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 | 1.34 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89933 | 0.671515 | 0.335758 | − | 0.941948i | \(-0.391008\pi\) | ||||
0.335758 | + | 0.941948i | \(0.391008\pi\) | |||||||
\(3\) | −6.15189 | −1.18393 | −0.591966 | − | 0.805963i | \(-0.701648\pi\) | ||||
−0.591966 | + | 0.805963i | \(0.701648\pi\) | |||||||
\(4\) | −4.39254 | −0.549068 | ||||||||
\(5\) | −1.87975 | −0.168130 | −0.0840651 | − | 0.996460i | \(-0.526790\pi\) | ||||
−0.0840651 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(6\) | −11.6845 | −0.795028 | ||||||||
\(7\) | 2.77777 | 0.149985 | 0.0749927 | − | 0.997184i | \(-0.476107\pi\) | ||||
0.0749927 | + | 0.997184i | \(0.476107\pi\) | |||||||
\(8\) | −23.5375 | −1.04022 | ||||||||
\(9\) | 10.8458 | 0.401696 | ||||||||
\(10\) | −3.57027 | −0.112902 | ||||||||
\(11\) | 5.01316 | 0.137411 | 0.0687056 | − | 0.997637i | \(-0.478113\pi\) | ||||
0.0687056 | + | 0.997637i | \(0.478113\pi\) | |||||||
\(12\) | 27.0224 | 0.650059 | ||||||||
\(13\) | −31.2928 | −0.667620 | −0.333810 | − | 0.942640i | \(-0.608334\pi\) | ||||
−0.333810 | + | 0.942640i | \(0.608334\pi\) | |||||||
\(14\) | 5.27590 | 0.100717 | ||||||||
\(15\) | 11.5640 | 0.199055 | ||||||||
\(16\) | −9.56527 | −0.149457 | ||||||||
\(17\) | 42.4153 | 0.605130 | 0.302565 | − | 0.953129i | \(-0.402157\pi\) | ||||
0.302565 | + | 0.953129i | \(0.402157\pi\) | |||||||
\(18\) | 20.5997 | 0.269745 | ||||||||
\(19\) | 2.31817 | 0.0279908 | 0.0139954 | − | 0.999902i | \(-0.495545\pi\) | ||||
0.0139954 | + | 0.999902i | \(0.495545\pi\) | |||||||
\(20\) | 8.25689 | 0.0923148 | ||||||||
\(21\) | −17.0885 | −0.177572 | ||||||||
\(22\) | 9.52164 | 0.0922737 | ||||||||
\(23\) | −10.8509 | −0.0983723 | −0.0491862 | − | 0.998790i | \(-0.515663\pi\) | ||||
−0.0491862 | + | 0.998790i | \(0.515663\pi\) | |||||||
\(24\) | 144.800 | 1.23155 | ||||||||
\(25\) | −121.467 | −0.971732 | ||||||||
\(26\) | −59.4353 | −0.448317 | ||||||||
\(27\) | 99.3790 | 0.708352 | ||||||||
\(28\) | −12.2015 | −0.0823521 | ||||||||
\(29\) | −82.1722 | −0.526173 | −0.263086 | − | 0.964772i | \(-0.584740\pi\) | ||||
−0.263086 | + | 0.964772i | \(0.584740\pi\) | |||||||
\(30\) | 21.9639 | 0.133668 | ||||||||
\(31\) | 296.425 | 1.71740 | 0.858702 | − | 0.512475i | \(-0.171271\pi\) | ||||
0.858702 | + | 0.512475i | \(0.171271\pi\) | |||||||
\(32\) | 170.133 | 0.939859 | ||||||||
\(33\) | −30.8404 | −0.162686 | ||||||||
\(34\) | 80.5606 | 0.406354 | ||||||||
\(35\) | −5.22151 | −0.0252171 | ||||||||
\(36\) | −47.6406 | −0.220558 | ||||||||
\(37\) | 186.475 | 0.828547 | 0.414273 | − | 0.910152i | \(-0.364036\pi\) | ||||
0.414273 | + | 0.910152i | \(0.364036\pi\) | |||||||
\(38\) | 4.40297 | 0.0187962 | ||||||||
\(39\) | 192.510 | 0.790416 | ||||||||
\(40\) | 44.2448 | 0.174893 | ||||||||
\(41\) | 343.407 | 1.30808 | 0.654039 | − | 0.756461i | \(-0.273073\pi\) | ||||
0.654039 | + | 0.756461i | \(0.273073\pi\) | |||||||
\(42\) | −32.4568 | −0.119243 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −22.0205 | −0.0754480 | ||||||||
\(45\) | −20.3874 | −0.0675372 | ||||||||
\(46\) | −20.6094 | −0.0660585 | ||||||||
\(47\) | −200.405 | −0.621960 | −0.310980 | − | 0.950417i | \(-0.600657\pi\) | ||||
−0.310980 | + | 0.950417i | \(0.600657\pi\) | |||||||
\(48\) | 58.8445 | 0.176947 | ||||||||
\(49\) | −335.284 | −0.977504 | ||||||||
\(50\) | −230.705 | −0.652533 | ||||||||
\(51\) | −260.934 | −0.716433 | ||||||||
\(52\) | 137.455 | 0.366568 | ||||||||
\(53\) | −500.508 | −1.29717 | −0.648585 | − | 0.761142i | \(-0.724639\pi\) | ||||
−0.648585 | + | 0.761142i | \(0.724639\pi\) | |||||||
\(54\) | 188.754 | 0.475669 | ||||||||
\(55\) | −9.42349 | −0.0231030 | ||||||||
\(56\) | −65.3818 | −0.156018 | ||||||||
\(57\) | −14.2611 | −0.0331392 | ||||||||
\(58\) | −156.072 | −0.353333 | ||||||||
\(59\) | 613.901 | 1.35463 | 0.677315 | − | 0.735693i | \(-0.263144\pi\) | ||||
0.677315 | + | 0.735693i | \(0.263144\pi\) | |||||||
\(60\) | −50.7955 | −0.109295 | ||||||||
\(61\) | 661.557 | 1.38858 | 0.694292 | − | 0.719693i | \(-0.255717\pi\) | ||||
0.694292 | + | 0.719693i | \(0.255717\pi\) | |||||||
\(62\) | 563.010 | 1.15326 | ||||||||
\(63\) | 30.1271 | 0.0602485 | ||||||||
\(64\) | 399.661 | 0.780587 | ||||||||
\(65\) | 58.8227 | 0.112247 | ||||||||
\(66\) | −58.5761 | −0.109246 | ||||||||
\(67\) | 198.433 | 0.361828 | 0.180914 | − | 0.983499i | \(-0.442094\pi\) | ||||
0.180914 | + | 0.983499i | \(0.442094\pi\) | |||||||
\(68\) | −186.311 | −0.332257 | ||||||||
\(69\) | 66.7534 | 0.116466 | ||||||||
\(70\) | −9.91739 | −0.0169336 | ||||||||
\(71\) | −896.331 | −1.49824 | −0.749119 | − | 0.662435i | \(-0.769523\pi\) | ||||
−0.749119 | + | 0.662435i | \(0.769523\pi\) | |||||||
\(72\) | −255.283 | −0.417853 | ||||||||
\(73\) | 619.729 | 0.993614 | 0.496807 | − | 0.867861i | \(-0.334506\pi\) | ||||
0.496807 | + | 0.867861i | \(0.334506\pi\) | |||||||
\(74\) | 354.177 | 0.556382 | ||||||||
\(75\) | 747.249 | 1.15047 | ||||||||
\(76\) | −10.1826 | −0.0153688 | ||||||||
\(77\) | 13.9254 | 0.0206097 | ||||||||
\(78\) | 365.640 | 0.530777 | ||||||||
\(79\) | 58.4019 | 0.0831737 | 0.0415868 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415868 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(80\) | 17.9803 | 0.0251283 | ||||||||
\(81\) | −904.205 | −1.24034 | ||||||||
\(82\) | 652.244 | 0.878394 | ||||||||
\(83\) | 188.055 | 0.248695 | 0.124348 | − | 0.992239i | \(-0.460316\pi\) | ||||
0.124348 | + | 0.992239i | \(0.460316\pi\) | |||||||
\(84\) | 75.0620 | 0.0974993 | ||||||||
\(85\) | −79.7302 | −0.101741 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 505.515 | 0.622953 | ||||||||
\(88\) | −117.997 | −0.142938 | ||||||||
\(89\) | 1323.82 | 1.57669 | 0.788343 | − | 0.615237i | \(-0.210939\pi\) | ||||
0.788343 | + | 0.615237i | \(0.210939\pi\) | |||||||
\(90\) | −38.7224 | −0.0453522 | ||||||||
\(91\) | −86.9240 | −0.100133 | ||||||||
\(92\) | 47.6629 | 0.0540130 | ||||||||
\(93\) | −1823.58 | −2.03329 | ||||||||
\(94\) | −380.636 | −0.417655 | ||||||||
\(95\) | −4.35758 | −0.00470609 | ||||||||
\(96\) | −1046.64 | −1.11273 | ||||||||
\(97\) | 1022.15 | 1.06993 | 0.534967 | − | 0.844873i | \(-0.320324\pi\) | ||||
0.534967 | + | 0.844873i | \(0.320324\pi\) | |||||||
\(98\) | −636.815 | −0.656409 | ||||||||
\(99\) | 54.3716 | 0.0551975 | ||||||||
\(100\) | 533.547 | 0.533547 | ||||||||
\(101\) | −532.767 | −0.524874 | −0.262437 | − | 0.964949i | \(-0.584526\pi\) | ||||
−0.262437 | + | 0.964949i | \(0.584526\pi\) | |||||||
\(102\) | −495.600 | −0.481096 | ||||||||
\(103\) | −1188.97 | −1.13740 | −0.568701 | − | 0.822544i | \(-0.692554\pi\) | ||||
−0.568701 | + | 0.822544i | \(0.692554\pi\) | |||||||
\(104\) | 736.555 | 0.694473 | ||||||||
\(105\) | 32.1222 | 0.0298553 | ||||||||
\(106\) | −950.631 | −0.871070 | ||||||||
\(107\) | 1016.86 | 0.918729 | 0.459364 | − | 0.888248i | \(-0.348077\pi\) | ||||
0.459364 | + | 0.888248i | \(0.348077\pi\) | |||||||
\(108\) | −436.526 | −0.388933 | ||||||||
\(109\) | −1514.02 | −1.33043 | −0.665215 | − | 0.746652i | \(-0.731660\pi\) | ||||
−0.665215 | + | 0.746652i | \(0.731660\pi\) | |||||||
\(110\) | −17.8983 | −0.0155140 | ||||||||
\(111\) | −1147.17 | −0.980943 | ||||||||
\(112\) | −26.5701 | −0.0224164 | ||||||||
\(113\) | −1252.63 | −1.04281 | −0.521403 | − | 0.853311i | \(-0.674591\pi\) | ||||
−0.521403 | + | 0.853311i | \(0.674591\pi\) | |||||||
\(114\) | −27.0866 | −0.0222534 | ||||||||
\(115\) | 20.3970 | 0.0165394 | ||||||||
\(116\) | 360.945 | 0.288904 | ||||||||
\(117\) | −339.395 | −0.268180 | ||||||||
\(118\) | 1166.00 | 0.909654 | ||||||||
\(119\) | 117.820 | 0.0907606 | ||||||||
\(120\) | −272.189 | −0.207061 | ||||||||
\(121\) | −1305.87 | −0.981118 | ||||||||
\(122\) | 1256.52 | 0.932456 | ||||||||
\(123\) | −2112.60 | −1.54868 | ||||||||
\(124\) | −1302.06 | −0.942971 | ||||||||
\(125\) | 463.296 | 0.331508 | ||||||||
\(126\) | 57.2213 | 0.0404578 | ||||||||
\(127\) | 1389.50 | 0.970855 | 0.485427 | − | 0.874277i | \(-0.338664\pi\) | ||||
0.485427 | + | 0.874277i | \(0.338664\pi\) | |||||||
\(128\) | −601.974 | −0.415683 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 111.724 | 0.0753755 | ||||||||
\(131\) | 801.787 | 0.534752 | 0.267376 | − | 0.963592i | \(-0.413843\pi\) | ||||
0.267376 | + | 0.963592i | \(0.413843\pi\) | |||||||
\(132\) | 135.468 | 0.0893254 | ||||||||
\(133\) | 6.43933 | 0.00419820 | ||||||||
\(134\) | 376.891 | 0.242973 | ||||||||
\(135\) | −186.808 | −0.119095 | ||||||||
\(136\) | −998.351 | −0.629470 | ||||||||
\(137\) | −161.623 | −0.100791 | −0.0503955 | − | 0.998729i | \(-0.516048\pi\) | ||||
−0.0503955 | + | 0.998729i | \(0.516048\pi\) | |||||||
\(138\) | 126.787 | 0.0782088 | ||||||||
\(139\) | −2295.60 | −1.40080 | −0.700398 | − | 0.713752i | \(-0.746994\pi\) | ||||
−0.700398 | + | 0.713752i | \(0.746994\pi\) | |||||||
\(140\) | 22.9357 | 0.0138459 | ||||||||
\(141\) | 1232.87 | 0.736358 | ||||||||
\(142\) | −1702.43 | −1.00609 | ||||||||
\(143\) | −156.876 | −0.0917384 | ||||||||
\(144\) | −103.743 | −0.0600364 | ||||||||
\(145\) | 154.463 | 0.0884655 | ||||||||
\(146\) | 1177.07 | 0.667226 | ||||||||
\(147\) | 2062.63 | 1.15730 | ||||||||
\(148\) | −819.097 | −0.454928 | ||||||||
\(149\) | −1133.28 | −0.623102 | −0.311551 | − | 0.950229i | \(-0.600848\pi\) | ||||
−0.311551 | + | 0.950229i | \(0.600848\pi\) | |||||||
\(150\) | 1419.27 | 0.772555 | ||||||||
\(151\) | 1357.22 | 0.731451 | 0.365725 | − | 0.930723i | \(-0.380821\pi\) | ||||
0.365725 | + | 0.930723i | \(0.380821\pi\) | |||||||
\(152\) | −54.5640 | −0.0291166 | ||||||||
\(153\) | 460.027 | 0.243078 | ||||||||
\(154\) | 26.4489 | 0.0138397 | ||||||||
\(155\) | −557.206 | −0.288747 | ||||||||
\(156\) | −845.607 | −0.433992 | ||||||||
\(157\) | −263.487 | −0.133940 | −0.0669698 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669698 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(158\) | 110.924 | 0.0558524 | ||||||||
\(159\) | 3079.07 | 1.53576 | ||||||||
\(160\) | −319.807 | −0.158019 | ||||||||
\(161\) | −30.1412 | −0.0147544 | ||||||||
\(162\) | −1717.39 | −0.832904 | ||||||||
\(163\) | 602.189 | 0.289369 | 0.144684 | − | 0.989478i | \(-0.453783\pi\) | ||||
0.144684 | + | 0.989478i | \(0.453783\pi\) | |||||||
\(164\) | −1508.43 | −0.718223 | ||||||||
\(165\) | 57.9723 | 0.0273524 | ||||||||
\(166\) | 357.179 | 0.167003 | ||||||||
\(167\) | −3100.06 | −1.43646 | −0.718232 | − | 0.695804i | \(-0.755048\pi\) | ||||
−0.718232 | + | 0.695804i | \(0.755048\pi\) | |||||||
\(168\) | 402.222 | 0.184715 | ||||||||
\(169\) | −1217.76 | −0.554284 | ||||||||
\(170\) | −151.434 | −0.0683204 | ||||||||
\(171\) | 25.1424 | 0.0112438 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −793.385 | −0.348670 | −0.174335 | − | 0.984686i | \(-0.555778\pi\) | ||||
−0.174335 | + | 0.984686i | \(0.555778\pi\) | |||||||
\(174\) | 960.140 | 0.418322 | ||||||||
\(175\) | −337.406 | −0.145746 | ||||||||
\(176\) | −47.9522 | −0.0205371 | ||||||||
\(177\) | −3776.66 | −1.60379 | ||||||||
\(178\) | 2514.38 | 1.05877 | ||||||||
\(179\) | −1832.74 | −0.765283 | −0.382642 | − | 0.923897i | \(-0.624986\pi\) | ||||
−0.382642 | + | 0.923897i | \(0.624986\pi\) | |||||||
\(180\) | 89.5525 | 0.0370825 | ||||||||
\(181\) | −3600.53 | −1.47859 | −0.739297 | − | 0.673380i | \(-0.764842\pi\) | ||||
−0.739297 | + | 0.673380i | \(0.764842\pi\) | |||||||
\(182\) | −165.098 | −0.0672409 | ||||||||
\(183\) | −4069.83 | −1.64399 | ||||||||
\(184\) | 255.403 | 0.102329 | ||||||||
\(185\) | −350.526 | −0.139304 | ||||||||
\(186\) | −3463.58 | −1.36539 | ||||||||
\(187\) | 212.634 | 0.0831517 | ||||||||
\(188\) | 880.288 | 0.341498 | ||||||||
\(189\) | 276.052 | 0.106242 | ||||||||
\(190\) | −8.27649 | −0.00316021 | ||||||||
\(191\) | −1718.34 | −0.650967 | −0.325484 | − | 0.945548i | \(-0.605527\pi\) | ||||
−0.325484 | + | 0.945548i | \(0.605527\pi\) | |||||||
\(192\) | −2458.67 | −0.924162 | ||||||||
\(193\) | −902.915 | −0.336753 | −0.168376 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168376 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(194\) | 1941.40 | 0.718476 | ||||||||
\(195\) | −361.871 | −0.132893 | ||||||||
\(196\) | 1472.75 | 0.536716 | ||||||||
\(197\) | −2564.17 | −0.927360 | −0.463680 | − | 0.886003i | \(-0.653471\pi\) | ||||
−0.463680 | + | 0.886003i | \(0.653471\pi\) | |||||||
\(198\) | 103.270 | 0.0370660 | ||||||||
\(199\) | −4092.54 | −1.45785 | −0.728925 | − | 0.684593i | \(-0.759980\pi\) | ||||
−0.728925 | + | 0.684593i | \(0.759980\pi\) | |||||||
\(200\) | 2859.02 | 1.01082 | ||||||||
\(201\) | −1220.74 | −0.428380 | ||||||||
\(202\) | −1011.90 | −0.352461 | ||||||||
\(203\) | −228.255 | −0.0789182 | ||||||||
\(204\) | 1146.16 | 0.393370 | ||||||||
\(205\) | −645.520 | −0.219927 | ||||||||
\(206\) | −2258.24 | −0.763783 | ||||||||
\(207\) | −117.686 | −0.0395157 | ||||||||
\(208\) | 299.324 | 0.0997806 | ||||||||
\(209\) | 11.6213 | 0.00384624 | ||||||||
\(210\) | 61.0107 | 0.0200483 | ||||||||
\(211\) | 1558.96 | 0.508640 | 0.254320 | − | 0.967120i | \(-0.418148\pi\) | ||||
0.254320 | + | 0.967120i | \(0.418148\pi\) | |||||||
\(212\) | 2198.50 | 0.712234 | ||||||||
\(213\) | 5514.13 | 1.77381 | ||||||||
\(214\) | 1931.36 | 0.616940 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2339.14 | −0.736843 | ||||||||
\(217\) | 823.400 | 0.257585 | ||||||||
\(218\) | −2875.63 | −0.893404 | ||||||||
\(219\) | −3812.51 | −1.17637 | ||||||||
\(220\) | 41.3931 | 0.0126851 | ||||||||
\(221\) | −1327.29 | −0.403997 | ||||||||
\(222\) | −2178.86 | −0.658718 | ||||||||
\(223\) | 5191.82 | 1.55906 | 0.779529 | − | 0.626366i | \(-0.215458\pi\) | ||||
0.779529 | + | 0.626366i | \(0.215458\pi\) | |||||||
\(224\) | 472.589 | 0.140965 | ||||||||
\(225\) | −1317.40 | −0.390341 | ||||||||
\(226\) | −2379.15 | −0.700260 | ||||||||
\(227\) | 6436.83 | 1.88206 | 0.941029 | − | 0.338325i | \(-0.109860\pi\) | ||||
0.941029 | + | 0.338325i | \(0.109860\pi\) | |||||||
\(228\) | 62.6426 | 0.0181956 | ||||||||
\(229\) | −5961.17 | −1.72020 | −0.860099 | − | 0.510127i | \(-0.829598\pi\) | ||||
−0.860099 | + | 0.510127i | \(0.829598\pi\) | |||||||
\(230\) | 38.7406 | 0.0111064 | ||||||||
\(231\) | −85.6674 | −0.0244005 | ||||||||
\(232\) | 1934.13 | 0.547336 | ||||||||
\(233\) | −1629.54 | −0.458174 | −0.229087 | − | 0.973406i | \(-0.573574\pi\) | ||||
−0.229087 | + | 0.973406i | \(0.573574\pi\) | |||||||
\(234\) | −644.623 | −0.180087 | ||||||||
\(235\) | 376.712 | 0.104570 | ||||||||
\(236\) | −2696.59 | −0.743783 | ||||||||
\(237\) | −359.282 | −0.0984720 | ||||||||
\(238\) | 223.779 | 0.0609471 | ||||||||
\(239\) | 1788.54 | 0.484064 | 0.242032 | − | 0.970268i | \(-0.422186\pi\) | ||||
0.242032 | + | 0.970268i | \(0.422186\pi\) | |||||||
\(240\) | −110.613 | −0.0297502 | ||||||||
\(241\) | 4933.89 | 1.31875 | 0.659377 | − | 0.751812i | \(-0.270820\pi\) | ||||
0.659377 | + | 0.751812i | \(0.270820\pi\) | |||||||
\(242\) | −2480.28 | −0.658836 | ||||||||
\(243\) | 2879.34 | 0.760123 | ||||||||
\(244\) | −2905.92 | −0.762427 | ||||||||
\(245\) | 630.251 | 0.164348 | ||||||||
\(246\) | −4012.53 | −1.03996 | ||||||||
\(247\) | −72.5419 | −0.0186872 | ||||||||
\(248\) | −6977.12 | −1.78648 | ||||||||
\(249\) | −1156.89 | −0.294439 | ||||||||
\(250\) | 879.953 | 0.222612 | ||||||||
\(251\) | 5862.79 | 1.47433 | 0.737163 | − | 0.675715i | \(-0.236165\pi\) | ||||
0.737163 | + | 0.675715i | \(0.236165\pi\) | |||||||
\(252\) | −132.334 | −0.0330805 | ||||||||
\(253\) | −54.3971 | −0.0135175 | ||||||||
\(254\) | 2639.13 | 0.651944 | ||||||||
\(255\) | 490.492 | 0.120454 | ||||||||
\(256\) | −4340.63 | −1.05972 | ||||||||
\(257\) | 1027.25 | 0.249332 | 0.124666 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124666 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 517.983 | 0.124270 | ||||||||
\(260\) | −258.381 | −0.0616312 | ||||||||
\(261\) | −891.223 | −0.211361 | ||||||||
\(262\) | 1522.86 | 0.359094 | ||||||||
\(263\) | −8377.92 | −1.96428 | −0.982138 | − | 0.188160i | \(-0.939748\pi\) | ||||
−0.982138 | + | 0.188160i | \(0.939748\pi\) | |||||||
\(264\) | 725.907 | 0.169229 | ||||||||
\(265\) | 940.831 | 0.218094 | ||||||||
\(266\) | 12.2304 | 0.00281916 | ||||||||
\(267\) | −8144.02 | −1.86669 | ||||||||
\(268\) | −871.626 | −0.198668 | ||||||||
\(269\) | −2853.05 | −0.646668 | −0.323334 | − | 0.946285i | \(-0.604804\pi\) | ||||
−0.323334 | + | 0.946285i | \(0.604804\pi\) | |||||||
\(270\) | −354.810 | −0.0799743 | ||||||||
\(271\) | −4091.04 | −0.917021 | −0.458511 | − | 0.888689i | \(-0.651617\pi\) | ||||
−0.458511 | + | 0.888689i | \(0.651617\pi\) | |||||||
\(272\) | −405.713 | −0.0904411 | ||||||||
\(273\) | 534.747 | 0.118551 | ||||||||
\(274\) | −306.975 | −0.0676827 | ||||||||
\(275\) | −608.931 | −0.133527 | ||||||||
\(276\) | −293.217 | −0.0639478 | ||||||||
\(277\) | −5795.51 | −1.25711 | −0.628553 | − | 0.777766i | \(-0.716353\pi\) | ||||
−0.628553 | + | 0.777766i | \(0.716353\pi\) | |||||||
\(278\) | −4360.11 | −0.940656 | ||||||||
\(279\) | 3214.96 | 0.689874 | ||||||||
\(280\) | 122.902 | 0.0262313 | ||||||||
\(281\) | 4930.69 | 1.04676 | 0.523382 | − | 0.852098i | \(-0.324670\pi\) | ||||
0.523382 | + | 0.852098i | \(0.324670\pi\) | |||||||
\(282\) | 2341.63 | 0.494476 | ||||||||
\(283\) | 3343.99 | 0.702402 | 0.351201 | − | 0.936300i | \(-0.385773\pi\) | ||||
0.351201 | + | 0.936300i | \(0.385773\pi\) | |||||||
\(284\) | 3937.17 | 0.822634 | ||||||||
\(285\) | 26.8074 | 0.00557169 | ||||||||
\(286\) | −297.959 | −0.0616037 | ||||||||
\(287\) | 953.905 | 0.196192 | ||||||||
\(288\) | 1845.22 | 0.377538 | ||||||||
\(289\) | −3113.95 | −0.633818 | ||||||||
\(290\) | 293.377 | 0.0594059 | ||||||||
\(291\) | −6288.15 | −1.26673 | ||||||||
\(292\) | −2722.18 | −0.545561 | ||||||||
\(293\) | 3791.10 | 0.755898 | 0.377949 | − | 0.925826i | \(-0.376629\pi\) | ||||
0.377949 | + | 0.925826i | \(0.376629\pi\) | |||||||
\(294\) | 3917.62 | 0.777144 | ||||||||
\(295\) | −1153.98 | −0.227754 | ||||||||
\(296\) | −4389.15 | −0.861873 | ||||||||
\(297\) | 498.202 | 0.0973355 | ||||||||
\(298\) | −2152.48 | −0.418422 | ||||||||
\(299\) | 339.554 | 0.0656753 | ||||||||
\(300\) | −3282.32 | −0.631683 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2577.81 | 0.491180 | ||||||||
\(303\) | 3277.52 | 0.621415 | ||||||||
\(304\) | −22.1739 | −0.00418342 | ||||||||
\(305\) | −1243.56 | −0.233463 | ||||||||
\(306\) | 873.743 | 0.163231 | ||||||||
\(307\) | −4492.58 | −0.835195 | −0.417598 | − | 0.908632i | \(-0.637128\pi\) | ||||
−0.417598 | + | 0.908632i | \(0.637128\pi\) | |||||||
\(308\) | −61.1678 | −0.0113161 | ||||||||
\(309\) | 7314.40 | 1.34661 | ||||||||
\(310\) | −1058.32 | −0.193898 | ||||||||
\(311\) | 5187.14 | 0.945774 | 0.472887 | − | 0.881123i | \(-0.343212\pi\) | ||||
0.472887 | + | 0.881123i | \(0.343212\pi\) | |||||||
\(312\) | −4531.21 | −0.822209 | ||||||||
\(313\) | 5096.23 | 0.920307 | 0.460153 | − | 0.887839i | \(-0.347794\pi\) | ||||
0.460153 | + | 0.887839i | \(0.347794\pi\) | |||||||
\(314\) | −500.448 | −0.0899425 | ||||||||
\(315\) | −56.6314 | −0.0101296 | ||||||||
\(316\) | −256.533 | −0.0456680 | ||||||||
\(317\) | −6988.00 | −1.23812 | −0.619062 | − | 0.785342i | \(-0.712487\pi\) | ||||
−0.619062 | + | 0.785342i | \(0.712487\pi\) | |||||||
\(318\) | 5848.18 | 1.03129 | ||||||||
\(319\) | −411.942 | −0.0723020 | ||||||||
\(320\) | −751.263 | −0.131240 | ||||||||
\(321\) | −6255.64 | −1.08771 | ||||||||
\(322\) | −57.2481 | −0.00990780 | ||||||||
\(323\) | 98.3257 | 0.0169380 | ||||||||
\(324\) | 3971.76 | 0.681028 | ||||||||
\(325\) | 3801.02 | 0.648747 | ||||||||
\(326\) | 1143.76 | 0.194315 | ||||||||
\(327\) | 9314.09 | 1.57514 | ||||||||
\(328\) | −8082.96 | −1.36069 | ||||||||
\(329\) | −556.679 | −0.0932848 | ||||||||
\(330\) | 110.109 | 0.0183675 | ||||||||
\(331\) | −2689.73 | −0.446650 | −0.223325 | − | 0.974744i | \(-0.571691\pi\) | ||||
−0.223325 | + | 0.974744i | \(0.571691\pi\) | |||||||
\(332\) | −826.039 | −0.136551 | ||||||||
\(333\) | 2022.46 | 0.332824 | ||||||||
\(334\) | −5888.03 | −0.964607 | ||||||||
\(335\) | −373.006 | −0.0608342 | ||||||||
\(336\) | 163.456 | 0.0265395 | ||||||||
\(337\) | 9821.54 | 1.58758 | 0.793788 | − | 0.608194i | \(-0.208106\pi\) | ||||
0.793788 | + | 0.608194i | \(0.208106\pi\) | |||||||
\(338\) | −2312.93 | −0.372210 | ||||||||
\(339\) | 7706.02 | 1.23461 | ||||||||
\(340\) | 350.218 | 0.0558625 | ||||||||
\(341\) | 1486.03 | 0.235991 | ||||||||
\(342\) | 47.7537 | 0.00755036 | ||||||||
\(343\) | −1884.12 | −0.296597 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −125.480 | −0.0195815 | ||||||||
\(346\) | −1506.90 | −0.234137 | ||||||||
\(347\) | 1195.67 | 0.184977 | 0.0924885 | − | 0.995714i | \(-0.470518\pi\) | ||||
0.0924885 | + | 0.995714i | \(0.470518\pi\) | |||||||
\(348\) | −2220.49 | −0.342043 | ||||||||
\(349\) | 2146.24 | 0.329186 | 0.164593 | − | 0.986362i | \(-0.447369\pi\) | ||||
0.164593 | + | 0.986362i | \(0.447369\pi\) | |||||||
\(350\) | −640.845 | −0.0978703 | ||||||||
\(351\) | −3109.84 | −0.472909 | ||||||||
\(352\) | 852.902 | 0.129147 | ||||||||
\(353\) | −11886.2 | −1.79217 | −0.896087 | − | 0.443879i | \(-0.853602\pi\) | ||||
−0.896087 | + | 0.443879i | \(0.853602\pi\) | |||||||
\(354\) | −7173.12 | −1.07697 | ||||||||
\(355\) | 1684.88 | 0.251899 | ||||||||
\(356\) | −5814.95 | −0.865707 | ||||||||
\(357\) | −724.814 | −0.107454 | ||||||||
\(358\) | −3480.99 | −0.513899 | ||||||||
\(359\) | −6715.29 | −0.987241 | −0.493621 | − | 0.869677i | \(-0.664327\pi\) | ||||
−0.493621 | + | 0.869677i | \(0.664327\pi\) | |||||||
\(360\) | 479.869 | 0.0702537 | ||||||||
\(361\) | −6853.63 | −0.999217 | ||||||||
\(362\) | −6838.60 | −0.992898 | ||||||||
\(363\) | 8033.56 | 1.16158 | ||||||||
\(364\) | 381.817 | 0.0549799 | ||||||||
\(365\) | −1164.94 | −0.167056 | ||||||||
\(366\) | −7729.95 | −1.10396 | ||||||||
\(367\) | −7744.24 | −1.10149 | −0.550744 | − | 0.834674i | \(-0.685656\pi\) | ||||
−0.550744 | + | 0.834674i | \(0.685656\pi\) | |||||||
\(368\) | 103.791 | 0.0147025 | ||||||||
\(369\) | 3724.52 | 0.525449 | ||||||||
\(370\) | −665.765 | −0.0935445 | ||||||||
\(371\) | −1390.29 | −0.194557 | ||||||||
\(372\) | 8010.13 | 1.11641 | ||||||||
\(373\) | −56.6698 | −0.00786662 | −0.00393331 | − | 0.999992i | \(-0.501252\pi\) | ||||
−0.00393331 | + | 0.999992i | \(0.501252\pi\) | |||||||
\(374\) | 403.863 | 0.0558376 | ||||||||
\(375\) | −2850.15 | −0.392483 | ||||||||
\(376\) | 4717.05 | 0.646976 | ||||||||
\(377\) | 2571.40 | 0.351283 | ||||||||
\(378\) | 524.314 | 0.0713433 | ||||||||
\(379\) | 2963.95 | 0.401709 | 0.200854 | − | 0.979621i | \(-0.435628\pi\) | ||||
0.200854 | + | 0.979621i | \(0.435628\pi\) | |||||||
\(380\) | 19.1409 | 0.00258396 | ||||||||
\(381\) | −8548.08 | −1.14943 | ||||||||
\(382\) | −3263.70 | −0.437134 | ||||||||
\(383\) | 1125.17 | 0.150114 | 0.0750570 | − | 0.997179i | \(-0.476086\pi\) | ||||
0.0750570 | + | 0.997179i | \(0.476086\pi\) | |||||||
\(384\) | 3703.28 | 0.492141 | ||||||||
\(385\) | −26.1763 | −0.00346511 | ||||||||
\(386\) | −1714.93 | −0.226134 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4489.83 | −0.587466 | ||||||||
\(389\) | 11051.0 | 1.44038 | 0.720189 | − | 0.693777i | \(-0.244055\pi\) | ||||
0.720189 | + | 0.693777i | \(0.244055\pi\) | |||||||
\(390\) | −687.313 | −0.0892395 | ||||||||
\(391\) | −460.242 | −0.0595280 | ||||||||
\(392\) | 7891.76 | 1.01682 | ||||||||
\(393\) | −4932.51 | −0.633110 | ||||||||
\(394\) | −4870.22 | −0.622736 | ||||||||
\(395\) | −109.781 | −0.0139840 | ||||||||
\(396\) | −238.830 | −0.0303072 | ||||||||
\(397\) | 6471.64 | 0.818142 | 0.409071 | − | 0.912503i | \(-0.365853\pi\) | ||||
0.409071 | + | 0.912503i | \(0.365853\pi\) | |||||||
\(398\) | −7773.08 | −0.978968 | ||||||||
\(399\) | −39.6141 | −0.00497039 | ||||||||
\(400\) | 1161.86 | 0.145232 | ||||||||
\(401\) | −3098.52 | −0.385867 | −0.192934 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192934 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(402\) | −2318.59 | −0.287664 | ||||||||
\(403\) | −9275.97 | −1.14657 | ||||||||
\(404\) | 2340.20 | 0.288191 | ||||||||
\(405\) | 1699.68 | 0.208538 | ||||||||
\(406\) | −433.533 | −0.0529947 | ||||||||
\(407\) | 934.826 | 0.113852 | ||||||||
\(408\) | 6141.75 | 0.745249 | ||||||||
\(409\) | 12700.2 | 1.53542 | 0.767710 | − | 0.640798i | \(-0.221396\pi\) | ||||
0.767710 | + | 0.640798i | \(0.221396\pi\) | |||||||
\(410\) | −1226.06 | −0.147684 | ||||||||
\(411\) | 994.286 | 0.119330 | ||||||||
\(412\) | 5222.59 | 0.624511 | ||||||||
\(413\) | 1705.27 | 0.203175 | ||||||||
\(414\) | −223.525 | −0.0265354 | ||||||||
\(415\) | −353.497 | −0.0418132 | ||||||||
\(416\) | −5323.92 | −0.627468 | ||||||||
\(417\) | 14122.3 | 1.65845 | ||||||||
\(418\) | 22.0728 | 0.00258281 | ||||||||
\(419\) | −8277.25 | −0.965084 | −0.482542 | − | 0.875873i | \(-0.660286\pi\) | ||||
−0.482542 | + | 0.875873i | \(0.660286\pi\) | |||||||
\(420\) | −141.098 | −0.0163926 | ||||||||
\(421\) | 6783.31 | 0.785269 | 0.392634 | − | 0.919695i | \(-0.371564\pi\) | ||||
0.392634 | + | 0.919695i | \(0.371564\pi\) | |||||||
\(422\) | 2960.98 | 0.341560 | ||||||||
\(423\) | −2173.55 | −0.249839 | ||||||||
\(424\) | 11780.7 | 1.34935 | ||||||||
\(425\) | −5152.03 | −0.588024 | ||||||||
\(426\) | 10473.2 | 1.19114 | ||||||||
\(427\) | 1837.65 | 0.208267 | ||||||||
\(428\) | −4466.62 | −0.504444 | ||||||||
\(429\) | 965.082 | 0.108612 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5654.52 | −0.631946 | −0.315973 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315973 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(432\) | −950.586 | −0.105868 | ||||||||
\(433\) | 2479.97 | 0.275242 | 0.137621 | − | 0.990485i | \(-0.456054\pi\) | ||||
0.137621 | + | 0.990485i | \(0.456054\pi\) | |||||||
\(434\) | 1563.91 | 0.172973 | ||||||||
\(435\) | −950.243 | −0.104737 | ||||||||
\(436\) | 6650.40 | 0.730496 | ||||||||
\(437\) | −25.1541 | −0.00275351 | ||||||||
\(438\) | −7241.21 | −0.789951 | ||||||||
\(439\) | −6930.24 | −0.753445 | −0.376723 | − | 0.926326i | \(-0.622949\pi\) | ||||
−0.376723 | + | 0.926326i | \(0.622949\pi\) | |||||||
\(440\) | 221.806 | 0.0240322 | ||||||||
\(441\) | −3636.42 | −0.392659 | ||||||||
\(442\) | −2520.97 | −0.271290 | ||||||||
\(443\) | −14683.8 | −1.57482 | −0.787412 | − | 0.616427i | \(-0.788580\pi\) | ||||
−0.787412 | + | 0.616427i | \(0.788580\pi\) | |||||||
\(444\) | 5039.00 | 0.538604 | ||||||||
\(445\) | −2488.46 | −0.265088 | ||||||||
\(446\) | 9860.99 | 1.04693 | ||||||||
\(447\) | 6971.84 | 0.737711 | ||||||||
\(448\) | 1110.16 | 0.117077 | ||||||||
\(449\) | 12567.9 | 1.32097 | 0.660487 | − | 0.750837i | \(-0.270350\pi\) | ||||
0.660487 | + | 0.750837i | \(0.270350\pi\) | |||||||
\(450\) | −2502.18 | −0.262120 | ||||||||
\(451\) | 1721.55 | 0.179745 | ||||||||
\(452\) | 5502.21 | 0.572571 | ||||||||
\(453\) | −8349.48 | −0.865988 | ||||||||
\(454\) | 12225.7 | 1.26383 | ||||||||
\(455\) | 163.396 | 0.0168354 | ||||||||
\(456\) | 335.672 | 0.0344721 | ||||||||
\(457\) | 3586.37 | 0.367097 | 0.183549 | − | 0.983011i | \(-0.441242\pi\) | ||||
0.183549 | + | 0.983011i | \(0.441242\pi\) | |||||||
\(458\) | −11322.2 | −1.15514 | ||||||||
\(459\) | 4215.18 | 0.428645 | ||||||||
\(460\) | −89.5944 | −0.00908122 | ||||||||
\(461\) | 11289.0 | 1.14053 | 0.570263 | − | 0.821462i | \(-0.306841\pi\) | ||||
0.570263 | + | 0.821462i | \(0.306841\pi\) | |||||||
\(462\) | −162.711 | −0.0163853 | ||||||||
\(463\) | 16287.2 | 1.63484 | 0.817419 | − | 0.576044i | \(-0.195404\pi\) | ||||
0.817419 | + | 0.576044i | \(0.195404\pi\) | |||||||
\(464\) | 785.999 | 0.0786403 | ||||||||
\(465\) | 3427.87 | 0.341858 | ||||||||
\(466\) | −3095.03 | −0.307671 | ||||||||
\(467\) | −544.522 | −0.0539561 | −0.0269780 | − | 0.999636i | \(-0.508588\pi\) | ||||
−0.0269780 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(468\) | 1490.81 | 0.147249 | ||||||||
\(469\) | 551.202 | 0.0542689 | ||||||||
\(470\) | 715.501 | 0.0702205 | ||||||||
\(471\) | 1620.94 | 0.158575 | ||||||||
\(472\) | −14449.7 | −1.40912 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −682.395 | −0.0661254 | ||||||||
\(475\) | −281.580 | −0.0271995 | ||||||||
\(476\) | −517.528 | −0.0498337 | ||||||||
\(477\) | −5428.40 | −0.521068 | ||||||||
\(478\) | 3397.04 | 0.325056 | ||||||||
\(479\) | −3992.32 | −0.380822 | −0.190411 | − | 0.981704i | \(-0.560982\pi\) | ||||
−0.190411 | + | 0.981704i | \(0.560982\pi\) | |||||||
\(480\) | 1967.42 | 0.187083 | ||||||||
\(481\) | −5835.31 | −0.553154 | ||||||||
\(482\) | 9371.09 | 0.885563 | ||||||||
\(483\) | 185.425 | 0.0174682 | ||||||||
\(484\) | 5736.08 | 0.538700 | ||||||||
\(485\) | −1921.39 | −0.179888 | ||||||||
\(486\) | 5468.82 | 0.510434 | ||||||||
\(487\) | −9965.60 | −0.927278 | −0.463639 | − | 0.886024i | \(-0.653457\pi\) | ||||
−0.463639 | + | 0.886024i | \(0.653457\pi\) | |||||||
\(488\) | −15571.4 | −1.44444 | ||||||||
\(489\) | −3704.60 | −0.342593 | ||||||||
\(490\) | 1197.06 | 0.110362 | ||||||||
\(491\) | 15698.8 | 1.44293 | 0.721463 | − | 0.692452i | \(-0.243470\pi\) | ||||
0.721463 | + | 0.692452i | \(0.243470\pi\) | |||||||
\(492\) | 9279.70 | 0.850327 | ||||||||
\(493\) | −3485.36 | −0.318403 | ||||||||
\(494\) | −137.781 | −0.0125487 | ||||||||
\(495\) | −102.205 | −0.00928037 | ||||||||
\(496\) | −2835.39 | −0.256679 | ||||||||
\(497\) | −2489.80 | −0.224714 | ||||||||
\(498\) | −2197.33 | −0.197720 | ||||||||
\(499\) | −2241.60 | −0.201098 | −0.100549 | − | 0.994932i | \(-0.532060\pi\) | ||||
−0.100549 | + | 0.994932i | \(0.532060\pi\) | |||||||
\(500\) | −2035.05 | −0.182020 | ||||||||
\(501\) | 19071.2 | 1.70068 | ||||||||
\(502\) | 11135.4 | 0.990032 | ||||||||
\(503\) | −5388.26 | −0.477635 | −0.238818 | − | 0.971064i | \(-0.576760\pi\) | ||||
−0.238818 | + | 0.971064i | \(0.576760\pi\) | |||||||
\(504\) | −709.117 | −0.0626718 | ||||||||
\(505\) | 1001.47 | 0.0882472 | ||||||||
\(506\) | −103.318 | −0.00907718 | ||||||||
\(507\) | 7491.54 | 0.656235 | ||||||||
\(508\) | −6103.45 | −0.533065 | ||||||||
\(509\) | −3055.68 | −0.266092 | −0.133046 | − | 0.991110i | \(-0.542476\pi\) | ||||
−0.133046 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(510\) | 931.606 | 0.0808867 | ||||||||
\(511\) | 1721.46 | 0.149027 | ||||||||
\(512\) | −3428.51 | −0.295938 | ||||||||
\(513\) | 230.377 | 0.0198273 | ||||||||
\(514\) | 1951.10 | 0.167430 | ||||||||
\(515\) | 2234.96 | 0.191232 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1004.66 | −0.0854642 | ||||||||
\(518\) | 983.821 | 0.0834491 | ||||||||
\(519\) | 4880.82 | 0.412802 | ||||||||
\(520\) | −1384.54 | −0.116762 | ||||||||
\(521\) | 13025.1 | 1.09528 | 0.547638 | − | 0.836716i | \(-0.315527\pi\) | ||||
0.547638 | + | 0.836716i | \(0.315527\pi\) | |||||||
\(522\) | −1692.73 | −0.141932 | ||||||||
\(523\) | 2116.73 | 0.176976 | 0.0884878 | − | 0.996077i | \(-0.471797\pi\) | ||||
0.0884878 | + | 0.996077i | \(0.471797\pi\) | |||||||
\(524\) | −3521.88 | −0.293615 | ||||||||
\(525\) | 2075.68 | 0.172553 | ||||||||
\(526\) | −15912.4 | −1.31904 | ||||||||
\(527\) | 12572.9 | 1.03925 | ||||||||
\(528\) | 294.997 | 0.0243145 | ||||||||
\(529\) | −12049.3 | −0.990323 | ||||||||
\(530\) | 1786.95 | 0.146453 | ||||||||
\(531\) | 6658.24 | 0.544149 | ||||||||
\(532\) | −28.2850 | −0.00230510 | ||||||||
\(533\) | −10746.2 | −0.873298 | ||||||||
\(534\) | −15468.2 | −1.25351 | ||||||||
\(535\) | −1911.45 | −0.154466 | ||||||||
\(536\) | −4670.63 | −0.376382 | ||||||||
\(537\) | 11274.8 | 0.906044 | ||||||||
\(538\) | −5418.89 | −0.434247 | ||||||||
\(539\) | −1680.83 | −0.134320 | ||||||||
\(540\) | 820.561 | 0.0653914 | ||||||||
\(541\) | −346.282 | −0.0275191 | −0.0137596 | − | 0.999905i | \(-0.504380\pi\) | ||||
−0.0137596 | + | 0.999905i | \(0.504380\pi\) | |||||||
\(542\) | −7770.24 | −0.615794 | ||||||||
\(543\) | 22150.1 | 1.75056 | ||||||||
\(544\) | 7216.22 | 0.568737 | ||||||||
\(545\) | 2845.98 | 0.223685 | ||||||||
\(546\) | 1015.66 | 0.0796087 | ||||||||
\(547\) | 21019.5 | 1.64301 | 0.821507 | − | 0.570198i | \(-0.193133\pi\) | ||||
0.821507 | + | 0.570198i | \(0.193133\pi\) | |||||||
\(548\) | 709.935 | 0.0553411 | ||||||||
\(549\) | 7175.10 | 0.557789 | ||||||||
\(550\) | −1156.56 | −0.0896653 | ||||||||
\(551\) | −190.489 | −0.0147280 | ||||||||
\(552\) | −1571.21 | −0.121151 | ||||||||
\(553\) | 162.227 | 0.0124748 | ||||||||
\(554\) | −11007.6 | −0.844166 | ||||||||
\(555\) | 2156.40 | 0.164926 | ||||||||
\(556\) | 10083.5 | 0.769132 | ||||||||
\(557\) | 16058.5 | 1.22158 | 0.610790 | − | 0.791792i | \(-0.290852\pi\) | ||||
0.610790 | + | 0.791792i | \(0.290852\pi\) | |||||||
\(558\) | 6106.28 | 0.463261 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 49.9452 | 0.00376887 | ||||||||
\(561\) | −1308.10 | −0.0984459 | ||||||||
\(562\) | 9365.02 | 0.702917 | ||||||||
\(563\) | −9252.27 | −0.692605 | −0.346302 | − | 0.938123i | \(-0.612563\pi\) | ||||
−0.346302 | + | 0.938123i | \(0.612563\pi\) | |||||||
\(564\) | −5415.44 | −0.404310 | ||||||||
\(565\) | 2354.63 | 0.175327 | ||||||||
\(566\) | 6351.35 | 0.471673 | ||||||||
\(567\) | −2511.67 | −0.186032 | ||||||||
\(568\) | 21097.4 | 1.55850 | ||||||||
\(569\) | 11700.9 | 0.862090 | 0.431045 | − | 0.902330i | \(-0.358145\pi\) | ||||
0.431045 | + | 0.902330i | \(0.358145\pi\) | |||||||
\(570\) | 50.9161 | 0.00374148 | ||||||||
\(571\) | −21685.1 | −1.58931 | −0.794653 | − | 0.607064i | \(-0.792347\pi\) | ||||
−0.794653 | + | 0.607064i | \(0.792347\pi\) | |||||||
\(572\) | 689.082 | 0.0503706 | ||||||||
\(573\) | 10571.0 | 0.770701 | ||||||||
\(574\) | 1811.78 | 0.131746 | ||||||||
\(575\) | 1318.02 | 0.0955915 | ||||||||
\(576\) | 4334.63 | 0.313559 | ||||||||
\(577\) | 6485.51 | 0.467929 | 0.233965 | − | 0.972245i | \(-0.424830\pi\) | ||||
0.233965 | + | 0.972245i | \(0.424830\pi\) | |||||||
\(578\) | −5914.42 | −0.425618 | ||||||||
\(579\) | 5554.64 | 0.398692 | ||||||||
\(580\) | −678.487 | −0.0485735 | ||||||||
\(581\) | 522.373 | 0.0373007 | ||||||||
\(582\) | −11943.3 | −0.850628 | ||||||||
\(583\) | −2509.12 | −0.178246 | ||||||||
\(584\) | −14586.9 | −1.03358 | ||||||||
\(585\) | 637.978 | 0.0450892 | ||||||||
\(586\) | 7200.55 | 0.507597 | ||||||||
\(587\) | −22400.2 | −1.57505 | −0.787524 | − | 0.616284i | \(-0.788637\pi\) | ||||
−0.787524 | + | 0.616284i | \(0.788637\pi\) | |||||||
\(588\) | −9060.19 | −0.635435 | ||||||||
\(589\) | 687.163 | 0.0480714 | ||||||||
\(590\) | −2191.80 | −0.152940 | ||||||||
\(591\) | 15774.5 | 1.09793 | ||||||||
\(592\) | −1783.68 | −0.123832 | ||||||||
\(593\) | −1760.43 | −0.121909 | −0.0609546 | − | 0.998141i | \(-0.519414\pi\) | ||||
−0.0609546 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(594\) | 946.251 | 0.0653622 | ||||||||
\(595\) | −221.472 | −0.0152596 | ||||||||
\(596\) | 4977.99 | 0.342125 | ||||||||
\(597\) | 25176.8 | 1.72600 | ||||||||
\(598\) | 644.925 | 0.0441019 | ||||||||
\(599\) | −8806.31 | −0.600695 | −0.300347 | − | 0.953830i | \(-0.597103\pi\) | ||||
−0.300347 | + | 0.953830i | \(0.597103\pi\) | |||||||
\(600\) | −17588.4 | −1.19674 | ||||||||
\(601\) | −3892.88 | −0.264216 | −0.132108 | − | 0.991235i | \(-0.542175\pi\) | ||||
−0.132108 | + | 0.991235i | \(0.542175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2152.17 | 0.145345 | ||||||||
\(604\) | −5961.65 | −0.401616 | ||||||||
\(605\) | 2454.71 | 0.164956 | ||||||||
\(606\) | 6225.10 | 0.417290 | ||||||||
\(607\) | −14131.4 | −0.944938 | −0.472469 | − | 0.881347i | \(-0.656637\pi\) | ||||
−0.472469 | + | 0.881347i | \(0.656637\pi\) | |||||||
\(608\) | 394.396 | 0.0263074 | ||||||||
\(609\) | 1404.20 | 0.0934338 | ||||||||
\(610\) | −2361.94 | −0.156774 | ||||||||
\(611\) | 6271.24 | 0.415232 | ||||||||
\(612\) | −2020.69 | −0.133466 | ||||||||
\(613\) | 21940.2 | 1.44561 | 0.722804 | − | 0.691053i | \(-0.242853\pi\) | ||||
0.722804 | + | 0.691053i | \(0.242853\pi\) | |||||||
\(614\) | −8532.89 | −0.560846 | ||||||||
\(615\) | 3971.17 | 0.260379 | ||||||||
\(616\) | −327.769 | −0.0214386 | ||||||||
\(617\) | 14064.3 | 0.917678 | 0.458839 | − | 0.888519i | \(-0.348265\pi\) | ||||
0.458839 | + | 0.888519i | \(0.348265\pi\) | |||||||
\(618\) | 13892.5 | 0.904267 | ||||||||
\(619\) | −12577.8 | −0.816714 | −0.408357 | − | 0.912822i | \(-0.633898\pi\) | ||||
−0.408357 | + | 0.912822i | \(0.633898\pi\) | |||||||
\(620\) | 2447.55 | 0.158542 | ||||||||
\(621\) | −1078.35 | −0.0696822 | ||||||||
\(622\) | 9852.10 | 0.635102 | ||||||||
\(623\) | 3677.27 | 0.236480 | ||||||||
\(624\) | −1841.41 | −0.118133 | ||||||||
\(625\) | 14312.4 | 0.915996 | ||||||||
\(626\) | 9679.43 | 0.618000 | ||||||||
\(627\) | −71.4932 | −0.00455369 | ||||||||
\(628\) | 1157.38 | 0.0735419 | ||||||||
\(629\) | 7909.37 | 0.501378 | ||||||||
\(630\) | −107.562 | −0.00680217 | ||||||||
\(631\) | −4073.63 | −0.257003 | −0.128501 | − | 0.991709i | \(-0.541017\pi\) | ||||
−0.128501 | + | 0.991709i | \(0.541017\pi\) | |||||||
\(632\) | −1374.64 | −0.0865191 | ||||||||
\(633\) | −9590.55 | −0.602196 | ||||||||
\(634\) | −13272.5 | −0.831419 | ||||||||
\(635\) | −2611.92 | −0.163230 | ||||||||
\(636\) | −13524.9 | −0.843237 | ||||||||
\(637\) | 10492.0 | 0.652601 | ||||||||
\(638\) | −782.415 | −0.0485519 | ||||||||
\(639\) | −9721.42 | −0.601836 | ||||||||
\(640\) | 1131.56 | 0.0698889 | ||||||||
\(641\) | −25739.7 | −1.58605 | −0.793023 | − | 0.609192i | \(-0.791494\pi\) | ||||
−0.793023 | + | 0.609192i | \(0.791494\pi\) | |||||||
\(642\) | −11881.5 | −0.730415 | ||||||||
\(643\) | −6453.80 | −0.395821 | −0.197911 | − | 0.980220i | \(-0.563416\pi\) | ||||
−0.197911 | + | 0.980220i | \(0.563416\pi\) | |||||||
\(644\) | 132.396 | 0.00810116 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 186.753 | 0.0113742 | ||||||||
\(647\) | −3686.03 | −0.223977 | −0.111988 | − | 0.993710i | \(-0.535722\pi\) | ||||
−0.111988 | + | 0.993710i | \(0.535722\pi\) | |||||||
\(648\) | 21282.8 | 1.29023 | ||||||||
\(649\) | 3077.58 | 0.186141 | ||||||||
\(650\) | 7219.41 | 0.435644 | ||||||||
\(651\) | −5065.47 | −0.304964 | ||||||||
\(652\) | −2645.14 | −0.158883 | ||||||||
\(653\) | 4652.32 | 0.278804 | 0.139402 | − | 0.990236i | \(-0.455482\pi\) | ||||
0.139402 | + | 0.990236i | \(0.455482\pi\) | |||||||
\(654\) | 17690.5 | 1.05773 | ||||||||
\(655\) | −1507.16 | −0.0899079 | ||||||||
\(656\) | −3284.78 | −0.195502 | ||||||||
\(657\) | 6721.45 | 0.399130 | ||||||||
\(658\) | −1057.32 | −0.0626422 | ||||||||
\(659\) | 19533.7 | 1.15467 | 0.577334 | − | 0.816508i | \(-0.304093\pi\) | ||||
0.577334 | + | 0.816508i | \(0.304093\pi\) | |||||||
\(660\) | −254.646 | −0.0150183 | ||||||||
\(661\) | 10301.4 | 0.606169 | 0.303085 | − | 0.952964i | \(-0.401984\pi\) | ||||
0.303085 | + | 0.952964i | \(0.401984\pi\) | |||||||
\(662\) | −5108.69 | −0.299932 | ||||||||
\(663\) | 8165.35 | 0.478305 | ||||||||
\(664\) | −4426.35 | −0.258698 | ||||||||
\(665\) | −12.1043 | −0.000705844 0 | ||||||||
\(666\) | 3841.33 | 0.223496 | ||||||||
\(667\) | 891.641 | 0.0517608 | ||||||||
\(668\) | 13617.1 | 0.788716 | ||||||||
\(669\) | −31939.5 | −1.84582 | ||||||||
\(670\) | −708.461 | −0.0408511 | ||||||||
\(671\) | 3316.49 | 0.190807 | ||||||||
\(672\) | −2907.32 | −0.166893 | ||||||||
\(673\) | −32709.1 | −1.87347 | −0.936734 | − | 0.350041i | \(-0.886168\pi\) | ||||
−0.936734 | + | 0.350041i | \(0.886168\pi\) | |||||||
\(674\) | 18654.4 | 1.06608 | ||||||||
\(675\) | −12071.2 | −0.688328 | ||||||||
\(676\) | 5349.07 | 0.304339 | ||||||||
\(677\) | 6223.46 | 0.353304 | 0.176652 | − | 0.984273i | \(-0.443473\pi\) | ||||
0.176652 | + | 0.984273i | \(0.443473\pi\) | |||||||
\(678\) | 14636.3 | 0.829060 | ||||||||
\(679\) | 2839.29 | 0.160474 | ||||||||
\(680\) | 1876.65 | 0.105833 | ||||||||
\(681\) | −39598.7 | −2.22823 | ||||||||
\(682\) | 2822.46 | 0.158471 | ||||||||
\(683\) | −14250.9 | −0.798380 | −0.399190 | − | 0.916868i | \(-0.630709\pi\) | ||||
−0.399190 | + | 0.916868i | \(0.630709\pi\) | |||||||
\(684\) | −110.439 | −0.00617359 | ||||||||
\(685\) | 303.811 | 0.0169460 | ||||||||
\(686\) | −3578.56 | −0.199169 | ||||||||
\(687\) | 36672.5 | 2.03660 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15662.3 | 0.866017 | ||||||||
\(690\) | −238.328 | −0.0131493 | ||||||||
\(691\) | −18569.4 | −1.02230 | −0.511152 | − | 0.859490i | \(-0.670781\pi\) | ||||
−0.511152 | + | 0.859490i | \(0.670781\pi\) | |||||||
\(692\) | 3484.98 | 0.191444 | ||||||||
\(693\) | 151.032 | 0.00827882 | ||||||||
\(694\) | 2270.98 | 0.124215 | ||||||||
\(695\) | 4315.17 | 0.235516 | ||||||||
\(696\) | −11898.6 | −0.648009 | ||||||||
\(697\) | 14565.7 | 0.791557 | ||||||||
\(698\) | 4076.43 | 0.221053 | ||||||||
\(699\) | 10024.7 | 0.542447 | ||||||||
\(700\) | 1482.07 | 0.0800242 | ||||||||
\(701\) | −3684.53 | −0.198520 | −0.0992602 | − | 0.995062i | \(-0.531648\pi\) | ||||
−0.0992602 | + | 0.995062i | \(0.531648\pi\) | |||||||
\(702\) | −5906.62 | −0.317566 | ||||||||
\(703\) | 432.279 | 0.0231916 | ||||||||
\(704\) | 2003.56 | 0.107261 | ||||||||
\(705\) | −2317.49 | −0.123804 | ||||||||
\(706\) | −22575.8 | −1.20347 | ||||||||
\(707\) | −1479.90 | −0.0787234 | ||||||||
\(708\) | 16589.1 | 0.880589 | ||||||||
\(709\) | −28799.5 | −1.52551 | −0.762757 | − | 0.646685i | \(-0.776155\pi\) | ||||
−0.762757 | + | 0.646685i | \(0.776155\pi\) | |||||||
\(710\) | 3200.15 | 0.169154 | ||||||||
\(711\) | 633.414 | 0.0334105 | ||||||||
\(712\) | −31159.5 | −1.64010 | ||||||||
\(713\) | −3216.47 | −0.168945 | ||||||||
\(714\) | −1376.66 | −0.0721573 | ||||||||
\(715\) | 294.887 | 0.0154240 | ||||||||
\(716\) | 8050.40 | 0.420192 | ||||||||
\(717\) | −11002.9 | −0.573099 | ||||||||
\(718\) | −12754.6 | −0.662947 | ||||||||
\(719\) | −3244.36 | −0.168281 | −0.0841406 | − | 0.996454i | \(-0.526814\pi\) | ||||
−0.0841406 | + | 0.996454i | \(0.526814\pi\) | |||||||
\(720\) | 195.011 | 0.0100939 | ||||||||
\(721\) | −3302.67 | −0.170594 | ||||||||
\(722\) | −13017.3 | −0.670989 | ||||||||
\(723\) | −30352.8 | −1.56132 | ||||||||
\(724\) | 15815.5 | 0.811848 | ||||||||
\(725\) | 9981.18 | 0.511299 | ||||||||
\(726\) | 15258.4 | 0.780017 | ||||||||
\(727\) | −26113.0 | −1.33216 | −0.666079 | − | 0.745881i | \(-0.732029\pi\) | ||||
−0.666079 | + | 0.745881i | \(0.732029\pi\) | |||||||
\(728\) | 2045.98 | 0.104161 | ||||||||
\(729\) | 6700.14 | 0.340403 | ||||||||
\(730\) | −2212.60 | −0.112181 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 17876.9 | 0.902662 | ||||||||
\(733\) | −8054.45 | −0.405863 | −0.202932 | − | 0.979193i | \(-0.565047\pi\) | ||||
−0.202932 | + | 0.979193i | \(0.565047\pi\) | |||||||
\(734\) | −14708.9 | −0.739666 | ||||||||
\(735\) | −3877.24 | −0.194577 | ||||||||
\(736\) | −1846.09 | −0.0924561 | ||||||||
\(737\) | 994.777 | 0.0497193 | ||||||||
\(738\) | 7074.10 | 0.352847 | ||||||||
\(739\) | 19543.4 | 0.972822 | 0.486411 | − | 0.873730i | \(-0.338306\pi\) | ||||
0.486411 | + | 0.873730i | \(0.338306\pi\) | |||||||
\(740\) | 1539.70 | 0.0764871 | ||||||||
\(741\) | 446.270 | 0.0221243 | ||||||||
\(742\) | −2640.63 | −0.130648 | ||||||||
\(743\) | 6207.63 | 0.306508 | 0.153254 | − | 0.988187i | \(-0.451025\pi\) | ||||
0.153254 | + | 0.988187i | \(0.451025\pi\) | |||||||
\(744\) | 42922.5 | 2.11507 | ||||||||
\(745\) | 2130.29 | 0.104762 | ||||||||
\(746\) | −107.635 | −0.00528256 | ||||||||
\(747\) | 2039.60 | 0.0998999 | ||||||||
\(748\) | −934.005 | −0.0456559 | ||||||||
\(749\) | 2824.61 | 0.137796 | ||||||||
\(750\) | −5413.38 | −0.263558 | ||||||||
\(751\) | 11820.4 | 0.574346 | 0.287173 | − | 0.957879i | \(-0.407285\pi\) | ||||
0.287173 | + | 0.957879i | \(0.407285\pi\) | |||||||
\(752\) | 1916.93 | 0.0929564 | ||||||||
\(753\) | −36067.2 | −1.74550 | ||||||||
\(754\) | 4883.94 | 0.235892 | ||||||||
\(755\) | −2551.24 | −0.122979 | ||||||||
\(756\) | −1212.57 | −0.0583342 | ||||||||
\(757\) | −23218.6 | −1.11479 | −0.557393 | − | 0.830249i | \(-0.688198\pi\) | ||||
−0.557393 | + | 0.830249i | \(0.688198\pi\) | |||||||
\(758\) | 5629.52 | 0.269754 | ||||||||
\(759\) | 334.645 | 0.0160038 | ||||||||
\(760\) | 102.567 | 0.00489538 | ||||||||
\(761\) | −14404.3 | −0.686144 | −0.343072 | − | 0.939309i | \(-0.611468\pi\) | ||||
−0.343072 | + | 0.939309i | \(0.611468\pi\) | |||||||
\(762\) | −16235.6 | −0.771857 | ||||||||
\(763\) | −4205.60 | −0.199545 | ||||||||
\(764\) | 7547.88 | 0.357425 | ||||||||
\(765\) | −864.737 | −0.0408688 | ||||||||
\(766\) | 2137.08 | 0.100804 | ||||||||
\(767\) | −19210.7 | −0.904377 | ||||||||
\(768\) | 26703.1 | 1.25464 | ||||||||
\(769\) | 2924.07 | 0.137119 | 0.0685597 | − | 0.997647i | \(-0.478160\pi\) | ||||
0.0685597 | + | 0.997647i | \(0.478160\pi\) | |||||||
\(770\) | −49.7174 | −0.00232687 | ||||||||
\(771\) | −6319.56 | −0.295192 | ||||||||
\(772\) | 3966.09 | 0.184900 | ||||||||
\(773\) | −1040.49 | −0.0484137 | −0.0242068 | − | 0.999707i | \(-0.507706\pi\) | ||||
−0.0242068 | + | 0.999707i | \(0.507706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36005.7 | −1.66886 | ||||||||
\(776\) | −24058.9 | −1.11297 | ||||||||
\(777\) | −3186.58 | −0.147127 | ||||||||
\(778\) | 20989.5 | 0.967236 | ||||||||
\(779\) | 796.075 | 0.0366141 | ||||||||
\(780\) | 1589.53 | 0.0729672 | ||||||||
\(781\) | −4493.45 | −0.205875 | ||||||||
\(782\) | −874.153 | −0.0399740 | ||||||||
\(783\) | −8166.19 | −0.372715 | ||||||||
\(784\) | 3207.08 | 0.146095 | ||||||||
\(785\) | 495.290 | 0.0225193 | ||||||||
\(786\) | −9368.47 | −0.425143 | ||||||||
\(787\) | 35796.2 | 1.62134 | 0.810671 | − | 0.585501i | \(-0.199102\pi\) | ||||
0.810671 | + | 0.585501i | \(0.199102\pi\) | |||||||
\(788\) | 11263.2 | 0.509183 | ||||||||
\(789\) | 51540.1 | 2.32557 | ||||||||
\(790\) | −208.511 | −0.00939047 | ||||||||
\(791\) | −3479.50 | −0.156406 | ||||||||
\(792\) | −1279.77 | −0.0574177 | ||||||||
\(793\) | −20701.9 | −0.927046 | ||||||||
\(794\) | 12291.8 | 0.549395 | ||||||||
\(795\) | −5787.89 | −0.258208 | ||||||||
\(796\) | 17976.6 | 0.800458 | ||||||||
\(797\) | 15694.6 | 0.697531 | 0.348766 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348766 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(798\) | −75.2403 | −0.00333769 | ||||||||
\(799\) | −8500.24 | −0.376366 | ||||||||
\(800\) | −20665.4 | −0.913292 | ||||||||
\(801\) | 14357.9 | 0.633348 | ||||||||
\(802\) | −5885.12 | −0.259116 | ||||||||
\(803\) | 3106.80 | 0.136534 | ||||||||
\(804\) | 5362.15 | 0.235210 | ||||||||
\(805\) | 56.6580 | 0.00248066 | ||||||||
\(806\) | −17618.1 | −0.769941 | ||||||||
\(807\) | 17551.7 | 0.765611 | ||||||||
\(808\) | 12540.0 | 0.545986 | ||||||||
\(809\) | −8749.05 | −0.380223 | −0.190111 | − | 0.981763i | \(-0.560885\pi\) | ||||
−0.190111 | + | 0.981763i | \(0.560885\pi\) | |||||||
\(810\) | 3228.26 | 0.140036 | ||||||||
\(811\) | −24508.1 | −1.06115 | −0.530577 | − | 0.847637i | \(-0.678025\pi\) | ||||
−0.530577 | + | 0.847637i | \(0.678025\pi\) | |||||||
\(812\) | 1002.62 | 0.0433314 | ||||||||
\(813\) | 25167.6 | 1.08569 | ||||||||
\(814\) | 1775.54 | 0.0764531 | ||||||||
\(815\) | −1131.97 | −0.0486516 | ||||||||
\(816\) | 2495.90 | 0.107076 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 24122.0 | 1.03106 | ||||||||
\(819\) | −942.760 | −0.0402231 | ||||||||
\(820\) | 2835.47 | 0.120755 | ||||||||
\(821\) | 43792.7 | 1.86160 | 0.930801 | − | 0.365527i | \(-0.119111\pi\) | ||||
0.930801 | + | 0.365527i | \(0.119111\pi\) | |||||||
\(822\) | 1888.48 | 0.0801317 | ||||||||
\(823\) | 39701.8 | 1.68155 | 0.840776 | − | 0.541384i | \(-0.182099\pi\) | ||||
0.840776 | + | 0.541384i | \(0.182099\pi\) | |||||||
\(824\) | 27985.4 | 1.18315 | ||||||||
\(825\) | 3746.08 | 0.158087 | ||||||||
\(826\) | 3238.88 | 0.136435 | ||||||||
\(827\) | 40351.2 | 1.69668 | 0.848338 | − | 0.529456i | \(-0.177604\pi\) | ||||
0.848338 | + | 0.529456i | \(0.177604\pi\) | |||||||
\(828\) | 516.942 | 0.0216968 | ||||||||
\(829\) | 22880.5 | 0.958593 | 0.479297 | − | 0.877653i | \(-0.340892\pi\) | ||||
0.479297 | + | 0.877653i | \(0.340892\pi\) | |||||||
\(830\) | −671.408 | −0.0280782 | ||||||||
\(831\) | 35653.4 | 1.48833 | ||||||||
\(832\) | −12506.5 | −0.521135 | ||||||||
\(833\) | −14221.2 | −0.591517 | ||||||||
\(834\) | 26823.0 | 1.11367 | ||||||||
\(835\) | 5827.34 | 0.241513 | ||||||||
\(836\) | −51.0472 | −0.00211185 | ||||||||
\(837\) | 29458.4 | 1.21653 | ||||||||
\(838\) | −15721.2 | −0.648069 | ||||||||
\(839\) | −9266.09 | −0.381288 | −0.190644 | − | 0.981659i | \(-0.561058\pi\) | ||||
−0.190644 | + | 0.981659i | \(0.561058\pi\) | |||||||
\(840\) | −756.078 | −0.0310561 | ||||||||
\(841\) | −17636.7 | −0.723142 | ||||||||
\(842\) | 12883.7 | 0.527320 | ||||||||
\(843\) | −30333.1 | −1.23930 | ||||||||
\(844\) | −6847.79 | −0.279278 | ||||||||
\(845\) | 2289.09 | 0.0931919 | ||||||||
\(846\) | −4128.30 | −0.167770 | ||||||||
\(847\) | −3627.40 | −0.147153 | ||||||||
\(848\) | 4787.49 | 0.193872 | ||||||||
\(849\) | −20571.9 | −0.831596 | ||||||||
\(850\) | −9785.42 | −0.394867 | ||||||||
\(851\) | −2023.41 | −0.0815061 | ||||||||
\(852\) | −24221.1 | −0.973944 | ||||||||
\(853\) | −21969.4 | −0.881852 | −0.440926 | − | 0.897544i | \(-0.645350\pi\) | ||||
−0.440926 | + | 0.897544i | \(0.645350\pi\) | |||||||
\(854\) | 3490.31 | 0.139855 | ||||||||
\(855\) | −47.2614 | −0.00189042 | ||||||||
\(856\) | −23934.5 | −0.955682 | ||||||||
\(857\) | −29898.7 | −1.19174 | −0.595869 | − | 0.803082i | \(-0.703192\pi\) | ||||
−0.595869 | + | 0.803082i | \(0.703192\pi\) | |||||||
\(858\) | 1833.01 | 0.0729346 | ||||||||
\(859\) | −7922.96 | −0.314701 | −0.157350 | − | 0.987543i | \(-0.550295\pi\) | ||||
−0.157350 | + | 0.987543i | \(0.550295\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5868.32 | −0.232279 | ||||||||
\(862\) | −10739.8 | −0.424361 | ||||||||
\(863\) | −48962.3 | −1.93128 | −0.965642 | − | 0.259877i | \(-0.916318\pi\) | ||||
−0.965642 | + | 0.259877i | \(0.916318\pi\) | |||||||
\(864\) | 16907.6 | 0.665751 | ||||||||
\(865\) | 1491.37 | 0.0586220 | ||||||||
\(866\) | 4710.28 | 0.184829 | ||||||||
\(867\) | 19156.7 | 0.750397 | ||||||||
\(868\) | −3616.82 | −0.141432 | ||||||||
\(869\) | 292.778 | 0.0114290 | ||||||||
\(870\) | −1804.83 | −0.0703326 | ||||||||
\(871\) | −6209.53 | −0.241564 | ||||||||
\(872\) | 35636.3 | 1.38394 | ||||||||
\(873\) | 11086.0 | 0.429788 | ||||||||
\(874\) | −47.7761 | −0.00184903 | ||||||||
\(875\) | 1286.93 | 0.0497213 | ||||||||
\(876\) | 16746.6 | 0.645907 | ||||||||
\(877\) | −2093.85 | −0.0806206 | −0.0403103 | − | 0.999187i | \(-0.512835\pi\) | ||||
−0.0403103 | + | 0.999187i | \(0.512835\pi\) | |||||||
\(878\) | −13162.8 | −0.505950 | ||||||||
\(879\) | −23322.4 | −0.894933 | ||||||||
\(880\) | 90.1382 | 0.00345291 | ||||||||
\(881\) | −48729.2 | −1.86348 | −0.931742 | − | 0.363121i | \(-0.881711\pi\) | ||||
−0.931742 | + | 0.363121i | \(0.881711\pi\) | |||||||
\(882\) | −6906.76 | −0.263677 | ||||||||
\(883\) | −12474.4 | −0.475422 | −0.237711 | − | 0.971336i | \(-0.576397\pi\) | ||||
−0.237711 | + | 0.971336i | \(0.576397\pi\) | |||||||
\(884\) | 5830.18 | 0.221821 | ||||||||
\(885\) | 7099.18 | 0.269645 | ||||||||
\(886\) | −27889.4 | −1.05752 | ||||||||
\(887\) | −24736.2 | −0.936371 | −0.468186 | − | 0.883630i | \(-0.655092\pi\) | ||||
−0.468186 | + | 0.883630i | \(0.655092\pi\) | |||||||
\(888\) | 27001.6 | 1.02040 | ||||||||
\(889\) | 3859.72 | 0.145614 | ||||||||
\(890\) | −4726.41 | −0.178011 | ||||||||
\(891\) | −4532.92 | −0.170436 | ||||||||
\(892\) | −22805.3 | −0.856029 | ||||||||
\(893\) | −464.573 | −0.0174091 | ||||||||
\(894\) | 13241.8 | 0.495384 | ||||||||
\(895\) | 3445.10 | 0.128667 | ||||||||
\(896\) | −1672.14 | −0.0623464 | ||||||||
\(897\) | −2088.90 | −0.0777551 | ||||||||
\(898\) | 23870.7 | 0.887054 | ||||||||
\(899\) | −24357.9 | −0.903651 | ||||||||
\(900\) | 5786.73 | 0.214323 | ||||||||
\(901\) | −21229.2 | −0.784957 | ||||||||
\(902\) | 3269.80 | 0.120701 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29483.7 | 1.08475 | ||||||||
\(905\) | 6768.11 | 0.248596 | ||||||||
\(906\) | −15858.4 | −0.581524 | ||||||||
\(907\) | −21133.9 | −0.773693 | −0.386846 | − | 0.922144i | \(-0.626436\pi\) | ||||
−0.386846 | + | 0.922144i | \(0.626436\pi\) | |||||||
\(908\) | −28274.0 | −1.03338 | ||||||||
\(909\) | −5778.28 | −0.210840 | ||||||||
\(910\) | 310.343 | 0.0113052 | ||||||||
\(911\) | −43910.9 | −1.59696 | −0.798480 | − | 0.602021i | \(-0.794362\pi\) | ||||
−0.798480 | + | 0.602021i | \(0.794362\pi\) | |||||||
\(912\) | 136.411 | 0.00495289 | ||||||||
\(913\) | 942.749 | 0.0341735 | ||||||||
\(914\) | 6811.71 | 0.246511 | ||||||||
\(915\) | 7650.27 | 0.276404 | ||||||||
\(916\) | 26184.7 | 0.944505 | ||||||||
\(917\) | 2227.18 | 0.0802049 | ||||||||
\(918\) | 8006.03 | 0.287841 | ||||||||
\(919\) | −24074.8 | −0.864151 | −0.432075 | − | 0.901837i | \(-0.642219\pi\) | ||||
−0.432075 | + | 0.901837i | \(0.642219\pi\) | |||||||
\(920\) | −480.094 | −0.0172046 | ||||||||
\(921\) | 27637.8 | 0.988814 | ||||||||
\(922\) | 21441.6 | 0.765880 | ||||||||
\(923\) | 28048.7 | 1.00025 | ||||||||
\(924\) | 376.298 | 0.0133975 | ||||||||
\(925\) | −22650.4 | −0.805126 | ||||||||
\(926\) | 30934.8 | 1.09782 | ||||||||
\(927\) | −12895.3 | −0.456890 | ||||||||
\(928\) | −13980.2 | −0.494528 | ||||||||
\(929\) | −4596.72 | −0.162340 | −0.0811699 | − | 0.996700i | \(-0.525866\pi\) | ||||
−0.0811699 | + | 0.996700i | \(0.525866\pi\) | |||||||
\(930\) | 6510.66 | 0.229562 | ||||||||
\(931\) | −777.245 | −0.0273611 | ||||||||
\(932\) | 7157.81 | 0.251568 | ||||||||
\(933\) | −31910.7 | −1.11973 | ||||||||
\(934\) | −1034.23 | −0.0362323 | ||||||||
\(935\) | −399.700 | −0.0139803 | ||||||||
\(936\) | 7988.52 | 0.278967 | ||||||||
\(937\) | 42751.3 | 1.49053 | 0.745264 | − | 0.666769i | \(-0.232323\pi\) | ||||
0.745264 | + | 0.666769i | \(0.232323\pi\) | |||||||
\(938\) | 1046.91 | 0.0364424 | ||||||||
\(939\) | −31351.5 | −1.08958 | ||||||||
\(940\) | −1654.72 | −0.0574161 | ||||||||
\(941\) | −30236.3 | −1.04747 | −0.523737 | − | 0.851880i | \(-0.675463\pi\) | ||||
−0.523737 | + | 0.851880i | \(0.675463\pi\) | |||||||
\(942\) | 3078.70 | 0.106486 | ||||||||
\(943\) | −3726.27 | −0.128679 | ||||||||
\(944\) | −5872.13 | −0.202459 | ||||||||
\(945\) | −518.909 | −0.0178625 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24630.0 | 0.845160 | 0.422580 | − | 0.906326i | \(-0.361125\pi\) | ||||
0.422580 | + | 0.906326i | \(0.361125\pi\) | |||||||
\(948\) | 1578.16 | 0.0540678 | ||||||||
\(949\) | −19393.0 | −0.663356 | ||||||||
\(950\) | −534.813 | −0.0182649 | ||||||||
\(951\) | 42989.4 | 1.46585 | ||||||||
\(952\) | −2773.19 | −0.0944112 | ||||||||
\(953\) | 25475.3 | 0.865925 | 0.432963 | − | 0.901412i | \(-0.357468\pi\) | ||||
0.432963 | + | 0.901412i | \(0.357468\pi\) | |||||||
\(954\) | −10310.3 | −0.349905 | ||||||||
\(955\) | 3230.05 | 0.109447 | ||||||||
\(956\) | −7856.25 | −0.265784 | ||||||||
\(957\) | 2534.23 | 0.0856007 | ||||||||
\(958\) | −7582.75 | −0.255728 | ||||||||
\(959\) | −448.950 | −0.0151172 | ||||||||
\(960\) | 4621.69 | 0.155380 | ||||||||
\(961\) | 58076.9 | 1.94948 | ||||||||
\(962\) | −11083.2 | −0.371451 | ||||||||
\(963\) | 11028.7 | 0.369050 | ||||||||
\(964\) | −21672.3 | −0.724085 | ||||||||
\(965\) | 1697.26 | 0.0566183 | ||||||||
\(966\) | 352.184 | 0.0117302 | ||||||||
\(967\) | −39005.4 | −1.29714 | −0.648568 | − | 0.761157i | \(-0.724632\pi\) | ||||
−0.648568 | + | 0.761157i | \(0.724632\pi\) | |||||||
\(968\) | 30736.9 | 1.02058 | ||||||||
\(969\) | −604.889 | −0.0200535 | ||||||||
\(970\) | −3649.35 | −0.120798 | ||||||||
\(971\) | 30577.5 | 1.01059 | 0.505293 | − | 0.862948i | \(-0.331384\pi\) | ||||
0.505293 | + | 0.862948i | \(0.331384\pi\) | |||||||
\(972\) | −12647.6 | −0.417359 | ||||||||
\(973\) | −6376.66 | −0.210099 | ||||||||
\(974\) | −18928.0 | −0.622681 | ||||||||
\(975\) | −23383.5 | −0.768073 | ||||||||
\(976\) | −6327.97 | −0.207534 | ||||||||
\(977\) | −22122.7 | −0.724428 | −0.362214 | − | 0.932095i | \(-0.617979\pi\) | ||||
−0.362214 | + | 0.932095i | \(0.617979\pi\) | |||||||
\(978\) | −7036.27 | −0.230056 | ||||||||
\(979\) | 6636.53 | 0.216654 | ||||||||
\(980\) | −2768.40 | −0.0902381 | ||||||||
\(981\) | −16420.7 | −0.534428 | ||||||||
\(982\) | 29817.2 | 0.968947 | ||||||||
\(983\) | −2783.02 | −0.0902998 | −0.0451499 | − | 0.998980i | \(-0.514377\pi\) | ||||
−0.0451499 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(984\) | 49725.5 | 1.61097 | ||||||||
\(985\) | 4820.01 | 0.155917 | ||||||||
\(986\) | −6619.85 | −0.213812 | ||||||||
\(987\) | 3424.63 | 0.110443 | ||||||||
\(988\) | 318.643 | 0.0102605 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −194.122 | −0.00623191 | ||||||||
\(991\) | −55111.8 | −1.76658 | −0.883291 | − | 0.468825i | \(-0.844677\pi\) | ||||
−0.883291 | + | 0.468825i | \(0.844677\pi\) | |||||||
\(992\) | 50431.6 | 1.61412 | ||||||||
\(993\) | 16546.9 | 0.528803 | ||||||||
\(994\) | −4728.96 | −0.150899 | ||||||||
\(995\) | 7692.96 | 0.245109 | ||||||||
\(996\) | 5081.70 | 0.161667 | ||||||||
\(997\) | 25817.4 | 0.820104 | 0.410052 | − | 0.912062i | \(-0.365511\pi\) | ||||
0.410052 | + | 0.912062i | \(0.365511\pi\) | |||||||
\(998\) | −4257.54 | −0.135040 | ||||||||
\(999\) | 18531.7 | 0.586902 |
(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.i.1.34 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.17 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.34 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.17 | yes | 50 | 43.42 | odd | 2 |