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: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.05882\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05882 | 0.0935869 | 0.0467935 | − | 0.998905i | \(-0.485100\pi\) | ||||
0.0467935 | + | 0.998905i | \(0.485100\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −126.879 | −0.991241 | ||||||||
\(5\) | −151.597 | −0.542370 | −0.271185 | − | 0.962527i | \(-0.587416\pi\) | ||||
−0.271185 | + | 0.962527i | \(0.587416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1574.54 | −1.73504 | −0.867522 | − | 0.497398i | \(-0.834289\pi\) | ||||
−0.867522 | + | 0.497398i | \(0.834289\pi\) | |||||||
\(8\) | −269.870 | −0.186354 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −160.513 | −0.0507587 | ||||||||
\(11\) | −1597.23 | −0.361819 | −0.180910 | − | 0.983500i | \(-0.557904\pi\) | ||||
−0.180910 | + | 0.983500i | \(0.557904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8756.36 | 1.10541 | 0.552703 | − | 0.833378i | \(-0.313596\pi\) | ||||
0.552703 | + | 0.833378i | \(0.313596\pi\) | |||||||
\(14\) | −1667.15 | −0.162378 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15954.8 | 0.973801 | ||||||||
\(17\) | −19841.7 | −0.979507 | −0.489754 | − | 0.871861i | \(-0.662913\pi\) | ||||
−0.489754 | + | 0.871861i | \(0.662913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4839.26 | −0.161861 | −0.0809304 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809304 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(20\) | 19234.5 | 0.537620 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1691.17 | −0.0338616 | ||||||||
\(23\) | 30741.2 | 0.526834 | 0.263417 | − | 0.964682i | \(-0.415151\pi\) | ||||
0.263417 | + | 0.964682i | \(0.415151\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −55143.3 | −0.705835 | ||||||||
\(26\) | 9271.37 | 0.103452 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 199776. | 1.71985 | ||||||||
\(29\) | −14740.2 | −0.112230 | −0.0561152 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561152 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72269.3 | 0.435700 | 0.217850 | − | 0.975982i | \(-0.430096\pi\) | ||||
0.217850 | + | 0.975982i | \(0.430096\pi\) | |||||||
\(32\) | 51436.5 | 0.277489 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −21008.7 | −0.0916691 | ||||||||
\(35\) | 238696. | 0.941036 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 357556. | 1.16048 | 0.580240 | − | 0.814445i | \(-0.302959\pi\) | ||||
0.580240 | + | 0.814445i | \(0.302959\pi\) | |||||||
\(38\) | −5123.88 | −0.0151480 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40911.4 | 0.101073 | ||||||||
\(41\) | −562020. | −1.27353 | −0.636764 | − | 0.771059i | \(-0.719727\pi\) | ||||
−0.636764 | + | 0.771059i | \(0.719727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 682037. | 1.30818 | 0.654092 | − | 0.756415i | \(-0.273051\pi\) | ||||
0.654092 | + | 0.756415i | \(0.273051\pi\) | |||||||
\(44\) | 202654. | 0.358650 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 32549.3 | 0.0493047 | ||||||||
\(47\) | 1.24121e6 | 1.74382 | 0.871911 | − | 0.489665i | \(-0.162881\pi\) | ||||
0.871911 | + | 0.489665i | \(0.162881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.65563e6 | 2.01038 | ||||||||
\(50\) | −58386.6 | −0.0660569 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.11100e6 | −1.09572 | ||||||||
\(53\) | 1.94069e6 | 1.79057 | 0.895286 | − | 0.445493i | \(-0.146972\pi\) | ||||
0.895286 | + | 0.445493i | \(0.146972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 242135. | 0.196240 | ||||||||
\(56\) | 424921. | 0.323333 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15607.1 | −0.0105033 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.48399e6 | −1.40119 | −0.700593 | − | 0.713561i | \(-0.747081\pi\) | ||||
−0.700593 | + | 0.713561i | \(0.747081\pi\) | |||||||
\(62\) | 76519.8 | 0.0407758 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.98775e6 | −0.947832 | ||||||||
\(65\) | −1.32744e6 | −0.599539 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.19534e6 | −0.485546 | −0.242773 | − | 0.970083i | \(-0.578057\pi\) | ||||
−0.242773 | + | 0.970083i | \(0.578057\pi\) | |||||||
\(68\) | 2.51749e6 | 0.970928 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 252735. | 0.0880687 | ||||||||
\(71\) | 5.50733e6 | 1.82615 | 0.913076 | − | 0.407789i | \(-0.133700\pi\) | ||||
0.913076 | + | 0.407789i | \(0.133700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03549e6 | −0.311542 | −0.155771 | − | 0.987793i | \(-0.549786\pi\) | ||||
−0.155771 | + | 0.987793i | \(0.549786\pi\) | |||||||
\(74\) | 378585. | 0.108606 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 614000. | 0.160443 | ||||||||
\(77\) | 2.51490e6 | 0.627773 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.05062e6 | −0.239745 | −0.119873 | − | 0.992789i | \(-0.538249\pi\) | ||||
−0.119873 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(80\) | −2.41869e6 | −0.528161 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −595075. | −0.119185 | ||||||||
\(83\) | −8.29947e6 | −1.59323 | −0.796613 | − | 0.604490i | \(-0.793377\pi\) | ||||
−0.796613 | + | 0.604490i | \(0.793377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00794e6 | 0.531256 | ||||||||
\(86\) | 722151. | 0.122429 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 431043. | 0.0674266 | ||||||||
\(89\) | −1.51623e6 | −0.227982 | −0.113991 | − | 0.993482i | \(-0.536363\pi\) | ||||
−0.113991 | + | 0.993482i | \(0.536363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.37872e7 | −1.91793 | ||||||||
\(92\) | −3.90041e6 | −0.522219 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.31421e6 | 0.163199 | ||||||||
\(95\) | 733618. | 0.0877884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.02696e7 | 1.14249 | 0.571247 | − | 0.820778i | \(-0.306460\pi\) | ||||
0.571247 | + | 0.820778i | \(0.306460\pi\) | |||||||
\(98\) | 1.75301e6 | 0.188145 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.99653e6 | 0.699653 | ||||||||
\(101\) | 1.21422e7 | 1.17267 | 0.586333 | − | 0.810070i | \(-0.300571\pi\) | ||||
0.586333 | + | 0.810070i | \(0.300571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.11994e7 | −1.91159 | −0.955793 | − | 0.294041i | \(-0.905000\pi\) | ||||
−0.955793 | + | 0.294041i | \(0.905000\pi\) | |||||||
\(104\) | −2.36308e6 | −0.205997 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.05484e6 | 0.167574 | ||||||||
\(107\) | −58058.2 | −0.00458163 | −0.00229082 | − | 0.999997i | \(-0.500729\pi\) | ||||
−0.00229082 | + | 0.999997i | \(0.500729\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.06543e7 | 0.788011 | 0.394005 | − | 0.919108i | \(-0.371089\pi\) | ||||
0.394005 | + | 0.919108i | \(0.371089\pi\) | |||||||
\(110\) | 256376. | 0.0183655 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.51214e7 | −1.68959 | ||||||||
\(113\) | 4.86803e6 | 0.317379 | 0.158690 | − | 0.987329i | \(-0.449273\pi\) | ||||
0.158690 | + | 0.987329i | \(0.449273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.66028e6 | −0.285739 | ||||||||
\(116\) | 1.87022e6 | 0.111247 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −217458. | −0.0121840 | ||||||||
\(119\) | 3.12416e7 | 1.69949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.69360e7 | −0.869087 | ||||||||
\(122\) | −2.63009e6 | −0.131133 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.16945e6 | −0.431884 | ||||||||
\(125\) | 2.02031e7 | 0.925194 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.32597e7 | −1.44081 | −0.720403 | − | 0.693556i | \(-0.756043\pi\) | ||||
−0.720403 | + | 0.693556i | \(0.756043\pi\) | |||||||
\(128\) | −8.68852e6 | −0.366194 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.40551e6 | −0.0561090 | ||||||||
\(131\) | −3.81285e6 | −0.148184 | −0.0740918 | − | 0.997251i | \(-0.523606\pi\) | ||||
−0.0740918 | + | 0.997251i | \(0.523606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.61961e6 | 0.280836 | ||||||||
\(134\) | −1.26565e6 | −0.0454407 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.35467e6 | 0.182535 | ||||||||
\(137\) | −4.60178e7 | −1.52899 | −0.764494 | − | 0.644630i | \(-0.777011\pi\) | ||||
−0.764494 | + | 0.644630i | \(0.777011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.52736e7 | 1.42986 | 0.714930 | − | 0.699196i | \(-0.246458\pi\) | ||||
0.714930 | + | 0.699196i | \(0.246458\pi\) | |||||||
\(140\) | −3.02855e7 | −0.932794 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.83125e6 | 0.170904 | ||||||||
\(143\) | −1.39859e7 | −0.399957 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.23457e6 | 0.0608704 | ||||||||
\(146\) | −1.09639e6 | −0.0291562 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.53663e7 | −1.15032 | ||||||||
\(149\) | −2.55791e7 | −0.633481 | −0.316740 | − | 0.948512i | \(-0.602588\pi\) | ||||
−0.316740 | + | 0.948512i | \(0.602588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.20103e7 | 0.520243 | 0.260121 | − | 0.965576i | \(-0.416237\pi\) | ||||
0.260121 | + | 0.965576i | \(0.416237\pi\) | |||||||
\(152\) | 1.30597e6 | 0.0301634 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.66281e6 | 0.0587513 | ||||||||
\(155\) | −1.09558e7 | −0.236311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.45776e7 | 0.506862 | 0.253431 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253431 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(158\) | −1.11241e6 | −0.0224370 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.79762e6 | −0.150502 | ||||||||
\(161\) | −4.84033e7 | −0.914080 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.12800e7 | −1.28917 | −0.644586 | − | 0.764532i | \(-0.722970\pi\) | ||||
−0.644586 | + | 0.764532i | \(0.722970\pi\) | |||||||
\(164\) | 7.13085e7 | 1.26237 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.78761e6 | −0.149105 | ||||||||
\(167\) | −1.72745e7 | −0.287010 | −0.143505 | − | 0.989650i | \(-0.545837\pi\) | ||||
−0.143505 | + | 0.989650i | \(0.545837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.39253e7 | 0.221923 | ||||||||
\(170\) | 3.18486e6 | 0.0497186 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.65361e7 | −1.29673 | ||||||||
\(173\) | 4.27240e7 | 0.627351 | 0.313676 | − | 0.949530i | \(-0.398440\pi\) | ||||
0.313676 | + | 0.949530i | \(0.398440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.68254e7 | 1.22465 | ||||||||
\(176\) | −2.54833e7 | −0.352340 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.60541e6 | −0.0213361 | ||||||||
\(179\) | −5.80252e7 | −0.756191 | −0.378095 | − | 0.925767i | \(-0.623421\pi\) | ||||
−0.378095 | + | 0.925767i | \(0.623421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.33616e7 | −0.543539 | −0.271769 | − | 0.962362i | \(-0.587609\pi\) | ||||
−0.271769 | + | 0.962362i | \(0.587609\pi\) | |||||||
\(182\) | −1.45981e7 | −0.179493 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.29612e6 | −0.0981777 | ||||||||
\(185\) | −5.42044e7 | −0.629410 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16917e7 | 0.354405 | ||||||||
\(188\) | −1.57483e8 | −1.72855 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 776766. | 0.00821585 | ||||||||
\(191\) | 6.93621e7 | 0.720287 | 0.360143 | − | 0.932897i | \(-0.382728\pi\) | ||||
0.360143 | + | 0.932897i | \(0.382728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.17140e7 | 0.317541 | 0.158771 | − | 0.987315i | \(-0.449247\pi\) | ||||
0.158771 | + | 0.987315i | \(0.449247\pi\) | |||||||
\(194\) | 1.08736e7 | 0.106922 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.10065e8 | −1.99277 | ||||||||
\(197\) | 1.33959e8 | 1.24836 | 0.624178 | − | 0.781282i | \(-0.285434\pi\) | ||||
0.624178 | + | 0.781282i | \(0.285434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.57957e7 | 0.681803 | 0.340902 | − | 0.940099i | \(-0.389268\pi\) | ||||
0.340902 | + | 0.940099i | \(0.389268\pi\) | |||||||
\(200\) | 1.48815e7 | 0.131535 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.28564e7 | 0.109746 | ||||||||
\(203\) | 2.32090e7 | 0.194725 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.52006e7 | 0.690723 | ||||||||
\(206\) | −2.24463e7 | −0.178899 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.39706e8 | 1.07645 | ||||||||
\(209\) | 7.72939e6 | 0.0585644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.11972e8 | −1.55343 | −0.776713 | − | 0.629854i | \(-0.783115\pi\) | ||||
−0.776713 | + | 0.629854i | \(0.783115\pi\) | |||||||
\(212\) | −2.46233e8 | −1.77489 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −61472.9 | −0.000428781 0 | ||||||||
\(215\) | −1.03395e8 | −0.709519 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.13791e8 | −0.755959 | ||||||||
\(218\) | 1.12809e7 | 0.0737475 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.07218e7 | −0.194521 | ||||||||
\(221\) | −1.73741e8 | −1.08275 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.80114e8 | −1.08763 | −0.543814 | − | 0.839206i | \(-0.683020\pi\) | ||||
−0.543814 | + | 0.839206i | \(0.683020\pi\) | |||||||
\(224\) | −8.09888e7 | −0.481456 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.15434e6 | 0.0297025 | ||||||||
\(227\) | −7.73940e7 | −0.439154 | −0.219577 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219577 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.39410e8 | 0.767134 | 0.383567 | − | 0.923513i | \(-0.374696\pi\) | ||||
0.383567 | + | 0.923513i | \(0.374696\pi\) | |||||||
\(230\) | −4.93437e6 | −0.0267414 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.97793e6 | 0.0209146 | ||||||||
\(233\) | −1.24112e8 | −0.642787 | −0.321393 | − | 0.946946i | \(-0.604151\pi\) | ||||
−0.321393 | + | 0.946946i | \(0.604151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.88163e8 | −0.945796 | ||||||||
\(236\) | 2.60583e7 | 0.129049 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.30790e7 | 0.159050 | ||||||||
\(239\) | 1.55356e8 | 0.736096 | 0.368048 | − | 0.929807i | \(-0.380026\pi\) | ||||
0.368048 | + | 0.929807i | \(0.380026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.44462e8 | 1.58519 | 0.792597 | − | 0.609746i | \(-0.208729\pi\) | ||||
0.792597 | + | 0.609746i | \(0.208729\pi\) | |||||||
\(242\) | −1.79321e7 | −0.0813352 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.15166e8 | 1.38891 | ||||||||
\(245\) | −2.50989e8 | −1.09037 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.23743e7 | −0.178922 | ||||||||
\(248\) | −1.95033e7 | −0.0811945 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.13913e7 | 0.0865860 | ||||||||
\(251\) | 4.67431e8 | 1.86578 | 0.932888 | − | 0.360166i | \(-0.117280\pi\) | ||||
0.932888 | + | 0.360166i | \(0.117280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.91007e7 | −0.190619 | ||||||||
\(254\) | −3.52159e7 | −0.134841 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.45232e8 | 0.913561 | ||||||||
\(257\) | 4.09247e8 | 1.50390 | 0.751952 | − | 0.659218i | \(-0.229113\pi\) | ||||
0.751952 | + | 0.659218i | \(0.229113\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.62986e8 | −2.01349 | ||||||||
\(260\) | 1.68424e8 | 0.594288 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.03710e6 | −0.0138680 | ||||||||
\(263\) | −1.04382e8 | −0.353818 | −0.176909 | − | 0.984227i | \(-0.556610\pi\) | ||||
−0.176909 | + | 0.984227i | \(0.556610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.94204e8 | −0.971152 | ||||||||
\(266\) | 8.06776e6 | 0.0262825 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.51664e8 | 0.481293 | ||||||||
\(269\) | 1.95159e8 | 0.611302 | 0.305651 | − | 0.952144i | \(-0.401126\pi\) | ||||
0.305651 | + | 0.952144i | \(0.401126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.63467e8 | 1.10936 | 0.554681 | − | 0.832063i | \(-0.312840\pi\) | ||||
0.554681 | + | 0.832063i | \(0.312840\pi\) | |||||||
\(272\) | −3.16570e8 | −0.953845 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.87244e7 | −0.143093 | ||||||||
\(275\) | 8.80763e7 | 0.255385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.76920e8 | −1.06554 | −0.532771 | − | 0.846260i | \(-0.678849\pi\) | ||||
−0.532771 | + | 0.846260i | \(0.678849\pi\) | |||||||
\(278\) | 4.79364e7 | 0.133816 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.44167e7 | −0.175366 | ||||||||
\(281\) | −3.38642e8 | −0.910475 | −0.455238 | − | 0.890370i | \(-0.650446\pi\) | ||||
−0.455238 | + | 0.890370i | \(0.650446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.79439e8 | −0.732882 | −0.366441 | − | 0.930441i | \(-0.619424\pi\) | ||||
−0.366441 | + | 0.930441i | \(0.619424\pi\) | |||||||
\(284\) | −6.98764e8 | −1.81016 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.48085e7 | −0.0374308 | ||||||||
\(287\) | 8.84923e8 | 2.20963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.66455e7 | −0.0405653 | ||||||||
\(290\) | 2.36600e6 | 0.00569667 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.31382e8 | 0.308813 | ||||||||
\(293\) | −6.25978e8 | −1.45386 | −0.726930 | − | 0.686712i | \(-0.759054\pi\) | ||||
−0.726930 | + | 0.686712i | \(0.759054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.11349e7 | 0.0706106 | ||||||||
\(296\) | −9.64935e7 | −0.216260 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.70836e7 | −0.0592855 | ||||||||
\(299\) | 2.69181e8 | 0.582365 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07390e9 | −2.26976 | ||||||||
\(302\) | 2.33048e7 | 0.0486879 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.72092e7 | −0.157620 | ||||||||
\(305\) | 3.76566e8 | 0.759962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.80506e8 | −0.553297 | −0.276649 | − | 0.960971i | \(-0.589224\pi\) | ||||
−0.276649 | + | 0.960971i | \(0.589224\pi\) | |||||||
\(308\) | −3.19087e8 | −0.622275 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.16002e7 | −0.0221156 | ||||||||
\(311\) | −3.02914e8 | −0.571029 | −0.285515 | − | 0.958374i | \(-0.592165\pi\) | ||||
−0.285515 | + | 0.958374i | \(0.592165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.65931e8 | −1.41184 | −0.705918 | − | 0.708294i | \(-0.749465\pi\) | ||||
−0.705918 | + | 0.708294i | \(0.749465\pi\) | |||||||
\(314\) | 2.60231e7 | 0.0474357 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.33301e8 | 0.237645 | ||||||||
\(317\) | 1.06128e9 | 1.87120 | 0.935601 | − | 0.353058i | \(-0.114858\pi\) | ||||
0.935601 | + | 0.353058i | \(0.114858\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.35434e7 | 0.0406071 | ||||||||
\(320\) | 3.01337e8 | 0.514076 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.12501e7 | −0.0855459 | ||||||||
\(323\) | 9.60192e7 | 0.158544 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.82855e8 | −0.780234 | ||||||||
\(326\) | −7.54724e7 | −0.120650 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.51672e8 | 0.237327 | ||||||||
\(329\) | −1.95433e9 | −3.02561 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.08627e8 | −0.467774 | −0.233887 | − | 0.972264i | \(-0.575145\pi\) | ||||
−0.233887 | + | 0.972264i | \(0.575145\pi\) | |||||||
\(332\) | 1.05303e9 | 1.57927 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.82905e7 | −0.0268604 | ||||||||
\(335\) | 1.81210e8 | 0.263346 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.55380e8 | −1.07513 | −0.537565 | − | 0.843222i | \(-0.680656\pi\) | ||||
−0.537565 | + | 0.843222i | \(0.680656\pi\) | |||||||
\(338\) | 1.47443e7 | 0.0207691 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.81645e8 | −0.526603 | ||||||||
\(341\) | −1.15430e8 | −0.157645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.31016e9 | −1.75306 | ||||||||
\(344\) | −1.84061e8 | −0.243785 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.52368e7 | 0.0587119 | ||||||||
\(347\) | 2.59655e8 | 0.333614 | 0.166807 | − | 0.985990i | \(-0.446654\pi\) | ||||
0.166807 | + | 0.985990i | \(0.446654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.22817e8 | −0.532431 | −0.266215 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266215 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(350\) | 9.19321e7 | 0.114612 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.21556e7 | −0.100401 | ||||||||
\(353\) | −1.55553e9 | −1.88221 | −0.941105 | − | 0.338116i | \(-0.890210\pi\) | ||||
−0.941105 | + | 0.338116i | \(0.890210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.34895e8 | −0.990450 | ||||||||
\(356\) | 1.92378e8 | 0.225985 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.14380e7 | −0.0707696 | ||||||||
\(359\) | 7.61688e8 | 0.868853 | 0.434427 | − | 0.900707i | \(-0.356951\pi\) | ||||
0.434427 | + | 0.900707i | \(0.356951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.70453e8 | −0.973801 | ||||||||
\(362\) | −4.59119e7 | −0.0508681 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.74931e9 | 1.90113 | ||||||||
\(365\) | 1.56977e8 | 0.168971 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37332e8 | 0.145024 | 0.0725122 | − | 0.997368i | \(-0.476898\pi\) | ||||
0.0725122 | + | 0.997368i | \(0.476898\pi\) | |||||||
\(368\) | 4.90469e8 | 0.513031 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.73924e7 | −0.0589045 | ||||||||
\(371\) | −3.05570e9 | −3.10672 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.94107e8 | −0.293443 | −0.146722 | − | 0.989178i | \(-0.546872\pi\) | ||||
−0.146722 | + | 0.989178i | \(0.546872\pi\) | |||||||
\(374\) | 3.35556e7 | 0.0331677 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.34964e8 | −0.324968 | ||||||||
\(377\) | −1.29070e8 | −0.124060 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.95112e8 | 0.655870 | 0.327935 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327935 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(380\) | −9.30806e7 | −0.0870195 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.34417e7 | 0.0674094 | ||||||||
\(383\) | 5.22431e8 | 0.475153 | 0.237576 | − | 0.971369i | \(-0.423647\pi\) | ||||
0.237576 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.81251e8 | −0.340485 | ||||||||
\(386\) | 3.35792e7 | 0.0297177 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.30300e9 | −1.13249 | ||||||||
\(389\) | 1.26347e9 | 1.08829 | 0.544143 | − | 0.838993i | \(-0.316855\pi\) | ||||
0.544143 | + | 0.838993i | \(0.316855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.09958e8 | −0.516038 | ||||||||
\(392\) | −4.46806e8 | −0.374643 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.41837e8 | 0.116830 | ||||||||
\(395\) | 1.59271e8 | 0.130031 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.32040e8 | 0.587175 | 0.293588 | − | 0.955932i | \(-0.405151\pi\) | ||||
0.293588 | + | 0.955932i | \(0.405151\pi\) | |||||||
\(398\) | 8.02537e7 | 0.0638079 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.79799e8 | −0.687343 | ||||||||
\(401\) | 1.29683e9 | 1.00434 | 0.502168 | − | 0.864770i | \(-0.332536\pi\) | ||||
0.502168 | + | 0.864770i | \(0.332536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.32816e8 | 0.481626 | ||||||||
\(404\) | −1.54060e9 | −1.16240 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.45741e7 | 0.0182237 | ||||||||
\(407\) | −5.71097e8 | −0.419884 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.56134e9 | 1.85113 | 0.925563 | − | 0.378594i | \(-0.123592\pi\) | ||||
0.925563 | + | 0.378594i | \(0.123592\pi\) | |||||||
\(410\) | 9.02116e7 | 0.0646426 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.68976e9 | 1.89484 | ||||||||
\(413\) | 3.23378e8 | 0.225884 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.25818e9 | 0.864118 | ||||||||
\(416\) | 4.50396e8 | 0.306738 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.18400e6 | 0.00548086 | ||||||||
\(419\) | 1.65931e9 | 1.10199 | 0.550995 | − | 0.834509i | \(-0.314248\pi\) | ||||
0.550995 | + | 0.834509i | \(0.314248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.44008e9 | −1.59374 | −0.796870 | − | 0.604151i | \(-0.793512\pi\) | ||||
−0.796870 | + | 0.604151i | \(0.793512\pi\) | |||||||
\(422\) | −2.24440e8 | −0.145380 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.23734e8 | −0.333680 | ||||||||
\(425\) | 1.09414e9 | 0.691370 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.91115e9 | 2.43112 | ||||||||
\(428\) | 7.36636e6 | 0.00454150 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.09476e8 | −0.0664017 | ||||||||
\(431\) | −5.66963e8 | −0.341102 | −0.170551 | − | 0.985349i | \(-0.554555\pi\) | ||||
−0.170551 | + | 0.985349i | \(0.554555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.17068e9 | −0.692996 | −0.346498 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346498 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(434\) | −1.20484e8 | −0.0707479 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.35181e9 | −0.781109 | ||||||||
\(437\) | −1.48765e8 | −0.0852737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.09400e9 | −0.617151 | −0.308575 | − | 0.951200i | \(-0.599852\pi\) | ||||
−0.308575 | + | 0.951200i | \(0.599852\pi\) | |||||||
\(440\) | −6.53448e7 | −0.0365701 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.83960e8 | −0.101332 | ||||||||
\(443\) | −1.26000e8 | −0.0688584 | −0.0344292 | − | 0.999407i | \(-0.510961\pi\) | ||||
−0.0344292 | + | 0.999407i | \(0.510961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.29856e8 | 0.123650 | ||||||||
\(446\) | −1.90707e8 | −0.101788 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.12979e9 | 1.64453 | ||||||||
\(449\) | 2.96820e8 | 0.154750 | 0.0773750 | − | 0.997002i | \(-0.475346\pi\) | ||||
0.0773750 | + | 0.997002i | \(0.475346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.97673e8 | 0.460787 | ||||||||
\(452\) | −6.17650e8 | −0.314599 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.19459e7 | −0.0410990 | ||||||||
\(455\) | 2.09011e9 | 1.04023 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.03128e8 | 0.0995552 | 0.0497776 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497776 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(458\) | 1.47610e8 | 0.0717937 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.91291e8 | 0.283236 | ||||||||
\(461\) | 1.66300e9 | 0.790567 | 0.395283 | − | 0.918559i | \(-0.370646\pi\) | ||||
0.395283 | + | 0.918559i | \(0.370646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.36357e8 | −0.391614 | −0.195807 | − | 0.980642i | \(-0.562733\pi\) | ||||
−0.195807 | + | 0.980642i | \(0.562733\pi\) | |||||||
\(464\) | −2.35176e8 | −0.109290 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.31411e8 | −0.0601564 | ||||||||
\(467\) | 3.67614e9 | 1.67026 | 0.835129 | − | 0.550054i | \(-0.185393\pi\) | ||||
0.835129 | + | 0.550054i | \(0.185393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.88211e9 | 0.842444 | ||||||||
\(470\) | −1.99230e8 | −0.0885142 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.54256e7 | 0.0242612 | ||||||||
\(473\) | −1.08937e9 | −0.473326 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.66853e8 | 0.114247 | ||||||||
\(476\) | −3.96390e9 | −1.68460 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.64493e8 | 0.0688890 | ||||||||
\(479\) | −4.47354e9 | −1.85985 | −0.929924 | − | 0.367752i | \(-0.880127\pi\) | ||||
−0.929924 | + | 0.367752i | \(0.880127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.13089e9 | 1.28280 | ||||||||
\(482\) | 3.64722e8 | 0.148353 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.14883e9 | 0.861475 | ||||||||
\(485\) | −1.55685e9 | −0.619654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.90180e8 | 0.231544 | 0.115772 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115772 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(488\) | 6.70354e8 | 0.261117 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.65751e8 | −0.102044 | ||||||||
\(491\) | −1.22115e9 | −0.465568 | −0.232784 | − | 0.972528i | \(-0.574784\pi\) | ||||
−0.232784 | + | 0.972528i | \(0.574784\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.92471e8 | 0.109930 | ||||||||
\(494\) | −4.48666e7 | −0.0167447 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.15304e9 | 0.424285 | ||||||||
\(497\) | −8.67151e9 | −3.16846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.48542e9 | 0.535176 | 0.267588 | − | 0.963533i | \(-0.413773\pi\) | ||||
0.267588 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(500\) | −2.56335e9 | −0.917090 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.94923e8 | 0.174612 | ||||||||
\(503\) | 2.28973e9 | 0.802224 | 0.401112 | − | 0.916029i | \(-0.368624\pi\) | ||||
0.401112 | + | 0.916029i | \(0.368624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.84073e9 | −0.636019 | ||||||||
\(506\) | −5.19885e7 | −0.0178394 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.21996e9 | 1.42819 | ||||||||
\(509\) | 4.18910e9 | 1.40802 | 0.704009 | − | 0.710191i | \(-0.251392\pi\) | ||||
0.704009 | + | 0.710191i | \(0.251392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63042e9 | 0.540539 | ||||||||
\(512\) | 1.37179e9 | 0.451691 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.33317e8 | 0.140746 | ||||||||
\(515\) | 3.21377e9 | 1.03679 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.98249e9 | −0.630948 | ||||||||
\(518\) | −5.96098e8 | −0.188436 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.58235e8 | 0.111727 | ||||||||
\(521\) | −1.43063e9 | −0.443196 | −0.221598 | − | 0.975138i | \(-0.571127\pi\) | ||||
−0.221598 | + | 0.975138i | \(0.571127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.34628e9 | 0.411509 | 0.205755 | − | 0.978604i | \(-0.434035\pi\) | ||||
0.205755 | + | 0.978604i | \(0.434035\pi\) | |||||||
\(524\) | 4.83770e8 | 0.146886 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.10521e8 | −0.0331127 | ||||||||
\(527\) | −1.43395e9 | −0.426772 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.45980e9 | −0.722446 | ||||||||
\(530\) | −3.11507e8 | −0.0908871 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.66768e8 | −0.278376 | ||||||||
\(533\) | −4.92125e9 | −1.40776 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.80145e6 | 0.00248494 | ||||||||
\(536\) | 3.22586e8 | 0.0904835 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.06637e8 | 0.0572099 | ||||||||
\(539\) | −2.64442e9 | −0.727395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.77248e9 | −1.02432 | −0.512162 | − | 0.858889i | \(-0.671155\pi\) | ||||
−0.512162 | + | 0.858889i | \(0.671155\pi\) | |||||||
\(542\) | 3.84845e8 | 0.103822 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.02059e9 | −0.271803 | ||||||||
\(545\) | −1.61516e9 | −0.427393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.81833e9 | 0.475026 | 0.237513 | − | 0.971384i | \(-0.423668\pi\) | ||||
0.237513 | + | 0.971384i | \(0.423668\pi\) | |||||||
\(548\) | 5.83869e9 | 1.51560 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.32566e7 | 0.0239007 | ||||||||
\(551\) | 7.13317e7 | 0.0181657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.65424e9 | 0.415969 | ||||||||
\(554\) | −3.99089e8 | −0.0997208 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.74427e9 | −1.41734 | ||||||||
\(557\) | 5.99186e7 | 0.0146916 | 0.00734579 | − | 0.999973i | \(-0.497662\pi\) | ||||
0.00734579 | + | 0.999973i | \(0.497662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.97216e9 | 1.44607 | ||||||||
\(560\) | 3.80833e9 | 0.916382 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.58559e8 | −0.0852086 | ||||||||
\(563\) | 5.52477e9 | 1.30477 | 0.652386 | − | 0.757887i | \(-0.273768\pi\) | ||||
0.652386 | + | 0.757887i | \(0.273768\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.37978e8 | −0.172137 | ||||||||
\(566\) | −2.95874e8 | −0.0685882 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.48626e9 | −0.340311 | ||||||||
\(569\) | 5.19237e9 | 1.18161 | 0.590803 | − | 0.806816i | \(-0.298811\pi\) | ||||
0.590803 | + | 0.806816i | \(0.298811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.98094e9 | 0.445293 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(572\) | 1.77451e9 | 0.396454 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.36970e8 | 0.206792 | ||||||||
\(575\) | −1.69517e9 | −0.371858 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.25873e9 | −0.706209 | −0.353104 | − | 0.935584i | \(-0.614874\pi\) | ||||
−0.353104 | + | 0.935584i | \(0.614874\pi\) | |||||||
\(578\) | −1.76245e7 | −0.00379638 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.83520e8 | −0.0603372 | ||||||||
\(581\) | 1.30679e10 | 2.76432 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.09973e9 | −0.647863 | ||||||||
\(584\) | 2.79448e8 | 0.0580571 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.62795e8 | −0.136062 | ||||||||
\(587\) | 7.32754e8 | 0.149529 | 0.0747643 | − | 0.997201i | \(-0.476180\pi\) | ||||
0.0747643 | + | 0.997201i | \(0.476180\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.49730e8 | −0.0705227 | ||||||||
\(590\) | 3.29661e7 | 0.00660823 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.70472e9 | 1.13008 | ||||||||
\(593\) | −7.42096e9 | −1.46140 | −0.730699 | − | 0.682700i | \(-0.760806\pi\) | ||||
−0.730699 | + | 0.682700i | \(0.760806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.73613e9 | −0.921752 | ||||||||
\(596\) | 3.24545e9 | 0.627933 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.85013e8 | 0.0545018 | ||||||||
\(599\) | 1.05376e9 | 0.200331 | 0.100165 | − | 0.994971i | \(-0.468063\pi\) | ||||
0.100165 | + | 0.994971i | \(0.468063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.07267e9 | −1.32899 | −0.664496 | − | 0.747292i | \(-0.731354\pi\) | ||||
−0.664496 | + | 0.747292i | \(0.731354\pi\) | |||||||
\(602\) | −1.13706e9 | −0.212420 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.79264e9 | −0.515686 | ||||||||
\(605\) | 2.56745e9 | 0.471367 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.55310e9 | 0.826317 | 0.413159 | − | 0.910659i | \(-0.364426\pi\) | ||||
0.413159 | + | 0.910659i | \(0.364426\pi\) | |||||||
\(608\) | −2.48914e8 | −0.0449146 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.98714e8 | 0.0711225 | ||||||||
\(611\) | 1.08685e10 | 1.92763 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.47628e9 | 1.13557 | 0.567785 | − | 0.823177i | \(-0.307800\pi\) | ||||
0.567785 | + | 0.823177i | \(0.307800\pi\) | |||||||
\(614\) | −2.97004e8 | −0.0517814 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.78694e8 | −0.116988 | ||||||||
\(617\) | −4.44035e9 | −0.761061 | −0.380531 | − | 0.924768i | \(-0.624259\pi\) | ||||
−0.380531 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.96260e9 | 0.502060 | 0.251030 | − | 0.967979i | \(-0.419231\pi\) | ||||
0.251030 | + | 0.967979i | \(0.419231\pi\) | |||||||
\(620\) | 1.39006e9 | 0.234241 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.20730e8 | −0.0534409 | ||||||||
\(623\) | 2.38737e9 | 0.395559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.24534e9 | 0.204037 | ||||||||
\(626\) | −8.10979e8 | −0.132129 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.11837e9 | −0.502423 | ||||||||
\(629\) | −7.09452e9 | −1.13670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.60390e9 | 0.254142 | 0.127071 | − | 0.991894i | \(-0.459442\pi\) | ||||
0.127071 | + | 0.991894i | \(0.459442\pi\) | |||||||
\(632\) | 2.83530e8 | 0.0446775 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.12369e9 | 0.175120 | ||||||||
\(635\) | 5.04207e9 | 0.781450 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44973e10 | 2.22229 | ||||||||
\(638\) | 2.49281e7 | 0.00380030 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.31715e9 | 0.198613 | ||||||||
\(641\) | 6.32307e8 | 0.0948254 | 0.0474127 | − | 0.998875i | \(-0.484902\pi\) | ||||
0.0474127 | + | 0.998875i | \(0.484902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.72453e9 | −0.700842 | −0.350421 | − | 0.936592i | \(-0.613961\pi\) | ||||
−0.350421 | + | 0.936592i | \(0.613961\pi\) | |||||||
\(644\) | 6.14136e9 | 0.906074 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.01667e8 | 0.0148376 | ||||||||
\(647\) | 6.52515e9 | 0.947165 | 0.473582 | − | 0.880750i | \(-0.342961\pi\) | ||||
0.473582 | + | 0.880750i | \(0.342961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.28037e8 | 0.0471049 | ||||||||
\(650\) | −5.11254e8 | −0.0730197 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.04393e9 | 1.27788 | ||||||||
\(653\) | 7.88114e9 | 1.10762 | 0.553812 | − | 0.832641i | \(-0.313172\pi\) | ||||
0.553812 | + | 0.832641i | \(0.313172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.78017e8 | 0.0803703 | ||||||||
\(656\) | −8.96689e9 | −1.24016 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.06928e9 | −0.283157 | ||||||||
\(659\) | −7.14701e9 | −0.972805 | −0.486402 | − | 0.873735i | \(-0.661691\pi\) | ||||
−0.486402 | + | 0.873735i | \(0.661691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.05842e9 | −0.681255 | −0.340627 | − | 0.940198i | \(-0.610639\pi\) | ||||
−0.340627 | + | 0.940198i | \(0.610639\pi\) | |||||||
\(662\) | −3.26779e8 | −0.0437776 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.23978e9 | 0.296904 | ||||||||
\(665\) | −1.15511e9 | −0.152317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.53132e8 | −0.0591267 | ||||||||
\(668\) | 2.19177e9 | 0.284496 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.91868e8 | 0.0246457 | ||||||||
\(671\) | 3.96750e9 | 0.506977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.46795e10 | −1.85634 | −0.928169 | − | 0.372158i | \(-0.878618\pi\) | ||||
−0.928169 | + | 0.372158i | \(0.878618\pi\) | |||||||
\(674\) | −7.99808e8 | −0.100618 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.76683e9 | −0.219979 | ||||||||
\(677\) | −8.90911e9 | −1.10350 | −0.551752 | − | 0.834008i | \(-0.686041\pi\) | ||||
−0.551752 | + | 0.834008i | \(0.686041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.61700e10 | −1.98228 | ||||||||
\(680\) | −8.11753e8 | −0.0990017 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.22219e8 | −0.0147535 | ||||||||
\(683\) | 1.04640e10 | 1.25668 | 0.628338 | − | 0.777940i | \(-0.283735\pi\) | ||||
0.628338 | + | 0.777940i | \(0.283735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.97617e9 | 0.829278 | ||||||||
\(686\) | −1.38722e9 | −0.164063 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.08817e10 | 1.27391 | ||||||||
\(689\) | 1.69934e10 | 1.97931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.56029e9 | −1.10230 | −0.551148 | − | 0.834408i | \(-0.685810\pi\) | ||||
−0.551148 | + | 0.834408i | \(0.685810\pi\) | |||||||
\(692\) | −5.42078e9 | −0.621857 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.74927e8 | 0.0312219 | ||||||||
\(695\) | −6.86335e9 | −0.775513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11514e10 | 1.24743 | ||||||||
\(698\) | −4.47685e8 | −0.0498285 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.10163e10 | −1.21393 | ||||||||
\(701\) | −4.24136e9 | −0.465041 | −0.232521 | − | 0.972591i | \(-0.574697\pi\) | ||||
−0.232521 | + | 0.972591i | \(0.574697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.73031e9 | −0.187836 | ||||||||
\(704\) | 3.17488e9 | 0.342944 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.64702e9 | −0.176150 | ||||||||
\(707\) | −1.91185e10 | −2.03463 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.04133e10 | 1.09730 | 0.548652 | − | 0.836051i | \(-0.315141\pi\) | ||||
0.548652 | + | 0.836051i | \(0.315141\pi\) | |||||||
\(710\) | −8.84000e8 | −0.0926932 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.09184e8 | 0.0424853 | ||||||||
\(713\) | 2.22164e9 | 0.229542 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.12022e9 | 0.216925 | ||||||||
\(716\) | 7.36218e9 | 0.749567 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.06487e8 | 0.0813133 | ||||||||
\(719\) | 6.99544e9 | 0.701882 | 0.350941 | − | 0.936398i | \(-0.385862\pi\) | ||||
0.350941 | + | 0.936398i | \(0.385862\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.33794e10 | 3.31669 | ||||||||
\(722\) | −9.21649e8 | −0.0911351 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.50168e9 | 0.538778 | ||||||||
\(725\) | 8.12824e8 | 0.0792161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.85412e10 | 1.78965 | 0.894824 | − | 0.446418i | \(-0.147301\pi\) | ||||
0.894824 | + | 0.446418i | \(0.147301\pi\) | |||||||
\(728\) | 3.72076e9 | 0.357414 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.66210e8 | 0.0158135 | ||||||||
\(731\) | −1.35328e10 | −1.28137 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.68407e9 | −0.720655 | −0.360327 | − | 0.932826i | \(-0.617335\pi\) | ||||
−0.360327 | + | 0.932826i | \(0.617335\pi\) | |||||||
\(734\) | 1.45409e8 | 0.0135724 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.58122e9 | 0.146191 | ||||||||
\(737\) | 1.90923e9 | 0.175680 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.62766e9 | −0.148357 | −0.0741785 | − | 0.997245i | \(-0.523633\pi\) | ||||
−0.0741785 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(740\) | 6.87740e9 | 0.623897 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.23542e9 | −0.290748 | ||||||||
\(743\) | 1.23451e9 | 0.110417 | 0.0552084 | − | 0.998475i | \(-0.482418\pi\) | ||||
0.0552084 | + | 0.998475i | \(0.482418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.87772e9 | 0.343581 | ||||||||
\(746\) | −3.11405e8 | −0.0274625 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.02101e9 | −0.351301 | ||||||||
\(749\) | 9.14149e7 | 0.00794934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.87234e10 | 1.61304 | 0.806520 | − | 0.591206i | \(-0.201348\pi\) | ||||
0.806520 | + | 0.591206i | \(0.201348\pi\) | |||||||
\(752\) | 1.98032e10 | 1.69814 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.36662e8 | −0.0116104 | ||||||||
\(755\) | −3.33669e9 | −0.282164 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.90822e9 | −0.327449 | −0.163724 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163724 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(758\) | 7.35995e8 | 0.0613809 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.97981e8 | −0.0163597 | ||||||||
\(761\) | −8.54296e9 | −0.702687 | −0.351344 | − | 0.936247i | \(-0.614275\pi\) | ||||
−0.351344 | + | 0.936247i | \(0.614275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.67756e10 | −1.36723 | ||||||||
\(764\) | −8.80059e9 | −0.713978 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.53158e8 | 0.0444681 | ||||||||
\(767\) | −1.79837e9 | −0.143912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.98742e9 | −0.712677 | −0.356338 | − | 0.934357i | \(-0.615975\pi\) | ||||
−0.356338 | + | 0.934357i | \(0.615975\pi\) | |||||||
\(770\) | −4.03674e8 | −0.0318650 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.02384e9 | −0.314760 | ||||||||
\(773\) | −7.14394e9 | −0.556301 | −0.278150 | − | 0.960538i | \(-0.589721\pi\) | ||||
−0.278150 | + | 0.960538i | \(0.589721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.98517e9 | −0.307532 | ||||||||
\(776\) | −2.77146e9 | −0.212908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.33779e9 | 0.101849 | ||||||||
\(779\) | 2.71976e9 | 0.206134 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.79645e9 | −0.660737 | ||||||||
\(782\) | −6.45833e8 | −0.0482944 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.64153e10 | 1.95771 | ||||||||
\(785\) | −3.72588e9 | −0.274907 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.12694e9 | 0.155541 | 0.0777705 | − | 0.996971i | \(-0.475220\pi\) | ||||
0.0777705 | + | 0.996971i | \(0.475220\pi\) | |||||||
\(788\) | −1.69965e10 | −1.23742 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.68638e8 | 0.0121692 | ||||||||
\(791\) | −7.66490e9 | −0.550667 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.17507e10 | −1.54888 | ||||||||
\(794\) | 7.75095e8 | 0.0549519 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.61688e9 | −0.675832 | ||||||||
\(797\) | 7.00833e9 | 0.490355 | 0.245177 | − | 0.969478i | \(-0.421154\pi\) | ||||
0.245177 | + | 0.969478i | \(0.421154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.46277e10 | −1.70809 | ||||||||
\(800\) | −2.83638e9 | −0.195862 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.37311e9 | 0.0939926 | ||||||||
\(803\) | 1.65391e9 | 0.112722 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.33780e9 | 0.495770 | ||||||||
\(806\) | 6.70035e8 | 0.0450739 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.27682e9 | −0.218531 | ||||||||
\(809\) | −2.24886e10 | −1.49329 | −0.746643 | − | 0.665225i | \(-0.768335\pi\) | ||||
−0.746643 | + | 0.665225i | \(0.768335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.32750e9 | −0.482373 | −0.241186 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241186 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(812\) | −2.94474e9 | −0.193019 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.04686e8 | −0.0392957 | ||||||||
\(815\) | 1.08058e10 | 0.699209 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.30056e9 | −0.211743 | ||||||||
\(818\) | 2.71199e9 | 0.173241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.08102e10 | −0.684673 | ||||||||
\(821\) | 1.86005e10 | 1.17307 | 0.586534 | − | 0.809924i | \(-0.300492\pi\) | ||||
0.586534 | + | 0.809924i | \(0.300492\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.44677e9 | −0.215532 | −0.107766 | − | 0.994176i | \(-0.534370\pi\) | ||||
−0.107766 | + | 0.994176i | \(0.534370\pi\) | |||||||
\(824\) | 5.72108e9 | 0.356232 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.42397e8 | 0.0211398 | ||||||||
\(827\) | −5.34418e9 | −0.328558 | −0.164279 | − | 0.986414i | \(-0.552530\pi\) | ||||
−0.164279 | + | 0.986414i | \(0.552530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.24427e10 | 0.758532 | 0.379266 | − | 0.925288i | \(-0.376176\pi\) | ||||
0.379266 | + | 0.925288i | \(0.376176\pi\) | |||||||
\(830\) | 1.33218e9 | 0.0808701 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.74054e10 | −1.04774 | ||||||||
\(833\) | −3.28506e10 | −1.96918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.61876e9 | 0.155666 | ||||||||
\(836\) | −9.80697e8 | −0.0580514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.75690e9 | 0.103132 | ||||||||
\(839\) | −2.08037e10 | −1.21611 | −0.608056 | − | 0.793894i | \(-0.708050\pi\) | ||||
−0.608056 | + | 0.793894i | \(0.708050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.70326e10 | −0.987404 | ||||||||
\(842\) | −2.58360e9 | −0.149153 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.68948e10 | 1.53982 | ||||||||
\(845\) | −2.11104e9 | −0.120364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.66665e10 | 1.50790 | ||||||||
\(848\) | 3.09633e10 | 1.74366 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.15849e9 | 0.0647032 | ||||||||
\(851\) | 1.09917e10 | 0.611380 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.30134e10 | 1.82125 | 0.910623 | − | 0.413239i | \(-0.135603\pi\) | ||||
0.910623 | + | 0.413239i | \(0.135603\pi\) | |||||||
\(854\) | 4.14118e9 | 0.227521 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.56681e7 | 0.000853806 0 | ||||||||
\(857\) | −7.37991e9 | −0.400515 | −0.200257 | − | 0.979743i | \(-0.564178\pi\) | ||||
−0.200257 | + | 0.979743i | \(0.564178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.66866e9 | 0.466633 | 0.233317 | − | 0.972401i | \(-0.425042\pi\) | ||||
0.233317 | + | 0.972401i | \(0.425042\pi\) | |||||||
\(860\) | 1.31186e10 | 0.703305 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00309e8 | −0.0319227 | ||||||||
\(863\) | 9.44417e8 | 0.0500180 | 0.0250090 | − | 0.999687i | \(-0.492039\pi\) | ||||
0.0250090 | + | 0.999687i | \(0.492039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.47684e9 | −0.340257 | ||||||||
\(866\) | −1.23953e9 | −0.0648554 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.44377e10 | 0.749338 | ||||||||
\(869\) | 1.67807e9 | 0.0867445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04668e10 | −0.536725 | ||||||||
\(872\) | −2.87527e9 | −0.146849 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.57514e8 | −0.00798050 | ||||||||
\(875\) | −3.18106e10 | −1.60525 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.94376e10 | −0.973071 | −0.486535 | − | 0.873661i | \(-0.661740\pi\) | ||||
−0.486535 | + | 0.873661i | \(0.661740\pi\) | |||||||
\(878\) | −1.15834e9 | −0.0577573 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.86320e9 | 0.191099 | ||||||||
\(881\) | −3.61733e10 | −1.78227 | −0.891134 | − | 0.453741i | \(-0.850089\pi\) | ||||
−0.891134 | + | 0.453741i | \(0.850089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.10672e10 | −1.02978 | −0.514890 | − | 0.857256i | \(-0.672167\pi\) | ||||
−0.514890 | + | 0.857256i | \(0.672167\pi\) | |||||||
\(884\) | 2.20441e10 | 1.07327 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.33410e8 | −0.00644424 | ||||||||
\(887\) | −3.08019e10 | −1.48199 | −0.740993 | − | 0.671512i | \(-0.765645\pi\) | ||||
−0.740993 | + | 0.671512i | \(0.765645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.23688e10 | 2.49986 | ||||||||
\(890\) | 2.43375e8 | 0.0115721 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.28527e10 | 1.07810 | ||||||||
\(893\) | −6.00653e9 | −0.282256 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.79645e9 | 0.410135 | ||||||||
\(896\) | 1.36804e10 | 0.635363 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.14277e8 | 0.0144826 | ||||||||
\(899\) | −1.06526e9 | −0.0488988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.85067e10 | −1.75388 | ||||||||
\(902\) | 9.50469e8 | 0.0431236 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.31373e9 | −0.0591449 | ||||||||
\(905\) | 6.57349e9 | 0.294799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.57628e10 | 0.701466 | 0.350733 | − | 0.936475i | \(-0.385932\pi\) | ||||
0.350733 | + | 0.936475i | \(0.385932\pi\) | |||||||
\(908\) | 9.81966e9 | 0.435307 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.21304e9 | 0.0973517 | ||||||||
\(911\) | −8.64623e9 | −0.378890 | −0.189445 | − | 0.981891i | \(-0.560669\pi\) | ||||
−0.189445 | + | 0.981891i | \(0.560669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.32561e10 | 0.576460 | ||||||||
\(914\) | 2.15075e8 | 0.00931706 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.76883e10 | −0.760415 | ||||||||
\(917\) | 6.00348e9 | 0.257105 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.72145e10 | −0.731628 | −0.365814 | − | 0.930688i | \(-0.619209\pi\) | ||||
−0.365814 | + | 0.930688i | \(0.619209\pi\) | |||||||
\(920\) | 1.25767e9 | 0.0532486 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.76081e9 | 0.0739867 | ||||||||
\(923\) | 4.82242e10 | 2.01864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.97168e10 | −0.819107 | ||||||||
\(926\) | −8.85547e8 | −0.0366499 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.58184e8 | −0.0311427 | ||||||||
\(929\) | −2.13454e10 | −0.873471 | −0.436735 | − | 0.899590i | \(-0.643865\pi\) | ||||
−0.436735 | + | 0.899590i | \(0.643865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.01205e9 | −0.325402 | ||||||||
\(932\) | 1.57472e10 | 0.637157 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.89236e9 | 0.156314 | ||||||||
\(935\) | −4.80436e9 | −0.192219 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.94917e9 | 0.117115 | 0.0585573 | − | 0.998284i | \(-0.481350\pi\) | ||||
0.0585573 | + | 0.998284i | \(0.481350\pi\) | |||||||
\(938\) | 1.99281e9 | 0.0788417 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.38740e10 | 0.937513 | ||||||||
\(941\) | −8.66911e9 | −0.339165 | −0.169582 | − | 0.985516i | \(-0.554242\pi\) | ||||
−0.169582 | + | 0.985516i | \(0.554242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.72772e10 | −0.670937 | ||||||||
\(944\) | −3.27677e9 | −0.126778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.15344e9 | −0.0442971 | ||||||||
\(947\) | −1.86313e10 | −0.712884 | −0.356442 | − | 0.934317i | \(-0.616010\pi\) | ||||
−0.356442 | + | 0.934317i | \(0.616010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.06713e9 | −0.344380 | ||||||||
\(950\) | 2.82548e8 | 0.0106920 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.43115e9 | −0.316707 | ||||||||
\(953\) | −3.78151e10 | −1.41527 | −0.707637 | − | 0.706576i | \(-0.750239\pi\) | ||||
−0.707637 | + | 0.706576i | \(0.750239\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.05151e10 | −0.390662 | ||||||||
\(956\) | −1.97114e10 | −0.729649 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.73666e9 | −0.174057 | ||||||||
\(959\) | 7.24570e10 | 2.65286 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.22898e10 | −0.810165 | ||||||||
\(962\) | 3.31503e9 | 0.120054 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.37050e10 | −1.57131 | ||||||||
\(965\) | −4.80775e9 | −0.172225 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.55682e10 | −1.26494 | −0.632470 | − | 0.774585i | \(-0.717959\pi\) | ||||
−0.632470 | + | 0.774585i | \(0.717959\pi\) | |||||||
\(968\) | 4.57052e9 | 0.161958 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.64841e9 | −0.0579915 | ||||||||
\(971\) | −2.79517e10 | −0.979806 | −0.489903 | − | 0.871777i | \(-0.662968\pi\) | ||||
−0.489903 | + | 0.871777i | \(0.662968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.12852e10 | −2.48087 | ||||||||
\(974\) | 6.24891e8 | 0.0216695 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.96315e10 | −1.36448 | ||||||||
\(977\) | 6.61358e9 | 0.226885 | 0.113443 | − | 0.993545i | \(-0.463812\pi\) | ||||
0.113443 | + | 0.993545i | \(0.463812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.42176e9 | 0.0824882 | ||||||||
\(980\) | 3.18453e10 | 1.08082 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.29297e9 | −0.0435711 | ||||||||
\(983\) | −1.77476e10 | −0.595939 | −0.297970 | − | 0.954575i | \(-0.596309\pi\) | ||||
−0.297970 | + | 0.954575i | \(0.596309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.03077e10 | −0.677071 | ||||||||
\(986\) | 3.09672e8 | 0.0102881 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.37641e9 | 0.177355 | ||||||||
\(989\) | 2.09667e10 | 0.689195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.22116e9 | −0.137776 | −0.0688880 | − | 0.997624i | \(-0.521945\pi\) | ||||
−0.0688880 | + | 0.997624i | \(0.521945\pi\) | |||||||
\(992\) | 3.71728e9 | 0.120902 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.18153e9 | −0.296526 | ||||||||
\(995\) | −1.14904e10 | −0.369790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.02379e10 | −0.646742 | −0.323371 | − | 0.946272i | \(-0.604816\pi\) | ||||
−0.323371 | + | 0.946272i | \(0.604816\pi\) | |||||||
\(998\) | 1.57278e9 | 0.0500854 | ||||||||
\(999\) | 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.b.1.8 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.9 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.9 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.8 | 16 | 1.1 | even | 1 | trivial |