Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.509800.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} + 5x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.66444\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.36360 | 1.41713 | 0.708563 | − | 0.705647i | \(-0.249344\pi\) | ||||
0.708563 | + | 0.705647i | \(0.249344\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.4926 | −1.38570 | −0.692850 | − | 0.721082i | \(-0.743645\pi\) | ||||
−0.692850 | + | 0.721082i | \(0.743645\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.2227 | 1.00825 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 49.0777 | 1.04705 | 0.523527 | − | 0.852009i | \(-0.324616\pi\) | ||||
0.523527 | + | 0.852009i | \(0.324616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −114.081 | −1.96371 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −34.1261 | −0.486871 | −0.243435 | − | 0.969917i | \(-0.578274\pi\) | ||||
−0.243435 | + | 0.969917i | \(0.578274\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 144.114 | 1.74011 | 0.870053 | − | 0.492958i | \(-0.164084\pi\) | ||||
0.870053 | + | 0.492958i | \(0.164084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 51.5452 | 0.535623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −118.906 | −1.07798 | −0.538992 | − | 0.842311i | \(-0.681195\pi\) | ||||
−0.538992 | + | 0.842311i | \(0.681195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 115.020 | 0.920164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.63966 | 0.0116872 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −63.6830 | −0.407780 | −0.203890 | − | 0.978994i | \(-0.565359\pi\) | ||||
−0.203890 | + | 0.978994i | \(0.565359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 212.912 | 1.23355 | 0.616777 | − | 0.787138i | \(-0.288438\pi\) | ||||
0.616777 | + | 0.787138i | \(0.288438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −80.9996 | −0.427280 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −108.448 | −0.523745 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −200.224 | −0.889638 | −0.444819 | − | 0.895620i | \(-0.646732\pi\) | ||||
−0.444819 | + | 0.895620i | \(0.646732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 361.389 | 1.48381 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 451.267 | 1.71893 | 0.859464 | − | 0.511197i | \(-0.170798\pi\) | ||||
0.859464 | + | 0.511197i | \(0.170798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 130.664 | 0.463396 | 0.231698 | − | 0.972788i | \(-0.425572\pi\) | ||||
0.231698 | + | 0.972788i | \(0.425572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −421.750 | −1.39713 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 176.271 | 0.547057 | 0.273529 | − | 0.961864i | \(-0.411809\pi\) | ||||
0.273529 | + | 0.961864i | \(0.411809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −251.291 | −0.689957 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −629.988 | −1.63274 | −0.816372 | − | 0.577526i | \(-0.804018\pi\) | ||||
−0.816372 | + | 0.577526i | \(0.804018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 170.419 | 0.417804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1061.20 | 2.46595 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 86.9318 | 0.191823 | 0.0959115 | − | 0.995390i | \(-0.469423\pi\) | ||||
0.0959115 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 644.248 | 1.35225 | 0.676127 | − | 0.736785i | \(-0.263657\pi\) | ||||
0.676127 | + | 0.736785i | \(0.263657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 190.559 | 0.381082 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −760.340 | −1.45090 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 400.974 | 0.731147 | 0.365573 | − | 0.930783i | \(-0.380873\pi\) | ||||
0.365573 | + | 0.930783i | \(0.380873\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −875.578 | −1.52764 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −507.611 | −0.848484 | −0.424242 | − | 0.905549i | \(-0.639459\pi\) | ||||
−0.424242 | + | 0.905549i | \(0.639459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 176.392 | 0.282811 | 0.141405 | − | 0.989952i | \(-0.454838\pi\) | ||||
0.141405 | + | 0.989952i | \(0.454838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 846.965 | 1.30399 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −77.0000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 701.122 | 0.998512 | 0.499256 | − | 0.866455i | \(-0.333607\pi\) | ||||
0.499256 | + | 0.866455i | \(0.333607\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −722.938 | −0.991685 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1259.27 | 1.66534 | 0.832670 | − | 0.553770i | \(-0.186811\pi\) | ||||
0.832670 | + | 0.553770i | \(0.186811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 528.702 | 0.674656 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −468.936 | −0.577876 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 788.394 | 0.938984 | 0.469492 | − | 0.882937i | \(-0.344437\pi\) | ||||
0.469492 | + | 0.882937i | \(0.344437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 343.544 | 0.395749 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1567.80 | 1.74810 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2232.70 | −2.41126 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 185.039 | 0.193689 | 0.0968446 | − | 0.995300i | \(-0.469125\pi\) | ||||
0.0968446 | + | 0.995300i | \(0.469125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −299.449 | −0.303998 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1243.55 | 1.22513 | 0.612565 | − | 0.790420i | \(-0.290138\pi\) | ||||
0.612565 | + | 0.790420i | \(0.290138\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1555.21 | 1.48776 | 0.743879 | − | 0.668315i | \(-0.232984\pi\) | ||||
0.743879 | + | 0.668315i | \(0.232984\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −798.569 | −0.742213 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 247.062 | 0.223218 | 0.111609 | − | 0.993752i | \(-0.464400\pi\) | ||||
0.111609 | + | 0.993752i | \(0.464400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1160.58 | 1.01985 | 0.509923 | − | 0.860220i | \(-0.329674\pi\) | ||||
0.509923 | + | 0.860220i | \(0.329674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1474.37 | −1.26073 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1738.50 | 1.44729 | 0.723646 | − | 0.690171i | \(-0.242465\pi\) | ||||
0.723646 | + | 0.690171i | \(0.242465\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1842.16 | 1.49376 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1336.03 | 1.05569 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −238.883 | −0.184020 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3322.95 | 2.43594 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 154.609 | 0.110629 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1507.65 | 1.05340 | 0.526701 | − | 0.850051i | \(-0.323429\pi\) | ||||
0.526701 | + | 0.850051i | \(0.323429\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 962.157 | 0.656691 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1327.55 | −0.885408 | −0.442704 | − | 0.896668i | \(-0.645981\pi\) | ||||
−0.442704 | + | 0.896668i | \(0.645981\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1008.80 | 0.657698 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −25.4026 | −0.0161949 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −441.531 | −0.275347 | −0.137674 | − | 0.990478i | \(-0.543962\pi\) | ||||
−0.137674 | + | 0.990478i | \(0.543962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −179.162 | −0.109326 | −0.0546631 | − | 0.998505i | \(-0.517408\pi\) | ||||
−0.0546631 | + | 0.998505i | \(0.517408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1297.99 | 0.775250 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −539.854 | −0.315698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 986.615 | 0.565061 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 360.817 | 0.202447 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1147.07 | −0.630680 | −0.315340 | − | 0.948979i | \(-0.602118\pi\) | ||||
−0.315340 | + | 0.948979i | \(0.602118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1873.03 | −1.00944 | −0.504719 | − | 0.863284i | \(-0.668404\pi\) | ||||
−0.504719 | + | 0.863284i | \(0.668404\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −929.004 | −0.490886 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3298.56 | −1.70933 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −643.927 | −0.327331 | −0.163665 | − | 0.986516i | \(-0.552332\pi\) | ||||
−0.163665 | + | 0.986516i | \(0.552332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4638.98 | −2.31381 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −832.343 | −0.407440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3044.47 | 1.46295 | 0.731477 | − | 0.681866i | \(-0.238831\pi\) | ||||
0.731477 | + | 0.681866i | \(0.238831\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1254.89 | 0.592081 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 337.038 | 0.156172 | 0.0780861 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780861 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 211.617 | 0.0963209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3923.17 | 1.75446 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3504.80 | −1.54026 | −0.770131 | − | 0.637886i | \(-0.779809\pi\) | ||||
−0.770131 | + | 0.637886i | \(0.779809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 805.143 | 0.347789 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 640.132 | 0.271837 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −221.078 | −0.0923135 | −0.0461568 | − | 0.998934i | \(-0.514697\pi\) | ||||
−0.0461568 | + | 0.998934i | \(0.514697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4561.63 | −1.87328 | −0.936640 | − | 0.350295i | \(-0.886081\pi\) | ||||
−0.936640 | + | 0.350295i | \(0.886081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4743.99 | 1.91631 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3101.99 | 1.23277 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 375.387 | 0.146797 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.4776 | 0.00441733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4180.40 | −1.58368 | −0.791841 | − | 0.610727i | \(-0.790877\pi\) | ||||
−0.791841 | + | 0.610727i | \(0.790877\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1942.59 | −0.724510 | −0.362255 | − | 0.932079i | \(-0.617993\pi\) | ||||
−0.362255 | + | 0.932079i | \(0.617993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5598.85 | −2.05611 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3775.15 | 1.36532 | 0.682660 | − | 0.730736i | \(-0.260823\pi\) | ||||
0.682660 | + | 0.730736i | \(0.260823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 993.760 | 0.353999 | 0.176999 | − | 0.984211i | \(-0.443361\pi\) | ||||
0.176999 | + | 0.984211i | \(0.443361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2952.62 | 1.03613 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −445.781 | −0.154127 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6991.29 | −2.38192 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3236.94 | −1.08687 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1585.25 | −0.524662 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2912.24 | 0.950176 | 0.475088 | − | 0.879938i | \(-0.342416\pi\) | ||||
0.475088 | + | 0.879938i | \(0.342416\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3737.85 | −1.20241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2024.32 | −0.642128 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1490.39 | 0.466239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1298.88 | 0.400778 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1674.83 | −0.509780 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5069.26 | −1.52225 | −0.761127 | − | 0.648603i | \(-0.775353\pi\) | ||||
−0.761127 | + | 0.648603i | \(0.775353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3131.16 | 0.927753 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5653.25 | 1.65295 | 0.826475 | − | 0.562974i | \(-0.190343\pi\) | ||||
0.826475 | + | 0.562974i | \(0.190343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5141.63 | −1.48371 | −0.741853 | − | 0.670563i | \(-0.766053\pi\) | ||||
−0.741853 | + | 0.670563i | \(0.766053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −566.998 | −0.161497 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 312.296 | 0.0878077 | 0.0439039 | − | 0.999036i | \(-0.486020\pi\) | ||||
0.0439039 | + | 0.999036i | \(0.486020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2730.89 | −0.758057 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5162.79 | 1.41502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4012.12 | 1.08587 | 0.542935 | − | 0.839775i | \(-0.317313\pi\) | ||||
0.542935 | + | 0.839775i | \(0.317313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 499.662 | 0.133552 | 0.0667761 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667761 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5367.70 | −1.41703 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −759.137 | −0.197957 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7072.78 | 1.82198 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9272.79 | 2.36000 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6112.34 | 1.53708 | 0.768541 | − | 0.639801i | \(-0.220983\pi\) | ||||
0.768541 | + | 0.639801i | \(0.220983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1307.97 | 0.325025 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3893.15 | 0.956073 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1910.22 | −0.463642 | −0.231821 | − | 0.972758i | \(-0.574468\pi\) | ||||
−0.231821 | + | 0.972758i | \(0.574468\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1401.57 | −0.336252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1733.62 | −0.411143 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1749.49 | −0.410184 | −0.205092 | − | 0.978743i | \(-0.565749\pi\) | ||||
−0.205092 | + | 0.978743i | \(0.565749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9760.14 | 2.26249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5805.42 | 1.33066 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2884.89 | −0.653883 | −0.326942 | − | 0.945045i | \(-0.606018\pi\) | ||||
−0.326942 | + | 0.945045i | \(0.606018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6065.04 | −1.35950 | −0.679751 | − | 0.733443i | \(-0.737912\pi\) | ||||
−0.679751 | + | 0.733443i | \(0.737912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2529.72 | 0.560826 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1265.23 | −0.277440 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3331.31 | −0.722595 | −0.361297 | − | 0.932451i | \(-0.617666\pi\) | ||||
−0.361297 | + | 0.932451i | \(0.617666\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5796.04 | 1.24373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −384.608 | −0.0816505 | −0.0408252 | − | 0.999166i | \(-0.512999\pi\) | ||||
−0.0408252 | + | 0.999166i | \(0.512999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1768.02 | −0.371371 | −0.185685 | − | 0.982609i | \(-0.559451\pi\) | ||||
−0.185685 | + | 0.982609i | \(0.559451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16440.7 | −3.41707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3158.87 | 0.649693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3748.41 | −0.762957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1362.55 | 0.274482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3801.87 | 0.758047 | 0.379023 | − | 0.925387i | \(-0.376260\pi\) | ||||
0.379023 | + | 0.925387i | \(0.376260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1346.80 | −0.265809 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0363 | −0.00352381 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5835.64 | −1.12871 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 914.647 | 0.175147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9157.03 | 1.73616 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9981.07 | −1.87382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 687.619 | 0.127832 | 0.0639161 | − | 0.997955i | \(-0.479641\pi\) | ||||
0.0639161 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11451.9 | 2.10834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2517.73 | 0.459059 | 0.229530 | − | 0.973302i | \(-0.426281\pi\) | ||||
0.229530 | + | 0.973302i | \(0.426281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4725.03 | −0.853274 | −0.426637 | − | 0.904423i | \(-0.640302\pi\) | ||||
−0.426637 | + | 0.904423i | \(0.640302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2952.25 | −0.528065 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2870.09 | 0.508519 | 0.254259 | − | 0.967136i | \(-0.418168\pi\) | ||||
0.254259 | + | 0.967136i | \(0.418168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 700.513 | 0.122950 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1819.26 | 0.316328 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4918.05 | −0.847207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5644.94 | 0.963461 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8546.03 | 1.44525 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1233.89 | 0.206768 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −365.467 | −0.0606885 | −0.0303443 | − | 0.999540i | \(-0.509660\pi\) | ||||
−0.0303443 | + | 0.999540i | \(0.509660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5450.63 | −0.896975 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6212.13 | −1.01315 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4292.33 | −0.693822 | −0.346911 | − | 0.937898i | \(-0.612769\pi\) | ||||
−0.346911 | + | 0.937898i | \(0.612769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12801.6 | 2.05100 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2342.03 | −0.371930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13565.0 | 2.11685 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6090.40 | 0.942218 | 0.471109 | − | 0.882075i | \(-0.343854\pi\) | ||||
0.471109 | + | 0.882075i | \(0.343854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6338.89 | 0.972244 | 0.486122 | − | 0.873891i | \(-0.338411\pi\) | ||||
0.486122 | + | 0.873891i | \(0.338411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 80.4709 | 0.0122371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5754.44 | 0.867643 | 0.433821 | − | 0.900999i | \(-0.357165\pi\) | ||||
0.433821 | + | 0.900999i | \(0.357165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7864.21 | 1.17574 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1759.04 | −0.260779 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7396.98 | −1.08746 | −0.543729 | − | 0.839261i | \(-0.682988\pi\) | ||||
−0.543729 | + | 0.839261i | \(0.682988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13909.8 | 2.02797 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 890.996 | 0.128830 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2732.78 | −0.391891 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4613.59 | 0.656205 | 0.328102 | − | 0.944642i | \(-0.393591\pi\) | ||||
0.328102 | + | 0.944642i | \(0.393591\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12284.7 | 1.73310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4409.91 | −0.617119 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4603.15 | 0.638986 | 0.319493 | − | 0.947589i | \(-0.396487\pi\) | ||||
0.319493 | + | 0.947589i | \(0.396487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1138.48 | 0.156775 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3125.41 | −0.426968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6982.50 | −0.946350 | −0.473175 | − | 0.880968i | \(-0.656892\pi\) | ||||
−0.473175 | + | 0.880968i | \(0.656892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11101.7 | 1.49280 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12743.5 | −1.70016 | −0.850079 | − | 0.526655i | \(-0.823446\pi\) | ||||
−0.850079 | + | 0.526655i | \(0.823446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1192.93 | 0.157915 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3557.02 | 0.467218 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1568.76 | 0.204471 | 0.102235 | − | 0.994760i | \(-0.467400\pi\) | ||||
0.102235 | + | 0.994760i | \(0.467400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4057.81 | 0.524839 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9775.54 | −1.25474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10862.2 | −1.38364 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9841.87 | 1.24420 | 0.622102 | − | 0.782936i | \(-0.286279\pi\) | ||||
0.622102 | + | 0.782936i | \(0.286279\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7428.39 | 0.932042 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5128.60 | 0.638679 | 0.319339 | − | 0.947640i | \(-0.396539\pi\) | ||||
0.319339 | + | 0.947640i | \(0.396539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10449.2 | 1.29160 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11200.2 | 1.37418 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2202.46 | 0.268236 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −87.6006 | −0.0105906 | −0.00529532 | − | 0.999986i | \(-0.501686\pi\) | ||||
−0.00529532 | + | 0.999986i | \(0.501686\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3251.26 | −0.390202 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 608.523 | 0.0725023 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19509.4 | −2.30766 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1319.28 | −0.154929 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7130.86 | 0.831420 | 0.415710 | − | 0.909497i | \(-0.363533\pi\) | ||||
0.415710 | + | 0.909497i | \(0.363533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6159.77 | 0.713085 | 0.356543 | − | 0.934279i | \(-0.383955\pi\) | ||||
0.356543 | + | 0.934279i | \(0.383955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4798.55 | 0.551569 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3925.20 | −0.448001 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4509.74 | 0.511104 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3975.27 | −0.447385 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12044.1 | −1.34604 | −0.673019 | − | 0.739625i | \(-0.735003\pi\) | ||||
−0.673019 | + | 0.739625i | \(0.735003\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9609.67 | −1.06654 | −0.533270 | − | 0.845945i | \(-0.679037\pi\) | ||||
−0.533270 | + | 0.845945i | \(0.679037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7265.04 | 0.800763 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17136.0 | −1.87581 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3122.62 | 0.339486 | 0.169743 | − | 0.985488i | \(-0.445706\pi\) | ||||
0.169743 | + | 0.985488i | \(0.445706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1333.91 | 0.144035 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9381.76 | −1.00619 | −0.503093 | − | 0.864232i | \(-0.667805\pi\) | ||||
−0.503093 | + | 0.864232i | \(0.667805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12214.3 | −1.30115 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8446.54 | −0.893753 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3407.36 | 0.358136 | 0.179068 | − | 0.983837i | \(-0.442692\pi\) | ||||
0.179068 | + | 0.983837i | \(0.442692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4963.93 | −0.518276 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13792.3 | −1.43050 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5322.38 | −0.548389 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13714.0 | −1.40375 | −0.701876 | − | 0.712299i | \(-0.747654\pi\) | ||||
−0.701876 | + | 0.712299i | \(0.747654\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −55.9554 | −0.00569014 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8864.54 | −0.895581 | −0.447790 | − | 0.894139i | \(-0.647789\pi\) | ||||
−0.447790 | + | 0.894139i | \(0.647789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14753.3 | 1.48087 | 0.740437 | − | 0.672126i | \(-0.234619\pi\) | ||||
0.740437 | + | 0.672126i | \(0.234619\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24289.3 | −2.42234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −488.428 | −0.0483977 | −0.0241989 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241989 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2806.82 | 0.276347 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4741.62 | −0.463869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1437.30 | −0.139719 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16576.1 | 1.60118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17149.9 | −1.64621 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1233.56 | 0.117668 | 0.0588338 | − | 0.998268i | \(-0.481262\pi\) | ||||
0.0588338 | + | 0.998268i | \(0.481262\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9826.52 | −0.931499 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6129.04 | −0.577394 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2866.73 | −0.268395 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16700.6 | −1.55395 | −0.776977 | − | 0.629529i | \(-0.783248\pi\) | ||||
−0.776977 | + | 0.629529i | \(0.783248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22418.3 | 2.07319 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2127.96 | 0.195587 | 0.0977937 | − | 0.995207i | \(-0.468821\pi\) | ||||
0.0977937 | + | 0.995207i | \(0.468821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2173.25 | 0.198536 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4639.25 | 0.421250 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3553.28 | −0.320697 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12341.5 | −1.10718 | −0.553590 | − | 0.832789i | \(-0.686742\pi\) | ||||
−0.553590 | + | 0.832789i | \(0.686742\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2481.81 | 0.221316 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3433.67 | 0.304374 | 0.152187 | − | 0.988352i | \(-0.451368\pi\) | ||||
0.152187 | + | 0.988352i | \(0.451368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19265.9 | −1.69766 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1558.26 | 0.136499 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1842.48 | −0.160445 | −0.0802223 | − | 0.996777i | \(-0.525563\pi\) | ||||
−0.0802223 | + | 0.996777i | \(0.525563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1234.75 | 0.106892 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 236.298 | 0.0203369 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24094.2 | −2.06158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1938.98 | −0.164944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25808.0 | −2.18275 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3532.65 | 0.297060 | 0.148530 | − | 0.988908i | \(-0.452546\pi\) | ||||
0.148530 | + | 0.988908i | \(0.452546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4497.20 | 0.376001 | 0.188001 | − | 0.982169i | \(-0.439799\pi\) | ||||
0.188001 | + | 0.982169i | \(0.439799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5928.76 | 0.492861 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7265.87 | −0.600581 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1971.67 | 0.162050 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2366.52 | 0.193405 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22147.1 | 1.79981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3827.62 | −0.309313 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1627.93 | −0.130820 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11426.0 | −0.908023 | −0.454011 | − | 0.890996i | \(-0.650007\pi\) | ||||
−0.454011 | + | 0.890996i | \(0.650007\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −33590.1 | −2.65467 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17980.4 | −1.41320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17875.3 | −1.39725 | −0.698623 | − | 0.715490i | \(-0.746204\pi\) | ||||
−0.698623 | + | 0.715490i | \(0.746204\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17538.2 | 1.36341 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9177.61 | −0.709581 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4907.86 | 0.377402 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22841.8 | 1.74699 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25343.4 | 1.92789 | 0.963946 | − | 0.266097i | \(-0.0857341\pi\) | ||||
0.963946 | + | 0.266097i | \(0.0857341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6412.68 | 0.485201 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2764.20 | 0.208030 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1597.92 | 0.119617 | 0.0598084 | − | 0.998210i | \(-0.480951\pi\) | ||||
0.0598084 | + | 0.998210i | \(0.480951\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26933.8 | −2.00551 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5060.57 | −0.374822 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11487.7 | −0.846377 | −0.423188 | − | 0.906042i | \(-0.639089\pi\) | ||||
−0.423188 | + | 0.906042i | \(0.639089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17027.0 | −1.24791 | −0.623957 | − | 0.781459i | \(-0.714476\pi\) | ||||
−0.623957 | + | 0.781459i | \(0.714476\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30782.8 | −2.24428 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13676.6 | −0.991922 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19368.0 | 1.39740 | 0.698701 | − | 0.715414i | \(-0.253762\pi\) | ||||
0.698701 | + | 0.715414i | \(0.253762\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14304.4 | −1.02672 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8814.91 | 0.629439 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6929.86 | 0.492291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20698.5 | −1.46287 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27035.0 | 1.90094 | 0.950472 | − | 0.310809i | \(-0.100600\pi\) | ||||
0.950472 | + | 0.310809i | \(0.100600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30683.6 | 2.14651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27798.7 | 1.93483 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9717.62 | −0.672943 | −0.336471 | − | 0.941694i | \(-0.609234\pi\) | ||||
−0.336471 | + | 0.941694i | \(0.609234\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3700.92 | 0.254996 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7317.65 | 0.501661 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18386.6 | 1.25418 | 0.627092 | − | 0.778945i | \(-0.284245\pi\) | ||||
0.627092 | + | 0.778945i | \(0.284245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3288.31 | −0.223183 | −0.111591 | − | 0.993754i | \(-0.535595\pi\) | ||||
−0.111591 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10915.6 | 0.737176 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1874.60 | −0.125973 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27356.2 | 1.82925 | 0.914623 | − | 0.404307i | \(-0.132487\pi\) | ||||
0.914623 | + | 0.404307i | \(0.132487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3282.55 | −0.218417 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8650.95 | 0.572798 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9573.59 | −0.630789 | −0.315395 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315395 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −51481.1 | −3.37548 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7506.76 | −0.489807 | −0.244903 | − | 0.969547i | \(-0.578756\pi\) | ||||
−0.244903 | + | 0.969547i | \(0.578756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9294.64 | 0.603527 | 0.301763 | − | 0.953383i | \(-0.402425\pi\) | ||||
0.301763 | + | 0.953383i | \(0.402425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −194.966 | −0.0125986 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5518.75 | 0.354902 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16772.8 | −1.07346 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11673.2 | −0.743512 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6832.87 | 0.433139 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4254.20 | −0.268395 | −0.134197 | − | 0.990955i | \(-0.542846\pi\) | ||||
−0.134197 | + | 0.990955i | \(0.542846\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21444.6 | 1.34652 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23357.4 | −1.45970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2404.81 | 0.149579 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13818.5 | −0.855482 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5112.91 | 0.315051 | 0.157526 | − | 0.987515i | \(-0.449648\pi\) | ||||
0.157526 | + | 0.987515i | \(0.449648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7296.68 | −0.447516 | −0.223758 | − | 0.974645i | \(-0.571833\pi\) | ||||
−0.223758 | + | 0.974645i | \(0.571833\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14906.3 | −0.909977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15612.1 | −0.948649 | −0.474324 | − | 0.880350i | \(-0.657308\pi\) | ||||
−0.474324 | + | 0.880350i | \(0.657308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −956.250 | −0.0578368 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10974.6 | 0.660720 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23160.6 | −1.38797 | −0.693986 | − | 0.719988i | \(-0.744147\pi\) | ||||
−0.693986 | + | 0.719988i | \(0.744147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20567.2 | 1.22691 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4801.87 | 0.285143 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5707.65 | 0.337388 | 0.168694 | − | 0.985668i | \(-0.446045\pi\) | ||||
0.168694 | + | 0.985668i | \(0.446045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16202.5 | −0.953411 | −0.476706 | − | 0.879063i | \(-0.658169\pi\) | ||||
−0.476706 | + | 0.879063i | \(0.658169\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12332.8 | −0.722422 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15628.9 | −0.911372 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7572.30 | 0.439581 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37328.0 | −2.15723 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7086.73 | −0.407720 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16956.2 | −0.971192 | −0.485596 | − | 0.874183i | \(-0.661397\pi\) | ||||
−0.485596 | + | 0.874183i | \(0.661397\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 188.595 | 0.0107541 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21259.0 | 1.20687 | 0.603433 | − | 0.797414i | \(-0.293799\pi\) | ||||
0.603433 | + | 0.797414i | \(0.293799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1295.27 | 0.0732076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41628.3 | 2.34244 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5867.98 | −0.328744 | −0.164372 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164372 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6840.46 | 0.381548 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37860.9 | −2.10260 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30918.3 | −1.70957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15583.0 | −0.857892 | −0.428946 | − | 0.903330i | \(-0.641115\pi\) | ||||
−0.428946 | + | 0.903330i | \(0.641115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2096.15 | −0.114900 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2775.69 | 0.151493 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15400.0 | −0.836895 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2299.63 | 0.124435 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19210.5 | −1.03505 | −0.517525 | − | 0.855668i | \(-0.673147\pi\) | ||||
−0.517525 | + | 0.855668i | \(0.673147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28855.1 | −1.54806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20109.2 | −1.07426 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8704.87 | 0.463055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1760.77 | −0.0932683 | −0.0466342 | − | 0.998912i | \(-0.514850\pi\) | ||||
−0.0466342 | + | 0.998912i | \(0.514850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19086.4 | 1.00675 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25316.6 | −1.32975 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8363.74 | 0.437463 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29543.7 | 1.53881 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10517.7 | −0.545541 | −0.272770 | − | 0.962079i | \(-0.587940\pi\) | ||||
−0.272770 | + | 0.962079i | \(0.587940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10886.4 | 0.562319 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3679.31 | 0.189260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7324.85 | −0.375225 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10483.4 | 0.534814 | 0.267407 | − | 0.963584i | \(-0.413833\pi\) | ||||
0.267407 | + | 0.963584i | \(0.413833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20006.3 | −1.01643 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4459.05 | −0.225614 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8568.83 | −0.431783 | −0.215892 | − | 0.976417i | \(-0.569266\pi\) | ||||
−0.215892 | + | 0.976417i | \(0.569266\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5589.99 | −0.280530 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4410.72 | −0.220449 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3089.07 | 0.153766 | 0.0768832 | − | 0.997040i | \(-0.475503\pi\) | ||||
0.0768832 | + | 0.997040i | \(0.475503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 52081.1 | 2.58198 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28558.8 | 1.41012 | 0.705060 | − | 0.709148i | \(-0.250920\pi\) | ||||
0.705060 | + | 0.709148i | \(0.250920\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17771.0 | 0.873933 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34280.8 | 1.67907 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1729.43 | 0.0843685 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2062.51 | 0.100216 | 0.0501078 | − | 0.998744i | \(-0.484044\pi\) | ||||
0.0501078 | + | 0.998744i | \(0.484044\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45008.9 | 2.17824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29018.1 | 1.39878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39089.1 | 1.87678 | 0.938388 | − | 0.345584i | \(-0.112319\pi\) | ||||
0.938388 | + | 0.345584i | \(0.112319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9631.35 | 0.460601 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13820.5 | −0.658337 | −0.329169 | − | 0.944271i | \(-0.606768\pi\) | ||||
−0.329169 | + | 0.944271i | \(0.606768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8124.04 | 0.385465 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14392.7 | 0.680220 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4266.41 | 0.200849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28495.1 | −1.33623 | −0.668115 | − | 0.744058i | \(-0.732899\pi\) | ||||
−0.668115 | + | 0.744058i | \(0.732899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14066.1 | −0.657040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1874.14 | 0.0872032 | 0.0436016 | − | 0.999049i | \(-0.486117\pi\) | ||||
0.0436016 | + | 0.999049i | \(0.486117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24489.3 | 1.13507 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10320.6 | −0.476511 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 65033.8 | 2.99112 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5583.72 | 0.255828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −104.419 | −0.00476580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9976.10 | 0.453582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16614.9 | −0.752551 | −0.376275 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376275 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12882.6 | −0.581282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12169.5 | 0.547025 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31618.2 | 1.41588 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 71869.8 | 3.20624 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19323.7 | 0.858823 | 0.429411 | − | 0.903109i | \(-0.358721\pi\) | ||||
0.429411 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6015.43 | −0.266346 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21462.2 | 0.946728 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1940.32 | −0.0852706 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12895.2 | 0.564589 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21243.2 | −0.926635 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15363.0 | −0.667657 | −0.333829 | − | 0.942634i | \(-0.608341\pi\) | ||||
−0.333829 | + | 0.942634i | \(0.608341\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11404.0 | −0.493771 | −0.246886 | − | 0.969045i | \(-0.579407\pi\) | ||||
−0.246886 | + | 0.969045i | \(0.579407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44660.6 | −1.92659 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47166.8 | −2.02722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18830.5 | 0.806359 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9352.18 | 0.399013 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5529.00 | 0.235035 | 0.117517 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117517 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12216.1 | 0.517407 | 0.258704 | − | 0.965957i | \(-0.416705\pi\) | ||||
0.258704 | + | 0.965957i | \(0.416705\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9316.62 | −0.393167 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29123.0 | 1.22455 | 0.612277 | − | 0.790643i | \(-0.290254\pi\) | ||||
0.612277 | + | 0.790643i | \(0.290254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25679.6 | 1.07586 | 0.537930 | − | 0.842990i | \(-0.319207\pi\) | ||||
0.537930 | + | 0.842990i | \(0.319207\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24530.4 | −1.02401 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1672.18 | −0.0695529 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5221.59 | −0.216408 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 349.104 | 0.0144167 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7009.97 | 0.288452 | 0.144226 | − | 0.989545i | \(-0.453931\pi\) | ||||
0.144226 | + | 0.989545i | \(0.453931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20333.5 | −0.833715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2832.10 | −0.115709 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3278.50 | −0.133472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13019.0 | −0.526279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23807.9 | 0.959016 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7430.54 | 0.298261 | 0.149131 | − | 0.988818i | \(-0.452353\pi\) | ||||
0.149131 | + | 0.988818i | \(0.452353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −60780.0 | −2.43115 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16112.3 | −0.642225 | −0.321113 | − | 0.947041i | \(-0.604057\pi\) | ||||
−0.321113 | + | 0.947041i | \(0.604057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46836.9 | −1.86037 | −0.930183 | − | 0.367097i | \(-0.880352\pi\) | ||||
−0.930183 | + | 0.367097i | \(0.880352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23260.6 | 0.920698 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2453.00 | 0.0967568 | 0.0483784 | − | 0.998829i | \(-0.484595\pi\) | ||||
0.0483784 | + | 0.998829i | \(0.484595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54298.5 | 2.13434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27601.8 | −1.08121 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7712.34 | −0.301063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19678.9 | 0.765549 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5037.25 | 0.195287 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1082.26 | 0.0418138 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23733.6 | 0.913829 | 0.456914 | − | 0.889511i | \(-0.348955\pi\) | ||||
0.456914 | + | 0.889511i | \(0.348955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27995.5 | 1.07425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10868.6 | 0.415634 | 0.207817 | − | 0.978168i | \(-0.433364\pi\) | ||||
0.207817 | + | 0.978168i | \(0.433364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43075.4 | 1.64168 | 0.820840 | − | 0.571158i | \(-0.193505\pi\) | ||||
0.820840 | + | 0.571158i | \(0.193505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9917.30 | −0.376685 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16224.0 | 0.614149 | 0.307075 | − | 0.951685i | \(-0.400650\pi\) | ||||
0.307075 | + | 0.951685i | \(0.400650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10553.5 | 0.398149 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7952.32 | 0.299004 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25403.1 | 0.951938 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3425.07 | 0.127919 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42971.3 | −1.59952 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13558.9 | −0.503019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21499.0 | 0.794935 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6735.10 | 0.248206 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 70671.5 | 2.59580 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39985.6 | −1.46384 | −0.731918 | − | 0.681392i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681392i | \(0.761375\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33852.8 | 1.23523 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20330.9 | −0.739398 | −0.369699 | − | 0.929152i | \(-0.620539\pi\) | ||||
−0.369699 | + | 0.929152i | \(0.620539\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13852.0 | −0.502119 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −73496.7 | −2.65544 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9292.84 | −0.334653 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3734.71 | 0.134055 | 0.0670275 | − | 0.997751i | \(-0.478648\pi\) | ||||
0.0670275 | + | 0.997751i | \(0.478648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5063.36 | 0.181154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24912.4 | −0.888408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23029.9 | −0.818613 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42336.9 | 1.50003 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30122.2 | 1.06381 | 0.531904 | − | 0.846805i | \(-0.321477\pi\) | ||||
0.531904 | + | 0.846805i | \(0.321477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7061.59 | 0.248587 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18539.6 | 0.650545 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5815.72 | −0.203417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33701.9 | −1.17502 | −0.587509 | − | 0.809217i | \(-0.699891\pi\) | ||||
−0.587509 | + | 0.809217i | \(0.699891\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34793.3 | −1.20920 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20897.3 | 0.723944 | 0.361972 | − | 0.932189i | \(-0.382104\pi\) | ||||
0.361972 | + | 0.932189i | \(0.382104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53658.4 | −1.85298 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −177.819 | −0.00612110 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43378.9 | 1.48852 | 0.744258 | − | 0.667892i | \(-0.232803\pi\) | ||||
0.744258 | + | 0.667892i | \(0.232803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8656.93 | 0.296118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21134.2 | 0.720635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36362.5 | −1.23599 | −0.617994 | − | 0.786183i | \(-0.712054\pi\) | ||||
−0.617994 | + | 0.786183i | \(0.712054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 64765.3 | 2.19451 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5158.30 | 0.174236 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3090.72 | −0.104071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15540.6 | 0.521654 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6725.67 | 0.225059 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30095.7 | 1.00395 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23769.2 | −0.790451 | −0.395225 | − | 0.918584i | \(-0.629333\pi\) | ||||
−0.395225 | + | 0.918584i | \(0.629333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36214.6 | −1.20060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27125.4 | 0.896494 | 0.448247 | − | 0.893910i | \(-0.352048\pi\) | ||||
0.448247 | + | 0.893910i | \(0.352048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1254.14 | −0.0413214 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41567.1 | 1.36535 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30145.5 | −0.987146 | −0.493573 | − | 0.869704i | \(-0.664309\pi\) | ||||
−0.493573 | + | 0.869704i | \(0.664309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8672.33 | −0.283114 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31594.0 | 1.02826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23037.5 | −0.747489 | −0.373745 | − | 0.927532i | \(-0.621926\pi\) | ||||
−0.373745 | + | 0.927532i | \(0.621926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58486.8 | −1.89192 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9085.91 | 0.293017 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15536.7 | −0.499534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13580.1 | −0.435303 | −0.217651 | − | 0.976027i | \(-0.569840\pi\) | ||||
−0.217651 | + | 0.976027i | \(0.569840\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2691.16 | −0.0860033 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15395.9 | −0.490536 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26627.3 | −0.845832 | −0.422916 | − | 0.906169i | \(-0.638993\pi\) | ||||
−0.422916 | + | 0.906169i | \(0.638993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −328.300 | −0.0103973 |
(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 | 1232.4.a.w.1.3 | 4 | ||
4.3 | odd | 2 | 77.4.a.c.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 693.4.a.m.1.1 | 4 | |||
20.19 | odd | 2 | 1925.4.a.q.1.1 | 4 | |||
28.27 | even | 2 | 539.4.a.f.1.4 | 4 | |||
44.43 | even | 2 | 847.4.a.e.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.c.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
539.4.a.f.1.4 | 4 | 28.27 | even | 2 | |||
693.4.a.m.1.1 | 4 | 12.11 | even | 2 | |||
847.4.a.e.1.1 | 4 | 44.43 | even | 2 | |||
1232.4.a.w.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1925.4.a.q.1.1 | 4 | 20.19 | odd | 2 |