Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.41 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.81936 | 1.35035 | 0.675175 | − | 0.737658i | \(-0.264068\pi\) | ||||
0.675175 | + | 0.737658i | \(0.264068\pi\) | |||||||
\(3\) | −8.34786 | −1.60655 | −0.803273 | − | 0.595611i | \(-0.796910\pi\) | ||||
−0.803273 | + | 0.595611i | \(0.796910\pi\) | |||||||
\(4\) | 6.58755 | 0.823443 | ||||||||
\(5\) | −2.56409 | −0.229339 | −0.114670 | − | 0.993404i | \(-0.536581\pi\) | ||||
−0.114670 | + | 0.993404i | \(0.536581\pi\) | |||||||
\(6\) | −31.8835 | −2.16940 | ||||||||
\(7\) | 3.42361 | 0.184858 | 0.0924288 | − | 0.995719i | \(-0.470537\pi\) | ||||
0.0924288 | + | 0.995719i | \(0.470537\pi\) | |||||||
\(8\) | −5.39467 | −0.238413 | ||||||||
\(9\) | 42.6867 | 1.58099 | ||||||||
\(10\) | −9.79321 | −0.309688 | ||||||||
\(11\) | −24.5225 | −0.672164 | −0.336082 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336082 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(12\) | −54.9919 | −1.32290 | ||||||||
\(13\) | −46.2969 | −0.987727 | −0.493864 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493864 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(14\) | 13.0760 | 0.249622 | ||||||||
\(15\) | 21.4047 | 0.368444 | ||||||||
\(16\) | −73.3046 | −1.14538 | ||||||||
\(17\) | 97.5824 | 1.39219 | 0.696095 | − | 0.717950i | \(-0.254919\pi\) | ||||
0.696095 | + | 0.717950i | \(0.254919\pi\) | |||||||
\(18\) | 163.036 | 2.13489 | ||||||||
\(19\) | 131.921 | 1.59288 | 0.796439 | − | 0.604719i | \(-0.206715\pi\) | ||||
0.796439 | + | 0.604719i | \(0.206715\pi\) | |||||||
\(20\) | −16.8911 | −0.188848 | ||||||||
\(21\) | −28.5798 | −0.296982 | ||||||||
\(22\) | −93.6603 | −0.907656 | ||||||||
\(23\) | 175.382 | 1.58998 | 0.794991 | − | 0.606621i | \(-0.207475\pi\) | ||||
0.794991 | + | 0.606621i | \(0.207475\pi\) | |||||||
\(24\) | 45.0339 | 0.383021 | ||||||||
\(25\) | −118.425 | −0.947403 | ||||||||
\(26\) | −176.825 | −1.33378 | ||||||||
\(27\) | −130.950 | −0.933385 | ||||||||
\(28\) | 22.5532 | 0.152220 | ||||||||
\(29\) | 83.1501 | 0.532434 | 0.266217 | − | 0.963913i | \(-0.414226\pi\) | ||||
0.266217 | + | 0.963913i | \(0.414226\pi\) | |||||||
\(30\) | 81.7523 | 0.497529 | ||||||||
\(31\) | 128.550 | 0.744783 | 0.372392 | − | 0.928076i | \(-0.378538\pi\) | ||||
0.372392 | + | 0.928076i | \(0.378538\pi\) | |||||||
\(32\) | −236.820 | −1.30826 | ||||||||
\(33\) | 204.710 | 1.07986 | ||||||||
\(34\) | 372.703 | 1.87994 | ||||||||
\(35\) | −8.77845 | −0.0423951 | ||||||||
\(36\) | 281.201 | 1.30186 | ||||||||
\(37\) | −301.363 | −1.33902 | −0.669510 | − | 0.742803i | \(-0.733496\pi\) | ||||
−0.669510 | + | 0.742803i | \(0.733496\pi\) | |||||||
\(38\) | 503.853 | 2.15094 | ||||||||
\(39\) | 386.480 | 1.58683 | ||||||||
\(40\) | 13.8324 | 0.0546775 | ||||||||
\(41\) | −201.066 | −0.765884 | −0.382942 | − | 0.923772i | \(-0.625089\pi\) | ||||
−0.382942 | + | 0.923772i | \(0.625089\pi\) | |||||||
\(42\) | −109.157 | −0.401030 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −161.543 | −0.553489 | ||||||||
\(45\) | −109.453 | −0.362583 | ||||||||
\(46\) | 669.846 | 2.14703 | ||||||||
\(47\) | −335.227 | −1.04038 | −0.520191 | − | 0.854050i | \(-0.674139\pi\) | ||||
−0.520191 | + | 0.854050i | \(0.674139\pi\) | |||||||
\(48\) | 611.936 | 1.84011 | ||||||||
\(49\) | −331.279 | −0.965828 | ||||||||
\(50\) | −452.310 | −1.27933 | ||||||||
\(51\) | −814.604 | −2.23662 | ||||||||
\(52\) | −304.983 | −0.813338 | ||||||||
\(53\) | 373.842 | 0.968891 | 0.484445 | − | 0.874822i | \(-0.339021\pi\) | ||||
0.484445 | + | 0.874822i | \(0.339021\pi\) | |||||||
\(54\) | −500.147 | −1.26040 | ||||||||
\(55\) | 62.8779 | 0.154154 | ||||||||
\(56\) | −18.4692 | −0.0440724 | ||||||||
\(57\) | −1101.25 | −2.55903 | ||||||||
\(58\) | 317.581 | 0.718972 | ||||||||
\(59\) | 578.431 | 1.27636 | 0.638180 | − | 0.769887i | \(-0.279688\pi\) | ||||
0.638180 | + | 0.769887i | \(0.279688\pi\) | |||||||
\(60\) | 141.004 | 0.303393 | ||||||||
\(61\) | 892.641 | 1.87362 | 0.936811 | − | 0.349835i | \(-0.113762\pi\) | ||||
0.936811 | + | 0.349835i | \(0.113762\pi\) | |||||||
\(62\) | 490.980 | 1.00572 | ||||||||
\(63\) | 146.143 | 0.292258 | ||||||||
\(64\) | −318.064 | −0.621218 | ||||||||
\(65\) | 118.710 | 0.226525 | ||||||||
\(66\) | 781.862 | 1.45819 | ||||||||
\(67\) | 2.66116 | 0.00485242 | 0.00242621 | − | 0.999997i | \(-0.499228\pi\) | ||||
0.00242621 | + | 0.999997i | \(0.499228\pi\) | |||||||
\(68\) | 642.829 | 1.14639 | ||||||||
\(69\) | −1464.06 | −2.55438 | ||||||||
\(70\) | −33.5281 | −0.0572482 | ||||||||
\(71\) | −467.961 | −0.782208 | −0.391104 | − | 0.920346i | \(-0.627907\pi\) | ||||
−0.391104 | + | 0.920346i | \(0.627907\pi\) | |||||||
\(72\) | −230.281 | −0.376928 | ||||||||
\(73\) | 481.550 | 0.772070 | 0.386035 | − | 0.922484i | \(-0.373844\pi\) | ||||
0.386035 | + | 0.922484i | \(0.373844\pi\) | |||||||
\(74\) | −1151.01 | −1.80814 | ||||||||
\(75\) | 988.598 | 1.52205 | ||||||||
\(76\) | 869.034 | 1.31164 | ||||||||
\(77\) | −83.9554 | −0.124255 | ||||||||
\(78\) | 1476.11 | 2.14277 | ||||||||
\(79\) | −296.213 | −0.421856 | −0.210928 | − | 0.977502i | \(-0.567649\pi\) | ||||
−0.210928 | + | 0.977502i | \(0.567649\pi\) | |||||||
\(80\) | 187.960 | 0.262682 | ||||||||
\(81\) | −59.3866 | −0.0814631 | ||||||||
\(82\) | −767.945 | −1.03421 | ||||||||
\(83\) | 122.365 | 0.161823 | 0.0809116 | − | 0.996721i | \(-0.474217\pi\) | ||||
0.0809116 | + | 0.996721i | \(0.474217\pi\) | |||||||
\(84\) | −188.271 | −0.244548 | ||||||||
\(85\) | −250.210 | −0.319284 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −694.125 | −0.855379 | ||||||||
\(88\) | 132.291 | 0.160253 | ||||||||
\(89\) | −746.209 | −0.888742 | −0.444371 | − | 0.895843i | \(-0.646573\pi\) | ||||
−0.444371 | + | 0.895843i | \(0.646573\pi\) | |||||||
\(90\) | −418.040 | −0.489614 | ||||||||
\(91\) | −158.503 | −0.182589 | ||||||||
\(92\) | 1155.33 | 1.30926 | ||||||||
\(93\) | −1073.12 | −1.19653 | ||||||||
\(94\) | −1280.36 | −1.40488 | ||||||||
\(95\) | −338.257 | −0.365310 | ||||||||
\(96\) | 1976.94 | 2.10177 | ||||||||
\(97\) | −1723.34 | −1.80390 | −0.901949 | − | 0.431842i | \(-0.857864\pi\) | ||||
−0.901949 | + | 0.431842i | \(0.857864\pi\) | |||||||
\(98\) | −1265.27 | −1.30420 | ||||||||
\(99\) | −1046.78 | −1.06268 | ||||||||
\(100\) | −780.133 | −0.780133 | ||||||||
\(101\) | −384.032 | −0.378343 | −0.189171 | − | 0.981944i | \(-0.560580\pi\) | ||||
−0.189171 | + | 0.981944i | \(0.560580\pi\) | |||||||
\(102\) | −3111.27 | −3.02021 | ||||||||
\(103\) | 187.491 | 0.179360 | 0.0896798 | − | 0.995971i | \(-0.471416\pi\) | ||||
0.0896798 | + | 0.995971i | \(0.471416\pi\) | |||||||
\(104\) | 249.757 | 0.235487 | ||||||||
\(105\) | 73.2813 | 0.0681097 | ||||||||
\(106\) | 1427.84 | 1.30834 | ||||||||
\(107\) | −1145.03 | −1.03453 | −0.517263 | − | 0.855827i | \(-0.673049\pi\) | ||||
−0.517263 | + | 0.855827i | \(0.673049\pi\) | |||||||
\(108\) | −862.641 | −0.768590 | ||||||||
\(109\) | −1108.95 | −0.974482 | −0.487241 | − | 0.873268i | \(-0.661997\pi\) | ||||
−0.487241 | + | 0.873268i | \(0.661997\pi\) | |||||||
\(110\) | 240.154 | 0.208161 | ||||||||
\(111\) | 2515.73 | 2.15120 | ||||||||
\(112\) | −250.966 | −0.211733 | ||||||||
\(113\) | 1450.93 | 1.20789 | 0.603947 | − | 0.797025i | \(-0.293594\pi\) | ||||
0.603947 | + | 0.797025i | \(0.293594\pi\) | |||||||
\(114\) | −4206.09 | −3.45558 | ||||||||
\(115\) | −449.695 | −0.364646 | ||||||||
\(116\) | 547.755 | 0.438429 | ||||||||
\(117\) | −1976.26 | −1.56159 | ||||||||
\(118\) | 2209.24 | 1.72353 | ||||||||
\(119\) | 334.084 | 0.257357 | ||||||||
\(120\) | −115.471 | −0.0878419 | ||||||||
\(121\) | −729.648 | −0.548196 | ||||||||
\(122\) | 3409.32 | 2.53004 | ||||||||
\(123\) | 1678.47 | 1.23043 | ||||||||
\(124\) | 846.830 | 0.613287 | ||||||||
\(125\) | 624.165 | 0.446616 | ||||||||
\(126\) | 558.172 | 0.394650 | ||||||||
\(127\) | −2025.38 | −1.41515 | −0.707574 | − | 0.706640i | \(-0.750210\pi\) | ||||
−0.707574 | + | 0.706640i | \(0.750210\pi\) | |||||||
\(128\) | 679.755 | 0.469394 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 453.395 | 0.305888 | ||||||||
\(131\) | −2553.08 | −1.70278 | −0.851390 | − | 0.524534i | \(-0.824240\pi\) | ||||
−0.851390 | + | 0.524534i | \(0.824240\pi\) | |||||||
\(132\) | 1348.54 | 0.889205 | ||||||||
\(133\) | 451.645 | 0.294455 | ||||||||
\(134\) | 10.1639 | 0.00655246 | ||||||||
\(135\) | 335.769 | 0.214062 | ||||||||
\(136\) | −526.425 | −0.331916 | ||||||||
\(137\) | 1338.26 | 0.834564 | 0.417282 | − | 0.908777i | \(-0.362983\pi\) | ||||
0.417282 | + | 0.908777i | \(0.362983\pi\) | |||||||
\(138\) | −5591.78 | −3.44930 | ||||||||
\(139\) | 687.366 | 0.419436 | 0.209718 | − | 0.977762i | \(-0.432745\pi\) | ||||
0.209718 | + | 0.977762i | \(0.432745\pi\) | |||||||
\(140\) | −57.8285 | −0.0349100 | ||||||||
\(141\) | 2798.43 | 1.67142 | ||||||||
\(142\) | −1787.31 | −1.05625 | ||||||||
\(143\) | 1135.31 | 0.663915 | ||||||||
\(144\) | −3129.13 | −1.81084 | ||||||||
\(145\) | −213.205 | −0.122108 | ||||||||
\(146\) | 1839.21 | 1.04256 | ||||||||
\(147\) | 2765.47 | 1.55165 | ||||||||
\(148\) | −1985.24 | −1.10261 | ||||||||
\(149\) | 467.843 | 0.257230 | 0.128615 | − | 0.991695i | \(-0.458947\pi\) | ||||
0.128615 | + | 0.991695i | \(0.458947\pi\) | |||||||
\(150\) | 3775.82 | 2.05530 | ||||||||
\(151\) | 1726.18 | 0.930293 | 0.465147 | − | 0.885234i | \(-0.346002\pi\) | ||||
0.465147 | + | 0.885234i | \(0.346002\pi\) | |||||||
\(152\) | −711.668 | −0.379763 | ||||||||
\(153\) | 4165.47 | 2.20104 | ||||||||
\(154\) | −320.656 | −0.167787 | ||||||||
\(155\) | −329.614 | −0.170808 | ||||||||
\(156\) | 2545.96 | 1.30666 | ||||||||
\(157\) | −488.504 | −0.248324 | −0.124162 | − | 0.992262i | \(-0.539624\pi\) | ||||
−0.124162 | + | 0.992262i | \(0.539624\pi\) | |||||||
\(158\) | −1131.35 | −0.569653 | ||||||||
\(159\) | −3120.78 | −1.55657 | ||||||||
\(160\) | 607.228 | 0.300035 | ||||||||
\(161\) | 600.438 | 0.293920 | ||||||||
\(162\) | −226.819 | −0.110004 | ||||||||
\(163\) | −1013.08 | −0.486814 | −0.243407 | − | 0.969924i | \(-0.578265\pi\) | ||||
−0.243407 | + | 0.969924i | \(0.578265\pi\) | |||||||
\(164\) | −1324.53 | −0.630662 | ||||||||
\(165\) | −524.896 | −0.247655 | ||||||||
\(166\) | 467.357 | 0.218518 | ||||||||
\(167\) | −916.697 | −0.424767 | −0.212384 | − | 0.977186i | \(-0.568123\pi\) | ||||
−0.212384 | + | 0.977186i | \(0.568123\pi\) | |||||||
\(168\) | 154.179 | 0.0708044 | ||||||||
\(169\) | −53.5953 | −0.0243948 | ||||||||
\(170\) | −955.645 | −0.431145 | ||||||||
\(171\) | 5631.26 | 2.51832 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4040.24 | −1.77557 | −0.887786 | − | 0.460257i | \(-0.847757\pi\) | ||||
−0.887786 | + | 0.460257i | \(0.847757\pi\) | |||||||
\(174\) | −2651.12 | −1.15506 | ||||||||
\(175\) | −405.442 | −0.175135 | ||||||||
\(176\) | 1797.61 | 0.769886 | ||||||||
\(177\) | −4828.65 | −2.05053 | ||||||||
\(178\) | −2850.04 | −1.20011 | ||||||||
\(179\) | 818.629 | 0.341828 | 0.170914 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170914 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(180\) | −721.025 | −0.298567 | ||||||||
\(181\) | −1761.43 | −0.723350 | −0.361675 | − | 0.932304i | \(-0.617795\pi\) | ||||
−0.361675 | + | 0.932304i | \(0.617795\pi\) | |||||||
\(182\) | −605.379 | −0.246559 | ||||||||
\(183\) | −7451.64 | −3.01006 | ||||||||
\(184\) | −946.126 | −0.379072 | ||||||||
\(185\) | 772.722 | 0.307090 | ||||||||
\(186\) | −4098.63 | −1.61573 | ||||||||
\(187\) | −2392.96 | −0.935779 | ||||||||
\(188\) | −2208.33 | −0.856696 | ||||||||
\(189\) | −448.323 | −0.172543 | ||||||||
\(190\) | −1291.93 | −0.493296 | ||||||||
\(191\) | −1206.69 | −0.457137 | −0.228568 | − | 0.973528i | \(-0.573404\pi\) | ||||
−0.228568 | + | 0.973528i | \(0.573404\pi\) | |||||||
\(192\) | 2655.15 | 0.998016 | ||||||||
\(193\) | −1227.19 | −0.457694 | −0.228847 | − | 0.973462i | \(-0.573496\pi\) | ||||
−0.228847 | + | 0.973462i | \(0.573496\pi\) | |||||||
\(194\) | −6582.05 | −2.43589 | ||||||||
\(195\) | −990.971 | −0.363922 | ||||||||
\(196\) | −2182.32 | −0.795305 | ||||||||
\(197\) | 2906.38 | 1.05112 | 0.525560 | − | 0.850756i | \(-0.323856\pi\) | ||||
0.525560 | + | 0.850756i | \(0.323856\pi\) | |||||||
\(198\) | −3998.05 | −1.43499 | ||||||||
\(199\) | −1960.29 | −0.698299 | −0.349149 | − | 0.937067i | \(-0.613529\pi\) | ||||
−0.349149 | + | 0.937067i | \(0.613529\pi\) | |||||||
\(200\) | 638.866 | 0.225873 | ||||||||
\(201\) | −22.2149 | −0.00779563 | ||||||||
\(202\) | −1466.76 | −0.510895 | ||||||||
\(203\) | 284.673 | 0.0984244 | ||||||||
\(204\) | −5366.24 | −1.84173 | ||||||||
\(205\) | 515.552 | 0.175647 | ||||||||
\(206\) | 716.097 | 0.242198 | ||||||||
\(207\) | 7486.46 | 2.51374 | ||||||||
\(208\) | 3393.78 | 1.13133 | ||||||||
\(209\) | −3235.02 | −1.07067 | ||||||||
\(210\) | 279.888 | 0.0919719 | ||||||||
\(211\) | −5227.84 | −1.70568 | −0.852841 | − | 0.522170i | \(-0.825123\pi\) | ||||
−0.852841 | + | 0.522170i | \(0.825123\pi\) | |||||||
\(212\) | 2462.70 | 0.797827 | ||||||||
\(213\) | 3906.47 | 1.25665 | ||||||||
\(214\) | −4373.29 | −1.39697 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 706.434 | 0.222531 | ||||||||
\(217\) | 440.105 | 0.137679 | ||||||||
\(218\) | −4235.50 | −1.31589 | ||||||||
\(219\) | −4019.91 | −1.24037 | ||||||||
\(220\) | 414.211 | 0.126937 | ||||||||
\(221\) | −4517.77 | −1.37510 | ||||||||
\(222\) | 9608.50 | 2.90487 | ||||||||
\(223\) | −1121.01 | −0.336631 | −0.168315 | − | 0.985733i | \(-0.553833\pi\) | ||||
−0.168315 | + | 0.985733i | \(0.553833\pi\) | |||||||
\(224\) | −810.778 | −0.241841 | ||||||||
\(225\) | −5055.19 | −1.49783 | ||||||||
\(226\) | 5541.63 | 1.63108 | ||||||||
\(227\) | −499.397 | −0.146018 | −0.0730092 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730092 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(228\) | −7254.57 | −2.10722 | ||||||||
\(229\) | 1384.89 | 0.399633 | 0.199817 | − | 0.979833i | \(-0.435965\pi\) | ||||
0.199817 | + | 0.979833i | \(0.435965\pi\) | |||||||
\(230\) | −1717.55 | −0.492399 | ||||||||
\(231\) | 700.847 | 0.199621 | ||||||||
\(232\) | −448.567 | −0.126939 | ||||||||
\(233\) | 259.379 | 0.0729291 | 0.0364646 | − | 0.999335i | \(-0.488390\pi\) | ||||
0.0364646 | + | 0.999335i | \(0.488390\pi\) | |||||||
\(234\) | −7548.07 | −2.10869 | ||||||||
\(235\) | 859.554 | 0.238601 | ||||||||
\(236\) | 3810.44 | 1.05101 | ||||||||
\(237\) | 2472.75 | 0.677730 | ||||||||
\(238\) | 1275.99 | 0.347521 | ||||||||
\(239\) | 4228.11 | 1.14432 | 0.572162 | − | 0.820140i | \(-0.306105\pi\) | ||||
0.572162 | + | 0.820140i | \(0.306105\pi\) | |||||||
\(240\) | −1569.06 | −0.422010 | ||||||||
\(241\) | −7388.11 | −1.97473 | −0.987365 | − | 0.158463i | \(-0.949346\pi\) | ||||
−0.987365 | + | 0.158463i | \(0.949346\pi\) | |||||||
\(242\) | −2786.79 | −0.740256 | ||||||||
\(243\) | 4031.41 | 1.06426 | ||||||||
\(244\) | 5880.32 | 1.54282 | ||||||||
\(245\) | 849.430 | 0.221502 | ||||||||
\(246\) | 6410.69 | 1.66151 | ||||||||
\(247\) | −6107.52 | −1.57333 | ||||||||
\(248\) | −693.485 | −0.177566 | ||||||||
\(249\) | −1021.49 | −0.259976 | ||||||||
\(250\) | 2383.92 | 0.603088 | ||||||||
\(251\) | −2006.43 | −0.504561 | −0.252280 | − | 0.967654i | \(-0.581180\pi\) | ||||
−0.252280 | + | 0.967654i | \(0.581180\pi\) | |||||||
\(252\) | 962.721 | 0.240658 | ||||||||
\(253\) | −4300.79 | −1.06873 | ||||||||
\(254\) | −7735.68 | −1.91094 | ||||||||
\(255\) | 2088.72 | 0.512944 | ||||||||
\(256\) | 5140.74 | 1.25506 | ||||||||
\(257\) | 356.050 | 0.0864195 | 0.0432098 | − | 0.999066i | \(-0.486242\pi\) | ||||
0.0432098 | + | 0.999066i | \(0.486242\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1031.75 | −0.247528 | ||||||||
\(260\) | 782.005 | 0.186530 | ||||||||
\(261\) | 3549.40 | 0.841772 | ||||||||
\(262\) | −9751.16 | −2.29935 | ||||||||
\(263\) | 2558.23 | 0.599800 | 0.299900 | − | 0.953971i | \(-0.403047\pi\) | ||||
0.299900 | + | 0.953971i | \(0.403047\pi\) | |||||||
\(264\) | −1104.34 | −0.257453 | ||||||||
\(265\) | −958.567 | −0.222205 | ||||||||
\(266\) | 1725.00 | 0.397618 | ||||||||
\(267\) | 6229.25 | 1.42780 | ||||||||
\(268\) | 17.5305 | 0.00399569 | ||||||||
\(269\) | 7645.48 | 1.73291 | 0.866455 | − | 0.499255i | \(-0.166393\pi\) | ||||
0.866455 | + | 0.499255i | \(0.166393\pi\) | |||||||
\(270\) | 1282.42 | 0.289059 | ||||||||
\(271\) | −2563.79 | −0.574683 | −0.287342 | − | 0.957828i | \(-0.592772\pi\) | ||||
−0.287342 | + | 0.957828i | \(0.592772\pi\) | |||||||
\(272\) | −7153.24 | −1.59459 | ||||||||
\(273\) | 1323.16 | 0.293337 | ||||||||
\(274\) | 5111.31 | 1.12695 | ||||||||
\(275\) | 2904.08 | 0.636810 | ||||||||
\(276\) | −9644.57 | −2.10339 | ||||||||
\(277\) | 5655.56 | 1.22675 | 0.613375 | − | 0.789792i | \(-0.289811\pi\) | ||||
0.613375 | + | 0.789792i | \(0.289811\pi\) | |||||||
\(278\) | 2625.30 | 0.566386 | ||||||||
\(279\) | 5487.38 | 1.17749 | ||||||||
\(280\) | 47.3568 | 0.0101075 | ||||||||
\(281\) | −6410.59 | −1.36094 | −0.680469 | − | 0.732777i | \(-0.738224\pi\) | ||||
−0.680469 | + | 0.732777i | \(0.738224\pi\) | |||||||
\(282\) | 10688.2 | 2.25700 | ||||||||
\(283\) | −8030.69 | −1.68684 | −0.843419 | − | 0.537256i | \(-0.819461\pi\) | ||||
−0.843419 | + | 0.537256i | \(0.819461\pi\) | |||||||
\(284\) | −3082.72 | −0.644104 | ||||||||
\(285\) | 2823.72 | 0.586887 | ||||||||
\(286\) | 4336.18 | 0.896517 | ||||||||
\(287\) | −688.372 | −0.141579 | ||||||||
\(288\) | −10109.0 | −2.06834 | ||||||||
\(289\) | 4609.33 | 0.938191 | ||||||||
\(290\) | −814.306 | −0.164889 | ||||||||
\(291\) | 14386.2 | 2.89805 | ||||||||
\(292\) | 3172.23 | 0.635756 | ||||||||
\(293\) | −3612.22 | −0.720232 | −0.360116 | − | 0.932908i | \(-0.617263\pi\) | ||||
−0.360116 | + | 0.932908i | \(0.617263\pi\) | |||||||
\(294\) | 10562.3 | 2.09526 | ||||||||
\(295\) | −1483.15 | −0.292720 | ||||||||
\(296\) | 1625.75 | 0.319240 | ||||||||
\(297\) | 3211.23 | 0.627388 | ||||||||
\(298\) | 1786.86 | 0.347350 | ||||||||
\(299\) | −8119.63 | −1.57047 | ||||||||
\(300\) | 6512.44 | 1.25332 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6592.90 | 1.25622 | ||||||||
\(303\) | 3205.84 | 0.607825 | ||||||||
\(304\) | −9670.39 | −1.82446 | ||||||||
\(305\) | −2288.81 | −0.429696 | ||||||||
\(306\) | 15909.5 | 2.97217 | ||||||||
\(307\) | −1282.10 | −0.238349 | −0.119174 | − | 0.992873i | \(-0.538025\pi\) | ||||
−0.119174 | + | 0.992873i | \(0.538025\pi\) | |||||||
\(308\) | −553.060 | −0.102317 | ||||||||
\(309\) | −1565.15 | −0.288149 | ||||||||
\(310\) | −1258.92 | −0.230651 | ||||||||
\(311\) | −9145.70 | −1.66754 | −0.833770 | − | 0.552111i | \(-0.813822\pi\) | ||||
−0.833770 | + | 0.552111i | \(0.813822\pi\) | |||||||
\(312\) | −2084.93 | −0.378321 | ||||||||
\(313\) | 3256.64 | 0.588103 | 0.294051 | − | 0.955790i | \(-0.404996\pi\) | ||||
0.294051 | + | 0.955790i | \(0.404996\pi\) | |||||||
\(314\) | −1865.78 | −0.335324 | ||||||||
\(315\) | −374.723 | −0.0670262 | ||||||||
\(316\) | −1951.32 | −0.347374 | ||||||||
\(317\) | 6460.36 | 1.14464 | 0.572319 | − | 0.820031i | \(-0.306044\pi\) | ||||
0.572319 | + | 0.820031i | \(0.306044\pi\) | |||||||
\(318\) | −11919.4 | −2.10191 | ||||||||
\(319\) | −2039.05 | −0.357883 | ||||||||
\(320\) | 815.545 | 0.142470 | ||||||||
\(321\) | 9558.54 | 1.66201 | ||||||||
\(322\) | 2293.29 | 0.396895 | ||||||||
\(323\) | 12873.1 | 2.21759 | ||||||||
\(324\) | −391.212 | −0.0670802 | ||||||||
\(325\) | 5482.73 | 0.935776 | ||||||||
\(326\) | −3869.33 | −0.657369 | ||||||||
\(327\) | 9257.39 | 1.56555 | ||||||||
\(328\) | 1084.69 | 0.182597 | ||||||||
\(329\) | −1147.69 | −0.192322 | ||||||||
\(330\) | −2004.77 | −0.334421 | ||||||||
\(331\) | 6472.81 | 1.07486 | 0.537429 | − | 0.843309i | \(-0.319396\pi\) | ||||
0.537429 | + | 0.843309i | \(0.319396\pi\) | |||||||
\(332\) | 806.086 | 0.133252 | ||||||||
\(333\) | −12864.2 | −2.11697 | ||||||||
\(334\) | −3501.20 | −0.573584 | ||||||||
\(335\) | −6.82345 | −0.00111285 | ||||||||
\(336\) | 2095.03 | 0.340159 | ||||||||
\(337\) | 1072.36 | 0.173339 | 0.0866695 | − | 0.996237i | \(-0.472378\pi\) | ||||
0.0866695 | + | 0.996237i | \(0.472378\pi\) | |||||||
\(338\) | −204.700 | −0.0329415 | ||||||||
\(339\) | −12112.2 | −1.94054 | ||||||||
\(340\) | −1648.27 | −0.262912 | ||||||||
\(341\) | −3152.37 | −0.500616 | ||||||||
\(342\) | 21507.8 | 3.40061 | ||||||||
\(343\) | −2308.47 | −0.363398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3753.99 | 0.585820 | ||||||||
\(346\) | −15431.2 | −2.39764 | ||||||||
\(347\) | −1353.35 | −0.209371 | −0.104686 | − | 0.994505i | \(-0.533384\pi\) | ||||
−0.104686 | + | 0.994505i | \(0.533384\pi\) | |||||||
\(348\) | −4572.58 | −0.704357 | ||||||||
\(349\) | −8713.86 | −1.33651 | −0.668256 | − | 0.743932i | \(-0.732959\pi\) | ||||
−0.668256 | + | 0.743932i | \(0.732959\pi\) | |||||||
\(350\) | −1548.53 | −0.236493 | ||||||||
\(351\) | 6062.60 | 0.921930 | ||||||||
\(352\) | 5807.40 | 0.879363 | ||||||||
\(353\) | 6064.05 | 0.914325 | 0.457163 | − | 0.889383i | \(-0.348866\pi\) | ||||
0.457163 | + | 0.889383i | \(0.348866\pi\) | |||||||
\(354\) | −18442.4 | −2.76893 | ||||||||
\(355\) | 1199.90 | 0.179391 | ||||||||
\(356\) | −4915.69 | −0.731829 | ||||||||
\(357\) | −2788.89 | −0.413455 | ||||||||
\(358\) | 3126.64 | 0.461587 | ||||||||
\(359\) | 2672.80 | 0.392939 | 0.196469 | − | 0.980510i | \(-0.437052\pi\) | ||||
0.196469 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(360\) | 590.461 | 0.0864445 | ||||||||
\(361\) | 10544.1 | 1.53726 | ||||||||
\(362\) | −6727.56 | −0.976775 | ||||||||
\(363\) | 6091.00 | 0.880701 | ||||||||
\(364\) | −1044.14 | −0.150352 | ||||||||
\(365\) | −1234.74 | −0.177066 | ||||||||
\(366\) | −28460.5 | −4.06463 | ||||||||
\(367\) | 3206.83 | 0.456117 | 0.228059 | − | 0.973647i | \(-0.426762\pi\) | ||||
0.228059 | + | 0.973647i | \(0.426762\pi\) | |||||||
\(368\) | −12856.3 | −1.82114 | ||||||||
\(369\) | −8582.85 | −1.21085 | ||||||||
\(370\) | 2951.31 | 0.414679 | ||||||||
\(371\) | 1279.89 | 0.179107 | ||||||||
\(372\) | −7069.22 | −0.985273 | ||||||||
\(373\) | 2341.81 | 0.325079 | 0.162539 | − | 0.986702i | \(-0.448032\pi\) | ||||
0.162539 | + | 0.986702i | \(0.448032\pi\) | |||||||
\(374\) | −9139.60 | −1.26363 | ||||||||
\(375\) | −5210.44 | −0.717510 | ||||||||
\(376\) | 1808.44 | 0.248041 | ||||||||
\(377\) | −3849.59 | −0.525900 | ||||||||
\(378\) | −1712.31 | −0.232994 | ||||||||
\(379\) | −12165.1 | −1.64876 | −0.824382 | − | 0.566034i | \(-0.808477\pi\) | ||||
−0.824382 | + | 0.566034i | \(0.808477\pi\) | |||||||
\(380\) | −2228.28 | −0.300812 | ||||||||
\(381\) | 16907.6 | 2.27350 | ||||||||
\(382\) | −4608.80 | −0.617295 | ||||||||
\(383\) | −10219.7 | −1.36345 | −0.681727 | − | 0.731606i | \(-0.738771\pi\) | ||||
−0.681727 | + | 0.731606i | \(0.738771\pi\) | |||||||
\(384\) | −5674.50 | −0.754103 | ||||||||
\(385\) | 215.269 | 0.0284965 | ||||||||
\(386\) | −4687.08 | −0.618047 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11352.6 | −1.48541 | ||||||||
\(389\) | 9610.28 | 1.25260 | 0.626299 | − | 0.779583i | \(-0.284569\pi\) | ||||
0.626299 | + | 0.779583i | \(0.284569\pi\) | |||||||
\(390\) | −3784.88 | −0.491422 | ||||||||
\(391\) | 17114.2 | 2.21356 | ||||||||
\(392\) | 1787.14 | 0.230266 | ||||||||
\(393\) | 21312.8 | 2.73559 | ||||||||
\(394\) | 11100.5 | 1.41938 | ||||||||
\(395\) | 759.518 | 0.0967481 | ||||||||
\(396\) | −6895.74 | −0.875060 | ||||||||
\(397\) | 8283.95 | 1.04725 | 0.523627 | − | 0.851948i | \(-0.324579\pi\) | ||||
0.523627 | + | 0.851948i | \(0.324579\pi\) | |||||||
\(398\) | −7487.07 | −0.942947 | ||||||||
\(399\) | −3770.26 | −0.473056 | ||||||||
\(400\) | 8681.13 | 1.08514 | ||||||||
\(401\) | −12685.4 | −1.57975 | −0.789874 | − | 0.613269i | \(-0.789854\pi\) | ||||
−0.789874 | + | 0.613269i | \(0.789854\pi\) | |||||||
\(402\) | −84.8470 | −0.0105268 | ||||||||
\(403\) | −5951.47 | −0.735643 | ||||||||
\(404\) | −2529.83 | −0.311544 | ||||||||
\(405\) | 152.273 | 0.0186827 | ||||||||
\(406\) | 1087.27 | 0.132907 | ||||||||
\(407\) | 7390.16 | 0.900040 | ||||||||
\(408\) | 4394.52 | 0.533238 | ||||||||
\(409\) | −981.857 | −0.118703 | −0.0593517 | − | 0.998237i | \(-0.518903\pi\) | ||||
−0.0593517 | + | 0.998237i | \(0.518903\pi\) | |||||||
\(410\) | 1969.08 | 0.237185 | ||||||||
\(411\) | −11171.6 | −1.34077 | ||||||||
\(412\) | 1235.11 | 0.147693 | ||||||||
\(413\) | 1980.32 | 0.235945 | ||||||||
\(414\) | 28593.5 | 3.39443 | ||||||||
\(415\) | −313.756 | −0.0371124 | ||||||||
\(416\) | 10964.0 | 1.29220 | ||||||||
\(417\) | −5738.03 | −0.673844 | ||||||||
\(418\) | −12355.7 | −1.44578 | ||||||||
\(419\) | 10930.0 | 1.27439 | 0.637193 | − | 0.770704i | \(-0.280095\pi\) | ||||
0.637193 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(420\) | 482.744 | 0.0560845 | ||||||||
\(421\) | 12352.3 | 1.42996 | 0.714980 | − | 0.699145i | \(-0.246436\pi\) | ||||
0.714980 | + | 0.699145i | \(0.246436\pi\) | |||||||
\(422\) | −19967.0 | −2.30327 | ||||||||
\(423\) | −14309.8 | −1.64483 | ||||||||
\(424\) | −2016.76 | −0.230996 | ||||||||
\(425\) | −11556.2 | −1.31896 | ||||||||
\(426\) | 14920.2 | 1.69692 | ||||||||
\(427\) | 3056.05 | 0.346353 | ||||||||
\(428\) | −7542.94 | −0.851873 | ||||||||
\(429\) | −9477.44 | −1.06661 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6534.96 | −0.730343 | −0.365172 | − | 0.930940i | \(-0.618990\pi\) | ||||
−0.365172 | + | 0.930940i | \(0.618990\pi\) | |||||||
\(432\) | 9599.26 | 1.06908 | ||||||||
\(433\) | 12272.7 | 1.36210 | 0.681048 | − | 0.732239i | \(-0.261524\pi\) | ||||
0.681048 | + | 0.732239i | \(0.261524\pi\) | |||||||
\(434\) | 1680.92 | 0.185914 | ||||||||
\(435\) | 1779.80 | 0.196172 | ||||||||
\(436\) | −7305.29 | −0.802431 | ||||||||
\(437\) | 23136.5 | 2.53265 | ||||||||
\(438\) | −15353.5 | −1.67493 | ||||||||
\(439\) | −2806.41 | −0.305108 | −0.152554 | − | 0.988295i | \(-0.548750\pi\) | ||||
−0.152554 | + | 0.988295i | \(0.548750\pi\) | |||||||
\(440\) | −339.205 | −0.0367522 | ||||||||
\(441\) | −14141.2 | −1.52696 | ||||||||
\(442\) | −17255.0 | −1.85687 | ||||||||
\(443\) | −9336.79 | −1.00136 | −0.500682 | − | 0.865631i | \(-0.666917\pi\) | ||||
−0.500682 | + | 0.865631i | \(0.666917\pi\) | |||||||
\(444\) | 16572.5 | 1.77139 | ||||||||
\(445\) | 1913.35 | 0.203824 | ||||||||
\(446\) | −4281.56 | −0.454569 | ||||||||
\(447\) | −3905.49 | −0.413251 | ||||||||
\(448\) | −1088.93 | −0.114837 | ||||||||
\(449\) | 7212.30 | 0.758062 | 0.379031 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379031 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(450\) | −19307.6 | −2.02260 | ||||||||
\(451\) | 4930.64 | 0.514800 | ||||||||
\(452\) | 9558.07 | 0.994632 | ||||||||
\(453\) | −14409.9 | −1.49456 | ||||||||
\(454\) | −1907.38 | −0.197176 | ||||||||
\(455\) | 406.415 | 0.0418748 | ||||||||
\(456\) | 5940.90 | 0.610106 | ||||||||
\(457\) | −1378.40 | −0.141091 | −0.0705455 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705455 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(458\) | 5289.40 | 0.539645 | ||||||||
\(459\) | −12778.4 | −1.29945 | ||||||||
\(460\) | −2962.39 | −0.300265 | ||||||||
\(461\) | −11245.2 | −1.13610 | −0.568048 | − | 0.822996i | \(-0.692301\pi\) | ||||
−0.568048 | + | 0.822996i | \(0.692301\pi\) | |||||||
\(462\) | 2676.79 | 0.269558 | ||||||||
\(463\) | 2077.54 | 0.208535 | 0.104267 | − | 0.994549i | \(-0.466750\pi\) | ||||
0.104267 | + | 0.994549i | \(0.466750\pi\) | |||||||
\(464\) | −6095.28 | −0.609842 | ||||||||
\(465\) | 2751.57 | 0.274411 | ||||||||
\(466\) | 990.663 | 0.0984798 | ||||||||
\(467\) | −2016.77 | −0.199839 | −0.0999197 | − | 0.994996i | \(-0.531859\pi\) | ||||
−0.0999197 | + | 0.994996i | \(0.531859\pi\) | |||||||
\(468\) | −13018.7 | −1.28588 | ||||||||
\(469\) | 9.11076 | 0.000897006 0 | ||||||||
\(470\) | 3282.95 | 0.322194 | ||||||||
\(471\) | 4077.96 | 0.398944 | ||||||||
\(472\) | −3120.44 | −0.304301 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9444.32 | 0.915173 | ||||||||
\(475\) | −15622.8 | −1.50910 | ||||||||
\(476\) | 2200.80 | 0.211919 | ||||||||
\(477\) | 15958.1 | 1.53181 | ||||||||
\(478\) | 16148.7 | 1.54524 | ||||||||
\(479\) | 10427.0 | 0.994620 | 0.497310 | − | 0.867573i | \(-0.334321\pi\) | ||||
0.497310 | + | 0.867573i | \(0.334321\pi\) | |||||||
\(480\) | −5069.05 | −0.482019 | ||||||||
\(481\) | 13952.2 | 1.32259 | ||||||||
\(482\) | −28217.9 | −2.66658 | ||||||||
\(483\) | −5012.37 | −0.472196 | ||||||||
\(484\) | −4806.59 | −0.451408 | ||||||||
\(485\) | 4418.79 | 0.413705 | ||||||||
\(486\) | 15397.4 | 1.43712 | ||||||||
\(487\) | −4165.93 | −0.387631 | −0.193815 | − | 0.981038i | \(-0.562086\pi\) | ||||
−0.193815 | + | 0.981038i | \(0.562086\pi\) | |||||||
\(488\) | −4815.50 | −0.446696 | ||||||||
\(489\) | 8457.06 | 0.782089 | ||||||||
\(490\) | 3244.28 | 0.299106 | ||||||||
\(491\) | −11303.6 | −1.03895 | −0.519475 | − | 0.854486i | \(-0.673873\pi\) | ||||
−0.519475 | + | 0.854486i | \(0.673873\pi\) | |||||||
\(492\) | 11057.0 | 1.01319 | ||||||||
\(493\) | 8113.99 | 0.741249 | ||||||||
\(494\) | −23326.8 | −2.12454 | ||||||||
\(495\) | 2684.05 | 0.243715 | ||||||||
\(496\) | −9423.31 | −0.853063 | ||||||||
\(497\) | −1602.12 | −0.144597 | ||||||||
\(498\) | −3901.43 | −0.351059 | ||||||||
\(499\) | 13070.3 | 1.17256 | 0.586281 | − | 0.810108i | \(-0.300592\pi\) | ||||
0.586281 | + | 0.810108i | \(0.300592\pi\) | |||||||
\(500\) | 4111.72 | 0.367763 | ||||||||
\(501\) | 7652.45 | 0.682408 | ||||||||
\(502\) | −7663.29 | −0.681333 | ||||||||
\(503\) | 9968.27 | 0.883625 | 0.441812 | − | 0.897107i | \(-0.354336\pi\) | ||||
0.441812 | + | 0.897107i | \(0.354336\pi\) | |||||||
\(504\) | −788.391 | −0.0696780 | ||||||||
\(505\) | 984.694 | 0.0867689 | ||||||||
\(506\) | −16426.3 | −1.44316 | ||||||||
\(507\) | 447.406 | 0.0391913 | ||||||||
\(508\) | −13342.3 | −1.16529 | ||||||||
\(509\) | 11910.6 | 1.03719 | 0.518594 | − | 0.855021i | \(-0.326456\pi\) | ||||
0.518594 | + | 0.855021i | \(0.326456\pi\) | |||||||
\(510\) | 7977.59 | 0.692654 | ||||||||
\(511\) | 1648.64 | 0.142723 | ||||||||
\(512\) | 14196.3 | 1.22538 | ||||||||
\(513\) | −17275.0 | −1.48677 | ||||||||
\(514\) | 1359.89 | 0.116697 | ||||||||
\(515\) | −480.744 | −0.0411342 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8220.61 | 0.699307 | ||||||||
\(518\) | −3940.62 | −0.334249 | ||||||||
\(519\) | 33727.4 | 2.85254 | ||||||||
\(520\) | −640.399 | −0.0540065 | ||||||||
\(521\) | −7264.31 | −0.610854 | −0.305427 | − | 0.952215i | \(-0.598799\pi\) | ||||
−0.305427 | + | 0.952215i | \(0.598799\pi\) | |||||||
\(522\) | 13556.5 | 1.13669 | ||||||||
\(523\) | −11647.5 | −0.973823 | −0.486912 | − | 0.873451i | \(-0.661877\pi\) | ||||
−0.486912 | + | 0.873451i | \(0.661877\pi\) | |||||||
\(524\) | −16818.6 | −1.40214 | ||||||||
\(525\) | 3384.57 | 0.281362 | ||||||||
\(526\) | 9770.83 | 0.809940 | ||||||||
\(527\) | 12544.2 | 1.03688 | ||||||||
\(528\) | −15006.2 | −1.23686 | ||||||||
\(529\) | 18591.7 | 1.52804 | ||||||||
\(530\) | −3661.12 | −0.300054 | ||||||||
\(531\) | 24691.3 | 2.01791 | ||||||||
\(532\) | 2975.23 | 0.242467 | ||||||||
\(533\) | 9308.74 | 0.756485 | ||||||||
\(534\) | 23791.8 | 1.92803 | ||||||||
\(535\) | 2935.96 | 0.237257 | ||||||||
\(536\) | −14.3561 | −0.00115688 | ||||||||
\(537\) | −6833.80 | −0.549162 | ||||||||
\(538\) | 29200.9 | 2.34003 | ||||||||
\(539\) | 8123.78 | 0.649195 | ||||||||
\(540\) | 2211.89 | 0.176268 | ||||||||
\(541\) | 3578.45 | 0.284380 | 0.142190 | − | 0.989839i | \(-0.454586\pi\) | ||||
0.142190 | + | 0.989839i | \(0.454586\pi\) | |||||||
\(542\) | −9792.05 | −0.776023 | ||||||||
\(543\) | 14704.2 | 1.16209 | ||||||||
\(544\) | −23109.4 | −1.82134 | ||||||||
\(545\) | 2843.46 | 0.223487 | ||||||||
\(546\) | 5053.62 | 0.396108 | ||||||||
\(547\) | −15440.8 | −1.20695 | −0.603475 | − | 0.797382i | \(-0.706218\pi\) | ||||
−0.603475 | + | 0.797382i | \(0.706218\pi\) | |||||||
\(548\) | 8815.86 | 0.687217 | ||||||||
\(549\) | 38103.9 | 2.96218 | ||||||||
\(550\) | 11091.8 | 0.859917 | ||||||||
\(551\) | 10969.2 | 0.848102 | ||||||||
\(552\) | 7898.12 | 0.608997 | ||||||||
\(553\) | −1014.12 | −0.0779832 | ||||||||
\(554\) | 21600.7 | 1.65654 | ||||||||
\(555\) | −6450.57 | −0.493354 | ||||||||
\(556\) | 4528.06 | 0.345382 | ||||||||
\(557\) | −2684.18 | −0.204187 | −0.102094 | − | 0.994775i | \(-0.532554\pi\) | ||||
−0.102094 | + | 0.994775i | \(0.532554\pi\) | |||||||
\(558\) | 20958.3 | 1.59003 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 643.501 | 0.0485587 | ||||||||
\(561\) | 19976.1 | 1.50337 | ||||||||
\(562\) | −24484.4 | −1.83774 | ||||||||
\(563\) | −10345.1 | −0.774412 | −0.387206 | − | 0.921993i | \(-0.626560\pi\) | ||||
−0.387206 | + | 0.921993i | \(0.626560\pi\) | |||||||
\(564\) | 18434.8 | 1.37632 | ||||||||
\(565\) | −3720.32 | −0.277018 | ||||||||
\(566\) | −30672.1 | −2.27782 | ||||||||
\(567\) | −203.316 | −0.0150591 | ||||||||
\(568\) | 2524.50 | 0.186489 | ||||||||
\(569\) | 60.6533 | 0.00446875 | 0.00223438 | − | 0.999998i | \(-0.499289\pi\) | ||||
0.00223438 | + | 0.999998i | \(0.499289\pi\) | |||||||
\(570\) | 10784.8 | 0.792502 | ||||||||
\(571\) | −2225.56 | −0.163111 | −0.0815557 | − | 0.996669i | \(-0.525989\pi\) | ||||
−0.0815557 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(572\) | 7478.94 | 0.546696 | ||||||||
\(573\) | 10073.3 | 0.734411 | ||||||||
\(574\) | −2629.14 | −0.191182 | ||||||||
\(575\) | −20769.6 | −1.50635 | ||||||||
\(576\) | −13577.1 | −0.982139 | ||||||||
\(577\) | −16249.2 | −1.17238 | −0.586190 | − | 0.810173i | \(-0.699373\pi\) | ||||
−0.586190 | + | 0.810173i | \(0.699373\pi\) | |||||||
\(578\) | 17604.7 | 1.26689 | ||||||||
\(579\) | 10244.4 | 0.735306 | ||||||||
\(580\) | −1404.50 | −0.100549 | ||||||||
\(581\) | 418.930 | 0.0299142 | ||||||||
\(582\) | 54946.0 | 3.91337 | ||||||||
\(583\) | −9167.54 | −0.651253 | ||||||||
\(584\) | −2597.80 | −0.184072 | ||||||||
\(585\) | 5067.32 | 0.358133 | ||||||||
\(586\) | −13796.4 | −0.972564 | ||||||||
\(587\) | 10104.6 | 0.710496 | 0.355248 | − | 0.934772i | \(-0.384396\pi\) | ||||
0.355248 | + | 0.934772i | \(0.384396\pi\) | |||||||
\(588\) | 18217.7 | 1.27769 | ||||||||
\(589\) | 16958.4 | 1.18635 | ||||||||
\(590\) | −5664.69 | −0.395274 | ||||||||
\(591\) | −24262.0 | −1.68867 | ||||||||
\(592\) | 22091.3 | 1.53369 | ||||||||
\(593\) | −10930.9 | −0.756962 | −0.378481 | − | 0.925609i | \(-0.623553\pi\) | ||||
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(594\) | 12264.8 | 0.847193 | ||||||||
\(595\) | −856.623 | −0.0590220 | ||||||||
\(596\) | 3081.94 | 0.211814 | ||||||||
\(597\) | 16364.2 | 1.12185 | ||||||||
\(598\) | −31011.8 | −2.12068 | ||||||||
\(599\) | −21584.2 | −1.47230 | −0.736149 | − | 0.676819i | \(-0.763358\pi\) | ||||
−0.736149 | + | 0.676819i | \(0.763358\pi\) | |||||||
\(600\) | −5333.16 | −0.362876 | ||||||||
\(601\) | −18226.1 | −1.23704 | −0.618519 | − | 0.785770i | \(-0.712267\pi\) | ||||
−0.618519 | + | 0.785770i | \(0.712267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 113.596 | 0.00767162 | ||||||||
\(604\) | 11371.3 | 0.766044 | ||||||||
\(605\) | 1870.89 | 0.125723 | ||||||||
\(606\) | 12244.3 | 0.820776 | ||||||||
\(607\) | −24757.1 | −1.65546 | −0.827728 | − | 0.561130i | \(-0.810367\pi\) | ||||
−0.827728 | + | 0.561130i | \(0.810367\pi\) | |||||||
\(608\) | −31241.4 | −2.08389 | ||||||||
\(609\) | −2376.41 | −0.158123 | ||||||||
\(610\) | −8741.82 | −0.580239 | ||||||||
\(611\) | 15520.0 | 1.02761 | ||||||||
\(612\) | 27440.2 | 1.81243 | ||||||||
\(613\) | −19983.4 | −1.31668 | −0.658339 | − | 0.752722i | \(-0.728741\pi\) | ||||
−0.658339 | + | 0.752722i | \(0.728741\pi\) | |||||||
\(614\) | −4896.79 | −0.321854 | ||||||||
\(615\) | −4303.76 | −0.282186 | ||||||||
\(616\) | 452.911 | 0.0296239 | ||||||||
\(617\) | 26758.7 | 1.74597 | 0.872985 | − | 0.487746i | \(-0.162181\pi\) | ||||
0.872985 | + | 0.487746i | \(0.162181\pi\) | |||||||
\(618\) | −5977.87 | −0.389102 | ||||||||
\(619\) | 3557.65 | 0.231008 | 0.115504 | − | 0.993307i | \(-0.463152\pi\) | ||||
0.115504 | + | 0.993307i | \(0.463152\pi\) | |||||||
\(620\) | −2171.35 | −0.140651 | ||||||||
\(621\) | −22966.3 | −1.48407 | ||||||||
\(622\) | −34930.8 | −2.25176 | ||||||||
\(623\) | −2554.73 | −0.164291 | ||||||||
\(624\) | −28330.8 | −1.81753 | ||||||||
\(625\) | 13202.8 | 0.844977 | ||||||||
\(626\) | 12438.3 | 0.794144 | ||||||||
\(627\) | 27005.5 | 1.72009 | ||||||||
\(628\) | −3218.05 | −0.204481 | ||||||||
\(629\) | −29407.7 | −1.86417 | ||||||||
\(630\) | −1431.20 | −0.0905088 | ||||||||
\(631\) | 22683.1 | 1.43106 | 0.715532 | − | 0.698580i | \(-0.246184\pi\) | ||||
0.715532 | + | 0.698580i | \(0.246184\pi\) | |||||||
\(632\) | 1597.97 | 0.100576 | ||||||||
\(633\) | 43641.2 | 2.74026 | ||||||||
\(634\) | 24674.5 | 1.54566 | ||||||||
\(635\) | 5193.27 | 0.324549 | ||||||||
\(636\) | −20558.3 | −1.28174 | ||||||||
\(637\) | 15337.2 | 0.953974 | ||||||||
\(638\) | −7787.86 | −0.483267 | ||||||||
\(639\) | −19975.7 | −1.23666 | ||||||||
\(640\) | −1742.96 | −0.107651 | ||||||||
\(641\) | 3214.41 | 0.198068 | 0.0990341 | − | 0.995084i | \(-0.468425\pi\) | ||||
0.0990341 | + | 0.995084i | \(0.468425\pi\) | |||||||
\(642\) | 36507.6 | 2.24430 | ||||||||
\(643\) | 5096.07 | 0.312550 | 0.156275 | − | 0.987714i | \(-0.450051\pi\) | ||||
0.156275 | + | 0.987714i | \(0.450051\pi\) | |||||||
\(644\) | 3955.42 | 0.242027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49167.2 | 2.99452 | ||||||||
\(647\) | 2031.59 | 0.123447 | 0.0617234 | − | 0.998093i | \(-0.480340\pi\) | ||||
0.0617234 | + | 0.998093i | \(0.480340\pi\) | |||||||
\(648\) | 320.371 | 0.0194218 | ||||||||
\(649\) | −14184.5 | −0.857923 | ||||||||
\(650\) | 20940.6 | 1.26362 | ||||||||
\(651\) | −3673.94 | −0.221187 | ||||||||
\(652\) | −6673.72 | −0.400864 | ||||||||
\(653\) | 6868.13 | 0.411594 | 0.205797 | − | 0.978595i | \(-0.434021\pi\) | ||||
0.205797 | + | 0.978595i | \(0.434021\pi\) | |||||||
\(654\) | 35357.3 | 2.11404 | ||||||||
\(655\) | 6546.35 | 0.390514 | ||||||||
\(656\) | 14739.1 | 0.877232 | ||||||||
\(657\) | 20555.8 | 1.22063 | ||||||||
\(658\) | −4383.44 | −0.259702 | ||||||||
\(659\) | −11046.0 | −0.652947 | −0.326474 | − | 0.945206i | \(-0.605860\pi\) | ||||
−0.326474 | + | 0.945206i | \(0.605860\pi\) | |||||||
\(660\) | −3457.78 | −0.203930 | ||||||||
\(661\) | 19990.5 | 1.17631 | 0.588156 | − | 0.808748i | \(-0.299854\pi\) | ||||
0.588156 | + | 0.808748i | \(0.299854\pi\) | |||||||
\(662\) | 24722.0 | 1.45143 | ||||||||
\(663\) | 37713.7 | 2.20917 | ||||||||
\(664\) | −660.120 | −0.0385807 | ||||||||
\(665\) | −1158.06 | −0.0675302 | ||||||||
\(666\) | −49133.0 | −2.85865 | ||||||||
\(667\) | 14583.0 | 0.846561 | ||||||||
\(668\) | −6038.78 | −0.349772 | ||||||||
\(669\) | 9358.06 | 0.540812 | ||||||||
\(670\) | −26.0612 | −0.00150274 | ||||||||
\(671\) | −21889.8 | −1.25938 | ||||||||
\(672\) | 6768.26 | 0.388529 | ||||||||
\(673\) | 17975.7 | 1.02958 | 0.514792 | − | 0.857315i | \(-0.327869\pi\) | ||||
0.514792 | + | 0.857315i | \(0.327869\pi\) | |||||||
\(674\) | 4095.74 | 0.234068 | ||||||||
\(675\) | 15507.8 | 0.884292 | ||||||||
\(676\) | −353.062 | −0.0200877 | ||||||||
\(677\) | 742.490 | 0.0421510 | 0.0210755 | − | 0.999778i | \(-0.493291\pi\) | ||||
0.0210755 | + | 0.999778i | \(0.493291\pi\) | |||||||
\(678\) | −46260.7 | −2.62040 | ||||||||
\(679\) | −5900.03 | −0.333464 | ||||||||
\(680\) | 1349.80 | 0.0761214 | ||||||||
\(681\) | 4168.90 | 0.234585 | ||||||||
\(682\) | −12040.0 | −0.676007 | ||||||||
\(683\) | 29791.7 | 1.66903 | 0.834514 | − | 0.550987i | \(-0.185748\pi\) | ||||
0.834514 | + | 0.550987i | \(0.185748\pi\) | |||||||
\(684\) | 37096.2 | 2.07370 | ||||||||
\(685\) | −3431.42 | −0.191399 | ||||||||
\(686\) | −8816.88 | −0.490714 | ||||||||
\(687\) | −11560.9 | −0.642029 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17307.7 | −0.957000 | ||||||||
\(690\) | 14337.8 | 0.791062 | ||||||||
\(691\) | 3361.09 | 0.185039 | 0.0925196 | − | 0.995711i | \(-0.470508\pi\) | ||||
0.0925196 | + | 0.995711i | \(0.470508\pi\) | |||||||
\(692\) | −26615.3 | −1.46208 | ||||||||
\(693\) | −3583.78 | −0.196445 | ||||||||
\(694\) | −5168.95 | −0.282724 | ||||||||
\(695\) | −1762.47 | −0.0961933 | ||||||||
\(696\) | 3744.58 | 0.203934 | ||||||||
\(697\) | −19620.5 | −1.06626 | ||||||||
\(698\) | −33281.4 | −1.80476 | ||||||||
\(699\) | −2165.26 | −0.117164 | ||||||||
\(700\) | −2670.87 | −0.144213 | ||||||||
\(701\) | 23288.1 | 1.25475 | 0.627373 | − | 0.778719i | \(-0.284130\pi\) | ||||
0.627373 | + | 0.778719i | \(0.284130\pi\) | |||||||
\(702\) | 23155.3 | 1.24493 | ||||||||
\(703\) | −39755.9 | −2.13289 | ||||||||
\(704\) | 7799.71 | 0.417561 | ||||||||
\(705\) | −7175.44 | −0.383323 | ||||||||
\(706\) | 23160.8 | 1.23466 | ||||||||
\(707\) | −1314.78 | −0.0699395 | ||||||||
\(708\) | −31809.0 | −1.68850 | ||||||||
\(709\) | 17503.7 | 0.927171 | 0.463585 | − | 0.886052i | \(-0.346563\pi\) | ||||
0.463585 | + | 0.886052i | \(0.346563\pi\) | |||||||
\(710\) | 4582.84 | 0.242241 | ||||||||
\(711\) | −12644.4 | −0.666949 | ||||||||
\(712\) | 4025.55 | 0.211888 | ||||||||
\(713\) | 22545.3 | 1.18419 | ||||||||
\(714\) | −10651.8 | −0.558309 | ||||||||
\(715\) | −2911.05 | −0.152262 | ||||||||
\(716\) | 5392.76 | 0.281476 | ||||||||
\(717\) | −35295.6 | −1.83841 | ||||||||
\(718\) | 10208.4 | 0.530605 | ||||||||
\(719\) | −10970.4 | −0.569024 | −0.284512 | − | 0.958673i | \(-0.591832\pi\) | ||||
−0.284512 | + | 0.958673i | \(0.591832\pi\) | |||||||
\(720\) | 8023.38 | 0.415297 | ||||||||
\(721\) | 641.896 | 0.0331560 | ||||||||
\(722\) | 40271.6 | 2.07584 | ||||||||
\(723\) | 61674.9 | 3.17249 | ||||||||
\(724\) | −11603.5 | −0.595638 | ||||||||
\(725\) | −9847.09 | −0.504430 | ||||||||
\(726\) | 23263.8 | 1.18925 | ||||||||
\(727\) | −747.962 | −0.0381573 | −0.0190787 | − | 0.999818i | \(-0.506073\pi\) | ||||
−0.0190787 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(728\) | 855.069 | 0.0435315 | ||||||||
\(729\) | −32050.2 | −1.62832 | ||||||||
\(730\) | −4715.91 | −0.239101 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −49088.0 | −2.47861 | ||||||||
\(733\) | −21811.3 | −1.09907 | −0.549534 | − | 0.835471i | \(-0.685195\pi\) | ||||
−0.549534 | + | 0.835471i | \(0.685195\pi\) | |||||||
\(734\) | 12248.0 | 0.615918 | ||||||||
\(735\) | −7090.92 | −0.355854 | ||||||||
\(736\) | −41533.8 | −2.08010 | ||||||||
\(737\) | −65.2581 | −0.00326162 | ||||||||
\(738\) | −32781.0 | −1.63508 | ||||||||
\(739\) | −13215.5 | −0.657834 | −0.328917 | − | 0.944359i | \(-0.606684\pi\) | ||||
−0.328917 | + | 0.944359i | \(0.606684\pi\) | |||||||
\(740\) | 5090.34 | 0.252871 | ||||||||
\(741\) | 50984.7 | 2.52762 | ||||||||
\(742\) | 4888.37 | 0.241857 | ||||||||
\(743\) | −25963.2 | −1.28196 | −0.640980 | − | 0.767558i | \(-0.721472\pi\) | ||||
−0.640980 | + | 0.767558i | \(0.721472\pi\) | |||||||
\(744\) | 5789.12 | 0.285268 | ||||||||
\(745\) | −1199.59 | −0.0589929 | ||||||||
\(746\) | 8944.24 | 0.438970 | ||||||||
\(747\) | 5223.36 | 0.255841 | ||||||||
\(748\) | −15763.8 | −0.770561 | ||||||||
\(749\) | −3920.13 | −0.191240 | ||||||||
\(750\) | −19900.6 | −0.968889 | ||||||||
\(751\) | 3717.93 | 0.180651 | 0.0903256 | − | 0.995912i | \(-0.471209\pi\) | ||||
0.0903256 | + | 0.995912i | \(0.471209\pi\) | |||||||
\(752\) | 24573.7 | 1.19164 | ||||||||
\(753\) | 16749.4 | 0.810600 | ||||||||
\(754\) | −14703.0 | −0.710148 | ||||||||
\(755\) | −4426.08 | −0.213353 | ||||||||
\(756\) | −2953.35 | −0.142080 | ||||||||
\(757\) | −120.818 | −0.00580079 | −0.00290039 | − | 0.999996i | \(-0.500923\pi\) | ||||
−0.00290039 | + | 0.999996i | \(0.500923\pi\) | |||||||
\(758\) | −46463.1 | −2.22641 | ||||||||
\(759\) | 35902.4 | 1.71696 | ||||||||
\(760\) | 1824.78 | 0.0870945 | ||||||||
\(761\) | −23248.7 | −1.10744 | −0.553722 | − | 0.832702i | \(-0.686793\pi\) | ||||
−0.553722 | + | 0.832702i | \(0.686793\pi\) | |||||||
\(762\) | 64576.3 | 3.07002 | ||||||||
\(763\) | −3796.62 | −0.180140 | ||||||||
\(764\) | −7949.14 | −0.376426 | ||||||||
\(765\) | −10680.7 | −0.504784 | ||||||||
\(766\) | −39032.8 | −1.84114 | ||||||||
\(767\) | −26779.6 | −1.26070 | ||||||||
\(768\) | −42914.2 | −2.01632 | ||||||||
\(769\) | 12713.4 | 0.596174 | 0.298087 | − | 0.954539i | \(-0.403651\pi\) | ||||
0.298087 | + | 0.954539i | \(0.403651\pi\) | |||||||
\(770\) | 822.192 | 0.0384802 | ||||||||
\(771\) | −2972.26 | −0.138837 | ||||||||
\(772\) | −8084.16 | −0.376885 | ||||||||
\(773\) | 6472.11 | 0.301146 | 0.150573 | − | 0.988599i | \(-0.451888\pi\) | ||||
0.150573 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15223.6 | −0.705610 | ||||||||
\(776\) | 9296.82 | 0.430073 | ||||||||
\(777\) | 8612.88 | 0.397665 | ||||||||
\(778\) | 36705.2 | 1.69144 | ||||||||
\(779\) | −26524.8 | −1.21996 | ||||||||
\(780\) | −6528.07 | −0.299670 | ||||||||
\(781\) | 11475.6 | 0.525772 | ||||||||
\(782\) | 65365.2 | 2.98907 | ||||||||
\(783\) | −10888.5 | −0.496966 | ||||||||
\(784\) | 24284.3 | 1.10624 | ||||||||
\(785\) | 1252.57 | 0.0569505 | ||||||||
\(786\) | 81401.3 | 3.69401 | ||||||||
\(787\) | −25596.9 | −1.15938 | −0.579689 | − | 0.814838i | \(-0.696826\pi\) | ||||
−0.579689 | + | 0.814838i | \(0.696826\pi\) | |||||||
\(788\) | 19145.9 | 0.865538 | ||||||||
\(789\) | −21355.8 | −0.963606 | ||||||||
\(790\) | 2900.88 | 0.130644 | ||||||||
\(791\) | 4967.42 | 0.223288 | ||||||||
\(792\) | 5647.05 | 0.253358 | ||||||||
\(793\) | −41326.5 | −1.85063 | ||||||||
\(794\) | 31639.4 | 1.41416 | ||||||||
\(795\) | 8001.98 | 0.356982 | ||||||||
\(796\) | −12913.5 | −0.575010 | ||||||||
\(797\) | −26835.0 | −1.19265 | −0.596327 | − | 0.802742i | \(-0.703374\pi\) | ||||
−0.596327 | + | 0.802742i | \(0.703374\pi\) | |||||||
\(798\) | −14400.0 | −0.638791 | ||||||||
\(799\) | −32712.3 | −1.44841 | ||||||||
\(800\) | 28045.5 | 1.23945 | ||||||||
\(801\) | −31853.2 | −1.40509 | ||||||||
\(802\) | −48450.2 | −2.13321 | ||||||||
\(803\) | −11808.8 | −0.518958 | ||||||||
\(804\) | −146.342 | −0.00641926 | ||||||||
\(805\) | −1539.58 | −0.0674075 | ||||||||
\(806\) | −22730.9 | −0.993375 | ||||||||
\(807\) | −63823.3 | −2.78400 | ||||||||
\(808\) | 2071.73 | 0.0902018 | ||||||||
\(809\) | −22386.4 | −0.972887 | −0.486443 | − | 0.873712i | \(-0.661706\pi\) | ||||
−0.486443 | + | 0.873712i | \(0.661706\pi\) | |||||||
\(810\) | 581.585 | 0.0252282 | ||||||||
\(811\) | 12050.9 | 0.521781 | 0.260891 | − | 0.965368i | \(-0.415984\pi\) | ||||
0.260891 | + | 0.965368i | \(0.415984\pi\) | |||||||
\(812\) | 1875.30 | 0.0810470 | ||||||||
\(813\) | 21402.2 | 0.923255 | ||||||||
\(814\) | 28225.7 | 1.21537 | ||||||||
\(815\) | 2597.64 | 0.111646 | ||||||||
\(816\) | 59714.2 | 2.56178 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3750.07 | −0.160291 | ||||||||
\(819\) | −6765.95 | −0.288671 | ||||||||
\(820\) | 3396.23 | 0.144636 | ||||||||
\(821\) | 2118.86 | 0.0900717 | 0.0450358 | − | 0.998985i | \(-0.485660\pi\) | ||||
0.0450358 | + | 0.998985i | \(0.485660\pi\) | |||||||
\(822\) | −42668.4 | −1.81050 | ||||||||
\(823\) | −15733.7 | −0.666396 | −0.333198 | − | 0.942857i | \(-0.608128\pi\) | ||||
−0.333198 | + | 0.942857i | \(0.608128\pi\) | |||||||
\(824\) | −1011.45 | −0.0427617 | ||||||||
\(825\) | −24242.9 | −1.02306 | ||||||||
\(826\) | 7563.57 | 0.318608 | ||||||||
\(827\) | −19983.4 | −0.840256 | −0.420128 | − | 0.907465i | \(-0.638015\pi\) | ||||
−0.420128 | + | 0.907465i | \(0.638015\pi\) | |||||||
\(828\) | 49317.4 | 2.06993 | ||||||||
\(829\) | 34475.6 | 1.44437 | 0.722187 | − | 0.691698i | \(-0.243137\pi\) | ||||
0.722187 | + | 0.691698i | \(0.243137\pi\) | |||||||
\(830\) | −1198.35 | −0.0501147 | ||||||||
\(831\) | −47211.8 | −1.97083 | ||||||||
\(832\) | 14725.4 | 0.613594 | ||||||||
\(833\) | −32327.0 | −1.34461 | ||||||||
\(834\) | −21915.6 | −0.909924 | ||||||||
\(835\) | 2350.50 | 0.0974159 | ||||||||
\(836\) | −21310.8 | −0.881640 | ||||||||
\(837\) | −16833.7 | −0.695170 | ||||||||
\(838\) | 41745.8 | 1.72087 | ||||||||
\(839\) | −9582.61 | −0.394313 | −0.197156 | − | 0.980372i | \(-0.563171\pi\) | ||||
−0.197156 | + | 0.980372i | \(0.563171\pi\) | |||||||
\(840\) | −395.328 | −0.0162382 | ||||||||
\(841\) | −17475.1 | −0.716514 | ||||||||
\(842\) | 47177.9 | 1.93095 | ||||||||
\(843\) | 53514.7 | 2.18641 | ||||||||
\(844\) | −34438.6 | −1.40453 | ||||||||
\(845\) | 137.423 | 0.00559468 | ||||||||
\(846\) | −54654.2 | −2.22110 | ||||||||
\(847\) | −2498.03 | −0.101338 | ||||||||
\(848\) | −27404.4 | −1.10975 | ||||||||
\(849\) | 67039.1 | 2.70998 | ||||||||
\(850\) | −44137.5 | −1.78106 | ||||||||
\(851\) | −52853.5 | −2.12902 | ||||||||
\(852\) | 25734.1 | 1.03478 | ||||||||
\(853\) | −31343.1 | −1.25811 | −0.629055 | − | 0.777361i | \(-0.716558\pi\) | ||||
−0.629055 | + | 0.777361i | \(0.716558\pi\) | |||||||
\(854\) | 11672.2 | 0.467698 | ||||||||
\(855\) | −14439.1 | −0.577550 | ||||||||
\(856\) | 6177.06 | 0.246644 | ||||||||
\(857\) | −3018.06 | −0.120298 | −0.0601488 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601488 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(858\) | −36197.8 | −1.44030 | ||||||||
\(859\) | −20259.2 | −0.804697 | −0.402349 | − | 0.915487i | \(-0.631806\pi\) | ||||
−0.402349 | + | 0.915487i | \(0.631806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5746.43 | 0.227454 | ||||||||
\(862\) | −24959.4 | −0.986219 | ||||||||
\(863\) | −40225.7 | −1.58667 | −0.793336 | − | 0.608785i | \(-0.791657\pi\) | ||||
−0.793336 | + | 0.608785i | \(0.791657\pi\) | |||||||
\(864\) | 31011.6 | 1.22111 | ||||||||
\(865\) | 10359.6 | 0.407209 | ||||||||
\(866\) | 46873.9 | 1.83931 | ||||||||
\(867\) | −38478.0 | −1.50725 | ||||||||
\(868\) | 2899.22 | 0.113371 | ||||||||
\(869\) | 7263.88 | 0.283556 | ||||||||
\(870\) | 6797.71 | 0.264901 | ||||||||
\(871\) | −123.203 | −0.00479286 | ||||||||
\(872\) | 5982.44 | 0.232329 | ||||||||
\(873\) | −73563.5 | −2.85194 | ||||||||
\(874\) | 88366.6 | 3.41996 | ||||||||
\(875\) | 2136.90 | 0.0825604 | ||||||||
\(876\) | −26481.3 | −1.02137 | ||||||||
\(877\) | 9078.63 | 0.349559 | 0.174780 | − | 0.984608i | \(-0.444079\pi\) | ||||
0.174780 | + | 0.984608i | \(0.444079\pi\) | |||||||
\(878\) | −10718.7 | −0.412003 | ||||||||
\(879\) | 30154.3 | 1.15708 | ||||||||
\(880\) | −4609.24 | −0.176565 | ||||||||
\(881\) | −1661.65 | −0.0635440 | −0.0317720 | − | 0.999495i | \(-0.510115\pi\) | ||||
−0.0317720 | + | 0.999495i | \(0.510115\pi\) | |||||||
\(882\) | −54010.4 | −2.06193 | ||||||||
\(883\) | 10862.1 | 0.413974 | 0.206987 | − | 0.978344i | \(-0.433634\pi\) | ||||
0.206987 | + | 0.978344i | \(0.433634\pi\) | |||||||
\(884\) | −29761.0 | −1.13232 | ||||||||
\(885\) | 12381.1 | 0.470268 | ||||||||
\(886\) | −35660.6 | −1.35219 | ||||||||
\(887\) | −12633.9 | −0.478248 | −0.239124 | − | 0.970989i | \(-0.576860\pi\) | ||||
−0.239124 | + | 0.970989i | \(0.576860\pi\) | |||||||
\(888\) | −13571.5 | −0.512873 | ||||||||
\(889\) | −6934.12 | −0.261601 | ||||||||
\(890\) | 7307.78 | 0.275233 | ||||||||
\(891\) | 1456.31 | 0.0547565 | ||||||||
\(892\) | −7384.73 | −0.277196 | ||||||||
\(893\) | −44223.4 | −1.65720 | ||||||||
\(894\) | −14916.5 | −0.558034 | ||||||||
\(895\) | −2099.04 | −0.0783946 | ||||||||
\(896\) | 2327.22 | 0.0867710 | ||||||||
\(897\) | 67781.5 | 2.52303 | ||||||||
\(898\) | 27546.4 | 1.02365 | ||||||||
\(899\) | 10689.0 | 0.396548 | ||||||||
\(900\) | −33301.3 | −1.23338 | ||||||||
\(901\) | 36480.4 | 1.34888 | ||||||||
\(902\) | 18831.9 | 0.695160 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7827.29 | −0.287977 | ||||||||
\(905\) | 4516.48 | 0.165893 | ||||||||
\(906\) | −55036.6 | −2.01818 | ||||||||
\(907\) | 43157.9 | 1.57997 | 0.789987 | − | 0.613124i | \(-0.210087\pi\) | ||||
0.789987 | + | 0.613124i | \(0.210087\pi\) | |||||||
\(908\) | −3289.80 | −0.120238 | ||||||||
\(909\) | −16393.1 | −0.598156 | ||||||||
\(910\) | 1552.25 | 0.0565456 | ||||||||
\(911\) | 8726.36 | 0.317363 | 0.158681 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158681 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(912\) | 80727.0 | 2.93107 | ||||||||
\(913\) | −3000.70 | −0.108772 | ||||||||
\(914\) | −5264.59 | −0.190522 | ||||||||
\(915\) | 19106.7 | 0.690325 | ||||||||
\(916\) | 9123.02 | 0.329076 | ||||||||
\(917\) | −8740.76 | −0.314772 | ||||||||
\(918\) | −48805.6 | −1.75471 | ||||||||
\(919\) | −25907.4 | −0.929932 | −0.464966 | − | 0.885328i | \(-0.653934\pi\) | ||||
−0.464966 | + | 0.885328i | \(0.653934\pi\) | |||||||
\(920\) | 2425.95 | 0.0869363 | ||||||||
\(921\) | 10702.8 | 0.382918 | ||||||||
\(922\) | −42949.4 | −1.53413 | ||||||||
\(923\) | 21665.2 | 0.772609 | ||||||||
\(924\) | 4616.86 | 0.164376 | ||||||||
\(925\) | 35689.0 | 1.26859 | ||||||||
\(926\) | 7934.89 | 0.281595 | ||||||||
\(927\) | 8003.37 | 0.283566 | ||||||||
\(928\) | −19691.6 | −0.696560 | ||||||||
\(929\) | −32728.1 | −1.15584 | −0.577919 | − | 0.816094i | \(-0.696135\pi\) | ||||
−0.577919 | + | 0.816094i | \(0.696135\pi\) | |||||||
\(930\) | 10509.3 | 0.370551 | ||||||||
\(931\) | −43702.5 | −1.53845 | ||||||||
\(932\) | 1708.67 | 0.0600530 | ||||||||
\(933\) | 76347.0 | 2.67898 | ||||||||
\(934\) | −7702.78 | −0.269853 | ||||||||
\(935\) | 6135.78 | 0.214611 | ||||||||
\(936\) | 10661.3 | 0.372302 | ||||||||
\(937\) | −5170.31 | −0.180263 | −0.0901316 | − | 0.995930i | \(-0.528729\pi\) | ||||
−0.0901316 | + | 0.995930i | \(0.528729\pi\) | |||||||
\(938\) | 34.7973 | 0.00121127 | ||||||||
\(939\) | −27186.0 | −0.944814 | ||||||||
\(940\) | 5662.36 | 0.196474 | ||||||||
\(941\) | −23338.4 | −0.808511 | −0.404255 | − | 0.914646i | \(-0.632469\pi\) | ||||
−0.404255 | + | 0.914646i | \(0.632469\pi\) | |||||||
\(942\) | 15575.2 | 0.538714 | ||||||||
\(943\) | −35263.3 | −1.21774 | ||||||||
\(944\) | −42401.6 | −1.46192 | ||||||||
\(945\) | 1149.54 | 0.0395710 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6979.11 | 0.239483 | 0.119742 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119742 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(948\) | 16289.3 | 0.558073 | ||||||||
\(949\) | −22294.3 | −0.762595 | ||||||||
\(950\) | −59669.0 | −2.03781 | ||||||||
\(951\) | −53930.2 | −1.83891 | ||||||||
\(952\) | −1802.27 | −0.0613572 | ||||||||
\(953\) | −15961.8 | −0.542552 | −0.271276 | − | 0.962502i | \(-0.587446\pi\) | ||||
−0.271276 | + | 0.962502i | \(0.587446\pi\) | |||||||
\(954\) | 60949.8 | 2.06847 | ||||||||
\(955\) | 3094.07 | 0.104840 | ||||||||
\(956\) | 27852.9 | 0.942287 | ||||||||
\(957\) | 17021.7 | 0.574955 | ||||||||
\(958\) | 39824.6 | 1.34308 | ||||||||
\(959\) | 4581.68 | 0.154276 | ||||||||
\(960\) | −6808.05 | −0.228884 | ||||||||
\(961\) | −13265.9 | −0.445298 | ||||||||
\(962\) | 53288.4 | 1.78595 | ||||||||
\(963\) | −48877.5 | −1.63557 | ||||||||
\(964\) | −48669.5 | −1.62608 | ||||||||
\(965\) | 3146.62 | 0.104967 | ||||||||
\(966\) | −19144.1 | −0.637630 | ||||||||
\(967\) | −15404.6 | −0.512283 | −0.256142 | − | 0.966639i | \(-0.582451\pi\) | ||||
−0.256142 | + | 0.966639i | \(0.582451\pi\) | |||||||
\(968\) | 3936.21 | 0.130697 | ||||||||
\(969\) | −107463. | −3.56265 | ||||||||
\(970\) | 16877.0 | 0.558646 | ||||||||
\(971\) | −814.407 | −0.0269161 | −0.0134581 | − | 0.999909i | \(-0.504284\pi\) | ||||
−0.0134581 | + | 0.999909i | \(0.504284\pi\) | |||||||
\(972\) | 26557.1 | 0.876357 | ||||||||
\(973\) | 2353.27 | 0.0775360 | ||||||||
\(974\) | −15911.2 | −0.523437 | ||||||||
\(975\) | −45769.1 | −1.50337 | ||||||||
\(976\) | −65434.7 | −2.14602 | ||||||||
\(977\) | 3952.69 | 0.129435 | 0.0647174 | − | 0.997904i | \(-0.479385\pi\) | ||||
0.0647174 | + | 0.997904i | \(0.479385\pi\) | |||||||
\(978\) | 32300.6 | 1.05609 | ||||||||
\(979\) | 18298.9 | 0.597380 | ||||||||
\(980\) | 5595.66 | 0.182395 | ||||||||
\(981\) | −47337.6 | −1.54064 | ||||||||
\(982\) | −43172.6 | −1.40295 | ||||||||
\(983\) | −2736.55 | −0.0887918 | −0.0443959 | − | 0.999014i | \(-0.514136\pi\) | ||||
−0.0443959 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(984\) | −9054.80 | −0.293350 | ||||||||
\(985\) | −7452.22 | −0.241063 | ||||||||
\(986\) | 30990.3 | 1.00094 | ||||||||
\(987\) | 9580.73 | 0.308975 | ||||||||
\(988\) | −40233.6 | −1.29555 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 10251.4 | 0.329101 | ||||||||
\(991\) | −24139.6 | −0.773783 | −0.386892 | − | 0.922125i | \(-0.626451\pi\) | ||||
−0.386892 | + | 0.922125i | \(0.626451\pi\) | |||||||
\(992\) | −30443.2 | −0.974367 | ||||||||
\(993\) | −54034.1 | −1.72681 | ||||||||
\(994\) | −6119.07 | −0.195257 | ||||||||
\(995\) | 5026.37 | 0.160147 | ||||||||
\(996\) | −6729.09 | −0.214076 | ||||||||
\(997\) | 27188.4 | 0.863656 | 0.431828 | − | 0.901956i | \(-0.357869\pi\) | ||||
0.431828 | + | 0.901956i | \(0.357869\pi\) | |||||||
\(998\) | 49920.3 | 1.58337 | ||||||||
\(999\) | 39463.5 | 1.24982 |
(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 | 1849.4.a.j.1.41 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.10 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.10 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.41 | yes | 50 | 1.1 | even | 1 | trivial |