Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,6,Mod(1,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.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: | \(138.571620318\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 286x^{4} + 1126x^{3} + 1345x^{2} - 3193x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-18.0466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 43.4968 | 0.778095 | 0.389047 | − | 0.921218i | \(-0.372804\pi\) | ||||
0.389047 | + | 0.921218i | \(0.372804\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −238.200 | −1.83737 | −0.918686 | − | 0.394990i | \(-0.870748\pi\) | ||||
−0.918686 | + | 0.394990i | \(0.870748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −628.981 | −1.56731 | −0.783656 | − | 0.621195i | \(-0.786648\pi\) | ||||
−0.783656 | + | 0.621195i | \(0.786648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −966.503 | −1.58615 | −0.793076 | − | 0.609122i | \(-0.791522\pi\) | ||||
−0.793076 | + | 0.609122i | \(0.791522\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 758.898 | 0.636885 | 0.318443 | − | 0.947942i | \(-0.396840\pi\) | ||||
0.318443 | + | 0.947942i | \(0.396840\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2229.53 | −1.41687 | −0.708434 | − | 0.705777i | \(-0.750598\pi\) | ||||
−0.708434 | + | 0.705777i | \(0.750598\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1535.42 | −0.605212 | −0.302606 | − | 0.953116i | \(-0.597857\pi\) | ||||
−0.302606 | + | 0.953116i | \(0.597857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1233.03 | −0.394568 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1721.68 | 0.380153 | 0.190077 | − | 0.981769i | \(-0.439126\pi\) | ||||
0.190077 | + | 0.981769i | \(0.439126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5893.78 | −1.10151 | −0.550757 | − | 0.834666i | \(-0.685661\pi\) | ||||
−0.550757 | + | 0.834666i | \(0.685661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10360.9 | −1.42965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2878.30 | −0.345646 | −0.172823 | − | 0.984953i | \(-0.555289\pi\) | ||||
−0.172823 | + | 0.984953i | \(0.555289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1744.06 | 0.162032 | 0.0810162 | − | 0.996713i | \(-0.474183\pi\) | ||||
0.0810162 | + | 0.996713i | \(0.474183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15025.3 | −1.23923 | −0.619613 | − | 0.784907i | \(-0.712711\pi\) | ||||
−0.619613 | + | 0.784907i | \(0.712711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 27880.9 | 1.84103 | 0.920517 | − | 0.390702i | \(-0.127768\pi\) | ||||
0.920517 | + | 0.390702i | \(0.127768\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 39932.3 | 2.37593 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36718.5 | 1.79554 | 0.897771 | − | 0.440462i | \(-0.145185\pi\) | ||||
0.897771 | + | 0.440462i | \(0.145185\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −27358.7 | −1.21952 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11248.2 | 0.420681 | 0.210340 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210340 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21070.7 | −0.725027 | −0.362513 | − | 0.931979i | \(-0.618081\pi\) | ||||
−0.362513 | + | 0.931979i | \(0.618081\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42039.8 | −1.23418 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 27761.0 | 0.755523 | 0.377761 | − | 0.925903i | \(-0.376694\pi\) | ||||
0.377761 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8983.56 | −0.211496 | −0.105748 | − | 0.994393i | \(-0.533724\pi\) | ||||
−0.105748 | + | 0.994393i | \(0.533724\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2793.24 | −0.0613481 | −0.0306740 | − | 0.999529i | \(-0.509765\pi\) | ||||
−0.0306740 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 149823. | 2.87974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21609.0 | 0.389554 | 0.194777 | − | 0.980848i | \(-0.437602\pi\) | ||||
0.194777 | + | 0.980848i | \(0.437602\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 48373.7 | 0.770750 | 0.385375 | − | 0.922760i | \(-0.374072\pi\) | ||||
0.385375 | + | 0.922760i | \(0.374072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33009.7 | 0.495557 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −136005. | −1.82004 | −0.910018 | − | 0.414569i | \(-0.863932\pi\) | ||||
−0.910018 | + | 0.414569i | \(0.863932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 230221. | 2.91435 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −96977.5 | −1.10246 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −130323. | −1.40634 | −0.703172 | − | 0.711019i | \(-0.748234\pi\) | ||||
−0.703172 | + | 0.711019i | \(0.748234\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −141630. | −1.38151 | −0.690753 | − | 0.723091i | \(-0.742721\pi\) | ||||
−0.690753 | + | 0.723091i | \(0.742721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 67778.9 | 0.629508 | 0.314754 | − | 0.949173i | \(-0.398078\pi\) | ||||
0.314754 | + | 0.949173i | \(0.398078\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −138518. | −1.16962 | −0.584811 | − | 0.811170i | \(-0.698831\pi\) | ||||
−0.584811 | + | 0.811170i | \(0.698831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116731. | 0.941066 | 0.470533 | − | 0.882382i | \(-0.344062\pi\) | ||||
0.470533 | + | 0.882382i | \(0.344062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 168277. | 1.23974 | 0.619869 | − | 0.784705i | \(-0.287186\pi\) | ||||
0.619869 | + | 0.784705i | \(0.287186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −66785.9 | −0.470912 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −180770. | −1.17019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 234566. | 1.45647 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −189560. | −1.08511 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −114407. | −0.629424 | −0.314712 | − | 0.949187i | \(-0.601908\pi\) | ||||
−0.314712 | + | 0.949187i | \(0.601908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 243693. | 1.24070 | 0.620348 | − | 0.784327i | \(-0.286991\pi\) | ||||
0.620348 | + | 0.784327i | \(0.286991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 531075. | 2.60331 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −245544. | −1.11771 | −0.558854 | − | 0.829266i | \(-0.688759\pi\) | ||||
−0.558854 | + | 0.829266i | \(0.688759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −274623. | −1.20559 | −0.602795 | − | 0.797896i | \(-0.705946\pi\) | ||||
−0.602795 | + | 0.797896i | \(0.705946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 607912. | 2.48600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 74887.8 | 0.295795 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 187023. | 0.690126 | 0.345063 | − | 0.938580i | \(-0.387858\pi\) | ||||
0.345063 | + | 0.938580i | \(0.387858\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −504788. | −1.80164 | −0.900818 | − | 0.434198i | \(-0.857032\pi\) | ||||
−0.900818 | + | 0.434198i | \(0.857032\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −256361. | −0.857082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −307900. | −0.996920 | −0.498460 | − | 0.866913i | \(-0.666101\pi\) | ||||
−0.498460 | + | 0.866913i | \(0.666101\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 365737. | 1.11200 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 269060. | 0.793194 | 0.396597 | − | 0.917993i | \(-0.370191\pi\) | ||||
0.396597 | + | 0.917993i | \(0.370191\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 136016. | 0.377396 | 0.188698 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188698 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 562836. | 1.51588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −654874. | −1.66358 | −0.831788 | − | 0.555094i | \(-0.812682\pi\) | ||||
−0.831788 | + | 0.555094i | \(0.812682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 293707. | 0.724968 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −306491. | −0.714965 | −0.357482 | − | 0.933920i | \(-0.616365\pi\) | ||||
−0.357482 | + | 0.933920i | \(0.616365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 330963. | 0.750901 | 0.375450 | − | 0.926842i | \(-0.377488\pi\) | ||||
0.375450 | + | 0.926842i | \(0.377488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −125197. | −0.268945 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −477333. | −0.998199 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 303420. | 0.601811 | 0.300906 | − | 0.953654i | \(-0.402711\pi\) | ||||
0.300906 | + | 0.953654i | \(0.402711\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −43319.2 | −0.0837119 | −0.0418559 | − | 0.999124i | \(-0.513327\pi\) | ||||
−0.0418559 | + | 0.999124i | \(0.513327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 160510. | 0.294671 | 0.147335 | − | 0.989087i | \(-0.452930\pi\) | ||||
0.147335 | + | 0.989087i | \(0.452930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −446301. | −0.798905 | −0.399452 | − | 0.916754i | \(-0.630800\pi\) | ||||
−0.399452 | + | 0.916754i | \(0.630800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −410105. | −0.698482 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 75861.1 | 0.126077 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.40233e6 | 2.22068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −295670. | −0.457195 | −0.228598 | − | 0.973521i | \(-0.573414\pi\) | ||||
−0.228598 | + | 0.973521i | \(0.573414\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −653551. | −0.964236 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.40390e6 | 2.02389 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −733478. | −1.01020 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 591927. | 0.797087 | 0.398544 | − | 0.917149i | \(-0.369516\pi\) | ||||
0.398544 | + | 0.917149i | \(0.369516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21754.7 | −0.0280213 | −0.0140106 | − | 0.999902i | \(-0.504460\pi\) | ||||
−0.0140106 | + | 0.999902i | \(0.504460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20550e6 | 1.51907 | 0.759536 | − | 0.650465i | \(-0.225426\pi\) | ||||
0.759536 | + | 0.650465i | \(0.225426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 482208. | 0.581895 | 0.290947 | − | 0.956739i | \(-0.406030\pi\) | ||||
0.290947 | + | 0.956739i | \(0.406030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.21273e6 | 1.43250 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 78381.2 | 0.0887600 | 0.0443800 | − | 0.999015i | \(-0.485869\pi\) | ||||
0.0443800 | + | 0.999015i | \(0.485869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.60921e6 | 1.78472 | 0.892359 | − | 0.451327i | \(-0.149049\pi\) | ||||
0.892359 | + | 0.451327i | \(0.149049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.73693e6 | 1.84870 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.15485e6 | 2.24737 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −902802. | −0.904499 | −0.452250 | − | 0.891891i | \(-0.649378\pi\) | ||||
−0.452250 | + | 0.891891i | \(0.649378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 965750. | 0.948556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −848294. | −0.801150 | −0.400575 | − | 0.916264i | \(-0.631190\pi\) | ||||
−0.400575 | + | 0.916264i | \(0.631190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 685611. | 0.635080 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.07974e6 | 0.962568 | 0.481284 | − | 0.876565i | \(-0.340171\pi\) | ||||
0.481284 | + | 0.876565i | \(0.340171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.59714e6 | 1.39710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.05599e6 | −0.889775 | −0.444888 | − | 0.895586i | \(-0.646756\pi\) | ||||
−0.444888 | + | 0.895586i | \(0.646756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 394981. | 0.326703 | 0.163351 | − | 0.986568i | \(-0.447770\pi\) | ||||
0.163351 | + | 0.986568i | \(0.447770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 775550. | 0.618412 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 613031. | 0.480046 | 0.240023 | − | 0.970767i | \(-0.422845\pi\) | ||||
0.240023 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 64392.2 | 0.0486483 | 0.0243241 | − | 0.999704i | \(-0.492257\pi\) | ||||
0.0243241 | + | 0.999704i | \(0.492257\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.21208e6 | −1.64186 | −0.820928 | − | 0.571032i | \(-0.806543\pi\) | ||||
−0.820928 | + | 0.571032i | \(0.806543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −415435. | −0.297713 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −843930. | −0.594377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.19315e6 | 0.811940 | 0.405970 | − | 0.913886i | \(-0.366934\pi\) | ||||
0.405970 | + | 0.913886i | \(0.366934\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 489260. | 0.327329 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.48399e6 | 0.959959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.57902e6 | 2.27692 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −916508. | −0.564139 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 218811. | 0.132503 | 0.0662513 | − | 0.997803i | \(-0.478896\pi\) | ||||
0.0662513 | + | 0.997803i | \(0.478896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.74472e6 | 1.60915 | 0.804577 | − | 0.593848i | \(-0.202392\pi\) | ||||
0.804577 | + | 0.593848i | \(0.202392\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.22904e6 | −0.709098 | −0.354549 | − | 0.935038i | \(-0.615366\pi\) | ||||
−0.354549 | + | 0.935038i | \(0.615366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −317742. | −0.177593 | −0.0887967 | − | 0.996050i | \(-0.528302\pi\) | ||||
−0.0887967 | + | 0.996050i | \(0.528302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08291e6 | −0.595819 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.69199e6 | −0.902383 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19172e6 | 0.625846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.64123e6 | −3.38266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.89037e6 | −1.45005 | −0.725026 | − | 0.688721i | \(-0.758172\pi\) | ||||
−0.725026 | + | 0.688721i | \(0.758172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.20751e6 | 0.587869 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −65398.3 | −0.0313683 | −0.0156842 | − | 0.999877i | \(-0.504993\pi\) | ||||
−0.0156842 | + | 0.999877i | \(0.504993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.70707e6 | 1.72642 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.50845e6 | −2.52810 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.54353e6 | −1.57984 | −0.789919 | − | 0.613211i | \(-0.789878\pi\) | ||||
−0.789919 | + | 0.613211i | \(0.789878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.13278e6 | −0.497833 | −0.248916 | − | 0.968525i | \(-0.580074\pi\) | ||||
−0.248916 | + | 0.968525i | \(0.580074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.33228e6 | 0.569063 | 0.284531 | − | 0.958667i | \(-0.408162\pi\) | ||||
0.284531 | + | 0.958667i | \(0.408162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −390756. | −0.164564 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17438.3 | −0.00714115 | −0.00357057 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357057 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.49471e6 | 1.00752 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −121497. | −0.0477346 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.92930e6 | 0.747713 | 0.373857 | − | 0.927486i | \(-0.378035\pi\) | ||||
0.373857 | + | 0.927486i | \(0.378035\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.74636e6 | −3.29908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.25187e6 | 0.838053 | 0.419026 | − | 0.907974i | \(-0.362372\pi\) | ||||
0.419026 | + | 0.907974i | \(0.362372\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.66401e6 | −0.602981 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −937118. | −0.335117 | −0.167558 | − | 0.985862i | \(-0.553588\pi\) | ||||
−0.167558 | + | 0.985862i | \(0.553588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.13598e6 | 1.78907 | 0.894533 | − | 0.447001i | \(-0.147508\pi\) | ||||
0.894533 | + | 0.447001i | \(0.147508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.51684e6 | 2.24071 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.90747e6 | −0.639123 | −0.319562 | − | 0.947566i | \(-0.603536\pi\) | ||||
−0.319562 | + | 0.947566i | \(0.603536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.16523e6 | −0.385451 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 939925. | 0.303110 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.88120e6 | 0.599045 | 0.299522 | − | 0.954089i | \(-0.403173\pi\) | ||||
0.299522 | + | 0.954089i | \(0.403173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.92637e6 | 1.21935 | 0.609677 | − | 0.792650i | \(-0.291299\pi\) | ||||
0.609677 | + | 0.792650i | \(0.291299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.69636e6 | 1.74717 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.81039e6 | 0.541735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.29230e6 | −0.381991 | −0.190996 | − | 0.981591i | \(-0.561172\pi\) | ||||
−0.190996 | + | 0.981591i | \(0.561172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.67932e6 | −0.772946 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.10410e6 | 0.599717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.51195e6 | −0.420729 | −0.210365 | − | 0.977623i | \(-0.567465\pi\) | ||||
−0.210365 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 728989. | 0.200454 | 0.100227 | − | 0.994965i | \(-0.468043\pi\) | ||||
0.100227 | + | 0.994965i | \(0.468043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −935741. | −0.251295 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.01904e6 | 1.33214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.55233e6 | −0.921127 | −0.460564 | − | 0.887627i | \(-0.652353\pi\) | ||||
−0.460564 | + | 0.887627i | \(0.652353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 912422. | 0.233871 | 0.116935 | − | 0.993140i | \(-0.462693\pi\) | ||||
0.116935 | + | 0.993140i | \(0.462693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.42327e6 | 0.857506 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 704468. | 0.174462 | 0.0872308 | − | 0.996188i | \(-0.472198\pi\) | ||||
0.0872308 | + | 0.996188i | \(0.472198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.89511e6 | 0.458801 | 0.229401 | − | 0.973332i | \(-0.426323\pi\) | ||||
0.229401 | + | 0.973332i | \(0.426323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.91579e6 | −1.41616 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.18292e6 | 1.21327 | 0.606637 | − | 0.794979i | \(-0.292518\pi\) | ||||
0.606637 | + | 0.794979i | \(0.292518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.09698e6 | −0.253955 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00139e7 | 2.26764 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.14278e6 | −0.703920 | −0.351960 | − | 0.936015i | \(-0.614485\pi\) | ||||
−0.351960 | + | 0.936015i | \(0.614485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.24377e6 | −1.80665 | −0.903324 | − | 0.428958i | \(-0.858881\pi\) | ||||
−0.903324 | + | 0.428958i | \(0.858881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.70691e6 | −0.370049 | −0.185025 | − | 0.982734i | \(-0.559236\pi\) | ||||
−0.185025 | + | 0.982734i | \(0.559236\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.29616e6 | −1.12375 | −0.561874 | − | 0.827223i | \(-0.689919\pi\) | ||||
−0.561874 | + | 0.827223i | \(0.689919\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.61267e6 | −1.38818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.45060e6 | 1.94226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.74907e6 | 0.559051 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.97109e6 | 1.18909 | 0.594545 | − | 0.804063i | \(-0.297332\pi\) | ||||
0.594545 | + | 0.804063i | \(0.297332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78188e6 | 0.548247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.66864e6 | −1.09427 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.86439e6 | 0.738344 | 0.369172 | − | 0.929361i | \(-0.379641\pi\) | ||||
0.369172 | + | 0.929361i | \(0.379641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.72054e6 | 0.883665 | 0.441832 | − | 0.897098i | \(-0.354329\pi\) | ||||
0.441832 | + | 0.897098i | \(0.354329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30658e6 | 0.242114 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.13988e6 | 0.388597 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.76698e6 | 1.03680 | 0.518402 | − | 0.855137i | \(-0.326527\pi\) | ||||
0.518402 | + | 0.855137i | \(0.326527\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.56779e6 | 0.276292 | 0.138146 | − | 0.990412i | \(-0.455886\pi\) | ||||
0.138146 | + | 0.990412i | \(0.455886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.16047e6 | −1.07494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.02710e7 | 1.75719 | 0.878594 | − | 0.477570i | \(-0.158482\pi\) | ||||
0.878594 | + | 0.477570i | \(0.158482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 665350. | 0.112719 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.94817e6 | 0.489817 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.75365e7 | −2.88548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −329958. | −0.0532554 | −0.0266277 | − | 0.999645i | \(-0.508477\pi\) | ||||
−0.0266277 | + | 0.999645i | \(0.508477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.54496e6 | −1.52588 | −0.762939 | − | 0.646470i | \(-0.776244\pi\) | ||||
−0.762939 | + | 0.646470i | \(0.776244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.47278e6 | −0.701538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.07883e6 | −0.633718 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.68564e6 | −0.257008 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.02508e6 | −0.910077 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.51166e7 | −3.72383 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.26583e7 | 1.85944 | 0.929721 | − | 0.368266i | \(-0.120048\pi\) | ||||
0.929721 | + | 0.368266i | \(0.120048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.07743e6 | 0.732239 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 852516. | 0.121824 | 0.0609122 | − | 0.998143i | \(-0.480599\pi\) | ||||
0.0609122 | + | 0.998143i | \(0.480599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.83855e6 | −0.538627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.14728e6 | −0.715755 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.73795e6 | 0.510500 | 0.255250 | − | 0.966875i | \(-0.417842\pi\) | ||||
0.255250 | + | 0.966875i | \(0.417842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.45220e7 | 1.96560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.40018e6 | 0.718021 | 0.359011 | − | 0.933333i | \(-0.383114\pi\) | ||||
0.359011 | + | 0.933333i | \(0.383114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.31954e6 | 0.964634 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.31015e6 | −0.946555 | −0.473277 | − | 0.880913i | \(-0.656929\pi\) | ||||
−0.473277 | + | 0.880913i | \(0.656929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.20437e6 | 0.154585 | 0.0772926 | − | 0.997008i | \(-0.475372\pi\) | ||||
0.0772926 | + | 0.997008i | \(0.475372\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.89321e6 | 0.238797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.18554e7 | −1.48244 | −0.741219 | − | 0.671263i | \(-0.765752\pi\) | ||||
−0.741219 | + | 0.671263i | \(0.765752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.15226e7 | −1.41615 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.30953e7 | −2.81418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −758999. | −0.0909172 | −0.0454586 | − | 0.998966i | \(-0.514475\pi\) | ||||
−0.0454586 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31404e7 | 1.56070 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.25788e7 | −1.46893 | −0.734466 | − | 0.678645i | \(-0.762567\pi\) | ||||
−0.734466 | + | 0.678645i | \(0.762567\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.86291e6 | −0.910523 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50146e7 | 1.70980 | 0.854902 | − | 0.518790i | \(-0.173617\pi\) | ||||
0.854902 | + | 0.518790i | \(0.173617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.13086e6 | −1.03116 | −0.515579 | − | 0.856842i | \(-0.672423\pi\) | ||||
−0.515579 | + | 0.856842i | \(0.672423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.02029e7 | 1.13327 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.70428e7 | −1.87745 | −0.938726 | − | 0.344664i | \(-0.887993\pi\) | ||||
−0.938726 | + | 0.344664i | \(0.887993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.69470e7 | −2.92016 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.33457e7 | −1.43447 | −0.717234 | − | 0.696833i | \(-0.754592\pi\) | ||||
−0.717234 | + | 0.696833i | \(0.754592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.54154e6 | −0.374524 | −0.187262 | − | 0.982310i | \(-0.559961\pi\) | ||||
−0.187262 | + | 0.982310i | \(0.559961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.40154e6 | −0.776417 | −0.388209 | − | 0.921571i | \(-0.626906\pi\) | ||||
−0.388209 | + | 0.921571i | \(0.626906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.23964e7 | 3.34408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.39207e6 | −0.449748 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.18434e6 | −0.220137 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.09670e6 | 0.409601 | 0.204801 | − | 0.978804i | \(-0.434345\pi\) | ||||
0.204801 | + | 0.978804i | \(0.434345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.97634e6 | −0.489752 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.85947e7 | −3.76859 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.04505e6 | −0.677234 | −0.338617 | − | 0.940924i | \(-0.609959\pi\) | ||||
−0.338617 | + | 0.940924i | \(0.609959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.48089e6 | −0.904319 | −0.452159 | − | 0.891937i | \(-0.649346\pi\) | ||||
−0.452159 | + | 0.891937i | \(0.649346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.50542e6 | −0.798794 | −0.399397 | − | 0.916778i | \(-0.630781\pi\) | ||||
−0.399397 | + | 0.916778i | \(0.630781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.07489e6 | −0.659338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.14712e7 | −1.05275 | −0.526374 | − | 0.850253i | \(-0.676449\pi\) | ||||
−0.526374 | + | 0.850253i | \(0.676449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.05999e7 | 0.965379 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.16294e7 | −1.04314 | −0.521571 | − | 0.853208i | \(-0.674654\pi\) | ||||
−0.521571 | + | 0.853208i | \(0.674654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.90433e6 | 0.614636 | 0.307318 | − | 0.951607i | \(-0.400568\pi\) | ||||
0.307318 | + | 0.951607i | \(0.400568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.31001e7 | 2.02562 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.64351e6 | −0.230073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.32531e7 | 1.13634 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.35548e6 | −0.285573 | −0.142787 | − | 0.989753i | \(-0.545606\pi\) | ||||
−0.142787 | + | 0.989753i | \(0.545606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.27857e6 | 0.526488 | 0.263244 | − | 0.964729i | \(-0.415208\pi\) | ||||
0.263244 | + | 0.964729i | \(0.415208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.10430e7 | 2.58398 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.03583e6 | 0.495091 | 0.247546 | − | 0.968876i | \(-0.420376\pi\) | ||||
0.247546 | + | 0.968876i | \(0.420376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.06804e7 | −0.869683 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.54886e7 | −2.84800 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.02558e6 | 0.161382 | 0.0806909 | − | 0.996739i | \(-0.474287\pi\) | ||||
0.0806909 | + | 0.996739i | \(0.474287\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.19452e7 | −0.938063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.32356e6 | 0.103196 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.24146e7 | 0.954199 | 0.477100 | − | 0.878849i | \(-0.341688\pi\) | ||||
0.477100 | + | 0.878849i | \(0.341688\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.41725e6 | 0.489735 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.37364e7 | 2.53834 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.81440e7 | −1.35555 | −0.677777 | − | 0.735267i | \(-0.737057\pi\) | ||||
−0.677777 | + | 0.735267i | \(0.737057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.04943e6 | 0.666649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.64422e7 | 1.93434 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.43642e7 | 1.03623 | 0.518117 | − | 0.855309i | \(-0.326633\pi\) | ||||
0.518117 | + | 0.855309i | \(0.326633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.61449e7 | −1.15664 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.12288e6 | −0.149996 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.61647e6 | 0.534463 | 0.267232 | − | 0.963632i | \(-0.413891\pi\) | ||||
0.267232 | + | 0.963632i | \(0.413891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.14026e7 | −0.789246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.52045e7 | −1.73268 | −0.866338 | − | 0.499457i | \(-0.833533\pi\) | ||||
−0.866338 | + | 0.499457i | \(0.833533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.74611e7 | −1.18414 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.76133e7 | 1.85998 | 0.929989 | − | 0.367587i | \(-0.119816\pi\) | ||||
0.929989 | + | 0.367587i | \(0.119816\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.37947e7 | 0.916728 | 0.458364 | − | 0.888764i | \(-0.348436\pi\) | ||||
0.458364 | + | 0.888764i | \(0.348436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.13489e6 | 0.536984 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.29949e7 | 2.14903 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.01785e6 | −0.259952 | −0.129976 | − | 0.991517i | \(-0.541490\pi\) | ||||
−0.129976 | + | 0.991517i | \(0.541490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.19567e7 | −1.40184 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.91655e7 | 1.21557 | 0.607787 | − | 0.794100i | \(-0.292058\pi\) | ||||
0.607787 | + | 0.794100i | \(0.292058\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.34719e7 | 0.843271 | 0.421635 | − | 0.906765i | \(-0.361456\pi\) | ||||
0.421635 | + | 0.906765i | \(0.361456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.78054e7 | −1.72909 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.08714e7 | −0.667264 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.03586e7 | −1.24146 | −0.620728 | − | 0.784026i | \(-0.713163\pi\) | ||||
−0.620728 | + | 0.784026i | \(0.713163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −606409. | −0.0365020 | −0.0182510 | − | 0.999833i | \(-0.505810\pi\) | ||||
−0.0182510 | + | 0.999833i | \(0.505810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.26718e6 | 0.434622 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.88843e6 | −0.229578 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.65049e6 | 0.331481 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.33927e7 | −0.775699 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.70088e7 | −1.55442 | −0.777211 | − | 0.629240i | \(-0.783366\pi\) | ||||
−0.777211 | + | 0.629240i | \(0.783366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00837e7 | −2.27786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03649e7 | 1.15000 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.67959e7 | −0.936608 | −0.468304 | − | 0.883567i | \(-0.655135\pi\) | ||||
−0.468304 | + | 0.883567i | \(0.655135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.11588e7 | 1.17253 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.75689e6 | 0.0961516 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.59084e7 | 0.865241 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.60402e7 | −0.861662 | −0.430831 | − | 0.902433i | \(-0.641780\pi\) | ||||
−0.430831 | + | 0.902433i | \(0.641780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.00506e6 | −0.373990 | −0.186995 | − | 0.982361i | \(-0.559875\pi\) | ||||
−0.186995 | + | 0.982361i | \(0.559875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.17032e7 | 0.617180 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.34993e7 | 1.75582 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.40734e7 | 0.728690 | 0.364345 | − | 0.931264i | \(-0.381293\pi\) | ||||
0.364345 | + | 0.931264i | \(0.381293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.03356e6 | −0.259045 | −0.129523 | − | 0.991576i | \(-0.541344\pi\) | ||||
−0.129523 | + | 0.991576i | \(0.541344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.14029e7 | −1.08820 | −0.544101 | − | 0.839020i | \(-0.683129\pi\) | ||||
−0.544101 | + | 0.839020i | \(0.683129\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.39490e7 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.03046e7 | 1.51320 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.91625e6 | 0.293650 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.21737e6 | 0.157796 | 0.0788981 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788981 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.75470e7 | −0.855484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.44816e7 | 1.17950 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.58736e7 | −2.67607 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.41940e6 | 0.209189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.11126e7 | −0.993502 | −0.496751 | − | 0.867893i | \(-0.665474\pi\) | ||||
−0.496751 | + | 0.867893i | \(0.665474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.91130e7 | 1.81915 | 0.909577 | − | 0.415535i | \(-0.136406\pi\) | ||||
0.909577 | + | 0.415535i | \(0.136406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.11440e7 | 1.44010 | 0.720049 | − | 0.693924i | \(-0.244119\pi\) | ||||
0.720049 | + | 0.693924i | \(0.244119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.12386e7 | −1.42779 | −0.713896 | − | 0.700251i | \(-0.753071\pi\) | ||||
−0.713896 | + | 0.700251i | \(0.753071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.84849e7 | −1.29442 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.35917e7 | −0.610553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.68311e7 | −1.19837 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.51533e7 | 1.99374 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06670e7 | 0.468320 | 0.234160 | − | 0.972198i | \(-0.424766\pi\) | ||||
0.234160 | + | 0.972198i | \(0.424766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.05809e7 | 0.459284 | 0.229642 | − | 0.973275i | \(-0.426244\pi\) | ||||
0.229642 | + | 0.973275i | \(0.426244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.05413e7 | 0.886596 | 0.443298 | − | 0.896374i | \(-0.353808\pi\) | ||||
0.443298 | + | 0.896374i | \(0.353808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.31469e7 | 1.41460 | 0.707301 | − | 0.706913i | \(-0.249913\pi\) | ||||
0.707301 | + | 0.706913i | \(0.249913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.72518e7 | 1.15649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.21613e7 | −2.60850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.33314e7 | −0.556310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.01472e7 | −0.418744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.78656e7 | 1.14355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.43958e7 | 0.584272 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.45989e7 | −0.589252 | −0.294626 | − | 0.955613i | \(-0.595195\pi\) | ||||
−0.294626 | + | 0.955613i | \(0.595195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.24495e7 | 0.896211 | 0.448106 | − | 0.893981i | \(-0.352099\pi\) | ||||
0.448106 | + | 0.893981i | \(0.352099\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.04261e7 | −1.20801 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.80478e7 | −2.27962 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −83468.9 | −0.00326014 | −0.00163007 | − | 0.999999i | \(-0.500519\pi\) | ||||
−0.00163007 | + | 0.999999i | \(0.500519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.68264e6 | 0.335465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54902e6 | 0.136381 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.39387e7 | 1.29020 | 0.645098 | − | 0.764100i | \(-0.276817\pi\) | ||||
0.645098 | + | 0.764100i | \(0.276817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.90303e7 | −3.36638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.07625e7 | −0.776693 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.39563e7 | −0.891397 | −0.445698 | − | 0.895183i | \(-0.647045\pi\) | ||||
−0.445698 | + | 0.895183i | \(0.647045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.54402e7 | 0.936582 | 0.468291 | − | 0.883574i | \(-0.344870\pi\) | ||||
0.468291 | + | 0.883574i | \(0.344870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.67786e6 | −0.0980639 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.63563e7 | −0.592665 | −0.296332 | − | 0.955085i | \(-0.595764\pi\) | ||||
−0.296332 | + | 0.955085i | \(0.595764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.69968e6 | 0.0973074 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.87396e7 | 1.38173 | 0.690865 | − | 0.722984i | \(-0.257230\pi\) | ||||
0.690865 | + | 0.722984i | \(0.257230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.31978e7 | 0.468266 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.84887e7 | 2.05364 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.10749e6 | 0.213331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.88425e6 | −0.0651358 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.27238e7 | 1.12538 | 0.562689 | − | 0.826669i | \(-0.309767\pi\) | ||||
0.562689 | + | 0.826669i | \(0.309767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.49297e7 | 0.508163 | 0.254082 | − | 0.967183i | \(-0.418227\pi\) | ||||
0.254082 | + | 0.967183i | \(0.418227\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.54151e7 | 2.21511 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.98709e6 | −0.0666011 | −0.0333005 | − | 0.999445i | \(-0.510602\pi\) | ||||
−0.0333005 | + | 0.999445i | \(0.510602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.55445e7 | 2.85257 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.35652e7 | 1.10791 | 0.553956 | − | 0.832546i | \(-0.313118\pi\) | ||||
0.553956 | + | 0.832546i | \(0.313118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.98168e6 | 0.229282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.30701e7 | 0.749995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.45527e7 | −0.794174 | −0.397087 | − | 0.917781i | \(-0.629979\pi\) | ||||
−0.397087 | + | 0.917781i | \(0.629979\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.94127e7 | −0.621624 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.76681e6 | 0.183737 | 0.0918687 | − | 0.995771i | \(-0.470716\pi\) | ||||
0.0918687 | + | 0.995771i | \(0.470716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 864.6.a.o.1.4 | yes | 6 | |
3.2 | odd | 2 | 864.6.a.p.1.3 | yes | 6 | ||
4.3 | odd | 2 | 864.6.a.p.1.4 | yes | 6 | ||
12.11 | even | 2 | inner | 864.6.a.o.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.6.a.o.1.3 | ✓ | 6 | 12.11 | even | 2 | inner | |
864.6.a.o.1.4 | yes | 6 | 1.1 | even | 1 | trivial | |
864.6.a.p.1.3 | yes | 6 | 3.2 | odd | 2 | ||
864.6.a.p.1.4 | yes | 6 | 4.3 | odd | 2 |