Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (of order \(2\), degree \(1\), 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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.1 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.40 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.81880i | − | 1.95470i | −0.211629 | − | 0.977350i | \(-0.567877\pi\) | ||
0.211629 | − | 0.977350i | \(-0.432123\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −45.1337 | −2.82085 | ||||||||
\(5\) | −21.3172 | −0.852690 | −0.426345 | − | 0.904561i | \(-0.640199\pi\) | ||||
−0.426345 | + | 0.904561i | \(0.640199\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.7266 | −0.627073 | −0.313537 | − | 0.949576i | \(-0.601514\pi\) | ||||
−0.313537 | + | 0.949576i | \(0.601514\pi\) | |||||||
\(8\) | 227.790i | 3.55922i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 166.675i | 1.66675i | ||||||||
\(11\) | 207.480i | 1.71471i | 0.514728 | + | 0.857353i | \(0.327893\pi\) | ||||
−0.514728 | + | 0.857353i | \(0.672107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 206.020i | − | 1.21905i | −0.792766 | − | 0.609526i | \(-0.791360\pi\) | ||
0.792766 | − | 0.609526i | \(-0.208640\pi\) | |||||||
\(14\) | 240.245i | 1.22574i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1058.91 | 4.13636 | ||||||||
\(17\) | 391.490 | 1.35464 | 0.677318 | − | 0.735690i | \(-0.263142\pi\) | ||||
0.677318 | + | 0.735690i | \(0.263142\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −321.627 | −0.890934 | −0.445467 | − | 0.895298i | \(-0.646962\pi\) | ||||
−0.445467 | + | 0.895298i | \(0.646962\pi\) | |||||||
\(20\) | 962.125 | 2.40531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1622.24 | 3.35174 | ||||||||
\(23\) | 287.967i | 0.544360i | 0.962246 | + | 0.272180i | \(0.0877447\pi\) | ||||
−0.962246 | + | 0.272180i | \(0.912255\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −170.575 | −0.272921 | ||||||||
\(26\) | −1610.83 | −2.38288 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1386.80 | 1.76888 | ||||||||
\(29\) | −1020.53 | −1.21347 | −0.606737 | − | 0.794902i | \(-0.707522\pi\) | ||||
−0.606737 | + | 0.794902i | \(0.707522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 560.747i | − | 0.583504i | −0.956494 | − | 0.291752i | \(-0.905762\pi\) | ||
0.956494 | − | 0.291752i | \(-0.0942381\pi\) | |||||||
\(32\) | − | 4634.75i | − | 4.52612i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3060.98i | − | 2.64791i | ||||||
\(35\) | 655.006 | 0.534699 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1257.89i | 0.918838i | 0.888220 | + | 0.459419i | \(0.151942\pi\) | ||||
−0.888220 | + | 0.459419i | \(0.848058\pi\) | |||||||
\(38\) | 2514.74i | 1.74151i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 4855.86i | − | 3.03491i | ||||||
\(41\) | 1524.79 | 0.907076 | 0.453538 | − | 0.891237i | \(-0.350162\pi\) | ||||
0.453538 | + | 0.891237i | \(0.350162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2155.53i | 1.16578i | 0.812550 | + | 0.582892i | \(0.198079\pi\) | ||||
−0.812550 | + | 0.582892i | \(0.801921\pi\) | |||||||
\(44\) | − | 9364.31i | − | 4.83694i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2251.55 | 1.06406 | ||||||||
\(47\) | − | 245.854i | − | 0.111296i | −0.998450 | − | 0.0556482i | \(-0.982277\pi\) | ||
0.998450 | − | 0.0556482i | \(-0.0177225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1456.88 | −0.606779 | ||||||||
\(50\) | 1333.69i | 0.533478i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9298.43i | 3.43877i | ||||||||
\(53\) | 1142.98 | 0.406899 | 0.203449 | − | 0.979085i | \(-0.434785\pi\) | ||||
0.203449 | + | 0.979085i | \(0.434785\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4422.89i | − | 1.46211i | ||||||
\(56\) | − | 6999.22i | − | 2.23189i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7979.34i | 2.37198i | ||||||||
\(59\) | 3465.52 | − | 327.946i | 0.995552 | − | 0.0942101i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 518.066i | 0.139228i | 0.997574 | + | 0.0696138i | \(0.0221767\pi\) | ||||
−0.997574 | + | 0.0696138i | \(0.977823\pi\) | |||||||
\(62\) | −4384.37 | −1.14057 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −19295.6 | −4.71085 | ||||||||
\(65\) | 4391.77i | 1.03947i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2495.71i | − | 0.555961i | −0.960587 | − | 0.277980i | \(-0.910335\pi\) | ||
0.960587 | − | 0.277980i | \(-0.0896650\pi\) | |||||||
\(68\) | −17669.4 | −3.82123 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 5121.36i | − | 1.04518i | ||||||
\(71\) | −9311.79 | −1.84721 | −0.923606 | − | 0.383344i | \(-0.874772\pi\) | ||||
−0.923606 | + | 0.383344i | \(0.874772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8005.70i | − | 1.50229i | −0.660138 | − | 0.751144i | \(-0.729502\pi\) | ||
0.660138 | − | 0.751144i | \(-0.270498\pi\) | |||||||
\(74\) | 9835.18 | 1.79605 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14516.2 | 2.51319 | ||||||||
\(77\) | − | 6375.14i | − | 1.07525i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5130.68 | 0.822093 | 0.411047 | − | 0.911614i | \(-0.365163\pi\) | ||||
0.411047 | + | 0.911614i | \(0.365163\pi\) | |||||||
\(80\) | −22573.0 | −3.52703 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 11922.1i | − | 1.77306i | ||||||
\(83\) | 13428.1i | 1.94921i | 0.223939 | + | 0.974603i | \(0.428108\pi\) | ||||
−0.223939 | + | 0.974603i | \(0.571892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8345.49 | −1.15508 | ||||||||
\(86\) | 16853.7 | 2.27876 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −47261.8 | −6.10302 | ||||||||
\(89\) | − | 3141.70i | − | 0.396630i | −0.980138 | − | 0.198315i | \(-0.936453\pi\) | ||
0.980138 | − | 0.198315i | \(-0.0635468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6330.29i | 0.764435i | ||||||||
\(92\) | − | 12997.0i | − | 1.53556i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1922.28 | −0.217551 | ||||||||
\(95\) | 6856.20 | 0.759690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5322.39i | − | 0.565670i | −0.959169 | − | 0.282835i | \(-0.908725\pi\) | ||
0.959169 | − | 0.282835i | \(-0.0912749\pi\) | |||||||
\(98\) | 11391.0i | 1.18607i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7698.69 | 0.769869 | ||||||||
\(101\) | − | 6022.91i | − | 0.590424i | −0.955432 | − | 0.295212i | \(-0.904610\pi\) | ||
0.955432 | − | 0.295212i | \(-0.0953902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3738.09i | 0.352350i | 0.984359 | + | 0.176175i | \(0.0563725\pi\) | ||||
−0.984359 | + | 0.176175i | \(0.943627\pi\) | |||||||
\(104\) | 46929.3 | 4.33888 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 8936.72i | − | 0.795365i | ||||||
\(107\) | −10702.1 | −0.934764 | −0.467382 | − | 0.884056i | \(-0.654803\pi\) | ||||
−0.467382 | + | 0.884056i | \(0.654803\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 21298.0i | − | 1.79261i | −0.443442 | − | 0.896303i | \(-0.646243\pi\) | ||
0.443442 | − | 0.896303i | \(-0.353757\pi\) | |||||||
\(110\) | −34581.7 | −2.85799 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32536.6 | −2.59380 | ||||||||
\(113\) | − | 16771.3i | − | 1.31344i | −0.754135 | − | 0.656720i | \(-0.771943\pi\) | ||
0.754135 | − | 0.656720i | \(-0.228057\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6138.65i | − | 0.464170i | ||||||
\(116\) | 46060.4 | 3.42303 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2564.14 | − | 27096.2i | −0.184153 | − | 1.94601i | ||||
\(119\) | −12029.2 | −0.849456 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28406.8 | −1.94022 | ||||||||
\(122\) | 4050.65 | 0.272148 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25308.6i | 1.64598i | ||||||||
\(125\) | 16959.5 | 1.08541 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27235.6 | 1.68861 | 0.844305 | − | 0.535863i | \(-0.180014\pi\) | ||||
0.844305 | + | 0.535863i | \(0.180014\pi\) | |||||||
\(128\) | 76712.8i | 4.68218i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 34338.4 | 2.03186 | ||||||||
\(131\) | 1718.72i | 0.100153i | 0.998745 | + | 0.0500763i | \(0.0159465\pi\) | ||||
−0.998745 | + | 0.0500763i | \(0.984054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9882.51 | 0.558681 | ||||||||
\(134\) | −19513.4 | −1.08674 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 89177.6i | 4.82145i | ||||||||
\(137\) | −8888.26 | −0.473560 | −0.236780 | − | 0.971563i | \(-0.576092\pi\) | ||||
−0.236780 | + | 0.971563i | \(0.576092\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2771.10 | 0.143424 | 0.0717121 | − | 0.997425i | \(-0.477154\pi\) | ||||
0.0717121 | + | 0.997425i | \(0.477154\pi\) | |||||||
\(140\) | −29562.8 | −1.50831 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 72807.1i | 3.61074i | ||||||||
\(143\) | 42744.9 | 2.09032 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21754.9 | 1.03472 | ||||||||
\(146\) | −62594.9 | −2.93652 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 56773.1i | − | 2.59191i | ||||||
\(149\) | 8123.08i | 0.365888i | 0.983123 | + | 0.182944i | \(0.0585627\pi\) | ||||
−0.983123 | + | 0.182944i | \(0.941437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2438.11i | 0.106930i | 0.998570 | + | 0.0534651i | \(0.0170266\pi\) | ||||
−0.998570 | + | 0.0534651i | \(0.982973\pi\) | |||||||
\(152\) | − | 73263.5i | − | 3.17103i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −49845.9 | −2.10179 | ||||||||
\(155\) | 11953.6i | 0.497547i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13811.6i | − | 0.560332i | −0.959952 | − | 0.280166i | \(-0.909611\pi\) | ||
0.959952 | − | 0.280166i | \(-0.0903895\pi\) | |||||||
\(158\) | − | 40115.8i | − | 1.60695i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 98800.0i | 3.85938i | ||||||||
\(161\) | − | 8848.23i | − | 0.341354i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14070.7 | −0.529593 | −0.264796 | − | 0.964304i | \(-0.585305\pi\) | ||||
−0.264796 | + | 0.964304i | \(0.585305\pi\) | |||||||
\(164\) | −68819.5 | −2.55873 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 104991. | 3.81011 | ||||||||
\(167\) | 37863.4 | 1.35765 | 0.678823 | − | 0.734302i | \(-0.262490\pi\) | ||||
0.678823 | + | 0.734302i | \(0.262490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13883.2 | −0.486089 | ||||||||
\(170\) | 65251.7i | 2.25784i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 97287.2i | − | 3.28851i | ||||||
\(173\) | 13221.6i | 0.441765i | 0.975300 | + | 0.220883i | \(0.0708938\pi\) | ||||
−0.975300 | + | 0.220883i | \(0.929106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5241.20 | 0.171141 | ||||||||
\(176\) | 219702.i | 7.09264i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24564.3 | −0.775292 | ||||||||
\(179\) | − | 398.257i | − | 0.0124296i | −0.999981 | − | 0.00621480i | \(-0.998022\pi\) | ||
0.999981 | − | 0.00621480i | \(-0.00197825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 46013.5 | 1.40452 | 0.702260 | − | 0.711920i | \(-0.252174\pi\) | ||||
0.702260 | + | 0.711920i | \(0.252174\pi\) | |||||||
\(182\) | 49495.3 | 1.49424 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −65596.0 | −1.93750 | ||||||||
\(185\) | − | 26814.7i | − | 0.783483i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 81226.2i | 2.32281i | ||||||||
\(188\) | 11096.3i | 0.313951i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 53607.3i | − | 1.48497i | ||||||
\(191\) | − | 60179.4i | − | 1.64961i | −0.565418 | − | 0.824804i | \(-0.691285\pi\) | ||
0.565418 | − | 0.824804i | \(-0.308715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31955.1 | −0.857879 | −0.428939 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428939 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(194\) | −41614.7 | −1.10572 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 65754.2 | 1.71163 | ||||||||
\(197\) | 34993.6 | 0.901689 | 0.450844 | − | 0.892603i | \(-0.351123\pi\) | ||||
0.450844 | + | 0.892603i | \(0.351123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3731.67 | 0.0942317 | 0.0471159 | − | 0.998889i | \(-0.484997\pi\) | ||||
0.0471159 | + | 0.998889i | \(0.484997\pi\) | |||||||
\(200\) | − | 38855.4i | − | 0.971385i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −47092.0 | −1.15410 | ||||||||
\(203\) | 31357.5 | 0.760938 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32504.4 | −0.773454 | ||||||||
\(206\) | 29227.4 | 0.688740 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 218156.i | − | 5.04244i | ||||||
\(209\) | − | 66731.1i | − | 1.52769i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13733.7i | − | 0.308476i | −0.988034 | − | 0.154238i | \(-0.950708\pi\) | ||
0.988034 | − | 0.154238i | \(-0.0492923\pi\) | |||||||
\(212\) | −51586.8 | −1.14780 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 83677.7i | 1.82718i | ||||||||
\(215\) | − | 45950.0i | − | 0.994052i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17229.8i | 0.365899i | ||||||||
\(218\) | −166524. | −3.50401 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 199621.i | 4.12441i | ||||||||
\(221\) | − | 80654.7i | − | 1.65137i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −62492.9 | −1.25667 | −0.628335 | − | 0.777943i | \(-0.716263\pi\) | ||||
−0.628335 | + | 0.777943i | \(0.716263\pi\) | |||||||
\(224\) | 142410.i | 2.83821i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −131132. | −2.56738 | ||||||||
\(227\) | 15746.2i | 0.305579i | 0.988259 | + | 0.152790i | \(0.0488257\pi\) | ||||
−0.988259 | + | 0.152790i | \(0.951174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 50347.4i | − | 0.960078i | −0.877247 | − | 0.480039i | \(-0.840623\pi\) | ||
0.877247 | − | 0.480039i | \(-0.159377\pi\) | |||||||
\(230\) | −47996.9 | −0.907314 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 232467.i | − | 4.31903i | ||||||
\(233\) | − | 54304.7i | − | 1.00029i | −0.865942 | − | 0.500144i | \(-0.833280\pi\) | ||
0.865942 | − | 0.500144i | \(-0.166720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5240.92i | 0.0949012i | ||||||||
\(236\) | −156411. | + | 14801.4i | −2.80831 | + | 0.265753i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 94053.6i | 1.66043i | ||||||||
\(239\) | −44247.5 | −0.774628 | −0.387314 | − | 0.921948i | \(-0.626597\pi\) | ||||
−0.387314 | + | 0.921948i | \(0.626597\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 93615.1 | 1.61180 | 0.805902 | − | 0.592050i | \(-0.201681\pi\) | ||||
0.805902 | + | 0.592050i | \(0.201681\pi\) | |||||||
\(242\) | 222107.i | 3.79255i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 23382.2i | − | 0.392741i | ||||||
\(245\) | 31056.6 | 0.517394 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 66261.6i | 1.08610i | ||||||||
\(248\) | 127733. | 2.07682 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 132603.i | − | 2.12164i | ||||||
\(251\) | 31025.2 | 0.492455 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −59747.2 | −0.933419 | ||||||||
\(254\) | − | 212950.i | − | 3.30073i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 291072. | 4.44141 | ||||||||
\(257\) | 51107.2 | 0.773777 | 0.386889 | − | 0.922126i | \(-0.373550\pi\) | ||||
0.386889 | + | 0.922126i | \(0.373550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 38650.6i | − | 0.576179i | ||||||
\(260\) | − | 198217.i | − | 2.93220i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13438.3 | 0.195768 | ||||||||
\(263\) | −83386.8 | −1.20555 | −0.602776 | − | 0.797911i | \(-0.705939\pi\) | ||||
−0.602776 | + | 0.797911i | \(0.705939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24365.1 | −0.346958 | ||||||||
\(266\) | − | 77269.3i | − | 1.09205i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 112640.i | 1.56828i | ||||||||
\(269\) | 55398.4i | 0.765584i | 0.923835 | + | 0.382792i | \(0.125037\pi\) | ||||
−0.923835 | + | 0.382792i | \(0.874963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 33799.6 | 0.460228 | 0.230114 | − | 0.973164i | \(-0.426090\pi\) | ||||
0.230114 | + | 0.973164i | \(0.426090\pi\) | |||||||
\(272\) | 414552. | 5.60326 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 69495.5i | 0.925669i | ||||||||
\(275\) | − | 35390.9i | − | 0.467979i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 71567.4 | 0.932730 | 0.466365 | − | 0.884592i | \(-0.345563\pi\) | ||||
0.466365 | + | 0.884592i | \(0.345563\pi\) | |||||||
\(278\) | − | 21666.7i | − | 0.280351i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 149204.i | 1.90311i | ||||||||
\(281\) | −121564. | −1.53955 | −0.769774 | − | 0.638316i | \(-0.779631\pi\) | ||||
−0.769774 | + | 0.638316i | \(0.779631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 142151.i | − | 1.77491i | −0.460890 | − | 0.887457i | \(-0.652470\pi\) | ||
0.460890 | − | 0.887457i | \(-0.347530\pi\) | |||||||
\(284\) | 420275. | 5.21071 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 334214.i | − | 4.08594i | ||||||
\(287\) | −46851.7 | −0.568803 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 69743.4 | 0.835041 | ||||||||
\(290\) | − | 170097.i | − | 2.02256i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 361326.i | 4.23774i | ||||||||
\(293\) | 96135.1 | 1.11982 | 0.559908 | − | 0.828555i | \(-0.310836\pi\) | ||||
0.559908 | + | 0.828555i | \(0.310836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73875.3 | + | 6990.89i | −0.848897 | + | 0.0803320i | ||||
\(296\) | −286535. | −3.27035 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 63512.8 | 0.715202 | ||||||||
\(299\) | 59326.9 | 0.663604 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 66232.2i | − | 0.731032i | ||||||
\(302\) | 19063.1 | 0.209016 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −340574. | −3.68522 | ||||||||
\(305\) | − | 11043.7i | − | 0.118718i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 35837.3 | 0.380240 | 0.190120 | − | 0.981761i | \(-0.439112\pi\) | ||||
0.190120 | + | 0.981761i | \(0.439112\pi\) | |||||||
\(308\) | 287733.i | 3.03311i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 93462.6 | 0.972556 | ||||||||
\(311\) | 55265.8 | 0.571394 | 0.285697 | − | 0.958320i | \(-0.407775\pi\) | ||||
0.285697 | + | 0.958320i | \(0.407775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 96714.2i | 0.987192i | 0.869691 | + | 0.493596i | \(0.164318\pi\) | ||||
−0.869691 | + | 0.493596i | \(0.835682\pi\) | |||||||
\(314\) | −107990. | −1.09528 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −231566. | −2.31900 | ||||||||
\(317\) | 132005. | 1.31363 | 0.656813 | − | 0.754053i | \(-0.271904\pi\) | ||||
0.656813 | + | 0.754053i | \(0.271904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 211740.i | − | 2.08075i | ||||||
\(320\) | 411330. | 4.01689 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −69182.6 | −0.667245 | ||||||||
\(323\) | −125914. | −1.20689 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35141.9i | 0.332705i | ||||||||
\(326\) | 110016.i | 1.03519i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 347333.i | 3.22848i | ||||||||
\(329\) | 7554.24i | 0.0697909i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 53983.3 | 0.492724 | 0.246362 | − | 0.969178i | \(-0.420765\pi\) | ||||
0.246362 | + | 0.969178i | \(0.420765\pi\) | |||||||
\(332\) | − | 606058.i | − | 5.49842i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 296046.i | − | 2.65379i | ||||||
\(335\) | 53201.6i | 0.474062i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 87020.3i | 0.766233i | 0.923700 | + | 0.383116i | \(0.125149\pi\) | ||||
−0.923700 | + | 0.383116i | \(0.874851\pi\) | |||||||
\(338\) | 108550.i | 0.950158i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 376662. | 3.25832 | ||||||||
\(341\) | 116344. | 1.00054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 118539. | 1.00757 | ||||||||
\(344\) | −491010. | −4.14928 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 103377. | 0.863519 | ||||||||
\(347\) | − | 74094.0i | − | 0.615353i | −0.951491 | − | 0.307677i | \(-0.900449\pi\) | ||
0.951491 | − | 0.307677i | \(-0.0995515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27934.6i | 0.229347i | 0.993403 | + | 0.114673i | \(0.0365821\pi\) | ||||
−0.993403 | + | 0.114673i | \(0.963418\pi\) | |||||||
\(350\) | − | 40979.9i | − | 0.334530i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 961615. | 7.76097 | ||||||||
\(353\) | − | 140969.i | − | 1.13129i | −0.824648 | − | 0.565647i | \(-0.808627\pi\) | ||
0.824648 | − | 0.565647i | \(-0.191373\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 198502. | 1.57510 | ||||||||
\(356\) | 141797.i | 1.11883i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3113.89 | −0.0242961 | ||||||||
\(359\) | 29736.8 | 0.230731 | 0.115365 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115365 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26877.0 | −0.206237 | ||||||||
\(362\) | − | 359770.i | − | 2.74542i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 285709.i | − | 2.15636i | ||||||
\(365\) | 170659.i | 1.28099i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 52026.5i | − | 0.386272i | −0.981172 | − | 0.193136i | \(-0.938134\pi\) | ||
0.981172 | − | 0.193136i | \(-0.0618658\pi\) | |||||||
\(368\) | 304930.i | 2.25167i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −209659. | −1.53148 | ||||||||
\(371\) | −35119.8 | −0.255155 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 70424.5 | 0.506181 | 0.253091 | − | 0.967443i | \(-0.418553\pi\) | ||||
0.253091 | + | 0.967443i | \(0.418553\pi\) | |||||||
\(374\) | 635091. | 4.54039 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 56003.0 | 0.396128 | ||||||||
\(377\) | 210250.i | 1.47929i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −39937.6 | −0.278038 | −0.139019 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139019 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(380\) | −309445. | −2.14297 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −470531. | −3.22449 | ||||||||
\(383\) | −155977. | −1.06332 | −0.531659 | − | 0.846959i | \(-0.678431\pi\) | ||||
−0.531659 | + | 0.846959i | \(0.678431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 135900.i | 0.916852i | ||||||||
\(386\) | 249851.i | 1.67690i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 240219.i | 1.59567i | ||||||||
\(389\) | 184572. | 1.21974 | 0.609870 | − | 0.792501i | \(-0.291222\pi\) | ||||
0.609870 | + | 0.792501i | \(0.291222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 112736.i | 0.737411i | ||||||||
\(392\) | − | 331862.i | − | 2.15966i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 273608.i | − | 1.76253i | ||||||
\(395\) | −109372. | −0.700990 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 216054.i | − | 1.37082i | −0.728155 | − | 0.685412i | \(-0.759622\pi\) | ||
0.728155 | − | 0.685412i | \(-0.240378\pi\) | |||||||
\(398\) | − | 29177.2i | − | 0.184195i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −180624. | −1.12890 | ||||||||
\(401\) | 186079.i | 1.15720i | 0.815611 | + | 0.578601i | \(0.196401\pi\) | ||||
−0.815611 | + | 0.578601i | \(0.803599\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −115525. | −0.711321 | ||||||||
\(404\) | 271836.i | 1.66550i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 245178.i | − | 1.48741i | ||||||
\(407\) | −260986. | −1.57554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 142032.i | − | 0.849064i | −0.905413 | − | 0.424532i | \(-0.860439\pi\) | ||
0.905413 | − | 0.424532i | \(-0.139561\pi\) | |||||||
\(410\) | 254145.i | 1.51187i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 168713.i | − | 0.993929i | ||||||
\(413\) | −106484. | + | 10076.6i | −0.624284 | + | 0.0590767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 286250.i | − | 1.66207i | ||||||
\(416\) | −954850. | −5.51758 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −521757. | −2.98618 | ||||||||
\(419\) | − | 305281.i | − | 1.73889i | −0.494032 | − | 0.869444i | \(-0.664477\pi\) | ||
0.494032 | − | 0.869444i | \(-0.335523\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 40020.9i | − | 0.225799i | −0.993606 | − | 0.112900i | \(-0.963986\pi\) | ||
0.993606 | − | 0.112900i | \(-0.0360139\pi\) | |||||||
\(422\) | −107381. | −0.602978 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 260359.i | 1.44824i | ||||||||
\(425\) | −66778.6 | −0.369708 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 15918.4i | − | 0.0873059i | ||||||
\(428\) | 483025. | 2.63683 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −359274. | −1.94307 | ||||||||
\(431\) | − | 199954.i | − | 1.07641i | −0.842815 | − | 0.538203i | \(-0.819103\pi\) | ||
0.842815 | − | 0.538203i | \(-0.180897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −173422. | −0.924972 | −0.462486 | − | 0.886627i | \(-0.653042\pi\) | ||||
−0.462486 | + | 0.886627i | \(0.653042\pi\) | |||||||
\(434\) | 134717. | 0.715224 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 961254.i | 5.05668i | ||||||||
\(437\) | − | 92617.9i | − | 0.484989i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 236050. | 1.22483 | 0.612415 | − | 0.790536i | \(-0.290198\pi\) | ||||
0.612415 | + | 0.790536i | \(0.290198\pi\) | |||||||
\(440\) | 1.00749e6 | 5.20398 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −630623. | −3.22794 | ||||||||
\(443\) | 390579.i | 1.99022i | 0.0987629 | + | 0.995111i | \(0.468511\pi\) | ||||
−0.0987629 | + | 0.995111i | \(0.531489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 66972.4i | 0.338202i | ||||||||
\(446\) | 488620.i | 2.45641i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 592889. | 2.95405 | ||||||||
\(449\) | −297658. | −1.47647 | −0.738236 | − | 0.674543i | \(-0.764341\pi\) | ||||
−0.738236 | + | 0.674543i | \(0.764341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 316364.i | 1.55537i | ||||||||
\(452\) | 756951.i | 3.70502i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 123116. | 0.597316 | ||||||||
\(455\) | − | 134944.i | − | 0.651826i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 138561.i | − | 0.663449i | −0.943376 | − | 0.331725i | \(-0.892370\pi\) | ||
0.943376 | − | 0.331725i | \(-0.107630\pi\) | |||||||
\(458\) | −393657. | −1.87666 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 277060.i | 1.30936i | ||||||||
\(461\) | 249929. | 1.17602 | 0.588010 | − | 0.808853i | \(-0.299911\pi\) | ||||
0.588010 | + | 0.808853i | \(0.299911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 101021.i | 0.471248i | 0.971844 | + | 0.235624i | \(0.0757134\pi\) | ||||
−0.971844 | + | 0.235624i | \(0.924287\pi\) | |||||||
\(464\) | −1.08065e6 | −5.01937 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −424597. | −1.95526 | ||||||||
\(467\) | 290164.i | 1.33048i | 0.746628 | + | 0.665242i | \(0.231672\pi\) | ||||
−0.746628 | + | 0.665242i | \(0.768328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 76684.6i | 0.348628i | ||||||||
\(470\) | 40977.7 | 0.185503 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 74702.8 | + | 789411.i | 0.335315 | + | 3.54339i | ||||
\(473\) | −447229. | −1.99898 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 54861.7 | 0.243154 | ||||||||
\(476\) | 542920. | 2.39619 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 345963.i | 1.51417i | ||||||||
\(479\) | 90383.7 | 0.393930 | 0.196965 | − | 0.980411i | \(-0.436891\pi\) | ||||
0.196965 | + | 0.980411i | \(0.436891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 259150. | 1.12011 | ||||||||
\(482\) | − | 731958.i | − | 3.15059i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.28210e6 | 5.47308 | ||||||||
\(485\) | 113459.i | 0.482341i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 151820. | 0.640132 | 0.320066 | − | 0.947395i | \(-0.396295\pi\) | ||||
0.320066 | + | 0.947395i | \(0.396295\pi\) | |||||||
\(488\) | −118010. | −0.495542 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 242825.i | − | 1.01135i | ||||||
\(491\) | 103785. | 0.430497 | 0.215249 | − | 0.976559i | \(-0.430944\pi\) | ||||
0.215249 | + | 0.976559i | \(0.430944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −399528. | −1.64382 | ||||||||
\(494\) | 518086. | 2.12299 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 593779.i | − | 2.41358i | ||||||
\(497\) | 286120. | 1.15834 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 469746. | 1.88652 | 0.943262 | − | 0.332049i | \(-0.107740\pi\) | ||||
0.943262 | + | 0.332049i | \(0.107740\pi\) | |||||||
\(500\) | −765443. | −3.06177 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 242580.i | − | 0.962602i | ||||||
\(503\) | 138093.i | 0.545801i | 0.962042 | + | 0.272901i | \(0.0879831\pi\) | ||||
−0.962042 | + | 0.272901i | \(0.912017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 128392.i | 0.503448i | ||||||||
\(506\) | 467151.i | 1.82455i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.22924e6 | −4.76332 | ||||||||
\(509\) | 123336.i | 0.476051i | 0.971259 | + | 0.238026i | \(0.0765002\pi\) | ||||
−0.971259 | + | 0.238026i | \(0.923500\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 245988.i | 0.942045i | ||||||||
\(512\) | − | 1.04843e6i | − | 3.99944i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 399597.i | − | 1.51250i | ||||||
\(515\) | − | 79685.7i | − | 0.300446i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51009.6 | 0.190841 | ||||||||
\(518\) | −302202. | −1.12626 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00040e6 | −3.69972 | ||||||||
\(521\) | 68858.9 | 0.253679 | 0.126840 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126840 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 269285. | 0.984482 | 0.492241 | − | 0.870459i | \(-0.336178\pi\) | ||||
0.492241 | + | 0.870459i | \(0.336178\pi\) | |||||||
\(524\) | − | 77572.1i | − | 0.282516i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 651985.i | 2.35649i | ||||||||
\(527\) | − | 219527.i | − | 0.790435i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 196916. | 0.703672 | ||||||||
\(530\) | 190506.i | 0.678199i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −446034. | −1.57596 | ||||||||
\(533\) | − | 314138.i | − | 1.10577i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 228139. | 0.797063 | ||||||||
\(536\) | 568498. | 1.97879 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 433149. | 1.49649 | ||||||||
\(539\) | − | 302272.i | − | 1.04045i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 110046.i | − | 0.375993i | −0.982170 | − | 0.187997i | \(-0.939801\pi\) | ||
0.982170 | − | 0.187997i | \(-0.0601994\pi\) | |||||||
\(542\) | − | 264272.i | − | 0.899607i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.81446e6i | − | 6.13125i | ||||||
\(545\) | 454014.i | 1.52854i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 163036. | 0.544889 | 0.272444 | − | 0.962172i | \(-0.412168\pi\) | ||||
0.272444 | + | 0.962172i | \(0.412168\pi\) | |||||||
\(548\) | 401159. | 1.33584 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −276714. | −0.914758 | ||||||||
\(551\) | 328231. | 1.08113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −157648. | −0.515513 | ||||||||
\(554\) | − | 559572.i | − | 1.82321i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −125070. | −0.404578 | ||||||||
\(557\) | 447290. | 1.44171 | 0.720857 | − | 0.693084i | \(-0.243749\pi\) | ||||
0.720857 | + | 0.693084i | \(0.243749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 444083. | 1.42115 | ||||||||
\(560\) | 693591. | 2.21171 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 950487.i | 3.00936i | ||||||||
\(563\) | 50595.3i | 0.159622i | 0.996810 | + | 0.0798111i | \(0.0254317\pi\) | ||||
−0.996810 | + | 0.0798111i | \(0.974568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 357518.i | 1.11996i | ||||||||
\(566\) | −1.11145e6 | −3.46943 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.12114e6i | − | 6.57464i | ||||||
\(569\) | 596739.i | 1.84315i | 0.388204 | + | 0.921573i | \(0.373096\pi\) | ||||
−0.388204 | + | 0.921573i | \(0.626904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2297.80i | 0.00704759i | 0.999994 | + | 0.00352379i | \(0.00112166\pi\) | ||||
−0.999994 | + | 0.00352379i | \(0.998878\pi\) | |||||||
\(572\) | −1.92923e6 | −5.89648 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 366324.i | 1.11184i | ||||||||
\(575\) | − | 49120.0i | − | 0.148567i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −635182. | −1.90786 | −0.953931 | − | 0.300027i | \(-0.903004\pi\) | ||||
−0.953931 | + | 0.300027i | \(0.903004\pi\) | |||||||
\(578\) | − | 545310.i | − | 1.63225i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −981880. | −2.91879 | ||||||||
\(581\) | − | 412599.i | − | 1.22229i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 237145.i | 0.697712i | ||||||||
\(584\) | 1.82362e6 | 5.34698 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 751661.i | − | 2.18891i | ||||||
\(587\) | − | 46453.2i | − | 0.134815i | −0.997726 | − | 0.0674077i | \(-0.978527\pi\) | ||
0.997726 | − | 0.0674077i | \(-0.0214728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 180351.i | 0.519863i | ||||||||
\(590\) | 54660.4 | + | 577616.i | 0.157025 | + | 1.65934i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.33199e6i | 3.80064i | ||||||||
\(593\) | 292298. | 0.831221 | 0.415611 | − | 0.909543i | \(-0.363568\pi\) | ||||
0.415611 | + | 0.909543i | \(0.363568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 256428. | 0.724323 | ||||||||
\(596\) | − | 366624.i | − | 1.03212i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 463865.i | − | 1.29715i | ||||||
\(599\) | −239592. | −0.667758 | −0.333879 | − | 0.942616i | \(-0.608358\pi\) | ||||
−0.333879 | + | 0.942616i | \(0.608358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 235688.i | 0.652512i | 0.945281 | + | 0.326256i | \(0.105787\pi\) | ||||
−0.945281 | + | 0.326256i | \(0.894213\pi\) | |||||||
\(602\) | −517857. | −1.42895 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 110041.i | − | 0.301634i | ||||||
\(605\) | 605554. | 1.65441 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 423021. | 1.14811 | 0.574056 | − | 0.818816i | \(-0.305369\pi\) | ||||
0.574056 | + | 0.818816i | \(0.305369\pi\) | |||||||
\(608\) | 1.49066e6i | 4.03247i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −86348.7 | −0.232058 | ||||||||
\(611\) | −50650.7 | −0.135676 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 210522.i | − | 0.560243i | −0.959965 | − | 0.280122i | \(-0.909625\pi\) | ||
0.959965 | − | 0.280122i | \(-0.0903748\pi\) | |||||||
\(614\) | − | 280205.i | − | 0.743256i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.45219e6 | 3.82704 | ||||||||
\(617\) | 342587. | 0.899914 | 0.449957 | − | 0.893050i | \(-0.351439\pi\) | ||||
0.449957 | + | 0.893050i | \(0.351439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −202870. | −0.529463 | −0.264732 | − | 0.964322i | \(-0.585283\pi\) | ||||
−0.264732 | + | 0.964322i | \(0.585283\pi\) | |||||||
\(620\) | − | 539508.i | − | 1.40351i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 432112.i | − | 1.11690i | ||||||
\(623\) | 96533.8i | 0.248716i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −254919. | −0.652594 | ||||||||
\(626\) | 756189. | 1.92966 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 623369.i | 1.58061i | ||||||||
\(629\) | 492451.i | 1.24469i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41966.6 | −0.105401 | −0.0527006 | − | 0.998610i | \(-0.516783\pi\) | ||||
−0.0527006 | + | 0.998610i | \(0.516783\pi\) | |||||||
\(632\) | 1.16872e6i | 2.92601i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.03212e6i | − | 2.56775i | ||||||
\(635\) | −580587. | −1.43986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 300146.i | 0.739696i | ||||||||
\(638\) | −1.65555e6 | −4.06725 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.63531e6i | − | 3.99245i | ||||||
\(641\) | 336370. | 0.818656 | 0.409328 | − | 0.912387i | \(-0.365763\pi\) | ||||
0.409328 | + | 0.912387i | \(0.365763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −387046. | −0.936140 | −0.468070 | − | 0.883691i | \(-0.655051\pi\) | ||||
−0.468070 | + | 0.883691i | \(0.655051\pi\) | |||||||
\(644\) | 399353.i | 0.962909i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 984495.i | 2.35911i | ||||||||
\(647\) | −640773. | −1.53072 | −0.765360 | − | 0.643602i | \(-0.777439\pi\) | ||||
−0.765360 | + | 0.643602i | \(0.777439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 68042.0 | + | 719024.i | 0.161543 | + | 1.70708i | ||||
\(650\) | 274768. | 0.650338 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 635064. | 1.49390 | ||||||||
\(653\) | −59695.3 | −0.139995 | −0.0699977 | − | 0.997547i | \(-0.522299\pi\) | ||||
−0.0699977 | + | 0.997547i | \(0.522299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 36638.4i | − | 0.0853991i | ||||||
\(656\) | 1.61462e6 | 3.75199 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 59065.1 | 0.136420 | ||||||||
\(659\) | 277090.i | 0.638043i | 0.947747 | + | 0.319022i | \(0.103354\pi\) | ||||
−0.947747 | + | 0.319022i | \(0.896646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −170596. | −0.390450 | −0.195225 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195225 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(662\) | − | 422085.i | − | 0.963128i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.05879e6 | −6.93766 | ||||||||
\(665\) | −210668. | −0.476381 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 293879.i | − | 0.660568i | ||||||
\(668\) | −1.70891e6 | −3.82972 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 415973. | 0.926649 | ||||||||
\(671\) | −107488. | −0.238734 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 124494.i | 0.274864i | 0.990511 | + | 0.137432i | \(0.0438848\pi\) | ||||
−0.990511 | + | 0.137432i | \(0.956115\pi\) | |||||||
\(674\) | 680394. | 1.49775 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 626599. | 1.37119 | ||||||||
\(677\) | −470982. | −1.02761 | −0.513804 | − | 0.857908i | \(-0.671764\pi\) | ||||
−0.513804 | + | 0.857908i | \(0.671764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 163539.i | 0.354716i | ||||||||
\(680\) | − | 1.90102e6i | − | 4.11120i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 909667.i | − | 1.95575i | ||||||
\(683\) | 543532.i | 1.16516i | 0.812775 | + | 0.582578i | \(0.197956\pi\) | ||||
−0.812775 | + | 0.582578i | \(0.802044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 189473. | 0.403800 | ||||||||
\(686\) | − | 926836.i | − | 1.96949i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.28251e6i | 4.82210i | ||||||||
\(689\) | − | 235476.i | − | 0.496031i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 466845.i | 0.977725i | 0.872361 | + | 0.488862i | \(0.162588\pi\) | ||||
−0.872361 | + | 0.488862i | \(0.837412\pi\) | |||||||
\(692\) | − | 596739.i | − | 1.24615i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −579327. | −1.20283 | ||||||||
\(695\) | −59072.1 | −0.122296 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 596942. | 1.22876 | ||||||||
\(698\) | 218415. | 0.448304 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −236554. | −0.482764 | ||||||||
\(701\) | − | 661106.i | − | 1.34535i | −0.739939 | − | 0.672674i | \(-0.765145\pi\) | ||
0.739939 | − | 0.672674i | \(-0.234855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 404571.i | − | 0.818624i | ||||||
\(704\) | − | 4.00345e6i | − | 8.07773i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.10221e6 | −2.21134 | ||||||||
\(707\) | 185064.i | 0.370239i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −64729.8 | −0.128769 | −0.0643845 | − | 0.997925i | \(-0.520508\pi\) | ||||
−0.0643845 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(710\) | − | 1.55205e6i | − | 3.07884i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 715649. | 1.41169 | ||||||||
\(713\) | 161476. | 0.317636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −911203. | −1.78239 | ||||||||
\(716\) | 17974.8i | 0.0350621i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 232506.i | − | 0.451009i | ||||||
\(719\) | 648569.i | 1.25458i | 0.778786 | + | 0.627290i | \(0.215836\pi\) | ||||
−0.778786 | + | 0.627290i | \(0.784164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 114859.i | − | 0.220950i | ||||||
\(722\) | 210146.i | 0.403131i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.07676e6 | −3.96195 | ||||||||
\(725\) | 174078. | 0.331182 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 201809. | 0.381831 | 0.190916 | − | 0.981606i | \(-0.438854\pi\) | ||||
0.190916 | + | 0.981606i | \(0.438854\pi\) | |||||||
\(728\) | −1.44198e6 | −2.72079 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.33435e6 | 2.50394 | ||||||||
\(731\) | 843870.i | 1.57921i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −517718. | −0.963575 | −0.481787 | − | 0.876288i | \(-0.660012\pi\) | ||||
−0.481787 | + | 0.876288i | \(0.660012\pi\) | |||||||
\(734\) | −406785. | −0.755045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.33465e6 | 2.46384 | ||||||||
\(737\) | 517808. | 0.953310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01019e6i | 1.84976i | 0.380263 | + | 0.924879i | \(0.375834\pi\) | ||||
−0.380263 | + | 0.924879i | \(0.624166\pi\) | |||||||
\(740\) | 1.21025e6i | 2.21009i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 274595.i | 0.498752i | ||||||||
\(743\) | 521556. | 0.944765 | 0.472382 | − | 0.881394i | \(-0.343394\pi\) | ||||
0.472382 | + | 0.881394i | \(0.343394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 173162.i | − | 0.311989i | ||||||
\(746\) | − | 550635.i | − | 0.989432i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.66603e6i | − | 6.55229i | ||||||
\(749\) | 328839. | 0.586165 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 879845.i | − | 1.56001i | −0.625776 | − | 0.780003i | \(-0.715217\pi\) | ||
0.625776 | − | 0.780003i | \(-0.284783\pi\) | |||||||
\(752\) | − | 260336.i | − | 0.460362i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.64390e6 | 2.89157 | ||||||||
\(755\) | − | 51973.9i | − | 0.0911782i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.05871e6 | −1.84750 | −0.923748 | − | 0.383000i | \(-0.874891\pi\) | ||||
−0.923748 | + | 0.383000i | \(0.874891\pi\) | |||||||
\(758\) | 312264.i | 0.543481i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.56178e6i | 2.70391i | ||||||||
\(761\) | 319446. | 0.551604 | 0.275802 | − | 0.961214i | \(-0.411057\pi\) | ||||
0.275802 | + | 0.961214i | \(0.411057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 654414.i | 1.12410i | ||||||||
\(764\) | 2.71612e6i | 4.65330i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.21955e6i | 2.07847i | ||||||||
\(767\) | −67563.3 | − | 713966.i | −0.114847 | − | 1.21363i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 547254.i | − | 0.925414i | −0.886511 | − | 0.462707i | \(-0.846878\pi\) | ||
0.886511 | − | 0.462707i | \(-0.153122\pi\) | |||||||
\(770\) | 1.06258e6 | 1.79217 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.44225e6 | 2.41995 | ||||||||
\(773\) | − | 385413.i | − | 0.645011i | −0.946568 | − | 0.322505i | \(-0.895475\pi\) | ||
0.946568 | − | 0.322505i | \(-0.104525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 95649.6i | 0.159250i | ||||||||
\(776\) | 1.21239e6 | 2.01335 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1.44313e6i | − | 2.38423i | ||||||
\(779\) | −490415. | −0.808144 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.93201e6i | − | 3.16743i | ||||||
\(782\) | 881461. | 1.44142 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.54270e6 | −2.50986 | ||||||||
\(785\) | 294426.i | 0.477789i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03990e6 | 1.67896 | 0.839481 | − | 0.543389i | \(-0.182859\pi\) | ||||
0.839481 | + | 0.543389i | \(0.182859\pi\) | |||||||
\(788\) | −1.57939e6 | −2.54353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 855158.i | 1.37023i | ||||||||
\(791\) | 515325.i | 0.823623i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 106732. | 0.169726 | ||||||||
\(794\) | −1.68929e6 | −2.67955 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −168424. | −0.265814 | ||||||||
\(797\) | − | 436583.i | − | 0.687306i | −0.939097 | − | 0.343653i | \(-0.888336\pi\) | ||
0.939097 | − | 0.343653i | \(-0.111664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 96249.2i | − | 0.150766i | ||||||
\(800\) | 790574.i | 1.23527i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.45492e6 | 2.26198 | ||||||||
\(803\) | 1.66102e6 | 2.57598 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 188620.i | 0.291069i | ||||||||
\(806\) | 903267.i | 1.39042i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.37196e6 | 2.10145 | ||||||||
\(809\) | − | 43381.1i | − | 0.0662832i | −0.999451 | − | 0.0331416i | \(-0.989449\pi\) | ||
0.999451 | − | 0.0331416i | \(-0.0105512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 112796.i | − | 0.171495i | −0.996317 | − | 0.0857476i | \(-0.972672\pi\) | ||
0.996317 | − | 0.0857476i | \(-0.0273279\pi\) | |||||||
\(812\) | −1.41528e6 | −2.14649 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.04060e6i | 3.07970i | ||||||||
\(815\) | 299949. | 0.451578 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 693279.i | − | 1.03864i | ||||||
\(818\) | −1.11052e6 | −1.65967 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.46704e6 | 2.18180 | ||||||||
\(821\) | 606308.i | 0.899512i | 0.893152 | + | 0.449756i | \(0.148489\pi\) | ||||
−0.893152 | + | 0.449756i | \(0.851511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 883912.i | 1.30500i | 0.757790 | + | 0.652499i | \(0.226279\pi\) | ||||
−0.757790 | + | 0.652499i | \(0.773721\pi\) | |||||||
\(824\) | −851500. | −1.25409 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 78787.3 | + | 832574.i | 0.115477 | + | 1.22029i | ||||
\(827\) | 4182.48 | 0.00611537 | 0.00305769 | − | 0.999995i | \(-0.499027\pi\) | ||||
0.00305769 | + | 0.999995i | \(0.499027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.03471e6 | 1.50561 | 0.752803 | − | 0.658246i | \(-0.228701\pi\) | ||||
0.752803 | + | 0.658246i | \(0.228701\pi\) | |||||||
\(830\) | −2.23813e6 | −3.24884 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.97529e6i | 5.74277i | ||||||||
\(833\) | −570353. | −0.821965 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −807143. | −1.15765 | ||||||||
\(836\) | 3.01182e6i | 4.30939i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.38693e6 | −3.39900 | ||||||||
\(839\) | − | 1.28432e6i | − | 1.82452i | −0.409611 | − | 0.912260i | \(-0.634336\pi\) | ||
0.409611 | − | 0.912260i | \(-0.365664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 334205. | 0.472521 | ||||||||
\(842\) | −312916. | −0.441370 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 619851.i | 0.870166i | ||||||||
\(845\) | 295951. | 0.414483 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 872843. | 1.21666 | ||||||||
\(848\) | 1.21031e6 | 1.68308 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 522128.i | 0.722669i | ||||||||
\(851\) | −362230. | −0.500179 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 131299. | 0.180452 | 0.0902262 | − | 0.995921i | \(-0.471241\pi\) | ||||
0.0902262 | + | 0.995921i | \(0.471241\pi\) | |||||||
\(854\) | −124463. | −0.170657 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 2.43784e6i | − | 3.32703i | ||||||
\(857\) | − | 41212.7i | − | 0.0561138i | −0.999606 | − | 0.0280569i | \(-0.991068\pi\) | ||
0.999606 | − | 0.0280569i | \(-0.00893196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 794929.i | − | 1.07731i | −0.842525 | − | 0.538657i | \(-0.818932\pi\) | ||
0.842525 | − | 0.538657i | \(-0.181068\pi\) | |||||||
\(860\) | 2.07389e6i | 2.80407i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.56340e6 | −2.10405 | ||||||||
\(863\) | 675152.i | 0.906525i | 0.891377 | + | 0.453263i | \(0.149740\pi\) | ||||
−0.891377 | + | 0.453263i | \(0.850260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 281848.i | − | 0.376689i | ||||||
\(866\) | 1.35595e6i | 1.80804i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 777646.i | − | 1.03215i | ||||||
\(869\) | 1.06451e6i | 1.40965i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −514165. | −0.677745 | ||||||||
\(872\) | 4.85147e6 | 6.38028 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −724161. | −0.948009 | ||||||||
\(875\) | −521107. | −0.680629 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 461113. | 0.599526 | 0.299763 | − | 0.954014i | \(-0.403092\pi\) | ||||
0.299763 | + | 0.954014i | \(0.403092\pi\) | |||||||
\(878\) | − | 1.84563e6i | − | 2.39418i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 4.68343e6i | − | 6.04782i | ||||||
\(881\) | 39808.0i | 0.0512883i | 0.999671 | + | 0.0256442i | \(0.00816368\pi\) | ||||
−0.999671 | + | 0.0256442i | \(0.991836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −206390. | −0.264708 | −0.132354 | − | 0.991203i | \(-0.542254\pi\) | ||||
−0.132354 | + | 0.991203i | \(0.542254\pi\) | |||||||
\(884\) | 3.64024e6i | 4.65828i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.05386e6 | 3.89029 | ||||||||
\(887\) | 488379.i | 0.620740i | 0.950616 | + | 0.310370i | \(0.100453\pi\) | ||||
−0.950616 | + | 0.310370i | \(0.899547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −836857. | −1.05888 | ||||||||
\(890\) | 523644. | 0.661083 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.82053e6 | 3.54488 | ||||||||
\(893\) | 79073.2i | 0.0991577i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8489.74i | 0.0105986i | ||||||||
\(896\) | − | 2.35712e6i | − | 2.93607i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.32733e6i | 2.88606i | ||||||||
\(899\) | 572260.i | 0.708067i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 447464. | 0.551200 | ||||||||
\(902\) | 2.47358e6 | 3.04028 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.82034e6 | 4.67482 | ||||||||
\(905\) | −980880. | −1.19762 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −664689. | −0.807986 | −0.403993 | − | 0.914762i | \(-0.632378\pi\) | ||||
−0.403993 | + | 0.914762i | \(0.632378\pi\) | |||||||
\(908\) | − | 710683.i | − | 0.861994i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.05510e6 | −1.27412 | ||||||||
\(911\) | −467295. | −0.563060 | −0.281530 | − | 0.959552i | \(-0.590842\pi\) | ||||
−0.281530 | + | 0.959552i | \(0.590842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.78605e6 | −3.34232 | ||||||||
\(914\) | −1.08338e6 | −1.29684 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.27236e6i | 2.70824i | ||||||||
\(917\) | − | 52810.4i | − | 0.0628030i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32821.0i | 0.0388616i | 0.999811 | + | 0.0194308i | \(0.00618541\pi\) | ||||
−0.999811 | + | 0.0194308i | \(0.993815\pi\) | |||||||
\(920\) | 1.39833e6 | 1.65209 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.95415e6i | − | 2.29877i | ||||||
\(923\) | 1.91841e6i | 2.25185i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 214565.i | − | 0.250770i | ||||||
\(926\) | 789863. | 0.921149 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.72991e6i | 5.49233i | ||||||||
\(929\) | − | 1.32545e6i | − | 1.53579i | −0.640577 | − | 0.767894i | \(-0.721305\pi\) | ||
0.640577 | − | 0.767894i | \(-0.278695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 468571. | 0.540600 | ||||||||
\(932\) | 2.45097e6i | 2.82167i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.26873e6 | 2.60070 | ||||||||
\(935\) | − | 1.73152e6i | − | 1.98063i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45039.7i | 0.0512998i | 0.999671 | + | 0.0256499i | \(0.00816552\pi\) | ||||
−0.999671 | + | 0.0256499i | \(0.991834\pi\) | |||||||
\(938\) | 599582. | 0.681463 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 236542.i | − | 0.267702i | ||||||
\(941\) | 517189.i | 0.584077i | 0.956407 | + | 0.292038i | \(0.0943335\pi\) | ||||
−0.956407 | + | 0.292038i | \(0.905667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 439090.i | 0.493776i | ||||||||
\(944\) | 3.66966e6 | − | 347264.i | 4.11796 | − | 0.389687i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.49680e6i | 3.90740i | ||||||||
\(947\) | −510466. | −0.569203 | −0.284601 | − | 0.958646i | \(-0.591861\pi\) | ||||
−0.284601 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.64933e6 | −1.83137 | ||||||||
\(950\) | − | 428953.i | − | 0.475294i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 2.74012e6i | − | 3.02340i | ||||||
\(953\) | 26017.8 | 0.0286473 | 0.0143237 | − | 0.999897i | \(-0.495440\pi\) | ||||
0.0143237 | + | 0.999897i | \(0.495440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.28286e6i | 1.40660i | ||||||||
\(956\) | 1.99705e6 | 2.18511 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 706692.i | − | 0.770015i | ||||||
\(959\) | 273106. | 0.296957 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 609084. | 0.659524 | ||||||||
\(962\) | − | 2.02624e6i | − | 2.18948i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.22519e6 | −4.54666 | ||||||||
\(965\) | 681195. | 0.731504 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 262570.i | − | 0.280797i | −0.990095 | − | 0.140399i | \(-0.955162\pi\) | ||
0.990095 | − | 0.140399i | \(-0.0448384\pi\) | |||||||
\(968\) | − | 6.47078e6i | − | 6.90567i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 887110. | 0.942832 | ||||||||
\(971\) | 787423. | 0.835160 | 0.417580 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417580 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −85146.4 | −0.0899374 | ||||||||
\(974\) | − | 1.18705e6i | − | 1.25127i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 548584.i | 0.575895i | ||||||||
\(977\) | − | 252812.i | − | 0.264855i | −0.991193 | − | 0.132428i | \(-0.957723\pi\) | ||
0.991193 | − | 0.132428i | \(-0.0422772\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 651839. | 0.680103 | ||||||||
\(980\) | −1.40170e6 | −1.45949 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 811472.i | − | 0.841493i | ||||||
\(983\) | − | 1.29505e6i | − | 1.34023i | −0.742256 | − | 0.670116i | \(-0.766244\pi\) | ||
0.742256 | − | 0.670116i | \(-0.233756\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −745968. | −0.768861 | ||||||||
\(986\) | 3.12383e6i | 3.21317i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 2.99063e6i | − | 3.06372i | ||||||
\(989\) | −620722. | −0.634607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.07822e6i | − | 1.09789i | −0.835857 | − | 0.548947i | \(-0.815029\pi\) | ||
0.835857 | − | 0.548947i | \(-0.184971\pi\) | |||||||
\(992\) | −2.59892e6 | −2.64101 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 2.23711e6i | − | 2.26420i | ||||||
\(995\) | −79548.9 | −0.0803504 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 565271. | 0.568678 | 0.284339 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284339 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(998\) | − | 3.67285e6i | − | 3.68759i | ||||||
\(999\) | 0 | 0 |
(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 | 531.5.c.d.235.1 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.40 | yes | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.40 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.1 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.1 | ✓ | 40 | 177.176 | even | 2 | ||
177.5.c.a.58.40 | yes | 40 | 3.2 | odd | 2 | ||
531.5.c.d.235.1 | 40 | 1.1 | even | 1 | trivial | ||
531.5.c.d.235.40 | 40 | 59.58 | odd | 2 | inner |