Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5929,2,Mod(1,5929)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5929, 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("5929.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5929 = 7^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5929.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: | \(47.3433033584\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.46673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5929.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46673 | −1.74424 | −0.872121 | − | 0.489290i | \(-0.837256\pi\) | ||||
−0.872121 | + | 0.489290i | \(0.837256\pi\) | |||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 4.08477 | 2.04238 | ||||||||
\(5\) | 3.46673 | 1.55037 | 0.775185 | − | 0.631735i | \(-0.217657\pi\) | ||||
0.775185 | + | 0.631735i | \(0.217657\pi\) | |||||||
\(6\) | −3.99126 | −1.62942 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.14256 | −1.81817 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | −8.55150 | −2.70422 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.60929 | 1.90794 | ||||||||
\(13\) | −0.653752 | −0.181318 | −0.0906590 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906590 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.60929 | 1.44831 | ||||||||
\(16\) | 4.51578 | 1.12894 | ||||||||
\(17\) | −1.13715 | −0.275800 | −0.137900 | − | 0.990446i | \(-0.544035\pi\) | ||||
−0.137900 | + | 0.990446i | \(0.544035\pi\) | |||||||
\(18\) | 0.942208 | 0.222080 | ||||||||
\(19\) | −6.07602 | −1.39393 | −0.696967 | − | 0.717103i | \(-0.745468\pi\) | ||||
−0.696967 | + | 0.717103i | \(0.745468\pi\) | |||||||
\(20\) | 14.1608 | 3.16645 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.66708 | −1.39018 | −0.695091 | − | 0.718921i | \(-0.744636\pi\) | ||||
−0.695091 | + | 0.718921i | \(0.744636\pi\) | |||||||
\(24\) | −8.32083 | −1.69848 | ||||||||
\(25\) | 7.01823 | 1.40365 | ||||||||
\(26\) | 1.61263 | 0.316263 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.57357 | 0.849291 | 0.424646 | − | 0.905360i | \(-0.360399\pi\) | ||||
0.424646 | + | 0.905360i | \(0.360399\pi\) | |||||||
\(30\) | −13.8366 | −2.52621 | ||||||||
\(31\) | −2.79631 | −0.502232 | −0.251116 | − | 0.967957i | \(-0.580798\pi\) | ||||
−0.251116 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(32\) | −0.854102 | −0.150985 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.80505 | 0.481063 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.56024 | −0.260040 | ||||||||
\(37\) | −0.439758 | −0.0722958 | −0.0361479 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361479 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(38\) | 14.9879 | 2.43136 | ||||||||
\(39\) | −1.05779 | −0.169382 | ||||||||
\(40\) | −17.8279 | −2.81883 | ||||||||
\(41\) | −5.90315 | −0.921917 | −0.460959 | − | 0.887422i | \(-0.652494\pi\) | ||||
−0.460959 | + | 0.887422i | \(0.652494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.70820 | −1.32799 | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32417 | −0.197396 | ||||||||
\(46\) | 16.4459 | 2.42482 | ||||||||
\(47\) | 0.604703 | 0.0882051 | 0.0441025 | − | 0.999027i | \(-0.485957\pi\) | ||||
0.0441025 | + | 0.999027i | \(0.485957\pi\) | |||||||
\(48\) | 7.30669 | 1.05463 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17.3121 | −2.44830 | ||||||||
\(51\) | −1.83995 | −0.257645 | ||||||||
\(52\) | −2.67042 | −0.370321 | ||||||||
\(53\) | 9.82247 | 1.34922 | 0.674610 | − | 0.738175i | \(-0.264312\pi\) | ||||
0.674610 | + | 0.738175i | \(0.264312\pi\) | |||||||
\(54\) | 13.4983 | 1.83688 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.83121 | −1.30218 | ||||||||
\(58\) | −11.2818 | −1.48137 | ||||||||
\(59\) | −1.69406 | −0.220547 | −0.110274 | − | 0.993901i | \(-0.535173\pi\) | ||||
−0.110274 | + | 0.993901i | \(0.535173\pi\) | |||||||
\(60\) | 22.9126 | 2.95801 | ||||||||
\(61\) | 6.85818 | 0.878100 | 0.439050 | − | 0.898463i | \(-0.355315\pi\) | ||||
0.439050 | + | 0.898463i | \(0.355315\pi\) | |||||||
\(62\) | 6.89775 | 0.876015 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.92472 | −0.865590 | ||||||||
\(65\) | −2.26638 | −0.281110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.17828 | −0.754797 | −0.377398 | − | 0.926051i | \(-0.623181\pi\) | ||||
−0.377398 | + | 0.926051i | \(0.623181\pi\) | |||||||
\(68\) | −4.64501 | −0.563290 | ||||||||
\(69\) | −10.7876 | −1.29867 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.41687 | −0.642864 | −0.321432 | − | 0.946933i | \(-0.604164\pi\) | ||||
−0.321432 | + | 0.946933i | \(0.604164\pi\) | |||||||
\(72\) | 1.96428 | 0.231493 | ||||||||
\(73\) | 6.70198 | 0.784408 | 0.392204 | − | 0.919878i | \(-0.371713\pi\) | ||||
0.392204 | + | 0.919878i | \(0.371713\pi\) | |||||||
\(74\) | 1.08477 | 0.126101 | ||||||||
\(75\) | 11.3557 | 1.31125 | ||||||||
\(76\) | −24.8191 | −2.84695 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.60929 | 0.295444 | ||||||||
\(79\) | −2.65375 | −0.298570 | −0.149285 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149285 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(80\) | 15.6550 | 1.75028 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 14.5615 | 1.60805 | ||||||||
\(83\) | 6.69658 | 0.735045 | 0.367522 | − | 0.930015i | \(-0.380206\pi\) | ||||
0.367522 | + | 0.930015i | \(0.380206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.94221 | −0.427592 | ||||||||
\(86\) | 21.4808 | 2.31633 | ||||||||
\(87\) | 7.40020 | 0.793384 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.698213 | 0.0740105 | 0.0370052 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370052 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(90\) | 3.26638 | 0.344307 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −27.2335 | −2.83929 | ||||||||
\(93\) | −4.52452 | −0.469171 | ||||||||
\(94\) | −1.49164 | −0.153851 | ||||||||
\(95\) | −21.0639 | −2.16111 | ||||||||
\(96\) | −1.38197 | −0.141046 | ||||||||
\(97\) | 14.8587 | 1.50867 | 0.754336 | − | 0.656489i | \(-0.227959\pi\) | ||||
0.754336 | + | 0.656489i | \(0.227959\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.6678 | 2.86678 | ||||||||
\(101\) | 8.61959 | 0.857682 | 0.428841 | − | 0.903380i | \(-0.358922\pi\) | ||||
0.428841 | + | 0.903380i | \(0.358922\pi\) | |||||||
\(102\) | 4.53867 | 0.449396 | ||||||||
\(103\) | 0.932958 | 0.0919271 | 0.0459636 | − | 0.998943i | \(-0.485364\pi\) | ||||
0.0459636 | + | 0.998943i | \(0.485364\pi\) | |||||||
\(104\) | 3.36196 | 0.329667 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.2294 | −2.35337 | ||||||||
\(107\) | −6.62212 | −0.640184 | −0.320092 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320092 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(108\) | −22.3524 | −2.15086 | ||||||||
\(109\) | 4.12507 | 0.395110 | 0.197555 | − | 0.980292i | \(-0.436700\pi\) | ||||
0.197555 | + | 0.980292i | \(0.436700\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.711544 | −0.0675368 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.8258 | −1.77098 | −0.885491 | − | 0.464656i | \(-0.846178\pi\) | ||||
−0.885491 | + | 0.464656i | \(0.846178\pi\) | |||||||
\(114\) | 24.2510 | 2.27131 | ||||||||
\(115\) | −23.1130 | −2.15530 | ||||||||
\(116\) | 18.6820 | 1.73458 | ||||||||
\(117\) | 0.249711 | 0.0230858 | ||||||||
\(118\) | 4.17878 | 0.384688 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −28.8461 | −2.63328 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.9173 | −1.53162 | ||||||||
\(123\) | −9.55150 | −0.861230 | ||||||||
\(124\) | −11.4223 | −1.02575 | ||||||||
\(125\) | 6.99666 | 0.625800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.96635 | 0.706899 | 0.353449 | − | 0.935454i | \(-0.385009\pi\) | ||||
0.353449 | + | 0.935454i | \(0.385009\pi\) | |||||||
\(128\) | 18.7896 | 1.66078 | ||||||||
\(129\) | −14.0902 | −1.24057 | ||||||||
\(130\) | 5.59056 | 0.490324 | ||||||||
\(131\) | −4.80505 | −0.419819 | −0.209910 | − | 0.977721i | \(-0.567317\pi\) | ||||
−0.209910 | + | 0.977721i | \(0.567317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.2401 | 1.31655 | ||||||||
\(135\) | −18.9704 | −1.63271 | ||||||||
\(136\) | 5.84788 | 0.501452 | ||||||||
\(137\) | −21.8777 | −1.86914 | −0.934571 | − | 0.355778i | \(-0.884216\pi\) | ||||
−0.934571 | + | 0.355778i | \(0.884216\pi\) | |||||||
\(138\) | 26.6100 | 2.26520 | ||||||||
\(139\) | −19.8137 | −1.68058 | −0.840289 | − | 0.542139i | \(-0.817615\pi\) | ||||
−0.840289 | + | 0.542139i | \(0.817615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.978431 | 0.0823987 | ||||||||
\(142\) | 13.3620 | 1.12131 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.72487 | −0.143740 | ||||||||
\(145\) | 15.8553 | 1.31672 | ||||||||
\(146\) | −16.5320 | −1.36820 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.79631 | −0.147656 | ||||||||
\(149\) | −3.16211 | −0.259050 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(150\) | −28.0115 | −2.28713 | ||||||||
\(151\) | −8.92806 | −0.726555 | −0.363278 | − | 0.931681i | \(-0.618342\pi\) | ||||
−0.363278 | + | 0.931681i | \(0.618342\pi\) | |||||||
\(152\) | 31.2463 | 2.53441 | ||||||||
\(153\) | 0.434354 | 0.0351155 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.69406 | −0.778645 | ||||||||
\(156\) | −4.32083 | −0.345944 | ||||||||
\(157\) | −1.13968 | −0.0909561 | −0.0454780 | − | 0.998965i | \(-0.514481\pi\) | ||||
−0.0454780 | + | 0.998965i | \(0.514481\pi\) | |||||||
\(158\) | 6.54609 | 0.520779 | ||||||||
\(159\) | 15.8931 | 1.26040 | ||||||||
\(160\) | −2.96094 | −0.234083 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 19.0141 | 1.49389 | ||||||||
\(163\) | −5.06728 | −0.396900 | −0.198450 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(164\) | −24.1130 | −1.88291 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.5187 | −1.28210 | ||||||||
\(167\) | −19.7069 | −1.52496 | −0.762482 | − | 0.647009i | \(-0.776019\pi\) | ||||
−0.762482 | + | 0.647009i | \(0.776019\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5726 | −0.967124 | ||||||||
\(170\) | 9.72437 | 0.745825 | ||||||||
\(171\) | 2.32083 | 0.177479 | ||||||||
\(172\) | −35.5710 | −2.71226 | ||||||||
\(173\) | −14.3948 | −1.09442 | −0.547208 | − | 0.836997i | \(-0.684309\pi\) | ||||
−0.547208 | + | 0.836997i | \(0.684309\pi\) | |||||||
\(174\) | −18.2543 | −1.38385 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.74104 | −0.206029 | ||||||||
\(178\) | −1.72230 | −0.129092 | ||||||||
\(179\) | −4.66420 | −0.348619 | −0.174309 | − | 0.984691i | \(-0.555769\pi\) | ||||
−0.174309 | + | 0.984691i | \(0.555769\pi\) | |||||||
\(180\) | −5.40894 | −0.403159 | ||||||||
\(181\) | −9.90805 | −0.736459 | −0.368230 | − | 0.929735i | \(-0.620036\pi\) | ||||
−0.368230 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0968 | 0.820297 | ||||||||
\(184\) | 34.2859 | 2.52759 | ||||||||
\(185\) | −1.52452 | −0.112085 | ||||||||
\(186\) | 11.1608 | 0.818349 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.47007 | 0.180148 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 51.9591 | 3.76951 | ||||||||
\(191\) | 9.94295 | 0.719447 | 0.359723 | − | 0.933059i | \(-0.382871\pi\) | ||||
0.359723 | + | 0.933059i | \(0.382871\pi\) | |||||||
\(192\) | −11.2044 | −0.808610 | ||||||||
\(193\) | −3.70665 | −0.266810 | −0.133405 | − | 0.991062i | \(-0.542591\pi\) | ||||
−0.133405 | + | 0.991062i | \(0.542591\pi\) | |||||||
\(194\) | −36.6524 | −2.63149 | ||||||||
\(195\) | −3.66708 | −0.262605 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.91982 | −0.421770 | −0.210885 | − | 0.977511i | \(-0.567635\pi\) | ||||
−0.210885 | + | 0.977511i | \(0.567635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4842 | −0.814095 | −0.407047 | − | 0.913407i | \(-0.633442\pi\) | ||||
−0.407047 | + | 0.913407i | \(0.633442\pi\) | |||||||
\(200\) | −36.0917 | −2.55207 | ||||||||
\(201\) | −9.99666 | −0.705110 | ||||||||
\(202\) | −21.2622 | −1.49600 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.51578 | −0.526210 | ||||||||
\(205\) | −20.4646 | −1.42931 | ||||||||
\(206\) | −2.30136 | −0.160343 | ||||||||
\(207\) | 2.54660 | 0.177001 | ||||||||
\(208\) | −2.95220 | −0.204698 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.72487 | −0.600645 | −0.300323 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300323 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(212\) | 40.1225 | 2.75562 | ||||||||
\(213\) | −8.76467 | −0.600546 | ||||||||
\(214\) | 16.3350 | 1.11664 | ||||||||
\(215\) | −30.1890 | −2.05887 | ||||||||
\(216\) | 28.1408 | 1.91474 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.1754 | −0.689168 | ||||||||
\(219\) | 10.8440 | 0.732772 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.743416 | 0.0500076 | ||||||||
\(222\) | 1.75519 | 0.117801 | ||||||||
\(223\) | −10.3328 | −0.691938 | −0.345969 | − | 0.938246i | \(-0.612450\pi\) | ||||
−0.345969 | + | 0.938246i | \(0.612450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.68073 | −0.178715 | ||||||||
\(226\) | 46.4382 | 3.08902 | ||||||||
\(227\) | −13.2690 | −0.880691 | −0.440346 | − | 0.897828i | \(-0.645144\pi\) | ||||
−0.440346 | + | 0.897828i | \(0.645144\pi\) | |||||||
\(228\) | −40.1582 | −2.65954 | ||||||||
\(229\) | 2.49623 | 0.164955 | 0.0824777 | − | 0.996593i | \(-0.473717\pi\) | ||||
0.0824777 | + | 0.996593i | \(0.473717\pi\) | |||||||
\(230\) | 57.0135 | 3.75936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.5199 | −1.54415 | ||||||||
\(233\) | 9.60389 | 0.629171 | 0.314586 | − | 0.949229i | \(-0.398134\pi\) | ||||
0.314586 | + | 0.949229i | \(0.398134\pi\) | |||||||
\(234\) | −0.615970 | −0.0402672 | ||||||||
\(235\) | 2.09634 | 0.136750 | ||||||||
\(236\) | −6.91982 | −0.450442 | ||||||||
\(237\) | −4.29386 | −0.278916 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.56327 | −0.359858 | −0.179929 | − | 0.983680i | \(-0.557587\pi\) | ||||
−0.179929 | + | 0.983680i | \(0.557587\pi\) | |||||||
\(240\) | 25.3303 | 1.63507 | ||||||||
\(241\) | 15.0208 | 0.967572 | 0.483786 | − | 0.875186i | \(-0.339261\pi\) | ||||
0.483786 | + | 0.875186i | \(0.339261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 28.0141 | 1.79342 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 23.5610 | 1.50219 | ||||||||
\(247\) | 3.97221 | 0.252746 | ||||||||
\(248\) | 14.3802 | 0.913143 | ||||||||
\(249\) | 10.8353 | 0.686659 | ||||||||
\(250\) | −17.2589 | −1.09155 | ||||||||
\(251\) | −27.6131 | −1.74292 | −0.871460 | − | 0.490466i | \(-0.836827\pi\) | ||||
−0.871460 | + | 0.490466i | \(0.836827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −19.6508 | −1.23300 | ||||||||
\(255\) | −6.37863 | −0.399445 | ||||||||
\(256\) | −32.4995 | −2.03122 | ||||||||
\(257\) | 28.4680 | 1.77578 | 0.887892 | − | 0.460052i | \(-0.152169\pi\) | ||||
0.887892 | + | 0.460052i | \(0.152169\pi\) | |||||||
\(258\) | 34.7567 | 2.16386 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.25764 | −0.574134 | ||||||||
\(261\) | −1.74695 | −0.108133 | ||||||||
\(262\) | 11.8528 | 0.732267 | ||||||||
\(263\) | −14.1803 | −0.874397 | −0.437199 | − | 0.899365i | \(-0.644029\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.0519 | 2.09179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.12973 | 0.0691385 | ||||||||
\(268\) | −25.2368 | −1.54158 | ||||||||
\(269\) | 24.1937 | 1.47511 | 0.737557 | − | 0.675285i | \(-0.235979\pi\) | ||||
0.737557 | + | 0.675285i | \(0.235979\pi\) | |||||||
\(270\) | 46.7950 | 2.84785 | ||||||||
\(271\) | 7.44975 | 0.452540 | 0.226270 | − | 0.974065i | \(-0.427347\pi\) | ||||
0.226270 | + | 0.974065i | \(0.427347\pi\) | |||||||
\(272\) | −5.13514 | −0.311363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 53.9665 | 3.26024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −44.0647 | −2.65238 | ||||||||
\(277\) | 19.1890 | 1.15296 | 0.576478 | − | 0.817113i | \(-0.304427\pi\) | ||||
0.576478 | + | 0.817113i | \(0.304427\pi\) | |||||||
\(278\) | 48.8751 | 2.93134 | ||||||||
\(279\) | 1.06810 | 0.0639452 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.90063 | 0.113382 | 0.0566910 | − | 0.998392i | \(-0.481945\pi\) | ||||
0.0566910 | + | 0.998392i | \(0.481945\pi\) | |||||||
\(282\) | −2.41353 | −0.143723 | ||||||||
\(283\) | 7.25178 | 0.431073 | 0.215537 | − | 0.976496i | \(-0.430850\pi\) | ||||
0.215537 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(284\) | −22.1266 | −1.31297 | ||||||||
\(285\) | −34.0822 | −2.01885 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.326238 | 0.0192238 | ||||||||
\(289\) | −15.7069 | −0.923934 | ||||||||
\(290\) | −39.1109 | −2.29667 | ||||||||
\(291\) | 24.0419 | 1.40936 | ||||||||
\(292\) | 27.3760 | 1.60206 | ||||||||
\(293\) | −3.27097 | −0.191092 | −0.0955460 | − | 0.995425i | \(-0.530460\pi\) | ||||
−0.0955460 | + | 0.995425i | \(0.530460\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.87284 | −0.341930 | ||||||||
\(296\) | 2.26148 | 0.131446 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.80008 | 0.451846 | ||||||||
\(299\) | 4.35862 | 0.252065 | ||||||||
\(300\) | 46.3855 | 2.67807 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 22.0231 | 1.26729 | ||||||||
\(303\) | 13.9468 | 0.801222 | ||||||||
\(304\) | −27.4380 | −1.57368 | ||||||||
\(305\) | 23.7755 | 1.36138 | ||||||||
\(306\) | −1.07144 | −0.0612499 | ||||||||
\(307\) | 31.6121 | 1.80420 | 0.902099 | − | 0.431530i | \(-0.142026\pi\) | ||||
0.902099 | + | 0.431530i | \(0.142026\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50956 | 0.0858758 | ||||||||
\(310\) | 23.9126 | 1.35815 | ||||||||
\(311\) | 9.03829 | 0.512514 | 0.256257 | − | 0.966609i | \(-0.417511\pi\) | ||||
0.256257 | + | 0.966609i | \(0.417511\pi\) | |||||||
\(312\) | 5.43976 | 0.307966 | ||||||||
\(313\) | −14.4990 | −0.819534 | −0.409767 | − | 0.912190i | \(-0.634390\pi\) | ||||
−0.409767 | + | 0.912190i | \(0.634390\pi\) | |||||||
\(314\) | 2.81128 | 0.158649 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.8400 | −0.609795 | ||||||||
\(317\) | −18.4174 | −1.03442 | −0.517211 | − | 0.855858i | \(-0.673030\pi\) | ||||
−0.517211 | + | 0.855858i | \(0.673030\pi\) | |||||||
\(318\) | −39.2040 | −2.19845 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −24.0061 | −1.34198 | ||||||||
\(321\) | −10.7148 | −0.598042 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.90937 | 0.384448 | ||||||||
\(324\) | −31.4862 | −1.74923 | ||||||||
\(325\) | −4.58818 | −0.254506 | ||||||||
\(326\) | 12.4996 | 0.692290 | ||||||||
\(327\) | 6.67450 | 0.369101 | ||||||||
\(328\) | 30.3573 | 1.67620 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.47653 | −0.355982 | −0.177991 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177991 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(332\) | 27.3540 | 1.50124 | ||||||||
\(333\) | 0.167973 | 0.00920485 | ||||||||
\(334\) | 48.6116 | 2.65991 | ||||||||
\(335\) | −21.4184 | −1.17021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.25682 | −0.340831 | −0.170415 | − | 0.985372i | \(-0.554511\pi\) | ||||
−0.170415 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(338\) | 31.0133 | 1.68690 | ||||||||
\(339\) | −30.4608 | −1.65440 | ||||||||
\(340\) | −16.1030 | −0.873308 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.72487 | −0.309566 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 44.7824 | 2.41451 | ||||||||
\(345\) | −37.3976 | −2.01342 | ||||||||
\(346\) | 35.5081 | 1.90893 | ||||||||
\(347\) | −22.7156 | −1.21944 | −0.609719 | − | 0.792617i | \(-0.708718\pi\) | ||||
−0.609719 | + | 0.792617i | \(0.708718\pi\) | |||||||
\(348\) | 30.2281 | 1.62039 | ||||||||
\(349\) | 29.6941 | 1.58949 | 0.794743 | − | 0.606946i | \(-0.207606\pi\) | ||||
0.794743 | + | 0.606946i | \(0.207606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.57742 | 0.190948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.82506 | 0.363262 | 0.181631 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181631 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(354\) | 6.76141 | 0.359365 | ||||||||
\(355\) | −18.7788 | −0.996676 | ||||||||
\(356\) | 2.85204 | 0.151158 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.5053 | 0.608076 | ||||||||
\(359\) | 7.25970 | 0.383152 | 0.191576 | − | 0.981478i | \(-0.438640\pi\) | ||||
0.191576 | + | 0.981478i | \(0.438640\pi\) | |||||||
\(360\) | 6.80964 | 0.358900 | ||||||||
\(361\) | 17.9180 | 0.943055 | ||||||||
\(362\) | 24.4405 | 1.28456 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.2340 | 1.21612 | ||||||||
\(366\) | −27.3728 | −1.43080 | ||||||||
\(367\) | 36.3366 | 1.89676 | 0.948378 | − | 0.317143i | \(-0.102723\pi\) | ||||
0.948378 | + | 0.317143i | \(0.102723\pi\) | |||||||
\(368\) | −30.1071 | −1.56944 | ||||||||
\(369\) | 2.25480 | 0.117380 | ||||||||
\(370\) | 3.76059 | 0.195504 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −18.4816 | −0.958227 | ||||||||
\(373\) | 14.2913 | 0.739977 | 0.369989 | − | 0.929036i | \(-0.379362\pi\) | ||||
0.369989 | + | 0.929036i | \(0.379362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.3208 | 0.584605 | ||||||||
\(376\) | −3.10972 | −0.160372 | ||||||||
\(377\) | −2.98998 | −0.153992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.54528 | −0.130742 | −0.0653710 | − | 0.997861i | \(-0.520823\pi\) | ||||
−0.0653710 | + | 0.997861i | \(0.520823\pi\) | |||||||
\(380\) | −86.0413 | −4.41382 | ||||||||
\(381\) | 12.8898 | 0.660365 | ||||||||
\(382\) | −24.5266 | −1.25489 | ||||||||
\(383\) | 23.1367 | 1.18223 | 0.591115 | − | 0.806587i | \(-0.298688\pi\) | ||||
0.591115 | + | 0.806587i | \(0.298688\pi\) | |||||||
\(384\) | 30.4023 | 1.55146 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.14330 | 0.465382 | ||||||||
\(387\) | 3.32624 | 0.169082 | ||||||||
\(388\) | 60.6943 | 3.08128 | ||||||||
\(389\) | 30.2615 | 1.53432 | 0.767158 | − | 0.641458i | \(-0.221670\pi\) | ||||
0.767158 | + | 0.641458i | \(0.221670\pi\) | |||||||
\(390\) | 9.04571 | 0.458047 | ||||||||
\(391\) | 7.58150 | 0.383413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.77474 | −0.392184 | ||||||||
\(394\) | 14.6026 | 0.735669 | ||||||||
\(395\) | −9.19985 | −0.462894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.6740 | 1.13798 | 0.568989 | − | 0.822345i | \(-0.307335\pi\) | ||||
0.568989 | + | 0.822345i | \(0.307335\pi\) | |||||||
\(398\) | 28.3285 | 1.41998 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 31.6928 | 1.58464 | ||||||||
\(401\) | −16.2186 | −0.809917 | −0.404959 | − | 0.914335i | \(-0.632714\pi\) | ||||
−0.404959 | + | 0.914335i | \(0.632714\pi\) | |||||||
\(402\) | 24.6591 | 1.22988 | ||||||||
\(403\) | 1.82809 | 0.0910637 | ||||||||
\(404\) | 35.2090 | 1.75171 | ||||||||
\(405\) | −26.7223 | −1.32784 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.46207 | 0.468442 | ||||||||
\(409\) | −35.0614 | −1.73368 | −0.866838 | − | 0.498590i | \(-0.833851\pi\) | ||||
−0.866838 | + | 0.498590i | \(0.833851\pi\) | |||||||
\(410\) | 50.4808 | 2.49307 | ||||||||
\(411\) | −35.3989 | −1.74610 | ||||||||
\(412\) | 3.81092 | 0.187750 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.28178 | −0.308732 | ||||||||
\(415\) | 23.2152 | 1.13959 | ||||||||
\(416\) | 0.558371 | 0.0273764 | ||||||||
\(417\) | −32.0593 | −1.56995 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.2633 | −1.38075 | −0.690376 | − | 0.723451i | \(-0.742555\pi\) | ||||
−0.690376 | + | 0.723451i | \(0.742555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7947 | −0.672311 | −0.336156 | − | 0.941806i | \(-0.609127\pi\) | ||||
−0.336156 | + | 0.941806i | \(0.609127\pi\) | |||||||
\(422\) | 21.5219 | 1.04767 | ||||||||
\(423\) | −0.230976 | −0.0112304 | ||||||||
\(424\) | −50.5126 | −2.45311 | ||||||||
\(425\) | −7.98081 | −0.387126 | ||||||||
\(426\) | 21.6201 | 1.04750 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.0498 | −1.30750 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 74.4682 | 3.59117 | ||||||||
\(431\) | −28.1700 | −1.35690 | −0.678451 | − | 0.734645i | \(-0.737349\pi\) | ||||
−0.678451 | + | 0.734645i | \(0.737349\pi\) | |||||||
\(432\) | −24.7110 | −1.18891 | ||||||||
\(433\) | −14.1793 | −0.681415 | −0.340708 | − | 0.940169i | \(-0.610667\pi\) | ||||
−0.340708 | + | 0.940169i | \(0.610667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.6545 | 1.23004 | ||||||||
\(436\) | 16.8499 | 0.806966 | ||||||||
\(437\) | 40.5093 | 1.93782 | ||||||||
\(438\) | −26.7493 | −1.27813 | ||||||||
\(439\) | 28.0185 | 1.33725 | 0.668625 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668625 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.83381 | −0.0872254 | ||||||||
\(443\) | 17.3370 | 0.823706 | 0.411853 | − | 0.911250i | \(-0.364882\pi\) | ||||
0.411853 | + | 0.911250i | \(0.364882\pi\) | |||||||
\(444\) | −2.90649 | −0.137936 | ||||||||
\(445\) | 2.42052 | 0.114744 | ||||||||
\(446\) | 25.4883 | 1.20691 | ||||||||
\(447\) | −5.11640 | −0.241998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.5215 | −1.39321 | −0.696603 | − | 0.717457i | \(-0.745306\pi\) | ||||
−0.696603 | + | 0.717457i | \(0.745306\pi\) | |||||||
\(450\) | 6.61263 | 0.311722 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −76.8990 | −3.61702 | ||||||||
\(453\) | −14.4459 | −0.678728 | ||||||||
\(454\) | 32.7309 | 1.53614 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 50.5576 | 2.36757 | ||||||||
\(457\) | −9.69725 | −0.453618 | −0.226809 | − | 0.973939i | \(-0.572829\pi\) | ||||
−0.226809 | + | 0.973939i | \(0.572829\pi\) | |||||||
\(458\) | −6.15752 | −0.287722 | ||||||||
\(459\) | 6.22266 | 0.290449 | ||||||||
\(460\) | −94.4111 | −4.40194 | ||||||||
\(461\) | −19.2216 | −0.895240 | −0.447620 | − | 0.894224i | \(-0.647728\pi\) | ||||
−0.447620 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5327 | 0.954235 | 0.477117 | − | 0.878840i | \(-0.341682\pi\) | ||||
0.477117 | + | 0.878840i | \(0.341682\pi\) | |||||||
\(464\) | 20.6532 | 0.958803 | ||||||||
\(465\) | −15.6853 | −0.727389 | ||||||||
\(466\) | −23.6902 | −1.09743 | ||||||||
\(467\) | −33.6714 | −1.55813 | −0.779064 | − | 0.626944i | \(-0.784305\pi\) | ||||
−0.779064 | + | 0.626944i | \(0.784305\pi\) | |||||||
\(468\) | 1.02001 | 0.0471500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.17112 | −0.238526 | ||||||||
\(471\) | −1.84403 | −0.0849686 | ||||||||
\(472\) | 8.71178 | 0.400992 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.5918 | 0.486498 | ||||||||
\(475\) | −42.6429 | −1.95659 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.75185 | −0.171785 | ||||||||
\(478\) | 13.7231 | 0.627680 | ||||||||
\(479\) | 14.1708 | 0.647479 | 0.323740 | − | 0.946146i | \(-0.395060\pi\) | ||||
0.323740 | + | 0.946146i | \(0.395060\pi\) | |||||||
\(480\) | −4.79091 | −0.218674 | ||||||||
\(481\) | 0.287493 | 0.0131085 | ||||||||
\(482\) | −37.0522 | −1.68768 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 51.5111 | 2.33900 | ||||||||
\(486\) | −9.72946 | −0.441337 | ||||||||
\(487\) | 27.7415 | 1.25709 | 0.628543 | − | 0.777775i | \(-0.283652\pi\) | ||||
0.628543 | + | 0.777775i | \(0.283652\pi\) | |||||||
\(488\) | −35.2686 | −1.59653 | ||||||||
\(489\) | −8.19903 | −0.370773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.44295 | 0.155378 | 0.0776891 | − | 0.996978i | \(-0.475246\pi\) | ||||
0.0776891 | + | 0.996978i | \(0.475246\pi\) | |||||||
\(492\) | −39.0156 | −1.75896 | ||||||||
\(493\) | −5.20086 | −0.234235 | ||||||||
\(494\) | −9.79837 | −0.440850 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.6275 | −0.566992 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.7278 | −1.19770 | ||||||||
\(499\) | −2.58923 | −0.115910 | −0.0579550 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579550 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(500\) | 28.5797 | 1.27812 | ||||||||
\(501\) | −31.8864 | −1.42458 | ||||||||
\(502\) | 68.1140 | 3.04008 | ||||||||
\(503\) | −22.9026 | −1.02118 | −0.510589 | − | 0.859825i | \(-0.670573\pi\) | ||||
−0.510589 | + | 0.859825i | \(0.670573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.8818 | 1.32972 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.3429 | −0.903460 | ||||||||
\(508\) | 32.5407 | 1.44376 | ||||||||
\(509\) | 24.0985 | 1.06815 | 0.534074 | − | 0.845438i | \(-0.320660\pi\) | ||||
0.534074 | + | 0.845438i | \(0.320660\pi\) | |||||||
\(510\) | 15.7344 | 0.696729 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 42.5884 | 1.88216 | ||||||||
\(513\) | 33.2488 | 1.46797 | ||||||||
\(514\) | −70.2229 | −3.09740 | ||||||||
\(515\) | 3.23432 | 0.142521 | ||||||||
\(516\) | −57.5550 | −2.53372 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.2913 | −1.02237 | ||||||||
\(520\) | 11.6550 | 0.511105 | ||||||||
\(521\) | 33.5057 | 1.46791 | 0.733956 | − | 0.679197i | \(-0.237672\pi\) | ||||
0.733956 | + | 0.679197i | \(0.237672\pi\) | |||||||
\(522\) | 4.30926 | 0.188611 | ||||||||
\(523\) | −31.1574 | −1.36242 | −0.681208 | − | 0.732090i | \(-0.738545\pi\) | ||||
−0.681208 | + | 0.732090i | \(0.738545\pi\) | |||||||
\(524\) | −19.6275 | −0.857432 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.9791 | 1.52516 | ||||||||
\(527\) | 3.17983 | 0.138516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4500 | 0.932608 | ||||||||
\(530\) | −83.9968 | −3.64859 | ||||||||
\(531\) | 0.647072 | 0.0280805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.85919 | 0.167160 | ||||||||
\(534\) | −2.78675 | −0.120594 | ||||||||
\(535\) | −22.9571 | −0.992522 | ||||||||
\(536\) | 31.7721 | 1.37235 | ||||||||
\(537\) | −7.54683 | −0.325670 | ||||||||
\(538\) | −59.6793 | −2.57296 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −77.4898 | −3.33463 | ||||||||
\(541\) | −22.6071 | −0.971957 | −0.485979 | − | 0.873971i | \(-0.661537\pi\) | ||||
−0.485979 | + | 0.873971i | \(0.661537\pi\) | |||||||
\(542\) | −18.3765 | −0.789340 | ||||||||
\(543\) | −16.0316 | −0.687980 | ||||||||
\(544\) | 0.971245 | 0.0416418 | ||||||||
\(545\) | 14.3005 | 0.612567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4442 | 1.17343 | 0.586715 | − | 0.809794i | \(-0.300421\pi\) | ||||
0.586715 | + | 0.809794i | \(0.300421\pi\) | |||||||
\(548\) | −89.3654 | −3.81750 | ||||||||
\(549\) | −2.61959 | −0.111801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.7891 | −1.18386 | ||||||||
\(552\) | 55.4757 | 2.36120 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −47.3341 | −2.01103 | ||||||||
\(555\) | −2.46673 | −0.104707 | ||||||||
\(556\) | −80.9344 | −3.43238 | ||||||||
\(557\) | 30.2504 | 1.28175 | 0.640875 | − | 0.767645i | \(-0.278572\pi\) | ||||
0.640875 | + | 0.767645i | \(0.278572\pi\) | |||||||
\(558\) | −2.63470 | −0.111536 | ||||||||
\(559\) | 5.69300 | 0.240788 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.68834 | −0.197766 | ||||||||
\(563\) | 7.46234 | 0.314500 | 0.157250 | − | 0.987559i | \(-0.449737\pi\) | ||||
0.157250 | + | 0.987559i | \(0.449737\pi\) | |||||||
\(564\) | 3.99666 | 0.168290 | ||||||||
\(565\) | −65.2640 | −2.74568 | ||||||||
\(566\) | −17.8882 | −0.751896 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.8565 | 1.16883 | ||||||||
\(569\) | −35.6483 | −1.49446 | −0.747228 | − | 0.664568i | \(-0.768616\pi\) | ||||
−0.747228 | + | 0.664568i | \(0.768616\pi\) | |||||||
\(570\) | 84.0716 | 3.52137 | ||||||||
\(571\) | −25.8902 | −1.08347 | −0.541737 | − | 0.840548i | \(-0.682233\pi\) | ||||
−0.541737 | + | 0.840548i | \(0.682233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0880 | 0.672087 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.7911 | −1.95132 | ||||||||
\(576\) | 2.64501 | 0.110209 | ||||||||
\(577\) | −8.16382 | −0.339864 | −0.169932 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169932 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(578\) | 38.7447 | 1.61157 | ||||||||
\(579\) | −5.99748 | −0.249247 | ||||||||
\(580\) | 64.7654 | 2.68924 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −59.3048 | −2.45826 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −34.4653 | −1.42619 | ||||||||
\(585\) | 0.865681 | 0.0357915 | ||||||||
\(586\) | 8.06860 | 0.333311 | ||||||||
\(587\) | 12.4634 | 0.514419 | 0.257210 | − | 0.966356i | \(-0.417197\pi\) | ||||
0.257210 | + | 0.966356i | \(0.417197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9904 | 0.700079 | ||||||||
\(590\) | 14.4867 | 0.596409 | ||||||||
\(591\) | −9.57847 | −0.394006 | ||||||||
\(592\) | −1.98585 | −0.0816180 | ||||||||
\(593\) | −23.6707 | −0.972037 | −0.486019 | − | 0.873948i | \(-0.661551\pi\) | ||||
−0.486019 | + | 0.873948i | \(0.661551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9165 | −0.529080 | ||||||||
\(597\) | −18.5819 | −0.760505 | ||||||||
\(598\) | −10.7515 | −0.439663 | ||||||||
\(599\) | 38.9809 | 1.59272 | 0.796358 | − | 0.604826i | \(-0.206757\pi\) | ||||
0.796358 | + | 0.604826i | \(0.206757\pi\) | |||||||
\(600\) | −58.3975 | −2.38407 | ||||||||
\(601\) | 30.5510 | 1.24620 | 0.623100 | − | 0.782142i | \(-0.285873\pi\) | ||||
0.623100 | + | 0.782142i | \(0.285873\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.35989 | 0.0961022 | ||||||||
\(604\) | −36.4690 | −1.48390 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −34.4030 | −1.39753 | ||||||||
\(607\) | 37.6173 | 1.52684 | 0.763420 | − | 0.645903i | \(-0.223519\pi\) | ||||
0.763420 | + | 0.645903i | \(0.223519\pi\) | |||||||
\(608\) | 5.18954 | 0.210464 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −58.6477 | −2.37458 | ||||||||
\(611\) | −0.395326 | −0.0159932 | ||||||||
\(612\) | 1.77423 | 0.0717192 | ||||||||
\(613\) | −17.6272 | −0.711956 | −0.355978 | − | 0.934494i | \(-0.615852\pi\) | ||||
−0.355978 | + | 0.934494i | \(0.615852\pi\) | |||||||
\(614\) | −77.9786 | −3.14696 | ||||||||
\(615\) | −33.1125 | −1.33522 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.4849 | −1.79089 | −0.895447 | − | 0.445168i | \(-0.853144\pi\) | ||||
−0.895447 | + | 0.445168i | \(0.853144\pi\) | |||||||
\(618\) | −3.72368 | −0.149788 | ||||||||
\(619\) | 6.20424 | 0.249369 | 0.124685 | − | 0.992196i | \(-0.460208\pi\) | ||||
0.124685 | + | 0.992196i | \(0.460208\pi\) | |||||||
\(620\) | −39.5979 | −1.59029 | ||||||||
\(621\) | 36.4832 | 1.46402 | ||||||||
\(622\) | −22.2950 | −0.893949 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.77676 | −0.191223 | ||||||||
\(625\) | −10.8356 | −0.433424 | ||||||||
\(626\) | 35.7652 | 1.42947 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.65531 | −0.185767 | ||||||||
\(629\) | 0.500073 | 0.0199392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.8057 | 1.78369 | 0.891844 | − | 0.452344i | \(-0.149412\pi\) | ||||
0.891844 | + | 0.452344i | \(0.149412\pi\) | |||||||
\(632\) | 13.6471 | 0.542851 | ||||||||
\(633\) | −14.1171 | −0.561106 | ||||||||
\(634\) | 45.4307 | 1.80428 | ||||||||
\(635\) | 27.6172 | 1.09595 | ||||||||
\(636\) | 64.9195 | 2.57423 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.06906 | 0.0818507 | ||||||||
\(640\) | 65.1386 | 2.57483 | ||||||||
\(641\) | −10.2756 | −0.405863 | −0.202932 | − | 0.979193i | \(-0.565047\pi\) | ||||
−0.202932 | + | 0.979193i | \(0.565047\pi\) | |||||||
\(642\) | 26.4306 | 1.04313 | ||||||||
\(643\) | 16.4446 | 0.648511 | 0.324255 | − | 0.945970i | \(-0.394886\pi\) | ||||
0.324255 | + | 0.945970i | \(0.394886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.8468 | −1.92334 | ||||||||
\(646\) | −17.0436 | −0.670570 | ||||||||
\(647\) | 26.9686 | 1.06025 | 0.530123 | − | 0.847920i | \(-0.322146\pi\) | ||||
0.530123 | + | 0.847920i | \(0.322146\pi\) | |||||||
\(648\) | 39.6399 | 1.55720 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 11.3178 | 0.443921 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.6986 | −0.810621 | ||||||||
\(653\) | 7.10602 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(654\) | −16.4642 | −0.643802 | ||||||||
\(655\) | −16.6578 | −0.650875 | ||||||||
\(656\) | −26.6573 | −1.04079 | ||||||||
\(657\) | −2.55993 | −0.0998724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6279 | 1.27100 | 0.635502 | − | 0.772099i | \(-0.280793\pi\) | ||||
0.635502 | + | 0.772099i | \(0.280793\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.8165 | 1.31531 | 0.657654 | − | 0.753320i | \(-0.271549\pi\) | ||||
0.657654 | + | 0.753320i | \(0.271549\pi\) | |||||||
\(662\) | 15.9759 | 0.620919 | ||||||||
\(663\) | 1.20287 | 0.0467157 | ||||||||
\(664\) | −34.4375 | −1.33644 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.414344 | −0.0160555 | ||||||||
\(667\) | −30.4924 | −1.18067 | ||||||||
\(668\) | −80.4980 | −3.11456 | ||||||||
\(669\) | −16.7189 | −0.646390 | ||||||||
\(670\) | 52.8335 | 2.04114 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.7496 | −0.915478 | −0.457739 | − | 0.889087i | \(-0.651341\pi\) | ||||
−0.457739 | + | 0.889087i | \(0.651341\pi\) | |||||||
\(674\) | 15.4339 | 0.594491 | ||||||||
\(675\) | −38.4047 | −1.47820 | ||||||||
\(676\) | −51.3562 | −1.97524 | ||||||||
\(677\) | −45.6311 | −1.75375 | −0.876874 | − | 0.480721i | \(-0.840375\pi\) | ||||
−0.876874 | + | 0.480721i | \(0.840375\pi\) | |||||||
\(678\) | 75.1386 | 2.88568 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.2730 | 0.777435 | ||||||||
\(681\) | −21.4696 | −0.822717 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.8727 | −1.10478 | −0.552392 | − | 0.833585i | \(-0.686285\pi\) | ||||
−0.552392 | + | 0.833585i | \(0.686285\pi\) | |||||||
\(684\) | 9.48006 | 0.362479 | ||||||||
\(685\) | −75.8442 | −2.89786 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.03898 | 0.154097 | ||||||||
\(688\) | −39.3243 | −1.49923 | ||||||||
\(689\) | −6.42145 | −0.244638 | ||||||||
\(690\) | 92.2498 | 3.51189 | ||||||||
\(691\) | 27.0635 | 1.02954 | 0.514772 | − | 0.857327i | \(-0.327877\pi\) | ||||
0.514772 | + | 0.857327i | \(0.327877\pi\) | |||||||
\(692\) | −58.7994 | −2.23522 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.0334 | 2.12700 | ||||||||
\(695\) | −68.6889 | −2.60552 | ||||||||
\(696\) | −38.0559 | −1.44251 | ||||||||
\(697\) | 6.71279 | 0.254265 | ||||||||
\(698\) | −73.2473 | −2.77245 | ||||||||
\(699\) | 15.5394 | 0.587755 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5156 | −1.45471 | −0.727357 | − | 0.686259i | \(-0.759252\pi\) | ||||
−0.727357 | + | 0.686259i | \(0.759252\pi\) | |||||||
\(702\) | −8.82453 | −0.333060 | ||||||||
\(703\) | 2.67198 | 0.100776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.39196 | 0.127748 | ||||||||
\(706\) | −16.8356 | −0.633616 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.1965 | −0.420790 | ||||||||
\(709\) | −1.89464 | −0.0711548 | −0.0355774 | − | 0.999367i | \(-0.511327\pi\) | ||||
−0.0355774 | + | 0.999367i | \(0.511327\pi\) | |||||||
\(710\) | 46.3223 | 1.73845 | ||||||||
\(711\) | 1.01364 | 0.0380146 | ||||||||
\(712\) | −3.59060 | −0.134564 | ||||||||
\(713\) | 18.6432 | 0.698194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.0522 | −0.712013 | ||||||||
\(717\) | −9.00156 | −0.336169 | ||||||||
\(718\) | −17.9077 | −0.668311 | ||||||||
\(719\) | −14.5772 | −0.543639 | −0.271819 | − | 0.962348i | \(-0.587625\pi\) | ||||
−0.271819 | + | 0.962348i | \(0.587625\pi\) | |||||||
\(720\) | −5.97968 | −0.222849 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −44.1990 | −1.64492 | ||||||||
\(723\) | 24.3041 | 0.903879 | ||||||||
\(724\) | −40.4721 | −1.50413 | ||||||||
\(725\) | 32.0984 | 1.19210 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.04780 | −0.150125 | −0.0750623 | − | 0.997179i | \(-0.523916\pi\) | ||||
−0.0750623 | + | 0.997179i | \(0.523916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | −57.3120 | −2.12121 | ||||||||
\(731\) | 9.90257 | 0.366260 | ||||||||
\(732\) | 45.3277 | 1.67536 | ||||||||
\(733\) | −23.5012 | −0.868036 | −0.434018 | − | 0.900904i | \(-0.642905\pi\) | ||||
−0.434018 | + | 0.900904i | \(0.642905\pi\) | |||||||
\(734\) | −89.6327 | −3.30840 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.69437 | 0.209897 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.56199 | −0.204740 | ||||||||
\(739\) | 32.6786 | 1.20210 | 0.601051 | − | 0.799210i | \(-0.294749\pi\) | ||||
0.601051 | + | 0.799210i | \(0.294749\pi\) | |||||||
\(740\) | −6.22732 | −0.228921 | ||||||||
\(741\) | 6.42717 | 0.236108 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1058 | 0.664237 | 0.332119 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332119 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(744\) | 23.2676 | 0.853033 | ||||||||
\(745\) | −10.9622 | −0.401624 | ||||||||
\(746\) | −35.2529 | −1.29070 | ||||||||
\(747\) | −2.55787 | −0.0935874 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −27.9255 | −1.01969 | ||||||||
\(751\) | 9.14357 | 0.333654 | 0.166827 | − | 0.985986i | \(-0.446648\pi\) | ||||
0.166827 | + | 0.985986i | \(0.446648\pi\) | |||||||
\(752\) | 2.73071 | 0.0995787 | ||||||||
\(753\) | −44.6789 | −1.62819 | ||||||||
\(754\) | 7.37548 | 0.268599 | ||||||||
\(755\) | −30.9512 | −1.12643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.3509 | 1.72100 | 0.860499 | − | 0.509452i | \(-0.170152\pi\) | ||||
0.860499 | + | 0.509452i | \(0.170152\pi\) | |||||||
\(758\) | 6.27851 | 0.228046 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 108.323 | 3.92927 | ||||||||
\(761\) | 3.44828 | 0.125000 | 0.0625000 | − | 0.998045i | \(-0.480093\pi\) | ||||
0.0625000 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(762\) | −31.7957 | −1.15184 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 40.6146 | 1.46939 | ||||||||
\(765\) | 1.50579 | 0.0544419 | ||||||||
\(766\) | −57.0720 | −2.06210 | ||||||||
\(767\) | 1.10749 | 0.0399892 | ||||||||
\(768\) | −52.5854 | −1.89751 | ||||||||
\(769\) | 34.9787 | 1.26137 | 0.630683 | − | 0.776041i | \(-0.282775\pi\) | ||||
0.630683 | + | 0.776041i | \(0.282775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.0622 | 1.65889 | ||||||||
\(772\) | −15.1408 | −0.544928 | ||||||||
\(773\) | −25.3794 | −0.912832 | −0.456416 | − | 0.889766i | \(-0.650867\pi\) | ||||
−0.456416 | + | 0.889766i | \(0.650867\pi\) | |||||||
\(774\) | −8.20494 | −0.294920 | ||||||||
\(775\) | −19.6251 | −0.704956 | ||||||||
\(776\) | −76.4117 | −2.74302 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −74.6469 | −2.67622 | ||||||||
\(779\) | 35.8677 | 1.28509 | ||||||||
\(780\) | −14.9792 | −0.536340 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.7015 | −0.668765 | ||||||||
\(783\) | −25.0272 | −0.894399 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.95095 | −0.141016 | ||||||||
\(786\) | 19.1782 | 0.684064 | ||||||||
\(787\) | 29.7552 | 1.06066 | 0.530329 | − | 0.847792i | \(-0.322068\pi\) | ||||
0.530329 | + | 0.847792i | \(0.322068\pi\) | |||||||
\(788\) | −24.1811 | −0.861415 | ||||||||
\(789\) | −22.9443 | −0.816838 | ||||||||
\(790\) | 22.6936 | 0.807400 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48355 | −0.159215 | ||||||||
\(794\) | −55.9308 | −1.98491 | ||||||||
\(795\) | 55.0971 | 1.95409 | ||||||||
\(796\) | −46.9103 | −1.66269 | ||||||||
\(797\) | 6.24330 | 0.221149 | 0.110575 | − | 0.993868i | \(-0.464731\pi\) | ||||
0.110575 | + | 0.993868i | \(0.464731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.687641 | −0.0243270 | ||||||||
\(800\) | −5.99428 | −0.211930 | ||||||||
\(801\) | −0.266694 | −0.00942316 | ||||||||
\(802\) | 40.0069 | 1.41269 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −40.8340 | −1.44010 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.50941 | −0.158837 | ||||||||
\(807\) | 39.1462 | 1.37801 | ||||||||
\(808\) | −44.3268 | −1.55941 | ||||||||
\(809\) | −39.1860 | −1.37771 | −0.688854 | − | 0.724900i | \(-0.741886\pi\) | ||||
−0.688854 | + | 0.724900i | \(0.741886\pi\) | |||||||
\(810\) | 65.9167 | 2.31608 | ||||||||
\(811\) | −12.3809 | −0.434753 | −0.217376 | − | 0.976088i | \(-0.569750\pi\) | ||||
−0.217376 | + | 0.976088i | \(0.569750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0539 | 0.422750 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.5669 | −0.615341 | ||||||||
\(816\) | −8.30883 | −0.290867 | ||||||||
\(817\) | 52.9112 | 1.85113 | ||||||||
\(818\) | 86.4871 | 3.02395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −83.5933 | −2.91920 | ||||||||
\(821\) | −47.6987 | −1.66470 | −0.832349 | − | 0.554252i | \(-0.813004\pi\) | ||||
−0.832349 | + | 0.554252i | \(0.813004\pi\) | |||||||
\(822\) | 87.3196 | 3.04562 | ||||||||
\(823\) | −14.5207 | −0.506161 | −0.253080 | − | 0.967445i | \(-0.581444\pi\) | ||||
−0.253080 | + | 0.967445i | \(0.581444\pi\) | |||||||
\(824\) | −4.79779 | −0.167139 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9372 | 1.07579 | 0.537896 | − | 0.843011i | \(-0.319219\pi\) | ||||
0.537896 | + | 0.843011i | \(0.319219\pi\) | |||||||
\(828\) | 10.4023 | 0.361504 | ||||||||
\(829\) | −0.0858057 | −0.00298015 | −0.00149008 | − | 0.999999i | \(-0.500474\pi\) | ||||
−0.00149008 | + | 0.999999i | \(0.500474\pi\) | |||||||
\(830\) | −57.2658 | −1.98772 | ||||||||
\(831\) | 31.0485 | 1.07706 | ||||||||
\(832\) | 4.52705 | 0.156947 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 79.0816 | 2.73837 | ||||||||
\(835\) | −68.3185 | −2.36426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.3018 | 0.528907 | ||||||||
\(838\) | 69.7179 | 2.40837 | ||||||||
\(839\) | −10.6905 | −0.369078 | −0.184539 | − | 0.982825i | \(-0.559079\pi\) | ||||
−0.184539 | + | 0.982825i | \(0.559079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.08244 | −0.278705 | ||||||||
\(842\) | 34.0278 | 1.17267 | ||||||||
\(843\) | 3.07528 | 0.105918 | ||||||||
\(844\) | −35.6391 | −1.22675 | ||||||||
\(845\) | −43.5859 | −1.49940 | ||||||||
\(846\) | 0.569756 | 0.0195886 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 44.3561 | 1.52319 | ||||||||
\(849\) | 11.7336 | 0.402697 | ||||||||
\(850\) | 19.6865 | 0.675242 | ||||||||
\(851\) | 2.93190 | 0.100504 | ||||||||
\(852\) | −35.8016 | −1.22654 | ||||||||
\(853\) | 21.2003 | 0.725884 | 0.362942 | − | 0.931812i | \(-0.381772\pi\) | ||||
0.362942 | + | 0.931812i | \(0.381772\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.04571 | 0.275157 | ||||||||
\(856\) | 34.0546 | 1.16396 | ||||||||
\(857\) | −9.45359 | −0.322929 | −0.161464 | − | 0.986879i | \(-0.551622\pi\) | ||||
−0.161464 | + | 0.986879i | \(0.551622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.8261 | 1.32473 | 0.662365 | − | 0.749181i | \(-0.269553\pi\) | ||||
0.662365 | + | 0.749181i | \(0.269553\pi\) | |||||||
\(860\) | −123.315 | −4.20501 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 69.4879 | 2.36677 | ||||||||
\(863\) | −37.6046 | −1.28008 | −0.640038 | − | 0.768343i | \(-0.721081\pi\) | ||||
−0.640038 | + | 0.768343i | \(0.721081\pi\) | |||||||
\(864\) | 4.67376 | 0.159005 | ||||||||
\(865\) | −49.9029 | −1.69675 | ||||||||
\(866\) | 34.9766 | 1.18855 | ||||||||
\(867\) | −25.4143 | −0.863114 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −63.2828 | −2.14549 | ||||||||
\(871\) | 4.03906 | 0.136858 | ||||||||
\(872\) | −21.2134 | −0.718377 | ||||||||
\(873\) | −5.67551 | −0.192087 | ||||||||
\(874\) | −99.9257 | −3.38004 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.2953 | 1.49660 | ||||||||
\(877\) | −22.0086 | −0.743178 | −0.371589 | − | 0.928397i | \(-0.621187\pi\) | ||||
−0.371589 | + | 0.928397i | \(0.621187\pi\) | |||||||
\(878\) | −69.1142 | −2.33249 | ||||||||
\(879\) | −5.29254 | −0.178513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.92969 | 0.233467 | 0.116734 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116734 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.3388 | 1.42481 | 0.712407 | − | 0.701767i | \(-0.247605\pi\) | ||||
0.712407 | + | 0.701767i | \(0.247605\pi\) | |||||||
\(884\) | 3.03668 | 0.102135 | ||||||||
\(885\) | −9.50245 | −0.319421 | ||||||||
\(886\) | −42.7657 | −1.43674 | ||||||||
\(887\) | 8.05647 | 0.270510 | 0.135255 | − | 0.990811i | \(-0.456815\pi\) | ||||
0.135255 | + | 0.990811i | \(0.456815\pi\) | |||||||
\(888\) | 3.65916 | 0.122793 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.97077 | −0.200141 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42.2072 | −1.41320 | ||||||||
\(893\) | −3.67419 | −0.122952 | ||||||||
\(894\) | 12.6208 | 0.422102 | ||||||||
\(895\) | −16.1695 | −0.540488 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.05239 | 0.235472 | ||||||||
\(898\) | 72.8216 | 2.43009 | ||||||||
\(899\) | −12.7891 | −0.426541 | ||||||||
\(900\) | −10.9501 | −0.365004 | ||||||||
\(901\) | −11.1697 | −0.372115 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 96.8128 | 3.21995 | ||||||||
\(905\) | −34.3485 | −1.14178 | ||||||||
\(906\) | 35.6342 | 1.18387 | ||||||||
\(907\) | 2.89429 | 0.0961033 | 0.0480517 | − | 0.998845i | \(-0.484699\pi\) | ||||
0.0480517 | + | 0.998845i | \(0.484699\pi\) | |||||||
\(908\) | −54.2006 | −1.79871 | ||||||||
\(909\) | −3.29239 | −0.109202 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2500 | −0.670912 | −0.335456 | − | 0.942056i | \(-0.608890\pi\) | ||||
−0.335456 | + | 0.942056i | \(0.608890\pi\) | |||||||
\(912\) | −44.3956 | −1.47008 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 23.9205 | 0.791220 | ||||||||
\(915\) | 38.4695 | 1.27176 | ||||||||
\(916\) | 10.1965 | 0.336902 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −15.3496 | −0.506613 | ||||||||
\(919\) | −18.7261 | −0.617718 | −0.308859 | − | 0.951108i | \(-0.599947\pi\) | ||||
−0.308859 | + | 0.951108i | \(0.599947\pi\) | |||||||
\(920\) | 118.860 | 3.91869 | ||||||||
\(921\) | 51.1494 | 1.68543 | ||||||||
\(922\) | 47.4146 | 1.56152 | ||||||||
\(923\) | 3.54128 | 0.116563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.08632 | −0.101478 | ||||||||
\(926\) | −50.6486 | −1.66442 | ||||||||
\(927\) | −0.356358 | −0.0117043 | ||||||||
\(928\) | −3.90630 | −0.128230 | ||||||||
\(929\) | 45.2701 | 1.48526 | 0.742631 | − | 0.669700i | \(-0.233577\pi\) | ||||
0.742631 | + | 0.669700i | \(0.233577\pi\) | |||||||
\(930\) | 38.6915 | 1.26874 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.2296 | 1.28501 | ||||||||
\(933\) | 14.6243 | 0.478777 | ||||||||
\(934\) | 83.0584 | 2.71775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.28415 | −0.0419738 | ||||||||
\(937\) | 29.4599 | 0.962413 | 0.481207 | − | 0.876607i | \(-0.340199\pi\) | ||||
0.481207 | + | 0.876607i | \(0.340199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.4599 | −0.765586 | ||||||||
\(940\) | 8.56308 | 0.279297 | ||||||||
\(941\) | 58.2346 | 1.89839 | 0.949197 | − | 0.314683i | \(-0.101898\pi\) | ||||
0.949197 | + | 0.314683i | \(0.101898\pi\) | |||||||
\(942\) | 4.54874 | 0.148206 | ||||||||
\(943\) | 39.3568 | 1.28163 | ||||||||
\(944\) | −7.64998 | −0.248986 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.3642 | 1.47414 | 0.737069 | − | 0.675818i | \(-0.236209\pi\) | ||||
0.737069 | + | 0.675818i | \(0.236209\pi\) | |||||||
\(948\) | −17.5394 | −0.569654 | ||||||||
\(949\) | −4.38143 | −0.142227 | ||||||||
\(950\) | 105.189 | 3.41277 | ||||||||
\(951\) | −29.7999 | −0.966329 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.3375 | 1.33905 | 0.669527 | − | 0.742788i | \(-0.266497\pi\) | ||||
0.669527 | + | 0.742788i | \(0.266497\pi\) | |||||||
\(954\) | 9.25480 | 0.299635 | ||||||||
\(955\) | 34.4695 | 1.11541 | ||||||||
\(956\) | −22.7247 | −0.734968 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.9555 | −1.12936 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −38.8428 | −1.25364 | ||||||||
\(961\) | −23.1807 | −0.747763 | ||||||||
\(962\) | −0.709167 | −0.0228645 | ||||||||
\(963\) | 2.52942 | 0.0815095 | ||||||||
\(964\) | 61.3563 | 1.97615 | ||||||||
\(965\) | −12.8499 | −0.413654 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.52818 | 0.209932 | 0.104966 | − | 0.994476i | \(-0.466527\pi\) | ||||
0.104966 | + | 0.994476i | \(0.466527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.1796 | 0.359140 | ||||||||
\(970\) | −127.064 | −4.07978 | ||||||||
\(971\) | −28.8587 | −0.926119 | −0.463060 | − | 0.886327i | \(-0.653248\pi\) | ||||
−0.463060 | + | 0.886327i | \(0.653248\pi\) | |||||||
\(972\) | 16.1114 | 0.516774 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −68.4308 | −2.19266 | ||||||||
\(975\) | −7.42383 | −0.237753 | ||||||||
\(976\) | 30.9700 | 0.991327 | ||||||||
\(977\) | −8.98453 | −0.287441 | −0.143720 | − | 0.989618i | \(-0.545907\pi\) | ||||
−0.143720 | + | 0.989618i | \(0.545907\pi\) | |||||||
\(978\) | 20.2248 | 0.646718 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.57564 | −0.0503062 | ||||||||
\(982\) | −8.49284 | −0.271017 | ||||||||
\(983\) | −36.8819 | −1.17635 | −0.588175 | − | 0.808734i | \(-0.700153\pi\) | ||||
−0.588175 | + | 0.808734i | \(0.700153\pi\) | |||||||
\(984\) | 49.1191 | 1.56586 | ||||||||
\(985\) | −20.5224 | −0.653899 | ||||||||
\(986\) | 12.8291 | 0.408562 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.2255 | 0.516203 | ||||||||
\(989\) | 58.0583 | 1.84615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.98352 | −0.0947746 | −0.0473873 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473873 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(992\) | 2.38833 | 0.0758297 | ||||||||
\(993\) | −10.4792 | −0.332549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.8127 | −1.26215 | ||||||||
\(996\) | 44.2596 | 1.40242 | ||||||||
\(997\) | 62.8553 | 1.99065 | 0.995324 | − | 0.0965930i | \(-0.0307945\pi\) | ||||
0.995324 | + | 0.0965930i | \(0.0307945\pi\) | |||||||
\(998\) | 6.38694 | 0.202175 | ||||||||
\(999\) | 2.40642 | 0.0761357 |
(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 | 5929.2.a.bb.1.1 | 4 | ||
7.6 | odd | 2 | 847.2.a.k.1.1 | 4 | |||
11.2 | odd | 10 | 539.2.f.d.246.1 | 8 | |||
11.6 | odd | 10 | 539.2.f.d.344.1 | 8 | |||
11.10 | odd | 2 | 5929.2.a.bi.1.4 | 4 | |||
21.20 | even | 2 | 7623.2.a.co.1.4 | 4 | |||
77.2 | odd | 30 | 539.2.q.b.312.1 | 16 | |||
77.6 | even | 10 | 77.2.f.a.36.1 | yes | 8 | ||
77.13 | even | 10 | 77.2.f.a.15.1 | ✓ | 8 | ||
77.17 | even | 30 | 539.2.q.c.520.1 | 16 | |||
77.20 | odd | 10 | 847.2.f.q.323.2 | 8 | |||
77.24 | even | 30 | 539.2.q.c.422.2 | 16 | |||
77.27 | odd | 10 | 847.2.f.q.729.2 | 8 | |||
77.39 | odd | 30 | 539.2.q.b.520.1 | 16 | |||
77.41 | even | 10 | 847.2.f.p.372.2 | 8 | |||
77.46 | odd | 30 | 539.2.q.b.422.2 | 16 | |||
77.48 | odd | 10 | 847.2.f.s.148.1 | 8 | |||
77.61 | even | 30 | 539.2.q.c.410.2 | 16 | |||
77.62 | even | 10 | 847.2.f.p.148.2 | 8 | |||
77.68 | even | 30 | 539.2.q.c.312.1 | 16 | |||
77.69 | odd | 10 | 847.2.f.s.372.1 | 8 | |||
77.72 | odd | 30 | 539.2.q.b.410.2 | 16 | |||
77.76 | even | 2 | 847.2.a.l.1.4 | 4 | |||
231.83 | odd | 10 | 693.2.m.g.190.2 | 8 | |||
231.167 | odd | 10 | 693.2.m.g.631.2 | 8 | |||
231.230 | odd | 2 | 7623.2.a.ch.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.1 | ✓ | 8 | 77.13 | even | 10 | ||
77.2.f.a.36.1 | yes | 8 | 77.6 | even | 10 | ||
539.2.f.d.246.1 | 8 | 11.2 | odd | 10 | |||
539.2.f.d.344.1 | 8 | 11.6 | odd | 10 | |||
539.2.q.b.312.1 | 16 | 77.2 | odd | 30 | |||
539.2.q.b.410.2 | 16 | 77.72 | odd | 30 | |||
539.2.q.b.422.2 | 16 | 77.46 | odd | 30 | |||
539.2.q.b.520.1 | 16 | 77.39 | odd | 30 | |||
539.2.q.c.312.1 | 16 | 77.68 | even | 30 | |||
539.2.q.c.410.2 | 16 | 77.61 | even | 30 | |||
539.2.q.c.422.2 | 16 | 77.24 | even | 30 | |||
539.2.q.c.520.1 | 16 | 77.17 | even | 30 | |||
693.2.m.g.190.2 | 8 | 231.83 | odd | 10 | |||
693.2.m.g.631.2 | 8 | 231.167 | odd | 10 | |||
847.2.a.k.1.1 | 4 | 7.6 | odd | 2 | |||
847.2.a.l.1.4 | 4 | 77.76 | even | 2 | |||
847.2.f.p.148.2 | 8 | 77.62 | even | 10 | |||
847.2.f.p.372.2 | 8 | 77.41 | even | 10 | |||
847.2.f.q.323.2 | 8 | 77.20 | odd | 10 | |||
847.2.f.q.729.2 | 8 | 77.27 | odd | 10 | |||
847.2.f.s.148.1 | 8 | 77.48 | odd | 10 | |||
847.2.f.s.372.1 | 8 | 77.69 | odd | 10 | |||
5929.2.a.bb.1.1 | 4 | 1.1 | even | 1 | trivial | ||
5929.2.a.bi.1.4 | 4 | 11.10 | odd | 2 | |||
7623.2.a.ch.1.1 | 4 | 231.230 | odd | 2 | |||
7623.2.a.co.1.4 | 4 | 21.20 | even | 2 |