Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,4,Mod(1,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.4979225328\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8184789.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 76x^{2} - 8x + 1048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-4.69357\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.70156 | 1.30870 | 0.654350 | − | 0.756192i | \(-0.272942\pi\) | ||||
0.654350 | + | 0.756192i | \(0.272942\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 5.70156 | 0.712695 | ||||||||
\(5\) | −5.05515 | −0.452146 | −0.226073 | − | 0.974110i | \(-0.572589\pi\) | ||||
−0.226073 | + | 0.974110i | \(0.572589\pi\) | |||||||
\(6\) | 11.1047 | 0.755578 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.50781 | −0.375996 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −18.7119 | −0.591724 | ||||||||
\(11\) | −31.4918 | −0.863195 | −0.431597 | − | 0.902066i | \(-0.642050\pi\) | ||||
−0.431597 | + | 0.902066i | \(0.642050\pi\) | |||||||
\(12\) | 17.1047 | 0.411475 | ||||||||
\(13\) | −59.0383 | −1.25956 | −0.629780 | − | 0.776773i | \(-0.716855\pi\) | ||||
−0.629780 | + | 0.776773i | \(0.716855\pi\) | |||||||
\(14\) | −25.9109 | −0.494642 | ||||||||
\(15\) | −15.1654 | −0.261047 | ||||||||
\(16\) | −77.1047 | −1.20476 | ||||||||
\(17\) | −116.499 | −1.66207 | −0.831037 | − | 0.556217i | \(-0.812252\pi\) | ||||
−0.831037 | + | 0.556217i | \(0.812252\pi\) | |||||||
\(18\) | 33.3141 | 0.436233 | ||||||||
\(19\) | 122.463 | 1.47868 | 0.739338 | − | 0.673334i | \(-0.235138\pi\) | ||||
0.739338 | + | 0.673334i | \(0.235138\pi\) | |||||||
\(20\) | −28.8222 | −0.322242 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −116.569 | −1.12966 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −25.5234 | −0.217081 | ||||||||
\(25\) | −99.4455 | −0.795564 | ||||||||
\(26\) | −218.534 | −1.64839 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −39.9109 | −0.269373 | ||||||||
\(29\) | 163.645 | 1.04787 | 0.523934 | − | 0.851759i | \(-0.324464\pi\) | ||||
0.523934 | + | 0.851759i | \(0.324464\pi\) | |||||||
\(30\) | −56.1358 | −0.341632 | ||||||||
\(31\) | 48.4738 | 0.280844 | 0.140422 | − | 0.990092i | \(-0.455154\pi\) | ||||
0.140422 | + | 0.990092i | \(0.455154\pi\) | |||||||
\(32\) | −217.345 | −1.20067 | ||||||||
\(33\) | −94.4755 | −0.498366 | ||||||||
\(34\) | −431.230 | −2.17516 | ||||||||
\(35\) | 35.3860 | 0.170895 | ||||||||
\(36\) | 51.3141 | 0.237565 | ||||||||
\(37\) | 405.482 | 1.80165 | 0.900823 | − | 0.434187i | \(-0.142964\pi\) | ||||
0.900823 | + | 0.434187i | \(0.142964\pi\) | |||||||
\(38\) | 453.303 | 1.93514 | ||||||||
\(39\) | −177.115 | −0.727208 | ||||||||
\(40\) | 43.0082 | 0.170005 | ||||||||
\(41\) | 62.7416 | 0.238990 | 0.119495 | − | 0.992835i | \(-0.461872\pi\) | ||||
0.119495 | + | 0.992835i | \(0.461872\pi\) | |||||||
\(42\) | −77.7328 | −0.285582 | ||||||||
\(43\) | −376.756 | −1.33616 | −0.668079 | − | 0.744090i | \(-0.732883\pi\) | ||||
−0.668079 | + | 0.744090i | \(0.732883\pi\) | |||||||
\(44\) | −179.553 | −0.615195 | ||||||||
\(45\) | −45.4963 | −0.150715 | ||||||||
\(46\) | −85.1359 | −0.272883 | ||||||||
\(47\) | −277.109 | −0.860011 | −0.430006 | − | 0.902826i | \(-0.641488\pi\) | ||||
−0.430006 | + | 0.902826i | \(0.641488\pi\) | |||||||
\(48\) | −231.314 | −0.695569 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −368.104 | −1.04115 | ||||||||
\(51\) | −349.498 | −0.959599 | ||||||||
\(52\) | −336.611 | −0.897683 | ||||||||
\(53\) | −478.867 | −1.24108 | −0.620542 | − | 0.784174i | \(-0.713087\pi\) | ||||
−0.620542 | + | 0.784174i | \(0.713087\pi\) | |||||||
\(54\) | 99.9422 | 0.251859 | ||||||||
\(55\) | 159.196 | 0.390290 | ||||||||
\(56\) | 59.5547 | 0.142113 | ||||||||
\(57\) | 367.388 | 0.853714 | ||||||||
\(58\) | 605.743 | 1.37134 | ||||||||
\(59\) | −64.0099 | −0.141244 | −0.0706218 | − | 0.997503i | \(-0.522498\pi\) | ||||
−0.0706218 | + | 0.997503i | \(0.522498\pi\) | |||||||
\(60\) | −86.4667 | −0.186047 | ||||||||
\(61\) | 456.987 | 0.959199 | 0.479600 | − | 0.877487i | \(-0.340782\pi\) | ||||
0.479600 | + | 0.877487i | \(0.340782\pi\) | |||||||
\(62\) | 179.429 | 0.367540 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −187.680 | −0.366562 | ||||||||
\(65\) | 298.447 | 0.569505 | ||||||||
\(66\) | −349.707 | −0.652211 | ||||||||
\(67\) | 230.437 | 0.420184 | 0.210092 | − | 0.977682i | \(-0.432624\pi\) | ||||
0.210092 | + | 0.977682i | \(0.432624\pi\) | |||||||
\(68\) | −664.228 | −1.18455 | ||||||||
\(69\) | −69.0000 | −0.120386 | ||||||||
\(70\) | 130.984 | 0.223650 | ||||||||
\(71\) | −372.871 | −0.623263 | −0.311631 | − | 0.950203i | \(-0.600875\pi\) | ||||
−0.311631 | + | 0.950203i | \(0.600875\pi\) | |||||||
\(72\) | −76.5703 | −0.125332 | ||||||||
\(73\) | −1163.37 | −1.86523 | −0.932615 | − | 0.360873i | \(-0.882479\pi\) | ||||
−0.932615 | + | 0.360873i | \(0.882479\pi\) | |||||||
\(74\) | 1500.92 | 2.35781 | ||||||||
\(75\) | −298.336 | −0.459319 | ||||||||
\(76\) | 698.228 | 1.05385 | ||||||||
\(77\) | 220.443 | 0.326257 | ||||||||
\(78\) | −655.602 | −0.951696 | ||||||||
\(79\) | −794.417 | −1.13138 | −0.565689 | − | 0.824618i | \(-0.691390\pi\) | ||||
−0.565689 | + | 0.824618i | \(0.691390\pi\) | |||||||
\(80\) | 389.776 | 0.544728 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 232.242 | 0.312766 | ||||||||
\(83\) | 579.797 | 0.766759 | 0.383380 | − | 0.923591i | \(-0.374760\pi\) | ||||
0.383380 | + | 0.923591i | \(0.374760\pi\) | |||||||
\(84\) | −119.733 | −0.155523 | ||||||||
\(85\) | 588.922 | 0.751500 | ||||||||
\(86\) | −1394.59 | −1.74863 | ||||||||
\(87\) | 490.936 | 0.604986 | ||||||||
\(88\) | 267.926 | 0.324557 | ||||||||
\(89\) | 983.546 | 1.17141 | 0.585706 | − | 0.810524i | \(-0.300817\pi\) | ||||
0.585706 | + | 0.810524i | \(0.300817\pi\) | |||||||
\(90\) | −168.407 | −0.197241 | ||||||||
\(91\) | 413.268 | 0.476069 | ||||||||
\(92\) | −131.136 | −0.148607 | ||||||||
\(93\) | 145.421 | 0.162145 | ||||||||
\(94\) | −1025.74 | −1.12550 | ||||||||
\(95\) | −619.067 | −0.668578 | ||||||||
\(96\) | −652.036 | −0.693210 | ||||||||
\(97\) | 1384.16 | 1.44887 | 0.724433 | − | 0.689346i | \(-0.242102\pi\) | ||||
0.724433 | + | 0.689346i | \(0.242102\pi\) | |||||||
\(98\) | 181.377 | 0.186957 | ||||||||
\(99\) | −283.426 | −0.287732 | ||||||||
\(100\) | −566.995 | −0.566995 | ||||||||
\(101\) | 177.049 | 0.174426 | 0.0872129 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872129 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(102\) | −1293.69 | −1.25583 | ||||||||
\(103\) | −1455.52 | −1.39239 | −0.696196 | − | 0.717852i | \(-0.745125\pi\) | ||||
−0.696196 | + | 0.717852i | \(0.745125\pi\) | |||||||
\(104\) | 502.287 | 0.473589 | ||||||||
\(105\) | 106.158 | 0.0986664 | ||||||||
\(106\) | −1772.56 | −1.62421 | ||||||||
\(107\) | −329.580 | −0.297773 | −0.148886 | − | 0.988854i | \(-0.547569\pi\) | ||||
−0.148886 | + | 0.988854i | \(0.547569\pi\) | |||||||
\(108\) | 153.942 | 0.137158 | ||||||||
\(109\) | 1486.26 | 1.30603 | 0.653016 | − | 0.757344i | \(-0.273503\pi\) | ||||
0.653016 | + | 0.757344i | \(0.273503\pi\) | |||||||
\(110\) | 589.273 | 0.510773 | ||||||||
\(111\) | 1216.45 | 1.04018 | ||||||||
\(112\) | 539.733 | 0.455357 | ||||||||
\(113\) | −1465.24 | −1.21981 | −0.609903 | − | 0.792476i | \(-0.708792\pi\) | ||||
−0.609903 | + | 0.792476i | \(0.708792\pi\) | |||||||
\(114\) | 1359.91 | 1.11726 | ||||||||
\(115\) | 116.268 | 0.0942790 | ||||||||
\(116\) | 933.033 | 0.746810 | ||||||||
\(117\) | −531.345 | −0.419853 | ||||||||
\(118\) | −236.936 | −0.184845 | ||||||||
\(119\) | 815.496 | 0.628205 | ||||||||
\(120\) | 129.025 | 0.0981524 | ||||||||
\(121\) | −339.265 | −0.254895 | ||||||||
\(122\) | 1691.57 | 1.25530 | ||||||||
\(123\) | 188.225 | 0.137981 | ||||||||
\(124\) | 276.376 | 0.200156 | ||||||||
\(125\) | 1134.60 | 0.811857 | ||||||||
\(126\) | −233.198 | −0.164881 | ||||||||
\(127\) | −305.856 | −0.213704 | −0.106852 | − | 0.994275i | \(-0.534077\pi\) | ||||
−0.106852 | + | 0.994275i | \(0.534077\pi\) | |||||||
\(128\) | 1044.05 | 0.720955 | ||||||||
\(129\) | −1130.27 | −0.771431 | ||||||||
\(130\) | 1104.72 | 0.745312 | ||||||||
\(131\) | −83.0214 | −0.0553711 | −0.0276856 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276856 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(132\) | −538.658 | −0.355183 | ||||||||
\(133\) | −857.239 | −0.558887 | ||||||||
\(134\) | 852.976 | 0.549895 | ||||||||
\(135\) | −136.489 | −0.0870156 | ||||||||
\(136\) | 991.155 | 0.624932 | ||||||||
\(137\) | −1055.46 | −0.658205 | −0.329103 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329103 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(138\) | −255.408 | −0.157549 | ||||||||
\(139\) | 1175.22 | 0.717128 | 0.358564 | − | 0.933505i | \(-0.383266\pi\) | ||||
0.358564 | + | 0.933505i | \(0.383266\pi\) | |||||||
\(140\) | 201.756 | 0.121796 | ||||||||
\(141\) | −831.328 | −0.496528 | ||||||||
\(142\) | −1380.21 | −0.815664 | ||||||||
\(143\) | 1859.22 | 1.08725 | ||||||||
\(144\) | −693.942 | −0.401587 | ||||||||
\(145\) | −827.250 | −0.473789 | ||||||||
\(146\) | −4306.27 | −2.44103 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 2311.88 | 1.28402 | ||||||||
\(149\) | 1729.41 | 0.950864 | 0.475432 | − | 0.879752i | \(-0.342292\pi\) | ||||
0.475432 | + | 0.879752i | \(0.342292\pi\) | |||||||
\(150\) | −1104.31 | −0.601111 | ||||||||
\(151\) | −378.487 | −0.203979 | −0.101990 | − | 0.994785i | \(-0.532521\pi\) | ||||
−0.101990 | + | 0.994785i | \(0.532521\pi\) | |||||||
\(152\) | −1041.89 | −0.555976 | ||||||||
\(153\) | −1048.49 | −0.554025 | ||||||||
\(154\) | 815.983 | 0.426972 | ||||||||
\(155\) | −245.042 | −0.126982 | ||||||||
\(156\) | −1009.83 | −0.518277 | ||||||||
\(157\) | −2853.73 | −1.45065 | −0.725325 | − | 0.688406i | \(-0.758311\pi\) | ||||
−0.725325 | + | 0.688406i | \(0.758311\pi\) | |||||||
\(158\) | −2940.58 | −1.48064 | ||||||||
\(159\) | −1436.60 | −0.716540 | ||||||||
\(160\) | 1098.71 | 0.542880 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 299.827 | 0.145411 | ||||||||
\(163\) | −617.784 | −0.296863 | −0.148431 | − | 0.988923i | \(-0.547422\pi\) | ||||
−0.148431 | + | 0.988923i | \(0.547422\pi\) | |||||||
\(164\) | 357.725 | 0.170327 | ||||||||
\(165\) | 477.587 | 0.225334 | ||||||||
\(166\) | 2146.16 | 1.00346 | ||||||||
\(167\) | 3609.26 | 1.67241 | 0.836207 | − | 0.548414i | \(-0.184768\pi\) | ||||
0.836207 | + | 0.548414i | \(0.184768\pi\) | |||||||
\(168\) | 178.664 | 0.0820490 | ||||||||
\(169\) | 1288.52 | 0.586492 | ||||||||
\(170\) | 2179.93 | 0.983488 | ||||||||
\(171\) | 1102.16 | 0.492892 | ||||||||
\(172\) | −2148.10 | −0.952273 | ||||||||
\(173\) | −2360.79 | −1.03750 | −0.518750 | − | 0.854926i | \(-0.673603\pi\) | ||||
−0.518750 | + | 0.854926i | \(0.673603\pi\) | |||||||
\(174\) | 1817.23 | 0.791746 | ||||||||
\(175\) | 696.118 | 0.300695 | ||||||||
\(176\) | 2428.17 | 1.03994 | ||||||||
\(177\) | −192.030 | −0.0815470 | ||||||||
\(178\) | 3640.66 | 1.53303 | ||||||||
\(179\) | −260.331 | −0.108704 | −0.0543522 | − | 0.998522i | \(-0.517309\pi\) | ||||
−0.0543522 | + | 0.998522i | \(0.517309\pi\) | |||||||
\(180\) | −259.400 | −0.107414 | ||||||||
\(181\) | 2786.16 | 1.14416 | 0.572082 | − | 0.820196i | \(-0.306136\pi\) | ||||
0.572082 | + | 0.820196i | \(0.306136\pi\) | |||||||
\(182\) | 1529.74 | 0.623032 | ||||||||
\(183\) | 1370.96 | 0.553794 | ||||||||
\(184\) | 195.680 | 0.0784005 | ||||||||
\(185\) | −2049.77 | −0.814607 | ||||||||
\(186\) | 538.286 | 0.212199 | ||||||||
\(187\) | 3668.78 | 1.43469 | ||||||||
\(188\) | −1579.96 | −0.612926 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −2291.51 | −0.874968 | ||||||||
\(191\) | −898.259 | −0.340292 | −0.170146 | − | 0.985419i | \(-0.554424\pi\) | ||||
−0.170146 | + | 0.985419i | \(0.554424\pi\) | |||||||
\(192\) | −563.039 | −0.211635 | ||||||||
\(193\) | −4200.40 | −1.56659 | −0.783294 | − | 0.621651i | \(-0.786462\pi\) | ||||
−0.783294 | + | 0.621651i | \(0.786462\pi\) | |||||||
\(194\) | 5123.55 | 1.89613 | ||||||||
\(195\) | 895.342 | 0.328804 | ||||||||
\(196\) | 279.377 | 0.101814 | ||||||||
\(197\) | −5068.61 | −1.83311 | −0.916557 | − | 0.399903i | \(-0.869044\pi\) | ||||
−0.916557 | + | 0.399903i | \(0.869044\pi\) | |||||||
\(198\) | −1049.12 | −0.376554 | ||||||||
\(199\) | −607.052 | −0.216245 | −0.108122 | − | 0.994138i | \(-0.534484\pi\) | ||||
−0.108122 | + | 0.994138i | \(0.534484\pi\) | |||||||
\(200\) | 846.063 | 0.299129 | ||||||||
\(201\) | 691.310 | 0.242593 | ||||||||
\(202\) | 655.357 | 0.228271 | ||||||||
\(203\) | −1145.52 | −0.396057 | ||||||||
\(204\) | −1992.69 | −0.683901 | ||||||||
\(205\) | −317.168 | −0.108058 | ||||||||
\(206\) | −5387.69 | −1.82222 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 4552.13 | 1.51747 | ||||||||
\(209\) | −3856.57 | −1.27639 | ||||||||
\(210\) | 392.951 | 0.129125 | ||||||||
\(211\) | −1114.86 | −0.363744 | −0.181872 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181872 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(212\) | −2730.29 | −0.884514 | ||||||||
\(213\) | −1118.61 | −0.359841 | ||||||||
\(214\) | −1219.96 | −0.389695 | ||||||||
\(215\) | 1904.56 | 0.604139 | ||||||||
\(216\) | −229.711 | −0.0723604 | ||||||||
\(217\) | −339.317 | −0.106149 | ||||||||
\(218\) | 5501.47 | 1.70920 | ||||||||
\(219\) | −3490.10 | −1.07689 | ||||||||
\(220\) | 907.665 | 0.278158 | ||||||||
\(221\) | 6877.93 | 2.09348 | ||||||||
\(222\) | 4502.75 | 1.36128 | ||||||||
\(223\) | −710.587 | −0.213383 | −0.106692 | − | 0.994292i | \(-0.534026\pi\) | ||||
−0.106692 | + | 0.994292i | \(0.534026\pi\) | |||||||
\(224\) | 1521.42 | 0.453812 | ||||||||
\(225\) | −895.009 | −0.265188 | ||||||||
\(226\) | −5423.68 | −1.59636 | ||||||||
\(227\) | 2095.70 | 0.612761 | 0.306380 | − | 0.951909i | \(-0.400882\pi\) | ||||
0.306380 | + | 0.951909i | \(0.400882\pi\) | |||||||
\(228\) | 2094.69 | 0.608438 | ||||||||
\(229\) | 5827.95 | 1.68176 | 0.840878 | − | 0.541225i | \(-0.182039\pi\) | ||||
0.840878 | + | 0.541225i | \(0.182039\pi\) | |||||||
\(230\) | 430.375 | 0.123383 | ||||||||
\(231\) | 661.328 | 0.188365 | ||||||||
\(232\) | −1392.26 | −0.393993 | ||||||||
\(233\) | 3397.06 | 0.955144 | 0.477572 | − | 0.878593i | \(-0.341517\pi\) | ||||
0.477572 | + | 0.878593i | \(0.341517\pi\) | |||||||
\(234\) | −1966.81 | −0.549462 | ||||||||
\(235\) | 1400.83 | 0.388851 | ||||||||
\(236\) | −364.956 | −0.100664 | ||||||||
\(237\) | −2383.25 | −0.653202 | ||||||||
\(238\) | 3018.61 | 0.822132 | ||||||||
\(239\) | −6151.78 | −1.66496 | −0.832480 | − | 0.554054i | \(-0.813080\pi\) | ||||
−0.832480 | + | 0.554054i | \(0.813080\pi\) | |||||||
\(240\) | 1169.33 | 0.314499 | ||||||||
\(241\) | 2792.09 | 0.746284 | 0.373142 | − | 0.927774i | \(-0.378280\pi\) | ||||
0.373142 | + | 0.927774i | \(0.378280\pi\) | |||||||
\(242\) | −1255.81 | −0.333581 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2605.54 | 0.683617 | ||||||||
\(245\) | −247.702 | −0.0645923 | ||||||||
\(246\) | 696.726 | 0.180576 | ||||||||
\(247\) | −7229.99 | −1.86248 | ||||||||
\(248\) | −412.406 | −0.105596 | ||||||||
\(249\) | 1739.39 | 0.442689 | ||||||||
\(250\) | 4199.81 | 1.06248 | ||||||||
\(251\) | −2264.50 | −0.569458 | −0.284729 | − | 0.958608i | \(-0.591904\pi\) | ||||
−0.284729 | + | 0.958608i | \(0.591904\pi\) | |||||||
\(252\) | −359.198 | −0.0897912 | ||||||||
\(253\) | 724.312 | 0.179989 | ||||||||
\(254\) | −1132.15 | −0.279674 | ||||||||
\(255\) | 1766.76 | 0.433879 | ||||||||
\(256\) | 5366.07 | 1.31008 | ||||||||
\(257\) | −5948.62 | −1.44383 | −0.721916 | − | 0.691981i | \(-0.756738\pi\) | ||||
−0.721916 | + | 0.691981i | \(0.756738\pi\) | |||||||
\(258\) | −4183.76 | −1.00957 | ||||||||
\(259\) | −2838.38 | −0.680958 | ||||||||
\(260\) | 1701.62 | 0.405884 | ||||||||
\(261\) | 1472.81 | 0.349289 | ||||||||
\(262\) | −307.309 | −0.0724642 | ||||||||
\(263\) | −6134.61 | −1.43831 | −0.719156 | − | 0.694848i | \(-0.755472\pi\) | ||||
−0.719156 | + | 0.694848i | \(0.755472\pi\) | |||||||
\(264\) | 803.779 | 0.187383 | ||||||||
\(265\) | 2420.74 | 0.561151 | ||||||||
\(266\) | −3173.12 | −0.731416 | ||||||||
\(267\) | 2950.64 | 0.676315 | ||||||||
\(268\) | 1313.85 | 0.299463 | ||||||||
\(269\) | −3089.28 | −0.700210 | −0.350105 | − | 0.936710i | \(-0.613854\pi\) | ||||
−0.350105 | + | 0.936710i | \(0.613854\pi\) | |||||||
\(270\) | −505.222 | −0.113877 | ||||||||
\(271\) | 4264.24 | 0.955846 | 0.477923 | − | 0.878402i | \(-0.341390\pi\) | ||||
0.477923 | + | 0.878402i | \(0.341390\pi\) | |||||||
\(272\) | 8982.65 | 2.00240 | ||||||||
\(273\) | 1239.80 | 0.274859 | ||||||||
\(274\) | −3906.85 | −0.861393 | ||||||||
\(275\) | 3131.72 | 0.686727 | ||||||||
\(276\) | −393.408 | −0.0857984 | ||||||||
\(277\) | 2445.88 | 0.530538 | 0.265269 | − | 0.964175i | \(-0.414539\pi\) | ||||
0.265269 | + | 0.964175i | \(0.414539\pi\) | |||||||
\(278\) | 4350.15 | 0.938505 | ||||||||
\(279\) | 436.264 | 0.0936145 | ||||||||
\(280\) | −301.058 | −0.0642558 | ||||||||
\(281\) | −6801.32 | −1.44389 | −0.721944 | − | 0.691951i | \(-0.756751\pi\) | ||||
−0.721944 | + | 0.691951i | \(0.756751\pi\) | |||||||
\(282\) | −3077.21 | −0.649806 | ||||||||
\(283\) | 8289.87 | 1.74128 | 0.870639 | − | 0.491922i | \(-0.163705\pi\) | ||||
0.870639 | + | 0.491922i | \(0.163705\pi\) | |||||||
\(284\) | −2125.95 | −0.444196 | ||||||||
\(285\) | −1857.20 | −0.386004 | ||||||||
\(286\) | 6882.03 | 1.42288 | ||||||||
\(287\) | −439.191 | −0.0903298 | ||||||||
\(288\) | −1956.11 | −0.400225 | ||||||||
\(289\) | 8659.11 | 1.76249 | ||||||||
\(290\) | −3062.12 | −0.620048 | ||||||||
\(291\) | 4152.47 | 0.836503 | ||||||||
\(292\) | −6633.01 | −1.32934 | ||||||||
\(293\) | 2479.89 | 0.494459 | 0.247229 | − | 0.968957i | \(-0.420480\pi\) | ||||
0.247229 | + | 0.968957i | \(0.420480\pi\) | |||||||
\(294\) | 544.130 | 0.107940 | ||||||||
\(295\) | 323.579 | 0.0638627 | ||||||||
\(296\) | −3449.77 | −0.677411 | ||||||||
\(297\) | −850.279 | −0.166122 | ||||||||
\(298\) | 6401.52 | 1.24440 | ||||||||
\(299\) | 1357.88 | 0.262636 | ||||||||
\(300\) | −1700.98 | −0.327355 | ||||||||
\(301\) | 2637.29 | 0.505020 | ||||||||
\(302\) | −1400.99 | −0.266948 | ||||||||
\(303\) | 531.146 | 0.100705 | ||||||||
\(304\) | −9442.44 | −1.78145 | ||||||||
\(305\) | −2310.14 | −0.433698 | ||||||||
\(306\) | −3881.07 | −0.725052 | ||||||||
\(307\) | −522.159 | −0.0970722 | −0.0485361 | − | 0.998821i | \(-0.515456\pi\) | ||||
−0.0485361 | + | 0.998821i | \(0.515456\pi\) | |||||||
\(308\) | 1256.87 | 0.232522 | ||||||||
\(309\) | −4366.55 | −0.803898 | ||||||||
\(310\) | −907.039 | −0.166182 | ||||||||
\(311\) | −2735.90 | −0.498838 | −0.249419 | − | 0.968396i | \(-0.580240\pi\) | ||||
−0.249419 | + | 0.968396i | \(0.580240\pi\) | |||||||
\(312\) | 1506.86 | 0.273427 | ||||||||
\(313\) | 6544.54 | 1.18185 | 0.590925 | − | 0.806726i | \(-0.298763\pi\) | ||||
0.590925 | + | 0.806726i | \(0.298763\pi\) | |||||||
\(314\) | −10563.2 | −1.89847 | ||||||||
\(315\) | 318.474 | 0.0569651 | ||||||||
\(316\) | −4529.42 | −0.806328 | ||||||||
\(317\) | −4130.52 | −0.731840 | −0.365920 | − | 0.930646i | \(-0.619246\pi\) | ||||
−0.365920 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(318\) | −5317.67 | −0.937735 | ||||||||
\(319\) | −5153.49 | −0.904513 | ||||||||
\(320\) | 948.748 | 0.165739 | ||||||||
\(321\) | −988.739 | −0.171919 | ||||||||
\(322\) | 595.952 | 0.103140 | ||||||||
\(323\) | −14266.8 | −2.45767 | ||||||||
\(324\) | 461.827 | 0.0791884 | ||||||||
\(325\) | 5871.09 | 1.00206 | ||||||||
\(326\) | −2286.77 | −0.388504 | ||||||||
\(327\) | 4458.77 | 0.754038 | ||||||||
\(328\) | −533.794 | −0.0898592 | ||||||||
\(329\) | 1939.76 | 0.325054 | ||||||||
\(330\) | 1767.82 | 0.294895 | ||||||||
\(331\) | 6616.50 | 1.09872 | 0.549359 | − | 0.835587i | \(-0.314872\pi\) | ||||
0.549359 | + | 0.835587i | \(0.314872\pi\) | |||||||
\(332\) | 3305.75 | 0.546466 | ||||||||
\(333\) | 3649.34 | 0.600549 | ||||||||
\(334\) | 13359.9 | 2.18869 | ||||||||
\(335\) | −1164.89 | −0.189984 | ||||||||
\(336\) | 1619.20 | 0.262900 | ||||||||
\(337\) | 4993.62 | 0.807180 | 0.403590 | − | 0.914940i | \(-0.367762\pi\) | ||||
0.403590 | + | 0.914940i | \(0.367762\pi\) | |||||||
\(338\) | 4769.55 | 0.767542 | ||||||||
\(339\) | −4395.72 | −0.704256 | ||||||||
\(340\) | 3357.77 | 0.535591 | ||||||||
\(341\) | −1526.53 | −0.242423 | ||||||||
\(342\) | 4079.73 | 0.645048 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 3205.37 | 0.502390 | ||||||||
\(345\) | 348.805 | 0.0544320 | ||||||||
\(346\) | −8738.61 | −1.35778 | ||||||||
\(347\) | −9965.27 | −1.54168 | −0.770841 | − | 0.637027i | \(-0.780164\pi\) | ||||
−0.770841 | + | 0.637027i | \(0.780164\pi\) | |||||||
\(348\) | 2799.10 | 0.431171 | ||||||||
\(349\) | −5902.15 | −0.905258 | −0.452629 | − | 0.891699i | \(-0.649514\pi\) | ||||
−0.452629 | + | 0.891699i | \(0.649514\pi\) | |||||||
\(350\) | 2576.73 | 0.393519 | ||||||||
\(351\) | −1594.03 | −0.242403 | ||||||||
\(352\) | 6844.60 | 1.03642 | ||||||||
\(353\) | 947.217 | 0.142820 | 0.0714098 | − | 0.997447i | \(-0.477250\pi\) | ||||
0.0714098 | + | 0.997447i | \(0.477250\pi\) | |||||||
\(354\) | −710.809 | −0.106721 | ||||||||
\(355\) | 1884.92 | 0.281806 | ||||||||
\(356\) | 5607.75 | 0.834860 | ||||||||
\(357\) | 2446.49 | 0.362694 | ||||||||
\(358\) | −963.633 | −0.142261 | ||||||||
\(359\) | −2733.14 | −0.401810 | −0.200905 | − | 0.979611i | \(-0.564388\pi\) | ||||
−0.200905 | + | 0.979611i | \(0.564388\pi\) | |||||||
\(360\) | 387.074 | 0.0566683 | ||||||||
\(361\) | 8138.10 | 1.18648 | ||||||||
\(362\) | 10313.1 | 1.49737 | ||||||||
\(363\) | −1017.80 | −0.147164 | ||||||||
\(364\) | 2356.27 | 0.339292 | ||||||||
\(365\) | 5880.99 | 0.843356 | ||||||||
\(366\) | 5074.70 | 0.724750 | ||||||||
\(367\) | −10099.4 | −1.43647 | −0.718237 | − | 0.695799i | \(-0.755051\pi\) | ||||
−0.718237 | + | 0.695799i | \(0.755051\pi\) | |||||||
\(368\) | 1773.41 | 0.251210 | ||||||||
\(369\) | 564.675 | 0.0796634 | ||||||||
\(370\) | −7587.36 | −1.06608 | ||||||||
\(371\) | 3352.07 | 0.469085 | ||||||||
\(372\) | 829.129 | 0.115560 | ||||||||
\(373\) | −1037.41 | −0.144008 | −0.0720039 | − | 0.997404i | \(-0.522939\pi\) | ||||
−0.0720039 | + | 0.997404i | \(0.522939\pi\) | |||||||
\(374\) | 13580.2 | 1.87758 | ||||||||
\(375\) | 3403.81 | 0.468726 | ||||||||
\(376\) | 2357.59 | 0.323361 | ||||||||
\(377\) | −9661.34 | −1.31985 | ||||||||
\(378\) | −699.595 | −0.0951939 | ||||||||
\(379\) | 5633.27 | 0.763487 | 0.381743 | − | 0.924268i | \(-0.375324\pi\) | ||||
0.381743 | + | 0.924268i | \(0.375324\pi\) | |||||||
\(380\) | −3529.65 | −0.476492 | ||||||||
\(381\) | −917.569 | −0.123382 | ||||||||
\(382\) | −3324.96 | −0.445340 | ||||||||
\(383\) | −1183.15 | −0.157849 | −0.0789247 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789247 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(384\) | 3132.16 | 0.416244 | ||||||||
\(385\) | −1114.37 | −0.147516 | ||||||||
\(386\) | −15548.0 | −2.05019 | ||||||||
\(387\) | −3390.81 | −0.445386 | ||||||||
\(388\) | 7891.86 | 1.03260 | ||||||||
\(389\) | −5825.10 | −0.759239 | −0.379620 | − | 0.925143i | \(-0.623945\pi\) | ||||
−0.379620 | + | 0.925143i | \(0.623945\pi\) | |||||||
\(390\) | 3314.16 | 0.430306 | ||||||||
\(391\) | 2679.49 | 0.346566 | ||||||||
\(392\) | −416.883 | −0.0537137 | ||||||||
\(393\) | −249.064 | −0.0319685 | ||||||||
\(394\) | −18761.8 | −2.39900 | ||||||||
\(395\) | 4015.90 | 0.511548 | ||||||||
\(396\) | −1615.97 | −0.205065 | ||||||||
\(397\) | −10610.7 | −1.34139 | −0.670697 | − | 0.741731i | \(-0.734005\pi\) | ||||
−0.670697 | + | 0.741731i | \(0.734005\pi\) | |||||||
\(398\) | −2247.04 | −0.283000 | ||||||||
\(399\) | −2571.72 | −0.322674 | ||||||||
\(400\) | 7667.71 | 0.958464 | ||||||||
\(401\) | 9348.78 | 1.16423 | 0.582114 | − | 0.813107i | \(-0.302226\pi\) | ||||
0.582114 | + | 0.813107i | \(0.302226\pi\) | |||||||
\(402\) | 2558.93 | 0.317482 | ||||||||
\(403\) | −2861.81 | −0.353739 | ||||||||
\(404\) | 1009.45 | 0.124312 | ||||||||
\(405\) | −409.467 | −0.0502385 | ||||||||
\(406\) | −4240.20 | −0.518319 | ||||||||
\(407\) | −12769.4 | −1.55517 | ||||||||
\(408\) | 2973.46 | 0.360805 | ||||||||
\(409\) | 11373.4 | 1.37501 | 0.687506 | − | 0.726179i | \(-0.258706\pi\) | ||||
0.687506 | + | 0.726179i | \(0.258706\pi\) | |||||||
\(410\) | −1174.02 | −0.141416 | ||||||||
\(411\) | −3166.38 | −0.380015 | ||||||||
\(412\) | −8298.72 | −0.992351 | ||||||||
\(413\) | 448.069 | 0.0533851 | ||||||||
\(414\) | −766.223 | −0.0909609 | ||||||||
\(415\) | −2930.96 | −0.346687 | ||||||||
\(416\) | 12831.7 | 1.51232 | ||||||||
\(417\) | 3525.66 | 0.414034 | ||||||||
\(418\) | −14275.3 | −1.67041 | ||||||||
\(419\) | 1459.66 | 0.170188 | 0.0850942 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850942 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(420\) | 605.267 | 0.0703191 | ||||||||
\(421\) | −16056.1 | −1.85873 | −0.929365 | − | 0.369163i | \(-0.879645\pi\) | ||||
−0.929365 | + | 0.369163i | \(0.879645\pi\) | |||||||
\(422\) | −4126.71 | −0.476031 | ||||||||
\(423\) | −2493.98 | −0.286670 | ||||||||
\(424\) | 4074.11 | 0.466642 | ||||||||
\(425\) | 11585.3 | 1.32229 | ||||||||
\(426\) | −4140.62 | −0.470924 | ||||||||
\(427\) | −3198.91 | −0.362543 | ||||||||
\(428\) | −1879.12 | −0.212221 | ||||||||
\(429\) | 5577.67 | 0.627722 | ||||||||
\(430\) | 7049.84 | 0.790636 | ||||||||
\(431\) | 9595.59 | 1.07240 | 0.536199 | − | 0.844092i | \(-0.319860\pi\) | ||||
0.536199 | + | 0.844092i | \(0.319860\pi\) | |||||||
\(432\) | −2081.83 | −0.231856 | ||||||||
\(433\) | −6863.20 | −0.761719 | −0.380859 | − | 0.924633i | \(-0.624372\pi\) | ||||
−0.380859 | + | 0.924633i | \(0.624372\pi\) | |||||||
\(434\) | −1256.00 | −0.138917 | ||||||||
\(435\) | −2481.75 | −0.273542 | ||||||||
\(436\) | 8473.98 | 0.930803 | ||||||||
\(437\) | −2816.64 | −0.308325 | ||||||||
\(438\) | −12918.8 | −1.40933 | ||||||||
\(439\) | 7540.01 | 0.819738 | 0.409869 | − | 0.912144i | \(-0.365574\pi\) | ||||
0.409869 | + | 0.912144i | \(0.365574\pi\) | |||||||
\(440\) | −1354.41 | −0.146747 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 25459.1 | 2.73974 | ||||||||
\(443\) | −10067.4 | −1.07973 | −0.539863 | − | 0.841753i | \(-0.681524\pi\) | ||||
−0.539863 | + | 0.841753i | \(0.681524\pi\) | |||||||
\(444\) | 6935.65 | 0.741332 | ||||||||
\(445\) | −4971.97 | −0.529649 | ||||||||
\(446\) | −2630.28 | −0.279254 | ||||||||
\(447\) | 5188.23 | 0.548982 | ||||||||
\(448\) | 1313.76 | 0.138547 | ||||||||
\(449\) | 530.162 | 0.0557236 | 0.0278618 | − | 0.999612i | \(-0.491130\pi\) | ||||
0.0278618 | + | 0.999612i | \(0.491130\pi\) | |||||||
\(450\) | −3312.93 | −0.347051 | ||||||||
\(451\) | −1975.85 | −0.206295 | ||||||||
\(452\) | −8354.15 | −0.869350 | ||||||||
\(453\) | −1135.46 | −0.117767 | ||||||||
\(454\) | 7757.38 | 0.801920 | ||||||||
\(455\) | −2089.13 | −0.215253 | ||||||||
\(456\) | −3125.67 | −0.320993 | ||||||||
\(457\) | −14568.7 | −1.49123 | −0.745617 | − | 0.666375i | \(-0.767845\pi\) | ||||
−0.745617 | + | 0.666375i | \(0.767845\pi\) | |||||||
\(458\) | 21572.5 | 2.20091 | ||||||||
\(459\) | −3145.48 | −0.319866 | ||||||||
\(460\) | 662.911 | 0.0671922 | ||||||||
\(461\) | −15985.4 | −1.61500 | −0.807498 | − | 0.589870i | \(-0.799179\pi\) | ||||
−0.807498 | + | 0.589870i | \(0.799179\pi\) | |||||||
\(462\) | 2447.95 | 0.246513 | ||||||||
\(463\) | −13491.0 | −1.35416 | −0.677082 | − | 0.735907i | \(-0.736756\pi\) | ||||
−0.677082 | + | 0.735907i | \(0.736756\pi\) | |||||||
\(464\) | −12617.8 | −1.26243 | ||||||||
\(465\) | −735.127 | −0.0733133 | ||||||||
\(466\) | 12574.4 | 1.25000 | ||||||||
\(467\) | 1504.25 | 0.149055 | 0.0745273 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745273 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(468\) | −3029.50 | −0.299228 | ||||||||
\(469\) | −1613.06 | −0.158815 | ||||||||
\(470\) | 5185.25 | 0.508889 | ||||||||
\(471\) | −8561.18 | −0.837534 | ||||||||
\(472\) | 544.584 | 0.0531070 | ||||||||
\(473\) | 11864.7 | 1.15336 | ||||||||
\(474\) | −8821.75 | −0.854845 | ||||||||
\(475\) | −12178.4 | −1.17638 | ||||||||
\(476\) | 4649.60 | 0.447719 | ||||||||
\(477\) | −4309.80 | −0.413694 | ||||||||
\(478\) | −22771.2 | −2.17893 | ||||||||
\(479\) | −10871.0 | −1.03697 | −0.518487 | − | 0.855085i | \(-0.673505\pi\) | ||||
−0.518487 | + | 0.855085i | \(0.673505\pi\) | |||||||
\(480\) | 3296.14 | 0.313432 | ||||||||
\(481\) | −23939.0 | −2.26928 | ||||||||
\(482\) | 10335.1 | 0.976661 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −1934.34 | −0.181662 | ||||||||
\(485\) | −6997.12 | −0.655099 | ||||||||
\(486\) | 899.480 | 0.0839531 | ||||||||
\(487\) | 16079.8 | 1.49619 | 0.748096 | − | 0.663591i | \(-0.230968\pi\) | ||||
0.748096 | + | 0.663591i | \(0.230968\pi\) | |||||||
\(488\) | −3887.96 | −0.360655 | ||||||||
\(489\) | −1853.35 | −0.171394 | ||||||||
\(490\) | −916.885 | −0.0845319 | ||||||||
\(491\) | −19353.9 | −1.77888 | −0.889441 | − | 0.457050i | \(-0.848906\pi\) | ||||
−0.889441 | + | 0.457050i | \(0.848906\pi\) | |||||||
\(492\) | 1073.18 | 0.0983384 | ||||||||
\(493\) | −19064.6 | −1.74163 | ||||||||
\(494\) | −26762.3 | −2.43743 | ||||||||
\(495\) | 1432.76 | 0.130097 | ||||||||
\(496\) | −3737.56 | −0.338349 | ||||||||
\(497\) | 2610.10 | 0.235571 | ||||||||
\(498\) | 6438.47 | 0.579346 | ||||||||
\(499\) | 13483.3 | 1.20961 | 0.604806 | − | 0.796373i | \(-0.293251\pi\) | ||||
0.604806 | + | 0.796373i | \(0.293251\pi\) | |||||||
\(500\) | 6469.02 | 0.578607 | ||||||||
\(501\) | 10827.8 | 0.965569 | ||||||||
\(502\) | −8382.18 | −0.745249 | ||||||||
\(503\) | −20352.0 | −1.80408 | −0.902039 | − | 0.431655i | \(-0.857930\pi\) | ||||
−0.902039 | + | 0.431655i | \(0.857930\pi\) | |||||||
\(504\) | 535.992 | 0.0473710 | ||||||||
\(505\) | −895.007 | −0.0788659 | ||||||||
\(506\) | 2681.09 | 0.235551 | ||||||||
\(507\) | 3865.57 | 0.338612 | ||||||||
\(508\) | −1743.86 | −0.152306 | ||||||||
\(509\) | −9128.10 | −0.794884 | −0.397442 | − | 0.917627i | \(-0.630102\pi\) | ||||
−0.397442 | + | 0.917627i | \(0.630102\pi\) | |||||||
\(510\) | 6539.79 | 0.567817 | ||||||||
\(511\) | 8143.57 | 0.704991 | ||||||||
\(512\) | 11510.4 | 0.993541 | ||||||||
\(513\) | 3306.49 | 0.284571 | ||||||||
\(514\) | −22019.2 | −1.88954 | ||||||||
\(515\) | 7357.85 | 0.629564 | ||||||||
\(516\) | −6444.30 | −0.549795 | ||||||||
\(517\) | 8726.67 | 0.742357 | ||||||||
\(518\) | −10506.4 | −0.891170 | ||||||||
\(519\) | −7082.37 | −0.599001 | ||||||||
\(520\) | −2539.13 | −0.214132 | ||||||||
\(521\) | 945.225 | 0.0794838 | 0.0397419 | − | 0.999210i | \(-0.487346\pi\) | ||||
0.0397419 | + | 0.999210i | \(0.487346\pi\) | |||||||
\(522\) | 5451.69 | 0.457115 | ||||||||
\(523\) | −14059.5 | −1.17548 | −0.587741 | − | 0.809049i | \(-0.699983\pi\) | ||||
−0.587741 | + | 0.809049i | \(0.699983\pi\) | |||||||
\(524\) | −473.352 | −0.0394627 | ||||||||
\(525\) | 2088.36 | 0.173606 | ||||||||
\(526\) | −22707.6 | −1.88232 | ||||||||
\(527\) | −5647.17 | −0.466783 | ||||||||
\(528\) | 7284.50 | 0.600411 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 8960.53 | 0.734378 | ||||||||
\(531\) | −576.089 | −0.0470812 | ||||||||
\(532\) | −4887.60 | −0.398316 | ||||||||
\(533\) | −3704.16 | −0.301022 | ||||||||
\(534\) | 10922.0 | 0.885093 | ||||||||
\(535\) | 1666.07 | 0.134637 | ||||||||
\(536\) | −1960.51 | −0.157987 | ||||||||
\(537\) | −780.994 | −0.0627605 | ||||||||
\(538\) | −11435.2 | −0.916365 | ||||||||
\(539\) | −1543.10 | −0.123314 | ||||||||
\(540\) | −778.200 | −0.0620156 | ||||||||
\(541\) | −23148.5 | −1.83961 | −0.919806 | − | 0.392374i | \(-0.871654\pi\) | ||||
−0.919806 | + | 0.392374i | \(0.871654\pi\) | |||||||
\(542\) | 15784.4 | 1.25092 | ||||||||
\(543\) | 8358.48 | 0.660583 | ||||||||
\(544\) | 25320.6 | 1.99561 | ||||||||
\(545\) | −7513.24 | −0.590518 | ||||||||
\(546\) | 4589.21 | 0.359707 | ||||||||
\(547\) | −6489.79 | −0.507282 | −0.253641 | − | 0.967298i | \(-0.581628\pi\) | ||||
−0.253641 | + | 0.967298i | \(0.581628\pi\) | |||||||
\(548\) | −6017.78 | −0.469100 | ||||||||
\(549\) | 4112.88 | 0.319733 | ||||||||
\(550\) | 11592.3 | 0.898719 | ||||||||
\(551\) | 20040.4 | 1.54946 | ||||||||
\(552\) | 587.039 | 0.0452646 | ||||||||
\(553\) | 5560.92 | 0.427621 | ||||||||
\(554\) | 9053.59 | 0.694314 | ||||||||
\(555\) | −6149.32 | −0.470314 | ||||||||
\(556\) | 6700.59 | 0.511094 | ||||||||
\(557\) | 1242.29 | 0.0945021 | 0.0472510 | − | 0.998883i | \(-0.484954\pi\) | ||||
0.0472510 | + | 0.998883i | \(0.484954\pi\) | |||||||
\(558\) | 1614.86 | 0.122513 | ||||||||
\(559\) | 22243.1 | 1.68297 | ||||||||
\(560\) | −2728.43 | −0.205888 | ||||||||
\(561\) | 11006.3 | 0.828321 | ||||||||
\(562\) | −25175.5 | −1.88962 | ||||||||
\(563\) | 15337.3 | 1.14812 | 0.574058 | − | 0.818814i | \(-0.305368\pi\) | ||||
0.574058 | + | 0.818814i | \(0.305368\pi\) | |||||||
\(564\) | −4739.87 | −0.353873 | ||||||||
\(565\) | 7407.00 | 0.551531 | ||||||||
\(566\) | 30685.5 | 2.27881 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 3172.32 | 0.234344 | ||||||||
\(569\) | 11775.1 | 0.867556 | 0.433778 | − | 0.901020i | \(-0.357180\pi\) | ||||
0.433778 | + | 0.901020i | \(0.357180\pi\) | |||||||
\(570\) | −6874.54 | −0.505163 | ||||||||
\(571\) | −12980.3 | −0.951331 | −0.475666 | − | 0.879626i | \(-0.657793\pi\) | ||||
−0.475666 | + | 0.879626i | \(0.657793\pi\) | |||||||
\(572\) | 10600.5 | 0.774875 | ||||||||
\(573\) | −2694.78 | −0.196468 | ||||||||
\(574\) | −1625.69 | −0.118215 | ||||||||
\(575\) | 2287.25 | 0.165887 | ||||||||
\(576\) | −1689.12 | −0.122187 | ||||||||
\(577\) | −17255.5 | −1.24499 | −0.622493 | − | 0.782626i | \(-0.713880\pi\) | ||||
−0.622493 | + | 0.782626i | \(0.713880\pi\) | |||||||
\(578\) | 32052.2 | 2.30657 | ||||||||
\(579\) | −12601.2 | −0.904470 | ||||||||
\(580\) | −4716.62 | −0.337667 | ||||||||
\(581\) | −4058.58 | −0.289808 | ||||||||
\(582\) | 15370.6 | 1.09473 | ||||||||
\(583\) | 15080.4 | 1.07130 | ||||||||
\(584\) | 9897.71 | 0.701318 | ||||||||
\(585\) | 2686.03 | 0.189835 | ||||||||
\(586\) | 9179.45 | 0.647098 | ||||||||
\(587\) | 10049.3 | 0.706606 | 0.353303 | − | 0.935509i | \(-0.385059\pi\) | ||||
0.353303 | + | 0.935509i | \(0.385059\pi\) | |||||||
\(588\) | 838.130 | 0.0587821 | ||||||||
\(589\) | 5936.23 | 0.415277 | ||||||||
\(590\) | 1197.75 | 0.0835772 | ||||||||
\(591\) | −15205.8 | −1.05835 | ||||||||
\(592\) | −31264.6 | −2.17055 | ||||||||
\(593\) | 16348.1 | 1.13210 | 0.566051 | − | 0.824371i | \(-0.308471\pi\) | ||||
0.566051 | + | 0.824371i | \(0.308471\pi\) | |||||||
\(594\) | −3147.36 | −0.217404 | ||||||||
\(595\) | −4122.45 | −0.284040 | ||||||||
\(596\) | 9860.34 | 0.677676 | ||||||||
\(597\) | −1821.15 | −0.124849 | ||||||||
\(598\) | 5026.28 | 0.343712 | ||||||||
\(599\) | 1849.87 | 0.126183 | 0.0630914 | − | 0.998008i | \(-0.479904\pi\) | ||||
0.0630914 | + | 0.998008i | \(0.479904\pi\) | |||||||
\(600\) | 2538.19 | 0.172702 | ||||||||
\(601\) | 18335.1 | 1.24443 | 0.622217 | − | 0.782845i | \(-0.286232\pi\) | ||||
0.622217 | + | 0.782845i | \(0.286232\pi\) | |||||||
\(602\) | 9762.11 | 0.660920 | ||||||||
\(603\) | 2073.93 | 0.140061 | ||||||||
\(604\) | −2157.97 | −0.145375 | ||||||||
\(605\) | 1715.03 | 0.115250 | ||||||||
\(606\) | 1966.07 | 0.131792 | ||||||||
\(607\) | 16265.7 | 1.08765 | 0.543826 | − | 0.839198i | \(-0.316975\pi\) | ||||
0.543826 | + | 0.839198i | \(0.316975\pi\) | |||||||
\(608\) | −26616.7 | −1.77541 | ||||||||
\(609\) | −3436.55 | −0.228663 | ||||||||
\(610\) | −8551.11 | −0.567581 | ||||||||
\(611\) | 16360.1 | 1.08324 | ||||||||
\(612\) | −5978.06 | −0.394851 | ||||||||
\(613\) | 19625.5 | 1.29309 | 0.646545 | − | 0.762875i | \(-0.276213\pi\) | ||||
0.646545 | + | 0.762875i | \(0.276213\pi\) | |||||||
\(614\) | −1932.80 | −0.127038 | ||||||||
\(615\) | −951.504 | −0.0623876 | ||||||||
\(616\) | −1875.49 | −0.122671 | ||||||||
\(617\) | 2886.80 | 0.188360 | 0.0941801 | − | 0.995555i | \(-0.469977\pi\) | ||||
0.0941801 | + | 0.995555i | \(0.469977\pi\) | |||||||
\(618\) | −16163.1 | −1.05206 | ||||||||
\(619\) | 767.335 | 0.0498252 | 0.0249126 | − | 0.999690i | \(-0.492069\pi\) | ||||
0.0249126 | + | 0.999690i | \(0.492069\pi\) | |||||||
\(620\) | −1397.12 | −0.0904997 | ||||||||
\(621\) | −621.000 | −0.0401286 | ||||||||
\(622\) | −10127.1 | −0.652829 | ||||||||
\(623\) | −6884.82 | −0.442752 | ||||||||
\(624\) | 13656.4 | 0.876111 | ||||||||
\(625\) | 6695.09 | 0.428486 | ||||||||
\(626\) | 24225.0 | 1.54669 | ||||||||
\(627\) | −11569.7 | −0.736922 | ||||||||
\(628\) | −16270.7 | −1.03387 | ||||||||
\(629\) | −47238.4 | −2.99447 | ||||||||
\(630\) | 1178.85 | 0.0745502 | ||||||||
\(631\) | 29321.3 | 1.84986 | 0.924931 | − | 0.380135i | \(-0.124123\pi\) | ||||
0.924931 | + | 0.380135i | \(0.124123\pi\) | |||||||
\(632\) | 6758.75 | 0.425393 | ||||||||
\(633\) | −3344.57 | −0.210008 | ||||||||
\(634\) | −15289.4 | −0.957759 | ||||||||
\(635\) | 1546.15 | 0.0966253 | ||||||||
\(636\) | −8190.87 | −0.510674 | ||||||||
\(637\) | −2892.88 | −0.179937 | ||||||||
\(638\) | −19075.9 | −1.18374 | ||||||||
\(639\) | −3355.84 | −0.207754 | ||||||||
\(640\) | −5277.85 | −0.325977 | ||||||||
\(641\) | −15027.9 | −0.926001 | −0.463000 | − | 0.886358i | \(-0.653227\pi\) | ||||
−0.463000 | + | 0.886358i | \(0.653227\pi\) | |||||||
\(642\) | −3659.88 | −0.224991 | ||||||||
\(643\) | 19893.0 | 1.22007 | 0.610034 | − | 0.792375i | \(-0.291156\pi\) | ||||
0.610034 | + | 0.792375i | \(0.291156\pi\) | |||||||
\(644\) | 917.952 | 0.0561683 | ||||||||
\(645\) | 5713.67 | 0.348800 | ||||||||
\(646\) | −52809.5 | −3.21635 | ||||||||
\(647\) | 6993.69 | 0.424962 | 0.212481 | − | 0.977165i | \(-0.431846\pi\) | ||||
0.212481 | + | 0.977165i | \(0.431846\pi\) | |||||||
\(648\) | −689.133 | −0.0417773 | ||||||||
\(649\) | 2015.79 | 0.121921 | ||||||||
\(650\) | 21732.2 | 1.31140 | ||||||||
\(651\) | −1017.95 | −0.0612851 | ||||||||
\(652\) | −3522.34 | −0.211573 | ||||||||
\(653\) | −7296.95 | −0.437292 | −0.218646 | − | 0.975804i | \(-0.570164\pi\) | ||||
−0.218646 | + | 0.975804i | \(0.570164\pi\) | |||||||
\(654\) | 16504.4 | 0.986810 | ||||||||
\(655\) | 419.686 | 0.0250358 | ||||||||
\(656\) | −4837.67 | −0.287926 | ||||||||
\(657\) | −10470.3 | −0.621743 | ||||||||
\(658\) | 7180.16 | 0.425398 | ||||||||
\(659\) | 17065.9 | 1.00879 | 0.504397 | − | 0.863472i | \(-0.331715\pi\) | ||||
0.504397 | + | 0.863472i | \(0.331715\pi\) | |||||||
\(660\) | 2722.99 | 0.160595 | ||||||||
\(661\) | −3802.18 | −0.223733 | −0.111867 | − | 0.993723i | \(-0.535683\pi\) | ||||
−0.111867 | + | 0.993723i | \(0.535683\pi\) | |||||||
\(662\) | 24491.4 | 1.43789 | ||||||||
\(663\) | 20633.8 | 1.20867 | ||||||||
\(664\) | −4932.80 | −0.288298 | ||||||||
\(665\) | 4333.47 | 0.252699 | ||||||||
\(666\) | 13508.3 | 0.785938 | ||||||||
\(667\) | −3763.84 | −0.218495 | ||||||||
\(668\) | 20578.4 | 1.19192 | ||||||||
\(669\) | −2131.76 | −0.123197 | ||||||||
\(670\) | −4311.92 | −0.248633 | ||||||||
\(671\) | −14391.3 | −0.827976 | ||||||||
\(672\) | 4564.25 | 0.262009 | ||||||||
\(673\) | 11806.0 | 0.676206 | 0.338103 | − | 0.941109i | \(-0.390215\pi\) | ||||
0.338103 | + | 0.941109i | \(0.390215\pi\) | |||||||
\(674\) | 18484.2 | 1.05636 | ||||||||
\(675\) | −2685.03 | −0.153106 | ||||||||
\(676\) | 7346.60 | 0.417990 | ||||||||
\(677\) | −821.416 | −0.0466316 | −0.0233158 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233158 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(678\) | −16271.0 | −0.921659 | ||||||||
\(679\) | −9689.10 | −0.547620 | ||||||||
\(680\) | −5010.43 | −0.282561 | ||||||||
\(681\) | 6287.11 | 0.353778 | ||||||||
\(682\) | −5650.54 | −0.317259 | ||||||||
\(683\) | 32952.5 | 1.84611 | 0.923053 | − | 0.384673i | \(-0.125686\pi\) | ||||
0.923053 | + | 0.384673i | \(0.125686\pi\) | |||||||
\(684\) | 6284.06 | 0.351282 | ||||||||
\(685\) | 5335.51 | 0.297605 | ||||||||
\(686\) | −1269.64 | −0.0706631 | ||||||||
\(687\) | 17483.9 | 0.970962 | ||||||||
\(688\) | 29049.7 | 1.60975 | ||||||||
\(689\) | 28271.5 | 1.56322 | ||||||||
\(690\) | 1291.12 | 0.0712351 | ||||||||
\(691\) | 14866.1 | 0.818429 | 0.409214 | − | 0.912438i | \(-0.365803\pi\) | ||||
0.409214 | + | 0.912438i | \(0.365803\pi\) | |||||||
\(692\) | −13460.2 | −0.739422 | ||||||||
\(693\) | 1983.98 | 0.108752 | ||||||||
\(694\) | −36887.1 | −2.01760 | ||||||||
\(695\) | −5940.91 | −0.324247 | ||||||||
\(696\) | −4176.79 | −0.227472 | ||||||||
\(697\) | −7309.36 | −0.397219 | ||||||||
\(698\) | −21847.2 | −1.18471 | ||||||||
\(699\) | 10191.2 | 0.551453 | ||||||||
\(700\) | 3968.96 | 0.214304 | ||||||||
\(701\) | −7493.89 | −0.403766 | −0.201883 | − | 0.979410i | \(-0.564706\pi\) | ||||
−0.201883 | + | 0.979410i | \(0.564706\pi\) | |||||||
\(702\) | −5900.42 | −0.317232 | ||||||||
\(703\) | 49656.4 | 2.66405 | ||||||||
\(704\) | 5910.37 | 0.316414 | ||||||||
\(705\) | 4202.48 | 0.224503 | ||||||||
\(706\) | 3506.18 | 0.186908 | ||||||||
\(707\) | −1239.34 | −0.0659268 | ||||||||
\(708\) | −1094.87 | −0.0581182 | ||||||||
\(709\) | −17896.5 | −0.947979 | −0.473989 | − | 0.880531i | \(-0.657186\pi\) | ||||
−0.473989 | + | 0.880531i | \(0.657186\pi\) | |||||||
\(710\) | 6977.14 | 0.368799 | ||||||||
\(711\) | −7149.75 | −0.377126 | ||||||||
\(712\) | −8367.82 | −0.440446 | ||||||||
\(713\) | −1114.90 | −0.0585599 | ||||||||
\(714\) | 9055.82 | 0.474658 | ||||||||
\(715\) | −9398.65 | −0.491594 | ||||||||
\(716\) | −1484.30 | −0.0774731 | ||||||||
\(717\) | −18455.3 | −0.961266 | ||||||||
\(718\) | −10116.9 | −0.525848 | ||||||||
\(719\) | −8470.81 | −0.439371 | −0.219686 | − | 0.975571i | \(-0.570503\pi\) | ||||
−0.219686 | + | 0.975571i | \(0.570503\pi\) | |||||||
\(720\) | 3507.98 | 0.181576 | ||||||||
\(721\) | 10188.6 | 0.526275 | ||||||||
\(722\) | 30123.7 | 1.55275 | ||||||||
\(723\) | 8376.27 | 0.430867 | ||||||||
\(724\) | 15885.5 | 0.815440 | ||||||||
\(725\) | −16273.8 | −0.833645 | ||||||||
\(726\) | −3767.43 | −0.192593 | ||||||||
\(727\) | 18742.9 | 0.956173 | 0.478086 | − | 0.878313i | \(-0.341331\pi\) | ||||
0.478086 | + | 0.878313i | \(0.341331\pi\) | |||||||
\(728\) | −3516.01 | −0.179000 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 21768.9 | 1.10370 | ||||||||
\(731\) | 43891.9 | 2.22079 | ||||||||
\(732\) | 7816.62 | 0.394686 | ||||||||
\(733\) | 18945.7 | 0.954671 | 0.477336 | − | 0.878721i | \(-0.341603\pi\) | ||||
0.477336 | + | 0.878721i | \(0.341603\pi\) | |||||||
\(734\) | −37383.7 | −1.87991 | ||||||||
\(735\) | −743.107 | −0.0372924 | ||||||||
\(736\) | 4998.94 | 0.250358 | ||||||||
\(737\) | −7256.87 | −0.362701 | ||||||||
\(738\) | 2090.18 | 0.104255 | ||||||||
\(739\) | 21028.3 | 1.04674 | 0.523369 | − | 0.852106i | \(-0.324675\pi\) | ||||
0.523369 | + | 0.852106i | \(0.324675\pi\) | |||||||
\(740\) | −11686.9 | −0.580567 | ||||||||
\(741\) | −21690.0 | −1.07530 | ||||||||
\(742\) | 12407.9 | 0.613892 | ||||||||
\(743\) | 10998.3 | 0.543053 | 0.271527 | − | 0.962431i | \(-0.412472\pi\) | ||||
0.271527 | + | 0.962431i | \(0.412472\pi\) | |||||||
\(744\) | −1237.22 | −0.0609659 | ||||||||
\(745\) | −8742.42 | −0.429929 | ||||||||
\(746\) | −3840.03 | −0.188463 | ||||||||
\(747\) | 5218.17 | 0.255586 | ||||||||
\(748\) | 20917.8 | 1.02250 | ||||||||
\(749\) | 2307.06 | 0.112548 | ||||||||
\(750\) | 12599.4 | 0.613422 | ||||||||
\(751\) | −27694.8 | −1.34567 | −0.672836 | − | 0.739792i | \(-0.734924\pi\) | ||||
−0.672836 | + | 0.739792i | \(0.734924\pi\) | |||||||
\(752\) | 21366.4 | 1.03611 | ||||||||
\(753\) | −6793.50 | −0.328777 | ||||||||
\(754\) | −35762.0 | −1.72729 | ||||||||
\(755\) | 1913.31 | 0.0922284 | ||||||||
\(756\) | −1077.60 | −0.0518410 | ||||||||
\(757\) | 11428.6 | 0.548719 | 0.274359 | − | 0.961627i | \(-0.411534\pi\) | ||||
0.274359 | + | 0.961627i | \(0.411534\pi\) | |||||||
\(758\) | 20851.9 | 0.999175 | ||||||||
\(759\) | 2172.94 | 0.103916 | ||||||||
\(760\) | 5266.90 | 0.251382 | ||||||||
\(761\) | −3125.54 | −0.148884 | −0.0744419 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744419 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(762\) | −3396.44 | −0.161470 | ||||||||
\(763\) | −10403.8 | −0.493634 | ||||||||
\(764\) | −5121.48 | −0.242524 | ||||||||
\(765\) | 5300.29 | 0.250500 | ||||||||
\(766\) | −4379.52 | −0.206578 | ||||||||
\(767\) | 3779.03 | 0.177905 | ||||||||
\(768\) | 16098.2 | 0.756373 | ||||||||
\(769\) | −9092.65 | −0.426384 | −0.213192 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213192 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(770\) | −4124.91 | −0.193054 | ||||||||
\(771\) | −17845.9 | −0.833597 | ||||||||
\(772\) | −23948.9 | −1.11650 | ||||||||
\(773\) | 35229.9 | 1.63924 | 0.819620 | − | 0.572908i | \(-0.194185\pi\) | ||||
0.819620 | + | 0.572908i | \(0.194185\pi\) | |||||||
\(774\) | −12551.3 | −0.582877 | ||||||||
\(775\) | −4820.50 | −0.223429 | ||||||||
\(776\) | −11776.2 | −0.544767 | ||||||||
\(777\) | −8515.13 | −0.393151 | ||||||||
\(778\) | −21562.0 | −0.993616 | ||||||||
\(779\) | 7683.50 | 0.353389 | ||||||||
\(780\) | 5104.85 | 0.234337 | ||||||||
\(781\) | 11742.4 | 0.537997 | ||||||||
\(782\) | 9918.28 | 0.453551 | ||||||||
\(783\) | 4418.42 | 0.201662 | ||||||||
\(784\) | −3778.13 | −0.172109 | ||||||||
\(785\) | 14426.0 | 0.655906 | ||||||||
\(786\) | −921.927 | −0.0418372 | ||||||||
\(787\) | 36470.6 | 1.65189 | 0.825945 | − | 0.563750i | \(-0.190642\pi\) | ||||
0.825945 | + | 0.563750i | \(0.190642\pi\) | |||||||
\(788\) | −28899.0 | −1.30645 | ||||||||
\(789\) | −18403.8 | −0.830410 | ||||||||
\(790\) | 14865.1 | 0.669463 | ||||||||
\(791\) | 10256.7 | 0.461044 | ||||||||
\(792\) | 2411.34 | 0.108186 | ||||||||
\(793\) | −26979.7 | −1.20817 | ||||||||
\(794\) | −39276.0 | −1.75548 | ||||||||
\(795\) | 7262.23 | 0.323981 | ||||||||
\(796\) | −3461.14 | −0.154117 | ||||||||
\(797\) | 26018.0 | 1.15634 | 0.578171 | − | 0.815916i | \(-0.303767\pi\) | ||||
0.578171 | + | 0.815916i | \(0.303767\pi\) | |||||||
\(798\) | −9519.36 | −0.422283 | ||||||||
\(799\) | 32283.1 | 1.42940 | ||||||||
\(800\) | 21614.0 | 0.955213 | ||||||||
\(801\) | 8851.91 | 0.390471 | ||||||||
\(802\) | 34605.1 | 1.52363 | ||||||||
\(803\) | 36636.5 | 1.61006 | ||||||||
\(804\) | 3941.55 | 0.172895 | ||||||||
\(805\) | −813.879 | −0.0356341 | ||||||||
\(806\) | −10593.2 | −0.462939 | ||||||||
\(807\) | −9267.83 | −0.404267 | ||||||||
\(808\) | −1506.30 | −0.0655833 | ||||||||
\(809\) | 9082.04 | 0.394694 | 0.197347 | − | 0.980334i | \(-0.436767\pi\) | ||||
0.197347 | + | 0.980334i | \(0.436767\pi\) | |||||||
\(810\) | −1515.67 | −0.0657471 | ||||||||
\(811\) | −16350.5 | −0.707944 | −0.353972 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353972 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(812\) | −6531.23 | −0.282268 | ||||||||
\(813\) | 12792.7 | 0.551858 | ||||||||
\(814\) | −47266.6 | −2.03525 | ||||||||
\(815\) | 3122.99 | 0.134225 | ||||||||
\(816\) | 26947.9 | 1.15609 | ||||||||
\(817\) | −46138.6 | −1.97575 | ||||||||
\(818\) | 42099.4 | 1.79948 | ||||||||
\(819\) | 3719.41 | 0.158690 | ||||||||
\(820\) | −1808.35 | −0.0770127 | ||||||||
\(821\) | 13198.1 | 0.561046 | 0.280523 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280523 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(822\) | −11720.6 | −0.497325 | ||||||||
\(823\) | −10005.0 | −0.423759 | −0.211879 | − | 0.977296i | \(-0.567958\pi\) | ||||
−0.211879 | + | 0.977296i | \(0.567958\pi\) | |||||||
\(824\) | 12383.3 | 0.523533 | ||||||||
\(825\) | 9395.16 | 0.396482 | ||||||||
\(826\) | 1658.56 | 0.0698650 | ||||||||
\(827\) | −26573.7 | −1.11736 | −0.558680 | − | 0.829383i | \(-0.688692\pi\) | ||||
−0.558680 | + | 0.829383i | \(0.688692\pi\) | |||||||
\(828\) | −1180.22 | −0.0495357 | ||||||||
\(829\) | −31676.3 | −1.32710 | −0.663549 | − | 0.748133i | \(-0.730951\pi\) | ||||
−0.663549 | + | 0.748133i | \(0.730951\pi\) | |||||||
\(830\) | −10849.1 | −0.453709 | ||||||||
\(831\) | 7337.65 | 0.306306 | ||||||||
\(832\) | 11080.3 | 0.461707 | ||||||||
\(833\) | −5708.47 | −0.237439 | ||||||||
\(834\) | 13050.4 | 0.541846 | ||||||||
\(835\) | −18245.4 | −0.756176 | ||||||||
\(836\) | −21988.5 | −0.909674 | ||||||||
\(837\) | 1308.79 | 0.0540484 | ||||||||
\(838\) | 5403.02 | 0.222726 | ||||||||
\(839\) | −16540.5 | −0.680623 | −0.340311 | − | 0.940313i | \(-0.610532\pi\) | ||||
−0.340311 | + | 0.940313i | \(0.610532\pi\) | |||||||
\(840\) | −903.173 | −0.0370981 | ||||||||
\(841\) | 2390.74 | 0.0980255 | ||||||||
\(842\) | −59432.6 | −2.43252 | ||||||||
\(843\) | −20404.0 | −0.833629 | ||||||||
\(844\) | −6356.43 | −0.259238 | ||||||||
\(845\) | −6513.68 | −0.265180 | ||||||||
\(846\) | −9231.63 | −0.375166 | ||||||||
\(847\) | 2374.86 | 0.0963412 | ||||||||
\(848\) | 36922.9 | 1.49521 | ||||||||
\(849\) | 24869.6 | 1.00533 | ||||||||
\(850\) | 42883.8 | 1.73048 | ||||||||
\(851\) | −9326.09 | −0.375669 | ||||||||
\(852\) | −6377.84 | −0.256457 | ||||||||
\(853\) | 4329.29 | 0.173777 | 0.0868887 | − | 0.996218i | \(-0.472308\pi\) | ||||
0.0868887 | + | 0.996218i | \(0.472308\pi\) | |||||||
\(854\) | −11841.0 | −0.474460 | ||||||||
\(855\) | −5571.60 | −0.222859 | ||||||||
\(856\) | 2804.00 | 0.111961 | ||||||||
\(857\) | −19109.8 | −0.761704 | −0.380852 | − | 0.924636i | \(-0.624369\pi\) | ||||
−0.380852 | + | 0.924636i | \(0.624369\pi\) | |||||||
\(858\) | 20646.1 | 0.821499 | ||||||||
\(859\) | −41024.1 | −1.62948 | −0.814740 | − | 0.579826i | \(-0.803121\pi\) | ||||
−0.814740 | + | 0.579826i | \(0.803121\pi\) | |||||||
\(860\) | 10859.0 | 0.430567 | ||||||||
\(861\) | −1317.57 | −0.0521519 | ||||||||
\(862\) | 35518.7 | 1.40345 | ||||||||
\(863\) | 30515.4 | 1.20366 | 0.601829 | − | 0.798625i | \(-0.294439\pi\) | ||||
0.601829 | + | 0.798625i | \(0.294439\pi\) | |||||||
\(864\) | −5868.32 | −0.231070 | ||||||||
\(865\) | 11934.1 | 0.469102 | ||||||||
\(866\) | −25404.5 | −0.996861 | ||||||||
\(867\) | 25977.3 | 1.01757 | ||||||||
\(868\) | −1934.63 | −0.0756518 | ||||||||
\(869\) | 25017.6 | 0.976600 | ||||||||
\(870\) | −9186.36 | −0.357985 | ||||||||
\(871\) | −13604.6 | −0.529247 | ||||||||
\(872\) | −12644.8 | −0.491063 | ||||||||
\(873\) | 12457.4 | 0.482955 | ||||||||
\(874\) | −10426.0 | −0.403505 | ||||||||
\(875\) | −7942.23 | −0.306853 | ||||||||
\(876\) | −19899.0 | −0.767495 | ||||||||
\(877\) | 5825.94 | 0.224319 | 0.112160 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112160 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(878\) | 27909.8 | 1.07279 | ||||||||
\(879\) | 7439.66 | 0.285476 | ||||||||
\(880\) | −12274.7 | −0.470206 | ||||||||
\(881\) | −6587.10 | −0.251901 | −0.125951 | − | 0.992037i | \(-0.540198\pi\) | ||||
−0.125951 | + | 0.992037i | \(0.540198\pi\) | |||||||
\(882\) | 1632.39 | 0.0623190 | ||||||||
\(883\) | 50190.6 | 1.91285 | 0.956426 | − | 0.291975i | \(-0.0943125\pi\) | ||||
0.956426 | + | 0.291975i | \(0.0943125\pi\) | |||||||
\(884\) | 39214.9 | 1.49201 | ||||||||
\(885\) | 970.738 | 0.0368712 | ||||||||
\(886\) | −37265.3 | −1.41304 | ||||||||
\(887\) | 10385.6 | 0.393139 | 0.196569 | − | 0.980490i | \(-0.437020\pi\) | ||||
0.196569 | + | 0.980490i | \(0.437020\pi\) | |||||||
\(888\) | −10349.3 | −0.391103 | ||||||||
\(889\) | 2140.99 | 0.0807724 | ||||||||
\(890\) | −18404.1 | −0.693152 | ||||||||
\(891\) | −2550.84 | −0.0959105 | ||||||||
\(892\) | −4051.46 | −0.152077 | ||||||||
\(893\) | −33935.5 | −1.27168 | ||||||||
\(894\) | 19204.5 | 0.718452 | ||||||||
\(895\) | 1316.01 | 0.0491503 | ||||||||
\(896\) | −7308.38 | −0.272495 | ||||||||
\(897\) | 4073.64 | 0.151633 | ||||||||
\(898\) | 1962.43 | 0.0729254 | ||||||||
\(899\) | 7932.50 | 0.294287 | ||||||||
\(900\) | −5102.95 | −0.188998 | ||||||||
\(901\) | 55787.7 | 2.06277 | ||||||||
\(902\) | −7313.72 | −0.269978 | ||||||||
\(903\) | 7911.88 | 0.291574 | ||||||||
\(904\) | 12466.0 | 0.458642 | ||||||||
\(905\) | −14084.4 | −0.517329 | ||||||||
\(906\) | −4202.98 | −0.154122 | ||||||||
\(907\) | 27202.9 | 0.995875 | 0.497938 | − | 0.867213i | \(-0.334091\pi\) | ||||
0.497938 | + | 0.867213i | \(0.334091\pi\) | |||||||
\(908\) | 11948.8 | 0.436712 | ||||||||
\(909\) | 1593.44 | 0.0581419 | ||||||||
\(910\) | −7733.05 | −0.281701 | ||||||||
\(911\) | −47046.7 | −1.71101 | −0.855503 | − | 0.517798i | \(-0.826752\pi\) | ||||
−0.855503 | + | 0.517798i | \(0.826752\pi\) | |||||||
\(912\) | −28327.3 | −1.02852 | ||||||||
\(913\) | −18258.9 | −0.661862 | ||||||||
\(914\) | −53926.8 | −1.95158 | ||||||||
\(915\) | −6930.41 | −0.250396 | ||||||||
\(916\) | 33228.4 | 1.19858 | ||||||||
\(917\) | 581.150 | 0.0209283 | ||||||||
\(918\) | −11643.2 | −0.418609 | ||||||||
\(919\) | 45639.4 | 1.63820 | 0.819099 | − | 0.573652i | \(-0.194474\pi\) | ||||
0.819099 | + | 0.573652i | \(0.194474\pi\) | |||||||
\(920\) | −989.189 | −0.0354485 | ||||||||
\(921\) | −1566.48 | −0.0560447 | ||||||||
\(922\) | −59170.9 | −2.11355 | ||||||||
\(923\) | 22013.7 | 0.785037 | ||||||||
\(924\) | 3770.60 | 0.134247 | ||||||||
\(925\) | −40323.4 | −1.43332 | ||||||||
\(926\) | −49937.6 | −1.77220 | ||||||||
\(927\) | −13099.7 | −0.464131 | ||||||||
\(928\) | −35567.5 | −1.25815 | ||||||||
\(929\) | −8934.94 | −0.315550 | −0.157775 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157775 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(930\) | −2721.12 | −0.0959451 | ||||||||
\(931\) | 6000.67 | 0.211240 | ||||||||
\(932\) | 19368.5 | 0.680726 | ||||||||
\(933\) | −8207.70 | −0.288004 | ||||||||
\(934\) | 5568.08 | 0.195068 | ||||||||
\(935\) | −18546.2 | −0.648691 | ||||||||
\(936\) | 4520.58 | 0.157863 | ||||||||
\(937\) | −44654.4 | −1.55688 | −0.778440 | − | 0.627719i | \(-0.783989\pi\) | ||||
−0.778440 | + | 0.627719i | \(0.783989\pi\) | |||||||
\(938\) | −5970.83 | −0.207841 | ||||||||
\(939\) | 19633.6 | 0.682342 | ||||||||
\(940\) | 7986.91 | 0.277132 | ||||||||
\(941\) | 6744.79 | 0.233660 | 0.116830 | − | 0.993152i | \(-0.462727\pi\) | ||||
0.116830 | + | 0.993152i | \(0.462727\pi\) | |||||||
\(942\) | −31689.7 | −1.09608 | ||||||||
\(943\) | −1443.06 | −0.0498329 | ||||||||
\(944\) | 4935.46 | 0.170165 | ||||||||
\(945\) | 955.423 | 0.0328888 | ||||||||
\(946\) | 43918.1 | 1.50941 | ||||||||
\(947\) | −2363.47 | −0.0811008 | −0.0405504 | − | 0.999177i | \(-0.512911\pi\) | ||||
−0.0405504 | + | 0.999177i | \(0.512911\pi\) | |||||||
\(948\) | −13588.3 | −0.465534 | ||||||||
\(949\) | 68683.2 | 2.34937 | ||||||||
\(950\) | −45078.9 | −1.53953 | ||||||||
\(951\) | −12391.6 | −0.422528 | ||||||||
\(952\) | −6938.08 | −0.236202 | ||||||||
\(953\) | 29812.2 | 1.01334 | 0.506670 | − | 0.862140i | \(-0.330876\pi\) | ||||
0.506670 | + | 0.862140i | \(0.330876\pi\) | |||||||
\(954\) | −15953.0 | −0.541402 | ||||||||
\(955\) | 4540.83 | 0.153862 | ||||||||
\(956\) | −35074.8 | −1.18661 | ||||||||
\(957\) | −15460.5 | −0.522221 | ||||||||
\(958\) | −40239.9 | −1.35709 | ||||||||
\(959\) | 7388.23 | 0.248778 | ||||||||
\(960\) | 2846.24 | 0.0956897 | ||||||||
\(961\) | −27441.3 | −0.921127 | ||||||||
\(962\) | −88611.7 | −2.96981 | ||||||||
\(963\) | −2966.22 | −0.0992576 | ||||||||
\(964\) | 15919.3 | 0.531873 | ||||||||
\(965\) | 21233.6 | 0.708327 | ||||||||
\(966\) | 1787.85 | 0.0595479 | ||||||||
\(967\) | −11175.2 | −0.371635 | −0.185818 | − | 0.982584i | \(-0.559493\pi\) | ||||
−0.185818 | + | 0.982584i | \(0.559493\pi\) | |||||||
\(968\) | 2886.40 | 0.0958394 | ||||||||
\(969\) | −42800.5 | −1.41894 | ||||||||
\(970\) | −25900.3 | −0.857328 | ||||||||
\(971\) | −4477.24 | −0.147973 | −0.0739863 | − | 0.997259i | \(-0.523572\pi\) | ||||
−0.0739863 | + | 0.997259i | \(0.523572\pi\) | |||||||
\(972\) | 1385.48 | 0.0457194 | ||||||||
\(973\) | −8226.54 | −0.271049 | ||||||||
\(974\) | 59520.4 | 1.95807 | ||||||||
\(975\) | 17613.3 | 0.578540 | ||||||||
\(976\) | −35235.8 | −1.15561 | ||||||||
\(977\) | 21591.9 | 0.707047 | 0.353524 | − | 0.935426i | \(-0.384983\pi\) | ||||
0.353524 | + | 0.935426i | \(0.384983\pi\) | |||||||
\(978\) | −6860.30 | −0.224303 | ||||||||
\(979\) | −30973.7 | −1.01116 | ||||||||
\(980\) | −1412.29 | −0.0460346 | ||||||||
\(981\) | 13376.3 | 0.435344 | ||||||||
\(982\) | −71639.8 | −2.32802 | ||||||||
\(983\) | −48547.2 | −1.57519 | −0.787597 | − | 0.616191i | \(-0.788675\pi\) | ||||
−0.787597 | + | 0.616191i | \(0.788675\pi\) | |||||||
\(984\) | −1601.38 | −0.0518803 | ||||||||
\(985\) | 25622.6 | 0.828836 | ||||||||
\(986\) | −70568.7 | −2.27927 | ||||||||
\(987\) | 5819.29 | 0.187670 | ||||||||
\(988\) | −41222.2 | −1.32738 | ||||||||
\(989\) | 8665.39 | 0.278608 | ||||||||
\(990\) | 5303.46 | 0.170258 | ||||||||
\(991\) | 7693.43 | 0.246609 | 0.123305 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123305 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(992\) | −10535.6 | −0.337202 | ||||||||
\(993\) | 19849.5 | 0.634345 | ||||||||
\(994\) | 9661.44 | 0.308292 | ||||||||
\(995\) | 3068.74 | 0.0977743 | ||||||||
\(996\) | 9917.25 | 0.315502 | ||||||||
\(997\) | 41546.8 | 1.31976 | 0.659879 | − | 0.751372i | \(-0.270607\pi\) | ||||
0.659879 | + | 0.751372i | \(0.270607\pi\) | |||||||
\(998\) | 49909.3 | 1.58302 | ||||||||
\(999\) | 10948.0 | 0.346727 |
(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 | 483.4.a.b.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 1449.4.a.d.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.4.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1449.4.a.d.1.1 | 4 | 3.2 | odd | 2 |