Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,4,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(31.3300142130\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.61734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.61734 | −1.63248 | −0.816238 | − | 0.577716i | \(-0.803944\pi\) | ||||
−0.816238 | + | 0.577716i | \(0.803944\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 13.3198 | 1.66498 | ||||||||
\(5\) | 3.21787 | 0.287815 | 0.143908 | − | 0.989591i | \(-0.454033\pi\) | ||||
0.143908 | + | 0.989591i | \(0.454033\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.9864 | 0.863187 | 0.431594 | − | 0.902068i | \(-0.357951\pi\) | ||||
0.431594 | + | 0.902068i | \(0.357951\pi\) | |||||||
\(8\) | −24.5634 | −1.08556 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.8580 | −0.469852 | ||||||||
\(11\) | −54.2052 | −1.48577 | −0.742886 | − | 0.669418i | \(-0.766544\pi\) | ||||
−0.742886 | + | 0.669418i | \(0.766544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 85.2841 | 1.81951 | 0.909753 | − | 0.415151i | \(-0.136271\pi\) | ||||
0.909753 | + | 0.415151i | \(0.136271\pi\) | |||||||
\(14\) | −73.8148 | −1.40913 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.85884 | 0.107169 | ||||||||
\(17\) | 48.1138 | 0.686430 | 0.343215 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343215 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 64.2348 | 0.775604 | 0.387802 | − | 0.921743i | \(-0.373235\pi\) | ||||
0.387802 | + | 0.921743i | \(0.373235\pi\) | |||||||
\(20\) | 42.8615 | 0.479206 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 250.284 | 2.42549 | ||||||||
\(23\) | 191.406 | 1.73525 | 0.867627 | − | 0.497216i | \(-0.165645\pi\) | ||||
0.867627 | + | 0.497216i | \(0.165645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −114.645 | −0.917162 | ||||||||
\(26\) | −393.786 | −2.97030 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 212.936 | 1.43719 | ||||||||
\(29\) | 15.0020 | 0.0960622 | 0.0480311 | − | 0.998846i | \(-0.484705\pi\) | ||||
0.0480311 | + | 0.998846i | \(0.484705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −209.724 | −1.21508 | −0.607542 | − | 0.794287i | \(-0.707844\pi\) | ||||
−0.607542 | + | 0.794287i | \(0.707844\pi\) | |||||||
\(32\) | 164.837 | 0.910606 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −222.158 | −1.12058 | ||||||||
\(35\) | 51.4424 | 0.248439 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 418.134 | 1.85786 | 0.928931 | − | 0.370254i | \(-0.120729\pi\) | ||||
0.928931 | + | 0.370254i | \(0.120729\pi\) | |||||||
\(38\) | −296.594 | −1.26615 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −79.0418 | −0.312440 | ||||||||
\(41\) | −226.787 | −0.863859 | −0.431929 | − | 0.901907i | \(-0.642167\pi\) | ||||
−0.431929 | + | 0.901907i | \(0.642167\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −207.102 | −0.734481 | −0.367241 | − | 0.930126i | \(-0.619697\pi\) | ||||
−0.367241 | + | 0.930126i | \(0.619697\pi\) | |||||||
\(44\) | −722.003 | −2.47377 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −883.784 | −2.83276 | ||||||||
\(47\) | −330.575 | −1.02594 | −0.512971 | − | 0.858406i | \(-0.671455\pi\) | ||||
−0.512971 | + | 0.858406i | \(0.671455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.4334 | −0.254908 | ||||||||
\(50\) | 529.356 | 1.49724 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1135.97 | 3.02943 | ||||||||
\(53\) | 449.141 | 1.16404 | 0.582021 | − | 0.813173i | \(-0.302262\pi\) | ||||
0.582021 | + | 0.813173i | \(0.302262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −174.426 | −0.427628 | ||||||||
\(56\) | −392.681 | −0.937039 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −69.2694 | −0.156819 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −393.282 | −0.825485 | −0.412743 | − | 0.910848i | \(-0.635429\pi\) | ||||
−0.412743 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(62\) | 968.368 | 1.98360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −815.980 | −1.59371 | ||||||||
\(65\) | 274.434 | 0.523682 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −67.7305 | −0.123501 | −0.0617507 | − | 0.998092i | \(-0.519668\pi\) | ||||
−0.0617507 | + | 0.998092i | \(0.519668\pi\) | |||||||
\(68\) | 640.866 | 1.14289 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −237.527 | −0.405570 | ||||||||
\(71\) | 589.737 | 0.985759 | 0.492879 | − | 0.870098i | \(-0.335944\pi\) | ||||
0.492879 | + | 0.870098i | \(0.335944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −229.329 | −0.367684 | −0.183842 | − | 0.982956i | \(-0.558853\pi\) | ||||
−0.183842 | + | 0.982956i | \(0.558853\pi\) | |||||||
\(74\) | −1930.67 | −3.03291 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 855.595 | 1.29136 | ||||||||
\(77\) | −866.549 | −1.28250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 563.476 | 0.802482 | 0.401241 | − | 0.915973i | \(-0.368579\pi\) | ||||
0.401241 | + | 0.915973i | \(0.368579\pi\) | |||||||
\(80\) | 22.0709 | 0.0308450 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1047.15 | 1.41023 | ||||||||
\(83\) | −1179.22 | −1.55947 | −0.779733 | − | 0.626112i | \(-0.784645\pi\) | ||||
−0.779733 | + | 0.626112i | \(0.784645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 154.824 | 0.197565 | ||||||||
\(86\) | 956.258 | 1.19902 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1331.46 | 1.61289 | ||||||||
\(89\) | 1335.45 | 1.59053 | 0.795266 | − | 0.606261i | \(-0.207331\pi\) | ||||
0.795266 | + | 0.606261i | \(0.207331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1363.39 | 1.57057 | ||||||||
\(92\) | 2549.49 | 2.88915 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1526.37 | 1.67482 | ||||||||
\(95\) | 206.699 | 0.223231 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1361.53 | 1.42518 | 0.712592 | − | 0.701578i | \(-0.247521\pi\) | ||||
0.712592 | + | 0.701578i | \(0.247521\pi\) | |||||||
\(98\) | 403.710 | 0.416131 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1527.05 | −1.52705 | ||||||||
\(101\) | −257.488 | −0.253673 | −0.126837 | − | 0.991924i | \(-0.540482\pi\) | ||||
−0.126837 | + | 0.991924i | \(0.540482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −343.256 | −0.328370 | −0.164185 | − | 0.986430i | \(-0.552499\pi\) | ||||
−0.164185 | + | 0.986430i | \(0.552499\pi\) | |||||||
\(104\) | −2094.86 | −1.97518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2073.84 | −1.90027 | ||||||||
\(107\) | 1319.34 | 1.19201 | 0.596007 | − | 0.802979i | \(-0.296753\pi\) | ||||
0.596007 | + | 0.802979i | \(0.296753\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 282.298 | 0.248067 | 0.124033 | − | 0.992278i | \(-0.460417\pi\) | ||||
0.124033 | + | 0.992278i | \(0.460417\pi\) | |||||||
\(110\) | 805.382 | 0.698092 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 109.648 | 0.0925072 | ||||||||
\(113\) | 2326.67 | 1.93695 | 0.968473 | − | 0.249119i | \(-0.0801411\pi\) | ||||
0.968473 | + | 0.249119i | \(0.0801411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 615.919 | 0.499433 | ||||||||
\(116\) | 199.824 | 0.159941 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −272.423 | −0.212530 | ||||||||
\(119\) | 769.169 | 0.592517 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1607.21 | 1.20752 | ||||||||
\(122\) | 1815.92 | 1.34758 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2793.49 | −2.02309 | ||||||||
\(125\) | −771.149 | −0.551789 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 660.219 | 0.461299 | 0.230650 | − | 0.973037i | \(-0.425915\pi\) | ||||
0.230650 | + | 0.973037i | \(0.425915\pi\) | |||||||
\(128\) | 2448.96 | 1.69109 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1267.15 | −0.854898 | ||||||||
\(131\) | −338.174 | −0.225545 | −0.112772 | − | 0.993621i | \(-0.535973\pi\) | ||||
−0.112772 | + | 0.993621i | \(0.535973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1026.89 | 0.669491 | ||||||||
\(134\) | 312.734 | 0.201613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1181.84 | −0.745159 | ||||||||
\(137\) | 1007.22 | 0.628121 | 0.314061 | − | 0.949403i | \(-0.398311\pi\) | ||||
0.314061 | + | 0.949403i | \(0.398311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2107.75 | 1.28617 | 0.643084 | − | 0.765796i | \(-0.277655\pi\) | ||||
0.643084 | + | 0.765796i | \(0.277655\pi\) | |||||||
\(140\) | 685.203 | 0.413644 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2723.01 | −1.60923 | ||||||||
\(143\) | −4622.85 | −2.70337 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 48.2746 | 0.0276482 | ||||||||
\(146\) | 1058.89 | 0.600235 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5569.47 | 3.09329 | ||||||||
\(149\) | 2275.39 | 1.25105 | 0.625527 | − | 0.780203i | \(-0.284884\pi\) | ||||
0.625527 | + | 0.780203i | \(0.284884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 396.997 | 0.213955 | 0.106977 | − | 0.994261i | \(-0.465883\pi\) | ||||
0.106977 | + | 0.994261i | \(0.465883\pi\) | |||||||
\(152\) | −1577.82 | −0.841962 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4001.15 | 2.09365 | ||||||||
\(155\) | −674.867 | −0.349720 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2285.11 | −1.16160 | −0.580802 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580802 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(158\) | −2601.76 | −1.31003 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 530.426 | 0.262086 | ||||||||
\(161\) | 3059.90 | 1.49785 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1433.49 | 0.688831 | 0.344415 | − | 0.938817i | \(-0.388077\pi\) | ||||
0.344415 | + | 0.938817i | \(0.388077\pi\) | |||||||
\(164\) | −3020.76 | −1.43830 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5444.84 | 2.54579 | ||||||||
\(167\) | −270.302 | −0.125249 | −0.0626246 | − | 0.998037i | \(-0.519947\pi\) | ||||
−0.0626246 | + | 0.998037i | \(0.519947\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5076.39 | 2.31060 | ||||||||
\(170\) | −714.875 | −0.322520 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2758.55 | −1.22289 | ||||||||
\(173\) | −1503.33 | −0.660673 | −0.330337 | − | 0.943863i | \(-0.607162\pi\) | ||||
−0.330337 | + | 0.943863i | \(0.607162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1832.77 | −0.791683 | ||||||||
\(176\) | −371.785 | −0.159229 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6166.22 | −2.59650 | ||||||||
\(179\) | −1741.30 | −0.727100 | −0.363550 | − | 0.931575i | \(-0.618435\pi\) | ||||
−0.363550 | + | 0.931575i | \(0.618435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3734.67 | −1.53368 | −0.766839 | − | 0.641839i | \(-0.778172\pi\) | ||||
−0.766839 | + | 0.641839i | \(0.778172\pi\) | |||||||
\(182\) | −6295.24 | −2.56392 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4701.56 | −1.88372 | ||||||||
\(185\) | 1345.50 | 0.534721 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2608.02 | −1.01988 | ||||||||
\(188\) | −4403.19 | −1.70817 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −954.401 | −0.364419 | ||||||||
\(191\) | −1504.04 | −0.569782 | −0.284891 | − | 0.958560i | \(-0.591957\pi\) | ||||
−0.284891 | + | 0.958560i | \(0.591957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2674.51 | 0.997488 | 0.498744 | − | 0.866749i | \(-0.333795\pi\) | ||||
0.498744 | + | 0.866749i | \(0.333795\pi\) | |||||||
\(194\) | −6286.67 | −2.32658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1164.60 | −0.424416 | ||||||||
\(197\) | 2496.55 | 0.902902 | 0.451451 | − | 0.892296i | \(-0.350907\pi\) | ||||
0.451451 | + | 0.892296i | \(0.350907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4410.90 | 1.57126 | 0.785629 | − | 0.618698i | \(-0.212339\pi\) | ||||
0.785629 | + | 0.618698i | \(0.212339\pi\) | |||||||
\(200\) | 2816.07 | 0.995632 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1188.91 | 0.414115 | ||||||||
\(203\) | 239.829 | 0.0829197 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −729.773 | −0.248632 | ||||||||
\(206\) | 1584.93 | 0.536055 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 584.950 | 0.194995 | ||||||||
\(209\) | −3481.86 | −1.15237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4046.61 | −1.32029 | −0.660143 | − | 0.751140i | \(-0.729504\pi\) | ||||
−0.660143 | + | 0.751140i | \(0.729504\pi\) | |||||||
\(212\) | 5982.47 | 1.93810 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6091.84 | −1.94593 | ||||||||
\(215\) | −666.427 | −0.211395 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3352.75 | −1.04885 | ||||||||
\(218\) | −1303.47 | −0.404963 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2323.32 | −0.711991 | ||||||||
\(221\) | 4103.34 | 1.24896 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3533.34 | 1.06103 | 0.530516 | − | 0.847675i | \(-0.321998\pi\) | ||||
0.530516 | + | 0.847675i | \(0.321998\pi\) | |||||||
\(224\) | 2635.16 | 0.786023 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10743.0 | −3.16202 | ||||||||
\(227\) | −96.7822 | −0.0282981 | −0.0141490 | − | 0.999900i | \(-0.504504\pi\) | ||||
−0.0141490 | + | 0.999900i | \(0.504504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1031.34 | 0.297611 | 0.148806 | − | 0.988866i | \(-0.452457\pi\) | ||||
0.148806 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(230\) | −2843.91 | −0.815312 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −368.500 | −0.104281 | ||||||||
\(233\) | −4689.07 | −1.31842 | −0.659208 | − | 0.751961i | \(-0.729108\pi\) | ||||
−0.659208 | + | 0.751961i | \(0.729108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1063.75 | −0.295282 | ||||||||
\(236\) | 785.869 | 0.216761 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3551.51 | −0.967270 | ||||||||
\(239\) | −234.661 | −0.0635103 | −0.0317551 | − | 0.999496i | \(-0.510110\pi\) | ||||
−0.0317551 | + | 0.999496i | \(0.510110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1334.65 | −0.356731 | −0.178365 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178365 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(242\) | −7421.01 | −1.97124 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5238.44 | −1.37441 | ||||||||
\(245\) | −281.350 | −0.0733664 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5478.21 | 1.41121 | ||||||||
\(248\) | 5151.54 | 1.31904 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3560.65 | 0.900782 | ||||||||
\(251\) | −1112.88 | −0.279859 | −0.139929 | − | 0.990161i | \(-0.544688\pi\) | ||||
−0.139929 | + | 0.990161i | \(0.544688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10375.2 | −2.57819 | ||||||||
\(254\) | −3048.46 | −0.753060 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4779.82 | −1.16695 | ||||||||
\(257\) | 2171.13 | 0.526971 | 0.263486 | − | 0.964663i | \(-0.415128\pi\) | ||||
0.263486 | + | 0.964663i | \(0.415128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6684.48 | 1.60368 | ||||||||
\(260\) | 3655.40 | 0.871918 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1561.46 | 0.368196 | ||||||||
\(263\) | 5098.53 | 1.19540 | 0.597698 | − | 0.801722i | \(-0.296082\pi\) | ||||
0.597698 | + | 0.801722i | \(0.296082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1445.28 | 0.335030 | ||||||||
\(266\) | −4741.48 | −1.09293 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −902.157 | −0.205627 | ||||||||
\(269\) | 2491.37 | 0.564689 | 0.282344 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282344 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2614.02 | −0.585943 | −0.292972 | − | 0.956121i | \(-0.594644\pi\) | ||||
−0.292972 | + | 0.956121i | \(0.594644\pi\) | |||||||
\(272\) | 330.005 | 0.0735642 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4650.67 | −1.02539 | ||||||||
\(275\) | 6214.37 | 1.36269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4270.47 | 0.926309 | 0.463154 | − | 0.886278i | \(-0.346718\pi\) | ||||
0.463154 | + | 0.886278i | \(0.346718\pi\) | |||||||
\(278\) | −9732.21 | −2.09964 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1263.60 | −0.269694 | ||||||||
\(281\) | 4081.99 | 0.866587 | 0.433294 | − | 0.901253i | \(-0.357351\pi\) | ||||
0.433294 | + | 0.901253i | \(0.357351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1547.60 | 0.325071 | 0.162535 | − | 0.986703i | \(-0.448033\pi\) | ||||
0.162535 | + | 0.986703i | \(0.448033\pi\) | |||||||
\(284\) | 7855.18 | 1.64127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21345.2 | 4.41318 | ||||||||
\(287\) | −3625.52 | −0.745672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2598.06 | −0.528814 | ||||||||
\(290\) | −222.900 | −0.0451350 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3054.62 | −0.612185 | ||||||||
\(293\) | −3046.36 | −0.607407 | −0.303703 | − | 0.952767i | \(-0.598223\pi\) | ||||
−0.303703 | + | 0.952767i | \(0.598223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 189.855 | 0.0374704 | ||||||||
\(296\) | −10270.8 | −2.01681 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10506.2 | −2.04231 | ||||||||
\(299\) | 16323.9 | 3.15730 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3310.82 | −0.633995 | ||||||||
\(302\) | −1833.07 | −0.349276 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 440.576 | 0.0831209 | ||||||||
\(305\) | −1265.53 | −0.237587 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5413.13 | 1.00633 | 0.503166 | − | 0.864190i | \(-0.332168\pi\) | ||||
0.503166 | + | 0.864190i | \(0.332168\pi\) | |||||||
\(308\) | −11542.3 | −2.13533 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3116.09 | 0.570909 | ||||||||
\(311\) | 945.000 | 0.172302 | 0.0861512 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861512 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4954.26 | 0.894669 | 0.447335 | − | 0.894367i | \(-0.352373\pi\) | ||||
0.447335 | + | 0.894367i | \(0.352373\pi\) | |||||||
\(314\) | 10551.1 | 1.89629 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7505.40 | 1.33611 | ||||||||
\(317\) | 3881.82 | 0.687775 | 0.343887 | − | 0.939011i | \(-0.388256\pi\) | ||||
0.343887 | + | 0.939011i | \(0.388256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −813.188 | −0.142727 | ||||||||
\(320\) | −2625.72 | −0.458695 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14128.6 | −2.44520 | ||||||||
\(323\) | 3090.58 | 0.532397 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9777.43 | −1.66878 | ||||||||
\(326\) | −6618.90 | −1.12450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5570.65 | 0.937768 | ||||||||
\(329\) | −5284.71 | −0.885580 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5526.01 | 0.917634 | 0.458817 | − | 0.888531i | \(-0.348273\pi\) | ||||
0.458817 | + | 0.888531i | \(0.348273\pi\) | |||||||
\(332\) | −15706.9 | −2.59647 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1248.08 | 0.204466 | ||||||||
\(335\) | −217.948 | −0.0355456 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3200.62 | 0.517356 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(338\) | −23439.4 | −3.77200 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2062.23 | 0.328941 | ||||||||
\(341\) | 11368.2 | 1.80534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6881.10 | −1.08322 | ||||||||
\(344\) | 5087.11 | 0.797321 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6941.40 | 1.07853 | ||||||||
\(347\) | 3533.99 | 0.546728 | 0.273364 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273364 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2116.90 | −0.324684 | −0.162342 | − | 0.986735i | \(-0.551905\pi\) | ||||
−0.162342 | + | 0.986735i | \(0.551905\pi\) | |||||||
\(350\) | 8462.52 | 1.29240 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8935.04 | −1.35295 | ||||||||
\(353\) | 1961.72 | 0.295784 | 0.147892 | − | 0.989004i | \(-0.452751\pi\) | ||||
0.147892 | + | 0.989004i | \(0.452751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1897.70 | 0.283717 | ||||||||
\(356\) | 17787.9 | 2.64820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8040.17 | 1.18697 | ||||||||
\(359\) | −4288.50 | −0.630469 | −0.315234 | − | 0.949014i | \(-0.602083\pi\) | ||||
−0.315234 | + | 0.949014i | \(0.602083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2732.89 | −0.398439 | ||||||||
\(362\) | 17244.2 | 2.50369 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18160.1 | 2.61497 | ||||||||
\(365\) | −737.952 | −0.105825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1246.33 | −0.177269 | −0.0886345 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886345 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(368\) | 1312.82 | 0.185966 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6212.65 | −0.872919 | ||||||||
\(371\) | 7180.17 | 1.00479 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11151.5 | 1.54799 | 0.773996 | − | 0.633190i | \(-0.218255\pi\) | ||||
0.773996 | + | 0.633190i | \(0.218255\pi\) | |||||||
\(374\) | 12042.1 | 1.66493 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8120.02 | 1.11372 | ||||||||
\(377\) | 1279.43 | 0.174786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6741.73 | 0.913719 | 0.456860 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456860 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(380\) | 2753.20 | 0.371674 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6944.65 | 0.930155 | ||||||||
\(383\) | −5172.09 | −0.690030 | −0.345015 | − | 0.938597i | \(-0.612126\pi\) | ||||
−0.345015 | + | 0.938597i | \(0.612126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2788.45 | −0.369123 | ||||||||
\(386\) | −12349.1 | −1.62837 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18135.4 | 2.37290 | ||||||||
\(389\) | −10739.9 | −1.39983 | −0.699914 | − | 0.714228i | \(-0.746778\pi\) | ||||
−0.699914 | + | 0.714228i | \(0.746778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9209.25 | 1.19113 | ||||||||
\(392\) | 2147.66 | 0.276717 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11527.4 | −1.47397 | ||||||||
\(395\) | 1813.20 | 0.230967 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3755.94 | 0.474825 | 0.237412 | − | 0.971409i | \(-0.423701\pi\) | ||||
0.237412 | + | 0.971409i | \(0.423701\pi\) | |||||||
\(398\) | −20366.6 | −2.56504 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −786.333 | −0.0982916 | ||||||||
\(401\) | −10542.2 | −1.31285 | −0.656424 | − | 0.754392i | \(-0.727932\pi\) | ||||
−0.656424 | + | 0.754392i | \(0.727932\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17886.2 | −2.21085 | ||||||||
\(404\) | −3429.69 | −0.422360 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1107.37 | −0.135364 | ||||||||
\(407\) | −22665.1 | −2.76036 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14298.9 | −1.72870 | −0.864348 | − | 0.502894i | \(-0.832269\pi\) | ||||
−0.864348 | + | 0.502894i | \(0.832269\pi\) | |||||||
\(410\) | 3369.61 | 0.405885 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4572.11 | −0.546727 | ||||||||
\(413\) | 943.201 | 0.112377 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3794.57 | −0.448839 | ||||||||
\(416\) | 14058.0 | 1.65685 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16076.9 | 1.88122 | ||||||||
\(419\) | −2605.91 | −0.303835 | −0.151917 | − | 0.988393i | \(-0.548545\pi\) | ||||
−0.151917 | + | 0.988393i | \(0.548545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11765.6 | −1.36204 | −0.681022 | − | 0.732263i | \(-0.738464\pi\) | ||||
−0.681022 | + | 0.732263i | \(0.738464\pi\) | |||||||
\(422\) | 18684.6 | 2.15534 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11032.4 | −1.26364 | ||||||||
\(425\) | −5516.02 | −0.629568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6287.18 | −0.712548 | ||||||||
\(428\) | 17573.4 | 1.98467 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3077.12 | 0.345097 | ||||||||
\(431\) | −11883.8 | −1.32813 | −0.664063 | − | 0.747677i | \(-0.731169\pi\) | ||||
−0.664063 | + | 0.747677i | \(0.731169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3187.43 | 0.353760 | 0.176880 | − | 0.984232i | \(-0.443400\pi\) | ||||
0.176880 | + | 0.984232i | \(0.443400\pi\) | |||||||
\(434\) | 15480.8 | 1.71221 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3760.16 | 0.413025 | ||||||||
\(437\) | 12294.9 | 1.34587 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16420.7 | 1.78524 | 0.892618 | − | 0.450814i | \(-0.148866\pi\) | ||||
0.892618 | + | 0.450814i | \(0.148866\pi\) | |||||||
\(440\) | 4284.48 | 0.464215 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18946.5 | −2.03890 | ||||||||
\(443\) | −632.306 | −0.0678143 | −0.0339072 | − | 0.999425i | \(-0.510795\pi\) | ||||
−0.0339072 | + | 0.999425i | \(0.510795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4297.31 | 0.457780 | ||||||||
\(446\) | −16314.6 | −1.73211 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13044.6 | −1.37567 | ||||||||
\(449\) | −6771.85 | −0.711767 | −0.355884 | − | 0.934530i | \(-0.615820\pi\) | ||||
−0.355884 | + | 0.934530i | \(0.615820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12293.0 | 1.28350 | ||||||||
\(452\) | 30990.8 | 3.22497 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 446.876 | 0.0461959 | ||||||||
\(455\) | 4387.22 | 0.452035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12278.5 | −1.25681 | −0.628406 | − | 0.777886i | \(-0.716292\pi\) | ||||
−0.628406 | + | 0.777886i | \(0.716292\pi\) | |||||||
\(458\) | −4762.06 | −0.485843 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8203.93 | 0.831543 | ||||||||
\(461\) | 10989.3 | 1.11024 | 0.555120 | − | 0.831770i | \(-0.312672\pi\) | ||||
0.555120 | + | 0.831770i | \(0.312672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12034.6 | −1.20798 | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||||
−0.603990 | + | 0.796992i | \(0.706423\pi\) | |||||||
\(464\) | 102.896 | 0.0102949 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21651.0 | 2.15228 | ||||||||
\(467\) | 9494.20 | 0.940769 | 0.470384 | − | 0.882462i | \(-0.344115\pi\) | ||||
0.470384 | + | 0.882462i | \(0.344115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1082.77 | −0.106605 | ||||||||
\(470\) | 4911.68 | 0.482040 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1449.24 | −0.141328 | ||||||||
\(473\) | 11226.0 | 1.09127 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7364.21 | −0.711354 | ||||||||
\(476\) | 10245.2 | 0.986527 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1083.51 | 0.103679 | ||||||||
\(479\) | −1700.69 | −0.162227 | −0.0811135 | − | 0.996705i | \(-0.525848\pi\) | ||||
−0.0811135 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35660.2 | 3.38039 | ||||||||
\(482\) | 6162.51 | 0.582354 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21407.7 | 2.01049 | ||||||||
\(485\) | 4381.25 | 0.410190 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3687.27 | 0.343093 | 0.171546 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171546 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(488\) | 9660.33 | 0.896112 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1299.09 | 0.119769 | ||||||||
\(491\) | −14020.6 | −1.28867 | −0.644337 | − | 0.764742i | \(-0.722866\pi\) | ||||
−0.644337 | + | 0.764742i | \(0.722866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 721.804 | 0.0659400 | ||||||||
\(494\) | −25294.7 | −2.30377 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1438.47 | −0.130220 | ||||||||
\(497\) | 9427.80 | 0.850894 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 831.548 | 0.0745996 | 0.0372998 | − | 0.999304i | \(-0.488124\pi\) | ||||
0.0372998 | + | 0.999304i | \(0.488124\pi\) | |||||||
\(500\) | −10271.6 | −0.918715 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5138.56 | 0.456862 | ||||||||
\(503\) | −14503.5 | −1.28565 | −0.642824 | − | 0.766014i | \(-0.722237\pi\) | ||||
−0.642824 | + | 0.766014i | \(0.722237\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −828.563 | −0.0730110 | ||||||||
\(506\) | 47905.7 | 4.20883 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8794.00 | 0.768052 | ||||||||
\(509\) | −3554.46 | −0.309526 | −0.154763 | − | 0.987952i | \(-0.549461\pi\) | ||||
−0.154763 | + | 0.987952i | \(0.549461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3666.16 | −0.317380 | ||||||||
\(512\) | 2478.40 | 0.213927 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10024.9 | −0.860267 | ||||||||
\(515\) | −1104.56 | −0.0945098 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17918.9 | 1.52431 | ||||||||
\(518\) | −30864.5 | −2.61797 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6741.01 | −0.568486 | ||||||||
\(521\) | −3095.33 | −0.260286 | −0.130143 | − | 0.991495i | \(-0.541544\pi\) | ||||
−0.130143 | + | 0.991495i | \(0.541544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10451.2 | −0.873802 | −0.436901 | − | 0.899510i | \(-0.643924\pi\) | ||||
−0.436901 | + | 0.899510i | \(0.643924\pi\) | |||||||
\(524\) | −4504.41 | −0.375527 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23541.6 | −1.95145 | ||||||||
\(527\) | −10090.6 | −0.834070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24469.1 | 2.01110 | ||||||||
\(530\) | −6673.35 | −0.546928 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13677.9 | 1.11469 | ||||||||
\(533\) | −19341.3 | −1.57179 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4245.47 | 0.343080 | ||||||||
\(536\) | 1663.69 | 0.134068 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11503.5 | −0.921841 | ||||||||
\(539\) | 4739.35 | 0.378735 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8714.59 | −0.692550 | −0.346275 | − | 0.938133i | \(-0.612554\pi\) | ||||
−0.346275 | + | 0.938133i | \(0.612554\pi\) | |||||||
\(542\) | 12069.8 | 0.956538 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7930.95 | 0.625067 | ||||||||
\(545\) | 908.401 | 0.0713975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7782.31 | −0.608314 | −0.304157 | − | 0.952622i | \(-0.598375\pi\) | ||||
−0.304157 | + | 0.952622i | \(0.598375\pi\) | |||||||
\(548\) | 13416.0 | 1.04581 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −28693.9 | −2.22456 | ||||||||
\(551\) | 963.651 | 0.0745062 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9007.99 | 0.692692 | ||||||||
\(554\) | −19718.2 | −1.51218 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28074.9 | 2.14144 | ||||||||
\(557\) | 12895.7 | 0.980982 | 0.490491 | − | 0.871446i | \(-0.336817\pi\) | ||||
0.490491 | + | 0.871446i | \(0.336817\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17662.5 | −1.33639 | ||||||||
\(560\) | 352.835 | 0.0266250 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18847.9 | −1.41468 | ||||||||
\(563\) | −10805.3 | −0.808863 | −0.404431 | − | 0.914568i | \(-0.632531\pi\) | ||||
−0.404431 | + | 0.914568i | \(0.632531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7486.94 | 0.557483 | ||||||||
\(566\) | −7145.78 | −0.530670 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14485.9 | −1.07010 | ||||||||
\(569\) | 11897.7 | 0.876589 | 0.438294 | − | 0.898831i | \(-0.355583\pi\) | ||||
0.438294 | + | 0.898831i | \(0.355583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20402.8 | 1.49532 | 0.747662 | − | 0.664080i | \(-0.231176\pi\) | ||||
0.747662 | + | 0.664080i | \(0.231176\pi\) | |||||||
\(572\) | −61575.4 | −4.50105 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16740.3 | 1.21729 | ||||||||
\(575\) | −21943.7 | −1.59151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21770.5 | 1.57074 | 0.785370 | − | 0.619027i | \(-0.212473\pi\) | ||||
0.785370 | + | 0.619027i | \(0.212473\pi\) | |||||||
\(578\) | 11996.1 | 0.863276 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 643.009 | 0.0460336 | ||||||||
\(581\) | −18851.5 | −1.34611 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24345.8 | −1.72950 | ||||||||
\(584\) | 5633.09 | 0.399142 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14066.1 | 0.991576 | ||||||||
\(587\) | −21616.4 | −1.51994 | −0.759970 | − | 0.649959i | \(-0.774786\pi\) | ||||
−0.759970 | + | 0.649959i | \(0.774786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13471.6 | −0.942424 | ||||||||
\(590\) | −876.623 | −0.0611695 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2867.91 | 0.199106 | ||||||||
\(593\) | 18257.7 | 1.26434 | 0.632172 | − | 0.774828i | \(-0.282164\pi\) | ||||
0.632172 | + | 0.774828i | \(0.282164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2475.09 | 0.170536 | ||||||||
\(596\) | 30307.7 | 2.08297 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −75372.8 | −5.15422 | ||||||||
\(599\) | 2679.25 | 0.182756 | 0.0913781 | − | 0.995816i | \(-0.470873\pi\) | ||||
0.0913781 | + | 0.995816i | \(0.470873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19874.2 | −1.34889 | −0.674447 | − | 0.738324i | \(-0.735618\pi\) | ||||
−0.674447 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(602\) | 15287.2 | 1.03498 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5287.93 | 0.356230 | ||||||||
\(605\) | 5171.79 | 0.347542 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20437.2 | −1.36659 | −0.683297 | − | 0.730141i | \(-0.739454\pi\) | ||||
−0.683297 | + | 0.730141i | \(0.739454\pi\) | |||||||
\(608\) | 10588.3 | 0.706269 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5843.39 | 0.387856 | ||||||||
\(611\) | −28192.8 | −1.86671 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19812.1 | 1.30539 | 0.652695 | − | 0.757621i | \(-0.273638\pi\) | ||||
0.652695 | + | 0.757621i | \(0.273638\pi\) | |||||||
\(614\) | −24994.3 | −1.64281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21285.4 | 1.39223 | ||||||||
\(617\) | −27960.5 | −1.82439 | −0.912194 | − | 0.409758i | \(-0.865613\pi\) | ||||
−0.912194 | + | 0.409758i | \(0.865613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28522.1 | −1.85202 | −0.926008 | − | 0.377503i | \(-0.876783\pi\) | ||||
−0.926008 | + | 0.377503i | \(0.876783\pi\) | |||||||
\(620\) | −8989.10 | −0.582276 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4363.38 | −0.281279 | ||||||||
\(623\) | 21349.1 | 1.37293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11849.2 | 0.758349 | ||||||||
\(626\) | −22875.5 | −1.46053 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30437.2 | −1.93404 | ||||||||
\(629\) | 20118.0 | 1.27529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13610.9 | −0.858706 | −0.429353 | − | 0.903137i | \(-0.641258\pi\) | ||||
−0.429353 | + | 0.903137i | \(0.641258\pi\) | |||||||
\(632\) | −13840.9 | −0.871140 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17923.7 | −1.12278 | ||||||||
\(635\) | 2124.50 | 0.132769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7456.68 | −0.463806 | ||||||||
\(638\) | 3754.76 | 0.232998 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7880.44 | 0.486721 | ||||||||
\(641\) | 19792.9 | 1.21961 | 0.609807 | − | 0.792550i | \(-0.291247\pi\) | ||||
0.609807 | + | 0.792550i | \(0.291247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14995.9 | 0.919719 | 0.459859 | − | 0.887992i | \(-0.347900\pi\) | ||||
0.459859 | + | 0.887992i | \(0.347900\pi\) | |||||||
\(644\) | 40757.2 | 2.49388 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14270.2 | −0.869126 | ||||||||
\(647\) | −29860.2 | −1.81441 | −0.907207 | − | 0.420684i | \(-0.861790\pi\) | ||||
−0.907207 | + | 0.420684i | \(0.861790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3198.11 | −0.193431 | ||||||||
\(650\) | 45145.7 | 2.72424 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19093.8 | 1.14689 | ||||||||
\(653\) | −17572.2 | −1.05307 | −0.526533 | − | 0.850155i | \(-0.676508\pi\) | ||||
−0.526533 | + | 0.850155i | \(0.676508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1088.20 | −0.0649153 | ||||||||
\(656\) | −1555.50 | −0.0925791 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24401.3 | 1.44569 | ||||||||
\(659\) | −14231.1 | −0.841222 | −0.420611 | − | 0.907241i | \(-0.638184\pi\) | ||||
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28811.1 | −1.69535 | −0.847673 | − | 0.530520i | \(-0.821997\pi\) | ||||
−0.847673 | + | 0.530520i | \(0.821997\pi\) | |||||||
\(662\) | −25515.4 | −1.49802 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28965.5 | 1.69289 | ||||||||
\(665\) | 3304.39 | 0.192690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2871.47 | 0.166692 | ||||||||
\(668\) | −3600.38 | −0.208537 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1006.34 | 0.0580273 | ||||||||
\(671\) | 21317.9 | 1.22648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16148.1 | 0.924909 | 0.462455 | − | 0.886643i | \(-0.346969\pi\) | ||||
0.462455 | + | 0.886643i | \(0.346969\pi\) | |||||||
\(674\) | −14778.4 | −0.844572 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 67616.5 | 3.84709 | ||||||||
\(677\) | −20624.3 | −1.17084 | −0.585418 | − | 0.810731i | \(-0.699070\pi\) | ||||
−0.585418 | + | 0.810731i | \(0.699070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21766.1 | 1.23020 | ||||||||
\(680\) | −3803.00 | −0.214468 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −52490.6 | −2.94717 | ||||||||
\(683\) | 26607.3 | 1.49063 | 0.745314 | − | 0.666714i | \(-0.232300\pi\) | ||||
0.745314 | + | 0.666714i | \(0.232300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3241.11 | 0.180783 | ||||||||
\(686\) | 31772.4 | 1.76833 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1420.48 | −0.0787138 | ||||||||
\(689\) | 38304.6 | 2.11798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31832.9 | 1.75251 | 0.876254 | − | 0.481850i | \(-0.160035\pi\) | ||||
0.876254 | + | 0.481850i | \(0.160035\pi\) | |||||||
\(692\) | −20024.1 | −1.10000 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16317.6 | −0.892520 | ||||||||
\(695\) | 6782.49 | 0.370179 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10911.6 | −0.592978 | ||||||||
\(698\) | 9774.42 | 0.530039 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24412.2 | −1.31813 | ||||||||
\(701\) | 26303.0 | 1.41719 | 0.708594 | − | 0.705616i | \(-0.249330\pi\) | ||||
0.708594 | + | 0.705616i | \(0.249330\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26858.8 | 1.44096 | ||||||||
\(704\) | 44230.4 | 2.36789 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9057.92 | −0.482860 | ||||||||
\(707\) | −4116.31 | −0.218967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31256.4 | 1.65565 | 0.827826 | − | 0.560984i | \(-0.189577\pi\) | ||||
0.827826 | + | 0.560984i | \(0.189577\pi\) | |||||||
\(710\) | −8762.32 | −0.463160 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −32803.1 | −1.72661 | ||||||||
\(713\) | −40142.4 | −2.10848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14875.7 | −0.778072 | ||||||||
\(716\) | −23193.8 | −1.21060 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19801.4 | 1.02922 | ||||||||
\(719\) | −20206.1 | −1.04807 | −0.524034 | − | 0.851697i | \(-0.675574\pi\) | ||||
−0.524034 | + | 0.851697i | \(0.675574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5487.45 | −0.283444 | ||||||||
\(722\) | 12618.7 | 0.650442 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −49745.1 | −2.55354 | ||||||||
\(725\) | −1719.91 | −0.0881047 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15044.8 | −0.767510 | −0.383755 | − | 0.923435i | \(-0.625369\pi\) | ||||
−0.383755 | + | 0.923435i | \(0.625369\pi\) | |||||||
\(728\) | −33489.5 | −1.70495 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3407.37 | 0.172757 | ||||||||
\(731\) | −9964.44 | −0.504170 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30276.0 | 1.52560 | 0.762802 | − | 0.646632i | \(-0.223823\pi\) | ||||
0.762802 | + | 0.646632i | \(0.223823\pi\) | |||||||
\(734\) | 5754.71 | 0.289387 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31550.8 | 1.58013 | ||||||||
\(737\) | 3671.35 | 0.183495 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7587.02 | −0.377663 | −0.188832 | − | 0.982009i | \(-0.560470\pi\) | ||||
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(740\) | 17921.9 | 0.890298 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33153.3 | −1.64029 | ||||||||
\(743\) | 12898.6 | 0.636882 | 0.318441 | − | 0.947943i | \(-0.396841\pi\) | ||||
0.318441 | + | 0.947943i | \(0.396841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7321.91 | 0.360072 | ||||||||
\(746\) | −51490.1 | −2.52706 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −34738.3 | −1.69807 | ||||||||
\(749\) | 21091.6 | 1.02893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18857.3 | −0.916260 | −0.458130 | − | 0.888885i | \(-0.651481\pi\) | ||||
−0.458130 | + | 0.888885i | \(0.651481\pi\) | |||||||
\(752\) | −2267.36 | −0.109949 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5907.58 | −0.285333 | ||||||||
\(755\) | 1277.49 | 0.0615795 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25156.1 | −1.20781 | −0.603905 | − | 0.797056i | \(-0.706390\pi\) | ||||
−0.603905 | + | 0.797056i | \(0.706390\pi\) | |||||||
\(758\) | −31128.9 | −1.49162 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5077.23 | −0.242330 | ||||||||
\(761\) | −2380.10 | −0.113375 | −0.0566875 | − | 0.998392i | \(-0.518054\pi\) | ||||
−0.0566875 | + | 0.998392i | \(0.518054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4512.95 | 0.214128 | ||||||||
\(764\) | −20033.5 | −0.948673 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23881.3 | 1.12646 | ||||||||
\(767\) | 5031.76 | 0.236879 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27770.6 | −1.30226 | −0.651128 | − | 0.758968i | \(-0.725704\pi\) | ||||
−0.651128 | + | 0.758968i | \(0.725704\pi\) | |||||||
\(770\) | 12875.2 | 0.602584 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35623.9 | 1.66079 | ||||||||
\(773\) | 15649.4 | 0.728165 | 0.364082 | − | 0.931367i | \(-0.381383\pi\) | ||||
0.364082 | + | 0.931367i | \(0.381383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24043.9 | 1.11443 | ||||||||
\(776\) | −33443.9 | −1.54712 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 49589.6 | 2.28518 | ||||||||
\(779\) | −14567.6 | −0.670012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31966.8 | −1.46461 | ||||||||
\(782\) | −42522.2 | −1.94449 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −599.691 | −0.0273183 | ||||||||
\(785\) | −7353.20 | −0.334327 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12216.7 | 0.553338 | 0.276669 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276669 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(788\) | 33253.6 | 1.50331 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8372.14 | −0.377047 | ||||||||
\(791\) | 37195.2 | 1.67195 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33540.7 | −1.50197 | ||||||||
\(794\) | −17342.5 | −0.775140 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 58752.3 | 2.61611 | ||||||||
\(797\) | −31212.6 | −1.38721 | −0.693605 | − | 0.720356i | \(-0.743979\pi\) | ||||
−0.693605 | + | 0.720356i | \(0.743979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15905.2 | −0.704237 | ||||||||
\(800\) | −18897.8 | −0.835173 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 48676.9 | 2.14319 | ||||||||
\(803\) | 12430.8 | 0.546295 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9846.36 | 0.431104 | ||||||||
\(806\) | 82586.5 | 3.60916 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6324.76 | 0.275377 | ||||||||
\(809\) | 27090.0 | 1.17730 | 0.588650 | − | 0.808388i | \(-0.299660\pi\) | ||||
0.588650 | + | 0.808388i | \(0.299660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2136.04 | 0.0924863 | 0.0462431 | − | 0.998930i | \(-0.485275\pi\) | ||||
0.0462431 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(812\) | 3194.48 | 0.138059 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 104652. | 4.50622 | ||||||||
\(815\) | 4612.78 | 0.198256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13303.1 | −0.569666 | ||||||||
\(818\) | 66023.0 | 2.82205 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9720.43 | −0.413966 | ||||||||
\(821\) | 13041.2 | 0.554373 | 0.277187 | − | 0.960816i | \(-0.410598\pi\) | ||||
0.277187 | + | 0.960816i | \(0.410598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15741.7 | −0.666734 | −0.333367 | − | 0.942797i | \(-0.608185\pi\) | ||||
−0.333367 | + | 0.942797i | \(0.608185\pi\) | |||||||
\(824\) | 8431.53 | 0.356464 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4355.08 | −0.183453 | ||||||||
\(827\) | −29188.2 | −1.22730 | −0.613648 | − | 0.789580i | \(-0.710299\pi\) | ||||
−0.613648 | + | 0.789580i | \(0.710299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23688.9 | −0.992461 | −0.496230 | − | 0.868191i | \(-0.665283\pi\) | ||||
−0.496230 | + | 0.868191i | \(0.665283\pi\) | |||||||
\(830\) | 17520.8 | 0.732718 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −69590.2 | −2.89977 | ||||||||
\(833\) | −4206.75 | −0.174976 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −869.799 | −0.0360487 | ||||||||
\(836\) | −46377.7 | −1.91867 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12032.3 | 0.496003 | ||||||||
\(839\) | −46609.6 | −1.91793 | −0.958965 | − | 0.283525i | \(-0.908496\pi\) | ||||
−0.958965 | + | 0.283525i | \(0.908496\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24163.9 | −0.990772 | ||||||||
\(842\) | 54325.8 | 2.22350 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −53900.1 | −2.19825 | ||||||||
\(845\) | 16335.2 | 0.665026 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25693.5 | 1.04231 | ||||||||
\(848\) | 3080.59 | 0.124750 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25469.3 | 1.02775 | ||||||||
\(851\) | 80033.2 | 3.22386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15069.2 | 0.604877 | 0.302439 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302439 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(854\) | 29030.1 | 1.16322 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32407.4 | −1.29400 | ||||||||
\(857\) | 32618.8 | 1.30016 | 0.650081 | − | 0.759865i | \(-0.274735\pi\) | ||||
0.650081 | + | 0.759865i | \(0.274735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6931.99 | −0.275339 | −0.137670 | − | 0.990478i | \(-0.543961\pi\) | ||||
−0.137670 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(860\) | −8876.68 | −0.351968 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 54871.5 | 2.16813 | ||||||||
\(863\) | −6692.94 | −0.263998 | −0.131999 | − | 0.991250i | \(-0.542140\pi\) | ||||
−0.131999 | + | 0.991250i | \(0.542140\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4837.54 | −0.190152 | ||||||||
\(866\) | −14717.4 | −0.577505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −44658.0 | −1.74630 | ||||||||
\(869\) | −30543.4 | −1.19230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5776.34 | −0.224711 | ||||||||
\(872\) | −6934.20 | −0.269291 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −56769.7 | −2.19710 | ||||||||
\(875\) | −12327.9 | −0.476297 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7773.39 | 0.299303 | 0.149652 | − | 0.988739i | \(-0.452185\pi\) | ||||
0.149652 | + | 0.988739i | \(0.452185\pi\) | |||||||
\(878\) | −75820.0 | −2.91435 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1196.36 | −0.0458286 | ||||||||
\(881\) | 8298.43 | 0.317345 | 0.158673 | − | 0.987331i | \(-0.449279\pi\) | ||||
0.158673 | + | 0.987331i | \(0.449279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30480.9 | −1.16168 | −0.580841 | − | 0.814017i | \(-0.697276\pi\) | ||||
−0.580841 | + | 0.814017i | \(0.697276\pi\) | |||||||
\(884\) | 54655.7 | 2.07949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2919.57 | 0.110705 | ||||||||
\(887\) | −7695.04 | −0.291290 | −0.145645 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145645 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10554.6 | 0.398188 | ||||||||
\(890\) | −19842.1 | −0.747314 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 47063.4 | 1.76659 | ||||||||
\(893\) | −21234.4 | −0.795724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5603.29 | −0.209271 | ||||||||
\(896\) | 39150.1 | 1.45973 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31267.9 | 1.16194 | ||||||||
\(899\) | −3146.29 | −0.116724 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21609.9 | 0.799034 | ||||||||
\(902\) | −56761.1 | −2.09528 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −57150.9 | −2.10267 | ||||||||
\(905\) | −12017.7 | −0.441416 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20682.7 | 0.757176 | 0.378588 | − | 0.925565i | \(-0.376410\pi\) | ||||
0.378588 | + | 0.925565i | \(0.376410\pi\) | |||||||
\(908\) | −1289.12 | −0.0471156 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20257.3 | −0.737937 | ||||||||
\(911\) | 27515.9 | 1.00071 | 0.500353 | − | 0.865822i | \(-0.333204\pi\) | ||||
0.500353 | + | 0.865822i | \(0.333204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63919.6 | 2.31701 | ||||||||
\(914\) | 56693.9 | 2.05171 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13737.3 | 0.495516 | ||||||||
\(917\) | −5406.19 | −0.194687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4136.30 | −0.148470 | −0.0742350 | − | 0.997241i | \(-0.523651\pi\) | ||||
−0.0742350 | + | 0.997241i | \(0.523651\pi\) | |||||||
\(920\) | −15129.0 | −0.542163 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −50741.1 | −1.81244 | ||||||||
\(923\) | 50295.2 | 1.79359 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47937.1 | −1.70396 | ||||||||
\(926\) | 55567.7 | 1.97200 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2472.89 | 0.0874748 | ||||||||
\(929\) | 41730.5 | 1.47377 | 0.736886 | − | 0.676017i | \(-0.236295\pi\) | ||||
0.736886 | + | 0.676017i | \(0.236295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5616.27 | −0.197708 | ||||||||
\(932\) | −62457.5 | −2.19513 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −43837.9 | −1.53578 | ||||||||
\(935\) | −8392.28 | −0.293537 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21380.2 | 0.745422 | 0.372711 | − | 0.927947i | \(-0.378428\pi\) | ||||
0.372711 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(938\) | 4999.51 | 0.174030 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14168.9 | −0.491637 | ||||||||
\(941\) | 21613.7 | 0.748764 | 0.374382 | − | 0.927275i | \(-0.377855\pi\) | ||||
0.374382 | + | 0.927275i | \(0.377855\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43408.3 | −1.49901 | ||||||||
\(944\) | 404.671 | 0.0139523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51834.2 | −1.78147 | ||||||||
\(947\) | 6008.44 | 0.206175 | 0.103088 | − | 0.994672i | \(-0.467128\pi\) | ||||
0.103088 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19558.1 | −0.669003 | ||||||||
\(950\) | 34003.1 | 1.16127 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18893.4 | −0.643212 | ||||||||
\(953\) | 5173.79 | 0.175861 | 0.0879305 | − | 0.996127i | \(-0.471975\pi\) | ||||
0.0879305 | + | 0.996127i | \(0.471975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4839.80 | −0.163992 | ||||||||
\(956\) | −3125.64 | −0.105743 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7852.68 | 0.264832 | ||||||||
\(959\) | 16101.9 | 0.542186 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14193.3 | 0.476430 | ||||||||
\(962\) | −164655. | −5.51840 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17777.2 | −0.593948 | ||||||||
\(965\) | 8606.22 | 0.287092 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26508.3 | 0.881540 | 0.440770 | − | 0.897620i | \(-0.354705\pi\) | ||||
0.440770 | + | 0.897620i | \(0.354705\pi\) | |||||||
\(968\) | −39478.4 | −1.31083 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20229.7 | −0.669625 | ||||||||
\(971\) | 22770.6 | 0.752569 | 0.376285 | − | 0.926504i | \(-0.377202\pi\) | ||||
0.376285 | + | 0.926504i | \(0.377202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33695.5 | 1.11020 | ||||||||
\(974\) | −17025.4 | −0.560091 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2697.46 | −0.0884667 | ||||||||
\(977\) | 10137.9 | 0.331974 | 0.165987 | − | 0.986128i | \(-0.446919\pi\) | ||||
0.165987 | + | 0.986128i | \(0.446919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72388.3 | −2.36317 | ||||||||
\(980\) | −3747.53 | −0.122153 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 64737.6 | 2.10373 | ||||||||
\(983\) | 19066.2 | 0.618635 | 0.309317 | − | 0.950959i | \(-0.399899\pi\) | ||||
0.309317 | + | 0.950959i | \(0.399899\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8033.58 | 0.259869 | ||||||||
\(986\) | −3332.81 | −0.107645 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 72968.7 | 2.34964 | ||||||||
\(989\) | −39640.4 | −1.27451 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17491.5 | −0.560681 | −0.280341 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280341 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(992\) | −34570.4 | −1.10646 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −43531.3 | −1.38906 | ||||||||
\(995\) | 14193.7 | 0.452232 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7297.85 | −0.231821 | −0.115910 | − | 0.993260i | \(-0.536979\pi\) | ||||
−0.115910 | + | 0.993260i | \(0.536979\pi\) | |||||||
\(998\) | −3839.54 | −0.121782 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.4.a.f.1.2 | 8 | ||
3.2 | odd | 2 | 177.4.a.c.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.7 | ✓ | 8 | 3.2 | odd | 2 | ||
531.4.a.f.1.2 | 8 | 1.1 | even | 1 | trivial |