Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
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: | \( x^{8} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.365778\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.365778 | 0.211182 | 0.105591 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105591 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.365778 | 0.149328 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.86621 | −0.955402 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.365778 | 0.105591 | ||||||||
\(13\) | −2.20049 | −0.610306 | −0.305153 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305153 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.365778 | −0.0944434 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.26330 | 1.51907 | 0.759537 | − | 0.650464i | \(-0.225425\pi\) | ||||
0.759537 | + | 0.650464i | \(0.225425\pi\) | |||||||
\(18\) | −2.86621 | −0.675571 | ||||||||
\(19\) | −6.00967 | −1.37871 | −0.689356 | − | 0.724422i | \(-0.742107\pi\) | ||||
−0.689356 | + | 0.724422i | \(0.742107\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.365778 | −0.0798193 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.452126 | 0.0942748 | 0.0471374 | − | 0.998888i | \(-0.484990\pi\) | ||||
0.0471374 | + | 0.998888i | \(0.484990\pi\) | |||||||
\(24\) | 0.365778 | 0.0746641 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.20049 | −0.431551 | ||||||||
\(27\) | −2.14573 | −0.412946 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.90770 | −0.354251 | −0.177126 | − | 0.984188i | \(-0.556680\pi\) | ||||
−0.177126 | + | 0.984188i | \(0.556680\pi\) | |||||||
\(30\) | −0.365778 | −0.0667816 | ||||||||
\(31\) | −6.05116 | −1.08682 | −0.543411 | − | 0.839467i | \(-0.682867\pi\) | ||||
−0.543411 | + | 0.839467i | \(0.682867\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.26330 | 1.07415 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.86621 | −0.477701 | ||||||||
\(37\) | 3.54127 | 0.582181 | 0.291090 | − | 0.956696i | \(-0.405982\pi\) | ||||
0.291090 | + | 0.956696i | \(0.405982\pi\) | |||||||
\(38\) | −6.00967 | −0.974897 | ||||||||
\(39\) | −0.804890 | −0.128886 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.0206760 | −0.00322905 | −0.00161452 | − | 0.999999i | \(-0.500514\pi\) | ||||
−0.00161452 | + | 0.999999i | \(0.500514\pi\) | |||||||
\(42\) | −0.365778 | −0.0564407 | ||||||||
\(43\) | 3.71582 | 0.566657 | 0.283329 | − | 0.959023i | \(-0.408561\pi\) | ||||
0.283329 | + | 0.959023i | \(0.408561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.86621 | 0.427269 | ||||||||
\(46\) | 0.452126 | 0.0666624 | ||||||||
\(47\) | 8.63329 | 1.25929 | 0.629647 | − | 0.776881i | \(-0.283199\pi\) | ||||
0.629647 | + | 0.776881i | \(0.283199\pi\) | |||||||
\(48\) | 0.365778 | 0.0527955 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.29098 | 0.320801 | ||||||||
\(52\) | −2.20049 | −0.305153 | ||||||||
\(53\) | 8.03517 | 1.10372 | 0.551858 | − | 0.833938i | \(-0.313919\pi\) | ||||
0.551858 | + | 0.833938i | \(0.313919\pi\) | |||||||
\(54\) | −2.14573 | −0.291997 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.19820 | −0.291159 | ||||||||
\(58\) | −1.90770 | −0.250493 | ||||||||
\(59\) | −12.7279 | −1.65703 | −0.828516 | − | 0.559965i | \(-0.810814\pi\) | ||||
−0.828516 | + | 0.559965i | \(0.810814\pi\) | |||||||
\(60\) | −0.365778 | −0.0472217 | ||||||||
\(61\) | 6.02013 | 0.770798 | 0.385399 | − | 0.922750i | \(-0.374064\pi\) | ||||
0.385399 | + | 0.922750i | \(0.374064\pi\) | |||||||
\(62\) | −6.05116 | −0.768499 | ||||||||
\(63\) | 2.86621 | 0.361108 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.20049 | 0.272937 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.19469 | 1.00114 | 0.500570 | − | 0.865696i | \(-0.333124\pi\) | ||||
0.500570 | + | 0.865696i | \(0.333124\pi\) | |||||||
\(68\) | 6.26330 | 0.759537 | ||||||||
\(69\) | 0.165378 | 0.0199091 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 15.7605 | 1.87043 | 0.935216 | − | 0.354077i | \(-0.115205\pi\) | ||||
0.935216 | + | 0.354077i | \(0.115205\pi\) | |||||||
\(72\) | −2.86621 | −0.337786 | ||||||||
\(73\) | 12.7842 | 1.49628 | 0.748139 | − | 0.663542i | \(-0.230947\pi\) | ||||
0.748139 | + | 0.663542i | \(0.230947\pi\) | |||||||
\(74\) | 3.54127 | 0.411664 | ||||||||
\(75\) | 0.365778 | 0.0422364 | ||||||||
\(76\) | −6.00967 | −0.689356 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.804890 | −0.0911358 | ||||||||
\(79\) | 10.7445 | 1.20885 | 0.604425 | − | 0.796662i | \(-0.293403\pi\) | ||||
0.604425 | + | 0.796662i | \(0.293403\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.81376 | 0.868196 | ||||||||
\(82\) | −0.0206760 | −0.00228328 | ||||||||
\(83\) | 10.9679 | 1.20388 | 0.601942 | − | 0.798540i | \(-0.294394\pi\) | ||||
0.601942 | + | 0.798540i | \(0.294394\pi\) | |||||||
\(84\) | −0.365778 | −0.0399096 | ||||||||
\(85\) | −6.26330 | −0.679351 | ||||||||
\(86\) | 3.71582 | 0.400687 | ||||||||
\(87\) | −0.697795 | −0.0748115 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.56469 | −1.01385 | −0.506927 | − | 0.861989i | \(-0.669219\pi\) | ||||
−0.506927 | + | 0.861989i | \(0.669219\pi\) | |||||||
\(90\) | 2.86621 | 0.302125 | ||||||||
\(91\) | 2.20049 | 0.230674 | ||||||||
\(92\) | 0.452126 | 0.0471374 | ||||||||
\(93\) | −2.21338 | −0.229517 | ||||||||
\(94\) | 8.63329 | 0.890455 | ||||||||
\(95\) | 6.00967 | 0.616579 | ||||||||
\(96\) | 0.365778 | 0.0373320 | ||||||||
\(97\) | −4.22569 | −0.429053 | −0.214527 | − | 0.976718i | \(-0.568821\pi\) | ||||
−0.214527 | + | 0.976718i | \(0.568821\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.0515 | −1.00016 | −0.500080 | − | 0.865979i | \(-0.666696\pi\) | ||||
−0.500080 | + | 0.865979i | \(0.666696\pi\) | |||||||
\(102\) | 2.29098 | 0.226841 | ||||||||
\(103\) | 14.6726 | 1.44573 | 0.722867 | − | 0.690987i | \(-0.242824\pi\) | ||||
0.722867 | + | 0.690987i | \(0.242824\pi\) | |||||||
\(104\) | −2.20049 | −0.215776 | ||||||||
\(105\) | 0.365778 | 0.0356963 | ||||||||
\(106\) | 8.03517 | 0.780445 | ||||||||
\(107\) | −1.85065 | −0.178909 | −0.0894545 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894545 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(108\) | −2.14573 | −0.206473 | ||||||||
\(109\) | −16.3800 | −1.56892 | −0.784459 | − | 0.620181i | \(-0.787059\pi\) | ||||
−0.784459 | + | 0.620181i | \(0.787059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.29532 | 0.122946 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −10.7686 | −1.01303 | −0.506514 | − | 0.862232i | \(-0.669066\pi\) | ||||
−0.506514 | + | 0.862232i | \(0.669066\pi\) | |||||||
\(114\) | −2.19820 | −0.205881 | ||||||||
\(115\) | −0.452126 | −0.0421610 | ||||||||
\(116\) | −1.90770 | −0.177126 | ||||||||
\(117\) | 6.30706 | 0.583087 | ||||||||
\(118\) | −12.7279 | −1.17170 | ||||||||
\(119\) | −6.26330 | −0.574156 | ||||||||
\(120\) | −0.365778 | −0.0333908 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.02013 | 0.545037 | ||||||||
\(123\) | −0.00756282 | −0.000681917 0 | ||||||||
\(124\) | −6.05116 | −0.543411 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.86621 | 0.255342 | ||||||||
\(127\) | 4.44315 | 0.394266 | 0.197133 | − | 0.980377i | \(-0.436837\pi\) | ||||
0.197133 | + | 0.980377i | \(0.436837\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.35916 | 0.119668 | ||||||||
\(130\) | 2.20049 | 0.192996 | ||||||||
\(131\) | −2.54949 | −0.222750 | −0.111375 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111375 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00967 | 0.521104 | ||||||||
\(134\) | 8.19469 | 0.707913 | ||||||||
\(135\) | 2.14573 | 0.184675 | ||||||||
\(136\) | 6.26330 | 0.537074 | ||||||||
\(137\) | −15.1630 | −1.29546 | −0.647730 | − | 0.761870i | \(-0.724281\pi\) | ||||
−0.647730 | + | 0.761870i | \(0.724281\pi\) | |||||||
\(138\) | 0.165378 | 0.0140779 | ||||||||
\(139\) | 4.56534 | 0.387227 | 0.193614 | − | 0.981078i | \(-0.437979\pi\) | ||||
0.193614 | + | 0.981078i | \(0.437979\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 3.15786 | 0.265940 | ||||||||
\(142\) | 15.7605 | 1.32260 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.86621 | −0.238851 | ||||||||
\(145\) | 1.90770 | 0.158426 | ||||||||
\(146\) | 12.7842 | 1.05803 | ||||||||
\(147\) | 0.365778 | 0.0301688 | ||||||||
\(148\) | 3.54127 | 0.291090 | ||||||||
\(149\) | 13.9113 | 1.13966 | 0.569830 | − | 0.821762i | \(-0.307009\pi\) | ||||
0.569830 | + | 0.821762i | \(0.307009\pi\) | |||||||
\(150\) | 0.365778 | 0.0298656 | ||||||||
\(151\) | 3.78025 | 0.307632 | 0.153816 | − | 0.988099i | \(-0.450844\pi\) | ||||
0.153816 | + | 0.988099i | \(0.450844\pi\) | |||||||
\(152\) | −6.00967 | −0.487449 | ||||||||
\(153\) | −17.9519 | −1.45133 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.05116 | 0.486041 | ||||||||
\(156\) | −0.804890 | −0.0644428 | ||||||||
\(157\) | 12.6782 | 1.01183 | 0.505916 | − | 0.862583i | \(-0.331154\pi\) | ||||
0.505916 | + | 0.862583i | \(0.331154\pi\) | |||||||
\(158\) | 10.7445 | 0.854787 | ||||||||
\(159\) | 2.93909 | 0.233085 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −0.452126 | −0.0356325 | ||||||||
\(162\) | 7.81376 | 0.613907 | ||||||||
\(163\) | 18.8534 | 1.47671 | 0.738356 | − | 0.674412i | \(-0.235603\pi\) | ||||
0.738356 | + | 0.674412i | \(0.235603\pi\) | |||||||
\(164\) | −0.0206760 | −0.00161452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9679 | 0.851274 | ||||||||
\(167\) | 15.5834 | 1.20588 | 0.602939 | − | 0.797787i | \(-0.293996\pi\) | ||||
0.602939 | + | 0.797787i | \(0.293996\pi\) | |||||||
\(168\) | −0.365778 | −0.0282204 | ||||||||
\(169\) | −8.15785 | −0.627527 | ||||||||
\(170\) | −6.26330 | −0.480374 | ||||||||
\(171\) | 17.2250 | 1.31723 | ||||||||
\(172\) | 3.71582 | 0.283329 | ||||||||
\(173\) | 6.79145 | 0.516344 | 0.258172 | − | 0.966099i | \(-0.416880\pi\) | ||||
0.258172 | + | 0.966099i | \(0.416880\pi\) | |||||||
\(174\) | −0.697795 | −0.0528997 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.65559 | −0.349935 | ||||||||
\(178\) | −9.56469 | −0.716904 | ||||||||
\(179\) | −23.7293 | −1.77361 | −0.886807 | − | 0.462139i | \(-0.847082\pi\) | ||||
−0.886807 | + | 0.462139i | \(0.847082\pi\) | |||||||
\(180\) | 2.86621 | 0.213634 | ||||||||
\(181\) | 14.5332 | 1.08024 | 0.540122 | − | 0.841587i | \(-0.318378\pi\) | ||||
0.540122 | + | 0.841587i | \(0.318378\pi\) | |||||||
\(182\) | 2.20049 | 0.163111 | ||||||||
\(183\) | 2.20203 | 0.162779 | ||||||||
\(184\) | 0.452126 | 0.0333312 | ||||||||
\(185\) | −3.54127 | −0.260359 | ||||||||
\(186\) | −2.21338 | −0.162293 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.63329 | 0.629647 | ||||||||
\(189\) | 2.14573 | 0.156079 | ||||||||
\(190\) | 6.00967 | 0.435987 | ||||||||
\(191\) | −6.74284 | −0.487895 | −0.243947 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243947 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(192\) | 0.365778 | 0.0263977 | ||||||||
\(193\) | −10.4918 | −0.755220 | −0.377610 | − | 0.925965i | \(-0.623254\pi\) | ||||
−0.377610 | + | 0.925965i | \(0.623254\pi\) | |||||||
\(194\) | −4.22569 | −0.303387 | ||||||||
\(195\) | 0.804890 | 0.0576394 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −8.40324 | −0.598706 | −0.299353 | − | 0.954142i | \(-0.596771\pi\) | ||||
−0.299353 | + | 0.954142i | \(0.596771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.41088 | 0.383567 | 0.191783 | − | 0.981437i | \(-0.438573\pi\) | ||||
0.191783 | + | 0.981437i | \(0.438573\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 2.99744 | 0.211423 | ||||||||
\(202\) | −10.0515 | −0.707220 | ||||||||
\(203\) | 1.90770 | 0.133894 | ||||||||
\(204\) | 2.29098 | 0.160401 | ||||||||
\(205\) | 0.0206760 | 0.00144407 | ||||||||
\(206\) | 14.6726 | 1.02229 | ||||||||
\(207\) | −1.29589 | −0.0900704 | ||||||||
\(208\) | −2.20049 | −0.152576 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.365778 | 0.0252411 | ||||||||
\(211\) | 8.53391 | 0.587499 | 0.293749 | − | 0.955882i | \(-0.405097\pi\) | ||||
0.293749 | + | 0.955882i | \(0.405097\pi\) | |||||||
\(212\) | 8.03517 | 0.551858 | ||||||||
\(213\) | 5.76486 | 0.395001 | ||||||||
\(214\) | −1.85065 | −0.126508 | ||||||||
\(215\) | −3.71582 | −0.253417 | ||||||||
\(216\) | −2.14573 | −0.145998 | ||||||||
\(217\) | 6.05116 | 0.410780 | ||||||||
\(218\) | −16.3800 | −1.10939 | ||||||||
\(219\) | 4.67618 | 0.315987 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7823 | −0.927100 | ||||||||
\(222\) | 1.29532 | 0.0869360 | ||||||||
\(223\) | −19.6449 | −1.31552 | −0.657760 | − | 0.753228i | \(-0.728496\pi\) | ||||
−0.657760 | + | 0.753228i | \(0.728496\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.86621 | −0.191080 | ||||||||
\(226\) | −10.7686 | −0.716318 | ||||||||
\(227\) | 2.37742 | 0.157795 | 0.0788975 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788975 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(228\) | −2.19820 | −0.145580 | ||||||||
\(229\) | 9.73039 | 0.643002 | 0.321501 | − | 0.946909i | \(-0.395813\pi\) | ||||
0.321501 | + | 0.946909i | \(0.395813\pi\) | |||||||
\(230\) | −0.452126 | −0.0298123 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.90770 | −0.125247 | ||||||||
\(233\) | 18.4540 | 1.20896 | 0.604482 | − | 0.796619i | \(-0.293380\pi\) | ||||
0.604482 | + | 0.796619i | \(0.293380\pi\) | |||||||
\(234\) | 6.30706 | 0.412305 | ||||||||
\(235\) | −8.63329 | −0.563173 | ||||||||
\(236\) | −12.7279 | −0.828516 | ||||||||
\(237\) | 3.93010 | 0.255287 | ||||||||
\(238\) | −6.26330 | −0.405990 | ||||||||
\(239\) | 17.6068 | 1.13889 | 0.569445 | − | 0.822030i | \(-0.307158\pi\) | ||||
0.569445 | + | 0.822030i | \(0.307158\pi\) | |||||||
\(240\) | −0.365778 | −0.0236109 | ||||||||
\(241\) | 17.4835 | 1.12621 | 0.563105 | − | 0.826385i | \(-0.309607\pi\) | ||||
0.563105 | + | 0.826385i | \(0.309607\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.29528 | 0.596293 | ||||||||
\(244\) | 6.02013 | 0.385399 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −0.00756282 | −0.000482188 0 | ||||||||
\(247\) | 13.2242 | 0.841436 | ||||||||
\(248\) | −6.05116 | −0.384249 | ||||||||
\(249\) | 4.01182 | 0.254239 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.9585 | −1.44913 | −0.724563 | − | 0.689209i | \(-0.757958\pi\) | ||||
−0.724563 | + | 0.689209i | \(0.757958\pi\) | |||||||
\(252\) | 2.86621 | 0.180554 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.44315 | 0.278788 | ||||||||
\(255\) | −2.29098 | −0.143467 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.2609 | 0.889569 | 0.444784 | − | 0.895638i | \(-0.353280\pi\) | ||||
0.444784 | + | 0.895638i | \(0.353280\pi\) | |||||||
\(258\) | 1.35916 | 0.0846179 | ||||||||
\(259\) | −3.54127 | −0.220044 | ||||||||
\(260\) | 2.20049 | 0.136469 | ||||||||
\(261\) | 5.46787 | 0.338452 | ||||||||
\(262\) | −2.54949 | −0.157508 | ||||||||
\(263\) | 9.29262 | 0.573007 | 0.286504 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286504 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.03517 | −0.493597 | ||||||||
\(266\) | 6.00967 | 0.368476 | ||||||||
\(267\) | −3.49855 | −0.214108 | ||||||||
\(268\) | 8.19469 | 0.500570 | ||||||||
\(269\) | 1.17894 | 0.0718811 | 0.0359405 | − | 0.999354i | \(-0.488557\pi\) | ||||
0.0359405 | + | 0.999354i | \(0.488557\pi\) | |||||||
\(270\) | 2.14573 | 0.130585 | ||||||||
\(271\) | −8.12467 | −0.493539 | −0.246769 | − | 0.969074i | \(-0.579369\pi\) | ||||
−0.246769 | + | 0.969074i | \(0.579369\pi\) | |||||||
\(272\) | 6.26330 | 0.379769 | ||||||||
\(273\) | 0.804890 | 0.0487142 | ||||||||
\(274\) | −15.1630 | −0.916028 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.165378 | 0.00995457 | ||||||||
\(277\) | 8.23042 | 0.494518 | 0.247259 | − | 0.968949i | \(-0.420470\pi\) | ||||
0.247259 | + | 0.968949i | \(0.420470\pi\) | |||||||
\(278\) | 4.56534 | 0.273811 | ||||||||
\(279\) | 17.3439 | 1.03835 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 21.0726 | 1.25709 | 0.628543 | − | 0.777775i | \(-0.283652\pi\) | ||||
0.628543 | + | 0.777775i | \(0.283652\pi\) | |||||||
\(282\) | 3.15786 | 0.188048 | ||||||||
\(283\) | 0.468381 | 0.0278423 | 0.0139212 | − | 0.999903i | \(-0.495569\pi\) | ||||
0.0139212 | + | 0.999903i | \(0.495569\pi\) | |||||||
\(284\) | 15.7605 | 0.935216 | ||||||||
\(285\) | 2.19820 | 0.130210 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0206760 | 0.00122047 | ||||||||
\(288\) | −2.86621 | −0.168893 | ||||||||
\(289\) | 22.2290 | 1.30759 | ||||||||
\(290\) | 1.90770 | 0.112024 | ||||||||
\(291\) | −1.54566 | −0.0906083 | ||||||||
\(292\) | 12.7842 | 0.748139 | ||||||||
\(293\) | −6.71911 | −0.392535 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(294\) | 0.365778 | 0.0213326 | ||||||||
\(295\) | 12.7279 | 0.741047 | ||||||||
\(296\) | 3.54127 | 0.205832 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.9113 | 0.805862 | ||||||||
\(299\) | −0.994899 | −0.0575365 | ||||||||
\(300\) | 0.365778 | 0.0211182 | ||||||||
\(301\) | −3.71582 | −0.214176 | ||||||||
\(302\) | 3.78025 | 0.217529 | ||||||||
\(303\) | −3.67661 | −0.211216 | ||||||||
\(304\) | −6.00967 | −0.344678 | ||||||||
\(305\) | −6.02013 | −0.344712 | ||||||||
\(306\) | −17.9519 | −1.02624 | ||||||||
\(307\) | 22.7190 | 1.29664 | 0.648321 | − | 0.761367i | \(-0.275471\pi\) | ||||
0.648321 | + | 0.761367i | \(0.275471\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.36691 | 0.305313 | ||||||||
\(310\) | 6.05116 | 0.343683 | ||||||||
\(311\) | −21.2105 | −1.20274 | −0.601368 | − | 0.798972i | \(-0.705377\pi\) | ||||
−0.601368 | + | 0.798972i | \(0.705377\pi\) | |||||||
\(312\) | −0.804890 | −0.0455679 | ||||||||
\(313\) | −3.70075 | −0.209179 | −0.104589 | − | 0.994515i | \(-0.533353\pi\) | ||||
−0.104589 | + | 0.994515i | \(0.533353\pi\) | |||||||
\(314\) | 12.6782 | 0.715474 | ||||||||
\(315\) | −2.86621 | −0.161492 | ||||||||
\(316\) | 10.7445 | 0.604425 | ||||||||
\(317\) | −7.71067 | −0.433074 | −0.216537 | − | 0.976274i | \(-0.569476\pi\) | ||||
−0.216537 | + | 0.976274i | \(0.569476\pi\) | |||||||
\(318\) | 2.93909 | 0.164816 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.676926 | −0.0377824 | ||||||||
\(322\) | −0.452126 | −0.0251960 | ||||||||
\(323\) | −37.6404 | −2.09437 | ||||||||
\(324\) | 7.81376 | 0.434098 | ||||||||
\(325\) | −2.20049 | −0.122061 | ||||||||
\(326\) | 18.8534 | 1.04419 | ||||||||
\(327\) | −5.99143 | −0.331327 | ||||||||
\(328\) | −0.0206760 | −0.00114164 | ||||||||
\(329\) | −8.63329 | −0.475968 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.2493 | 1.77258 | 0.886291 | − | 0.463128i | \(-0.153273\pi\) | ||||
0.886291 | + | 0.463128i | \(0.153273\pi\) | |||||||
\(332\) | 10.9679 | 0.601942 | ||||||||
\(333\) | −10.1500 | −0.556217 | ||||||||
\(334\) | 15.5834 | 0.852684 | ||||||||
\(335\) | −8.19469 | −0.447724 | ||||||||
\(336\) | −0.365778 | −0.0199548 | ||||||||
\(337\) | 33.2152 | 1.80935 | 0.904673 | − | 0.426106i | \(-0.140115\pi\) | ||||
0.904673 | + | 0.426106i | \(0.140115\pi\) | |||||||
\(338\) | −8.15785 | −0.443728 | ||||||||
\(339\) | −3.93892 | −0.213933 | ||||||||
\(340\) | −6.26330 | −0.339675 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 17.2250 | 0.931419 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.71582 | 0.200344 | ||||||||
\(345\) | −0.165378 | −0.00890364 | ||||||||
\(346\) | 6.79145 | 0.365111 | ||||||||
\(347\) | −3.37780 | −0.181330 | −0.0906649 | − | 0.995881i | \(-0.528899\pi\) | ||||
−0.0906649 | + | 0.995881i | \(0.528899\pi\) | |||||||
\(348\) | −0.697795 | −0.0374057 | ||||||||
\(349\) | −31.4117 | −1.68143 | −0.840716 | − | 0.541477i | \(-0.817865\pi\) | ||||
−0.840716 | + | 0.541477i | \(0.817865\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 4.72165 | 0.252023 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.9041 | 1.85776 | 0.928879 | − | 0.370383i | \(-0.120774\pi\) | ||||
0.928879 | + | 0.370383i | \(0.120774\pi\) | |||||||
\(354\) | −4.65559 | −0.247442 | ||||||||
\(355\) | −15.7605 | −0.836483 | ||||||||
\(356\) | −9.56469 | −0.506927 | ||||||||
\(357\) | −2.29098 | −0.121251 | ||||||||
\(358\) | −23.7293 | −1.25414 | ||||||||
\(359\) | 32.4765 | 1.71404 | 0.857022 | − | 0.515280i | \(-0.172312\pi\) | ||||
0.857022 | + | 0.515280i | \(0.172312\pi\) | |||||||
\(360\) | 2.86621 | 0.151062 | ||||||||
\(361\) | 17.1161 | 0.900849 | ||||||||
\(362\) | 14.5332 | 0.763848 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.20049 | 0.115337 | ||||||||
\(365\) | −12.7842 | −0.669156 | ||||||||
\(366\) | 2.20203 | 0.115102 | ||||||||
\(367\) | −28.7289 | −1.49963 | −0.749817 | − | 0.661645i | \(-0.769859\pi\) | ||||
−0.749817 | + | 0.661645i | \(0.769859\pi\) | |||||||
\(368\) | 0.452126 | 0.0235687 | ||||||||
\(369\) | 0.0592617 | 0.00308504 | ||||||||
\(370\) | −3.54127 | −0.184102 | ||||||||
\(371\) | −8.03517 | −0.417165 | ||||||||
\(372\) | −2.21338 | −0.114758 | ||||||||
\(373\) | −36.4802 | −1.88887 | −0.944437 | − | 0.328691i | \(-0.893392\pi\) | ||||
−0.944437 | + | 0.328691i | \(0.893392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.365778 | −0.0188887 | ||||||||
\(376\) | 8.63329 | 0.445228 | ||||||||
\(377\) | 4.19788 | 0.216202 | ||||||||
\(378\) | 2.14573 | 0.110364 | ||||||||
\(379\) | 0.299074 | 0.0153624 | 0.00768120 | − | 0.999970i | \(-0.497555\pi\) | ||||
0.00768120 | + | 0.999970i | \(0.497555\pi\) | |||||||
\(380\) | 6.00967 | 0.308290 | ||||||||
\(381\) | 1.62521 | 0.0832619 | ||||||||
\(382\) | −6.74284 | −0.344994 | ||||||||
\(383\) | −15.7020 | −0.802337 | −0.401168 | − | 0.916004i | \(-0.631396\pi\) | ||||
−0.401168 | + | 0.916004i | \(0.631396\pi\) | |||||||
\(384\) | 0.365778 | 0.0186660 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.4918 | −0.534021 | ||||||||
\(387\) | −10.6503 | −0.541386 | ||||||||
\(388\) | −4.22569 | −0.214527 | ||||||||
\(389\) | −9.66386 | −0.489977 | −0.244989 | − | 0.969526i | \(-0.578784\pi\) | ||||
−0.244989 | + | 0.969526i | \(0.578784\pi\) | |||||||
\(390\) | 0.804890 | 0.0407572 | ||||||||
\(391\) | 2.83180 | 0.143211 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −0.932548 | −0.0470408 | ||||||||
\(394\) | −8.40324 | −0.423349 | ||||||||
\(395\) | −10.7445 | −0.540615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7947 | 0.893090 | 0.446545 | − | 0.894761i | \(-0.352654\pi\) | ||||
0.446545 | + | 0.894761i | \(0.352654\pi\) | |||||||
\(398\) | 5.41088 | 0.271223 | ||||||||
\(399\) | 2.19820 | 0.110048 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 37.5083 | 1.87308 | 0.936538 | − | 0.350566i | \(-0.114011\pi\) | ||||
0.936538 | + | 0.350566i | \(0.114011\pi\) | |||||||
\(402\) | 2.99744 | 0.149498 | ||||||||
\(403\) | 13.3155 | 0.663293 | ||||||||
\(404\) | −10.0515 | −0.500080 | ||||||||
\(405\) | −7.81376 | −0.388269 | ||||||||
\(406\) | 1.90770 | 0.0946776 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.29098 | 0.113420 | ||||||||
\(409\) | 21.9950 | 1.08758 | 0.543791 | − | 0.839221i | \(-0.316988\pi\) | ||||
0.543791 | + | 0.839221i | \(0.316988\pi\) | |||||||
\(410\) | 0.0206760 | 0.00102112 | ||||||||
\(411\) | −5.54628 | −0.273578 | ||||||||
\(412\) | 14.6726 | 0.722867 | ||||||||
\(413\) | 12.7279 | 0.626299 | ||||||||
\(414\) | −1.29589 | −0.0636894 | ||||||||
\(415\) | −10.9679 | −0.538393 | ||||||||
\(416\) | −2.20049 | −0.107888 | ||||||||
\(417\) | 1.66990 | 0.0817754 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.6014 | −0.713327 | −0.356664 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356664 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(420\) | 0.365778 | 0.0178481 | ||||||||
\(421\) | −36.1140 | −1.76009 | −0.880044 | − | 0.474893i | \(-0.842487\pi\) | ||||
−0.880044 | + | 0.474893i | \(0.842487\pi\) | |||||||
\(422\) | 8.53391 | 0.415424 | ||||||||
\(423\) | −24.7448 | −1.20313 | ||||||||
\(424\) | 8.03517 | 0.390223 | ||||||||
\(425\) | 6.26330 | 0.303815 | ||||||||
\(426\) | 5.76486 | 0.279308 | ||||||||
\(427\) | −6.02013 | −0.291334 | ||||||||
\(428\) | −1.85065 | −0.0894545 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.71582 | −0.179193 | ||||||||
\(431\) | 1.92226 | 0.0925922 | 0.0462961 | − | 0.998928i | \(-0.485258\pi\) | ||||
0.0462961 | + | 0.998928i | \(0.485258\pi\) | |||||||
\(432\) | −2.14573 | −0.103236 | ||||||||
\(433\) | −8.11232 | −0.389853 | −0.194927 | − | 0.980818i | \(-0.562447\pi\) | ||||
−0.194927 | + | 0.980818i | \(0.562447\pi\) | |||||||
\(434\) | 6.05116 | 0.290465 | ||||||||
\(435\) | 0.697795 | 0.0334567 | ||||||||
\(436\) | −16.3800 | −0.784459 | ||||||||
\(437\) | −2.71713 | −0.129978 | ||||||||
\(438\) | 4.67618 | 0.223437 | ||||||||
\(439\) | 3.97670 | 0.189797 | 0.0948987 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0948987 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86621 | −0.136486 | ||||||||
\(442\) | −13.7823 | −0.655559 | ||||||||
\(443\) | −7.61310 | −0.361709 | −0.180855 | − | 0.983510i | \(-0.557886\pi\) | ||||
−0.180855 | + | 0.983510i | \(0.557886\pi\) | |||||||
\(444\) | 1.29532 | 0.0614730 | ||||||||
\(445\) | 9.56469 | 0.453410 | ||||||||
\(446\) | −19.6449 | −0.930213 | ||||||||
\(447\) | 5.08846 | 0.240676 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 3.27630 | 0.154618 | 0.0773090 | − | 0.997007i | \(-0.475367\pi\) | ||||
0.0773090 | + | 0.997007i | \(0.475367\pi\) | |||||||
\(450\) | −2.86621 | −0.135114 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −10.7686 | −0.506514 | ||||||||
\(453\) | 1.38273 | 0.0649664 | ||||||||
\(454\) | 2.37742 | 0.111578 | ||||||||
\(455\) | −2.20049 | −0.103161 | ||||||||
\(456\) | −2.19820 | −0.102940 | ||||||||
\(457\) | 8.41968 | 0.393856 | 0.196928 | − | 0.980418i | \(-0.436903\pi\) | ||||
0.196928 | + | 0.980418i | \(0.436903\pi\) | |||||||
\(458\) | 9.73039 | 0.454671 | ||||||||
\(459\) | −13.4393 | −0.627295 | ||||||||
\(460\) | −0.452126 | −0.0210805 | ||||||||
\(461\) | −22.7631 | −1.06018 | −0.530091 | − | 0.847941i | \(-0.677842\pi\) | ||||
−0.530091 | + | 0.847941i | \(0.677842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6401 | 1.14512 | 0.572561 | − | 0.819862i | \(-0.305950\pi\) | ||||
0.572561 | + | 0.819862i | \(0.305950\pi\) | |||||||
\(464\) | −1.90770 | −0.0885628 | ||||||||
\(465\) | 2.21338 | 0.102643 | ||||||||
\(466\) | 18.4540 | 0.854867 | ||||||||
\(467\) | 4.38924 | 0.203110 | 0.101555 | − | 0.994830i | \(-0.467618\pi\) | ||||
0.101555 | + | 0.994830i | \(0.467618\pi\) | |||||||
\(468\) | 6.30706 | 0.291544 | ||||||||
\(469\) | −8.19469 | −0.378396 | ||||||||
\(470\) | −8.63329 | −0.398224 | ||||||||
\(471\) | 4.63741 | 0.213681 | ||||||||
\(472\) | −12.7279 | −0.585849 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.93010 | 0.180516 | ||||||||
\(475\) | −6.00967 | −0.275743 | ||||||||
\(476\) | −6.26330 | −0.287078 | ||||||||
\(477\) | −23.0305 | −1.05449 | ||||||||
\(478\) | 17.6068 | 0.805316 | ||||||||
\(479\) | −10.1427 | −0.463433 | −0.231716 | − | 0.972783i | \(-0.574434\pi\) | ||||
−0.231716 | + | 0.972783i | \(0.574434\pi\) | |||||||
\(480\) | −0.365778 | −0.0166954 | ||||||||
\(481\) | −7.79252 | −0.355308 | ||||||||
\(482\) | 17.4835 | 0.796351 | ||||||||
\(483\) | −0.165378 | −0.00752495 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.22569 | 0.191879 | ||||||||
\(486\) | 9.29528 | 0.421643 | ||||||||
\(487\) | −22.6195 | −1.02499 | −0.512494 | − | 0.858691i | \(-0.671278\pi\) | ||||
−0.512494 | + | 0.858691i | \(0.671278\pi\) | |||||||
\(488\) | 6.02013 | 0.272518 | ||||||||
\(489\) | 6.89615 | 0.311855 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 2.55144 | 0.115145 | 0.0575724 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575724 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(492\) | −0.00756282 | −0.000340958 0 | ||||||||
\(493\) | −11.9485 | −0.538134 | ||||||||
\(494\) | 13.2242 | 0.594985 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.05116 | −0.271705 | ||||||||
\(497\) | −15.7605 | −0.706957 | ||||||||
\(498\) | 4.01182 | 0.179774 | ||||||||
\(499\) | 4.35625 | 0.195012 | 0.0975062 | − | 0.995235i | \(-0.468913\pi\) | ||||
0.0975062 | + | 0.995235i | \(0.468913\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.70005 | 0.254660 | ||||||||
\(502\) | −22.9585 | −1.02469 | ||||||||
\(503\) | 23.2545 | 1.03687 | 0.518433 | − | 0.855118i | \(-0.326515\pi\) | ||||
0.518433 | + | 0.855118i | \(0.326515\pi\) | |||||||
\(504\) | 2.86621 | 0.127671 | ||||||||
\(505\) | 10.0515 | 0.447285 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.98396 | −0.132522 | ||||||||
\(508\) | 4.44315 | 0.197133 | ||||||||
\(509\) | −2.94487 | −0.130529 | −0.0652646 | − | 0.997868i | \(-0.520789\pi\) | ||||
−0.0652646 | + | 0.997868i | \(0.520789\pi\) | |||||||
\(510\) | −2.29098 | −0.101446 | ||||||||
\(511\) | −12.7842 | −0.565540 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.8951 | 0.569333 | ||||||||
\(514\) | 14.2609 | 0.629020 | ||||||||
\(515\) | −14.6726 | −0.646552 | ||||||||
\(516\) | 1.35916 | 0.0598339 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.54127 | −0.155594 | ||||||||
\(519\) | 2.48416 | 0.109043 | ||||||||
\(520\) | 2.20049 | 0.0964978 | ||||||||
\(521\) | −35.1983 | −1.54207 | −0.771034 | − | 0.636794i | \(-0.780260\pi\) | ||||
−0.771034 | + | 0.636794i | \(0.780260\pi\) | |||||||
\(522\) | 5.46787 | 0.239322 | ||||||||
\(523\) | 4.34730 | 0.190094 | 0.0950470 | − | 0.995473i | \(-0.469700\pi\) | ||||
0.0950470 | + | 0.995473i | \(0.469700\pi\) | |||||||
\(524\) | −2.54949 | −0.111375 | ||||||||
\(525\) | −0.365778 | −0.0159639 | ||||||||
\(526\) | 9.29262 | 0.405177 | ||||||||
\(527\) | −37.9003 | −1.65096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7956 | −0.991112 | ||||||||
\(530\) | −8.03517 | −0.349026 | ||||||||
\(531\) | 36.4808 | 1.58313 | ||||||||
\(532\) | 6.00967 | 0.260552 | ||||||||
\(533\) | 0.0454973 | 0.00197071 | ||||||||
\(534\) | −3.49855 | −0.151397 | ||||||||
\(535\) | 1.85065 | 0.0800105 | ||||||||
\(536\) | 8.19469 | 0.353957 | ||||||||
\(537\) | −8.67967 | −0.374555 | ||||||||
\(538\) | 1.17894 | 0.0508276 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.14573 | 0.0923374 | ||||||||
\(541\) | 19.7931 | 0.850973 | 0.425486 | − | 0.904965i | \(-0.360103\pi\) | ||||
0.425486 | + | 0.904965i | \(0.360103\pi\) | |||||||
\(542\) | −8.12467 | −0.348985 | ||||||||
\(543\) | 5.31592 | 0.228128 | ||||||||
\(544\) | 6.26330 | 0.268537 | ||||||||
\(545\) | 16.3800 | 0.701641 | ||||||||
\(546\) | 0.804890 | 0.0344461 | ||||||||
\(547\) | 12.4719 | 0.533260 | 0.266630 | − | 0.963799i | \(-0.414090\pi\) | ||||
0.266630 | + | 0.963799i | \(0.414090\pi\) | |||||||
\(548\) | −15.1630 | −0.647730 | ||||||||
\(549\) | −17.2549 | −0.736423 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4647 | 0.488411 | ||||||||
\(552\) | 0.165378 | 0.00703894 | ||||||||
\(553\) | −10.7445 | −0.456903 | ||||||||
\(554\) | 8.23042 | 0.349677 | ||||||||
\(555\) | −1.29532 | −0.0549831 | ||||||||
\(556\) | 4.56534 | 0.193614 | ||||||||
\(557\) | 30.3225 | 1.28480 | 0.642402 | − | 0.766368i | \(-0.277938\pi\) | ||||
0.642402 | + | 0.766368i | \(0.277938\pi\) | |||||||
\(558\) | 17.3439 | 0.734225 | ||||||||
\(559\) | −8.17662 | −0.345834 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.0726 | 0.888894 | ||||||||
\(563\) | −19.1404 | −0.806671 | −0.403336 | − | 0.915052i | \(-0.632149\pi\) | ||||
−0.403336 | + | 0.915052i | \(0.632149\pi\) | |||||||
\(564\) | 3.15786 | 0.132970 | ||||||||
\(565\) | 10.7686 | 0.453040 | ||||||||
\(566\) | 0.468381 | 0.0196875 | ||||||||
\(567\) | −7.81376 | −0.328147 | ||||||||
\(568\) | 15.7605 | 0.661298 | ||||||||
\(569\) | 9.22473 | 0.386721 | 0.193360 | − | 0.981128i | \(-0.438061\pi\) | ||||
0.193360 | + | 0.981128i | \(0.438061\pi\) | |||||||
\(570\) | 2.19820 | 0.0920726 | ||||||||
\(571\) | 26.6182 | 1.11394 | 0.556968 | − | 0.830534i | \(-0.311965\pi\) | ||||
0.556968 | + | 0.830534i | \(0.311965\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.46638 | −0.103035 | ||||||||
\(574\) | 0.0206760 | 0.000863000 0 | ||||||||
\(575\) | 0.452126 | 0.0188550 | ||||||||
\(576\) | −2.86621 | −0.119425 | ||||||||
\(577\) | −8.14831 | −0.339219 | −0.169609 | − | 0.985511i | \(-0.554251\pi\) | ||||
−0.169609 | + | 0.985511i | \(0.554251\pi\) | |||||||
\(578\) | 22.2290 | 0.924604 | ||||||||
\(579\) | −3.83768 | −0.159489 | ||||||||
\(580\) | 1.90770 | 0.0792130 | ||||||||
\(581\) | −10.9679 | −0.455025 | ||||||||
\(582\) | −1.54566 | −0.0640698 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.7842 | 0.529014 | ||||||||
\(585\) | −6.30706 | −0.260765 | ||||||||
\(586\) | −6.71911 | −0.277564 | ||||||||
\(587\) | −18.1817 | −0.750440 | −0.375220 | − | 0.926936i | \(-0.622433\pi\) | ||||
−0.375220 | + | 0.926936i | \(0.622433\pi\) | |||||||
\(588\) | 0.365778 | 0.0150844 | ||||||||
\(589\) | 36.3655 | 1.49841 | ||||||||
\(590\) | 12.7279 | 0.524000 | ||||||||
\(591\) | −3.07372 | −0.126436 | ||||||||
\(592\) | 3.54127 | 0.145545 | ||||||||
\(593\) | −14.6040 | −0.599715 | −0.299857 | − | 0.953984i | \(-0.596939\pi\) | ||||
−0.299857 | + | 0.953984i | \(0.596939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.26330 | 0.256770 | ||||||||
\(596\) | 13.9113 | 0.569830 | ||||||||
\(597\) | 1.97918 | 0.0810024 | ||||||||
\(598\) | −0.994899 | −0.0406844 | ||||||||
\(599\) | −15.9571 | −0.651990 | −0.325995 | − | 0.945371i | \(-0.605699\pi\) | ||||
−0.325995 | + | 0.945371i | \(0.605699\pi\) | |||||||
\(600\) | 0.365778 | 0.0149328 | ||||||||
\(601\) | 22.0047 | 0.897591 | 0.448796 | − | 0.893634i | \(-0.351853\pi\) | ||||
0.448796 | + | 0.893634i | \(0.351853\pi\) | |||||||
\(602\) | −3.71582 | −0.151446 | ||||||||
\(603\) | −23.4877 | −0.956492 | ||||||||
\(604\) | 3.78025 | 0.153816 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.67661 | −0.149352 | ||||||||
\(607\) | −17.4148 | −0.706846 | −0.353423 | − | 0.935464i | \(-0.614982\pi\) | ||||
−0.353423 | + | 0.935464i | \(0.614982\pi\) | |||||||
\(608\) | −6.00967 | −0.243724 | ||||||||
\(609\) | 0.697795 | 0.0282761 | ||||||||
\(610\) | −6.02013 | −0.243748 | ||||||||
\(611\) | −18.9975 | −0.768555 | ||||||||
\(612\) | −17.9519 | −0.725664 | ||||||||
\(613\) | −18.4109 | −0.743611 | −0.371805 | − | 0.928311i | \(-0.621261\pi\) | ||||
−0.371805 | + | 0.928311i | \(0.621261\pi\) | |||||||
\(614\) | 22.7190 | 0.916864 | ||||||||
\(615\) | 0.00756282 | 0.000304963 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.54431 | −0.223206 | −0.111603 | − | 0.993753i | \(-0.535598\pi\) | ||||
−0.111603 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(618\) | 5.36691 | 0.215889 | ||||||||
\(619\) | −27.3331 | −1.09861 | −0.549305 | − | 0.835622i | \(-0.685108\pi\) | ||||
−0.549305 | + | 0.835622i | \(0.685108\pi\) | |||||||
\(620\) | 6.05116 | 0.243021 | ||||||||
\(621\) | −0.970140 | −0.0389304 | ||||||||
\(622\) | −21.2105 | −0.850463 | ||||||||
\(623\) | 9.56469 | 0.383201 | ||||||||
\(624\) | −0.804890 | −0.0322214 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.70075 | −0.147912 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.6782 | 0.505916 | ||||||||
\(629\) | 22.1800 | 0.884376 | ||||||||
\(630\) | −2.86621 | −0.114192 | ||||||||
\(631\) | 33.1472 | 1.31957 | 0.659785 | − | 0.751454i | \(-0.270647\pi\) | ||||
0.659785 | + | 0.751454i | \(0.270647\pi\) | |||||||
\(632\) | 10.7445 | 0.427393 | ||||||||
\(633\) | 3.12152 | 0.124069 | ||||||||
\(634\) | −7.71067 | −0.306230 | ||||||||
\(635\) | −4.44315 | −0.176321 | ||||||||
\(636\) | 2.93909 | 0.116542 | ||||||||
\(637\) | −2.20049 | −0.0871865 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.1730 | −1.78702 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 1.55259 | 0.0613236 | 0.0306618 | − | 0.999530i | \(-0.490239\pi\) | ||||
0.0306618 | + | 0.999530i | \(0.490239\pi\) | |||||||
\(642\) | −0.676926 | −0.0267162 | ||||||||
\(643\) | 7.60419 | 0.299880 | 0.149940 | − | 0.988695i | \(-0.452092\pi\) | ||||
0.149940 | + | 0.988695i | \(0.452092\pi\) | |||||||
\(644\) | −0.452126 | −0.0178163 | ||||||||
\(645\) | −1.35916 | −0.0535171 | ||||||||
\(646\) | −37.6404 | −1.48094 | ||||||||
\(647\) | 8.45292 | 0.332319 | 0.166159 | − | 0.986099i | \(-0.446863\pi\) | ||||
0.166159 | + | 0.986099i | \(0.446863\pi\) | |||||||
\(648\) | 7.81376 | 0.306953 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.20049 | −0.0863103 | ||||||||
\(651\) | 2.21338 | 0.0867493 | ||||||||
\(652\) | 18.8534 | 0.738356 | ||||||||
\(653\) | 32.5646 | 1.27435 | 0.637175 | − | 0.770719i | \(-0.280103\pi\) | ||||
0.637175 | + | 0.770719i | \(0.280103\pi\) | |||||||
\(654\) | −5.99143 | −0.234284 | ||||||||
\(655\) | 2.54949 | 0.0996169 | ||||||||
\(656\) | −0.0206760 | −0.000807262 0 | ||||||||
\(657\) | −36.6422 | −1.42955 | ||||||||
\(658\) | −8.63329 | −0.336561 | ||||||||
\(659\) | 37.9922 | 1.47997 | 0.739983 | − | 0.672626i | \(-0.234834\pi\) | ||||
0.739983 | + | 0.672626i | \(0.234834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0403 | −0.584999 | −0.292499 | − | 0.956266i | \(-0.594487\pi\) | ||||
−0.292499 | + | 0.956266i | \(0.594487\pi\) | |||||||
\(662\) | 32.2493 | 1.25341 | ||||||||
\(663\) | −5.04127 | −0.195787 | ||||||||
\(664\) | 10.9679 | 0.425637 | ||||||||
\(665\) | −6.00967 | −0.233045 | ||||||||
\(666\) | −10.1500 | −0.393305 | ||||||||
\(667\) | −0.862522 | −0.0333970 | ||||||||
\(668\) | 15.5834 | 0.602939 | ||||||||
\(669\) | −7.18567 | −0.277814 | ||||||||
\(670\) | −8.19469 | −0.316588 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.365778 | −0.0141102 | ||||||||
\(673\) | −38.3805 | −1.47946 | −0.739729 | − | 0.672905i | \(-0.765046\pi\) | ||||
−0.739729 | + | 0.672905i | \(0.765046\pi\) | |||||||
\(674\) | 33.2152 | 1.27940 | ||||||||
\(675\) | −2.14573 | −0.0825891 | ||||||||
\(676\) | −8.15785 | −0.313763 | ||||||||
\(677\) | −30.8004 | −1.18375 | −0.591877 | − | 0.806028i | \(-0.701613\pi\) | ||||
−0.591877 | + | 0.806028i | \(0.701613\pi\) | |||||||
\(678\) | −3.93892 | −0.151274 | ||||||||
\(679\) | 4.22569 | 0.162167 | ||||||||
\(680\) | −6.26330 | −0.240187 | ||||||||
\(681\) | 0.869608 | 0.0333234 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.0974 | 1.76387 | 0.881935 | − | 0.471371i | \(-0.156241\pi\) | ||||
0.881935 | + | 0.471371i | \(0.156241\pi\) | |||||||
\(684\) | 17.2250 | 0.658613 | ||||||||
\(685\) | 15.1630 | 0.579347 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 3.55916 | 0.135790 | ||||||||
\(688\) | 3.71582 | 0.141664 | ||||||||
\(689\) | −17.6813 | −0.673604 | ||||||||
\(690\) | −0.165378 | −0.00629582 | ||||||||
\(691\) | −26.6683 | −1.01451 | −0.507255 | − | 0.861796i | \(-0.669340\pi\) | ||||
−0.507255 | + | 0.861796i | \(0.669340\pi\) | |||||||
\(692\) | 6.79145 | 0.258172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.37780 | −0.128220 | ||||||||
\(695\) | −4.56534 | −0.173173 | ||||||||
\(696\) | −0.697795 | −0.0264498 | ||||||||
\(697\) | −0.129500 | −0.00490517 | ||||||||
\(698\) | −31.4117 | −1.18895 | ||||||||
\(699\) | 6.75008 | 0.255311 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 15.2735 | 0.576872 | 0.288436 | − | 0.957499i | \(-0.406865\pi\) | ||||
0.288436 | + | 0.957499i | \(0.406865\pi\) | |||||||
\(702\) | 4.72165 | 0.178207 | ||||||||
\(703\) | −21.2818 | −0.802660 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.15786 | −0.118932 | ||||||||
\(706\) | 34.9041 | 1.31363 | ||||||||
\(707\) | 10.0515 | 0.378025 | ||||||||
\(708\) | −4.65559 | −0.174968 | ||||||||
\(709\) | −23.2892 | −0.874645 | −0.437323 | − | 0.899305i | \(-0.644073\pi\) | ||||
−0.437323 | + | 0.899305i | \(0.644073\pi\) | |||||||
\(710\) | −15.7605 | −0.591483 | ||||||||
\(711\) | −30.7960 | −1.15494 | ||||||||
\(712\) | −9.56469 | −0.358452 | ||||||||
\(713\) | −2.73589 | −0.102460 | ||||||||
\(714\) | −2.29098 | −0.0857377 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.7293 | −0.886807 | ||||||||
\(717\) | 6.44018 | 0.240513 | ||||||||
\(718\) | 32.4765 | 1.21201 | ||||||||
\(719\) | 6.64924 | 0.247975 | 0.123987 | − | 0.992284i | \(-0.460432\pi\) | ||||
0.123987 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(720\) | 2.86621 | 0.106817 | ||||||||
\(721\) | −14.6726 | −0.546436 | ||||||||
\(722\) | 17.1161 | 0.636996 | ||||||||
\(723\) | 6.39507 | 0.237835 | ||||||||
\(724\) | 14.5332 | 0.540122 | ||||||||
\(725\) | −1.90770 | −0.0708502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.8003 | −1.36485 | −0.682424 | − | 0.730956i | \(-0.739074\pi\) | ||||
−0.682424 | + | 0.730956i | \(0.739074\pi\) | |||||||
\(728\) | 2.20049 | 0.0815555 | ||||||||
\(729\) | −20.0413 | −0.742269 | ||||||||
\(730\) | −12.7842 | −0.473165 | ||||||||
\(731\) | 23.2733 | 0.860795 | ||||||||
\(732\) | 2.20203 | 0.0813893 | ||||||||
\(733\) | −6.60763 | −0.244058 | −0.122029 | − | 0.992527i | \(-0.538940\pi\) | ||||
−0.122029 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(734\) | −28.7289 | −1.06040 | ||||||||
\(735\) | −0.365778 | −0.0134919 | ||||||||
\(736\) | 0.452126 | 0.0166656 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0592617 | 0.00218145 | ||||||||
\(739\) | −14.1761 | −0.521476 | −0.260738 | − | 0.965410i | \(-0.583966\pi\) | ||||
−0.260738 | + | 0.965410i | \(0.583966\pi\) | |||||||
\(740\) | −3.54127 | −0.130180 | ||||||||
\(741\) | 4.83712 | 0.177696 | ||||||||
\(742\) | −8.03517 | −0.294980 | ||||||||
\(743\) | −21.8533 | −0.801719 | −0.400859 | − | 0.916140i | \(-0.631288\pi\) | ||||
−0.400859 | + | 0.916140i | \(0.631288\pi\) | |||||||
\(744\) | −2.21338 | −0.0811465 | ||||||||
\(745\) | −13.9113 | −0.509672 | ||||||||
\(746\) | −36.4802 | −1.33564 | ||||||||
\(747\) | −31.4363 | −1.15019 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.85065 | 0.0676213 | ||||||||
\(750\) | −0.365778 | −0.0133563 | ||||||||
\(751\) | −18.3253 | −0.668700 | −0.334350 | − | 0.942449i | \(-0.608517\pi\) | ||||
−0.334350 | + | 0.942449i | \(0.608517\pi\) | |||||||
\(752\) | 8.63329 | 0.314824 | ||||||||
\(753\) | −8.39770 | −0.306029 | ||||||||
\(754\) | 4.19788 | 0.152878 | ||||||||
\(755\) | −3.78025 | −0.137577 | ||||||||
\(756\) | 2.14573 | 0.0780394 | ||||||||
\(757\) | −11.6388 | −0.423020 | −0.211510 | − | 0.977376i | \(-0.567838\pi\) | ||||
−0.211510 | + | 0.977376i | \(0.567838\pi\) | |||||||
\(758\) | 0.299074 | 0.0108629 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00967 | 0.217994 | ||||||||
\(761\) | 25.4547 | 0.922731 | 0.461366 | − | 0.887210i | \(-0.347360\pi\) | ||||
0.461366 | + | 0.887210i | \(0.347360\pi\) | |||||||
\(762\) | 1.62521 | 0.0588750 | ||||||||
\(763\) | 16.3800 | 0.592995 | ||||||||
\(764\) | −6.74284 | −0.243947 | ||||||||
\(765\) | 17.9519 | 0.649053 | ||||||||
\(766\) | −15.7020 | −0.567338 | ||||||||
\(767\) | 28.0076 | 1.01130 | ||||||||
\(768\) | 0.365778 | 0.0131989 | ||||||||
\(769\) | 41.1644 | 1.48442 | 0.742212 | − | 0.670165i | \(-0.233777\pi\) | ||||
0.742212 | + | 0.670165i | \(0.233777\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.21631 | 0.187861 | ||||||||
\(772\) | −10.4918 | −0.377610 | ||||||||
\(773\) | 3.93221 | 0.141432 | 0.0707159 | − | 0.997496i | \(-0.477472\pi\) | ||||
0.0707159 | + | 0.997496i | \(0.477472\pi\) | |||||||
\(774\) | −10.6503 | −0.382817 | ||||||||
\(775\) | −6.05116 | −0.217364 | ||||||||
\(776\) | −4.22569 | −0.151693 | ||||||||
\(777\) | −1.29532 | −0.0464692 | ||||||||
\(778\) | −9.66386 | −0.346466 | ||||||||
\(779\) | 0.124256 | 0.00445193 | ||||||||
\(780\) | 0.804890 | 0.0288197 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.83180 | 0.101265 | ||||||||
\(783\) | 4.09341 | 0.146286 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −12.6782 | −0.452505 | ||||||||
\(786\) | −0.932548 | −0.0332629 | ||||||||
\(787\) | −34.2138 | −1.21959 | −0.609796 | − | 0.792558i | \(-0.708749\pi\) | ||||
−0.609796 | + | 0.792558i | \(0.708749\pi\) | |||||||
\(788\) | −8.40324 | −0.299353 | ||||||||
\(789\) | 3.39903 | 0.121009 | ||||||||
\(790\) | −10.7445 | −0.382272 | ||||||||
\(791\) | 10.7686 | 0.382888 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2472 | −0.470423 | ||||||||
\(794\) | 17.7947 | 0.631510 | ||||||||
\(795\) | −2.93909 | −0.104239 | ||||||||
\(796\) | 5.41088 | 0.191783 | ||||||||
\(797\) | 0.946359 | 0.0335217 | 0.0167609 | − | 0.999860i | \(-0.494665\pi\) | ||||
0.0167609 | + | 0.999860i | \(0.494665\pi\) | |||||||
\(798\) | 2.19820 | 0.0778156 | ||||||||
\(799\) | 54.0729 | 1.91296 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 27.4144 | 0.968639 | ||||||||
\(802\) | 37.5083 | 1.32446 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.99744 | 0.105711 | ||||||||
\(805\) | 0.452126 | 0.0159354 | ||||||||
\(806\) | 13.3155 | 0.469019 | ||||||||
\(807\) | 0.431229 | 0.0151800 | ||||||||
\(808\) | −10.0515 | −0.353610 | ||||||||
\(809\) | −12.0510 | −0.423692 | −0.211846 | − | 0.977303i | \(-0.567947\pi\) | ||||
−0.211846 | + | 0.977303i | \(0.567947\pi\) | |||||||
\(810\) | −7.81376 | −0.274548 | ||||||||
\(811\) | 31.6751 | 1.11226 | 0.556132 | − | 0.831094i | \(-0.312285\pi\) | ||||
0.556132 | + | 0.831094i | \(0.312285\pi\) | |||||||
\(812\) | 1.90770 | 0.0669472 | ||||||||
\(813\) | −2.97182 | −0.104226 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.8534 | −0.660405 | ||||||||
\(816\) | 2.29098 | 0.0802003 | ||||||||
\(817\) | −22.3309 | −0.781258 | ||||||||
\(818\) | 21.9950 | 0.769037 | ||||||||
\(819\) | −6.30706 | −0.220386 | ||||||||
\(820\) | 0.0206760 | 0.000722037 0 | ||||||||
\(821\) | 24.4294 | 0.852591 | 0.426296 | − | 0.904584i | \(-0.359818\pi\) | ||||
0.426296 | + | 0.904584i | \(0.359818\pi\) | |||||||
\(822\) | −5.54628 | −0.193449 | ||||||||
\(823\) | −28.4472 | −0.991607 | −0.495803 | − | 0.868435i | \(-0.665126\pi\) | ||||
−0.495803 | + | 0.868435i | \(0.665126\pi\) | |||||||
\(824\) | 14.6726 | 0.511144 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.7279 | 0.442860 | ||||||||
\(827\) | 43.6508 | 1.51789 | 0.758943 | − | 0.651157i | \(-0.225716\pi\) | ||||
0.758943 | + | 0.651157i | \(0.225716\pi\) | |||||||
\(828\) | −1.29589 | −0.0450352 | ||||||||
\(829\) | 0.554570 | 0.0192610 | 0.00963050 | − | 0.999954i | \(-0.496934\pi\) | ||||
0.00963050 | + | 0.999954i | \(0.496934\pi\) | |||||||
\(830\) | −10.9679 | −0.380701 | ||||||||
\(831\) | 3.01051 | 0.104433 | ||||||||
\(832\) | −2.20049 | −0.0762882 | ||||||||
\(833\) | 6.26330 | 0.217011 | ||||||||
\(834\) | 1.66990 | 0.0578239 | ||||||||
\(835\) | −15.5834 | −0.539285 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.9842 | 0.448798 | ||||||||
\(838\) | −14.6014 | −0.504399 | ||||||||
\(839\) | −2.69760 | −0.0931315 | −0.0465658 | − | 0.998915i | \(-0.514828\pi\) | ||||
−0.0465658 | + | 0.998915i | \(0.514828\pi\) | |||||||
\(840\) | 0.365778 | 0.0126205 | ||||||||
\(841\) | −25.3607 | −0.874506 | ||||||||
\(842\) | −36.1140 | −1.24457 | ||||||||
\(843\) | 7.70789 | 0.265474 | ||||||||
\(844\) | 8.53391 | 0.293749 | ||||||||
\(845\) | 8.15785 | 0.280639 | ||||||||
\(846\) | −24.7448 | −0.850743 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.03517 | 0.275929 | ||||||||
\(849\) | 0.171323 | 0.00587980 | ||||||||
\(850\) | 6.26330 | 0.214830 | ||||||||
\(851\) | 1.60110 | 0.0548850 | ||||||||
\(852\) | 5.76486 | 0.197501 | ||||||||
\(853\) | 9.81741 | 0.336142 | 0.168071 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168071 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(854\) | −6.02013 | −0.206005 | ||||||||
\(855\) | −17.2250 | −0.589081 | ||||||||
\(856\) | −1.85065 | −0.0632539 | ||||||||
\(857\) | 38.1531 | 1.30329 | 0.651643 | − | 0.758526i | \(-0.274080\pi\) | ||||
0.651643 | + | 0.758526i | \(0.274080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.51538 | 0.256421 | 0.128211 | − | 0.991747i | \(-0.459077\pi\) | ||||
0.128211 | + | 0.991747i | \(0.459077\pi\) | |||||||
\(860\) | −3.71582 | −0.126708 | ||||||||
\(861\) | 0.00756282 | 0.000257740 0 | ||||||||
\(862\) | 1.92226 | 0.0654726 | ||||||||
\(863\) | 57.5800 | 1.96005 | 0.980024 | − | 0.198880i | \(-0.0637305\pi\) | ||||
0.980024 | + | 0.198880i | \(0.0637305\pi\) | |||||||
\(864\) | −2.14573 | −0.0729992 | ||||||||
\(865\) | −6.79145 | −0.230916 | ||||||||
\(866\) | −8.11232 | −0.275668 | ||||||||
\(867\) | 8.13087 | 0.276139 | ||||||||
\(868\) | 6.05116 | 0.205390 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.697795 | 0.0236575 | ||||||||
\(871\) | −18.0323 | −0.611002 | ||||||||
\(872\) | −16.3800 | −0.554696 | ||||||||
\(873\) | 12.1117 | 0.409919 | ||||||||
\(874\) | −2.71713 | −0.0919083 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 4.67618 | 0.157994 | ||||||||
\(877\) | −29.0321 | −0.980343 | −0.490172 | − | 0.871626i | \(-0.663066\pi\) | ||||
−0.490172 | + | 0.871626i | \(0.663066\pi\) | |||||||
\(878\) | 3.97670 | 0.134207 | ||||||||
\(879\) | −2.45770 | −0.0828963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.6656 | −1.63958 | −0.819792 | − | 0.572661i | \(-0.805911\pi\) | ||||
−0.819792 | + | 0.572661i | \(0.805911\pi\) | |||||||
\(882\) | −2.86621 | −0.0965102 | ||||||||
\(883\) | 47.0038 | 1.58180 | 0.790902 | − | 0.611943i | \(-0.209612\pi\) | ||||
0.790902 | + | 0.611943i | \(0.209612\pi\) | |||||||
\(884\) | −13.7823 | −0.463550 | ||||||||
\(885\) | 4.65559 | 0.156496 | ||||||||
\(886\) | −7.61310 | −0.255767 | ||||||||
\(887\) | 30.2777 | 1.01662 | 0.508312 | − | 0.861173i | \(-0.330270\pi\) | ||||
0.508312 | + | 0.861173i | \(0.330270\pi\) | |||||||
\(888\) | 1.29532 | 0.0434680 | ||||||||
\(889\) | −4.44315 | −0.149019 | ||||||||
\(890\) | 9.56469 | 0.320609 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.6449 | −0.657760 | ||||||||
\(893\) | −51.8832 | −1.73621 | ||||||||
\(894\) | 5.08846 | 0.170183 | ||||||||
\(895\) | 23.7293 | 0.793185 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.363912 | −0.0121507 | ||||||||
\(898\) | 3.27630 | 0.109331 | ||||||||
\(899\) | 11.5438 | 0.385008 | ||||||||
\(900\) | −2.86621 | −0.0955402 | ||||||||
\(901\) | 50.3267 | 1.67663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.35916 | −0.0452302 | ||||||||
\(904\) | −10.7686 | −0.358159 | ||||||||
\(905\) | −14.5332 | −0.483100 | ||||||||
\(906\) | 1.38273 | 0.0459382 | ||||||||
\(907\) | 48.9263 | 1.62457 | 0.812285 | − | 0.583261i | \(-0.198223\pi\) | ||||
0.812285 | + | 0.583261i | \(0.198223\pi\) | |||||||
\(908\) | 2.37742 | 0.0788975 | ||||||||
\(909\) | 28.8096 | 0.955556 | ||||||||
\(910\) | −2.20049 | −0.0729455 | ||||||||
\(911\) | 42.4585 | 1.40671 | 0.703357 | − | 0.710837i | \(-0.251684\pi\) | ||||
0.703357 | + | 0.710837i | \(0.251684\pi\) | |||||||
\(912\) | −2.19820 | −0.0727898 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.41968 | 0.278498 | ||||||||
\(915\) | −2.20203 | −0.0727968 | ||||||||
\(916\) | 9.73039 | 0.321501 | ||||||||
\(917\) | 2.54949 | 0.0841917 | ||||||||
\(918\) | −13.4393 | −0.443565 | ||||||||
\(919\) | 40.5258 | 1.33682 | 0.668412 | − | 0.743791i | \(-0.266974\pi\) | ||||
0.668412 | + | 0.743791i | \(0.266974\pi\) | |||||||
\(920\) | −0.452126 | −0.0149062 | ||||||||
\(921\) | 8.31011 | 0.273827 | ||||||||
\(922\) | −22.7631 | −0.749662 | ||||||||
\(923\) | −34.6809 | −1.14154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54127 | 0.116436 | ||||||||
\(926\) | 24.6401 | 0.809724 | ||||||||
\(927\) | −42.0547 | −1.38126 | ||||||||
\(928\) | −1.90770 | −0.0626234 | ||||||||
\(929\) | 40.3461 | 1.32371 | 0.661856 | − | 0.749631i | \(-0.269769\pi\) | ||||
0.661856 | + | 0.749631i | \(0.269769\pi\) | |||||||
\(930\) | 2.21338 | 0.0725796 | ||||||||
\(931\) | −6.00967 | −0.196959 | ||||||||
\(932\) | 18.4540 | 0.604482 | ||||||||
\(933\) | −7.75833 | −0.253996 | ||||||||
\(934\) | 4.38924 | 0.143620 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.30706 | 0.206153 | ||||||||
\(937\) | 33.7379 | 1.10217 | 0.551084 | − | 0.834450i | \(-0.314214\pi\) | ||||
0.551084 | + | 0.834450i | \(0.314214\pi\) | |||||||
\(938\) | −8.19469 | −0.267566 | ||||||||
\(939\) | −1.35365 | −0.0441747 | ||||||||
\(940\) | −8.63329 | −0.281587 | ||||||||
\(941\) | 12.3247 | 0.401773 | 0.200887 | − | 0.979614i | \(-0.435618\pi\) | ||||
0.200887 | + | 0.979614i | \(0.435618\pi\) | |||||||
\(942\) | 4.63741 | 0.151095 | ||||||||
\(943\) | −0.00934817 | −0.000304418 0 | ||||||||
\(944\) | −12.7279 | −0.414258 | ||||||||
\(945\) | −2.14573 | −0.0698005 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.817385 | −0.0265615 | −0.0132807 | − | 0.999912i | \(-0.504228\pi\) | ||||
−0.0132807 | + | 0.999912i | \(0.504228\pi\) | |||||||
\(948\) | 3.93010 | 0.127644 | ||||||||
\(949\) | −28.1315 | −0.913188 | ||||||||
\(950\) | −6.00967 | −0.194979 | ||||||||
\(951\) | −2.82039 | −0.0914575 | ||||||||
\(952\) | −6.26330 | −0.202995 | ||||||||
\(953\) | 6.96194 | 0.225519 | 0.112760 | − | 0.993622i | \(-0.464031\pi\) | ||||
0.112760 | + | 0.993622i | \(0.464031\pi\) | |||||||
\(954\) | −23.0305 | −0.745639 | ||||||||
\(955\) | 6.74284 | 0.218193 | ||||||||
\(956\) | 17.6068 | 0.569445 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.1427 | −0.327696 | ||||||||
\(959\) | 15.1630 | 0.489638 | ||||||||
\(960\) | −0.365778 | −0.0118054 | ||||||||
\(961\) | 5.61659 | 0.181180 | ||||||||
\(962\) | −7.79252 | −0.251241 | ||||||||
\(963\) | 5.30434 | 0.170930 | ||||||||
\(964\) | 17.4835 | 0.563105 | ||||||||
\(965\) | 10.4918 | 0.337744 | ||||||||
\(966\) | −0.165378 | −0.00532094 | ||||||||
\(967\) | −5.35673 | −0.172261 | −0.0861304 | − | 0.996284i | \(-0.527450\pi\) | ||||
−0.0861304 | + | 0.996284i | \(0.527450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.7680 | −0.442293 | ||||||||
\(970\) | 4.22569 | 0.135679 | ||||||||
\(971\) | −17.4088 | −0.558676 | −0.279338 | − | 0.960193i | \(-0.590115\pi\) | ||||
−0.279338 | + | 0.960193i | \(0.590115\pi\) | |||||||
\(972\) | 9.29528 | 0.298146 | ||||||||
\(973\) | −4.56534 | −0.146358 | ||||||||
\(974\) | −22.6195 | −0.724776 | ||||||||
\(975\) | −0.804890 | −0.0257771 | ||||||||
\(976\) | 6.02013 | 0.192700 | ||||||||
\(977\) | 5.42269 | 0.173487 | 0.0867437 | − | 0.996231i | \(-0.472354\pi\) | ||||
0.0867437 | + | 0.996231i | \(0.472354\pi\) | |||||||
\(978\) | 6.89615 | 0.220515 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 46.9484 | 1.49895 | ||||||||
\(982\) | 2.55144 | 0.0814197 | ||||||||
\(983\) | 12.9202 | 0.412092 | 0.206046 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206046 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(984\) | −0.00756282 | −0.000241094 0 | ||||||||
\(985\) | 8.40324 | 0.267750 | ||||||||
\(986\) | −11.9485 | −0.380518 | ||||||||
\(987\) | −3.15786 | −0.100516 | ||||||||
\(988\) | 13.2242 | 0.420718 | ||||||||
\(989\) | 1.68002 | 0.0534215 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6040 | −0.845104 | −0.422552 | − | 0.906339i | \(-0.638866\pi\) | ||||
−0.422552 | + | 0.906339i | \(0.638866\pi\) | |||||||
\(992\) | −6.05116 | −0.192125 | ||||||||
\(993\) | 11.7961 | 0.374337 | ||||||||
\(994\) | −15.7605 | −0.499894 | ||||||||
\(995\) | −5.41088 | −0.171536 | ||||||||
\(996\) | 4.01182 | 0.127119 | ||||||||
\(997\) | −57.0633 | −1.80721 | −0.903606 | − | 0.428365i | \(-0.859090\pi\) | ||||
−0.903606 | + | 0.428365i | \(0.859090\pi\) | |||||||
\(998\) | 4.35625 | 0.137895 | ||||||||
\(999\) | −7.59860 | −0.240409 |
(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 | 8470.2.a.dh.1.5 | 8 | ||
11.3 | even | 5 | 770.2.n.k.141.3 | yes | 16 | ||
11.4 | even | 5 | 770.2.n.k.71.3 | ✓ | 16 | ||
11.10 | odd | 2 | 8470.2.a.dg.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.k.71.3 | ✓ | 16 | 11.4 | even | 5 | ||
770.2.n.k.141.3 | yes | 16 | 11.3 | even | 5 | ||
8470.2.a.dg.1.5 | 8 | 11.10 | odd | 2 | |||
8470.2.a.dh.1.5 | 8 | 1.1 | even | 1 | trivial |