Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, 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("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.14785 | −1.82004 | −0.910020 | − | 0.414565i | \(-0.863934\pi\) | ||||
−0.910020 | + | 0.414565i | \(0.863934\pi\) | |||||||
\(3\) | −6.96013 | −1.33948 | −0.669739 | − | 0.742596i | \(-0.733594\pi\) | ||||
−0.669739 | + | 0.742596i | \(0.733594\pi\) | |||||||
\(4\) | 18.5003 | 2.31254 | ||||||||
\(5\) | −3.24701 | −0.290421 | −0.145210 | − | 0.989401i | \(-0.546386\pi\) | ||||
−0.145210 | + | 0.989401i | \(0.546386\pi\) | |||||||
\(6\) | 35.8297 | 2.43790 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −54.0542 | −2.38888 | ||||||||
\(9\) | 21.4435 | 0.794203 | ||||||||
\(10\) | 16.7151 | 0.528578 | ||||||||
\(11\) | 58.8488 | 1.61305 | 0.806526 | − | 0.591199i | \(-0.201345\pi\) | ||||
0.806526 | + | 0.591199i | \(0.201345\pi\) | |||||||
\(12\) | −128.765 | −3.09760 | ||||||||
\(13\) | −47.9754 | −1.02354 | −0.511768 | − | 0.859123i | \(-0.671009\pi\) | ||||
−0.511768 | + | 0.859123i | \(0.671009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.5996 | 0.389013 | ||||||||
\(16\) | 130.260 | 2.03531 | ||||||||
\(17\) | 84.9507 | 1.21197 | 0.605987 | − | 0.795474i | \(-0.292778\pi\) | ||||
0.605987 | + | 0.795474i | \(0.292778\pi\) | |||||||
\(18\) | −110.388 | −1.44548 | ||||||||
\(19\) | −54.8763 | −0.662605 | −0.331302 | − | 0.943525i | \(-0.607488\pi\) | ||||
−0.331302 | + | 0.943525i | \(0.607488\pi\) | |||||||
\(20\) | −60.0707 | −0.671611 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −302.944 | −2.93582 | ||||||||
\(23\) | 150.540 | 1.36477 | 0.682385 | − | 0.730993i | \(-0.260943\pi\) | ||||
0.682385 | + | 0.730993i | \(0.260943\pi\) | |||||||
\(24\) | 376.225 | 3.19986 | ||||||||
\(25\) | −114.457 | −0.915656 | ||||||||
\(26\) | 246.970 | 1.86288 | ||||||||
\(27\) | 38.6742 | 0.275661 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 44.2844 | 0.283566 | 0.141783 | − | 0.989898i | \(-0.454717\pi\) | ||||
0.141783 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(30\) | −116.339 | −0.708018 | ||||||||
\(31\) | −95.7503 | −0.554750 | −0.277375 | − | 0.960762i | \(-0.589464\pi\) | ||||
−0.277375 | + | 0.960762i | \(0.589464\pi\) | |||||||
\(32\) | −238.126 | −1.31547 | ||||||||
\(33\) | −409.595 | −2.16065 | ||||||||
\(34\) | −437.313 | −2.20584 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 396.712 | 1.83663 | ||||||||
\(37\) | 209.605 | 0.931321 | 0.465661 | − | 0.884963i | \(-0.345817\pi\) | ||||
0.465661 | + | 0.884963i | \(0.345817\pi\) | |||||||
\(38\) | 282.495 | 1.20597 | ||||||||
\(39\) | 333.915 | 1.37101 | ||||||||
\(40\) | 175.514 | 0.693781 | ||||||||
\(41\) | −354.943 | −1.35202 | −0.676010 | − | 0.736893i | \(-0.736292\pi\) | ||||
−0.676010 | + | 0.736893i | \(0.736292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 221.030 | 0.783877 | 0.391939 | − | 0.919991i | \(-0.371805\pi\) | ||||
0.391939 | + | 0.919991i | \(0.371805\pi\) | |||||||
\(44\) | 1088.72 | 3.73025 | ||||||||
\(45\) | −69.6271 | −0.230653 | ||||||||
\(46\) | −774.956 | −2.48394 | ||||||||
\(47\) | 235.194 | 0.729928 | 0.364964 | − | 0.931022i | \(-0.381081\pi\) | ||||
0.364964 | + | 0.931022i | \(0.381081\pi\) | |||||||
\(48\) | −906.628 | −2.72626 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 589.207 | 1.66653 | ||||||||
\(51\) | −591.268 | −1.62341 | ||||||||
\(52\) | −887.561 | −2.36697 | ||||||||
\(53\) | −508.784 | −1.31862 | −0.659310 | − | 0.751871i | \(-0.729151\pi\) | ||||
−0.659310 | + | 0.751871i | \(0.729151\pi\) | |||||||
\(54\) | −199.089 | −0.501714 | ||||||||
\(55\) | −191.082 | −0.468464 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 381.947 | 0.887545 | ||||||||
\(58\) | −227.969 | −0.516101 | ||||||||
\(59\) | −439.523 | −0.969847 | −0.484924 | − | 0.874556i | \(-0.661153\pi\) | ||||
−0.484924 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(60\) | 418.100 | 0.899609 | ||||||||
\(61\) | 51.4628 | 0.108019 | 0.0540093 | − | 0.998540i | \(-0.482800\pi\) | ||||
0.0540093 | + | 0.998540i | \(0.482800\pi\) | |||||||
\(62\) | 492.908 | 1.00967 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 183.755 | 0.358896 | ||||||||
\(65\) | 155.776 | 0.297257 | ||||||||
\(66\) | 2108.53 | 3.93246 | ||||||||
\(67\) | −263.337 | −0.480175 | −0.240087 | − | 0.970751i | \(-0.577176\pi\) | ||||
−0.240087 | + | 0.970751i | \(0.577176\pi\) | |||||||
\(68\) | 1571.62 | 2.80274 | ||||||||
\(69\) | −1047.78 | −1.82808 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 203.727 | 0.340534 | 0.170267 | − | 0.985398i | \(-0.445537\pi\) | ||||
0.170267 | + | 0.985398i | \(0.445537\pi\) | |||||||
\(72\) | −1159.11 | −1.89726 | ||||||||
\(73\) | 679.617 | 1.08963 | 0.544816 | − | 0.838556i | \(-0.316600\pi\) | ||||
0.544816 | + | 0.838556i | \(0.316600\pi\) | |||||||
\(74\) | −1079.02 | −1.69504 | ||||||||
\(75\) | 796.636 | 1.22650 | ||||||||
\(76\) | −1015.23 | −1.53230 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1718.94 | −2.49528 | ||||||||
\(79\) | −189.020 | −0.269196 | −0.134598 | − | 0.990900i | \(-0.542974\pi\) | ||||
−0.134598 | + | 0.990900i | \(0.542974\pi\) | |||||||
\(80\) | −422.955 | −0.591098 | ||||||||
\(81\) | −848.151 | −1.16344 | ||||||||
\(82\) | 1827.19 | 2.46073 | ||||||||
\(83\) | −520.046 | −0.687740 | −0.343870 | − | 0.939017i | \(-0.611738\pi\) | ||||
−0.343870 | + | 0.939017i | \(0.611738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −275.835 | −0.351983 | ||||||||
\(86\) | −1137.83 | −1.42669 | ||||||||
\(87\) | −308.225 | −0.379830 | ||||||||
\(88\) | −3181.02 | −3.85339 | ||||||||
\(89\) | −1494.87 | −1.78041 | −0.890203 | − | 0.455565i | \(-0.849437\pi\) | ||||
−0.890203 | + | 0.455565i | \(0.849437\pi\) | |||||||
\(90\) | 358.430 | 0.419798 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2785.04 | 3.15609 | ||||||||
\(93\) | 666.435 | 0.743076 | ||||||||
\(94\) | −1210.74 | −1.32850 | ||||||||
\(95\) | 178.184 | 0.192434 | ||||||||
\(96\) | 1657.39 | 1.76205 | ||||||||
\(97\) | −712.036 | −0.745322 | −0.372661 | − | 0.927967i | \(-0.621555\pi\) | ||||
−0.372661 | + | 0.927967i | \(0.621555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1261.92 | 1.28109 | ||||||||
\(100\) | −2117.49 | −2.11749 | ||||||||
\(101\) | −51.9916 | −0.0512214 | −0.0256107 | − | 0.999672i | \(-0.508153\pi\) | ||||
−0.0256107 | + | 0.999672i | \(0.508153\pi\) | |||||||
\(102\) | 3043.76 | 2.95468 | ||||||||
\(103\) | 187.146 | 0.179030 | 0.0895149 | − | 0.995985i | \(-0.471468\pi\) | ||||
0.0895149 | + | 0.995985i | \(0.471468\pi\) | |||||||
\(104\) | 2593.27 | 2.44511 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2619.14 | 2.39994 | ||||||||
\(107\) | 626.000 | 0.565586 | 0.282793 | − | 0.959181i | \(-0.408739\pi\) | ||||
0.282793 | + | 0.959181i | \(0.408739\pi\) | |||||||
\(108\) | 715.486 | 0.637478 | ||||||||
\(109\) | −444.254 | −0.390384 | −0.195192 | − | 0.980765i | \(-0.562533\pi\) | ||||
−0.195192 | + | 0.980765i | \(0.562533\pi\) | |||||||
\(110\) | 983.662 | 0.852623 | ||||||||
\(111\) | −1458.88 | −1.24748 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2043.53 | −1.70123 | −0.850616 | − | 0.525787i | \(-0.823771\pi\) | ||||
−0.850616 | + | 0.525787i | \(0.823771\pi\) | |||||||
\(114\) | −1966.20 | −1.61537 | ||||||||
\(115\) | −488.803 | −0.396358 | ||||||||
\(116\) | 819.276 | 0.655758 | ||||||||
\(117\) | −1028.76 | −0.812896 | ||||||||
\(118\) | 2262.60 | 1.76516 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1221.60 | −0.929305 | ||||||||
\(121\) | 2132.18 | 1.60194 | ||||||||
\(122\) | −264.923 | −0.196598 | ||||||||
\(123\) | 2470.45 | 1.81100 | ||||||||
\(124\) | −1771.41 | −1.28288 | ||||||||
\(125\) | 777.518 | 0.556347 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −36.3506 | −0.0253984 | −0.0126992 | − | 0.999919i | \(-0.504042\pi\) | ||||
−0.0126992 | + | 0.999919i | \(0.504042\pi\) | |||||||
\(128\) | 959.065 | 0.662267 | ||||||||
\(129\) | −1538.40 | −1.04999 | ||||||||
\(130\) | −801.913 | −0.541019 | ||||||||
\(131\) | −327.576 | −0.218477 | −0.109238 | − | 0.994016i | \(-0.534841\pi\) | ||||
−0.109238 | + | 0.994016i | \(0.534841\pi\) | |||||||
\(132\) | −7577.66 | −4.99659 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1355.62 | 0.873937 | ||||||||
\(135\) | −125.575 | −0.0800577 | ||||||||
\(136\) | −4591.94 | −2.89526 | ||||||||
\(137\) | 384.045 | 0.239498 | 0.119749 | − | 0.992804i | \(-0.461791\pi\) | ||||
0.119749 | + | 0.992804i | \(0.461791\pi\) | |||||||
\(138\) | 5393.80 | 3.32718 | ||||||||
\(139\) | 215.972 | 0.131788 | 0.0658938 | − | 0.997827i | \(-0.479010\pi\) | ||||
0.0658938 | + | 0.997827i | \(0.479010\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1636.98 | −0.977723 | ||||||||
\(142\) | −1048.75 | −0.619785 | ||||||||
\(143\) | −2823.29 | −1.65102 | ||||||||
\(144\) | 2793.23 | 1.61645 | ||||||||
\(145\) | −143.792 | −0.0823534 | ||||||||
\(146\) | −3498.56 | −1.98317 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3877.77 | 2.15372 | ||||||||
\(149\) | 1874.22 | 1.03048 | 0.515242 | − | 0.857045i | \(-0.327702\pi\) | ||||
0.515242 | + | 0.857045i | \(0.327702\pi\) | |||||||
\(150\) | −4100.96 | −2.23228 | ||||||||
\(151\) | −227.877 | −0.122811 | −0.0614053 | − | 0.998113i | \(-0.519558\pi\) | ||||
−0.0614053 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(152\) | 2966.30 | 1.58288 | ||||||||
\(153\) | 1821.64 | 0.962554 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 310.902 | 0.161111 | ||||||||
\(156\) | 6177.55 | 3.17051 | ||||||||
\(157\) | −1353.42 | −0.687992 | −0.343996 | − | 0.938971i | \(-0.611781\pi\) | ||||
−0.343996 | + | 0.938971i | \(0.611781\pi\) | |||||||
\(158\) | 973.049 | 0.489947 | ||||||||
\(159\) | 3541.21 | 1.76626 | ||||||||
\(160\) | 773.196 | 0.382041 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4366.15 | 2.11752 | ||||||||
\(163\) | 2541.27 | 1.22115 | 0.610575 | − | 0.791958i | \(-0.290938\pi\) | ||||
0.610575 | + | 0.791958i | \(0.290938\pi\) | |||||||
\(164\) | −6566.57 | −3.12660 | ||||||||
\(165\) | 1329.96 | 0.627497 | ||||||||
\(166\) | 2677.12 | 1.25171 | ||||||||
\(167\) | −187.723 | −0.0869847 | −0.0434923 | − | 0.999054i | \(-0.513848\pi\) | ||||
−0.0434923 | + | 0.999054i | \(0.513848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 104.638 | 0.0476276 | ||||||||
\(170\) | 1419.96 | 0.640623 | ||||||||
\(171\) | −1176.74 | −0.526243 | ||||||||
\(172\) | 4089.13 | 1.81275 | ||||||||
\(173\) | 2854.37 | 1.25441 | 0.627206 | − | 0.778853i | \(-0.284198\pi\) | ||||
0.627206 | + | 0.778853i | \(0.284198\pi\) | |||||||
\(174\) | 1586.70 | 0.691306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7665.65 | 3.28307 | ||||||||
\(177\) | 3059.14 | 1.29909 | ||||||||
\(178\) | 7695.37 | 3.24041 | ||||||||
\(179\) | 355.983 | 0.148645 | 0.0743225 | − | 0.997234i | \(-0.476321\pi\) | ||||
0.0743225 | + | 0.997234i | \(0.476321\pi\) | |||||||
\(180\) | −1288.13 | −0.533395 | ||||||||
\(181\) | −266.530 | −0.109453 | −0.0547266 | − | 0.998501i | \(-0.517429\pi\) | ||||
−0.0547266 | + | 0.998501i | \(0.517429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −358.188 | −0.144689 | ||||||||
\(184\) | −8137.31 | −3.26027 | ||||||||
\(185\) | −680.589 | −0.270475 | ||||||||
\(186\) | −3430.71 | −1.35243 | ||||||||
\(187\) | 4999.24 | 1.95498 | ||||||||
\(188\) | 4351.18 | 1.68799 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −917.263 | −0.350238 | ||||||||
\(191\) | 4485.01 | 1.69908 | 0.849540 | − | 0.527525i | \(-0.176880\pi\) | ||||
0.849540 | + | 0.527525i | \(0.176880\pi\) | |||||||
\(192\) | −1278.96 | −0.480733 | ||||||||
\(193\) | 3487.25 | 1.30061 | 0.650304 | − | 0.759674i | \(-0.274641\pi\) | ||||
0.650304 | + | 0.759674i | \(0.274641\pi\) | |||||||
\(194\) | 3665.45 | 1.35652 | ||||||||
\(195\) | −1084.22 | −0.398169 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2415.21 | −0.873486 | −0.436743 | − | 0.899586i | \(-0.643868\pi\) | ||||
−0.436743 | + | 0.899586i | \(0.643868\pi\) | |||||||
\(198\) | −6496.18 | −2.33163 | ||||||||
\(199\) | 5226.68 | 1.86186 | 0.930928 | − | 0.365203i | \(-0.119000\pi\) | ||||
0.930928 | + | 0.365203i | \(0.119000\pi\) | |||||||
\(200\) | 6186.88 | 2.18739 | ||||||||
\(201\) | 1832.86 | 0.643184 | ||||||||
\(202\) | 267.645 | 0.0932249 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10938.7 | −3.75422 | ||||||||
\(205\) | 1152.50 | 0.392655 | ||||||||
\(206\) | −963.400 | −0.325841 | ||||||||
\(207\) | 3228.10 | 1.08390 | ||||||||
\(208\) | −6249.28 | −2.08322 | ||||||||
\(209\) | −3229.40 | −1.06882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2239.69 | −0.730743 | −0.365372 | − | 0.930862i | \(-0.619058\pi\) | ||||
−0.365372 | + | 0.930862i | \(0.619058\pi\) | |||||||
\(212\) | −9412.68 | −3.04937 | ||||||||
\(213\) | −1417.97 | −0.456138 | ||||||||
\(214\) | −3222.56 | −1.02939 | ||||||||
\(215\) | −717.685 | −0.227654 | ||||||||
\(216\) | −2090.50 | −0.658521 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2286.95 | 0.710514 | ||||||||
\(219\) | −4730.22 | −1.45954 | ||||||||
\(220\) | −3535.09 | −1.08334 | ||||||||
\(221\) | −4075.54 | −1.24050 | ||||||||
\(222\) | 7510.10 | 2.27047 | ||||||||
\(223\) | 1381.27 | 0.414784 | 0.207392 | − | 0.978258i | \(-0.433502\pi\) | ||||
0.207392 | + | 0.978258i | \(0.433502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2454.35 | −0.727216 | ||||||||
\(226\) | 10519.8 | 3.09631 | ||||||||
\(227\) | −295.331 | −0.0863515 | −0.0431757 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431757 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(228\) | 7066.14 | 2.05249 | ||||||||
\(229\) | −4468.09 | −1.28934 | −0.644672 | − | 0.764459i | \(-0.723006\pi\) | ||||
−0.644672 | + | 0.764459i | \(0.723006\pi\) | |||||||
\(230\) | 2516.29 | 0.721387 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2393.76 | −0.677405 | ||||||||
\(233\) | −2322.69 | −0.653065 | −0.326533 | − | 0.945186i | \(-0.605880\pi\) | ||||
−0.326533 | + | 0.945186i | \(0.605880\pi\) | |||||||
\(234\) | 5295.90 | 1.47950 | ||||||||
\(235\) | −763.677 | −0.211986 | ||||||||
\(236\) | −8131.33 | −2.24281 | ||||||||
\(237\) | 1315.61 | 0.360582 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.49690 | 0.000675777 0 | 0.000337889 | − | 1.00000i | \(-0.499892\pi\) | ||||
0.000337889 | 1.00000i | \(0.499892\pi\) | ||||||||
\(240\) | 2943.83 | 0.791763 | ||||||||
\(241\) | 5914.89 | 1.58096 | 0.790480 | − | 0.612487i | \(-0.209831\pi\) | ||||
0.790480 | + | 0.612487i | \(0.209831\pi\) | |||||||
\(242\) | −10976.1 | −2.91559 | ||||||||
\(243\) | 4859.04 | 1.28275 | ||||||||
\(244\) | 952.080 | 0.249798 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12717.5 | −3.29609 | ||||||||
\(247\) | 2632.71 | 0.678200 | ||||||||
\(248\) | 5175.70 | 1.32523 | ||||||||
\(249\) | 3619.59 | 0.921213 | ||||||||
\(250\) | −4002.55 | −1.01257 | ||||||||
\(251\) | 596.482 | 0.149998 | 0.0749992 | − | 0.997184i | \(-0.476105\pi\) | ||||
0.0749992 | + | 0.997184i | \(0.476105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8859.08 | 2.20144 | ||||||||
\(254\) | 187.127 | 0.0462261 | ||||||||
\(255\) | 1919.85 | 0.471473 | ||||||||
\(256\) | −6407.16 | −1.56425 | ||||||||
\(257\) | 1023.45 | 0.248409 | 0.124205 | − | 0.992257i | \(-0.460362\pi\) | ||||
0.124205 | + | 0.992257i | \(0.460362\pi\) | |||||||
\(258\) | 7919.44 | 1.91102 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2881.92 | 0.687419 | ||||||||
\(261\) | 949.611 | 0.225209 | ||||||||
\(262\) | 1686.31 | 0.397636 | ||||||||
\(263\) | 876.156 | 0.205422 | 0.102711 | − | 0.994711i | \(-0.467248\pi\) | ||||
0.102711 | + | 0.994711i | \(0.467248\pi\) | |||||||
\(264\) | 22140.3 | 5.16153 | ||||||||
\(265\) | 1652.02 | 0.382955 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10404.5 | 2.38481 | ||||||||
\(268\) | −4871.82 | −1.11043 | ||||||||
\(269\) | −1408.69 | −0.319291 | −0.159645 | − | 0.987174i | \(-0.551035\pi\) | ||||
−0.159645 | + | 0.987174i | \(0.551035\pi\) | |||||||
\(270\) | 646.442 | 0.145708 | ||||||||
\(271\) | 1230.79 | 0.275885 | 0.137943 | − | 0.990440i | \(-0.455951\pi\) | ||||
0.137943 | + | 0.990440i | \(0.455951\pi\) | |||||||
\(272\) | 11065.7 | 2.46675 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1977.01 | −0.435896 | ||||||||
\(275\) | −6735.65 | −1.47700 | ||||||||
\(276\) | −19384.2 | −4.22751 | ||||||||
\(277\) | 6840.25 | 1.48372 | 0.741860 | − | 0.670555i | \(-0.233944\pi\) | ||||
0.741860 | + | 0.670555i | \(0.233944\pi\) | |||||||
\(278\) | −1111.79 | −0.239859 | ||||||||
\(279\) | −2053.22 | −0.440584 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2831.45 | 0.601104 | 0.300552 | − | 0.953765i | \(-0.402829\pi\) | ||||
0.300552 | + | 0.953765i | \(0.402829\pi\) | |||||||
\(282\) | 8426.95 | 1.77949 | ||||||||
\(283\) | 7110.88 | 1.49363 | 0.746816 | − | 0.665031i | \(-0.231582\pi\) | ||||
0.746816 | + | 0.665031i | \(0.231582\pi\) | |||||||
\(284\) | 3769.02 | 0.787500 | ||||||||
\(285\) | −1240.18 | −0.257762 | ||||||||
\(286\) | 14533.9 | 3.00492 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5106.24 | −1.04475 | ||||||||
\(289\) | 2303.62 | 0.468883 | ||||||||
\(290\) | 740.217 | 0.149886 | ||||||||
\(291\) | 4955.86 | 0.998343 | ||||||||
\(292\) | 12573.1 | 2.51982 | ||||||||
\(293\) | −6463.86 | −1.28881 | −0.644407 | − | 0.764682i | \(-0.722896\pi\) | ||||
−0.644407 | + | 0.764682i | \(0.722896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1427.13 | 0.281664 | ||||||||
\(296\) | −11330.0 | −2.22482 | ||||||||
\(297\) | 2275.93 | 0.444655 | ||||||||
\(298\) | −9648.20 | −1.87552 | ||||||||
\(299\) | −7222.20 | −1.39689 | ||||||||
\(300\) | 14738.0 | 2.83634 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1173.08 | 0.223520 | ||||||||
\(303\) | 361.869 | 0.0686099 | ||||||||
\(304\) | −7148.20 | −1.34861 | ||||||||
\(305\) | −167.100 | −0.0313709 | ||||||||
\(306\) | −9377.52 | −1.75189 | ||||||||
\(307\) | 6566.61 | 1.22077 | 0.610384 | − | 0.792105i | \(-0.291015\pi\) | ||||
0.610384 | + | 0.792105i | \(0.291015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1302.56 | −0.239806 | ||||||||
\(310\) | −1600.47 | −0.293228 | ||||||||
\(311\) | −7227.56 | −1.31781 | −0.658903 | − | 0.752228i | \(-0.728979\pi\) | ||||
−0.658903 | + | 0.752228i | \(0.728979\pi\) | |||||||
\(312\) | −18049.5 | −3.27517 | ||||||||
\(313\) | −8437.42 | −1.52368 | −0.761839 | − | 0.647767i | \(-0.775703\pi\) | ||||
−0.761839 | + | 0.647767i | \(0.775703\pi\) | |||||||
\(314\) | 6967.20 | 1.25217 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3496.94 | −0.622527 | ||||||||
\(317\) | 7128.11 | 1.26295 | 0.631474 | − | 0.775397i | \(-0.282450\pi\) | ||||
0.631474 | + | 0.775397i | \(0.282450\pi\) | |||||||
\(318\) | −18229.6 | −3.21467 | ||||||||
\(319\) | 2606.08 | 0.457406 | ||||||||
\(320\) | −596.652 | −0.104231 | ||||||||
\(321\) | −4357.05 | −0.757591 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4661.78 | −0.803060 | ||||||||
\(324\) | −15691.1 | −2.69052 | ||||||||
\(325\) | 5491.12 | 0.937207 | ||||||||
\(326\) | −13082.1 | −2.22254 | ||||||||
\(327\) | 3092.07 | 0.522911 | ||||||||
\(328\) | 19186.2 | 3.22981 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6846.42 | −1.14207 | ||||||||
\(331\) | −3626.78 | −0.602254 | −0.301127 | − | 0.953584i | \(-0.597363\pi\) | ||||
−0.301127 | + | 0.953584i | \(0.597363\pi\) | |||||||
\(332\) | −9621.03 | −1.59043 | ||||||||
\(333\) | 4494.66 | 0.739658 | ||||||||
\(334\) | 966.370 | 0.158316 | ||||||||
\(335\) | 855.056 | 0.139453 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1275.65 | −0.206199 | −0.103099 | − | 0.994671i | \(-0.532876\pi\) | ||||
−0.103099 | + | 0.994671i | \(0.532876\pi\) | |||||||
\(338\) | −538.659 | −0.0866840 | ||||||||
\(339\) | 14223.3 | 2.27876 | ||||||||
\(340\) | −5103.05 | −0.813976 | ||||||||
\(341\) | −5634.78 | −0.894841 | ||||||||
\(342\) | 6057.67 | 0.957782 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11947.6 | −1.87259 | ||||||||
\(345\) | 3402.14 | 0.530913 | ||||||||
\(346\) | −14693.8 | −2.28308 | ||||||||
\(347\) | −6043.73 | −0.934998 | −0.467499 | − | 0.883994i | \(-0.654845\pi\) | ||||
−0.467499 | + | 0.883994i | \(0.654845\pi\) | |||||||
\(348\) | −5702.27 | −0.878374 | ||||||||
\(349\) | −2389.00 | −0.366419 | −0.183210 | − | 0.983074i | \(-0.558649\pi\) | ||||
−0.183210 | + | 0.983074i | \(0.558649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1855.41 | −0.282149 | ||||||||
\(352\) | −14013.4 | −2.12192 | ||||||||
\(353\) | 2524.06 | 0.380573 | 0.190287 | − | 0.981729i | \(-0.439058\pi\) | ||||
0.190287 | + | 0.981729i | \(0.439058\pi\) | |||||||
\(354\) | −15748.0 | −2.36439 | ||||||||
\(355\) | −661.502 | −0.0988982 | ||||||||
\(356\) | −27655.7 | −4.11727 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1832.55 | −0.270540 | ||||||||
\(359\) | 4138.63 | 0.608437 | 0.304218 | − | 0.952602i | \(-0.401605\pi\) | ||||
0.304218 | + | 0.952602i | \(0.401605\pi\) | |||||||
\(360\) | 3763.64 | 0.551003 | ||||||||
\(361\) | −3847.59 | −0.560955 | ||||||||
\(362\) | 1372.06 | 0.199209 | ||||||||
\(363\) | −14840.2 | −2.14576 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2206.72 | −0.316452 | ||||||||
\(366\) | 1843.90 | 0.263339 | ||||||||
\(367\) | 7614.50 | 1.08303 | 0.541517 | − | 0.840690i | \(-0.317850\pi\) | ||||
0.541517 | + | 0.840690i | \(0.317850\pi\) | |||||||
\(368\) | 19609.3 | 2.77774 | ||||||||
\(369\) | −7611.21 | −1.07378 | ||||||||
\(370\) | 3503.57 | 0.492276 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12329.3 | 1.71840 | ||||||||
\(373\) | −7415.95 | −1.02945 | −0.514723 | − | 0.857357i | \(-0.672105\pi\) | ||||
−0.514723 | + | 0.857357i | \(0.672105\pi\) | |||||||
\(374\) | −25735.3 | −3.55814 | ||||||||
\(375\) | −5411.63 | −0.745214 | ||||||||
\(376\) | −12713.2 | −1.74371 | ||||||||
\(377\) | −2124.56 | −0.290240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 73.8067 | 0.0100032 | 0.00500158 | − | 0.999987i | \(-0.498408\pi\) | ||||
0.00500158 | + | 0.999987i | \(0.498408\pi\) | |||||||
\(380\) | 3296.46 | 0.445013 | ||||||||
\(381\) | 253.005 | 0.0340206 | ||||||||
\(382\) | −23088.2 | −3.09239 | ||||||||
\(383\) | 8475.40 | 1.13074 | 0.565369 | − | 0.824838i | \(-0.308734\pi\) | ||||
0.565369 | + | 0.824838i | \(0.308734\pi\) | |||||||
\(384\) | −6675.22 | −0.887093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17951.8 | −2.36716 | ||||||||
\(387\) | 4739.65 | 0.622558 | ||||||||
\(388\) | −13172.9 | −1.72359 | ||||||||
\(389\) | −7897.26 | −1.02932 | −0.514662 | − | 0.857393i | \(-0.672082\pi\) | ||||
−0.514662 | + | 0.857393i | \(0.672082\pi\) | |||||||
\(390\) | 5581.42 | 0.724683 | ||||||||
\(391\) | 12788.5 | 1.65407 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2279.97 | 0.292645 | ||||||||
\(394\) | 12433.1 | 1.58978 | ||||||||
\(395\) | 613.750 | 0.0781801 | ||||||||
\(396\) | 23346.0 | 2.96258 | ||||||||
\(397\) | 10827.9 | 1.36886 | 0.684431 | − | 0.729077i | \(-0.260051\pi\) | ||||
0.684431 | + | 0.729077i | \(0.260051\pi\) | |||||||
\(398\) | −26906.1 | −3.38865 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14909.2 | −1.86365 | ||||||||
\(401\) | −2773.97 | −0.345450 | −0.172725 | − | 0.984970i | \(-0.555257\pi\) | ||||
−0.172725 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(402\) | −9435.29 | −1.17062 | ||||||||
\(403\) | 4593.66 | 0.567807 | ||||||||
\(404\) | −961.863 | −0.118452 | ||||||||
\(405\) | 2753.95 | 0.337889 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12335.0 | 1.50227 | ||||||||
\(408\) | 31960.5 | 3.87814 | ||||||||
\(409\) | −14660.0 | −1.77235 | −0.886175 | − | 0.463350i | \(-0.846647\pi\) | ||||
−0.886175 | + | 0.463350i | \(0.846647\pi\) | |||||||
\(410\) | −5932.91 | −0.714647 | ||||||||
\(411\) | −2673.01 | −0.320802 | ||||||||
\(412\) | 3462.27 | 0.414014 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16617.7 | −1.97275 | ||||||||
\(415\) | 1688.59 | 0.199734 | ||||||||
\(416\) | 11424.2 | 1.34643 | ||||||||
\(417\) | −1503.19 | −0.176527 | ||||||||
\(418\) | 16624.5 | 1.94529 | ||||||||
\(419\) | −7935.55 | −0.925243 | −0.462622 | − | 0.886556i | \(-0.653091\pi\) | ||||
−0.462622 | + | 0.886556i | \(0.653091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12583.7 | −1.45675 | −0.728376 | − | 0.685177i | \(-0.759725\pi\) | ||||
−0.728376 | + | 0.685177i | \(0.759725\pi\) | |||||||
\(422\) | 11529.6 | 1.32998 | ||||||||
\(423\) | 5043.38 | 0.579711 | ||||||||
\(424\) | 27501.9 | 3.15003 | ||||||||
\(425\) | −9723.20 | −1.10975 | ||||||||
\(426\) | 7299.47 | 0.830189 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11581.2 | 1.30794 | ||||||||
\(429\) | 19650.5 | 2.21150 | ||||||||
\(430\) | 3694.53 | 0.414340 | ||||||||
\(431\) | −5401.64 | −0.603684 | −0.301842 | − | 0.953358i | \(-0.597602\pi\) | ||||
−0.301842 | + | 0.953358i | \(0.597602\pi\) | |||||||
\(432\) | 5037.70 | 0.561057 | ||||||||
\(433\) | −5989.02 | −0.664697 | −0.332349 | − | 0.943157i | \(-0.607841\pi\) | ||||
−0.332349 | + | 0.943157i | \(0.607841\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1000.81 | 0.110311 | ||||||||
\(436\) | −8218.86 | −0.902780 | ||||||||
\(437\) | −8261.07 | −0.904303 | ||||||||
\(438\) | 24350.5 | 2.65642 | ||||||||
\(439\) | −13191.9 | −1.43421 | −0.717103 | − | 0.696967i | \(-0.754532\pi\) | ||||
−0.717103 | + | 0.696967i | \(0.754532\pi\) | |||||||
\(440\) | 10328.8 | 1.11910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20980.3 | 2.25776 | ||||||||
\(443\) | −15538.1 | −1.66645 | −0.833225 | − | 0.552934i | \(-0.813508\pi\) | ||||
−0.833225 | + | 0.552934i | \(0.813508\pi\) | |||||||
\(444\) | −26989.8 | −2.88486 | ||||||||
\(445\) | 4853.86 | 0.517067 | ||||||||
\(446\) | −7110.58 | −0.754923 | ||||||||
\(447\) | −13044.8 | −1.38031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7092.05 | 0.745422 | 0.372711 | − | 0.927948i | \(-0.378428\pi\) | ||||
0.372711 | + | 0.927948i | \(0.378428\pi\) | |||||||
\(450\) | 12634.6 | 1.32356 | ||||||||
\(451\) | −20888.0 | −2.18088 | ||||||||
\(452\) | −37806.0 | −3.93417 | ||||||||
\(453\) | 1586.06 | 0.164502 | ||||||||
\(454\) | 1520.32 | 0.157163 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20645.8 | −2.12024 | ||||||||
\(457\) | 8539.94 | 0.874139 | 0.437069 | − | 0.899428i | \(-0.356016\pi\) | ||||
0.437069 | + | 0.899428i | \(0.356016\pi\) | |||||||
\(458\) | 23001.1 | 2.34666 | ||||||||
\(459\) | 3285.40 | 0.334094 | ||||||||
\(460\) | −9043.03 | −0.916595 | ||||||||
\(461\) | 6167.30 | 0.623080 | 0.311540 | − | 0.950233i | \(-0.399155\pi\) | ||||
0.311540 | + | 0.950233i | \(0.399155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8115.61 | −0.814610 | −0.407305 | − | 0.913292i | \(-0.633531\pi\) | ||||
−0.407305 | + | 0.913292i | \(0.633531\pi\) | |||||||
\(464\) | 5768.49 | 0.577145 | ||||||||
\(465\) | −2163.92 | −0.215805 | ||||||||
\(466\) | 11956.8 | 1.18860 | ||||||||
\(467\) | −10883.1 | −1.07840 | −0.539199 | − | 0.842178i | \(-0.681273\pi\) | ||||
−0.539199 | + | 0.842178i | \(0.681273\pi\) | |||||||
\(468\) | −19032.4 | −1.87986 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3931.29 | 0.385824 | ||||||||
\(471\) | 9419.99 | 0.921550 | ||||||||
\(472\) | 23758.1 | 2.31685 | ||||||||
\(473\) | 13007.3 | 1.26443 | ||||||||
\(474\) | −6772.55 | −0.656273 | ||||||||
\(475\) | 6280.98 | 0.606718 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10910.1 | −1.04725 | ||||||||
\(478\) | −12.8536 | −0.00122994 | ||||||||
\(479\) | −14758.0 | −1.40775 | −0.703873 | − | 0.710326i | \(-0.748548\pi\) | ||||
−0.703873 | + | 0.710326i | \(0.748548\pi\) | |||||||
\(480\) | −5381.55 | −0.511735 | ||||||||
\(481\) | −10055.9 | −0.953241 | ||||||||
\(482\) | −30449.0 | −2.87741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39446.0 | 3.70454 | ||||||||
\(485\) | 2311.98 | 0.216457 | ||||||||
\(486\) | −25013.6 | −2.33465 | ||||||||
\(487\) | −2369.67 | −0.220493 | −0.110246 | − | 0.993904i | \(-0.535164\pi\) | ||||
−0.110246 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(488\) | −2781.78 | −0.258044 | ||||||||
\(489\) | −17687.6 | −1.63570 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17347.1 | 1.59443 | 0.797214 | − | 0.603696i | \(-0.206306\pi\) | ||||
0.797214 | + | 0.603696i | \(0.206306\pi\) | |||||||
\(492\) | 45704.2 | 4.18802 | ||||||||
\(493\) | 3761.99 | 0.343674 | ||||||||
\(494\) | −13552.8 | −1.23435 | ||||||||
\(495\) | −4097.47 | −0.372055 | ||||||||
\(496\) | −12472.4 | −1.12909 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −18633.1 | −1.67664 | ||||||||
\(499\) | −14617.0 | −1.31132 | −0.655659 | − | 0.755058i | \(-0.727609\pi\) | ||||
−0.655659 | + | 0.755058i | \(0.727609\pi\) | |||||||
\(500\) | 14384.4 | 1.28658 | ||||||||
\(501\) | 1306.58 | 0.116514 | ||||||||
\(502\) | −3070.60 | −0.273003 | ||||||||
\(503\) | −13355.9 | −1.18392 | −0.591958 | − | 0.805969i | \(-0.701645\pi\) | ||||
−0.591958 | + | 0.805969i | \(0.701645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 168.817 | 0.0148758 | ||||||||
\(506\) | −45605.2 | −4.00672 | ||||||||
\(507\) | −728.293 | −0.0637961 | ||||||||
\(508\) | −672.499 | −0.0587349 | ||||||||
\(509\) | 1359.50 | 0.118386 | 0.0591932 | − | 0.998247i | \(-0.481147\pi\) | ||||
0.0591932 | + | 0.998247i | \(0.481147\pi\) | |||||||
\(510\) | −9883.10 | −0.858100 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25310.6 | 2.18473 | ||||||||
\(513\) | −2122.30 | −0.182654 | ||||||||
\(514\) | −5268.57 | −0.452114 | ||||||||
\(515\) | −607.665 | −0.0519940 | ||||||||
\(516\) | −28460.9 | −2.42814 | ||||||||
\(517\) | 13840.9 | 1.17741 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19866.8 | −1.68026 | ||||||||
\(520\) | −8420.37 | −0.710111 | ||||||||
\(521\) | 10272.6 | 0.863817 | 0.431909 | − | 0.901917i | \(-0.357840\pi\) | ||||
0.431909 | + | 0.901917i | \(0.357840\pi\) | |||||||
\(522\) | −4888.45 | −0.409888 | ||||||||
\(523\) | 17081.2 | 1.42812 | 0.714060 | − | 0.700084i | \(-0.246854\pi\) | ||||
0.714060 | + | 0.700084i | \(0.246854\pi\) | |||||||
\(524\) | −6060.27 | −0.505237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4510.32 | −0.373877 | ||||||||
\(527\) | −8134.05 | −0.672343 | ||||||||
\(528\) | −53353.9 | −4.39760 | ||||||||
\(529\) | 10495.2 | 0.862597 | ||||||||
\(530\) | −8504.37 | −0.696993 | ||||||||
\(531\) | −9424.90 | −0.770255 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17028.5 | 1.38384 | ||||||||
\(534\) | −53560.8 | −4.34046 | ||||||||
\(535\) | −2032.63 | −0.164258 | ||||||||
\(536\) | 14234.5 | 1.14708 | ||||||||
\(537\) | −2477.69 | −0.199107 | ||||||||
\(538\) | 7251.71 | 0.581122 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2323.19 | −0.185137 | ||||||||
\(541\) | 10729.6 | 0.852683 | 0.426341 | − | 0.904562i | \(-0.359802\pi\) | ||||
0.426341 | + | 0.904562i | \(0.359802\pi\) | |||||||
\(542\) | −6335.90 | −0.502122 | ||||||||
\(543\) | 1855.08 | 0.146610 | ||||||||
\(544\) | −20229.0 | −1.59432 | ||||||||
\(545\) | 1442.50 | 0.113376 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20050.0 | 1.56724 | 0.783618 | − | 0.621243i | \(-0.213372\pi\) | ||||
0.783618 | + | 0.621243i | \(0.213372\pi\) | |||||||
\(548\) | 7104.97 | 0.553849 | ||||||||
\(549\) | 1103.54 | 0.0857887 | ||||||||
\(550\) | 34674.1 | 2.68820 | ||||||||
\(551\) | −2430.16 | −0.187892 | ||||||||
\(552\) | 56636.8 | 4.36707 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35212.5 | −2.70043 | ||||||||
\(555\) | 4736.99 | 0.362296 | ||||||||
\(556\) | 3995.55 | 0.304765 | ||||||||
\(557\) | 12051.4 | 0.916759 | 0.458380 | − | 0.888757i | \(-0.348430\pi\) | ||||
0.458380 | + | 0.888757i | \(0.348430\pi\) | |||||||
\(558\) | 10569.7 | 0.801880 | ||||||||
\(559\) | −10604.0 | −0.802327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34795.4 | −2.61865 | ||||||||
\(562\) | −14575.9 | −1.09403 | ||||||||
\(563\) | −13594.0 | −1.01762 | −0.508810 | − | 0.860879i | \(-0.669914\pi\) | ||||
−0.508810 | + | 0.860879i | \(0.669914\pi\) | |||||||
\(564\) | −30284.8 | −2.26103 | ||||||||
\(565\) | 6635.36 | 0.494074 | ||||||||
\(566\) | −36605.7 | −2.71847 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11012.3 | −0.813495 | ||||||||
\(569\) | −10657.3 | −0.785197 | −0.392598 | − | 0.919710i | \(-0.628424\pi\) | ||||
−0.392598 | + | 0.919710i | \(0.628424\pi\) | |||||||
\(570\) | 6384.27 | 0.469136 | ||||||||
\(571\) | −12337.4 | −0.904209 | −0.452105 | − | 0.891965i | \(-0.649327\pi\) | ||||
−0.452105 | + | 0.891965i | \(0.649327\pi\) | |||||||
\(572\) | −52231.9 | −3.81805 | ||||||||
\(573\) | −31216.3 | −2.27588 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17230.3 | −1.24966 | ||||||||
\(576\) | 3940.34 | 0.285036 | ||||||||
\(577\) | 14808.4 | 1.06843 | 0.534214 | − | 0.845349i | \(-0.320608\pi\) | ||||
0.534214 | + | 0.845349i | \(0.320608\pi\) | |||||||
\(578\) | −11858.7 | −0.853385 | ||||||||
\(579\) | −24271.7 | −1.74214 | ||||||||
\(580\) | −2660.19 | −0.190446 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −25512.0 | −1.81702 | ||||||||
\(583\) | −29941.3 | −2.12700 | ||||||||
\(584\) | −36736.2 | −2.60300 | ||||||||
\(585\) | 3340.39 | 0.236082 | ||||||||
\(586\) | 33275.0 | 2.34569 | ||||||||
\(587\) | −9084.07 | −0.638739 | −0.319369 | − | 0.947630i | \(-0.603471\pi\) | ||||
−0.319369 | + | 0.947630i | \(0.603471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5254.42 | 0.367580 | ||||||||
\(590\) | −7346.66 | −0.512640 | ||||||||
\(591\) | 16810.2 | 1.17002 | ||||||||
\(592\) | 27303.2 | 1.89553 | ||||||||
\(593\) | −27554.3 | −1.90813 | −0.954065 | − | 0.299600i | \(-0.903147\pi\) | ||||
−0.954065 | + | 0.299600i | \(0.903147\pi\) | |||||||
\(594\) | −11716.1 | −0.809290 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34673.7 | 2.38304 | ||||||||
\(597\) | −36378.4 | −2.49392 | ||||||||
\(598\) | 37178.8 | 2.54240 | ||||||||
\(599\) | 15408.8 | 1.05106 | 0.525530 | − | 0.850775i | \(-0.323867\pi\) | ||||
0.525530 | + | 0.850775i | \(0.323867\pi\) | |||||||
\(600\) | −43061.5 | −2.92997 | ||||||||
\(601\) | −26852.7 | −1.82254 | −0.911270 | − | 0.411810i | \(-0.864897\pi\) | ||||
−0.911270 | + | 0.411810i | \(0.864897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5646.86 | −0.381356 | ||||||||
\(604\) | −4215.81 | −0.284005 | ||||||||
\(605\) | −6923.19 | −0.465236 | ||||||||
\(606\) | −1862.85 | −0.124873 | ||||||||
\(607\) | 12580.2 | 0.841213 | 0.420607 | − | 0.907243i | \(-0.361817\pi\) | ||||
0.420607 | + | 0.907243i | \(0.361817\pi\) | |||||||
\(608\) | 13067.5 | 0.871638 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 860.206 | 0.0570963 | ||||||||
\(611\) | −11283.5 | −0.747108 | ||||||||
\(612\) | 33700.9 | 2.22595 | ||||||||
\(613\) | 11022.4 | 0.726246 | 0.363123 | − | 0.931741i | \(-0.381710\pi\) | ||||
0.363123 | + | 0.931741i | \(0.381710\pi\) | |||||||
\(614\) | −33803.9 | −2.22185 | ||||||||
\(615\) | −8021.57 | −0.525953 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18154.9 | 1.18459 | 0.592293 | − | 0.805723i | \(-0.298223\pi\) | ||||
0.592293 | + | 0.805723i | \(0.298223\pi\) | |||||||
\(618\) | 6705.40 | 0.436457 | ||||||||
\(619\) | 6517.56 | 0.423203 | 0.211602 | − | 0.977356i | \(-0.432132\pi\) | ||||
0.211602 | + | 0.977356i | \(0.432132\pi\) | |||||||
\(620\) | 5751.79 | 0.372576 | ||||||||
\(621\) | 5822.00 | 0.376214 | ||||||||
\(622\) | 37206.4 | 2.39846 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 43495.8 | 2.79043 | ||||||||
\(625\) | 11782.5 | 0.754081 | ||||||||
\(626\) | 43434.5 | 2.77315 | ||||||||
\(627\) | 22477.1 | 1.43166 | ||||||||
\(628\) | −25038.7 | −1.59101 | ||||||||
\(629\) | 17806.1 | 1.12874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −928.861 | −0.0586012 | −0.0293006 | − | 0.999571i | \(-0.509328\pi\) | ||||
−0.0293006 | + | 0.999571i | \(0.509328\pi\) | |||||||
\(632\) | 10217.4 | 0.643077 | ||||||||
\(633\) | 15588.6 | 0.978815 | ||||||||
\(634\) | −36694.5 | −2.29862 | ||||||||
\(635\) | 118.031 | 0.00737622 | ||||||||
\(636\) | 65513.5 | 4.08456 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13415.7 | −0.832497 | ||||||||
\(639\) | 4368.61 | 0.270453 | ||||||||
\(640\) | −3114.09 | −0.192336 | ||||||||
\(641\) | 26729.8 | 1.64706 | 0.823528 | − | 0.567275i | \(-0.192002\pi\) | ||||
0.823528 | + | 0.567275i | \(0.192002\pi\) | |||||||
\(642\) | 22429.4 | 1.37885 | ||||||||
\(643\) | −5311.51 | −0.325763 | −0.162881 | − | 0.986646i | \(-0.552079\pi\) | ||||
−0.162881 | + | 0.986646i | \(0.552079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4995.18 | 0.304938 | ||||||||
\(646\) | 23998.1 | 1.46160 | ||||||||
\(647\) | −10529.7 | −0.639822 | −0.319911 | − | 0.947448i | \(-0.603653\pi\) | ||||
−0.319911 | + | 0.947448i | \(0.603653\pi\) | |||||||
\(648\) | 45846.1 | 2.77933 | ||||||||
\(649\) | −25865.4 | −1.56441 | ||||||||
\(650\) | −28267.4 | −1.70575 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 47014.4 | 2.82396 | ||||||||
\(653\) | 247.029 | 0.0148039 | 0.00740197 | − | 0.999973i | \(-0.497644\pi\) | ||||
0.00740197 | + | 0.999973i | \(0.497644\pi\) | |||||||
\(654\) | −15917.5 | −0.951718 | ||||||||
\(655\) | 1063.64 | 0.0634503 | ||||||||
\(656\) | −46234.9 | −2.75178 | ||||||||
\(657\) | 14573.3 | 0.865389 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1307.57 | −0.0772925 | −0.0386463 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386463 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(660\) | 24604.7 | 1.45112 | ||||||||
\(661\) | 32906.1 | 1.93631 | 0.968153 | − | 0.250361i | \(-0.0805491\pi\) | ||||
0.968153 | + | 0.250361i | \(0.0805491\pi\) | |||||||
\(662\) | 18670.1 | 1.09613 | ||||||||
\(663\) | 28366.3 | 1.66162 | ||||||||
\(664\) | 28110.7 | 1.64293 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23137.9 | −1.34621 | ||||||||
\(667\) | 6666.56 | 0.387002 | ||||||||
\(668\) | −3472.94 | −0.201156 | ||||||||
\(669\) | −9613.84 | −0.555594 | ||||||||
\(670\) | −4401.70 | −0.253810 | ||||||||
\(671\) | 3028.52 | 0.174240 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16392.4 | −0.938900 | −0.469450 | − | 0.882959i | \(-0.655548\pi\) | ||||
−0.469450 | + | 0.882959i | \(0.655548\pi\) | |||||||
\(674\) | 6566.85 | 0.375290 | ||||||||
\(675\) | −4426.53 | −0.252411 | ||||||||
\(676\) | 1935.84 | 0.110141 | ||||||||
\(677\) | −5112.42 | −0.290231 | −0.145115 | − | 0.989415i | \(-0.546355\pi\) | ||||
−0.145115 | + | 0.989415i | \(0.546355\pi\) | |||||||
\(678\) | −73219.2 | −4.14744 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14910.1 | 0.840845 | ||||||||
\(681\) | 2055.54 | 0.115666 | ||||||||
\(682\) | 29007.0 | 1.62865 | ||||||||
\(683\) | −9655.89 | −0.540955 | −0.270477 | − | 0.962726i | \(-0.587182\pi\) | ||||
−0.270477 | + | 0.962726i | \(0.587182\pi\) | |||||||
\(684\) | −21770.1 | −1.21696 | ||||||||
\(685\) | −1247.00 | −0.0695552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31098.5 | 1.72705 | ||||||||
\(688\) | 28791.4 | 1.59544 | ||||||||
\(689\) | 24409.1 | 1.34966 | ||||||||
\(690\) | −17513.7 | −0.966282 | ||||||||
\(691\) | 13905.7 | 0.765552 | 0.382776 | − | 0.923841i | \(-0.374968\pi\) | ||||
0.382776 | + | 0.923841i | \(0.374968\pi\) | |||||||
\(692\) | 52806.8 | 2.90088 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31112.2 | 1.70173 | ||||||||
\(695\) | −701.261 | −0.0382739 | ||||||||
\(696\) | 16660.9 | 0.907369 | ||||||||
\(697\) | −30152.7 | −1.63861 | ||||||||
\(698\) | 12298.2 | 0.666898 | ||||||||
\(699\) | 16166.2 | 0.874767 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28770.3 | 1.55013 | 0.775064 | − | 0.631883i | \(-0.217718\pi\) | ||||
0.775064 | + | 0.631883i | \(0.217718\pi\) | |||||||
\(702\) | 9551.36 | 0.513523 | ||||||||
\(703\) | −11502.4 | −0.617098 | ||||||||
\(704\) | 10813.7 | 0.578917 | ||||||||
\(705\) | 5315.30 | 0.283951 | ||||||||
\(706\) | −12993.5 | −0.692658 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 56595.1 | 3.00420 | ||||||||
\(709\) | −2627.73 | −0.139191 | −0.0695956 | − | 0.997575i | \(-0.522171\pi\) | ||||
−0.0695956 | + | 0.997575i | \(0.522171\pi\) | |||||||
\(710\) | 3405.31 | 0.179999 | ||||||||
\(711\) | −4053.26 | −0.213796 | ||||||||
\(712\) | 80804.1 | 4.25318 | ||||||||
\(713\) | −14414.2 | −0.757106 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9167.24 | 0.479490 | ||||||||
\(716\) | 6585.82 | 0.343748 | ||||||||
\(717\) | −17.3787 | −0.000905189 0 | ||||||||
\(718\) | −21305.1 | −1.10738 | ||||||||
\(719\) | −1386.68 | −0.0719258 | −0.0359629 | − | 0.999353i | \(-0.511450\pi\) | ||||
−0.0359629 | + | 0.999353i | \(0.511450\pi\) | |||||||
\(720\) | −9069.63 | −0.469452 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19806.8 | 1.02096 | ||||||||
\(723\) | −41168.4 | −2.11766 | ||||||||
\(724\) | −4930.90 | −0.253115 | ||||||||
\(725\) | −5068.65 | −0.259648 | ||||||||
\(726\) | 76395.3 | 3.90536 | ||||||||
\(727\) | −28039.0 | −1.43041 | −0.715205 | − | 0.698915i | \(-0.753667\pi\) | ||||
−0.715205 | + | 0.698915i | \(0.753667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10919.5 | −0.554769 | ||||||||
\(730\) | 11359.9 | 0.575955 | ||||||||
\(731\) | 18776.6 | 0.950040 | ||||||||
\(732\) | −6626.61 | −0.334599 | ||||||||
\(733\) | 23145.9 | 1.16632 | 0.583161 | − | 0.812356i | \(-0.301816\pi\) | ||||
0.583161 | + | 0.812356i | \(0.301816\pi\) | |||||||
\(734\) | −39198.3 | −1.97117 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35847.4 | −1.79532 | ||||||||
\(737\) | −15497.0 | −0.774547 | ||||||||
\(738\) | 39181.4 | 1.95432 | ||||||||
\(739\) | −10745.8 | −0.534902 | −0.267451 | − | 0.963572i | \(-0.586181\pi\) | ||||
−0.267451 | + | 0.963572i | \(0.586181\pi\) | |||||||
\(740\) | −12591.1 | −0.625486 | ||||||||
\(741\) | −18324.0 | −0.908435 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25041.1 | −1.23643 | −0.618216 | − | 0.786008i | \(-0.712144\pi\) | ||||
−0.618216 | + | 0.786008i | \(0.712144\pi\) | |||||||
\(744\) | −36023.6 | −1.77512 | ||||||||
\(745\) | −6085.60 | −0.299274 | ||||||||
\(746\) | 38176.2 | 1.87363 | ||||||||
\(747\) | −11151.6 | −0.546205 | ||||||||
\(748\) | 92487.7 | 4.52097 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 27858.3 | 1.35632 | ||||||||
\(751\) | 32944.8 | 1.60076 | 0.800381 | − | 0.599492i | \(-0.204631\pi\) | ||||
0.800381 | + | 0.599492i | \(0.204631\pi\) | |||||||
\(752\) | 30636.4 | 1.48563 | ||||||||
\(753\) | −4151.59 | −0.200920 | ||||||||
\(754\) | 10936.9 | 0.528248 | ||||||||
\(755\) | 739.919 | 0.0356668 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23803.0 | −1.14285 | −0.571424 | − | 0.820655i | \(-0.693609\pi\) | ||||
−0.571424 | + | 0.820655i | \(0.693609\pi\) | |||||||
\(758\) | −379.946 | −0.0182061 | ||||||||
\(759\) | −61660.4 | −2.94879 | ||||||||
\(760\) | −9631.58 | −0.459703 | ||||||||
\(761\) | −34675.2 | −1.65174 | −0.825871 | − | 0.563858i | \(-0.809316\pi\) | ||||
−0.825871 | + | 0.563858i | \(0.809316\pi\) | |||||||
\(762\) | −1302.43 | −0.0619188 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 82974.3 | 3.92919 | ||||||||
\(765\) | −5914.87 | −0.279546 | ||||||||
\(766\) | −43630.1 | −2.05799 | ||||||||
\(767\) | 21086.3 | 0.992674 | ||||||||
\(768\) | 44594.7 | 2.09528 | ||||||||
\(769\) | −28935.5 | −1.35688 | −0.678441 | − | 0.734655i | \(-0.737344\pi\) | ||||
−0.678441 | + | 0.734655i | \(0.737344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7123.36 | −0.332739 | ||||||||
\(772\) | 64515.3 | 3.00771 | ||||||||
\(773\) | 16964.0 | 0.789331 | 0.394665 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394665 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(774\) | −24399.0 | −1.13308 | ||||||||
\(775\) | 10959.3 | 0.507960 | ||||||||
\(776\) | 38488.5 | 1.78049 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 40653.9 | 1.87341 | ||||||||
\(779\) | 19478.0 | 0.895854 | ||||||||
\(780\) | −20058.5 | −0.920783 | ||||||||
\(781\) | 11989.1 | 0.549299 | ||||||||
\(782\) | −65833.0 | −3.01047 | ||||||||
\(783\) | 1712.66 | 0.0781680 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4394.56 | 0.199807 | ||||||||
\(786\) | −11737.0 | −0.532626 | ||||||||
\(787\) | −17051.3 | −0.772318 | −0.386159 | − | 0.922432i | \(-0.626198\pi\) | ||||
−0.386159 | + | 0.922432i | \(0.626198\pi\) | |||||||
\(788\) | −44682.3 | −2.01997 | ||||||||
\(789\) | −6098.16 | −0.275159 | ||||||||
\(790\) | −3159.49 | −0.142291 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −68212.2 | −3.06037 | ||||||||
\(793\) | −2468.95 | −0.110561 | ||||||||
\(794\) | −55740.6 | −2.49138 | ||||||||
\(795\) | −11498.3 | −0.512960 | ||||||||
\(796\) | 96695.4 | 4.30562 | ||||||||
\(797\) | 2866.63 | 0.127404 | 0.0637021 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637021 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19979.9 | 0.884654 | ||||||||
\(800\) | 27255.2 | 1.20452 | ||||||||
\(801\) | −32055.2 | −1.41400 | ||||||||
\(802\) | 14280.0 | 0.628732 | ||||||||
\(803\) | 39994.6 | 1.75763 | ||||||||
\(804\) | 33908.6 | 1.48739 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −23647.4 | −1.03343 | ||||||||
\(807\) | 9804.66 | 0.427683 | ||||||||
\(808\) | 2810.37 | 0.122362 | ||||||||
\(809\) | 5452.85 | 0.236974 | 0.118487 | − | 0.992956i | \(-0.462196\pi\) | ||||
0.118487 | + | 0.992956i | \(0.462196\pi\) | |||||||
\(810\) | −14176.9 | −0.614971 | ||||||||
\(811\) | 3643.68 | 0.157764 | 0.0788822 | − | 0.996884i | \(-0.474865\pi\) | ||||
0.0788822 | + | 0.996884i | \(0.474865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8566.44 | −0.369543 | ||||||||
\(814\) | −63498.7 | −2.73419 | ||||||||
\(815\) | −8251.51 | −0.354648 | ||||||||
\(816\) | −77018.7 | −3.30416 | ||||||||
\(817\) | −12129.3 | −0.519401 | ||||||||
\(818\) | 75467.6 | 3.22575 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21321.7 | 0.908031 | ||||||||
\(821\) | 21790.0 | 0.926281 | 0.463141 | − | 0.886285i | \(-0.346723\pi\) | ||||
0.463141 | + | 0.886285i | \(0.346723\pi\) | |||||||
\(822\) | 13760.2 | 0.583873 | ||||||||
\(823\) | −5238.96 | −0.221894 | −0.110947 | − | 0.993826i | \(-0.535388\pi\) | ||||
−0.110947 | + | 0.993826i | \(0.535388\pi\) | |||||||
\(824\) | −10116.0 | −0.427681 | ||||||||
\(825\) | 46881.0 | 1.97841 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8639.97 | −0.363291 | −0.181645 | − | 0.983364i | \(-0.558142\pi\) | ||||
−0.181645 | + | 0.983364i | \(0.558142\pi\) | |||||||
\(828\) | 59720.9 | 2.50658 | ||||||||
\(829\) | 32197.9 | 1.34895 | 0.674474 | − | 0.738298i | \(-0.264370\pi\) | ||||
0.674474 | + | 0.738298i | \(0.264370\pi\) | |||||||
\(830\) | −8692.61 | −0.363524 | ||||||||
\(831\) | −47609.0 | −1.98741 | ||||||||
\(832\) | −8815.70 | −0.367343 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7738.21 | 0.321286 | ||||||||
\(835\) | 609.538 | 0.0252622 | ||||||||
\(836\) | −59745.1 | −2.47168 | ||||||||
\(837\) | −3703.06 | −0.152923 | ||||||||
\(838\) | 40851.0 | 1.68398 | ||||||||
\(839\) | 40283.6 | 1.65762 | 0.828810 | − | 0.559530i | \(-0.189018\pi\) | ||||
0.828810 | + | 0.559530i | \(0.189018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22427.9 | −0.919591 | ||||||||
\(842\) | 64779.1 | 2.65135 | ||||||||
\(843\) | −19707.3 | −0.805166 | ||||||||
\(844\) | −41435.1 | −1.68988 | ||||||||
\(845\) | −339.759 | −0.0138320 | ||||||||
\(846\) | −25962.6 | −1.05510 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −66274.3 | −2.68381 | ||||||||
\(849\) | −49492.7 | −2.00069 | ||||||||
\(850\) | 50053.6 | 2.01979 | ||||||||
\(851\) | 31553.9 | 1.27104 | ||||||||
\(852\) | −26232.9 | −1.05484 | ||||||||
\(853\) | −44150.6 | −1.77220 | −0.886100 | − | 0.463493i | \(-0.846596\pi\) | ||||
−0.886100 | + | 0.463493i | \(0.846596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3820.88 | 0.152832 | ||||||||
\(856\) | −33838.0 | −1.35112 | ||||||||
\(857\) | −32361.4 | −1.28990 | −0.644951 | − | 0.764224i | \(-0.723122\pi\) | ||||
−0.644951 | + | 0.764224i | \(0.723122\pi\) | |||||||
\(858\) | −101158. | −4.02502 | ||||||||
\(859\) | −44224.6 | −1.75660 | −0.878302 | − | 0.478107i | \(-0.841323\pi\) | ||||
−0.878302 | + | 0.478107i | \(0.841323\pi\) | |||||||
\(860\) | −13277.4 | −0.526461 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27806.8 | 1.09873 | ||||||||
\(863\) | 6285.13 | 0.247912 | 0.123956 | − | 0.992288i | \(-0.460442\pi\) | ||||
0.123956 | + | 0.992288i | \(0.460442\pi\) | |||||||
\(864\) | −9209.32 | −0.362624 | ||||||||
\(865\) | −9268.14 | −0.364308 | ||||||||
\(866\) | 30830.6 | 1.20978 | ||||||||
\(867\) | −16033.5 | −0.628058 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11123.6 | −0.434227 | ||||||||
\(870\) | −5152.01 | −0.200770 | ||||||||
\(871\) | 12633.7 | 0.491477 | ||||||||
\(872\) | 24013.8 | 0.932581 | ||||||||
\(873\) | −15268.5 | −0.591937 | ||||||||
\(874\) | 42526.7 | 1.64587 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −87510.8 | −3.37525 | ||||||||
\(877\) | 10959.1 | 0.421963 | 0.210981 | − | 0.977490i | \(-0.432334\pi\) | ||||
0.210981 | + | 0.977490i | \(0.432334\pi\) | |||||||
\(878\) | 67910.1 | 2.61031 | ||||||||
\(879\) | 44989.3 | 1.72634 | ||||||||
\(880\) | −24890.4 | −0.953472 | ||||||||
\(881\) | 9900.29 | 0.378603 | 0.189301 | − | 0.981919i | \(-0.439378\pi\) | ||||
0.189301 | + | 0.981919i | \(0.439378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48125.0 | −1.83413 | −0.917065 | − | 0.398738i | \(-0.869448\pi\) | ||||
−0.917065 | + | 0.398738i | \(0.869448\pi\) | |||||||
\(884\) | −75399.0 | −2.86871 | ||||||||
\(885\) | −9933.04 | −0.377283 | ||||||||
\(886\) | 79987.8 | 3.03300 | ||||||||
\(887\) | 334.271 | 0.0126536 | 0.00632680 | − | 0.999980i | \(-0.497986\pi\) | ||||
0.00632680 | + | 0.999980i | \(0.497986\pi\) | |||||||
\(888\) | 78858.6 | 2.98009 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −24986.9 | −0.941083 | ||||||||
\(891\) | −49912.6 | −1.87670 | ||||||||
\(892\) | 25554.0 | 0.959206 | ||||||||
\(893\) | −12906.6 | −0.483654 | ||||||||
\(894\) | 67152.7 | 2.51222 | ||||||||
\(895\) | −1155.88 | −0.0431696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50267.5 | 1.87111 | ||||||||
\(898\) | −36508.8 | −1.35670 | ||||||||
\(899\) | −4240.24 | −0.157308 | ||||||||
\(900\) | −45406.4 | −1.68172 | ||||||||
\(901\) | −43221.6 | −1.59813 | ||||||||
\(902\) | 107528. | 3.96928 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 110461. | 4.06404 | ||||||||
\(905\) | 865.424 | 0.0317875 | ||||||||
\(906\) | −8164.78 | −0.299400 | ||||||||
\(907\) | 41015.9 | 1.50155 | 0.750777 | − | 0.660556i | \(-0.229679\pi\) | ||||
0.750777 | + | 0.660556i | \(0.229679\pi\) | |||||||
\(908\) | −5463.72 | −0.199692 | ||||||||
\(909\) | −1114.88 | −0.0406802 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40481.5 | −1.47224 | −0.736121 | − | 0.676849i | \(-0.763345\pi\) | ||||
−0.736121 | + | 0.676849i | \(0.763345\pi\) | |||||||
\(912\) | 49752.4 | 1.80643 | ||||||||
\(913\) | −30604.0 | −1.10936 | ||||||||
\(914\) | −43962.3 | −1.59097 | ||||||||
\(915\) | 1163.04 | 0.0420206 | ||||||||
\(916\) | −82661.3 | −2.98167 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16912.7 | −0.608065 | ||||||||
\(919\) | 4752.86 | 0.170601 | 0.0853005 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0853005 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(920\) | 26421.9 | 0.946852 | ||||||||
\(921\) | −45704.5 | −1.63519 | ||||||||
\(922\) | −31748.3 | −1.13403 | ||||||||
\(923\) | −9773.87 | −0.348549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23990.8 | −0.852770 | ||||||||
\(926\) | 41777.9 | 1.48262 | ||||||||
\(927\) | 4013.06 | 0.142186 | ||||||||
\(928\) | −10545.3 | −0.373023 | ||||||||
\(929\) | 32762.8 | 1.15707 | 0.578533 | − | 0.815659i | \(-0.303626\pi\) | ||||
0.578533 | + | 0.815659i | \(0.303626\pi\) | |||||||
\(930\) | 11139.5 | 0.392773 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −42970.5 | −1.51024 | ||||||||
\(933\) | 50304.8 | 1.76517 | ||||||||
\(934\) | 56024.8 | 1.96273 | ||||||||
\(935\) | −16232.6 | −0.567766 | ||||||||
\(936\) | 55608.8 | 1.94191 | ||||||||
\(937\) | −37520.9 | −1.30817 | −0.654085 | − | 0.756421i | \(-0.726946\pi\) | ||||
−0.654085 | + | 0.756421i | \(0.726946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 58725.6 | 2.04093 | ||||||||
\(940\) | −14128.3 | −0.490228 | ||||||||
\(941\) | −8686.80 | −0.300937 | −0.150468 | − | 0.988615i | \(-0.548078\pi\) | ||||
−0.150468 | + | 0.988615i | \(0.548078\pi\) | |||||||
\(942\) | −48492.7 | −1.67726 | ||||||||
\(943\) | −53433.0 | −1.84520 | ||||||||
\(944\) | −57252.3 | −1.97394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −66959.8 | −2.30132 | ||||||||
\(947\) | 16321.2 | 0.560049 | 0.280024 | − | 0.959993i | \(-0.409657\pi\) | ||||
0.280024 | + | 0.959993i | \(0.409657\pi\) | |||||||
\(948\) | 24339.2 | 0.833861 | ||||||||
\(949\) | −32604.9 | −1.11528 | ||||||||
\(950\) | −32333.5 | −1.10425 | ||||||||
\(951\) | −49612.6 | −1.69169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16610.3 | 0.564596 | 0.282298 | − | 0.959327i | \(-0.408903\pi\) | ||||
0.282298 | + | 0.959327i | \(0.408903\pi\) | |||||||
\(954\) | 56163.5 | 1.90604 | ||||||||
\(955\) | −14562.9 | −0.493448 | ||||||||
\(956\) | 46.1934 | 0.00156276 | ||||||||
\(957\) | −18138.7 | −0.612685 | ||||||||
\(958\) | 75972.0 | 2.56215 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4152.78 | 0.139615 | ||||||||
\(961\) | −20622.9 | −0.692252 | ||||||||
\(962\) | 51766.2 | 1.73494 | ||||||||
\(963\) | 13423.6 | 0.449190 | ||||||||
\(964\) | 109428. | 3.65604 | ||||||||
\(965\) | −11323.1 | −0.377724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7530.63 | −0.250433 | −0.125216 | − | 0.992129i | \(-0.539963\pi\) | ||||
−0.125216 | + | 0.992129i | \(0.539963\pi\) | |||||||
\(968\) | −115253. | −3.82683 | ||||||||
\(969\) | 32446.6 | 1.07568 | ||||||||
\(970\) | −11901.7 | −0.393961 | ||||||||
\(971\) | 3882.76 | 0.128325 | 0.0641625 | − | 0.997939i | \(-0.479562\pi\) | ||||
0.0641625 | + | 0.997939i | \(0.479562\pi\) | |||||||
\(972\) | 89894.0 | 2.96641 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12198.7 | 0.401305 | ||||||||
\(975\) | −38218.9 | −1.25537 | ||||||||
\(976\) | 6703.56 | 0.219852 | ||||||||
\(977\) | −8185.31 | −0.268036 | −0.134018 | − | 0.990979i | \(-0.542788\pi\) | ||||
−0.134018 | + | 0.990979i | \(0.542788\pi\) | |||||||
\(978\) | 91052.9 | 2.97705 | ||||||||
\(979\) | −87971.3 | −2.87189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9526.36 | −0.310044 | ||||||||
\(982\) | −89300.3 | −2.90192 | ||||||||
\(983\) | −29363.9 | −0.952761 | −0.476381 | − | 0.879239i | \(-0.658052\pi\) | ||||
−0.476381 | + | 0.879239i | \(0.658052\pi\) | |||||||
\(984\) | −133538. | −4.32627 | ||||||||
\(985\) | 7842.21 | 0.253679 | ||||||||
\(986\) | −19366.1 | −0.625501 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48706.1 | 1.56837 | ||||||||
\(989\) | 33273.8 | 1.06981 | ||||||||
\(990\) | 21093.1 | 0.677155 | ||||||||
\(991\) | 24197.0 | 0.775623 | 0.387811 | − | 0.921739i | \(-0.373231\pi\) | ||||
0.387811 | + | 0.921739i | \(0.373231\pi\) | |||||||
\(992\) | 22800.6 | 0.729758 | ||||||||
\(993\) | 25242.9 | 0.806706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16971.0 | −0.540722 | ||||||||
\(996\) | 66963.6 | 2.13035 | ||||||||
\(997\) | −37381.7 | −1.18745 | −0.593726 | − | 0.804667i | \(-0.702344\pi\) | ||||
−0.593726 | + | 0.804667i | \(0.702344\pi\) | |||||||
\(998\) | 75246.2 | 2.38665 | ||||||||
\(999\) | 8106.31 | 0.256729 |
(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 | 2401.4.a.c.1.3 | 39 | ||
7.6 | odd | 2 | 2401.4.a.d.1.3 | 39 | |||
49.13 | odd | 14 | 49.4.e.a.22.13 | ✓ | 78 | ||
49.34 | odd | 14 | 49.4.e.a.29.13 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.22.13 | ✓ | 78 | 49.13 | odd | 14 | ||
49.4.e.a.29.13 | yes | 78 | 49.34 | odd | 14 | ||
2401.4.a.c.1.3 | 39 | 1.1 | even | 1 | trivial | ||
2401.4.a.d.1.3 | 39 | 7.6 | odd | 2 |