Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.78487 | −1.69171 | −0.845854 | − | 0.533415i | \(-0.820909\pi\) | ||||
−0.845854 | + | 0.533415i | \(0.820909\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.8950 | 1.86187 | ||||||||
\(5\) | 19.8446 | 1.77495 | 0.887477 | − | 0.460852i | \(-0.152456\pi\) | ||||
0.887477 | + | 0.460852i | \(0.152456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.72473 | 0.525086 | 0.262543 | − | 0.964920i | \(-0.415439\pi\) | ||||
0.262543 | + | 0.964920i | \(0.415439\pi\) | |||||||
\(8\) | −32.9917 | −1.45804 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −94.9538 | −3.00270 | ||||||||
\(11\) | 8.54762 | 0.234291 | 0.117146 | − | 0.993115i | \(-0.462626\pi\) | ||||
0.117146 | + | 0.993115i | \(0.462626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70.2704 | 1.49919 | 0.749596 | − | 0.661896i | \(-0.230248\pi\) | ||||
0.749596 | + | 0.661896i | \(0.230248\pi\) | |||||||
\(14\) | −46.5316 | −0.888292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 38.7010 | 0.604703 | ||||||||
\(17\) | 97.0361 | 1.38439 | 0.692197 | − | 0.721709i | \(-0.256643\pi\) | ||||
0.692197 | + | 0.721709i | \(0.256643\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.5866 | 0.876448 | 0.438224 | − | 0.898866i | \(-0.355608\pi\) | ||||
0.438224 | + | 0.898866i | \(0.355608\pi\) | |||||||
\(20\) | 295.585 | 3.30474 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −40.8993 | −0.396352 | ||||||||
\(23\) | −147.733 | −1.33933 | −0.669663 | − | 0.742665i | \(-0.733561\pi\) | ||||
−0.669663 | + | 0.742665i | \(0.733561\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 268.808 | 2.15046 | ||||||||
\(26\) | −336.235 | −2.53619 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 144.850 | 0.977644 | ||||||||
\(29\) | −33.0087 | −0.211364 | −0.105682 | − | 0.994400i | \(-0.533703\pi\) | ||||
−0.105682 | + | 0.994400i | \(0.533703\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 113.100 | 0.655271 | 0.327636 | − | 0.944804i | \(-0.393748\pi\) | ||||
0.327636 | + | 0.944804i | \(0.393748\pi\) | |||||||
\(32\) | 78.7542 | 0.435059 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −464.305 | −2.34199 | ||||||||
\(35\) | 192.983 | 0.932003 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 185.104 | 0.822458 | 0.411229 | − | 0.911532i | \(-0.365100\pi\) | ||||
0.411229 | + | 0.911532i | \(0.365100\pi\) | |||||||
\(38\) | −347.318 | −1.48269 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −654.706 | −2.58795 | ||||||||
\(41\) | −347.392 | −1.32326 | −0.661629 | − | 0.749832i | \(-0.730134\pi\) | ||||
−0.661629 | + | 0.749832i | \(0.730134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 332.997 | 1.18097 | 0.590484 | − | 0.807050i | \(-0.298937\pi\) | ||||
0.590484 | + | 0.807050i | \(0.298937\pi\) | |||||||
\(44\) | 127.317 | 0.436221 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 706.884 | 2.26575 | ||||||||
\(47\) | 161.096 | 0.499964 | 0.249982 | − | 0.968250i | \(-0.419575\pi\) | ||||
0.249982 | + | 0.968250i | \(0.419575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −248.430 | −0.724285 | ||||||||
\(50\) | −1286.21 | −3.63795 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1046.68 | 2.79131 | ||||||||
\(53\) | −550.417 | −1.42652 | −0.713261 | − | 0.700899i | \(-0.752782\pi\) | ||||
−0.713261 | + | 0.700899i | \(0.752782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 169.624 | 0.415856 | ||||||||
\(56\) | −320.835 | −0.765596 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 157.942 | 0.357566 | ||||||||
\(59\) | 103.680 | 0.228780 | 0.114390 | − | 0.993436i | \(-0.463509\pi\) | ||||
0.114390 | + | 0.993436i | \(0.463509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 280.648 | 0.589070 | 0.294535 | − | 0.955641i | \(-0.404835\pi\) | ||||
0.294535 | + | 0.955641i | \(0.404835\pi\) | |||||||
\(62\) | −541.170 | −1.10853 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −686.437 | −1.34070 | ||||||||
\(65\) | 1394.49 | 2.66100 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −408.830 | −0.745470 | −0.372735 | − | 0.927938i | \(-0.621580\pi\) | ||||
−0.372735 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(68\) | 1445.35 | 2.57757 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −923.400 | −1.57668 | ||||||||
\(71\) | −530.048 | −0.885988 | −0.442994 | − | 0.896525i | \(-0.646084\pi\) | ||||
−0.442994 | + | 0.896525i | \(0.646084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 549.032 | 0.880265 | 0.440132 | − | 0.897933i | \(-0.354931\pi\) | ||||
0.440132 | + | 0.897933i | \(0.354931\pi\) | |||||||
\(74\) | −885.699 | −1.39136 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1081.18 | 1.63184 | ||||||||
\(77\) | 83.1232 | 0.123023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 934.908 | 1.33146 | 0.665730 | − | 0.746192i | \(-0.268120\pi\) | ||||
0.665730 | + | 0.746192i | \(0.268120\pi\) | |||||||
\(80\) | 768.005 | 1.07332 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1662.23 | 2.23856 | ||||||||
\(83\) | 786.990 | 1.04076 | 0.520382 | − | 0.853934i | \(-0.325790\pi\) | ||||
0.520382 | + | 0.853934i | \(0.325790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1925.64 | 2.45724 | ||||||||
\(86\) | −1593.35 | −1.99785 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −282.000 | −0.341606 | ||||||||
\(89\) | 741.961 | 0.883682 | 0.441841 | − | 0.897093i | \(-0.354325\pi\) | ||||
0.441841 | + | 0.897093i | \(0.354325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 683.360 | 0.787204 | ||||||||
\(92\) | −2200.48 | −2.49366 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −770.825 | −0.845793 | ||||||||
\(95\) | 1440.45 | 1.55565 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −611.445 | −0.640029 | −0.320015 | − | 0.947413i | \(-0.603688\pi\) | ||||
−0.320015 | + | 0.947413i | \(0.603688\pi\) | |||||||
\(98\) | 1188.70 | 1.22528 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4003.89 | 4.00389 | ||||||||
\(101\) | 694.672 | 0.684380 | 0.342190 | − | 0.939631i | \(-0.388831\pi\) | ||||
0.342190 | + | 0.939631i | \(0.388831\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1438.35 | 1.37597 | 0.687984 | − | 0.725726i | \(-0.258496\pi\) | ||||
0.687984 | + | 0.725726i | \(0.258496\pi\) | |||||||
\(104\) | −2318.34 | −2.18588 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2633.68 | 2.41326 | ||||||||
\(107\) | 1029.81 | 0.930426 | 0.465213 | − | 0.885199i | \(-0.345978\pi\) | ||||
0.465213 | + | 0.885199i | \(0.345978\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 861.356 | 0.756908 | 0.378454 | − | 0.925620i | \(-0.376456\pi\) | ||||
0.378454 | + | 0.925620i | \(0.376456\pi\) | |||||||
\(110\) | −811.629 | −0.703507 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 376.357 | 0.317521 | ||||||||
\(113\) | 703.757 | 0.585875 | 0.292938 | − | 0.956132i | \(-0.405367\pi\) | ||||
0.292938 | + | 0.956132i | \(0.405367\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2931.70 | −2.37724 | ||||||||
\(116\) | −491.665 | −0.393534 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −496.097 | −0.387029 | ||||||||
\(119\) | 943.649 | 0.726926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1257.94 | −0.945108 | ||||||||
\(122\) | −1342.86 | −0.996535 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1684.63 | 1.22003 | ||||||||
\(125\) | 2853.80 | 2.04201 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 64.5337 | 0.0450901 | 0.0225450 | − | 0.999746i | \(-0.492823\pi\) | ||||
0.0225450 | + | 0.999746i | \(0.492823\pi\) | |||||||
\(128\) | 2654.48 | 1.83301 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6672.44 | −4.50163 | ||||||||
\(131\) | −18.7940 | −0.0125346 | −0.00626732 | − | 0.999980i | \(-0.501995\pi\) | ||||
−0.00626732 | + | 0.999980i | \(0.501995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 705.885 | 0.460210 | ||||||||
\(134\) | 1956.20 | 1.26112 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3201.38 | −2.01850 | ||||||||
\(137\) | −1154.78 | −0.720142 | −0.360071 | − | 0.932925i | \(-0.617248\pi\) | ||||
−0.360071 | + | 0.932925i | \(0.617248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1892.52 | −1.15483 | −0.577414 | − | 0.816452i | \(-0.695938\pi\) | ||||
−0.577414 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(140\) | 2874.48 | 1.73527 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2536.21 | 1.49883 | ||||||||
\(143\) | 600.644 | 0.351247 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −655.044 | −0.375162 | ||||||||
\(146\) | −2627.05 | −1.48915 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2757.13 | 1.53131 | ||||||||
\(149\) | −1645.18 | −0.904553 | −0.452276 | − | 0.891878i | \(-0.649388\pi\) | ||||
−0.452276 | + | 0.891878i | \(0.649388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2245.47 | −1.21016 | −0.605078 | − | 0.796166i | \(-0.706858\pi\) | ||||
−0.605078 | + | 0.796166i | \(0.706858\pi\) | |||||||
\(152\) | −2394.75 | −1.27790 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −397.734 | −0.208119 | ||||||||
\(155\) | 2244.43 | 1.16308 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2419.98 | −1.23016 | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||||
−0.615081 | + | 0.788464i | \(0.710877\pi\) | |||||||
\(158\) | −4473.42 | −2.25244 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1562.84 | 0.772210 | ||||||||
\(161\) | −1436.66 | −0.703261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −722.645 | −0.347251 | −0.173626 | − | 0.984812i | \(-0.555548\pi\) | ||||
−0.173626 | + | 0.984812i | \(0.555548\pi\) | |||||||
\(164\) | −5174.41 | −2.46374 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3765.65 | −1.76067 | ||||||||
\(167\) | 2807.10 | 1.30072 | 0.650358 | − | 0.759628i | \(-0.274619\pi\) | ||||
0.650358 | + | 0.759628i | \(0.274619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2740.92 | 1.24758 | ||||||||
\(170\) | −9213.94 | −4.15692 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4959.99 | 2.19881 | ||||||||
\(173\) | −4063.67 | −1.78587 | −0.892933 | − | 0.450190i | \(-0.851356\pi\) | ||||
−0.892933 | + | 0.450190i | \(0.851356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2614.08 | 1.12918 | ||||||||
\(176\) | 330.801 | 0.141677 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3550.19 | −1.49493 | ||||||||
\(179\) | −2575.22 | −1.07531 | −0.537656 | − | 0.843164i | \(-0.680690\pi\) | ||||
−0.537656 | + | 0.843164i | \(0.680690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1161.25 | 0.476877 | 0.238438 | − | 0.971158i | \(-0.423365\pi\) | ||||
0.238438 | + | 0.971158i | \(0.423365\pi\) | |||||||
\(182\) | −3269.79 | −1.33172 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4873.96 | 1.95279 | ||||||||
\(185\) | 3673.31 | 1.45982 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 829.427 | 0.324351 | ||||||||
\(188\) | 2399.53 | 0.930871 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6892.37 | −2.63171 | ||||||||
\(191\) | −3619.78 | −1.37130 | −0.685650 | − | 0.727931i | \(-0.740482\pi\) | ||||
−0.685650 | + | 0.727931i | \(0.740482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3105.81 | 1.15835 | 0.579174 | − | 0.815204i | \(-0.303375\pi\) | ||||
0.579174 | + | 0.815204i | \(0.303375\pi\) | |||||||
\(194\) | 2925.69 | 1.08274 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3700.36 | −1.34853 | ||||||||
\(197\) | −499.680 | −0.180715 | −0.0903573 | − | 0.995909i | \(-0.528801\pi\) | ||||
−0.0903573 | + | 0.995909i | \(0.528801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1884.46 | −0.671286 | −0.335643 | − | 0.941989i | \(-0.608953\pi\) | ||||
−0.335643 | + | 0.941989i | \(0.608953\pi\) | |||||||
\(200\) | −8868.42 | −3.13546 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3323.92 | −1.15777 | ||||||||
\(203\) | −321.001 | −0.110984 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6893.85 | −2.34872 | ||||||||
\(206\) | −6882.32 | −2.32774 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2719.53 | 0.906566 | ||||||||
\(209\) | 620.442 | 0.205344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4769.84 | −1.55625 | −0.778127 | − | 0.628107i | \(-0.783830\pi\) | ||||
−0.778127 | + | 0.628107i | \(0.783830\pi\) | |||||||
\(212\) | −8198.46 | −2.65600 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4927.51 | −1.57401 | ||||||||
\(215\) | 6608.19 | 2.09616 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1099.87 | 0.344074 | ||||||||
\(218\) | −4121.48 | −1.28047 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2526.55 | 0.774272 | ||||||||
\(221\) | 6818.76 | 2.07547 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6102.53 | −1.83254 | −0.916268 | − | 0.400565i | \(-0.868814\pi\) | ||||
−0.916268 | + | 0.400565i | \(0.868814\pi\) | |||||||
\(224\) | 765.863 | 0.228444 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3367.39 | −0.991130 | ||||||||
\(227\) | −6734.80 | −1.96918 | −0.984591 | − | 0.174875i | \(-0.944048\pi\) | ||||
−0.984591 | + | 0.174875i | \(0.944048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4481.93 | 1.29334 | 0.646669 | − | 0.762771i | \(-0.276161\pi\) | ||||
0.646669 | + | 0.762771i | \(0.276161\pi\) | |||||||
\(230\) | 14027.8 | 4.02160 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1089.01 | 0.308178 | ||||||||
\(233\) | −3307.94 | −0.930087 | −0.465044 | − | 0.885288i | \(-0.653961\pi\) | ||||
−0.465044 | + | 0.885288i | \(0.653961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3196.89 | 0.887413 | ||||||||
\(236\) | 1544.32 | 0.425960 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4515.24 | −1.22975 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5155.80 | 1.37807 | 0.689033 | − | 0.724730i | \(-0.258035\pi\) | ||||
0.689033 | + | 0.724730i | \(0.258035\pi\) | |||||||
\(242\) | 6019.07 | 1.59885 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4180.25 | 1.09678 | ||||||||
\(245\) | −4929.98 | −1.28557 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5100.69 | 1.31396 | ||||||||
\(248\) | −3731.37 | −0.955412 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13655.1 | −3.45449 | ||||||||
\(251\) | 2292.76 | 0.576564 | 0.288282 | − | 0.957546i | \(-0.406916\pi\) | ||||
0.288282 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1262.77 | −0.313792 | ||||||||
\(254\) | −308.786 | −0.0762792 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7209.84 | −1.76022 | ||||||||
\(257\) | 7868.90 | 1.90992 | 0.954958 | − | 0.296741i | \(-0.0958999\pi\) | ||||
0.954958 | + | 0.296741i | \(0.0958999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1800.09 | 0.431861 | ||||||||
\(260\) | 20770.9 | 4.95444 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 89.9268 | 0.0212050 | ||||||||
\(263\) | −4584.99 | −1.07499 | −0.537495 | − | 0.843267i | \(-0.680629\pi\) | ||||
−0.537495 | + | 0.843267i | \(0.680629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10922.8 | −2.53201 | ||||||||
\(266\) | −3377.57 | −0.778541 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6089.52 | −1.38797 | ||||||||
\(269\) | 3099.36 | 0.702497 | 0.351248 | − | 0.936282i | \(-0.385757\pi\) | ||||
0.351248 | + | 0.936282i | \(0.385757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 74.6626 | 0.0167359 | 0.00836795 | − | 0.999965i | \(-0.497336\pi\) | ||||
0.00836795 | + | 0.999965i | \(0.497336\pi\) | |||||||
\(272\) | 3755.39 | 0.837147 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5525.47 | 1.21827 | ||||||||
\(275\) | 2297.66 | 0.503834 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4505.76 | 0.977346 | 0.488673 | − | 0.872467i | \(-0.337481\pi\) | ||||
0.488673 | + | 0.872467i | \(0.337481\pi\) | |||||||
\(278\) | 9055.44 | 1.95363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6366.84 | −1.35890 | ||||||||
\(281\) | 1282.60 | 0.272290 | 0.136145 | − | 0.990689i | \(-0.456529\pi\) | ||||
0.136145 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7160.55 | 1.50406 | 0.752032 | − | 0.659126i | \(-0.229074\pi\) | ||||
0.752032 | + | 0.659126i | \(0.229074\pi\) | |||||||
\(284\) | −7895.07 | −1.64960 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2874.00 | −0.594208 | ||||||||
\(287\) | −3378.29 | −0.694824 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4503.00 | 0.916547 | ||||||||
\(290\) | 3134.30 | 0.634664 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8177.83 | 1.63894 | ||||||||
\(293\) | 4723.96 | 0.941900 | 0.470950 | − | 0.882160i | \(-0.343911\pi\) | ||||
0.470950 | + | 0.882160i | \(0.343911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2057.49 | 0.406074 | ||||||||
\(296\) | −6106.90 | −1.19918 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7871.97 | 1.53024 | ||||||||
\(299\) | −10381.3 | −2.00791 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3238.31 | 0.620109 | ||||||||
\(302\) | 10744.3 | 2.04723 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2809.17 | 0.529991 | ||||||||
\(305\) | 5569.34 | 1.04557 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −932.353 | −0.173330 | −0.0866648 | − | 0.996238i | \(-0.527621\pi\) | ||||
−0.0866648 | + | 0.996238i | \(0.527621\pi\) | |||||||
\(308\) | 1238.12 | 0.229053 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10739.3 | −1.96758 | ||||||||
\(311\) | −8737.59 | −1.59313 | −0.796565 | − | 0.604553i | \(-0.793352\pi\) | ||||
−0.796565 | + | 0.604553i | \(0.793352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9685.91 | −1.74914 | −0.874569 | − | 0.484902i | \(-0.838855\pi\) | ||||
−0.874569 | + | 0.484902i | \(0.838855\pi\) | |||||||
\(314\) | 11579.3 | 2.08107 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13925.5 | 2.47901 | ||||||||
\(317\) | −7268.72 | −1.28786 | −0.643931 | − | 0.765084i | \(-0.722698\pi\) | ||||
−0.643931 | + | 0.765084i | \(0.722698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −282.146 | −0.0495208 | ||||||||
\(320\) | −13622.1 | −2.37967 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6874.25 | 1.18971 | ||||||||
\(323\) | 7043.52 | 1.21335 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18889.2 | 3.22395 | ||||||||
\(326\) | 3457.77 | 0.587448 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11461.1 | 1.92936 | ||||||||
\(329\) | 1566.62 | 0.262524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2629.34 | −0.436622 | −0.218311 | − | 0.975879i | \(-0.570055\pi\) | ||||
−0.218311 | + | 0.975879i | \(0.570055\pi\) | |||||||
\(332\) | 11722.2 | 1.93777 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13431.6 | −2.20043 | ||||||||
\(335\) | −8113.06 | −1.32318 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −822.253 | −0.132911 | −0.0664555 | − | 0.997789i | \(-0.521169\pi\) | ||||
−0.0664555 | + | 0.997789i | \(0.521169\pi\) | |||||||
\(338\) | −13115.0 | −2.11053 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 28682.4 | 4.57507 | ||||||||
\(341\) | 966.738 | 0.153524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5751.49 | −0.905398 | ||||||||
\(344\) | −10986.1 | −1.72190 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19444.1 | 3.02116 | ||||||||
\(347\) | −2068.50 | −0.320009 | −0.160004 | − | 0.987116i | \(-0.551151\pi\) | ||||
−0.160004 | + | 0.987116i | \(0.551151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4309.43 | 0.660970 | 0.330485 | − | 0.943811i | \(-0.392788\pi\) | ||||
0.330485 | + | 0.943811i | \(0.392788\pi\) | |||||||
\(350\) | −12508.0 | −1.91024 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 673.161 | 0.101931 | ||||||||
\(353\) | −1240.22 | −0.186998 | −0.0934989 | − | 0.995619i | \(-0.529805\pi\) | ||||
−0.0934989 | + | 0.995619i | \(0.529805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10518.6 | −1.57259 | ||||||||
\(356\) | 11051.5 | 1.64531 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12322.1 | 1.81911 | ||||||||
\(359\) | −7485.52 | −1.10048 | −0.550238 | − | 0.835008i | \(-0.685463\pi\) | ||||
−0.550238 | + | 0.835008i | \(0.685463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1590.18 | −0.231839 | ||||||||
\(362\) | −5556.41 | −0.806736 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10178.6 | 1.46568 | ||||||||
\(365\) | 10895.3 | 1.56243 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8439.72 | −1.20041 | −0.600204 | − | 0.799847i | \(-0.704914\pi\) | ||||
−0.600204 | + | 0.799847i | \(0.704914\pi\) | |||||||
\(368\) | −5717.42 | −0.809894 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17576.3 | −2.46960 | ||||||||
\(371\) | −5352.66 | −0.749046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12520.7 | 1.73807 | 0.869033 | − | 0.494755i | \(-0.164742\pi\) | ||||
0.869033 | + | 0.494755i | \(0.164742\pi\) | |||||||
\(374\) | −3968.70 | −0.548708 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5314.84 | −0.728968 | ||||||||
\(377\) | −2319.53 | −0.316875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1526.01 | 0.206824 | 0.103412 | − | 0.994639i | \(-0.467024\pi\) | ||||
0.103412 | + | 0.994639i | \(0.467024\pi\) | |||||||
\(380\) | 21455.5 | 2.89643 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17320.2 | 2.31984 | ||||||||
\(383\) | 10304.4 | 1.37475 | 0.687375 | − | 0.726302i | \(-0.258763\pi\) | ||||
0.687375 | + | 0.726302i | \(0.258763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1649.55 | 0.218360 | ||||||||
\(386\) | −14860.9 | −1.95959 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9107.47 | −1.19165 | ||||||||
\(389\) | 10412.4 | 1.35714 | 0.678571 | − | 0.734534i | \(-0.262599\pi\) | ||||
0.678571 | + | 0.734534i | \(0.262599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14335.4 | −1.85415 | ||||||||
\(392\) | 8196.11 | 1.05604 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2390.91 | 0.305716 | ||||||||
\(395\) | 18552.9 | 2.36328 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −432.529 | −0.0546801 | −0.0273400 | − | 0.999626i | \(-0.508704\pi\) | ||||
−0.0273400 | + | 0.999626i | \(0.508704\pi\) | |||||||
\(398\) | 9016.90 | 1.13562 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10403.1 | 1.30039 | ||||||||
\(401\) | −7984.92 | −0.994384 | −0.497192 | − | 0.867641i | \(-0.665636\pi\) | ||||
−0.497192 | + | 0.867641i | \(0.665636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7947.60 | 0.982377 | ||||||||
\(404\) | 10347.1 | 1.27423 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1535.95 | 0.187753 | ||||||||
\(407\) | 1582.20 | 0.192695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2505.56 | 0.302914 | 0.151457 | − | 0.988464i | \(-0.451604\pi\) | ||||
0.151457 | + | 0.988464i | \(0.451604\pi\) | |||||||
\(410\) | 32986.2 | 3.97335 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21424.2 | 2.56188 | ||||||||
\(413\) | 1008.26 | 0.120129 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15617.5 | 1.84731 | ||||||||
\(416\) | 5534.08 | 0.652237 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2968.74 | −0.347382 | ||||||||
\(419\) | 2380.41 | 0.277543 | 0.138772 | − | 0.990324i | \(-0.455685\pi\) | ||||
0.138772 | + | 0.990324i | \(0.455685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2540.60 | 0.294112 | 0.147056 | − | 0.989128i | \(-0.453020\pi\) | ||||
0.147056 | + | 0.989128i | \(0.453020\pi\) | |||||||
\(422\) | 22823.1 | 2.63273 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18159.2 | 2.07993 | ||||||||
\(425\) | 26084.0 | 2.97709 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2729.23 | 0.309313 | ||||||||
\(428\) | 15339.0 | 1.73234 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −31619.3 | −3.54609 | ||||||||
\(431\) | −6366.35 | −0.711500 | −0.355750 | − | 0.934581i | \(-0.615774\pi\) | ||||
−0.355750 | + | 0.934581i | \(0.615774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7620.55 | 0.845774 | 0.422887 | − | 0.906182i | \(-0.361017\pi\) | ||||
0.422887 | + | 0.906182i | \(0.361017\pi\) | |||||||
\(434\) | −5262.73 | −0.582072 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12829.9 | 1.40927 | ||||||||
\(437\) | −10723.4 | −1.17385 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −222.146 | −0.0241513 | −0.0120757 | − | 0.999927i | \(-0.503844\pi\) | ||||
−0.0120757 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(440\) | −5596.18 | −0.606335 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32626.9 | −3.51109 | ||||||||
\(443\) | −3699.08 | −0.396724 | −0.198362 | − | 0.980129i | \(-0.563562\pi\) | ||||
−0.198362 | + | 0.980129i | \(0.563562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14723.9 | 1.56850 | ||||||||
\(446\) | 29199.8 | 3.10012 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6675.41 | −0.703981 | ||||||||
\(449\) | 14076.6 | 1.47954 | 0.739772 | − | 0.672858i | \(-0.234933\pi\) | ||||
0.739772 | + | 0.672858i | \(0.234933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2969.38 | −0.310028 | ||||||||
\(452\) | 10482.5 | 1.09083 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32225.1 | 3.33128 | ||||||||
\(455\) | 13561.0 | 1.39725 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13989.7 | −1.43197 | −0.715987 | − | 0.698114i | \(-0.754023\pi\) | ||||
−0.715987 | + | 0.698114i | \(0.754023\pi\) | |||||||
\(458\) | −21445.5 | −2.18795 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −43667.7 | −4.42612 | ||||||||
\(461\) | 2517.77 | 0.254369 | 0.127185 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127185 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19554.7 | −1.96281 | −0.981406 | − | 0.191942i | \(-0.938522\pi\) | ||||
−0.981406 | + | 0.191942i | \(0.938522\pi\) | |||||||
\(464\) | −1277.47 | −0.127813 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15828.1 | 1.57344 | ||||||||
\(467\) | −5374.11 | −0.532514 | −0.266257 | − | 0.963902i | \(-0.585787\pi\) | ||||
−0.266257 | + | 0.963902i | \(0.585787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3975.76 | −0.391436 | ||||||||
\(470\) | −15296.7 | −1.50124 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3420.59 | −0.333571 | ||||||||
\(473\) | 2846.33 | 0.276690 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19511.8 | 1.88477 | ||||||||
\(476\) | 14055.7 | 1.35344 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1143.58 | −0.109427 | ||||||||
\(479\) | −7240.49 | −0.690660 | −0.345330 | − | 0.938481i | \(-0.612233\pi\) | ||||
−0.345330 | + | 0.938481i | \(0.612233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13007.3 | 1.23302 | ||||||||
\(482\) | −24669.8 | −2.33129 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18737.0 | −1.75967 | ||||||||
\(485\) | −12133.9 | −1.13602 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12572.3 | −1.16983 | −0.584913 | − | 0.811096i | \(-0.698871\pi\) | ||||
−0.584913 | + | 0.811096i | \(0.698871\pi\) | |||||||
\(488\) | −9259.05 | −0.858888 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23589.3 | 2.17481 | ||||||||
\(491\) | −6112.04 | −0.561777 | −0.280888 | − | 0.959740i | \(-0.590629\pi\) | ||||
−0.280888 | + | 0.959740i | \(0.590629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3203.03 | −0.292611 | ||||||||
\(494\) | −24406.1 | −2.22284 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4377.09 | 0.396244 | ||||||||
\(497\) | −5154.57 | −0.465220 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8599.20 | −0.771449 | −0.385724 | − | 0.922614i | \(-0.626048\pi\) | ||||
−0.385724 | + | 0.922614i | \(0.626048\pi\) | |||||||
\(500\) | 42507.4 | 3.80198 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10970.6 | −0.975378 | ||||||||
\(503\) | 1731.25 | 0.153465 | 0.0767324 | − | 0.997052i | \(-0.475551\pi\) | ||||
0.0767324 | + | 0.997052i | \(0.475551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13785.5 | 1.21474 | ||||||||
\(506\) | 6042.17 | 0.530845 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 961.229 | 0.0839521 | ||||||||
\(509\) | −9134.65 | −0.795454 | −0.397727 | − | 0.917504i | \(-0.630201\pi\) | ||||
−0.397727 | + | 0.917504i | \(0.630201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5339.19 | 0.462215 | ||||||||
\(512\) | 13262.4 | 1.14476 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −37651.7 | −3.23102 | ||||||||
\(515\) | 28543.4 | 2.44228 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1376.99 | 0.117137 | ||||||||
\(518\) | −8613.18 | −0.730582 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −46006.4 | −3.87984 | ||||||||
\(521\) | 4233.05 | 0.355956 | 0.177978 | − | 0.984034i | \(-0.443044\pi\) | ||||
0.177978 | + | 0.984034i | \(0.443044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9909.37 | 0.828502 | 0.414251 | − | 0.910163i | \(-0.364044\pi\) | ||||
0.414251 | + | 0.910163i | \(0.364044\pi\) | |||||||
\(524\) | −279.937 | −0.0233379 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21938.6 | 1.81857 | ||||||||
\(527\) | 10974.8 | 0.907154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9658.08 | 0.793793 | ||||||||
\(530\) | 52264.2 | 4.28342 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10514.2 | 0.856854 | ||||||||
\(533\) | −24411.4 | −1.98382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20436.2 | 1.65146 | ||||||||
\(536\) | 13488.0 | 1.08693 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14830.1 | −1.18842 | ||||||||
\(539\) | −2123.48 | −0.169694 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20780.5 | −1.65143 | −0.825714 | − | 0.564089i | \(-0.809227\pi\) | ||||
−0.825714 | + | 0.564089i | \(0.809227\pi\) | |||||||
\(542\) | −357.251 | −0.0283123 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7641.99 | 0.602294 | ||||||||
\(545\) | 17093.3 | 1.34348 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17988.3 | −1.40608 | −0.703040 | − | 0.711150i | \(-0.748175\pi\) | ||||
−0.703040 | + | 0.711150i | \(0.748175\pi\) | |||||||
\(548\) | −17200.4 | −1.34081 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10994.0 | −0.852340 | ||||||||
\(551\) | −2395.99 | −0.185250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9091.73 | 0.699131 | ||||||||
\(554\) | −21559.5 | −1.65338 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28189.0 | −2.15014 | ||||||||
\(557\) | −5673.16 | −0.431561 | −0.215781 | − | 0.976442i | \(-0.569230\pi\) | ||||
−0.215781 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23399.8 | 1.77050 | ||||||||
\(560\) | 7468.64 | 0.563585 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6137.07 | −0.460635 | ||||||||
\(563\) | 10444.6 | 0.781862 | 0.390931 | − | 0.920420i | \(-0.372153\pi\) | ||||
0.390931 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13965.8 | 1.03990 | ||||||||
\(566\) | −34262.3 | −2.54444 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17487.2 | 1.29181 | ||||||||
\(569\) | 18182.8 | 1.33965 | 0.669827 | − | 0.742517i | \(-0.266368\pi\) | ||||
0.669827 | + | 0.742517i | \(0.266368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3278.87 | −0.240309 | −0.120154 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120154 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(572\) | 8946.59 | 0.653979 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16164.7 | 1.17544 | ||||||||
\(575\) | −39711.8 | −2.88017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11157.3 | 0.805000 | 0.402500 | − | 0.915420i | \(-0.368141\pi\) | ||||
0.402500 | + | 0.915420i | \(0.368141\pi\) | |||||||
\(578\) | −21546.3 | −1.55053 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9756.88 | −0.698504 | ||||||||
\(581\) | 7653.27 | 0.546490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4704.76 | −0.334221 | ||||||||
\(584\) | −18113.5 | −1.28346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22603.5 | −1.59342 | ||||||||
\(587\) | 16447.0 | 1.15646 | 0.578230 | − | 0.815874i | \(-0.303744\pi\) | ||||
0.578230 | + | 0.815874i | \(0.303744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8209.56 | 0.574311 | ||||||||
\(590\) | −9844.84 | −0.686959 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7163.71 | 0.497343 | ||||||||
\(593\) | 19783.1 | 1.36997 | 0.684987 | − | 0.728556i | \(-0.259808\pi\) | ||||
0.684987 | + | 0.728556i | \(0.259808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18726.3 | 1.29026 | ||||||||
\(596\) | −24504.9 | −1.68416 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 49673.0 | 3.39679 | ||||||||
\(599\) | −8064.17 | −0.550072 | −0.275036 | − | 0.961434i | \(-0.588690\pi\) | ||||
−0.275036 | + | 0.961434i | \(0.588690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12131.3 | 0.823368 | 0.411684 | − | 0.911327i | \(-0.364941\pi\) | ||||
0.411684 | + | 0.911327i | \(0.364941\pi\) | |||||||
\(602\) | −15494.9 | −1.04904 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33446.2 | −2.25316 | ||||||||
\(605\) | −24963.3 | −1.67752 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −374.686 | −0.0250544 | −0.0125272 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125272 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(608\) | 5716.50 | 0.381307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26648.6 | −1.76880 | ||||||||
\(611\) | 11320.3 | 0.749542 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10459.3 | −0.689144 | −0.344572 | − | 0.938760i | \(-0.611976\pi\) | ||||
−0.344572 | + | 0.938760i | \(0.611976\pi\) | |||||||
\(614\) | 4461.19 | 0.293223 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2742.38 | −0.179372 | ||||||||
\(617\) | −8628.61 | −0.563006 | −0.281503 | − | 0.959560i | \(-0.590833\pi\) | ||||
−0.281503 | + | 0.959560i | \(0.590833\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −66.5127 | −0.00431885 | −0.00215943 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215943 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(620\) | 33430.7 | 2.16550 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41808.3 | 2.69511 | ||||||||
\(623\) | 7215.37 | 0.464009 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23031.6 | 1.47402 | ||||||||
\(626\) | 46345.8 | 2.95903 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36045.6 | −2.29041 | ||||||||
\(629\) | 17961.8 | 1.13861 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18876.9 | 1.19093 | 0.595466 | − | 0.803381i | \(-0.296968\pi\) | ||||
0.595466 | + | 0.803381i | \(0.296968\pi\) | |||||||
\(632\) | −30844.2 | −1.94132 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34779.9 | 2.17869 | ||||||||
\(635\) | 1280.64 | 0.0800328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17457.2 | −1.08584 | ||||||||
\(638\) | 1350.03 | 0.0837747 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 52677.0 | 3.25350 | ||||||||
\(641\) | 18816.8 | 1.15947 | 0.579734 | − | 0.814806i | \(-0.303157\pi\) | ||||
0.579734 | + | 0.814806i | \(0.303157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12561.3 | 0.770403 | 0.385202 | − | 0.922832i | \(-0.374132\pi\) | ||||
0.385202 | + | 0.922832i | \(0.374132\pi\) | |||||||
\(644\) | −21399.1 | −1.30938 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33702.3 | −2.05263 | ||||||||
\(647\) | 12355.1 | 0.750740 | 0.375370 | − | 0.926875i | \(-0.377516\pi\) | ||||
0.375370 | + | 0.926875i | \(0.377516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 886.220 | 0.0536012 | ||||||||
\(650\) | −90382.4 | −5.45399 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10763.8 | −0.646538 | ||||||||
\(653\) | 16862.8 | 1.01056 | 0.505278 | − | 0.862957i | \(-0.331390\pi\) | ||||
0.505278 | + | 0.862957i | \(0.331390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −372.959 | −0.0222484 | ||||||||
\(656\) | −13444.4 | −0.800178 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7496.07 | −0.444114 | ||||||||
\(659\) | 101.409 | 0.00599441 | 0.00299721 | − | 0.999996i | \(-0.499046\pi\) | ||||
0.00299721 | + | 0.999996i | \(0.499046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 780.657 | 0.0459365 | 0.0229682 | − | 0.999736i | \(-0.492688\pi\) | ||||
0.0229682 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(662\) | 12581.1 | 0.738636 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25964.1 | −1.51748 | ||||||||
\(665\) | 14008.0 | 0.816852 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4876.48 | 0.283086 | ||||||||
\(668\) | 41811.7 | 2.42177 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38820.0 | 2.23843 | ||||||||
\(671\) | 2398.87 | 0.138014 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8497.67 | −0.486718 | −0.243359 | − | 0.969936i | \(-0.578249\pi\) | ||||
−0.243359 | + | 0.969936i | \(0.578249\pi\) | |||||||
\(674\) | 3934.38 | 0.224846 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 40826.0 | 2.32283 | ||||||||
\(677\) | 3736.10 | 0.212098 | 0.106049 | − | 0.994361i | \(-0.466180\pi\) | ||||
0.106049 | + | 0.994361i | \(0.466180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5946.13 | −0.336070 | ||||||||
\(680\) | −63530.1 | −3.58275 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4625.72 | −0.259718 | ||||||||
\(683\) | −29098.8 | −1.63021 | −0.815107 | − | 0.579311i | \(-0.803322\pi\) | ||||
−0.815107 | + | 0.579311i | \(0.803322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22916.1 | −1.27822 | ||||||||
\(686\) | 27520.2 | 1.53167 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12887.3 | 0.714134 | ||||||||
\(689\) | −38678.0 | −2.13863 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5688.32 | 0.313160 | 0.156580 | − | 0.987665i | \(-0.449953\pi\) | ||||
0.156580 | + | 0.987665i | \(0.449953\pi\) | |||||||
\(692\) | −60528.3 | −3.32506 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9897.51 | 0.541361 | ||||||||
\(695\) | −37556.2 | −2.04977 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33709.6 | −1.83191 | ||||||||
\(698\) | −20620.1 | −1.11817 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 38936.7 | 2.10239 | ||||||||
\(701\) | −21585.3 | −1.16300 | −0.581502 | − | 0.813545i | \(-0.697535\pi\) | ||||
−0.581502 | + | 0.813545i | \(0.697535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13436.1 | 0.720841 | ||||||||
\(704\) | −5867.40 | −0.314113 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5934.29 | 0.316346 | ||||||||
\(707\) | 6755.49 | 0.359358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28328.5 | 1.50057 | 0.750283 | − | 0.661117i | \(-0.229917\pi\) | ||||
0.750283 | + | 0.661117i | \(0.229917\pi\) | |||||||
\(710\) | 50330.1 | 2.66036 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24478.5 | −1.28844 | ||||||||
\(713\) | −16708.7 | −0.877621 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11919.5 | 0.623448 | ||||||||
\(716\) | −38357.9 | −2.00210 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35817.3 | 1.86168 | ||||||||
\(719\) | 22840.1 | 1.18469 | 0.592344 | − | 0.805685i | \(-0.298202\pi\) | ||||
0.592344 | + | 0.805685i | \(0.298202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13987.6 | 0.722502 | ||||||||
\(722\) | 7608.83 | 0.392204 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17296.7 | 0.887885 | ||||||||
\(725\) | −8872.99 | −0.454531 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25402.2 | −1.29590 | −0.647948 | − | 0.761685i | \(-0.724372\pi\) | ||||
−0.647948 | + | 0.761685i | \(0.724372\pi\) | |||||||
\(728\) | −22545.2 | −1.14778 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −52132.7 | −2.64317 | ||||||||
\(731\) | 32312.7 | 1.63492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27288.3 | −1.37505 | −0.687527 | − | 0.726159i | \(-0.741304\pi\) | ||||
−0.687527 | + | 0.726159i | \(0.741304\pi\) | |||||||
\(734\) | 40383.0 | 2.03074 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11634.6 | −0.582686 | ||||||||
\(737\) | −3494.52 | −0.174657 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36966.9 | 1.84012 | 0.920061 | − | 0.391775i | \(-0.128139\pi\) | ||||
0.920061 | + | 0.391775i | \(0.128139\pi\) | |||||||
\(740\) | 54714.0 | 2.71801 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25611.8 | 1.26717 | ||||||||
\(743\) | 1086.94 | 0.0536686 | 0.0268343 | − | 0.999640i | \(-0.491457\pi\) | ||||
0.0268343 | + | 0.999640i | \(0.491457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32647.9 | −1.60554 | ||||||||
\(746\) | −59910.0 | −2.94030 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12354.3 | 0.603902 | ||||||||
\(749\) | 10014.6 | 0.488553 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28459.7 | 1.38284 | 0.691418 | − | 0.722455i | \(-0.256986\pi\) | ||||
0.691418 | + | 0.722455i | \(0.256986\pi\) | |||||||
\(752\) | 6234.59 | 0.302330 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11098.7 | 0.536061 | ||||||||
\(755\) | −44560.4 | −2.14797 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23083.0 | 1.10828 | 0.554139 | − | 0.832424i | \(-0.313048\pi\) | ||||
0.554139 | + | 0.832424i | \(0.313048\pi\) | |||||||
\(758\) | −7301.79 | −0.349885 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47522.9 | −2.26821 | ||||||||
\(761\) | 36.9783 | 0.00176145 | 0.000880724 | − | 1.00000i | \(-0.499720\pi\) | ||||
0.000880724 | 1.00000i | \(0.499720\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8376.45 | 0.397442 | ||||||||
\(764\) | −53916.7 | −2.55319 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49305.2 | −2.32568 | ||||||||
\(767\) | 7285.65 | 0.342985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9659.87 | −0.452983 | −0.226492 | − | 0.974013i | \(-0.572726\pi\) | ||||
−0.226492 | + | 0.974013i | \(0.572726\pi\) | |||||||
\(770\) | −7892.87 | −0.369402 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 46261.1 | 2.15670 | ||||||||
\(773\) | −35662.2 | −1.65935 | −0.829676 | − | 0.558245i | \(-0.811475\pi\) | ||||
−0.829676 | + | 0.558245i | \(0.811475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30402.2 | 1.40913 | ||||||||
\(776\) | 20172.6 | 0.933188 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −49821.9 | −2.29589 | ||||||||
\(779\) | −25216.0 | −1.15977 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4530.65 | −0.207579 | ||||||||
\(782\) | 68593.2 | 3.13669 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9614.48 | −0.437977 | ||||||||
\(785\) | −48023.5 | −2.18348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39166.5 | 1.77400 | 0.886999 | − | 0.461771i | \(-0.152786\pi\) | ||||
0.886999 | + | 0.461771i | \(0.152786\pi\) | |||||||
\(788\) | −7442.74 | −0.336468 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −88773.1 | −3.99798 | ||||||||
\(791\) | 6843.85 | 0.307635 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19721.2 | 0.883129 | ||||||||
\(794\) | 2069.59 | 0.0925027 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −28069.0 | −1.24985 | ||||||||
\(797\) | 2563.21 | 0.113919 | 0.0569595 | − | 0.998376i | \(-0.481859\pi\) | ||||
0.0569595 | + | 0.998376i | \(0.481859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15632.2 | 0.692148 | ||||||||
\(800\) | 21169.7 | 0.935578 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38206.8 | 1.68221 | ||||||||
\(803\) | 4692.92 | 0.206238 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28510.0 | −1.24826 | ||||||||
\(806\) | −38028.2 | −1.66189 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22918.4 | −0.997854 | ||||||||
\(809\) | 13667.1 | 0.593954 | 0.296977 | − | 0.954885i | \(-0.404022\pi\) | ||||
0.296977 | + | 0.954885i | \(0.404022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7391.23 | 0.320026 | 0.160013 | − | 0.987115i | \(-0.448846\pi\) | ||||
0.160013 | + | 0.987115i | \(0.448846\pi\) | |||||||
\(812\) | −4781.30 | −0.206639 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7570.62 | −0.325983 | ||||||||
\(815\) | −14340.6 | −0.616355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24171.1 | 1.03506 | ||||||||
\(818\) | −11988.8 | −0.512442 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −102684. | −4.37302 | ||||||||
\(821\) | 40299.0 | 1.71309 | 0.856544 | − | 0.516074i | \(-0.172607\pi\) | ||||
0.856544 | + | 0.516074i | \(0.172607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41727.0 | 1.76733 | 0.883664 | − | 0.468121i | \(-0.155069\pi\) | ||||
0.883664 | + | 0.468121i | \(0.155069\pi\) | |||||||
\(824\) | −47453.6 | −2.00622 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4824.41 | −0.203224 | ||||||||
\(827\) | 34063.5 | 1.43229 | 0.716145 | − | 0.697952i | \(-0.245905\pi\) | ||||
0.716145 | + | 0.697952i | \(0.245905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36976.2 | −1.54914 | −0.774571 | − | 0.632488i | \(-0.782034\pi\) | ||||
−0.774571 | + | 0.632488i | \(0.782034\pi\) | |||||||
\(830\) | −74727.7 | −3.12511 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −48236.1 | −2.00996 | ||||||||
\(833\) | −24106.6 | −1.00270 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55705.7 | 2.30871 | ||||||||
\(836\) | 9241.49 | 0.382325 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11390.0 | −0.469522 | ||||||||
\(839\) | −9709.26 | −0.399524 | −0.199762 | − | 0.979844i | \(-0.564017\pi\) | ||||
−0.199762 | + | 0.979844i | \(0.564017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23299.4 | −0.955325 | ||||||||
\(842\) | −12156.4 | −0.497552 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −71046.8 | −2.89755 | ||||||||
\(845\) | 54392.5 | 2.21439 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12233.1 | −0.496263 | ||||||||
\(848\) | −21301.7 | −0.862622 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −124809. | −5.03636 | ||||||||
\(851\) | −27346.0 | −1.10154 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30934.7 | 1.24172 | 0.620858 | − | 0.783923i | \(-0.286784\pi\) | ||||
0.620858 | + | 0.783923i | \(0.286784\pi\) | |||||||
\(854\) | −13059.0 | −0.523266 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33975.2 | −1.35660 | ||||||||
\(857\) | −17180.4 | −0.684799 | −0.342400 | − | 0.939554i | \(-0.611240\pi\) | ||||
−0.342400 | + | 0.939554i | \(0.611240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18577.7 | −0.737910 | −0.368955 | − | 0.929447i | \(-0.620284\pi\) | ||||
−0.368955 | + | 0.929447i | \(0.620284\pi\) | |||||||
\(860\) | 98429.0 | 3.90279 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30462.2 | 1.20365 | ||||||||
\(863\) | −35850.9 | −1.41411 | −0.707056 | − | 0.707158i | \(-0.749977\pi\) | ||||
−0.707056 | + | 0.707158i | \(0.749977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80641.8 | −3.16983 | ||||||||
\(866\) | −36463.4 | −1.43080 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16382.5 | 0.640622 | ||||||||
\(869\) | 7991.24 | 0.311950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28728.6 | −1.11760 | ||||||||
\(872\) | −28417.6 | −1.10360 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 51310.3 | 1.98581 | ||||||||
\(875\) | 27752.4 | 1.07223 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34877.5 | −1.34291 | −0.671454 | − | 0.741046i | \(-0.734330\pi\) | ||||
−0.671454 | + | 0.741046i | \(0.734330\pi\) | |||||||
\(878\) | 1062.94 | 0.0408570 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6564.61 | 0.251469 | ||||||||
\(881\) | 40799.7 | 1.56025 | 0.780124 | − | 0.625625i | \(-0.215156\pi\) | ||||
0.780124 | + | 0.625625i | \(0.215156\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20747.1 | −0.790710 | −0.395355 | − | 0.918528i | \(-0.629378\pi\) | ||||
−0.395355 | + | 0.918528i | \(0.629378\pi\) | |||||||
\(884\) | 101565. | 3.86427 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17699.6 | 0.671141 | ||||||||
\(887\) | −35205.1 | −1.33266 | −0.666332 | − | 0.745655i | \(-0.732137\pi\) | ||||
−0.666332 | + | 0.745655i | \(0.732137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 627.573 | 0.0236762 | ||||||||
\(890\) | −70452.0 | −2.65344 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −90897.2 | −3.41195 | ||||||||
\(893\) | 11693.4 | 0.438193 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51104.1 | −1.90863 | ||||||||
\(896\) | 25814.1 | 0.962486 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −67354.7 | −2.50296 | ||||||||
\(899\) | −3733.29 | −0.138501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53410.3 | −1.97487 | ||||||||
\(902\) | 14208.1 | 0.524476 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23218.1 | −0.854230 | ||||||||
\(905\) | 23044.4 | 0.846434 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33086.7 | 1.21127 | 0.605636 | − | 0.795741i | \(-0.292919\pi\) | ||||
0.605636 | + | 0.795741i | \(0.292919\pi\) | |||||||
\(908\) | −100315. | −3.66637 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −64887.6 | −2.36374 | ||||||||
\(911\) | 19349.1 | 0.703693 | 0.351846 | − | 0.936058i | \(-0.385554\pi\) | ||||
0.351846 | + | 0.936058i | \(0.385554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6726.89 | 0.243842 | ||||||||
\(914\) | 66939.1 | 2.42248 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 66758.4 | 2.40803 | ||||||||
\(917\) | −182.766 | −0.00658177 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7490.62 | −0.268871 | −0.134436 | − | 0.990922i | \(-0.542922\pi\) | ||||
−0.134436 | + | 0.990922i | \(0.542922\pi\) | |||||||
\(920\) | 96721.8 | 3.46611 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12047.2 | −0.430318 | ||||||||
\(923\) | −37246.7 | −1.32827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49757.4 | 1.76866 | ||||||||
\(926\) | 93566.6 | 3.32051 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2599.57 | −0.0919560 | ||||||||
\(929\) | 14979.3 | 0.529013 | 0.264507 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264507 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18032.7 | −0.634798 | ||||||||
\(932\) | −49271.7 | −1.73171 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25714.4 | 0.900858 | ||||||||
\(935\) | 16459.6 | 0.575709 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35932.6 | 1.25279 | 0.626397 | − | 0.779504i | \(-0.284529\pi\) | ||||
0.626397 | + | 0.779504i | \(0.284529\pi\) | |||||||
\(938\) | 19023.5 | 0.662195 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 47617.7 | 1.65225 | ||||||||
\(941\) | 40959.5 | 1.41896 | 0.709480 | − | 0.704726i | \(-0.248930\pi\) | ||||
0.709480 | + | 0.704726i | \(0.248930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51321.3 | 1.77227 | ||||||||
\(944\) | 4012.53 | 0.138344 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13619.3 | −0.468079 | ||||||||
\(947\) | −25559.8 | −0.877068 | −0.438534 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438534 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38580.7 | 1.31969 | ||||||||
\(950\) | −93361.6 | −3.18847 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −31132.6 | −1.05989 | ||||||||
\(953\) | 49571.0 | 1.68496 | 0.842478 | − | 0.538731i | \(-0.181096\pi\) | ||||
0.842478 | + | 0.538731i | \(0.181096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −71833.1 | −2.43400 | ||||||||
\(956\) | 3559.90 | 0.120435 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34644.8 | 1.16840 | ||||||||
\(959\) | −11229.9 | −0.378136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16999.3 | −0.570620 | ||||||||
\(962\) | −62238.4 | −2.08591 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 76795.6 | 2.56579 | ||||||||
\(965\) | 61633.5 | 2.05601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17045.0 | −0.566837 | −0.283419 | − | 0.958996i | \(-0.591469\pi\) | ||||
−0.283419 | + | 0.958996i | \(0.591469\pi\) | |||||||
\(968\) | 41501.5 | 1.37800 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 58059.0 | 1.92182 | ||||||||
\(971\) | 55060.0 | 1.81973 | 0.909866 | − | 0.414902i | \(-0.136184\pi\) | ||||
0.909866 | + | 0.414902i | \(0.136184\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18404.2 | −0.606384 | ||||||||
\(974\) | 60156.8 | 1.97900 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10861.4 | 0.356213 | ||||||||
\(977\) | 4980.17 | 0.163080 | 0.0815402 | − | 0.996670i | \(-0.474016\pi\) | ||||
0.0815402 | + | 0.996670i | \(0.474016\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6342.00 | 0.207039 | ||||||||
\(980\) | −73432.1 | −2.39357 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29245.3 | 0.950362 | ||||||||
\(983\) | −44793.9 | −1.45341 | −0.726706 | − | 0.686949i | \(-0.758950\pi\) | ||||
−0.726706 | + | 0.686949i | \(0.758950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9915.95 | −0.320760 | ||||||||
\(986\) | 15326.1 | 0.495013 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 75974.7 | 2.44644 | ||||||||
\(989\) | −49194.7 | −1.58170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14339.8 | −0.459657 | −0.229829 | − | 0.973231i | \(-0.573817\pi\) | ||||
−0.229829 | + | 0.973231i | \(0.573817\pi\) | |||||||
\(992\) | 8907.12 | 0.285082 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24664.0 | 0.787016 | ||||||||
\(995\) | −37396.3 | −1.19150 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34566.7 | −1.09803 | −0.549017 | − | 0.835811i | \(-0.684998\pi\) | ||||
−0.549017 | + | 0.835811i | \(0.684998\pi\) | |||||||
\(998\) | 41146.1 | 1.30507 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.4.a.e.1.5 | 32 | ||
3.2 | odd | 2 | 717.4.a.c.1.28 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.c.1.28 | ✓ | 32 | 3.2 | odd | 2 | ||
2151.4.a.e.1.5 | 32 | 1.1 | even | 1 | trivial |