Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(513,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.513");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(60.4179558459\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 36x^{8} + 405x^{6} + 1380x^{4} + 420x^{2} + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 513.2 | ||
Root | \(0.357936i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.513 |
Dual form | 1024.4.b.j.513.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 7.77277i | − 1.49587i | −0.663771 | − | 0.747935i | \(-0.731045\pi\) | ||||
0.663771 | − | 0.747935i | \(-0.268955\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.59550i | 0.589919i | 0.955510 | + | 0.294960i | \(0.0953062\pi\) | ||||
−0.955510 | + | 0.294960i | \(0.904694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.8965 | −1.34429 | −0.672143 | − | 0.740422i | \(-0.734626\pi\) | ||||
−0.672143 | + | 0.740422i | \(0.734626\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −33.4160 | −1.23763 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 31.5979i | 0.866103i | 0.901369 | + | 0.433052i | \(0.142563\pi\) | ||||
−0.901369 | + | 0.433052i | \(0.857437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 15.9402i | − 0.340078i | −0.985437 | − | 0.170039i | \(-0.945611\pi\) | ||||
0.985437 | − | 0.170039i | \(-0.0543893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 51.2653 | 0.882443 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 88.4846 | 1.26239 | 0.631196 | − | 0.775623i | \(-0.282564\pi\) | ||||
0.631196 | + | 0.775623i | \(0.282564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.4838i | 0.645790i | 0.946435 | + | 0.322895i | \(0.104656\pi\) | ||||
−0.946435 | + | 0.322895i | \(0.895344\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 193.515i | 2.01088i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.1224 | −0.436270 | −0.218135 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218135 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 81.4994 | 0.651995 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 49.8702i | 0.355464i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 14.7689i | − 0.0945692i | −0.998881 | − | 0.0472846i | \(-0.984943\pi\) | ||||
0.998881 | − | 0.0472846i | \(-0.0150568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −96.9578 | −0.561746 | −0.280873 | − | 0.959745i | \(-0.590624\pi\) | ||||
−0.280873 | + | 0.959745i | \(0.590624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 245.604 | 1.29558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 164.205i | − 0.793020i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 230.911i | 1.02599i | 0.858392 | + | 0.512994i | \(0.171464\pi\) | ||||
−0.858392 | + | 0.512994i | \(0.828536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −123.899 | −0.508713 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 360.519 | 1.37326 | 0.686629 | − | 0.727008i | \(-0.259090\pi\) | ||||
0.686629 | + | 0.727008i | \(0.259090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 141.774i | − 0.502797i | −0.967884 | − | 0.251398i | \(-0.919110\pi\) | ||||
0.967884 | − | 0.251398i | \(-0.0808905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 220.395i | − 0.730102i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −220.669 | −0.684849 | −0.342425 | − | 0.939545i | \(-0.611248\pi\) | ||||
−0.342425 | + | 0.939545i | \(0.611248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 276.837 | 0.807104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 687.771i | − 1.88838i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 248.551i | − 0.644172i | −0.946710 | − | 0.322086i | \(-0.895616\pi\) | ||||
0.946710 | − | 0.322086i | \(-0.104384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −208.404 | −0.510931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 415.717 | 0.966019 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 572.767i | − 1.26386i | −0.775024 | − | 0.631932i | \(-0.782262\pi\) | ||||
0.775024 | − | 0.631932i | \(-0.217738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 939.852i | − 1.97272i | −0.164614 | − | 0.986358i | \(-0.552638\pi\) | ||||
0.164614 | − | 0.986358i | \(-0.447362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 831.942 | 1.66373 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 105.133 | 0.200619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 151.854i | 0.276894i | 0.990370 | + | 0.138447i | \(0.0442111\pi\) | ||||
−0.990370 | + | 0.138447i | \(0.955789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 374.045i | 0.652604i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 215.050 | 0.359461 | 0.179731 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179731 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 668.587 | 1.07195 | 0.535974 | − | 0.844235i | \(-0.319945\pi\) | ||||
0.535974 | + | 0.844235i | \(0.319945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 633.476i | − 0.975300i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 786.679i | − 1.16429i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 822.956 | 1.17202 | 0.586012 | − | 0.810303i | \(-0.300697\pi\) | ||||
0.586012 | + | 0.810303i | \(0.300697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −514.603 | −0.705902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 462.269i | 0.611332i | 0.952139 | + | 0.305666i | \(0.0988791\pi\) | ||||
−0.952139 | + | 0.305666i | \(0.901121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 583.600i | 0.744710i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −114.795 | −0.141463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −262.733 | −0.312918 | −0.156459 | − | 0.987684i | \(-0.550008\pi\) | ||||
−0.156459 | + | 0.987684i | \(0.550008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 396.855i | 0.457162i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 753.631i | 0.840300i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −352.752 | −0.380964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −150.801 | −0.157850 | −0.0789251 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789251 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1055.88i | − 1.07192i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 690.115i | − 0.679891i | −0.940445 | − | 0.339945i | \(-0.889591\pi\) | ||||
0.940445 | − | 0.339945i | \(-0.110409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1840.58 | −1.76075 | −0.880377 | − | 0.474275i | \(-0.842710\pi\) | ||||
−0.880377 | + | 0.474275i | \(0.842710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1276.33 | −1.18626 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 112.302i | − 0.101464i | −0.998712 | − | 0.0507322i | \(-0.983845\pi\) | ||||
0.998712 | − | 0.0507322i | \(-0.0161555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1347.72i | 1.18429i | 0.805831 | + | 0.592146i | \(0.201719\pi\) | ||||
−0.805831 | + | 0.592146i | \(0.798281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1794.82 | 1.53475 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 720.469 | 0.599788 | 0.299894 | − | 0.953973i | \(-0.403049\pi\) | ||||
0.299894 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 317.391i | − 0.257364i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 532.657i | 0.420890i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2202.96 | −1.69702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 332.571 | 0.249865 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2802.23i | − 2.05422i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1361.97i | 0.974544i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2622.35 | 1.83225 | 0.916124 | − | 0.400895i | \(-0.131301\pi\) | ||||
0.916124 | + | 0.400895i | \(0.131301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1101.97 | −0.752119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 929.950i | − 0.620230i | −0.950699 | − | 0.310115i | \(-0.899632\pi\) | ||||
0.950699 | − | 0.310115i | \(-0.100368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1331.56i | − 0.868127i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −328.919 | −0.209695 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2511.52 | −1.56623 | −0.783117 | − | 0.621874i | \(-0.786371\pi\) | ||||
−0.783117 | + | 0.621874i | \(0.786371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1535.86i | − 0.937195i | −0.883412 | − | 0.468598i | \(-0.844759\pi\) | ||||
0.883412 | − | 0.468598i | \(-0.155241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1715.21i | 1.02445i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 503.677 | 0.294543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 97.4080 | 0.0557882 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2151.79i | − 1.20732i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3230.96i | − 1.77645i | −0.459413 | − | 0.888223i | \(-0.651940\pi\) | ||||
0.459413 | − | 0.888223i | \(-0.348060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2814.39 | 1.51677 | 0.758383 | − | 0.651809i | \(-0.225990\pi\) | ||||
0.758383 | + | 0.651809i | \(0.225990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2956.80 | −1.56237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 639.485i | − 0.331385i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1281.71i | 0.651541i | 0.945449 | + | 0.325770i | \(0.105624\pi\) | ||||
−0.945449 | + | 0.325770i | \(0.894376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1931.93 | −0.963598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1198.08 | 0.586472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1969.09i | − 0.946204i | −0.881008 | − | 0.473102i | \(-0.843134\pi\) | ||||
0.881008 | − | 0.473102i | \(-0.156866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1619.88i | 0.764287i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1221.66 | −0.566075 | −0.283038 | − | 0.959109i | \(-0.591342\pi\) | ||||
−0.283038 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1942.91 | 0.884347 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1787.21i | − 0.799249i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 796.794i | − 0.350168i | −0.984553 | − | 0.175084i | \(-0.943980\pi\) | ||||
0.984553 | − | 0.175084i | \(-0.0560198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2029.05 | −0.876468 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4451.99 | −1.89058 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3114.42i | − 1.30046i | −0.759737 | − | 0.650230i | \(-0.774672\pi\) | ||||
0.759737 | − | 0.650230i | \(-0.225328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 171.535i | 0.0704425i | 0.999380 | + | 0.0352213i | \(0.0112136\pi\) | ||||
−0.999380 | + | 0.0352213i | \(0.988786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7305.26 | −2.95093 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1522.98 | −0.605251 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2795.93i | 1.09336i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1241.59i | − 0.477845i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3927.65 | 1.48793 | 0.743966 | − | 0.668218i | \(-0.232942\pi\) | ||||
0.743966 | + | 0.668218i | \(0.232942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3249.02 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 817.179i | − 0.300099i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3423.68i | − 1.23821i | −0.785309 | − | 0.619103i | \(-0.787496\pi\) | ||||
0.785309 | − | 0.619103i | \(-0.212504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1371.30 | 0.488488 | 0.244244 | − | 0.969714i | \(-0.421460\pi\) | ||||
0.244244 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1180.33 | 0.414198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 367.693i | 0.127128i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2377.80i | 0.810112i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1608.06 | 0.539941 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1689.98 | −0.559321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2291.73i | − 0.747721i | −0.927485 | − | 0.373861i | \(-0.878034\pi\) | ||||
0.927485 | − | 0.373861i | \(-0.121966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1671.54i | − 0.537708i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 935.068 | 0.296610 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2413.91 | 0.755148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5196.77i | − 1.60349i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1410.46i | − 0.429312i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −419.617 | −0.126007 | −0.0630036 | − | 0.998013i | \(-0.520068\pi\) | ||||
−0.0630036 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2723.38 | −0.806929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3017.42i | 0.882262i | 0.897443 | + | 0.441131i | \(0.145423\pi\) | ||||
−0.897443 | + | 0.441131i | \(0.854577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2226.56i | 0.642513i | 0.946992 | + | 0.321256i | \(0.104105\pi\) | ||||
−0.946992 | + | 0.321256i | \(0.895895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6114.67 | −1.74163 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1194.86 | −0.335957 | −0.167978 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167978 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1455.42i | − 0.404006i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 6396.65i | − 1.75320i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4241.03 | 1.14782 | 0.573911 | − | 0.818917i | \(-0.305425\pi\) | ||||
0.573911 | + | 0.818917i | \(0.305425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5571.19 | 1.48910 | 0.744548 | − | 0.667569i | \(-0.232665\pi\) | ||||
0.744548 | + | 0.667569i | \(0.232665\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5346.38i | 1.41140i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1825.88i | 0.476126i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 852.541 | 0.219619 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3593.11 | 0.914474 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 682.681i | 0.171675i | 0.996309 | + | 0.0858375i | \(0.0273566\pi\) | ||||
−0.996309 | + | 0.0858375i | \(0.972643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1520.57i | − 0.377855i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4536.19 | 1.11399 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8093.12 | 1.96434 | 0.982169 | − | 0.188002i | \(-0.0602013\pi\) | ||||
0.982169 | + | 0.188002i | \(0.0602013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5748.89i | − 1.37922i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 493.516i | 0.117042i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −410.300 | −0.0961984 | −0.0480992 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480992 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1639.32 | 0.380009 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2042.17i | 0.468085i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6.75940i | − 0.00153207i | −1.00000 | 0.000766037i | \(-0.999756\pi\) | |||||
1.00000 | 0.000766037i | \(-0.000243837\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2833.98 | 0.635247 | 0.317623 | − | 0.948217i | \(-0.397115\pi\) | ||||
0.317623 | + | 0.948217i | \(0.397115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3084.67 | 0.683855 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2575.21i | 0.564695i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2157.81i | 0.468052i | 0.972230 | + | 0.234026i | \(0.0751900\pi\) | ||||
−0.972230 | + | 0.234026i | \(0.924810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3239.94 | 0.695234 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4750.23 | 1.00845 | 0.504226 | − | 0.863572i | \(-0.331778\pi\) | ||||
0.504226 | + | 0.863572i | \(0.331778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 910.900i | − 0.191334i | −0.995413 | − | 0.0956668i | \(-0.969502\pi\) | ||||
0.995413 | − | 0.0956668i | \(-0.0304983\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2741.86i | 0.569873i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8975.67 | −1.84605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2916.53 | 0.593635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1172.14i | 0.236124i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2026.80i | 0.404119i | 0.979373 | + | 0.202060i | \(0.0647635\pi\) | ||||
−0.979373 | + | 0.202060i | \(0.935237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3777.69 | 0.745578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1575.79 | −0.307868 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 767.080i | 0.148366i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3529.67i | 0.675903i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5364.10 | −1.01703 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6198.79 | 1.16374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 326.981i | − 0.0607877i | −0.999538 | − | 0.0303938i | \(-0.990324\pi\) | ||||
0.999538 | − | 0.0303938i | \(-0.00967615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14306.4i | 2.63386i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −871.410 | −0.158885 | −0.0794423 | − | 0.996839i | \(-0.525314\pi\) | ||||
−0.0794423 | + | 0.996839i | \(0.525314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3515.02 | −0.634762 | −0.317381 | − | 0.948298i | \(-0.602803\pi\) | ||||
−0.317381 | + | 0.948298i | \(0.602803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5487.07i | 0.981465i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6680.42i | − 1.18363i | −0.806075 | − | 0.591814i | \(-0.798412\pi\) | ||||
0.806075 | − | 0.591814i | \(-0.201588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 466.665 | 0.0819067 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −872.901 | −0.151778 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4732.49i | 0.815241i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1299.12i | − 0.221729i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10475.5 | 1.77155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5493.90 | 0.920633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2574.24i | − 0.427471i | −0.976892 | − | 0.213736i | \(-0.931437\pi\) | ||||
0.976892 | − | 0.213736i | \(-0.0685631\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7716.13i | − 1.26979i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1001.55 | −0.163345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −74.0970 | −0.0119772 | −0.00598861 | − | 0.999982i | \(-0.501906\pi\) | ||||
−0.00598861 | + | 0.999982i | \(0.501906\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 5600.04i | − 0.897205i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3063.67i | − 0.486530i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1647.24 | 0.259307 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2467.01 | −0.384984 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2973.72i | − 0.460050i | −0.973185 | − | 0.230025i | \(-0.926119\pi\) | ||||
0.973185 | − | 0.230025i | \(-0.0738808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9351.98i | 1.43438i | 0.696875 | + | 0.717192i | \(0.254573\pi\) | ||||
−0.696875 | + | 0.717192i | \(0.745427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 794.940 | 0.120885 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2216.90 | 0.334259 | 0.167130 | − | 0.985935i | \(-0.446550\pi\) | ||||
0.167130 | + | 0.985935i | \(0.446550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1418.36i | 0.212053i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17123.1i | 2.53852i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2082.23 | −0.306117 | −0.153059 | − | 0.988217i | \(-0.548912\pi\) | ||||
−0.153059 | + | 0.988217i | \(0.548912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3998.49 | 0.582955 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2585.00i | − 0.373766i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4409.66i | 0.632362i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4509.22 | −0.641360 | −0.320680 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320680 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12047.1 | −1.69959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6188.05i | 0.865951i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12249.3i | − 1.70039i | −0.526470 | − | 0.850194i | \(-0.676485\pi\) | ||||
0.526470 | − | 0.850194i | \(-0.323515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10586.3 | 1.45779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −235.418 | −0.0321609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 4981.51i | − 0.675153i | −0.941298 | − | 0.337576i | \(-0.890393\pi\) | ||||
0.941298 | − | 0.337576i | \(-0.109607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 20382.9i | − 2.74081i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3044.88 | 0.406229 | 0.203115 | − | 0.979155i | \(-0.434894\pi\) | ||||
0.203115 | + | 0.979155i | \(0.434894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5188.54 | 0.686837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4737.51i | 0.622277i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2733.30i | − 0.356256i | −0.984007 | − | 0.178128i | \(-0.942996\pi\) | ||||
0.984007 | − | 0.178128i | \(-0.0570042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4258.09 | −0.550744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7228.29 | −0.927784 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5427.81i | 0.691399i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 950.997i | − 0.120225i | −0.998192 | − | 0.0601123i | \(-0.980854\pi\) | ||||
0.998192 | − | 0.0601123i | \(-0.0191459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10349.9 | −1.29861 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7606.74 | 0.947288 | 0.473644 | − | 0.880716i | \(-0.342938\pi\) | ||||
0.473644 | + | 0.880716i | \(0.342938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1545.53i | 0.191037i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3394.06i | − 0.416425i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7296.32 | −0.888612 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4981.58 | 0.602257 | 0.301129 | − | 0.953584i | \(-0.402637\pi\) | ||||
0.301129 | + | 0.953584i | \(0.402637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19521.5i | 2.34288i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14259.9i | 1.69899i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3048.89 | −0.360637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11937.9 | −1.40192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4855.53i | 0.566129i | 0.959101 | + | 0.283065i | \(0.0913511\pi\) | ||||
−0.959101 | + | 0.283065i | \(0.908649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 11276.5i | − 1.30543i | −0.757604 | − | 0.652714i | \(-0.773630\pi\) | ||||
0.757604 | − | 0.652714i | \(-0.226370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7373.88 | 0.847590 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7211.44 | 0.823074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23399.0i | 2.65189i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3914.97i | − 0.440598i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4800.16 | −0.536463 | −0.268232 | − | 0.963354i | \(-0.586439\pi\) | ||||
−0.268232 | + | 0.963354i | \(0.586439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6242.32 | −0.692810 | −0.346405 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346405 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 757.130i | − 0.0834520i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2573.77i | − 0.281739i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4929.27 | −0.535903 | −0.267951 | − | 0.963432i | \(-0.586347\pi\) | ||||
−0.267951 | + | 0.963432i | \(0.586347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9250.77 | −0.998896 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10848.0i | 1.16344i | 0.813390 | + | 0.581718i | \(0.197619\pi\) | ||||
−0.813390 | + | 0.581718i | \(0.802381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1732.86i | − 0.184596i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25113.5 | −2.65733 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11515.2 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11391.7i | 1.18938i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 21875.6i | − 2.26889i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2617.46 | −0.269689 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4829.89 | −0.494383 | −0.247191 | − | 0.968967i | \(-0.579508\pi\) | ||||
−0.247191 | + | 0.968967i | \(0.579508\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4412.74i | 0.448735i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11689.6i | 1.18100i | 0.807039 | + | 0.590498i | \(0.201069\pi\) | ||||
−0.807039 | + | 0.590498i | \(0.798931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5043.86 | 0.506281 | 0.253141 | − | 0.967430i | \(-0.418536\pi\) | ||||
0.253141 | + | 0.967430i | \(0.418536\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4970.57 | −0.495709 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17591.1i | 1.74308i | 0.490321 | + | 0.871542i | \(0.336880\pi\) | ||||
−0.490321 | + | 0.871542i | \(0.663120\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 3780.63i | − 0.372225i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9962.47 | 0.974621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4479.75 | 0.435474 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4358.89i | 0.421052i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8305.58i | 0.797246i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13059.7 | 1.24575 | 0.622875 | − | 0.782321i | \(-0.285964\pi\) | ||||
0.622875 | + | 0.782321i | \(0.285964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3680.77 | 0.348916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 9312.41i | − 0.877286i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 994.605i | − 0.0931189i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15549.3 | 1.44683 | 0.723414 | − | 0.690414i | \(-0.242572\pi\) | ||||
0.723414 | + | 0.690414i | \(0.242572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15305.3 | −1.41540 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12202.3i | − 1.12155i | −0.827967 | − | 0.560777i | \(-0.810503\pi\) | ||||
0.827967 | − | 0.560777i | \(-0.189497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1306.82i | − 0.119383i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6964.03 | 0.632344 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5354.00 | −0.483219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2450.01i | 0.219794i | 0.993943 | + | 0.109897i | \(0.0350521\pi\) | ||||
−0.993943 | + | 0.109897i | \(0.964948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9495.65i | 0.846775i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16579.6 | 1.46968 | 0.734839 | − | 0.678241i | \(-0.237258\pi\) | ||||
0.734839 | + | 0.678241i | \(0.237258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4551.65 | 0.401081 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 15101.8i | − 1.32287i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11074.6i | 0.964387i | 0.876065 | + | 0.482193i | \(0.160160\pi\) | ||||
−0.876065 | + | 0.482193i | \(0.839840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16645.5 | −1.44100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2667.24 | −0.229555 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12139.5i | − 1.03870i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6972.69i | − 0.593150i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6193.30 | −0.523807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3400.02 | 0.285907 | 0.142953 | − | 0.989729i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989729i | \(0.454340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2856.01i | − 0.238785i | −0.992847 | − | 0.119393i | \(-0.961905\pi\) | ||||
0.992847 | − | 0.119393i | \(-0.0380947\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15771.4i | 1.31108i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8579.28 | −0.709144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9851.23 | −0.809668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19139.6i | 1.56420i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5746.74i | − 0.467015i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 740.691 | 0.0598558 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24207.7 | −1.94532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8747.47i | 0.699035i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18996.6i | 1.50966i | 0.655921 | + | 0.754829i | \(0.272280\pi\) | ||||
−0.655921 | + | 0.754829i | \(0.727720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1333.30 | 0.105373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8888.86 | −0.698637 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7603.46i | 0.594333i | 0.954826 | + | 0.297167i | \(0.0960417\pi\) | ||||
−0.954826 | + | 0.297167i | \(0.903958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31406.1i | 2.44149i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 789.894 | 0.0610719 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20488.7 | −1.57553 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11837.7i | 0.905377i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2936.30i | − 0.223367i | −0.993744 | − | 0.111683i | \(-0.964376\pi\) | ||||
0.993744 | − | 0.111683i | \(-0.0356242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2259.90 | −0.170990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21732.1 | 1.63553 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 23536.9i | − 1.76192i | −0.473188 | − | 0.880961i | \(-0.656897\pi\) | ||||
0.473188 | − | 0.880961i | \(-0.343103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4751.85i | 0.353826i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12811.8 | 0.948934 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5659.60 | 0.416982 | 0.208491 | − | 0.978024i | \(-0.433145\pi\) | ||||
0.208491 | + | 0.978024i | \(0.433145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 6891.00i | − 0.505043i | −0.967591 | − | 0.252521i | \(-0.918740\pi\) | ||||
0.967591 | − | 0.252521i | \(-0.0812598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 30528.8i | − 2.22575i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3921.95 | −0.284446 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10652.2 | 0.768556 | 0.384278 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384278 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25253.9i | 1.81264i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 11508.9i | − 0.821805i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7853.69 | 0.557919 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3513.14 | −0.248291 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14006.3i | 0.984841i | 0.870357 | + | 0.492421i | \(0.163888\pi\) | ||||
−0.870357 | + | 0.492421i | \(0.836112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5185.67i | − 0.362770i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26611.5 | −1.85220 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3528.04 | 0.244316 | 0.122158 | − | 0.992511i | \(-0.461019\pi\) | ||||
0.122158 | + | 0.992511i | \(0.461019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 14529.6i | − 1.00110i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 10658.8i | − 0.730715i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19024.9 | −1.29772 | −0.648861 | − | 0.760907i | \(-0.724754\pi\) | ||||
−0.648861 | + | 0.760907i | \(0.724754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1065.92 | 0.0723460 | 0.0361730 | − | 0.999346i | \(-0.488483\pi\) | ||||
0.0361730 | + | 0.999346i | \(0.488483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5074.35i | − 0.342692i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2193.47i | 0.147400i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12909.7 | 0.863242 | 0.431621 | − | 0.902055i | \(-0.357942\pi\) | ||||
0.431621 | + | 0.902055i | \(0.357942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2858.00 | 0.190167 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3517.51i | 0.232902i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12393.3i | 0.816578i | 0.912853 | + | 0.408289i | \(0.133874\pi\) | ||||
−0.912853 | + | 0.408289i | \(0.866126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18482.1 | 1.21182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18921.2 | 1.23459 | 0.617293 | − | 0.786733i | \(-0.288229\pi\) | ||||
0.617293 | + | 0.786733i | \(0.288229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 21378.2i | − 1.38814i | −0.719906 | − | 0.694072i | \(-0.755815\pi\) | ||||
0.719906 | − | 0.694072i | \(-0.244185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2399.87i | − 0.155078i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6541.15 | 0.420651 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1204.57 | 0.0770926 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13135.8i | 0.836672i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20432.1i | 1.29520i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9602.80 | 0.605834 | 0.302917 | − | 0.953017i | \(-0.402039\pi\) | ||||
0.302917 | + | 0.953017i | \(0.402039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17813.1 | −1.11849 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17295.7i | 1.08088i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4412.83i | − 0.274478i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7186.12 | −0.444880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4450.84 | 0.274256 | 0.137128 | − | 0.990553i | \(-0.456213\pi\) | ||||
0.137128 | + | 0.990553i | \(0.456213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 9180.04i | − 0.563026i | −0.959557 | − | 0.281513i | \(-0.909164\pi\) | ||||
0.959557 | − | 0.281513i | \(-0.0908362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 7268.07i | − 0.443690i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5546.17 | −0.337005 | −0.168503 | − | 0.985701i | \(-0.553893\pi\) | ||||
−0.168503 | + | 0.985701i | \(0.553893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18098.3 | 1.09464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 18762.8i | − 1.12960i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8948.56i | 0.536270i | 0.963381 | + | 0.268135i | \(0.0864073\pi\) | ||||
−0.963381 | + | 0.268135i | \(0.913593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6133.49 | 0.365886 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22341.5 | −1.32667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21404.4i | 1.26525i | 0.774460 | + | 0.632623i | \(0.218022\pi\) | ||||
−0.774460 | + | 0.632623i | \(0.781978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 33177.6i | − 1.95228i | −0.217140 | − | 0.976140i | \(-0.569673\pi\) | ||||
0.217140 | − | 0.976140i | \(-0.430327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10963.2 | −0.642195 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8782.30 | 0.512125 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 710.713i | 0.0412577i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3261.59i | 0.188491i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29697.4 | 1.70858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30638.5 | 1.75487 | 0.877436 | − | 0.479694i | \(-0.159252\pi\) | ||||
0.877436 | + | 0.479694i | \(0.159252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4064.39i | 0.231760i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17633.7i | 1.00106i | 0.865720 | + | 0.500529i | \(0.166861\pi\) | ||||
−0.865720 | + | 0.500529i | \(0.833139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3754.41 | 0.212196 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23453.8 | 1.31975 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19570.6i | 1.09641i | 0.836344 | + | 0.548206i | \(0.184689\pi\) | ||||
−0.836344 | + | 0.548206i | \(0.815311\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 16564.8i | − 0.923952i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17306.6 | 0.961116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3961.95 | −0.219068 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 149.923i | − 0.00825375i | −0.999991 | − | 0.00412688i | \(-0.998686\pi\) | ||||
0.999991 | − | 0.00412688i | \(-0.00131363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26287.7i | 1.44096i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10129.8 | 0.552870 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31900.4 | 1.73359 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9287.38i | 0.502548i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 11086.5i | − 0.597335i | −0.954357 | − | 0.298667i | \(-0.903458\pi\) | ||||
0.954357 | − | 0.298667i | \(-0.0965421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12350.0 | −0.662574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11312.7 | −0.604341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17181.5i | 0.913968i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 3858.40i | − 0.204380i | −0.994765 | − | 0.102190i | \(-0.967415\pi\) | ||||
0.994765 | − | 0.102190i | \(-0.0325850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27499.9 | −1.45053 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4665.84 | 0.245073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3322.00i | 0.173756i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 32964.6i | − 1.71699i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32717.8 | 1.69704 | 0.848519 | − | 0.529166i | \(-0.177495\pi\) | ||||
0.848519 | + | 0.529166i | \(0.177495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45824.0 | 2.36696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 43303.6i | − 2.22750i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1203.65i | − 0.0616587i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25847.2 | −1.31859 | −0.659297 | − | 0.751883i | \(-0.729146\pi\) | ||||
−0.659297 | + | 0.751883i | \(0.729146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27662.0 | 1.40537 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 12544.8i | − 0.634727i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 14328.7i | − 0.722023i | −0.932561 | − | 0.361011i | \(-0.882432\pi\) | ||||
0.932561 | − | 0.361011i | \(-0.117568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14192.1 | 0.712223 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4798.27 | −0.239819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 27101.5i | − 1.34905i | −0.738253 | − | 0.674524i | \(-0.764349\pi\) | ||||
0.738253 | − | 0.674524i | \(-0.235651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 6626.61i | − 0.328522i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23322.1 | −1.15155 | −0.575777 | − | 0.817607i | \(-0.695301\pi\) | ||||
−0.575777 | + | 0.817607i | \(0.695301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21309.8 | 1.04796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 15447.2i | − 0.756603i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2795.94i | 0.136397i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25994.0 | −1.26303 | −0.631515 | − | 0.775364i | \(-0.717566\pi\) | ||||
−0.631515 | + | 0.775364i | \(0.717566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5306.32 | 0.256804 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18562.3i | 0.894770i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31317.8i | 1.50365i | 0.659363 | + | 0.751825i | \(0.270826\pi\) | ||||
−0.659363 | + | 0.751825i | \(0.729174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11819.0 | −0.565222 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16497.5 | 0.785853 | 0.392926 | − | 0.919570i | \(-0.371463\pi\) | ||||
0.392926 | + | 0.919570i | \(0.371463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 33553.4i | − 1.59203i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 19501.6i | − 0.921675i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9130.02 | −0.429812 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24867.3 | −1.16611 | −0.583055 | − | 0.812433i | \(-0.698143\pi\) | ||||
−0.583055 | + | 0.812433i | \(0.698143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 62905.9i | − 2.93839i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2661.15i | − 0.123823i | −0.998082 | − | 0.0619114i | \(-0.980280\pi\) | ||||
0.998082 | − | 0.0619114i | \(-0.0197196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7902.00 | −0.366256 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44684.8 | −2.06314 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19281.9i | 0.886837i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6795.14i | 0.311331i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 736.525 | 0.0336159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8453.54 | −0.384356 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 11018.1i | − 0.499049i | −0.968369 | − | 0.249524i | \(-0.919726\pi\) | ||||
0.968369 | − | 0.249524i | \(-0.0802742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3189.17i | 0.143900i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17937.2 | −0.806286 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14981.4 | −0.670877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 12742.0i | − 0.568445i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5953.61i | 0.264602i | 0.991210 | + | 0.132301i | \(0.0422365\pi\) | ||||
−0.991210 | + | 0.132301i | \(0.957763\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19525.8 | −0.864549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8779.50 | 0.387276 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21126.0i | 0.928417i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7901.94i | 0.345971i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −52.5393 | −0.00229178 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27554.3 | −1.19747 | −0.598737 | − | 0.800946i | \(-0.704330\pi\) | ||||
−0.598737 | + | 0.800946i | \(0.704330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4817.57i | 0.208592i | 0.994546 | + | 0.104296i | \(0.0332589\pi\) | ||||
−0.994546 | + | 0.104296i | \(0.966741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 22027.9i | − 0.950247i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12987.1 | 0.558184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7582.59 | 0.324701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 13261.3i | − 0.565797i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 13914.6i | − 0.591504i | −0.955265 | − | 0.295752i | \(-0.904430\pi\) | ||||
0.955265 | − | 0.295752i | \(-0.0955701\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36653.5 | 1.55244 | 0.776221 | − | 0.630461i | \(-0.217134\pi\) | ||||
0.776221 | + | 0.630461i | \(0.217134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20016.5 | 0.844711 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31428.3i | 1.32149i | 0.750612 | + | 0.660743i | \(0.229759\pi\) | ||||
−0.750612 | + | 0.660743i | \(0.770241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 20810.9i | − 0.871885i | −0.899975 | − | 0.435942i | \(-0.856415\pi\) | ||||
0.899975 | − | 0.435942i | \(-0.143585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16772.2 | 0.700145 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24495.8 | 1.01888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8057.43i | − 0.333939i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4835.30i | − 0.199680i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11010.0 | −0.453050 | −0.226525 | − | 0.974005i | \(-0.572737\pi\) | ||||
−0.226525 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24170.9 | 0.991057 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 36922.5i | − 1.50852i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12814.5i | 0.521694i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8279.85 | −0.335890 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7080.22 | −0.286210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 11112.0i | − 0.447608i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18116.0i | 0.727175i | 0.931560 | + | 0.363587i | \(0.118448\pi\) | ||||
−0.931560 | + | 0.363587i | \(0.881552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11787.6 | 0.471493 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38510.8 | −1.53501 | −0.767505 | − | 0.641043i | \(-0.778502\pi\) | ||||
−0.767505 | + | 0.641043i | \(0.778502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 32858.7i | − 1.30515i | −0.757723 | − | 0.652576i | \(-0.773688\pi\) | ||||
0.757723 | − | 0.652576i | \(-0.226312\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 69765.8i | 2.76146i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22079.5 | −0.870911 | −0.435456 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435456 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5255.26 | 0.206571 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 22669.5i | − 0.888001i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26003.7i | 1.01509i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2420.58 | 0.0941656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5039.15 | 0.195360 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 33908.2i | − 1.31007i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5773.00i | 0.222281i | 0.993805 | + | 0.111140i | \(0.0354504\pi\) | ||||
−0.993805 | + | 0.111140i | \(0.964550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15753.9 | 0.604510 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7132.59 | −0.272762 | −0.136381 | − | 0.990656i | \(-0.543547\pi\) | ||||
−0.136381 | + | 0.990656i | \(0.543547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27110.4i | 1.03323i | 0.856219 | + | 0.516613i | \(0.172807\pi\) | ||||
−0.856219 | + | 0.516613i | \(0.827193\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 29363.1i | − 1.11529i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45045.7 | −1.70517 | −0.852585 | − | 0.522589i | \(-0.824966\pi\) | ||||
−0.852585 | + | 0.522589i | \(0.824966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65287.3 | −2.46306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 16260.4i | − 0.611384i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 11802.2i | − 0.442269i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20541.1 | 0.767167 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5962.34 | 0.221936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1431.96i | 0.0531239i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 21992.9i | − 0.813197i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27435.3 | 1.01106 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1131.36 | −0.0415554 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 47599.9i | − 1.74259i | −0.490760 | − | 0.871295i | \(-0.663281\pi\) | ||||
0.490760 | − | 0.871295i | \(-0.336719\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23060.9i | 0.841453i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42503.8 | 1.54579 | 0.772895 | − | 0.634534i | \(-0.218808\pi\) | ||||
0.772895 | + | 0.634534i | \(0.218808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14606.7 | −0.529477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 48181.8i | − 1.74081i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23152.5i | 0.833766i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8819.41 | −0.316568 | −0.158284 | − | 0.987394i | \(-0.550596\pi\) | ||||
−0.158284 | + | 0.987394i | \(0.550596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2541.55 | −0.0909305 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3427.94i | − 0.122245i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18819.1i | 0.668940i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 61504.8 | 2.17916 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14155.6 | −0.499925 | −0.249963 | − | 0.968256i | \(-0.580418\pi\) | ||||
−0.249963 | + | 0.968256i | \(0.580418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14806.3i | 0.521220i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6773.27i | 0.237671i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18440.6 | −0.644996 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38518.7 | −1.34296 | −0.671479 | − | 0.741023i | \(-0.734341\pi\) | ||||
−0.671479 | + | 0.741023i | \(0.734341\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27321.4i | 0.949523i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39595.4i | 1.37170i | 0.727741 | + | 0.685852i | \(0.240570\pi\) | ||||
−0.727741 | + | 0.685852i | \(0.759430\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17349.0 | −0.599112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8188.93 | 0.281890 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46442.1i | − 1.59363i | −0.604225 | − | 0.796814i | \(-0.706517\pi\) | ||||
0.604225 | − | 0.796814i | \(-0.293483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 10657.4i | − 0.364545i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51925.4 | −1.77055 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20600.1 | 0.700211 | 0.350106 | − | 0.936710i | \(-0.386146\pi\) | ||||
0.350106 | + | 0.936710i | \(0.386146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25904.8i | 0.877760i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 3627.28i | − 0.122522i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 62528.2 | 2.10547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20390.2 | −0.684441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3752.70i | 0.125575i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 21428.9i | − 0.714841i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38210.9 | −1.27071 | −0.635356 | − | 0.772219i | \(-0.719147\pi\) | ||||
−0.635356 | + | 0.772219i | \(0.719147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36784.6 | 1.21950 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52643.9i | 1.73988i | 0.493157 | + | 0.869941i | \(0.335843\pi\) | ||||
−0.493157 | + | 0.869941i | \(0.664157\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38237.6i | 1.25986i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10097.7 | −0.331678 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7985.95 | −0.261508 | −0.130754 | − | 0.991415i | \(-0.541740\pi\) | ||||
−0.130754 | + | 0.991415i | \(0.541740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 8301.83i | − 0.271019i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 45035.3i | − 1.46571i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10703.1 | −0.347279 | −0.173639 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173639 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22580.9 | 0.730442 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 42702.8i | − 1.37715i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6822.49i | 0.219355i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23945.4 | −0.767558 | −0.383779 | − | 0.923425i | \(-0.625377\pi\) | ||||
−0.383779 | + | 0.923425i | \(0.625377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20009.0 | −0.639442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9044.42i | 0.288168i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20212.7i | 0.642068i | 0.947068 | + | 0.321034i | \(0.104030\pi\) | ||||
−0.947068 | + | 0.321034i | \(0.895970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11515.6 | −0.364702 |
(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 | 1024.4.b.j.513.2 | 10 | ||
4.3 | odd | 2 | 1024.4.b.k.513.9 | 10 | |||
8.3 | odd | 2 | 1024.4.b.k.513.2 | 10 | |||
8.5 | even | 2 | inner | 1024.4.b.j.513.9 | 10 | ||
16.3 | odd | 4 | 1024.4.a.m.1.2 | 10 | |||
16.5 | even | 4 | 1024.4.a.n.1.2 | 10 | |||
16.11 | odd | 4 | 1024.4.a.m.1.9 | 10 | |||
16.13 | even | 4 | 1024.4.a.n.1.9 | 10 | |||
32.3 | odd | 8 | 64.4.e.a.49.1 | 10 | |||
32.5 | even | 8 | 16.4.e.a.13.1 | yes | 10 | ||
32.11 | odd | 8 | 128.4.e.a.33.5 | 10 | |||
32.13 | even | 8 | 128.4.e.b.97.1 | 10 | |||
32.19 | odd | 8 | 128.4.e.a.97.5 | 10 | |||
32.21 | even | 8 | 128.4.e.b.33.1 | 10 | |||
32.27 | odd | 8 | 64.4.e.a.17.1 | 10 | |||
32.29 | even | 8 | 16.4.e.a.5.1 | ✓ | 10 | ||
96.5 | odd | 8 | 144.4.k.a.109.5 | 10 | |||
96.29 | odd | 8 | 144.4.k.a.37.5 | 10 | |||
96.35 | even | 8 | 576.4.k.a.433.4 | 10 | |||
96.59 | even | 8 | 576.4.k.a.145.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.1 | ✓ | 10 | 32.29 | even | 8 | ||
16.4.e.a.13.1 | yes | 10 | 32.5 | even | 8 | ||
64.4.e.a.17.1 | 10 | 32.27 | odd | 8 | |||
64.4.e.a.49.1 | 10 | 32.3 | odd | 8 | |||
128.4.e.a.33.5 | 10 | 32.11 | odd | 8 | |||
128.4.e.a.97.5 | 10 | 32.19 | odd | 8 | |||
128.4.e.b.33.1 | 10 | 32.21 | even | 8 | |||
128.4.e.b.97.1 | 10 | 32.13 | even | 8 | |||
144.4.k.a.37.5 | 10 | 96.29 | odd | 8 | |||
144.4.k.a.109.5 | 10 | 96.5 | odd | 8 | |||
576.4.k.a.145.4 | 10 | 96.59 | even | 8 | |||
576.4.k.a.433.4 | 10 | 96.35 | even | 8 | |||
1024.4.a.m.1.2 | 10 | 16.3 | odd | 4 | |||
1024.4.a.m.1.9 | 10 | 16.11 | odd | 4 | |||
1024.4.a.n.1.2 | 10 | 16.5 | even | 4 | |||
1024.4.a.n.1.9 | 10 | 16.13 | even | 4 | |||
1024.4.b.j.513.2 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.b.j.513.9 | 10 | 8.5 | even | 2 | inner | ||
1024.4.b.k.513.2 | 10 | 8.3 | odd | 2 | |||
1024.4.b.k.513.9 | 10 | 4.3 | odd | 2 |