Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3680,2,Mod(1,3680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3680 = 2^{5} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3680.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: | \(29.3849479438\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.876604.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} + 8x^{2} + 18x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.895130\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3680.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.94825 | −1.70217 | −0.851087 | − | 0.525025i | \(-0.824056\pi\) | ||||
−0.851087 | + | 0.525025i | \(0.824056\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13809 | −0.808120 | −0.404060 | − | 0.914732i | \(-0.632401\pi\) | ||||
−0.404060 | + | 0.914732i | \(0.632401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.69219 | 1.89740 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.67228 | −1.71026 | −0.855129 | − | 0.518416i | \(-0.826522\pi\) | ||||
−0.855129 | + | 0.518416i | \(0.826522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.04212 | −1.39843 | −0.699217 | − | 0.714910i | \(-0.746468\pi\) | ||||
−0.699217 | + | 0.714910i | \(0.746468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.94825 | −0.761235 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.545195 | 0.132229 | 0.0661146 | − | 0.997812i | \(-0.478940\pi\) | ||||
0.0661146 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.74531 | −1.54748 | −0.773740 | − | 0.633503i | \(-0.781617\pi\) | ||||
−0.773740 | + | 0.633503i | \(0.781617\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.30361 | 1.37556 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.93725 | −1.52753 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.11378 | −0.949605 | −0.474803 | − | 0.880092i | \(-0.657481\pi\) | ||||
−0.474803 | + | 0.880092i | \(0.657481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.64464 | −0.834202 | −0.417101 | − | 0.908860i | \(-0.636954\pi\) | ||||
−0.417101 | + | 0.908860i | \(0.636954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.7233 | 2.91116 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.13809 | −0.361402 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.21748 | −0.364551 | −0.182275 | − | 0.983248i | \(-0.558346\pi\) | ||||
−0.182275 | + | 0.983248i | \(0.558346\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.8655 | 2.38038 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2264 | −1.59709 | −0.798547 | − | 0.601933i | \(-0.794397\pi\) | ||||
−0.798547 | + | 0.601933i | \(0.794397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5377 | 1.60698 | 0.803491 | − | 0.595317i | \(-0.202974\pi\) | ||||
0.803491 | + | 0.595317i | \(0.202974\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.69219 | 0.848542 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.61280 | 0.381116 | 0.190558 | − | 0.981676i | \(-0.438970\pi\) | ||||
0.190558 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.42859 | −0.346942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.60737 | −0.225077 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.67366 | 1.19142 | 0.595709 | − | 0.803200i | \(-0.296871\pi\) | ||||
0.595709 | + | 0.803200i | \(0.296871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.67228 | −0.764850 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.8869 | 2.63408 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.777152 | 0.101177 | 0.0505883 | − | 0.998720i | \(-0.483890\pi\) | ||||
0.0505883 | + | 0.998720i | \(0.483890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00137 | −0.896434 | −0.448217 | − | 0.893925i | \(-0.647941\pi\) | ||||
−0.448217 | + | 0.893925i | \(0.647941\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.1704 | −1.53332 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.04212 | −0.625399 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.27040 | −0.888221 | −0.444110 | − | 0.895972i | \(-0.646480\pi\) | ||||
−0.444110 | + | 0.895972i | \(0.646480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.94825 | −0.354928 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.40168 | 0.403705 | 0.201853 | − | 0.979416i | \(-0.435304\pi\) | ||||
0.201853 | + | 0.979416i | \(0.435304\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.34436 | −0.742552 | −0.371276 | − | 0.928523i | \(-0.621080\pi\) | ||||
−0.371276 | + | 0.928523i | \(0.621080\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.94825 | −0.340435 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.1278 | 1.38209 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.07651 | −0.458644 | −0.229322 | − | 0.973351i | \(-0.573651\pi\) | ||||
−0.229322 | + | 0.973351i | \(0.573651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.32446 | 0.702717 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.51409 | −0.166193 | −0.0830964 | − | 0.996542i | \(-0.526481\pi\) | ||||
−0.0830964 | + | 0.996542i | \(0.526481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.545195 | 0.0591347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.0767 | 1.61639 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.79799 | −1.03859 | −0.519293 | − | 0.854596i | \(-0.673805\pi\) | ||||
−0.519293 | + | 0.854596i | \(0.673805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.7805 | 1.13010 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.6936 | 1.41996 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.74531 | −0.692054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.60389 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32.2877 | −3.24504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6915 | −1.26285 | −0.631425 | − | 0.775437i | \(-0.717529\pi\) | ||||
−0.631425 | + | 0.775437i | \(0.717529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3271 | −1.01756 | −0.508778 | − | 0.860898i | \(-0.669903\pi\) | ||||
−0.508778 | + | 0.860898i | \(0.669903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.30361 | 0.615170 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9221 | −1.15255 | −0.576275 | − | 0.817256i | \(-0.695494\pi\) | ||||
−0.576275 | + | 0.817256i | \(0.695494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.06552 | −0.676754 | −0.338377 | − | 0.941011i | \(-0.609878\pi\) | ||||
−0.338377 | + | 0.941011i | \(0.609878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.53768 | 0.620529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.5134 | 1.83567 | 0.917835 | − | 0.396963i | \(-0.129936\pi\) | ||||
0.917835 | + | 0.396963i | \(0.129936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.7007 | −2.65338 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.16567 | −0.106857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.1748 | 1.92498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.1500 | 2.71853 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1007 | 1.25123 | 0.625616 | − | 0.780131i | \(-0.284848\pi\) | ||||
0.625616 | + | 0.780131i | \(0.284848\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −31.0677 | −2.73536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0470 | 1.66414 | 0.832071 | − | 0.554669i | \(-0.187155\pi\) | ||||
0.832071 | + | 0.554669i | \(0.187155\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4221 | 1.25055 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.93725 | −0.683130 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5943 | 0.905129 | 0.452565 | − | 0.891732i | \(-0.350509\pi\) | ||||
0.452565 | + | 0.891732i | \(0.350509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3997 | 1.22136 | 0.610681 | − | 0.791877i | \(-0.290896\pi\) | ||||
0.610681 | + | 0.791877i | \(0.290896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.70319 | −0.648725 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.6004 | 2.39168 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.11378 | −0.424676 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.16010 | 0.590555 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.81908 | −0.230948 | −0.115474 | − | 0.993311i | \(-0.536839\pi\) | ||||
−0.115474 | + | 0.993311i | \(0.536839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.704562 | −0.0573365 | −0.0286682 | − | 0.999589i | \(-0.509127\pi\) | ||||
−0.0286682 | + | 0.999589i | \(0.509127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.10335 | 0.250891 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.64464 | −0.373066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.0793 | −1.28326 | −0.641632 | − | 0.767012i | \(-0.721743\pi\) | ||||
−0.641632 | + | 0.767012i | \(0.721743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.5721 | −2.02800 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.13809 | −0.168505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1665 | −0.952951 | −0.476475 | − | 0.879188i | \(-0.658086\pi\) | ||||
−0.476475 | + | 0.879188i | \(0.658086\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.7233 | 1.30191 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.6031 | −1.74908 | −0.874538 | − | 0.484956i | \(-0.838835\pi\) | ||||
−0.874538 | + | 0.484956i | \(0.838835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4230 | 0.955617 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −38.3956 | −2.93618 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.50538 | 0.494595 | 0.247297 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247297 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.13809 | −0.161624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.29124 | −0.172220 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.90981 | −0.740694 | −0.370347 | − | 0.928893i | \(-0.620761\pi\) | ||||
−0.370347 | + | 0.928893i | \(0.620761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.95505 | 0.219647 | 0.109824 | − | 0.993951i | \(-0.464971\pi\) | ||||
0.109824 | + | 0.993951i | \(0.464971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.6418 | 1.52589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.21748 | −0.163032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.09250 | −0.226146 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.9705 | 1.23442 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.46155 | 0.395184 | 0.197592 | − | 0.980284i | \(-0.436688\pi\) | ||||
0.197592 | + | 0.980284i | \(0.436688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.778917 | −0.0560677 | −0.0280338 | − | 0.999607i | \(-0.508925\pi\) | ||||
−0.0280338 | + | 0.999607i | \(0.508925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.8655 | 1.06454 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9363 | 1.20666 | 0.603332 | − | 0.797490i | \(-0.293839\pi\) | ||||
0.603332 | + | 0.797490i | \(0.293839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.78489 | −0.480968 | −0.240484 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240484 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.4350 | 1.51191 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.9337 | 0.767395 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2264 | −0.714242 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.69219 | 0.395635 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.2613 | 2.64659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8197 | 1.15792 | 0.578959 | − | 0.815357i | \(-0.303459\pi\) | ||||
0.578959 | + | 0.815357i | \(0.303459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0290 | −0.687177 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.5377 | 0.718664 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.93063 | 0.674135 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.7048 | 1.26395 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.74894 | −0.184914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2013 | 1.35278 | 0.676391 | − | 0.736543i | \(-0.263543\pi\) | ||||
0.676391 | + | 0.736543i | \(0.263543\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.69219 | 0.379479 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.2353 | −1.34306 | −0.671532 | − | 0.740976i | \(-0.734363\pi\) | ||||
−0.671532 | + | 0.740976i | \(0.734363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2264 | 1.40268 | 0.701340 | − | 0.712827i | \(-0.252585\pi\) | ||||
0.701340 | + | 0.712827i | \(0.252585\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.7559 | −2.35256 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1243 | −0.859799 | −0.429900 | − | 0.902877i | \(-0.641451\pi\) | ||||
−0.429900 | + | 0.902877i | \(0.641451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.61280 | 0.170440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0186 | 0.780691 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.02691 | −0.519218 | −0.259609 | − | 0.965714i | \(-0.583594\pi\) | ||||
−0.259609 | + | 0.965714i | \(0.583594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.788006 | 0.0507599 | 0.0253800 | − | 0.999678i | \(-0.491920\pi\) | ||||
0.0253800 | + | 0.999678i | \(0.491920\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.16567 | 0.331378 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.42859 | −0.155157 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.0107 | 2.16405 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.46392 | 0.282889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.8373 | 1.94643 | 0.973216 | − | 0.229891i | \(-0.0738368\pi\) | ||||
0.973216 | + | 0.229891i | \(0.0738368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.67228 | −0.356613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.60737 | −0.100658 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2362 | 0.825649 | 0.412824 | − | 0.910811i | \(-0.364542\pi\) | ||||
0.412824 | + | 0.910811i | \(0.364542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.74115 | 0.294601 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.1086 | −1.80178 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.7546 | 1.64976 | 0.824879 | − | 0.565310i | \(-0.191243\pi\) | ||||
0.824879 | + | 0.565310i | \(0.191243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.67366 | 0.532818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.8870 | 1.76785 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.2672 | 1.41863 | 0.709313 | − | 0.704893i | \(-0.249005\pi\) | ||||
0.709313 | + | 0.704893i | \(0.249005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.119207 | −0.00724133 | −0.00362067 | − | 0.999993i | \(-0.501152\pi\) | ||||
−0.00362067 | + | 0.999993i | \(0.501152\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −31.7836 | −1.92363 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.67228 | −0.342051 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.49882 | 0.390476 | 0.195238 | − | 0.980756i | \(-0.437452\pi\) | ||||
0.195238 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.4382 | −1.58281 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.59753 | 0.214610 | 0.107305 | − | 0.994226i | \(-0.465778\pi\) | ||||
0.107305 | + | 0.994226i | \(0.465778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.7552 | −1.11488 | −0.557439 | − | 0.830218i | \(-0.688216\pi\) | ||||
−0.557439 | + | 0.830218i | \(0.688216\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.8869 | 1.17800 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.8649 | 1.29064 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7028 | −0.982515 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5734 | −0.795688 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.19938 | 0.0700687 | 0.0350344 | − | 0.999386i | \(-0.488846\pi\) | ||||
0.0350344 | + | 0.999386i | \(0.488846\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.777152 | 0.0452476 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 45.0223 | 2.61246 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.04212 | −0.291594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5305 | −1.29863 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.4177 | 2.14959 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00137 | −0.400898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.14771 | −0.465014 | −0.232507 | − | 0.972595i | \(-0.574693\pi\) | ||||
−0.232507 | + | 0.972595i | \(0.574693\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.4468 | 1.73206 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.7342 | 1.91289 | 0.956447 | − | 0.291907i | \(-0.0942898\pi\) | ||||
0.956447 | + | 0.291907i | \(0.0942898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.24043 | 0.183160 | 0.0915799 | − | 0.995798i | \(-0.470808\pi\) | ||||
0.0915799 | + | 0.995798i | \(0.470808\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.1704 | −0.685724 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.89626 | −0.331167 | −0.165584 | − | 0.986196i | \(-0.552951\pi\) | ||||
−0.165584 | + | 0.986196i | \(0.552951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.0068 | 1.62407 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.1492 | 1.96184 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.67751 | −0.204622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.04212 | −0.279687 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.8309 | 1.15195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.58638 | −0.307987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.57807 | −0.0867383 | −0.0433691 | − | 0.999059i | \(-0.513809\pi\) | ||||
−0.0433691 | + | 0.999059i | \(0.513809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6223 | −0.691698 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.27040 | −0.397224 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.55835 | −0.0848888 | −0.0424444 | − | 0.999099i | \(-0.513515\pi\) | ||||
−0.0424444 | + | 0.999099i | \(0.513515\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −57.5305 | −3.12463 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.3457 | 1.42670 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1591 | 1.08849 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.94825 | −0.158729 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.4997 | −1.74468 | −0.872339 | − | 0.488902i | \(-0.837397\pi\) | ||||
−0.872339 | + | 0.488902i | \(0.837397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9841 | 1.12325 | 0.561626 | − | 0.827391i | \(-0.310176\pi\) | ||||
0.561626 | + | 0.827391i | \(0.310176\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.0206 | 2.13614 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.2614 | −1.61065 | −0.805327 | − | 0.592831i | \(-0.798010\pi\) | ||||
−0.805327 | + | 0.592831i | \(0.798010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.40168 | 0.180543 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.43670 | 0.181889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.8907 | 0.680347 | 0.340173 | − | 0.940363i | \(-0.389514\pi\) | ||||
0.340173 | + | 0.940363i | \(0.389514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4992 | 1.39470 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −62.4286 | −3.27665 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.34436 | −0.332079 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.49484 | −0.495627 | −0.247813 | − | 0.968808i | \(-0.579712\pi\) | ||||
−0.247813 | + | 0.968808i | \(0.579712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −58.2105 | −3.03032 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.5450 | −0.962809 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3732 | −0.795996 | −0.397998 | − | 0.917386i | \(-0.630295\pi\) | ||||
−0.397998 | + | 0.917386i | \(0.630295\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.94825 | −0.152247 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.7843 | 1.32796 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.7952 | −1.78731 | −0.893655 | − | 0.448756i | \(-0.851867\pi\) | ||||
−0.893655 | + | 0.448756i | \(0.851867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −41.5723 | −2.12982 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.6026 | 1.35933 | 0.679666 | − | 0.733522i | \(-0.262125\pi\) | ||||
0.679666 | + | 0.733522i | \(0.262125\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1278 | 0.618091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 59.9825 | 3.04908 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.0795 | −1.67720 | −0.838598 | − | 0.544751i | \(-0.816624\pi\) | ||||
−0.838598 | + | 0.544751i | \(0.816624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.545195 | 0.0275717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −56.1553 | −2.83266 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.07651 | −0.205112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8019 | 1.69647 | 0.848235 | − | 0.529620i | \(-0.177666\pi\) | ||||
0.848235 | + | 0.529620i | \(0.177666\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −42.5198 | −2.12865 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.1390 | −1.15551 | −0.577754 | − | 0.816211i | \(-0.696071\pi\) | ||||
−0.577754 | + | 0.816211i | \(0.696071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.4188 | 1.16658 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.32446 | 0.314265 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.5782 | 0.623476 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.9838 | −1.13648 | −0.568239 | − | 0.822864i | \(-0.692375\pi\) | ||||
−0.568239 | + | 0.822864i | \(0.692375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.2346 | −1.54069 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.66162 | −0.0817629 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.51409 | −0.0743237 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.4538 | −2.07897 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.5935 | 1.15262 | 0.576308 | − | 0.817233i | \(-0.304493\pi\) | ||||
0.576308 | + | 0.817233i | \(0.304493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0768 | 1.70954 | 0.854769 | − | 0.519009i | \(-0.173699\pi\) | ||||
0.854769 | + | 0.519009i | \(0.173699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.8725 | 0.723128 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.545195 | 0.0264458 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9695 | 0.724427 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −84.3210 | −4.07106 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0434 | −0.869119 | −0.434559 | − | 0.900643i | \(-0.643096\pi\) | ||||
−0.434559 | + | 0.900643i | \(0.643096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0698 | −1.06061 | −0.530304 | − | 0.847808i | \(-0.677922\pi\) | ||||
−0.530304 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.0767 | 0.722873 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.74531 | −0.322672 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0314 | 1.00377 | 0.501887 | − | 0.864933i | \(-0.332639\pi\) | ||||
0.501887 | + | 0.864933i | \(0.332639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8240 | −0.658286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.4291 | −0.638037 | −0.319019 | − | 0.947748i | \(-0.603353\pi\) | ||||
−0.319019 | + | 0.947748i | \(0.603353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.79799 | −0.464469 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.31135 | 0.393113 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.57879 | −0.310472 | −0.155236 | − | 0.987877i | \(-0.549614\pi\) | ||||
−0.155236 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.0069 | 2.73144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.07723 | 0.0975966 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7805 | 0.505397 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.3604 | 1.88798 | 0.943990 | − | 0.329973i | \(-0.107040\pi\) | ||||
0.943990 | + | 0.329973i | \(0.107040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.32735 | −0.201983 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.83330 | −0.178534 | −0.0892672 | − | 0.996008i | \(-0.528453\pi\) | ||||
−0.0892672 | + | 0.996008i | \(0.528453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6251 | −1.46974 | −0.734871 | − | 0.678207i | \(-0.762757\pi\) | ||||
−0.734871 | + | 0.678207i | \(0.762757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6936 | 0.635024 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3994 | 0.481225 | 0.240612 | − | 0.970621i | \(-0.422652\pi\) | ||||
0.240612 | + | 0.970621i | \(0.422652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5447 | 0.717789 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 47.4057 | 2.18434 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −59.7727 | −2.74835 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.74531 | −0.309496 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 49.3721 | 2.26059 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.7475 | −1.72473 | −0.862365 | − | 0.506288i | \(-0.831017\pi\) | ||||
−0.862365 | + | 0.506288i | \(0.831017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1808 | 0.509800 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.30361 | 0.286824 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.60389 | 0.209052 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.15350 | −0.369470 | −0.184735 | − | 0.982788i | \(-0.559143\pi\) | ||||
−0.184735 | + | 0.982788i | \(0.559143\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.8698 | 1.62209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.9268 | −1.12493 | −0.562466 | − | 0.826820i | \(-0.690147\pi\) | ||||
−0.562466 | + | 0.826820i | \(0.690147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.78801 | −0.125565 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.2877 | −1.45122 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.27309 | −0.326243 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.59825 | −0.384911 | −0.192455 | − | 0.981306i | \(-0.561645\pi\) | ||||
−0.192455 | + | 0.981306i | \(0.561645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 66.6395 | 2.97723 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.6459 | −1.76772 | −0.883861 | − | 0.467750i | \(-0.845065\pi\) | ||||
−0.883861 | + | 0.467750i | \(0.845065\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.6915 | −0.564763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.6262 | −1.62663 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.7612 | −1.31914 | −0.659572 | − | 0.751642i | \(-0.729262\pi\) | ||||
−0.659572 | + | 0.751642i | \(0.729262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5648 | 0.600071 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 53.5393 | 2.36382 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3271 | −0.455065 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.8205 | −0.651806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.1795 | −0.841886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.9544 | −1.35614 | −0.678069 | − | 0.734998i | \(-0.737183\pi\) | ||||
−0.678069 | + | 0.734998i | \(0.737183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3392 | −1.23919 | −0.619593 | − | 0.784923i | \(-0.712702\pi\) | ||||
−0.619593 | + | 0.784923i | \(0.712702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.30361 | 0.275112 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.53223 | −0.110306 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.42370 | 0.191972 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.5627 | 2.23343 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9221 | −0.515436 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.2166 | 1.26079 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.7757 | 0.593360 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72062 | 0.116969 | 0.0584844 | − | 0.998288i | \(-0.481373\pi\) | ||||
0.0584844 | + | 0.998288i | \(0.481373\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.71224 | −0.373878 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.06552 | −0.302653 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8646 | 1.49070 | 0.745352 | − | 0.666671i | \(-0.232282\pi\) | ||||
0.745352 | + | 0.666671i | \(0.232282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.8532 | −1.70089 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4940 | 1.46950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71593 | 0.370639 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.53768 | 0.277509 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.424068 | −0.0179684 | −0.00898418 | − | 0.999960i | \(-0.502860\pi\) | ||||
−0.00898418 | + | 0.999960i | \(0.502860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.1323 | −2.24726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.11746 | 0.384940 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.2454 | 1.56971 | 0.784853 | − | 0.619682i | \(-0.212738\pi\) | ||||
0.784853 | + | 0.619682i | \(0.212738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.5134 | 0.820936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.5222 | −0.567880 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.31757 | 0.0971574 | 0.0485787 | − | 0.998819i | \(-0.484531\pi\) | ||||
0.0485787 | + | 0.998819i | \(0.484531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6079 | 1.40645 | 0.703224 | − | 0.710968i | \(-0.251743\pi\) | ||||
0.703224 | + | 0.710968i | \(0.251743\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.1020 | −0.672672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.59589 | 0.316221 | 0.158110 | − | 0.987421i | \(-0.449460\pi\) | ||||
0.158110 | + | 0.987421i | \(0.449460\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.29644 | 0.0954369 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.23725 | 0.134304 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.1994 | −2.03763 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.7007 | −1.18663 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.6838 | −1.30773 | −0.653864 | − | 0.756612i | \(-0.726853\pi\) | ||||
−0.653864 | + | 0.756612i | \(0.726853\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3295 | 1.29091 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.9326 | −2.05395 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.4910 | −1.37531 | −0.687656 | − | 0.726037i | \(-0.741360\pi\) | ||||
−0.687656 | + | 0.726037i | \(0.741360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.16567 | −0.0477879 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.0036 | 0.818691 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.59861 | 0.351330 | 0.175665 | − | 0.984450i | \(-0.443792\pi\) | ||||
0.175665 | + | 0.984450i | \(0.443792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.84676 | 0.116122 | 0.0580608 | − | 0.998313i | \(-0.481508\pi\) | ||||
0.0580608 | + | 0.998313i | \(0.481508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.3845 | −1.68531 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1748 | 0.860877 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.1716 | −1.34639 | −0.673197 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673197 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.2353 | −1.30624 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.1741 | −0.532965 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.2327 | 1.74615 | 0.873076 | − | 0.487583i | \(-0.162121\pi\) | ||||
0.873076 | + | 0.487583i | \(0.162121\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.1500 | 1.21576 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.55753 | −0.223738 | −0.111869 | − | 0.993723i | \(-0.535684\pi\) | ||||
−0.111869 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.89126 | 0.116210 | 0.0581048 | − | 0.998310i | \(-0.481494\pi\) | ||||
0.0581048 | + | 0.998310i | \(0.481494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.93725 | −0.318511 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.9489 | 0.839302 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −112.804 | −4.50496 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.20896 | −0.0482043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2178 | 0.406763 | 0.203381 | − | 0.979100i | \(-0.434807\pi\) | ||||
0.203381 | + | 0.979100i | \(0.434807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −49.5888 | −1.97098 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.1007 | 0.559568 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2453 | 0.485175 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.3630 | 0.765989 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.0639 | −1.10846 | −0.554229 | − | 0.832364i | \(-0.686987\pi\) | ||||
−0.554229 | + | 0.832364i | \(0.686987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4578 | −0.688467 | −0.344234 | − | 0.938884i | \(-0.611861\pi\) | ||||
−0.344234 | + | 0.938884i | \(0.611861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.0677 | −1.22329 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.1560 | 1.81458 | 0.907290 | − | 0.420506i | \(-0.138147\pi\) | ||||
0.907290 | + | 0.420506i | \(0.138147\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.40823 | −0.173038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.2780 | −1.14750 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.6636 | 1.31736 | 0.658680 | − | 0.752423i | \(-0.271115\pi\) | ||||
0.658680 | + | 0.752423i | \(0.271115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.0470 | 0.744227 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.1133 | −1.40891 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.63197 | −0.180436 | −0.0902180 | − | 0.995922i | \(-0.528756\pi\) | ||||
−0.0902180 | + | 0.995922i | \(0.528756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7286 | 0.456191 | 0.228095 | − | 0.973639i | \(-0.426750\pi\) | ||||
0.228095 | + | 0.973639i | \(0.426750\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.10457 | 0.314755 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4221 | 0.559263 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.11378 | −0.198006 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −59.5587 | −2.30267 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7138 | 1.53313 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.4703 | −1.63711 | −0.818555 | − | 0.574428i | \(-0.805224\pi\) | ||||
−0.818555 | + | 0.574428i | \(0.805224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.93725 | −0.305505 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.4373 | −0.785471 | −0.392735 | − | 0.919651i | \(-0.628471\pi\) | ||||
−0.392735 | + | 0.919651i | \(0.628471\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.84350 | −0.377759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 59.6588 | 2.28613 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.289606 | 0.0110815 | 0.00554073 | − | 0.999985i | \(-0.498236\pi\) | ||||
0.00554073 | + | 0.999985i | \(0.498236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.5943 | 0.404786 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −62.5808 | −2.38761 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.7337 | −1.66612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.96253 | −0.0746583 | −0.0373291 | − | 0.999303i | \(-0.511885\pi\) | ||||
−0.0373291 | + | 0.999303i | \(0.511885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 69.0339 | 2.62238 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.3997 | 0.546210 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.57537 | −0.211182 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.6936 | 1.46353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.2259 | −1.40600 | −0.703001 | − | 0.711189i | \(-0.748157\pi\) | ||||
−0.703001 | + | 0.711189i | \(0.748157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.9576 | 0.564136 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.70319 | −0.290119 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.1355 | 1.02053 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1006 | −0.679782 | −0.339891 | − | 0.940465i | \(-0.610390\pi\) | ||||
−0.339891 | + | 0.940465i | \(0.610390\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.2043 | −0.870229 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.64464 | −0.173943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.6004 | 1.06959 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.6654 | 0.883799 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.5147 | −1.10071 | −0.550357 | − | 0.834930i | \(-0.685508\pi\) | ||||
−0.550357 | + | 0.834930i | \(0.685508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0801 | 0.822307 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.32324 | −0.0864023 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.11378 | −0.189921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.92069 | −0.108322 | −0.0541611 | − | 0.998532i | \(-0.517248\pi\) | ||||
−0.0541611 | + | 0.998532i | \(0.517248\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.2031 | −1.26678 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.74509 | 0.212490 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8857 | −0.845304 | −0.422652 | − | 0.906292i | \(-0.638901\pi\) | ||||
−0.422652 | + | 0.906292i | \(0.638901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.16010 | 0.264104 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.2398 | 1.51909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.48850 | −0.128327 | −0.0641633 | − | 0.997939i | \(-0.520438\pi\) | ||||
−0.0641633 | + | 0.997939i | \(0.520438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −100.272 | −3.68359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.54065 | 0.350013 | 0.175006 | − | 0.984567i | \(-0.444005\pi\) | ||||
0.175006 | + | 0.984567i | \(0.444005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.81908 | −0.103283 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.61848 | −0.315334 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.4904 | 0.931398 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.84212 | −0.249673 | −0.124836 | − | 0.992177i | \(-0.539841\pi\) | ||||
−0.124836 | + | 0.992177i | \(0.539841\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −90.9161 | −3.31317 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.704562 | −0.0256416 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.2647 | 1.46344 | 0.731722 | − | 0.681603i | \(-0.238717\pi\) | ||||
0.731722 | + | 0.681603i | \(0.238717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.7233 | 0.607018 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.1615 | −1.67335 | −0.836677 | − | 0.547697i | \(-0.815505\pi\) | ||||
−0.836677 | + | 0.547697i | \(0.815505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1067 | 0.546898 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.10335 | 0.112202 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.91850 | −0.141489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.4559 | 1.81949 | 0.909744 | − | 0.415171i | \(-0.136278\pi\) | ||||
0.909744 | + | 0.415171i | \(0.136278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.0235 | −1.40540 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.52270 | 0.270573 | 0.135286 | − | 0.990807i | \(-0.456805\pi\) | ||||
0.135286 | + | 0.990807i | \(0.456805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.64464 | −0.166840 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.9781 | −0.501462 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 68.9802 | 2.47147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2953 | −0.690440 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.5894 | 1.45055 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0793 | −0.573893 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.7815 | −0.598195 | −0.299098 | − | 0.954223i | \(-0.596686\pi\) | ||||
−0.299098 | + | 0.954223i | \(0.596686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.8792 | −2.80817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.7214 | −1.48344 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.3018 | 1.25360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.5721 | −0.906950 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.89231 | 0.314982 | 0.157491 | − | 0.987520i | \(-0.449659\pi\) | ||||
0.157491 | + | 0.987520i | \(0.449659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.42448 | 0.0503946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −55.7720 | −1.97061 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.9870 | 1.26995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.13809 | −0.0753576 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −68.5976 | −2.41475 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6388 | 1.11236 | 0.556180 | − | 0.831062i | \(-0.312266\pi\) | ||||
0.556180 | + | 0.831062i | \(0.312266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.2436 | −0.429932 | −0.214966 | − | 0.976622i | \(-0.568964\pi\) | ||||
−0.214966 | + | 0.976622i | \(0.568964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.351453 | 0.0123260 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1665 | −0.426173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −71.0799 | −2.48677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 61.3646 | 2.14425 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.9559 | 1.88307 | 0.941536 | − | 0.336912i | \(-0.109382\pi\) | ||||
0.941536 | + | 0.336912i | \(0.109382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.8887 | −0.937282 | −0.468641 | − | 0.883389i | \(-0.655256\pi\) | ||||
−0.468641 | + | 0.883389i | \(0.655256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.7233 | 0.582231 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6209 | 0.369324 | 0.184662 | − | 0.982802i | \(-0.440881\pi\) | ||||
0.184662 | + | 0.982802i | \(0.440881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.6878 | −0.822710 | −0.411355 | − | 0.911475i | \(-0.634944\pi\) | ||||
−0.411355 | + | 0.911475i | \(0.634944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.1602 | −0.664658 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.32406 | −0.0458758 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.6031 | −0.782211 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.8657 | 1.27426 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.7151 | −0.404449 | −0.202225 | − | 0.979339i | \(-0.564817\pi\) | ||||
−0.202225 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.84925 | −0.0982499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6064 | −0.365304 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4230 | 0.427365 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.2735 | −1.55562 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.2949 | 1.89772 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.21748 | −0.0760141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8775 | 1.26266 | 0.631331 | − | 0.775513i | \(-0.282509\pi\) | ||||
0.631331 | + | 0.775513i | \(0.282509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.3956 | −1.31310 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.6431 | −1.55914 | −0.779569 | − | 0.626317i | \(-0.784562\pi\) | ||||
−0.779569 | + | 0.626317i | \(0.784562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.3689 | −1.10441 | −0.552206 | − | 0.833708i | \(-0.686214\pi\) | ||||
−0.552206 | + | 0.833708i | \(0.686214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −64.4632 | −2.19690 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.9540 | 0.849443 | 0.424722 | − | 0.905324i | \(-0.360372\pi\) | ||||
0.424722 | + | 0.905324i | \(0.360372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.50538 | 0.221190 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 49.2440 | 1.67241 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.1231 | 0.784399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.6583 | 1.24212 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.2062 | 0.886946 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.13809 | −0.0722805 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.1405 | −1.25415 | −0.627073 | − | 0.778960i | \(-0.715747\pi\) | ||||
−0.627073 | + | 0.778960i | \(0.715747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.53608 | −0.119269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1005 | 0.710894 | 0.355447 | − | 0.934696i | \(-0.384329\pi\) | ||||
0.355447 | + | 0.934696i | \(0.384329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.57577 | −0.120334 | −0.0601672 | − | 0.998188i | \(-0.519163\pi\) | ||||
−0.0601672 | + | 0.998188i | \(0.519163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.29124 | −0.0770192 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.6213 | 1.83401 | 0.917003 | − | 0.398881i | \(-0.130601\pi\) | ||||
0.917003 | + | 0.398881i | \(0.130601\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.1484 | −1.01115 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.8741 | −1.20183 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.6241 | −0.589769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.90981 | −0.331248 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8655 | 0.496343 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.7517 | 0.792162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.72883 | 0.157540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 66.4255 | 2.21050 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.95505 | 0.0982293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5957 | 1.28155 | 0.640775 | − | 0.767729i | \(-0.278613\pi\) | ||||
0.640775 | + | 0.767729i | \(0.278613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −72.2423 | −2.39613 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.81812 | 0.325289 | 0.162644 | − | 0.986685i | \(-0.447998\pi\) | ||||
0.162644 | + | 0.986685i | \(0.447998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.58834 | 0.284233 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.6418 | 0.682397 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.7241 | −1.34483 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.64000 | 0.285007 | 0.142504 | − | 0.989794i | \(-0.454485\pi\) | ||||
0.142504 | + | 0.989794i | \(0.454485\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0215 | 0.791535 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.1517 | −0.564555 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.21748 | −0.0729102 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −58.7836 | −1.93071 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.4687 | −0.704367 | −0.352183 | − | 0.935931i | \(-0.614561\pi\) | ||||
−0.352183 | + | 0.935931i | \(0.614561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3816 | 0.536886 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −99.4570 | −3.25608 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.09250 | −0.101136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9844 | 0.685531 | 0.342765 | − | 0.939421i | \(-0.388636\pi\) | ||||
0.342765 | + | 0.939421i | \(0.388636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.55360 | −0.311770 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.4942 | −0.863687 | −0.431844 | − | 0.901948i | \(-0.642137\pi\) | ||||
−0.431844 | + | 0.901948i | \(0.642137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2264 | −0.333017 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.9705 | 0.552051 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.9572 | −0.421053 | −0.210527 | − | 0.977588i | \(-0.567518\pi\) | ||||
−0.210527 | + | 0.977588i | \(0.567518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9891 | 1.03841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3837 | 0.563704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.87158 | 0.125413 | 0.0627064 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627064 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.46155 | 0.176732 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −85.5194 | −2.76445 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.6514 | −0.731453 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.42733 | −0.304108 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −67.8626 | −2.18684 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.778917 | −0.0250742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.7264 | 1.11673 | 0.558363 | − | 0.829597i | \(-0.311430\pi\) | ||||
0.558363 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.8422 | 0.348302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4154 | −0.334245 | −0.167123 | − | 0.985936i | \(-0.553448\pi\) | ||||
−0.167123 | + | 0.985936i | \(0.553448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.7877 | −0.987008 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.8655 | 0.476076 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.6802 | −1.30148 | −0.650738 | − | 0.759303i | \(-0.725540\pi\) | ||||
−0.650738 | + | 0.759303i | \(0.725540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55.5770 | 1.77625 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.2183 | −1.28407 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5016 | 0.717688 | 0.358844 | − | 0.933397i | \(-0.383171\pi\) | ||||
0.358844 | + | 0.933397i | \(0.383171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.9363 | 0.539637 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.4701 | 0.524248 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.5377 | 0.335079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.71659 | −0.276892 | −0.138446 | − | 0.990370i | \(-0.544211\pi\) | ||||
−0.138446 | + | 0.990370i | \(0.544211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.65253 | 0.147644 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.78489 | −0.215095 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.1186 | 0.668832 | 0.334416 | − | 0.942426i | \(-0.391461\pi\) | ||||
0.334416 | + | 0.942426i | \(0.391461\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.6007 | 0.556861 |
(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 | 3680.2.a.x.1.1 | ✓ | 5 | |
4.3 | odd | 2 | 3680.2.a.ba.1.5 | yes | 5 | ||
8.3 | odd | 2 | 7360.2.a.cl.1.1 | 5 | |||
8.5 | even | 2 | 7360.2.a.cq.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.x.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
3680.2.a.ba.1.5 | yes | 5 | 4.3 | odd | 2 | ||
7360.2.a.cl.1.1 | 5 | 8.3 | odd | 2 | |||
7360.2.a.cq.1.5 | 5 | 8.5 | even | 2 |