Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 24x^{2} - 3x + 46 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.52801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52801 | 0.540232 | 0.270116 | − | 0.962828i | \(-0.412938\pi\) | ||||
0.270116 | + | 0.962828i | \(0.412938\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.66519 | −0.708149 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −20.8805 | −0.922797 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.3481 | −1.40746 | −0.703729 | − | 0.710469i | \(-0.748483\pi\) | ||||
−0.703729 | + | 0.710469i | \(0.748483\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.2268 | −1.86095 | −0.930476 | − | 0.366353i | \(-0.880606\pi\) | ||||
−0.930476 | + | 0.366353i | \(0.880606\pi\) | |||||||
\(14\) | 10.6960 | 0.204189 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.4160 | 0.209625 | ||||||||
\(17\) | −80.6781 | −1.15102 | −0.575509 | − | 0.817795i | \(-0.695196\pi\) | ||||
−0.575509 | + | 0.817795i | \(0.695196\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −29.8288 | −0.360168 | −0.180084 | − | 0.983651i | \(-0.557637\pi\) | ||||
−0.180084 | + | 0.983651i | \(0.557637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −78.4602 | −0.760354 | ||||||||
\(23\) | −1.71385 | −0.0155375 | −0.00776874 | − | 0.999970i | \(-0.502473\pi\) | ||||
−0.00776874 | + | 0.999970i | \(0.502473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −133.283 | −1.00535 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −39.6564 | −0.267655 | ||||||||
\(29\) | 204.810 | 1.31146 | 0.655730 | − | 0.754996i | \(-0.272361\pi\) | ||||
0.655730 | + | 0.754996i | \(0.272361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −150.176 | −0.870080 | −0.435040 | − | 0.900411i | \(-0.643266\pi\) | ||||
−0.435040 | + | 0.900411i | \(0.643266\pi\) | |||||||
\(32\) | 187.544 | 1.03604 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −123.277 | −0.621817 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 366.397 | 1.62798 | 0.813990 | − | 0.580879i | \(-0.197291\pi\) | ||||
0.813990 | + | 0.580879i | \(0.197291\pi\) | |||||||
\(38\) | −45.5786 | −0.194575 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −176.696 | −0.673057 | −0.336528 | − | 0.941673i | \(-0.609253\pi\) | ||||
−0.336528 | + | 0.941673i | \(0.609253\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 394.793 | 1.40013 | 0.700063 | − | 0.714081i | \(-0.253155\pi\) | ||||
0.700063 | + | 0.714081i | \(0.253155\pi\) | |||||||
\(44\) | 290.897 | 0.996690 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.61877 | −0.00839385 | ||||||||
\(47\) | −507.757 | −1.57583 | −0.787915 | − | 0.615784i | \(-0.788839\pi\) | ||||
−0.787915 | + | 0.615784i | \(0.788839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 494.157 | 1.31783 | ||||||||
\(53\) | 149.869 | 0.388416 | 0.194208 | − | 0.980960i | \(-0.437786\pi\) | ||||
0.194208 | + | 0.980960i | \(0.437786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −146.164 | −0.348785 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 312.952 | 0.708493 | ||||||||
\(59\) | −463.249 | −1.02220 | −0.511101 | − | 0.859521i | \(-0.670762\pi\) | ||||
−0.511101 | + | 0.859521i | \(0.670762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 380.956 | 0.799613 | 0.399807 | − | 0.916600i | \(-0.369077\pi\) | ||||
0.399807 | + | 0.916600i | \(0.369077\pi\) | |||||||
\(62\) | −229.471 | −0.470045 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 179.240 | 0.350079 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −797.666 | −1.45448 | −0.727242 | − | 0.686381i | \(-0.759198\pi\) | ||||
−0.727242 | + | 0.686381i | \(0.759198\pi\) | |||||||
\(68\) | 457.057 | 0.815093 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 220.174 | 0.368025 | 0.184013 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184013 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1013.61 | 1.62512 | 0.812559 | − | 0.582878i | \(-0.198074\pi\) | ||||
0.812559 | + | 0.582878i | \(0.198074\pi\) | |||||||
\(74\) | 559.857 | 0.879487 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 168.986 | 0.255053 | ||||||||
\(77\) | −359.437 | −0.531969 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −111.805 | −0.159228 | −0.0796140 | − | 0.996826i | \(-0.525369\pi\) | ||||
−0.0796140 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −269.993 | −0.363607 | ||||||||
\(83\) | −853.761 | −1.12907 | −0.564533 | − | 0.825411i | \(-0.690944\pi\) | ||||
−0.564533 | + | 0.825411i | \(0.690944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 603.247 | 0.756393 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1072.17 | 1.29880 | ||||||||
\(89\) | 935.860 | 1.11462 | 0.557309 | − | 0.830305i | \(-0.311834\pi\) | ||||
0.557309 | + | 0.830305i | \(0.311834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −610.588 | −0.703374 | ||||||||
\(92\) | 9.70929 | 0.0110029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −775.857 | −0.851314 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 783.811 | 0.820453 | 0.410227 | − | 0.911984i | \(-0.365450\pi\) | ||||
0.410227 | + | 0.911984i | \(0.365450\pi\) | |||||||
\(98\) | 74.8723 | 0.0771760 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1805.17 | −1.77842 | −0.889212 | − | 0.457495i | \(-0.848747\pi\) | ||||
−0.889212 | + | 0.457495i | \(0.848747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 578.608 | 0.553514 | 0.276757 | − | 0.960940i | \(-0.410740\pi\) | ||||
0.276757 | + | 0.960940i | \(0.410740\pi\) | |||||||
\(104\) | 1821.34 | 1.71728 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 229.000 | 0.209835 | ||||||||
\(107\) | 214.800 | 0.194070 | 0.0970349 | − | 0.995281i | \(-0.469064\pi\) | ||||
0.0970349 | + | 0.995281i | \(0.469064\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 812.409 | 0.713896 | 0.356948 | − | 0.934124i | \(-0.383817\pi\) | ||||
0.356948 | + | 0.934124i | \(0.383817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 93.9119 | 0.0792307 | ||||||||
\(113\) | −1596.30 | −1.32891 | −0.664457 | − | 0.747326i | \(-0.731337\pi\) | ||||
−0.664457 | + | 0.747326i | \(0.731337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1160.29 | −0.928709 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −707.848 | −0.552227 | ||||||||
\(119\) | −564.747 | −0.435044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1305.63 | 0.980936 | ||||||||
\(122\) | 582.103 | 0.431977 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 850.778 | 0.616146 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1469.71 | 1.02690 | 0.513449 | − | 0.858120i | \(-0.328368\pi\) | ||||
0.513449 | + | 0.858120i | \(0.328368\pi\) | |||||||
\(128\) | −1226.47 | −0.846919 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1217.36 | 0.811919 | 0.405959 | − | 0.913891i | \(-0.366937\pi\) | ||||
0.405959 | + | 0.913891i | \(0.366937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −208.802 | −0.136131 | ||||||||
\(134\) | −1218.84 | −0.785759 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1684.60 | 1.06216 | ||||||||
\(137\) | −1637.23 | −1.02101 | −0.510503 | − | 0.859876i | \(-0.670541\pi\) | ||||
−0.510503 | + | 0.859876i | \(0.670541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 44.7736 | 0.0273212 | 0.0136606 | − | 0.999907i | \(-0.495652\pi\) | ||||
0.0136606 | + | 0.999907i | \(0.495652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 336.427 | 0.198819 | ||||||||
\(143\) | 4478.93 | 2.61921 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1548.80 | 0.877941 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2075.71 | −1.15285 | ||||||||
\(149\) | 2153.29 | 1.18392 | 0.591960 | − | 0.805967i | \(-0.298354\pi\) | ||||
0.591960 | + | 0.805967i | \(0.298354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3037.34 | −1.63692 | −0.818461 | − | 0.574562i | \(-0.805172\pi\) | ||||
−0.818461 | + | 0.574562i | \(0.805172\pi\) | |||||||
\(152\) | 622.841 | 0.332362 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −549.222 | −0.287387 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1353.92 | −0.688245 | −0.344122 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344122 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(158\) | −170.838 | −0.0860201 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.9969 | −0.00587262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3174.14 | 1.52526 | 0.762631 | − | 0.646834i | \(-0.223907\pi\) | ||||
0.762631 | + | 0.646834i | \(0.223907\pi\) | |||||||
\(164\) | 1001.02 | 0.476625 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1304.55 | −0.609957 | ||||||||
\(167\) | 999.272 | 0.463030 | 0.231515 | − | 0.972831i | \(-0.425632\pi\) | ||||
0.231515 | + | 0.972831i | \(0.425632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5411.52 | 2.46314 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2236.58 | −0.991499 | ||||||||
\(173\) | 1208.55 | 0.531122 | 0.265561 | − | 0.964094i | \(-0.414443\pi\) | ||||
0.265561 | + | 0.964094i | \(0.414443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −688.885 | −0.295038 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1430.00 | 0.602152 | ||||||||
\(179\) | 894.985 | 0.373711 | 0.186856 | − | 0.982387i | \(-0.440170\pi\) | ||||
0.186856 | + | 0.982387i | \(0.440170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2030.68 | 0.833917 | 0.416959 | − | 0.908925i | \(-0.363096\pi\) | ||||
0.416959 | + | 0.908925i | \(0.363096\pi\) | |||||||
\(182\) | −932.983 | −0.379985 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 35.7861 | 0.0143379 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4142.67 | 1.62001 | ||||||||
\(188\) | 2876.54 | 1.11592 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4527.59 | 1.71521 | 0.857604 | − | 0.514311i | \(-0.171952\pi\) | ||||
0.857604 | + | 0.514311i | \(0.171952\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2539.92 | −0.947294 | −0.473647 | − | 0.880715i | \(-0.657063\pi\) | ||||
−0.473647 | + | 0.880715i | \(0.657063\pi\) | |||||||
\(194\) | 1197.67 | 0.443235 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −277.595 | −0.101164 | ||||||||
\(197\) | −2344.75 | −0.848002 | −0.424001 | − | 0.905662i | \(-0.639375\pi\) | ||||
−0.424001 | + | 0.905662i | \(0.639375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3253.14 | 1.15884 | 0.579420 | − | 0.815029i | \(-0.303279\pi\) | ||||
0.579420 | + | 0.815029i | \(0.303279\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2758.31 | −0.960762 | ||||||||
\(203\) | 1433.67 | 0.495685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 884.117 | 0.299026 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1170.23 | −0.390101 | ||||||||
\(209\) | 1531.65 | 0.506922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2528.43 | 0.824949 | 0.412475 | − | 0.910969i | \(-0.364665\pi\) | ||||
0.412475 | + | 0.910969i | \(0.364665\pi\) | |||||||
\(212\) | −849.035 | −0.275056 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 328.215 | 0.104843 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1051.23 | −0.328859 | ||||||||
\(218\) | 1241.37 | 0.385669 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7037.30 | 2.14199 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3930.00 | −1.18015 | −0.590073 | − | 0.807350i | \(-0.700901\pi\) | ||||
−0.590073 | + | 0.807350i | \(0.700901\pi\) | |||||||
\(224\) | 1312.81 | 0.391587 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2439.16 | −0.717922 | ||||||||
\(227\) | −512.698 | −0.149907 | −0.0749536 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749536 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1865.41 | 0.538296 | 0.269148 | − | 0.963099i | \(-0.413258\pi\) | ||||
0.269148 | + | 0.963099i | \(0.413258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4276.55 | −1.21021 | ||||||||
\(233\) | 1509.17 | 0.424329 | 0.212165 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212165 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2624.40 | 0.723872 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −862.937 | −0.235025 | ||||||||
\(239\) | 5852.90 | 1.58407 | 0.792035 | − | 0.610476i | \(-0.209022\pi\) | ||||
0.792035 | + | 0.610476i | \(0.209022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3050.88 | −0.815454 | −0.407727 | − | 0.913104i | \(-0.633678\pi\) | ||||
−0.407727 | + | 0.913104i | \(0.633678\pi\) | |||||||
\(242\) | 1995.01 | 0.529933 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2158.19 | −0.566246 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2601.87 | 0.670256 | ||||||||
\(248\) | 3135.76 | 0.802907 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5905.16 | −1.48498 | −0.742491 | − | 0.669856i | \(-0.766356\pi\) | ||||
−0.742491 | + | 0.669856i | \(0.766356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 88.0029 | 0.0218684 | ||||||||
\(254\) | 2245.73 | 0.554763 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3307.98 | −0.807612 | ||||||||
\(257\) | −544.470 | −0.132152 | −0.0660761 | − | 0.997815i | \(-0.521048\pi\) | ||||
−0.0660761 | + | 0.997815i | \(0.521048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2564.78 | 0.615319 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1860.14 | 0.438625 | ||||||||
\(263\) | 1706.22 | 0.400039 | 0.200019 | − | 0.979792i | \(-0.435900\pi\) | ||||
0.200019 | + | 0.979792i | \(0.435900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −319.051 | −0.0735423 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4518.93 | 1.02999 | ||||||||
\(269\) | −289.872 | −0.0657019 | −0.0328509 | − | 0.999460i | \(-0.510459\pi\) | ||||
−0.0328509 | + | 0.999460i | \(0.510459\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1408.35 | −0.315687 | −0.157843 | − | 0.987464i | \(-0.550454\pi\) | ||||
−0.157843 | + | 0.987464i | \(0.550454\pi\) | |||||||
\(272\) | −1082.38 | −0.241282 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2501.70 | −0.551580 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6467.17 | −1.40280 | −0.701398 | − | 0.712770i | \(-0.747440\pi\) | ||||
−0.701398 | + | 0.712770i | \(0.747440\pi\) | |||||||
\(278\) | 68.4144 | 0.0147598 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4271.00 | 0.906714 | 0.453357 | − | 0.891329i | \(-0.350226\pi\) | ||||
0.453357 | + | 0.891329i | \(0.350226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3761.13 | −0.790021 | −0.395011 | − | 0.918677i | \(-0.629259\pi\) | ||||
−0.395011 | + | 0.918677i | \(0.629259\pi\) | |||||||
\(284\) | −1247.33 | −0.260617 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6843.84 | 1.41498 | ||||||||
\(287\) | −1236.87 | −0.254392 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1595.96 | 0.324843 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5742.28 | −1.15083 | ||||||||
\(293\) | −468.982 | −0.0935093 | −0.0467547 | − | 0.998906i | \(-0.514888\pi\) | ||||
−0.0467547 | + | 0.998906i | \(0.514888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7650.56 | −1.50230 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3290.24 | 0.639592 | ||||||||
\(299\) | 149.494 | 0.0289145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2763.55 | 0.529198 | ||||||||
\(302\) | −4641.08 | −0.884318 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −400.183 | −0.0755002 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4130.28 | 0.767841 | 0.383921 | − | 0.923366i | \(-0.374574\pi\) | ||||
0.383921 | + | 0.923366i | \(0.374574\pi\) | |||||||
\(308\) | 2036.28 | 0.376713 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3179.75 | 0.579765 | 0.289883 | − | 0.957062i | \(-0.406384\pi\) | ||||
0.289883 | + | 0.957062i | \(0.406384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4719.06 | −0.852194 | −0.426097 | − | 0.904677i | \(-0.640112\pi\) | ||||
−0.426097 | + | 0.904677i | \(0.640112\pi\) | |||||||
\(314\) | −2068.80 | −0.371812 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 633.395 | 0.112757 | ||||||||
\(317\) | −4807.13 | −0.851720 | −0.425860 | − | 0.904789i | \(-0.640028\pi\) | ||||
−0.425860 | + | 0.904789i | \(0.640028\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10516.6 | −1.84582 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.3314 | −0.00317258 | ||||||||
\(323\) | 2406.53 | 0.414561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4850.10 | 0.823995 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3689.51 | 0.621095 | ||||||||
\(329\) | −3554.30 | −0.595608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2243.42 | −0.372537 | −0.186268 | − | 0.982499i | \(-0.559639\pi\) | ||||
−0.186268 | + | 0.982499i | \(0.559639\pi\) | |||||||
\(332\) | 4836.72 | 0.799547 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1526.89 | 0.250144 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −760.365 | −0.122907 | −0.0614536 | − | 0.998110i | \(-0.519574\pi\) | ||||
−0.0614536 | + | 0.998110i | \(0.519574\pi\) | |||||||
\(338\) | 8268.84 | 1.33067 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7711.27 | 1.22460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −8243.49 | −1.29203 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1846.67 | 0.286929 | ||||||||
\(347\) | 2619.75 | 0.405289 | 0.202645 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202645 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5950.25 | 0.912635 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9630.02 | −1.45819 | ||||||||
\(353\) | 1571.79 | 0.236991 | 0.118496 | − | 0.992955i | \(-0.462193\pi\) | ||||
0.118496 | + | 0.992955i | \(0.462193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5301.83 | −0.789315 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1367.54 | 0.201891 | ||||||||
\(359\) | 1292.38 | 0.189998 | 0.0949988 | − | 0.995477i | \(-0.469715\pi\) | ||||
0.0949988 | + | 0.995477i | \(0.469715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5969.24 | −0.870279 | ||||||||
\(362\) | 3102.89 | 0.450509 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3459.10 | 0.498094 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1193.60 | 0.169770 | 0.0848849 | − | 0.996391i | \(-0.472948\pi\) | ||||
0.0848849 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(368\) | −22.9930 | −0.00325704 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1049.08 | 0.146807 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1817.49 | 0.252295 | 0.126148 | − | 0.992011i | \(-0.459739\pi\) | ||||
0.126148 | + | 0.992011i | \(0.459739\pi\) | |||||||
\(374\) | 6330.02 | 0.875181 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10602.2 | 1.45417 | ||||||||
\(377\) | −17865.0 | −2.44056 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2201.44 | −0.298366 | −0.149183 | − | 0.988810i | \(-0.547664\pi\) | ||||
−0.149183 | + | 0.988810i | \(0.547664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6918.18 | 0.926610 | ||||||||
\(383\) | −11487.2 | −1.53255 | −0.766275 | − | 0.642512i | \(-0.777892\pi\) | ||||
−0.766275 | + | 0.642512i | \(0.777892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3881.02 | −0.511758 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4440.44 | −0.581003 | ||||||||
\(389\) | 284.996 | 0.0371462 | 0.0185731 | − | 0.999828i | \(-0.494088\pi\) | ||||
0.0185731 | + | 0.999828i | \(0.494088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 138.270 | 0.0178839 | ||||||||
\(392\) | −1023.15 | −0.131828 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3582.79 | −0.458118 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9446.19 | −1.19418 | −0.597092 | − | 0.802173i | \(-0.703677\pi\) | ||||
−0.597092 | + | 0.802173i | \(0.703677\pi\) | |||||||
\(398\) | 4970.82 | 0.626042 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11303.8 | −1.40769 | −0.703845 | − | 0.710353i | \(-0.748535\pi\) | ||||
−0.703845 | + | 0.710353i | \(0.748535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13099.4 | 1.61918 | ||||||||
\(404\) | 10226.6 | 1.25939 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2190.66 | 0.267785 | ||||||||
\(407\) | −18813.8 | −2.29131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10022.2 | 1.21165 | 0.605827 | − | 0.795596i | \(-0.292842\pi\) | ||||
0.605827 | + | 0.795596i | \(0.292842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3277.92 | −0.391970 | ||||||||
\(413\) | −3242.75 | −0.386356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16358.9 | −1.92803 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2340.38 | 0.273855 | ||||||||
\(419\) | −9033.23 | −1.05323 | −0.526614 | − | 0.850105i | \(-0.676538\pi\) | ||||
−0.526614 | + | 0.850105i | \(0.676538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13162.6 | 1.52377 | 0.761883 | − | 0.647715i | \(-0.224275\pi\) | ||||
0.761883 | + | 0.647715i | \(0.224275\pi\) | |||||||
\(422\) | 3863.46 | 0.445664 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3129.34 | −0.358429 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2666.69 | 0.302225 | ||||||||
\(428\) | −1216.88 | −0.137430 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15992.1 | 1.78727 | 0.893634 | − | 0.448796i | \(-0.148147\pi\) | ||||
0.893634 | + | 0.448796i | \(0.148147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1526.80 | −0.169453 | −0.0847266 | − | 0.996404i | \(-0.527002\pi\) | ||||
−0.0847266 | + | 0.996404i | \(0.527002\pi\) | |||||||
\(434\) | −1606.29 | −0.177660 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4602.45 | −0.505545 | ||||||||
\(437\) | 51.1221 | 0.00559611 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8620.34 | 0.937190 | 0.468595 | − | 0.883413i | \(-0.344760\pi\) | ||||
0.468595 | + | 0.883413i | \(0.344760\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10753.0 | 1.15717 | ||||||||
\(443\) | −17733.9 | −1.90194 | −0.950972 | − | 0.309278i | \(-0.899913\pi\) | ||||
−0.950972 | + | 0.309278i | \(0.899913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6005.07 | −0.637552 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1254.68 | 0.132317 | ||||||||
\(449\) | 12508.1 | 1.31469 | 0.657344 | − | 0.753591i | \(-0.271680\pi\) | ||||
0.657344 | + | 0.753591i | \(0.271680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9073.02 | 0.947299 | ||||||||
\(452\) | 9043.35 | 0.941070 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −783.406 | −0.0809847 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6138.41 | −0.628321 | −0.314160 | − | 0.949370i | \(-0.601723\pi\) | ||||
−0.314160 | + | 0.949370i | \(0.601723\pi\) | |||||||
\(458\) | 2850.36 | 0.290805 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −534.711 | −0.0540216 | −0.0270108 | − | 0.999635i | \(-0.508599\pi\) | ||||
−0.0270108 | + | 0.999635i | \(0.508599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5081.20 | 0.510029 | 0.255014 | − | 0.966937i | \(-0.417920\pi\) | ||||
0.255014 | + | 0.966937i | \(0.417920\pi\) | |||||||
\(464\) | 2747.73 | 0.274914 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2306.02 | 0.229236 | ||||||||
\(467\) | 17073.9 | 1.69183 | 0.845915 | − | 0.533318i | \(-0.179055\pi\) | ||||
0.845915 | + | 0.533318i | \(0.179055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5583.66 | −0.549743 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9672.89 | 0.943285 | ||||||||
\(473\) | −20271.9 | −1.97062 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3199.40 | 0.308076 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8943.27 | 0.855765 | ||||||||
\(479\) | 7075.25 | 0.674899 | 0.337449 | − | 0.941344i | \(-0.390436\pi\) | ||||
0.337449 | + | 0.941344i | \(0.390436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31959.6 | −3.02959 | ||||||||
\(482\) | −4661.76 | −0.440534 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7396.63 | −0.694649 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15770.2 | −1.46738 | −0.733690 | − | 0.679485i | \(-0.762203\pi\) | ||||
−0.733690 | + | 0.679485i | \(0.762203\pi\) | |||||||
\(488\) | −7954.56 | −0.737881 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8301.12 | −0.762982 | −0.381491 | − | 0.924373i | \(-0.624589\pi\) | ||||
−0.381491 | + | 0.924373i | \(0.624589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16523.7 | −1.50951 | ||||||||
\(494\) | 3975.68 | 0.362094 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2014.76 | −0.182390 | ||||||||
\(497\) | 1541.22 | 0.139101 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3575.29 | −0.320745 | −0.160373 | − | 0.987057i | \(-0.551270\pi\) | ||||
−0.160373 | + | 0.987057i | \(0.551270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9023.13 | −0.802235 | ||||||||
\(503\) | −11686.3 | −1.03592 | −0.517960 | − | 0.855405i | \(-0.673308\pi\) | ||||
−0.517960 | + | 0.855405i | \(0.673308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 134.469 | 0.0118140 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8326.21 | −0.727197 | ||||||||
\(509\) | 7736.09 | 0.673666 | 0.336833 | − | 0.941564i | \(-0.390644\pi\) | ||||
0.336833 | + | 0.941564i | \(0.390644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7095.25 | 0.614237 | ||||||||
\(512\) | 4757.14 | 0.410621 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −831.955 | −0.0713929 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26072.4 | 2.21791 | ||||||||
\(518\) | 3919.00 | 0.332415 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −47.6564 | −0.00400741 | −0.00200371 | − | 0.999998i | \(-0.500638\pi\) | ||||
−0.00200371 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13429.0 | 1.12277 | 0.561385 | − | 0.827555i | \(-0.310269\pi\) | ||||
0.561385 | + | 0.827555i | \(0.310269\pi\) | |||||||
\(524\) | −6896.59 | −0.574960 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2607.12 | 0.216114 | ||||||||
\(527\) | 12115.9 | 1.00148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12164.1 | −0.999759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1182.90 | 0.0964010 | ||||||||
\(533\) | 15412.7 | 1.25253 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16655.7 | 1.34219 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −442.926 | −0.0354943 | ||||||||
\(539\) | −2516.06 | −0.201065 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13627.6 | 1.08299 | 0.541493 | − | 0.840705i | \(-0.317859\pi\) | ||||
0.541493 | + | 0.840705i | \(0.317859\pi\) | |||||||
\(542\) | −2151.97 | −0.170544 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15130.7 | −1.19250 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1691.42 | −0.132212 | −0.0661058 | − | 0.997813i | \(-0.521057\pi\) | ||||
−0.0661058 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(548\) | 9275.21 | 0.723024 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6109.25 | −0.472346 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −782.633 | −0.0601825 | ||||||||
\(554\) | −9881.88 | −0.757836 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −253.651 | −0.0193475 | ||||||||
\(557\) | 4741.73 | 0.360706 | 0.180353 | − | 0.983602i | \(-0.442276\pi\) | ||||
0.180353 | + | 0.983602i | \(0.442276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34436.6 | −2.60557 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6526.12 | 0.489836 | ||||||||
\(563\) | −1073.78 | −0.0803808 | −0.0401904 | − | 0.999192i | \(-0.512796\pi\) | ||||
−0.0401904 | + | 0.999192i | \(0.512796\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5747.03 | −0.426795 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4597.34 | −0.339613 | ||||||||
\(569\) | −3530.34 | −0.260105 | −0.130052 | − | 0.991507i | \(-0.541515\pi\) | ||||
−0.130052 | + | 0.991507i | \(0.541515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2949.59 | −0.216176 | −0.108088 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108088 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(572\) | −25374.0 | −1.85479 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1889.95 | −0.137430 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22580.2 | 1.62916 | 0.814580 | − | 0.580051i | \(-0.196968\pi\) | ||||
0.814580 | + | 0.580051i | \(0.196968\pi\) | |||||||
\(578\) | 2438.63 | 0.175491 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5976.32 | −0.426747 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7695.47 | −0.546679 | ||||||||
\(584\) | −21164.6 | −1.49965 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −716.608 | −0.0505168 | ||||||||
\(587\) | 18289.4 | 1.28600 | 0.643002 | − | 0.765864i | \(-0.277689\pi\) | ||||
0.643002 | + | 0.765864i | \(0.277689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4479.58 | 0.313375 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4915.57 | 0.341265 | ||||||||
\(593\) | −9131.08 | −0.632325 | −0.316162 | − | 0.948705i | \(-0.602394\pi\) | ||||
−0.316162 | + | 0.948705i | \(0.602394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12198.8 | −0.838393 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 228.427 | 0.0156206 | ||||||||
\(599\) | −5457.56 | −0.372270 | −0.186135 | − | 0.982524i | \(-0.559596\pi\) | ||||
−0.186135 | + | 0.982524i | \(0.559596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6527.79 | 0.443052 | 0.221526 | − | 0.975154i | \(-0.428896\pi\) | ||||
0.221526 | + | 0.975154i | \(0.428896\pi\) | |||||||
\(602\) | 4222.73 | 0.285890 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17207.1 | 1.15919 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10959.4 | 0.732833 | 0.366416 | − | 0.930451i | \(-0.380585\pi\) | ||||
0.366416 | + | 0.930451i | \(0.380585\pi\) | |||||||
\(608\) | −5594.21 | −0.373150 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44290.1 | 2.93254 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28164.2 | 1.85569 | 0.927846 | − | 0.372963i | \(-0.121658\pi\) | ||||
0.927846 | + | 0.372963i | \(0.121658\pi\) | |||||||
\(614\) | 6311.09 | 0.414813 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7505.22 | 0.490899 | ||||||||
\(617\) | 20764.0 | 1.35483 | 0.677413 | − | 0.735603i | \(-0.263101\pi\) | ||||
0.677413 | + | 0.735603i | \(0.263101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.21158 | −0.000598134 0 | −0.000299067 | − | 1.00000i | \(-0.500095\pi\) | ||||
−0.000299067 | 1.00000i | \(0.500095\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4858.68 | 0.313208 | ||||||||
\(623\) | 6551.02 | 0.421286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7210.75 | −0.460383 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7670.21 | 0.487380 | ||||||||
\(629\) | −29560.2 | −1.87384 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15005.5 | −0.946684 | −0.473342 | − | 0.880879i | \(-0.656953\pi\) | ||||
−0.473342 | + | 0.880879i | \(0.656953\pi\) | |||||||
\(632\) | 2334.54 | 0.146935 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7345.32 | −0.460126 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4274.12 | −0.265850 | ||||||||
\(638\) | −16069.5 | −0.997173 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19610.6 | 1.20838 | 0.604191 | − | 0.796839i | \(-0.293496\pi\) | ||||
0.604191 | + | 0.796839i | \(0.293496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26668.9 | −1.63564 | −0.817820 | − | 0.575474i | \(-0.804818\pi\) | ||||
−0.817820 | + | 0.575474i | \(0.804818\pi\) | |||||||
\(644\) | 67.9650 | 0.00415869 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3677.20 | 0.223959 | ||||||||
\(647\) | 6895.91 | 0.419020 | 0.209510 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209510 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23787.0 | 1.43871 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17982.1 | −1.08011 | ||||||||
\(653\) | 18809.2 | 1.12720 | 0.563598 | − | 0.826049i | \(-0.309417\pi\) | ||||
0.563598 | + | 0.826049i | \(0.309417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2370.55 | −0.141089 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5431.00 | −0.321766 | ||||||||
\(659\) | 6285.52 | 0.371547 | 0.185773 | − | 0.982593i | \(-0.440521\pi\) | ||||
0.185773 | + | 0.982593i | \(0.440521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1910.45 | 0.112418 | 0.0562088 | − | 0.998419i | \(-0.482099\pi\) | ||||
0.0562088 | + | 0.998419i | \(0.482099\pi\) | |||||||
\(662\) | −3427.97 | −0.201256 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17827.0 | 1.04190 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −351.014 | −0.0203768 | ||||||||
\(668\) | −5661.07 | −0.327894 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19561.4 | −1.12542 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22754.2 | −1.30328 | −0.651641 | − | 0.758528i | \(-0.725919\pi\) | ||||
−0.651641 | + | 0.758528i | \(0.725919\pi\) | |||||||
\(674\) | −1161.84 | −0.0663984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30657.3 | −1.74427 | ||||||||
\(677\) | 6327.54 | 0.359213 | 0.179606 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179606 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5486.68 | 0.310102 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11782.9 | 0.661568 | ||||||||
\(683\) | −12440.7 | −0.696969 | −0.348484 | − | 0.937315i | \(-0.613304\pi\) | ||||
−0.348484 | + | 0.937315i | \(0.613304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 524.106 | 0.0291698 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5296.54 | 0.293501 | ||||||||
\(689\) | −13072.6 | −0.722823 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13421.5 | −0.738898 | −0.369449 | − | 0.929251i | \(-0.620454\pi\) | ||||
−0.369449 | + | 0.929251i | \(0.620454\pi\) | |||||||
\(692\) | −6846.65 | −0.376114 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4002.99 | 0.218950 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14255.5 | 0.774701 | ||||||||
\(698\) | 9092.03 | 0.493035 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3484.08 | −0.187720 | −0.0938601 | − | 0.995585i | \(-0.529921\pi\) | ||||
−0.0938601 | + | 0.995585i | \(0.529921\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10929.2 | −0.586347 | ||||||||
\(704\) | −9203.66 | −0.492721 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2401.70 | 0.128030 | ||||||||
\(707\) | −12636.2 | −0.672181 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22952.1 | 1.21578 | 0.607888 | − | 0.794023i | \(-0.292017\pi\) | ||||
0.607888 | + | 0.794023i | \(0.292017\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19541.2 | −1.02857 | ||||||||
\(713\) | 257.380 | 0.0135189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5070.26 | −0.264643 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1974.76 | 0.102643 | ||||||||
\(719\) | −11393.3 | −0.590957 | −0.295479 | − | 0.955349i | \(-0.595479\pi\) | ||||
−0.295479 | + | 0.955349i | \(0.595479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4050.25 | 0.209209 | ||||||||
\(722\) | −9121.04 | −0.470152 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11504.2 | −0.590538 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22822.6 | 1.16430 | 0.582149 | − | 0.813082i | \(-0.302212\pi\) | ||||
0.582149 | + | 0.813082i | \(0.302212\pi\) | |||||||
\(728\) | 12749.4 | 0.649071 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31851.2 | −1.61157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7923.03 | −0.399241 | −0.199621 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199621 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(734\) | 1823.83 | 0.0917150 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −321.422 | −0.0160975 | ||||||||
\(737\) | 40958.6 | 2.04712 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23588.4 | 1.17417 | 0.587087 | − | 0.809524i | \(-0.300275\pi\) | ||||
0.587087 | + | 0.809524i | \(0.300275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1603.00 | 0.0793101 | ||||||||
\(743\) | −30296.2 | −1.49591 | −0.747953 | − | 0.663752i | \(-0.768963\pi\) | ||||
−0.747953 | + | 0.663752i | \(0.768963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2777.14 | 0.136298 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23469.0 | −1.14721 | ||||||||
\(749\) | 1503.60 | 0.0733515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3326.15 | −0.161615 | −0.0808076 | − | 0.996730i | \(-0.525750\pi\) | ||||
−0.0808076 | + | 0.996730i | \(0.525750\pi\) | |||||||
\(752\) | −6812.06 | −0.330333 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27297.8 | −1.31847 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21829.2 | −1.04808 | −0.524040 | − | 0.851694i | \(-0.675576\pi\) | ||||
−0.524040 | + | 0.851694i | \(0.675576\pi\) | |||||||
\(758\) | −3363.82 | −0.161187 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32402.3 | −1.54347 | −0.771736 | − | 0.635943i | \(-0.780611\pi\) | ||||
−0.771736 | + | 0.635943i | \(0.780611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5686.86 | 0.269827 | ||||||||
\(764\) | −25649.7 | −1.21462 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17552.5 | −0.827933 | ||||||||
\(767\) | 40407.8 | 1.90227 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12942.0 | 0.606894 | 0.303447 | − | 0.952848i | \(-0.401863\pi\) | ||||
0.303447 | + | 0.952848i | \(0.401863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14389.2 | 0.670825 | ||||||||
\(773\) | 33087.0 | 1.53953 | 0.769766 | − | 0.638326i | \(-0.220373\pi\) | ||||
0.769766 | + | 0.638326i | \(0.220373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16366.4 | −0.757112 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 435.476 | 0.0200676 | ||||||||
\(779\) | 5270.64 | 0.242414 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11305.5 | −0.517980 | ||||||||
\(782\) | 211.278 | 0.00966148 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 657.383 | 0.0299464 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30248.7 | −1.37008 | −0.685038 | − | 0.728507i | \(-0.740215\pi\) | ||||
−0.685038 | + | 0.728507i | \(0.740215\pi\) | |||||||
\(788\) | 13283.5 | 0.600512 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11174.1 | −0.502282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33229.6 | −1.48804 | ||||||||
\(794\) | −14433.8 | −0.645136 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18429.7 | −0.820631 | ||||||||
\(797\) | −3123.69 | −0.138829 | −0.0694145 | − | 0.997588i | \(-0.522113\pi\) | ||||
−0.0694145 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40964.9 | 1.81381 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17272.3 | −0.760480 | ||||||||
\(803\) | −52046.8 | −2.28729 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20016.0 | 0.874731 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 37692.8 | 1.64112 | ||||||||
\(809\) | −35088.2 | −1.52489 | −0.762444 | − | 0.647055i | \(-0.776001\pi\) | ||||
−0.762444 | + | 0.647055i | \(0.776001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29394.0 | −1.27271 | −0.636353 | − | 0.771398i | \(-0.719558\pi\) | ||||
−0.636353 | + | 0.771398i | \(0.719558\pi\) | |||||||
\(812\) | −8122.03 | −0.351019 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28747.6 | −1.23784 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11776.2 | −0.504281 | ||||||||
\(818\) | 15314.0 | 0.654575 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36702.5 | 1.56020 | 0.780100 | − | 0.625654i | \(-0.215168\pi\) | ||||
0.780100 | + | 0.625654i | \(0.215168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21436.3 | −0.907924 | −0.453962 | − | 0.891021i | \(-0.649990\pi\) | ||||
−0.453962 | + | 0.891021i | \(0.649990\pi\) | |||||||
\(824\) | −12081.6 | −0.510781 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4954.94 | −0.208722 | ||||||||
\(827\) | −4079.17 | −0.171520 | −0.0857598 | − | 0.996316i | \(-0.527332\pi\) | ||||
−0.0857598 | + | 0.996316i | \(0.527332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35727.1 | −1.49681 | −0.748404 | − | 0.663244i | \(-0.769179\pi\) | ||||
−0.748404 | + | 0.663244i | \(0.769179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15634.6 | −0.651480 | ||||||||
\(833\) | −3953.23 | −0.164431 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8677.11 | −0.358976 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13802.8 | −0.568987 | ||||||||
\(839\) | 22421.8 | 0.922628 | 0.461314 | − | 0.887237i | \(-0.347378\pi\) | ||||
0.461314 | + | 0.887237i | \(0.347378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17558.3 | 0.719927 | ||||||||
\(842\) | 20112.5 | 0.823187 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14324.0 | −0.584187 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9139.38 | 0.370759 | ||||||||
\(848\) | 2010.64 | 0.0814216 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −627.949 | −0.0252947 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43300.2 | −1.73807 | −0.869034 | − | 0.494753i | \(-0.835259\pi\) | ||||
−0.869034 | + | 0.494753i | \(0.835259\pi\) | |||||||
\(854\) | 4074.72 | 0.163272 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4485.13 | −0.179087 | ||||||||
\(857\) | 44562.7 | 1.77623 | 0.888116 | − | 0.459619i | \(-0.152014\pi\) | ||||
0.888116 | + | 0.459619i | \(0.152014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26003.7 | −1.03287 | −0.516434 | − | 0.856327i | \(-0.672741\pi\) | ||||
−0.516434 | + | 0.856327i | \(0.672741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24436.1 | 0.965540 | ||||||||
\(863\) | 28719.8 | 1.13283 | 0.566416 | − | 0.824119i | \(-0.308329\pi\) | ||||
0.566416 | + | 0.824119i | \(0.308329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2332.96 | −0.0915441 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5955.45 | 0.232881 | ||||||||
\(869\) | 5740.96 | 0.224107 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 69577.9 | 2.70672 | ||||||||
\(872\) | −16963.5 | −0.658781 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 78.1149 | 0.00302320 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4042.01 | −0.155632 | −0.0778159 | − | 0.996968i | \(-0.524795\pi\) | ||||
−0.0778159 | + | 0.996968i | \(0.524795\pi\) | |||||||
\(878\) | 13171.9 | 0.506300 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45388.8 | 1.73574 | 0.867871 | − | 0.496790i | \(-0.165488\pi\) | ||||
0.867871 | + | 0.496790i | \(0.165488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10622.5 | 0.404842 | 0.202421 | − | 0.979299i | \(-0.435119\pi\) | ||||
0.202421 | + | 0.979299i | \(0.435119\pi\) | |||||||
\(884\) | −39867.6 | −1.51685 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27097.5 | −1.02749 | ||||||||
\(887\) | −943.623 | −0.0357201 | −0.0178601 | − | 0.999840i | \(-0.505685\pi\) | ||||
−0.0178601 | + | 0.999840i | \(0.505685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10288.0 | 0.388131 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22264.2 | 0.835719 | ||||||||
\(893\) | 15145.8 | 0.567564 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8585.29 | −0.320105 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19112.5 | 0.710236 | ||||||||
\(899\) | −30757.7 | −1.14107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12091.1 | −0.447074 | ||||||||
\(902\) | 13863.6 | 0.511761 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33331.6 | 1.22632 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24087.8 | 0.881834 | 0.440917 | − | 0.897548i | \(-0.354653\pi\) | ||||
0.440917 | + | 0.897548i | \(0.354653\pi\) | |||||||
\(908\) | 2904.53 | 0.106157 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44542.8 | −1.61994 | −0.809972 | − | 0.586468i | \(-0.800518\pi\) | ||||
−0.809972 | + | 0.586468i | \(0.800518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43839.0 | 1.58911 | ||||||||
\(914\) | −9379.53 | −0.339439 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10567.9 | −0.381194 | ||||||||
\(917\) | 8521.53 | 0.306876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22333.9 | −0.801661 | −0.400830 | − | 0.916152i | \(-0.631278\pi\) | ||||
−0.400830 | + | 0.916152i | \(0.631278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −817.042 | −0.0291842 | ||||||||
\(923\) | −19205.1 | −0.684878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7764.11 | 0.275534 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 38410.9 | 1.35873 | ||||||||
\(929\) | 48395.4 | 1.70915 | 0.854576 | − | 0.519327i | \(-0.173817\pi\) | ||||
0.854576 | + | 0.519327i | \(0.173817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1461.61 | −0.0514526 | ||||||||
\(932\) | −8549.71 | −0.300488 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26089.0 | 0.913981 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10547.8 | 0.367749 | 0.183874 | − | 0.982950i | \(-0.441136\pi\) | ||||
0.183874 | + | 0.982950i | \(0.441136\pi\) | |||||||
\(938\) | −8531.88 | −0.296989 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47214.8 | 1.63566 | 0.817831 | − | 0.575458i | \(-0.195176\pi\) | ||||
0.817831 | + | 0.575458i | \(0.195176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 302.831 | 0.0104576 | ||||||||
\(944\) | −6214.94 | −0.214279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30975.6 | −1.06459 | ||||||||
\(947\) | −30737.7 | −1.05474 | −0.527370 | − | 0.849635i | \(-0.676822\pi\) | ||||
−0.527370 | + | 0.849635i | \(0.676822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −88413.7 | −3.02427 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11792.2 | 0.401457 | ||||||||
\(953\) | 17032.1 | 0.578933 | 0.289466 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289466 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33157.8 | −1.12176 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10811.0 | 0.364602 | ||||||||
\(959\) | −11460.6 | −0.385904 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7238.05 | −0.242961 | ||||||||
\(962\) | −48834.6 | −1.63668 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17283.8 | 0.577463 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7597.47 | 0.252656 | 0.126328 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126328 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(968\) | −27262.1 | −0.905205 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19134.9 | −0.632410 | −0.316205 | − | 0.948691i | \(-0.602409\pi\) | ||||
−0.316205 | + | 0.948691i | \(0.602409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 313.415 | 0.0103265 | ||||||||
\(974\) | −24096.9 | −0.792726 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5110.90 | 0.167619 | ||||||||
\(977\) | 44846.1 | 1.46853 | 0.734266 | − | 0.678862i | \(-0.237527\pi\) | ||||
0.734266 | + | 0.678862i | \(0.237527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48054.6 | −1.56878 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12684.2 | −0.412187 | ||||||||
\(983\) | −7385.31 | −0.239628 | −0.119814 | − | 0.992796i | \(-0.538230\pi\) | ||||
−0.119814 | + | 0.992796i | \(0.538230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25248.3 | −0.815488 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14740.1 | −0.474641 | ||||||||
\(989\) | −676.616 | −0.0217545 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56089.0 | 1.79791 | 0.898953 | − | 0.438045i | \(-0.144329\pi\) | ||||
0.898953 | + | 0.438045i | \(0.144329\pi\) | |||||||
\(992\) | −28164.7 | −0.901440 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2354.99 | 0.0751466 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11762.2 | 0.373633 | 0.186816 | − | 0.982395i | \(-0.440183\pi\) | ||||
0.186816 | + | 0.982395i | \(0.440183\pi\) | |||||||
\(998\) | −5463.07 | −0.173277 | ||||||||
\(999\) | 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 | 1575.4.a.bk.1.3 | 4 | ||
3.2 | odd | 2 | 525.4.a.u.1.2 | yes | 4 | ||
5.4 | even | 2 | 1575.4.a.bj.1.2 | 4 | |||
15.2 | even | 4 | 525.4.d.n.274.3 | 8 | |||
15.8 | even | 4 | 525.4.d.n.274.6 | 8 | |||
15.14 | odd | 2 | 525.4.a.t.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.t.1.3 | ✓ | 4 | 15.14 | odd | 2 | ||
525.4.a.u.1.2 | yes | 4 | 3.2 | odd | 2 | ||
525.4.d.n.274.3 | 8 | 15.2 | even | 4 | |||
525.4.d.n.274.6 | 8 | 15.8 | even | 4 | |||
1575.4.a.bj.1.2 | 4 | 5.4 | even | 2 | |||
1575.4.a.bk.1.3 | 4 | 1.1 | even | 1 | trivial |