Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, 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("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 46x^{7} + 145x^{6} + 680x^{5} - 1501x^{4} - 3203x^{3} + 4784x^{2} + 3584x - 4096 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.84018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.84018 | −1.71126 | −0.855630 | − | 0.517587i | \(-0.826830\pi\) | ||||
−0.855630 | + | 0.517587i | \(0.826830\pi\) | |||||||
\(3\) | −6.19662 | −1.19254 | −0.596270 | − | 0.802784i | \(-0.703351\pi\) | ||||
−0.596270 | + | 0.802784i | \(0.703351\pi\) | |||||||
\(4\) | 15.4273 | 1.92841 | ||||||||
\(5\) | 15.2399 | 1.36309 | 0.681547 | − | 0.731774i | \(-0.261308\pi\) | ||||
0.681547 | + | 0.731774i | \(0.261308\pi\) | |||||||
\(6\) | 29.9927 | 2.04075 | ||||||||
\(7\) | 4.31620 | 0.233053 | 0.116527 | − | 0.993188i | \(-0.462824\pi\) | ||||
0.116527 | + | 0.993188i | \(0.462824\pi\) | |||||||
\(8\) | −35.9495 | −1.58876 | ||||||||
\(9\) | 11.3981 | 0.422151 | ||||||||
\(10\) | −73.7636 | −2.33261 | ||||||||
\(11\) | 24.5691 | 0.673443 | 0.336722 | − | 0.941604i | \(-0.390682\pi\) | ||||
0.336722 | + | 0.941604i | \(0.390682\pi\) | |||||||
\(12\) | −95.5971 | −2.29971 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −20.8912 | −0.398815 | ||||||||
\(15\) | −94.4355 | −1.62554 | ||||||||
\(16\) | 50.5834 | 0.790365 | ||||||||
\(17\) | −127.160 | −1.81417 | −0.907086 | − | 0.420944i | \(-0.861699\pi\) | ||||
−0.907086 | + | 0.420944i | \(0.861699\pi\) | |||||||
\(18\) | −55.1687 | −0.722410 | ||||||||
\(19\) | 51.7462 | 0.624810 | 0.312405 | − | 0.949949i | \(-0.398865\pi\) | ||||
0.312405 | + | 0.949949i | \(0.398865\pi\) | |||||||
\(20\) | 235.110 | 2.62861 | ||||||||
\(21\) | −26.7459 | −0.277925 | ||||||||
\(22\) | −118.919 | −1.15244 | ||||||||
\(23\) | 87.3684 | 0.792068 | 0.396034 | − | 0.918236i | \(-0.370386\pi\) | ||||
0.396034 | + | 0.918236i | \(0.370386\pi\) | |||||||
\(24\) | 222.765 | 1.89466 | ||||||||
\(25\) | 107.253 | 0.858024 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 96.6792 | 0.689108 | ||||||||
\(28\) | 66.5874 | 0.449423 | ||||||||
\(29\) | 225.726 | 1.44539 | 0.722693 | − | 0.691169i | \(-0.242904\pi\) | ||||
0.722693 | + | 0.691169i | \(0.242904\pi\) | |||||||
\(30\) | 457.085 | 2.78173 | ||||||||
\(31\) | −108.720 | −0.629895 | −0.314948 | − | 0.949109i | \(-0.601987\pi\) | ||||
−0.314948 | + | 0.949109i | \(0.601987\pi\) | |||||||
\(32\) | 42.7634 | 0.236237 | ||||||||
\(33\) | −152.246 | −0.803108 | ||||||||
\(34\) | 615.479 | 3.10452 | ||||||||
\(35\) | 65.7783 | 0.317673 | ||||||||
\(36\) | 175.842 | 0.814081 | ||||||||
\(37\) | −115.756 | −0.514330 | −0.257165 | − | 0.966367i | \(-0.582788\pi\) | ||||
−0.257165 | + | 0.966367i | \(0.582788\pi\) | |||||||
\(38\) | −250.461 | −1.06921 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −547.865 | −2.16563 | ||||||||
\(41\) | 191.885 | 0.730912 | 0.365456 | − | 0.930829i | \(-0.380913\pi\) | ||||
0.365456 | + | 0.930829i | \(0.380913\pi\) | |||||||
\(42\) | 129.455 | 0.475602 | ||||||||
\(43\) | −123.301 | −0.437284 | −0.218642 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218642 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(44\) | 379.036 | 1.29868 | ||||||||
\(45\) | 173.705 | 0.575431 | ||||||||
\(46\) | −422.878 | −1.35543 | ||||||||
\(47\) | 36.7339 | 0.114004 | 0.0570020 | − | 0.998374i | \(-0.481846\pi\) | ||||
0.0570020 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(48\) | −313.446 | −0.942542 | ||||||||
\(49\) | −324.370 | −0.945686 | ||||||||
\(50\) | −519.124 | −1.46830 | ||||||||
\(51\) | 787.965 | 2.16347 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 119.162 | 0.308833 | 0.154416 | − | 0.988006i | \(-0.450650\pi\) | ||||
0.154416 | + | 0.988006i | \(0.450650\pi\) | |||||||
\(54\) | −467.944 | −1.17924 | ||||||||
\(55\) | 374.430 | 0.917966 | ||||||||
\(56\) | −155.165 | −0.370265 | ||||||||
\(57\) | −320.651 | −0.745110 | ||||||||
\(58\) | −1092.55 | −2.47343 | ||||||||
\(59\) | 804.553 | 1.77532 | 0.887660 | − | 0.460500i | \(-0.152330\pi\) | ||||
0.887660 | + | 0.460500i | \(0.152330\pi\) | |||||||
\(60\) | −1456.89 | −3.13472 | ||||||||
\(61\) | 678.886 | 1.42496 | 0.712479 | − | 0.701693i | \(-0.247572\pi\) | ||||
0.712479 | + | 0.701693i | \(0.247572\pi\) | |||||||
\(62\) | 526.226 | 1.07791 | ||||||||
\(63\) | 49.1964 | 0.0983835 | ||||||||
\(64\) | −611.650 | −1.19463 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 736.896 | 1.37433 | ||||||||
\(67\) | 87.4806 | 0.159514 | 0.0797571 | − | 0.996814i | \(-0.474586\pi\) | ||||
0.0797571 | + | 0.996814i | \(0.474586\pi\) | |||||||
\(68\) | −1961.74 | −3.49848 | ||||||||
\(69\) | −541.388 | −0.944572 | ||||||||
\(70\) | −318.379 | −0.543622 | ||||||||
\(71\) | 981.049 | 1.63985 | 0.819923 | − | 0.572473i | \(-0.194016\pi\) | ||||
0.819923 | + | 0.572473i | \(0.194016\pi\) | |||||||
\(72\) | −409.755 | −0.670695 | ||||||||
\(73\) | −263.862 | −0.423051 | −0.211526 | − | 0.977372i | \(-0.567843\pi\) | ||||
−0.211526 | + | 0.977372i | \(0.567843\pi\) | |||||||
\(74\) | 560.281 | 0.880153 | ||||||||
\(75\) | −664.606 | −1.02323 | ||||||||
\(76\) | 798.304 | 1.20489 | ||||||||
\(77\) | 106.045 | 0.156948 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 321.051 | 0.457228 | 0.228614 | − | 0.973517i | \(-0.426581\pi\) | ||||
0.228614 | + | 0.973517i | \(0.426581\pi\) | |||||||
\(80\) | 770.883 | 1.07734 | ||||||||
\(81\) | −906.832 | −1.24394 | ||||||||
\(82\) | −928.757 | −1.25078 | ||||||||
\(83\) | 1042.54 | 1.37872 | 0.689362 | − | 0.724417i | \(-0.257891\pi\) | ||||
0.689362 | + | 0.724417i | \(0.257891\pi\) | |||||||
\(84\) | −412.617 | −0.535955 | ||||||||
\(85\) | −1937.91 | −2.47289 | ||||||||
\(86\) | 596.798 | 0.748307 | ||||||||
\(87\) | −1398.74 | −1.72368 | ||||||||
\(88\) | −883.248 | −1.06994 | ||||||||
\(89\) | 344.746 | 0.410595 | 0.205298 | − | 0.978700i | \(-0.434184\pi\) | ||||
0.205298 | + | 0.978700i | \(0.434184\pi\) | |||||||
\(90\) | −840.762 | −0.984712 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1347.86 | 1.52743 | ||||||||
\(93\) | 673.698 | 0.751175 | ||||||||
\(94\) | −177.799 | −0.195091 | ||||||||
\(95\) | 788.604 | 0.851674 | ||||||||
\(96\) | −264.989 | −0.281722 | ||||||||
\(97\) | 482.521 | 0.505079 | 0.252539 | − | 0.967587i | \(-0.418734\pi\) | ||||
0.252539 | + | 0.967587i | \(0.418734\pi\) | |||||||
\(98\) | 1570.01 | 1.61832 | ||||||||
\(99\) | 280.041 | 0.284295 | ||||||||
\(100\) | 1654.63 | 1.65463 | ||||||||
\(101\) | 839.779 | 0.827338 | 0.413669 | − | 0.910427i | \(-0.364247\pi\) | ||||
0.413669 | + | 0.910427i | \(0.364247\pi\) | |||||||
\(102\) | −3813.89 | −3.70227 | ||||||||
\(103\) | 159.823 | 0.152892 | 0.0764459 | − | 0.997074i | \(-0.475643\pi\) | ||||
0.0764459 | + | 0.997074i | \(0.475643\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −407.603 | −0.378838 | ||||||||
\(106\) | −576.764 | −0.528494 | ||||||||
\(107\) | 1075.62 | 0.971818 | 0.485909 | − | 0.874009i | \(-0.338489\pi\) | ||||
0.485909 | + | 0.874009i | \(0.338489\pi\) | |||||||
\(108\) | 1491.50 | 1.32889 | ||||||||
\(109\) | 1161.67 | 1.02080 | 0.510401 | − | 0.859936i | \(-0.329497\pi\) | ||||
0.510401 | + | 0.859936i | \(0.329497\pi\) | |||||||
\(110\) | −1812.31 | −1.57088 | ||||||||
\(111\) | 717.298 | 0.613359 | ||||||||
\(112\) | 218.328 | 0.184197 | ||||||||
\(113\) | −1463.48 | −1.21834 | −0.609172 | − | 0.793038i | \(-0.708498\pi\) | ||||
−0.609172 | + | 0.793038i | \(0.708498\pi\) | |||||||
\(114\) | 1552.01 | 1.27508 | ||||||||
\(115\) | 1331.48 | 1.07966 | ||||||||
\(116\) | 3482.34 | 2.78730 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3894.18 | −3.03803 | ||||||||
\(119\) | −548.851 | −0.422799 | ||||||||
\(120\) | 3394.91 | 2.58259 | ||||||||
\(121\) | −727.357 | −0.546474 | ||||||||
\(122\) | −3285.93 | −2.43848 | ||||||||
\(123\) | −1189.04 | −0.871641 | ||||||||
\(124\) | −1677.26 | −1.21470 | ||||||||
\(125\) | −270.461 | −0.193526 | ||||||||
\(126\) | −238.119 | −0.168360 | ||||||||
\(127\) | 289.923 | 0.202571 | 0.101285 | − | 0.994857i | \(-0.467704\pi\) | ||||
0.101285 | + | 0.994857i | \(0.467704\pi\) | |||||||
\(128\) | 2618.38 | 1.80808 | ||||||||
\(129\) | 764.048 | 0.521478 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1201.97 | −0.801653 | −0.400826 | − | 0.916154i | \(-0.631277\pi\) | ||||
−0.400826 | + | 0.916154i | \(0.631277\pi\) | |||||||
\(132\) | −2348.74 | −1.54872 | ||||||||
\(133\) | 223.347 | 0.145614 | ||||||||
\(134\) | −423.422 | −0.272971 | ||||||||
\(135\) | 1473.38 | 0.939319 | ||||||||
\(136\) | 4571.35 | 2.88228 | ||||||||
\(137\) | −779.620 | −0.486186 | −0.243093 | − | 0.970003i | \(-0.578162\pi\) | ||||
−0.243093 | + | 0.970003i | \(0.578162\pi\) | |||||||
\(138\) | 2620.41 | 1.61641 | ||||||||
\(139\) | 2031.48 | 1.23963 | 0.619814 | − | 0.784749i | \(-0.287208\pi\) | ||||
0.619814 | + | 0.784749i | \(0.287208\pi\) | |||||||
\(140\) | 1014.78 | 0.612605 | ||||||||
\(141\) | −227.626 | −0.135954 | ||||||||
\(142\) | −4748.45 | −2.80621 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 576.553 | 0.333653 | ||||||||
\(145\) | 3440.03 | 1.97020 | ||||||||
\(146\) | 1277.14 | 0.723951 | ||||||||
\(147\) | 2010.00 | 1.12777 | ||||||||
\(148\) | −1785.81 | −0.991841 | ||||||||
\(149\) | −2603.60 | −1.43151 | −0.715757 | − | 0.698350i | \(-0.753918\pi\) | ||||
−0.715757 | + | 0.698350i | \(0.753918\pi\) | |||||||
\(150\) | 3216.81 | 1.75101 | ||||||||
\(151\) | −206.776 | −0.111438 | −0.0557192 | − | 0.998446i | \(-0.517745\pi\) | ||||
−0.0557192 | + | 0.998446i | \(0.517745\pi\) | |||||||
\(152\) | −1860.25 | −0.992671 | ||||||||
\(153\) | −1449.38 | −0.765854 | ||||||||
\(154\) | −513.279 | −0.268579 | ||||||||
\(155\) | −1656.88 | −0.858606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 699.208 | 0.355433 | 0.177716 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177716 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(158\) | −1553.94 | −0.782437 | ||||||||
\(159\) | −738.400 | −0.368295 | ||||||||
\(160\) | 651.708 | 0.322013 | ||||||||
\(161\) | 377.100 | 0.184594 | ||||||||
\(162\) | 4389.23 | 2.12870 | ||||||||
\(163\) | 2944.14 | 1.41474 | 0.707371 | − | 0.706842i | \(-0.249881\pi\) | ||||
0.707371 | + | 0.706842i | \(0.249881\pi\) | |||||||
\(164\) | 2960.27 | 1.40950 | ||||||||
\(165\) | −2320.20 | −1.09471 | ||||||||
\(166\) | −5046.10 | −2.35936 | ||||||||
\(167\) | 2740.82 | 1.27000 | 0.635002 | − | 0.772510i | \(-0.280999\pi\) | ||||
0.635002 | + | 0.772510i | \(0.280999\pi\) | |||||||
\(168\) | 961.500 | 0.441556 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9379.81 | 4.23176 | ||||||||
\(171\) | 589.806 | 0.263764 | ||||||||
\(172\) | −1902.20 | −0.843264 | ||||||||
\(173\) | 338.812 | 0.148898 | 0.0744491 | − | 0.997225i | \(-0.476280\pi\) | ||||
0.0744491 | + | 0.997225i | \(0.476280\pi\) | |||||||
\(174\) | 6770.13 | 2.94967 | ||||||||
\(175\) | 462.926 | 0.199965 | ||||||||
\(176\) | 1242.79 | 0.532266 | ||||||||
\(177\) | −4985.51 | −2.11714 | ||||||||
\(178\) | −1668.63 | −0.702635 | ||||||||
\(179\) | −1094.40 | −0.456979 | −0.228489 | − | 0.973546i | \(-0.573379\pi\) | ||||
−0.228489 | + | 0.973546i | \(0.573379\pi\) | |||||||
\(180\) | 2679.80 | 1.10967 | ||||||||
\(181\) | −1420.26 | −0.583243 | −0.291622 | − | 0.956534i | \(-0.594195\pi\) | ||||
−0.291622 | + | 0.956534i | \(0.594195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4206.80 | −1.69932 | ||||||||
\(184\) | −3140.85 | −1.25840 | ||||||||
\(185\) | −1764.11 | −0.701080 | ||||||||
\(186\) | −3260.82 | −1.28546 | ||||||||
\(187\) | −3124.22 | −1.22174 | ||||||||
\(188\) | 566.705 | 0.219847 | ||||||||
\(189\) | 417.287 | 0.160599 | ||||||||
\(190\) | −3816.98 | −1.45744 | ||||||||
\(191\) | −896.779 | −0.339731 | −0.169866 | − | 0.985467i | \(-0.554333\pi\) | ||||
−0.169866 | + | 0.985467i | \(0.554333\pi\) | |||||||
\(192\) | 3790.16 | 1.42464 | ||||||||
\(193\) | −2589.97 | −0.965959 | −0.482980 | − | 0.875632i | \(-0.660445\pi\) | ||||
−0.482980 | + | 0.875632i | \(0.660445\pi\) | |||||||
\(194\) | −2335.49 | −0.864321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5004.16 | −1.82367 | ||||||||
\(197\) | −1481.87 | −0.535932 | −0.267966 | − | 0.963428i | \(-0.586352\pi\) | ||||
−0.267966 | + | 0.963428i | \(0.586352\pi\) | |||||||
\(198\) | −1355.45 | −0.486502 | ||||||||
\(199\) | −3599.45 | −1.28220 | −0.641101 | − | 0.767456i | \(-0.721522\pi\) | ||||
−0.641101 | + | 0.767456i | \(0.721522\pi\) | |||||||
\(200\) | −3855.69 | −1.36319 | ||||||||
\(201\) | −542.084 | −0.190227 | ||||||||
\(202\) | −4064.68 | −1.41579 | ||||||||
\(203\) | 974.278 | 0.336852 | ||||||||
\(204\) | 12156.2 | 4.17207 | ||||||||
\(205\) | 2924.30 | 0.996301 | ||||||||
\(206\) | −773.572 | −0.261638 | ||||||||
\(207\) | 995.830 | 0.334372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1271.36 | 0.420774 | ||||||||
\(210\) | 1972.87 | 0.648291 | ||||||||
\(211\) | 3051.22 | 0.995518 | 0.497759 | − | 0.867315i | \(-0.334156\pi\) | ||||
0.497759 | + | 0.867315i | \(0.334156\pi\) | |||||||
\(212\) | 1838.35 | 0.595557 | ||||||||
\(213\) | −6079.19 | −1.95558 | ||||||||
\(214\) | −5206.21 | −1.66303 | ||||||||
\(215\) | −1879.09 | −0.596059 | ||||||||
\(216\) | −3475.57 | −1.09483 | ||||||||
\(217\) | −469.259 | −0.146799 | ||||||||
\(218\) | −5622.67 | −1.74686 | ||||||||
\(219\) | 1635.05 | 0.504506 | ||||||||
\(220\) | 5776.45 | 1.77022 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3471.85 | −1.04962 | ||||||||
\(223\) | −2599.87 | −0.780718 | −0.390359 | − | 0.920663i | \(-0.627649\pi\) | ||||
−0.390359 | + | 0.920663i | \(0.627649\pi\) | |||||||
\(224\) | 184.576 | 0.0550558 | ||||||||
\(225\) | 1222.48 | 0.362216 | ||||||||
\(226\) | 7083.52 | 2.08491 | ||||||||
\(227\) | −993.208 | −0.290403 | −0.145202 | − | 0.989402i | \(-0.546383\pi\) | ||||
−0.145202 | + | 0.989402i | \(0.546383\pi\) | |||||||
\(228\) | −4946.79 | −1.43688 | ||||||||
\(229\) | 437.772 | 0.126327 | 0.0631633 | − | 0.998003i | \(-0.479881\pi\) | ||||
0.0631633 | + | 0.998003i | \(0.479881\pi\) | |||||||
\(230\) | −6444.60 | −1.84758 | ||||||||
\(231\) | −657.123 | −0.187167 | ||||||||
\(232\) | −8114.72 | −2.29637 | ||||||||
\(233\) | 2933.08 | 0.824689 | 0.412344 | − | 0.911028i | \(-0.364710\pi\) | ||||
0.412344 | + | 0.911028i | \(0.364710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 559.819 | 0.155398 | ||||||||
\(236\) | 12412.1 | 3.42355 | ||||||||
\(237\) | −1989.43 | −0.545263 | ||||||||
\(238\) | 2656.53 | 0.723519 | ||||||||
\(239\) | 5813.48 | 1.57340 | 0.786700 | − | 0.617335i | \(-0.211788\pi\) | ||||
0.786700 | + | 0.617335i | \(0.211788\pi\) | |||||||
\(240\) | −4776.87 | −1.28477 | ||||||||
\(241\) | 1148.25 | 0.306910 | 0.153455 | − | 0.988156i | \(-0.450960\pi\) | ||||
0.153455 | + | 0.988156i | \(0.450960\pi\) | |||||||
\(242\) | 3520.54 | 0.935160 | ||||||||
\(243\) | 3008.95 | 0.794339 | ||||||||
\(244\) | 10473.4 | 2.74791 | ||||||||
\(245\) | −4943.36 | −1.28906 | ||||||||
\(246\) | 5755.15 | 1.49161 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3908.44 | 1.00075 | ||||||||
\(249\) | −6460.24 | −1.64418 | ||||||||
\(250\) | 1309.08 | 0.331174 | ||||||||
\(251\) | −3255.80 | −0.818741 | −0.409371 | − | 0.912368i | \(-0.634252\pi\) | ||||
−0.409371 | + | 0.912368i | \(0.634252\pi\) | |||||||
\(252\) | 758.968 | 0.189724 | ||||||||
\(253\) | 2146.57 | 0.533413 | ||||||||
\(254\) | −1403.28 | −0.346652 | ||||||||
\(255\) | 12008.5 | 2.94902 | ||||||||
\(256\) | −7780.24 | −1.89947 | ||||||||
\(257\) | 6320.90 | 1.53419 | 0.767095 | − | 0.641534i | \(-0.221702\pi\) | ||||
0.767095 | + | 0.641534i | \(0.221702\pi\) | |||||||
\(258\) | −3698.13 | −0.892386 | ||||||||
\(259\) | −499.628 | −0.119866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2572.84 | 0.610171 | ||||||||
\(262\) | 5817.74 | 1.37184 | ||||||||
\(263\) | −6168.99 | −1.44637 | −0.723187 | − | 0.690653i | \(-0.757323\pi\) | ||||
−0.723187 | + | 0.690653i | \(0.757323\pi\) | |||||||
\(264\) | 5473.15 | 1.27594 | ||||||||
\(265\) | 1816.01 | 0.420968 | ||||||||
\(266\) | −1081.04 | −0.249183 | ||||||||
\(267\) | −2136.26 | −0.489651 | ||||||||
\(268\) | 1349.59 | 0.307609 | ||||||||
\(269\) | 843.598 | 0.191209 | 0.0956043 | − | 0.995419i | \(-0.469522\pi\) | ||||
0.0956043 | + | 0.995419i | \(0.469522\pi\) | |||||||
\(270\) | −7131.40 | −1.60742 | ||||||||
\(271\) | −2063.06 | −0.462442 | −0.231221 | − | 0.972901i | \(-0.574272\pi\) | ||||
−0.231221 | + | 0.972901i | \(0.574272\pi\) | |||||||
\(272\) | −6432.20 | −1.43386 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3773.50 | 0.831990 | ||||||||
\(275\) | 2635.12 | 0.577831 | ||||||||
\(276\) | −8352.16 | −1.82153 | ||||||||
\(277\) | 6582.49 | 1.42781 | 0.713905 | − | 0.700242i | \(-0.246925\pi\) | ||||
0.713905 | + | 0.700242i | \(0.246925\pi\) | |||||||
\(278\) | −9832.74 | −2.12133 | ||||||||
\(279\) | −1239.20 | −0.265911 | ||||||||
\(280\) | −2364.70 | −0.504706 | ||||||||
\(281\) | −935.025 | −0.198502 | −0.0992508 | − | 0.995062i | \(-0.531645\pi\) | ||||
−0.0992508 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(282\) | 1101.75 | 0.232653 | ||||||||
\(283\) | −5338.77 | −1.12140 | −0.560701 | − | 0.828018i | \(-0.689468\pi\) | ||||
−0.560701 | + | 0.828018i | \(0.689468\pi\) | |||||||
\(284\) | 15134.9 | 3.16230 | ||||||||
\(285\) | −4886.68 | −1.01566 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 828.215 | 0.170341 | ||||||||
\(288\) | 487.421 | 0.0997276 | ||||||||
\(289\) | 11256.8 | 2.29122 | ||||||||
\(290\) | −16650.3 | −3.37152 | ||||||||
\(291\) | −2990.00 | −0.602326 | ||||||||
\(292\) | −4070.69 | −0.815818 | ||||||||
\(293\) | −1763.76 | −0.351673 | −0.175837 | − | 0.984419i | \(-0.556263\pi\) | ||||
−0.175837 | + | 0.984419i | \(0.556263\pi\) | |||||||
\(294\) | −9728.75 | −1.92991 | ||||||||
\(295\) | 12261.3 | 2.41993 | ||||||||
\(296\) | 4161.38 | 0.817146 | ||||||||
\(297\) | 2375.33 | 0.464075 | ||||||||
\(298\) | 12601.9 | 2.44969 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10253.1 | −1.97321 | ||||||||
\(301\) | −532.192 | −0.101910 | ||||||||
\(302\) | 1000.83 | 0.190700 | ||||||||
\(303\) | −5203.79 | −0.986634 | ||||||||
\(304\) | 2617.50 | 0.493828 | ||||||||
\(305\) | 10346.1 | 1.94235 | ||||||||
\(306\) | 7015.27 | 1.31058 | ||||||||
\(307\) | −4736.59 | −0.880558 | −0.440279 | − | 0.897861i | \(-0.645121\pi\) | ||||
−0.440279 | + | 0.897861i | \(0.645121\pi\) | |||||||
\(308\) | 1636.00 | 0.302661 | ||||||||
\(309\) | −990.363 | −0.182329 | ||||||||
\(310\) | 8019.60 | 1.46930 | ||||||||
\(311\) | −4746.90 | −0.865505 | −0.432753 | − | 0.901513i | \(-0.642458\pi\) | ||||
−0.432753 | + | 0.901513i | \(0.642458\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10115.9 | 1.82679 | 0.913393 | − | 0.407078i | \(-0.133452\pi\) | ||||
0.913393 | + | 0.407078i | \(0.133452\pi\) | |||||||
\(314\) | −3384.29 | −0.608238 | ||||||||
\(315\) | 749.746 | 0.134106 | ||||||||
\(316\) | 4952.95 | 0.881725 | ||||||||
\(317\) | −5906.13 | −1.04644 | −0.523219 | − | 0.852198i | \(-0.675269\pi\) | ||||
−0.523219 | + | 0.852198i | \(0.675269\pi\) | |||||||
\(318\) | 3573.99 | 0.630249 | ||||||||
\(319\) | 5545.89 | 0.973386 | ||||||||
\(320\) | −9321.45 | −1.62839 | ||||||||
\(321\) | −6665.23 | −1.15893 | ||||||||
\(322\) | −1825.23 | −0.315888 | ||||||||
\(323\) | −6580.07 | −1.13351 | ||||||||
\(324\) | −13990.0 | −2.39883 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14250.2 | −2.42099 | ||||||||
\(327\) | −7198.41 | −1.21735 | ||||||||
\(328\) | −6898.16 | −1.16124 | ||||||||
\(329\) | 158.551 | 0.0265690 | ||||||||
\(330\) | 11230.2 | 1.87334 | ||||||||
\(331\) | −2802.82 | −0.465429 | −0.232715 | − | 0.972545i | \(-0.574761\pi\) | ||||
−0.232715 | + | 0.972545i | \(0.574761\pi\) | |||||||
\(332\) | 16083.6 | 2.65875 | ||||||||
\(333\) | −1319.40 | −0.217125 | ||||||||
\(334\) | −13266.0 | −2.17331 | ||||||||
\(335\) | 1333.19 | 0.217433 | ||||||||
\(336\) | −1352.90 | −0.219662 | ||||||||
\(337\) | −244.919 | −0.0395892 | −0.0197946 | − | 0.999804i | \(-0.506301\pi\) | ||||
−0.0197946 | + | 0.999804i | \(0.506301\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9068.65 | 1.45292 | ||||||||
\(340\) | −29896.7 | −4.76875 | ||||||||
\(341\) | −2671.17 | −0.424199 | ||||||||
\(342\) | −2854.77 | −0.451369 | ||||||||
\(343\) | −2880.51 | −0.453448 | ||||||||
\(344\) | 4432.60 | 0.694738 | ||||||||
\(345\) | −8250.68 | −1.28754 | ||||||||
\(346\) | −1639.91 | −0.254804 | ||||||||
\(347\) | 10356.8 | 1.60226 | 0.801129 | − | 0.598492i | \(-0.204233\pi\) | ||||
0.801129 | + | 0.598492i | \(0.204233\pi\) | |||||||
\(348\) | −21578.7 | −3.32397 | ||||||||
\(349\) | −8433.58 | −1.29352 | −0.646761 | − | 0.762693i | \(-0.723877\pi\) | ||||
−0.646761 | + | 0.762693i | \(0.723877\pi\) | |||||||
\(350\) | −2240.64 | −0.342193 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1050.66 | 0.159092 | ||||||||
\(353\) | 4733.72 | 0.713741 | 0.356871 | − | 0.934154i | \(-0.383844\pi\) | ||||
0.356871 | + | 0.934154i | \(0.383844\pi\) | |||||||
\(354\) | 24130.7 | 3.62298 | ||||||||
\(355\) | 14951.0 | 2.23526 | ||||||||
\(356\) | 5318.50 | 0.791797 | ||||||||
\(357\) | 3401.02 | 0.504204 | ||||||||
\(358\) | 5297.08 | 0.782010 | ||||||||
\(359\) | 7561.34 | 1.11162 | 0.555811 | − | 0.831309i | \(-0.312408\pi\) | ||||
0.555811 | + | 0.831309i | \(0.312408\pi\) | |||||||
\(360\) | −6244.60 | −0.914220 | ||||||||
\(361\) | −4181.33 | −0.609613 | ||||||||
\(362\) | 6874.30 | 0.998081 | ||||||||
\(363\) | 4507.15 | 0.651692 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4021.22 | −0.576659 | ||||||||
\(366\) | 20361.6 | 2.90798 | ||||||||
\(367\) | −11940.0 | −1.69826 | −0.849130 | − | 0.528184i | \(-0.822873\pi\) | ||||
−0.849130 | + | 0.528184i | \(0.822873\pi\) | |||||||
\(368\) | 4419.39 | 0.626023 | ||||||||
\(369\) | 2187.12 | 0.308555 | ||||||||
\(370\) | 8538.60 | 1.19973 | ||||||||
\(371\) | 514.327 | 0.0719745 | ||||||||
\(372\) | 10393.4 | 1.44858 | ||||||||
\(373\) | −5797.12 | −0.804728 | −0.402364 | − | 0.915480i | \(-0.631811\pi\) | ||||
−0.402364 | + | 0.915480i | \(0.631811\pi\) | |||||||
\(374\) | 15121.8 | 2.09072 | ||||||||
\(375\) | 1675.94 | 0.230788 | ||||||||
\(376\) | −1320.56 | −0.181125 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2019.74 | −0.274826 | ||||||||
\(379\) | 8846.31 | 1.19896 | 0.599478 | − | 0.800391i | \(-0.295375\pi\) | ||||
0.599478 | + | 0.800391i | \(0.295375\pi\) | |||||||
\(380\) | 12166.0 | 1.64238 | ||||||||
\(381\) | −1796.54 | −0.241574 | ||||||||
\(382\) | 4340.57 | 0.581369 | ||||||||
\(383\) | 1047.61 | 0.139766 | 0.0698830 | − | 0.997555i | \(-0.477737\pi\) | ||||
0.0698830 | + | 0.997555i | \(0.477737\pi\) | |||||||
\(384\) | −16225.1 | −2.15621 | ||||||||
\(385\) | 1616.12 | 0.213935 | ||||||||
\(386\) | 12535.9 | 1.65301 | ||||||||
\(387\) | −1405.39 | −0.184600 | ||||||||
\(388\) | 7444.01 | 0.974000 | ||||||||
\(389\) | −11858.4 | −1.54562 | −0.772808 | − | 0.634640i | \(-0.781148\pi\) | ||||
−0.772808 | + | 0.634640i | \(0.781148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11109.8 | −1.43695 | ||||||||
\(392\) | 11660.9 | 1.50247 | ||||||||
\(393\) | 7448.14 | 0.956003 | ||||||||
\(394\) | 7172.50 | 0.917120 | ||||||||
\(395\) | 4892.76 | 0.623245 | ||||||||
\(396\) | 4320.28 | 0.548238 | ||||||||
\(397\) | 10480.3 | 1.32492 | 0.662460 | − | 0.749097i | \(-0.269512\pi\) | ||||
0.662460 | + | 0.749097i | \(0.269512\pi\) | |||||||
\(398\) | 17422.0 | 2.19418 | ||||||||
\(399\) | −1384.00 | −0.173650 | ||||||||
\(400\) | 5425.22 | 0.678152 | ||||||||
\(401\) | 7936.40 | 0.988341 | 0.494171 | − | 0.869365i | \(-0.335472\pi\) | ||||
0.494171 | + | 0.869365i | \(0.335472\pi\) | |||||||
\(402\) | 2623.78 | 0.325528 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12955.5 | 1.59545 | ||||||||
\(405\) | −13820.0 | −1.69561 | ||||||||
\(406\) | −4715.68 | −0.576441 | ||||||||
\(407\) | −2844.03 | −0.346372 | ||||||||
\(408\) | −28326.9 | −3.43723 | ||||||||
\(409\) | −5835.68 | −0.705516 | −0.352758 | − | 0.935715i | \(-0.614756\pi\) | ||||
−0.352758 | + | 0.935715i | \(0.614756\pi\) | |||||||
\(410\) | −14154.1 | −1.70493 | ||||||||
\(411\) | 4831.01 | 0.579796 | ||||||||
\(412\) | 2465.64 | 0.294838 | ||||||||
\(413\) | 3472.61 | 0.413744 | ||||||||
\(414\) | −4820.00 | −0.572198 | ||||||||
\(415\) | 15888.2 | 1.87933 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12588.3 | −1.47830 | ||||||||
\(418\) | −6153.60 | −0.720054 | ||||||||
\(419\) | −8544.29 | −0.996219 | −0.498109 | − | 0.867114i | \(-0.665972\pi\) | ||||
−0.498109 | + | 0.867114i | \(0.665972\pi\) | |||||||
\(420\) | −6288.22 | −0.730556 | ||||||||
\(421\) | −16524.6 | −1.91297 | −0.956484 | − | 0.291786i | \(-0.905750\pi\) | ||||
−0.956484 | + | 0.291786i | \(0.905750\pi\) | |||||||
\(422\) | −14768.4 | −1.70359 | ||||||||
\(423\) | 418.696 | 0.0481269 | ||||||||
\(424\) | −4283.81 | −0.490661 | ||||||||
\(425\) | −13638.3 | −1.55660 | ||||||||
\(426\) | 29424.3 | 3.34651 | ||||||||
\(427\) | 2930.21 | 0.332091 | ||||||||
\(428\) | 16594.0 | 1.87407 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9095.11 | 1.02001 | ||||||||
\(431\) | −6836.58 | −0.764052 | −0.382026 | − | 0.924152i | \(-0.624774\pi\) | ||||
−0.382026 | + | 0.924152i | \(0.624774\pi\) | |||||||
\(432\) | 4890.36 | 0.544647 | ||||||||
\(433\) | −6290.65 | −0.698174 | −0.349087 | − | 0.937090i | \(-0.613508\pi\) | ||||
−0.349087 | + | 0.937090i | \(0.613508\pi\) | |||||||
\(434\) | 2271.30 | 0.251211 | ||||||||
\(435\) | −21316.5 | −2.34954 | ||||||||
\(436\) | 17921.4 | 1.96853 | ||||||||
\(437\) | 4520.98 | 0.494892 | ||||||||
\(438\) | −7913.95 | −0.863340 | ||||||||
\(439\) | 8868.59 | 0.964180 | 0.482090 | − | 0.876122i | \(-0.339878\pi\) | ||||
0.482090 | + | 0.876122i | \(0.339878\pi\) | |||||||
\(440\) | −13460.6 | −1.45843 | ||||||||
\(441\) | −3697.20 | −0.399222 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4310.67 | −0.462316 | −0.231158 | − | 0.972916i | \(-0.574251\pi\) | ||||
−0.231158 | + | 0.972916i | \(0.574251\pi\) | |||||||
\(444\) | 11066.0 | 1.18281 | ||||||||
\(445\) | 5253.87 | 0.559680 | ||||||||
\(446\) | 12583.8 | 1.33601 | ||||||||
\(447\) | 16133.5 | 1.70714 | ||||||||
\(448\) | −2640.00 | −0.278412 | ||||||||
\(449\) | −4604.48 | −0.483962 | −0.241981 | − | 0.970281i | \(-0.577797\pi\) | ||||
−0.241981 | + | 0.970281i | \(0.577797\pi\) | |||||||
\(450\) | −5917.01 | −0.619845 | ||||||||
\(451\) | 4714.45 | 0.492228 | ||||||||
\(452\) | −22577.6 | −2.34947 | ||||||||
\(453\) | 1281.31 | 0.132895 | ||||||||
\(454\) | 4807.30 | 0.496956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11527.2 | 1.18380 | ||||||||
\(457\) | 16379.2 | 1.67656 | 0.838281 | − | 0.545238i | \(-0.183561\pi\) | ||||
0.838281 | + | 0.545238i | \(0.183561\pi\) | |||||||
\(458\) | −2118.89 | −0.216178 | ||||||||
\(459\) | −12293.8 | −1.25016 | ||||||||
\(460\) | 20541.2 | 2.08204 | ||||||||
\(461\) | 9631.51 | 0.973068 | 0.486534 | − | 0.873662i | \(-0.338261\pi\) | ||||
0.486534 | + | 0.873662i | \(0.338261\pi\) | |||||||
\(462\) | 3180.59 | 0.320291 | ||||||||
\(463\) | −17855.0 | −1.79220 | −0.896102 | − | 0.443848i | \(-0.853613\pi\) | ||||
−0.896102 | + | 0.443848i | \(0.853613\pi\) | |||||||
\(464\) | 11418.0 | 1.14238 | ||||||||
\(465\) | 10267.1 | 1.02392 | ||||||||
\(466\) | −14196.6 | −1.41126 | ||||||||
\(467\) | 8220.28 | 0.814538 | 0.407269 | − | 0.913308i | \(-0.366481\pi\) | ||||
0.407269 | + | 0.913308i | \(0.366481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 377.584 | 0.0371753 | ||||||||
\(470\) | −2709.62 | −0.265927 | ||||||||
\(471\) | −4332.73 | −0.423867 | ||||||||
\(472\) | −28923.3 | −2.82055 | ||||||||
\(473\) | −3029.40 | −0.294486 | ||||||||
\(474\) | 9629.18 | 0.933087 | ||||||||
\(475\) | 5549.93 | 0.536102 | ||||||||
\(476\) | −8467.29 | −0.815331 | ||||||||
\(477\) | 1358.22 | 0.130374 | ||||||||
\(478\) | −28138.3 | −2.69250 | ||||||||
\(479\) | −3164.10 | −0.301819 | −0.150909 | − | 0.988548i | \(-0.548220\pi\) | ||||
−0.150909 | + | 0.988548i | \(0.548220\pi\) | |||||||
\(480\) | −4038.39 | −0.384013 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5557.73 | −0.525203 | ||||||||
\(483\) | −2336.74 | −0.220136 | ||||||||
\(484\) | −11221.2 | −1.05383 | ||||||||
\(485\) | 7353.55 | 0.688469 | ||||||||
\(486\) | −14563.9 | −1.35932 | ||||||||
\(487\) | −7487.99 | −0.696741 | −0.348371 | − | 0.937357i | \(-0.613265\pi\) | ||||
−0.348371 | + | 0.937357i | \(0.613265\pi\) | |||||||
\(488\) | −24405.6 | −2.26391 | ||||||||
\(489\) | −18243.7 | −1.68714 | ||||||||
\(490\) | 23926.7 | 2.20592 | ||||||||
\(491\) | −16013.7 | −1.47187 | −0.735933 | − | 0.677054i | \(-0.763256\pi\) | ||||
−0.735933 | + | 0.677054i | \(0.763256\pi\) | |||||||
\(492\) | −18343.6 | −1.68089 | ||||||||
\(493\) | −28703.4 | −2.62218 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4267.78 | 0.387520 | ||||||||
\(496\) | −5499.44 | −0.497847 | ||||||||
\(497\) | 4234.41 | 0.382171 | ||||||||
\(498\) | 31268.7 | 2.81362 | ||||||||
\(499\) | 10343.2 | 0.927904 | 0.463952 | − | 0.885860i | \(-0.346431\pi\) | ||||
0.463952 | + | 0.885860i | \(0.346431\pi\) | |||||||
\(500\) | −4172.48 | −0.373198 | ||||||||
\(501\) | −16983.8 | −1.51453 | ||||||||
\(502\) | 15758.6 | 1.40108 | ||||||||
\(503\) | −18615.3 | −1.65013 | −0.825063 | − | 0.565040i | \(-0.808861\pi\) | ||||
−0.825063 | + | 0.565040i | \(0.808861\pi\) | |||||||
\(504\) | −1768.58 | −0.156308 | ||||||||
\(505\) | 12798.1 | 1.12774 | ||||||||
\(506\) | −10389.8 | −0.912809 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4472.73 | 0.390641 | ||||||||
\(509\) | −3628.41 | −0.315965 | −0.157983 | − | 0.987442i | \(-0.550499\pi\) | ||||
−0.157983 | + | 0.987442i | \(0.550499\pi\) | |||||||
\(510\) | −58123.1 | −5.04654 | ||||||||
\(511\) | −1138.88 | −0.0985935 | ||||||||
\(512\) | 16710.7 | 1.44241 | ||||||||
\(513\) | 5002.78 | 0.430562 | ||||||||
\(514\) | −30594.3 | −2.62540 | ||||||||
\(515\) | 2435.68 | 0.208406 | ||||||||
\(516\) | 11787.2 | 1.00563 | ||||||||
\(517\) | 902.521 | 0.0767753 | ||||||||
\(518\) | 2418.29 | 0.205122 | ||||||||
\(519\) | −2099.49 | −0.177567 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3105.46 | −0.261137 | −0.130569 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130569 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(522\) | −12453.0 | −1.04416 | ||||||||
\(523\) | 1911.23 | 0.159794 | 0.0798969 | − | 0.996803i | \(-0.474541\pi\) | ||||
0.0798969 | + | 0.996803i | \(0.474541\pi\) | |||||||
\(524\) | −18543.1 | −1.54592 | ||||||||
\(525\) | −2868.58 | −0.238467 | ||||||||
\(526\) | 29859.0 | 2.47512 | ||||||||
\(527\) | 13824.9 | 1.14274 | ||||||||
\(528\) | −7701.10 | −0.634748 | ||||||||
\(529\) | −4533.77 | −0.372628 | ||||||||
\(530\) | −8789.80 | −0.720386 | ||||||||
\(531\) | 9170.35 | 0.749452 | ||||||||
\(532\) | 3445.64 | 0.280804 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10339.9 | 0.837920 | ||||||||
\(535\) | 16392.4 | 1.32468 | ||||||||
\(536\) | −3144.88 | −0.253430 | ||||||||
\(537\) | 6781.57 | 0.544965 | ||||||||
\(538\) | −4083.16 | −0.327208 | ||||||||
\(539\) | −7969.50 | −0.636866 | ||||||||
\(540\) | 22730.2 | 1.81140 | ||||||||
\(541\) | −15251.2 | −1.21202 | −0.606008 | − | 0.795459i | \(-0.707230\pi\) | ||||
−0.606008 | + | 0.795459i | \(0.707230\pi\) | |||||||
\(542\) | 9985.55 | 0.791358 | ||||||||
\(543\) | 8800.80 | 0.695541 | ||||||||
\(544\) | −5437.82 | −0.428575 | ||||||||
\(545\) | 17703.6 | 1.39145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1838.85 | 0.143736 | 0.0718681 | − | 0.997414i | \(-0.477104\pi\) | ||||
0.0718681 | + | 0.997414i | \(0.477104\pi\) | |||||||
\(548\) | −12027.4 | −0.937567 | ||||||||
\(549\) | 7737.99 | 0.601547 | ||||||||
\(550\) | −12754.4 | −0.988819 | ||||||||
\(551\) | 11680.4 | 0.903091 | ||||||||
\(552\) | 19462.6 | 1.50070 | ||||||||
\(553\) | 1385.72 | 0.106558 | ||||||||
\(554\) | −31860.4 | −2.44336 | ||||||||
\(555\) | 10931.5 | 0.836066 | ||||||||
\(556\) | 31340.3 | 2.39051 | ||||||||
\(557\) | 6301.29 | 0.479343 | 0.239672 | − | 0.970854i | \(-0.422960\pi\) | ||||
0.239672 | + | 0.970854i | \(0.422960\pi\) | |||||||
\(558\) | 5997.96 | 0.455042 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3327.29 | 0.251078 | ||||||||
\(561\) | 19359.6 | 1.45698 | ||||||||
\(562\) | 4525.69 | 0.339688 | ||||||||
\(563\) | 11759.8 | 0.880316 | 0.440158 | − | 0.897920i | \(-0.354922\pi\) | ||||
0.440158 | + | 0.897920i | \(0.354922\pi\) | |||||||
\(564\) | −3511.66 | −0.262176 | ||||||||
\(565\) | −22303.3 | −1.66072 | ||||||||
\(566\) | 25840.6 | 1.91901 | ||||||||
\(567\) | −3914.07 | −0.289904 | ||||||||
\(568\) | −35268.2 | −2.60532 | ||||||||
\(569\) | −17219.4 | −1.26867 | −0.634337 | − | 0.773056i | \(-0.718727\pi\) | ||||
−0.634337 | + | 0.773056i | \(0.718727\pi\) | |||||||
\(570\) | 23652.4 | 1.73805 | ||||||||
\(571\) | 825.501 | 0.0605011 | 0.0302506 | − | 0.999542i | \(-0.490369\pi\) | ||||
0.0302506 | + | 0.999542i | \(0.490369\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5557.00 | 0.405143 | ||||||||
\(574\) | −4008.71 | −0.291498 | ||||||||
\(575\) | 9370.52 | 0.679614 | ||||||||
\(576\) | −6971.62 | −0.504313 | ||||||||
\(577\) | 1073.19 | 0.0774308 | 0.0387154 | − | 0.999250i | \(-0.487673\pi\) | ||||
0.0387154 | + | 0.999250i | \(0.487673\pi\) | |||||||
\(578\) | −54484.8 | −3.92088 | ||||||||
\(579\) | 16049.1 | 1.15194 | ||||||||
\(580\) | 53070.3 | 3.79935 | ||||||||
\(581\) | 4499.83 | 0.321316 | ||||||||
\(582\) | 14472.1 | 1.03074 | ||||||||
\(583\) | 2927.71 | 0.207981 | ||||||||
\(584\) | 9485.71 | 0.672126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8536.93 | 0.601804 | ||||||||
\(587\) | −14939.4 | −1.05045 | −0.525225 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525225 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(588\) | 31008.9 | 2.17480 | ||||||||
\(589\) | −5625.86 | −0.393565 | ||||||||
\(590\) | −59346.7 | −4.14113 | ||||||||
\(591\) | 9182.57 | 0.639121 | ||||||||
\(592\) | −5855.34 | −0.406509 | ||||||||
\(593\) | 6296.13 | 0.436006 | 0.218003 | − | 0.975948i | \(-0.430046\pi\) | ||||
0.218003 | + | 0.975948i | \(0.430046\pi\) | |||||||
\(594\) | −11497.0 | −0.794154 | ||||||||
\(595\) | −8364.40 | −0.576314 | ||||||||
\(596\) | −40166.6 | −2.76055 | ||||||||
\(597\) | 22304.4 | 1.52908 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3518.96 | −0.240035 | −0.120017 | − | 0.992772i | \(-0.538295\pi\) | ||||
−0.120017 | + | 0.992772i | \(0.538295\pi\) | |||||||
\(600\) | 23892.2 | 1.62566 | ||||||||
\(601\) | 5380.65 | 0.365194 | 0.182597 | − | 0.983188i | \(-0.441550\pi\) | ||||
0.182597 | + | 0.983188i | \(0.441550\pi\) | |||||||
\(602\) | 2575.90 | 0.174395 | ||||||||
\(603\) | 997.110 | 0.0673391 | ||||||||
\(604\) | −3190.00 | −0.214899 | ||||||||
\(605\) | −11084.8 | −0.744895 | ||||||||
\(606\) | 25187.3 | 1.68839 | ||||||||
\(607\) | 20708.6 | 1.38474 | 0.692369 | − | 0.721543i | \(-0.256567\pi\) | ||||
0.692369 | + | 0.721543i | \(0.256567\pi\) | |||||||
\(608\) | 2212.84 | 0.147603 | ||||||||
\(609\) | −6037.23 | −0.401709 | ||||||||
\(610\) | −50077.1 | −3.32387 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −22360.1 | −1.47688 | ||||||||
\(613\) | 8563.66 | 0.564246 | 0.282123 | − | 0.959378i | \(-0.408961\pi\) | ||||
0.282123 | + | 0.959378i | \(0.408961\pi\) | |||||||
\(614\) | 22925.9 | 1.50687 | ||||||||
\(615\) | −18120.8 | −1.18813 | ||||||||
\(616\) | −3812.28 | −0.249352 | ||||||||
\(617\) | 30449.6 | 1.98680 | 0.993400 | − | 0.114703i | \(-0.0365915\pi\) | ||||
0.993400 | + | 0.114703i | \(0.0365915\pi\) | |||||||
\(618\) | 4793.53 | 0.312013 | ||||||||
\(619\) | 26233.1 | 1.70339 | 0.851693 | − | 0.524041i | \(-0.175576\pi\) | ||||
0.851693 | + | 0.524041i | \(0.175576\pi\) | |||||||
\(620\) | −25561.2 | −1.65575 | ||||||||
\(621\) | 8446.70 | 0.545820 | ||||||||
\(622\) | 22975.8 | 1.48111 | ||||||||
\(623\) | 1487.99 | 0.0956905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17528.4 | −1.12182 | ||||||||
\(626\) | −48962.7 | −3.12611 | ||||||||
\(627\) | −7878.13 | −0.501790 | ||||||||
\(628\) | 10786.9 | 0.685421 | ||||||||
\(629\) | 14719.6 | 0.933084 | ||||||||
\(630\) | −3628.90 | −0.229490 | ||||||||
\(631\) | −20639.5 | −1.30213 | −0.651066 | − | 0.759021i | \(-0.725678\pi\) | ||||
−0.651066 | + | 0.759021i | \(0.725678\pi\) | |||||||
\(632\) | −11541.6 | −0.726425 | ||||||||
\(633\) | −18907.2 | −1.18719 | ||||||||
\(634\) | 28586.7 | 1.79073 | ||||||||
\(635\) | 4418.38 | 0.276123 | ||||||||
\(636\) | −11391.5 | −0.710226 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −26843.1 | −1.66572 | ||||||||
\(639\) | 11182.1 | 0.692262 | ||||||||
\(640\) | 39903.8 | 2.46459 | ||||||||
\(641\) | −4431.77 | −0.273080 | −0.136540 | − | 0.990635i | \(-0.543598\pi\) | ||||
−0.136540 | + | 0.990635i | \(0.543598\pi\) | |||||||
\(642\) | 32260.9 | 1.98323 | ||||||||
\(643\) | 14176.1 | 0.869439 | 0.434719 | − | 0.900566i | \(-0.356848\pi\) | ||||
0.434719 | + | 0.900566i | \(0.356848\pi\) | |||||||
\(644\) | 5817.63 | 0.355973 | ||||||||
\(645\) | 11644.0 | 0.710824 | ||||||||
\(646\) | 31848.7 | 1.93974 | ||||||||
\(647\) | 5650.79 | 0.343362 | 0.171681 | − | 0.985153i | \(-0.445080\pi\) | ||||
0.171681 | + | 0.985153i | \(0.445080\pi\) | |||||||
\(648\) | 32600.1 | 1.97632 | ||||||||
\(649\) | 19767.2 | 1.19558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2907.82 | 0.175064 | ||||||||
\(652\) | 45420.2 | 2.72821 | ||||||||
\(653\) | −18436.3 | −1.10485 | −0.552425 | − | 0.833562i | \(-0.686298\pi\) | ||||
−0.552425 | + | 0.833562i | \(0.686298\pi\) | |||||||
\(654\) | 34841.6 | 2.08320 | ||||||||
\(655\) | −18317.8 | −1.09273 | ||||||||
\(656\) | 9706.18 | 0.577687 | ||||||||
\(657\) | −3007.52 | −0.178591 | ||||||||
\(658\) | −767.415 | −0.0454665 | ||||||||
\(659\) | −15331.9 | −0.906294 | −0.453147 | − | 0.891436i | \(-0.649699\pi\) | ||||
−0.453147 | + | 0.891436i | \(0.649699\pi\) | |||||||
\(660\) | −35794.4 | −2.11106 | ||||||||
\(661\) | −22295.1 | −1.31192 | −0.655961 | − | 0.754795i | \(-0.727736\pi\) | ||||
−0.655961 | + | 0.754795i | \(0.727736\pi\) | |||||||
\(662\) | 13566.2 | 0.796471 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37478.9 | −2.19046 | ||||||||
\(665\) | 3403.78 | 0.198485 | ||||||||
\(666\) | 6386.12 | 0.371557 | ||||||||
\(667\) | 19721.3 | 1.14484 | ||||||||
\(668\) | 42283.4 | 2.44909 | ||||||||
\(669\) | 16110.4 | 0.931037 | ||||||||
\(670\) | −6452.88 | −0.372084 | ||||||||
\(671\) | 16679.7 | 0.959629 | ||||||||
\(672\) | −1143.75 | −0.0656562 | ||||||||
\(673\) | −16171.7 | −0.926259 | −0.463129 | − | 0.886291i | \(-0.653274\pi\) | ||||
−0.463129 | + | 0.886291i | \(0.653274\pi\) | |||||||
\(674\) | 1185.45 | 0.0677475 | ||||||||
\(675\) | 10369.1 | 0.591272 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33614.4 | 1.90828 | 0.954141 | − | 0.299358i | \(-0.0967725\pi\) | ||||
0.954141 | + | 0.299358i | \(0.0967725\pi\) | |||||||
\(678\) | −43893.9 | −2.48633 | ||||||||
\(679\) | 2082.66 | 0.117710 | ||||||||
\(680\) | 69666.7 | 3.92882 | ||||||||
\(681\) | 6154.53 | 0.346318 | ||||||||
\(682\) | 12928.9 | 0.725915 | ||||||||
\(683\) | −22477.5 | −1.25926 | −0.629632 | − | 0.776893i | \(-0.716794\pi\) | ||||
−0.629632 | + | 0.776893i | \(0.716794\pi\) | |||||||
\(684\) | 9099.12 | 0.508646 | ||||||||
\(685\) | −11881.3 | −0.662717 | ||||||||
\(686\) | 13942.2 | 0.775968 | ||||||||
\(687\) | −2712.70 | −0.150649 | ||||||||
\(688\) | −6236.97 | −0.345614 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 39934.7 | 2.20332 | ||||||||
\(691\) | −7618.93 | −0.419447 | −0.209723 | − | 0.977761i | \(-0.567256\pi\) | ||||
−0.209723 | + | 0.977761i | \(0.567256\pi\) | |||||||
\(692\) | 5226.95 | 0.287137 | ||||||||
\(693\) | 1208.71 | 0.0662558 | ||||||||
\(694\) | −50128.9 | −2.74188 | ||||||||
\(695\) | 30959.5 | 1.68973 | ||||||||
\(696\) | 50283.8 | 2.73851 | ||||||||
\(697\) | −24400.2 | −1.32600 | ||||||||
\(698\) | 40820.0 | 2.21355 | ||||||||
\(699\) | −18175.2 | −0.983474 | ||||||||
\(700\) | 7141.70 | 0.385616 | ||||||||
\(701\) | −18164.3 | −0.978684 | −0.489342 | − | 0.872092i | \(-0.662763\pi\) | ||||
−0.489342 | + | 0.872092i | \(0.662763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5989.95 | −0.321359 | ||||||||
\(704\) | −15027.7 | −0.804514 | ||||||||
\(705\) | −3468.99 | −0.185319 | ||||||||
\(706\) | −22912.0 | −1.22140 | ||||||||
\(707\) | 3624.66 | 0.192814 | ||||||||
\(708\) | −76912.9 | −4.08272 | ||||||||
\(709\) | 16706.5 | 0.884945 | 0.442472 | − | 0.896782i | \(-0.354101\pi\) | ||||
0.442472 | + | 0.896782i | \(0.354101\pi\) | |||||||
\(710\) | −72365.7 | −3.82512 | ||||||||
\(711\) | 3659.36 | 0.193019 | ||||||||
\(712\) | −12393.4 | −0.652336 | ||||||||
\(713\) | −9498.72 | −0.498920 | ||||||||
\(714\) | −16461.5 | −0.862825 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16883.6 | −0.881244 | ||||||||
\(717\) | −36023.9 | −1.87634 | ||||||||
\(718\) | −36598.2 | −1.90227 | ||||||||
\(719\) | 4549.39 | 0.235972 | 0.117986 | − | 0.993015i | \(-0.462356\pi\) | ||||
0.117986 | + | 0.993015i | \(0.462356\pi\) | |||||||
\(720\) | 8786.58 | 0.454800 | ||||||||
\(721\) | 689.830 | 0.0356319 | ||||||||
\(722\) | 20238.4 | 1.04321 | ||||||||
\(723\) | −7115.26 | −0.366002 | ||||||||
\(724\) | −21910.8 | −1.12473 | ||||||||
\(725\) | 24209.8 | 1.24018 | ||||||||
\(726\) | −21815.4 | −1.11521 | ||||||||
\(727\) | −6246.70 | −0.318676 | −0.159338 | − | 0.987224i | \(-0.550936\pi\) | ||||
−0.159338 | + | 0.987224i | \(0.550936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5839.14 | 0.296659 | ||||||||
\(730\) | 19463.4 | 0.986813 | ||||||||
\(731\) | 15679.0 | 0.793309 | ||||||||
\(732\) | −64899.6 | −3.27699 | ||||||||
\(733\) | −3447.16 | −0.173702 | −0.0868511 | − | 0.996221i | \(-0.527680\pi\) | ||||
−0.0868511 | + | 0.996221i | \(0.527680\pi\) | |||||||
\(734\) | 57791.6 | 2.90617 | ||||||||
\(735\) | 30632.1 | 1.53725 | ||||||||
\(736\) | 3736.17 | 0.187116 | ||||||||
\(737\) | 2149.32 | 0.107424 | ||||||||
\(738\) | −10586.0 | −0.528018 | ||||||||
\(739\) | 37032.9 | 1.84341 | 0.921703 | − | 0.387895i | \(-0.126798\pi\) | ||||
0.921703 | + | 0.387895i | \(0.126798\pi\) | |||||||
\(740\) | −27215.4 | −1.35197 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2489.43 | −0.123167 | ||||||||
\(743\) | 15298.0 | 0.755356 | 0.377678 | − | 0.925937i | \(-0.376723\pi\) | ||||
0.377678 | + | 0.925937i | \(0.376723\pi\) | |||||||
\(744\) | −24219.1 | −1.19343 | ||||||||
\(745\) | −39678.5 | −1.95129 | ||||||||
\(746\) | 28059.1 | 1.37710 | ||||||||
\(747\) | 11883.0 | 0.582029 | ||||||||
\(748\) | −48198.4 | −2.35603 | ||||||||
\(749\) | 4642.62 | 0.226485 | ||||||||
\(750\) | −8111.86 | −0.394938 | ||||||||
\(751\) | −9844.54 | −0.478339 | −0.239169 | − | 0.970978i | \(-0.576875\pi\) | ||||
−0.239169 | + | 0.970978i | \(0.576875\pi\) | |||||||
\(752\) | 1858.12 | 0.0901048 | ||||||||
\(753\) | 20174.9 | 0.976382 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3151.24 | −0.151901 | ||||||||
\(756\) | 6437.62 | 0.309701 | ||||||||
\(757\) | 5921.31 | 0.284298 | 0.142149 | − | 0.989845i | \(-0.454599\pi\) | ||||
0.142149 | + | 0.989845i | \(0.454599\pi\) | |||||||
\(758\) | −42817.7 | −2.05173 | ||||||||
\(759\) | −13301.4 | −0.636116 | ||||||||
\(760\) | −28349.9 | −1.35310 | ||||||||
\(761\) | −17872.5 | −0.851348 | −0.425674 | − | 0.904877i | \(-0.639963\pi\) | ||||
−0.425674 | + | 0.904877i | \(0.639963\pi\) | |||||||
\(762\) | 8695.58 | 0.413396 | ||||||||
\(763\) | 5013.99 | 0.237901 | ||||||||
\(764\) | −13834.9 | −0.655142 | ||||||||
\(765\) | −22088.4 | −1.04393 | ||||||||
\(766\) | −5070.61 | −0.239176 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 48211.2 | 2.26520 | ||||||||
\(769\) | −11265.2 | −0.528262 | −0.264131 | − | 0.964487i | \(-0.585085\pi\) | ||||
−0.264131 | + | 0.964487i | \(0.585085\pi\) | |||||||
\(770\) | −7822.29 | −0.366099 | ||||||||
\(771\) | −39168.2 | −1.82958 | ||||||||
\(772\) | −39956.3 | −1.86277 | ||||||||
\(773\) | −27603.7 | −1.28439 | −0.642196 | − | 0.766540i | \(-0.721977\pi\) | ||||
−0.642196 | + | 0.766540i | \(0.721977\pi\) | |||||||
\(774\) | 6802.35 | 0.315898 | ||||||||
\(775\) | −11660.6 | −0.540465 | ||||||||
\(776\) | −17346.4 | −0.802447 | ||||||||
\(777\) | 3096.00 | 0.142945 | ||||||||
\(778\) | 57396.7 | 2.64495 | ||||||||
\(779\) | 9929.31 | 0.456681 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24103.5 | 1.10434 | ||||||||
\(782\) | 53773.4 | 2.45899 | ||||||||
\(783\) | 21823.0 | 0.996027 | ||||||||
\(784\) | −16407.7 | −0.747437 | ||||||||
\(785\) | 10655.8 | 0.484488 | ||||||||
\(786\) | −36050.3 | −1.63597 | ||||||||
\(787\) | −24163.1 | −1.09444 | −0.547218 | − | 0.836990i | \(-0.684313\pi\) | ||||
−0.547218 | + | 0.836990i | \(0.684313\pi\) | |||||||
\(788\) | −22861.2 | −1.03350 | ||||||||
\(789\) | 38226.9 | 1.72486 | ||||||||
\(790\) | −23681.8 | −1.06653 | ||||||||
\(791\) | −6316.70 | −0.283939 | ||||||||
\(792\) | −10067.3 | −0.451675 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −50726.7 | −2.26728 | ||||||||
\(795\) | −11253.1 | −0.502021 | ||||||||
\(796\) | −55529.8 | −2.47262 | ||||||||
\(797\) | 30385.6 | 1.35046 | 0.675228 | − | 0.737609i | \(-0.264045\pi\) | ||||
0.675228 | + | 0.737609i | \(0.264045\pi\) | |||||||
\(798\) | 6698.79 | 0.297161 | ||||||||
\(799\) | −4671.10 | −0.206823 | ||||||||
\(800\) | 4586.51 | 0.202697 | ||||||||
\(801\) | 3929.43 | 0.173333 | ||||||||
\(802\) | −38413.6 | −1.69131 | ||||||||
\(803\) | −6482.87 | −0.284901 | ||||||||
\(804\) | −8362.89 | −0.366836 | ||||||||
\(805\) | 5746.94 | 0.251619 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5227.46 | −0.228024 | ||||||||
\(808\) | −30189.6 | −1.31444 | ||||||||
\(809\) | −41976.9 | −1.82426 | −0.912131 | − | 0.409899i | \(-0.865564\pi\) | ||||
−0.912131 | + | 0.409899i | \(0.865564\pi\) | |||||||
\(810\) | 66891.2 | 2.90162 | ||||||||
\(811\) | −9674.05 | −0.418868 | −0.209434 | − | 0.977823i | \(-0.567162\pi\) | ||||
−0.209434 | + | 0.977823i | \(0.567162\pi\) | |||||||
\(812\) | 15030.5 | 0.649590 | ||||||||
\(813\) | 12784.0 | 0.551480 | ||||||||
\(814\) | 13765.6 | 0.592733 | ||||||||
\(815\) | 44868.3 | 1.92843 | ||||||||
\(816\) | 39857.9 | 1.70993 | ||||||||
\(817\) | −6380.35 | −0.273219 | ||||||||
\(818\) | 28245.7 | 1.20732 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 45114.0 | 1.92128 | ||||||||
\(821\) | 25426.0 | 1.08085 | 0.540423 | − | 0.841394i | \(-0.318264\pi\) | ||||
0.540423 | + | 0.841394i | \(0.318264\pi\) | |||||||
\(822\) | −23382.9 | −0.992181 | ||||||||
\(823\) | 14388.3 | 0.609408 | 0.304704 | − | 0.952447i | \(-0.401442\pi\) | ||||
0.304704 | + | 0.952447i | \(0.401442\pi\) | |||||||
\(824\) | −5745.56 | −0.242908 | ||||||||
\(825\) | −16328.8 | −0.689086 | ||||||||
\(826\) | −16808.1 | −0.708024 | ||||||||
\(827\) | 3850.25 | 0.161894 | 0.0809469 | − | 0.996718i | \(-0.474206\pi\) | ||||
0.0809469 | + | 0.996718i | \(0.474206\pi\) | |||||||
\(828\) | 15363.0 | 0.644807 | ||||||||
\(829\) | −1918.58 | −0.0803802 | −0.0401901 | − | 0.999192i | \(-0.512796\pi\) | ||||
−0.0401901 | + | 0.999192i | \(0.512796\pi\) | |||||||
\(830\) | −76901.7 | −3.21602 | ||||||||
\(831\) | −40789.2 | −1.70272 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41247.1 | 1.71564 | ||||||||
\(834\) | 60929.7 | 2.52977 | ||||||||
\(835\) | 41769.6 | 1.73113 | ||||||||
\(836\) | 19613.7 | 0.811426 | ||||||||
\(837\) | −10511.0 | −0.434066 | ||||||||
\(838\) | 41355.9 | 1.70479 | ||||||||
\(839\) | 31412.1 | 1.29257 | 0.646285 | − | 0.763096i | \(-0.276322\pi\) | ||||
0.646285 | + | 0.763096i | \(0.276322\pi\) | |||||||
\(840\) | 14653.1 | 0.601882 | ||||||||
\(841\) | 26563.1 | 1.08914 | ||||||||
\(842\) | 79981.9 | 3.27359 | ||||||||
\(843\) | 5793.99 | 0.236721 | ||||||||
\(844\) | 47072.0 | 1.91977 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2026.56 | −0.0823577 | ||||||||
\(847\) | −3139.42 | −0.127357 | ||||||||
\(848\) | 6027.61 | 0.244091 | ||||||||
\(849\) | 33082.3 | 1.33732 | ||||||||
\(850\) | 66012.0 | 2.66376 | ||||||||
\(851\) | −10113.4 | −0.407384 | ||||||||
\(852\) | −93785.5 | −3.77117 | ||||||||
\(853\) | 18315.5 | 0.735184 | 0.367592 | − | 0.929987i | \(-0.380182\pi\) | ||||
0.367592 | + | 0.929987i | \(0.380182\pi\) | |||||||
\(854\) | −14182.7 | −0.568295 | ||||||||
\(855\) | 8988.56 | 0.359535 | ||||||||
\(856\) | −38668.1 | −1.54398 | ||||||||
\(857\) | 9579.31 | 0.381824 | 0.190912 | − | 0.981607i | \(-0.438856\pi\) | ||||
0.190912 | + | 0.981607i | \(0.438856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7136.55 | −0.283465 | −0.141732 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141732 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(860\) | −28989.3 | −1.14945 | ||||||||
\(861\) | −5132.13 | −0.203139 | ||||||||
\(862\) | 33090.3 | 1.30749 | ||||||||
\(863\) | 17239.2 | 0.679986 | 0.339993 | − | 0.940428i | \(-0.389575\pi\) | ||||
0.339993 | + | 0.940428i | \(0.389575\pi\) | |||||||
\(864\) | 4134.34 | 0.162793 | ||||||||
\(865\) | 5163.44 | 0.202962 | ||||||||
\(866\) | 30447.8 | 1.19476 | ||||||||
\(867\) | −69754.0 | −2.73237 | ||||||||
\(868\) | −7239.41 | −0.283089 | ||||||||
\(869\) | 7887.94 | 0.307917 | ||||||||
\(870\) | 103176. | 4.02067 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −41761.3 | −1.62181 | ||||||||
\(873\) | 5499.81 | 0.213219 | ||||||||
\(874\) | −21882.3 | −0.846889 | ||||||||
\(875\) | −1167.36 | −0.0451019 | ||||||||
\(876\) | 25224.5 | 0.972895 | ||||||||
\(877\) | −33048.7 | −1.27249 | −0.636247 | − | 0.771486i | \(-0.719514\pi\) | ||||
−0.636247 | + | 0.771486i | \(0.719514\pi\) | |||||||
\(878\) | −42925.6 | −1.64996 | ||||||||
\(879\) | 10929.4 | 0.419384 | ||||||||
\(880\) | 18939.9 | 0.725529 | ||||||||
\(881\) | 19527.8 | 0.746775 | 0.373387 | − | 0.927676i | \(-0.378196\pi\) | ||||
0.373387 | + | 0.927676i | \(0.378196\pi\) | |||||||
\(882\) | 17895.1 | 0.683173 | ||||||||
\(883\) | −26361.3 | −1.00467 | −0.502337 | − | 0.864672i | \(-0.667526\pi\) | ||||
−0.502337 | + | 0.864672i | \(0.667526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −75978.4 | −2.88586 | ||||||||
\(886\) | 20864.4 | 0.791144 | ||||||||
\(887\) | 21405.8 | 0.810301 | 0.405151 | − | 0.914250i | \(-0.367219\pi\) | ||||
0.405151 | + | 0.914250i | \(0.367219\pi\) | |||||||
\(888\) | −25786.5 | −0.974479 | ||||||||
\(889\) | 1251.37 | 0.0472098 | ||||||||
\(890\) | −25429.7 | −0.957758 | ||||||||
\(891\) | −22280.1 | −0.837723 | ||||||||
\(892\) | −40109.0 | −1.50555 | ||||||||
\(893\) | 1900.84 | 0.0712308 | ||||||||
\(894\) | −78089.1 | −2.92136 | ||||||||
\(895\) | −16678.5 | −0.622905 | ||||||||
\(896\) | 11301.5 | 0.421379 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22286.5 | 0.828184 | ||||||||
\(899\) | −24541.0 | −0.910442 | ||||||||
\(900\) | 18859.5 | 0.698501 | ||||||||
\(901\) | −15152.7 | −0.560276 | ||||||||
\(902\) | −22818.8 | −0.842330 | ||||||||
\(903\) | 3297.79 | 0.121532 | ||||||||
\(904\) | 52611.5 | 1.93565 | ||||||||
\(905\) | −21644.5 | −0.795015 | ||||||||
\(906\) | −6201.78 | −0.227418 | ||||||||
\(907\) | 28887.5 | 1.05754 | 0.528772 | − | 0.848764i | \(-0.322653\pi\) | ||||
0.528772 | + | 0.848764i | \(0.322653\pi\) | |||||||
\(908\) | −15322.5 | −0.560018 | ||||||||
\(909\) | 9571.86 | 0.349261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31360.9 | −1.14054 | −0.570271 | − | 0.821456i | \(-0.693162\pi\) | ||||
−0.570271 | + | 0.821456i | \(0.693162\pi\) | |||||||
\(912\) | −16219.6 | −0.588909 | ||||||||
\(913\) | 25614.4 | 0.928492 | ||||||||
\(914\) | −79278.4 | −2.86903 | ||||||||
\(915\) | −64111.0 | −2.31633 | ||||||||
\(916\) | 6753.64 | 0.243610 | ||||||||
\(917\) | −5187.94 | −0.186828 | ||||||||
\(918\) | 59504.0 | 2.13935 | ||||||||
\(919\) | −1104.61 | −0.0396493 | −0.0198246 | − | 0.999803i | \(-0.506311\pi\) | ||||
−0.0198246 | + | 0.999803i | \(0.506311\pi\) | |||||||
\(920\) | −47866.0 | −1.71532 | ||||||||
\(921\) | 29350.8 | 1.05010 | ||||||||
\(922\) | −46618.2 | −1.66517 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −10137.6 | −0.360935 | ||||||||
\(925\) | −12415.2 | −0.441308 | ||||||||
\(926\) | 86421.2 | 3.06693 | ||||||||
\(927\) | 1821.68 | 0.0645433 | ||||||||
\(928\) | 9652.81 | 0.341454 | ||||||||
\(929\) | −38435.8 | −1.35742 | −0.678708 | − | 0.734409i | \(-0.737460\pi\) | ||||
−0.678708 | + | 0.734409i | \(0.737460\pi\) | |||||||
\(930\) | −49694.4 | −1.75220 | ||||||||
\(931\) | −16784.9 | −0.590874 | ||||||||
\(932\) | 45249.5 | 1.59034 | ||||||||
\(933\) | 29414.7 | 1.03215 | ||||||||
\(934\) | −39787.6 | −1.39389 | ||||||||
\(935\) | −47612.7 | −1.66535 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21008.7 | 0.732469 | 0.366235 | − | 0.930522i | \(-0.380647\pi\) | ||||
0.366235 | + | 0.930522i | \(0.380647\pi\) | |||||||
\(938\) | −1827.57 | −0.0636166 | ||||||||
\(939\) | −62684.3 | −2.17852 | ||||||||
\(940\) | 8636.50 | 0.299672 | ||||||||
\(941\) | −12695.6 | −0.439814 | −0.219907 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219907 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(942\) | 20971.2 | 0.725348 | ||||||||
\(943\) | 16764.7 | 0.578932 | ||||||||
\(944\) | 40697.0 | 1.40315 | ||||||||
\(945\) | 6359.40 | 0.218911 | ||||||||
\(946\) | 14662.8 | 0.503942 | ||||||||
\(947\) | −48719.4 | −1.67177 | −0.835886 | − | 0.548902i | \(-0.815046\pi\) | ||||
−0.835886 | + | 0.548902i | \(0.815046\pi\) | |||||||
\(948\) | −30691.5 | −1.05149 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −26862.7 | −0.917410 | ||||||||
\(951\) | 36598.0 | 1.24792 | ||||||||
\(952\) | 19730.9 | 0.671725 | ||||||||
\(953\) | −11347.3 | −0.385704 | −0.192852 | − | 0.981228i | \(-0.561774\pi\) | ||||
−0.192852 | + | 0.981228i | \(0.561774\pi\) | |||||||
\(954\) | −6574.00 | −0.223104 | ||||||||
\(955\) | −13666.8 | −0.463085 | ||||||||
\(956\) | 89686.3 | 3.03417 | ||||||||
\(957\) | −34365.7 | −1.16080 | ||||||||
\(958\) | 15314.8 | 0.516491 | ||||||||
\(959\) | −3365.00 | −0.113307 | ||||||||
\(960\) | 57761.4 | 1.94192 | ||||||||
\(961\) | −17970.9 | −0.603232 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12260.0 | 0.410254 | ||||||||
\(964\) | 17714.4 | 0.591849 | ||||||||
\(965\) | −39470.8 | −1.31669 | ||||||||
\(966\) | 11310.2 | 0.376709 | ||||||||
\(967\) | 10585.2 | 0.352014 | 0.176007 | − | 0.984389i | \(-0.443682\pi\) | ||||
0.176007 | + | 0.984389i | \(0.443682\pi\) | |||||||
\(968\) | 26148.1 | 0.868215 | ||||||||
\(969\) | 40774.2 | 1.35176 | ||||||||
\(970\) | −35592.5 | −1.17815 | ||||||||
\(971\) | −53730.8 | −1.77580 | −0.887900 | − | 0.460036i | \(-0.847836\pi\) | ||||
−0.887900 | + | 0.460036i | \(0.847836\pi\) | |||||||
\(972\) | 46420.0 | 1.53181 | ||||||||
\(973\) | 8768.30 | 0.288899 | ||||||||
\(974\) | 36243.2 | 1.19231 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34340.4 | 1.12624 | ||||||||
\(977\) | −9534.31 | −0.312210 | −0.156105 | − | 0.987740i | \(-0.549894\pi\) | ||||
−0.156105 | + | 0.987740i | \(0.549894\pi\) | |||||||
\(978\) | 88302.8 | 2.88713 | ||||||||
\(979\) | 8470.11 | 0.276513 | ||||||||
\(980\) | −76262.7 | −2.48584 | ||||||||
\(981\) | 13240.8 | 0.430933 | ||||||||
\(982\) | 77508.9 | 2.51875 | ||||||||
\(983\) | −8972.94 | −0.291142 | −0.145571 | − | 0.989348i | \(-0.546502\pi\) | ||||
−0.145571 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(984\) | 42745.3 | 1.38483 | ||||||||
\(985\) | −22583.4 | −0.730526 | ||||||||
\(986\) | 138929. | 4.48723 | ||||||||
\(987\) | −982.480 | −0.0316846 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10772.6 | −0.346359 | ||||||||
\(990\) | −20656.8 | −0.663148 | ||||||||
\(991\) | −34900.6 | −1.11872 | −0.559362 | − | 0.828924i | \(-0.688954\pi\) | ||||
−0.559362 | + | 0.828924i | \(0.688954\pi\) | |||||||
\(992\) | −4649.26 | −0.148804 | ||||||||
\(993\) | 17368.0 | 0.555043 | ||||||||
\(994\) | −20495.3 | −0.653995 | ||||||||
\(995\) | −54855.1 | −1.74776 | ||||||||
\(996\) | −99664.2 | −3.17066 | ||||||||
\(997\) | −48154.9 | −1.52967 | −0.764836 | − | 0.644225i | \(-0.777180\pi\) | ||||
−0.764836 | + | 0.644225i | \(0.777180\pi\) | |||||||
\(998\) | −50062.8 | −1.58788 | ||||||||
\(999\) | −11191.2 | −0.354429 |
(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 | 169.4.a.l.1.1 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.bg.1.9 | 9 | |||
13.2 | odd | 12 | 169.4.e.h.147.2 | 36 | |||
13.3 | even | 3 | 169.4.c.k.22.9 | 18 | |||
13.4 | even | 6 | 169.4.c.l.146.1 | 18 | |||
13.5 | odd | 4 | 169.4.b.g.168.17 | 18 | |||
13.6 | odd | 12 | 169.4.e.h.23.17 | 36 | |||
13.7 | odd | 12 | 169.4.e.h.23.2 | 36 | |||
13.8 | odd | 4 | 169.4.b.g.168.2 | 18 | |||
13.9 | even | 3 | 169.4.c.k.146.9 | 18 | |||
13.10 | even | 6 | 169.4.c.l.22.1 | 18 | |||
13.11 | odd | 12 | 169.4.e.h.147.17 | 36 | |||
13.12 | even | 2 | 169.4.a.k.1.9 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bh.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.9 | ✓ | 9 | 13.12 | even | 2 | ||
169.4.a.l.1.1 | yes | 9 | 1.1 | even | 1 | trivial | |
169.4.b.g.168.2 | 18 | 13.8 | odd | 4 | |||
169.4.b.g.168.17 | 18 | 13.5 | odd | 4 | |||
169.4.c.k.22.9 | 18 | 13.3 | even | 3 | |||
169.4.c.k.146.9 | 18 | 13.9 | even | 3 | |||
169.4.c.l.22.1 | 18 | 13.10 | even | 6 | |||
169.4.c.l.146.1 | 18 | 13.4 | even | 6 | |||
169.4.e.h.23.2 | 36 | 13.7 | odd | 12 | |||
169.4.e.h.23.17 | 36 | 13.6 | odd | 12 | |||
169.4.e.h.147.2 | 36 | 13.2 | odd | 12 | |||
169.4.e.h.147.17 | 36 | 13.11 | odd | 12 | |||
1521.4.a.bg.1.9 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bh.1.1 | 9 | 39.38 | odd | 2 |