Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3173728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 29x^{2} + 118 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.90965\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.90965 | 1.73582 | 0.867912 | − | 0.496718i | \(-0.165462\pi\) | ||||
0.867912 | + | 0.496718i | \(0.165462\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.1047 | 2.01309 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10469 | −0.113642 | −0.0568212 | − | 0.998384i | \(-0.518096\pi\) | ||||
−0.0568212 | + | 0.998384i | \(0.518096\pi\) | |||||||
\(8\) | 39.7912 | 1.75854 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.3052 | 1.10477 | 0.552385 | − | 0.833589i | \(-0.313718\pi\) | ||||
0.552385 | + | 0.833589i | \(0.313718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.7328 | −1.31705 | −0.658523 | − | 0.752561i | \(-0.728818\pi\) | ||||
−0.658523 | + | 0.752561i | \(0.728818\pi\) | |||||||
\(14\) | −10.3333 | −0.197263 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 66.5234 | 1.03943 | ||||||||
\(17\) | 99.2210 | 1.41557 | 0.707783 | − | 0.706430i | \(-0.249695\pi\) | ||||
0.707783 | + | 0.706430i | \(0.249695\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 134.523 | 1.62430 | 0.812152 | − | 0.583445i | \(-0.198296\pi\) | ||||
0.812152 | + | 0.583445i | \(0.198296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 197.884 | 1.91769 | ||||||||
\(23\) | 76.4985 | 0.693524 | 0.346762 | − | 0.937953i | \(-0.387281\pi\) | ||||
0.346762 | + | 0.937953i | \(0.387281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −303.087 | −2.28616 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −33.8953 | −0.228772 | ||||||||
\(29\) | 236.691 | 1.51560 | 0.757801 | − | 0.652486i | \(-0.226274\pi\) | ||||
0.757801 | + | 0.652486i | \(0.226274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 243.628 | 1.41151 | 0.705756 | − | 0.708455i | \(-0.250607\pi\) | ||||
0.705756 | + | 0.708455i | \(0.250607\pi\) | |||||||
\(32\) | 8.27738 | 0.0457265 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 487.141 | 2.45717 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −57.4187 | −0.255124 | −0.127562 | − | 0.991831i | \(-0.540715\pi\) | ||||
−0.127562 | + | 0.991831i | \(0.540715\pi\) | |||||||
\(38\) | 660.463 | 2.81951 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −411.383 | −1.56701 | −0.783503 | − | 0.621389i | \(-0.786569\pi\) | ||||
−0.783503 | + | 0.621389i | \(0.786569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −102.884 | −0.364877 | −0.182439 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182439 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(44\) | 649.102 | 2.22400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 375.581 | 1.20384 | ||||||||
\(47\) | −260.442 | −0.808283 | −0.404142 | − | 0.914696i | \(-0.632430\pi\) | ||||
−0.404142 | + | 0.914696i | \(0.632430\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −338.570 | −0.987085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −994.187 | −2.65133 | ||||||||
\(53\) | 75.4706 | 0.195598 | 0.0977989 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977989 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −83.7480 | −0.199845 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1162.07 | 2.63082 | ||||||||
\(59\) | −39.2772 | −0.0866688 | −0.0433344 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433344 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −675.851 | −1.41859 | −0.709294 | − | 0.704912i | \(-0.750986\pi\) | ||||
−0.709294 | + | 0.704912i | \(0.750986\pi\) | |||||||
\(62\) | 1196.13 | 2.45014 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −491.548 | −0.960055 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 601.176 | 1.09620 | 0.548100 | − | 0.836413i | \(-0.315351\pi\) | ||||
0.548100 | + | 0.836413i | \(0.315351\pi\) | |||||||
\(68\) | 1597.92 | 2.84966 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 222.192 | 0.371400 | 0.185700 | − | 0.982607i | \(-0.440545\pi\) | ||||
0.185700 | + | 0.982607i | \(0.440545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 297.419 | 0.476852 | 0.238426 | − | 0.971161i | \(-0.423368\pi\) | ||||
0.238426 | + | 0.971161i | \(0.423368\pi\) | |||||||
\(74\) | −281.906 | −0.442850 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2166.46 | 3.26986 | ||||||||
\(77\) | −84.8297 | −0.125549 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −95.6999 | −0.136292 | −0.0681461 | − | 0.997675i | \(-0.521708\pi\) | ||||
−0.0681461 | + | 0.997675i | \(0.521708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2019.75 | −2.72005 | ||||||||
\(83\) | −3.08384 | −0.00407826 | −0.00203913 | − | 0.999998i | \(-0.500649\pi\) | ||||
−0.00203913 | + | 0.999998i | \(0.500649\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −505.126 | −0.633363 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1603.79 | 1.94278 | ||||||||
\(89\) | 1342.73 | 1.59920 | 0.799601 | − | 0.600532i | \(-0.205044\pi\) | ||||
0.799601 | + | 0.600532i | \(0.205044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 129.928 | 0.149672 | ||||||||
\(92\) | 1231.99 | 1.39612 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1278.68 | −1.40304 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1482.57 | −1.55188 | −0.775941 | − | 0.630806i | \(-0.782724\pi\) | ||||
−0.775941 | + | 0.630806i | \(0.782724\pi\) | |||||||
\(98\) | −1662.26 | −1.71341 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1535.82 | −1.51306 | −0.756532 | − | 0.653957i | \(-0.773108\pi\) | ||||
−0.756532 | + | 0.653957i | \(0.773108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 356.581 | 0.341116 | 0.170558 | − | 0.985348i | \(-0.445443\pi\) | ||||
0.170558 | + | 0.985348i | \(0.445443\pi\) | |||||||
\(104\) | −2456.42 | −2.31608 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 370.534 | 0.339523 | ||||||||
\(107\) | −1580.23 | −1.42773 | −0.713864 | − | 0.700285i | \(-0.753056\pi\) | ||||
−0.713864 | + | 0.700285i | \(0.753056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1189.98 | 1.04568 | 0.522842 | − | 0.852430i | \(-0.324872\pi\) | ||||
0.522842 | + | 0.852430i | \(0.324872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −140.011 | −0.118123 | ||||||||
\(113\) | −369.022 | −0.307209 | −0.153605 | − | 0.988132i | \(-0.549088\pi\) | ||||
−0.153605 | + | 0.988132i | \(0.549088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3811.84 | 3.05104 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −192.837 | −0.150442 | ||||||||
\(119\) | −208.829 | −0.160868 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 293.506 | 0.220516 | ||||||||
\(122\) | −3318.20 | −2.46242 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3923.55 | 2.84150 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1414.84 | 0.988560 | 0.494280 | − | 0.869303i | \(-0.335432\pi\) | ||||
0.494280 | + | 0.869303i | \(0.335432\pi\) | |||||||
\(128\) | −2479.55 | −1.71221 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −155.161 | −0.103484 | −0.0517422 | − | 0.998660i | \(-0.516477\pi\) | ||||
−0.0517422 | + | 0.998660i | \(0.516477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −283.130 | −0.184590 | ||||||||
\(134\) | 2951.57 | 1.90281 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3948.12 | 2.48933 | ||||||||
\(137\) | −2447.63 | −1.52639 | −0.763194 | − | 0.646169i | \(-0.776370\pi\) | ||||
−0.763194 | + | 0.646169i | \(0.776370\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1463.98 | 0.893329 | 0.446665 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446665 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1090.89 | 0.644685 | ||||||||
\(143\) | −2488.15 | −1.45503 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1460.22 | 0.827732 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −924.711 | −0.513586 | ||||||||
\(149\) | −3363.34 | −1.84923 | −0.924616 | − | 0.380899i | \(-0.875614\pi\) | ||||
−0.924616 | + | 0.380899i | \(0.875614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2004.07 | 1.08006 | 0.540029 | − | 0.841647i | \(-0.318413\pi\) | ||||
0.540029 | + | 0.841647i | \(0.318413\pi\) | |||||||
\(152\) | 5352.85 | 2.85640 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −416.485 | −0.217930 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 951.144 | 0.483500 | 0.241750 | − | 0.970339i | \(-0.422279\pi\) | ||||
0.241750 | + | 0.970339i | \(0.422279\pi\) | |||||||
\(158\) | −469.853 | −0.236579 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −161.005 | −0.0788137 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3152.95 | −1.51508 | −0.757539 | − | 0.652790i | \(-0.773598\pi\) | ||||
−0.757539 | + | 0.652790i | \(0.773598\pi\) | |||||||
\(164\) | −6625.19 | −3.15452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.1406 | −0.00707914 | ||||||||
\(167\) | −1886.55 | −0.874165 | −0.437083 | − | 0.899421i | \(-0.643988\pi\) | ||||
−0.437083 | + | 0.899421i | \(0.643988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1613.94 | 0.734610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1656.92 | −0.734529 | ||||||||
\(173\) | −1036.73 | −0.455615 | −0.227808 | − | 0.973706i | \(-0.573156\pi\) | ||||
−0.227808 | + | 0.973706i | \(0.573156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2681.24 | 1.14833 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6592.33 | 2.77593 | ||||||||
\(179\) | 3790.25 | 1.58266 | 0.791332 | − | 0.611387i | \(-0.209388\pi\) | ||||
0.791332 | + | 0.611387i | \(0.209388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 946.498 | 0.388689 | 0.194344 | − | 0.980933i | \(-0.437742\pi\) | ||||
0.194344 | + | 0.980933i | \(0.437742\pi\) | |||||||
\(182\) | 637.902 | 0.259805 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3043.97 | 1.21959 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3999.12 | 1.56387 | ||||||||
\(188\) | −4194.33 | −1.62714 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2618.92 | 0.992137 | 0.496068 | − | 0.868284i | \(-0.334777\pi\) | ||||
0.496068 | + | 0.868284i | \(0.334777\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2587.20 | −0.964927 | −0.482463 | − | 0.875916i | \(-0.660258\pi\) | ||||
−0.482463 | + | 0.875916i | \(0.660258\pi\) | |||||||
\(194\) | −7278.92 | −2.69379 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5452.57 | −1.98709 | ||||||||
\(197\) | 628.328 | 0.227241 | 0.113621 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2892.44 | −1.03035 | −0.515175 | − | 0.857085i | \(-0.672273\pi\) | ||||
−0.515175 | + | 0.857085i | \(0.672273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7540.32 | −2.62641 | ||||||||
\(203\) | −498.161 | −0.172237 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1750.69 | 0.592118 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4106.68 | −1.36898 | ||||||||
\(209\) | 5421.99 | 1.79448 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2864.38 | −0.934560 | −0.467280 | − | 0.884109i | \(-0.654766\pi\) | ||||
−0.467280 | + | 0.884109i | \(0.654766\pi\) | |||||||
\(212\) | 1215.43 | 0.393755 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7758.39 | −2.47828 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −512.761 | −0.160408 | ||||||||
\(218\) | 5842.39 | 1.81512 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6125.19 | −1.86437 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2244.32 | 0.673950 | 0.336975 | − | 0.941514i | \(-0.390596\pi\) | ||||
0.336975 | + | 0.941514i | \(0.390596\pi\) | |||||||
\(224\) | −17.4213 | −0.00519647 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1811.77 | −0.533261 | ||||||||
\(227\) | −5959.64 | −1.74253 | −0.871267 | − | 0.490809i | \(-0.836701\pi\) | ||||
−0.871267 | + | 0.490809i | \(0.836701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2181.56 | 0.629527 | 0.314764 | − | 0.949170i | \(-0.398075\pi\) | ||||
0.314764 | + | 0.949170i | \(0.398075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9418.23 | 2.66525 | ||||||||
\(233\) | −4013.04 | −1.12834 | −0.564170 | − | 0.825659i | \(-0.690804\pi\) | ||||
−0.564170 | + | 0.825659i | \(0.690804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −632.547 | −0.174472 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1025.28 | −0.279239 | ||||||||
\(239\) | 6489.56 | 1.75638 | 0.878190 | − | 0.478312i | \(-0.158751\pi\) | ||||
0.878190 | + | 0.478312i | \(0.158751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1886.47 | 0.504224 | 0.252112 | − | 0.967698i | \(-0.418875\pi\) | ||||
0.252112 | + | 0.967698i | \(0.418875\pi\) | |||||||
\(242\) | 1441.01 | 0.382777 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10884.4 | −2.85574 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8304.51 | −2.13928 | ||||||||
\(248\) | 9694.25 | 2.48220 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6307.08 | −1.58605 | −0.793026 | − | 0.609187i | \(-0.791496\pi\) | ||||
−0.793026 | + | 0.609187i | \(0.791496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3083.29 | 0.766184 | ||||||||
\(254\) | 6946.39 | 1.71597 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8241.35 | −2.01205 | ||||||||
\(257\) | −4384.12 | −1.06410 | −0.532050 | − | 0.846713i | \(-0.678578\pi\) | ||||
−0.532050 | + | 0.846713i | \(0.678578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 120.848 | 0.0289929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −761.785 | −0.179631 | ||||||||
\(263\) | 2927.40 | 0.686353 | 0.343177 | − | 0.939271i | \(-0.388497\pi\) | ||||
0.343177 | + | 0.939271i | \(0.388497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1390.07 | −0.320416 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9681.76 | 2.20674 | ||||||||
\(269\) | −1869.35 | −0.423703 | −0.211852 | − | 0.977302i | \(-0.567949\pi\) | ||||
−0.211852 | + | 0.977302i | \(0.567949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −111.800 | −0.0250603 | −0.0125302 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125302 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(272\) | 6600.52 | 1.47138 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12017.0 | −2.64954 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4454.02 | 0.966124 | 0.483062 | − | 0.875586i | \(-0.339525\pi\) | ||||
0.483062 | + | 0.875586i | \(0.339525\pi\) | |||||||
\(278\) | 7187.61 | 1.55066 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2236.64 | 0.474828 | 0.237414 | − | 0.971409i | \(-0.423700\pi\) | ||||
0.237414 | + | 0.971409i | \(0.423700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1629.67 | −0.342309 | −0.171155 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171155 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(284\) | 3578.34 | 0.747660 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12216.0 | −2.52568 | ||||||||
\(287\) | 865.832 | 0.178078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4931.81 | 1.00383 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4789.84 | 0.959945 | ||||||||
\(293\) | −2540.47 | −0.506538 | −0.253269 | − | 0.967396i | \(-0.581506\pi\) | ||||
−0.253269 | + | 0.967396i | \(0.581506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2284.76 | −0.448645 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16512.8 | −3.20994 | ||||||||
\(299\) | −4722.47 | −0.913403 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 216.539 | 0.0414655 | ||||||||
\(302\) | 9839.27 | 1.87479 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8948.96 | 1.68835 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4752.32 | 0.883482 | 0.441741 | − | 0.897143i | \(-0.354361\pi\) | ||||
0.441741 | + | 0.897143i | \(0.354361\pi\) | |||||||
\(308\) | −1366.16 | −0.252740 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7665.82 | −1.39771 | −0.698857 | − | 0.715262i | \(-0.746308\pi\) | ||||
−0.698857 | + | 0.715262i | \(0.746308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7864.29 | −1.42018 | −0.710089 | − | 0.704112i | \(-0.751345\pi\) | ||||
−0.710089 | + | 0.704112i | \(0.751345\pi\) | |||||||
\(314\) | 4669.78 | 0.839271 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1541.22 | −0.274368 | ||||||||
\(317\) | 3845.65 | 0.681367 | 0.340684 | − | 0.940178i | \(-0.389342\pi\) | ||||
0.340684 | + | 0.940178i | \(0.389342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9539.88 | 1.67439 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −790.481 | −0.136807 | ||||||||
\(323\) | 13347.5 | 2.29931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15479.9 | −2.62991 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16369.4 | −2.75564 | ||||||||
\(329\) | 548.148 | 0.0918553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −700.894 | −0.116389 | −0.0581943 | − | 0.998305i | \(-0.518534\pi\) | ||||
−0.0581943 | + | 0.998305i | \(0.518534\pi\) | |||||||
\(332\) | −49.6643 | −0.00820989 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9262.30 | −1.51740 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12070.9 | 1.95118 | 0.975588 | − | 0.219610i | \(-0.0704786\pi\) | ||||
0.975588 | + | 0.219610i | \(0.0704786\pi\) | |||||||
\(338\) | 7923.88 | 1.27515 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9819.47 | 1.55940 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1434.49 | 0.225817 | ||||||||
\(344\) | −4093.89 | −0.641651 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5090.01 | −0.790868 | ||||||||
\(347\) | 8064.60 | 1.24764 | 0.623819 | − | 0.781569i | \(-0.285580\pi\) | ||||
0.623819 | + | 0.781569i | \(0.285580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8726.16 | 1.33840 | 0.669199 | − | 0.743083i | \(-0.266637\pi\) | ||||
0.669199 | + | 0.743083i | \(0.266637\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 333.621 | 0.0505173 | ||||||||
\(353\) | 6125.68 | 0.923618 | 0.461809 | − | 0.886979i | \(-0.347201\pi\) | ||||
0.461809 | + | 0.886979i | \(0.347201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21624.2 | 3.21933 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18608.8 | 2.74723 | ||||||||
\(359\) | −567.297 | −0.0834005 | −0.0417002 | − | 0.999130i | \(-0.513277\pi\) | ||||
−0.0417002 | + | 0.999130i | \(0.513277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11237.6 | 1.63837 | ||||||||
\(362\) | 4646.98 | 0.674695 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2092.45 | 0.301303 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −380.770 | −0.0541581 | −0.0270791 | − | 0.999633i | \(-0.508621\pi\) | ||||
−0.0270791 | + | 0.999633i | \(0.508621\pi\) | |||||||
\(368\) | 5088.95 | 0.720869 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −158.842 | −0.0222282 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1049.75 | 0.145721 | 0.0728604 | − | 0.997342i | \(-0.476787\pi\) | ||||
0.0728604 | + | 0.997342i | \(0.476787\pi\) | |||||||
\(374\) | 19634.3 | 2.71461 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10363.3 | −1.42140 | ||||||||
\(377\) | −14611.6 | −1.99612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3574.95 | 0.484520 | 0.242260 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242260 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12858.0 | 1.72217 | ||||||||
\(383\) | −14221.2 | −1.89731 | −0.948656 | − | 0.316310i | \(-0.897556\pi\) | ||||
−0.948656 | + | 0.316310i | \(0.897556\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12702.3 | −1.67494 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23876.4 | −3.12407 | ||||||||
\(389\) | 7982.31 | 1.04041 | 0.520205 | − | 0.854042i | \(-0.325856\pi\) | ||||
0.520205 | + | 0.854042i | \(0.325856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7590.26 | 0.981729 | ||||||||
\(392\) | −13472.1 | −1.73583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3084.87 | 0.394451 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2355.10 | 0.297731 | 0.148865 | − | 0.988857i | \(-0.452438\pi\) | ||||
0.148865 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(398\) | −14200.9 | −1.78851 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6419.98 | −0.799498 | −0.399749 | − | 0.916625i | \(-0.630903\pi\) | ||||
−0.399749 | + | 0.916625i | \(0.630903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15039.8 | −1.85903 | ||||||||
\(404\) | −24733.8 | −3.04593 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2445.80 | −0.298973 | ||||||||
\(407\) | −2314.27 | −0.281853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8435.21 | −1.01979 | −0.509895 | − | 0.860236i | \(-0.670316\pi\) | ||||
−0.509895 | + | 0.860236i | \(0.670316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5742.63 | 0.686697 | ||||||||
\(413\) | 82.6662 | 0.00984925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −510.986 | −0.0602239 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26620.1 | 3.11491 | ||||||||
\(419\) | −9663.61 | −1.12673 | −0.563363 | − | 0.826210i | \(-0.690493\pi\) | ||||
−0.563363 | + | 0.826210i | \(0.690493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3723.76 | −0.431081 | −0.215540 | − | 0.976495i | \(-0.569151\pi\) | ||||
−0.215540 | + | 0.976495i | \(0.569151\pi\) | |||||||
\(422\) | −14063.1 | −1.62223 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3003.07 | 0.343966 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1422.46 | 0.161212 | ||||||||
\(428\) | −25449.2 | −2.87414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2671.60 | 0.298577 | 0.149288 | − | 0.988794i | \(-0.452302\pi\) | ||||
0.149288 | + | 0.988794i | \(0.452302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2723.52 | −0.302273 | −0.151137 | − | 0.988513i | \(-0.548293\pi\) | ||||
−0.151137 | + | 0.988513i | \(0.548293\pi\) | |||||||
\(434\) | −2517.48 | −0.278440 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19164.3 | 2.10505 | ||||||||
\(437\) | 10290.8 | 1.12649 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8281.91 | 0.900396 | 0.450198 | − | 0.892929i | \(-0.351353\pi\) | ||||
0.450198 | + | 0.892929i | \(0.351353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30072.6 | −3.23621 | ||||||||
\(443\) | −6286.69 | −0.674243 | −0.337121 | − | 0.941461i | \(-0.609453\pi\) | ||||
−0.337121 | + | 0.941461i | \(0.609453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11018.8 | 1.16986 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1034.56 | 0.109103 | ||||||||
\(449\) | −4737.77 | −0.497971 | −0.248986 | − | 0.968507i | \(-0.580097\pi\) | ||||
−0.248986 | + | 0.968507i | \(0.580097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16580.9 | −1.73118 | ||||||||
\(452\) | −5942.98 | −0.618439 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29259.8 | −3.02473 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13151.5 | −1.34617 | −0.673085 | − | 0.739565i | \(-0.735031\pi\) | ||||
−0.673085 | + | 0.739565i | \(0.735031\pi\) | |||||||
\(458\) | 10710.7 | 1.09275 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18163.7 | 1.83507 | 0.917533 | − | 0.397658i | \(-0.130177\pi\) | ||||
0.917533 | + | 0.397658i | \(0.130177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12788.0 | −1.28361 | −0.641803 | − | 0.766869i | \(-0.721813\pi\) | ||||
−0.641803 | + | 0.766869i | \(0.721813\pi\) | |||||||
\(464\) | 15745.5 | 1.57536 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19702.6 | −1.95860 | ||||||||
\(467\) | 3978.90 | 0.394265 | 0.197132 | − | 0.980377i | \(-0.436837\pi\) | ||||
0.197132 | + | 0.980377i | \(0.436837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1265.29 | −0.124575 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1562.89 | −0.152410 | ||||||||
\(473\) | −4146.77 | −0.403105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3363.13 | −0.323842 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 31861.5 | 3.04877 | ||||||||
\(479\) | 1095.93 | 0.104539 | 0.0522694 | − | 0.998633i | \(-0.483355\pi\) | ||||
0.0522694 | + | 0.998633i | \(0.483355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3544.62 | 0.336010 | ||||||||
\(482\) | 9261.90 | 0.875244 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4726.83 | 0.443917 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15345.9 | 1.42790 | 0.713951 | − | 0.700196i | \(-0.246904\pi\) | ||||
0.713951 | + | 0.700196i | \(0.246904\pi\) | |||||||
\(488\) | −26892.9 | −2.49464 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2148.29 | −0.197457 | −0.0987283 | − | 0.995114i | \(-0.531477\pi\) | ||||
−0.0987283 | + | 0.995114i | \(0.531477\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23484.7 | 2.14544 | ||||||||
\(494\) | −40772.3 | −3.71342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16207.0 | 1.46717 | ||||||||
\(497\) | −467.645 | −0.0422068 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 771.203 | 0.0691860 | 0.0345930 | − | 0.999401i | \(-0.488987\pi\) | ||||
0.0345930 | + | 0.999401i | \(0.488987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30965.6 | −2.75311 | ||||||||
\(503\) | −4031.11 | −0.357333 | −0.178666 | − | 0.983910i | \(-0.557178\pi\) | ||||
−0.178666 | + | 0.983910i | \(0.557178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15137.9 | 1.32996 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22785.6 | 1.99006 | ||||||||
\(509\) | −7337.75 | −0.638979 | −0.319489 | − | 0.947590i | \(-0.603511\pi\) | ||||
−0.319489 | + | 0.947590i | \(0.603511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −625.973 | −0.0541907 | ||||||||
\(512\) | −20625.7 | −1.78035 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21524.5 | −1.84709 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10497.1 | −0.892967 | ||||||||
\(518\) | 593.324 | 0.0503266 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6972.35 | −0.586304 | −0.293152 | − | 0.956066i | \(-0.594704\pi\) | ||||
−0.293152 | + | 0.956066i | \(0.594704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9040.75 | −0.755878 | −0.377939 | − | 0.925830i | \(-0.623367\pi\) | ||||
−0.377939 | + | 0.925830i | \(0.623367\pi\) | |||||||
\(524\) | −2498.81 | −0.208323 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14372.5 | 1.19139 | ||||||||
\(527\) | 24173.0 | 1.99809 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6314.97 | −0.519025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4559.71 | −0.371595 | ||||||||
\(533\) | 25395.8 | 2.06382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 23921.5 | 1.92771 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9177.85 | −0.735475 | ||||||||
\(539\) | −13646.1 | −1.09050 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22956.9 | 1.82439 | 0.912196 | − | 0.409755i | \(-0.134386\pi\) | ||||
0.912196 | + | 0.409755i | \(0.134386\pi\) | |||||||
\(542\) | −548.898 | −0.0435003 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 821.290 | 0.0647289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −734.019 | −0.0573755 | −0.0286877 | − | 0.999588i | \(-0.509133\pi\) | ||||
−0.0286877 | + | 0.999588i | \(0.509133\pi\) | |||||||
\(548\) | −39418.3 | −3.07275 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31840.5 | 2.46180 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 201.418 | 0.0154886 | ||||||||
\(554\) | 21867.7 | 1.67702 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 23576.9 | 1.79835 | ||||||||
\(557\) | 8428.97 | 0.641197 | 0.320599 | − | 0.947215i | \(-0.396116\pi\) | ||||
0.320599 | + | 0.947215i | \(0.396116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6351.34 | 0.480560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10981.1 | 0.824218 | ||||||||
\(563\) | −9091.27 | −0.680553 | −0.340276 | − | 0.940325i | \(-0.610521\pi\) | ||||
−0.340276 | + | 0.940325i | \(0.610521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8001.09 | −0.594189 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8841.30 | 0.653121 | ||||||||
\(569\) | −6766.12 | −0.498507 | −0.249253 | − | 0.968438i | \(-0.580185\pi\) | ||||
−0.249253 | + | 0.968438i | \(0.580185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3864.13 | −0.283203 | −0.141602 | − | 0.989924i | \(-0.545225\pi\) | ||||
−0.141602 | + | 0.989924i | \(0.545225\pi\) | |||||||
\(572\) | −40070.9 | −2.92911 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4250.93 | 0.309112 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3572.62 | 0.257765 | 0.128882 | − | 0.991660i | \(-0.458861\pi\) | ||||
0.128882 | + | 0.991660i | \(0.458861\pi\) | |||||||
\(578\) | 24213.5 | 1.74247 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.49052 | 0.000463463 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3041.85 | 0.216090 | ||||||||
\(584\) | 11834.6 | 0.838564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12472.8 | −0.879262 | ||||||||
\(587\) | −10186.2 | −0.716236 | −0.358118 | − | 0.933676i | \(-0.616581\pi\) | ||||
−0.358118 | + | 0.933676i | \(0.616581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32773.7 | 2.29273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3819.69 | −0.265183 | ||||||||
\(593\) | 2691.78 | 0.186405 | 0.0932025 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0932025 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −54165.6 | −3.72266 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23185.7 | −1.58551 | ||||||||
\(599\) | 4236.48 | 0.288978 | 0.144489 | − | 0.989506i | \(-0.453846\pi\) | ||||
0.144489 | + | 0.989506i | \(0.453846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10749.6 | 0.729595 | 0.364798 | − | 0.931087i | \(-0.381138\pi\) | ||||
0.364798 | + | 0.931087i | \(0.381138\pi\) | |||||||
\(602\) | 1063.13 | 0.0719768 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32274.9 | 2.17425 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19499.1 | 1.30386 | 0.651932 | − | 0.758278i | \(-0.273959\pi\) | ||||
0.651932 | + | 0.758278i | \(0.273959\pi\) | |||||||
\(608\) | 1113.50 | 0.0742738 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16077.8 | 1.06455 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1509.82 | −0.0994796 | −0.0497398 | − | 0.998762i | \(-0.515839\pi\) | ||||
−0.0497398 | + | 0.998762i | \(0.515839\pi\) | |||||||
\(614\) | 23332.2 | 1.53357 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3375.48 | −0.220782 | ||||||||
\(617\) | 27905.1 | 1.82077 | 0.910387 | − | 0.413758i | \(-0.135784\pi\) | ||||
0.910387 | + | 0.413758i | \(0.135784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1448.88 | 0.0940801 | 0.0470401 | − | 0.998893i | \(-0.485021\pi\) | ||||
0.0470401 | + | 0.998893i | \(0.485021\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37636.5 | −2.42619 | ||||||||
\(623\) | −2826.02 | −0.181737 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −38610.9 | −2.46518 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15317.9 | 0.973327 | ||||||||
\(629\) | −5697.15 | −0.361145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7476.02 | 0.471657 | 0.235829 | − | 0.971795i | \(-0.424220\pi\) | ||||
0.235829 | + | 0.971795i | \(0.424220\pi\) | |||||||
\(632\) | −3808.01 | −0.239675 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18880.8 | 1.18273 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20900.9 | 1.30004 | ||||||||
\(638\) | 46837.5 | 2.90645 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 50.3581 | 0.00310301 | 0.00155150 | − | 0.999999i | \(-0.499506\pi\) | ||||
0.00155150 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16728.8 | 1.02600 | 0.513002 | − | 0.858387i | \(-0.328533\pi\) | ||||
0.513002 | + | 0.858387i | \(0.328533\pi\) | |||||||
\(644\) | −2592.94 | −0.158659 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 65531.8 | 3.99120 | ||||||||
\(647\) | 13149.5 | 0.799010 | 0.399505 | − | 0.916731i | \(-0.369182\pi\) | ||||
0.399505 | + | 0.916731i | \(0.369182\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1583.07 | −0.0957490 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −50777.2 | −3.04998 | ||||||||
\(653\) | −4131.96 | −0.247620 | −0.123810 | − | 0.992306i | \(-0.539511\pi\) | ||||
−0.123810 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27366.6 | −1.62879 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2691.22 | 0.159445 | ||||||||
\(659\) | 4141.95 | 0.244837 | 0.122419 | − | 0.992479i | \(-0.460935\pi\) | ||||
0.122419 | + | 0.992479i | \(0.460935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25593.3 | −1.50600 | −0.753000 | − | 0.658021i | \(-0.771394\pi\) | ||||
−0.753000 | + | 0.658021i | \(0.771394\pi\) | |||||||
\(662\) | −3441.15 | −0.202030 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −122.710 | −0.00717178 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18106.5 | 1.05111 | ||||||||
\(668\) | −30382.3 | −1.75977 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27240.3 | −1.56721 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27185.3 | −1.55708 | −0.778541 | − | 0.627593i | \(-0.784040\pi\) | ||||
−0.778541 | + | 0.627593i | \(0.784040\pi\) | |||||||
\(674\) | 59264.1 | 3.38690 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25992.0 | 1.47883 | ||||||||
\(677\) | 3359.82 | 0.190736 | 0.0953680 | − | 0.995442i | \(-0.469597\pi\) | ||||
0.0953680 | + | 0.995442i | \(0.469597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3120.35 | 0.176360 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48210.2 | 2.70684 | ||||||||
\(683\) | 25176.1 | 1.41045 | 0.705223 | − | 0.708985i | \(-0.250847\pi\) | ||||
0.705223 | + | 0.708985i | \(0.250847\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7042.86 | 0.391979 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6844.22 | −0.379264 | ||||||||
\(689\) | −4659.01 | −0.257611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5980.72 | −0.329258 | −0.164629 | − | 0.986356i | \(-0.552643\pi\) | ||||
−0.164629 | + | 0.986356i | \(0.552643\pi\) | |||||||
\(692\) | −16696.3 | −0.917193 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 39594.4 | 2.16568 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40817.8 | −2.21820 | ||||||||
\(698\) | 42842.4 | 2.32322 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8195.53 | 0.441570 | 0.220785 | − | 0.975322i | \(-0.429138\pi\) | ||||
0.220785 | + | 0.975322i | \(0.429138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7724.17 | −0.414399 | ||||||||
\(704\) | −19811.9 | −1.06064 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30075.0 | 1.60324 | ||||||||
\(707\) | 3232.41 | 0.171948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6700.56 | 0.354929 | 0.177465 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177465 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 53428.8 | 2.81226 | ||||||||
\(713\) | 18637.2 | 0.978918 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 61040.8 | 3.18604 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2785.23 | −0.144769 | ||||||||
\(719\) | 319.573 | 0.0165759 | 0.00828794 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828794 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −750.492 | −0.0387653 | ||||||||
\(722\) | 55172.5 | 2.84392 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15243.1 | 0.782464 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4869.19 | 0.248402 | 0.124201 | − | 0.992257i | \(-0.460363\pi\) | ||||
0.124201 | + | 0.992257i | \(0.460363\pi\) | |||||||
\(728\) | 5170.00 | 0.263204 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10208.3 | −0.516508 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26969.4 | −1.35899 | −0.679495 | − | 0.733681i | \(-0.737801\pi\) | ||||
−0.679495 | + | 0.733681i | \(0.737801\pi\) | |||||||
\(734\) | −1869.45 | −0.0940090 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 633.208 | 0.0317124 | ||||||||
\(737\) | 24230.5 | 1.21105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29544.7 | −1.47066 | −0.735331 | − | 0.677708i | \(-0.762973\pi\) | ||||
−0.735331 | + | 0.677708i | \(0.762973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −779.859 | −0.0385842 | ||||||||
\(743\) | 37991.6 | 1.87588 | 0.937939 | − | 0.346800i | \(-0.112732\pi\) | ||||
0.937939 | + | 0.346800i | \(0.112732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5153.90 | 0.252946 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 64404.6 | 3.14821 | ||||||||
\(749\) | 3325.89 | 0.162250 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18817.9 | −0.914349 | −0.457174 | − | 0.889377i | \(-0.651138\pi\) | ||||
−0.457174 | + | 0.889377i | \(0.651138\pi\) | |||||||
\(752\) | −17325.5 | −0.840153 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −71738.0 | −3.46491 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6255.42 | 0.300339 | 0.150170 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150170 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(758\) | 17551.8 | 0.841041 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4900.19 | 0.233419 | 0.116709 | − | 0.993166i | \(-0.462765\pi\) | ||||
0.116709 | + | 0.993166i | \(0.462765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2504.54 | −0.118834 | ||||||||
\(764\) | 42176.8 | 1.99726 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −69821.3 | −3.29340 | ||||||||
\(767\) | 2424.69 | 0.114147 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21378.4 | 1.00250 | 0.501252 | − | 0.865301i | \(-0.332873\pi\) | ||||
0.501252 | + | 0.865301i | \(0.332873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41666.1 | −1.94248 | ||||||||
\(773\) | 7694.82 | 0.358038 | 0.179019 | − | 0.983846i | \(-0.442708\pi\) | ||||
0.179019 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −58993.4 | −2.72904 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39190.4 | 1.80597 | ||||||||
\(779\) | −55340.6 | −2.54529 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8955.50 | 0.410311 | ||||||||
\(782\) | 37265.5 | 1.70411 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22522.9 | −1.02600 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26712.1 | −1.20989 | −0.604945 | − | 0.796267i | \(-0.706805\pi\) | ||||
−0.604945 | + | 0.796267i | \(0.706805\pi\) | |||||||
\(788\) | 10119.0 | 0.457456 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 776.675 | 0.0349120 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41722.2 | 1.86835 | ||||||||
\(794\) | 11562.7 | 0.516808 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −46581.8 | −2.07418 | ||||||||
\(797\) | −12894.2 | −0.573070 | −0.286535 | − | 0.958070i | \(-0.592503\pi\) | ||||
−0.286535 | + | 0.958070i | \(0.592503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25841.3 | −1.14418 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −31519.9 | −1.38779 | ||||||||
\(803\) | 11987.5 | 0.526812 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −73840.4 | −3.22695 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −61111.9 | −2.66078 | ||||||||
\(809\) | 13581.6 | 0.590241 | 0.295120 | − | 0.955460i | \(-0.404640\pi\) | ||||
0.295120 | + | 0.955460i | \(0.404640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29019.1 | 1.25647 | 0.628235 | − | 0.778023i | \(-0.283777\pi\) | ||||
0.628235 | + | 0.778023i | \(0.283777\pi\) | |||||||
\(812\) | −8022.72 | −0.346727 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11362.3 | −0.489247 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13840.4 | −0.592672 | ||||||||
\(818\) | −41414.0 | −1.77018 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7950.00 | 0.337950 | 0.168975 | − | 0.985620i | \(-0.445954\pi\) | ||||
0.168975 | + | 0.985620i | \(0.445954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10499.7 | −0.444708 | −0.222354 | − | 0.974966i | \(-0.571374\pi\) | ||||
−0.222354 | + | 0.974966i | \(0.571374\pi\) | |||||||
\(824\) | 14188.8 | 0.599867 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 405.862 | 0.0170966 | ||||||||
\(827\) | −27097.0 | −1.13936 | −0.569682 | − | 0.821865i | \(-0.692934\pi\) | ||||
−0.569682 | + | 0.821865i | \(0.692934\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.331 | 0.0136299 | 0.00681497 | − | 0.999977i | \(-0.497831\pi\) | ||||
0.00681497 | + | 0.999977i | \(0.497831\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30344.7 | 1.26444 | ||||||||
\(833\) | −33593.3 | −1.39728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 87319.4 | 3.61245 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47444.9 | −1.95580 | ||||||||
\(839\) | 30523.3 | 1.25600 | 0.627999 | − | 0.778214i | \(-0.283874\pi\) | ||||
0.627999 | + | 0.778214i | \(0.283874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31633.8 | 1.29705 | ||||||||
\(842\) | −18282.4 | −0.748281 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −46130.0 | −1.88135 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −617.739 | −0.0250599 | ||||||||
\(848\) | 5020.56 | 0.203310 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4392.45 | −0.176935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32915.4 | 1.32122 | 0.660612 | − | 0.750728i | \(-0.270297\pi\) | ||||
0.660612 | + | 0.750728i | \(0.270297\pi\) | |||||||
\(854\) | 6983.76 | 0.279835 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −62879.3 | −2.51071 | ||||||||
\(857\) | −18915.5 | −0.753959 | −0.376979 | − | 0.926222i | \(-0.623037\pi\) | ||||
−0.376979 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31407.3 | −1.24750 | −0.623750 | − | 0.781624i | \(-0.714392\pi\) | ||||
−0.623750 | + | 0.781624i | \(0.714392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13116.6 | 0.518277 | ||||||||
\(863\) | −39038.2 | −1.53983 | −0.769916 | − | 0.638146i | \(-0.779702\pi\) | ||||
−0.769916 | + | 0.638146i | \(0.779702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13371.6 | −0.524693 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8257.85 | −0.322914 | ||||||||
\(869\) | −3857.20 | −0.150571 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37112.3 | −1.44375 | ||||||||
\(872\) | 47350.8 | 1.83888 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 50524.5 | 1.95540 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47360.9 | −1.82356 | −0.911781 | − | 0.410677i | \(-0.865293\pi\) | ||||
−0.911781 | + | 0.410677i | \(0.865293\pi\) | |||||||
\(878\) | 40661.3 | 1.56293 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5167.57 | −0.197616 | −0.0988081 | − | 0.995107i | \(-0.531503\pi\) | ||||
−0.0988081 | + | 0.995107i | \(0.531503\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31450.1 | 1.19862 | 0.599308 | − | 0.800518i | \(-0.295442\pi\) | ||||
0.599308 | + | 0.800518i | \(0.295442\pi\) | |||||||
\(884\) | −98644.3 | −3.75313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30865.4 | −1.17037 | ||||||||
\(887\) | −7264.18 | −0.274980 | −0.137490 | − | 0.990503i | \(-0.543904\pi\) | ||||
−0.137490 | + | 0.990503i | \(0.543904\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2977.80 | −0.112342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36144.1 | 1.35672 | ||||||||
\(893\) | −35035.5 | −1.31290 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5218.68 | 0.194580 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23260.8 | −0.864391 | ||||||||
\(899\) | 57664.6 | 2.13929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7488.27 | 0.276882 | ||||||||
\(902\) | −81406.2 | −3.00502 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14683.8 | −0.540239 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9535.80 | 0.349097 | 0.174549 | − | 0.984649i | \(-0.444153\pi\) | ||||
0.174549 | + | 0.984649i | \(0.444153\pi\) | |||||||
\(908\) | −95978.2 | −3.50787 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50779.1 | 1.84675 | 0.923373 | − | 0.383904i | \(-0.125421\pi\) | ||||
0.923373 | + | 0.383904i | \(0.125421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −124.295 | −0.00450554 | ||||||||
\(914\) | −64569.1 | −2.33671 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35133.4 | 1.26729 | ||||||||
\(917\) | 326.564 | 0.0117602 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44669.7 | −1.60339 | −0.801696 | − | 0.597732i | \(-0.796069\pi\) | ||||
−0.801696 | + | 0.597732i | \(0.796069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 89177.2 | 3.18535 | ||||||||
\(923\) | −13716.6 | −0.489151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −62784.8 | −2.22812 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1959.18 | 0.0693032 | ||||||||
\(929\) | −23431.4 | −0.827513 | −0.413756 | − | 0.910388i | \(-0.635783\pi\) | ||||
−0.413756 | + | 0.910388i | \(0.635783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45545.6 | −1.60333 | ||||||||
\(932\) | −64628.8 | −2.27144 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19535.0 | 0.684375 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25234.2 | 0.879792 | 0.439896 | − | 0.898049i | \(-0.355015\pi\) | ||||
0.439896 | + | 0.898049i | \(0.355015\pi\) | |||||||
\(938\) | −6212.12 | −0.216240 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47812.7 | −1.65637 | −0.828187 | − | 0.560452i | \(-0.810628\pi\) | ||||
−0.828187 | + | 0.560452i | \(0.810628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31470.2 | −1.08676 | ||||||||
\(944\) | −2612.86 | −0.0900860 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20359.2 | −0.699720 | ||||||||
\(947\) | 26024.4 | 0.893007 | 0.446504 | − | 0.894782i | \(-0.352669\pi\) | ||||
0.446504 | + | 0.894782i | \(0.352669\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18360.5 | −0.628037 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8309.56 | −0.282893 | ||||||||
\(953\) | −32403.9 | −1.10143 | −0.550716 | − | 0.834692i | \(-0.685645\pi\) | ||||
−0.550716 | + | 0.834692i | \(0.685645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 104512. | 3.53574 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5380.61 | 0.181461 | ||||||||
\(959\) | 5151.49 | 0.173462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29563.7 | 0.992369 | ||||||||
\(962\) | 17402.9 | 0.583254 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30381.0 | 1.01505 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50840.1 | 1.69070 | 0.845350 | − | 0.534213i | \(-0.179392\pi\) | ||||
0.845350 | + | 0.534213i | \(0.179392\pi\) | |||||||
\(968\) | 11679.0 | 0.387785 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17336.6 | 0.572975 | 0.286488 | − | 0.958084i | \(-0.407512\pi\) | ||||
0.286488 | + | 0.958084i | \(0.407512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3081.21 | −0.101520 | ||||||||
\(974\) | 75342.9 | 2.47859 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44960.0 | −1.47452 | ||||||||
\(977\) | 48360.1 | 1.58360 | 0.791799 | − | 0.610781i | \(-0.209145\pi\) | ||||
0.791799 | + | 0.610781i | \(0.209145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54118.9 | 1.76675 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10547.4 | −0.342750 | ||||||||
\(983\) | 56102.8 | 1.82035 | 0.910174 | − | 0.414226i | \(-0.135948\pi\) | ||||
0.910174 | + | 0.414226i | \(0.135948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 115302. | 3.72410 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −133742. | −4.30656 | ||||||||
\(989\) | −7870.50 | −0.253051 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46186.7 | −1.48049 | −0.740247 | − | 0.672335i | \(-0.765291\pi\) | ||||
−0.740247 | + | 0.672335i | \(0.765291\pi\) | |||||||
\(992\) | 2016.60 | 0.0645436 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2295.98 | −0.0732635 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16073.7 | −0.510592 | −0.255296 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255296 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(998\) | 3786.34 | 0.120095 | ||||||||
\(999\) | 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 | 675.4.a.x.1.4 | yes | 4 | |
3.2 | odd | 2 | inner | 675.4.a.x.1.1 | yes | 4 | |
5.2 | odd | 4 | 675.4.b.o.649.7 | 8 | |||
5.3 | odd | 4 | 675.4.b.o.649.2 | 8 | |||
5.4 | even | 2 | 675.4.a.w.1.1 | ✓ | 4 | ||
15.2 | even | 4 | 675.4.b.o.649.1 | 8 | |||
15.8 | even | 4 | 675.4.b.o.649.8 | 8 | |||
15.14 | odd | 2 | 675.4.a.w.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.w.1.1 | ✓ | 4 | 5.4 | even | 2 | ||
675.4.a.w.1.4 | yes | 4 | 15.14 | odd | 2 | ||
675.4.a.x.1.1 | yes | 4 | 3.2 | odd | 2 | inner | |
675.4.a.x.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
675.4.b.o.649.1 | 8 | 15.2 | even | 4 | |||
675.4.b.o.649.2 | 8 | 5.3 | odd | 4 | |||
675.4.b.o.649.7 | 8 | 5.2 | odd | 4 | |||
675.4.b.o.649.8 | 8 | 15.8 | even | 4 |