Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(59,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.59");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.h (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: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 59.2 | ||
Root | \(1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.59 |
Dual form | 60.4.h.a.59.4 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 1.00000i | ||||||
\(3\) | 1.58114 | + | 4.94975i | 0.304290 | + | 0.952579i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 11.1803i | 1.00000i | ||||||||
\(6\) | 14.0000 | − | 4.47214i | 0.952579 | − | 0.304290i | ||||
\(7\) | 34.7851 | 1.87822 | 0.939108 | − | 0.343622i | \(-0.111654\pi\) | ||||
0.939108 | + | 0.343622i | \(0.111654\pi\) | |||||||
\(8\) | 22.6274i | 1.00000i | ||||||||
\(9\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(10\) | 31.6228 | 1.00000 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −12.6491 | − | 39.5980i | −0.304290 | − | 0.952579i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | − | 98.3870i | − | 1.87822i | ||||||
\(15\) | −55.3399 | + | 17.6777i | −0.952579 | + | 0.304290i | ||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 44.2719 | + | 62.2254i | 0.579721 | + | 0.814815i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | − | 89.4427i | − | 1.00000i | ||||||
\(21\) | 55.0000 | + | 172.177i | 0.571523 | + | 1.78915i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 94.7523i | − | 0.859010i | −0.903065 | − | 0.429505i | \(-0.858688\pi\) | ||
0.903065 | − | 0.429505i | \(-0.141312\pi\) | |||||||
\(24\) | −112.000 | + | 35.7771i | −0.952579 | + | 0.304290i | ||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −112.261 | − | 84.1457i | −0.800171 | − | 0.599772i | ||||
\(28\) | −278.280 | −1.87822 | ||||||||
\(29\) | 62.6099i | 0.400909i | 0.979703 | + | 0.200455i | \(0.0642419\pi\) | ||||
−0.979703 | + | 0.200455i | \(0.935758\pi\) | |||||||
\(30\) | 50.0000 | + | 156.525i | 0.304290 | + | 0.952579i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 181.019i | − | 1.00000i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 388.909i | 1.87822i | ||||||||
\(36\) | 176.000 | − | 125.220i | 0.814815 | − | 0.579721i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −252.982 | −1.00000 | ||||||||
\(41\) | − | 460.630i | − | 1.75459i | −0.479949 | − | 0.877297i | \(-0.659345\pi\) | ||
0.479949 | − | 0.877297i | \(-0.340655\pi\) | |||||||
\(42\) | 486.991 | − | 155.563i | 1.78915 | − | 0.571523i | ||||
\(43\) | 376.311 | 1.33458 | 0.667289 | − | 0.744798i | \(-0.267454\pi\) | ||||
0.667289 | + | 0.744798i | \(0.267454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −175.000 | − | 245.967i | −0.579721 | − | 0.814815i | ||||
\(46\) | −268.000 | −0.859010 | ||||||||
\(47\) | − | 425.678i | − | 1.32110i | −0.750783 | − | 0.660549i | \(-0.770324\pi\) | ||
0.750783 | − | 0.660549i | \(-0.229676\pi\) | |||||||
\(48\) | 101.193 | + | 316.784i | 0.304290 | + | 0.952579i | ||||
\(49\) | 867.000 | 2.52770 | ||||||||
\(50\) | 353.553i | 1.00000i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −238.000 | + | 317.522i | −0.599772 | + | 0.800171i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 787.096i | 1.87822i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 177.088 | 0.400909 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 442.719 | − | 141.421i | 0.952579 | − | 0.304290i | ||||
\(61\) | −952.000 | −1.99821 | −0.999107 | − | 0.0422409i | \(-0.986550\pi\) | ||||
−0.999107 | + | 0.0422409i | \(0.986550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −765.271 | + | 544.472i | −1.53040 | + | 1.08884i | ||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 774.758 | 1.41271 | 0.706356 | − | 0.707856i | \(-0.250338\pi\) | ||||
0.706356 | + | 0.707856i | \(0.250338\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 469.000 | − | 149.817i | 0.818275 | − | 0.261388i | ||||
\(70\) | 1100.00 | 1.87822 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −354.175 | − | 497.803i | −0.579721 | − | 0.814815i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −197.642 | − | 618.718i | −0.304290 | − | 0.952579i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 715.542i | 1.00000i | ||||||||
\(81\) | 239.000 | − | 688.709i | 0.327846 | − | 0.944731i | ||||
\(82\) | −1302.86 | −1.75459 | ||||||||
\(83\) | 108.894i | 0.144009i | 0.997404 | + | 0.0720043i | \(0.0229395\pi\) | ||||
−0.997404 | + | 0.0720043i | \(0.977060\pi\) | |||||||
\(84\) | −440.000 | − | 1377.42i | −0.571523 | − | 1.78915i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1064.37i | − | 1.33458i | ||||||
\(87\) | −309.903 | + | 98.9949i | −0.381898 | + | 0.121993i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 948.093i | 1.12919i | 0.825369 | + | 0.564593i | \(0.190967\pi\) | ||||
−0.825369 | + | 0.564593i | \(0.809033\pi\) | |||||||
\(90\) | −695.701 | + | 494.975i | −0.814815 | + | 0.579721i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 758.018i | 0.859010i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1204.00 | −1.32110 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 896.000 | − | 286.217i | 0.952579 | − | 0.304290i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | − | 2452.25i | − | 2.52770i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1000.00 | 1.00000 | ||||||||
\(101\) | 1994.57i | 1.96502i | 0.186200 | + | 0.982512i | \(0.440383\pi\) | ||||
−0.186200 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −932.872 | −0.892414 | −0.446207 | − | 0.894930i | \(-0.647225\pi\) | ||||
−0.446207 | + | 0.894930i | \(0.647225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1925.00 | + | 614.919i | −1.78915 | + | 0.571523i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 312.541i | 0.282378i | 0.989983 | + | 0.141189i | \(0.0450926\pi\) | ||||
−0.989983 | + | 0.141189i | \(0.954907\pi\) | |||||||
\(108\) | 898.087 | + | 673.166i | 0.800171 | + | 0.599772i | ||||
\(109\) | 1136.00 | 0.998248 | 0.499124 | − | 0.866530i | \(-0.333655\pi\) | ||||
0.499124 | + | 0.866530i | \(0.333655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2226.24 | 1.87822 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1059.36 | 0.859010 | ||||||||
\(116\) | − | 500.879i | − | 0.400909i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −400.000 | − | 1252.20i | −0.304290 | − | 0.952579i | ||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 2692.66i | 1.99821i | ||||||||
\(123\) | 2280.00 | − | 728.320i | 1.67139 | − | 0.533906i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1397.54i | − | 1.00000i | ||||||
\(126\) | 1540.00 | + | 2164.51i | 1.08884 | + | 1.53040i | ||||
\(127\) | −2412.82 | −1.68585 | −0.842925 | − | 0.538031i | \(-0.819168\pi\) | ||||
−0.842925 | + | 0.538031i | \(0.819168\pi\) | |||||||
\(128\) | 1448.15i | 1.00000i | ||||||||
\(129\) | 595.000 | + | 1862.64i | 0.406099 | + | 1.27129i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2191.35i | − | 1.41271i | ||||||
\(135\) | 940.778 | − | 1255.11i | 0.599772 | − | 0.800171i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −423.745 | − | 1326.53i | −0.261388 | − | 0.818275i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | − | 3111.27i | − | 1.87822i | ||||||
\(141\) | 2107.00 | − | 673.056i | 1.25845 | − | 0.401997i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1408.00 | + | 1001.76i | −0.814815 | + | 0.579721i | ||||
\(145\) | −700.000 | −0.400909 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1370.85 | + | 4291.43i | 0.769154 | + | 2.40783i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1909.60i | − | 1.04994i | −0.851121 | − | 0.524969i | \(-0.824077\pi\) | ||
0.851121 | − | 0.524969i | \(-0.175923\pi\) | |||||||
\(150\) | −1750.00 | + | 559.017i | −0.952579 | + | 0.304290i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2023.86 | 1.00000 | ||||||||
\(161\) | − | 3295.96i | − | 1.61341i | ||||||
\(162\) | −1947.96 | − | 675.994i | −0.944731 | − | 0.327846i | ||||
\(163\) | −22.1359 | −0.0106369 | −0.00531847 | − | 0.999986i | \(-0.501693\pi\) | ||||
−0.00531847 | + | 0.999986i | \(0.501693\pi\) | |||||||
\(164\) | 3685.04i | 1.75459i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 308.000 | 0.144009 | ||||||||
\(167\) | − | 1851.21i | − | 0.857788i | −0.903355 | − | 0.428894i | \(-0.858903\pi\) | ||
0.903355 | − | 0.428894i | \(-0.141097\pi\) | |||||||
\(168\) | −3895.93 | + | 1244.51i | −1.78915 | + | 0.571523i | ||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3010.49 | −1.33458 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 280.000 | + | 876.539i | 0.121993 | + | 0.381898i | ||||
\(175\) | −4348.13 | −1.87822 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2681.61 | 1.12919 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 1400.00 | + | 1967.74i | 0.579721 | + | 0.814815i | ||||
\(181\) | −1078.00 | −0.442691 | −0.221346 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221346 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1505.24 | − | 4712.16i | −0.608037 | − | 1.90346i | ||||
\(184\) | 2144.00 | 0.859010 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3405.43i | 1.32110i | ||||||||
\(189\) | −3905.00 | − | 2927.01i | −1.50289 | − | 1.12650i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −809.543 | − | 2534.27i | −0.304290 | − | 0.952579i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6936.00 | −2.52770 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | − | 2828.43i | − | 1.00000i | ||||||
\(201\) | 1225.00 | + | 3834.86i | 0.429875 | + | 1.34572i | ||||
\(202\) | 5641.50 | 1.96502 | ||||||||
\(203\) | 2177.89i | 0.752994i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5150.00 | 1.75459 | ||||||||
\(206\) | 2638.56i | 0.892414i | ||||||||
\(207\) | 1483.11 | + | 2084.55i | 0.497986 | + | 0.699934i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1739.25 | + | 5444.72i | 0.571523 | + | 1.78915i | ||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 884.000 | 0.282378 | ||||||||
\(215\) | 4207.29i | 1.33458i | ||||||||
\(216\) | 1904.00 | − | 2540.17i | 0.599772 | − | 0.800171i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 3213.09i | − | 0.998248i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2083.94 | 0.625789 | 0.312895 | − | 0.949788i | \(-0.398701\pi\) | ||||
0.312895 | + | 0.949788i | \(0.398701\pi\) | |||||||
\(224\) | − | 6296.77i | − | 1.87822i | ||||||
\(225\) | 2750.00 | − | 1956.56i | 0.814815 | − | 0.579721i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5771.41i | − | 1.68750i | −0.536739 | − | 0.843748i | \(-0.680344\pi\) | ||
0.536739 | − | 0.843748i | \(-0.319656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6874.00 | −1.98361 | −0.991805 | − | 0.127761i | \(-0.959221\pi\) | ||||
−0.991805 | + | 0.127761i | \(0.959221\pi\) | |||||||
\(230\) | − | 2996.33i | − | 0.859010i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1416.70 | −0.400909 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4759.23 | 1.32110 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −3541.75 | + | 1131.37i | −0.952579 | + | 0.304290i | ||||
\(241\) | −1708.00 | −0.456523 | −0.228261 | − | 0.973600i | \(-0.573304\pi\) | ||||
−0.228261 | + | 0.973600i | \(0.573304\pi\) | |||||||
\(242\) | 3764.64i | 1.00000i | ||||||||
\(243\) | 3786.83 | + | 94.0452i | 0.999692 | + | 0.0248272i | ||||
\(244\) | 7616.00 | 1.99821 | ||||||||
\(245\) | 9693.35i | 2.52770i | ||||||||
\(246\) | −2060.00 | − | 6448.82i | −0.533906 | − | 1.67139i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −539.000 | + | 172.177i | −0.137180 | + | 0.0438204i | ||||
\(250\) | −3952.85 | −1.00000 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 6122.17 | − | 4355.78i | 1.53040 | − | 1.08884i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6824.48i | 1.68585i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 5268.35 | − | 1682.91i | 1.27129 | − | 0.406099i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −980.000 | − | 1377.42i | −0.232416 | − | 0.326667i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8509.32i | 1.99508i | 0.0700645 | + | 0.997542i | \(0.477679\pi\) | ||||
−0.0700645 | + | 0.997542i | \(0.522321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4692.82 | + | 1499.07i | −1.07564 | + | 0.343601i | ||||
\(268\) | −6198.06 | −1.41271 | ||||||||
\(269\) | 6864.73i | 1.55595i | 0.628297 | + | 0.777974i | \(0.283752\pi\) | ||||
−0.628297 | + | 0.777974i | \(0.716248\pi\) | |||||||
\(270\) | −3550.00 | − | 2660.92i | −0.800171 | − | 0.599772i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3752.00 | + | 1198.53i | −0.818275 | + | 0.261388i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8800.00 | −1.87822 | ||||||||
\(281\) | 4288.78i | 0.910488i | 0.890367 | + | 0.455244i | \(0.150448\pi\) | ||||
−0.890367 | + | 0.455244i | \(0.849552\pi\) | |||||||
\(282\) | −1903.69 | − | 5959.50i | −0.401997 | − | 1.25845i | ||||
\(283\) | −9471.02 | −1.98938 | −0.994689 | − | 0.102929i | \(-0.967178\pi\) | ||||
−0.994689 | + | 0.102929i | \(0.967178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 16023.0i | − | 3.29551i | ||||||
\(288\) | 2833.40 | + | 3982.43i | 0.579721 | + | 0.814815i | ||||
\(289\) | −4913.00 | −1.00000 | ||||||||
\(290\) | 1979.90i | 0.400909i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 12138.0 | − | 3877.34i | 2.40783 | − | 0.769154i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5401.17 | −1.04994 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1581.14 | + | 4949.75i | 0.304290 | + | 0.952579i | ||||
\(301\) | 13090.0 | 2.50663 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9872.63 | + | 3153.70i | −1.87184 | + | 0.597938i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 10643.7i | − | 1.99821i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10052.9 | 1.86889 | 0.934443 | − | 0.356112i | \(-0.115898\pi\) | ||||
0.934443 | + | 0.356112i | \(0.115898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1475.00 | − | 4617.48i | −0.271553 | − | 0.850095i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6087.38 | − | 8555.99i | −1.08884 | − | 1.53040i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 5724.33i | − | 1.00000i | ||||||
\(321\) | −1547.00 | + | 494.171i | −0.268988 | + | 0.0859250i | ||||
\(322\) | −9322.39 | −1.61341 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1912.00 | + | 5509.67i | −0.327846 | + | 0.944731i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 62.6099i | 0.0106369i | ||||||||
\(327\) | 1796.17 | + | 5622.91i | 0.303757 | + | 0.950911i | ||||
\(328\) | 10422.9 | 1.75459 | ||||||||
\(329\) | − | 14807.2i | − | 2.48131i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | − | 871.156i | − | 0.144009i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5236.00 | −0.857788 | ||||||||
\(335\) | 8662.06i | 1.41271i | ||||||||
\(336\) | 3520.00 | + | 11019.3i | 0.571523 | + | 1.78915i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 6214.05i | − | 1.00000i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18227.4 | 2.86935 | ||||||||
\(344\) | 8514.95i | 1.33458i | ||||||||
\(345\) | 1675.00 | + | 5243.58i | 0.261388 | + | 0.818275i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11131.3i | 1.72207i | 0.508546 | + | 0.861035i | \(0.330183\pi\) | ||||
−0.508546 | + | 0.861035i | \(0.669817\pi\) | |||||||
\(348\) | 2479.23 | − | 791.960i | 0.381898 | − | 0.121993i | ||||
\(349\) | −9646.00 | −1.47948 | −0.739740 | − | 0.672893i | \(-0.765052\pi\) | ||||
−0.739740 | + | 0.672893i | \(0.765052\pi\) | |||||||
\(350\) | 12298.4i | 1.87822i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7584.74i | − | 1.12919i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 5565.61 | − | 3959.80i | 0.814815 | − | 0.579721i | ||||
\(361\) | 6859.00 | 1.00000 | ||||||||
\(362\) | 3049.04i | 0.442691i | ||||||||
\(363\) | −2104.50 | − | 6588.11i | −0.304290 | − | 0.952579i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13328.0 | + | 4257.47i | −1.90346 | + | 0.608037i | ||||
\(367\) | 3450.04 | 0.490711 | 0.245355 | − | 0.969433i | \(-0.421095\pi\) | ||||
0.245355 | + | 0.969433i | \(0.421095\pi\) | |||||||
\(368\) | − | 6064.15i | − | 0.859010i | ||||||
\(369\) | 7210.00 | + | 10133.9i | 1.01718 | + | 1.42967i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6917.48 | − | 2209.71i | 0.952579 | − | 0.304290i | ||||
\(376\) | 9632.00 | 1.32110 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8278.84 | + | 11045.0i | −1.12650 | + | 1.50289i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3815.00 | − | 11942.8i | −0.512988 | − | 1.60591i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11473.5i | − | 1.53073i | −0.643597 | − | 0.765365i | \(-0.722559\pi\) | ||
0.643597 | − | 0.765365i | \(-0.277441\pi\) | |||||||
\(384\) | −7168.00 | + | 2289.73i | −0.952579 | + | 0.304290i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8278.84 | + | 5890.20i | −1.08743 | + | 0.773684i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5854.03i | − | 0.763010i | −0.924367 | − | 0.381505i | \(-0.875406\pi\) | ||
0.924367 | − | 0.381505i | \(-0.124594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 19618.0i | 2.52770i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8000.00 | −1.00000 | ||||||||
\(401\) | − | 2754.84i | − | 0.343067i | −0.985178 | − | 0.171534i | \(-0.945128\pi\) | ||
0.985178 | − | 0.171534i | \(-0.0548722\pi\) | |||||||
\(402\) | 10846.6 | − | 3464.82i | 1.34572 | − | 0.429875i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 15956.6i | − | 1.96502i | ||||||
\(405\) | 7700.00 | + | 2672.10i | 0.944731 | + | 0.327846i | ||||
\(406\) | 6160.00 | 0.752994 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4844.00 | 0.585624 | 0.292812 | − | 0.956170i | \(-0.405409\pi\) | ||||
0.292812 | + | 0.956170i | \(0.405409\pi\) | |||||||
\(410\) | − | 14566.4i | − | 1.75459i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7462.98 | 0.892414 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5896.00 | − | 4194.86i | 0.699934 | − | 0.497986i | ||||
\(415\) | −1217.48 | −0.144009 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 15400.0 | − | 4919.35i | 1.78915 | − | 0.571523i | ||||
\(421\) | −9592.00 | −1.11042 | −0.555208 | − | 0.831711i | \(-0.687362\pi\) | ||||
−0.555208 | + | 0.831711i | \(0.687362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6662.92 | + | 9364.92i | 0.765868 | + | 1.07645i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33115.4 | −3.75308 | ||||||||
\(428\) | − | 2500.33i | − | 0.282378i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11900.0 | 1.33458 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −7184.69 | − | 5385.33i | −0.800171 | − | 0.599772i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1106.80 | − | 3464.82i | −0.121993 | − | 0.381898i | ||||
\(436\) | −9088.00 | −0.998248 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19074.0 | + | 13570.7i | −2.05960 | + | 1.46536i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14477.3i | − | 1.55268i | −0.630314 | − | 0.776340i | \(-0.717074\pi\) | ||
0.630314 | − | 0.776340i | \(-0.282926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10600.0 | −1.12919 | ||||||||
\(446\) | − | 5894.28i | − | 0.625789i | ||||||
\(447\) | 9452.05 | − | 3019.35i | 1.00015 | − | 0.319486i | ||||
\(448\) | −17809.9 | −1.87822 | ||||||||
\(449\) | 18939.5i | 1.99067i | 0.0964880 | + | 0.995334i | \(0.469239\pi\) | ||||
−0.0964880 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(450\) | −5533.99 | − | 7778.17i | −0.579721 | − | 0.814815i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16324.0 | −1.68750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 19442.6i | 1.98361i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8474.90 | −0.859010 | ||||||||
\(461\) | 11654.4i | 1.17744i | 0.808338 | + | 0.588719i | \(0.200368\pi\) | ||||
−0.808338 | + | 0.588719i | \(0.799632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12374.0 | −1.24205 | −0.621024 | − | 0.783792i | \(-0.713283\pi\) | ||||
−0.621024 | + | 0.783792i | \(0.713283\pi\) | |||||||
\(464\) | 4007.03i | 0.400909i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11156.7i | 1.10551i | 0.833345 | + | 0.552754i | \(0.186423\pi\) | ||||
−0.833345 | + | 0.552754i | \(0.813577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26950.0 | 2.65338 | ||||||||
\(470\) | − | 13461.1i | − | 1.32110i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 3200.00 | + | 10017.6i | 0.304290 | + | 0.952579i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4830.95i | 0.456523i | ||||||||
\(483\) | 16314.2 | − | 5211.38i | 1.53690 | − | 0.490944i | ||||
\(484\) | 10648.0 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 266.000 | − | 10710.8i | 0.0248272 | − | 0.999692i | ||||
\(487\) | 21494.0 | 1.99997 | 0.999986 | − | 0.00532938i | \(-0.00169640\pi\) | ||||
0.999986 | + | 0.00532938i | \(0.00169640\pi\) | |||||||
\(488\) | − | 21541.3i | − | 1.99821i | ||||||
\(489\) | −35.0000 | − | 109.567i | −0.00323672 | − | 0.0101325i | ||||
\(490\) | 27416.9 | 2.52770 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −18240.0 | + | 5826.56i | −1.67139 | + | 0.533906i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 486.991 | + | 1524.52i | 0.0438204 | + | 0.137180i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 11180.3i | 1.00000i | ||||||||
\(501\) | 9163.00 | − | 2927.01i | 0.817111 | − | 0.261017i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18106.2i | 1.60500i | 0.596653 | + | 0.802499i | \(0.296497\pi\) | ||||
−0.596653 | + | 0.802499i | \(0.703503\pi\) | |||||||
\(504\) | −12320.0 | − | 17316.1i | −1.08884 | − | 1.53040i | ||||
\(505\) | −22300.0 | −1.96502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3473.76 | + | 10874.6i | 0.304290 | + | 0.952579i | ||||
\(508\) | 19302.5 | 1.68585 | ||||||||
\(509\) | 21153.2i | 1.84204i | 0.389513 | + | 0.921021i | \(0.372643\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11585.2i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 10429.8i | − | 0.892414i | ||||||
\(516\) | −4760.00 | − | 14901.2i | −0.406099 | − | 1.27129i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22235.5i | − | 1.86978i | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||
0.354943 | − | 0.934888i | \(-0.384500\pi\) | |||||||
\(522\) | −3895.93 | + | 2771.86i | −0.326667 | + | 0.232416i | ||||
\(523\) | −12487.8 | −1.04408 | −0.522041 | − | 0.852920i | \(-0.674829\pi\) | ||||
−0.522041 | + | 0.852920i | \(0.674829\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6875.00 | − | 21522.2i | −0.571523 | − | 1.78915i | ||||
\(526\) | 24068.0 | 1.99508 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3189.00 | 0.262102 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4240.00 | + | 13273.3i | 0.343601 | + | 1.07564i | ||||
\(535\) | −3494.32 | −0.282378 | ||||||||
\(536\) | 17530.8i | 1.41271i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19416.4 | 1.55595 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7526.22 | + | 10040.9i | −0.599772 | + | 0.800171i | ||||
\(541\) | −6802.00 | −0.540556 | −0.270278 | − | 0.962782i | \(-0.587116\pi\) | ||||
−0.270278 | + | 0.962782i | \(0.587116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1704.47 | − | 5335.83i | −0.134707 | − | 0.421699i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12700.9i | 0.998248i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5157.67 | 0.403156 | 0.201578 | − | 0.979472i | \(-0.435393\pi\) | ||||
0.201578 | + | 0.979472i | \(0.435393\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20944.0 | − | 14901.2i | 1.62818 | − | 1.15841i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3389.96 | + | 10612.3i | 0.261388 | + | 0.818275i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24890.2i | 1.87822i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12130.5 | 0.910488 | ||||||||
\(563\) | − | 2385.78i | − | 0.178594i | −0.996005 | − | 0.0892971i | \(-0.971538\pi\) | ||
0.996005 | − | 0.0892971i | \(-0.0284621\pi\) | |||||||
\(564\) | −16856.0 | + | 5384.45i | −1.25845 | + | 0.401997i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26788.1i | 1.98938i | ||||||||
\(567\) | 8313.63 | − | 23956.8i | 0.615766 | − | 1.77441i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22758.7i | − | 1.67679i | −0.545062 | − | 0.838396i | \(-0.683494\pi\) | ||
0.545062 | − | 0.838396i | \(-0.316506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −45320.0 | −3.29551 | ||||||||
\(575\) | 11844.0i | 0.859010i | ||||||||
\(576\) | 11264.0 | − | 8014.07i | 0.814815 | − | 0.579721i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 13896.1i | 1.00000i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5600.00 | 0.400909 | ||||||||
\(581\) | 3787.90i | 0.270479i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16462.9i | − | 1.15757i | −0.815479 | − | 0.578786i | \(-0.803527\pi\) | ||
0.815479 | − | 0.578786i | \(-0.196473\pi\) | |||||||
\(588\) | −10966.8 | − | 34331.4i | −0.769154 | − | 2.40783i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15276.8i | 1.04994i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 14000.0 | − | 4472.14i | 0.952579 | − | 0.304290i | ||||
\(601\) | 28532.0 | 1.93651 | 0.968257 | − | 0.249958i | \(-0.0804168\pi\) | ||||
0.968257 | + | 0.249958i | \(0.0804168\pi\) | |||||||
\(602\) | − | 37024.1i | − | 2.50663i | ||||||
\(603\) | −17044.7 | + | 12126.9i | −1.15110 | + | 0.818980i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 14881.0i | − | 1.00000i | ||||||
\(606\) | 8920.00 | + | 27924.0i | 0.597938 | + | 1.87184i | ||||
\(607\) | −24839.7 | −1.66098 | −0.830488 | − | 0.557037i | \(-0.811938\pi\) | ||||
−0.830488 | + | 0.557037i | \(0.811938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10780.0 | + | 3443.54i | −0.717287 | + | 0.229129i | ||||
\(610\) | −30104.9 | −1.99821 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | − | 28433.8i | − | 1.86889i | ||||||
\(615\) | 8142.86 | + | 25491.2i | 0.533906 | + | 1.67139i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | −13060.2 | + | 4171.93i | −0.850095 | + | 0.271553i | ||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7973.00 | + | 10637.0i | −0.515210 | + | 0.687354i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32979.5i | 2.12086i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −24200.0 | + | 17217.7i | −1.53040 | + | 1.08884i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 26976.1i | − | 1.68585i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16190.9 | −1.00000 | ||||||||
\(641\) | − | 24449.2i | − | 1.50653i | −0.657719 | − | 0.753264i | \(-0.728478\pi\) | ||
0.657719 | − | 0.753264i | \(-0.271522\pi\) | |||||||
\(642\) | 1397.73 | + | 4375.58i | 0.0859250 | + | 0.268988i | ||||
\(643\) | 9825.20 | 0.602594 | 0.301297 | − | 0.953530i | \(-0.402580\pi\) | ||||
0.301297 | + | 0.953530i | \(0.402580\pi\) | |||||||
\(644\) | 26367.7i | 1.61341i | ||||||||
\(645\) | −20825.0 | + | 6652.30i | −1.27129 | + | 0.406099i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 29470.8i | − | 1.79075i | −0.445311 | − | 0.895376i | \(-0.646907\pi\) | ||
0.445311 | − | 0.895376i | \(-0.353093\pi\) | |||||||
\(648\) | 15583.7 | + | 5407.95i | 0.944731 | + | 0.327846i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 177.088 | 0.0106369 | ||||||||
\(653\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(654\) | 15904.0 | − | 5080.35i | 0.950911 | − | 0.303757i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 29480.3i | − | 1.75459i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −41881.2 | −2.48131 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30688.0 | −1.80579 | −0.902893 | − | 0.429865i | \(-0.858561\pi\) | ||||
−0.902893 | + | 0.429865i | \(0.858561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2464.00 | −0.144009 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5932.43 | 0.344385 | ||||||||
\(668\) | 14809.6i | 0.857788i | ||||||||
\(669\) | 3295.00 | + | 10315.0i | 0.190422 | + | 0.596114i | ||||
\(670\) | 24500.0 | 1.41271 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 31167.4 | − | 9956.06i | 1.78915 | − | 0.571523i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14032.6 | + | 10518.2i | 0.800171 | + | 0.599772i | ||||
\(676\) | −17576.0 | −1.00000 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28567.0 | − | 9125.39i | 1.60747 | − | 0.513489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5567.76i | − | 0.311924i | −0.987763 | − | 0.155962i | \(-0.950152\pi\) | ||
0.987763 | − | 0.155962i | \(-0.0498478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 51554.8i | − | 2.86935i | ||||||
\(687\) | −10868.7 | − | 34024.6i | −0.603593 | − | 1.88955i | ||||
\(688\) | 24083.9 | 1.33458 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 14831.1 | − | 4737.62i | 0.818275 | − | 0.261388i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31484.0 | 1.72207 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2240.00 | − | 7012.31i | −0.121993 | − | 0.381898i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 27283.0i | 1.47948i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 34785.1 | 1.87822 | ||||||||
\(701\) | 35844.2i | 1.93126i | 0.259914 | + | 0.965632i | \(0.416306\pi\) | ||||
−0.259914 | + | 0.965632i | \(0.583694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7525.00 | + | 23557.0i | 0.401997 | + | 1.25845i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69381.3i | 3.69074i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 506.000 | 0.0268029 | 0.0134014 | − | 0.999910i | \(-0.495734\pi\) | ||||
0.0134014 | + | 0.999910i | \(0.495734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21452.9 | −1.12919 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −11200.0 | − | 15741.9i | −0.579721 | − | 0.814815i | ||||
\(721\) | −32450.0 | −1.67615 | ||||||||
\(722\) | − | 19400.2i | − | 1.00000i | ||||||
\(723\) | −2700.59 | − | 8454.17i | −0.138915 | − | 0.434874i | ||||
\(724\) | 8624.00 | 0.442691 | ||||||||
\(725\) | − | 7826.24i | − | 0.400909i | ||||||
\(726\) | −18634.0 | + | 5952.41i | −0.952579 | + | 0.304290i | ||||
\(727\) | 38114.9 | 1.94444 | 0.972218 | − | 0.234078i | \(-0.0752072\pi\) | ||||
0.972218 | + | 0.234078i | \(0.0752072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5522.00 | + | 18892.5i | 0.280547 | + | 0.959840i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 12042.0 | + | 37697.3i | 0.608037 | + | 1.90346i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | − | 9758.20i | − | 0.490711i | ||||||
\(735\) | −47979.7 | + | 15326.5i | −2.40783 | + | 0.769154i | ||||
\(736\) | −17152.0 | −0.859010 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 28662.9 | − | 20393.0i | 1.42967 | − | 1.01718i | ||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40493.2i | − | 1.99940i | −0.0245922 | − | 0.999698i | \(-0.507829\pi\) | ||
0.0245922 | − | 0.999698i | \(-0.492171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21350.0 | 1.04994 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1704.47 | − | 2395.68i | −0.0834849 | − | 0.117340i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10871.8i | 0.530368i | ||||||||
\(750\) | −6250.00 | − | 19565.6i | −0.304290 | − | 0.952579i | ||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | − | 27243.4i | − | 1.32110i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 31240.0 | + | 23416.1i | 1.50289 | + | 1.12650i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35884.4i | 1.70934i | 0.519170 | + | 0.854671i | \(0.326241\pi\) | ||||
−0.519170 | + | 0.854671i | \(0.673759\pi\) | |||||||
\(762\) | −33779.4 | + | 10790.4i | −1.60591 | + | 0.512988i | ||||
\(763\) | 39515.8 | 1.87493 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32452.0 | −1.53073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6476.34 | + | 20274.2i | 0.304290 | + | 0.952579i | ||||
\(769\) | −29554.0 | −1.38588 | −0.692942 | − | 0.720994i | \(-0.743686\pi\) | ||||
−0.692942 | + | 0.720994i | \(0.743686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 16660.0 | + | 23416.1i | 0.773684 | + | 1.08743i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16557.7 | −0.763010 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5268.35 | − | 7028.64i | 0.240454 | − | 0.320796i | ||||
\(784\) | 55488.0 | 2.52770 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27584.5 | 1.24941 | 0.624703 | − | 0.780862i | \(-0.285220\pi\) | ||||
0.624703 | + | 0.780862i | \(0.285220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42119.0 | + | 13454.4i | −1.90048 | + | 0.607085i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 22627.4i | 1.00000i | ||||||||
\(801\) | −14840.0 | − | 20858.0i | −0.654614 | − | 0.920078i | ||||
\(802\) | −7791.85 | −0.343067 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −9800.00 | − | 30678.9i | −0.429875 | − | 1.34572i | ||||
\(805\) | 36850.0 | 1.61341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33978.7 | + | 10854.1i | −1.48216 | + | 0.473460i | ||||
\(808\) | −45132.0 | −1.96502 | ||||||||
\(809\) | − | 37691.2i | − | 1.63801i | −0.573786 | − | 0.819005i | \(-0.694526\pi\) | ||
0.573786 | − | 0.819005i | \(-0.305474\pi\) | |||||||
\(810\) | 7557.84 | − | 21778.9i | 0.327846 | − | 0.944731i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | − | 17423.1i | − | 0.752994i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 247.487i | − | 0.0106369i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 13700.9i | − | 0.585624i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −41200.0 | −1.75459 | ||||||||
\(821\) | − | 46425.2i | − | 1.97351i | −0.162216 | − | 0.986755i | \(-0.551864\pi\) | ||
0.162216 | − | 0.986755i | \(-0.448136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35085.5 | −1.48603 | −0.743015 | − | 0.669275i | \(-0.766605\pi\) | ||||
−0.743015 | + | 0.669275i | \(0.766605\pi\) | |||||||
\(824\) | − | 21108.5i | − | 0.892414i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46285.8i | 1.94621i | 0.230364 | + | 0.973104i | \(0.426008\pi\) | ||||
−0.230364 | + | 0.973104i | \(0.573992\pi\) | |||||||
\(828\) | −11864.9 | − | 16676.4i | −0.497986 | − | 0.699934i | ||||
\(829\) | 36344.0 | 1.52265 | 0.761326 | − | 0.648369i | \(-0.224548\pi\) | ||||
0.761326 | + | 0.648369i | \(0.224548\pi\) | |||||||
\(830\) | 3443.54i | 0.144009i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20697.1 | 0.857788 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −13914.0 | − | 43557.8i | −0.571523 | − | 1.78915i | ||||
\(841\) | 20469.0 | 0.839272 | ||||||||
\(842\) | 27130.3i | 1.11042i | ||||||||
\(843\) | −21228.4 | + | 6781.15i | −0.867312 | + | 0.277053i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24563.2i | 1.00000i | ||||||||
\(846\) | 26488.0 | − | 18845.6i | 1.07645 | − | 0.765868i | ||||
\(847\) | −46298.9 | −1.87822 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14975.0 | − | 46879.2i | −0.605348 | − | 1.89504i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 93664.4i | 3.75308i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7072.00 | −0.282378 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | − | 33658.3i | − | 1.33458i | ||||||
\(861\) | 79310.0 | − | 25334.7i | 3.13923 | − | 1.00279i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44820.7i | − | 1.76792i | −0.467564 | − | 0.883959i | \(-0.654868\pi\) | ||
0.467564 | − | 0.883959i | \(-0.345132\pi\) | |||||||
\(864\) | −15232.0 | + | 20321.4i | −0.599772 | + | 0.800171i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7768.14 | − | 24318.1i | −0.304290 | − | 0.952579i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9800.00 | + | 3130.50i | −0.381898 | + | 0.121993i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 25704.7i | 0.998248i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 48613.6i | − | 1.87822i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42847.5i | 1.63856i | 0.573395 | + | 0.819279i | \(0.305626\pi\) | ||||
−0.573395 | + | 0.819279i | \(0.694374\pi\) | |||||||
\(882\) | 38383.7 | + | 53949.4i | 1.46536 | + | 2.05960i | ||||
\(883\) | 47791.5 | 1.82142 | 0.910709 | − | 0.413049i | \(-0.135536\pi\) | ||||
0.910709 | + | 0.413049i | \(0.135536\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40948.0 | −1.55268 | ||||||||
\(887\) | 4029.09i | 0.152518i | 0.997088 | + | 0.0762592i | \(0.0242976\pi\) | ||||
−0.997088 | + | 0.0762592i | \(0.975702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −83930.0 | −3.16639 | ||||||||
\(890\) | 29981.3i | 1.12919i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16671.5 | −0.625789 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −8540.00 | − | 26734.4i | −0.319486 | − | 1.00015i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50374.1i | 1.87822i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 53569.0 | 1.99067 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −22000.0 | + | 15652.5i | −0.814815 | + | 0.579721i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20697.1 | + | 64792.2i | 0.762743 | + | 2.38776i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12052.4i | − | 0.442691i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53414.0 | −1.95544 | −0.977720 | − | 0.209914i | \(-0.932682\pi\) | ||||
−0.977720 | + | 0.209914i | \(0.932682\pi\) | |||||||
\(908\) | 46171.2i | 1.68750i | ||||||||
\(909\) | −31220.0 | − | 43880.6i | −1.13917 | − | 1.60113i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 52683.5 | − | 16829.1i | 1.90346 | − | 0.608037i | ||||
\(916\) | 54992.0 | 1.98361 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 23970.6i | 0.859010i | ||||||||
\(921\) | 15895.0 | + | 49759.2i | 0.568684 | + | 1.78026i | ||||
\(922\) | 32963.6 | 1.17744 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34998.9i | 1.24205i | ||||||||
\(927\) | 20523.2 | − | 14601.8i | 0.727152 | − | 0.517351i | ||||
\(928\) | 11333.6 | 0.400909 | ||||||||
\(929\) | 18054.0i | 0.637603i | 0.947822 | + | 0.318801i | \(0.103280\pi\) | ||||
−0.947822 | + | 0.318801i | \(0.896720\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31556.0 | 1.10551 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | − | 76226.1i | − | 2.65338i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −38073.8 | −1.32110 | ||||||||
\(941\) | − | 36805.7i | − | 1.27506i | −0.770426 | − | 0.637530i | \(-0.779956\pi\) | ||
0.770426 | − | 0.637530i | \(-0.220044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43645.8 | −1.50721 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32725.0 | − | 43659.2i | 1.12650 | − | 1.50289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52115.2i | 1.78830i | 0.447772 | + | 0.894148i | \(0.352218\pi\) | ||||
−0.447772 | + | 0.894148i | \(0.647782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 28334.0 | − | 9050.97i | 0.952579 | − | 0.304290i | ||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4892.04 | − | 6875.91i | −0.163701 | − | 0.230086i | ||||
\(964\) | 13664.0 | 0.456523 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14740.0 | − | 46143.5i | −0.490944 | − | 1.53690i | ||||
\(967\) | 49783.7 | 1.65557 | 0.827785 | − | 0.561045i | \(-0.189600\pi\) | ||||
0.827785 | + | 0.561045i | \(0.189600\pi\) | |||||||
\(968\) | − | 30117.1i | − | 1.00000i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −30294.6 | − | 752.362i | −0.999692 | − | 0.0248272i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 60794.2i | − | 1.99997i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60928.0 | −1.99821 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | −309.903 | + | 98.9949i | −0.0101325 | + | 0.00323672i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 77546.8i | − | 2.52770i | ||||||
\(981\) | −24992.0 | + | 17781.2i | −0.813388 | + | 0.578706i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51962.4i | 1.68601i | 0.537908 | + | 0.843003i | \(0.319215\pi\) | ||||
−0.537908 | + | 0.843003i | \(0.680785\pi\) | |||||||
\(984\) | 16480.0 | + | 51590.6i | 0.533906 | + | 1.67139i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 73292.1 | − | 23412.3i | 2.36364 | − | 0.755037i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 35656.3i | − | 1.14642i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4312.00 | − | 1377.42i | 0.137180 | − | 0.0438204i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 60.4.h.a.59.2 | yes | 4 | |
3.2 | odd | 2 | inner | 60.4.h.a.59.4 | yes | 4 | |
4.3 | odd | 2 | inner | 60.4.h.a.59.3 | yes | 4 | |
5.4 | even | 2 | inner | 60.4.h.a.59.3 | yes | 4 | |
12.11 | even | 2 | inner | 60.4.h.a.59.1 | ✓ | 4 | |
15.14 | odd | 2 | inner | 60.4.h.a.59.1 | ✓ | 4 | |
20.19 | odd | 2 | CM | 60.4.h.a.59.2 | yes | 4 | |
60.59 | even | 2 | inner | 60.4.h.a.59.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.h.a.59.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
60.4.h.a.59.1 | ✓ | 4 | 15.14 | odd | 2 | inner | |
60.4.h.a.59.2 | yes | 4 | 1.1 | even | 1 | trivial | |
60.4.h.a.59.2 | yes | 4 | 20.19 | odd | 2 | CM | |
60.4.h.a.59.3 | yes | 4 | 4.3 | odd | 2 | inner | |
60.4.h.a.59.3 | yes | 4 | 5.4 | even | 2 | inner | |
60.4.h.a.59.4 | yes | 4 | 3.2 | odd | 2 | inner | |
60.4.h.a.59.4 | yes | 4 | 60.59 | even | 2 | inner |