Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 204 x^{8} + 42 x^{7} + 12958 x^{6} + 5872 x^{5} - 259871 x^{4} - 149461 x^{3} + 1222472 x^{2} + 627136 x - 43712 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.66698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.66698 | −0.513261 | −0.256631 | − | 0.966510i | \(-0.582612\pi\) | ||||
−0.256631 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.5699 | 1.75861 | 0.879304 | − | 0.476261i | \(-0.158008\pi\) | ||||
0.879304 | + | 0.476261i | \(0.158008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19.8872 | −0.736563 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.2916 | 1.40591 | 0.702955 | − | 0.711235i | \(-0.251864\pi\) | ||||
0.702955 | + | 0.711235i | \(0.251864\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.1984 | 0.857617 | 0.428808 | − | 0.903395i | \(-0.358934\pi\) | ||||
0.428808 | + | 0.903395i | \(0.358934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.3349 | 0.229538 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 93.3680 | 1.33206 | 0.666032 | − | 0.745923i | \(-0.267992\pi\) | ||||
0.666032 | + | 0.745923i | \(0.267992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61.9187 | 0.747638 | 0.373819 | − | 0.927502i | \(-0.378048\pi\) | ||||
0.373819 | + | 0.927502i | \(0.378048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −86.8634 | −0.902626 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 125.047 | 0.891311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −160.031 | −1.02472 | −0.512361 | − | 0.858770i | \(-0.671229\pi\) | ||||
−0.512361 | + | 0.858770i | \(0.671229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 295.881 | 1.71425 | 0.857124 | − | 0.515109i | \(-0.172249\pi\) | ||||
0.857124 | + | 0.515109i | \(0.172249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −136.794 | −0.721599 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −162.849 | −0.786473 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 401.688 | 1.78479 | 0.892393 | − | 0.451258i | \(-0.149025\pi\) | ||||
0.892393 | + | 0.451258i | \(0.149025\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −107.208 | −0.440182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 310.046 | 1.18100 | 0.590501 | − | 0.807037i | \(-0.298930\pi\) | ||||
0.590501 | + | 0.807037i | \(0.298930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −506.024 | −1.79460 | −0.897302 | − | 0.441417i | \(-0.854476\pi\) | ||||
−0.897302 | + | 0.441417i | \(0.854476\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 99.4360 | 0.329401 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −188.492 | −0.584987 | −0.292494 | − | 0.956267i | \(-0.594485\pi\) | ||||
−0.292494 | + | 0.956267i | \(0.594485\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 717.796 | 2.09270 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −249.011 | −0.683697 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 162.682 | 0.421623 | 0.210812 | − | 0.977527i | \(-0.432389\pi\) | ||||
0.210812 | + | 0.977527i | \(0.432389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −256.458 | −0.628742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −165.136 | −0.383734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 206.969 | 0.456697 | 0.228348 | − | 0.973579i | \(-0.426667\pi\) | ||||
0.228348 | + | 0.973579i | \(0.426667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −856.676 | −1.79813 | −0.899067 | − | 0.437811i | \(-0.855754\pi\) | ||||
−0.899067 | + | 0.437811i | \(0.855754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −647.723 | −1.29532 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −200.992 | −0.383538 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −435.055 | −0.793289 | −0.396645 | − | 0.917972i | \(-0.629825\pi\) | ||||
−0.396645 | + | 0.917972i | \(0.629825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 61.3407 | 0.107022 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −132.120 | −0.220841 | −0.110421 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110421 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −675.451 | −1.08295 | −0.541477 | − | 0.840716i | \(-0.682135\pi\) | ||||
−0.541477 | + | 0.840716i | \(0.682135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −66.6746 | −0.102652 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1670.56 | 2.47244 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −802.451 | −1.14282 | −0.571410 | − | 0.820665i | \(-0.693603\pi\) | ||||
−0.571410 | + | 0.820665i | \(0.693603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 203.455 | 0.279087 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 657.368 | 0.869344 | 0.434672 | − | 0.900589i | \(-0.356864\pi\) | ||||
0.434672 | + | 0.900589i | \(0.356864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −466.840 | −0.595717 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 426.799 | 0.525950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1588.25 | 1.89163 | 0.945813 | − | 0.324713i | \(-0.105268\pi\) | ||||
0.945813 | + | 0.324713i | \(0.105268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1309.26 | 1.50821 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −789.109 | −0.879858 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −309.594 | −0.334354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1549.02 | −1.62144 | −0.810719 | − | 0.585436i | \(-0.800923\pi\) | ||||
−0.810719 | + | 0.585436i | \(0.800923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1020.05 | −1.03554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 520.718 | 0.513003 | 0.256502 | − | 0.966544i | \(-0.417430\pi\) | ||||
0.256502 | + | 0.966544i | \(0.417430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −233.521 | −0.223394 | −0.111697 | − | 0.993742i | \(-0.535629\pi\) | ||||
−0.111697 | + | 0.993742i | \(0.535629\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 434.317 | 0.403666 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −632.552 | −0.571506 | −0.285753 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285753 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 608.347 | 0.534579 | 0.267289 | − | 0.963616i | \(-0.413872\pi\) | ||||
0.267289 | + | 0.963616i | \(0.413872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1071.30 | −0.916062 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1508.50 | −1.25582 | −0.627910 | − | 0.778286i | \(-0.716090\pi\) | ||||
−0.627910 | + | 0.778286i | \(0.716090\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −799.432 | −0.631688 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3040.98 | 2.34258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1299.83 | 0.976581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −826.889 | −0.606163 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 399.499 | 0.279132 | 0.139566 | − | 0.990213i | \(-0.455429\pi\) | ||||
0.139566 | + | 0.990213i | \(0.455429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1349.56 | 0.921101 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1687.36 | 1.12538 | 0.562692 | − | 0.826666i | \(-0.309766\pi\) | ||||
0.562692 | + | 0.826666i | \(0.309766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2016.68 | 1.31480 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −625.237 | −0.398606 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1788.43 | 1.11530 | 0.557649 | − | 0.830077i | \(-0.311704\pi\) | ||||
0.557649 | + | 0.830077i | \(0.311704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3172.31 | −1.93577 | −0.967885 | − | 0.251392i | \(-0.919112\pi\) | ||||
−0.967885 | + | 0.251392i | \(0.919112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 502.706 | 0.300252 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2061.84 | 1.20573 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 800.153 | 0.458269 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1914.35 | −1.07410 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −578.448 | −0.318043 | −0.159021 | − | 0.987275i | \(-0.550834\pi\) | ||||
−0.159021 | + | 0.987275i | \(0.550834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −76.8056 | −0.0413930 | −0.0206965 | − | 0.999786i | \(-0.506588\pi\) | ||||
−0.0206965 | + | 0.999786i | \(0.506588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1856.83 | −0.981148 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1479.40 | −0.766635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2206.33 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −433.869 | −0.216403 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −749.107 | −0.366695 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1613.69 | 0.775425 | 0.387713 | − | 0.921780i | \(-0.373265\pi\) | ||||
0.387713 | + | 0.921780i | \(0.373265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 683.970 | 0.322709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 432.118 | 0.200229 | 0.100115 | − | 0.994976i | \(-0.468079\pi\) | ||||
0.100115 | + | 0.994976i | \(0.468079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −581.093 | −0.264494 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1231.39 | −0.550682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 56.1129 | 0.0246600 | 0.0123300 | − | 0.999924i | \(-0.496075\pi\) | ||||
0.0123300 | + | 0.999924i | \(0.496075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 814.247 | 0.351722 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −551.984 | −0.234405 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3253.75 | −1.35864 | −0.679320 | − | 0.733842i | \(-0.737725\pi\) | ||||
−0.679320 | + | 0.733842i | \(0.737725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −934.727 | −0.383855 | −0.191927 | − | 0.981409i | \(-0.561474\pi\) | ||||
−0.191927 | + | 0.981409i | \(0.561474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2284.74 | 0.922913 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2008.44 | −0.798181 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4789.00 | 1.87276 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4072.78 | 1.56747 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 592.378 | 0.224414 | 0.112207 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112207 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −533.680 | −0.199042 | −0.0995211 | − | 0.995035i | \(-0.531731\pi\) | ||||
−0.0995211 | + | 0.995035i | \(0.531731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 536.042 | 0.196855 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1721.56 | 0.622621 | 0.311311 | − | 0.950308i | \(-0.399232\pi\) | ||||
0.311311 | + | 0.950308i | \(0.399232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3237.34 | 1.15321 | 0.576605 | − | 0.817023i | \(-0.304377\pi\) | ||||
0.576605 | + | 0.817023i | \(0.304377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1160.28 | 0.407165 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5212.17 | −1.80208 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1550.23 | −0.528160 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 457.405 | 0.153584 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3175.91 | 1.05111 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4559.29 | −1.48756 | −0.743779 | − | 0.668426i | \(-0.766969\pi\) | ||||
−0.743779 | + | 0.668426i | \(0.766969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 352.362 | 0.113349 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2530.12 | 0.802571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9636.79 | 3.01469 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1801.42 | 0.555838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3753.24 | 1.14240 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −373.549 | −0.112173 | −0.0560867 | − | 0.998426i | \(-0.517862\pi\) | ||||
−0.0560867 | + | 0.998426i | \(0.517862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −497.180 | −0.147313 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1609.88 | 0.470712 | 0.235356 | − | 0.971909i | \(-0.424374\pi\) | ||||
0.235356 | + | 0.971909i | \(0.424374\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3940.09 | 1.13698 | 0.568490 | − | 0.822690i | \(-0.307528\pi\) | ||||
0.568490 | + | 0.822690i | \(0.307528\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4455.36 | −1.26901 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1589.71 | −0.446976 | −0.223488 | − | 0.974707i | \(-0.571744\pi\) | ||||
−0.223488 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 942.461 | 0.261614 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2140.12 | 0.586565 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6822.07 | 1.84637 | 0.923186 | − | 0.384354i | \(-0.125576\pi\) | ||||
0.923186 | + | 0.384354i | \(0.125576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1652.64 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3918.89 | −1.03456 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3588.98 | −0.935884 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2489.03 | 0.641187 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1753.19 | −0.446201 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 416.739 | 0.104798 | 0.0523991 | − | 0.998626i | \(-0.483313\pi\) | ||||
0.0523991 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1179.71 | −0.293152 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1245.06 | 0.305759 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6716.52 | 1.63021 | 0.815107 | − | 0.579310i | \(-0.196678\pi\) | ||||
0.815107 | + | 0.579310i | \(0.196678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13082.9 | 3.13874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3182.56 | 0.754772 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3740.77 | −0.877055 | −0.438528 | − | 0.898718i | \(-0.644500\pi\) | ||||
−0.438528 | + | 0.898718i | \(0.644500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −813.408 | −0.188556 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4235.85 | −0.970898 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7097.85 | −1.60879 | −0.804393 | − | 0.594097i | \(-0.797509\pi\) | ||||
−0.804393 | + | 0.594097i | \(0.797509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6263.03 | 1.40388 | 0.701941 | − | 0.712235i | \(-0.252317\pi\) | ||||
0.701941 | + | 0.712235i | \(0.252317\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3491.76 | −0.774107 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1282.29 | 0.281182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2907.85 | −0.630742 | −0.315371 | − | 0.948968i | \(-0.602129\pi\) | ||||
−0.315371 | + | 0.948968i | \(0.602129\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5884.23 | −1.26265 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8189.11 | 1.73851 | 0.869255 | − | 0.494364i | \(-0.164599\pi\) | ||||
0.869255 | + | 0.494364i | \(0.164599\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1639.18 | −0.344307 | −0.172154 | − | 0.985070i | \(-0.555073\pi\) | ||||
−0.172154 | + | 0.985070i | \(0.555073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 825.681 | 0.171611 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10098.2 | 2.07692 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3804.59 | 0.774393 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4131.22 | 0.832222 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5752.39 | 1.14696 | 0.573478 | − | 0.819221i | \(-0.305594\pi\) | ||||
0.573478 | + | 0.819221i | \(0.305594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1034.85 | −0.204241 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6413.88 | 1.25310 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −924.562 | −0.178825 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16481.1 | −3.15600 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1388.75 | −0.263305 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4283.38 | 0.804150 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 158.191 | 0.0294086 | 0.0147043 | − | 0.999892i | \(-0.495319\pi\) | ||||
0.0147043 | + | 0.999892i | \(0.495319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 622.798 | 0.114659 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4931.03 | 0.899078 | 0.449539 | − | 0.893261i | \(-0.351588\pi\) | ||||
0.449539 | + | 0.893261i | \(0.351588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7376.79 | 1.33214 | 0.666072 | − | 0.745888i | \(-0.267974\pi\) | ||||
0.666072 | + | 0.745888i | \(0.267974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3238.62 | 0.579287 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10018.1 | −1.77499 | −0.887497 | − | 0.460813i | \(-0.847558\pi\) | ||||
−0.887497 | + | 0.460813i | \(0.847558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8208.23 | −1.44067 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1687.01 | 0.293332 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5781.23 | 0.995901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1004.96 | 0.171523 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1622.45 | −0.274379 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6139.17 | −1.02876 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4863.38 | −0.807599 | −0.403800 | − | 0.914848i | \(-0.632311\pi\) | ||||
−0.403800 | + | 0.914848i | \(0.632311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7988.45 | −1.31461 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2175.27 | 0.354770 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3986.67 | 0.644415 | 0.322207 | − | 0.946669i | \(-0.395575\pi\) | ||||
0.322207 | + | 0.946669i | \(0.395575\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4023.15 | 0.644564 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15176.2 | 2.41008 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12207.1 | 1.92163 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −306.703 | −0.0478619 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8106.64 | −1.25414 | −0.627071 | − | 0.778962i | \(-0.715747\pi\) | ||||
−0.627071 | + | 0.778962i | \(0.715747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7883.34 | −1.20913 | −0.604564 | − | 0.796557i | \(-0.706652\pi\) | ||||
−0.604564 | + | 0.796557i | \(0.706652\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5026.70 | 0.764403 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8183.51 | 1.23389 | 0.616946 | − | 0.787005i | \(-0.288370\pi\) | ||||
0.616946 | + | 0.787005i | \(0.288370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 660.599 | 0.0987633 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8110.26 | −1.20235 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4731.13 | −0.695542 | −0.347771 | − | 0.937580i | \(-0.613061\pi\) | ||||
−0.347771 | + | 0.937580i | \(0.613061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3025.07 | −0.441037 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3466.63 | −0.501242 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3377.26 | 0.484312 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9595.07 | −1.36474 | −0.682368 | − | 0.731009i | \(-0.739050\pi\) | ||||
−0.682368 | + | 0.731009i | \(0.739050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6165.95 | −0.869882 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5298.52 | 0.741470 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9329.41 | −1.29506 | −0.647532 | − | 0.762038i | \(-0.724199\pi\) | ||||
−0.647532 | + | 0.762038i | \(0.724199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 333.373 | 0.0459075 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6432.96 | −0.878818 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1735.50 | −0.235216 | −0.117608 | − | 0.993060i | \(-0.537523\pi\) | ||||
−0.117608 | + | 0.993060i | \(0.537523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1065.46 | −0.143268 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4477.97 | 0.597425 | 0.298712 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298712 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8352.81 | −1.10571 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10063.4 | 1.32184 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4131.24 | 0.538463 | 0.269232 | − | 0.963075i | \(-0.413230\pi\) | ||||
0.269232 | + | 0.963075i | \(0.413230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2147.46 | −0.277754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4500.17 | −0.577617 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4012.25 | 0.511084 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7836.84 | 0.990730 | 0.495365 | − | 0.868685i | \(-0.335034\pi\) | ||||
0.495365 | + | 0.868685i | \(0.335034\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5378.47 | −0.674837 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4396.01 | −0.547447 | −0.273723 | − | 0.961808i | \(-0.588255\pi\) | ||||
−0.273723 | + | 0.961808i | \(0.588255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11893.9 | 1.47017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1017.27 | −0.124812 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20603.2 | 2.50925 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7113.24 | 0.859968 | 0.429984 | − | 0.902836i | \(-0.358519\pi\) | ||||
0.429984 | + | 0.902836i | \(0.358519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4769.71 | −0.572439 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6740.96 | 0.803150 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3286.84 | −0.388782 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8460.51 | 0.993557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6600.86 | −0.769625 | −0.384812 | − | 0.922995i | \(-0.625734\pi\) | ||||
−0.384812 | + | 0.922995i | \(0.625734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5950.49 | 0.688858 | 0.344429 | − | 0.938812i | \(-0.388073\pi\) | ||||
0.344429 | + | 0.938812i | \(0.388073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3748.58 | 0.430880 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2334.20 | 0.266413 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27901.8 | −3.16221 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5498.89 | −0.618855 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10387.9 | 1.16094 | 0.580470 | − | 0.814281i | \(-0.302869\pi\) | ||||
0.580470 | + | 0.814281i | \(0.302869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −953.901 | −0.105870 | −0.0529348 | − | 0.998598i | \(-0.516858\pi\) | ||||
−0.0529348 | + | 0.998598i | \(0.516858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2134.00 | −0.235212 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1424.13 | −0.155893 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1178.30 | −0.128103 | −0.0640516 | − | 0.997947i | \(-0.520402\pi\) | ||||
−0.0640516 | + | 0.997947i | \(0.520402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14275.0 | −1.54141 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7649.98 | 0.820455 | 0.410228 | − | 0.911983i | \(-0.365449\pi\) | ||||
0.410228 | + | 0.911983i | \(0.365449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7941.27 | −0.845960 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1542.71 | 0.163239 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8823.48 | −0.927407 | −0.463704 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463704 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15902.8 | 1.66038 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 204.839 | 0.0212454 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6546.28 | −0.674493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8649.10 | 0.885312 | 0.442656 | − | 0.896691i | \(-0.354036\pi\) | ||||
0.442656 | + | 0.896691i | \(0.354036\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11675.4 | 1.18728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6286.95 | 0.635168 | 0.317584 | − | 0.948230i | \(-0.397128\pi\) | ||||
0.317584 | + | 0.948230i | \(0.397128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5621.96 | −0.564309 | −0.282154 | − | 0.959369i | \(-0.591049\pi\) | ||||
−0.282154 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3945.54 | 0.393484 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6971.08 | 0.690757 | 0.345378 | − | 0.938464i | \(-0.387751\pi\) | ||||
0.345378 | + | 0.938464i | \(0.387751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14169.7 | −1.39508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5884.25 | −0.575651 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25954.8 | −2.52305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1547.97 | 0.149528 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3235.28 | −0.310552 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17953.1 | −1.71252 | −0.856259 | − | 0.516546i | \(-0.827217\pi\) | ||||
−0.856259 | + | 0.516546i | \(0.827217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16147.2 | 1.53066 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1997.86 | 0.188210 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7745.12 | 0.725129 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7211.61 | 0.671025 | 0.335513 | − | 0.942036i | \(-0.391090\pi\) | ||||
0.335513 | + | 0.942036i | \(0.391090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4303.70 | −0.397996 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17059.5 | −1.56799 | −0.783997 | − | 0.620764i | \(-0.786822\pi\) | ||||
−0.783997 | + | 0.620764i | \(0.786822\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14941.7 | −1.36499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5100.23 | 0.463108 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4303.13 | −0.388374 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7033.90 | 0.631023 | 0.315512 | − | 0.948922i | \(-0.397824\pi\) | ||||
0.315512 | + | 0.948922i | \(0.397824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1152.45 | −0.102770 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6905.46 | 0.612125 | 0.306063 | − | 0.952011i | \(-0.400988\pi\) | ||||
0.306063 | + | 0.952011i | \(0.400988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2603.59 | −0.229422 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1549.77 | 0.135754 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17053.4 | −1.48502 | −0.742512 | − | 0.669833i | \(-0.766366\pi\) | ||||
−0.742512 | + | 0.669833i | \(0.766366\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21999.4 | −1.90449 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7742.78 | 0.666378 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1167.61 | 0.0999047 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9668.07 | −0.822439 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −149.652 | −0.0126570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8408.62 | 0.707080 | 0.353540 | − | 0.935419i | \(-0.384978\pi\) | ||||
0.353540 | + | 0.935419i | \(0.384978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10039.2 | 0.839358 | 0.419679 | − | 0.907672i | \(-0.362143\pi\) | ||||
0.419679 | + | 0.907672i | \(0.362143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2171.58 | −0.180525 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27625.8 | 2.28349 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4116.04 | −0.336386 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12463.3 | 1.01285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3162.76 | 0.255585 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8677.70 | 0.697338 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36816.9 | 2.94215 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20681.5 | −1.64356 | −0.821780 | − | 0.569805i | \(-0.807019\pi\) | ||||
−0.821780 | + | 0.569805i | \(0.807019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2492.90 | 0.197018 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3041.74 | −0.239071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14433.2 | −1.12819 | −0.564095 | − | 0.825710i | \(-0.690775\pi\) | ||||
−0.564095 | + | 0.825710i | \(0.690775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17036.9 | 1.32444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9908.89 | −0.766121 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26135.7 | −2.00977 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5356.48 | 0.409675 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3260.33 | −0.248016 | −0.124008 | − | 0.992281i | \(-0.539575\pi\) | ||||
−0.124008 | + | 0.992281i | \(0.539575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20341.3 | −1.53908 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12772.2 | −0.961216 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20472.8 | 1.53255 | 0.766275 | − | 0.642513i | \(-0.222108\pi\) | ||||
0.766275 | + | 0.642513i | \(0.222108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7542.50 | 0.561620 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6626.49 | 0.490805 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6713.38 | 0.494621 | 0.247311 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247311 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16917.1 | −1.23986 | −0.619930 | − | 0.784657i | \(-0.712839\pi\) | ||||
−0.619930 | + | 0.784657i | \(0.712839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1579.86 | −0.115183 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24924.6 | 1.79831 | 0.899155 | − | 0.437631i | \(-0.144182\pi\) | ||||
0.899155 | + | 0.437631i | \(0.144182\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1423.32 | 0.102161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21410.4 | 1.52883 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8344.20 | 0.592764 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3997.16 | 0.282500 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14178.0 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18320.5 | 1.28164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4591.39 | −0.319568 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −202.904 | −0.0140510 | −0.00702552 | − | 0.999975i | \(-0.502236\pi\) | ||||
−0.00702552 | + | 0.999975i | \(0.502236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15204.9 | −1.04763 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8633.92 | −0.591898 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11092.1 | −0.756614 | −0.378307 | − | 0.925680i | \(-0.623494\pi\) | ||||
−0.378307 | + | 0.925680i | \(0.623494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8006.00 | 0.543380 | 0.271690 | − | 0.962385i | \(-0.412417\pi\) | ||||
0.271690 | + | 0.962385i | \(0.412417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8652.02 | 0.584307 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6499.15 | −0.436740 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19772.8 | −1.32216 | −0.661080 | − | 0.750315i | \(-0.729902\pi\) | ||||
−0.661080 | + | 0.750315i | \(0.729902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13900.8 | 0.924940 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7577.08 | −0.501695 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16760.8 | 1.10434 | 0.552171 | − | 0.833731i | \(-0.313800\pi\) | ||||
0.552171 | + | 0.833731i | \(0.313800\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4134.44 | 0.271084 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2059.18 | −0.134359 | −0.0671793 | − | 0.997741i | \(-0.521400\pi\) | ||||
−0.0671793 | + | 0.997741i | \(0.521400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9225.99 | 0.599070 | 0.299535 | − | 0.954085i | \(-0.403169\pi\) | ||||
0.299535 | + | 0.954085i | \(0.403169\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2876.09 | −0.185851 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51729.2 | 3.32663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8470.11 | −0.539495 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37504.8 | 2.37745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16197.8 | −1.02191 | −0.510954 | − | 0.859608i | \(-0.670708\pi\) | ||||
−0.510954 | + | 0.859608i | \(0.670708\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12159.6 | 0.763506 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1997.49 | −0.124832 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28854.2 | 1.79474 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2627.49 | 0.162664 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17673.4 | −1.08901 | −0.544506 | − | 0.838757i | \(-0.683283\pi\) | ||||
−0.544506 | + | 0.838757i | \(0.683283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26012.7 | −1.59540 | −0.797698 | − | 0.603057i | \(-0.793949\pi\) | ||||
−0.797698 | + | 0.603057i | \(0.793949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6747.80 | −0.411929 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23339.4 | −1.41818 | −0.709092 | − | 0.705116i | \(-0.750895\pi\) | ||||
−0.709092 | + | 0.705116i | \(0.750895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10615.8 | 0.642074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25701.2 | −1.54732 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13540.1 | −0.811434 | −0.405717 | − | 0.913999i | \(-0.632978\pi\) | ||||
−0.405717 | + | 0.913999i | \(0.632978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8436.80 | −0.503287 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13432.8 | 0.797663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4110.58 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6854.43 | 0.403338 | 0.201669 | − | 0.979454i | \(-0.435363\pi\) | ||||
0.201669 | + | 0.979454i | \(0.435363\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10009.8 | −0.586350 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10083.4 | −0.587997 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3680.70 | 0.213669 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 996.249 | 0.0575743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −43940.3 | −2.52801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −604.990 | −0.0346518 | −0.0173259 | − | 0.999850i | \(-0.505515\pi\) | ||||
−0.0173259 | + | 0.999850i | \(0.505515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3126.19 | 0.178262 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17954.2 | −1.01925 | −0.509627 | − | 0.860395i | \(-0.670217\pi\) | ||||
−0.509627 | + | 0.860395i | \(0.670217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −50451.5 | −2.85147 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4293.53 | −0.241598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17456.8 | 0.977987 | 0.488993 | − | 0.872288i | \(-0.337364\pi\) | ||||
0.488993 | + | 0.872288i | \(0.337364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8942.14 | −0.498776 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10508.2 | −0.583568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6539.53 | 0.361591 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17092.8 | 0.941013 | 0.470507 | − | 0.882397i | \(-0.344071\pi\) | ||||
0.470507 | + | 0.882397i | \(0.344071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −33222.8 | −1.82111 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15861.6 | 0.865703 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28948.4 | 1.57317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4239.73 | 0.229415 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24311.0 | −1.30986 | −0.654932 | − | 0.755687i | \(-0.727303\pi\) | ||||
−0.654932 | + | 0.755687i | \(0.727303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24872.0 | 1.33437 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2513.53 | −0.134277 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16959.7 | 0.902172 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26445.7 | −1.40083 | −0.700415 | − | 0.713736i | \(-0.747002\pi\) | ||||
−0.700415 | + | 0.713736i | \(0.747002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15958.5 | 0.841758 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6805.25 | −0.357446 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10309.2 | −0.539219 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18194.3 | −0.947671 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3042.17 | 0.157794 | 0.0788970 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788970 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7605.76 | −0.392862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4407.57 | −0.226721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4000.76 | −0.204944 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2285.89 | 0.116615 | 0.0583073 | − | 0.998299i | \(-0.481430\pi\) | ||||
0.0583073 | + | 0.998299i | \(0.481430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4958.35 | 0.251910 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47246.5 | −2.39053 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11996.9 | 0.604523 | 0.302262 | − | 0.953225i | \(-0.402258\pi\) | ||||
0.302262 | + | 0.953225i | \(0.402258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9571.76 | 0.480353 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22314.7 | −1.11529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6071.38 | −0.302218 | −0.151109 | − | 0.988517i | \(-0.548284\pi\) | ||||
−0.151109 | + | 0.988517i | \(0.548284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6638.21 | −0.329097 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4243.30 | −0.209517 | −0.104759 | − | 0.994498i | \(-0.533407\pi\) | ||||
−0.104759 | + | 0.994498i | \(0.533407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2892.24 | 0.142233 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13073.2 | −0.640326 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20602.1 | −1.00505 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34214.9 | −1.66248 | −0.831238 | − | 0.555917i | \(-0.812367\pi\) | ||||
−0.831238 | + | 0.555917i | \(0.812367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1111.44 | −0.0537889 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 384.028 | 0.0185115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13048.3 | 0.626485 | 0.313243 | − | 0.949673i | \(-0.398585\pi\) | ||||
0.313243 | + | 0.949673i | \(0.398585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3146.26 | 0.150464 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12372.4 | 0.589353 | 0.294676 | − | 0.955597i | \(-0.404788\pi\) | ||||
0.294676 | + | 0.955597i | \(0.404788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19813.8 | 0.940115 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9284.14 | 0.438783 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8319.82 | 0.391671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16603.3 | 0.778585 | 0.389292 | − | 0.921114i | \(-0.372720\pi\) | ||||
0.389292 | + | 0.921114i | \(0.372720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17912.9 | −0.836726 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16184.3 | −0.753050 | −0.376525 | − | 0.926406i | \(-0.622881\pi\) | ||||
−0.376525 | + | 0.926406i | \(0.622881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7397.01 | 0.342850 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34892.0 | −1.61099 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19197.7 | 0.882962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6776.64 | −0.310483 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20011.4 | −0.913345 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11031.6 | −0.501575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8065.72 | −0.365326 | −0.182663 | − | 0.983176i | \(-0.558472\pi\) | ||||
−0.182663 | + | 0.983176i | \(0.558472\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9976.57 | 0.450159 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49131.6 | −2.20850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34437.0 | −1.54211 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2169.35 | 0.0967784 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −543.463 | −0.0241536 | −0.0120768 | − | 0.999927i | \(-0.503844\pi\) | ||||
−0.0120768 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17599.1 | −0.779240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31585.9 | −1.39330 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34645.0 | −1.52253 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3745.54 | 0.163991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18929.9 | 0.825728 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7792.84 | 0.338667 | 0.169333 | − | 0.985559i | \(-0.445839\pi\) | ||||
0.169333 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20977.8 | −0.908300 | −0.454150 | − | 0.890925i | \(-0.650057\pi\) | ||||
−0.454150 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16703.4 | −0.720559 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8068.47 | −0.346781 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31332.4 | −1.34171 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26037.4 | −1.11089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21076.3 | −0.895940 | −0.447970 | − | 0.894049i | \(-0.647853\pi\) | ||||
−0.447970 | + | 0.894049i | \(0.647853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23531.1 | −0.996650 | −0.498325 | − | 0.866990i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866990i | \(0.666051\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3419.85 | −0.144320 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16665.2 | −0.700733 | −0.350367 | − | 0.936613i | \(-0.613943\pi\) | ||||
−0.350367 | + | 0.936613i | \(0.613943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7011.28 | −0.293741 | −0.146871 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146871 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7755.18 | 0.323735 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 67019.2 | 2.78761 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2160.59 | −0.0895452 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36999.1 | 1.52793 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14366.1 | 0.591149 | 0.295575 | − | 0.955320i | \(-0.404489\pi\) | ||||
0.295575 | + | 0.955320i | \(0.404489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1220.78 | 0.0500544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21840.2 | −0.892310 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2905.46 | 0.118285 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42335.3 | 1.71742 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4371.66 | 0.176720 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9238.82 | −0.372154 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15450.3 | 0.620172 | 0.310086 | − | 0.950709i | \(-0.399642\pi\) | ||||
0.310086 | + | 0.950709i | \(0.399642\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6156.95 | 0.246273 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 615.237 | 0.0245229 | 0.0122614 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122614 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40420.2 | 1.60550 | 0.802748 | − | 0.596319i | \(-0.203370\pi\) | ||||
0.802748 | + | 0.596319i | \(0.203370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26931.7 | −1.06600 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.1816 | 0.00162438 | 0.000812189 | − | 1.00000i | \(-0.499741\pi\) | ||||
0.000812189 | 1.00000i | \(0.499741\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −280.564 | −0.0110283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10146.8 | −0.397466 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41159.0 | −1.60670 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17488.5 | −0.680338 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30805.7 | 1.19429 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4071.23 | −0.157295 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16812.3 | 0.647332 | 0.323666 | − | 0.946171i | \(-0.395085\pi\) | ||||
0.323666 | + | 0.946171i | \(0.395085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15341.5 | −0.588689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7044.58 | 0.269396 | 0.134698 | − | 0.990887i | \(-0.456994\pi\) | ||||
0.134698 | + | 0.990887i | \(0.456994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43578.5 | −1.66085 | −0.830427 | − | 0.557127i | \(-0.811904\pi\) | ||||
−0.830427 | + | 0.557127i | \(0.811904\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2759.92 | 0.104829 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7888.43 | 0.298611 | 0.149305 | − | 0.988791i | \(-0.452296\pi\) | ||||
0.149305 | + | 0.988791i | \(0.452296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13011.6 | 0.490884 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10435.5 | 0.392371 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11671.2 | −0.437359 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16268.7 | 0.607602 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2465.79 | 0.0917842 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47349.9 | −1.75663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15189.3 | 0.561629 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 43955.0 | 1.61986 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4673.63 | 0.171665 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25762.6 | −0.943146 | −0.471573 | − | 0.881827i | \(-0.656314\pi\) | ||||
−0.471573 | + | 0.881827i | \(0.656314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10355.6 | −0.377859 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14667.6 | 0.533437 | 0.266718 | − | 0.963775i | \(-0.414061\pi\) | ||||
0.266718 | + | 0.963775i | \(0.414061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33717.5 | 1.22222 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11423.7 | −0.412739 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54957.1 | 1.97911 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13259.9 | 0.475957 | 0.237979 | − | 0.971270i | \(-0.423515\pi\) | ||||
0.237979 | + | 0.971270i | \(0.423515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −421.893 | −0.0150943 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5311.00 | −0.189397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10042.2 | 0.356957 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4644.09 | 0.164543 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22354.5 | −0.789482 | −0.394741 | − | 0.918792i | \(-0.629166\pi\) | ||||
−0.394741 | + | 0.918792i | \(0.629166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44445.0 | 1.56458 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13151.0 | −0.461462 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23945.0 | −0.837524 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32943.0 | 1.14856 | 0.574281 | − | 0.818659i | \(-0.305282\pi\) | ||||
0.574281 | + | 0.818659i | \(0.305282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19673.8 | −0.683738 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25878.6 | 0.896514 | 0.448257 | − | 0.893905i | \(-0.352045\pi\) | ||||
0.448257 | + | 0.893905i | \(0.352045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7131.06 | −0.246256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20363.9 | −0.700992 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4350.14 | −0.149272 | −0.0746360 | − | 0.997211i | \(-0.523779\pi\) | ||||
−0.0746360 | + | 0.997211i | \(0.523779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27152.0 | −0.928759 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26718.2 | 0.911037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31637.6 | 1.07539 | 0.537693 | − | 0.843140i | \(-0.319296\pi\) | ||||
0.537693 | + | 0.843140i | \(0.319296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2961.89 | −0.100361 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21891.2 | 0.739438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58248.9 | 1.96137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57754.3 | 1.93865 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12579.7 | 0.420950 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2668.40 | 0.0890144 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 882.920 | 0.0293617 | 0.0146809 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146809 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15418.5 | −0.511158 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22292.9 | −0.736781 | −0.368391 | − | 0.929671i | \(-0.620091\pi\) | ||||
−0.368391 | + | 0.929671i | \(0.620091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −103322. | −3.40426 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2680.21 | −0.0880363 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43227.9 | 1.41554 | 0.707770 | − | 0.706443i | \(-0.249702\pi\) | ||||
0.707770 | + | 0.706443i | \(0.249702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 81464.1 | 2.65945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12098.3 | −0.393751 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5466.42 | 0.177367 | 0.0886835 | − | 0.996060i | \(-0.471734\pi\) | ||||
0.0886835 | + | 0.996060i | \(0.471734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8607.82 | −0.278445 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16373.1 | 0.528025 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11638.6 | 0.374201 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18988.2 | 0.608658 | 0.304329 | − | 0.952567i | \(-0.401568\pi\) | ||||
0.304329 | + | 0.952567i | \(0.401568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12970.5 | 0.414509 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16186.7 | −0.515731 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38646.6 | −1.22763 | −0.613817 | − | 0.789449i | \(-0.710367\pi\) | ||||
−0.613817 | + | 0.789449i | \(0.710367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50230.1 | 1.59080 |
(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 | 1840.4.a.bb.1.4 | 10 | ||
4.3 | odd | 2 | 920.4.a.g.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.g.1.7 | ✓ | 10 | 4.3 | odd | 2 | ||
1840.4.a.bb.1.4 | 10 | 1.1 | even | 1 | trivial |