Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,4,Mod(1,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.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: | \(40.8883236340\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.54138 | −1.60562 | −0.802810 | − | 0.596234i | \(-0.796663\pi\) | ||||
−0.802810 | + | 0.596234i | \(0.796663\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.6241 | 1.57802 | ||||||||
\(5\) | −13.1655 | −1.17756 | −0.588780 | − | 0.808293i | \(-0.700392\pi\) | ||||
−0.588780 | + | 0.808293i | \(0.700392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 59.7897 | 1.89072 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.8345 | −1.16987 | −0.584936 | − | 0.811079i | \(-0.698881\pi\) | ||||
−0.584936 | + | 0.811079i | \(0.698881\pi\) | |||||||
\(14\) | −31.7897 | −0.606868 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.62414 | −0.0878772 | ||||||||
\(17\) | 79.9104 | 1.14007 | 0.570033 | − | 0.821622i | \(-0.306930\pi\) | ||||
0.570033 | + | 0.821622i | \(0.306930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.2551 | 0.256645 | 0.128323 | − | 0.991732i | \(-0.459041\pi\) | ||||
0.128323 | + | 0.991732i | \(0.459041\pi\) | |||||||
\(20\) | −166.203 | −1.85821 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −49.9552 | −0.484113 | ||||||||
\(23\) | −119.414 | −1.08259 | −0.541294 | − | 0.840834i | \(-0.682065\pi\) | ||||
−0.541294 | + | 0.840834i | \(0.682065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 48.3311 | 0.386648 | ||||||||
\(26\) | 249.024 | 1.87837 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 88.3690 | 0.596435 | ||||||||
\(29\) | 87.4829 | 0.560178 | 0.280089 | − | 0.959974i | \(-0.409636\pi\) | ||||
0.280089 | + | 0.959974i | \(0.409636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 191.248 | 1.10804 | 0.554019 | − | 0.832504i | \(-0.313093\pi\) | ||||
0.554019 | + | 0.832504i | \(0.313093\pi\) | |||||||
\(32\) | 193.541 | 1.06918 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −362.904 | −1.83051 | ||||||||
\(35\) | −92.1587 | −0.445076 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 91.6484 | 0.407214 | 0.203607 | − | 0.979053i | \(-0.434734\pi\) | ||||
0.203607 | + | 0.979053i | \(0.434734\pi\) | |||||||
\(38\) | −96.5277 | −0.412075 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 276.476 | 1.09287 | ||||||||
\(41\) | 60.4829 | 0.230386 | 0.115193 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115193 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −213.552 | −0.757357 | −0.378679 | − | 0.925528i | \(-0.623621\pi\) | ||||
−0.378679 | + | 0.925528i | \(0.623621\pi\) | |||||||
\(44\) | 138.866 | 0.475790 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 542.304 | 1.73822 | ||||||||
\(47\) | −417.421 | −1.29547 | −0.647735 | − | 0.761866i | \(-0.724283\pi\) | ||||
−0.647735 | + | 0.761866i | \(0.724283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −219.490 | −0.620811 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −692.238 | −1.84608 | ||||||||
\(53\) | 414.904 | 1.07531 | 0.537655 | − | 0.843165i | \(-0.319310\pi\) | ||||
0.537655 | + | 0.843165i | \(0.319310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −144.821 | −0.355048 | ||||||||
\(56\) | −147.000 | −0.350780 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −397.293 | −0.899433 | ||||||||
\(59\) | 358.069 | 0.790112 | 0.395056 | − | 0.918657i | \(-0.370725\pi\) | ||||
0.395056 | + | 0.918657i | \(0.370725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 515.297 | 1.08159 | 0.540795 | − | 0.841154i | \(-0.318123\pi\) | ||||
0.540795 | + | 0.841154i | \(0.318123\pi\) | |||||||
\(62\) | −868.531 | −1.77909 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −833.952 | −1.62881 | ||||||||
\(65\) | 721.925 | 1.37760 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −107.572 | −0.196150 | −0.0980752 | − | 0.995179i | \(-0.531269\pi\) | ||||
−0.0980752 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(68\) | 1008.80 | 1.79904 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 418.528 | 0.714623 | ||||||||
\(71\) | 711.793 | 1.18978 | 0.594890 | − | 0.803807i | \(-0.297196\pi\) | ||||
0.594890 | + | 0.803807i | \(0.297196\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 131.773 | 0.211272 | 0.105636 | − | 0.994405i | \(-0.466312\pi\) | ||||
0.105636 | + | 0.994405i | \(0.466312\pi\) | |||||||
\(74\) | −416.210 | −0.653831 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 268.328 | 0.404991 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4966 | 0.0149488 | 0.00747441 | − | 0.999972i | \(-0.497621\pi\) | ||||
0.00747441 | + | 0.999972i | \(0.497621\pi\) | |||||||
\(80\) | 74.0448 | 0.103481 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −274.676 | −0.369913 | ||||||||
\(83\) | 618.352 | 0.817747 | 0.408873 | − | 0.912591i | \(-0.365922\pi\) | ||||
0.408873 | + | 0.912591i | \(0.365922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1052.06 | −1.34250 | ||||||||
\(86\) | 969.821 | 1.21603 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −231.000 | −0.279826 | ||||||||
\(89\) | −1376.44 | −1.63935 | −0.819677 | − | 0.572826i | \(-0.805847\pi\) | ||||
−0.819677 | + | 0.572826i | \(0.805847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −383.841 | −0.442170 | ||||||||
\(92\) | −1507.50 | −1.70834 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1895.67 | 2.08003 | ||||||||
\(95\) | −279.835 | −0.302215 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −534.752 | −0.559751 | −0.279875 | − | 0.960036i | \(-0.590293\pi\) | ||||
−0.279875 | + | 0.960036i | \(0.590293\pi\) | |||||||
\(98\) | −222.528 | −0.229374 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 610.138 | 0.610138 | ||||||||
\(101\) | −1620.01 | −1.59601 | −0.798004 | − | 0.602652i | \(-0.794111\pi\) | ||||
−0.798004 | + | 0.602652i | \(0.794111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 822.814 | 0.787129 | 0.393564 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393564 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(104\) | 1151.52 | 1.08573 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1884.24 | −1.72654 | ||||||||
\(107\) | 1749.78 | 1.58091 | 0.790456 | − | 0.612518i | \(-0.209843\pi\) | ||||
0.790456 | + | 0.612518i | \(0.209843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −647.607 | −0.569078 | −0.284539 | − | 0.958665i | \(-0.591840\pi\) | ||||
−0.284539 | + | 0.958665i | \(0.591840\pi\) | |||||||
\(110\) | 657.686 | 0.570072 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −39.3690 | −0.0332145 | ||||||||
\(113\) | −1151.50 | −0.958622 | −0.479311 | − | 0.877645i | \(-0.659113\pi\) | ||||
−0.479311 | + | 0.877645i | \(0.659113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1572.15 | 1.27481 | ||||||||
\(116\) | 1104.40 | 0.883971 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1626.13 | −1.26862 | ||||||||
\(119\) | 559.373 | 0.430904 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2340.16 | −1.73662 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2414.35 | 1.74851 | ||||||||
\(125\) | 1009.39 | 0.722259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 278.146 | 0.194342 | 0.0971710 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971710 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(128\) | 2238.96 | 1.54608 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3278.54 | −2.21190 | ||||||||
\(131\) | −2332.22 | −1.55547 | −0.777737 | − | 0.628590i | \(-0.783633\pi\) | ||||
−0.777737 | + | 0.628590i | \(0.783633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 148.786 | 0.0970028 | ||||||||
\(134\) | 488.528 | 0.314943 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1678.12 | −1.05807 | ||||||||
\(137\) | −2612.23 | −1.62903 | −0.814517 | − | 0.580139i | \(-0.802998\pi\) | ||||
−0.814517 | + | 0.580139i | \(0.802998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2884.68 | −1.76025 | −0.880126 | − | 0.474740i | \(-0.842542\pi\) | ||||
−0.880126 | + | 0.474740i | \(0.842542\pi\) | |||||||
\(140\) | −1163.42 | −0.702338 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3232.53 | −1.91033 | ||||||||
\(143\) | −603.179 | −0.352730 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1151.76 | −0.659643 | ||||||||
\(146\) | −598.431 | −0.339222 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1156.98 | 0.642590 | ||||||||
\(149\) | −2909.54 | −1.59972 | −0.799862 | − | 0.600184i | \(-0.795094\pi\) | ||||
−0.799862 | + | 0.600184i | \(0.795094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2327.06 | −1.25413 | −0.627063 | − | 0.778968i | \(-0.715743\pi\) | ||||
−0.627063 | + | 0.778968i | \(0.715743\pi\) | |||||||
\(152\) | −446.358 | −0.238187 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −349.686 | −0.182977 | ||||||||
\(155\) | −2517.88 | −1.30478 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −927.572 | −0.471518 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(158\) | −47.6689 | −0.0240021 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2548.07 | −1.25902 | ||||||||
\(161\) | −835.897 | −0.409179 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2966.31 | −1.42539 | −0.712696 | − | 0.701473i | \(-0.752526\pi\) | ||||
−0.712696 | + | 0.701473i | \(0.752526\pi\) | |||||||
\(164\) | 763.545 | 0.363554 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2808.17 | −1.31299 | ||||||||
\(167\) | −3856.35 | −1.78691 | −0.893454 | − | 0.449156i | \(-0.851725\pi\) | ||||
−0.893454 | + | 0.449156i | \(0.851725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 809.820 | 0.368602 | ||||||||
\(170\) | 4777.82 | 2.15554 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2695.91 | −1.19512 | ||||||||
\(173\) | 2699.52 | 1.18636 | 0.593181 | − | 0.805069i | \(-0.297872\pi\) | ||||
0.593181 | + | 0.805069i | \(0.297872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 338.317 | 0.146139 | ||||||||
\(176\) | −61.8656 | −0.0264960 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6250.95 | 2.63218 | ||||||||
\(179\) | −1328.58 | −0.554764 | −0.277382 | − | 0.960760i | \(-0.589467\pi\) | ||||
−0.277382 | + | 0.960760i | \(0.589467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 534.944 | 0.219680 | 0.109840 | − | 0.993949i | \(-0.464966\pi\) | ||||
0.109840 | + | 0.993949i | \(0.464966\pi\) | |||||||
\(182\) | 1743.17 | 0.709958 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2507.69 | 1.00472 | ||||||||
\(185\) | −1206.60 | −0.479519 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 879.014 | 0.343743 | ||||||||
\(188\) | −5269.58 | −2.04427 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1270.84 | 0.485243 | ||||||||
\(191\) | 3456.20 | 1.30933 | 0.654665 | − | 0.755919i | \(-0.272810\pi\) | ||||
0.654665 | + | 0.755919i | \(0.272810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3106.02 | −1.15843 | −0.579213 | − | 0.815176i | \(-0.696640\pi\) | ||||
−0.579213 | + | 0.815176i | \(0.696640\pi\) | |||||||
\(194\) | 2428.51 | 0.898747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 618.583 | 0.225431 | ||||||||
\(197\) | −4886.49 | −1.76725 | −0.883623 | − | 0.468198i | \(-0.844903\pi\) | ||||
−0.883623 | + | 0.468198i | \(0.844903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3319.74 | 1.18257 | 0.591283 | − | 0.806464i | \(-0.298622\pi\) | ||||
0.591283 | + | 0.806464i | \(0.298622\pi\) | |||||||
\(200\) | −1014.95 | −0.358840 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7357.07 | 2.56258 | ||||||||
\(203\) | 612.380 | 0.211727 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −796.289 | −0.271294 | ||||||||
\(206\) | −3736.71 | −1.26383 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 308.397 | 0.102805 | ||||||||
\(209\) | 233.807 | 0.0773815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4262.51 | 1.39073 | 0.695364 | − | 0.718658i | \(-0.255243\pi\) | ||||
0.695364 | + | 0.718658i | \(0.255243\pi\) | |||||||
\(212\) | 5237.80 | 1.69686 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7946.42 | −2.53835 | ||||||||
\(215\) | 2811.52 | 0.891834 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1338.74 | 0.418799 | ||||||||
\(218\) | 2941.03 | 0.913723 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1828.24 | −0.560272 | ||||||||
\(221\) | −4381.84 | −1.33373 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2766.16 | 0.830655 | 0.415328 | − | 0.909672i | \(-0.363667\pi\) | ||||
0.415328 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(224\) | 1354.79 | 0.404110 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5229.42 | 1.53918 | ||||||||
\(227\) | −545.724 | −0.159564 | −0.0797818 | − | 0.996812i | \(-0.525422\pi\) | ||||
−0.0797818 | + | 0.996812i | \(0.525422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3197.48 | 0.922688 | 0.461344 | − | 0.887221i | \(-0.347367\pi\) | ||||
0.461344 | + | 0.887221i | \(0.347367\pi\) | |||||||
\(230\) | −7139.71 | −2.04686 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1837.14 | −0.519889 | ||||||||
\(233\) | −4203.76 | −1.18196 | −0.590982 | − | 0.806684i | \(-0.701260\pi\) | ||||
−0.590982 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5495.56 | 1.52549 | ||||||||
\(236\) | 4520.32 | 1.24681 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2540.32 | −0.691869 | ||||||||
\(239\) | −5720.73 | −1.54830 | −0.774150 | − | 0.633003i | \(-0.781822\pi\) | ||||
−0.774150 | + | 0.633003i | \(0.781822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5191.77 | 1.38768 | 0.693841 | − | 0.720128i | \(-0.255917\pi\) | ||||
0.693841 | + | 0.720128i | \(0.255917\pi\) | |||||||
\(242\) | −549.507 | −0.145966 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6505.18 | 1.70677 | ||||||||
\(245\) | −645.111 | −0.168223 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1165.51 | −0.300243 | ||||||||
\(248\) | −4016.21 | −1.02835 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4584.01 | −1.15967 | ||||||||
\(251\) | −847.944 | −0.213234 | −0.106617 | − | 0.994300i | \(-0.534002\pi\) | ||||
−0.106617 | + | 0.994300i | \(0.534002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1313.55 | −0.326412 | ||||||||
\(254\) | −1263.16 | −0.312039 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3496.37 | −0.853606 | ||||||||
\(257\) | 1493.87 | 0.362588 | 0.181294 | − | 0.983429i | \(-0.441971\pi\) | ||||
0.181294 | + | 0.983429i | \(0.441971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 641.539 | 0.153912 | ||||||||
\(260\) | 9113.68 | 2.17387 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10591.5 | 2.49750 | ||||||||
\(263\) | −135.848 | −0.0318507 | −0.0159253 | − | 0.999873i | \(-0.505069\pi\) | ||||
−0.0159253 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5462.42 | −1.26624 | ||||||||
\(266\) | −675.694 | −0.155750 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1358.01 | −0.309529 | ||||||||
\(269\) | 739.406 | 0.167593 | 0.0837963 | − | 0.996483i | \(-0.473295\pi\) | ||||
0.0837963 | + | 0.996483i | \(0.473295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4360.29 | 0.977375 | 0.488688 | − | 0.872459i | \(-0.337476\pi\) | ||||
0.488688 | + | 0.872459i | \(0.337476\pi\) | |||||||
\(272\) | −449.428 | −0.100186 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11863.1 | 2.61561 | ||||||||
\(275\) | 531.642 | 0.116579 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5779.74 | −1.25369 | −0.626843 | − | 0.779146i | \(-0.715653\pi\) | ||||
−0.626843 | + | 0.779146i | \(0.715653\pi\) | |||||||
\(278\) | 13100.4 | 2.82630 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1935.33 | 0.413065 | ||||||||
\(281\) | 4366.84 | 0.927059 | 0.463530 | − | 0.886081i | \(-0.346583\pi\) | ||||
0.463530 | + | 0.886081i | \(0.346583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8294.14 | −1.74218 | −0.871088 | − | 0.491128i | \(-0.836585\pi\) | ||||
−0.871088 | + | 0.491128i | \(0.836585\pi\) | |||||||
\(284\) | 8985.78 | 1.87749 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2739.27 | 0.566351 | ||||||||
\(287\) | 423.380 | 0.0870778 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1472.67 | 0.299750 | ||||||||
\(290\) | 5230.57 | 1.05914 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1663.52 | 0.333391 | ||||||||
\(293\) | −2434.82 | −0.485473 | −0.242736 | − | 0.970092i | \(-0.578045\pi\) | ||||
−0.242736 | + | 0.970092i | \(0.578045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4714.17 | −0.930405 | ||||||||
\(296\) | −1924.62 | −0.377926 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13213.3 | 2.56855 | ||||||||
\(299\) | 6547.99 | 1.26649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1494.86 | −0.286254 | ||||||||
\(302\) | 10568.1 | 2.01365 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −119.542 | −0.0225533 | ||||||||
\(305\) | −6784.15 | −1.27364 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5972.33 | −1.11029 | −0.555145 | − | 0.831754i | \(-0.687337\pi\) | ||||
−0.555145 | + | 0.831754i | \(0.687337\pi\) | |||||||
\(308\) | 972.059 | 0.179832 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11434.7 | 2.09499 | ||||||||
\(311\) | 8278.65 | 1.50945 | 0.754725 | − | 0.656041i | \(-0.227770\pi\) | ||||
0.754725 | + | 0.656041i | \(0.227770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1386.60 | −0.250400 | −0.125200 | − | 0.992131i | \(-0.539957\pi\) | ||||
−0.125200 | + | 0.992131i | \(0.539957\pi\) | |||||||
\(314\) | 4212.46 | 0.757079 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 132.510 | 0.0235895 | ||||||||
\(317\) | −11.2346 | −0.00199053 | −0.000995264 | − | 1.00000i | \(-0.500317\pi\) | ||||
−0.000995264 | 1.00000i | \(0.500317\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 962.312 | 0.168900 | ||||||||
\(320\) | 10979.4 | 1.91803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3796.13 | 0.656987 | ||||||||
\(323\) | 1698.51 | 0.292593 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2650.21 | −0.452329 | ||||||||
\(326\) | 13471.1 | 2.28864 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1270.14 | −0.213816 | ||||||||
\(329\) | −2921.94 | −0.489641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4516.29 | −0.749963 | −0.374981 | − | 0.927032i | \(-0.622351\pi\) | ||||
−0.374981 | + | 0.927032i | \(0.622351\pi\) | |||||||
\(332\) | 7806.17 | 1.29042 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17513.2 | 2.86910 | ||||||||
\(335\) | 1416.25 | 0.230979 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −676.780 | −0.109396 | −0.0546982 | − | 0.998503i | \(-0.517420\pi\) | ||||
−0.0546982 | + | 0.998503i | \(0.517420\pi\) | |||||||
\(338\) | −3677.70 | −0.591836 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13281.4 | −2.11848 | ||||||||
\(341\) | 2103.73 | 0.334086 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 4484.59 | 0.702886 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12259.5 | −1.90485 | ||||||||
\(347\) | −7619.43 | −1.17877 | −0.589384 | − | 0.807853i | \(-0.700629\pi\) | ||||
−0.589384 | + | 0.807853i | \(0.700629\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3178.35 | 0.487488 | 0.243744 | − | 0.969840i | \(-0.421624\pi\) | ||||
0.243744 | + | 0.969840i | \(0.421624\pi\) | |||||||
\(350\) | −1536.43 | −0.234644 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2128.96 | 0.322368 | ||||||||
\(353\) | −1776.12 | −0.267800 | −0.133900 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133900 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9371.13 | −1.40104 | ||||||||
\(356\) | −17376.4 | −2.58693 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6033.59 | 0.890740 | ||||||||
\(359\) | 11425.3 | 1.67968 | 0.839838 | − | 0.542838i | \(-0.182650\pi\) | ||||
0.839838 | + | 0.542838i | \(0.182650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6407.22 | −0.934133 | ||||||||
\(362\) | −2429.38 | −0.352722 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4845.67 | −0.697753 | ||||||||
\(365\) | −1734.86 | −0.248785 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1321.34 | −0.187938 | −0.0939689 | − | 0.995575i | \(-0.529955\pi\) | ||||
−0.0939689 | + | 0.995575i | \(0.529955\pi\) | |||||||
\(368\) | 671.600 | 0.0951348 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5479.63 | 0.769925 | ||||||||
\(371\) | 2904.32 | 0.406429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2011.16 | −0.279180 | −0.139590 | − | 0.990209i | \(-0.544578\pi\) | ||||
−0.139590 | + | 0.990209i | \(0.544578\pi\) | |||||||
\(374\) | −3991.94 | −0.551920 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8765.83 | 1.20230 | ||||||||
\(377\) | −4797.08 | −0.655337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1376.20 | −0.186519 | −0.0932597 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932597 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(380\) | −3532.68 | −0.476901 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15695.9 | −2.10229 | ||||||||
\(383\) | −68.4429 | −0.00913125 | −0.00456563 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456563 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1013.75 | −0.134195 | ||||||||
\(386\) | 14105.6 | 1.85999 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6750.78 | −0.883297 | ||||||||
\(389\) | 1796.33 | 0.234133 | 0.117066 | − | 0.993124i | \(-0.462651\pi\) | ||||
0.117066 | + | 0.993124i | \(0.462651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9542.40 | −1.23422 | ||||||||
\(392\) | −1029.00 | −0.132583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22191.4 | 2.83753 | ||||||||
\(395\) | −138.193 | −0.0176031 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4175.59 | 0.527876 | 0.263938 | − | 0.964540i | \(-0.414978\pi\) | ||||
0.263938 | + | 0.964540i | \(0.414978\pi\) | |||||||
\(398\) | −15076.2 | −1.89875 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −271.821 | −0.0339776 | ||||||||
\(401\) | 5735.25 | 0.714226 | 0.357113 | − | 0.934061i | \(-0.383761\pi\) | ||||
0.357113 | + | 0.934061i | \(0.383761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10487.0 | −1.29626 | ||||||||
\(404\) | −20451.2 | −2.51853 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2781.05 | −0.339954 | ||||||||
\(407\) | 1008.13 | 0.122780 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4552.26 | 0.550355 | 0.275177 | − | 0.961394i | \(-0.411263\pi\) | ||||
0.275177 | + | 0.961394i | \(0.411263\pi\) | |||||||
\(410\) | 3616.25 | 0.435595 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10387.3 | 1.24210 | ||||||||
\(413\) | 2506.48 | 0.298634 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8140.93 | −0.962946 | ||||||||
\(416\) | −10612.7 | −1.25080 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1061.80 | −0.124245 | ||||||||
\(419\) | −12761.1 | −1.48788 | −0.743940 | − | 0.668247i | \(-0.767045\pi\) | ||||
−0.743940 | + | 0.668247i | \(0.767045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2838.93 | −0.328649 | −0.164324 | − | 0.986406i | \(-0.552544\pi\) | ||||
−0.164324 | + | 0.986406i | \(0.552544\pi\) | |||||||
\(422\) | −19357.7 | −2.23298 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8712.97 | −0.997970 | ||||||||
\(425\) | 3862.15 | 0.440805 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3607.08 | 0.408803 | ||||||||
\(428\) | 22089.5 | 2.49471 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12768.2 | −1.43195 | ||||||||
\(431\) | 12820.2 | 1.43277 | 0.716387 | − | 0.697704i | \(-0.245795\pi\) | ||||
0.716387 | + | 0.697704i | \(0.245795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12570.9 | −1.39519 | −0.697595 | − | 0.716493i | \(-0.745746\pi\) | ||||
−0.697595 | + | 0.716493i | \(0.745746\pi\) | |||||||
\(434\) | −6079.72 | −0.672433 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8175.48 | −0.898015 | ||||||||
\(437\) | −2538.16 | −0.277841 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11589.8 | −1.26003 | −0.630013 | − | 0.776585i | \(-0.716950\pi\) | ||||
−0.630013 | + | 0.776585i | \(0.716950\pi\) | |||||||
\(440\) | 3041.24 | 0.329512 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19899.6 | 2.14147 | ||||||||
\(443\) | −15298.1 | −1.64071 | −0.820355 | − | 0.571855i | \(-0.806224\pi\) | ||||
−0.820355 | + | 0.571855i | \(0.806224\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18121.6 | 1.93044 | ||||||||
\(446\) | −12562.2 | −1.33372 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5837.66 | −0.615633 | ||||||||
\(449\) | −3370.37 | −0.354249 | −0.177125 | − | 0.984188i | \(-0.556680\pi\) | ||||
−0.177125 | + | 0.984188i | \(0.556680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 665.312 | 0.0694641 | ||||||||
\(452\) | −14536.7 | −1.51272 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2478.34 | 0.256199 | ||||||||
\(455\) | 5053.47 | 0.520682 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2682.12 | −0.274539 | −0.137269 | − | 0.990534i | \(-0.543833\pi\) | ||||
−0.137269 | + | 0.990534i | \(0.543833\pi\) | |||||||
\(458\) | −14521.0 | −1.48149 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19847.0 | 2.01168 | ||||||||
\(461\) | −1313.76 | −0.132729 | −0.0663645 | − | 0.997795i | \(-0.521140\pi\) | ||||
−0.0663645 | + | 0.997795i | \(0.521140\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17339.2 | 1.74043 | 0.870215 | − | 0.492672i | \(-0.163980\pi\) | ||||
0.870215 | + | 0.492672i | \(0.163980\pi\) | |||||||
\(464\) | −492.016 | −0.0492269 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19090.9 | 1.89779 | ||||||||
\(467\) | 8810.22 | 0.872995 | 0.436497 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −753.007 | −0.0741379 | ||||||||
\(470\) | −24957.4 | −2.44936 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7519.45 | −0.733285 | ||||||||
\(473\) | −2349.07 | −0.228352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1027.28 | 0.0992315 | ||||||||
\(476\) | 7061.60 | 0.679975 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25980.0 | 2.48598 | ||||||||
\(479\) | 708.948 | 0.0676256 | 0.0338128 | − | 0.999428i | \(-0.489235\pi\) | ||||
0.0338128 | + | 0.999428i | \(0.489235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5025.49 | −0.476388 | ||||||||
\(482\) | −23577.8 | −2.22809 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1527.52 | 0.143456 | ||||||||
\(485\) | 7040.29 | 0.659140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12253.6 | 1.14017 | 0.570085 | − | 0.821586i | \(-0.306910\pi\) | ||||
0.570085 | + | 0.821586i | \(0.306910\pi\) | |||||||
\(488\) | −10821.2 | −1.00380 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2929.69 | 0.270102 | ||||||||
\(491\) | 5429.37 | 0.499031 | 0.249515 | − | 0.968371i | \(-0.419729\pi\) | ||||
0.249515 | + | 0.968371i | \(0.419729\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6990.79 | 0.638640 | ||||||||
\(494\) | 5293.04 | 0.482076 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1075.61 | −0.0973714 | ||||||||
\(497\) | 4982.55 | 0.449694 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14531.6 | −1.30366 | −0.651829 | − | 0.758366i | \(-0.725998\pi\) | ||||
−0.651829 | + | 0.758366i | \(0.725998\pi\) | |||||||
\(500\) | 12742.6 | 1.13974 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3850.83 | 0.342373 | ||||||||
\(503\) | 6349.27 | 0.562823 | 0.281412 | − | 0.959587i | \(-0.409197\pi\) | ||||
0.281412 | + | 0.959587i | \(0.409197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21328.2 | 1.87940 | ||||||||
\(506\) | 5965.34 | 0.524094 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3511.35 | 0.306675 | ||||||||
\(509\) | 2082.16 | 0.181317 | 0.0906585 | − | 0.995882i | \(-0.471103\pi\) | ||||
0.0906585 | + | 0.995882i | \(0.471103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 922.410 | 0.0798532 | ||||||||
\(512\) | −2033.36 | −0.175513 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6784.24 | −0.582179 | ||||||||
\(515\) | −10832.8 | −0.926892 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4591.63 | −0.390599 | ||||||||
\(518\) | −2913.47 | −0.247125 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15160.4 | −1.27852 | ||||||||
\(521\) | 17339.3 | 1.45806 | 0.729030 | − | 0.684481i | \(-0.239971\pi\) | ||||
0.729030 | + | 0.684481i | \(0.239971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11310.6 | −0.945660 | −0.472830 | − | 0.881154i | \(-0.656768\pi\) | ||||
−0.472830 | + | 0.881154i | \(0.656768\pi\) | |||||||
\(524\) | −29442.3 | −2.45457 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 616.936 | 0.0511401 | ||||||||
\(527\) | 15282.7 | 1.26324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2092.66 | 0.171995 | ||||||||
\(530\) | 24806.9 | 2.03310 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1878.30 | 0.153072 | ||||||||
\(533\) | −3316.55 | −0.269523 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23036.8 | −1.86162 | ||||||||
\(536\) | 2259.02 | 0.182043 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3357.93 | −0.269090 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1483.01 | −0.117855 | −0.0589275 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589275 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(542\) | −19801.7 | −1.56929 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15466.0 | 1.21893 | ||||||||
\(545\) | 8526.08 | 0.670123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3512.31 | 0.274544 | 0.137272 | − | 0.990533i | \(-0.456167\pi\) | ||||
0.137272 | + | 0.990533i | \(0.456167\pi\) | |||||||
\(548\) | −32977.2 | −2.57065 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2414.39 | −0.187181 | ||||||||
\(551\) | 1859.46 | 0.143767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.4760 | 0.00565012 | ||||||||
\(554\) | 26248.0 | 2.01294 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36416.6 | −2.77771 | ||||||||
\(557\) | −14069.1 | −1.07025 | −0.535123 | − | 0.844774i | \(-0.679735\pi\) | ||||
−0.535123 | + | 0.844774i | \(0.679735\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11710.0 | 0.886012 | ||||||||
\(560\) | 518.314 | 0.0391121 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19831.5 | −1.48851 | ||||||||
\(563\) | −12982.7 | −0.971860 | −0.485930 | − | 0.873998i | \(-0.661519\pi\) | ||||
−0.485930 | + | 0.873998i | \(0.661519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15160.1 | 1.12884 | ||||||||
\(566\) | 37666.9 | 2.79727 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14947.7 | −1.10421 | ||||||||
\(569\) | 1668.21 | 0.122909 | 0.0614545 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614545 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22037.1 | −1.61510 | −0.807552 | − | 0.589797i | \(-0.799208\pi\) | ||||
−0.807552 | + | 0.589797i | \(0.799208\pi\) | |||||||
\(572\) | −7614.62 | −0.556614 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1922.73 | −0.139814 | ||||||||
\(575\) | −5771.39 | −0.418581 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22415.8 | 1.61730 | 0.808649 | − | 0.588292i | \(-0.200199\pi\) | ||||
0.808649 | + | 0.588292i | \(0.200199\pi\) | |||||||
\(578\) | −6687.96 | −0.481284 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14540.0 | −1.04093 | ||||||||
\(581\) | 4328.47 | 0.309079 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4563.94 | 0.324218 | ||||||||
\(584\) | −2767.23 | −0.196077 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11057.4 | 0.779485 | ||||||||
\(587\) | 24252.2 | 1.70527 | 0.852636 | − | 0.522506i | \(-0.175003\pi\) | ||||
0.852636 | + | 0.522506i | \(0.175003\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4065.01 | 0.284373 | ||||||||
\(590\) | 21408.8 | 1.49388 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −515.444 | −0.0357848 | ||||||||
\(593\) | −18666.9 | −1.29268 | −0.646340 | − | 0.763050i | \(-0.723701\pi\) | ||||
−0.646340 | + | 0.763050i | \(0.723701\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7364.44 | −0.507416 | ||||||||
\(596\) | −36730.5 | −2.52439 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29736.9 | −2.03350 | ||||||||
\(599\) | 11400.1 | 0.777620 | 0.388810 | − | 0.921318i | \(-0.372886\pi\) | ||||
0.388810 | + | 0.921318i | \(0.372886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9722.11 | −0.659856 | −0.329928 | − | 0.944006i | \(-0.607024\pi\) | ||||
−0.329928 | + | 0.944006i | \(0.607024\pi\) | |||||||
\(602\) | 6788.75 | 0.459616 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −29377.1 | −1.97903 | ||||||||
\(605\) | −1593.03 | −0.107051 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20616.5 | −1.37858 | −0.689291 | − | 0.724484i | \(-0.742078\pi\) | ||||
−0.689291 | + | 0.724484i | \(0.742078\pi\) | |||||||
\(608\) | 4113.75 | 0.274399 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30809.4 | 2.04498 | ||||||||
\(611\) | 22889.0 | 1.51553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −363.351 | −0.0239406 | −0.0119703 | − | 0.999928i | \(-0.503810\pi\) | ||||
−0.0119703 | + | 0.999928i | \(0.503810\pi\) | |||||||
\(614\) | 27122.6 | 1.78270 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1617.00 | −0.105764 | ||||||||
\(617\) | 19599.7 | 1.27886 | 0.639429 | − | 0.768850i | \(-0.279171\pi\) | ||||
0.639429 | + | 0.768850i | \(0.279171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10178.6 | 0.660926 | 0.330463 | − | 0.943819i | \(-0.392795\pi\) | ||||
0.330463 | + | 0.943819i | \(0.392795\pi\) | |||||||
\(620\) | −31786.1 | −2.05897 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37596.5 | −2.42361 | ||||||||
\(623\) | −9635.09 | −0.619618 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19330.5 | −1.23715 | ||||||||
\(626\) | 6297.08 | 0.402048 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11709.8 | −0.744064 | ||||||||
\(629\) | 7323.66 | 0.464250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13503.9 | −0.851949 | −0.425975 | − | 0.904735i | \(-0.640069\pi\) | ||||
−0.425975 | + | 0.904735i | \(0.640069\pi\) | |||||||
\(632\) | −220.428 | −0.0138737 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 51.0205 | 0.00319603 | ||||||||
\(635\) | −3661.93 | −0.228849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2686.89 | −0.167125 | ||||||||
\(638\) | −4370.22 | −0.271189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −29477.1 | −1.82060 | ||||||||
\(641\) | −29389.5 | −1.81095 | −0.905473 | − | 0.424404i | \(-0.860483\pi\) | ||||
−0.905473 | + | 0.424404i | \(0.860483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11632.9 | −0.713461 | −0.356730 | − | 0.934207i | \(-0.616108\pi\) | ||||
−0.356730 | + | 0.934207i | \(0.616108\pi\) | |||||||
\(644\) | −10552.5 | −0.645692 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7713.56 | −0.469793 | ||||||||
\(647\) | 7522.70 | 0.457106 | 0.228553 | − | 0.973531i | \(-0.426601\pi\) | ||||
0.228553 | + | 0.973531i | \(0.426601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3938.76 | 0.238228 | ||||||||
\(650\) | 12035.6 | 0.726270 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37447.1 | −2.24929 | ||||||||
\(653\) | −31890.8 | −1.91115 | −0.955577 | − | 0.294743i | \(-0.904766\pi\) | ||||
−0.955577 | + | 0.294743i | \(0.904766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30704.9 | 1.83166 | ||||||||
\(656\) | −340.164 | −0.0202457 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13269.7 | 0.786178 | ||||||||
\(659\) | −20234.0 | −1.19606 | −0.598029 | − | 0.801474i | \(-0.704049\pi\) | ||||
−0.598029 | + | 0.801474i | \(0.704049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16493.0 | 0.970505 | 0.485252 | − | 0.874374i | \(-0.338728\pi\) | ||||
0.485252 | + | 0.874374i | \(0.338728\pi\) | |||||||
\(662\) | 20510.2 | 1.20416 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12985.4 | −0.758932 | ||||||||
\(665\) | −1958.85 | −0.114227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10446.7 | −0.606441 | ||||||||
\(668\) | −48683.1 | −2.81977 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6431.72 | −0.370864 | ||||||||
\(671\) | 5668.26 | 0.326112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7338.87 | 0.420346 | 0.210173 | − | 0.977664i | \(-0.432597\pi\) | ||||
0.210173 | + | 0.977664i | \(0.432597\pi\) | |||||||
\(674\) | 3073.52 | 0.175649 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10223.3 | 0.581661 | ||||||||
\(677\) | −10296.8 | −0.584549 | −0.292274 | − | 0.956334i | \(-0.594412\pi\) | ||||
−0.292274 | + | 0.956334i | \(0.594412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3743.26 | −0.211566 | ||||||||
\(680\) | 22093.3 | 1.24594 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9553.85 | −0.536416 | ||||||||
\(683\) | −19884.5 | −1.11400 | −0.556998 | − | 0.830514i | \(-0.688047\pi\) | ||||
−0.556998 | + | 0.830514i | \(0.688047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34391.4 | 1.91829 | ||||||||
\(686\) | −1557.69 | −0.0866954 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1201.05 | 0.0665545 | ||||||||
\(689\) | −22751.0 | −1.25797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26756.6 | 1.47304 | 0.736519 | − | 0.676417i | \(-0.236468\pi\) | ||||
0.736519 | + | 0.676417i | \(0.236468\pi\) | |||||||
\(692\) | 34079.1 | 1.87210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34602.7 | 1.89265 | ||||||||
\(695\) | 37978.3 | 2.07280 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4833.21 | 0.262656 | ||||||||
\(698\) | −14434.1 | −0.782720 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4270.97 | 0.230611 | ||||||||
\(701\) | 7556.29 | 0.407128 | 0.203564 | − | 0.979062i | \(-0.434747\pi\) | ||||
0.203564 | + | 0.979062i | \(0.434747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1948.00 | 0.104510 | ||||||||
\(704\) | −9173.47 | −0.491105 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8066.03 | 0.429985 | ||||||||
\(707\) | −11340.1 | −0.603234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18371.1 | 0.973117 | 0.486558 | − | 0.873648i | \(-0.338252\pi\) | ||||
0.486558 | + | 0.873648i | \(0.338252\pi\) | |||||||
\(710\) | 42557.9 | 2.24953 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28905.3 | 1.52145 | ||||||||
\(713\) | −22837.7 | −1.19955 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7941.17 | 0.415361 | ||||||||
\(716\) | −16772.2 | −0.875427 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −51886.6 | −2.69692 | ||||||||
\(719\) | −24627.6 | −1.27740 | −0.638702 | − | 0.769454i | \(-0.720528\pi\) | ||||
−0.638702 | + | 0.769454i | \(0.720528\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5759.70 | 0.297507 | ||||||||
\(722\) | 29097.6 | 1.49986 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6753.20 | 0.346659 | ||||||||
\(725\) | 4228.14 | 0.216592 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19040.6 | 0.971360 | 0.485680 | − | 0.874137i | \(-0.338572\pi\) | ||||
0.485680 | + | 0.874137i | \(0.338572\pi\) | |||||||
\(728\) | 8060.67 | 0.410368 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7878.65 | 0.399455 | ||||||||
\(731\) | −17065.0 | −0.863437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35623.2 | −1.79505 | −0.897526 | − | 0.440961i | \(-0.854638\pi\) | ||||
−0.897526 | + | 0.440961i | \(0.854638\pi\) | |||||||
\(734\) | 6000.69 | 0.301757 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23111.5 | −1.15748 | ||||||||
\(737\) | −1183.30 | −0.0591415 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7248.54 | 0.360814 | 0.180407 | − | 0.983592i | \(-0.442258\pi\) | ||||
0.180407 | + | 0.983592i | \(0.442258\pi\) | |||||||
\(740\) | −15232.3 | −0.756689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13189.6 | −0.652570 | ||||||||
\(743\) | 29033.2 | 1.43354 | 0.716772 | − | 0.697307i | \(-0.245619\pi\) | ||||
0.716772 | + | 0.697307i | \(0.245619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38305.6 | 1.88377 | ||||||||
\(746\) | 9133.46 | 0.448257 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11096.8 | 0.542432 | ||||||||
\(749\) | 12248.5 | 0.597529 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32062.0 | −1.55787 | −0.778933 | − | 0.627107i | \(-0.784239\pi\) | ||||
−0.778933 | + | 0.627107i | \(0.784239\pi\) | |||||||
\(752\) | 2347.63 | 0.113842 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21785.4 | 1.05222 | ||||||||
\(755\) | 30636.9 | 1.47681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16132.9 | 0.774584 | 0.387292 | − | 0.921957i | \(-0.373411\pi\) | ||||
0.387292 | + | 0.921957i | \(0.373411\pi\) | |||||||
\(758\) | 6249.87 | 0.299479 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5876.54 | 0.280479 | ||||||||
\(761\) | 37232.9 | 1.77358 | 0.886789 | − | 0.462175i | \(-0.152931\pi\) | ||||
0.886789 | + | 0.462175i | \(0.152931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4533.25 | −0.215091 | ||||||||
\(764\) | 43631.6 | 2.06615 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 310.825 | 0.0146613 | ||||||||
\(767\) | −19634.5 | −0.924331 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36009.7 | 1.68861 | 0.844305 | − | 0.535862i | \(-0.180013\pi\) | ||||
0.844305 | + | 0.535862i | \(0.180013\pi\) | |||||||
\(770\) | 4603.80 | 0.215467 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −39210.9 | −1.82802 | ||||||||
\(773\) | −20156.0 | −0.937856 | −0.468928 | − | 0.883236i | \(-0.655360\pi\) | ||||
−0.468928 | + | 0.883236i | \(0.655360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9243.23 | 0.428421 | ||||||||
\(776\) | 11229.8 | 0.519492 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8157.83 | −0.375929 | ||||||||
\(779\) | 1285.57 | 0.0591276 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7829.73 | 0.358732 | ||||||||
\(782\) | 43335.7 | 1.98169 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −275.583 | −0.0125539 | ||||||||
\(785\) | 12212.0 | 0.555241 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19711.9 | −0.892823 | −0.446411 | − | 0.894828i | \(-0.647298\pi\) | ||||
−0.446411 | + | 0.894828i | \(0.647298\pi\) | |||||||
\(788\) | −61687.7 | −2.78875 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 627.587 | 0.0282640 | ||||||||
\(791\) | −8060.52 | −0.362325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28256.0 | −1.26532 | ||||||||
\(794\) | −18963.0 | −0.847569 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41908.9 | 1.86611 | ||||||||
\(797\) | 8274.02 | 0.367730 | 0.183865 | − | 0.982952i | \(-0.441139\pi\) | ||||
0.183865 | + | 0.982952i | \(0.441139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33356.2 | −1.47692 | ||||||||
\(800\) | 9354.06 | 0.413395 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26045.9 | −1.14678 | ||||||||
\(803\) | 1449.50 | 0.0637009 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11005.0 | 0.481833 | ||||||||
\(806\) | 47625.5 | 2.08131 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34020.2 | 1.48122 | ||||||||
\(809\) | −15039.4 | −0.653593 | −0.326797 | − | 0.945095i | \(-0.605969\pi\) | ||||
−0.326797 | + | 0.945095i | \(0.605969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31217.1 | −1.35164 | −0.675820 | − | 0.737067i | \(-0.736210\pi\) | ||||
−0.675820 | + | 0.737067i | \(0.736210\pi\) | |||||||
\(812\) | 7730.77 | 0.334110 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4578.31 | −0.197137 | ||||||||
\(815\) | 39053.0 | 1.67849 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4539.08 | −0.194372 | ||||||||
\(818\) | −20673.6 | −0.883661 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10052.5 | −0.428106 | ||||||||
\(821\) | −6151.17 | −0.261483 | −0.130741 | − | 0.991417i | \(-0.541736\pi\) | ||||
−0.130741 | + | 0.991417i | \(0.541736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34084.1 | −1.44362 | −0.721808 | − | 0.692093i | \(-0.756689\pi\) | ||||
−0.721808 | + | 0.692093i | \(0.756689\pi\) | |||||||
\(824\) | −17279.1 | −0.730517 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11382.9 | −0.479494 | ||||||||
\(827\) | −19451.9 | −0.817907 | −0.408953 | − | 0.912555i | \(-0.634106\pi\) | ||||
−0.408953 | + | 0.912555i | \(0.634106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26492.7 | 1.10993 | 0.554963 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554963 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(830\) | 36971.1 | 1.54613 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 45729.3 | 1.90550 | ||||||||
\(833\) | 3915.61 | 0.162867 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50770.9 | 2.10419 | ||||||||
\(836\) | 2951.61 | 0.122109 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 57953.1 | 2.38897 | ||||||||
\(839\) | 8978.20 | 0.369442 | 0.184721 | − | 0.982791i | \(-0.440862\pi\) | ||||
0.184721 | + | 0.982791i | \(0.440862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16735.7 | −0.686201 | ||||||||
\(842\) | 12892.7 | 0.527685 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 53810.6 | 2.19459 | ||||||||
\(845\) | −10661.7 | −0.434052 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | −2333.48 | −0.0944952 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17539.5 | −0.707765 | ||||||||
\(851\) | −10944.1 | −0.440844 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27980.8 | −1.12315 | −0.561574 | − | 0.827427i | \(-0.689804\pi\) | ||||
−0.561574 | + | 0.827427i | \(0.689804\pi\) | |||||||
\(854\) | −16381.1 | −0.656382 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36745.4 | −1.46721 | ||||||||
\(857\) | 4175.08 | 0.166416 | 0.0832078 | − | 0.996532i | \(-0.473483\pi\) | ||||
0.0832078 | + | 0.996532i | \(0.473483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38793.4 | 1.54088 | 0.770439 | − | 0.637514i | \(-0.220037\pi\) | ||||
0.770439 | + | 0.637514i | \(0.220037\pi\) | |||||||
\(860\) | 35493.1 | 1.40733 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −58221.2 | −2.30049 | ||||||||
\(863\) | 19429.6 | 0.766385 | 0.383193 | − | 0.923668i | \(-0.374825\pi\) | ||||
0.383193 | + | 0.923668i | \(0.374825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35540.6 | −1.39701 | ||||||||
\(866\) | 57089.1 | 2.24015 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16900.4 | 0.660873 | ||||||||
\(869\) | 115.462 | 0.00450724 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5898.68 | 0.229471 | ||||||||
\(872\) | 13599.7 | 0.528148 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11526.7 | 0.446107 | ||||||||
\(875\) | 7065.71 | 0.272988 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17547.9 | −0.675656 | −0.337828 | − | 0.941208i | \(-0.609692\pi\) | ||||
−0.337828 | + | 0.941208i | \(0.609692\pi\) | |||||||
\(878\) | 52633.8 | 2.02312 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 814.493 | 0.0312006 | ||||||||
\(881\) | 44948.7 | 1.71891 | 0.859455 | − | 0.511212i | \(-0.170803\pi\) | ||||
0.859455 | + | 0.511212i | \(0.170803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37819.3 | −1.44136 | −0.720680 | − | 0.693268i | \(-0.756170\pi\) | ||||
−0.720680 | + | 0.693268i | \(0.756170\pi\) | |||||||
\(884\) | −55317.0 | −2.10465 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 69474.4 | 2.63436 | ||||||||
\(887\) | 7203.82 | 0.272695 | 0.136348 | − | 0.990661i | \(-0.456464\pi\) | ||||
0.136348 | + | 0.990661i | \(0.456464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1947.02 | 0.0734543 | ||||||||
\(890\) | −82297.0 | −3.09955 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 34920.5 | 1.31079 | ||||||||
\(893\) | −8872.33 | −0.332476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17491.5 | 0.653268 | ||||||||
\(896\) | 15672.7 | 0.584363 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15306.2 | 0.568790 | ||||||||
\(899\) | 16731.0 | 0.620699 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33155.1 | 1.22592 | ||||||||
\(902\) | −3021.43 | −0.111533 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24181.6 | 0.889676 | ||||||||
\(905\) | −7042.81 | −0.258686 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9420.96 | 0.344893 | 0.172446 | − | 0.985019i | \(-0.444833\pi\) | ||||
0.172446 | + | 0.985019i | \(0.444833\pi\) | |||||||
\(908\) | −6889.30 | −0.251794 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22949.7 | −0.836018 | ||||||||
\(911\) | −40045.0 | −1.45637 | −0.728184 | − | 0.685382i | \(-0.759635\pi\) | ||||
−0.728184 | + | 0.685382i | \(0.759635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6801.87 | 0.246560 | ||||||||
\(914\) | 12180.5 | 0.440805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40365.5 | 1.45602 | ||||||||
\(917\) | −16325.6 | −0.587914 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8881.69 | −0.318803 | −0.159402 | − | 0.987214i | \(-0.550956\pi\) | ||||
−0.159402 | + | 0.987214i | \(0.550956\pi\) | |||||||
\(920\) | −33015.1 | −1.18312 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5966.30 | 0.213112 | ||||||||
\(923\) | −39030.8 | −1.39189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4429.46 | 0.157448 | ||||||||
\(926\) | −78743.7 | −2.79447 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16931.6 | 0.598928 | ||||||||
\(929\) | −39037.4 | −1.37866 | −0.689331 | − | 0.724447i | \(-0.742095\pi\) | ||||
−0.689331 | + | 0.724447i | \(0.742095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1041.50 | 0.0366636 | ||||||||
\(932\) | −53068.9 | −1.86516 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40010.6 | −1.40170 | ||||||||
\(935\) | −11572.7 | −0.404778 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17549.7 | 0.611870 | 0.305935 | − | 0.952052i | \(-0.401031\pi\) | ||||
0.305935 | + | 0.952052i | \(0.401031\pi\) | |||||||
\(938\) | 3419.69 | 0.119037 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 69376.8 | 2.40726 | ||||||||
\(941\) | 28176.8 | 0.976128 | 0.488064 | − | 0.872808i | \(-0.337703\pi\) | ||||
0.488064 | + | 0.872808i | \(0.337703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7222.49 | −0.249413 | ||||||||
\(944\) | −2013.83 | −0.0694329 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10668.0 | 0.366646 | ||||||||
\(947\) | 11092.6 | 0.380636 | 0.190318 | − | 0.981722i | \(-0.439048\pi\) | ||||
0.190318 | + | 0.981722i | \(0.439048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7225.69 | −0.247161 | ||||||||
\(950\) | −4665.28 | −0.159328 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11746.8 | −0.399913 | ||||||||
\(953\) | −21883.0 | −0.743820 | −0.371910 | − | 0.928269i | \(-0.621297\pi\) | ||||
−0.371910 | + | 0.928269i | \(0.621297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45502.7 | −1.54181 | ||||||||
\(956\) | −72219.4 | −2.44324 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3219.60 | −0.108581 | ||||||||
\(959\) | −18285.6 | −0.615717 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6784.91 | 0.227750 | ||||||||
\(962\) | 22822.7 | 0.764899 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 65541.7 | 2.18979 | ||||||||
\(965\) | 40892.4 | 1.36412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40235.4 | 1.33804 | 0.669019 | − | 0.743245i | \(-0.266714\pi\) | ||||
0.669019 | + | 0.743245i | \(0.266714\pi\) | |||||||
\(968\) | −2541.00 | −0.0843707 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31972.6 | −1.05833 | ||||||||
\(971\) | −44470.2 | −1.46974 | −0.734870 | − | 0.678208i | \(-0.762757\pi\) | ||||
−0.734870 | + | 0.678208i | \(0.762757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20192.7 | −0.665313 | ||||||||
\(974\) | −55648.2 | −1.83068 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2898.10 | −0.0950472 | ||||||||
\(977\) | 55989.4 | 1.83343 | 0.916715 | − | 0.399542i | \(-0.130831\pi\) | ||||
0.916715 | + | 0.399542i | \(0.130831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15140.9 | −0.494284 | ||||||||
\(980\) | −8143.97 | −0.265459 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24656.8 | −0.801254 | ||||||||
\(983\) | 5987.22 | 0.194265 | 0.0971326 | − | 0.995271i | \(-0.469033\pi\) | ||||
0.0971326 | + | 0.995271i | \(0.469033\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64333.1 | 2.08104 | ||||||||
\(986\) | −31747.8 | −1.02541 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14713.6 | −0.473788 | ||||||||
\(989\) | 25501.1 | 0.819905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1965.53 | −0.0630043 | −0.0315022 | − | 0.999504i | \(-0.510029\pi\) | ||||
−0.0315022 | + | 0.999504i | \(0.510029\pi\) | |||||||
\(992\) | 37014.5 | 1.18469 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22627.7 | −0.722039 | ||||||||
\(995\) | −43706.2 | −1.39254 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10802.9 | −0.343161 | −0.171581 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(998\) | 65993.7 | 2.09318 | ||||||||
\(999\) | 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 | 693.4.a.h.1.1 | 2 | ||
3.2 | odd | 2 | 231.4.a.i.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 1617.4.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.4.a.i.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
693.4.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1617.4.a.l.1.2 | 2 | 21.20 | even | 2 |