Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.82709\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.95630 | 1.38331 | 0.691655 | − | 0.722228i | \(-0.256882\pi\) | ||||
0.691655 | + | 0.722228i | \(0.256882\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.82709 | 0.913545 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.95630 | 0.798654 | ||||||||
\(7\) | −1.54732 | −0.584831 | −0.292416 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292416 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(8\) | −0.338261 | −0.119593 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.82709 | 0.527436 | ||||||||
\(13\) | −4.15622 | −1.15273 | −0.576363 | − | 0.817194i | \(-0.695529\pi\) | ||||
−0.576363 | + | 0.817194i | \(0.695529\pi\) | |||||||
\(14\) | −3.02701 | −0.809003 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.31592 | −1.07898 | ||||||||
\(17\) | −0.741591 | −0.179862 | −0.0899312 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899312 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(18\) | 1.95630 | 0.461103 | ||||||||
\(19\) | 7.48127 | 1.71632 | 0.858161 | − | 0.513381i | \(-0.171607\pi\) | ||||
0.858161 | + | 0.513381i | \(0.171607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.54732 | −0.337652 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.15622 | 0.241088 | 0.120544 | − | 0.992708i | \(-0.461536\pi\) | ||||
0.120544 | + | 0.992708i | \(0.461536\pi\) | |||||||
\(24\) | −0.338261 | −0.0690473 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.13078 | −1.59458 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.82709 | −0.534270 | ||||||||
\(29\) | 6.88558 | 1.27862 | 0.639310 | − | 0.768949i | \(-0.279220\pi\) | ||||
0.639310 | + | 0.768949i | \(0.279220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.77583 | 1.21697 | 0.608487 | − | 0.793564i | \(-0.291777\pi\) | ||||
0.608487 | + | 0.793564i | \(0.291777\pi\) | |||||||
\(32\) | −7.76669 | −1.37297 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.45077 | −0.248805 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82709 | 0.304515 | ||||||||
\(37\) | −3.92015 | −0.644468 | −0.322234 | − | 0.946660i | \(-0.604434\pi\) | ||||
−0.322234 | + | 0.946660i | \(0.604434\pi\) | |||||||
\(38\) | 14.6356 | 2.37420 | ||||||||
\(39\) | −4.15622 | −0.665527 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0345680 | 0.00539862 | 0.00269931 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269931 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(42\) | −3.02701 | −0.467078 | ||||||||
\(43\) | 11.1726 | 1.70380 | 0.851901 | − | 0.523703i | \(-0.175450\pi\) | ||||
0.851901 | + | 0.523703i | \(0.175450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.26190 | 0.333499 | ||||||||
\(47\) | 7.04179 | 1.02715 | 0.513576 | − | 0.858044i | \(-0.328321\pi\) | ||||
0.513576 | + | 0.858044i | \(0.328321\pi\) | |||||||
\(48\) | −4.31592 | −0.622949 | ||||||||
\(49\) | −4.60581 | −0.657972 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.741591 | −0.103844 | ||||||||
\(52\) | −7.59378 | −1.05307 | ||||||||
\(53\) | 1.22384 | 0.168107 | 0.0840537 | − | 0.996461i | \(-0.473213\pi\) | ||||
0.0840537 | + | 0.996461i | \(0.473213\pi\) | |||||||
\(54\) | 1.95630 | 0.266218 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.523398 | 0.0699420 | ||||||||
\(57\) | 7.48127 | 0.990919 | ||||||||
\(58\) | 13.4702 | 1.76873 | ||||||||
\(59\) | −4.30934 | −0.561028 | −0.280514 | − | 0.959850i | \(-0.590505\pi\) | ||||
−0.280514 | + | 0.959850i | \(0.590505\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.55488 | 0.839266 | 0.419633 | − | 0.907694i | \(-0.362159\pi\) | ||||
0.419633 | + | 0.907694i | \(0.362159\pi\) | |||||||
\(62\) | 13.2555 | 1.68345 | ||||||||
\(63\) | −1.54732 | −0.194944 | ||||||||
\(64\) | −6.56210 | −0.820263 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.55199 | 0.433944 | 0.216972 | − | 0.976178i | \(-0.430382\pi\) | ||||
0.216972 | + | 0.976178i | \(0.430382\pi\) | |||||||
\(68\) | −1.35495 | −0.164312 | ||||||||
\(69\) | 1.15622 | 0.139192 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.88558 | 0.698490 | 0.349245 | − | 0.937031i | \(-0.386438\pi\) | ||||
0.349245 | + | 0.937031i | \(0.386438\pi\) | |||||||
\(72\) | −0.338261 | −0.0398645 | ||||||||
\(73\) | −4.57880 | −0.535907 | −0.267954 | − | 0.963432i | \(-0.586347\pi\) | ||||
−0.267954 | + | 0.963432i | \(0.586347\pi\) | |||||||
\(74\) | −7.66897 | −0.891499 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.6690 | 1.56794 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.13078 | −0.920630 | ||||||||
\(79\) | 6.17758 | 0.695032 | 0.347516 | − | 0.937674i | \(-0.387025\pi\) | ||||
0.347516 | + | 0.937674i | \(0.387025\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.0676252 | 0.00746796 | ||||||||
\(83\) | 15.1493 | 1.66285 | 0.831424 | − | 0.555639i | \(-0.187526\pi\) | ||||
0.831424 | + | 0.555639i | \(0.187526\pi\) | |||||||
\(84\) | −2.82709 | −0.308461 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 21.8569 | 2.35689 | ||||||||
\(87\) | 6.88558 | 0.738212 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.5582 | −1.86117 | −0.930585 | − | 0.366076i | \(-0.880701\pi\) | ||||
−0.930585 | + | 0.366076i | \(0.880701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.43099 | 0.674151 | ||||||||
\(92\) | 2.11251 | 0.220244 | ||||||||
\(93\) | 6.77583 | 0.702621 | ||||||||
\(94\) | 13.7758 | 1.42087 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.76669 | −0.792685 | ||||||||
\(97\) | 0.144318 | 0.0146533 | 0.00732665 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732665 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(98\) | −9.01032 | −0.910179 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.50073 | −0.348335 | −0.174168 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174168 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(102\) | −1.45077 | −0.143648 | ||||||||
\(103\) | −12.1151 | −1.19373 | −0.596866 | − | 0.802341i | \(-0.703588\pi\) | ||||
−0.596866 | + | 0.802341i | \(0.703588\pi\) | |||||||
\(104\) | 1.40589 | 0.137859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.39419 | 0.232545 | ||||||||
\(107\) | 3.77307 | 0.364756 | 0.182378 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182378 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(108\) | 1.82709 | 0.175812 | ||||||||
\(109\) | 18.3140 | 1.75416 | 0.877082 | − | 0.480341i | \(-0.159487\pi\) | ||||
0.877082 | + | 0.480341i | \(0.159487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.92015 | −0.372084 | ||||||||
\(112\) | 6.67810 | 0.631021 | ||||||||
\(113\) | 14.3333 | 1.34836 | 0.674180 | − | 0.738567i | \(-0.264497\pi\) | ||||
0.674180 | + | 0.738567i | \(0.264497\pi\) | |||||||
\(114\) | 14.6356 | 1.37075 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.5806 | 1.16808 | ||||||||
\(117\) | −4.15622 | −0.384242 | ||||||||
\(118\) | −8.43034 | −0.776076 | ||||||||
\(119\) | 1.14748 | 0.105189 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 12.8233 | 1.16096 | ||||||||
\(123\) | 0.0345680 | 0.00311689 | ||||||||
\(124\) | 12.3801 | 1.11176 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.02701 | −0.269668 | ||||||||
\(127\) | 14.4648 | 1.28354 | 0.641771 | − | 0.766896i | \(-0.278200\pi\) | ||||
0.641771 | + | 0.766896i | \(0.278200\pi\) | |||||||
\(128\) | 2.69598 | 0.238293 | ||||||||
\(129\) | 11.1726 | 0.983691 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6523 | 1.28017 | 0.640087 | − | 0.768302i | \(-0.278898\pi\) | ||||
0.640087 | + | 0.768302i | \(0.278898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5759 | −1.00376 | ||||||||
\(134\) | 6.94874 | 0.600280 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.250852 | 0.0215103 | ||||||||
\(137\) | −10.4178 | −0.890051 | −0.445026 | − | 0.895518i | \(-0.646805\pi\) | ||||
−0.445026 | + | 0.895518i | \(0.646805\pi\) | |||||||
\(138\) | 2.26190 | 0.192546 | ||||||||
\(139\) | −1.73212 | −0.146917 | −0.0734584 | − | 0.997298i | \(-0.523404\pi\) | ||||
−0.0734584 | + | 0.997298i | \(0.523404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.04179 | 0.593026 | ||||||||
\(142\) | 11.5139 | 0.966228 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.31592 | −0.359660 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.95748 | −0.741326 | ||||||||
\(147\) | −4.60581 | −0.379881 | ||||||||
\(148\) | −7.16247 | −0.588751 | ||||||||
\(149\) | −12.4580 | −1.02060 | −0.510299 | − | 0.859997i | \(-0.670465\pi\) | ||||
−0.510299 | + | 0.859997i | \(0.670465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6070 | 1.43284 | 0.716418 | − | 0.697671i | \(-0.245780\pi\) | ||||
0.716418 | + | 0.697671i | \(0.245780\pi\) | |||||||
\(152\) | −2.53062 | −0.205261 | ||||||||
\(153\) | −0.741591 | −0.0599541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.59378 | −0.607989 | ||||||||
\(157\) | −15.8594 | −1.26572 | −0.632860 | − | 0.774266i | \(-0.718119\pi\) | ||||
−0.632860 | + | 0.774266i | \(0.718119\pi\) | |||||||
\(158\) | 12.0852 | 0.961444 | ||||||||
\(159\) | 1.22384 | 0.0970569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.78903 | −0.140996 | ||||||||
\(162\) | 1.95630 | 0.153701 | ||||||||
\(163\) | −8.51958 | −0.667305 | −0.333652 | − | 0.942696i | \(-0.608281\pi\) | ||||
−0.333652 | + | 0.942696i | \(0.608281\pi\) | |||||||
\(164\) | 0.0631589 | 0.00493188 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.6364 | 2.30023 | ||||||||
\(167\) | −14.5293 | −1.12431 | −0.562156 | − | 0.827031i | \(-0.690028\pi\) | ||||
−0.562156 | + | 0.827031i | \(0.690028\pi\) | |||||||
\(168\) | 0.523398 | 0.0403810 | ||||||||
\(169\) | 4.27413 | 0.328779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.48127 | 0.572107 | ||||||||
\(172\) | 20.4133 | 1.55650 | ||||||||
\(173\) | 10.1366 | 0.770674 | 0.385337 | − | 0.922776i | \(-0.374085\pi\) | ||||
0.385337 | + | 0.922776i | \(0.374085\pi\) | |||||||
\(174\) | 13.4702 | 1.02118 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.30934 | −0.323910 | ||||||||
\(178\) | −34.3491 | −2.57457 | ||||||||
\(179\) | 26.6506 | 1.99196 | 0.995978 | − | 0.0895936i | \(-0.0285568\pi\) | ||||
0.995978 | + | 0.0895936i | \(0.0285568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0593 | 1.63966 | 0.819829 | − | 0.572609i | \(-0.194069\pi\) | ||||
0.819829 | + | 0.572609i | \(0.194069\pi\) | |||||||
\(182\) | 12.5809 | 0.932559 | ||||||||
\(183\) | 6.55488 | 0.484550 | ||||||||
\(184\) | −0.391103 | −0.0288325 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.2555 | 0.971942 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.8660 | 0.938349 | ||||||||
\(189\) | −1.54732 | −0.112551 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6234 | 0.768679 | 0.384339 | − | 0.923192i | \(-0.374429\pi\) | ||||
0.384339 | + | 0.923192i | \(0.374429\pi\) | |||||||
\(192\) | −6.56210 | −0.473579 | ||||||||
\(193\) | 2.68375 | 0.193180 | 0.0965902 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965902 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(194\) | 0.282329 | 0.0202700 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.41523 | −0.601088 | ||||||||
\(197\) | −17.2838 | −1.23142 | −0.615709 | − | 0.787973i | \(-0.711130\pi\) | ||||
−0.615709 | + | 0.787973i | \(0.711130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.39386 | −0.595025 | −0.297513 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297513 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.55199 | 0.250538 | ||||||||
\(202\) | −6.84846 | −0.481856 | ||||||||
\(203\) | −10.6542 | −0.747777 | ||||||||
\(204\) | −1.35495 | −0.0948658 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.7006 | −1.65130 | ||||||||
\(207\) | 1.15622 | 0.0803625 | ||||||||
\(208\) | 17.9379 | 1.24377 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6434 | −1.62768 | −0.813840 | − | 0.581089i | \(-0.802627\pi\) | ||||
−0.813840 | + | 0.581089i | \(0.802627\pi\) | |||||||
\(212\) | 2.23607 | 0.153574 | ||||||||
\(213\) | 5.88558 | 0.403273 | ||||||||
\(214\) | 7.38124 | 0.504571 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.338261 | −0.0230158 | ||||||||
\(217\) | −10.4844 | −0.711725 | ||||||||
\(218\) | 35.8276 | 2.42655 | ||||||||
\(219\) | −4.57880 | −0.309406 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.08221 | 0.207332 | ||||||||
\(222\) | −7.66897 | −0.514707 | ||||||||
\(223\) | 23.7007 | 1.58712 | 0.793559 | − | 0.608494i | \(-0.208226\pi\) | ||||
0.793559 | + | 0.608494i | \(0.208226\pi\) | |||||||
\(224\) | 12.0175 | 0.802956 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.0401 | 1.86520 | ||||||||
\(227\) | 14.4080 | 0.956295 | 0.478148 | − | 0.878279i | \(-0.341308\pi\) | ||||
0.478148 | + | 0.878279i | \(0.341308\pi\) | |||||||
\(228\) | 13.6690 | 0.905249 | ||||||||
\(229\) | −20.6000 | −1.36129 | −0.680644 | − | 0.732614i | \(-0.738300\pi\) | ||||
−0.680644 | + | 0.732614i | \(0.738300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.32912 | −0.152915 | ||||||||
\(233\) | −10.1634 | −0.665829 | −0.332915 | − | 0.942957i | \(-0.608032\pi\) | ||||
−0.332915 | + | 0.942957i | \(0.608032\pi\) | |||||||
\(234\) | −8.13078 | −0.531526 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.87356 | −0.512525 | ||||||||
\(237\) | 6.17758 | 0.401277 | ||||||||
\(238\) | 2.24481 | 0.145509 | ||||||||
\(239\) | −8.52498 | −0.551435 | −0.275717 | − | 0.961239i | \(-0.588915\pi\) | ||||
−0.275717 | + | 0.961239i | \(0.588915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.81966 | 0.310462 | 0.155231 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155231 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.9764 | 0.766707 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0676252 | 0.00431163 | ||||||||
\(247\) | −31.0938 | −1.97845 | ||||||||
\(248\) | −2.29200 | −0.145542 | ||||||||
\(249\) | 15.1493 | 0.960045 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0612 | −0.887538 | −0.443769 | − | 0.896141i | \(-0.646359\pi\) | ||||
−0.443769 | + | 0.896141i | \(0.646359\pi\) | |||||||
\(252\) | −2.82709 | −0.178090 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 28.2974 | 1.77554 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.3983 | 1.14990 | ||||||||
\(257\) | −11.6340 | −0.725709 | −0.362854 | − | 0.931846i | \(-0.618198\pi\) | ||||
−0.362854 | + | 0.931846i | \(0.618198\pi\) | |||||||
\(258\) | 21.8569 | 1.36075 | ||||||||
\(259\) | 6.06572 | 0.376905 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.88558 | 0.426207 | ||||||||
\(262\) | 28.6642 | 1.77088 | ||||||||
\(263\) | 11.0280 | 0.680015 | 0.340007 | − | 0.940423i | \(-0.389570\pi\) | ||||
0.340007 | + | 0.940423i | \(0.389570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.6459 | −1.38851 | ||||||||
\(267\) | −17.5582 | −1.07455 | ||||||||
\(268\) | 6.48981 | 0.396428 | ||||||||
\(269\) | 18.9754 | 1.15695 | 0.578476 | − | 0.815700i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815700i | \(0.303648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5699 | 0.945802 | 0.472901 | − | 0.881116i | \(-0.343207\pi\) | ||||
0.472901 | + | 0.881116i | \(0.343207\pi\) | |||||||
\(272\) | 3.20065 | 0.194068 | ||||||||
\(273\) | 6.43099 | 0.389221 | ||||||||
\(274\) | −20.3803 | −1.23122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.11251 | 0.127158 | ||||||||
\(277\) | −5.91319 | −0.355289 | −0.177645 | − | 0.984095i | \(-0.556848\pi\) | ||||
−0.177645 | + | 0.984095i | \(0.556848\pi\) | |||||||
\(278\) | −3.38855 | −0.203232 | ||||||||
\(279\) | 6.77583 | 0.405658 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.7543 | 1.65569 | 0.827843 | − | 0.560961i | \(-0.189568\pi\) | ||||
0.827843 | + | 0.560961i | \(0.189568\pi\) | |||||||
\(282\) | 13.7758 | 0.820339 | ||||||||
\(283\) | −19.7440 | −1.17366 | −0.586830 | − | 0.809710i | \(-0.699624\pi\) | ||||
−0.586830 | + | 0.809710i | \(0.699624\pi\) | |||||||
\(284\) | 10.7535 | 0.638102 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0534877 | −0.00315728 | ||||||||
\(288\) | −7.76669 | −0.457657 | ||||||||
\(289\) | −16.4500 | −0.967650 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.144318 | 0.00846008 | ||||||||
\(292\) | −8.36588 | −0.489576 | ||||||||
\(293\) | −19.8794 | −1.16137 | −0.580684 | − | 0.814129i | \(-0.697215\pi\) | ||||
−0.580684 | + | 0.814129i | \(0.697215\pi\) | |||||||
\(294\) | −9.01032 | −0.525492 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.32603 | 0.0770741 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.3715 | −1.41180 | ||||||||
\(299\) | −4.80548 | −0.277908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.2875 | −0.996437 | ||||||||
\(302\) | 34.4445 | 1.98206 | ||||||||
\(303\) | −3.50073 | −0.201112 | ||||||||
\(304\) | −32.2886 | −1.85188 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.45077 | −0.0829351 | ||||||||
\(307\) | 10.3072 | 0.588262 | 0.294131 | − | 0.955765i | \(-0.404970\pi\) | ||||
0.294131 | + | 0.955765i | \(0.404970\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1151 | −0.689202 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.36316 | 0.474231 | 0.237116 | − | 0.971481i | \(-0.423798\pi\) | ||||
0.237116 | + | 0.971481i | \(0.423798\pi\) | |||||||
\(312\) | 1.40589 | 0.0795926 | ||||||||
\(313\) | 7.12380 | 0.402661 | 0.201331 | − | 0.979523i | \(-0.435473\pi\) | ||||
0.201331 | + | 0.979523i | \(0.435473\pi\) | |||||||
\(314\) | −31.0257 | −1.75088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2870 | 0.634943 | ||||||||
\(317\) | −27.5894 | −1.54957 | −0.774786 | − | 0.632223i | \(-0.782143\pi\) | ||||
−0.774786 | + | 0.632223i | \(0.782143\pi\) | |||||||
\(318\) | 2.39419 | 0.134260 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.77307 | 0.210592 | ||||||||
\(322\) | −3.49988 | −0.195040 | ||||||||
\(323\) | −5.54805 | −0.308702 | ||||||||
\(324\) | 1.82709 | 0.101505 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.6668 | −0.923089 | ||||||||
\(327\) | 18.3140 | 1.01277 | ||||||||
\(328\) | −0.0116930 | −0.000645639 0 | ||||||||
\(329\) | −10.8959 | −0.600710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.9410 | −0.876195 | −0.438098 | − | 0.898927i | \(-0.644348\pi\) | ||||
−0.438098 | + | 0.898927i | \(0.644348\pi\) | |||||||
\(332\) | 27.6791 | 1.51909 | ||||||||
\(333\) | −3.92015 | −0.214823 | ||||||||
\(334\) | −28.4236 | −1.55527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.67810 | 0.364320 | ||||||||
\(337\) | −11.9554 | −0.651250 | −0.325625 | − | 0.945499i | \(-0.605575\pi\) | ||||
−0.325625 | + | 0.945499i | \(0.605575\pi\) | |||||||
\(338\) | 8.36145 | 0.454803 | ||||||||
\(339\) | 14.3333 | 0.778476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 14.6356 | 0.791401 | ||||||||
\(343\) | 17.9579 | 0.969634 | ||||||||
\(344\) | −3.77925 | −0.203764 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8303 | 1.06608 | ||||||||
\(347\) | 2.19367 | 0.117762 | 0.0588812 | − | 0.998265i | \(-0.481247\pi\) | ||||
0.0588812 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(348\) | 12.5806 | 0.674390 | ||||||||
\(349\) | −4.82985 | −0.258536 | −0.129268 | − | 0.991610i | \(-0.541263\pi\) | ||||
−0.129268 | + | 0.991610i | \(0.541263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.15622 | −0.221842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1032 | 0.590962 | 0.295481 | − | 0.955349i | \(-0.404520\pi\) | ||||
0.295481 | + | 0.955349i | \(0.404520\pi\) | |||||||
\(354\) | −8.43034 | −0.448068 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −32.0805 | −1.70026 | ||||||||
\(357\) | 1.14748 | 0.0607310 | ||||||||
\(358\) | 52.1364 | 2.75549 | ||||||||
\(359\) | −12.5790 | −0.663894 | −0.331947 | − | 0.943298i | \(-0.607706\pi\) | ||||
−0.331947 | + | 0.943298i | \(0.607706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.9694 | 1.94576 | ||||||||
\(362\) | 43.1546 | 2.26815 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.7500 | 0.615867 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.8233 | 0.670283 | ||||||||
\(367\) | 20.9190 | 1.09197 | 0.545983 | − | 0.837796i | \(-0.316156\pi\) | ||||
0.545983 | + | 0.837796i | \(0.316156\pi\) | |||||||
\(368\) | −4.99013 | −0.260129 | ||||||||
\(369\) | 0.0345680 | 0.00179954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.89367 | −0.0983145 | ||||||||
\(372\) | 12.3801 | 0.641876 | ||||||||
\(373\) | −9.62019 | −0.498115 | −0.249057 | − | 0.968489i | \(-0.580121\pi\) | ||||
−0.249057 | + | 0.968489i | \(0.580121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.38197 | −0.122841 | ||||||||
\(377\) | −28.6180 | −1.47390 | ||||||||
\(378\) | −3.02701 | −0.155693 | ||||||||
\(379\) | −29.8900 | −1.53534 | −0.767672 | − | 0.640843i | \(-0.778585\pi\) | ||||
−0.767672 | + | 0.640843i | \(0.778585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4648 | 0.741053 | ||||||||
\(382\) | 20.7824 | 1.06332 | ||||||||
\(383\) | 28.0360 | 1.43257 | 0.716287 | − | 0.697806i | \(-0.245840\pi\) | ||||
0.716287 | + | 0.697806i | \(0.245840\pi\) | |||||||
\(384\) | 2.69598 | 0.137578 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.25021 | 0.267228 | ||||||||
\(387\) | 11.1726 | 0.567934 | ||||||||
\(388\) | 0.263682 | 0.0133864 | ||||||||
\(389\) | 9.89338 | 0.501614 | 0.250807 | − | 0.968037i | \(-0.419304\pi\) | ||||
0.250807 | + | 0.968037i | \(0.419304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.857439 | −0.0433626 | ||||||||
\(392\) | 1.55797 | 0.0786892 | ||||||||
\(393\) | 14.6523 | 0.739109 | ||||||||
\(394\) | −33.8122 | −1.70343 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7457 | −0.740067 | −0.370033 | − | 0.929018i | \(-0.620654\pi\) | ||||
−0.370033 | + | 0.929018i | \(0.620654\pi\) | |||||||
\(398\) | −16.4209 | −0.823104 | ||||||||
\(399\) | −11.5759 | −0.579520 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3793 | −0.718067 | −0.359034 | − | 0.933325i | \(-0.616894\pi\) | ||||
−0.359034 | + | 0.933325i | \(0.616894\pi\) | |||||||
\(402\) | 6.94874 | 0.346572 | ||||||||
\(403\) | −28.1618 | −1.40284 | ||||||||
\(404\) | −6.39615 | −0.318220 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.8427 | −1.03441 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.250852 | 0.0124190 | ||||||||
\(409\) | −11.0034 | −0.544083 | −0.272042 | − | 0.962285i | \(-0.587699\pi\) | ||||
−0.272042 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4178 | −0.513871 | ||||||||
\(412\) | −22.1353 | −1.09053 | ||||||||
\(413\) | 6.66792 | 0.328107 | ||||||||
\(414\) | 2.26190 | 0.111166 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 32.2800 | 1.58266 | ||||||||
\(417\) | −1.73212 | −0.0848225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.80166 | −0.136870 | −0.0684350 | − | 0.997656i | \(-0.521801\pi\) | ||||
−0.0684350 | + | 0.997656i | \(0.521801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0116 | −0.877830 | −0.438915 | − | 0.898529i | \(-0.644637\pi\) | ||||
−0.438915 | + | 0.898529i | \(0.644637\pi\) | |||||||
\(422\) | −46.2535 | −2.25158 | ||||||||
\(423\) | 7.04179 | 0.342384 | ||||||||
\(424\) | −0.413978 | −0.0201045 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.5139 | 0.557852 | ||||||||
\(427\) | −10.1425 | −0.490829 | ||||||||
\(428\) | 6.89374 | 0.333221 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.9751 | −0.673159 | −0.336580 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336580 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(432\) | −4.31592 | −0.207650 | ||||||||
\(433\) | −0.370876 | −0.0178232 | −0.00891159 | − | 0.999960i | \(-0.502837\pi\) | ||||
−0.00891159 | + | 0.999960i | \(0.502837\pi\) | |||||||
\(434\) | −20.5105 | −0.984536 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.4614 | 1.60251 | ||||||||
\(437\) | 8.64996 | 0.413784 | ||||||||
\(438\) | −8.95748 | −0.428005 | ||||||||
\(439\) | −11.2753 | −0.538141 | −0.269071 | − | 0.963120i | \(-0.586716\pi\) | ||||
−0.269071 | + | 0.963120i | \(0.586716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.60581 | −0.219324 | ||||||||
\(442\) | 6.02972 | 0.286805 | ||||||||
\(443\) | −29.5638 | −1.40462 | −0.702308 | − | 0.711873i | \(-0.747847\pi\) | ||||
−0.702308 | + | 0.711873i | \(0.747847\pi\) | |||||||
\(444\) | −7.16247 | −0.339916 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 46.3656 | 2.19547 | ||||||||
\(447\) | −12.4580 | −0.589243 | ||||||||
\(448\) | 10.1537 | 0.479715 | ||||||||
\(449\) | 1.13716 | 0.0536659 | 0.0268330 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268330 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 26.1882 | 1.23179 | ||||||||
\(453\) | 17.6070 | 0.827248 | ||||||||
\(454\) | 28.1864 | 1.32285 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.53062 | −0.118507 | ||||||||
\(457\) | 7.03740 | 0.329196 | 0.164598 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164598 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(458\) | −40.2997 | −1.88308 | ||||||||
\(459\) | −0.741591 | −0.0346145 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7977 | −0.875497 | −0.437748 | − | 0.899098i | \(-0.644224\pi\) | ||||
−0.437748 | + | 0.899098i | \(0.644224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.0376 | 1.72128 | 0.860642 | − | 0.509211i | \(-0.170063\pi\) | ||||
0.860642 | + | 0.509211i | \(0.170063\pi\) | |||||||
\(464\) | −29.7176 | −1.37961 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.8827 | −0.921048 | ||||||||
\(467\) | −0.579204 | −0.0268024 | −0.0134012 | − | 0.999910i | \(-0.504266\pi\) | ||||
−0.0134012 | + | 0.999910i | \(0.504266\pi\) | |||||||
\(468\) | −7.59378 | −0.351023 | ||||||||
\(469\) | −5.49606 | −0.253784 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.8594 | −0.730763 | ||||||||
\(472\) | 1.45768 | 0.0670953 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.0852 | 0.555090 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.09655 | 0.0960950 | ||||||||
\(477\) | 1.22384 | 0.0560358 | ||||||||
\(478\) | −16.6774 | −0.762805 | ||||||||
\(479\) | 11.9258 | 0.544903 | 0.272452 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272452 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2930 | 0.742896 | ||||||||
\(482\) | 9.42868 | 0.429465 | ||||||||
\(483\) | −1.78903 | −0.0814038 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.95630 | 0.0887394 | ||||||||
\(487\) | −21.8411 | −0.989715 | −0.494857 | − | 0.868974i | \(-0.664780\pi\) | ||||
−0.494857 | + | 0.868974i | \(0.664780\pi\) | |||||||
\(488\) | −2.21726 | −0.100371 | ||||||||
\(489\) | −8.51958 | −0.385269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.47542 | −0.382490 | −0.191245 | − | 0.981542i | \(-0.561253\pi\) | ||||
−0.191245 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(492\) | 0.0631589 | 0.00284742 | ||||||||
\(493\) | −5.10629 | −0.229976 | ||||||||
\(494\) | −60.8286 | −2.73681 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.2439 | −1.31309 | ||||||||
\(497\) | −9.10686 | −0.408499 | ||||||||
\(498\) | 29.6364 | 1.32804 | ||||||||
\(499\) | 2.54042 | 0.113725 | 0.0568624 | − | 0.998382i | \(-0.481890\pi\) | ||||
0.0568624 | + | 0.998382i | \(0.481890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.5293 | −0.649122 | ||||||||
\(502\) | −27.5080 | −1.22774 | ||||||||
\(503\) | −32.6484 | −1.45572 | −0.727860 | − | 0.685725i | \(-0.759485\pi\) | ||||
−0.727860 | + | 0.685725i | \(0.759485\pi\) | |||||||
\(504\) | 0.523398 | 0.0233140 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.27413 | 0.189821 | ||||||||
\(508\) | 26.4285 | 1.17257 | ||||||||
\(509\) | −4.32103 | −0.191526 | −0.0957632 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957632 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.08485 | 0.313415 | ||||||||
\(512\) | 30.6006 | 1.35237 | ||||||||
\(513\) | 7.48127 | 0.330306 | ||||||||
\(514\) | −22.7595 | −1.00388 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 20.4133 | 0.898646 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.8663 | 0.521377 | ||||||||
\(519\) | 10.1366 | 0.444949 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3715 | −1.02392 | −0.511962 | − | 0.859008i | \(-0.671081\pi\) | ||||
−0.511962 | + | 0.859008i | \(0.671081\pi\) | |||||||
\(522\) | 13.4702 | 0.589576 | ||||||||
\(523\) | 29.1251 | 1.27355 | 0.636775 | − | 0.771050i | \(-0.280268\pi\) | ||||
0.636775 | + | 0.771050i | \(0.280268\pi\) | |||||||
\(524\) | 26.7710 | 1.16950 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5740 | 0.940671 | ||||||||
\(527\) | −5.02490 | −0.218888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6632 | −0.941877 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.30934 | −0.187009 | ||||||||
\(532\) | −21.1502 | −0.916979 | ||||||||
\(533\) | −0.143672 | −0.00622313 | ||||||||
\(534\) | −34.3491 | −1.48643 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.20150 | −0.0518969 | ||||||||
\(537\) | 26.6506 | 1.15006 | ||||||||
\(538\) | 37.1215 | 1.60042 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.1724 | 1.12524 | 0.562619 | − | 0.826716i | \(-0.309794\pi\) | ||||
0.562619 | + | 0.826716i | \(0.309794\pi\) | |||||||
\(542\) | 30.4592 | 1.30834 | ||||||||
\(543\) | 22.0593 | 0.946657 | ||||||||
\(544\) | 5.75971 | 0.246946 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.5809 | 0.538413 | ||||||||
\(547\) | −3.58440 | −0.153258 | −0.0766289 | − | 0.997060i | \(-0.524416\pi\) | ||||
−0.0766289 | + | 0.997060i | \(0.524416\pi\) | |||||||
\(548\) | −19.0342 | −0.813102 | ||||||||
\(549\) | 6.55488 | 0.279755 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.5129 | 2.19452 | ||||||||
\(552\) | −0.391103 | −0.0166464 | ||||||||
\(553\) | −9.55868 | −0.406476 | ||||||||
\(554\) | −11.5680 | −0.491475 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.16475 | −0.134215 | ||||||||
\(557\) | −18.5029 | −0.783992 | −0.391996 | − | 0.919967i | \(-0.628215\pi\) | ||||
−0.391996 | + | 0.919967i | \(0.628215\pi\) | |||||||
\(558\) | 13.2555 | 0.561151 | ||||||||
\(559\) | −46.4356 | −1.96402 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 54.2957 | 2.29033 | ||||||||
\(563\) | 31.3801 | 1.32251 | 0.661257 | − | 0.750159i | \(-0.270023\pi\) | ||||
0.661257 | + | 0.750159i | \(0.270023\pi\) | |||||||
\(564\) | 12.8660 | 0.541756 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −38.6251 | −1.62354 | ||||||||
\(567\) | −1.54732 | −0.0649813 | ||||||||
\(568\) | −1.99086 | −0.0835348 | ||||||||
\(569\) | −0.944229 | −0.0395841 | −0.0197921 | − | 0.999804i | \(-0.506300\pi\) | ||||
−0.0197921 | + | 0.999804i | \(0.506300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.0576 | 1.59266 | 0.796331 | − | 0.604861i | \(-0.206771\pi\) | ||||
0.796331 | + | 0.604861i | \(0.206771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6234 | 0.443797 | ||||||||
\(574\) | −0.104638 | −0.00436749 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.56210 | −0.273421 | ||||||||
\(577\) | 46.2896 | 1.92706 | 0.963531 | − | 0.267596i | \(-0.0862291\pi\) | ||||
0.963531 | + | 0.267596i | \(0.0862291\pi\) | |||||||
\(578\) | −32.1811 | −1.33856 | ||||||||
\(579\) | 2.68375 | 0.111533 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.4407 | −0.972485 | ||||||||
\(582\) | 0.282329 | 0.0117029 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.54883 | 0.0640910 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.8900 | −1.60653 | ||||||||
\(587\) | 15.5435 | 0.641549 | 0.320774 | − | 0.947156i | \(-0.396057\pi\) | ||||
0.320774 | + | 0.947156i | \(0.396057\pi\) | |||||||
\(588\) | −8.41523 | −0.347038 | ||||||||
\(589\) | 50.6918 | 2.08872 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.2838 | −0.710960 | ||||||||
\(592\) | 16.9190 | 0.695368 | ||||||||
\(593\) | −11.8521 | −0.486709 | −0.243355 | − | 0.969937i | \(-0.578248\pi\) | ||||
−0.243355 | + | 0.969937i | \(0.578248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.7619 | −0.932364 | ||||||||
\(597\) | −8.39386 | −0.343538 | ||||||||
\(598\) | −9.40094 | −0.384433 | ||||||||
\(599\) | 29.7295 | 1.21471 | 0.607357 | − | 0.794429i | \(-0.292230\pi\) | ||||
0.607357 | + | 0.794429i | \(0.292230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7234 | 0.763743 | 0.381871 | − | 0.924215i | \(-0.375280\pi\) | ||||
0.381871 | + | 0.924215i | \(0.375280\pi\) | |||||||
\(602\) | −33.8195 | −1.37838 | ||||||||
\(603\) | 3.55199 | 0.144648 | ||||||||
\(604\) | 32.1696 | 1.30896 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.84846 | −0.278199 | ||||||||
\(607\) | −41.6415 | −1.69018 | −0.845088 | − | 0.534627i | \(-0.820452\pi\) | ||||
−0.845088 | + | 0.534627i | \(0.820452\pi\) | |||||||
\(608\) | −58.1047 | −2.35646 | ||||||||
\(609\) | −10.6542 | −0.431729 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.2672 | −1.18402 | ||||||||
\(612\) | −1.35495 | −0.0547708 | ||||||||
\(613\) | −20.6594 | −0.834424 | −0.417212 | − | 0.908809i | \(-0.636993\pi\) | ||||
−0.417212 | + | 0.908809i | \(0.636993\pi\) | |||||||
\(614\) | 20.1639 | 0.813748 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.0784 | −1.85505 | −0.927524 | − | 0.373764i | \(-0.878067\pi\) | ||||
−0.927524 | + | 0.373764i | \(0.878067\pi\) | |||||||
\(618\) | −23.7006 | −0.953380 | ||||||||
\(619\) | −20.3065 | −0.816187 | −0.408093 | − | 0.912940i | \(-0.633806\pi\) | ||||
−0.408093 | + | 0.912940i | \(0.633806\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15622 | 0.0463973 | ||||||||
\(622\) | 16.3608 | 0.656009 | ||||||||
\(623\) | 27.1682 | 1.08847 | ||||||||
\(624\) | 17.9379 | 0.718091 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.9363 | 0.557005 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.9766 | −1.15629 | ||||||||
\(629\) | 2.90715 | 0.115916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.4810 | 0.576479 | 0.288240 | − | 0.957558i | \(-0.406930\pi\) | ||||
0.288240 | + | 0.957558i | \(0.406930\pi\) | |||||||
\(632\) | −2.08964 | −0.0831212 | ||||||||
\(633\) | −23.6434 | −0.939741 | ||||||||
\(634\) | −53.9729 | −2.14354 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.23607 | 0.0886659 | ||||||||
\(637\) | 19.1427 | 0.758462 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.88558 | 0.232830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.61474 | 0.103276 | 0.0516380 | − | 0.998666i | \(-0.483556\pi\) | ||||
0.0516380 | + | 0.998666i | \(0.483556\pi\) | |||||||
\(642\) | 7.38124 | 0.291314 | ||||||||
\(643\) | −15.8227 | −0.623985 | −0.311993 | − | 0.950085i | \(-0.600996\pi\) | ||||
−0.311993 | + | 0.950085i | \(0.600996\pi\) | |||||||
\(644\) | −3.26873 | −0.128806 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.8536 | −0.427030 | ||||||||
\(647\) | 41.2841 | 1.62305 | 0.811523 | − | 0.584321i | \(-0.198639\pi\) | ||||
0.811523 | + | 0.584321i | \(0.198639\pi\) | |||||||
\(648\) | −0.338261 | −0.0132882 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4844 | −0.410915 | ||||||||
\(652\) | −15.5660 | −0.609613 | ||||||||
\(653\) | 28.9158 | 1.13156 | 0.565781 | − | 0.824556i | \(-0.308575\pi\) | ||||
0.565781 | + | 0.824556i | \(0.308575\pi\) | |||||||
\(654\) | 35.8276 | 1.40097 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.149193 | −0.00582500 | ||||||||
\(657\) | −4.57880 | −0.178636 | ||||||||
\(658\) | −21.3156 | −0.830968 | ||||||||
\(659\) | −9.25143 | −0.360384 | −0.180192 | − | 0.983631i | \(-0.557672\pi\) | ||||
−0.180192 | + | 0.983631i | \(0.557672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4522 | 0.717706 | 0.358853 | − | 0.933394i | \(-0.383168\pi\) | ||||
0.358853 | + | 0.933394i | \(0.383168\pi\) | |||||||
\(662\) | −31.1853 | −1.21205 | ||||||||
\(663\) | 3.08221 | 0.119703 | ||||||||
\(664\) | −5.12441 | −0.198866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.66897 | −0.297166 | ||||||||
\(667\) | 7.96121 | 0.308259 | ||||||||
\(668\) | −26.5464 | −1.02711 | ||||||||
\(669\) | 23.7007 | 0.916323 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 12.0175 | 0.463587 | ||||||||
\(673\) | 12.0185 | 0.463278 | 0.231639 | − | 0.972802i | \(-0.425591\pi\) | ||||
0.231639 | + | 0.972802i | \(0.425591\pi\) | |||||||
\(674\) | −23.3882 | −0.900880 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.80922 | 0.300354 | ||||||||
\(677\) | −8.09542 | −0.311132 | −0.155566 | − | 0.987825i | \(-0.549720\pi\) | ||||
−0.155566 | + | 0.987825i | \(0.549720\pi\) | |||||||
\(678\) | 28.0401 | 1.07687 | ||||||||
\(679\) | −0.223306 | −0.00856970 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4080 | 0.552117 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5755 | 0.672507 | 0.336253 | − | 0.941772i | \(-0.390840\pi\) | ||||
0.336253 | + | 0.941772i | \(0.390840\pi\) | |||||||
\(684\) | 13.6690 | 0.522646 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 35.1309 | 1.34130 | ||||||||
\(687\) | −20.6000 | −0.785940 | ||||||||
\(688\) | −48.2200 | −1.83837 | ||||||||
\(689\) | −5.08654 | −0.193782 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.1921 | −1.03444 | −0.517218 | − | 0.855854i | \(-0.673032\pi\) | ||||
−0.517218 | + | 0.855854i | \(0.673032\pi\) | |||||||
\(692\) | 18.5206 | 0.704046 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.29147 | 0.162902 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.32912 | −0.0882852 | ||||||||
\(697\) | −0.0256353 | −0.000971008 0 | ||||||||
\(698\) | −9.44861 | −0.357635 | ||||||||
\(699\) | −10.1634 | −0.384417 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.103001 | 0.00389029 | 0.00194514 | − | 0.999998i | \(-0.499381\pi\) | ||||
0.00194514 | + | 0.999998i | \(0.499381\pi\) | |||||||
\(702\) | −8.13078 | −0.306877 | ||||||||
\(703\) | −29.3277 | −1.10611 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.7211 | 0.817484 | ||||||||
\(707\) | 5.41674 | 0.203717 | ||||||||
\(708\) | −7.87356 | −0.295906 | ||||||||
\(709\) | −40.4949 | −1.52082 | −0.760408 | − | 0.649445i | \(-0.775001\pi\) | ||||
−0.760408 | + | 0.649445i | \(0.775001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.17758 | 0.231677 | ||||||||
\(712\) | 5.93927 | 0.222584 | ||||||||
\(713\) | 7.83432 | 0.293397 | ||||||||
\(714\) | 2.24481 | 0.0840097 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 48.6930 | 1.81974 | ||||||||
\(717\) | −8.52498 | −0.318371 | ||||||||
\(718\) | −24.6082 | −0.918371 | ||||||||
\(719\) | 48.9879 | 1.82694 | 0.913471 | − | 0.406905i | \(-0.133392\pi\) | ||||
0.913471 | + | 0.406905i | \(0.133392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.7459 | 0.698132 | ||||||||
\(722\) | 72.3231 | 2.69159 | ||||||||
\(723\) | 4.81966 | 0.179245 | ||||||||
\(724\) | 40.3044 | 1.49790 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.4370 | 0.498352 | 0.249176 | − | 0.968458i | \(-0.419840\pi\) | ||||
0.249176 | + | 0.968458i | \(0.419840\pi\) | |||||||
\(728\) | −2.17535 | −0.0806240 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.28549 | −0.306450 | ||||||||
\(732\) | 11.9764 | 0.442659 | ||||||||
\(733\) | 31.0641 | 1.14738 | 0.573688 | − | 0.819074i | \(-0.305512\pi\) | ||||
0.573688 | + | 0.819074i | \(0.305512\pi\) | |||||||
\(734\) | 40.9238 | 1.51053 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.97997 | −0.331006 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.0676252 | 0.00248932 | ||||||||
\(739\) | 31.4225 | 1.15589 | 0.577947 | − | 0.816074i | \(-0.303854\pi\) | ||||
0.577947 | + | 0.816074i | \(0.303854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.0938 | −1.14226 | ||||||||
\(742\) | −3.70458 | −0.135999 | ||||||||
\(743\) | −1.74334 | −0.0639569 | −0.0319785 | − | 0.999489i | \(-0.510181\pi\) | ||||
−0.0319785 | + | 0.999489i | \(0.510181\pi\) | |||||||
\(744\) | −2.29200 | −0.0840288 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.8199 | −0.689047 | ||||||||
\(747\) | 15.1493 | 0.554283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.83814 | −0.213321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4075 | 0.781172 | 0.390586 | − | 0.920566i | \(-0.372272\pi\) | ||||
0.390586 | + | 0.920566i | \(0.372272\pi\) | |||||||
\(752\) | −30.3918 | −1.10828 | ||||||||
\(753\) | −14.0612 | −0.512420 | ||||||||
\(754\) | −55.9852 | −2.03886 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.82709 | −0.102820 | ||||||||
\(757\) | −0.444930 | −0.0161712 | −0.00808562 | − | 0.999967i | \(-0.502574\pi\) | ||||
−0.00808562 | + | 0.999967i | \(0.502574\pi\) | |||||||
\(758\) | −58.4736 | −2.12386 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.0823 | 1.16298 | 0.581492 | − | 0.813552i | \(-0.302469\pi\) | ||||
0.581492 | + | 0.813552i | \(0.302469\pi\) | |||||||
\(762\) | 28.2974 | 1.02511 | ||||||||
\(763\) | −28.3376 | −1.02589 | ||||||||
\(764\) | 19.4098 | 0.702223 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.8467 | 1.98169 | ||||||||
\(767\) | 17.9105 | 0.646712 | ||||||||
\(768\) | 18.3983 | 0.663893 | ||||||||
\(769\) | 38.9434 | 1.40433 | 0.702167 | − | 0.712012i | \(-0.252216\pi\) | ||||
0.702167 | + | 0.712012i | \(0.252216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6340 | −0.418988 | ||||||||
\(772\) | 4.90345 | 0.176479 | ||||||||
\(773\) | −22.7930 | −0.819809 | −0.409904 | − | 0.912128i | \(-0.634438\pi\) | ||||
−0.409904 | + | 0.912128i | \(0.634438\pi\) | |||||||
\(774\) | 21.8569 | 0.785629 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0488172 | −0.00175244 | ||||||||
\(777\) | 6.06572 | 0.217606 | ||||||||
\(778\) | 19.3544 | 0.693888 | ||||||||
\(779\) | 0.258613 | 0.00926576 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.67740 | −0.0599839 | ||||||||
\(783\) | 6.88558 | 0.246071 | ||||||||
\(784\) | 19.8783 | 0.709939 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 28.6642 | 1.02242 | ||||||||
\(787\) | 19.7845 | 0.705242 | 0.352621 | − | 0.935766i | \(-0.385290\pi\) | ||||
0.352621 | + | 0.935766i | \(0.385290\pi\) | |||||||
\(788\) | −31.5790 | −1.12496 | ||||||||
\(789\) | 11.0280 | 0.392607 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.1781 | −0.788563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.2435 | −0.967444 | ||||||||
\(794\) | −28.8470 | −1.02374 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.3364 | −0.543583 | ||||||||
\(797\) | −12.3662 | −0.438035 | −0.219018 | − | 0.975721i | \(-0.570285\pi\) | ||||
−0.219018 | + | 0.975721i | \(0.570285\pi\) | |||||||
\(798\) | −22.6459 | −0.801656 | ||||||||
\(799\) | −5.22213 | −0.184746 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.5582 | −0.620390 | ||||||||
\(802\) | −28.1301 | −0.993309 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.48981 | 0.228878 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55.0928 | −1.94056 | ||||||||
\(807\) | 18.9754 | 0.667966 | ||||||||
\(808\) | 1.18416 | 0.0416586 | ||||||||
\(809\) | 20.4155 | 0.717772 | 0.358886 | − | 0.933381i | \(-0.383157\pi\) | ||||
0.358886 | + | 0.933381i | \(0.383157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0367 | −0.352437 | −0.176219 | − | 0.984351i | \(-0.556387\pi\) | ||||
−0.176219 | + | 0.984351i | \(0.556387\pi\) | |||||||
\(812\) | −19.4662 | −0.683128 | ||||||||
\(813\) | 15.5699 | 0.546059 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.20065 | 0.112045 | ||||||||
\(817\) | 83.5851 | 2.92427 | ||||||||
\(818\) | −21.5259 | −0.752636 | ||||||||
\(819\) | 6.43099 | 0.224717 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3699 | −0.361913 | −0.180957 | − | 0.983491i | \(-0.557919\pi\) | ||||
−0.180957 | + | 0.983491i | \(0.557919\pi\) | |||||||
\(822\) | −20.3803 | −0.710843 | ||||||||
\(823\) | −48.6023 | −1.69417 | −0.847085 | − | 0.531457i | \(-0.821645\pi\) | ||||
−0.847085 | + | 0.531457i | \(0.821645\pi\) | |||||||
\(824\) | 4.09806 | 0.142763 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.0444 | 0.453873 | ||||||||
\(827\) | −10.5295 | −0.366147 | −0.183074 | − | 0.983099i | \(-0.558605\pi\) | ||||
−0.183074 | + | 0.983099i | \(0.558605\pi\) | |||||||
\(828\) | 2.11251 | 0.0734148 | ||||||||
\(829\) | −29.2410 | −1.01558 | −0.507791 | − | 0.861480i | \(-0.669538\pi\) | ||||
−0.507791 | + | 0.861480i | \(0.669538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.91319 | −0.205126 | ||||||||
\(832\) | 27.2735 | 0.945539 | ||||||||
\(833\) | 3.41563 | 0.118344 | ||||||||
\(834\) | −3.38855 | −0.117336 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.77583 | 0.234207 | ||||||||
\(838\) | −5.48087 | −0.189334 | ||||||||
\(839\) | −22.0625 | −0.761681 | −0.380840 | − | 0.924641i | \(-0.624365\pi\) | ||||
−0.380840 | + | 0.924641i | \(0.624365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.4112 | 0.634869 | ||||||||
\(842\) | −35.2359 | −1.21431 | ||||||||
\(843\) | 27.7543 | 0.955910 | ||||||||
\(844\) | −43.1987 | −1.48696 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.7758 | 0.473623 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.28200 | −0.181385 | ||||||||
\(849\) | −19.7440 | −0.677613 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.53253 | −0.155373 | ||||||||
\(852\) | 10.7535 | 0.368408 | ||||||||
\(853\) | 1.43827 | 0.0492455 | 0.0246227 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246227 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(854\) | −19.8417 | −0.678968 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.27628 | −0.0436224 | ||||||||
\(857\) | −34.3766 | −1.17428 | −0.587141 | − | 0.809485i | \(-0.699746\pi\) | ||||
−0.587141 | + | 0.809485i | \(0.699746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4635 | −0.493489 | −0.246744 | − | 0.969081i | \(-0.579361\pi\) | ||||
−0.246744 | + | 0.969081i | \(0.579361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0534877 | −0.00182286 | ||||||||
\(862\) | −27.3395 | −0.931187 | ||||||||
\(863\) | −21.9433 | −0.746958 | −0.373479 | − | 0.927639i | \(-0.621835\pi\) | ||||
−0.373479 | + | 0.927639i | \(0.621835\pi\) | |||||||
\(864\) | −7.76669 | −0.264228 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.725544 | −0.0246550 | ||||||||
\(867\) | −16.4500 | −0.558673 | ||||||||
\(868\) | −19.1559 | −0.650193 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7628 | −0.500219 | ||||||||
\(872\) | −6.19492 | −0.209786 | ||||||||
\(873\) | 0.144318 | 0.00488443 | ||||||||
\(874\) | 16.9219 | 0.572391 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.36588 | −0.282657 | ||||||||
\(877\) | 12.6435 | 0.426940 | 0.213470 | − | 0.976950i | \(-0.431523\pi\) | ||||
0.213470 | + | 0.976950i | \(0.431523\pi\) | |||||||
\(878\) | −22.0578 | −0.744416 | ||||||||
\(879\) | −19.8794 | −0.670516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.38769 | −0.215207 | −0.107603 | − | 0.994194i | \(-0.534318\pi\) | ||||
−0.107603 | + | 0.994194i | \(0.534318\pi\) | |||||||
\(882\) | −9.01032 | −0.303393 | ||||||||
\(883\) | 40.8573 | 1.37496 | 0.687478 | − | 0.726205i | \(-0.258718\pi\) | ||||
0.687478 | + | 0.726205i | \(0.258718\pi\) | |||||||
\(884\) | 5.63148 | 0.189407 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −57.8354 | −1.94302 | ||||||||
\(887\) | −2.81682 | −0.0945794 | −0.0472897 | − | 0.998881i | \(-0.515058\pi\) | ||||
−0.0472897 | + | 0.998881i | \(0.515058\pi\) | |||||||
\(888\) | 1.32603 | 0.0444988 | ||||||||
\(889\) | −22.3816 | −0.750655 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.3034 | 1.44990 | ||||||||
\(893\) | 52.6816 | 1.76292 | ||||||||
\(894\) | −24.3715 | −0.815106 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.17153 | −0.139361 | ||||||||
\(897\) | −4.80548 | −0.160450 | ||||||||
\(898\) | 2.22462 | 0.0742366 | ||||||||
\(899\) | 46.6555 | 1.55605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.907590 | −0.0302362 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.2875 | −0.575293 | ||||||||
\(904\) | −4.84839 | −0.161255 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.4445 | 1.14434 | ||||||||
\(907\) | 13.0949 | 0.434808 | 0.217404 | − | 0.976082i | \(-0.430241\pi\) | ||||
0.217404 | + | 0.976082i | \(0.430241\pi\) | |||||||
\(908\) | 26.3248 | 0.873619 | ||||||||
\(909\) | −3.50073 | −0.116112 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.5351 | 0.382175 | 0.191087 | − | 0.981573i | \(-0.438799\pi\) | ||||
0.191087 | + | 0.981573i | \(0.438799\pi\) | |||||||
\(912\) | −32.2886 | −1.06918 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.7672 | 0.455379 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37.6381 | −1.24360 | ||||||||
\(917\) | −22.6717 | −0.748686 | ||||||||
\(918\) | −1.45077 | −0.0478826 | ||||||||
\(919\) | 7.82709 | 0.258192 | 0.129096 | − | 0.991632i | \(-0.458792\pi\) | ||||
0.129096 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3072 | 0.339633 | ||||||||
\(922\) | −36.7739 | −1.21108 | ||||||||
\(923\) | −24.4617 | −0.805168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 72.4565 | 2.38107 | ||||||||
\(927\) | −12.1151 | −0.397911 | ||||||||
\(928\) | −53.4782 | −1.75551 | ||||||||
\(929\) | −28.5710 | −0.937386 | −0.468693 | − | 0.883361i | \(-0.655275\pi\) | ||||
−0.468693 | + | 0.883361i | \(0.655275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.4573 | −1.12929 | ||||||||
\(932\) | −18.5695 | −0.608265 | ||||||||
\(933\) | 8.36316 | 0.273798 | ||||||||
\(934\) | −1.13309 | −0.0370760 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.40589 | 0.0459528 | ||||||||
\(937\) | −39.0877 | −1.27694 | −0.638470 | − | 0.769647i | \(-0.720432\pi\) | ||||
−0.638470 | + | 0.769647i | \(0.720432\pi\) | |||||||
\(938\) | −10.7519 | −0.351062 | ||||||||
\(939\) | 7.12380 | 0.232477 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.3575 | 0.435443 | 0.217721 | − | 0.976011i | \(-0.430138\pi\) | ||||
0.217721 | + | 0.976011i | \(0.430138\pi\) | |||||||
\(942\) | −31.0257 | −1.01087 | ||||||||
\(943\) | 0.0399681 | 0.00130154 | ||||||||
\(944\) | 18.5988 | 0.605338 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.22435 | −0.267255 | −0.133628 | − | 0.991032i | \(-0.542663\pi\) | ||||
−0.133628 | + | 0.991032i | \(0.542663\pi\) | |||||||
\(948\) | 11.2870 | 0.366585 | ||||||||
\(949\) | 19.0305 | 0.617755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.5894 | −0.894646 | ||||||||
\(952\) | −0.388147 | −0.0125799 | ||||||||
\(953\) | 55.7519 | 1.80598 | 0.902991 | − | 0.429661i | \(-0.141367\pi\) | ||||
0.902991 | + | 0.429661i | \(0.141367\pi\) | |||||||
\(954\) | 2.39419 | 0.0775149 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.5759 | −0.503761 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.3304 | 0.753770 | ||||||||
\(959\) | 16.1196 | 0.520530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9119 | 0.481028 | ||||||||
\(962\) | 31.8739 | 1.02765 | ||||||||
\(963\) | 3.77307 | 0.121585 | ||||||||
\(964\) | 8.80596 | 0.283621 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.49988 | −0.112607 | ||||||||
\(967\) | −1.68449 | −0.0541695 | −0.0270847 | − | 0.999633i | \(-0.508622\pi\) | ||||
−0.0270847 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.54805 | −0.178229 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −61.1384 | −1.96202 | −0.981012 | − | 0.193945i | \(-0.937872\pi\) | ||||
−0.981012 | + | 0.193945i | \(0.937872\pi\) | |||||||
\(972\) | 1.82709 | 0.0586040 | ||||||||
\(973\) | 2.68015 | 0.0859216 | ||||||||
\(974\) | −42.7276 | −1.36908 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.2903 | −0.905551 | ||||||||
\(977\) | −22.9369 | −0.733817 | −0.366909 | − | 0.930257i | \(-0.619584\pi\) | ||||
−0.366909 | + | 0.930257i | \(0.619584\pi\) | |||||||
\(978\) | −16.6668 | −0.532946 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.3140 | 0.584721 | ||||||||
\(982\) | −16.5804 | −0.529103 | ||||||||
\(983\) | −6.68730 | −0.213292 | −0.106646 | − | 0.994297i | \(-0.534011\pi\) | ||||
−0.106646 | + | 0.994297i | \(0.534011\pi\) | |||||||
\(984\) | −0.0116930 | −0.000372760 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.98940 | −0.318127 | ||||||||
\(987\) | −10.8959 | −0.346820 | ||||||||
\(988\) | −56.8112 | −1.80740 | ||||||||
\(989\) | 12.9179 | 0.410766 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.65123 | −0.115985 | −0.0579925 | − | 0.998317i | \(-0.518470\pi\) | ||||
−0.0579925 | + | 0.998317i | \(0.518470\pi\) | |||||||
\(992\) | −52.6258 | −1.67087 | ||||||||
\(993\) | −15.9410 | −0.505872 | ||||||||
\(994\) | −17.8157 | −0.565080 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.6791 | 0.877045 | ||||||||
\(997\) | −8.31754 | −0.263419 | −0.131710 | − | 0.991288i | \(-0.542047\pi\) | ||||
−0.131710 | + | 0.991288i | \(0.542047\pi\) | |||||||
\(998\) | 4.96981 | 0.157317 | ||||||||
\(999\) | −3.92015 | −0.124028 |
(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 | 9075.2.a.co.1.4 | 4 | ||
5.4 | even | 2 | 1815.2.a.u.1.1 | 4 | |||
11.5 | even | 5 | 825.2.n.j.751.1 | 8 | |||
11.9 | even | 5 | 825.2.n.j.301.1 | 8 | |||
11.10 | odd | 2 | 9075.2.a.df.1.1 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bj.1.4 | 4 | |||
55.9 | even | 10 | 165.2.m.c.136.2 | yes | 8 | ||
55.27 | odd | 20 | 825.2.bx.e.124.1 | 16 | |||
55.38 | odd | 20 | 825.2.bx.e.124.4 | 16 | |||
55.42 | odd | 20 | 825.2.bx.e.499.4 | 16 | |||
55.49 | even | 10 | 165.2.m.c.91.2 | ✓ | 8 | ||
55.53 | odd | 20 | 825.2.bx.e.499.1 | 16 | |||
55.54 | odd | 2 | 1815.2.a.q.1.4 | 4 | |||
165.104 | odd | 10 | 495.2.n.c.91.1 | 8 | |||
165.119 | odd | 10 | 495.2.n.c.136.1 | 8 | |||
165.164 | even | 2 | 5445.2.a.bq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.c.91.2 | ✓ | 8 | 55.49 | even | 10 | ||
165.2.m.c.136.2 | yes | 8 | 55.9 | even | 10 | ||
495.2.n.c.91.1 | 8 | 165.104 | odd | 10 | |||
495.2.n.c.136.1 | 8 | 165.119 | odd | 10 | |||
825.2.n.j.301.1 | 8 | 11.9 | even | 5 | |||
825.2.n.j.751.1 | 8 | 11.5 | even | 5 | |||
825.2.bx.e.124.1 | 16 | 55.27 | odd | 20 | |||
825.2.bx.e.124.4 | 16 | 55.38 | odd | 20 | |||
825.2.bx.e.499.1 | 16 | 55.53 | odd | 20 | |||
825.2.bx.e.499.4 | 16 | 55.42 | odd | 20 | |||
1815.2.a.q.1.4 | 4 | 55.54 | odd | 2 | |||
1815.2.a.u.1.1 | 4 | 5.4 | even | 2 | |||
5445.2.a.bj.1.4 | 4 | 15.14 | odd | 2 | |||
5445.2.a.bq.1.1 | 4 | 165.164 | even | 2 | |||
9075.2.a.co.1.4 | 4 | 1.1 | even | 1 | trivial | ||
9075.2.a.df.1.1 | 4 | 11.10 | odd | 2 |