Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.52050 | 1.59824 | 0.799120 | − | 0.601172i | \(-0.205299\pi\) | ||||
0.799120 | + | 0.601172i | \(0.205299\pi\) | |||||||
\(3\) | 1.75128 | 0.337034 | 0.168517 | − | 0.985699i | \(-0.446102\pi\) | ||||
0.168517 | + | 0.985699i | \(0.446102\pi\) | |||||||
\(4\) | 12.4349 | 1.55437 | ||||||||
\(5\) | 13.0472 | 1.16698 | 0.583488 | − | 0.812122i | \(-0.301687\pi\) | ||||
0.583488 | + | 0.812122i | \(0.301687\pi\) | |||||||
\(6\) | 7.91667 | 0.538661 | ||||||||
\(7\) | −4.32755 | −0.233666 | −0.116833 | − | 0.993152i | \(-0.537274\pi\) | ||||
−0.116833 | + | 0.993152i | \(0.537274\pi\) | |||||||
\(8\) | 20.0482 | 0.886013 | ||||||||
\(9\) | −23.9330 | −0.886408 | ||||||||
\(10\) | 58.9799 | 1.86511 | ||||||||
\(11\) | −55.2516 | −1.51445 | −0.757227 | − | 0.653152i | \(-0.773446\pi\) | ||||
−0.757227 | + | 0.653152i | \(0.773446\pi\) | |||||||
\(12\) | 21.7771 | 0.523875 | ||||||||
\(13\) | −37.7658 | −0.805719 | −0.402860 | − | 0.915262i | \(-0.631984\pi\) | ||||
−0.402860 | + | 0.915262i | \(0.631984\pi\) | |||||||
\(14\) | −19.5627 | −0.373454 | ||||||||
\(15\) | 22.8493 | 0.393311 | ||||||||
\(16\) | −8.85170 | −0.138308 | ||||||||
\(17\) | −24.9093 | −0.355376 | −0.177688 | − | 0.984087i | \(-0.556862\pi\) | ||||
−0.177688 | + | 0.984087i | \(0.556862\pi\) | |||||||
\(18\) | −108.189 | −1.41669 | ||||||||
\(19\) | −39.7201 | −0.479601 | −0.239800 | − | 0.970822i | \(-0.577082\pi\) | ||||
−0.239800 | + | 0.970822i | \(0.577082\pi\) | |||||||
\(20\) | 162.241 | 1.81391 | ||||||||
\(21\) | −7.57876 | −0.0787534 | ||||||||
\(22\) | −249.765 | −2.42046 | ||||||||
\(23\) | −2.55110 | −0.0231279 | −0.0115639 | − | 0.999933i | \(-0.503681\pi\) | ||||
−0.0115639 | + | 0.999933i | \(0.503681\pi\) | |||||||
\(24\) | 35.1100 | 0.298617 | ||||||||
\(25\) | 45.2293 | 0.361834 | ||||||||
\(26\) | −170.720 | −1.28773 | ||||||||
\(27\) | −89.1980 | −0.635784 | ||||||||
\(28\) | −53.8129 | −0.363203 | ||||||||
\(29\) | 238.086 | 1.52454 | 0.762268 | − | 0.647262i | \(-0.224086\pi\) | ||||
0.762268 | + | 0.647262i | \(0.224086\pi\) | |||||||
\(30\) | 103.290 | 0.628605 | ||||||||
\(31\) | 263.063 | 1.52411 | 0.762056 | − | 0.647512i | \(-0.224190\pi\) | ||||
0.762056 | + | 0.647512i | \(0.224190\pi\) | |||||||
\(32\) | −200.400 | −1.10706 | ||||||||
\(33\) | −96.7611 | −0.510423 | ||||||||
\(34\) | −112.603 | −0.567977 | ||||||||
\(35\) | −56.4624 | −0.272682 | ||||||||
\(36\) | −297.606 | −1.37780 | ||||||||
\(37\) | −353.428 | −1.57036 | −0.785178 | − | 0.619270i | \(-0.787429\pi\) | ||||
−0.785178 | + | 0.619270i | \(0.787429\pi\) | |||||||
\(38\) | −179.555 | −0.766517 | ||||||||
\(39\) | −66.1386 | −0.271555 | ||||||||
\(40\) | 261.573 | 1.03396 | ||||||||
\(41\) | 254.188 | 0.968233 | 0.484117 | − | 0.875004i | \(-0.339141\pi\) | ||||
0.484117 | + | 0.875004i | \(0.339141\pi\) | |||||||
\(42\) | −34.2598 | −0.125867 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −687.051 | −2.35402 | ||||||||
\(45\) | −312.259 | −1.03442 | ||||||||
\(46\) | −11.5323 | −0.0369639 | ||||||||
\(47\) | −386.866 | −1.20064 | −0.600321 | − | 0.799759i | \(-0.704961\pi\) | ||||
−0.600321 | + | 0.799759i | \(0.704961\pi\) | |||||||
\(48\) | −15.5018 | −0.0466145 | ||||||||
\(49\) | −324.272 | −0.945400 | ||||||||
\(50\) | 204.459 | 0.578297 | ||||||||
\(51\) | −43.6232 | −0.119774 | ||||||||
\(52\) | −469.616 | −1.25238 | ||||||||
\(53\) | −35.7551 | −0.0926668 | −0.0463334 | − | 0.998926i | \(-0.514754\pi\) | ||||
−0.0463334 | + | 0.998926i | \(0.514754\pi\) | |||||||
\(54\) | −403.220 | −1.01614 | ||||||||
\(55\) | −720.878 | −1.76733 | ||||||||
\(56\) | −86.7595 | −0.207031 | ||||||||
\(57\) | −69.5611 | −0.161642 | ||||||||
\(58\) | 1076.27 | 2.43657 | ||||||||
\(59\) | −87.4154 | −0.192890 | −0.0964451 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964451 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(60\) | 284.130 | 0.611350 | ||||||||
\(61\) | −890.643 | −1.86943 | −0.934714 | − | 0.355400i | \(-0.884345\pi\) | ||||
−0.934714 | + | 0.355400i | \(0.884345\pi\) | |||||||
\(62\) | 1189.18 | 2.43589 | ||||||||
\(63\) | 103.571 | 0.207123 | ||||||||
\(64\) | −835.093 | −1.63104 | ||||||||
\(65\) | −492.738 | −0.940256 | ||||||||
\(66\) | −437.409 | −0.815777 | ||||||||
\(67\) | −998.120 | −1.82000 | −0.909998 | − | 0.414612i | \(-0.863917\pi\) | ||||
−0.909998 | + | 0.414612i | \(0.863917\pi\) | |||||||
\(68\) | −309.746 | −0.552386 | ||||||||
\(69\) | −4.46769 | −0.00779489 | ||||||||
\(70\) | −255.238 | −0.435812 | ||||||||
\(71\) | −443.994 | −0.742146 | −0.371073 | − | 0.928604i | \(-0.621010\pi\) | ||||
−0.371073 | + | 0.928604i | \(0.621010\pi\) | |||||||
\(72\) | −479.813 | −0.785369 | ||||||||
\(73\) | 70.5226 | 0.113069 | 0.0565346 | − | 0.998401i | \(-0.481995\pi\) | ||||
0.0565346 | + | 0.998401i | \(0.481995\pi\) | |||||||
\(74\) | −1597.67 | −2.50980 | ||||||||
\(75\) | 79.2092 | 0.121951 | ||||||||
\(76\) | −493.917 | −0.745476 | ||||||||
\(77\) | 239.104 | 0.353876 | ||||||||
\(78\) | −298.980 | −0.434010 | ||||||||
\(79\) | 975.256 | 1.38892 | 0.694461 | − | 0.719530i | \(-0.255643\pi\) | ||||
0.694461 | + | 0.719530i | \(0.255643\pi\) | |||||||
\(80\) | −115.490 | −0.161402 | ||||||||
\(81\) | 489.980 | 0.672127 | ||||||||
\(82\) | 1149.06 | 1.54747 | ||||||||
\(83\) | 836.712 | 1.10652 | 0.553260 | − | 0.833009i | \(-0.313384\pi\) | ||||
0.553260 | + | 0.833009i | \(0.313384\pi\) | |||||||
\(84\) | −94.2415 | −0.122412 | ||||||||
\(85\) | −324.997 | −0.414716 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 416.956 | 0.513821 | ||||||||
\(88\) | −1107.69 | −1.34182 | ||||||||
\(89\) | 1086.38 | 1.29389 | 0.646944 | − | 0.762537i | \(-0.276047\pi\) | ||||
0.646944 | + | 0.762537i | \(0.276047\pi\) | |||||||
\(90\) | −1411.57 | −1.65325 | ||||||||
\(91\) | 163.434 | 0.188269 | ||||||||
\(92\) | −31.7228 | −0.0359492 | ||||||||
\(93\) | 460.697 | 0.513678 | ||||||||
\(94\) | −1748.83 | −1.91891 | ||||||||
\(95\) | −518.236 | −0.559683 | ||||||||
\(96\) | −350.956 | −0.373118 | ||||||||
\(97\) | −1132.50 | −1.18544 | −0.592720 | − | 0.805408i | \(-0.701946\pi\) | ||||
−0.592720 | + | 0.805408i | \(0.701946\pi\) | |||||||
\(98\) | −1465.87 | −1.51098 | ||||||||
\(99\) | 1322.34 | 1.34242 | ||||||||
\(100\) | 562.423 | 0.562423 | ||||||||
\(101\) | 1437.96 | 1.41665 | 0.708326 | − | 0.705885i | \(-0.249450\pi\) | ||||
0.708326 | + | 0.705885i | \(0.249450\pi\) | |||||||
\(102\) | −197.199 | −0.191428 | ||||||||
\(103\) | 1763.53 | 1.68704 | 0.843521 | − | 0.537096i | \(-0.180479\pi\) | ||||
0.843521 | + | 0.537096i | \(0.180479\pi\) | |||||||
\(104\) | −757.136 | −0.713878 | ||||||||
\(105\) | −98.8816 | −0.0919033 | ||||||||
\(106\) | −161.631 | −0.148104 | ||||||||
\(107\) | 166.103 | 0.150073 | 0.0750365 | − | 0.997181i | \(-0.476093\pi\) | ||||
0.0750365 | + | 0.997181i | \(0.476093\pi\) | |||||||
\(108\) | −1109.17 | −0.988243 | ||||||||
\(109\) | −441.796 | −0.388224 | −0.194112 | − | 0.980979i | \(-0.562182\pi\) | ||||
−0.194112 | + | 0.980979i | \(0.562182\pi\) | |||||||
\(110\) | −3258.73 | −2.82462 | ||||||||
\(111\) | −618.951 | −0.529264 | ||||||||
\(112\) | 38.3062 | 0.0323178 | ||||||||
\(113\) | 971.442 | 0.808722 | 0.404361 | − | 0.914599i | \(-0.367494\pi\) | ||||
0.404361 | + | 0.914599i | \(0.367494\pi\) | |||||||
\(114\) | −314.451 | −0.258342 | ||||||||
\(115\) | −33.2847 | −0.0269897 | ||||||||
\(116\) | 2960.59 | 2.36969 | ||||||||
\(117\) | 903.850 | 0.714196 | ||||||||
\(118\) | −395.162 | −0.308285 | ||||||||
\(119\) | 107.796 | 0.0830393 | ||||||||
\(120\) | 458.087 | 0.348479 | ||||||||
\(121\) | 1721.74 | 1.29357 | ||||||||
\(122\) | −4026.15 | −2.98779 | ||||||||
\(123\) | 445.155 | 0.326328 | ||||||||
\(124\) | 3271.17 | 2.36903 | ||||||||
\(125\) | −1040.78 | −0.744725 | ||||||||
\(126\) | 468.195 | 0.331032 | ||||||||
\(127\) | −1595.77 | −1.11498 | −0.557489 | − | 0.830185i | \(-0.688235\pi\) | ||||
−0.557489 | + | 0.830185i | \(0.688235\pi\) | |||||||
\(128\) | −2171.84 | −1.49973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2227.42 | −1.50275 | ||||||||
\(131\) | −55.8044 | −0.0372187 | −0.0186094 | − | 0.999827i | \(-0.505924\pi\) | ||||
−0.0186094 | + | 0.999827i | \(0.505924\pi\) | |||||||
\(132\) | −1203.22 | −0.793385 | ||||||||
\(133\) | 171.891 | 0.112066 | ||||||||
\(134\) | −4512.00 | −2.90879 | ||||||||
\(135\) | −1163.78 | −0.741945 | ||||||||
\(136\) | −499.387 | −0.314868 | ||||||||
\(137\) | −137.795 | −0.0859316 | −0.0429658 | − | 0.999077i | \(-0.513681\pi\) | ||||
−0.0429658 | + | 0.999077i | \(0.513681\pi\) | |||||||
\(138\) | −20.1962 | −0.0124581 | ||||||||
\(139\) | 1016.38 | 0.620206 | 0.310103 | − | 0.950703i | \(-0.399637\pi\) | ||||
0.310103 | + | 0.950703i | \(0.399637\pi\) | |||||||
\(140\) | −702.107 | −0.423849 | ||||||||
\(141\) | −677.511 | −0.404658 | ||||||||
\(142\) | −2007.08 | −1.18613 | ||||||||
\(143\) | 2086.62 | 1.22022 | ||||||||
\(144\) | 211.848 | 0.122597 | ||||||||
\(145\) | 3106.36 | 1.77910 | ||||||||
\(146\) | 318.798 | 0.180712 | ||||||||
\(147\) | −567.892 | −0.318632 | ||||||||
\(148\) | −4394.85 | −2.44091 | ||||||||
\(149\) | 2725.90 | 1.49876 | 0.749378 | − | 0.662142i | \(-0.230352\pi\) | ||||
0.749378 | + | 0.662142i | \(0.230352\pi\) | |||||||
\(150\) | 358.065 | 0.194906 | ||||||||
\(151\) | −1350.49 | −0.727822 | −0.363911 | − | 0.931434i | \(-0.618559\pi\) | ||||
−0.363911 | + | 0.931434i | \(0.618559\pi\) | |||||||
\(152\) | −796.315 | −0.424932 | ||||||||
\(153\) | 596.155 | 0.315008 | ||||||||
\(154\) | 1080.87 | 0.565578 | ||||||||
\(155\) | 3432.23 | 1.77860 | ||||||||
\(156\) | −822.430 | −0.422097 | ||||||||
\(157\) | −2623.54 | −1.33364 | −0.666818 | − | 0.745220i | \(-0.732344\pi\) | ||||
−0.666818 | + | 0.745220i | \(0.732344\pi\) | |||||||
\(158\) | 4408.65 | 2.21983 | ||||||||
\(159\) | −62.6172 | −0.0312319 | ||||||||
\(160\) | −2614.65 | −1.29192 | ||||||||
\(161\) | 11.0400 | 0.00540419 | ||||||||
\(162\) | 2214.96 | 1.07422 | ||||||||
\(163\) | −407.303 | −0.195721 | −0.0978603 | − | 0.995200i | \(-0.531200\pi\) | ||||
−0.0978603 | + | 0.995200i | \(0.531200\pi\) | |||||||
\(164\) | 3160.82 | 1.50499 | ||||||||
\(165\) | −1262.46 | −0.595651 | ||||||||
\(166\) | 3782.36 | 1.76848 | ||||||||
\(167\) | 1743.79 | 0.808015 | 0.404008 | − | 0.914756i | \(-0.367617\pi\) | ||||
0.404008 | + | 0.914756i | \(0.367617\pi\) | |||||||
\(168\) | −151.940 | −0.0697765 | ||||||||
\(169\) | −770.743 | −0.350816 | ||||||||
\(170\) | −1469.15 | −0.662815 | ||||||||
\(171\) | 950.621 | 0.425122 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1182.29 | 0.519584 | 0.259792 | − | 0.965665i | \(-0.416346\pi\) | ||||
0.259792 | + | 0.965665i | \(0.416346\pi\) | |||||||
\(174\) | 1884.85 | 0.821208 | ||||||||
\(175\) | −195.732 | −0.0845483 | ||||||||
\(176\) | 489.071 | 0.209461 | ||||||||
\(177\) | −153.089 | −0.0650106 | ||||||||
\(178\) | 4910.99 | 2.06794 | ||||||||
\(179\) | −4505.20 | −1.88120 | −0.940600 | − | 0.339517i | \(-0.889737\pi\) | ||||
−0.940600 | + | 0.339517i | \(0.889737\pi\) | |||||||
\(180\) | −3882.92 | −1.60787 | ||||||||
\(181\) | −2610.79 | −1.07215 | −0.536073 | − | 0.844172i | \(-0.680093\pi\) | ||||
−0.536073 | + | 0.844172i | \(0.680093\pi\) | |||||||
\(182\) | 738.802 | 0.300899 | ||||||||
\(183\) | −1559.77 | −0.630061 | ||||||||
\(184\) | −51.1449 | −0.0204916 | ||||||||
\(185\) | −4611.24 | −1.83257 | ||||||||
\(186\) | 2082.58 | 0.820980 | ||||||||
\(187\) | 1376.28 | 0.538201 | ||||||||
\(188\) | −4810.66 | −1.86624 | ||||||||
\(189\) | 386.009 | 0.148561 | ||||||||
\(190\) | −2342.69 | −0.894507 | ||||||||
\(191\) | −2992.98 | −1.13384 | −0.566922 | − | 0.823771i | \(-0.691866\pi\) | ||||
−0.566922 | + | 0.823771i | \(0.691866\pi\) | |||||||
\(192\) | −1462.48 | −0.549717 | ||||||||
\(193\) | −842.048 | −0.314051 | −0.157026 | − | 0.987595i | \(-0.550191\pi\) | ||||
−0.157026 | + | 0.987595i | \(0.550191\pi\) | |||||||
\(194\) | −5119.46 | −1.89462 | ||||||||
\(195\) | −862.923 | −0.316898 | ||||||||
\(196\) | −4032.31 | −1.46950 | ||||||||
\(197\) | 1391.04 | 0.503082 | 0.251541 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251541 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(198\) | 5977.63 | 2.14551 | ||||||||
\(199\) | −989.587 | −0.352512 | −0.176256 | − | 0.984344i | \(-0.556399\pi\) | ||||
−0.176256 | + | 0.984344i | \(0.556399\pi\) | |||||||
\(200\) | 906.764 | 0.320590 | ||||||||
\(201\) | −1747.99 | −0.613401 | ||||||||
\(202\) | 6500.28 | 2.26415 | ||||||||
\(203\) | −1030.33 | −0.356232 | ||||||||
\(204\) | −542.453 | −0.186173 | ||||||||
\(205\) | 3316.45 | 1.12991 | ||||||||
\(206\) | 7972.02 | 2.69630 | ||||||||
\(207\) | 61.0555 | 0.0205007 | ||||||||
\(208\) | 334.292 | 0.111437 | ||||||||
\(209\) | 2194.60 | 0.726333 | ||||||||
\(210\) | −446.994 | −0.146884 | ||||||||
\(211\) | 943.172 | 0.307728 | 0.153864 | − | 0.988092i | \(-0.450828\pi\) | ||||
0.153864 | + | 0.988092i | \(0.450828\pi\) | |||||||
\(212\) | −444.612 | −0.144038 | ||||||||
\(213\) | −777.558 | −0.250129 | ||||||||
\(214\) | 750.871 | 0.239853 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1788.26 | −0.563313 | ||||||||
\(217\) | −1138.42 | −0.356133 | ||||||||
\(218\) | −1997.14 | −0.620474 | ||||||||
\(219\) | 123.505 | 0.0381082 | ||||||||
\(220\) | −8964.08 | −2.74708 | ||||||||
\(221\) | 940.721 | 0.286334 | ||||||||
\(222\) | −2797.97 | −0.845890 | ||||||||
\(223\) | −4371.74 | −1.31280 | −0.656398 | − | 0.754415i | \(-0.727921\pi\) | ||||
−0.656398 | + | 0.754415i | \(0.727921\pi\) | |||||||
\(224\) | 867.240 | 0.258682 | ||||||||
\(225\) | −1082.47 | −0.320733 | ||||||||
\(226\) | 4391.41 | 1.29253 | ||||||||
\(227\) | 1293.65 | 0.378249 | 0.189124 | − | 0.981953i | \(-0.439435\pi\) | ||||
0.189124 | + | 0.981953i | \(0.439435\pi\) | |||||||
\(228\) | −864.988 | −0.251251 | ||||||||
\(229\) | 2720.83 | 0.785141 | 0.392570 | − | 0.919722i | \(-0.371586\pi\) | ||||
0.392570 | + | 0.919722i | \(0.371586\pi\) | |||||||
\(230\) | −150.464 | −0.0431360 | ||||||||
\(231\) | 418.739 | 0.119268 | ||||||||
\(232\) | 4773.20 | 1.35076 | ||||||||
\(233\) | 1824.91 | 0.513108 | 0.256554 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256554 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(234\) | 4085.86 | 1.14146 | ||||||||
\(235\) | −5047.52 | −1.40112 | ||||||||
\(236\) | −1087.01 | −0.299822 | ||||||||
\(237\) | 1707.95 | 0.468114 | ||||||||
\(238\) | 487.294 | 0.132717 | ||||||||
\(239\) | 2517.89 | 0.681460 | 0.340730 | − | 0.940161i | \(-0.389326\pi\) | ||||
0.340730 | + | 0.940161i | \(0.389326\pi\) | |||||||
\(240\) | −202.255 | −0.0543980 | ||||||||
\(241\) | 2023.30 | 0.540797 | 0.270398 | − | 0.962749i | \(-0.412845\pi\) | ||||
0.270398 | + | 0.962749i | \(0.412845\pi\) | |||||||
\(242\) | 7783.13 | 2.06743 | ||||||||
\(243\) | 3266.44 | 0.862314 | ||||||||
\(244\) | −11075.1 | −2.90578 | ||||||||
\(245\) | −4230.84 | −1.10326 | ||||||||
\(246\) | 2012.33 | 0.521550 | ||||||||
\(247\) | 1500.06 | 0.386424 | ||||||||
\(248\) | 5273.93 | 1.35038 | ||||||||
\(249\) | 1465.32 | 0.372935 | ||||||||
\(250\) | −4704.87 | −1.19025 | ||||||||
\(251\) | −2200.46 | −0.553355 | −0.276677 | − | 0.960963i | \(-0.589233\pi\) | ||||
−0.276677 | + | 0.960963i | \(0.589233\pi\) | |||||||
\(252\) | 1287.90 | 0.321946 | ||||||||
\(253\) | 140.952 | 0.0350261 | ||||||||
\(254\) | −7213.71 | −1.78200 | ||||||||
\(255\) | −569.161 | −0.139773 | ||||||||
\(256\) | −3137.08 | −0.765890 | ||||||||
\(257\) | −869.760 | −0.211106 | −0.105553 | − | 0.994414i | \(-0.533661\pi\) | ||||
−0.105553 | + | 0.994414i | \(0.533661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1529.48 | 0.366938 | ||||||||
\(260\) | −6127.17 | −1.46150 | ||||||||
\(261\) | −5698.12 | −1.35136 | ||||||||
\(262\) | −252.264 | −0.0594844 | ||||||||
\(263\) | 4849.52 | 1.13701 | 0.568506 | − | 0.822679i | \(-0.307522\pi\) | ||||
0.568506 | + | 0.822679i | \(0.307522\pi\) | |||||||
\(264\) | −1939.88 | −0.452241 | ||||||||
\(265\) | −466.503 | −0.108140 | ||||||||
\(266\) | 777.032 | 0.179109 | ||||||||
\(267\) | 1902.56 | 0.436085 | ||||||||
\(268\) | −12411.6 | −2.82894 | ||||||||
\(269\) | 432.453 | 0.0980191 | 0.0490096 | − | 0.998798i | \(-0.484394\pi\) | ||||
0.0490096 | + | 0.998798i | \(0.484394\pi\) | |||||||
\(270\) | −5260.89 | −1.18581 | ||||||||
\(271\) | 861.175 | 0.193036 | 0.0965179 | − | 0.995331i | \(-0.469230\pi\) | ||||
0.0965179 | + | 0.995331i | \(0.469230\pi\) | |||||||
\(272\) | 220.490 | 0.0491514 | ||||||||
\(273\) | 286.218 | 0.0634531 | ||||||||
\(274\) | −622.903 | −0.137339 | ||||||||
\(275\) | −2498.99 | −0.547981 | ||||||||
\(276\) | −55.5555 | −0.0121161 | ||||||||
\(277\) | 2228.63 | 0.483412 | 0.241706 | − | 0.970350i | \(-0.422293\pi\) | ||||
0.241706 | + | 0.970350i | \(0.422293\pi\) | |||||||
\(278\) | 4594.57 | 0.991237 | ||||||||
\(279\) | −6295.88 | −1.35098 | ||||||||
\(280\) | −1131.97 | −0.241600 | ||||||||
\(281\) | −5991.67 | −1.27200 | −0.636002 | − | 0.771688i | \(-0.719413\pi\) | ||||
−0.636002 | + | 0.771688i | \(0.719413\pi\) | |||||||
\(282\) | −3062.69 | −0.646740 | ||||||||
\(283\) | 1125.62 | 0.236434 | 0.118217 | − | 0.992988i | \(-0.462282\pi\) | ||||
0.118217 | + | 0.992988i | \(0.462282\pi\) | |||||||
\(284\) | −5521.04 | −1.15357 | ||||||||
\(285\) | −907.577 | −0.188632 | ||||||||
\(286\) | 9432.58 | 1.95021 | ||||||||
\(287\) | −1100.01 | −0.226243 | ||||||||
\(288\) | 4796.17 | 0.981308 | ||||||||
\(289\) | −4292.53 | −0.873708 | ||||||||
\(290\) | 14042.3 | 2.84342 | ||||||||
\(291\) | −1983.32 | −0.399534 | ||||||||
\(292\) | 876.945 | 0.175751 | ||||||||
\(293\) | 6457.05 | 1.28746 | 0.643729 | − | 0.765254i | \(-0.277387\pi\) | ||||
0.643729 | + | 0.765254i | \(0.277387\pi\) | |||||||
\(294\) | −2567.16 | −0.509251 | ||||||||
\(295\) | −1140.53 | −0.225098 | ||||||||
\(296\) | −7085.58 | −1.39136 | ||||||||
\(297\) | 4928.33 | 0.962865 | ||||||||
\(298\) | 12322.5 | 2.39537 | ||||||||
\(299\) | 96.3444 | 0.0186346 | ||||||||
\(300\) | 984.962 | 0.189556 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6104.88 | −1.16323 | ||||||||
\(303\) | 2518.27 | 0.477461 | ||||||||
\(304\) | 351.590 | 0.0663325 | ||||||||
\(305\) | −11620.4 | −2.18158 | ||||||||
\(306\) | 2694.92 | 0.503459 | ||||||||
\(307\) | 7900.21 | 1.46869 | 0.734347 | − | 0.678775i | \(-0.237489\pi\) | ||||
0.734347 | + | 0.678775i | \(0.237489\pi\) | |||||||
\(308\) | 2973.25 | 0.550053 | ||||||||
\(309\) | 3088.43 | 0.568591 | ||||||||
\(310\) | 15515.4 | 2.84263 | ||||||||
\(311\) | 3923.50 | 0.715374 | 0.357687 | − | 0.933841i | \(-0.383565\pi\) | ||||
0.357687 | + | 0.933841i | \(0.383565\pi\) | |||||||
\(312\) | −1325.96 | −0.240601 | ||||||||
\(313\) | 7259.87 | 1.31103 | 0.655515 | − | 0.755182i | \(-0.272452\pi\) | ||||
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(314\) | −11859.7 | −2.13147 | ||||||||
\(315\) | 1351.32 | 0.241708 | ||||||||
\(316\) | 12127.3 | 2.15890 | ||||||||
\(317\) | −5967.29 | −1.05728 | −0.528638 | − | 0.848847i | \(-0.677297\pi\) | ||||
−0.528638 | + | 0.848847i | \(0.677297\pi\) | |||||||
\(318\) | −283.061 | −0.0499160 | ||||||||
\(319\) | −13154.7 | −2.30884 | ||||||||
\(320\) | −10895.6 | −1.90339 | ||||||||
\(321\) | 290.894 | 0.0505798 | ||||||||
\(322\) | 49.9064 | 0.00863719 | ||||||||
\(323\) | 989.401 | 0.170439 | ||||||||
\(324\) | 6092.88 | 1.04473 | ||||||||
\(325\) | −1708.12 | −0.291537 | ||||||||
\(326\) | −1841.22 | −0.312808 | ||||||||
\(327\) | −773.709 | −0.130845 | ||||||||
\(328\) | 5096.01 | 0.857867 | ||||||||
\(329\) | 1674.18 | 0.280549 | ||||||||
\(330\) | −5706.96 | −0.951993 | ||||||||
\(331\) | −7412.74 | −1.23094 | −0.615470 | − | 0.788161i | \(-0.711034\pi\) | ||||
−0.615470 | + | 0.788161i | \(0.711034\pi\) | |||||||
\(332\) | 10404.5 | 1.71994 | ||||||||
\(333\) | 8458.59 | 1.39198 | ||||||||
\(334\) | 7882.81 | 1.29140 | ||||||||
\(335\) | −13022.7 | −2.12389 | ||||||||
\(336\) | 67.0849 | 0.0108922 | ||||||||
\(337\) | 12010.9 | 1.94147 | 0.970733 | − | 0.240160i | \(-0.0771998\pi\) | ||||
0.970733 | + | 0.240160i | \(0.0771998\pi\) | |||||||
\(338\) | −3484.15 | −0.560688 | ||||||||
\(339\) | 1701.27 | 0.272567 | ||||||||
\(340\) | −4041.32 | −0.644621 | ||||||||
\(341\) | −14534.6 | −2.30819 | ||||||||
\(342\) | 4297.29 | 0.679446 | ||||||||
\(343\) | 2887.66 | 0.454574 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −58.2909 | −0.00909645 | ||||||||
\(346\) | 5344.56 | 0.830419 | ||||||||
\(347\) | 2376.88 | 0.367716 | 0.183858 | − | 0.982953i | \(-0.441141\pi\) | ||||
0.183858 | + | 0.982953i | \(0.441141\pi\) | |||||||
\(348\) | 5184.83 | 0.798666 | ||||||||
\(349\) | 2443.29 | 0.374747 | 0.187373 | − | 0.982289i | \(-0.440003\pi\) | ||||
0.187373 | + | 0.982289i | \(0.440003\pi\) | |||||||
\(350\) | −884.807 | −0.135128 | ||||||||
\(351\) | 3368.64 | 0.512264 | ||||||||
\(352\) | 11072.4 | 1.67659 | ||||||||
\(353\) | −6845.61 | −1.03217 | −0.516084 | − | 0.856538i | \(-0.672611\pi\) | ||||
−0.516084 | + | 0.856538i | \(0.672611\pi\) | |||||||
\(354\) | −692.039 | −0.103902 | ||||||||
\(355\) | −5792.88 | −0.866067 | ||||||||
\(356\) | 13509.1 | 2.01118 | ||||||||
\(357\) | 188.782 | 0.0279871 | ||||||||
\(358\) | −20365.8 | −3.00661 | ||||||||
\(359\) | −8886.04 | −1.30637 | −0.653185 | − | 0.757198i | \(-0.726568\pi\) | ||||
−0.653185 | + | 0.757198i | \(0.726568\pi\) | |||||||
\(360\) | −6260.22 | −0.916507 | ||||||||
\(361\) | −5281.31 | −0.769983 | ||||||||
\(362\) | −11802.1 | −1.71354 | ||||||||
\(363\) | 3015.25 | 0.435977 | ||||||||
\(364\) | 2032.29 | 0.292639 | ||||||||
\(365\) | 920.122 | 0.131949 | ||||||||
\(366\) | −7050.93 | −1.00699 | ||||||||
\(367\) | 1772.16 | 0.252060 | 0.126030 | − | 0.992026i | \(-0.459776\pi\) | ||||
0.126030 | + | 0.992026i | \(0.459776\pi\) | |||||||
\(368\) | 22.5816 | 0.00319877 | ||||||||
\(369\) | −6083.49 | −0.858249 | ||||||||
\(370\) | −20845.1 | −2.92888 | ||||||||
\(371\) | 154.732 | 0.0216531 | ||||||||
\(372\) | 5728.74 | 0.798444 | ||||||||
\(373\) | −2089.79 | −0.290095 | −0.145047 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145047 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(374\) | 6221.48 | 0.860174 | ||||||||
\(375\) | −1822.71 | −0.250998 | ||||||||
\(376\) | −7755.96 | −1.06378 | ||||||||
\(377\) | −8991.53 | −1.22835 | ||||||||
\(378\) | 1744.96 | 0.237436 | ||||||||
\(379\) | −12958.0 | −1.75622 | −0.878108 | − | 0.478462i | \(-0.841194\pi\) | ||||
−0.878108 | + | 0.478462i | \(0.841194\pi\) | |||||||
\(380\) | −6444.23 | −0.869953 | ||||||||
\(381\) | −2794.65 | −0.375786 | ||||||||
\(382\) | −13529.8 | −1.81215 | ||||||||
\(383\) | 2891.35 | 0.385747 | 0.192874 | − | 0.981224i | \(-0.438219\pi\) | ||||
0.192874 | + | 0.981224i | \(0.438219\pi\) | |||||||
\(384\) | −3803.51 | −0.505461 | ||||||||
\(385\) | 3119.64 | 0.412965 | ||||||||
\(386\) | −3806.48 | −0.501929 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14082.5 | −1.84261 | ||||||||
\(389\) | 8007.52 | 1.04370 | 0.521848 | − | 0.853039i | \(-0.325243\pi\) | ||||
0.521848 | + | 0.853039i | \(0.325243\pi\) | |||||||
\(390\) | −3900.84 | −0.506479 | ||||||||
\(391\) | 63.5462 | 0.00821910 | ||||||||
\(392\) | −6501.07 | −0.837637 | ||||||||
\(393\) | −97.7292 | −0.0125440 | ||||||||
\(394\) | 6288.18 | 0.804046 | ||||||||
\(395\) | 12724.4 | 1.62084 | ||||||||
\(396\) | 16443.2 | 2.08662 | ||||||||
\(397\) | −5407.44 | −0.683606 | −0.341803 | − | 0.939772i | \(-0.611038\pi\) | ||||
−0.341803 | + | 0.939772i | \(0.611038\pi\) | |||||||
\(398\) | −4473.43 | −0.563399 | ||||||||
\(399\) | 301.029 | 0.0377702 | ||||||||
\(400\) | −400.356 | −0.0500445 | ||||||||
\(401\) | −11696.4 | −1.45658 | −0.728290 | − | 0.685269i | \(-0.759684\pi\) | ||||
−0.728290 | + | 0.685269i | \(0.759684\pi\) | |||||||
\(402\) | −7901.79 | −0.980362 | ||||||||
\(403\) | −9934.78 | −1.22801 | ||||||||
\(404\) | 17880.9 | 2.20200 | ||||||||
\(405\) | 6392.87 | 0.784356 | ||||||||
\(406\) | −4657.61 | −0.569344 | ||||||||
\(407\) | 19527.4 | 2.37823 | ||||||||
\(408\) | −874.567 | −0.106121 | ||||||||
\(409\) | 4629.41 | 0.559681 | 0.279840 | − | 0.960047i | \(-0.409718\pi\) | ||||
0.279840 | + | 0.960047i | \(0.409718\pi\) | |||||||
\(410\) | 14992.0 | 1.80586 | ||||||||
\(411\) | −241.318 | −0.0289619 | ||||||||
\(412\) | 21929.4 | 2.62229 | ||||||||
\(413\) | 378.295 | 0.0450718 | ||||||||
\(414\) | 276.002 | 0.0327651 | ||||||||
\(415\) | 10916.7 | 1.29128 | ||||||||
\(416\) | 7568.25 | 0.891981 | ||||||||
\(417\) | 1779.97 | 0.209031 | ||||||||
\(418\) | 9920.69 | 1.16085 | ||||||||
\(419\) | −3307.85 | −0.385678 | −0.192839 | − | 0.981230i | \(-0.561770\pi\) | ||||
−0.192839 | + | 0.981230i | \(0.561770\pi\) | |||||||
\(420\) | −1229.59 | −0.142852 | ||||||||
\(421\) | 242.081 | 0.0280245 | 0.0140122 | − | 0.999902i | \(-0.495540\pi\) | ||||
0.0140122 | + | 0.999902i | \(0.495540\pi\) | |||||||
\(422\) | 4263.61 | 0.491823 | ||||||||
\(423\) | 9258.87 | 1.06426 | ||||||||
\(424\) | −716.824 | −0.0821039 | ||||||||
\(425\) | −1126.63 | −0.128587 | ||||||||
\(426\) | −3514.95 | −0.399766 | ||||||||
\(427\) | 3854.30 | 0.436821 | ||||||||
\(428\) | 2065.49 | 0.233269 | ||||||||
\(429\) | 3654.26 | 0.411257 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16410.0 | −1.83398 | −0.916989 | − | 0.398913i | \(-0.869387\pi\) | ||||
−0.916989 | + | 0.398913i | \(0.869387\pi\) | |||||||
\(432\) | 789.555 | 0.0879339 | ||||||||
\(433\) | −6230.06 | −0.691450 | −0.345725 | − | 0.938336i | \(-0.612367\pi\) | ||||
−0.345725 | + | 0.938336i | \(0.612367\pi\) | |||||||
\(434\) | −5146.22 | −0.569185 | ||||||||
\(435\) | 5440.11 | 0.599617 | ||||||||
\(436\) | −5493.71 | −0.603442 | ||||||||
\(437\) | 101.330 | 0.0110921 | ||||||||
\(438\) | 558.305 | 0.0609060 | ||||||||
\(439\) | −4436.43 | −0.482322 | −0.241161 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241161 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(440\) | −14452.3 | −1.56588 | ||||||||
\(441\) | 7760.81 | 0.838010 | ||||||||
\(442\) | 4252.53 | 0.457630 | ||||||||
\(443\) | −13607.7 | −1.45941 | −0.729707 | − | 0.683760i | \(-0.760343\pi\) | ||||
−0.729707 | + | 0.683760i | \(0.760343\pi\) | |||||||
\(444\) | −7696.63 | −0.822671 | ||||||||
\(445\) | 14174.2 | 1.50994 | ||||||||
\(446\) | −19762.5 | −2.09816 | ||||||||
\(447\) | 4773.82 | 0.505132 | ||||||||
\(448\) | 3613.91 | 0.381119 | ||||||||
\(449\) | 3677.16 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(450\) | −4893.32 | −0.512607 | ||||||||
\(451\) | −14044.3 | −1.46634 | ||||||||
\(452\) | 12079.8 | 1.25705 | ||||||||
\(453\) | −2365.08 | −0.245301 | ||||||||
\(454\) | 5847.94 | 0.604532 | ||||||||
\(455\) | 2132.35 | 0.219706 | ||||||||
\(456\) | −1394.57 | −0.143217 | ||||||||
\(457\) | −9654.94 | −0.988270 | −0.494135 | − | 0.869385i | \(-0.664515\pi\) | ||||
−0.494135 | + | 0.869385i | \(0.664515\pi\) | |||||||
\(458\) | 12299.5 | 1.25484 | ||||||||
\(459\) | 2221.86 | 0.225943 | ||||||||
\(460\) | −413.893 | −0.0419519 | ||||||||
\(461\) | 6387.32 | 0.645308 | 0.322654 | − | 0.946517i | \(-0.395425\pi\) | ||||
0.322654 | + | 0.946517i | \(0.395425\pi\) | |||||||
\(462\) | 1892.91 | 0.190619 | ||||||||
\(463\) | −8369.16 | −0.840060 | −0.420030 | − | 0.907510i | \(-0.637981\pi\) | ||||
−0.420030 | + | 0.907510i | \(0.637981\pi\) | |||||||
\(464\) | −2107.47 | −0.210855 | ||||||||
\(465\) | 6010.80 | 0.599450 | ||||||||
\(466\) | 8249.53 | 0.820069 | ||||||||
\(467\) | 11897.9 | 1.17895 | 0.589475 | − | 0.807786i | \(-0.299334\pi\) | ||||
0.589475 | + | 0.807786i | \(0.299334\pi\) | |||||||
\(468\) | 11239.3 | 1.11012 | ||||||||
\(469\) | 4319.41 | 0.425271 | ||||||||
\(470\) | −22817.3 | −2.23933 | ||||||||
\(471\) | −4594.55 | −0.449481 | ||||||||
\(472\) | −1752.52 | −0.170903 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7720.78 | 0.748159 | ||||||||
\(475\) | −1796.51 | −0.173536 | ||||||||
\(476\) | 1340.44 | 0.129074 | ||||||||
\(477\) | 855.727 | 0.0821405 | ||||||||
\(478\) | 11382.1 | 1.08914 | ||||||||
\(479\) | −5313.81 | −0.506877 | −0.253438 | − | 0.967352i | \(-0.581562\pi\) | ||||
−0.253438 | + | 0.967352i | \(0.581562\pi\) | |||||||
\(480\) | −4578.99 | −0.435420 | ||||||||
\(481\) | 13347.5 | 1.26527 | ||||||||
\(482\) | 9146.32 | 0.864322 | ||||||||
\(483\) | 19.3342 | 0.00182140 | ||||||||
\(484\) | 21409.7 | 2.01068 | ||||||||
\(485\) | −14775.9 | −1.38338 | ||||||||
\(486\) | 14766.0 | 1.37818 | ||||||||
\(487\) | 10792.5 | 1.00422 | 0.502110 | − | 0.864804i | \(-0.332557\pi\) | ||||
0.502110 | + | 0.864804i | \(0.332557\pi\) | |||||||
\(488\) | −17855.8 | −1.65634 | ||||||||
\(489\) | −713.303 | −0.0659645 | ||||||||
\(490\) | −19125.5 | −1.76327 | ||||||||
\(491\) | 2458.96 | 0.226011 | 0.113006 | − | 0.993594i | \(-0.463952\pi\) | ||||
0.113006 | + | 0.993594i | \(0.463952\pi\) | |||||||
\(492\) | 5535.48 | 0.507233 | ||||||||
\(493\) | −5930.57 | −0.541784 | ||||||||
\(494\) | 6781.03 | 0.617597 | ||||||||
\(495\) | 17252.8 | 1.56658 | ||||||||
\(496\) | −2328.55 | −0.210797 | ||||||||
\(497\) | 1921.41 | 0.173414 | ||||||||
\(498\) | 6623.98 | 0.596039 | ||||||||
\(499\) | 8744.82 | 0.784513 | 0.392256 | − | 0.919856i | \(-0.371695\pi\) | ||||
0.392256 | + | 0.919856i | \(0.371695\pi\) | |||||||
\(500\) | −12942.1 | −1.15758 | ||||||||
\(501\) | 3053.87 | 0.272329 | ||||||||
\(502\) | −9947.20 | −0.884393 | ||||||||
\(503\) | −12931.7 | −1.14631 | −0.573157 | − | 0.819446i | \(-0.694281\pi\) | ||||
−0.573157 | + | 0.819446i | \(0.694281\pi\) | |||||||
\(504\) | 2076.42 | 0.183514 | ||||||||
\(505\) | 18761.3 | 1.65320 | ||||||||
\(506\) | 637.175 | 0.0559800 | ||||||||
\(507\) | −1349.79 | −0.118237 | ||||||||
\(508\) | −19843.4 | −1.73309 | ||||||||
\(509\) | 19155.2 | 1.66805 | 0.834026 | − | 0.551726i | \(-0.186030\pi\) | ||||
0.834026 | + | 0.551726i | \(0.186030\pi\) | |||||||
\(510\) | −2572.89 | −0.223391 | ||||||||
\(511\) | −305.190 | −0.0264204 | ||||||||
\(512\) | 3193.56 | 0.275658 | ||||||||
\(513\) | 3542.95 | 0.304923 | ||||||||
\(514\) | −3931.75 | −0.337397 | ||||||||
\(515\) | 23009.1 | 1.96874 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21375.0 | 1.81832 | ||||||||
\(518\) | 6914.00 | 0.586455 | ||||||||
\(519\) | 2070.53 | 0.175118 | ||||||||
\(520\) | −9878.50 | −0.833079 | ||||||||
\(521\) | 2030.86 | 0.170775 | 0.0853875 | − | 0.996348i | \(-0.472787\pi\) | ||||
0.0853875 | + | 0.996348i | \(0.472787\pi\) | |||||||
\(522\) | −25758.4 | −2.15980 | ||||||||
\(523\) | −13361.0 | −1.11708 | −0.558542 | − | 0.829477i | \(-0.688639\pi\) | ||||
−0.558542 | + | 0.829477i | \(0.688639\pi\) | |||||||
\(524\) | −693.925 | −0.0578516 | ||||||||
\(525\) | −342.782 | −0.0284957 | ||||||||
\(526\) | 21922.2 | 1.81722 | ||||||||
\(527\) | −6552.71 | −0.541633 | ||||||||
\(528\) | 856.501 | 0.0705955 | ||||||||
\(529\) | −12160.5 | −0.999465 | ||||||||
\(530\) | −2108.83 | −0.172833 | ||||||||
\(531\) | 2092.11 | 0.170979 | ||||||||
\(532\) | 2137.45 | 0.174192 | ||||||||
\(533\) | −9599.63 | −0.780124 | ||||||||
\(534\) | 8600.52 | 0.696968 | ||||||||
\(535\) | 2167.18 | 0.175132 | ||||||||
\(536\) | −20010.5 | −1.61254 | ||||||||
\(537\) | −7889.88 | −0.634029 | ||||||||
\(538\) | 1954.91 | 0.156658 | ||||||||
\(539\) | 17916.6 | 1.43176 | ||||||||
\(540\) | −14471.6 | −1.15326 | ||||||||
\(541\) | −1543.79 | −0.122685 | −0.0613425 | − | 0.998117i | \(-0.519538\pi\) | ||||
−0.0613425 | + | 0.998117i | \(0.519538\pi\) | |||||||
\(542\) | 3892.95 | 0.308517 | ||||||||
\(543\) | −4572.22 | −0.361350 | ||||||||
\(544\) | 4991.82 | 0.393424 | ||||||||
\(545\) | −5764.20 | −0.453048 | ||||||||
\(546\) | 1293.85 | 0.101413 | ||||||||
\(547\) | −15805.6 | −1.23546 | −0.617731 | − | 0.786390i | \(-0.711948\pi\) | ||||
−0.617731 | + | 0.786390i | \(0.711948\pi\) | |||||||
\(548\) | −1713.47 | −0.133569 | ||||||||
\(549\) | 21315.8 | 1.65708 | ||||||||
\(550\) | −11296.7 | −0.875804 | ||||||||
\(551\) | −9456.81 | −0.731168 | ||||||||
\(552\) | −89.5691 | −0.00690637 | ||||||||
\(553\) | −4220.47 | −0.324544 | ||||||||
\(554\) | 10074.5 | 0.772608 | ||||||||
\(555\) | −8075.58 | −0.617638 | ||||||||
\(556\) | 12638.7 | 0.964028 | ||||||||
\(557\) | 552.342 | 0.0420170 | 0.0210085 | − | 0.999779i | \(-0.493312\pi\) | ||||
0.0210085 | + | 0.999779i | \(0.493312\pi\) | |||||||
\(558\) | −28460.6 | −2.15920 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 499.788 | 0.0377141 | ||||||||
\(561\) | 2410.25 | 0.181392 | ||||||||
\(562\) | −27085.4 | −2.03297 | ||||||||
\(563\) | 12098.2 | 0.905644 | 0.452822 | − | 0.891601i | \(-0.350417\pi\) | ||||
0.452822 | + | 0.891601i | \(0.350417\pi\) | |||||||
\(564\) | −8424.81 | −0.628987 | ||||||||
\(565\) | 12674.6 | 0.943760 | ||||||||
\(566\) | 5088.35 | 0.377878 | ||||||||
\(567\) | −2120.42 | −0.157053 | ||||||||
\(568\) | −8901.27 | −0.657551 | ||||||||
\(569\) | 519.978 | 0.0383104 | 0.0191552 | − | 0.999817i | \(-0.493902\pi\) | ||||
0.0191552 | + | 0.999817i | \(0.493902\pi\) | |||||||
\(570\) | −4102.70 | −0.301479 | ||||||||
\(571\) | −13553.9 | −0.993365 | −0.496682 | − | 0.867932i | \(-0.665449\pi\) | ||||
−0.496682 | + | 0.867932i | \(0.665449\pi\) | |||||||
\(572\) | 25947.0 | 1.89668 | ||||||||
\(573\) | −5241.55 | −0.382144 | ||||||||
\(574\) | −4972.61 | −0.361590 | ||||||||
\(575\) | −115.384 | −0.00836845 | ||||||||
\(576\) | 19986.3 | 1.44577 | ||||||||
\(577\) | −6324.19 | −0.456290 | −0.228145 | − | 0.973627i | \(-0.573266\pi\) | ||||
−0.228145 | + | 0.973627i | \(0.573266\pi\) | |||||||
\(578\) | −19404.4 | −1.39639 | ||||||||
\(579\) | −1474.66 | −0.105846 | ||||||||
\(580\) | 38627.4 | 2.76537 | ||||||||
\(581\) | −3620.92 | −0.258556 | ||||||||
\(582\) | −8965.61 | −0.638551 | ||||||||
\(583\) | 1975.53 | 0.140339 | ||||||||
\(584\) | 1413.85 | 0.100181 | ||||||||
\(585\) | 11792.7 | 0.833450 | ||||||||
\(586\) | 29189.1 | 2.05766 | ||||||||
\(587\) | −21394.9 | −1.50437 | −0.752183 | − | 0.658954i | \(-0.770999\pi\) | ||||
−0.752183 | + | 0.658954i | \(0.770999\pi\) | |||||||
\(588\) | −7061.71 | −0.495272 | ||||||||
\(589\) | −10448.9 | −0.730965 | ||||||||
\(590\) | −5155.75 | −0.359761 | ||||||||
\(591\) | 2436.10 | 0.169556 | ||||||||
\(592\) | 3128.44 | 0.217193 | ||||||||
\(593\) | 17243.2 | 1.19409 | 0.597043 | − | 0.802209i | \(-0.296342\pi\) | ||||
0.597043 | + | 0.802209i | \(0.296342\pi\) | |||||||
\(594\) | 22278.5 | 1.53889 | ||||||||
\(595\) | 1406.44 | 0.0969049 | ||||||||
\(596\) | 33896.5 | 2.32962 | ||||||||
\(597\) | −1733.04 | −0.118809 | ||||||||
\(598\) | 435.525 | 0.0297825 | ||||||||
\(599\) | 1214.43 | 0.0828387 | 0.0414193 | − | 0.999142i | \(-0.486812\pi\) | ||||
0.0414193 | + | 0.999142i | \(0.486812\pi\) | |||||||
\(600\) | 1588.00 | 0.108050 | ||||||||
\(601\) | 3251.39 | 0.220677 | 0.110338 | − | 0.993894i | \(-0.464807\pi\) | ||||
0.110338 | + | 0.993894i | \(0.464807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23888.0 | 1.61326 | ||||||||
\(604\) | −16793.2 | −1.13130 | ||||||||
\(605\) | 22463.9 | 1.50956 | ||||||||
\(606\) | 11383.8 | 0.763096 | ||||||||
\(607\) | 13945.8 | 0.932526 | 0.466263 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466263 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(608\) | 7959.89 | 0.530948 | ||||||||
\(609\) | −1804.40 | −0.120062 | ||||||||
\(610\) | −52530.0 | −3.48668 | ||||||||
\(611\) | 14610.3 | 0.967381 | ||||||||
\(612\) | 7413.16 | 0.489639 | ||||||||
\(613\) | 8980.34 | 0.591701 | 0.295850 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295850 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(614\) | 35712.9 | 2.34732 | ||||||||
\(615\) | 5808.03 | 0.380817 | ||||||||
\(616\) | 4793.60 | 0.313539 | ||||||||
\(617\) | −9450.64 | −0.616642 | −0.308321 | − | 0.951282i | \(-0.599767\pi\) | ||||
−0.308321 | + | 0.951282i | \(0.599767\pi\) | |||||||
\(618\) | 13961.3 | 0.908745 | ||||||||
\(619\) | −9340.01 | −0.606473 | −0.303237 | − | 0.952915i | \(-0.598067\pi\) | ||||
−0.303237 | + | 0.952915i | \(0.598067\pi\) | |||||||
\(620\) | 42679.6 | 2.76460 | ||||||||
\(621\) | 227.553 | 0.0147043 | ||||||||
\(622\) | 17736.2 | 1.14334 | ||||||||
\(623\) | −4701.37 | −0.302337 | ||||||||
\(624\) | 585.439 | 0.0375582 | ||||||||
\(625\) | −19233.0 | −1.23091 | ||||||||
\(626\) | 32818.3 | 2.09534 | ||||||||
\(627\) | 3843.36 | 0.244799 | ||||||||
\(628\) | −32623.5 | −2.07296 | ||||||||
\(629\) | 8803.65 | 0.558067 | ||||||||
\(630\) | 6108.62 | 0.386307 | ||||||||
\(631\) | −9633.83 | −0.607792 | −0.303896 | − | 0.952705i | \(-0.598288\pi\) | ||||
−0.303896 | + | 0.952705i | \(0.598288\pi\) | |||||||
\(632\) | 19552.1 | 1.23060 | ||||||||
\(633\) | 1651.76 | 0.103715 | ||||||||
\(634\) | −26975.2 | −1.68978 | ||||||||
\(635\) | −20820.4 | −1.30115 | ||||||||
\(636\) | −778.642 | −0.0485458 | ||||||||
\(637\) | 12246.4 | 0.761727 | ||||||||
\(638\) | −59465.6 | −3.69007 | ||||||||
\(639\) | 10626.1 | 0.657844 | ||||||||
\(640\) | −28336.5 | −1.75015 | ||||||||
\(641\) | −10806.5 | −0.665885 | −0.332943 | − | 0.942947i | \(-0.608042\pi\) | ||||
−0.332943 | + | 0.942947i | \(0.608042\pi\) | |||||||
\(642\) | 1314.99 | 0.0808386 | ||||||||
\(643\) | 5396.16 | 0.330955 | 0.165477 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165477 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(644\) | 137.282 | 0.00840011 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4472.59 | 0.272402 | ||||||||
\(647\) | 13276.4 | 0.806722 | 0.403361 | − | 0.915041i | \(-0.367842\pi\) | ||||
0.403361 | + | 0.915041i | \(0.367842\pi\) | |||||||
\(648\) | 9823.22 | 0.595513 | ||||||||
\(649\) | 4829.84 | 0.292123 | ||||||||
\(650\) | −7721.56 | −0.465945 | ||||||||
\(651\) | −1993.69 | −0.120029 | ||||||||
\(652\) | −5064.79 | −0.304222 | ||||||||
\(653\) | 7560.53 | 0.453088 | 0.226544 | − | 0.974001i | \(-0.427257\pi\) | ||||
0.226544 | + | 0.974001i | \(0.427257\pi\) | |||||||
\(654\) | −3497.55 | −0.209121 | ||||||||
\(655\) | −728.091 | −0.0434334 | ||||||||
\(656\) | −2250.00 | −0.133914 | ||||||||
\(657\) | −1687.82 | −0.100225 | ||||||||
\(658\) | 7568.15 | 0.448385 | ||||||||
\(659\) | 17888.9 | 1.05744 | 0.528718 | − | 0.848797i | \(-0.322673\pi\) | ||||
0.528718 | + | 0.848797i | \(0.322673\pi\) | |||||||
\(660\) | −15698.6 | −0.925861 | ||||||||
\(661\) | 28643.1 | 1.68546 | 0.842729 | − | 0.538337i | \(-0.180947\pi\) | ||||
0.842729 | + | 0.538337i | \(0.180947\pi\) | |||||||
\(662\) | −33509.3 | −1.96733 | ||||||||
\(663\) | 1647.47 | 0.0965043 | ||||||||
\(664\) | 16774.6 | 0.980390 | ||||||||
\(665\) | 2242.69 | 0.130779 | ||||||||
\(666\) | 38237.1 | 2.22471 | ||||||||
\(667\) | −607.382 | −0.0352593 | ||||||||
\(668\) | 21683.9 | 1.25595 | ||||||||
\(669\) | −7656.15 | −0.442457 | ||||||||
\(670\) | −58869.0 | −3.39449 | ||||||||
\(671\) | 49209.4 | 2.83116 | ||||||||
\(672\) | 1518.78 | 0.0871849 | ||||||||
\(673\) | −26681.2 | −1.52821 | −0.764105 | − | 0.645091i | \(-0.776819\pi\) | ||||
−0.764105 | + | 0.645091i | \(0.776819\pi\) | |||||||
\(674\) | 54295.2 | 3.10293 | ||||||||
\(675\) | −4034.36 | −0.230048 | ||||||||
\(676\) | −9584.15 | −0.545297 | ||||||||
\(677\) | −24196.9 | −1.37365 | −0.686826 | − | 0.726821i | \(-0.740997\pi\) | ||||
−0.686826 | + | 0.726821i | \(0.740997\pi\) | |||||||
\(678\) | 7690.59 | 0.435627 | ||||||||
\(679\) | 4900.94 | 0.276997 | ||||||||
\(680\) | −6515.60 | −0.367444 | ||||||||
\(681\) | 2265.54 | 0.127483 | ||||||||
\(682\) | −65703.8 | −3.68905 | ||||||||
\(683\) | 33758.8 | 1.89128 | 0.945641 | − | 0.325213i | \(-0.105436\pi\) | ||||
0.945641 | + | 0.325213i | \(0.105436\pi\) | |||||||
\(684\) | 11820.9 | 0.660796 | ||||||||
\(685\) | −1797.84 | −0.100280 | ||||||||
\(686\) | 13053.7 | 0.726517 | ||||||||
\(687\) | 4764.93 | 0.264619 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1350.32 | 0.0746634 | ||||||||
\(690\) | −263.504 | −0.0145383 | ||||||||
\(691\) | 18145.5 | 0.998970 | 0.499485 | − | 0.866322i | \(-0.333523\pi\) | ||||
0.499485 | + | 0.866322i | \(0.333523\pi\) | |||||||
\(692\) | 14701.7 | 0.807625 | ||||||||
\(693\) | −5722.48 | −0.313678 | ||||||||
\(694\) | 10744.7 | 0.587698 | ||||||||
\(695\) | 13261.0 | 0.723765 | ||||||||
\(696\) | 8359.21 | 0.455252 | ||||||||
\(697\) | −6331.66 | −0.344087 | ||||||||
\(698\) | 11044.9 | 0.598935 | ||||||||
\(699\) | 3195.94 | 0.172935 | ||||||||
\(700\) | −2433.92 | −0.131419 | ||||||||
\(701\) | −21944.9 | −1.18238 | −0.591189 | − | 0.806533i | \(-0.701341\pi\) | ||||
−0.591189 | + | 0.806533i | \(0.701341\pi\) | |||||||
\(702\) | 15227.9 | 0.818720 | ||||||||
\(703\) | 14038.2 | 0.753144 | ||||||||
\(704\) | 46140.2 | 2.47014 | ||||||||
\(705\) | −8839.62 | −0.472226 | ||||||||
\(706\) | −30945.6 | −1.64965 | ||||||||
\(707\) | −6222.83 | −0.331023 | ||||||||
\(708\) | −1903.65 | −0.101050 | ||||||||
\(709\) | −36958.0 | −1.95767 | −0.978834 | − | 0.204656i | \(-0.934392\pi\) | ||||
−0.978834 | + | 0.204656i | \(0.934392\pi\) | |||||||
\(710\) | −26186.7 | −1.38418 | ||||||||
\(711\) | −23340.8 | −1.23115 | ||||||||
\(712\) | 21779.9 | 1.14640 | ||||||||
\(713\) | −671.099 | −0.0352494 | ||||||||
\(714\) | 853.389 | 0.0447301 | ||||||||
\(715\) | 27224.6 | 1.42397 | ||||||||
\(716\) | −56022.0 | −2.92408 | ||||||||
\(717\) | 4409.54 | 0.229675 | ||||||||
\(718\) | −40169.4 | −2.08789 | ||||||||
\(719\) | 5395.23 | 0.279845 | 0.139922 | − | 0.990162i | \(-0.455315\pi\) | ||||
0.139922 | + | 0.990162i | \(0.455315\pi\) | |||||||
\(720\) | 2764.02 | 0.143068 | ||||||||
\(721\) | −7631.75 | −0.394204 | ||||||||
\(722\) | −23874.2 | −1.23062 | ||||||||
\(723\) | 3543.36 | 0.182267 | ||||||||
\(724\) | −32465.0 | −1.66651 | ||||||||
\(725\) | 10768.5 | 0.551629 | ||||||||
\(726\) | 13630.4 | 0.696795 | ||||||||
\(727\) | −9561.59 | −0.487785 | −0.243892 | − | 0.969802i | \(-0.578424\pi\) | ||||
−0.243892 | + | 0.969802i | \(0.578424\pi\) | |||||||
\(728\) | 3276.54 | 0.166809 | ||||||||
\(729\) | −7509.02 | −0.381497 | ||||||||
\(730\) | 4159.42 | 0.210886 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −19395.6 | −0.979347 | ||||||||
\(733\) | 13308.7 | 0.670623 | 0.335312 | − | 0.942107i | \(-0.391158\pi\) | ||||
0.335312 | + | 0.942107i | \(0.391158\pi\) | |||||||
\(734\) | 8011.05 | 0.402852 | ||||||||
\(735\) | −7409.40 | −0.371836 | ||||||||
\(736\) | 511.239 | 0.0256040 | ||||||||
\(737\) | 55147.7 | 2.75630 | ||||||||
\(738\) | −27500.5 | −1.37169 | ||||||||
\(739\) | −16167.3 | −0.804768 | −0.402384 | − | 0.915471i | \(-0.631818\pi\) | ||||
−0.402384 | + | 0.915471i | \(0.631818\pi\) | |||||||
\(740\) | −57340.5 | −2.84849 | ||||||||
\(741\) | 2627.03 | 0.130238 | ||||||||
\(742\) | 699.466 | 0.0346068 | ||||||||
\(743\) | −25680.2 | −1.26799 | −0.633994 | − | 0.773338i | \(-0.718585\pi\) | ||||
−0.633994 | + | 0.773338i | \(0.718585\pi\) | |||||||
\(744\) | 9236.13 | 0.455125 | ||||||||
\(745\) | 35565.4 | 1.74901 | ||||||||
\(746\) | −9446.91 | −0.463641 | ||||||||
\(747\) | −20025.0 | −0.980828 | ||||||||
\(748\) | 17114.0 | 0.836562 | ||||||||
\(749\) | −718.821 | −0.0350669 | ||||||||
\(750\) | −8239.55 | −0.401154 | ||||||||
\(751\) | −12689.2 | −0.616559 | −0.308279 | − | 0.951296i | \(-0.599753\pi\) | ||||
−0.308279 | + | 0.951296i | \(0.599753\pi\) | |||||||
\(752\) | 3424.42 | 0.166058 | ||||||||
\(753\) | −3853.63 | −0.186500 | ||||||||
\(754\) | −40646.2 | −1.96319 | ||||||||
\(755\) | −17620.1 | −0.849351 | ||||||||
\(756\) | 4800.00 | 0.230918 | ||||||||
\(757\) | 17431.3 | 0.836926 | 0.418463 | − | 0.908234i | \(-0.362569\pi\) | ||||
0.418463 | + | 0.908234i | \(0.362569\pi\) | |||||||
\(758\) | −58576.5 | −2.80685 | ||||||||
\(759\) | 246.847 | 0.0118050 | ||||||||
\(760\) | −10389.7 | −0.495886 | ||||||||
\(761\) | 16997.5 | 0.809670 | 0.404835 | − | 0.914390i | \(-0.367329\pi\) | ||||
0.404835 | + | 0.914390i | \(0.367329\pi\) | |||||||
\(762\) | −12633.2 | −0.600595 | ||||||||
\(763\) | 1911.89 | 0.0907146 | ||||||||
\(764\) | −37217.5 | −1.76241 | ||||||||
\(765\) | 7778.15 | 0.367607 | ||||||||
\(766\) | 13070.4 | 0.616516 | ||||||||
\(767\) | 3301.31 | 0.155415 | ||||||||
\(768\) | −5493.92 | −0.258131 | ||||||||
\(769\) | −29896.1 | −1.40193 | −0.700963 | − | 0.713198i | \(-0.747246\pi\) | ||||
−0.700963 | + | 0.713198i | \(0.747246\pi\) | |||||||
\(770\) | 14102.3 | 0.660017 | ||||||||
\(771\) | −1523.19 | −0.0711498 | ||||||||
\(772\) | −10470.8 | −0.488152 | ||||||||
\(773\) | 18464.3 | 0.859138 | 0.429569 | − | 0.903034i | \(-0.358665\pi\) | ||||
0.429569 | + | 0.903034i | \(0.358665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11898.1 | 0.551475 | ||||||||
\(776\) | −22704.5 | −1.05032 | ||||||||
\(777\) | 2678.54 | 0.123671 | ||||||||
\(778\) | 36198.0 | 1.66807 | ||||||||
\(779\) | −10096.4 | −0.464365 | ||||||||
\(780\) | −10730.4 | −0.492577 | ||||||||
\(781\) | 24531.4 | 1.12395 | ||||||||
\(782\) | 287.261 | 0.0131361 | ||||||||
\(783\) | −21236.8 | −0.969275 | ||||||||
\(784\) | 2870.36 | 0.130756 | ||||||||
\(785\) | −34229.8 | −1.55632 | ||||||||
\(786\) | −441.785 | −0.0200483 | ||||||||
\(787\) | −7383.94 | −0.334446 | −0.167223 | − | 0.985919i | \(-0.553480\pi\) | ||||
−0.167223 | + | 0.985919i | \(0.553480\pi\) | |||||||
\(788\) | 17297.5 | 0.781975 | ||||||||
\(789\) | 8492.87 | 0.383212 | ||||||||
\(790\) | 57520.5 | 2.59049 | ||||||||
\(791\) | −4203.97 | −0.188971 | ||||||||
\(792\) | 26510.5 | 1.18940 | ||||||||
\(793\) | 33635.9 | 1.50623 | ||||||||
\(794\) | −24444.3 | −1.09257 | ||||||||
\(795\) | −816.979 | −0.0364469 | ||||||||
\(796\) | −12305.5 | −0.547934 | ||||||||
\(797\) | 23799.0 | 1.05772 | 0.528860 | − | 0.848709i | \(-0.322620\pi\) | ||||
0.528860 | + | 0.848709i | \(0.322620\pi\) | |||||||
\(798\) | 1360.80 | 0.0603658 | ||||||||
\(799\) | 9636.57 | 0.426680 | ||||||||
\(800\) | −9063.93 | −0.400573 | ||||||||
\(801\) | −26000.4 | −1.14691 | ||||||||
\(802\) | −52873.4 | −2.32796 | ||||||||
\(803\) | −3896.49 | −0.171238 | ||||||||
\(804\) | −21736.1 | −0.953451 | ||||||||
\(805\) | 144.041 | 0.00630657 | ||||||||
\(806\) | −44910.2 | −1.96265 | ||||||||
\(807\) | 757.348 | 0.0330358 | ||||||||
\(808\) | 28828.4 | 1.25517 | ||||||||
\(809\) | 2665.36 | 0.115833 | 0.0579166 | − | 0.998321i | \(-0.481554\pi\) | ||||
0.0579166 | + | 0.998321i | \(0.481554\pi\) | |||||||
\(810\) | 28899.0 | 1.25359 | ||||||||
\(811\) | −36736.8 | −1.59063 | −0.795317 | − | 0.606194i | \(-0.792695\pi\) | ||||
−0.795317 | + | 0.606194i | \(0.792695\pi\) | |||||||
\(812\) | −12812.1 | −0.553715 | ||||||||
\(813\) | 1508.16 | 0.0650597 | ||||||||
\(814\) | 88273.9 | 3.80098 | ||||||||
\(815\) | −5314.16 | −0.228401 | ||||||||
\(816\) | 386.140 | 0.0165657 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 20927.2 | 0.894504 | ||||||||
\(819\) | −3911.46 | −0.166883 | ||||||||
\(820\) | 41239.8 | 1.75629 | ||||||||
\(821\) | −13460.1 | −0.572180 | −0.286090 | − | 0.958203i | \(-0.592356\pi\) | ||||
−0.286090 | + | 0.958203i | \(0.592356\pi\) | |||||||
\(822\) | −1090.88 | −0.0462880 | ||||||||
\(823\) | −25589.3 | −1.08382 | −0.541912 | − | 0.840435i | \(-0.682300\pi\) | ||||
−0.541912 | + | 0.840435i | \(0.682300\pi\) | |||||||
\(824\) | 35355.5 | 1.49474 | ||||||||
\(825\) | −4376.43 | −0.184688 | ||||||||
\(826\) | 1710.08 | 0.0720355 | ||||||||
\(827\) | 24201.4 | 1.01761 | 0.508807 | − | 0.860881i | \(-0.330087\pi\) | ||||
0.508807 | + | 0.860881i | \(0.330087\pi\) | |||||||
\(828\) | 759.222 | 0.0318657 | ||||||||
\(829\) | −15933.9 | −0.667560 | −0.333780 | − | 0.942651i | \(-0.608324\pi\) | ||||
−0.333780 | + | 0.942651i | \(0.608324\pi\) | |||||||
\(830\) | 49349.2 | 2.06378 | ||||||||
\(831\) | 3902.95 | 0.162926 | ||||||||
\(832\) | 31538.0 | 1.31416 | ||||||||
\(833\) | 8077.41 | 0.335973 | ||||||||
\(834\) | 8046.38 | 0.334081 | ||||||||
\(835\) | 22751.6 | 0.942935 | ||||||||
\(836\) | 27289.7 | 1.12899 | ||||||||
\(837\) | −23464.7 | −0.969006 | ||||||||
\(838\) | −14953.2 | −0.616406 | ||||||||
\(839\) | −23536.8 | −0.968512 | −0.484256 | − | 0.874926i | \(-0.660910\pi\) | ||||
−0.484256 | + | 0.874926i | \(0.660910\pi\) | |||||||
\(840\) | −1982.40 | −0.0814275 | ||||||||
\(841\) | 32296.1 | 1.32421 | ||||||||
\(842\) | 1094.33 | 0.0447898 | ||||||||
\(843\) | −10493.1 | −0.428709 | ||||||||
\(844\) | 11728.3 | 0.478323 | ||||||||
\(845\) | −10056.0 | −0.409394 | ||||||||
\(846\) | 41854.7 | 1.70094 | ||||||||
\(847\) | −7450.91 | −0.302263 | ||||||||
\(848\) | 316.493 | 0.0128165 | ||||||||
\(849\) | 1971.27 | 0.0796864 | ||||||||
\(850\) | −5092.94 | −0.205513 | ||||||||
\(851\) | 901.629 | 0.0363190 | ||||||||
\(852\) | −9668.90 | −0.388792 | ||||||||
\(853\) | 14346.0 | 0.575845 | 0.287923 | − | 0.957654i | \(-0.407035\pi\) | ||||
0.287923 | + | 0.957654i | \(0.407035\pi\) | |||||||
\(854\) | 17423.4 | 0.698145 | ||||||||
\(855\) | 12402.9 | 0.496107 | ||||||||
\(856\) | 3330.07 | 0.132967 | ||||||||
\(857\) | −25049.7 | −0.998462 | −0.499231 | − | 0.866469i | \(-0.666384\pi\) | ||||
−0.499231 | + | 0.866469i | \(0.666384\pi\) | |||||||
\(858\) | 16519.1 | 0.657288 | ||||||||
\(859\) | −26179.1 | −1.03983 | −0.519917 | − | 0.854217i | \(-0.674037\pi\) | ||||
−0.519917 | + | 0.854217i | \(0.674037\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1926.43 | −0.0762516 | ||||||||
\(862\) | −74181.7 | −2.93113 | ||||||||
\(863\) | 10987.8 | 0.433404 | 0.216702 | − | 0.976238i | \(-0.430470\pi\) | ||||
0.216702 | + | 0.976238i | \(0.430470\pi\) | |||||||
\(864\) | 17875.3 | 0.703852 | ||||||||
\(865\) | 15425.6 | 0.606342 | ||||||||
\(866\) | −28163.0 | −1.10510 | ||||||||
\(867\) | −7517.42 | −0.294469 | ||||||||
\(868\) | −14156.2 | −0.553561 | ||||||||
\(869\) | −53884.4 | −2.10346 | ||||||||
\(870\) | 24592.0 | 0.958331 | ||||||||
\(871\) | 37694.8 | 1.46641 | ||||||||
\(872\) | −8857.20 | −0.343971 | ||||||||
\(873\) | 27104.1 | 1.05078 | ||||||||
\(874\) | 458.062 | 0.0177279 | ||||||||
\(875\) | 4504.05 | 0.174017 | ||||||||
\(876\) | 1535.78 | 0.0592341 | ||||||||
\(877\) | 43452.2 | 1.67306 | 0.836531 | − | 0.547919i | \(-0.184580\pi\) | ||||
0.836531 | + | 0.547919i | \(0.184580\pi\) | |||||||
\(878\) | −20054.9 | −0.770865 | ||||||||
\(879\) | 11308.1 | 0.433917 | ||||||||
\(880\) | 6381.00 | 0.244436 | ||||||||
\(881\) | −10548.4 | −0.403389 | −0.201694 | − | 0.979449i | \(-0.564645\pi\) | ||||
−0.201694 | + | 0.979449i | \(0.564645\pi\) | |||||||
\(882\) | 35082.8 | 1.33934 | ||||||||
\(883\) | −12217.7 | −0.465637 | −0.232818 | − | 0.972520i | \(-0.574795\pi\) | ||||
−0.232818 | + | 0.972520i | \(0.574795\pi\) | |||||||
\(884\) | 11697.8 | 0.445068 | ||||||||
\(885\) | −1997.38 | −0.0758658 | ||||||||
\(886\) | −61513.5 | −2.33249 | ||||||||
\(887\) | −39821.5 | −1.50741 | −0.753706 | − | 0.657212i | \(-0.771736\pi\) | ||||
−0.753706 | + | 0.657212i | \(0.771736\pi\) | |||||||
\(888\) | −12408.9 | −0.468934 | ||||||||
\(889\) | 6905.80 | 0.260532 | ||||||||
\(890\) | 64074.6 | 2.41324 | ||||||||
\(891\) | −27072.2 | −1.01790 | ||||||||
\(892\) | −54362.4 | −2.04057 | ||||||||
\(893\) | 15366.4 | 0.575829 | ||||||||
\(894\) | 21580.1 | 0.807322 | ||||||||
\(895\) | −58780.3 | −2.19532 | ||||||||
\(896\) | 9398.77 | 0.350436 | ||||||||
\(897\) | 168.726 | 0.00628049 | ||||||||
\(898\) | 16622.6 | 0.617710 | ||||||||
\(899\) | 62631.6 | 2.32356 | ||||||||
\(900\) | −13460.5 | −0.498537 | ||||||||
\(901\) | 890.635 | 0.0329316 | ||||||||
\(902\) | −63487.4 | −2.34357 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19475.6 | 0.716538 | ||||||||
\(905\) | −34063.4 | −1.25117 | ||||||||
\(906\) | −10691.4 | −0.392049 | ||||||||
\(907\) | −32895.0 | −1.20426 | −0.602128 | − | 0.798399i | \(-0.705680\pi\) | ||||
−0.602128 | + | 0.798399i | \(0.705680\pi\) | |||||||
\(908\) | 16086.5 | 0.587938 | ||||||||
\(909\) | −34414.6 | −1.25573 | ||||||||
\(910\) | 9639.29 | 0.351142 | ||||||||
\(911\) | −14491.2 | −0.527019 | −0.263509 | − | 0.964657i | \(-0.584880\pi\) | ||||
−0.263509 | + | 0.964657i | \(0.584880\pi\) | |||||||
\(912\) | 615.734 | 0.0223563 | ||||||||
\(913\) | −46229.7 | −1.67577 | ||||||||
\(914\) | −43645.2 | −1.57949 | ||||||||
\(915\) | −20350.6 | −0.735267 | ||||||||
\(916\) | 33833.3 | 1.22040 | ||||||||
\(917\) | 241.496 | 0.00869675 | ||||||||
\(918\) | 10043.9 | 0.361110 | ||||||||
\(919\) | 3819.84 | 0.137111 | 0.0685554 | − | 0.997647i | \(-0.478161\pi\) | ||||
0.0685554 | + | 0.997647i | \(0.478161\pi\) | |||||||
\(920\) | −667.298 | −0.0239132 | ||||||||
\(921\) | 13835.5 | 0.495000 | ||||||||
\(922\) | 28873.9 | 1.03136 | ||||||||
\(923\) | 16767.8 | 0.597962 | ||||||||
\(924\) | 5206.99 | 0.185387 | ||||||||
\(925\) | −15985.3 | −0.568208 | ||||||||
\(926\) | −37832.8 | −1.34262 | ||||||||
\(927\) | −42206.5 | −1.49541 | ||||||||
\(928\) | −47712.4 | −1.68775 | ||||||||
\(929\) | 6597.01 | 0.232983 | 0.116491 | − | 0.993192i | \(-0.462835\pi\) | ||||
0.116491 | + | 0.993192i | \(0.462835\pi\) | |||||||
\(930\) | 27171.8 | 0.958064 | ||||||||
\(931\) | 12880.1 | 0.453415 | ||||||||
\(932\) | 22692.7 | 0.797559 | ||||||||
\(933\) | 6871.16 | 0.241106 | ||||||||
\(934\) | 53784.6 | 1.88425 | ||||||||
\(935\) | 17956.6 | 0.628068 | ||||||||
\(936\) | 18120.5 | 0.632787 | ||||||||
\(937\) | −22841.5 | −0.796370 | −0.398185 | − | 0.917305i | \(-0.630360\pi\) | ||||
−0.398185 | + | 0.917305i | \(0.630360\pi\) | |||||||
\(938\) | 19525.9 | 0.679685 | ||||||||
\(939\) | 12714.1 | 0.441862 | ||||||||
\(940\) | −62765.6 | −2.17786 | ||||||||
\(941\) | 36677.3 | 1.27061 | 0.635306 | − | 0.772261i | \(-0.280874\pi\) | ||||
0.635306 | + | 0.772261i | \(0.280874\pi\) | |||||||
\(942\) | −20769.7 | −0.718378 | ||||||||
\(943\) | −648.460 | −0.0223932 | ||||||||
\(944\) | 773.775 | 0.0266782 | ||||||||
\(945\) | 5036.34 | 0.173367 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19733.4 | −0.677138 | −0.338569 | − | 0.940942i | \(-0.609943\pi\) | ||||
−0.338569 | + | 0.940942i | \(0.609943\pi\) | |||||||
\(948\) | 21238.2 | 0.727622 | ||||||||
\(949\) | −2663.34 | −0.0911020 | ||||||||
\(950\) | −8121.13 | −0.277352 | ||||||||
\(951\) | −10450.4 | −0.356338 | ||||||||
\(952\) | 2161.12 | 0.0735739 | ||||||||
\(953\) | −12496.6 | −0.424768 | −0.212384 | − | 0.977186i | \(-0.568123\pi\) | ||||
−0.212384 | + | 0.977186i | \(0.568123\pi\) | |||||||
\(954\) | 3868.32 | 0.131280 | ||||||||
\(955\) | −39050.0 | −1.32317 | ||||||||
\(956\) | 31309.9 | 1.05924 | ||||||||
\(957\) | −23037.5 | −0.778157 | ||||||||
\(958\) | −24021.1 | −0.810111 | ||||||||
\(959\) | 596.315 | 0.0200793 | ||||||||
\(960\) | −19081.3 | −0.641507 | ||||||||
\(961\) | 39411.0 | 1.32291 | ||||||||
\(962\) | 60337.4 | 2.02220 | ||||||||
\(963\) | −3975.35 | −0.133026 | ||||||||
\(964\) | 25159.6 | 0.840597 | ||||||||
\(965\) | −10986.4 | −0.366491 | ||||||||
\(966\) | 87.4002 | 0.00291103 | ||||||||
\(967\) | −1702.88 | −0.0566297 | −0.0283149 | − | 0.999599i | \(-0.509014\pi\) | ||||
−0.0283149 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(968\) | 34517.7 | 1.14612 | ||||||||
\(969\) | 1732.72 | 0.0574437 | ||||||||
\(970\) | −66794.6 | −2.21097 | ||||||||
\(971\) | −3923.91 | −0.129685 | −0.0648426 | − | 0.997896i | \(-0.520655\pi\) | ||||
−0.0648426 | + | 0.997896i | \(0.520655\pi\) | |||||||
\(972\) | 40618.0 | 1.34035 | ||||||||
\(973\) | −4398.45 | −0.144921 | ||||||||
\(974\) | 48787.5 | 1.60498 | ||||||||
\(975\) | −2991.40 | −0.0982579 | ||||||||
\(976\) | 7883.71 | 0.258557 | ||||||||
\(977\) | −24540.8 | −0.803614 | −0.401807 | − | 0.915724i | \(-0.631618\pi\) | ||||
−0.401807 | + | 0.915724i | \(0.631618\pi\) | |||||||
\(978\) | −3224.49 | −0.105427 | ||||||||
\(979\) | −60024.2 | −1.95953 | ||||||||
\(980\) | −52610.3 | −1.71487 | ||||||||
\(981\) | 10573.5 | 0.344124 | ||||||||
\(982\) | 11115.8 | 0.361220 | ||||||||
\(983\) | 10646.8 | 0.345453 | 0.172727 | − | 0.984970i | \(-0.444742\pi\) | ||||
0.172727 | + | 0.984970i | \(0.444742\pi\) | |||||||
\(984\) | 8924.56 | 0.289131 | ||||||||
\(985\) | 18149.1 | 0.587085 | ||||||||
\(986\) | −26809.2 | −0.865900 | ||||||||
\(987\) | 2931.96 | 0.0945547 | ||||||||
\(988\) | 18653.2 | 0.600645 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 77991.3 | 2.50376 | ||||||||
\(991\) | 68.7730 | 0.00220449 | 0.00110224 | − | 0.999999i | \(-0.499649\pi\) | ||||
0.00110224 | + | 0.999999i | \(0.499649\pi\) | |||||||
\(992\) | −52717.6 | −1.68729 | ||||||||
\(993\) | −12981.8 | −0.414869 | ||||||||
\(994\) | 8685.72 | 0.277157 | ||||||||
\(995\) | −12911.3 | −0.411373 | ||||||||
\(996\) | 18221.2 | 0.579678 | ||||||||
\(997\) | 56204.3 | 1.78536 | 0.892682 | − | 0.450686i | \(-0.148821\pi\) | ||||
0.892682 | + | 0.450686i | \(0.148821\pi\) | |||||||
\(998\) | 39531.0 | 1.25384 | ||||||||
\(999\) | 31525.1 | 0.998407 |
(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 | 1849.4.a.j.1.43 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.8 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.8 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.43 | yes | 50 | 1.1 | even | 1 | trivial |