Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-15.9892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17.9892 | 1.59004 | 0.795018 | − | 0.606585i | \(-0.207461\pi\) | ||||
0.795018 | + | 0.606585i | \(0.207461\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 195.612 | 1.52822 | ||||||||
\(5\) | 98.9095 | 0.353869 | 0.176935 | − | 0.984223i | \(-0.443382\pi\) | ||||
0.176935 | + | 0.984223i | \(0.443382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 159.201 | 0.175429 | 0.0877147 | − | 0.996146i | \(-0.472044\pi\) | ||||
0.0877147 | + | 0.996146i | \(0.472044\pi\) | |||||||
\(8\) | 1216.28 | 0.839884 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1779.30 | 0.562665 | ||||||||
\(11\) | 4884.97 | 1.10659 | 0.553296 | − | 0.832985i | \(-0.313370\pi\) | ||||
0.553296 | + | 0.832985i | \(0.313370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11664.5 | 1.47253 | 0.736265 | − | 0.676694i | \(-0.236588\pi\) | ||||
0.736265 | + | 0.676694i | \(0.236588\pi\) | |||||||
\(14\) | 2863.90 | 0.278939 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3158.35 | −0.192770 | ||||||||
\(17\) | 10463.7 | 0.516550 | 0.258275 | − | 0.966071i | \(-0.416846\pi\) | ||||
0.258275 | + | 0.966071i | \(0.416846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14966.8 | 0.500599 | 0.250300 | − | 0.968168i | \(-0.419471\pi\) | ||||
0.250300 | + | 0.968168i | \(0.419471\pi\) | |||||||
\(20\) | 19347.9 | 0.540789 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 87876.7 | 1.75952 | ||||||||
\(23\) | 88.0105 | 0.00150830 | 0.000754148 | − | 1.00000i | \(-0.499760\pi\) | ||||
0.000754148 | 1.00000i | \(0.499760\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −68341.9 | −0.874776 | ||||||||
\(26\) | 209835. | 2.34138 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 31141.6 | 0.268094 | ||||||||
\(29\) | 102600. | 0.781185 | 0.390592 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390592 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −287624. | −1.73404 | −0.867019 | − | 0.498275i | \(-0.833967\pi\) | ||||
−0.867019 | + | 0.498275i | \(0.833967\pi\) | |||||||
\(32\) | −212500. | −1.14640 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 188233. | 0.821333 | ||||||||
\(35\) | 15746.5 | 0.0620791 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 566144. | 1.83747 | 0.918737 | − | 0.394870i | \(-0.129210\pi\) | ||||
0.918737 | + | 0.394870i | \(0.129210\pi\) | |||||||
\(38\) | 269240. | 0.795971 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 120302. | 0.297209 | ||||||||
\(41\) | −296117. | −0.670995 | −0.335497 | − | 0.942041i | \(-0.608904\pi\) | ||||
−0.335497 | + | 0.942041i | \(0.608904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 740471. | 1.42026 | 0.710131 | − | 0.704070i | \(-0.248636\pi\) | ||||
0.710131 | + | 0.704070i | \(0.248636\pi\) | |||||||
\(44\) | 955557. | 1.69111 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1583.24 | 0.00239825 | ||||||||
\(47\) | −958168. | −1.34617 | −0.673084 | − | 0.739566i | \(-0.735031\pi\) | ||||
−0.673084 | + | 0.739566i | \(0.735031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −798198. | −0.969225 | ||||||||
\(50\) | −1.22942e6 | −1.39093 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.28171e6 | 2.25034 | ||||||||
\(53\) | 732872. | 0.676181 | 0.338090 | − | 0.941114i | \(-0.390219\pi\) | ||||
0.338090 | + | 0.941114i | \(0.390219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 483170. | 0.391589 | ||||||||
\(56\) | 193633. | 0.147340 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.84569e6 | 1.24211 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28293e6 | 1.28777 | 0.643884 | − | 0.765123i | \(-0.277322\pi\) | ||||
0.643884 | + | 0.765123i | \(0.277322\pi\) | |||||||
\(62\) | −5.17412e6 | −2.75718 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.41844e6 | −1.63004 | ||||||||
\(65\) | 1.15373e6 | 0.521083 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.29840e6 | −1.74600 | −0.873001 | − | 0.487719i | \(-0.837829\pi\) | ||||
−0.873001 | + | 0.487719i | \(0.837829\pi\) | |||||||
\(68\) | 2.04681e6 | 0.789400 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 283267. | 0.0987080 | ||||||||
\(71\) | 4.99901e6 | 1.65760 | 0.828800 | − | 0.559545i | \(-0.189024\pi\) | ||||
0.828800 | + | 0.559545i | \(0.189024\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.66974e6 | 1.10409 | 0.552046 | − | 0.833814i | \(-0.313847\pi\) | ||||
0.552046 | + | 0.833814i | \(0.313847\pi\) | |||||||
\(74\) | 1.01845e7 | 2.92165 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.92768e6 | 0.765024 | ||||||||
\(77\) | 777691. | 0.194129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.18719e6 | 0.727300 | 0.363650 | − | 0.931536i | \(-0.381530\pi\) | ||||
0.363650 | + | 0.931536i | \(0.381530\pi\) | |||||||
\(80\) | −312391. | −0.0682155 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.32690e6 | −1.06691 | ||||||||
\(83\) | 4.43945e6 | 0.852228 | 0.426114 | − | 0.904670i | \(-0.359882\pi\) | ||||
0.426114 | + | 0.904670i | \(0.359882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.03496e6 | 0.182791 | ||||||||
\(86\) | 1.33205e7 | 2.25827 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.94150e6 | 0.929409 | ||||||||
\(89\) | 1.07216e7 | 1.61211 | 0.806056 | − | 0.591839i | \(-0.201598\pi\) | ||||
0.806056 | + | 0.591839i | \(0.201598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.85700e6 | 0.258325 | ||||||||
\(92\) | 17215.9 | 0.00230500 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.72367e7 | −2.14046 | ||||||||
\(95\) | 1.48036e6 | 0.177147 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.05589e6 | −0.451216 | −0.225608 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(98\) | −1.43590e7 | −1.54110 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.33685e7 | −1.33685 | ||||||||
\(101\) | 1.05360e7 | 1.01754 | 0.508768 | − | 0.860904i | \(-0.330101\pi\) | ||||
0.508768 | + | 0.860904i | \(0.330101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.49129e6 | −0.855845 | −0.427922 | − | 0.903816i | \(-0.640754\pi\) | ||||
−0.427922 | + | 0.903816i | \(0.640754\pi\) | |||||||
\(104\) | 1.41873e7 | 1.23675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.31838e7 | 1.07515 | ||||||||
\(107\) | 7.68612e6 | 0.606547 | 0.303273 | − | 0.952904i | \(-0.401921\pi\) | ||||
0.303273 | + | 0.952904i | \(0.401921\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.46696e7 | 1.08499 | 0.542494 | − | 0.840059i | \(-0.317480\pi\) | ||||
0.542494 | + | 0.840059i | \(0.317480\pi\) | |||||||
\(110\) | 8.69185e6 | 0.622641 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −502812. | −0.0338176 | ||||||||
\(113\) | 1.52191e7 | 0.992234 | 0.496117 | − | 0.868256i | \(-0.334759\pi\) | ||||
0.496117 | + | 0.868256i | \(0.334759\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8705.07 | 0.000533740 0 | ||||||||
\(116\) | 2.00697e7 | 1.19382 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.69461e6 | 0.207005 | ||||||||
\(119\) | 1.66582e6 | 0.0906180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.37575e6 | 0.224545 | ||||||||
\(122\) | 4.10680e7 | 2.04760 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.62626e7 | −2.64999 | ||||||||
\(125\) | −1.44870e7 | −0.663426 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.49590e7 | 0.648021 | 0.324011 | − | 0.946053i | \(-0.394969\pi\) | ||||
0.324011 | + | 0.946053i | \(0.394969\pi\) | |||||||
\(128\) | −3.42951e7 | −1.44543 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.07547e7 | 0.828541 | ||||||||
\(131\) | 2.82534e7 | 1.09805 | 0.549024 | − | 0.835807i | \(-0.315000\pi\) | ||||
0.549024 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.38272e6 | 0.0878198 | ||||||||
\(134\) | −7.73248e7 | −2.77621 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.27268e7 | 0.433842 | ||||||||
\(137\) | −4.47666e7 | −1.48741 | −0.743707 | − | 0.668506i | \(-0.766934\pi\) | ||||
−0.743707 | + | 0.668506i | \(0.766934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.23885e7 | −1.33874 | −0.669370 | − | 0.742929i | \(-0.733436\pi\) | ||||
−0.669370 | + | 0.742929i | \(0.733436\pi\) | |||||||
\(140\) | 3.08020e6 | 0.0948703 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.99283e7 | 2.63565 | ||||||||
\(143\) | 5.69807e7 | 1.62949 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.01481e7 | 0.276437 | ||||||||
\(146\) | 6.60157e7 | 1.75555 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.10744e8 | 2.80806 | ||||||||
\(149\) | 3.46535e7 | 0.858214 | 0.429107 | − | 0.903254i | \(-0.358828\pi\) | ||||
0.429107 | + | 0.903254i | \(0.358828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.67555e7 | −1.81422 | −0.907110 | − | 0.420893i | \(-0.861717\pi\) | ||||
−0.907110 | + | 0.420893i | \(0.861717\pi\) | |||||||
\(152\) | 1.82038e7 | 0.420445 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.39901e7 | 0.308672 | ||||||||
\(155\) | −2.84487e7 | −0.613623 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.08764e7 | −1.25545 | −0.627726 | − | 0.778434i | \(-0.716014\pi\) | ||||
−0.627726 | + | 0.778434i | \(0.716014\pi\) | |||||||
\(158\) | 5.73351e7 | 1.15643 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.10183e7 | −0.405675 | ||||||||
\(161\) | 14011.3 | 0.000264600 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.26090e7 | −1.67493 | −0.837465 | − | 0.546491i | \(-0.815963\pi\) | ||||
−0.837465 | + | 0.546491i | \(0.815963\pi\) | |||||||
\(164\) | −5.79239e7 | −1.02543 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.98622e7 | 1.35507 | ||||||||
\(167\) | −6.05390e7 | −1.00584 | −0.502918 | − | 0.864334i | \(-0.667740\pi\) | ||||
−0.502918 | + | 0.864334i | \(0.667740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.33117e7 | 1.16834 | ||||||||
\(170\) | 1.86180e7 | 0.290645 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.44845e8 | 2.17047 | ||||||||
\(173\) | −6.39593e6 | −0.0939166 | −0.0469583 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469583 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.08801e7 | −0.153461 | ||||||||
\(176\) | −1.54284e7 | −0.213318 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.92873e8 | 2.56332 | ||||||||
\(179\) | 1.31141e8 | 1.70904 | 0.854519 | − | 0.519421i | \(-0.173852\pi\) | ||||
0.854519 | + | 0.519421i | \(0.173852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.39901e7 | −0.426066 | −0.213033 | − | 0.977045i | \(-0.568334\pi\) | ||||
−0.213033 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(182\) | 3.34059e7 | 0.410746 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 107046. | 0.00126679 | ||||||||
\(185\) | 5.59971e7 | 0.650226 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.11147e7 | 0.571610 | ||||||||
\(188\) | −1.87429e8 | −2.05724 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.66304e7 | 0.281670 | ||||||||
\(191\) | −1.52054e8 | −1.57899 | −0.789497 | − | 0.613755i | \(-0.789658\pi\) | ||||
−0.789497 | + | 0.613755i | \(0.789658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.77384e6 | 0.0578115 | 0.0289057 | − | 0.999582i | \(-0.490798\pi\) | ||||
0.0289057 | + | 0.999582i | \(0.490798\pi\) | |||||||
\(194\) | −7.29622e7 | −0.717450 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.56137e8 | −1.48119 | ||||||||
\(197\) | 1.02503e8 | 0.955221 | 0.477611 | − | 0.878572i | \(-0.341503\pi\) | ||||
0.477611 | + | 0.878572i | \(0.341503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.62017e7 | 0.775408 | 0.387704 | − | 0.921784i | \(-0.373268\pi\) | ||||
0.387704 | + | 0.921784i | \(0.373268\pi\) | |||||||
\(200\) | −8.31230e7 | −0.734711 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.89534e8 | 1.61792 | ||||||||
\(203\) | 1.63340e7 | 0.137043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.92887e7 | −0.237445 | ||||||||
\(206\) | −1.70741e8 | −1.36082 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.68405e7 | −0.283860 | ||||||||
\(209\) | 7.31122e7 | 0.553959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.46914e7 | 0.180949 | 0.0904746 | − | 0.995899i | \(-0.471162\pi\) | ||||
0.0904746 | + | 0.995899i | \(0.471162\pi\) | |||||||
\(212\) | 1.43358e8 | 1.03335 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.38267e8 | 0.964431 | ||||||||
\(215\) | 7.32396e7 | 0.502587 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.57899e7 | −0.304201 | ||||||||
\(218\) | 2.63894e8 | 1.72517 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.45137e7 | 0.598433 | ||||||||
\(221\) | 1.22053e8 | 0.760635 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.55302e7 | 0.274936 | 0.137468 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137468 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(224\) | −3.38302e7 | −0.201111 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.73780e8 | 1.57769 | ||||||||
\(227\) | 2.56384e8 | 1.45479 | 0.727395 | − | 0.686219i | \(-0.240731\pi\) | ||||
0.727395 | + | 0.686219i | \(0.240731\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.44709e8 | −1.89683 | −0.948415 | − | 0.317033i | \(-0.897314\pi\) | ||||
−0.948415 | + | 0.317033i | \(0.897314\pi\) | |||||||
\(230\) | 156597. | 0.000848667 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24790e8 | 0.656104 | ||||||||
\(233\) | 1.44767e8 | 0.749762 | 0.374881 | − | 0.927073i | \(-0.377684\pi\) | ||||
0.374881 | + | 0.927073i | \(0.377684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.47720e7 | −0.476368 | ||||||||
\(236\) | 4.01745e7 | 0.198957 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.99669e7 | 0.144086 | ||||||||
\(239\) | 2.45941e8 | 1.16530 | 0.582650 | − | 0.812723i | \(-0.302016\pi\) | ||||
0.582650 | + | 0.812723i | \(0.302016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.54396e8 | 1.17071 | 0.585357 | − | 0.810775i | \(-0.300954\pi\) | ||||
0.585357 | + | 0.810775i | \(0.300954\pi\) | |||||||
\(242\) | 7.87164e7 | 0.357035 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.46567e8 | 1.96799 | ||||||||
\(245\) | −7.89494e7 | −0.342979 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.74580e8 | 0.737147 | ||||||||
\(248\) | −3.49831e8 | −1.45639 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.60609e8 | −1.05487 | ||||||||
\(251\) | −3.25172e8 | −1.29794 | −0.648971 | − | 0.760813i | \(-0.724800\pi\) | ||||
−0.648971 | + | 0.760813i | \(0.724800\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 429928. | 0.00166907 | ||||||||
\(254\) | 2.69100e8 | 1.03038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.79381e8 | −0.668245 | ||||||||
\(257\) | −2.54981e8 | −0.937003 | −0.468502 | − | 0.883463i | \(-0.655206\pi\) | ||||
−0.468502 | + | 0.883463i | \(0.655206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.01307e7 | 0.322347 | ||||||||
\(260\) | 2.25683e8 | 0.796328 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.08256e8 | 1.74594 | ||||||||
\(263\) | −4.19400e8 | −1.42162 | −0.710809 | − | 0.703385i | \(-0.751671\pi\) | ||||
−0.710809 | + | 0.703385i | \(0.751671\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.24880e7 | 0.239280 | ||||||||
\(266\) | 4.28633e7 | 0.139637 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.40817e8 | −2.66827 | ||||||||
\(269\) | 4.15320e8 | 1.30092 | 0.650459 | − | 0.759541i | \(-0.274576\pi\) | ||||
0.650459 | + | 0.759541i | \(0.274576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50963e7 | −0.168163 | −0.0840814 | − | 0.996459i | \(-0.526796\pi\) | ||||
−0.0840814 | + | 0.996459i | \(0.526796\pi\) | |||||||
\(272\) | −3.30479e7 | −0.0995755 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.05315e8 | −2.36504 | ||||||||
\(275\) | −3.33848e8 | −0.968020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.16584e8 | −0.612275 | −0.306138 | − | 0.951987i | \(-0.599037\pi\) | ||||
−0.306138 | + | 0.951987i | \(0.599037\pi\) | |||||||
\(278\) | −7.62536e8 | −2.12865 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.91522e7 | 0.0521392 | ||||||||
\(281\) | 1.30596e8 | 0.351123 | 0.175561 | − | 0.984468i | \(-0.443826\pi\) | ||||
0.175561 | + | 0.984468i | \(0.443826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.03750e8 | 1.05891 | 0.529457 | − | 0.848337i | \(-0.322396\pi\) | ||||
0.529457 | + | 0.848337i | \(0.322396\pi\) | |||||||
\(284\) | 9.77865e8 | 2.53317 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.02504e9 | 2.59095 | ||||||||
\(287\) | −4.71420e7 | −0.117712 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00851e8 | −0.733176 | ||||||||
\(290\) | 1.82556e8 | 0.439546 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.17844e8 | 1.68729 | ||||||||
\(293\) | −1.61200e8 | −0.374394 | −0.187197 | − | 0.982322i | \(-0.559940\pi\) | ||||
−0.187197 | + | 0.982322i | \(0.559940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.03139e7 | 0.0460699 | ||||||||
\(296\) | 6.88591e8 | 1.54327 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.23390e8 | 1.36459 | ||||||||
\(299\) | 1.02660e6 | 0.00222101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17884e8 | 0.249156 | ||||||||
\(302\) | −1.38077e9 | −2.88468 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.72702e7 | −0.0965007 | ||||||||
\(305\) | 2.25803e8 | 0.455701 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.32355e8 | −1.44457 | −0.722283 | − | 0.691597i | \(-0.756907\pi\) | ||||
−0.722283 | + | 0.691597i | \(0.756907\pi\) | |||||||
\(308\) | 1.52126e8 | 0.296671 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.11770e8 | −0.975683 | ||||||||
\(311\) | −1.98727e8 | −0.374624 | −0.187312 | − | 0.982300i | \(-0.559978\pi\) | ||||
−0.187312 | + | 0.982300i | \(0.559978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.25644e8 | 0.415929 | 0.207964 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207964 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(314\) | −1.09512e9 | −1.99622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.23453e8 | 1.11147 | ||||||||
\(317\) | −5.60321e8 | −0.987937 | −0.493968 | − | 0.869480i | \(-0.664454\pi\) | ||||
−0.493968 | + | 0.869480i | \(0.664454\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.01197e8 | 0.864452 | ||||||||
\(320\) | −3.38117e8 | −0.576822 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 252053. | 0.000420723 0 | ||||||||
\(323\) | 1.56607e8 | 0.258585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.97173e8 | −1.28813 | ||||||||
\(326\) | −1.66596e9 | −2.66320 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.60161e8 | −0.563558 | ||||||||
\(329\) | −1.52541e8 | −0.236157 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.88144e7 | 0.0739861 | 0.0369930 | − | 0.999316i | \(-0.488222\pi\) | ||||
0.0369930 | + | 0.999316i | \(0.488222\pi\) | |||||||
\(332\) | 8.68408e8 | 1.30239 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.08905e9 | −1.59932 | ||||||||
\(335\) | −4.25152e8 | −0.617857 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.98448e8 | −0.709439 | −0.354720 | − | 0.934973i | \(-0.615424\pi\) | ||||
−0.354720 | + | 0.934973i | \(0.615424\pi\) | |||||||
\(338\) | 1.31882e9 | 1.85771 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.02449e8 | 0.279345 | ||||||||
\(341\) | −1.40503e9 | −1.91887 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.58183e8 | −0.345460 | ||||||||
\(344\) | 9.00621e8 | 1.19286 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.15058e8 | −0.149331 | ||||||||
\(347\) | −4.64305e8 | −0.596554 | −0.298277 | − | 0.954479i | \(-0.596412\pi\) | ||||
−0.298277 | + | 0.954479i | \(0.596412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.75860e8 | −0.473301 | −0.236651 | − | 0.971595i | \(-0.576050\pi\) | ||||
−0.236651 | + | 0.971595i | \(0.576050\pi\) | |||||||
\(350\) | −1.95724e8 | −0.244009 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.03806e9 | −1.26859 | ||||||||
\(353\) | 6.79230e8 | 0.821874 | 0.410937 | − | 0.911664i | \(-0.365202\pi\) | ||||
0.410937 | + | 0.911664i | \(0.365202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.94450e8 | 0.586574 | ||||||||
\(356\) | 2.09727e9 | 2.46366 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.35912e9 | 2.71743 | ||||||||
\(359\) | −4.73258e8 | −0.539843 | −0.269922 | − | 0.962882i | \(-0.586998\pi\) | ||||
−0.269922 | + | 0.962882i | \(0.586998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.69868e8 | −0.749400 | ||||||||
\(362\) | −6.11455e8 | −0.677461 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.63250e8 | 0.394776 | ||||||||
\(365\) | 3.62972e8 | 0.390704 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.29401e9 | 1.36649 | 0.683245 | − | 0.730189i | \(-0.260568\pi\) | ||||
0.683245 | + | 0.730189i | \(0.260568\pi\) | |||||||
\(368\) | −277968. | −0.000290755 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00734e9 | 1.03388 | ||||||||
\(371\) | 1.16674e8 | 0.118622 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.91706e8 | −0.690146 | −0.345073 | − | 0.938576i | \(-0.612146\pi\) | ||||
−0.345073 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(374\) | 9.19512e8 | 0.908881 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.16540e9 | −1.13062 | ||||||||
\(377\) | 1.19677e9 | 1.15032 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.69203e8 | −0.914487 | −0.457243 | − | 0.889342i | \(-0.651163\pi\) | ||||
−0.457243 | + | 0.889342i | \(0.651163\pi\) | |||||||
\(380\) | 2.89575e8 | 0.270719 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.73533e9 | −2.51066 | ||||||||
\(383\) | 1.28084e9 | 1.16493 | 0.582465 | − | 0.812856i | \(-0.302088\pi\) | ||||
0.582465 | + | 0.812856i | \(0.302088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.69211e7 | 0.0686962 | ||||||||
\(386\) | 1.03867e8 | 0.0919224 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.93379e8 | −0.689556 | ||||||||
\(389\) | −1.19302e9 | −1.02760 | −0.513802 | − | 0.857909i | \(-0.671763\pi\) | ||||
−0.513802 | + | 0.857909i | \(0.671763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 920911. | 0.000779111 0 | ||||||||
\(392\) | −9.70834e8 | −0.814036 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.84394e9 | 1.51884 | ||||||||
\(395\) | 3.15244e8 | 0.257369 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.46557e7 | −0.0358187 | −0.0179094 | − | 0.999840i | \(-0.505701\pi\) | ||||
−0.0179094 | + | 0.999840i | \(0.505701\pi\) | |||||||
\(398\) | 1.55070e9 | 1.23293 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.15847e8 | 0.168631 | ||||||||
\(401\) | −5.52185e8 | −0.427641 | −0.213821 | − | 0.976873i | \(-0.568591\pi\) | ||||
−0.213821 | + | 0.976873i | \(0.568591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.35498e9 | −2.55342 | ||||||||
\(404\) | 2.06096e9 | 1.55501 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.93835e8 | 0.217903 | ||||||||
\(407\) | 2.76560e9 | 2.03333 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.01492e8 | 0.579252 | 0.289626 | − | 0.957140i | \(-0.406469\pi\) | ||||
0.289626 | + | 0.957140i | \(0.406469\pi\) | |||||||
\(410\) | −5.26881e8 | −0.377546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.85661e9 | −1.30792 | ||||||||
\(413\) | 3.26965e7 | 0.0228390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.39104e8 | 0.301577 | ||||||||
\(416\) | −2.47871e9 | −1.68810 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.31523e9 | 0.880815 | ||||||||
\(419\) | 3.06611e8 | 0.203629 | 0.101814 | − | 0.994803i | \(-0.467535\pi\) | ||||
0.101814 | + | 0.994803i | \(0.467535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.08219e9 | 0.706832 | 0.353416 | − | 0.935466i | \(-0.385020\pi\) | ||||
0.353416 | + | 0.935466i | \(0.385020\pi\) | |||||||
\(422\) | 4.44178e8 | 0.287716 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.91379e8 | 0.567913 | ||||||||
\(425\) | −7.15106e8 | −0.451866 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.63444e8 | 0.225912 | ||||||||
\(428\) | 1.50350e9 | 0.926935 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.31752e9 | 0.799132 | ||||||||
\(431\) | −1.67605e9 | −1.00836 | −0.504182 | − | 0.863597i | \(-0.668206\pi\) | ||||
−0.504182 | + | 0.863597i | \(0.668206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.51807e9 | 1.49060 | 0.745300 | − | 0.666730i | \(-0.232306\pi\) | ||||
0.745300 | + | 0.666730i | \(0.232306\pi\) | |||||||
\(434\) | −8.23725e8 | −0.483691 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.86954e9 | 1.65810 | ||||||||
\(437\) | 1.31723e6 | 0.000755053 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.36932e9 | −0.772465 | −0.386232 | − | 0.922402i | \(-0.626224\pi\) | ||||
−0.386232 | + | 0.922402i | \(0.626224\pi\) | |||||||
\(440\) | 5.87671e8 | 0.328889 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.19564e9 | 1.20944 | ||||||||
\(443\) | 3.62914e7 | 0.0198331 | 0.00991656 | − | 0.999951i | \(-0.496843\pi\) | ||||
0.00991656 | + | 0.999951i | \(0.496843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.06047e9 | 0.570477 | ||||||||
\(446\) | 8.19052e8 | 0.437159 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.44219e8 | −0.285957 | ||||||||
\(449\) | 2.01372e9 | 1.04987 | 0.524937 | − | 0.851141i | \(-0.324089\pi\) | ||||
0.524937 | + | 0.851141i | \(0.324089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.44652e9 | −0.742517 | ||||||||
\(452\) | 2.97703e9 | 1.51635 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.61214e9 | 2.31317 | ||||||||
\(455\) | 1.83675e8 | 0.0914133 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.10905e8 | −0.0543554 | −0.0271777 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271777 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(458\) | −6.20104e9 | −3.01603 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.70281e6 | 0.000815671 0 | ||||||||
\(461\) | −3.59226e9 | −1.70771 | −0.853856 | − | 0.520510i | \(-0.825742\pi\) | ||||
−0.853856 | + | 0.520510i | \(0.825742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.38603e9 | −1.11723 | −0.558614 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558614 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(464\) | −3.24046e8 | −0.150589 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.60424e9 | 1.19215 | ||||||||
\(467\) | −1.97044e9 | −0.895271 | −0.447636 | − | 0.894216i | \(-0.647734\pi\) | ||||
−0.447636 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.84308e8 | −0.306300 | ||||||||
\(470\) | −1.70487e9 | −0.757442 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.49799e8 | 0.109344 | ||||||||
\(473\) | 3.61718e9 | 1.57165 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.02286e9 | −0.437913 | ||||||||
\(476\) | 3.25855e8 | 0.138484 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.42428e9 | 1.85287 | ||||||||
\(479\) | −4.56276e9 | −1.89694 | −0.948469 | − | 0.316869i | \(-0.897368\pi\) | ||||
−0.948469 | + | 0.316869i | \(0.897368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.60378e9 | 2.70573 | ||||||||
\(482\) | 4.57639e9 | 1.86148 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.55949e8 | 0.343154 | ||||||||
\(485\) | −4.01166e8 | −0.159672 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.91958e9 | 1.14543 | 0.572715 | − | 0.819754i | \(-0.305890\pi\) | ||||
0.572715 | + | 0.819754i | \(0.305890\pi\) | |||||||
\(488\) | 2.77668e9 | 1.08158 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.42024e9 | −0.545349 | ||||||||
\(491\) | 8.15321e8 | 0.310845 | 0.155422 | − | 0.987848i | \(-0.450326\pi\) | ||||
0.155422 | + | 0.987848i | \(0.450326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.07357e9 | 0.403521 | ||||||||
\(494\) | 3.14055e9 | 1.17209 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.08415e8 | 0.334271 | ||||||||
\(497\) | 7.95847e8 | 0.290792 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.24554e9 | −1.16932 | −0.584662 | − | 0.811277i | \(-0.698773\pi\) | ||||
−0.584662 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(500\) | −2.83382e9 | −1.01386 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.84959e9 | −2.06378 | ||||||||
\(503\) | 4.45372e9 | 1.56040 | 0.780198 | − | 0.625532i | \(-0.215118\pi\) | ||||
0.780198 | + | 0.625532i | \(0.215118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04211e9 | 0.360075 | ||||||||
\(506\) | 7.73407e6 | 0.00265388 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.92615e9 | 0.990317 | ||||||||
\(509\) | −4.82014e9 | −1.62012 | −0.810060 | − | 0.586347i | \(-0.800565\pi\) | ||||
−0.810060 | + | 0.586347i | \(0.800565\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.84226e8 | 0.193690 | ||||||||
\(512\) | 1.16285e9 | 0.382896 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.58690e9 | −1.48987 | ||||||||
\(515\) | −9.38779e8 | −0.302857 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.68062e9 | −1.48966 | ||||||||
\(518\) | 1.62138e9 | 0.512543 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.40326e9 | 0.437649 | ||||||||
\(521\) | 3.16646e9 | 0.980939 | 0.490469 | − | 0.871458i | \(-0.336825\pi\) | ||||
0.490469 | + | 0.871458i | \(0.336825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.33084e9 | −0.406790 | −0.203395 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203395 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(524\) | 5.52670e9 | 1.67806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.54467e9 | −2.26042 | ||||||||
\(527\) | −3.00960e9 | −0.895717 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.40482e9 | −0.999998 | ||||||||
\(530\) | 1.30400e9 | 0.380463 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.66088e8 | 0.134208 | ||||||||
\(533\) | −3.45405e9 | −0.988059 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.60231e8 | 0.214638 | ||||||||
\(536\) | −5.22806e9 | −1.46644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.47128e9 | 2.06851 | ||||||||
\(539\) | −3.89917e9 | −1.07254 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.45311e8 | 0.0666081 | 0.0333040 | − | 0.999445i | \(-0.489397\pi\) | ||||
0.0333040 | + | 0.999445i | \(0.489397\pi\) | |||||||
\(542\) | −9.91139e8 | −0.267385 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.22353e9 | −0.592171 | ||||||||
\(545\) | 1.45096e9 | 0.383944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.35454e9 | 0.353865 | 0.176933 | − | 0.984223i | \(-0.443383\pi\) | ||||
0.176933 | + | 0.984223i | \(0.443383\pi\) | |||||||
\(548\) | −8.75687e9 | −2.27309 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00566e9 | −1.53919 | ||||||||
\(551\) | 1.53559e9 | 0.391061 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.07404e8 | 0.127590 | ||||||||
\(554\) | −3.89617e9 | −0.973540 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.29169e9 | −2.04589 | ||||||||
\(557\) | 2.79389e9 | 0.685041 | 0.342520 | − | 0.939510i | \(-0.388719\pi\) | ||||
0.342520 | + | 0.939510i | \(0.388719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.63721e9 | 2.09138 | ||||||||
\(560\) | −4.97329e7 | −0.0119670 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.34933e9 | 0.558298 | ||||||||
\(563\) | −1.29186e9 | −0.305095 | −0.152548 | − | 0.988296i | \(-0.548748\pi\) | ||||
−0.152548 | + | 0.988296i | \(0.548748\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.50531e9 | 0.351121 | ||||||||
\(566\) | 7.26315e9 | 1.68371 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.08021e9 | 1.39219 | ||||||||
\(569\) | −2.83891e9 | −0.646040 | −0.323020 | − | 0.946392i | \(-0.604698\pi\) | ||||
−0.323020 | + | 0.946392i | \(0.604698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.52009e9 | −0.566487 | −0.283243 | − | 0.959048i | \(-0.591410\pi\) | ||||
−0.283243 | + | 0.959048i | \(0.591410\pi\) | |||||||
\(572\) | 1.11461e10 | 2.49021 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.48048e8 | −0.187167 | ||||||||
\(575\) | −6.01480e6 | −0.00131942 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.41099e9 | −1.60606 | −0.803028 | − | 0.595941i | \(-0.796779\pi\) | ||||
−0.803028 | + | 0.595941i | \(0.796779\pi\) | |||||||
\(578\) | −5.41206e9 | −1.16578 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.98509e9 | 0.422456 | ||||||||
\(581\) | 7.06764e8 | 0.149506 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.58006e9 | 0.748256 | ||||||||
\(584\) | 4.46344e9 | 0.927309 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.89987e9 | −0.595301 | ||||||||
\(587\) | 2.54336e9 | 0.519008 | 0.259504 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259504 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.30480e9 | −0.868058 | ||||||||
\(590\) | 3.65432e8 | 0.0732528 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.78808e9 | −0.354210 | ||||||||
\(593\) | −9.16399e9 | −1.80465 | −0.902326 | − | 0.431055i | \(-0.858142\pi\) | ||||
−0.902326 | + | 0.431055i | \(0.858142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.64766e8 | 0.0320670 | ||||||||
\(596\) | 6.77864e9 | 1.31154 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.84677e7 | 0.00353149 | ||||||||
\(599\) | 5.47291e9 | 1.04046 | 0.520229 | − | 0.854027i | \(-0.325847\pi\) | ||||
0.520229 | + | 0.854027i | \(0.325847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.19336e9 | −0.787955 | −0.393977 | − | 0.919120i | \(-0.628901\pi\) | ||||
−0.393977 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(602\) | 2.12063e9 | 0.396167 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.50143e10 | −2.77252 | ||||||||
\(605\) | 4.32804e8 | 0.0794598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.57768e9 | 1.19375 | 0.596874 | − | 0.802335i | \(-0.296409\pi\) | ||||
0.596874 | + | 0.802335i | \(0.296409\pi\) | |||||||
\(608\) | −3.18044e9 | −0.573885 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.06202e9 | 0.724582 | ||||||||
\(611\) | −1.11765e10 | −1.98227 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.04485e9 | −1.23527 | −0.617633 | − | 0.786467i | \(-0.711908\pi\) | ||||
−0.617633 | + | 0.786467i | \(0.711908\pi\) | |||||||
\(614\) | −1.31745e10 | −2.29691 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.45892e8 | 0.163046 | ||||||||
\(617\) | 4.68870e9 | 0.803627 | 0.401813 | − | 0.915722i | \(-0.368380\pi\) | ||||
0.401813 | + | 0.915722i | \(0.368380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.66470e9 | −1.12944 | −0.564720 | − | 0.825282i | \(-0.691016\pi\) | ||||
−0.564720 | + | 0.825282i | \(0.691016\pi\) | |||||||
\(620\) | −5.56490e9 | −0.937749 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.57495e9 | −0.595667 | ||||||||
\(623\) | 1.70689e9 | 0.282812 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.90631e9 | 0.640010 | ||||||||
\(626\) | 4.05916e9 | 0.661342 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.19081e10 | −1.91860 | ||||||||
\(629\) | 5.92394e9 | 0.949147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.09161e8 | 0.0965227 | 0.0482614 | − | 0.998835i | \(-0.484632\pi\) | ||||
0.0482614 | + | 0.998835i | \(0.484632\pi\) | |||||||
\(632\) | 3.87653e9 | 0.610848 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00797e10 | −1.57086 | ||||||||
\(635\) | 1.47959e9 | 0.229315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.31057e9 | −1.42721 | ||||||||
\(638\) | 9.01614e9 | 1.37451 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.39211e9 | −0.511493 | ||||||||
\(641\) | 3.31465e7 | 0.00497089 | 0.00248545 | − | 0.999997i | \(-0.499209\pi\) | ||||
0.00248545 | + | 0.999997i | \(0.499209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.47226e9 | −0.663421 | −0.331710 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331710 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(644\) | 2.74078e6 | 0.000404366 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.81724e9 | 0.411159 | ||||||||
\(647\) | 4.33561e9 | 0.629340 | 0.314670 | − | 0.949201i | \(-0.398106\pi\) | ||||
0.314670 | + | 0.949201i | \(0.398106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.00327e9 | 0.144066 | ||||||||
\(650\) | −1.43405e10 | −2.04818 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.81154e10 | −2.55966 | ||||||||
\(653\) | 5.43227e9 | 0.763458 | 0.381729 | − | 0.924274i | \(-0.375329\pi\) | ||||
0.381729 | + | 0.924274i | \(0.375329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.79453e9 | 0.388566 | ||||||||
\(656\) | 9.35239e8 | 0.129348 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.74410e9 | −0.375499 | ||||||||
\(659\) | −5.26358e9 | −0.716444 | −0.358222 | − | 0.933636i | \(-0.616617\pi\) | ||||
−0.358222 | + | 0.933636i | \(0.616617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.51100e9 | 0.203497 | 0.101749 | − | 0.994810i | \(-0.467556\pi\) | ||||
0.101749 | + | 0.994810i | \(0.467556\pi\) | |||||||
\(662\) | 8.78133e8 | 0.117641 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.39962e9 | 0.715772 | ||||||||
\(665\) | 2.35674e8 | 0.0310768 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.02986e6 | 0.00117826 | ||||||||
\(668\) | −1.18421e10 | −1.53714 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.64816e9 | −0.982415 | ||||||||
\(671\) | 1.11520e10 | 1.42503 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.92429e8 | 0.0622717 | 0.0311359 | − | 0.999515i | \(-0.490088\pi\) | ||||
0.0311359 | + | 0.999515i | \(0.490088\pi\) | |||||||
\(674\) | −8.96668e9 | −1.12803 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.43406e10 | 1.78548 | ||||||||
\(677\) | −1.38348e10 | −1.71361 | −0.856805 | − | 0.515640i | \(-0.827554\pi\) | ||||
−0.856805 | + | 0.515640i | \(0.827554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.45701e8 | −0.0791566 | ||||||||
\(680\) | 1.25880e9 | 0.153523 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.52754e10 | −3.05108 | ||||||||
\(683\) | −8.01482e8 | −0.0962545 | −0.0481273 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481273 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.42784e9 | −0.526350 | ||||||||
\(686\) | −4.64450e9 | −0.549294 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.33866e9 | −0.273784 | ||||||||
\(689\) | 8.54858e9 | 0.995696 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.59241e9 | −0.298903 | −0.149452 | − | 0.988769i | \(-0.547751\pi\) | ||||
−0.149452 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(692\) | −1.25112e9 | −0.143525 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.35247e9 | −0.948543 | ||||||||
\(695\) | −4.19263e9 | −0.473739 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.09846e9 | −0.346602 | ||||||||
\(698\) | −6.76143e9 | −0.752566 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.12827e9 | −0.234522 | ||||||||
\(701\) | −1.40491e10 | −1.54040 | −0.770201 | − | 0.637801i | \(-0.779844\pi\) | ||||
−0.770201 | + | 0.637801i | \(0.779844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.47335e9 | 0.919838 | ||||||||
\(704\) | −1.66990e10 | −1.80379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.22188e10 | 1.30681 | ||||||||
\(707\) | 1.67733e9 | 0.178506 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.39937e9 | −0.990460 | −0.495230 | − | 0.868762i | \(-0.664916\pi\) | ||||
−0.495230 | + | 0.868762i | \(0.664916\pi\) | |||||||
\(710\) | 8.89476e9 | 0.932675 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.30405e10 | 1.35399 | ||||||||
\(713\) | −2.53139e7 | −0.00261544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.63593e9 | 0.576626 | ||||||||
\(716\) | 2.56526e10 | 2.61178 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.51354e9 | −0.858371 | ||||||||
\(719\) | −1.11397e10 | −1.11769 | −0.558846 | − | 0.829272i | \(-0.688756\pi\) | ||||
−0.558846 | + | 0.829272i | \(0.688756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51102e9 | −0.150140 | ||||||||
\(722\) | −1.20504e10 | −1.19157 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.64886e9 | −0.651122 | ||||||||
\(725\) | −7.01187e9 | −0.683362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.70625e9 | −0.936874 | −0.468437 | − | 0.883497i | \(-0.655183\pi\) | ||||
−0.468437 | + | 0.883497i | \(0.655183\pi\) | |||||||
\(728\) | 2.25863e9 | 0.216963 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.52958e9 | 0.621234 | ||||||||
\(731\) | 7.74803e9 | 0.733636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.02746e9 | 0.377718 | 0.188859 | − | 0.982004i | \(-0.439521\pi\) | ||||
0.188859 | + | 0.982004i | \(0.439521\pi\) | |||||||
\(734\) | 2.32782e10 | 2.17277 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.87022e7 | −0.00172911 | ||||||||
\(737\) | −2.09975e10 | −1.93211 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.14088e10 | 1.03989 | 0.519943 | − | 0.854201i | \(-0.325953\pi\) | ||||
0.519943 | + | 0.854201i | \(0.325953\pi\) | |||||||
\(740\) | 1.09537e10 | 0.993686 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.09887e9 | 0.188613 | ||||||||
\(743\) | 3.48068e9 | 0.311317 | 0.155659 | − | 0.987811i | \(-0.450250\pi\) | ||||
0.155659 | + | 0.987811i | \(0.450250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.42757e9 | 0.303696 | ||||||||
\(746\) | −1.24432e10 | −1.09736 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.99863e9 | 0.873544 | ||||||||
\(749\) | 1.22364e9 | 0.106406 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.06375e10 | −0.916433 | −0.458217 | − | 0.888841i | \(-0.651512\pi\) | ||||
−0.458217 | + | 0.888841i | \(0.651512\pi\) | |||||||
\(752\) | 3.02623e9 | 0.259501 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.15290e10 | 1.82905 | ||||||||
\(755\) | −7.59185e9 | −0.641997 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.08009e10 | 1.74279 | 0.871397 | − | 0.490578i | \(-0.163214\pi\) | ||||
0.871397 | + | 0.490578i | \(0.163214\pi\) | |||||||
\(758\) | −1.74352e10 | −1.45407 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.80053e9 | 0.148783 | ||||||||
\(761\) | −1.33150e9 | −0.109521 | −0.0547604 | − | 0.998500i | \(-0.517439\pi\) | ||||
−0.0547604 | + | 0.998500i | \(0.517439\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.33541e9 | 0.190339 | ||||||||
\(764\) | −2.97435e10 | −2.41304 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.30413e10 | 1.85228 | ||||||||
\(767\) | 2.39564e9 | 0.191707 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.19213e10 | −1.73830 | −0.869148 | − | 0.494553i | \(-0.835332\pi\) | ||||
−0.869148 | + | 0.494553i | \(0.835332\pi\) | |||||||
\(770\) | 1.38375e9 | 0.109230 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.12943e9 | 0.0883485 | ||||||||
\(773\) | −3.83517e9 | −0.298646 | −0.149323 | − | 0.988788i | \(-0.547709\pi\) | ||||
−0.149323 | + | 0.988788i | \(0.547709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.96567e10 | 1.51690 | ||||||||
\(776\) | −4.93310e9 | −0.378969 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.14616e10 | −1.63393 | ||||||||
\(779\) | −4.43191e9 | −0.335900 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.44200e10 | 1.83429 | ||||||||
\(782\) | 1.65665e7 | 0.00123881 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.52099e9 | 0.186838 | ||||||||
\(785\) | −6.02126e9 | −0.444266 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.79274e10 | 1.31101 | 0.655504 | − | 0.755192i | \(-0.272456\pi\) | ||||
0.655504 | + | 0.755192i | \(0.272456\pi\) | |||||||
\(788\) | 2.00508e10 | 1.45979 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.67099e9 | 0.409227 | ||||||||
\(791\) | 2.42289e9 | 0.174067 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.66292e10 | 1.89627 | ||||||||
\(794\) | −8.03321e8 | −0.0569531 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.68621e10 | 1.18499 | ||||||||
\(797\) | 5.47185e9 | 0.382851 | 0.191426 | − | 0.981507i | \(-0.438689\pi\) | ||||
0.191426 | + | 0.981507i | \(0.438689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.00259e10 | −0.695363 | ||||||||
\(800\) | 1.45227e10 | 1.00284 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.93338e9 | −0.679965 | ||||||||
\(803\) | 1.79266e10 | 1.22178 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38586e6 | 9.36337e−5 0 | ||||||||
\(806\) | −6.03535e10 | −4.06003 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.28147e10 | 0.854612 | ||||||||
\(809\) | −2.20226e9 | −0.146234 | −0.0731171 | − | 0.997323i | \(-0.523295\pi\) | ||||
−0.0731171 | + | 0.997323i | \(0.523295\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.11433e9 | −0.336679 | −0.168339 | − | 0.985729i | \(-0.553840\pi\) | ||||
−0.168339 | + | 0.985729i | \(0.553840\pi\) | |||||||
\(812\) | 3.19512e9 | 0.209431 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.97509e10 | 3.23307 | ||||||||
\(815\) | −9.15991e9 | −0.592707 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.10825e10 | 0.710982 | ||||||||
\(818\) | 1.44182e10 | 0.921032 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.72922e9 | −0.362867 | ||||||||
\(821\) | 4.81471e9 | 0.303647 | 0.151824 | − | 0.988408i | \(-0.451485\pi\) | ||||
0.151824 | + | 0.988408i | \(0.451485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.90096e10 | −1.81402 | −0.907011 | − | 0.421107i | \(-0.861642\pi\) | ||||
−0.907011 | + | 0.421107i | \(0.861642\pi\) | |||||||
\(824\) | −1.15441e10 | −0.718810 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.88185e8 | 0.0363148 | ||||||||
\(827\) | −5.95215e9 | −0.365936 | −0.182968 | − | 0.983119i | \(-0.558570\pi\) | ||||
−0.182968 | + | 0.983119i | \(0.558570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00332e10 | 0.611643 | 0.305821 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305821 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(830\) | 7.89913e9 | 0.479519 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.98744e10 | −2.40028 | ||||||||
\(833\) | −8.35207e9 | −0.500653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.98788e9 | −0.355935 | ||||||||
\(836\) | 1.43016e10 | 0.846570 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.51569e9 | 0.323777 | ||||||||
\(839\) | −7.75973e9 | −0.453607 | −0.226803 | − | 0.973941i | \(-0.572827\pi\) | ||||
−0.226803 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.72315e9 | −0.389751 | ||||||||
\(842\) | 1.94677e10 | 1.12389 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.82992e9 | 0.276529 | ||||||||
\(845\) | 7.25123e9 | 0.413441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.96624e8 | 0.0393919 | ||||||||
\(848\) | −2.31466e9 | −0.130347 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.28642e10 | −0.718483 | ||||||||
\(851\) | 4.98266e7 | 0.00277146 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.15852e10 | 1.74246 | 0.871229 | − | 0.490877i | \(-0.163324\pi\) | ||||
0.871229 | + | 0.490877i | \(0.163324\pi\) | |||||||
\(854\) | 6.53807e9 | 0.359209 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.34849e9 | 0.509429 | ||||||||
\(857\) | 1.81369e10 | 0.984304 | 0.492152 | − | 0.870509i | \(-0.336210\pi\) | ||||
0.492152 | + | 0.870509i | \(0.336210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.80979e10 | 1.51251 | 0.756253 | − | 0.654279i | \(-0.227028\pi\) | ||||
0.756253 | + | 0.654279i | \(0.227028\pi\) | |||||||
\(860\) | 1.43265e10 | 0.768062 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.01509e10 | −1.60334 | ||||||||
\(863\) | 1.12434e10 | 0.595467 | 0.297734 | − | 0.954649i | \(-0.403769\pi\) | ||||
0.297734 | + | 0.954649i | \(0.403769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.32618e8 | −0.0332342 | ||||||||
\(866\) | 4.52982e10 | 2.37011 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.95705e9 | −0.464885 | ||||||||
\(869\) | 1.55693e10 | 0.804824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.01386e10 | −2.57104 | ||||||||
\(872\) | 1.78424e10 | 0.911265 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.36960e7 | 0.00120056 | ||||||||
\(875\) | −2.30634e9 | −0.116384 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.39725e10 | −0.699481 | −0.349740 | − | 0.936847i | \(-0.613730\pi\) | ||||
−0.349740 | + | 0.936847i | \(0.613730\pi\) | |||||||
\(878\) | −2.46330e10 | −1.22825 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.52602e9 | −0.0754867 | ||||||||
\(881\) | 1.05370e10 | 0.519158 | 0.259579 | − | 0.965722i | \(-0.416416\pi\) | ||||
0.259579 | + | 0.965722i | \(0.416416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.48119e10 | 1.21282 | 0.606412 | − | 0.795151i | \(-0.292608\pi\) | ||||
0.606412 | + | 0.795151i | \(0.292608\pi\) | |||||||
\(884\) | 2.38750e10 | 1.16242 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.52854e8 | 0.0315354 | ||||||||
\(887\) | −3.02069e10 | −1.45336 | −0.726680 | − | 0.686976i | \(-0.758938\pi\) | ||||
−0.726680 | + | 0.686976i | \(0.758938\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.38148e9 | 0.113682 | ||||||||
\(890\) | 1.90770e10 | 0.907080 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.90624e9 | 0.420162 | ||||||||
\(893\) | −1.43407e10 | −0.673891 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.29711e10 | 0.604776 | ||||||||
\(896\) | −5.45981e9 | −0.253571 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.62253e10 | 1.66934 | ||||||||
\(899\) | −2.95101e10 | −1.35460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.66853e9 | 0.349281 | ||||||||
\(902\) | −2.60218e10 | −1.18063 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.85107e10 | 0.833362 | ||||||||
\(905\) | −3.36194e9 | −0.150772 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.15712e10 | 0.514937 | 0.257468 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257468 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(908\) | 5.01517e10 | 2.22323 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.30416e9 | 0.145350 | ||||||||
\(911\) | 1.60273e10 | 0.702338 | 0.351169 | − | 0.936312i | \(-0.385784\pi\) | ||||
0.351169 | + | 0.936312i | \(0.385784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.16866e10 | 0.943068 | ||||||||
\(914\) | −1.99509e9 | −0.0864271 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.74291e10 | −2.89877 | ||||||||
\(917\) | 4.49797e9 | 0.192630 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.52685e9 | 0.404897 | 0.202449 | − | 0.979293i | \(-0.435110\pi\) | ||||
0.202449 | + | 0.979293i | \(0.435110\pi\) | |||||||
\(920\) | 1.05878e7 | 0.000448280 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.46219e10 | −2.71532 | ||||||||
\(923\) | 5.83109e10 | 2.44086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.86914e10 | −1.60738 | ||||||||
\(926\) | −4.29228e10 | −1.77643 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.18025e10 | −0.895547 | ||||||||
\(929\) | −7.62148e9 | −0.311878 | −0.155939 | − | 0.987767i | \(-0.549840\pi\) | ||||
−0.155939 | + | 0.987767i | \(0.549840\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.19464e10 | −0.485193 | ||||||||
\(932\) | 2.83181e10 | 1.14580 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.54467e10 | −1.42351 | ||||||||
\(935\) | 5.05573e9 | 0.202275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.55429e9 | 0.101434 | 0.0507168 | − | 0.998713i | \(-0.483849\pi\) | ||||
0.0507168 | + | 0.998713i | \(0.483849\pi\) | |||||||
\(938\) | −1.23102e10 | −0.487028 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.85385e10 | −0.727993 | ||||||||
\(941\) | 1.11902e10 | 0.437797 | 0.218898 | − | 0.975748i | \(-0.429754\pi\) | ||||
0.218898 | + | 0.975748i | \(0.429754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.60613e7 | −0.00101206 | ||||||||
\(944\) | −6.48658e8 | −0.0250965 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.50702e10 | 2.49898 | ||||||||
\(947\) | −2.91042e10 | −1.11361 | −0.556803 | − | 0.830645i | \(-0.687972\pi\) | ||||
−0.556803 | + | 0.830645i | \(0.687972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.28056e10 | 1.62581 | ||||||||
\(950\) | −1.84004e10 | −0.696297 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.02611e9 | 0.0761087 | ||||||||
\(953\) | −1.18538e10 | −0.443643 | −0.221821 | − | 0.975087i | \(-0.571200\pi\) | ||||
−0.221821 | + | 0.975087i | \(0.571200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50396e10 | −0.558758 | ||||||||
\(956\) | 4.81089e10 | 1.78083 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.20804e10 | −3.01620 | ||||||||
\(959\) | −7.12688e9 | −0.260936 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.52147e10 | 2.00689 | ||||||||
\(962\) | 1.18797e11 | 4.30222 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.97629e10 | 1.78911 | ||||||||
\(965\) | 5.71088e8 | 0.0204577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.91605e10 | −1.39269 | −0.696347 | − | 0.717705i | \(-0.745193\pi\) | ||||
−0.696347 | + | 0.717705i | \(0.745193\pi\) | |||||||
\(968\) | 5.32215e9 | 0.188592 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.21666e9 | −0.253884 | ||||||||
\(971\) | −4.49711e10 | −1.57640 | −0.788200 | − | 0.615419i | \(-0.788987\pi\) | ||||
−0.788200 | + | 0.615419i | \(0.788987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.74829e9 | −0.234854 | ||||||||
\(974\) | 5.25209e10 | 1.82128 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.21027e9 | −0.248243 | ||||||||
\(977\) | 3.26239e10 | 1.11919 | 0.559597 | − | 0.828765i | \(-0.310956\pi\) | ||||
0.559597 | + | 0.828765i | \(0.310956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.23748e10 | 1.78395 | ||||||||
\(980\) | −1.54434e10 | −0.524146 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.46670e10 | 0.494254 | ||||||||
\(983\) | 4.19068e10 | 1.40717 | 0.703585 | − | 0.710611i | \(-0.251581\pi\) | ||||
0.703585 | + | 0.710611i | \(0.251581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.01385e10 | 0.338024 | ||||||||
\(986\) | 1.93127e10 | 0.641613 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.41498e10 | 1.12652 | ||||||||
\(989\) | 6.51692e7 | 0.00214218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.39919e10 | 0.456687 | 0.228343 | − | 0.973581i | \(-0.426669\pi\) | ||||
0.228343 | + | 0.973581i | \(0.426669\pi\) | |||||||
\(992\) | 6.11201e10 | 1.98789 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.43167e10 | 0.462370 | ||||||||
\(995\) | 8.52617e9 | 0.274393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.75080e10 | 1.83779 | 0.918893 | − | 0.394506i | \(-0.129084\pi\) | ||||
0.918893 | + | 0.394506i | \(0.129084\pi\) | |||||||
\(998\) | −5.83846e10 | −1.85927 | ||||||||
\(999\) | 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 | 531.8.a.d.1.15 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.3 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.3 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.15 | 17 | 1.1 | even | 1 | trivial |