Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(1,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("117.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.20905 | −1.48812 | −0.744062 | − | 0.668111i | \(-0.767103\pi\) | ||||
−0.744062 | + | 0.668111i | \(0.767103\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.71610 | 1.21451 | ||||||||
\(5\) | 11.4322 | 1.02253 | 0.511264 | − | 0.859424i | \(-0.329178\pi\) | ||||
0.511264 | + | 0.859424i | \(0.329178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.2543 | −0.607675 | −0.303838 | − | 0.952724i | \(-0.598268\pi\) | ||||
−0.303838 | + | 0.952724i | \(0.598268\pi\) | |||||||
\(8\) | −7.22315 | −0.319221 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −48.1187 | −1.52165 | ||||||||
\(11\) | −25.8785 | −0.709333 | −0.354666 | − | 0.934993i | \(-0.615406\pi\) | ||||
−0.354666 | + | 0.934993i | \(0.615406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 47.3699 | 0.904296 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −47.3262 | −0.739472 | ||||||||
\(17\) | 20.3276 | 0.290010 | 0.145005 | − | 0.989431i | \(-0.453680\pi\) | ||||
0.145005 | + | 0.989431i | \(0.453680\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 154.712 | 1.86807 | 0.934035 | − | 0.357181i | \(-0.116262\pi\) | ||||
0.934035 | + | 0.357181i | \(0.116262\pi\) | |||||||
\(20\) | 111.076 | 1.24187 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 108.924 | 1.05558 | ||||||||
\(23\) | 180.418 | 1.63565 | 0.817823 | − | 0.575471i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575471i | \(0.195181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.69520 | 0.0455616 | ||||||||
\(26\) | −54.7176 | −0.412731 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −109.348 | −0.738029 | ||||||||
\(29\) | 20.4522 | 0.130961 | 0.0654806 | − | 0.997854i | \(-0.479142\pi\) | ||||
0.0654806 | + | 0.997854i | \(0.479142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 266.424 | 1.54359 | 0.771794 | − | 0.635873i | \(-0.219360\pi\) | ||||
0.771794 | + | 0.635873i | \(0.219360\pi\) | |||||||
\(32\) | 256.984 | 1.41965 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −85.5599 | −0.431571 | ||||||||
\(35\) | −128.661 | −0.621364 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 115.984 | 0.515340 | 0.257670 | − | 0.966233i | \(-0.417045\pi\) | ||||
0.257670 | + | 0.966233i | \(0.417045\pi\) | |||||||
\(38\) | −651.190 | −2.77992 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −82.5765 | −0.326412 | ||||||||
\(41\) | −391.184 | −1.49006 | −0.745032 | − | 0.667029i | \(-0.767566\pi\) | ||||
−0.745032 | + | 0.667029i | \(0.767566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 151.407 | 0.536963 | 0.268482 | − | 0.963285i | \(-0.413478\pi\) | ||||
0.268482 | + | 0.963285i | \(0.413478\pi\) | |||||||
\(44\) | −251.438 | −0.861494 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −759.390 | −2.43404 | ||||||||
\(47\) | 467.365 | 1.45047 | 0.725236 | − | 0.688500i | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −216.341 | −0.630731 | ||||||||
\(50\) | −23.9714 | −0.0678012 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 126.309 | 0.336845 | ||||||||
\(53\) | −79.9842 | −0.207296 | −0.103648 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103648 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −295.848 | −0.725312 | ||||||||
\(56\) | 81.2915 | 0.193983 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −86.0843 | −0.194887 | ||||||||
\(59\) | 873.710 | 1.92792 | 0.963960 | − | 0.266045i | \(-0.0857171\pi\) | ||||
0.963960 | + | 0.266045i | \(0.0857171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −187.068 | −0.392649 | −0.196325 | − | 0.980539i | \(-0.562901\pi\) | ||||
−0.196325 | + | 0.980539i | \(0.562901\pi\) | |||||||
\(62\) | −1121.39 | −2.29705 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −703.047 | −1.37314 | ||||||||
\(65\) | 148.619 | 0.283598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −609.204 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(68\) | 197.505 | 0.352221 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 541.542 | 0.924667 | ||||||||
\(71\) | −248.038 | −0.414601 | −0.207301 | − | 0.978277i | \(-0.566468\pi\) | ||||
−0.207301 | + | 0.978277i | \(0.566468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 852.765 | 1.36724 | 0.683621 | − | 0.729838i | \(-0.260404\pi\) | ||||
0.683621 | + | 0.729838i | \(0.260404\pi\) | |||||||
\(74\) | −488.181 | −0.766890 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1503.20 | 2.26880 | ||||||||
\(77\) | 291.244 | 0.431044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −331.221 | −0.471712 | −0.235856 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235856 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(80\) | −541.043 | −0.756130 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1646.51 | 2.21740 | ||||||||
\(83\) | 435.432 | 0.575842 | 0.287921 | − | 0.957654i | \(-0.407036\pi\) | ||||
0.287921 | + | 0.957654i | \(0.407036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 232.389 | 0.296543 | ||||||||
\(86\) | −637.281 | −0.799067 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 186.924 | 0.226434 | ||||||||
\(89\) | −259.233 | −0.308749 | −0.154375 | − | 0.988012i | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −146.306 | −0.168539 | ||||||||
\(92\) | 1752.96 | 1.98651 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1967.16 | −2.15848 | ||||||||
\(95\) | 1768.70 | 1.91015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1225.17 | 1.28245 | 0.641223 | − | 0.767355i | \(-0.278428\pi\) | ||||
0.641223 | + | 0.767355i | \(0.278428\pi\) | |||||||
\(98\) | 910.589 | 0.938606 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 55.3351 | 0.0553351 | ||||||||
\(101\) | −645.416 | −0.635855 | −0.317927 | − | 0.948115i | \(-0.602987\pi\) | ||||
−0.317927 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −511.137 | −0.488969 | −0.244484 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244484 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(104\) | −93.9010 | −0.0885360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 336.657 | 0.308482 | ||||||||
\(107\) | −608.195 | −0.549499 | −0.274750 | − | 0.961516i | \(-0.588595\pi\) | ||||
−0.274750 | + | 0.961516i | \(0.588595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1300.04 | −1.14239 | −0.571197 | − | 0.820813i | \(-0.693521\pi\) | ||||
−0.571197 | + | 0.820813i | \(0.693521\pi\) | |||||||
\(110\) | 1245.24 | 1.07935 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 532.623 | 0.449359 | ||||||||
\(113\) | −42.1953 | −0.0351274 | −0.0175637 | − | 0.999846i | \(-0.505591\pi\) | ||||
−0.0175637 | + | 0.999846i | \(0.505591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2062.58 | 1.67249 | ||||||||
\(116\) | 198.716 | 0.159054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3677.49 | −2.86899 | ||||||||
\(119\) | −228.773 | −0.176232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −661.303 | −0.496847 | ||||||||
\(122\) | 787.378 | 0.584311 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2588.61 | 1.87471 | ||||||||
\(125\) | −1363.92 | −0.975939 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −311.018 | −0.217310 | −0.108655 | − | 0.994080i | \(-0.534654\pi\) | ||||
−0.108655 | + | 0.994080i | \(0.534654\pi\) | |||||||
\(128\) | 903.291 | 0.623753 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −625.543 | −0.422029 | ||||||||
\(131\) | −2000.98 | −1.33456 | −0.667278 | − | 0.744809i | \(-0.732541\pi\) | ||||
−0.667278 | + | 0.744809i | \(0.732541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1741.17 | −1.13518 | ||||||||
\(134\) | 2564.17 | 1.65306 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −146.829 | −0.0925773 | ||||||||
\(137\) | −1038.53 | −0.647644 | −0.323822 | − | 0.946118i | \(-0.604968\pi\) | ||||
−0.323822 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2858.46 | −1.74426 | −0.872128 | − | 0.489277i | \(-0.837261\pi\) | ||||
−0.872128 | + | 0.489277i | \(0.837261\pi\) | |||||||
\(140\) | −1250.09 | −0.754655 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1044.00 | 0.616978 | ||||||||
\(143\) | −336.421 | −0.196734 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 233.814 | 0.133911 | ||||||||
\(146\) | −3589.33 | −2.03462 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1126.91 | 0.625887 | ||||||||
\(149\) | −743.479 | −0.408780 | −0.204390 | − | 0.978890i | \(-0.565521\pi\) | ||||
−0.204390 | + | 0.978890i | \(0.565521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2277.24 | 1.22728 | 0.613640 | − | 0.789586i | \(-0.289705\pi\) | ||||
0.613640 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(152\) | −1117.51 | −0.596328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1225.86 | −0.641447 | ||||||||
\(155\) | 3045.82 | 1.57836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3173.51 | 1.61321 | 0.806605 | − | 0.591091i | \(-0.201303\pi\) | ||||
0.806605 | + | 0.591091i | \(0.201303\pi\) | |||||||
\(158\) | 1394.12 | 0.701966 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2937.89 | 1.45163 | ||||||||
\(161\) | −2030.48 | −0.993941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2314.65 | −1.11225 | −0.556126 | − | 0.831098i | \(-0.687713\pi\) | ||||
−0.556126 | + | 0.831098i | \(0.687713\pi\) | |||||||
\(164\) | −3800.78 | −1.80970 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1832.76 | −0.856925 | ||||||||
\(167\) | 2665.65 | 1.23517 | 0.617587 | − | 0.786502i | \(-0.288110\pi\) | ||||
0.617587 | + | 0.786502i | \(0.288110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −978.138 | −0.441293 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1471.09 | 0.652148 | ||||||||
\(173\) | 165.243 | 0.0726198 | 0.0363099 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363099 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −64.0954 | −0.0276866 | ||||||||
\(176\) | 1224.73 | 0.524532 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1091.13 | 0.459457 | ||||||||
\(179\) | −712.339 | −0.297446 | −0.148723 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148723 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2206.53 | 0.906133 | 0.453066 | − | 0.891477i | \(-0.350330\pi\) | ||||
0.453066 | + | 0.891477i | \(0.350330\pi\) | |||||||
\(182\) | 615.809 | 0.250806 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1303.19 | −0.522132 | ||||||||
\(185\) | 1325.95 | 0.526949 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −526.048 | −0.205714 | ||||||||
\(188\) | 4540.96 | 1.76162 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7444.54 | −2.84254 | ||||||||
\(191\) | −1470.64 | −0.557129 | −0.278565 | − | 0.960417i | \(-0.589859\pi\) | ||||
−0.278565 | + | 0.960417i | \(0.589859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 369.560 | 0.137832 | 0.0689158 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689158 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(194\) | −5156.80 | −1.90844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2101.99 | −0.766031 | ||||||||
\(197\) | 4273.41 | 1.54552 | 0.772761 | − | 0.634697i | \(-0.218875\pi\) | ||||
0.772761 | + | 0.634697i | \(0.218875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4154.31 | 1.47985 | 0.739927 | − | 0.672687i | \(-0.234860\pi\) | ||||
0.739927 | + | 0.672687i | \(0.234860\pi\) | |||||||
\(200\) | −41.1373 | −0.0145442 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2716.59 | 0.946230 | ||||||||
\(203\) | −230.175 | −0.0795819 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4472.09 | −1.52363 | ||||||||
\(206\) | 2151.40 | 0.727646 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −615.241 | −0.205093 | ||||||||
\(209\) | −4003.71 | −1.32508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1231.59 | 0.401830 | 0.200915 | − | 0.979609i | \(-0.435608\pi\) | ||||
0.200915 | + | 0.979609i | \(0.435608\pi\) | |||||||
\(212\) | −777.134 | −0.251763 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2559.92 | 0.817723 | ||||||||
\(215\) | 1730.92 | 0.549059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2998.42 | −0.938000 | ||||||||
\(218\) | 5471.92 | 1.70002 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2874.49 | −0.880901 | ||||||||
\(221\) | 264.259 | 0.0804343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2187.24 | −0.656809 | −0.328404 | − | 0.944537i | \(-0.606511\pi\) | ||||
−0.328404 | + | 0.944537i | \(0.606511\pi\) | |||||||
\(224\) | −2892.17 | −0.862684 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 177.602 | 0.0522739 | ||||||||
\(227\) | −4138.67 | −1.21010 | −0.605051 | − | 0.796187i | \(-0.706847\pi\) | ||||
−0.605051 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −835.354 | −0.241056 | −0.120528 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120528 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(230\) | −8681.50 | −2.48887 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −147.729 | −0.0418056 | ||||||||
\(233\) | −3685.51 | −1.03625 | −0.518124 | − | 0.855305i | \(-0.673370\pi\) | ||||
−0.518124 | + | 0.855305i | \(0.673370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5343.01 | 1.48315 | ||||||||
\(236\) | 8489.05 | 2.34148 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 962.917 | 0.262255 | ||||||||
\(239\) | −3026.21 | −0.819034 | −0.409517 | − | 0.912303i | \(-0.634303\pi\) | ||||
−0.409517 | + | 0.912303i | \(0.634303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3265.58 | 0.872839 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(242\) | 2783.46 | 0.739370 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1817.57 | −0.476877 | ||||||||
\(245\) | −2473.25 | −0.644940 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2011.25 | 0.518110 | ||||||||
\(248\) | −1924.42 | −0.492746 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5740.79 | 1.45232 | ||||||||
\(251\) | 6363.16 | 1.60016 | 0.800078 | − | 0.599897i | \(-0.204792\pi\) | ||||
0.800078 | + | 0.599897i | \(0.204792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4668.96 | −1.16022 | ||||||||
\(254\) | 1309.09 | 0.323385 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1822.38 | 0.444917 | ||||||||
\(257\) | 6085.36 | 1.47702 | 0.738511 | − | 0.674242i | \(-0.235529\pi\) | ||||
0.738511 | + | 0.674242i | \(0.235529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1305.31 | −0.313159 | ||||||||
\(260\) | 1443.99 | 0.344433 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8422.24 | 1.98598 | ||||||||
\(263\) | −123.227 | −0.0288916 | −0.0144458 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144458 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −914.395 | −0.211965 | ||||||||
\(266\) | 7328.69 | 1.68929 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5919.08 | −1.34913 | ||||||||
\(269\) | 1935.79 | 0.438763 | 0.219381 | − | 0.975639i | \(-0.429596\pi\) | ||||
0.219381 | + | 0.975639i | \(0.429596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4612.69 | −1.03395 | −0.516976 | − | 0.856000i | \(-0.672942\pi\) | ||||
−0.516976 | + | 0.856000i | \(0.672942\pi\) | |||||||
\(272\) | −962.028 | −0.214454 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4371.20 | 0.963774 | ||||||||
\(275\) | −147.383 | −0.0323183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5834.30 | −1.26552 | −0.632761 | − | 0.774347i | \(-0.718078\pi\) | ||||
−0.632761 | + | 0.774347i | \(0.718078\pi\) | |||||||
\(278\) | 12031.4 | 2.59567 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 929.341 | 0.198353 | ||||||||
\(281\) | −4691.91 | −0.996071 | −0.498036 | − | 0.867157i | \(-0.665945\pi\) | ||||
−0.498036 | + | 0.867157i | \(0.665945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3465.60 | 0.727945 | 0.363973 | − | 0.931410i | \(-0.381420\pi\) | ||||
0.363973 | + | 0.931410i | \(0.381420\pi\) | |||||||
\(284\) | −2409.96 | −0.503539 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1416.01 | 0.292764 | ||||||||
\(287\) | 4402.50 | 0.905475 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4499.79 | −0.915894 | ||||||||
\(290\) | −984.133 | −0.199277 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8285.55 | 1.66053 | ||||||||
\(293\) | −2677.31 | −0.533822 | −0.266911 | − | 0.963721i | \(-0.586003\pi\) | ||||
−0.266911 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9988.43 | 1.97135 | ||||||||
\(296\) | −837.767 | −0.164507 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3129.34 | 0.608315 | ||||||||
\(299\) | 2345.44 | 0.453646 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1703.98 | −0.326299 | ||||||||
\(302\) | −9585.02 | −1.82634 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7321.93 | −1.38139 | ||||||||
\(305\) | −2138.60 | −0.401494 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 471.915 | 0.0877316 | 0.0438658 | − | 0.999037i | \(-0.486033\pi\) | ||||
0.0438658 | + | 0.999037i | \(0.486033\pi\) | |||||||
\(308\) | 2829.76 | 0.523508 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12820.0 | −2.34880 | ||||||||
\(311\) | 1518.52 | 0.276872 | 0.138436 | − | 0.990371i | \(-0.455793\pi\) | ||||
0.138436 | + | 0.990371i | \(0.455793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4049.86 | 0.731348 | 0.365674 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(314\) | −13357.5 | −2.40066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3218.17 | −0.572900 | ||||||||
\(317\) | −3253.96 | −0.576532 | −0.288266 | − | 0.957550i | \(-0.593079\pi\) | ||||
−0.288266 | + | 0.957550i | \(0.593079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −529.272 | −0.0928951 | ||||||||
\(320\) | −8037.37 | −1.40407 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8546.40 | 1.47911 | ||||||||
\(323\) | 3144.92 | 0.541759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74.0375 | 0.0126365 | ||||||||
\(326\) | 9742.46 | 1.65517 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2825.58 | 0.475660 | ||||||||
\(329\) | −5259.86 | −0.881415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3422.45 | −0.568322 | −0.284161 | − | 0.958777i | \(-0.591715\pi\) | ||||
−0.284161 | + | 0.958777i | \(0.591715\pi\) | |||||||
\(332\) | 4230.71 | 0.699368 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11219.8 | −1.83809 | ||||||||
\(335\) | −6964.54 | −1.13586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9301.67 | −1.50354 | −0.751772 | − | 0.659423i | \(-0.770801\pi\) | ||||
−0.751772 | + | 0.659423i | \(0.770801\pi\) | |||||||
\(338\) | −711.329 | −0.114471 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2257.92 | 0.360155 | ||||||||
\(341\) | −6894.66 | −1.09492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6294.99 | 0.990955 | ||||||||
\(344\) | −1093.64 | −0.171410 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −695.518 | −0.108067 | ||||||||
\(347\) | −216.898 | −0.0335554 | −0.0167777 | − | 0.999859i | \(-0.505341\pi\) | ||||
−0.0167777 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4809.84 | −0.737721 | −0.368861 | − | 0.929485i | \(-0.620252\pi\) | ||||
−0.368861 | + | 0.929485i | \(0.620252\pi\) | |||||||
\(350\) | 269.781 | 0.0412011 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6650.35 | −1.00700 | ||||||||
\(353\) | 2859.64 | 0.431170 | 0.215585 | − | 0.976485i | \(-0.430834\pi\) | ||||
0.215585 | + | 0.976485i | \(0.430834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2835.62 | −0.423941 | ||||||||
\(356\) | −2518.74 | −0.374980 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2998.27 | 0.442636 | ||||||||
\(359\) | −3686.04 | −0.541899 | −0.270949 | − | 0.962594i | \(-0.587338\pi\) | ||||
−0.270949 | + | 0.962594i | \(0.587338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17076.8 | 2.48969 | ||||||||
\(362\) | −9287.39 | −1.34844 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1421.52 | −0.204692 | ||||||||
\(365\) | 9748.98 | 1.39804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3470.59 | −0.493633 | −0.246816 | − | 0.969062i | \(-0.579384\pi\) | ||||
−0.246816 | + | 0.969062i | \(0.579384\pi\) | |||||||
\(368\) | −8538.52 | −1.20951 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5580.98 | −0.784166 | ||||||||
\(371\) | 900.166 | 0.125968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11963.4 | −1.66070 | −0.830352 | − | 0.557240i | \(-0.811860\pi\) | ||||
−0.830352 | + | 0.557240i | \(0.811860\pi\) | |||||||
\(374\) | 2214.16 | 0.306127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3375.85 | −0.463021 | ||||||||
\(377\) | 265.879 | 0.0363221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 345.604 | 0.0468403 | 0.0234202 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234202 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(380\) | 17184.8 | 2.31990 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6189.99 | 0.829078 | ||||||||
\(383\) | 3386.40 | 0.451793 | 0.225897 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225897 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3329.56 | 0.440754 | ||||||||
\(386\) | −1555.49 | −0.205110 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11903.9 | 1.55755 | ||||||||
\(389\) | 1629.88 | 0.212438 | 0.106219 | − | 0.994343i | \(-0.466126\pi\) | ||||
0.106219 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3667.47 | 0.474353 | ||||||||
\(392\) | 1562.66 | 0.201343 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17987.0 | −2.29993 | ||||||||
\(395\) | −3786.58 | −0.482338 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7938.94 | 1.00364 | 0.501819 | − | 0.864973i | \(-0.332664\pi\) | ||||
0.501819 | + | 0.864973i | \(0.332664\pi\) | |||||||
\(398\) | −17485.7 | −2.20221 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −269.532 | −0.0336915 | ||||||||
\(401\) | −214.402 | −0.0267001 | −0.0133500 | − | 0.999911i | \(-0.504250\pi\) | ||||
−0.0133500 | + | 0.999911i | \(0.504250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3463.52 | 0.428114 | ||||||||
\(404\) | −6270.93 | −0.772253 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 968.819 | 0.118428 | ||||||||
\(407\) | −3001.48 | −0.365548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4783.73 | −0.578338 | −0.289169 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289169 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(410\) | 18823.2 | 2.26735 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4966.25 | −0.593859 | ||||||||
\(413\) | −9832.99 | −1.17155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4977.95 | 0.588815 | ||||||||
\(416\) | 3340.79 | 0.393739 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16851.8 | 1.97189 | ||||||||
\(419\) | 9903.67 | 1.15472 | 0.577358 | − | 0.816491i | \(-0.304084\pi\) | ||||
0.577358 | + | 0.816491i | \(0.304084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12120.6 | −1.40314 | −0.701572 | − | 0.712598i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712598i | \(0.747518\pi\) | |||||||
\(422\) | −5183.82 | −0.597973 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 577.738 | 0.0661732 | ||||||||
\(425\) | 115.770 | 0.0132133 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2105.32 | 0.238603 | ||||||||
\(428\) | −5909.28 | −0.667374 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7285.53 | −0.817068 | ||||||||
\(431\) | 13672.6 | 1.52805 | 0.764023 | − | 0.645189i | \(-0.223221\pi\) | ||||
0.764023 | + | 0.645189i | \(0.223221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7113.10 | 0.789455 | 0.394727 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394727 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(434\) | 12620.5 | 1.39586 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12631.3 | −1.38745 | ||||||||
\(437\) | 27912.9 | 3.05550 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6022.04 | −0.654707 | −0.327353 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327353 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(440\) | 2136.96 | 0.231535 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1112.28 | −0.119696 | ||||||||
\(443\) | 12994.4 | 1.39364 | 0.696821 | − | 0.717245i | \(-0.254597\pi\) | ||||
0.696821 | + | 0.717245i | \(0.254597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2963.61 | −0.315704 | ||||||||
\(446\) | 9206.20 | 0.977413 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7912.30 | 0.834422 | ||||||||
\(449\) | −10984.3 | −1.15452 | −0.577260 | − | 0.816560i | \(-0.695878\pi\) | ||||
−0.577260 | + | 0.816560i | \(0.695878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10123.2 | 1.05695 | ||||||||
\(452\) | −409.973 | −0.0426627 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17419.9 | 1.80078 | ||||||||
\(455\) | −1672.60 | −0.172335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9834.10 | 1.00661 | 0.503304 | − | 0.864109i | \(-0.332118\pi\) | ||||
0.503304 | + | 0.864109i | \(0.332118\pi\) | |||||||
\(458\) | 3516.05 | 0.358721 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 20040.2 | 2.03126 | ||||||||
\(461\) | −3401.42 | −0.343644 | −0.171822 | − | 0.985128i | \(-0.554965\pi\) | ||||
−0.171822 | + | 0.985128i | \(0.554965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1739.42 | 0.174596 | 0.0872979 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872979 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(464\) | −967.925 | −0.0968422 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15512.5 | 1.54207 | ||||||||
\(467\) | 7958.82 | 0.788630 | 0.394315 | − | 0.918975i | \(-0.370982\pi\) | ||||
0.394315 | + | 0.918975i | \(0.370982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6856.16 | 0.675028 | ||||||||
\(470\) | −22489.0 | −2.20711 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6310.94 | −0.615433 | ||||||||
\(473\) | −3918.20 | −0.380886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 881.114 | 0.0851122 | ||||||||
\(476\) | −2222.78 | −0.214036 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12737.5 | 1.21882 | ||||||||
\(479\) | −8431.98 | −0.804315 | −0.402158 | − | 0.915570i | \(-0.631740\pi\) | ||||
−0.402158 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1507.79 | 0.142930 | ||||||||
\(482\) | −13745.0 | −1.29889 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6425.29 | −0.603427 | ||||||||
\(485\) | 14006.4 | 1.31133 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11684.7 | −1.08723 | −0.543617 | − | 0.839334i | \(-0.682945\pi\) | ||||
−0.543617 | + | 0.839334i | \(0.682945\pi\) | |||||||
\(488\) | 1351.22 | 0.125342 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10410.0 | 0.959750 | ||||||||
\(491\) | 3954.70 | 0.363489 | 0.181745 | − | 0.983346i | \(-0.441826\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 415.744 | 0.0379801 | ||||||||
\(494\) | −8465.47 | −0.771011 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12608.8 | −1.14144 | ||||||||
\(497\) | 2791.49 | 0.251943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5690.37 | −0.510493 | −0.255246 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(500\) | −13251.9 | −1.18529 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26782.8 | −2.38123 | ||||||||
\(503\) | −10859.1 | −0.962595 | −0.481298 | − | 0.876557i | \(-0.659834\pi\) | ||||
−0.481298 | + | 0.876557i | \(0.659834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7378.53 | −0.650178 | ||||||||
\(506\) | 19651.9 | 1.72655 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3021.88 | −0.263926 | ||||||||
\(509\) | 18558.6 | 1.61610 | 0.808049 | − | 0.589115i | \(-0.200524\pi\) | ||||
0.808049 | + | 0.589115i | \(0.200524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9597.27 | −0.830838 | ||||||||
\(512\) | −14896.8 | −1.28584 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25613.6 | −2.19799 | ||||||||
\(515\) | −5843.42 | −0.499984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12094.7 | −1.02887 | ||||||||
\(518\) | 5494.13 | 0.466020 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1073.49 | −0.0905305 | ||||||||
\(521\) | −17297.5 | −1.45454 | −0.727271 | − | 0.686350i | \(-0.759212\pi\) | ||||
−0.727271 | + | 0.686350i | \(0.759212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5016.11 | −0.419386 | −0.209693 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209693 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(524\) | −19441.8 | −1.62084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 518.667 | 0.0429942 | ||||||||
\(527\) | 5415.77 | 0.447656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20383.8 | 1.67533 | ||||||||
\(530\) | 3848.73 | 0.315431 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16917.4 | −1.37869 | ||||||||
\(533\) | −5085.39 | −0.413269 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6953.01 | −0.561878 | ||||||||
\(536\) | 4400.37 | 0.354603 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8147.83 | −0.652933 | ||||||||
\(539\) | 5598.57 | 0.447398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17642.3 | 1.40204 | 0.701018 | − | 0.713144i | \(-0.252729\pi\) | ||||
0.701018 | + | 0.713144i | \(0.252729\pi\) | |||||||
\(542\) | 19415.0 | 1.53865 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5223.86 | 0.411712 | ||||||||
\(545\) | −14862.3 | −1.16813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18414.9 | −1.43943 | −0.719713 | − | 0.694271i | \(-0.755727\pi\) | ||||
−0.719713 | + | 0.694271i | \(0.755727\pi\) | |||||||
\(548\) | −10090.4 | −0.786571 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 620.343 | 0.0480937 | ||||||||
\(551\) | 3164.20 | 0.244645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3727.66 | 0.286648 | ||||||||
\(554\) | 24556.9 | 1.88325 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27773.1 | −2.11842 | ||||||||
\(557\) | −8179.15 | −0.622193 | −0.311096 | − | 0.950378i | \(-0.600696\pi\) | ||||
−0.311096 | + | 0.950378i | \(0.600696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1968.30 | 0.148927 | ||||||||
\(560\) | 6089.05 | 0.459481 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19748.5 | 1.48228 | ||||||||
\(563\) | 1880.07 | 0.140738 | 0.0703690 | − | 0.997521i | \(-0.477582\pi\) | ||||
0.0703690 | + | 0.997521i | \(0.477582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −482.385 | −0.0359187 | ||||||||
\(566\) | −14586.9 | −1.08327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1791.62 | 0.132350 | ||||||||
\(569\) | −10118.3 | −0.745485 | −0.372743 | − | 0.927935i | \(-0.621583\pi\) | ||||
−0.372743 | + | 0.927935i | \(0.621583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23428.9 | 1.71711 | 0.858555 | − | 0.512721i | \(-0.171362\pi\) | ||||
0.858555 | + | 0.512721i | \(0.171362\pi\) | |||||||
\(572\) | −3268.70 | −0.238935 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18530.3 | −1.34746 | ||||||||
\(575\) | 1027.52 | 0.0745225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20508.1 | 1.47966 | 0.739831 | − | 0.672793i | \(-0.234906\pi\) | ||||
0.739831 | + | 0.672793i | \(0.234906\pi\) | |||||||
\(578\) | 18939.8 | 1.36296 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2271.76 | 0.162637 | ||||||||
\(581\) | −4900.49 | −0.349925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2069.87 | 0.147042 | ||||||||
\(584\) | −6159.65 | −0.436452 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11268.9 | 0.794394 | ||||||||
\(587\) | 5968.43 | 0.419665 | 0.209833 | − | 0.977737i | \(-0.432708\pi\) | ||||
0.209833 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41219.0 | 2.88353 | ||||||||
\(590\) | −42041.8 | −2.93361 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5489.06 | −0.381080 | ||||||||
\(593\) | 14659.5 | 1.01517 | 0.507584 | − | 0.861602i | \(-0.330539\pi\) | ||||
0.507584 | + | 0.861602i | \(0.330539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2615.38 | −0.180202 | ||||||||
\(596\) | −7223.72 | −0.496468 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9872.07 | −0.675082 | ||||||||
\(599\) | −23635.9 | −1.61225 | −0.806125 | − | 0.591746i | \(-0.798439\pi\) | ||||
−0.806125 | + | 0.591746i | \(0.798439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11527.0 | −0.782356 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(602\) | 7172.15 | 0.485573 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22125.9 | 1.49055 | ||||||||
\(605\) | −7560.15 | −0.508039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5098.56 | −0.340930 | −0.170465 | − | 0.985364i | \(-0.554527\pi\) | ||||
−0.170465 | + | 0.985364i | \(0.554527\pi\) | |||||||
\(608\) | 39758.4 | 2.65200 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9001.47 | 0.597473 | ||||||||
\(611\) | 6075.74 | 0.402288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1516.39 | 0.0999128 | 0.0499564 | − | 0.998751i | \(-0.484092\pi\) | ||||
0.0499564 | + | 0.998751i | \(0.484092\pi\) | |||||||
\(614\) | −1986.31 | −0.130556 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2103.70 | −0.137598 | ||||||||
\(617\) | −18539.3 | −1.20966 | −0.604832 | − | 0.796353i | \(-0.706760\pi\) | ||||
−0.604832 | + | 0.796353i | \(0.706760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25684.9 | 1.66779 | 0.833897 | − | 0.551920i | \(-0.186105\pi\) | ||||
0.833897 | + | 0.551920i | \(0.186105\pi\) | |||||||
\(620\) | 29593.5 | 1.91694 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6391.51 | −0.412020 | ||||||||
\(623\) | 2917.49 | 0.187619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16304.5 | −1.04349 | ||||||||
\(626\) | −17046.1 | −1.08834 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30834.2 | 1.95926 | ||||||||
\(629\) | 2357.67 | 0.149454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22410.9 | −1.41389 | −0.706945 | − | 0.707269i | \(-0.749927\pi\) | ||||
−0.706945 | + | 0.707269i | \(0.749927\pi\) | |||||||
\(632\) | 2392.46 | 0.150580 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13696.1 | 0.857950 | ||||||||
\(635\) | −3555.62 | −0.222206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2812.43 | −0.174933 | ||||||||
\(638\) | 2227.73 | 0.138239 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10326.6 | 0.637804 | ||||||||
\(641\) | −6827.81 | −0.420721 | −0.210361 | − | 0.977624i | \(-0.567464\pi\) | ||||
−0.210361 | + | 0.977624i | \(0.567464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23264.3 | −1.42684 | −0.713418 | − | 0.700738i | \(-0.752854\pi\) | ||||
−0.713418 | + | 0.700738i | \(0.752854\pi\) | |||||||
\(644\) | −19728.4 | −1.20715 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13237.1 | −0.806204 | ||||||||
\(647\) | −14745.9 | −0.896014 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22610.3 | −1.36754 | ||||||||
\(650\) | −311.628 | −0.0188047 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22489.3 | −1.35084 | ||||||||
\(653\) | −10909.0 | −0.653755 | −0.326878 | − | 0.945067i | \(-0.605997\pi\) | ||||
−0.326878 | + | 0.945067i | \(0.605997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22875.7 | −1.36462 | ||||||||
\(656\) | 18513.2 | 1.10186 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22139.0 | 1.31166 | ||||||||
\(659\) | 4182.99 | 0.247263 | 0.123631 | − | 0.992328i | \(-0.460546\pi\) | ||||
0.123631 | + | 0.992328i | \(0.460546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2224.23 | 0.130881 | 0.0654406 | − | 0.997856i | \(-0.479155\pi\) | ||||
0.0654406 | + | 0.997856i | \(0.479155\pi\) | |||||||
\(662\) | 14405.2 | 0.845734 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3145.19 | −0.183821 | ||||||||
\(665\) | −19905.4 | −1.16075 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3689.95 | 0.214206 | ||||||||
\(668\) | 25899.7 | 1.50013 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29314.1 | 1.69030 | ||||||||
\(671\) | 4841.04 | 0.278519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24152.5 | −1.38337 | −0.691687 | − | 0.722197i | \(-0.743132\pi\) | ||||
−0.691687 | + | 0.722197i | \(0.743132\pi\) | |||||||
\(674\) | 39151.2 | 2.23746 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1642.02 | 0.0934240 | ||||||||
\(677\) | 15310.7 | 0.869187 | 0.434593 | − | 0.900627i | \(-0.356892\pi\) | ||||
0.434593 | + | 0.900627i | \(0.356892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13788.4 | −0.779310 | ||||||||
\(680\) | −1678.58 | −0.0946628 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29020.0 | 1.62937 | ||||||||
\(683\) | −11399.6 | −0.638646 | −0.319323 | − | 0.947646i | \(-0.603455\pi\) | ||||
−0.319323 | + | 0.947646i | \(0.603455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11872.6 | −0.662233 | ||||||||
\(686\) | −26495.9 | −1.47466 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7165.54 | −0.397069 | ||||||||
\(689\) | −1039.79 | −0.0574935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3323.23 | −0.182955 | −0.0914773 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914773 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(692\) | 1605.52 | 0.0881976 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 912.936 | 0.0499345 | ||||||||
\(695\) | −32678.5 | −1.78355 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7951.82 | −0.432133 | ||||||||
\(698\) | 20244.8 | 1.09782 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −622.758 | −0.0336257 | ||||||||
\(701\) | 12670.4 | 0.682673 | 0.341336 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341336 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17944.0 | 0.962692 | ||||||||
\(704\) | 18193.8 | 0.974012 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12036.4 | −0.641635 | ||||||||
\(707\) | 7263.71 | 0.386393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13075.2 | 0.692594 | 0.346297 | − | 0.938125i | \(-0.387439\pi\) | ||||
0.346297 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(710\) | 11935.3 | 0.630877 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1872.48 | 0.0985592 | ||||||||
\(713\) | 48067.8 | 2.52476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3846.03 | −0.201165 | ||||||||
\(716\) | −6921.16 | −0.361251 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15514.7 | 0.806412 | ||||||||
\(719\) | 2988.41 | 0.155005 | 0.0775026 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5752.48 | 0.297134 | ||||||||
\(722\) | −71877.0 | −3.70496 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21438.9 | 1.10051 | ||||||||
\(725\) | 116.479 | 0.00596680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5507.46 | −0.280963 | −0.140482 | − | 0.990083i | \(-0.544865\pi\) | ||||
−0.140482 | + | 0.990083i | \(0.544865\pi\) | |||||||
\(728\) | 1056.79 | 0.0538011 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41033.9 | −2.08046 | ||||||||
\(731\) | 3077.75 | 0.155725 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36585.2 | −1.84353 | −0.921764 | − | 0.387751i | \(-0.873252\pi\) | ||||
−0.921764 | + | 0.387751i | \(0.873252\pi\) | |||||||
\(734\) | 14607.9 | 0.734587 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46364.6 | 2.32204 | ||||||||
\(737\) | 15765.3 | 0.787953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6425.89 | 0.319865 | 0.159933 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159933 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(740\) | 12883.0 | 0.639986 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3788.84 | −0.187457 | ||||||||
\(743\) | −20411.0 | −1.00782 | −0.503908 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503908 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8499.60 | −0.417988 | ||||||||
\(746\) | 50354.6 | 2.47133 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5111.13 | −0.249842 | ||||||||
\(749\) | 6844.81 | 0.333917 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24259.5 | −1.17875 | −0.589375 | − | 0.807860i | \(-0.700626\pi\) | ||||
−0.589375 | + | 0.807860i | \(0.700626\pi\) | |||||||
\(752\) | −22118.6 | −1.07258 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1119.10 | −0.0540518 | ||||||||
\(755\) | 26033.9 | 1.25493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9295.39 | 0.446297 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(758\) | −1454.66 | −0.0697042 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12775.6 | −0.609761 | ||||||||
\(761\) | 21974.7 | 1.04676 | 0.523378 | − | 0.852101i | \(-0.324672\pi\) | ||||
0.523378 | + | 0.852101i | \(0.324672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14631.0 | 0.694204 | ||||||||
\(764\) | −14288.9 | −0.676641 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14253.5 | −0.672324 | ||||||||
\(767\) | 11358.2 | 0.534709 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22987.4 | 1.07795 | 0.538977 | − | 0.842320i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842320i | \(0.318811\pi\) | |||||||
\(770\) | −14014.3 | −0.655897 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3590.68 | 0.167398 | ||||||||
\(773\) | −31970.9 | −1.48760 | −0.743799 | − | 0.668404i | \(-0.766978\pi\) | ||||
−0.743799 | + | 0.668404i | \(0.766978\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1517.34 | 0.0703283 | ||||||||
\(776\) | −8849.59 | −0.409384 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6860.25 | −0.316133 | ||||||||
\(779\) | −60520.8 | −2.78354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6418.85 | 0.294090 | ||||||||
\(782\) | −15436.6 | −0.705896 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10238.6 | 0.466408 | ||||||||
\(785\) | 36280.2 | 1.64955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6087.26 | 0.275715 | 0.137857 | − | 0.990452i | \(-0.455978\pi\) | ||||
0.137857 | + | 0.990452i | \(0.455978\pi\) | |||||||
\(788\) | 41520.9 | 1.87706 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15937.9 | 0.717779 | ||||||||
\(791\) | 474.878 | 0.0213460 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2431.88 | −0.108901 | ||||||||
\(794\) | −33415.4 | −1.49354 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 40363.6 | 1.79730 | ||||||||
\(797\) | −23080.0 | −1.02577 | −0.512883 | − | 0.858458i | \(-0.671423\pi\) | ||||
−0.512883 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9500.41 | 0.420651 | ||||||||
\(800\) | 1463.57 | 0.0646813 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 902.429 | 0.0397330 | ||||||||
\(803\) | −22068.3 | −0.969829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23212.9 | −1.01633 | ||||||||
\(806\) | −14578.1 | −0.637087 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4661.94 | 0.202978 | ||||||||
\(809\) | 32377.8 | 1.40710 | 0.703550 | − | 0.710646i | \(-0.251597\pi\) | ||||
0.703550 | + | 0.710646i | \(0.251597\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26352.8 | 1.14103 | 0.570513 | − | 0.821288i | \(-0.306744\pi\) | ||||
0.570513 | + | 0.821288i | \(0.306744\pi\) | |||||||
\(812\) | −2236.40 | −0.0966532 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12633.4 | 0.543980 | ||||||||
\(815\) | −26461.5 | −1.13731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23424.5 | 1.00308 | ||||||||
\(818\) | 20135.0 | 0.860638 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43451.3 | −1.85047 | ||||||||
\(821\) | −35355.3 | −1.50294 | −0.751468 | − | 0.659770i | \(-0.770654\pi\) | ||||
−0.751468 | + | 0.659770i | \(0.770654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12663.3 | −0.536347 | −0.268173 | − | 0.963371i | \(-0.586420\pi\) | ||||
−0.268173 | + | 0.963371i | \(0.586420\pi\) | |||||||
\(824\) | 3692.02 | 0.156089 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41387.6 | 1.74341 | ||||||||
\(827\) | 16295.2 | 0.685176 | 0.342588 | − | 0.939486i | \(-0.388697\pi\) | ||||
0.342588 | + | 0.939486i | \(0.388697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13638.9 | 0.571411 | 0.285705 | − | 0.958318i | \(-0.407772\pi\) | ||||
0.285705 | + | 0.958318i | \(0.407772\pi\) | |||||||
\(830\) | −20952.4 | −0.876229 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9139.61 | −0.380840 | ||||||||
\(833\) | −4397.69 | −0.182918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30474.2 | 1.26300 | ||||||||
\(836\) | −38900.5 | −1.60933 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −41685.0 | −1.71836 | ||||||||
\(839\) | 1890.31 | 0.0777838 | 0.0388919 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388919 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23970.7 | −0.982849 | ||||||||
\(842\) | 51016.4 | 2.08805 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11966.3 | 0.488028 | ||||||||
\(845\) | 1932.04 | 0.0786559 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7442.50 | 0.301921 | ||||||||
\(848\) | 3785.35 | 0.153289 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −487.280 | −0.0196630 | ||||||||
\(851\) | 20925.6 | 0.842914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1620.21 | 0.0650351 | 0.0325175 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325175 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(854\) | −8861.39 | −0.355071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4393.08 | 0.175412 | ||||||||
\(857\) | 14508.4 | 0.578292 | 0.289146 | − | 0.957285i | \(-0.406629\pi\) | ||||
0.289146 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29639.8 | 1.17730 | 0.588648 | − | 0.808389i | \(-0.299660\pi\) | ||||
0.588648 | + | 0.808389i | \(0.299660\pi\) | |||||||
\(860\) | 16817.8 | 0.666839 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −57548.8 | −2.27392 | ||||||||
\(863\) | −21528.8 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1889.10 | 0.0742557 | ||||||||
\(866\) | −29939.4 | −1.17481 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −29132.9 | −1.13921 | ||||||||
\(869\) | 8571.50 | 0.334601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7919.65 | −0.308091 | ||||||||
\(872\) | 9390.36 | 0.364676 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −117487. | −4.54696 | ||||||||
\(875\) | 15349.9 | 0.593054 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14865.3 | 0.572366 | 0.286183 | − | 0.958175i | \(-0.407613\pi\) | ||||
0.286183 | + | 0.958175i | \(0.407613\pi\) | |||||||
\(878\) | 25347.1 | 0.974285 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14001.4 | 0.536348 | ||||||||
\(881\) | 21336.0 | 0.815921 | 0.407961 | − | 0.913000i | \(-0.366240\pi\) | ||||
0.407961 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37538.2 | 1.43065 | 0.715323 | − | 0.698794i | \(-0.246280\pi\) | ||||
0.715323 | + | 0.698794i | \(0.246280\pi\) | |||||||
\(884\) | 2567.57 | 0.0976884 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −54694.1 | −2.07391 | ||||||||
\(887\) | −34575.0 | −1.30881 | −0.654406 | − | 0.756144i | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756144i | \(0.727081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3500.29 | 0.132054 | ||||||||
\(890\) | 12474.0 | 0.469807 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21251.4 | −0.797703 | ||||||||
\(893\) | 72306.9 | 2.70958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8143.61 | −0.304146 | ||||||||
\(896\) | −10165.9 | −0.379039 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46233.3 | 1.71807 | ||||||||
\(899\) | 5448.96 | 0.202150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1625.89 | −0.0601178 | ||||||||
\(902\) | −42609.2 | −1.57287 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 304.783 | 0.0112134 | ||||||||
\(905\) | 25225.5 | 0.926545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10424.8 | −0.381641 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(908\) | −40211.7 | −1.46968 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7040.05 | 0.256456 | ||||||||
\(911\) | −10961.8 | −0.398661 | −0.199331 | − | 0.979932i | \(-0.563877\pi\) | ||||
−0.199331 | + | 0.979932i | \(0.563877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11268.3 | −0.408464 | ||||||||
\(914\) | −41392.2 | −1.49796 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8116.38 | −0.292765 | ||||||||
\(917\) | 22519.7 | 0.810976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10779.2 | −0.386914 | −0.193457 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193457 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(920\) | −14898.3 | −0.533895 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14316.7 | 0.511384 | ||||||||
\(923\) | −3224.49 | −0.114990 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 660.549 | 0.0234797 | ||||||||
\(926\) | −7321.32 | −0.259820 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5255.88 | 0.185919 | ||||||||
\(929\) | −5429.07 | −0.191735 | −0.0958675 | − | 0.995394i | \(-0.530563\pi\) | ||||
−0.0958675 | + | 0.995394i | \(0.530563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33470.5 | −1.17825 | ||||||||
\(932\) | −35808.8 | −1.25854 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33499.1 | −1.17358 | ||||||||
\(935\) | −6013.88 | −0.210348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21300.1 | −0.742631 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(938\) | −28857.9 | −1.00453 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51913.2 | 1.80130 | ||||||||
\(941\) | −26851.2 | −0.930207 | −0.465103 | − | 0.885256i | \(-0.653983\pi\) | ||||
−0.465103 | + | 0.885256i | \(0.653983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −70576.7 | −2.43722 | ||||||||
\(944\) | −41349.4 | −1.42564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16491.9 | 0.566805 | ||||||||
\(947\) | 8021.68 | 0.275258 | 0.137629 | − | 0.990484i | \(-0.456052\pi\) | ||||
0.137629 | + | 0.990484i | \(0.456052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11085.9 | 0.379204 | ||||||||
\(950\) | −3708.65 | −0.126658 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1652.46 | 0.0562569 | ||||||||
\(953\) | −35715.0 | −1.21398 | −0.606990 | − | 0.794709i | \(-0.707623\pi\) | ||||
−0.606990 | + | 0.794709i | \(0.707623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16812.6 | −0.569680 | ||||||||
\(956\) | −29402.9 | −0.994726 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35490.6 | 1.19692 | ||||||||
\(959\) | 11687.9 | 0.393557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41190.9 | 1.38266 | ||||||||
\(962\) | −6346.35 | −0.212697 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31728.7 | 1.06007 | ||||||||
\(965\) | 4224.88 | 0.140936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53338.8 | 1.77380 | 0.886898 | − | 0.461965i | \(-0.152855\pi\) | ||||
0.886898 | + | 0.461965i | \(0.152855\pi\) | |||||||
\(968\) | 4776.69 | 0.158604 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −58953.6 | −1.95143 | ||||||||
\(971\) | −23112.9 | −0.763882 | −0.381941 | − | 0.924187i | \(-0.624744\pi\) | ||||
−0.381941 | + | 0.924187i | \(0.624744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32170.0 | 1.05994 | ||||||||
\(974\) | 49181.3 | 1.61794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8853.22 | 0.290353 | ||||||||
\(977\) | 52874.6 | 1.73143 | 0.865715 | − | 0.500538i | \(-0.166864\pi\) | ||||
0.865715 | + | 0.500538i | \(0.166864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6708.57 | 0.219006 | ||||||||
\(980\) | −24030.4 | −0.783287 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16645.5 | −0.540917 | ||||||||
\(983\) | −45173.1 | −1.46572 | −0.732858 | − | 0.680381i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680381i | \(0.761814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48854.5 | 1.58034 | ||||||||
\(986\) | −1749.89 | −0.0565190 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19541.6 | 0.629251 | ||||||||
\(989\) | 27316.7 | 0.878281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60485.6 | 1.93884 | 0.969418 | − | 0.245414i | \(-0.0789239\pi\) | ||||
0.969418 | + | 0.245414i | \(0.0789239\pi\) | |||||||
\(992\) | 68466.7 | 2.19135 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11749.5 | −0.374922 | ||||||||
\(995\) | 47492.8 | 1.51319 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18108.1 | −0.575214 | −0.287607 | − | 0.957749i | \(-0.592860\pi\) | ||||
−0.287607 | + | 0.957749i | \(0.592860\pi\) | |||||||
\(998\) | 23951.1 | 0.759677 | ||||||||
\(999\) | 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 | 117.4.a.f.1.1 | 3 | ||
3.2 | odd | 2 | 39.4.a.c.1.3 | ✓ | 3 | ||
4.3 | odd | 2 | 1872.4.a.bk.1.3 | 3 | |||
12.11 | even | 2 | 624.4.a.t.1.1 | 3 | |||
13.12 | even | 2 | 1521.4.a.u.1.3 | 3 | |||
15.14 | odd | 2 | 975.4.a.l.1.1 | 3 | |||
21.20 | even | 2 | 1911.4.a.k.1.3 | 3 | |||
24.5 | odd | 2 | 2496.4.a.bl.1.3 | 3 | |||
24.11 | even | 2 | 2496.4.a.bp.1.3 | 3 | |||
39.5 | even | 4 | 507.4.b.g.337.1 | 6 | |||
39.8 | even | 4 | 507.4.b.g.337.6 | 6 | |||
39.38 | odd | 2 | 507.4.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
117.4.a.f.1.1 | 3 | 1.1 | even | 1 | trivial | ||
507.4.a.h.1.1 | 3 | 39.38 | odd | 2 | |||
507.4.b.g.337.1 | 6 | 39.5 | even | 4 | |||
507.4.b.g.337.6 | 6 | 39.8 | even | 4 | |||
624.4.a.t.1.1 | 3 | 12.11 | even | 2 | |||
975.4.a.l.1.1 | 3 | 15.14 | odd | 2 | |||
1521.4.a.u.1.3 | 3 | 13.12 | even | 2 | |||
1872.4.a.bk.1.3 | 3 | 4.3 | odd | 2 | |||
1911.4.a.k.1.3 | 3 | 21.20 | even | 2 | |||
2496.4.a.bl.1.3 | 3 | 24.5 | odd | 2 | |||
2496.4.a.bp.1.3 | 3 | 24.11 | even | 2 |