Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.60620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.60620 | 1.13575 | 0.567877 | − | 0.823114i | \(-0.307765\pi\) | ||||
0.567877 | + | 0.823114i | \(0.307765\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.579871 | 0.289935 | ||||||||
\(5\) | 3.54808 | 1.58675 | 0.793375 | − | 0.608733i | \(-0.208322\pi\) | ||||
0.793375 | + | 0.608733i | \(0.208322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.28101 | −0.806458 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.69892 | 1.80216 | ||||||||
\(11\) | 2.78529 | 0.839796 | 0.419898 | − | 0.907571i | \(-0.362066\pi\) | ||||
0.419898 | + | 0.907571i | \(0.362066\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.43579 | 0.675567 | 0.337784 | − | 0.941224i | \(-0.390323\pi\) | ||||
0.337784 | + | 0.941224i | \(0.390323\pi\) | |||||||
\(14\) | 1.60620 | 0.429274 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.82349 | −1.20587 | ||||||||
\(17\) | 6.06028 | 1.46983 | 0.734917 | − | 0.678158i | \(-0.237221\pi\) | ||||
0.734917 | + | 0.678158i | \(0.237221\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.93658 | −0.444283 | −0.222141 | − | 0.975014i | \(-0.571305\pi\) | ||||
−0.222141 | + | 0.975014i | \(0.571305\pi\) | |||||||
\(20\) | 2.05743 | 0.460055 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.47373 | 0.953802 | ||||||||
\(23\) | −3.19860 | −0.666955 | −0.333477 | − | 0.942758i | \(-0.608222\pi\) | ||||
−0.333477 | + | 0.942758i | \(0.608222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.58887 | 1.51777 | ||||||||
\(26\) | 3.91236 | 0.767277 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.579871 | 0.109585 | ||||||||
\(29\) | −2.42395 | −0.450116 | −0.225058 | − | 0.974345i | \(-0.572257\pi\) | ||||
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.23823 | 0.581603 | 0.290801 | − | 0.956783i | \(-0.406078\pi\) | ||||
0.290801 | + | 0.956783i | \(0.406078\pi\) | |||||||
\(32\) | −3.18546 | −0.563116 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.73400 | 1.66937 | ||||||||
\(35\) | 3.54808 | 0.599735 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.06507 | −0.175097 | −0.0875484 | − | 0.996160i | \(-0.527903\pi\) | ||||
−0.0875484 | + | 0.996160i | \(0.527903\pi\) | |||||||
\(38\) | −3.11054 | −0.504596 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.09320 | −1.27965 | ||||||||
\(41\) | 3.51151 | 0.548406 | 0.274203 | − | 0.961672i | \(-0.411586\pi\) | ||||
0.274203 | + | 0.961672i | \(0.411586\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.82642 | 0.888521 | 0.444260 | − | 0.895898i | \(-0.353466\pi\) | ||||
0.444260 | + | 0.895898i | \(0.353466\pi\) | |||||||
\(44\) | 1.61511 | 0.243487 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.13759 | −0.757496 | ||||||||
\(47\) | 2.39519 | 0.349375 | 0.174687 | − | 0.984624i | \(-0.444109\pi\) | ||||
0.174687 | + | 0.984624i | \(0.444109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 12.1892 | 1.72382 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41244 | 0.195871 | ||||||||
\(53\) | −11.1491 | −1.53145 | −0.765723 | − | 0.643171i | \(-0.777619\pi\) | ||||
−0.765723 | + | 0.643171i | \(0.777619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.88243 | 1.33255 | ||||||||
\(56\) | −2.28101 | −0.304813 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.89334 | −0.511221 | ||||||||
\(59\) | 2.80705 | 0.365447 | 0.182723 | − | 0.983164i | \(-0.441509\pi\) | ||||
0.182723 | + | 0.983164i | \(0.441509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.16721 | 1.04570 | 0.522852 | − | 0.852423i | \(-0.324868\pi\) | ||||
0.522852 | + | 0.852423i | \(0.324868\pi\) | |||||||
\(62\) | 5.20123 | 0.660557 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.53050 | 0.566312 | ||||||||
\(65\) | 8.64238 | 1.07196 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.97952 | 0.730515 | 0.365257 | − | 0.930907i | \(-0.380981\pi\) | ||||
0.365257 | + | 0.930907i | \(0.380981\pi\) | |||||||
\(68\) | 3.51418 | 0.426157 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.69892 | 0.681151 | ||||||||
\(71\) | −12.1587 | −1.44297 | −0.721484 | − | 0.692431i | \(-0.756540\pi\) | ||||
−0.721484 | + | 0.692431i | \(0.756540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.47476 | 0.289649 | 0.144824 | − | 0.989457i | \(-0.453738\pi\) | ||||
0.144824 | + | 0.989457i | \(0.453738\pi\) | |||||||
\(74\) | −1.71072 | −0.198867 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12297 | −0.128813 | ||||||||
\(77\) | 2.78529 | 0.317413 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.02097 | −0.339885 | −0.169943 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169943 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(80\) | −17.1141 | −1.91342 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.64018 | 0.622854 | ||||||||
\(83\) | 10.1939 | 1.11893 | 0.559465 | − | 0.828854i | \(-0.311007\pi\) | ||||
0.559465 | + | 0.828854i | \(0.311007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.5023 | 2.33226 | ||||||||
\(86\) | 9.35838 | 1.00914 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.35327 | −0.677261 | ||||||||
\(89\) | 2.30092 | 0.243897 | 0.121949 | − | 0.992536i | \(-0.461086\pi\) | ||||
0.121949 | + | 0.992536i | \(0.461086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.43579 | 0.255340 | ||||||||
\(92\) | −1.85478 | −0.193374 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.84715 | 0.396804 | ||||||||
\(95\) | −6.87116 | −0.704966 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.707978 | −0.0718843 | −0.0359422 | − | 0.999354i | \(-0.511443\pi\) | ||||
−0.0359422 | + | 0.999354i | \(0.511443\pi\) | |||||||
\(98\) | 1.60620 | 0.162250 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.40057 | 0.440057 | ||||||||
\(101\) | −11.1926 | −1.11371 | −0.556853 | − | 0.830611i | \(-0.687991\pi\) | ||||
−0.556853 | + | 0.830611i | \(0.687991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.42373 | 0.928548 | 0.464274 | − | 0.885692i | \(-0.346315\pi\) | ||||
0.464274 | + | 0.885692i | \(0.346315\pi\) | |||||||
\(104\) | −5.55606 | −0.544817 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.9076 | −1.73934 | ||||||||
\(107\) | 6.56198 | 0.634371 | 0.317185 | − | 0.948364i | \(-0.397262\pi\) | ||||
0.317185 | + | 0.948364i | \(0.397262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.5034 | −1.48495 | −0.742476 | − | 0.669872i | \(-0.766349\pi\) | ||||
−0.742476 | + | 0.669872i | \(0.766349\pi\) | |||||||
\(110\) | 15.8731 | 1.51344 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.82349 | −0.455777 | ||||||||
\(113\) | −14.8683 | −1.39869 | −0.699344 | − | 0.714786i | \(-0.746524\pi\) | ||||
−0.699344 | + | 0.714786i | \(0.746524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.3489 | −1.05829 | ||||||||
\(116\) | −1.40558 | −0.130505 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.50868 | 0.415057 | ||||||||
\(119\) | 6.06028 | 0.555545 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.24216 | −0.294742 | ||||||||
\(122\) | 13.1182 | 1.18766 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.87775 | 0.168627 | ||||||||
\(125\) | 9.18552 | 0.821578 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 13.6478 | 1.20631 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.8814 | 1.21748 | ||||||||
\(131\) | 16.9371 | 1.47981 | 0.739903 | − | 0.672714i | \(-0.234871\pi\) | ||||
0.739903 | + | 0.672714i | \(0.234871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93658 | −0.167923 | ||||||||
\(134\) | 9.60429 | 0.829684 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.8235 | −1.18536 | ||||||||
\(137\) | 8.14622 | 0.695979 | 0.347989 | − | 0.937498i | \(-0.386865\pi\) | ||||
0.347989 | + | 0.937498i | \(0.386865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0461 | −0.852099 | −0.426050 | − | 0.904700i | \(-0.640095\pi\) | ||||
−0.426050 | + | 0.904700i | \(0.640095\pi\) | |||||||
\(140\) | 2.05743 | 0.173884 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19.5292 | −1.63886 | ||||||||
\(143\) | 6.78439 | 0.567339 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.60037 | −0.714222 | ||||||||
\(146\) | 3.97495 | 0.328969 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.617604 | −0.0507667 | ||||||||
\(149\) | 4.50378 | 0.368964 | 0.184482 | − | 0.982836i | \(-0.440939\pi\) | ||||
0.184482 | + | 0.982836i | \(0.440939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3733 | −1.08831 | −0.544154 | − | 0.838986i | \(-0.683149\pi\) | ||||
−0.544154 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(152\) | 4.41736 | 0.358296 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.47373 | 0.360503 | ||||||||
\(155\) | 11.4895 | 0.922858 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.76796 | −0.619951 | −0.309975 | − | 0.950745i | \(-0.600321\pi\) | ||||
−0.309975 | + | 0.950745i | \(0.600321\pi\) | |||||||
\(158\) | −4.85227 | −0.386026 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.3023 | −0.893524 | ||||||||
\(161\) | −3.19860 | −0.252085 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3737 | 0.890858 | 0.445429 | − | 0.895317i | \(-0.353051\pi\) | ||||
0.445429 | + | 0.895317i | \(0.353051\pi\) | |||||||
\(164\) | 2.03622 | 0.159002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.3735 | 1.27083 | ||||||||
\(167\) | −2.47601 | −0.191600 | −0.0957998 | − | 0.995401i | \(-0.530541\pi\) | ||||
−0.0957998 | + | 0.995401i | \(0.530541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.06692 | −0.543609 | ||||||||
\(170\) | 34.5370 | 2.64887 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.37857 | 0.257614 | ||||||||
\(173\) | 10.7831 | 0.819820 | 0.409910 | − | 0.912126i | \(-0.365560\pi\) | ||||
0.409910 | + | 0.912126i | \(0.365560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.58887 | 0.573665 | ||||||||
\(176\) | −13.4348 | −1.01269 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.69573 | 0.277007 | ||||||||
\(179\) | 12.0233 | 0.898667 | 0.449333 | − | 0.893364i | \(-0.351662\pi\) | ||||
0.449333 | + | 0.893364i | \(0.351662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0378 | 1.26641 | 0.633204 | − | 0.773985i | \(-0.281739\pi\) | ||||
0.633204 | + | 0.773985i | \(0.281739\pi\) | |||||||
\(182\) | 3.91236 | 0.290004 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.29604 | 0.537871 | ||||||||
\(185\) | −3.77896 | −0.277835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8796 | 1.23436 | ||||||||
\(188\) | 1.38890 | 0.101296 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.0364 | −0.800667 | ||||||||
\(191\) | −13.9297 | −1.00792 | −0.503959 | − | 0.863727i | \(-0.668124\pi\) | ||||
−0.503959 | + | 0.863727i | \(0.668124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.5610 | −1.69596 | −0.847979 | − | 0.530030i | \(-0.822181\pi\) | ||||
−0.847979 | + | 0.530030i | \(0.822181\pi\) | |||||||
\(194\) | −1.13715 | −0.0816428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.579871 | 0.0414193 | ||||||||
\(197\) | 6.52931 | 0.465194 | 0.232597 | − | 0.972573i | \(-0.425278\pi\) | ||||
0.232597 | + | 0.972573i | \(0.425278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0272 | 1.34881 | 0.674403 | − | 0.738364i | \(-0.264401\pi\) | ||||
0.674403 | + | 0.738364i | \(0.264401\pi\) | |||||||
\(200\) | −17.3103 | −1.22402 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.9776 | −1.26490 | ||||||||
\(203\) | −2.42395 | −0.170128 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4591 | 0.870182 | ||||||||
\(206\) | 15.1364 | 1.05460 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.7490 | −0.814648 | ||||||||
\(209\) | −5.39395 | −0.373107 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5670 | −0.865151 | −0.432575 | − | 0.901598i | \(-0.642395\pi\) | ||||
−0.432575 | + | 0.901598i | \(0.642395\pi\) | |||||||
\(212\) | −6.46503 | −0.444020 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.5398 | 0.720489 | ||||||||
\(215\) | 20.6726 | 1.40986 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.23823 | 0.219825 | ||||||||
\(218\) | −24.9015 | −1.68654 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.73053 | 0.386352 | ||||||||
\(221\) | 14.7616 | 0.992971 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.9633 | 1.87256 | 0.936280 | − | 0.351255i | \(-0.114245\pi\) | ||||
0.936280 | + | 0.351255i | \(0.114245\pi\) | |||||||
\(224\) | −3.18546 | −0.212838 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.8814 | −1.58856 | ||||||||
\(227\) | 17.2281 | 1.14347 | 0.571733 | − | 0.820440i | \(-0.306271\pi\) | ||||
0.571733 | + | 0.820440i | \(0.306271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.7667 | −1.17406 | −0.587030 | − | 0.809565i | \(-0.699703\pi\) | ||||
−0.587030 | + | 0.809565i | \(0.699703\pi\) | |||||||
\(230\) | −18.2286 | −1.20196 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.52905 | 0.363000 | ||||||||
\(233\) | −14.0286 | −0.919043 | −0.459521 | − | 0.888167i | \(-0.651979\pi\) | ||||
−0.459521 | + | 0.888167i | \(0.651979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.49834 | 0.554370 | ||||||||
\(236\) | 1.62773 | 0.105956 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.73400 | 0.630962 | ||||||||
\(239\) | 21.4428 | 1.38702 | 0.693510 | − | 0.720447i | \(-0.256063\pi\) | ||||
0.693510 | + | 0.720447i | \(0.256063\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.57437 | −0.294661 | −0.147331 | − | 0.989087i | \(-0.547068\pi\) | ||||
−0.147331 | + | 0.989087i | \(0.547068\pi\) | |||||||
\(242\) | −5.20755 | −0.334754 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.73593 | 0.303187 | ||||||||
\(245\) | 3.54808 | 0.226679 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.71712 | −0.300143 | ||||||||
\(248\) | −7.38642 | −0.469038 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.7538 | 0.933110 | ||||||||
\(251\) | −11.2949 | −0.712925 | −0.356462 | − | 0.934310i | \(-0.616017\pi\) | ||||
−0.356462 | + | 0.934310i | \(0.616017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.90903 | −0.560106 | ||||||||
\(254\) | 1.60620 | 0.100782 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.8601 | 0.803755 | ||||||||
\(257\) | 27.1572 | 1.69402 | 0.847010 | − | 0.531576i | \(-0.178400\pi\) | ||||
0.847010 | + | 0.531576i | \(0.178400\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.06507 | −0.0661803 | ||||||||
\(260\) | 5.01147 | 0.310798 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 27.2044 | 1.68069 | ||||||||
\(263\) | −1.15314 | −0.0711058 | −0.0355529 | − | 0.999368i | \(-0.511319\pi\) | ||||
−0.0355529 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.5579 | −2.43002 | ||||||||
\(266\) | −3.11054 | −0.190719 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.46735 | 0.211802 | ||||||||
\(269\) | −15.9024 | −0.969584 | −0.484792 | − | 0.874629i | \(-0.661105\pi\) | ||||
−0.484792 | + | 0.874629i | \(0.661105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.54720 | 0.215477 | 0.107739 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107739 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(272\) | −29.2317 | −1.77243 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.0844 | 0.790460 | ||||||||
\(275\) | 21.1372 | 1.27462 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.879357 | 0.0528355 | 0.0264177 | − | 0.999651i | \(-0.491590\pi\) | ||||
0.0264177 | + | 0.999651i | \(0.491590\pi\) | |||||||
\(278\) | −16.1360 | −0.967774 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.09320 | −0.483661 | ||||||||
\(281\) | −15.5204 | −0.925868 | −0.462934 | − | 0.886393i | \(-0.653203\pi\) | ||||
−0.462934 | + | 0.886393i | \(0.653203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.1358 | −1.61306 | −0.806528 | − | 0.591196i | \(-0.798656\pi\) | ||||
−0.806528 | + | 0.591196i | \(0.798656\pi\) | |||||||
\(284\) | −7.05046 | −0.418368 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8971 | 0.644357 | ||||||||
\(287\) | 3.51151 | 0.207278 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.7270 | 1.16041 | ||||||||
\(290\) | −13.8139 | −0.811180 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.43504 | 0.0839794 | ||||||||
\(293\) | 13.8186 | 0.807294 | 0.403647 | − | 0.914915i | \(-0.367742\pi\) | ||||
0.403647 | + | 0.914915i | \(0.367742\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.95964 | 0.579873 | ||||||||
\(296\) | 2.42944 | 0.141208 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.23396 | 0.419052 | ||||||||
\(299\) | −7.79113 | −0.450573 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.82642 | 0.335829 | ||||||||
\(302\) | −21.4802 | −1.23605 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.34110 | 0.535749 | ||||||||
\(305\) | 28.9779 | 1.65927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.8063 | −1.41577 | −0.707885 | − | 0.706328i | \(-0.750350\pi\) | ||||
−0.707885 | + | 0.706328i | \(0.750350\pi\) | |||||||
\(308\) | 1.61511 | 0.0920293 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.4544 | 1.04814 | ||||||||
\(311\) | 14.3789 | 0.815355 | 0.407677 | − | 0.913126i | \(-0.366339\pi\) | ||||
0.407677 | + | 0.913126i | \(0.366339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.43949 | 0.307458 | 0.153729 | − | 0.988113i | \(-0.450872\pi\) | ||||
0.153729 | + | 0.988113i | \(0.450872\pi\) | |||||||
\(314\) | −12.4769 | −0.704111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.75177 | −0.0985448 | ||||||||
\(317\) | 0.807453 | 0.0453511 | 0.0226755 | − | 0.999743i | \(-0.492782\pi\) | ||||
0.0226755 | + | 0.999743i | \(0.492782\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.75141 | −0.378006 | ||||||||
\(320\) | 16.0746 | 0.898596 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.13759 | −0.286307 | ||||||||
\(323\) | −11.7362 | −0.653022 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.4849 | 1.02536 | ||||||||
\(326\) | 18.2684 | 1.01180 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.00978 | −0.442266 | ||||||||
\(329\) | 2.39519 | 0.132051 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.60565 | −0.253150 | −0.126575 | − | 0.991957i | \(-0.540398\pi\) | ||||
−0.126575 | + | 0.991957i | \(0.540398\pi\) | |||||||
\(332\) | 5.91117 | 0.324417 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.97697 | −0.217610 | ||||||||
\(335\) | 21.2158 | 1.15914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.71254 | 0.202235 | 0.101118 | − | 0.994874i | \(-0.467758\pi\) | ||||
0.101118 | + | 0.994874i | \(0.467758\pi\) | |||||||
\(338\) | −11.3509 | −0.617406 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.4686 | 0.676204 | ||||||||
\(341\) | 9.01940 | 0.488428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −13.2901 | −0.716555 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.3197 | 0.931113 | ||||||||
\(347\) | 5.38943 | 0.289320 | 0.144660 | − | 0.989481i | \(-0.453791\pi\) | ||||
0.144660 | + | 0.989481i | \(0.453791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3138 | 0.873257 | 0.436629 | − | 0.899642i | \(-0.356172\pi\) | ||||
0.436629 | + | 0.899642i | \(0.356172\pi\) | |||||||
\(350\) | 12.1892 | 0.651542 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.87244 | −0.472903 | ||||||||
\(353\) | −3.10479 | −0.165251 | −0.0826256 | − | 0.996581i | \(-0.526331\pi\) | ||||
−0.0826256 | + | 0.996581i | \(0.526331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.1399 | −2.28963 | ||||||||
\(356\) | 1.33424 | 0.0707144 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.3119 | 1.02066 | ||||||||
\(359\) | 0.513047 | 0.0270776 | 0.0135388 | − | 0.999908i | \(-0.495690\pi\) | ||||
0.0135388 | + | 0.999908i | \(0.495690\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2496 | −0.802613 | ||||||||
\(362\) | 27.3660 | 1.43833 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.41244 | 0.0740322 | ||||||||
\(365\) | 8.78064 | 0.459600 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.45004 | 0.127891 | 0.0639456 | − | 0.997953i | \(-0.479632\pi\) | ||||
0.0639456 | + | 0.997953i | \(0.479632\pi\) | |||||||
\(368\) | 15.4284 | 0.804262 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.06976 | −0.315552 | ||||||||
\(371\) | −11.1491 | −0.578832 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.9564 | −1.49930 | −0.749652 | − | 0.661832i | \(-0.769779\pi\) | ||||
−0.749652 | + | 0.661832i | \(0.769779\pi\) | |||||||
\(374\) | 27.1120 | 1.40193 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.46346 | −0.281756 | ||||||||
\(377\) | −5.90424 | −0.304084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.9005 | 0.559919 | 0.279959 | − | 0.960012i | \(-0.409679\pi\) | ||||
0.279959 | + | 0.960012i | \(0.409679\pi\) | |||||||
\(380\) | −3.98438 | −0.204395 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.3739 | −1.14475 | ||||||||
\(383\) | 16.5606 | 0.846208 | 0.423104 | − | 0.906081i | \(-0.360941\pi\) | ||||
0.423104 | + | 0.906081i | \(0.360941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.88243 | 0.503655 | ||||||||
\(386\) | −37.8436 | −1.92619 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.410536 | −0.0208418 | ||||||||
\(389\) | 12.9612 | 0.657157 | 0.328578 | − | 0.944477i | \(-0.393431\pi\) | ||||
0.328578 | + | 0.944477i | \(0.393431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3844 | −0.980312 | ||||||||
\(392\) | −2.28101 | −0.115208 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.4874 | 0.528346 | ||||||||
\(395\) | −10.7186 | −0.539313 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.8068 | −1.59634 | −0.798168 | − | 0.602435i | \(-0.794197\pi\) | ||||
−0.798168 | + | 0.602435i | \(0.794197\pi\) | |||||||
\(398\) | 30.5615 | 1.53191 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −36.6049 | −1.83024 | ||||||||
\(401\) | −36.4319 | −1.81932 | −0.909660 | − | 0.415353i | \(-0.863658\pi\) | ||||
−0.909660 | + | 0.415353i | \(0.863658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.88765 | 0.392912 | ||||||||
\(404\) | −6.49027 | −0.322903 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.89334 | −0.193223 | ||||||||
\(407\) | −2.96653 | −0.147046 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0186891 | −0.000924115 0 | −0.000462058 | − | 1.00000i | \(-0.500147\pi\) | ||||
−0.000462058 | 1.00000i | \(0.500147\pi\) | ||||||||
\(410\) | 20.0118 | 0.988313 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.46455 | 0.269219 | ||||||||
\(413\) | 2.80705 | 0.138126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.1689 | 1.77546 | ||||||||
\(416\) | −7.75913 | −0.380423 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.66375 | −0.423758 | ||||||||
\(419\) | 20.4211 | 0.997637 | 0.498819 | − | 0.866706i | \(-0.333767\pi\) | ||||
0.498819 | + | 0.866706i | \(0.333767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.7357 | 1.01060 | 0.505299 | − | 0.862944i | \(-0.331382\pi\) | ||||
0.505299 | + | 0.862944i | \(0.331382\pi\) | |||||||
\(422\) | −20.1852 | −0.982598 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.4312 | 1.23505 | ||||||||
\(425\) | 45.9907 | 2.23087 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.16721 | 0.395239 | ||||||||
\(428\) | 3.80510 | 0.183927 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.2043 | 1.60125 | ||||||||
\(431\) | −26.7720 | −1.28956 | −0.644782 | − | 0.764367i | \(-0.723052\pi\) | ||||
−0.644782 | + | 0.764367i | \(0.723052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.45697 | −0.358359 | −0.179179 | − | 0.983816i | \(-0.557344\pi\) | ||||
−0.179179 | + | 0.983816i | \(0.557344\pi\) | |||||||
\(434\) | 5.20123 | 0.249667 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.98995 | −0.430540 | ||||||||
\(437\) | 6.19436 | 0.296317 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.491516 | 0.0234588 | 0.0117294 | − | 0.999931i | \(-0.496266\pi\) | ||||
0.0117294 | + | 0.999931i | \(0.496266\pi\) | |||||||
\(440\) | −22.5419 | −1.07464 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.7100 | 1.12777 | ||||||||
\(443\) | −16.3582 | −0.777203 | −0.388602 | − | 0.921406i | \(-0.627042\pi\) | ||||
−0.388602 | + | 0.921406i | \(0.627042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.16385 | 0.387004 | ||||||||
\(446\) | 44.9146 | 2.12677 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.53050 | 0.214046 | ||||||||
\(449\) | −21.0828 | −0.994957 | −0.497478 | − | 0.867476i | \(-0.665741\pi\) | ||||
−0.497478 | + | 0.867476i | \(0.665741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.78057 | 0.460549 | ||||||||
\(452\) | −8.62167 | −0.405529 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.6717 | 1.29870 | ||||||||
\(455\) | 8.64238 | 0.405161 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.58237 | 0.448245 | 0.224122 | − | 0.974561i | \(-0.428049\pi\) | ||||
0.224122 | + | 0.974561i | \(0.428049\pi\) | |||||||
\(458\) | −28.5369 | −1.33344 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.58089 | −0.306836 | ||||||||
\(461\) | 26.0159 | 1.21168 | 0.605841 | − | 0.795586i | \(-0.292837\pi\) | ||||
0.605841 | + | 0.795586i | \(0.292837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0319 | −0.698590 | −0.349295 | − | 0.937013i | \(-0.613579\pi\) | ||||
−0.349295 | + | 0.937013i | \(0.613579\pi\) | |||||||
\(464\) | 11.6919 | 0.542783 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.5327 | −1.04381 | ||||||||
\(467\) | 7.12952 | 0.329915 | 0.164957 | − | 0.986301i | \(-0.447251\pi\) | ||||
0.164957 | + | 0.986301i | \(0.447251\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.97952 | 0.276109 | ||||||||
\(470\) | 13.6500 | 0.629628 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.40290 | −0.294718 | ||||||||
\(473\) | 16.2283 | 0.746177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.6965 | −0.674321 | ||||||||
\(476\) | 3.51418 | 0.161072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.4414 | 1.57531 | ||||||||
\(479\) | 2.79072 | 0.127511 | 0.0637557 | − | 0.997966i | \(-0.479692\pi\) | ||||
0.0637557 | + | 0.997966i | \(0.479692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.59429 | −0.118290 | ||||||||
\(482\) | −7.34735 | −0.334662 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.88004 | −0.0854561 | ||||||||
\(485\) | −2.51196 | −0.114062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.2763 | 1.46258 | 0.731289 | − | 0.682067i | \(-0.238919\pi\) | ||||
0.731289 | + | 0.682067i | \(0.238919\pi\) | |||||||
\(488\) | −18.6295 | −0.843317 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.69892 | 0.257451 | ||||||||
\(491\) | 30.0985 | 1.35833 | 0.679163 | − | 0.733987i | \(-0.262343\pi\) | ||||
0.679163 | + | 0.733987i | \(0.262343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6898 | −0.661596 | ||||||||
\(494\) | −7.57662 | −0.340888 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.6196 | −0.701339 | ||||||||
\(497\) | −12.1587 | −0.545391 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.8366 | 1.42520 | 0.712602 | − | 0.701569i | \(-0.247517\pi\) | ||||
0.712602 | + | 0.701569i | \(0.247517\pi\) | |||||||
\(500\) | 5.32642 | 0.238205 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.1418 | −0.809707 | ||||||||
\(503\) | 42.3948 | 1.89029 | 0.945145 | − | 0.326651i | \(-0.105920\pi\) | ||||
0.945145 | + | 0.326651i | \(0.105920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7123 | −1.76717 | ||||||||
\(506\) | −14.3097 | −0.636142 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.579871 | 0.0257276 | ||||||||
\(509\) | −15.5022 | −0.687125 | −0.343562 | − | 0.939130i | \(-0.611634\pi\) | ||||
−0.343562 | + | 0.939130i | \(0.611634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.47476 | 0.109477 | ||||||||
\(512\) | −6.63978 | −0.293440 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 43.6199 | 1.92399 | ||||||||
\(515\) | 33.4362 | 1.47337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.67131 | 0.293404 | ||||||||
\(518\) | −1.71072 | −0.0751645 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.7133 | −0.864487 | ||||||||
\(521\) | −37.1898 | −1.62931 | −0.814657 | − | 0.579943i | \(-0.803075\pi\) | ||||
−0.814657 | + | 0.579943i | \(0.803075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.4445 | −1.89970 | −0.949848 | − | 0.312712i | \(-0.898763\pi\) | ||||
−0.949848 | + | 0.312712i | \(0.898763\pi\) | |||||||
\(524\) | 9.82136 | 0.429048 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.85217 | −0.0807586 | ||||||||
\(527\) | 19.6246 | 0.854859 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.7689 | −0.555172 | ||||||||
\(530\) | −63.5378 | −2.75990 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.12297 | −0.0486869 | ||||||||
\(533\) | 8.55331 | 0.370485 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2824 | 1.00659 | ||||||||
\(536\) | −13.6393 | −0.589130 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.5423 | −1.10121 | ||||||||
\(539\) | 2.78529 | 0.119971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.77004 | −0.248074 | −0.124037 | − | 0.992278i | \(-0.539584\pi\) | ||||
−0.124037 | + | 0.992278i | \(0.539584\pi\) | |||||||
\(542\) | 5.69751 | 0.244729 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.3048 | −0.827686 | ||||||||
\(545\) | −55.0072 | −2.35625 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.9425 | −1.49403 | −0.747016 | − | 0.664806i | \(-0.768514\pi\) | ||||
−0.747016 | + | 0.664806i | \(0.768514\pi\) | |||||||
\(548\) | 4.72376 | 0.201789 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 33.9505 | 1.44766 | ||||||||
\(551\) | 4.69419 | 0.199979 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.02097 | −0.128465 | ||||||||
\(554\) | 1.41242 | 0.0600080 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.82544 | −0.247054 | ||||||||
\(557\) | 17.9223 | 0.759392 | 0.379696 | − | 0.925111i | \(-0.376029\pi\) | ||||
0.379696 | + | 0.925111i | \(0.376029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.1919 | 0.600255 | ||||||||
\(560\) | −17.1141 | −0.723204 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.9288 | −1.05156 | ||||||||
\(563\) | −17.5956 | −0.741568 | −0.370784 | − | 0.928719i | \(-0.620911\pi\) | ||||
−0.370784 | + | 0.928719i | \(0.620911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −52.7537 | −2.21937 | ||||||||
\(566\) | −43.5855 | −1.83203 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.7340 | 1.16369 | ||||||||
\(569\) | −32.1201 | −1.34654 | −0.673272 | − | 0.739395i | \(-0.735112\pi\) | ||||
−0.673272 | + | 0.739395i | \(0.735112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9633 | 0.751739 | 0.375870 | − | 0.926673i | \(-0.377344\pi\) | ||||
0.375870 | + | 0.926673i | \(0.377344\pi\) | |||||||
\(572\) | 3.93407 | 0.164492 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.64018 | 0.235416 | ||||||||
\(575\) | −24.2738 | −1.01229 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.0564 | −1.20963 | −0.604816 | − | 0.796365i | \(-0.706753\pi\) | ||||
−0.604816 | + | 0.796365i | \(0.706753\pi\) | |||||||
\(578\) | 31.6854 | 1.31794 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.98711 | −0.207078 | ||||||||
\(581\) | 10.1939 | 0.422916 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.0535 | −1.28610 | ||||||||
\(584\) | −5.64494 | −0.233589 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.1955 | 0.916886 | ||||||||
\(587\) | 6.10638 | 0.252037 | 0.126019 | − | 0.992028i | \(-0.459780\pi\) | ||||
0.126019 | + | 0.992028i | \(0.459780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.27110 | −0.258396 | ||||||||
\(590\) | 15.9971 | 0.658592 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.13736 | 0.211144 | ||||||||
\(593\) | 9.02500 | 0.370612 | 0.185306 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185306 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.5023 | 0.881510 | ||||||||
\(596\) | 2.61161 | 0.106976 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.5141 | −0.511739 | ||||||||
\(599\) | −5.06194 | −0.206825 | −0.103413 | − | 0.994639i | \(-0.532976\pi\) | ||||
−0.103413 | + | 0.994639i | \(0.532976\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.99790 | −0.367032 | −0.183516 | − | 0.983017i | \(-0.558748\pi\) | ||||
−0.183516 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(602\) | 9.35838 | 0.381419 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.75481 | −0.315539 | ||||||||
\(605\) | −11.5034 | −0.467682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7806 | 0.518749 | 0.259375 | − | 0.965777i | \(-0.416484\pi\) | ||||
0.259375 | + | 0.965777i | \(0.416484\pi\) | |||||||
\(608\) | 6.16892 | 0.250183 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 46.5443 | 1.88452 | ||||||||
\(611\) | 5.83419 | 0.236026 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1381 | −0.692201 | −0.346101 | − | 0.938197i | \(-0.612494\pi\) | ||||
−0.346101 | + | 0.938197i | \(0.612494\pi\) | |||||||
\(614\) | −39.8438 | −1.60797 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.35327 | −0.255980 | ||||||||
\(617\) | 45.8447 | 1.84564 | 0.922820 | − | 0.385232i | \(-0.125879\pi\) | ||||
0.922820 | + | 0.385232i | \(0.125879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.5262 | 1.87005 | 0.935023 | − | 0.354587i | \(-0.115378\pi\) | ||||
0.935023 | + | 0.354587i | \(0.115378\pi\) | |||||||
\(620\) | 6.66242 | 0.267569 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.0954 | 0.926042 | ||||||||
\(623\) | 2.30092 | 0.0921845 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.35340 | −0.214136 | ||||||||
\(626\) | 8.73690 | 0.349197 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.50441 | −0.179746 | ||||||||
\(629\) | −6.45463 | −0.257363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7725 | −0.548273 | −0.274136 | − | 0.961691i | \(-0.588392\pi\) | ||||
−0.274136 | + | 0.961691i | \(0.588392\pi\) | |||||||
\(632\) | 6.89085 | 0.274103 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.29693 | 0.0515076 | ||||||||
\(635\) | 3.54808 | 0.140801 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.43579 | 0.0965096 | ||||||||
\(638\) | −10.8441 | −0.429322 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.4235 | 1.91411 | ||||||||
\(641\) | 0.860650 | 0.0339937 | 0.0169968 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169968 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.6792 | −1.64367 | −0.821834 | − | 0.569727i | \(-0.807049\pi\) | ||||
−0.821834 | + | 0.569727i | \(0.807049\pi\) | |||||||
\(644\) | −1.85478 | −0.0730884 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.8507 | −0.741672 | ||||||||
\(647\) | −19.3518 | −0.760798 | −0.380399 | − | 0.924822i | \(-0.624213\pi\) | ||||
−0.380399 | + | 0.924822i | \(0.624213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.81845 | 0.306901 | ||||||||
\(650\) | 29.6904 | 1.16455 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.59529 | 0.258291 | ||||||||
\(653\) | −8.67139 | −0.339338 | −0.169669 | − | 0.985501i | \(-0.554270\pi\) | ||||
−0.169669 | + | 0.985501i | \(0.554270\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.0944 | 2.34808 | ||||||||
\(656\) | −16.9377 | −0.661308 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.84715 | 0.149978 | ||||||||
\(659\) | −22.3147 | −0.869257 | −0.434629 | − | 0.900610i | \(-0.643120\pi\) | ||||
−0.434629 | + | 0.900610i | \(0.643120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0803059 | −0.00312354 | −0.00156177 | − | 0.999999i | \(-0.500497\pi\) | ||||
−0.00156177 | + | 0.999999i | \(0.500497\pi\) | |||||||
\(662\) | −7.39759 | −0.287516 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.2525 | −0.902370 | ||||||||
\(665\) | −6.87116 | −0.266452 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.75325 | 0.300207 | ||||||||
\(668\) | −1.43577 | −0.0555515 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34.0768 | 1.31650 | ||||||||
\(671\) | 22.7481 | 0.878179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.2767 | 1.39836 | 0.699182 | − | 0.714944i | \(-0.253548\pi\) | ||||
0.699182 | + | 0.714944i | \(0.253548\pi\) | |||||||
\(674\) | 5.96308 | 0.229689 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.09790 | −0.157612 | ||||||||
\(677\) | −10.2419 | −0.393629 | −0.196815 | − | 0.980441i | \(-0.563060\pi\) | ||||
−0.196815 | + | 0.980441i | \(0.563060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.707978 | −0.0271697 | ||||||||
\(680\) | −49.0470 | −1.88087 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.4869 | 0.554734 | ||||||||
\(683\) | −2.86486 | −0.109621 | −0.0548104 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548104 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9034 | 1.10434 | ||||||||
\(686\) | 1.60620 | 0.0613249 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.1037 | −1.07144 | ||||||||
\(689\) | −27.1569 | −1.03459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.83501 | −0.183932 | −0.0919662 | − | 0.995762i | \(-0.529315\pi\) | ||||
−0.0919662 | + | 0.995762i | \(0.529315\pi\) | |||||||
\(692\) | 6.25278 | 0.237695 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.65649 | 0.328596 | ||||||||
\(695\) | −35.6444 | −1.35207 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2807 | 0.806065 | ||||||||
\(698\) | 26.2032 | 0.991804 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.40057 | 0.166326 | ||||||||
\(701\) | 25.9468 | 0.979998 | 0.489999 | − | 0.871723i | \(-0.336997\pi\) | ||||
0.489999 | + | 0.871723i | \(0.336997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.06260 | 0.0777925 | ||||||||
\(704\) | 12.6187 | 0.475587 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.98691 | −0.187685 | ||||||||
\(707\) | −11.1926 | −0.420942 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.5065 | −0.957918 | −0.478959 | − | 0.877837i | \(-0.658986\pi\) | ||||
−0.478959 | + | 0.877837i | \(0.658986\pi\) | |||||||
\(710\) | −69.2912 | −2.60045 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.24842 | −0.196693 | ||||||||
\(713\) | −10.3578 | −0.387903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0715 | 0.900225 | ||||||||
\(716\) | 6.97199 | 0.260555 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.824054 | 0.0307534 | ||||||||
\(719\) | −39.6442 | −1.47848 | −0.739240 | − | 0.673442i | \(-0.764815\pi\) | ||||
−0.739240 | + | 0.673442i | \(0.764815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.42373 | 0.350958 | ||||||||
\(722\) | −24.4939 | −0.911570 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.87971 | 0.367177 | ||||||||
\(725\) | −18.3951 | −0.683175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1557 | 0.562094 | 0.281047 | − | 0.959694i | \(-0.409318\pi\) | ||||
0.281047 | + | 0.959694i | \(0.409318\pi\) | |||||||
\(728\) | −5.55606 | −0.205921 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.1034 | 0.521992 | ||||||||
\(731\) | 35.3097 | 1.30598 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.36022 | −0.308792 | −0.154396 | − | 0.988009i | \(-0.549343\pi\) | ||||
−0.154396 | + | 0.988009i | \(0.549343\pi\) | |||||||
\(734\) | 3.93525 | 0.145253 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.1890 | 0.375573 | ||||||||
\(737\) | 16.6547 | 0.613484 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.2136 | −0.890712 | −0.445356 | − | 0.895354i | \(-0.646923\pi\) | ||||
−0.445356 | + | 0.895354i | \(0.646923\pi\) | |||||||
\(740\) | −2.19131 | −0.0805541 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.9076 | −0.657410 | ||||||||
\(743\) | −28.8264 | −1.05754 | −0.528768 | − | 0.848766i | \(-0.677346\pi\) | ||||
−0.528768 | + | 0.848766i | \(0.677346\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9798 | 0.585454 | ||||||||
\(746\) | −46.5097 | −1.70284 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.78800 | 0.357885 | ||||||||
\(749\) | 6.56198 | 0.239770 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1065 | −0.405283 | −0.202641 | − | 0.979253i | \(-0.564953\pi\) | ||||
−0.202641 | + | 0.979253i | \(0.564953\pi\) | |||||||
\(752\) | −11.5532 | −0.421302 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.48338 | −0.345364 | ||||||||
\(755\) | −47.4497 | −1.72687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6799 | −0.569897 | −0.284949 | − | 0.958543i | \(-0.591977\pi\) | ||||
−0.284949 | + | 0.958543i | \(0.591977\pi\) | |||||||
\(758\) | 17.5083 | 0.635930 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.6732 | 0.568525 | ||||||||
\(761\) | −26.4513 | −0.958857 | −0.479429 | − | 0.877581i | \(-0.659156\pi\) | ||||
−0.479429 | + | 0.877581i | \(0.659156\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5034 | −0.561259 | ||||||||
\(764\) | −8.07743 | −0.292231 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.5996 | 0.961083 | ||||||||
\(767\) | 6.83739 | 0.246884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.07969 | −0.291361 | −0.145681 | − | 0.989332i | \(-0.546537\pi\) | ||||
−0.145681 | + | 0.989332i | \(0.546537\pi\) | |||||||
\(770\) | 15.8731 | 0.572028 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.6623 | −0.491718 | ||||||||
\(773\) | −42.2559 | −1.51984 | −0.759919 | − | 0.650018i | \(-0.774761\pi\) | ||||
−0.759919 | + | 0.650018i | \(0.774761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.5745 | 0.882742 | ||||||||
\(776\) | 1.61490 | 0.0579717 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8182 | 0.746368 | ||||||||
\(779\) | −6.80033 | −0.243647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.8654 | −1.21180 | ||||||||
\(782\) | −31.1352 | −1.11339 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.82349 | −0.172268 | ||||||||
\(785\) | −27.5613 | −0.983707 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.9478 | −1.17446 | −0.587231 | − | 0.809420i | \(-0.699782\pi\) | ||||
−0.587231 | + | 0.809420i | \(0.699782\pi\) | |||||||
\(788\) | 3.78616 | 0.134876 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.2162 | −0.612526 | ||||||||
\(791\) | −14.8683 | −0.528654 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.8936 | 0.706444 | ||||||||
\(794\) | −51.0879 | −1.81304 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0333 | 0.391067 | ||||||||
\(797\) | 10.7795 | 0.381831 | 0.190915 | − | 0.981607i | \(-0.438854\pi\) | ||||
0.190915 | + | 0.981607i | \(0.438854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.5155 | 0.513523 | ||||||||
\(800\) | −24.1741 | −0.854683 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −58.5168 | −2.06630 | ||||||||
\(803\) | 6.89292 | 0.243246 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.3489 | −0.399996 | ||||||||
\(806\) | 12.6691 | 0.446251 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.5304 | 0.898158 | ||||||||
\(809\) | 11.5058 | 0.404521 | 0.202260 | − | 0.979332i | \(-0.435171\pi\) | ||||
0.202260 | + | 0.979332i | \(0.435171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.28050 | 0.255653 | 0.127826 | − | 0.991797i | \(-0.459200\pi\) | ||||
0.127826 | + | 0.991797i | \(0.459200\pi\) | |||||||
\(812\) | −1.40558 | −0.0493261 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.76484 | −0.167008 | ||||||||
\(815\) | 40.3549 | 1.41357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.2834 | −0.394755 | ||||||||
\(818\) | −0.0300184 | −0.00104957 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.22468 | 0.252297 | ||||||||
\(821\) | 23.7546 | 0.829041 | 0.414521 | − | 0.910040i | \(-0.363949\pi\) | ||||
0.414521 | + | 0.910040i | \(0.363949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.5319 | 1.90086 | 0.950431 | − | 0.310936i | \(-0.100642\pi\) | ||||
0.950431 | + | 0.310936i | \(0.100642\pi\) | |||||||
\(824\) | −21.4956 | −0.748835 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.50868 | 0.156877 | ||||||||
\(827\) | −16.7507 | −0.582478 | −0.291239 | − | 0.956650i | \(-0.594068\pi\) | ||||
−0.291239 | + | 0.956650i | \(0.594068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2568 | 0.599355 | 0.299677 | − | 0.954041i | \(-0.403121\pi\) | ||||
0.299677 | + | 0.954041i | \(0.403121\pi\) | |||||||
\(830\) | 58.0944 | 2.01649 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.0353 | 0.382582 | ||||||||
\(833\) | 6.06028 | 0.209976 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.78509 | −0.304021 | ||||||||
\(836\) | −3.12779 | −0.108177 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.8004 | 1.13307 | ||||||||
\(839\) | 4.63330 | 0.159959 | 0.0799796 | − | 0.996797i | \(-0.474514\pi\) | ||||
0.0799796 | + | 0.996797i | \(0.474514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1245 | −0.797395 | ||||||||
\(842\) | 33.3057 | 1.14779 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.28726 | −0.250838 | ||||||||
\(845\) | −25.0740 | −0.862572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.24216 | −0.111402 | ||||||||
\(848\) | 53.7776 | 1.84673 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 73.8701 | 2.53372 | ||||||||
\(851\) | 3.40674 | 0.116782 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.0413 | −1.23403 | −0.617016 | − | 0.786951i | \(-0.711659\pi\) | ||||
−0.617016 | + | 0.786951i | \(0.711659\pi\) | |||||||
\(854\) | 13.1182 | 0.448894 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9679 | −0.511594 | ||||||||
\(857\) | 38.5445 | 1.31665 | 0.658327 | − | 0.752732i | \(-0.271264\pi\) | ||||
0.658327 | + | 0.752732i | \(0.271264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.3488 | −1.00137 | −0.500685 | − | 0.865630i | \(-0.666918\pi\) | ||||
−0.500685 | + | 0.865630i | \(0.666918\pi\) | |||||||
\(860\) | 11.9874 | 0.408768 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.0012 | −1.46463 | ||||||||
\(863\) | 2.89395 | 0.0985111 | 0.0492555 | − | 0.998786i | \(-0.484315\pi\) | ||||
0.0492555 | + | 0.998786i | \(0.484315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.2591 | 1.30085 | ||||||||
\(866\) | −11.9774 | −0.407007 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.87775 | 0.0637351 | ||||||||
\(869\) | −8.41427 | −0.285434 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5649 | 0.493512 | ||||||||
\(872\) | 35.3633 | 1.19755 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.94937 | 0.336542 | ||||||||
\(875\) | 9.18552 | 0.310527 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.8638 | −0.704519 | −0.352259 | − | 0.935902i | \(-0.614587\pi\) | ||||
−0.352259 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(878\) | 0.789471 | 0.0266434 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −47.6678 | −1.60688 | ||||||||
\(881\) | 37.4032 | 1.26015 | 0.630074 | − | 0.776535i | \(-0.283025\pi\) | ||||
0.630074 | + | 0.776535i | \(0.283025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.668193 | 0.0224865 | 0.0112433 | − | 0.999937i | \(-0.496421\pi\) | ||||
0.0112433 | + | 0.999937i | \(0.496421\pi\) | |||||||
\(884\) | 8.55981 | 0.287897 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.2746 | −0.882711 | ||||||||
\(887\) | −15.8528 | −0.532286 | −0.266143 | − | 0.963934i | \(-0.585749\pi\) | ||||
−0.266143 | + | 0.963934i | \(0.585749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 13.1128 | 0.439541 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.2151 | 0.542921 | ||||||||
\(893\) | −4.63849 | −0.155221 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.6598 | 1.42596 | ||||||||
\(896\) | 13.6478 | 0.455941 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.8631 | −1.13003 | ||||||||
\(899\) | −7.84931 | −0.261789 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −67.5666 | −2.25097 | ||||||||
\(902\) | 15.7095 | 0.523070 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33.9146 | 1.12798 | ||||||||
\(905\) | 60.4514 | 2.00947 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.26158 | −0.108299 | −0.0541496 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541496 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(908\) | 9.99005 | 0.331531 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.8814 | 0.460163 | ||||||||
\(911\) | −50.2514 | −1.66490 | −0.832451 | − | 0.554099i | \(-0.813063\pi\) | ||||
−0.832451 | + | 0.554099i | \(0.813063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.3931 | 0.939674 | ||||||||
\(914\) | 15.3912 | 0.509095 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.3024 | −0.340401 | ||||||||
\(917\) | 16.9371 | 0.559314 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1516 | 0.730713 | 0.365356 | − | 0.930868i | \(-0.380947\pi\) | ||||
0.365356 | + | 0.930868i | \(0.380947\pi\) | |||||||
\(920\) | 25.8869 | 0.853466 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41.7867 | 1.37617 | ||||||||
\(923\) | −29.6160 | −0.974822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.08269 | −0.265757 | ||||||||
\(926\) | −24.1442 | −0.793426 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.72141 | 0.253468 | ||||||||
\(929\) | −17.8794 | −0.586605 | −0.293302 | − | 0.956020i | \(-0.594754\pi\) | ||||
−0.293302 | + | 0.956020i | \(0.594754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93658 | −0.0634690 | ||||||||
\(932\) | −8.13477 | −0.266463 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.4514 | 0.374702 | ||||||||
\(935\) | 59.8903 | 1.95862 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.2241 | −1.34673 | −0.673366 | − | 0.739310i | \(-0.735152\pi\) | ||||
−0.673366 | + | 0.739310i | \(0.735152\pi\) | |||||||
\(938\) | 9.60429 | 0.313591 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.92794 | 0.160732 | ||||||||
\(941\) | −18.6993 | −0.609581 | −0.304791 | − | 0.952419i | \(-0.598586\pi\) | ||||
−0.304791 | + | 0.952419i | \(0.598586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.2319 | −0.365762 | ||||||||
\(944\) | −13.5398 | −0.440682 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.0658 | 0.847473 | ||||||||
\(947\) | −35.5049 | −1.15376 | −0.576878 | − | 0.816830i | \(-0.695729\pi\) | ||||
−0.576878 | + | 0.816830i | \(0.695729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.02799 | 0.195677 | ||||||||
\(950\) | −23.6055 | −0.765862 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.8235 | −0.448024 | ||||||||
\(953\) | −8.77896 | −0.284378 | −0.142189 | − | 0.989839i | \(-0.545414\pi\) | ||||
−0.142189 | + | 0.989839i | \(0.545414\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.4237 | −1.59931 | ||||||||
\(956\) | 12.4341 | 0.402146 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.48245 | 0.144821 | ||||||||
\(959\) | 8.14622 | 0.263055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5139 | −0.661738 | ||||||||
\(962\) | −4.16695 | −0.134348 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.65255 | −0.0854327 | ||||||||
\(965\) | −83.5963 | −2.69106 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.9391 | 0.898461 | 0.449230 | − | 0.893416i | \(-0.351698\pi\) | ||||
0.449230 | + | 0.893416i | \(0.351698\pi\) | |||||||
\(968\) | 7.39540 | 0.237697 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.03471 | −0.129547 | ||||||||
\(971\) | −59.3843 | −1.90573 | −0.952867 | − | 0.303389i | \(-0.901882\pi\) | ||||
−0.952867 | + | 0.303389i | \(0.901882\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0461 | −0.322063 | ||||||||
\(974\) | 51.8421 | 1.66113 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.3945 | −1.26099 | ||||||||
\(977\) | 15.7565 | 0.504094 | 0.252047 | − | 0.967715i | \(-0.418896\pi\) | ||||
0.252047 | + | 0.967715i | \(0.418896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.40873 | 0.204824 | ||||||||
\(980\) | 2.05743 | 0.0657221 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.3442 | 1.54272 | ||||||||
\(983\) | 38.6686 | 1.23334 | 0.616668 | − | 0.787223i | \(-0.288482\pi\) | ||||
0.616668 | + | 0.787223i | \(0.288482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.1665 | 0.738146 | ||||||||
\(986\) | −23.5947 | −0.751410 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.73532 | −0.0870221 | ||||||||
\(989\) | −18.6364 | −0.592603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.4853 | 1.31783 | 0.658913 | − | 0.752219i | \(-0.271017\pi\) | ||||
0.658913 | + | 0.752219i | \(0.271017\pi\) | |||||||
\(992\) | −10.3153 | −0.327510 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.5292 | −0.619429 | ||||||||
\(995\) | 67.5102 | 2.14022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.2478 | 1.90807 | 0.954034 | − | 0.299698i | \(-0.0968859\pi\) | ||||
0.954034 | + | 0.299698i | \(0.0968859\pi\) | |||||||
\(998\) | 51.1359 | 1.61868 | ||||||||
\(999\) | 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 | 8001.2.a.u.1.13 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.6 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.6 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.13 | 18 | 1.1 | even | 1 | trivial |