Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.07227\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.756417 | 0.534868 | 0.267434 | − | 0.963576i | \(-0.413824\pi\) | ||||
0.267434 | + | 0.963576i | \(0.413824\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.42783 | −0.713916 | ||||||||
\(5\) | −0.386144 | −0.172689 | −0.0863445 | − | 0.996265i | \(-0.527519\pi\) | ||||
−0.0863445 | + | 0.996265i | \(0.527519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.194914 | 0.0736704 | 0.0368352 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368352 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(8\) | −2.59287 | −0.916719 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.292086 | −0.0923657 | ||||||||
\(11\) | −2.36326 | −0.712549 | −0.356275 | − | 0.934381i | \(-0.615953\pi\) | ||||
−0.356275 | + | 0.934381i | \(0.615953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.22636 | −0.340131 | −0.170065 | − | 0.985433i | \(-0.554398\pi\) | ||||
−0.170065 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(14\) | 0.147436 | 0.0394039 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.894372 | 0.223593 | ||||||||
\(17\) | 5.04830 | 1.22439 | 0.612197 | − | 0.790705i | \(-0.290286\pi\) | ||||
0.612197 | + | 0.790705i | \(0.290286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24460 | 0.973779 | 0.486890 | − | 0.873464i | \(-0.338131\pi\) | ||||
0.486890 | + | 0.873464i | \(0.338131\pi\) | |||||||
\(20\) | 0.551349 | 0.123285 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.78761 | −0.381120 | ||||||||
\(23\) | −1.53457 | −0.319980 | −0.159990 | − | 0.987119i | \(-0.551146\pi\) | ||||
−0.159990 | + | 0.987119i | \(0.551146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.85089 | −0.970179 | ||||||||
\(26\) | −0.927639 | −0.181925 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.278304 | −0.0525945 | ||||||||
\(29\) | 7.31602 | 1.35855 | 0.679275 | − | 0.733883i | \(-0.262294\pi\) | ||||
0.679275 | + | 0.733883i | \(0.262294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.33893 | 0.599690 | 0.299845 | − | 0.953988i | \(-0.403065\pi\) | ||||
0.299845 | + | 0.953988i | \(0.403065\pi\) | |||||||
\(32\) | 5.86226 | 1.03631 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.81863 | 0.654889 | ||||||||
\(35\) | −0.0752647 | −0.0127221 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.17138 | −0.356973 | −0.178487 | − | 0.983942i | \(-0.557120\pi\) | ||||
−0.178487 | + | 0.983942i | \(0.557120\pi\) | |||||||
\(38\) | 3.21069 | 0.520843 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00122 | 0.158307 | ||||||||
\(41\) | 1.04840 | 0.163733 | 0.0818663 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818663 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53067 | −0.233425 | −0.116712 | − | 0.993166i | \(-0.537236\pi\) | ||||
−0.116712 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(44\) | 3.37434 | 0.508701 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.16077 | −0.171147 | ||||||||
\(47\) | 1.08422 | 0.158150 | 0.0790748 | − | 0.996869i | \(-0.474803\pi\) | ||||
0.0790748 | + | 0.996869i | \(0.474803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96201 | −0.994573 | ||||||||
\(50\) | −3.66930 | −0.518917 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.75104 | 0.242825 | ||||||||
\(53\) | −1.55308 | −0.213332 | −0.106666 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106666 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.912558 | 0.123049 | ||||||||
\(56\) | −0.505386 | −0.0675350 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.53396 | 0.726645 | ||||||||
\(59\) | −14.8451 | −1.93267 | −0.966334 | − | 0.257293i | \(-0.917170\pi\) | ||||
−0.966334 | + | 0.257293i | \(0.917170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.45056 | −0.697873 | −0.348936 | − | 0.937146i | \(-0.613457\pi\) | ||||
−0.348936 | + | 0.937146i | \(0.613457\pi\) | |||||||
\(62\) | 2.52563 | 0.320755 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.64557 | 0.330697 | ||||||||
\(65\) | 0.473551 | 0.0587368 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3202 | −1.38298 | −0.691490 | − | 0.722386i | \(-0.743045\pi\) | ||||
−0.691490 | + | 0.722386i | \(0.743045\pi\) | |||||||
\(68\) | −7.20814 | −0.874115 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0569315 | −0.00680462 | ||||||||
\(71\) | 11.4236 | 1.35573 | 0.677864 | − | 0.735187i | \(-0.262906\pi\) | ||||
0.677864 | + | 0.735187i | \(0.262906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.902229 | −0.105598 | −0.0527990 | − | 0.998605i | \(-0.516814\pi\) | ||||
−0.0527990 | + | 0.998605i | \(0.516814\pi\) | |||||||
\(74\) | −1.64247 | −0.190933 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.06059 | −0.695197 | ||||||||
\(77\) | −0.460631 | −0.0524938 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7431 | −1.43371 | −0.716853 | − | 0.697225i | \(-0.754418\pi\) | ||||
−0.716853 | + | 0.697225i | \(0.754418\pi\) | |||||||
\(80\) | −0.345356 | −0.0386120 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.793029 | 0.0875753 | ||||||||
\(83\) | −6.10241 | −0.669826 | −0.334913 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334913 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.94937 | −0.211439 | ||||||||
\(86\) | −1.15782 | −0.124851 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.12763 | 0.653207 | ||||||||
\(89\) | −6.44432 | −0.683097 | −0.341548 | − | 0.939864i | \(-0.610951\pi\) | ||||
−0.341548 | + | 0.939864i | \(0.610951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.239034 | −0.0250576 | ||||||||
\(92\) | 2.19111 | 0.228439 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.820122 | 0.0845892 | ||||||||
\(95\) | −1.63903 | −0.168161 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9886 | −1.31879 | −0.659394 | − | 0.751797i | \(-0.729187\pi\) | ||||
−0.659394 | + | 0.751797i | \(0.729187\pi\) | |||||||
\(98\) | −5.26618 | −0.531965 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.92626 | 0.692626 | ||||||||
\(101\) | −6.18139 | −0.615072 | −0.307536 | − | 0.951537i | \(-0.599504\pi\) | ||||
−0.307536 | + | 0.951537i | \(0.599504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.78250 | 0.766833 | 0.383416 | − | 0.923576i | \(-0.374747\pi\) | ||||
0.383416 | + | 0.923576i | \(0.374747\pi\) | |||||||
\(104\) | 3.17979 | 0.311804 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.17477 | −0.114104 | ||||||||
\(107\) | 8.18217 | 0.791000 | 0.395500 | − | 0.918466i | \(-0.370571\pi\) | ||||
0.395500 | + | 0.918466i | \(0.370571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.32486 | −0.510029 | −0.255015 | − | 0.966937i | \(-0.582080\pi\) | ||||
−0.255015 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(110\) | 0.690275 | 0.0658151 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.174325 | 0.0164722 | ||||||||
\(113\) | 3.60573 | 0.339199 | 0.169599 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169599 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.592565 | 0.0552570 | ||||||||
\(116\) | −10.4461 | −0.969892 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2291 | −1.03372 | ||||||||
\(119\) | 0.983983 | 0.0902016 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.41501 | −0.492274 | ||||||||
\(122\) | −4.12290 | −0.373270 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.76744 | −0.428129 | ||||||||
\(125\) | 3.80386 | 0.340228 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8352 | −1.58262 | −0.791308 | − | 0.611418i | \(-0.790599\pi\) | ||||
−0.791308 | + | 0.611418i | \(0.790599\pi\) | |||||||
\(128\) | −9.72337 | −0.859432 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.358202 | 0.0314164 | ||||||||
\(131\) | 12.1841 | 1.06453 | 0.532267 | − | 0.846577i | \(-0.321340\pi\) | ||||
0.532267 | + | 0.846577i | \(0.321340\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.827331 | 0.0717387 | ||||||||
\(134\) | −8.56278 | −0.739711 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.0896 | −1.12242 | ||||||||
\(137\) | 13.9009 | 1.18764 | 0.593819 | − | 0.804599i | \(-0.297620\pi\) | ||||
0.593819 | + | 0.804599i | \(0.297620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.99920 | 0.424027 | 0.212013 | − | 0.977267i | \(-0.431998\pi\) | ||||
0.212013 | + | 0.977267i | \(0.431998\pi\) | |||||||
\(140\) | 0.107465 | 0.00908249 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.64099 | 0.725135 | ||||||||
\(143\) | 2.89820 | 0.242360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.82504 | −0.234607 | ||||||||
\(146\) | −0.682462 | −0.0564809 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.10037 | 0.254849 | ||||||||
\(149\) | −17.4937 | −1.43314 | −0.716570 | − | 0.697515i | \(-0.754289\pi\) | ||||
−0.716570 | + | 0.697515i | \(0.754289\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.480306 | 0.0390867 | 0.0195434 | − | 0.999809i | \(-0.493779\pi\) | ||||
0.0195434 | + | 0.999809i | \(0.493779\pi\) | |||||||
\(152\) | −11.0057 | −0.892682 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.348429 | −0.0280772 | ||||||||
\(155\) | −1.28931 | −0.103560 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.117389 | 0.00936869 | 0.00468434 | − | 0.999989i | \(-0.498509\pi\) | ||||
0.00468434 | + | 0.999989i | \(0.498509\pi\) | |||||||
\(158\) | −9.63907 | −0.766843 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.26368 | −0.178959 | ||||||||
\(161\) | −0.299108 | −0.0235730 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.5273 | −0.981210 | −0.490605 | − | 0.871382i | \(-0.663224\pi\) | ||||
−0.490605 | + | 0.871382i | \(0.663224\pi\) | |||||||
\(164\) | −1.49694 | −0.116891 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.61597 | −0.358268 | ||||||||
\(167\) | 0.744061 | 0.0575772 | 0.0287886 | − | 0.999586i | \(-0.490835\pi\) | ||||
0.0287886 | + | 0.999586i | \(0.490835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4960 | −0.884311 | ||||||||
\(170\) | −1.47454 | −0.113092 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.18554 | 0.166646 | ||||||||
\(173\) | −11.6073 | −0.882484 | −0.441242 | − | 0.897388i | \(-0.645462\pi\) | ||||
−0.441242 | + | 0.897388i | \(0.645462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.945505 | −0.0714734 | ||||||||
\(176\) | −2.11363 | −0.159321 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.87460 | −0.365367 | ||||||||
\(179\) | 21.1974 | 1.58437 | 0.792183 | − | 0.610284i | \(-0.208945\pi\) | ||||
0.792183 | + | 0.610284i | \(0.208945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9508 | 0.888299 | 0.444150 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444150 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(182\) | −0.180809 | −0.0134025 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.97894 | 0.293332 | ||||||||
\(185\) | 0.838467 | 0.0616453 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.9304 | −0.872441 | ||||||||
\(188\) | −1.54808 | −0.112906 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.23979 | −0.0899438 | ||||||||
\(191\) | −24.2243 | −1.75281 | −0.876406 | − | 0.481574i | \(-0.840065\pi\) | ||||
−0.876406 | + | 0.481574i | \(0.840065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.78545 | −0.416446 | −0.208223 | − | 0.978081i | \(-0.566768\pi\) | ||||
−0.208223 | + | 0.978081i | \(0.566768\pi\) | |||||||
\(194\) | −9.82478 | −0.705378 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.94058 | 0.710042 | ||||||||
\(197\) | −4.06793 | −0.289828 | −0.144914 | − | 0.989444i | \(-0.546291\pi\) | ||||
−0.144914 | + | 0.989444i | \(0.546291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4204 | −0.809571 | −0.404785 | − | 0.914412i | \(-0.632654\pi\) | ||||
−0.404785 | + | 0.914412i | \(0.632654\pi\) | |||||||
\(200\) | 12.5777 | 0.889381 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.67571 | −0.328982 | ||||||||
\(203\) | 1.42599 | 0.100085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.404834 | −0.0282748 | ||||||||
\(206\) | 5.88682 | 0.410154 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.09682 | −0.0760509 | ||||||||
\(209\) | −10.0311 | −0.693866 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0941 | 1.24565 | 0.622824 | − | 0.782362i | \(-0.285985\pi\) | ||||
0.622824 | + | 0.782362i | \(0.285985\pi\) | |||||||
\(212\) | 2.21753 | 0.152301 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.18913 | 0.423080 | ||||||||
\(215\) | 0.591058 | 0.0403098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.650804 | 0.0441794 | ||||||||
\(218\) | −4.02782 | −0.272798 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.30298 | −0.0878469 | ||||||||
\(221\) | −6.19103 | −0.416454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.1665 | −1.41741 | −0.708706 | − | 0.705504i | \(-0.750721\pi\) | ||||
−0.708706 | + | 0.705504i | \(0.750721\pi\) | |||||||
\(224\) | 1.14263 | 0.0763455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.72744 | 0.181426 | ||||||||
\(227\) | 13.3828 | 0.888248 | 0.444124 | − | 0.895965i | \(-0.353515\pi\) | ||||
0.444124 | + | 0.895965i | \(0.353515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5484 | −0.829225 | −0.414612 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414612 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(230\) | 0.448226 | 0.0295552 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.9695 | −1.24541 | ||||||||
\(233\) | −15.6538 | −1.02551 | −0.512757 | − | 0.858534i | \(-0.671376\pi\) | ||||
−0.512757 | + | 0.858534i | \(0.671376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.418665 | −0.0273107 | ||||||||
\(236\) | 21.1963 | 1.37976 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.744302 | 0.0482459 | ||||||||
\(239\) | −3.45659 | −0.223588 | −0.111794 | − | 0.993731i | \(-0.535660\pi\) | ||||
−0.111794 | + | 0.993731i | \(0.535660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.7843 | 1.85416 | 0.927080 | − | 0.374864i | \(-0.122311\pi\) | ||||
0.927080 | + | 0.374864i | \(0.122311\pi\) | |||||||
\(242\) | −4.09601 | −0.263301 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.78249 | 0.498223 | ||||||||
\(245\) | 2.68834 | 0.171752 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.20541 | −0.331212 | ||||||||
\(248\) | −8.65743 | −0.549747 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.87731 | 0.181977 | ||||||||
\(251\) | 1.82824 | 0.115397 | 0.0576986 | − | 0.998334i | \(-0.481624\pi\) | ||||
0.0576986 | + | 0.998334i | \(0.481624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.62658 | 0.228001 | ||||||||
\(254\) | −13.4908 | −0.846490 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.6461 | −0.790380 | ||||||||
\(257\) | −3.65882 | −0.228231 | −0.114116 | − | 0.993467i | \(-0.536403\pi\) | ||||
−0.114116 | + | 0.993467i | \(0.536403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.423232 | −0.0262983 | ||||||||
\(260\) | −0.676152 | −0.0419332 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.21630 | 0.569385 | ||||||||
\(263\) | 13.1581 | 0.811362 | 0.405681 | − | 0.914015i | \(-0.367034\pi\) | ||||
0.405681 | + | 0.914015i | \(0.367034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.599712 | 0.0368400 | ||||||||
\(266\) | 0.625807 | 0.0383707 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.1633 | 0.987332 | ||||||||
\(269\) | 30.0225 | 1.83050 | 0.915251 | − | 0.402885i | \(-0.131992\pi\) | ||||
0.915251 | + | 0.402885i | \(0.131992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.04876 | −0.549673 | −0.274837 | − | 0.961491i | \(-0.588624\pi\) | ||||
−0.274837 | + | 0.961491i | \(0.588624\pi\) | |||||||
\(272\) | 4.51506 | 0.273766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.5149 | 0.635229 | ||||||||
\(275\) | 11.4639 | 0.691300 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3482 | 0.621762 | 0.310881 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310881 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(278\) | 3.78148 | 0.226798 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.195152 | 0.0116625 | ||||||||
\(281\) | 19.3686 | 1.15543 | 0.577716 | − | 0.816238i | \(-0.303944\pi\) | ||||
0.577716 | + | 0.816238i | \(0.303944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.72949 | 0.578358 | 0.289179 | − | 0.957275i | \(-0.406618\pi\) | ||||
0.289179 | + | 0.957275i | \(0.406618\pi\) | |||||||
\(284\) | −16.3109 | −0.967876 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.19225 | 0.129631 | ||||||||
\(287\) | 0.204347 | 0.0120622 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48538 | 0.499140 | ||||||||
\(290\) | −2.13691 | −0.125484 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.28823 | 0.0753881 | ||||||||
\(293\) | −26.2321 | −1.53249 | −0.766247 | − | 0.642546i | \(-0.777878\pi\) | ||||
−0.766247 | + | 0.642546i | \(0.777878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.73235 | 0.333750 | ||||||||
\(296\) | 5.63012 | 0.327244 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.2325 | −0.766540 | ||||||||
\(299\) | 1.88193 | 0.108835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.298348 | −0.0171965 | ||||||||
\(302\) | 0.363312 | 0.0209062 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.79626 | 0.217730 | ||||||||
\(305\) | 2.10470 | 0.120515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7097 | −0.782455 | −0.391228 | − | 0.920294i | \(-0.627950\pi\) | ||||
−0.391228 | + | 0.920294i | \(0.627950\pi\) | |||||||
\(308\) | 0.657704 | 0.0374762 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.975257 | −0.0553909 | ||||||||
\(311\) | −30.9043 | −1.75242 | −0.876212 | − | 0.481926i | \(-0.839937\pi\) | ||||
−0.876212 | + | 0.481926i | \(0.839937\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2287 | −1.59558 | −0.797790 | − | 0.602935i | \(-0.793998\pi\) | ||||
−0.797790 | + | 0.602935i | \(0.793998\pi\) | |||||||
\(314\) | 0.0887953 | 0.00501101 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.1949 | 1.02355 | ||||||||
\(317\) | 7.55793 | 0.424496 | 0.212248 | − | 0.977216i | \(-0.431922\pi\) | ||||
0.212248 | + | 0.977216i | \(0.431922\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.2896 | −0.968034 | ||||||||
\(320\) | −1.02157 | −0.0571077 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.226251 | −0.0126085 | ||||||||
\(323\) | 21.4281 | 1.19229 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.94894 | 0.329988 | ||||||||
\(326\) | −9.47583 | −0.524818 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.71837 | −0.150097 | ||||||||
\(329\) | 0.211329 | 0.0116509 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4225 | 1.12252 | 0.561260 | − | 0.827640i | \(-0.310317\pi\) | ||||
0.561260 | + | 0.827640i | \(0.310317\pi\) | |||||||
\(332\) | 8.71322 | 0.478200 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.562821 | 0.0307962 | ||||||||
\(335\) | 4.37122 | 0.238825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7603 | 0.912994 | 0.456497 | − | 0.889725i | \(-0.349104\pi\) | ||||
0.456497 | + | 0.889725i | \(0.349104\pi\) | |||||||
\(338\) | −8.69581 | −0.472990 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.78338 | 0.150950 | ||||||||
\(341\) | −7.89077 | −0.427309 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.72138 | −0.146941 | ||||||||
\(344\) | 3.96882 | 0.213985 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.77994 | −0.472012 | ||||||||
\(347\) | −14.1418 | −0.759171 | −0.379586 | − | 0.925157i | \(-0.623933\pi\) | ||||
−0.379586 | + | 0.925157i | \(0.623933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.1523 | −1.18579 | −0.592893 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592893 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(350\) | −0.715196 | −0.0382288 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.8540 | −0.738423 | ||||||||
\(353\) | −17.2209 | −0.916574 | −0.458287 | − | 0.888804i | \(-0.651537\pi\) | ||||
−0.458287 | + | 0.888804i | \(0.651537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.41114 | −0.234119 | ||||||||
\(356\) | 9.20141 | 0.487674 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.0341 | 0.847426 | ||||||||
\(359\) | −21.9672 | −1.15938 | −0.579692 | − | 0.814836i | \(-0.696827\pi\) | ||||
−0.579692 | + | 0.814836i | \(0.696827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.983329 | −0.0517541 | ||||||||
\(362\) | 9.03983 | 0.475123 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.341300 | 0.0178890 | ||||||||
\(365\) | 0.348390 | 0.0182356 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1841 | −0.688202 | −0.344101 | − | 0.938933i | \(-0.611816\pi\) | ||||
−0.344101 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(368\) | −1.37248 | −0.0715452 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.634231 | 0.0329721 | ||||||||
\(371\) | −0.302716 | −0.0157162 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.2516 | −1.82526 | −0.912630 | − | 0.408787i | \(-0.865952\pi\) | ||||
−0.912630 | + | 0.408787i | \(0.865952\pi\) | |||||||
\(374\) | −9.02440 | −0.466641 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.81124 | −0.144979 | ||||||||
\(377\) | −8.97207 | −0.462085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6003 | 1.21227 | 0.606134 | − | 0.795363i | \(-0.292720\pi\) | ||||
0.606134 | + | 0.795363i | \(0.292720\pi\) | |||||||
\(380\) | 2.34026 | 0.120053 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.3237 | −0.937522 | ||||||||
\(383\) | 13.1311 | 0.670970 | 0.335485 | − | 0.942046i | \(-0.391100\pi\) | ||||
0.335485 | + | 0.942046i | \(0.391100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.177870 | 0.00906509 | ||||||||
\(386\) | −4.37622 | −0.222744 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.5455 | 0.941505 | ||||||||
\(389\) | −29.2216 | −1.48159 | −0.740797 | − | 0.671729i | \(-0.765552\pi\) | ||||
−0.740797 | + | 0.671729i | \(0.765552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.74697 | −0.391781 | ||||||||
\(392\) | 18.0516 | 0.911743 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.07706 | −0.155020 | ||||||||
\(395\) | 4.92065 | 0.247585 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.2129 | 1.31559 | 0.657795 | − | 0.753197i | \(-0.271489\pi\) | ||||
0.657795 | + | 0.753197i | \(0.271489\pi\) | |||||||
\(398\) | −8.63859 | −0.433013 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.33850 | −0.216925 | ||||||||
\(401\) | 24.3910 | 1.21803 | 0.609014 | − | 0.793160i | \(-0.291565\pi\) | ||||
0.609014 | + | 0.793160i | \(0.291565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.09473 | −0.203973 | ||||||||
\(404\) | 8.82599 | 0.439110 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.07864 | 0.0535322 | ||||||||
\(407\) | 5.13154 | 0.254361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2071 | 0.653051 | 0.326526 | − | 0.945188i | \(-0.394122\pi\) | ||||
0.326526 | + | 0.945188i | \(0.394122\pi\) | |||||||
\(410\) | −0.306223 | −0.0151233 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.1121 | −0.547454 | ||||||||
\(413\) | −2.89351 | −0.142380 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.35641 | 0.115672 | ||||||||
\(416\) | −7.18924 | −0.352481 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.58770 | −0.371126 | ||||||||
\(419\) | −15.8597 | −0.774799 | −0.387400 | − | 0.921912i | \(-0.626627\pi\) | ||||
−0.387400 | + | 0.921912i | \(0.626627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.53957 | −0.221245 | −0.110622 | − | 0.993863i | \(-0.535284\pi\) | ||||
−0.110622 | + | 0.993863i | \(0.535284\pi\) | |||||||
\(422\) | 13.6867 | 0.666257 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.02693 | 0.195565 | ||||||||
\(425\) | −24.4888 | −1.18788 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.06239 | −0.0514126 | ||||||||
\(428\) | −11.6828 | −0.564708 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.447087 | 0.0215604 | ||||||||
\(431\) | 24.0460 | 1.15825 | 0.579126 | − | 0.815238i | \(-0.303394\pi\) | ||||
0.579126 | + | 0.815238i | \(0.303394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.8069 | −0.999914 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(434\) | 0.492279 | 0.0236302 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.60301 | 0.364118 | ||||||||
\(437\) | −6.51364 | −0.311590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0822 | −1.29256 | −0.646282 | − | 0.763098i | \(-0.723677\pi\) | ||||
−0.646282 | + | 0.763098i | \(0.723677\pi\) | |||||||
\(440\) | −2.36615 | −0.112802 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.68301 | −0.222748 | ||||||||
\(443\) | −26.1108 | −1.24056 | −0.620282 | − | 0.784379i | \(-0.712982\pi\) | ||||
−0.620282 | + | 0.784379i | \(0.712982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48844 | 0.117963 | ||||||||
\(446\) | −16.0107 | −0.758129 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.515658 | 0.0243626 | ||||||||
\(449\) | −18.4224 | −0.869407 | −0.434703 | − | 0.900574i | \(-0.643147\pi\) | ||||
−0.434703 | + | 0.900574i | \(0.643147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.47764 | −0.116668 | ||||||||
\(452\) | −5.14838 | −0.242159 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.1230 | 0.475095 | ||||||||
\(455\) | 0.0923016 | 0.00432716 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.55147 | −0.166131 | −0.0830654 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830654 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(458\) | −9.49186 | −0.443526 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.846084 | −0.0394489 | ||||||||
\(461\) | 2.86665 | 0.133513 | 0.0667565 | − | 0.997769i | \(-0.478735\pi\) | ||||
0.0667565 | + | 0.997769i | \(0.478735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.5287 | 1.41879 | 0.709395 | − | 0.704811i | \(-0.248968\pi\) | ||||
0.709395 | + | 0.704811i | \(0.248968\pi\) | |||||||
\(464\) | 6.54324 | 0.303762 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8408 | −0.548515 | ||||||||
\(467\) | −18.7000 | −0.865332 | −0.432666 | − | 0.901554i | \(-0.642427\pi\) | ||||
−0.432666 | + | 0.901554i | \(0.642427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.20646 | −0.101885 | ||||||||
\(470\) | −0.316685 | −0.0146076 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 38.4914 | 1.77171 | ||||||||
\(473\) | 3.61736 | 0.166326 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.5901 | −0.944740 | ||||||||
\(476\) | −1.40496 | −0.0643964 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.61463 | −0.119590 | ||||||||
\(479\) | −7.50976 | −0.343130 | −0.171565 | − | 0.985173i | \(-0.554882\pi\) | ||||
−0.171565 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.66289 | 0.121418 | ||||||||
\(482\) | 21.7729 | 0.991730 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.73173 | 0.351442 | ||||||||
\(485\) | 5.01546 | 0.227740 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6786 | 1.48081 | 0.740404 | − | 0.672162i | \(-0.234634\pi\) | ||||
0.740404 | + | 0.672162i | \(0.234634\pi\) | |||||||
\(488\) | 14.1326 | 0.639753 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.03351 | 0.0918644 | ||||||||
\(491\) | −2.81716 | −0.127137 | −0.0635683 | − | 0.997977i | \(-0.520248\pi\) | ||||
−0.0635683 | + | 0.997977i | \(0.520248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.9335 | 1.66340 | ||||||||
\(494\) | −3.93746 | −0.177155 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.98625 | 0.134087 | ||||||||
\(497\) | 2.22661 | 0.0998770 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0591 | 1.30086 | 0.650432 | − | 0.759564i | \(-0.274588\pi\) | ||||
0.650432 | + | 0.759564i | \(0.274588\pi\) | |||||||
\(500\) | −5.43128 | −0.242894 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.38291 | 0.0617223 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.38691 | 0.106216 | ||||||||
\(506\) | 2.74321 | 0.121951 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.4656 | 1.12986 | ||||||||
\(509\) | −7.58042 | −0.335996 | −0.167998 | − | 0.985787i | \(-0.553730\pi\) | ||||
−0.167998 | + | 0.985787i | \(0.553730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.175857 | −0.00777944 | ||||||||
\(512\) | 9.88103 | 0.436684 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.76760 | −0.122074 | ||||||||
\(515\) | −3.00517 | −0.132423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.56229 | −0.112689 | ||||||||
\(518\) | −0.320140 | −0.0140661 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.22786 | −0.0538451 | ||||||||
\(521\) | 8.90148 | 0.389981 | 0.194990 | − | 0.980805i | \(-0.437532\pi\) | ||||
0.194990 | + | 0.980805i | \(0.437532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7311 | 1.64986 | 0.824932 | − | 0.565232i | \(-0.191213\pi\) | ||||
0.824932 | + | 0.565232i | \(0.191213\pi\) | |||||||
\(524\) | −17.3969 | −0.759988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.95301 | 0.433972 | ||||||||
\(527\) | 16.8560 | 0.734257 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6451 | −0.897613 | ||||||||
\(530\) | 0.453632 | 0.0197045 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.18129 | −0.0512154 | ||||||||
\(533\) | −1.28572 | −0.0556905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.15950 | −0.136597 | ||||||||
\(536\) | 29.3518 | 1.26780 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.7095 | 0.979076 | ||||||||
\(539\) | 16.4530 | 0.708682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6293 | 0.499981 | 0.249990 | − | 0.968248i | \(-0.419573\pi\) | ||||
0.249990 | + | 0.968248i | \(0.419573\pi\) | |||||||
\(542\) | −6.84464 | −0.294003 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 29.5945 | 1.26885 | ||||||||
\(545\) | 2.05616 | 0.0880764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4958 | −0.577040 | −0.288520 | − | 0.957474i | \(-0.593163\pi\) | ||||
−0.288520 | + | 0.957474i | \(0.593163\pi\) | |||||||
\(548\) | −19.8482 | −0.847874 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.67150 | 0.369754 | ||||||||
\(551\) | 31.0536 | 1.32293 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.48379 | −0.105622 | ||||||||
\(554\) | 7.82754 | 0.332560 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.13803 | −0.302720 | ||||||||
\(557\) | 34.2002 | 1.44911 | 0.724554 | − | 0.689218i | \(-0.242046\pi\) | ||||
0.724554 | + | 0.689218i | \(0.242046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.87715 | 0.0793949 | ||||||||
\(560\) | −0.0673146 | −0.00284456 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.6507 | 0.618003 | ||||||||
\(563\) | −25.6005 | −1.07893 | −0.539467 | − | 0.842007i | \(-0.681374\pi\) | ||||
−0.539467 | + | 0.842007i | \(0.681374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.39233 | −0.0585758 | ||||||||
\(566\) | 7.35956 | 0.309345 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.6199 | −1.24282 | ||||||||
\(569\) | 17.2311 | 0.722363 | 0.361182 | − | 0.932495i | \(-0.382373\pi\) | ||||
0.361182 | + | 0.932495i | \(0.382373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.79325 | 0.116894 | 0.0584470 | − | 0.998291i | \(-0.481385\pi\) | ||||
0.0584470 | + | 0.998291i | \(0.481385\pi\) | |||||||
\(572\) | −4.13815 | −0.173025 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.154572 | 0.00645171 | ||||||||
\(575\) | 7.44403 | 0.310438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.1143 | −1.66998 | −0.834991 | − | 0.550264i | \(-0.814527\pi\) | ||||
−0.834991 | + | 0.550264i | \(0.814527\pi\) | |||||||
\(578\) | 6.41849 | 0.266974 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.03368 | 0.167490 | ||||||||
\(581\) | −1.18944 | −0.0493464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.67032 | 0.152009 | ||||||||
\(584\) | 2.33936 | 0.0968036 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8424 | −0.819682 | ||||||||
\(587\) | 38.5445 | 1.59090 | 0.795451 | − | 0.606018i | \(-0.207234\pi\) | ||||
0.795451 | + | 0.606018i | \(0.207234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1725 | 0.583966 | ||||||||
\(590\) | 4.33605 | 0.178512 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.94202 | −0.0798167 | ||||||||
\(593\) | 25.0372 | 1.02816 | 0.514078 | − | 0.857744i | \(-0.328134\pi\) | ||||
0.514078 | + | 0.857744i | \(0.328134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.379959 | −0.0155768 | ||||||||
\(596\) | 24.9781 | 1.02314 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.42353 | 0.0582123 | ||||||||
\(599\) | 23.0220 | 0.940655 | 0.470328 | − | 0.882492i | \(-0.344136\pi\) | ||||
0.470328 | + | 0.882492i | \(0.344136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.9451 | −1.38465 | −0.692326 | − | 0.721585i | \(-0.743414\pi\) | ||||
−0.692326 | + | 0.721585i | \(0.743414\pi\) | |||||||
\(602\) | −0.225675 | −0.00919784 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.685796 | −0.0279046 | ||||||||
\(605\) | 2.09097 | 0.0850102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3039 | 0.986467 | 0.493233 | − | 0.869897i | \(-0.335815\pi\) | ||||
0.493233 | + | 0.869897i | \(0.335815\pi\) | |||||||
\(608\) | 24.8830 | 1.00914 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.59203 | 0.0644595 | ||||||||
\(611\) | −1.32964 | −0.0537916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.5604 | 1.39588 | 0.697940 | − | 0.716156i | \(-0.254100\pi\) | ||||
0.697940 | + | 0.716156i | \(0.254100\pi\) | |||||||
\(614\) | −10.3703 | −0.418510 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.19436 | 0.0481220 | ||||||||
\(617\) | −34.3607 | −1.38331 | −0.691655 | − | 0.722228i | \(-0.743118\pi\) | ||||
−0.691655 | + | 0.722228i | \(0.743118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.08451 | 0.0435902 | 0.0217951 | − | 0.999762i | \(-0.493062\pi\) | ||||
0.0217951 | + | 0.999762i | \(0.493062\pi\) | |||||||
\(620\) | 1.84092 | 0.0739331 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.3766 | −0.937315 | ||||||||
\(623\) | −1.25609 | −0.0503240 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7856 | 0.911425 | ||||||||
\(626\) | −21.3527 | −0.853425 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.167612 | −0.00668846 | ||||||||
\(629\) | −10.9618 | −0.437076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.03426 | −0.240220 | −0.120110 | − | 0.992761i | \(-0.538325\pi\) | ||||
−0.120110 | + | 0.992761i | \(0.538325\pi\) | |||||||
\(632\) | 33.0411 | 1.31430 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.71695 | 0.227049 | ||||||||
\(635\) | 6.88695 | 0.273300 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.53792 | 0.338285 | ||||||||
\(638\) | −13.0782 | −0.517770 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.75462 | 0.148414 | ||||||||
\(641\) | 22.0716 | 0.871778 | 0.435889 | − | 0.900001i | \(-0.356434\pi\) | ||||
0.435889 | + | 0.900001i | \(0.356434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.6373 | −1.60258 | −0.801290 | − | 0.598277i | \(-0.795852\pi\) | ||||
−0.801290 | + | 0.598277i | \(0.795852\pi\) | |||||||
\(644\) | 0.427077 | 0.0168292 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.2086 | 0.637717 | ||||||||
\(647\) | −22.9719 | −0.903118 | −0.451559 | − | 0.892241i | \(-0.649132\pi\) | ||||
−0.451559 | + | 0.892241i | \(0.649132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0828 | 1.37712 | ||||||||
\(650\) | 4.49988 | 0.176500 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.8868 | 0.700502 | ||||||||
\(653\) | 39.0459 | 1.52798 | 0.763992 | − | 0.645226i | \(-0.223237\pi\) | ||||
0.763992 | + | 0.645226i | \(0.223237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.70483 | −0.183833 | ||||||||
\(656\) | 0.937660 | 0.0366095 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.159853 | 0.00623172 | ||||||||
\(659\) | 26.6054 | 1.03640 | 0.518199 | − | 0.855260i | \(-0.326603\pi\) | ||||
0.518199 | + | 0.855260i | \(0.326603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.3661 | −1.53116 | −0.765582 | − | 0.643338i | \(-0.777549\pi\) | ||||
−0.765582 | + | 0.643338i | \(0.777549\pi\) | |||||||
\(662\) | 15.4479 | 0.600400 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.8228 | 0.614042 | ||||||||
\(665\) | −0.319469 | −0.0123885 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2269 | −0.434709 | ||||||||
\(668\) | −1.06239 | −0.0411053 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.30647 | 0.127740 | ||||||||
\(671\) | 12.8811 | 0.497269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4145 | −0.517090 | −0.258545 | − | 0.965999i | \(-0.583243\pi\) | ||||
−0.258545 | + | 0.965999i | \(0.583243\pi\) | |||||||
\(674\) | 12.6778 | 0.488331 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.4144 | 0.631324 | ||||||||
\(677\) | 2.13435 | 0.0820299 | 0.0410149 | − | 0.999159i | \(-0.486941\pi\) | ||||
0.0410149 | + | 0.999159i | \(0.486941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.53165 | −0.0971557 | ||||||||
\(680\) | 5.05448 | 0.193830 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.96871 | −0.228554 | ||||||||
\(683\) | −21.3544 | −0.817105 | −0.408552 | − | 0.912735i | \(-0.633966\pi\) | ||||
−0.408552 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.36777 | −0.205092 | ||||||||
\(686\) | −2.05850 | −0.0785940 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.36899 | −0.0521921 | ||||||||
\(689\) | 1.90463 | 0.0725606 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8167 | 0.525614 | 0.262807 | − | 0.964848i | \(-0.415352\pi\) | ||||
0.262807 | + | 0.964848i | \(0.415352\pi\) | |||||||
\(692\) | 16.5732 | 0.630020 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.6971 | −0.406056 | ||||||||
\(695\) | −1.93041 | −0.0732247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.29265 | 0.200473 | ||||||||
\(698\) | −16.7564 | −0.634238 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.35002 | 0.0510260 | ||||||||
\(701\) | −45.1209 | −1.70419 | −0.852097 | − | 0.523385i | \(-0.824669\pi\) | ||||
−0.852097 | + | 0.523385i | \(0.824669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.21666 | −0.347613 | ||||||||
\(704\) | −6.25217 | −0.235638 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.0262 | −0.490246 | ||||||||
\(707\) | −1.20484 | −0.0453126 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.6350 | −1.41341 | −0.706706 | − | 0.707507i | \(-0.749820\pi\) | ||||
−0.706706 | + | 0.707507i | \(0.749820\pi\) | |||||||
\(710\) | −3.33667 | −0.125223 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.7093 | 0.626208 | ||||||||
\(713\) | −5.12383 | −0.191889 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.11912 | −0.0418529 | ||||||||
\(716\) | −30.2663 | −1.13110 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.6164 | −0.620117 | ||||||||
\(719\) | 34.9860 | 1.30476 | 0.652380 | − | 0.757892i | \(-0.273771\pi\) | ||||
0.652380 | + | 0.757892i | \(0.273771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.51691 | 0.0564929 | ||||||||
\(722\) | −0.743807 | −0.0276816 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.0638 | −0.634171 | ||||||||
\(725\) | −35.4892 | −1.31804 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0594046 | 0.00220319 | 0.00110160 | − | 0.999999i | \(-0.499649\pi\) | ||||
0.00110160 | + | 0.999999i | \(0.499649\pi\) | |||||||
\(728\) | 0.619784 | 0.0229707 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.263529 | 0.00975363 | ||||||||
\(731\) | −7.72727 | −0.285804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6914 | −0.875060 | −0.437530 | − | 0.899204i | \(-0.644147\pi\) | ||||
−0.437530 | + | 0.899204i | \(0.644147\pi\) | |||||||
\(734\) | −9.97265 | −0.368097 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.99605 | −0.331599 | ||||||||
\(737\) | 26.7525 | 0.985441 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2539 | −0.487551 | −0.243776 | − | 0.969832i | \(-0.578386\pi\) | ||||
−0.243776 | + | 0.969832i | \(0.578386\pi\) | |||||||
\(740\) | −1.19719 | −0.0440096 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.228979 | −0.00840610 | ||||||||
\(743\) | 13.7983 | 0.506210 | 0.253105 | − | 0.967439i | \(-0.418548\pi\) | ||||
0.253105 | + | 0.967439i | \(0.418548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.75509 | 0.247487 | ||||||||
\(746\) | −26.6649 | −0.976273 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.0347 | 0.622850 | ||||||||
\(749\) | 1.59481 | 0.0582733 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.82043 | 0.139410 | 0.0697048 | − | 0.997568i | \(-0.477794\pi\) | ||||
0.0697048 | + | 0.997568i | \(0.477794\pi\) | |||||||
\(752\) | 0.969695 | 0.0353611 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.78663 | −0.247154 | ||||||||
\(755\) | −0.185467 | −0.00674984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6215 | 0.713157 | 0.356578 | − | 0.934265i | \(-0.383943\pi\) | ||||
0.356578 | + | 0.934265i | \(0.383943\pi\) | |||||||
\(758\) | 17.8517 | 0.648403 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.24979 | 0.154156 | ||||||||
\(761\) | −47.5141 | −1.72238 | −0.861192 | − | 0.508280i | \(-0.830281\pi\) | ||||
−0.861192 | + | 0.508280i | \(0.830281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.03789 | −0.0375741 | ||||||||
\(764\) | 34.5883 | 1.25136 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.93262 | 0.358880 | ||||||||
\(767\) | 18.2054 | 0.657360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0139 | −0.361111 | −0.180556 | − | 0.983565i | \(-0.557790\pi\) | ||||
−0.180556 | + | 0.983565i | \(0.557790\pi\) | |||||||
\(770\) | 0.134544 | 0.00484863 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.26066 | 0.297308 | ||||||||
\(773\) | 35.8956 | 1.29108 | 0.645538 | − | 0.763728i | \(-0.276633\pi\) | ||||
0.645538 | + | 0.763728i | \(0.276633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.1968 | −0.581807 | ||||||||
\(776\) | 33.6777 | 1.20896 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.1037 | −0.792457 | ||||||||
\(779\) | 4.45005 | 0.159439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.9968 | −0.966023 | ||||||||
\(782\) | −5.85995 | −0.209551 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.22662 | −0.222379 | ||||||||
\(785\) | −0.0453292 | −0.00161787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.89211 | 0.0674464 | 0.0337232 | − | 0.999431i | \(-0.489264\pi\) | ||||
0.0337232 | + | 0.999431i | \(0.489264\pi\) | |||||||
\(788\) | 5.80833 | 0.206913 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.72207 | 0.132425 | ||||||||
\(791\) | 0.702806 | 0.0249889 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.68434 | 0.237368 | ||||||||
\(794\) | 19.8279 | 0.703667 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.3064 | 0.577966 | ||||||||
\(797\) | −24.4028 | −0.864393 | −0.432197 | − | 0.901779i | \(-0.642261\pi\) | ||||
−0.432197 | + | 0.901779i | \(0.642261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.47347 | 0.193637 | ||||||||
\(800\) | −28.4372 | −1.00541 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.4498 | 0.651484 | ||||||||
\(803\) | 2.13220 | 0.0752437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.115499 | 0.00407080 | ||||||||
\(806\) | −3.09733 | −0.109099 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.0276 | 0.563848 | ||||||||
\(809\) | 32.9341 | 1.15790 | 0.578951 | − | 0.815363i | \(-0.303462\pi\) | ||||
0.578951 | + | 0.815363i | \(0.303462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.8145 | −1.50342 | −0.751711 | − | 0.659493i | \(-0.770771\pi\) | ||||
−0.751711 | + | 0.659493i | \(0.770771\pi\) | |||||||
\(812\) | −2.03608 | −0.0714523 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.88158 | 0.136049 | ||||||||
\(815\) | 4.83732 | 0.169444 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.49708 | −0.227304 | ||||||||
\(818\) | 9.99011 | 0.349296 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.578035 | 0.0201859 | ||||||||
\(821\) | 28.2632 | 0.986393 | 0.493196 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493196 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4127 | 0.362962 | 0.181481 | − | 0.983394i | \(-0.441911\pi\) | ||||
0.181481 | + | 0.983394i | \(0.441911\pi\) | |||||||
\(824\) | −20.1790 | −0.702970 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.18870 | −0.0761547 | ||||||||
\(827\) | 0.0841446 | 0.00292600 | 0.00146300 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146300 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.3470 | 1.60970 | 0.804850 | − | 0.593479i | \(-0.202246\pi\) | ||||
0.804850 | + | 0.593479i | \(0.202246\pi\) | |||||||
\(830\) | 1.78243 | 0.0618690 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.24442 | −0.112480 | ||||||||
\(833\) | −35.1463 | −1.21775 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.287315 | −0.00994294 | ||||||||
\(836\) | 14.3227 | 0.495362 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.9966 | −0.414415 | ||||||||
\(839\) | 13.9611 | 0.481990 | 0.240995 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240995 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.5241 | 0.845660 | ||||||||
\(842\) | −3.43381 | −0.118337 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.8353 | −0.889289 | ||||||||
\(845\) | 4.43913 | 0.152711 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.05546 | −0.0362660 | ||||||||
\(848\) | −1.38903 | −0.0476994 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.5237 | −0.635359 | ||||||||
\(851\) | 3.33214 | 0.114224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.5527 | −1.86785 | −0.933924 | − | 0.357472i | \(-0.883639\pi\) | ||||
−0.933924 | + | 0.357472i | \(0.883639\pi\) | |||||||
\(854\) | −0.803609 | −0.0274989 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.2153 | −0.725124 | ||||||||
\(857\) | −27.6798 | −0.945525 | −0.472762 | − | 0.881190i | \(-0.656743\pi\) | ||||
−0.472762 | + | 0.881190i | \(0.656743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.1497 | 0.926336 | 0.463168 | − | 0.886270i | \(-0.346713\pi\) | ||||
0.463168 | + | 0.886270i | \(0.346713\pi\) | |||||||
\(860\) | −0.843932 | −0.0287778 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.1888 | 0.619512 | ||||||||
\(863\) | −25.9641 | −0.883827 | −0.441913 | − | 0.897058i | \(-0.645700\pi\) | ||||
−0.441913 | + | 0.897058i | \(0.645700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.48208 | 0.152395 | ||||||||
\(866\) | −15.7387 | −0.534822 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.929239 | −0.0315404 | ||||||||
\(869\) | 30.1151 | 1.02159 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8826 | 0.470394 | ||||||||
\(872\) | 13.8067 | 0.467554 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.92703 | −0.166659 | ||||||||
\(875\) | 0.741425 | 0.0250647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.2176 | 1.25675 | 0.628374 | − | 0.777911i | \(-0.283721\pi\) | ||||
0.628374 | + | 0.777911i | \(0.283721\pi\) | |||||||
\(878\) | −20.4855 | −0.691351 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.816166 | 0.0275130 | ||||||||
\(881\) | 6.44185 | 0.217031 | 0.108516 | − | 0.994095i | \(-0.465390\pi\) | ||||
0.108516 | + | 0.994095i | \(0.465390\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.9727 | 1.54711 | 0.773553 | − | 0.633732i | \(-0.218478\pi\) | ||||
0.773553 | + | 0.633732i | \(0.218478\pi\) | |||||||
\(884\) | 8.83976 | 0.297313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.7507 | −0.663538 | ||||||||
\(887\) | 28.3187 | 0.950849 | 0.475425 | − | 0.879756i | \(-0.342294\pi\) | ||||
0.475425 | + | 0.879756i | \(0.342294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.47632 | −0.116592 | ||||||||
\(890\) | 1.88230 | 0.0630947 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.2222 | 1.01191 | ||||||||
\(893\) | 4.60208 | 0.154003 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.18524 | −0.273602 | ||||||||
\(896\) | −1.89522 | −0.0633147 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.9350 | −0.465018 | ||||||||
\(899\) | 24.4277 | 0.814710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.84041 | −0.261202 | ||||||||
\(902\) | −1.87413 | −0.0624017 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.34920 | −0.310950 | ||||||||
\(905\) | −4.61475 | −0.153399 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.5099 | −0.415384 | −0.207692 | − | 0.978194i | \(-0.566595\pi\) | ||||
−0.207692 | + | 0.978194i | \(0.566595\pi\) | |||||||
\(908\) | −19.1084 | −0.634135 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0698185 | 0.00231446 | ||||||||
\(911\) | −2.41940 | −0.0801584 | −0.0400792 | − | 0.999197i | \(-0.512761\pi\) | ||||
−0.0400792 | + | 0.999197i | \(0.512761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4216 | 0.477284 | ||||||||
\(914\) | −2.68639 | −0.0888580 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.9171 | 0.591997 | ||||||||
\(917\) | 2.37485 | 0.0784246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.3462 | 1.66077 | 0.830384 | − | 0.557192i | \(-0.188121\pi\) | ||||
0.830384 | + | 0.557192i | \(0.188121\pi\) | |||||||
\(920\) | −1.53645 | −0.0506551 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.16838 | 0.0714118 | ||||||||
\(923\) | −14.0094 | −0.461125 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5331 | 0.346328 | ||||||||
\(926\) | 23.0924 | 0.758865 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 42.8884 | 1.40788 | ||||||||
\(929\) | 32.9858 | 1.08223 | 0.541115 | − | 0.840948i | \(-0.318002\pi\) | ||||
0.541115 | + | 0.840948i | \(0.318002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.5510 | −0.968494 | ||||||||
\(932\) | 22.3510 | 0.732131 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.1450 | −0.462838 | ||||||||
\(935\) | 4.60687 | 0.150661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9023 | 1.56490 | 0.782450 | − | 0.622714i | \(-0.213970\pi\) | ||||
0.782450 | + | 0.622714i | \(0.213970\pi\) | |||||||
\(938\) | −1.66900 | −0.0544948 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.597783 | 0.0194975 | ||||||||
\(941\) | 4.42362 | 0.144206 | 0.0721030 | − | 0.997397i | \(-0.477029\pi\) | ||||
0.0721030 | + | 0.997397i | \(0.477029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60884 | −0.0523912 | ||||||||
\(944\) | −13.2770 | −0.432131 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.73624 | 0.0889627 | ||||||||
\(947\) | −19.3253 | −0.627987 | −0.313994 | − | 0.949425i | \(-0.601667\pi\) | ||||
−0.313994 | + | 0.949425i | \(0.601667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.10646 | 0.0359171 | ||||||||
\(950\) | −15.5747 | −0.505311 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.55134 | −0.0826895 | ||||||||
\(953\) | −30.0968 | −0.974931 | −0.487465 | − | 0.873142i | \(-0.662078\pi\) | ||||
−0.487465 | + | 0.873142i | \(0.662078\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.35408 | 0.302691 | ||||||||
\(956\) | 4.93544 | 0.159623 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.68051 | −0.183529 | ||||||||
\(959\) | 2.70948 | 0.0874937 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8515 | −0.640371 | ||||||||
\(962\) | 2.01426 | 0.0649423 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.0992 | −1.32372 | ||||||||
\(965\) | 2.23402 | 0.0719156 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.6607 | −1.37187 | −0.685937 | − | 0.727661i | \(-0.740608\pi\) | ||||
−0.685937 | + | 0.727661i | \(0.740608\pi\) | |||||||
\(968\) | 14.0404 | 0.451277 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.79378 | 0.121811 | ||||||||
\(971\) | −33.0050 | −1.05918 | −0.529591 | − | 0.848253i | \(-0.677655\pi\) | ||||
−0.529591 | + | 0.848253i | \(0.677655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.974412 | 0.0312382 | ||||||||
\(974\) | 24.7187 | 0.792037 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.87483 | −0.156039 | ||||||||
\(977\) | 5.79949 | 0.185542 | 0.0927710 | − | 0.995687i | \(-0.470428\pi\) | ||||
0.0927710 | + | 0.995687i | \(0.470428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.2296 | 0.486740 | ||||||||
\(980\) | −3.83850 | −0.122616 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.13095 | −0.0680013 | ||||||||
\(983\) | 35.2304 | 1.12367 | 0.561837 | − | 0.827248i | \(-0.310095\pi\) | ||||
0.561837 | + | 0.827248i | \(0.310095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.57081 | 0.0500501 | ||||||||
\(986\) | 27.9371 | 0.889700 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.43245 | 0.236458 | ||||||||
\(989\) | 2.34891 | 0.0746911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.08023 | 0.288443 | 0.144221 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144221 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(992\) | 19.5737 | 0.621466 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.68424 | 0.0534210 | ||||||||
\(995\) | 4.40992 | 0.139804 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.6440 | 1.88894 | 0.944472 | − | 0.328591i | \(-0.106574\pi\) | ||||
0.944472 | + | 0.328591i | \(0.106574\pi\) | |||||||
\(998\) | 21.9808 | 0.695791 | ||||||||
\(999\) | 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 | 4527.2.a.k.1.6 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.5 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.5 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.6 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.10 | 10 | 12.11 | even | 2 |