Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{109}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.72015\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −3.55969 | −0.228354 | −0.114177 | − | 0.993460i | \(-0.536423\pi\) | ||||
−0.114177 | + | 0.993460i | \(0.536423\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −41.6418 | −0.744912 | −0.372456 | − | 0.928050i | \(-0.621484\pi\) | ||||
−0.372456 | + | 0.928050i | \(0.621484\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −230.329 | −0.947854 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −110.754 | −0.275979 | −0.137989 | − | 0.990434i | \(-0.544064\pi\) | ||||
−0.137989 | + | 0.990434i | \(0.544064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 179.135 | 0.293982 | 0.146991 | − | 0.989138i | \(-0.453041\pi\) | ||||
0.146991 | + | 0.989138i | \(0.453041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 148.232 | 0.170104 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −355.567 | −0.298401 | −0.149200 | − | 0.988807i | \(-0.547670\pi\) | ||||
−0.149200 | + | 0.988807i | \(0.547670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1955.96 | −1.24302 | −0.621508 | − | 0.783408i | \(-0.713480\pi\) | ||||
−0.621508 | + | 0.783408i | \(0.713480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1546.73 | −0.609668 | −0.304834 | − | 0.952405i | \(-0.598601\pi\) | ||||
−0.304834 | + | 0.952405i | \(0.598601\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1390.96 | −0.445106 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1684.90 | 0.444801 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6273.94 | 1.38531 | 0.692653 | − | 0.721271i | \(-0.256442\pi\) | ||||
0.692653 | + | 0.721271i | \(0.256442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6004.18 | −1.12215 | −0.561073 | − | 0.827767i | \(-0.689611\pi\) | ||||
−0.561073 | + | 0.827767i | \(0.689611\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 394.249 | 0.0630210 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9688.45 | −1.16346 | −0.581728 | − | 0.813383i | \(-0.697623\pi\) | ||||
−0.581728 | + | 0.813383i | \(0.697623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −637.665 | −0.0671322 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10577.3 | 0.982686 | 0.491343 | − | 0.870966i | \(-0.336506\pi\) | ||||
0.491343 | + | 0.870966i | \(0.336506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6716.00 | −0.553910 | −0.276955 | − | 0.960883i | \(-0.589325\pi\) | ||||
−0.276955 | + | 0.960883i | \(0.589325\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9591.31 | 0.706068 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27240.8 | −1.79877 | −0.899384 | − | 0.437159i | \(-0.855985\pi\) | ||||
−0.899384 | + | 0.437159i | \(0.855985\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1265.71 | 0.0681411 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32679.4 | −1.59803 | −0.799014 | − | 0.601312i | \(-0.794645\pi\) | ||||
−0.799014 | + | 0.601312i | \(0.794645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4611.98 | 0.205580 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6962.63 | 0.283848 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 492.663 | 0.0184255 | 0.00921277 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921277 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40552.2 | 1.39537 | 0.697686 | − | 0.716403i | \(-0.254213\pi\) | ||||
0.697686 | + | 0.716403i | \(0.254213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7459.50 | −0.218991 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7688.15 | 0.209235 | 0.104618 | − | 0.994513i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994513i | \(0.466638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5505.87 | 0.139220 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −77879.3 | −1.83348 | −0.916740 | − | 0.399484i | \(-0.869189\pi\) | ||||
−0.916740 | + | 0.399484i | \(0.869189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73915.9 | 1.62342 | 0.811710 | − | 0.584061i | \(-0.198537\pi\) | ||||
0.811710 | + | 0.584061i | \(0.198537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4951.38 | 0.101642 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43933.1 | 0.791998 | 0.395999 | − | 0.918251i | \(-0.370398\pi\) | ||||
0.395999 | + | 0.918251i | \(0.370398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49972.1 | 0.846282 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −41194.2 | −0.656359 | −0.328179 | − | 0.944615i | \(-0.606435\pi\) | ||||
−0.328179 | + | 0.944615i | \(0.606435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14806.5 | 0.222282 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22333.3 | −0.316341 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 65724.6 | 0.879534 | 0.439767 | − | 0.898112i | \(-0.355061\pi\) | ||||
0.439767 | + | 0.898112i | \(0.355061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21373.0 | 0.256247 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 81449.9 | 0.925937 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −68534.5 | −0.739571 | −0.369786 | − | 0.929117i | \(-0.620569\pi\) | ||||
−0.369786 | + | 0.929117i | \(0.620569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25509.7 | 0.261588 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −117358. | −1.14475 | −0.572375 | − | 0.819992i | \(-0.693978\pi\) | ||||
−0.572375 | + | 0.819992i | \(0.693978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10819.0 | 0.100484 | 0.0502418 | − | 0.998737i | \(-0.484001\pi\) | ||||
0.0502418 | + | 0.998737i | \(0.484001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −110400. | −0.932203 | −0.466101 | − | 0.884731i | \(-0.654342\pi\) | ||||
−0.466101 | + | 0.884731i | \(0.654342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12261.2 | 0.0988476 | 0.0494238 | − | 0.998778i | \(-0.484262\pi\) | ||||
0.0494238 | + | 0.998778i | \(0.484262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34487.9 | 0.265680 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −122314. | −0.901117 | −0.450558 | − | 0.892747i | \(-0.648775\pi\) | ||||
−0.450558 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64408.5 | 0.454149 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −41259.8 | −0.278652 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −148785. | −0.923836 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −37651.9 | −0.224401 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 188053. | 1.07648 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 169073. | 0.930174 | 0.465087 | − | 0.885265i | \(-0.346023\pi\) | ||||
0.465087 | + | 0.885265i | \(0.346023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23906.9 | 0.126488 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 377451. | 1.92168 | 0.960842 | − | 0.277096i | \(-0.0893720\pi\) | ||||
0.960842 | + | 0.277096i | \(0.0893720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −70162.5 | −0.331338 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 316630. | 1.44129 | 0.720643 | − | 0.693306i | \(-0.243847\pi\) | ||||
0.720643 | + | 0.693306i | \(0.243847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 229447. | 1.00727 | 0.503634 | − | 0.863917i | \(-0.331996\pi\) | ||||
0.503634 | + | 0.863917i | \(0.331996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 96968.9 | 0.410757 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19839.8 | −0.0811330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −261259. | −1.03193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 157502. | 0.581191 | 0.290596 | − | 0.956846i | \(-0.406147\pi\) | ||||
0.290596 | + | 0.956846i | \(0.406147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 146785. | 0.523888 | 0.261944 | − | 0.965083i | \(-0.415636\pi\) | ||||
0.261944 | + | 0.965083i | \(0.415636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 81897.3 | 0.282840 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 250025. | 0.835899 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −327485. | −1.06033 | −0.530166 | − | 0.847894i | \(-0.677870\pi\) | ||||
−0.530166 | + | 0.847894i | \(0.677870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 116329. | 0.364917 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −348187. | −1.02646 | −0.513231 | − | 0.858250i | \(-0.671552\pi\) | ||||
−0.513231 | + | 0.858250i | \(0.671552\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16417.2 | −0.0469451 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 547771. | 1.51987 | 0.759937 | − | 0.649996i | \(-0.225230\pi\) | ||||
0.759937 | + | 0.649996i | \(0.225230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −339204. | −0.913574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 450514. | 1.17820 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 182541. | 0.463708 | 0.231854 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231854 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1753.73 | −0.00420755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −136123. | −0.317541 | −0.158770 | − | 0.987316i | \(-0.550753\pi\) | ||||
−0.158770 | + | 0.987316i | \(0.550753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 591381. | 1.34175 | 0.670874 | − | 0.741571i | \(-0.265919\pi\) | ||||
0.670874 | + | 0.741571i | \(0.265919\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −144354. | −0.318640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 403445. | 0.866672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39380.4 | 0.0823523 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 441191. | 0.875071 | 0.437536 | − | 0.899201i | \(-0.355851\pi\) | ||||
0.437536 | + | 0.899201i | \(0.355851\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 448375. | 0.866459 | 0.433230 | − | 0.901284i | \(-0.357374\pi\) | ||||
0.433230 | + | 0.901284i | \(0.357374\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26553.5 | 0.0500076 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −542019. | −0.995059 | −0.497530 | − | 0.867447i | \(-0.665759\pi\) | ||||
−0.497530 | + | 0.867447i | \(0.665759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 197959. | 0.354358 | 0.177179 | − | 0.984179i | \(-0.443303\pi\) | ||||
0.177179 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27367.4 | −0.0477798 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −440458. | −0.732014 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 356255. | 0.577877 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 216630. | 0.343046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13658e6 | −1.75749 | −0.878745 | − | 0.477292i | \(-0.841618\pi\) | ||||
−0.878745 | + | 0.477292i | \(0.841618\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 277226. | 0.418683 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 279667. | 0.412614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −263118. | −0.370715 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −63694.5 | −0.0877245 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 497078. | 0.669364 | 0.334682 | − | 0.942331i | \(-0.391371\pi\) | ||||
0.334682 | + | 0.942331i | \(0.391371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 320377. | 0.421896 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −934539. | −1.20374 | −0.601870 | − | 0.798594i | \(-0.705578\pi\) | ||||
−0.601870 | + | 0.798594i | \(0.705578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.05206e6 | 1.32572 | 0.662860 | − | 0.748743i | \(-0.269343\pi\) | ||||
0.662860 | + | 0.748743i | \(0.269343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 414582. | 0.500289 | 0.250145 | − | 0.968209i | \(-0.419522\pi\) | ||||
0.250145 | + | 0.968209i | \(0.419522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.13436e6 | 1.33992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −156388. | −0.180856 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −481799. | −0.545596 | −0.272798 | − | 0.962071i | \(-0.587949\pi\) | ||||
−0.272798 | + | 0.962071i | \(0.587949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28961.0 | 0.0321197 | 0.0160598 | − | 0.999871i | \(-0.494888\pi\) | ||||
0.0160598 | + | 0.999871i | \(0.494888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −587317. | −0.638053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −350381. | −0.365425 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 146639. | 0.149882 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −553855. | −0.554896 | −0.277448 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277448 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 171305. | 0.168256 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −52706.5 | −0.0507591 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.87969e6 | 1.77522 | 0.887612 | − | 0.460592i | \(-0.152363\pi\) | ||||
0.887612 | + | 0.460592i | \(0.152363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.44507e6 | −1.31307 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.08337e6 | 0.965801 | 0.482900 | − | 0.875675i | \(-0.339583\pi\) | ||||
0.482900 | + | 0.875675i | \(0.339583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36083e6 | 1.19039 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −233959. | −0.200846 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.10814e6 | 0.933710 | 0.466855 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466855 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 322007. | 0.266344 | 0.133172 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133172 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 154053. | 0.122840 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.45746e6 | 1.14130 | 0.570648 | − | 0.821195i | \(-0.306692\pi\) | ||||
0.570648 | + | 0.821195i | \(0.306692\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.38293e6 | 1.06363 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.03123e6 | 0.779092 | 0.389546 | − | 0.921007i | \(-0.372632\pi\) | ||||
0.389546 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −79664.8 | −0.0591290 | −0.0295645 | − | 0.999563i | \(-0.509412\pi\) | ||||
−0.0295645 | + | 0.999563i | \(0.509412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −289937. | −0.211442 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.29343e6 | −0.910957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 243962. | 0.168884 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.44146e6 | 0.980920 | 0.490460 | − | 0.871464i | \(-0.336829\pi\) | ||||
0.490460 | + | 0.871464i | \(0.336829\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20515.4 | −0.0137254 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −186609. | −0.122756 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −277072. | −0.179232 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 417760. | 0.261409 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.68867e6 | −1.03943 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.71962e6 | 1.04132 | 0.520662 | − | 0.853763i | \(-0.325685\pi\) | ||||
0.520662 | + | 0.853763i | \(0.325685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38512.4 | −0.0229459 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 159609. | 0.0935745 | 0.0467873 | − | 0.998905i | \(-0.485102\pi\) | ||||
0.0467873 | + | 0.998905i | \(0.485102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 452617. | 0.261138 | 0.130569 | − | 0.991439i | \(-0.458320\pi\) | ||||
0.130569 | + | 0.991439i | \(0.458320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.82631e6 | 1.02076 | 0.510382 | − | 0.859948i | \(-0.329504\pi\) | ||||
0.510382 | + | 0.859948i | \(0.329504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −694862. | −0.382315 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 392991. | 0.212873 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 695477. | 0.370917 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −249169. | −0.130853 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −43646.0 | −0.0225723 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.08212e6 | −1.04457 | −0.522283 | − | 0.852772i | \(-0.674919\pi\) | ||||
−0.522283 | + | 0.852772i | \(0.674919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.23153e6 | 1.10279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −320149. | −0.155862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 329493. | 0.158041 | 0.0790207 | − | 0.996873i | \(-0.474821\pi\) | ||||
0.0790207 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 435401. | 0.205774 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 664984. | 0.309689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −229274. | −0.103707 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.24318e6 | 0.554256 | 0.277128 | − | 0.960833i | \(-0.410617\pi\) | ||||
0.277128 | + | 0.960833i | \(0.410617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.07921e6 | −0.474287 | −0.237143 | − | 0.971475i | \(-0.576211\pi\) | ||||
−0.237143 | + | 0.971475i | \(0.576211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 301825. | 0.130764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −526521. | −0.224895 | −0.112447 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112447 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.24304e6 | 1.36578 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.42758e6 | −0.584606 | −0.292303 | − | 0.956326i | \(-0.594422\pi\) | ||||
−0.292303 | + | 0.956326i | \(0.594422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.34969e6 | 0.545088 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 529628. | 0.210962 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.07799e6 | −1.20930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.97129e6 | 0.763986 | 0.381993 | − | 0.924165i | \(-0.375238\pi\) | ||||
0.381993 | + | 0.924165i | \(0.375238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.43625e6 | −0.931443 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.64517e6 | −0.984422 | −0.492211 | − | 0.870476i | \(-0.663811\pi\) | ||||
−0.492211 | + | 0.870476i | \(0.663811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −669410. | −0.245818 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12388e6 | 0.407255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.17483e6 | 0.420123 | 0.210062 | − | 0.977688i | \(-0.432634\pi\) | ||||
0.210062 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −601847. | −0.212409 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.90876e6 | 1.36158 | 0.680788 | − | 0.732480i | \(-0.261637\pi\) | ||||
0.680788 | + | 0.732480i | \(0.261637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.54689e6 | 0.525026 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 195479. | 0.0654978 | 0.0327489 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327489 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 549965. | 0.181925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.34361e6 | −0.438825 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.82946e6 | −0.589969 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.30425e6 | −1.05220 | −0.526099 | − | 0.850424i | \(-0.676346\pi\) | ||||
−0.526099 | + | 0.850424i | \(0.676346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.38638e6 | 1.36221 | 0.681107 | − | 0.732184i | \(-0.261499\pi\) | ||||
0.681107 | + | 0.732184i | \(0.261499\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.07556e6 | −0.329891 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.08093e6 | −0.630405 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.07303e6 | 0.321089 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.21445e6 | −0.950163 | −0.475081 | − | 0.879942i | \(-0.657581\pi\) | ||||
−0.475081 | + | 0.879942i | \(0.657581\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.12710e6 | −0.329124 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.71540e6 | 0.488929 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −816761. | −0.230014 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.48815e6 | −1.24891 | −0.624457 | − | 0.781059i | \(-0.714680\pi\) | ||||
−0.624457 | + | 0.781059i | \(0.714680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.05150e6 | −1.11406 | −0.557032 | − | 0.830491i | \(-0.688060\pi\) | ||||
−0.557032 | + | 0.830491i | \(0.688060\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.27434e6 | 1.70497 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 494579. | 0.132820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 70623.6 | 0.0185271 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.83082e6 | −0.734039 | −0.367019 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367019 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.39735e6 | −0.870804 | −0.435402 | − | 0.900236i | \(-0.643394\pi\) | ||||
−0.435402 | + | 0.900236i | \(0.643394\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 930000. | 0.235646 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.02534e6 | 0.757827 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.39261e6 | −0.840181 | −0.420091 | − | 0.907482i | \(-0.638002\pi\) | ||||
−0.420091 | + | 0.907482i | \(0.638002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.66957e6 | −1.13049 | −0.565246 | − | 0.824922i | \(-0.691219\pi\) | ||||
−0.565246 | + | 0.824922i | \(0.691219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.73689e6 | −0.655175 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −560657. | −0.132718 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −782382. | −0.183148 | −0.0915742 | − | 0.995798i | \(-0.529190\pi\) | ||||
−0.0915742 | + | 0.995798i | \(0.529190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.17147e6 | −0.271201 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −522508. | −0.119632 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −531415. | −0.119026 | −0.0595132 | − | 0.998228i | \(-0.518955\pi\) | ||||
−0.0595132 | + | 0.998228i | \(0.518955\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −599097. | −0.132729 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.34721e6 | −0.295245 | −0.147623 | − | 0.989044i | \(-0.547162\pi\) | ||||
−0.147623 | + | 0.989044i | \(0.547162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.81207e6 | −1.47682 | −0.738409 | − | 0.674354i | \(-0.764422\pi\) | ||||
−0.738409 | + | 0.674354i | \(0.764422\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −890012. | −0.190881 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.02154e6 | 0.216752 | 0.108376 | − | 0.994110i | \(-0.465435\pi\) | ||||
0.108376 | + | 0.994110i | \(0.465435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.16575e6 | 0.242132 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 743821. | 0.152868 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72066e6 | 0.553274 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.52700e6 | 1.51470 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.31826e6 | −1.65651 | −0.828254 | − | 0.560353i | \(-0.810666\pi\) | ||||
−0.828254 | + | 0.560353i | \(0.810666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.73554e6 | −0.342036 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.85390e6 | 0.550916 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −602725. | −0.115159 | −0.0575793 | − | 0.998341i | \(-0.518338\pi\) | ||||
−0.0575793 | + | 0.998341i | \(0.518338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.23944e6 | 0.234397 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.27617e6 | 0.987678 | 0.493839 | − | 0.869553i | \(-0.335593\pi\) | ||||
0.493839 | + | 0.869553i | \(0.335593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.23081e6 | −0.413376 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.06227e6 | −0.194860 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.19577e6 | 1.47346 | 0.736730 | − | 0.676187i | \(-0.236369\pi\) | ||||
0.736730 | + | 0.676187i | \(0.236369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.94990e6 | −0.347070 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.81947e6 | −0.673106 | −0.336553 | − | 0.941665i | \(-0.609261\pi\) | ||||
−0.336553 | + | 0.941665i | \(0.609261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.88702e6 | 0.852739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.20746e6 | 0.208619 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00040e6 | 0.342233 | 0.171116 | − | 0.985251i | \(-0.445263\pi\) | ||||
0.171116 | + | 0.985251i | \(0.445263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.29561e6 | −0.552895 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −450524. | −0.0748514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.01702e6 | 0.496422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −649790. | −0.105890 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.16663e7 | 1.88295 | 0.941477 | − | 0.337077i | \(-0.109438\pi\) | ||||
0.941477 | + | 0.337077i | \(0.109438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.08222e7 | −1.73006 | −0.865029 | − | 0.501723i | \(-0.832700\pi\) | ||||
−0.865029 | + | 0.501723i | \(0.832700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.13489e6 | 0.334849 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.04398e6 | −0.628305 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −113474. | −0.0174647 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.89476e6 | 0.288892 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.59727e6 | 0.694409 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 484557. | 0.0725118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.08714e6 | 0.159695 | 0.0798477 | − | 0.996807i | \(-0.474557\pi\) | ||||
0.0798477 | + | 0.996807i | \(0.474557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.10513e6 | −0.306394 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −510578. | −0.0736327 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −413333. | −0.0590652 | −0.0295326 | − | 0.999564i | \(-0.509402\pi\) | ||||
−0.0295326 | + | 0.999564i | \(0.509402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.34034e6 | −1.32261 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.22716e7 | −1.72196 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.43614e6 | −0.197908 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.20182e7 | −1.64135 | −0.820673 | − | 0.571398i | \(-0.806401\pi\) | ||||
−0.820673 | + | 0.571398i | \(0.806401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.20307e6 | −0.162840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −140182. | −0.0188055 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.42532e7 | −1.89514 | −0.947569 | − | 0.319551i | \(-0.896468\pi\) | ||||
−0.947569 | + | 0.319551i | \(0.896468\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.09339e6 | 0.671253 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.73389e6 | 0.353998 | 0.176999 | − | 0.984211i | \(-0.443361\pi\) | ||||
0.176999 | + | 0.984211i | \(0.443361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.60896e6 | 0.463225 | 0.231612 | − | 0.972808i | \(-0.425600\pi\) | ||||
0.231612 | + | 0.972808i | \(0.425600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.57051e6 | −0.199826 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.15143e6 | 0.271367 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.62585e6 | −0.203302 | −0.101651 | − | 0.994820i | \(-0.532413\pi\) | ||||
−0.101651 | + | 0.994820i | \(0.532413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.59608e6 | −0.197860 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.61936e6 | 0.441022 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.71814e6 | 0.207572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.69220e6 | −1.16099 | −0.580493 | − | 0.814265i | \(-0.697140\pi\) | ||||
−0.580493 | + | 0.814265i | \(0.697140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.17439e7 | 1.39484 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.92942e6 | 0.227226 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.64266e6 | −0.425384 | −0.212692 | − | 0.977119i | \(-0.568223\pi\) | ||||
−0.212692 | + | 0.977119i | \(0.568223\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −704672. | −0.0809191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −657286. | −0.0748492 | −0.0374246 | − | 0.999299i | \(-0.511915\pi\) | ||||
−0.0374246 | + | 0.999299i | \(0.511915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45544e7 | −1.64365 | −0.821824 | − | 0.569742i | \(-0.807043\pi\) | ||||
−0.821824 | + | 0.569742i | \(0.807043\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.77080e6 | −0.198324 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.19567e6 | 0.688176 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.40843e7 | 1.55154 | 0.775770 | − | 0.631015i | \(-0.217362\pi\) | ||||
0.775770 | + | 0.631015i | \(0.217362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.87977e6 | −0.528806 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.44096e6 | 0.369853 | 0.184926 | − | 0.982752i | \(-0.440795\pi\) | ||||
0.184926 | + | 0.982752i | \(0.440795\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.56789e6 | 0.167159 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.03183e6 | 0.637876 | 0.318938 | − | 0.947776i | \(-0.396674\pi\) | ||||
0.318938 | + | 0.947776i | \(0.396674\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.14635e7 | −1.20252 | −0.601259 | − | 0.799054i | \(-0.705334\pi\) | ||||
−0.601259 | + | 0.799054i | \(0.705334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.60608e6 | −0.271181 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.48412e6 | −0.356774 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −771136. | −0.0783361 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.44490e6 | 0.347176 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −536107. | −0.0536016 | −0.0268008 | − | 0.999641i | \(-0.508532\pi\) | ||||
−0.0268008 | + | 0.999641i | \(0.508532\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.04587e6 | 0.401331 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.04050e6 | −0.692898 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.79378e7 | 1.73787 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.91174e6 | 0.279903 | 0.139952 | − | 0.990158i | \(-0.455305\pi\) | ||||
0.139952 | + | 0.990158i | \(0.455305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.93974e7 | −1.85019 | −0.925096 | − | 0.379732i | \(-0.876016\pi\) | ||||
−0.925096 | + | 0.379732i | \(0.876016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −995527. | −0.0942223 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.40085e7 | 1.31562 | 0.657811 | − | 0.753183i | \(-0.271483\pi\) | ||||
0.657811 | + | 0.753183i | \(0.271483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54564.2 | −0.00508506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.11062e7 | 1.01926 | 0.509629 | − | 0.860394i | \(-0.329783\pi\) | ||||
0.509629 | + | 0.860394i | \(0.329783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.57177e7 | −1.43149 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.70249e7 | −1.53877 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.00615e7 | 0.902502 | 0.451251 | − | 0.892397i | \(-0.350978\pi\) | ||||
0.451251 | + | 0.892397i | \(0.350978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.42867e7 | −1.27183 | −0.635916 | − | 0.771758i | \(-0.719377\pi\) | ||||
−0.635916 | + | 0.771758i | \(0.719377\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 226733. | 0.0200323 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.70406e6 | −0.844577 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.76944e6 | −0.152852 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.49130e6 | −0.385094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.05348e7 | −1.74764 | −0.873822 | − | 0.486245i | \(-0.838366\pi\) | ||||
−0.873822 | + | 0.486245i | \(0.838366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.34363e6 | −0.197984 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.59295e6 | −0.301287 | −0.150643 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150643 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.32667e6 | 0.274879 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.19204e7 | 0.977773 | 0.488886 | − | 0.872347i | \(-0.337403\pi\) | ||||
0.488886 | + | 0.872347i | \(0.337403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.31850e7 | −1.07363 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.74501e6 | −0.302734 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.85402e6 | −0.469792 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.28101e6 | 0.341076 | 0.170538 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170538 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.55459e6 | −0.750326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.76094e6 | −0.293234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.47579e6 | −0.114243 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.79081e6 | −0.675669 | −0.337834 | − | 0.941206i | \(-0.609694\pi\) | ||||
−0.337834 | + | 0.941206i | \(0.609694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.89502e7 | 1.44619 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.03796e6 | −0.305978 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.97977e6 | 0.297332 | 0.148666 | − | 0.988887i | \(-0.452502\pi\) | ||||
0.148666 | + | 0.988887i | \(0.452502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.01191e7 | −0.750699 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.28681e6 | 0.684136 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 826166. | 0.0604369 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.71506e6 | 0.124589 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.88818e6 | 0.208354 | 0.104177 | − | 0.994559i | \(-0.466779\pi\) | ||||
0.104177 | + | 0.994559i | \(0.466779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −103092. | −0.00733467 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.72679e6 | −0.616608 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.12040e7 | 1.48793 | 0.743963 | − | 0.668221i | \(-0.232944\pi\) | ||||
0.743963 | + | 0.668221i | \(0.232944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00526e7 | −0.700580 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.38799e6 | 0.165287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.95972e7 | −1.34720 | −0.673602 | − | 0.739094i | \(-0.735254\pi\) | ||||
−0.673602 | + | 0.739094i | \(0.735254\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −851490. | −0.0577445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.41132e7 | −1.62422 | −0.812108 | − | 0.583507i | \(-0.801680\pi\) | ||||
−0.812108 | + | 0.583507i | \(0.801680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.24725e6 | 0.0834464 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.79774e6 | 0.518199 | 0.259100 | − | 0.965851i | \(-0.416574\pi\) | ||||
0.259100 | + | 0.965851i | \(0.416574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.55865e6 | −0.432936 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.48821e6 | 0.622132 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.01687e7 | 1.30490 | 0.652450 | − | 0.757832i | \(-0.273741\pi\) | ||||
0.652450 | + | 0.757832i | \(0.273741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.97155e6 | 0.126713 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.11238e6 | −0.390250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.80945e6 | −0.178190 | −0.0890948 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890948 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −609794. | −0.0384219 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.87055e7 | −1.17087 | −0.585433 | − | 0.810721i | \(-0.699075\pi\) | ||||
−0.585433 | + | 0.810721i | \(0.699075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.41036e6 | −0.210691 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 88253.1 | 0.00541679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.25184e7 | 1.37316 | 0.686580 | − | 0.727054i | \(-0.259111\pi\) | ||||
0.686580 | + | 0.727054i | \(0.259111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.69111e6 | −0.405380 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.24941e7 | 1.35400 | 0.677001 | − | 0.735982i | \(-0.263279\pi\) | ||||
0.677001 | + | 0.735982i | \(0.263279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.35155e6 | 0.499474 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.06888e7 | −1.22149 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.62541e6 | 0.506002 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.05710e7 | 0.616186 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.36371e7 | 0.789854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.80027e6 | −0.564029 | −0.282014 | − | 0.959410i | \(-0.591003\pi\) | ||||
−0.282014 | + | 0.959410i | \(0.591003\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.85647e6 | −0.220545 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.26431e6 | 0.410215 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.84414e6 | −0.271831 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.21486e7 | −0.677456 | −0.338728 | − | 0.940884i | \(-0.609997\pi\) | ||||
−0.338728 | + | 0.940884i | \(0.609997\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.68594e6 | 0.536753 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.51382e7 | −0.833670 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.18645e6 | −0.448030 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.94462e6 | −0.213217 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.73864e6 | −0.308275 | −0.154137 | − | 0.988049i | \(-0.549260\pi\) | ||||
−0.154137 | + | 0.988049i | \(0.549260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14111e7 | −0.609220 | −0.304610 | − | 0.952477i | \(-0.598526\pi\) | ||||
−0.304610 | + | 0.952477i | \(0.598526\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.14625e6 | −0.0608208 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.44991e7 | 0.764624 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31362e7 | 0.688519 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.53935e7 | −0.797038 | −0.398519 | − | 0.917160i | \(-0.630476\pi\) | ||||
−0.398519 | + | 0.917160i | \(0.630476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.69192e7 | 0.870722 | 0.435361 | − | 0.900256i | \(-0.356621\pi\) | ||||
0.435361 | + | 0.900256i | \(0.356621\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −548383. | −0.0280511 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.64225e7 | 1.34341 | 0.671707 | − | 0.740817i | \(-0.265561\pi\) | ||||
0.671707 | + | 0.740817i | \(0.265561\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.97821e6 | −0.0999737 | −0.0499869 | − | 0.998750i | \(-0.515918\pi\) | ||||
−0.0499869 | + | 0.998750i | \(0.515918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.18812e6 | −0.260620 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.28102e7 | −1.13217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.01165e7 | −0.499132 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.20079e7 | 1.07938 | 0.539689 | − | 0.841865i | \(-0.318542\pi\) | ||||
0.539689 | + | 0.841865i | \(0.318542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.88512e7 | 0.919071 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.67086e6 | −0.177909 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.41251e7 | 0.680532 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 283582. | 0.0135024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.49854e7 | 0.709322 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.53601e6 | −0.119338 | −0.0596689 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596689 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.87602e7 | −0.877653 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.14631e6 | −0.0533151 | −0.0266576 | − | 0.999645i | \(-0.508486\pi\) | ||||
−0.0266576 | + | 0.999645i | \(0.508486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.67759e7 | −0.775717 | −0.387858 | − | 0.921719i | \(-0.626785\pi\) | ||||
−0.387858 | + | 0.921719i | \(0.626785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.84806e7 | 0.844672 | 0.422336 | − | 0.906439i | \(-0.361210\pi\) | ||||
0.422336 | + | 0.906439i | \(0.361210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.60134e6 | −0.345422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.60421e6 | 0.208021 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.86575e6 | −0.218575 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.37721e6 | 0.0615115 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.57855e7 | 0.701006 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.61410e6 | −0.290383 | −0.145192 | − | 0.989404i | \(-0.546380\pi\) | ||||
−0.145192 | + | 0.989404i | \(0.546380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.13115e6 | −0.223997 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.43282e7 | 1.49009 | 0.745043 | − | 0.667016i | \(-0.232429\pi\) | ||||
0.745043 | + | 0.667016i | \(0.232429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.51963e6 | −0.238236 | −0.119118 | − | 0.992880i | \(-0.538007\pi\) | ||||
−0.119118 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 73028.6 | 0.00313426 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.55469e6 | 0.322410 | 0.161205 | − | 0.986921i | \(-0.448462\pi\) | ||||
0.161205 | + | 0.986921i | \(0.448462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.53459e6 | −0.233556 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.32820e7 | 2.23590 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.66842e6 | 0.236540 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 986292. | 0.0409284 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.76699e7 | −1.55451 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16197e7 | 0.476853 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.46262e7 | −0.999484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.38270e7 | 1.36536 | 0.682678 | − | 0.730720i | \(-0.260815\pi\) | ||||
0.682678 | + | 0.730720i | \(0.260815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.70310e7 | 1.08506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.27859e7 | −1.30885 | −0.654426 | − | 0.756126i | \(-0.727090\pi\) | ||||
−0.654426 | + | 0.756126i | \(0.727090\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.56241e6 | 0.181141 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.01115e6 | 0.237358 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.69872e7 | 1.83523 | 0.917615 | − | 0.397470i | \(-0.130112\pi\) | ||||
0.917615 | + | 0.397470i | \(0.130112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.12131e6 | −0.237791 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.39509e7 | −0.539011 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34762e7 | 0.517862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.49193e6 | −0.0952438 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.95603e7 | 1.50390 | 0.751952 | − | 0.659218i | \(-0.229112\pi\) | ||||
0.751952 | + | 0.659218i | \(0.229112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −568161. | −0.0213682 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.63987e6 | −0.0613452 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.90483e7 | −1.08086 | −0.540432 | − | 0.841387i | \(-0.681739\pi\) | ||||
−0.540432 | + | 0.841387i | \(0.681739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.61118e6 | −0.0596320 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.31199e7 | 1.21931 | 0.609656 | − | 0.792666i | \(-0.291307\pi\) | ||||
0.609656 | + | 0.792666i | \(0.291307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63602e7 | −0.599112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.99131e7 | −1.44624 | −0.723121 | − | 0.690721i | \(-0.757293\pi\) | ||||
−0.723121 | + | 0.690721i | \(0.757293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.32409e7 | 0.477257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.50109e6 | −0.233096 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.23250e7 | 0.439596 | 0.219798 | − | 0.975545i | \(-0.429460\pi\) | ||||
0.219798 | + | 0.975545i | \(0.429460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.83720e7 | −0.651851 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.47349e6 | 0.0873034 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.42097e6 | 0.259210 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.54283e7 | 0.883592 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.86712e7 | −0.645436 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.13540e7 | −1.42217 | −0.711084 | − | 0.703107i | \(-0.751796\pi\) | ||||
−0.711084 | + | 0.703107i | \(0.751796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.47568e6 | −0.0847004 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.88317e7 | 0.981345 | 0.490672 | − | 0.871344i | \(-0.336751\pi\) | ||||
0.490672 | + | 0.871344i | \(0.336751\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 886964. | 0.0298810 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.85143e6 | −0.296672 | −0.148336 | − | 0.988937i | \(-0.547392\pi\) | ||||
−0.148336 | + | 0.988937i | \(0.547392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.27923e6 | −0.242733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.82410e6 | −0.0936931 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.77705e7 | 0.916643 | 0.458322 | − | 0.888786i | \(-0.348451\pi\) | ||||
0.458322 | + | 0.888786i | \(0.348451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.25707e7 | 0.741232 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.03878e7 | 0.337702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.45725e7 | 1.76518 | 0.882591 | − | 0.470141i | \(-0.155797\pi\) | ||||
0.882591 | + | 0.470141i | \(0.155797\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.41171e6 | 0.238531 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.24336e6 | −0.263965 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.63991e7 | 0.522494 | 0.261247 | − | 0.965272i | \(-0.415866\pi\) | ||||
0.261247 | + | 0.965272i | \(0.415866\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.63241e7 | −0.517507 |
(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 | 784.6.a.o.1.2 | 2 | ||
4.3 | odd | 2 | 196.6.a.j.1.1 | 2 | |||
7.2 | even | 3 | 112.6.i.e.81.1 | 4 | |||
7.4 | even | 3 | 112.6.i.e.65.1 | 4 | |||
7.6 | odd | 2 | 784.6.a.bd.1.1 | 2 | |||
28.3 | even | 6 | 196.6.e.k.177.1 | 4 | |||
28.11 | odd | 6 | 28.6.e.b.9.2 | ✓ | 4 | ||
28.19 | even | 6 | 196.6.e.k.165.1 | 4 | |||
28.23 | odd | 6 | 28.6.e.b.25.2 | yes | 4 | ||
28.27 | even | 2 | 196.6.a.h.1.2 | 2 | |||
84.11 | even | 6 | 252.6.k.d.37.1 | 4 | |||
84.23 | even | 6 | 252.6.k.d.109.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.e.b.9.2 | ✓ | 4 | 28.11 | odd | 6 | ||
28.6.e.b.25.2 | yes | 4 | 28.23 | odd | 6 | ||
112.6.i.e.65.1 | 4 | 7.4 | even | 3 | |||
112.6.i.e.81.1 | 4 | 7.2 | even | 3 | |||
196.6.a.h.1.2 | 2 | 28.27 | even | 2 | |||
196.6.a.j.1.1 | 2 | 4.3 | odd | 2 | |||
196.6.e.k.165.1 | 4 | 28.19 | even | 6 | |||
196.6.e.k.177.1 | 4 | 28.3 | even | 6 | |||
252.6.k.d.37.1 | 4 | 84.11 | even | 6 | |||
252.6.k.d.109.1 | 4 | 84.23 | even | 6 | |||
784.6.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
784.6.a.bd.1.1 | 2 | 7.6 | odd | 2 |