Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.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: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.94567 | −0.888152 | −0.444076 | − | 0.895989i | \(-0.646468\pi\) | ||||
−0.444076 | + | 0.895989i | \(0.646468\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.28415 | 0.356158 | 0.178079 | − | 0.984016i | \(-0.443012\pi\) | ||||
0.178079 | + | 0.984016i | \(0.443012\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.22982 | 1.02588 | 0.512940 | − | 0.858424i | \(-0.328556\pi\) | ||||
0.512940 | + | 0.858424i | \(0.328556\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.22982 | 1.42922 | 0.714609 | − | 0.699524i | \(-0.246605\pi\) | ||||
0.714609 | + | 0.699524i | \(0.246605\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −2.94567 | −0.628018 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.28415 | 0.251842 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.94567 | 0.918387 | 0.459194 | − | 0.888336i | \(-0.348138\pi\) | ||||
0.459194 | + | 0.888336i | \(0.348138\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −2.22982 | −0.400487 | −0.200243 | − | 0.979746i | \(-0.564173\pi\) | ||||
−0.200243 | + | 0.979746i | \(0.564173\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.94567 | 0.512775 | ||||||||
\(34\) | 4.22982 | 0.725407 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.45963 | −1.06196 | −0.530978 | − | 0.847385i | \(-0.678175\pi\) | ||||
−0.530978 | + | 0.847385i | \(0.678175\pi\) | |||||||
\(38\) | 6.22982 | 1.01061 | ||||||||
\(39\) | −1.28415 | −0.205628 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.4596 | −1.63352 | −0.816760 | − | 0.576978i | \(-0.804232\pi\) | ||||
−0.816760 | + | 0.576978i | \(0.804232\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 10.9457 | 1.66920 | 0.834599 | − | 0.550857i | \(-0.185699\pi\) | ||||
0.834599 | + | 0.550857i | \(0.185699\pi\) | |||||||
\(44\) | −2.94567 | −0.444076 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −2.22982 | −0.325252 | −0.162626 | − | 0.986688i | \(-0.551996\pi\) | ||||
−0.162626 | + | 0.986688i | \(0.551996\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.22982 | −0.592293 | ||||||||
\(52\) | 1.28415 | 0.178079 | ||||||||
\(53\) | −6.45963 | −0.887298 | −0.443649 | − | 0.896201i | \(-0.646316\pi\) | ||||
−0.443649 | + | 0.896201i | \(0.646316\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.94567 | −0.397194 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −6.22982 | −0.825159 | ||||||||
\(58\) | 4.94567 | 0.649398 | ||||||||
\(59\) | 8.45963 | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314370\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314370\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −2.22982 | −0.283187 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.28415 | 0.159279 | ||||||||
\(66\) | 2.94567 | 0.362587 | ||||||||
\(67\) | 2.94567 | 0.359871 | 0.179935 | − | 0.983678i | \(-0.442411\pi\) | ||||
0.179935 | + | 0.983678i | \(0.442411\pi\) | |||||||
\(68\) | 4.22982 | 0.512940 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 12.8370 | 1.52347 | 0.761736 | − | 0.647888i | \(-0.224347\pi\) | ||||
0.761736 | + | 0.647888i | \(0.224347\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 3.43171 | 0.401651 | 0.200825 | − | 0.979627i | \(-0.435638\pi\) | ||||
0.200825 | + | 0.979627i | \(0.435638\pi\) | |||||||
\(74\) | −6.45963 | −0.750917 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 6.22982 | 0.714609 | ||||||||
\(77\) | −2.94567 | −0.335690 | ||||||||
\(78\) | −1.28415 | −0.145401 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.4596 | −1.15507 | ||||||||
\(83\) | −4.79811 | −0.526661 | −0.263330 | − | 0.964706i | \(-0.584821\pi\) | ||||
−0.263330 | + | 0.964706i | \(0.584821\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 4.22982 | 0.458788 | ||||||||
\(86\) | 10.9457 | 1.18030 | ||||||||
\(87\) | −4.94567 | −0.530231 | ||||||||
\(88\) | −2.94567 | −0.314009 | ||||||||
\(89\) | 3.17548 | 0.336601 | 0.168300 | − | 0.985736i | \(-0.446172\pi\) | ||||
0.168300 | + | 0.985736i | \(0.446172\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 1.28415 | 0.134615 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 2.22982 | 0.231221 | ||||||||
\(94\) | −2.22982 | −0.229988 | ||||||||
\(95\) | 6.22982 | 0.639166 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 15.6351 | 1.58751 | 0.793753 | − | 0.608241i | \(-0.208124\pi\) | ||||
0.793753 | + | 0.608241i | \(0.208124\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −2.94567 | −0.296051 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.17548 | 0.713987 | 0.356994 | − | 0.934107i | \(-0.383802\pi\) | ||||
0.356994 | + | 0.934107i | \(0.383802\pi\) | |||||||
\(102\) | −4.22982 | −0.418814 | ||||||||
\(103\) | 5.89134 | 0.580491 | 0.290245 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290245 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(104\) | 1.28415 | 0.125921 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −6.45963 | −0.627415 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 3.89134 | 0.372722 | 0.186361 | − | 0.982481i | \(-0.440331\pi\) | ||||
0.186361 | + | 0.982481i | \(0.440331\pi\) | |||||||
\(110\) | −2.94567 | −0.280858 | ||||||||
\(111\) | 6.45963 | 0.613121 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −2.45963 | −0.231383 | −0.115691 | − | 0.993285i | \(-0.536908\pi\) | ||||
−0.115691 | + | 0.993285i | \(0.536908\pi\) | |||||||
\(114\) | −6.22982 | −0.583476 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 4.94567 | 0.459194 | ||||||||
\(117\) | 1.28415 | 0.118719 | ||||||||
\(118\) | 8.45963 | 0.778772 | ||||||||
\(119\) | 4.22982 | 0.387747 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −2.32304 | −0.211186 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 10.4596 | 0.943113 | ||||||||
\(124\) | −2.22982 | −0.200243 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 13.5140 | 1.19917 | 0.599585 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599585 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.9457 | −0.963712 | ||||||||
\(130\) | 1.28415 | 0.112627 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 2.94567 | 0.256387 | ||||||||
\(133\) | 6.22982 | 0.540193 | ||||||||
\(134\) | 2.94567 | 0.254467 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 4.22982 | 0.362704 | ||||||||
\(137\) | −17.7827 | −1.51928 | −0.759638 | − | 0.650346i | \(-0.774624\pi\) | ||||
−0.759638 | + | 0.650346i | \(0.774624\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −2.56829 | −0.217840 | −0.108920 | − | 0.994051i | \(-0.534739\pi\) | ||||
−0.108920 | + | 0.994051i | \(0.534739\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 2.22982 | 0.187784 | ||||||||
\(142\) | 12.8370 | 1.07726 | ||||||||
\(143\) | −3.78267 | −0.316323 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.94567 | 0.410715 | ||||||||
\(146\) | 3.43171 | 0.284010 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −6.45963 | −0.530978 | ||||||||
\(149\) | −9.32304 | −0.763773 | −0.381887 | − | 0.924209i | \(-0.624726\pi\) | ||||
−0.381887 | + | 0.924209i | \(0.624726\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −1.43171 | −0.116511 | −0.0582553 | − | 0.998302i | \(-0.518554\pi\) | ||||
−0.0582553 | + | 0.998302i | \(0.518554\pi\) | |||||||
\(152\) | 6.22982 | 0.505305 | ||||||||
\(153\) | 4.22982 | 0.341960 | ||||||||
\(154\) | −2.94567 | −0.237369 | ||||||||
\(155\) | −2.22982 | −0.179103 | ||||||||
\(156\) | −1.28415 | −0.102814 | ||||||||
\(157\) | −13.0279 | −1.03974 | −0.519871 | − | 0.854245i | \(-0.674020\pi\) | ||||
−0.519871 | + | 0.854245i | \(0.674020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.45963 | 0.512282 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 10.5683 | 0.827773 | 0.413886 | − | 0.910329i | \(-0.364171\pi\) | ||||
0.413886 | + | 0.910329i | \(0.364171\pi\) | |||||||
\(164\) | −10.4596 | −0.816760 | ||||||||
\(165\) | 2.94567 | 0.229320 | ||||||||
\(166\) | −4.79811 | −0.372406 | ||||||||
\(167\) | 21.2577 | 1.64497 | 0.822487 | − | 0.568784i | \(-0.192586\pi\) | ||||
0.822487 | + | 0.568784i | \(0.192586\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −11.3510 | −0.873151 | ||||||||
\(170\) | 4.22982 | 0.324412 | ||||||||
\(171\) | 6.22982 | 0.476406 | ||||||||
\(172\) | 10.9457 | 0.834599 | ||||||||
\(173\) | −16.6894 | −1.26888 | −0.634438 | − | 0.772974i | \(-0.718768\pi\) | ||||
−0.634438 | + | 0.772974i | \(0.718768\pi\) | |||||||
\(174\) | −4.94567 | −0.374930 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −2.94567 | −0.222038 | ||||||||
\(177\) | −8.45963 | −0.635865 | ||||||||
\(178\) | 3.17548 | 0.238013 | ||||||||
\(179\) | −7.02792 | −0.525292 | −0.262646 | − | 0.964892i | \(-0.584595\pi\) | ||||
−0.262646 | + | 0.964892i | \(0.584595\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 1.28415 | 0.0951873 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −6.45963 | −0.474921 | ||||||||
\(186\) | 2.22982 | 0.163498 | ||||||||
\(187\) | −12.4596 | −0.911138 | ||||||||
\(188\) | −2.22982 | −0.162626 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 6.22982 | 0.451958 | ||||||||
\(191\) | 20.4596 | 1.48041 | 0.740203 | − | 0.672383i | \(-0.234729\pi\) | ||||
0.740203 | + | 0.672383i | \(0.234729\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 22.4596 | 1.61668 | 0.808340 | − | 0.588716i | \(-0.200366\pi\) | ||||
0.808340 | + | 0.588716i | \(0.200366\pi\) | |||||||
\(194\) | 15.6351 | 1.12254 | ||||||||
\(195\) | −1.28415 | −0.0919597 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 22.2423 | 1.58470 | 0.792349 | − | 0.610068i | \(-0.208858\pi\) | ||||
0.792349 | + | 0.610068i | \(0.208858\pi\) | |||||||
\(198\) | −2.94567 | −0.209339 | ||||||||
\(199\) | 12.4596 | 0.883240 | 0.441620 | − | 0.897202i | \(-0.354404\pi\) | ||||
0.441620 | + | 0.897202i | \(0.354404\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.94567 | −0.207771 | ||||||||
\(202\) | 7.17548 | 0.504865 | ||||||||
\(203\) | 4.94567 | 0.347118 | ||||||||
\(204\) | −4.22982 | −0.296146 | ||||||||
\(205\) | −10.4596 | −0.730532 | ||||||||
\(206\) | 5.89134 | 0.410469 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 1.28415 | 0.0890396 | ||||||||
\(209\) | −18.3510 | −1.26936 | ||||||||
\(210\) | −1.00000 | −0.0690066 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −6.45963 | −0.443649 | ||||||||
\(213\) | −12.8370 | −0.879577 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 10.9457 | 0.746488 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.22982 | −0.151370 | ||||||||
\(218\) | 3.89134 | 0.263555 | ||||||||
\(219\) | −3.43171 | −0.231893 | ||||||||
\(220\) | −2.94567 | −0.198597 | ||||||||
\(221\) | 5.43171 | 0.365376 | ||||||||
\(222\) | 6.45963 | 0.433542 | ||||||||
\(223\) | −2.60719 | −0.174590 | −0.0872951 | − | 0.996182i | \(-0.527822\pi\) | ||||
−0.0872951 | + | 0.996182i | \(0.527822\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.45963 | −0.163612 | ||||||||
\(227\) | −14.2298 | −0.944466 | −0.472233 | − | 0.881474i | \(-0.656552\pi\) | ||||
−0.472233 | + | 0.881474i | \(0.656552\pi\) | |||||||
\(228\) | −6.22982 | −0.412580 | ||||||||
\(229\) | 3.89134 | 0.257147 | 0.128573 | − | 0.991700i | \(-0.458960\pi\) | ||||
0.128573 | + | 0.991700i | \(0.458960\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 2.94567 | 0.193811 | ||||||||
\(232\) | 4.94567 | 0.324699 | ||||||||
\(233\) | −10.4596 | −0.685233 | −0.342617 | − | 0.939475i | \(-0.611313\pi\) | ||||
−0.342617 | + | 0.939475i | \(0.611313\pi\) | |||||||
\(234\) | 1.28415 | 0.0839473 | ||||||||
\(235\) | −2.22982 | −0.145457 | ||||||||
\(236\) | 8.45963 | 0.550675 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.22982 | 0.274178 | ||||||||
\(239\) | 20.8370 | 1.34783 | 0.673917 | − | 0.738807i | \(-0.264611\pi\) | ||||
0.673917 | + | 0.738807i | \(0.264611\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −20.6894 | −1.33272 | −0.666362 | − | 0.745628i | \(-0.732150\pi\) | ||||
−0.666362 | + | 0.745628i | \(0.732150\pi\) | |||||||
\(242\) | −2.32304 | −0.149331 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 10.4596 | 0.666882 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | −2.22982 | −0.141593 | ||||||||
\(249\) | 4.79811 | 0.304068 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.17548 | 0.326674 | 0.163337 | − | 0.986570i | \(-0.447774\pi\) | ||||
0.163337 | + | 0.986570i | \(0.447774\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 2.94567 | 0.185193 | ||||||||
\(254\) | 13.5140 | 0.847941 | ||||||||
\(255\) | −4.22982 | −0.264881 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.3230 | −1.33009 | −0.665047 | − | 0.746801i | \(-0.731589\pi\) | ||||
−0.665047 | + | 0.746801i | \(0.731589\pi\) | |||||||
\(258\) | −10.9457 | −0.681448 | ||||||||
\(259\) | −6.45963 | −0.401382 | ||||||||
\(260\) | 1.28415 | 0.0796394 | ||||||||
\(261\) | 4.94567 | 0.306129 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | 23.4876 | 1.44830 | 0.724152 | − | 0.689640i | \(-0.242231\pi\) | ||||
0.724152 | + | 0.689640i | \(0.242231\pi\) | |||||||
\(264\) | 2.94567 | 0.181293 | ||||||||
\(265\) | −6.45963 | −0.396812 | ||||||||
\(266\) | 6.22982 | 0.381974 | ||||||||
\(267\) | −3.17548 | −0.194336 | ||||||||
\(268\) | 2.94567 | 0.179935 | ||||||||
\(269\) | 10.2034 | 0.622113 | 0.311056 | − | 0.950391i | \(-0.399317\pi\) | ||||
0.311056 | + | 0.950391i | \(0.399317\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −14.0125 | −0.851198 | −0.425599 | − | 0.904912i | \(-0.639937\pi\) | ||||
−0.425599 | + | 0.904912i | \(0.639937\pi\) | |||||||
\(272\) | 4.22982 | 0.256470 | ||||||||
\(273\) | −1.28415 | −0.0777201 | ||||||||
\(274\) | −17.7827 | −1.07429 | ||||||||
\(275\) | −2.94567 | −0.177630 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −7.51396 | −0.451470 | −0.225735 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225735 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(278\) | −2.56829 | −0.154036 | ||||||||
\(279\) | −2.22982 | −0.133496 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −1.40530 | −0.0838330 | −0.0419165 | − | 0.999121i | \(-0.513346\pi\) | ||||
−0.0419165 | + | 0.999121i | \(0.513346\pi\) | |||||||
\(282\) | 2.22982 | 0.132784 | ||||||||
\(283\) | −8.20341 | −0.487642 | −0.243821 | − | 0.969820i | \(-0.578401\pi\) | ||||
−0.243821 | + | 0.969820i | \(0.578401\pi\) | |||||||
\(284\) | 12.8370 | 0.761736 | ||||||||
\(285\) | −6.22982 | −0.369022 | ||||||||
\(286\) | −3.78267 | −0.223674 | ||||||||
\(287\) | −10.4596 | −0.617412 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.891336 | 0.0524315 | ||||||||
\(290\) | 4.94567 | 0.290420 | ||||||||
\(291\) | −15.6351 | −0.916547 | ||||||||
\(292\) | 3.43171 | 0.200825 | ||||||||
\(293\) | −7.89134 | −0.461017 | −0.230508 | − | 0.973070i | \(-0.574039\pi\) | ||||
−0.230508 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 8.45963 | 0.492539 | ||||||||
\(296\) | −6.45963 | −0.375458 | ||||||||
\(297\) | 2.94567 | 0.170925 | ||||||||
\(298\) | −9.32304 | −0.540069 | ||||||||
\(299\) | −1.28415 | −0.0742642 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 10.9457 | 0.630898 | ||||||||
\(302\) | −1.43171 | −0.0823854 | ||||||||
\(303\) | −7.17548 | −0.412221 | ||||||||
\(304\) | 6.22982 | 0.357304 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 4.22982 | 0.241802 | ||||||||
\(307\) | −10.8106 | −0.616993 | −0.308497 | − | 0.951225i | \(-0.599826\pi\) | ||||
−0.308497 | + | 0.951225i | \(0.599826\pi\) | |||||||
\(308\) | −2.94567 | −0.167845 | ||||||||
\(309\) | −5.89134 | −0.335146 | ||||||||
\(310\) | −2.22982 | −0.126645 | ||||||||
\(311\) | −7.74378 | −0.439109 | −0.219555 | − | 0.975600i | \(-0.570460\pi\) | ||||
−0.219555 | + | 0.975600i | \(0.570460\pi\) | |||||||
\(312\) | −1.28415 | −0.0727005 | ||||||||
\(313\) | 17.0668 | 0.964674 | 0.482337 | − | 0.875986i | \(-0.339788\pi\) | ||||
0.482337 | + | 0.875986i | \(0.339788\pi\) | |||||||
\(314\) | −13.0279 | −0.735208 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.56829 | −0.481243 | −0.240622 | − | 0.970619i | \(-0.577351\pi\) | ||||
−0.240622 | + | 0.970619i | \(0.577351\pi\) | |||||||
\(318\) | 6.45963 | 0.362238 | ||||||||
\(319\) | −14.5683 | −0.815668 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 26.3510 | 1.46621 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.28415 | 0.0712317 | ||||||||
\(326\) | 10.5683 | 0.585324 | ||||||||
\(327\) | −3.89134 | −0.215191 | ||||||||
\(328\) | −10.4596 | −0.577536 | ||||||||
\(329\) | −2.22982 | −0.122934 | ||||||||
\(330\) | 2.94567 | 0.162154 | ||||||||
\(331\) | 30.3510 | 1.66824 | 0.834120 | − | 0.551583i | \(-0.185976\pi\) | ||||
0.834120 | + | 0.551583i | \(0.185976\pi\) | |||||||
\(332\) | −4.79811 | −0.263330 | ||||||||
\(333\) | −6.45963 | −0.353986 | ||||||||
\(334\) | 21.2577 | 1.16317 | ||||||||
\(335\) | 2.94567 | 0.160939 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 27.2966 | 1.48694 | 0.743471 | − | 0.668768i | \(-0.233178\pi\) | ||||
0.743471 | + | 0.668768i | \(0.233178\pi\) | |||||||
\(338\) | −11.3510 | −0.617411 | ||||||||
\(339\) | 2.45963 | 0.133589 | ||||||||
\(340\) | 4.22982 | 0.229394 | ||||||||
\(341\) | 6.56829 | 0.355693 | ||||||||
\(342\) | 6.22982 | 0.336870 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.9457 | 0.590151 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −16.6894 | −0.897230 | ||||||||
\(347\) | 14.3510 | 0.770400 | 0.385200 | − | 0.922833i | \(-0.374132\pi\) | ||||
0.385200 | + | 0.922833i | \(0.374132\pi\) | |||||||
\(348\) | −4.94567 | −0.265116 | ||||||||
\(349\) | 4.01249 | 0.214783 | 0.107392 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107392 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −1.28415 | −0.0685427 | ||||||||
\(352\) | −2.94567 | −0.157005 | ||||||||
\(353\) | 24.8106 | 1.32053 | 0.660267 | − | 0.751031i | \(-0.270443\pi\) | ||||
0.660267 | + | 0.751031i | \(0.270443\pi\) | |||||||
\(354\) | −8.45963 | −0.449624 | ||||||||
\(355\) | 12.8370 | 0.681317 | ||||||||
\(356\) | 3.17548 | 0.168300 | ||||||||
\(357\) | −4.22982 | −0.223866 | ||||||||
\(358\) | −7.02792 | −0.371437 | ||||||||
\(359\) | −0.676959 | −0.0357285 | −0.0178643 | − | 0.999840i | \(-0.505687\pi\) | ||||
−0.0178643 | + | 0.999840i | \(0.505687\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 19.8106 | 1.04266 | ||||||||
\(362\) | 6.00000 | 0.315353 | ||||||||
\(363\) | 2.32304 | 0.121928 | ||||||||
\(364\) | 1.28415 | 0.0673076 | ||||||||
\(365\) | 3.43171 | 0.179624 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | −0.754747 | −0.0393975 | −0.0196987 | − | 0.999806i | \(-0.506271\pi\) | ||||
−0.0196987 | + | 0.999806i | \(0.506271\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −10.4596 | −0.544507 | ||||||||
\(370\) | −6.45963 | −0.335820 | ||||||||
\(371\) | −6.45963 | −0.335367 | ||||||||
\(372\) | 2.22982 | 0.115611 | ||||||||
\(373\) | 6.67696 | 0.345720 | 0.172860 | − | 0.984946i | \(-0.444699\pi\) | ||||
0.172860 | + | 0.984946i | \(0.444699\pi\) | |||||||
\(374\) | −12.4596 | −0.644272 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −2.22982 | −0.114994 | ||||||||
\(377\) | 6.35097 | 0.327091 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −7.78267 | −0.399769 | −0.199884 | − | 0.979819i | \(-0.564057\pi\) | ||||
−0.199884 | + | 0.979819i | \(0.564057\pi\) | |||||||
\(380\) | 6.22982 | 0.319583 | ||||||||
\(381\) | −13.5140 | −0.692341 | ||||||||
\(382\) | 20.4596 | 1.04681 | ||||||||
\(383\) | −27.0279 | −1.38106 | −0.690531 | − | 0.723303i | \(-0.742623\pi\) | ||||
−0.690531 | + | 0.723303i | \(0.742623\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.94567 | −0.150125 | ||||||||
\(386\) | 22.4596 | 1.14317 | ||||||||
\(387\) | 10.9457 | 0.556400 | ||||||||
\(388\) | 15.6351 | 0.793753 | ||||||||
\(389\) | 4.81060 | 0.243907 | 0.121953 | − | 0.992536i | \(-0.461084\pi\) | ||||
0.121953 | + | 0.992536i | \(0.461084\pi\) | |||||||
\(390\) | −1.28415 | −0.0650253 | ||||||||
\(391\) | −4.22982 | −0.213911 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 22.2423 | 1.12055 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.94567 | −0.148025 | ||||||||
\(397\) | 1.28415 | 0.0644495 | 0.0322248 | − | 0.999481i | \(-0.489741\pi\) | ||||
0.0322248 | + | 0.999481i | \(0.489741\pi\) | |||||||
\(398\) | 12.4596 | 0.624545 | ||||||||
\(399\) | −6.22982 | −0.311881 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.62263 | 0.0810301 | 0.0405151 | − | 0.999179i | \(-0.487100\pi\) | ||||
0.0405151 | + | 0.999179i | \(0.487100\pi\) | |||||||
\(402\) | −2.94567 | −0.146917 | ||||||||
\(403\) | −2.86341 | −0.142637 | ||||||||
\(404\) | 7.17548 | 0.356994 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 4.94567 | 0.245449 | ||||||||
\(407\) | 19.0279 | 0.943179 | ||||||||
\(408\) | −4.22982 | −0.209407 | ||||||||
\(409\) | −8.10866 | −0.400948 | −0.200474 | − | 0.979699i | \(-0.564248\pi\) | ||||
−0.200474 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(410\) | −10.4596 | −0.516564 | ||||||||
\(411\) | 17.7827 | 0.877154 | ||||||||
\(412\) | 5.89134 | 0.290245 | ||||||||
\(413\) | 8.45963 | 0.416271 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −4.79811 | −0.235530 | ||||||||
\(416\) | 1.28415 | 0.0629605 | ||||||||
\(417\) | 2.56829 | 0.125770 | ||||||||
\(418\) | −18.3510 | −0.897575 | ||||||||
\(419\) | −28.4985 | −1.39224 | −0.696122 | − | 0.717924i | \(-0.745093\pi\) | ||||
−0.696122 | + | 0.717924i | \(0.745093\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | 20.5683 | 1.00244 | 0.501219 | − | 0.865321i | \(-0.332885\pi\) | ||||
0.501219 | + | 0.865321i | \(0.332885\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | −2.22982 | −0.108417 | ||||||||
\(424\) | −6.45963 | −0.313707 | ||||||||
\(425\) | 4.22982 | 0.205176 | ||||||||
\(426\) | −12.8370 | −0.621955 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 3.78267 | 0.182629 | ||||||||
\(430\) | 10.9457 | 0.527847 | ||||||||
\(431\) | −17.5962 | −0.847580 | −0.423790 | − | 0.905760i | \(-0.639301\pi\) | ||||
−0.423790 | + | 0.905760i | \(0.639301\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −9.28415 | −0.446168 | −0.223084 | − | 0.974799i | \(-0.571612\pi\) | ||||
−0.223084 | + | 0.974799i | \(0.571612\pi\) | |||||||
\(434\) | −2.22982 | −0.107035 | ||||||||
\(435\) | −4.94567 | −0.237127 | ||||||||
\(436\) | 3.89134 | 0.186361 | ||||||||
\(437\) | −6.22982 | −0.298012 | ||||||||
\(438\) | −3.43171 | −0.163973 | ||||||||
\(439\) | −19.6615 | −0.938393 | −0.469197 | − | 0.883094i | \(-0.655456\pi\) | ||||
−0.469197 | + | 0.883094i | \(0.655456\pi\) | |||||||
\(440\) | −2.94567 | −0.140429 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 5.43171 | 0.258360 | ||||||||
\(443\) | 39.2702 | 1.86578 | 0.932892 | − | 0.360155i | \(-0.117276\pi\) | ||||
0.932892 | + | 0.360155i | \(0.117276\pi\) | |||||||
\(444\) | 6.45963 | 0.306560 | ||||||||
\(445\) | 3.17548 | 0.150532 | ||||||||
\(446\) | −2.60719 | −0.123454 | ||||||||
\(447\) | 9.32304 | 0.440965 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −13.4876 | −0.636517 | −0.318259 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318259 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 30.8106 | 1.45081 | ||||||||
\(452\) | −2.45963 | −0.115691 | ||||||||
\(453\) | 1.43171 | 0.0672674 | ||||||||
\(454\) | −14.2298 | −0.667838 | ||||||||
\(455\) | 1.28415 | 0.0602018 | ||||||||
\(456\) | −6.22982 | −0.291738 | ||||||||
\(457\) | 40.5110 | 1.89503 | 0.947513 | − | 0.319719i | \(-0.103588\pi\) | ||||
0.947513 | + | 0.319719i | \(0.103588\pi\) | |||||||
\(458\) | 3.89134 | 0.181830 | ||||||||
\(459\) | −4.22982 | −0.197431 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | −21.5264 | −1.00259 | −0.501293 | − | 0.865277i | \(-0.667142\pi\) | ||||
−0.501293 | + | 0.865277i | \(0.667142\pi\) | |||||||
\(462\) | 2.94567 | 0.137045 | ||||||||
\(463\) | −13.7563 | −0.639308 | −0.319654 | − | 0.947534i | \(-0.603567\pi\) | ||||
−0.319654 | + | 0.947534i | \(0.603567\pi\) | |||||||
\(464\) | 4.94567 | 0.229597 | ||||||||
\(465\) | 2.22982 | 0.103405 | ||||||||
\(466\) | −10.4596 | −0.484533 | ||||||||
\(467\) | −0.338479 | −0.0156630 | −0.00783148 | − | 0.999969i | \(-0.502493\pi\) | ||||
−0.00783148 | + | 0.999969i | \(0.502493\pi\) | |||||||
\(468\) | 1.28415 | 0.0593597 | ||||||||
\(469\) | 2.94567 | 0.136018 | ||||||||
\(470\) | −2.22982 | −0.102854 | ||||||||
\(471\) | 13.0279 | 0.600295 | ||||||||
\(472\) | 8.45963 | 0.389386 | ||||||||
\(473\) | −32.2423 | −1.48250 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.22982 | 0.285844 | ||||||||
\(476\) | 4.22982 | 0.193873 | ||||||||
\(477\) | −6.45963 | −0.295766 | ||||||||
\(478\) | 20.8370 | 0.953062 | ||||||||
\(479\) | −35.9472 | −1.64247 | −0.821234 | − | 0.570591i | \(-0.806714\pi\) | ||||
−0.821234 | + | 0.570591i | \(0.806714\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −8.29512 | −0.378225 | ||||||||
\(482\) | −20.6894 | −0.942378 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −2.32304 | −0.105593 | ||||||||
\(485\) | 15.6351 | 0.709954 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.05433 | −0.0477764 | −0.0238882 | − | 0.999715i | \(-0.507605\pi\) | ||||
−0.0238882 | + | 0.999715i | \(0.507605\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | −10.5683 | −0.477915 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −12.9193 | −0.583038 | −0.291519 | − | 0.956565i | \(-0.594161\pi\) | ||||
−0.291519 | + | 0.956565i | \(0.594161\pi\) | |||||||
\(492\) | 10.4596 | 0.471557 | ||||||||
\(493\) | 20.9193 | 0.942156 | ||||||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | −2.94567 | −0.132398 | ||||||||
\(496\) | −2.22982 | −0.100122 | ||||||||
\(497\) | 12.8370 | 0.575818 | ||||||||
\(498\) | 4.79811 | 0.215008 | ||||||||
\(499\) | −29.8385 | −1.33576 | −0.667878 | − | 0.744271i | \(-0.732797\pi\) | ||||
−0.667878 | + | 0.744271i | \(0.732797\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −21.2577 | −0.949726 | ||||||||
\(502\) | 5.17548 | 0.230993 | ||||||||
\(503\) | 14.8106 | 0.660372 | 0.330186 | − | 0.943916i | \(-0.392889\pi\) | ||||
0.330186 | + | 0.943916i | \(0.392889\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 7.17548 | 0.319305 | ||||||||
\(506\) | 2.94567 | 0.130951 | ||||||||
\(507\) | 11.3510 | 0.504114 | ||||||||
\(508\) | 13.5140 | 0.599585 | ||||||||
\(509\) | −28.6072 | −1.26799 | −0.633996 | − | 0.773337i | \(-0.718586\pi\) | ||||
−0.633996 | + | 0.773337i | \(0.718586\pi\) | |||||||
\(510\) | −4.22982 | −0.187299 | ||||||||
\(511\) | 3.43171 | 0.151810 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.22982 | −0.275053 | ||||||||
\(514\) | −21.3230 | −0.940519 | ||||||||
\(515\) | 5.89134 | 0.259603 | ||||||||
\(516\) | −10.9457 | −0.481856 | ||||||||
\(517\) | 6.56829 | 0.288873 | ||||||||
\(518\) | −6.45963 | −0.283820 | ||||||||
\(519\) | 16.6894 | 0.732585 | ||||||||
\(520\) | 1.28415 | 0.0563136 | ||||||||
\(521\) | 0.312072 | 0.0136721 | 0.00683606 | − | 0.999977i | \(-0.497824\pi\) | ||||
0.00683606 | + | 0.999977i | \(0.497824\pi\) | |||||||
\(522\) | 4.94567 | 0.216466 | ||||||||
\(523\) | −8.20341 | −0.358710 | −0.179355 | − | 0.983784i | \(-0.557401\pi\) | ||||
−0.179355 | + | 0.983784i | \(0.557401\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 23.4876 | 1.02411 | ||||||||
\(527\) | −9.43171 | −0.410852 | ||||||||
\(528\) | 2.94567 | 0.128194 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.45963 | −0.280588 | ||||||||
\(531\) | 8.45963 | 0.367117 | ||||||||
\(532\) | 6.22982 | 0.270097 | ||||||||
\(533\) | −13.4317 | −0.581792 | ||||||||
\(534\) | −3.17548 | −0.137417 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 2.94567 | 0.127233 | ||||||||
\(537\) | 7.02792 | 0.303277 | ||||||||
\(538\) | 10.2034 | 0.439900 | ||||||||
\(539\) | −2.94567 | −0.126879 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 0.108664 | 0.00467185 | 0.00233592 | − | 0.999997i | \(-0.499256\pi\) | ||||
0.00233592 | + | 0.999997i | \(0.499256\pi\) | |||||||
\(542\) | −14.0125 | −0.601888 | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 4.22982 | 0.181352 | ||||||||
\(545\) | 3.89134 | 0.166687 | ||||||||
\(546\) | −1.28415 | −0.0549564 | ||||||||
\(547\) | 5.59622 | 0.239277 | 0.119639 | − | 0.992818i | \(-0.461826\pi\) | ||||
0.119639 | + | 0.992818i | \(0.461826\pi\) | |||||||
\(548\) | −17.7827 | −0.759638 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | −2.94567 | −0.125604 | ||||||||
\(551\) | 30.8106 | 1.31258 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.51396 | −0.319238 | ||||||||
\(555\) | 6.45963 | 0.274196 | ||||||||
\(556\) | −2.56829 | −0.108920 | ||||||||
\(557\) | 40.5933 | 1.71999 | 0.859996 | − | 0.510301i | \(-0.170466\pi\) | ||||
0.859996 | + | 0.510301i | \(0.170466\pi\) | |||||||
\(558\) | −2.22982 | −0.0943956 | ||||||||
\(559\) | 14.0558 | 0.594499 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 12.4596 | 0.526046 | ||||||||
\(562\) | −1.40530 | −0.0592789 | ||||||||
\(563\) | −4.79811 | −0.202216 | −0.101108 | − | 0.994875i | \(-0.532239\pi\) | ||||
−0.101108 | + | 0.994875i | \(0.532239\pi\) | |||||||
\(564\) | 2.22982 | 0.0938922 | ||||||||
\(565\) | −2.45963 | −0.103477 | ||||||||
\(566\) | −8.20341 | −0.344815 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 12.8370 | 0.538629 | ||||||||
\(569\) | −22.3774 | −0.938108 | −0.469054 | − | 0.883169i | \(-0.655405\pi\) | ||||
−0.469054 | + | 0.883169i | \(0.655405\pi\) | |||||||
\(570\) | −6.22982 | −0.260938 | ||||||||
\(571\) | −16.4596 | −0.688814 | −0.344407 | − | 0.938820i | \(-0.611920\pi\) | ||||
−0.344407 | + | 0.938820i | \(0.611920\pi\) | |||||||
\(572\) | −3.78267 | −0.158161 | ||||||||
\(573\) | −20.4596 | −0.854713 | ||||||||
\(574\) | −10.4596 | −0.436577 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −38.9193 | −1.62023 | −0.810115 | − | 0.586271i | \(-0.800595\pi\) | ||||
−0.810115 | + | 0.586271i | \(0.800595\pi\) | |||||||
\(578\) | 0.891336 | 0.0370747 | ||||||||
\(579\) | −22.4596 | −0.933390 | ||||||||
\(580\) | 4.94567 | 0.205358 | ||||||||
\(581\) | −4.79811 | −0.199059 | ||||||||
\(582\) | −15.6351 | −0.648096 | ||||||||
\(583\) | 19.0279 | 0.788056 | ||||||||
\(584\) | 3.43171 | 0.142005 | ||||||||
\(585\) | 1.28415 | 0.0530930 | ||||||||
\(586\) | −7.89134 | −0.325988 | ||||||||
\(587\) | −3.32304 | −0.137157 | −0.0685783 | − | 0.997646i | \(-0.521846\pi\) | ||||
−0.0685783 | + | 0.997646i | \(0.521846\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −13.8913 | −0.572383 | ||||||||
\(590\) | 8.45963 | 0.348277 | ||||||||
\(591\) | −22.2423 | −0.914926 | ||||||||
\(592\) | −6.45963 | −0.265489 | ||||||||
\(593\) | −46.2423 | −1.89894 | −0.949472 | − | 0.313852i | \(-0.898380\pi\) | ||||
−0.949472 | + | 0.313852i | \(0.898380\pi\) | |||||||
\(594\) | 2.94567 | 0.120862 | ||||||||
\(595\) | 4.22982 | 0.173406 | ||||||||
\(596\) | −9.32304 | −0.381887 | ||||||||
\(597\) | −12.4596 | −0.509939 | ||||||||
\(598\) | −1.28415 | −0.0525127 | ||||||||
\(599\) | −33.2966 | −1.36046 | −0.680232 | − | 0.732997i | \(-0.738121\pi\) | ||||
−0.680232 | + | 0.732997i | \(0.738121\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −37.4876 | −1.52915 | −0.764575 | − | 0.644535i | \(-0.777051\pi\) | ||||
−0.764575 | + | 0.644535i | \(0.777051\pi\) | |||||||
\(602\) | 10.9457 | 0.446112 | ||||||||
\(603\) | 2.94567 | 0.119957 | ||||||||
\(604\) | −1.43171 | −0.0582553 | ||||||||
\(605\) | −2.32304 | −0.0944451 | ||||||||
\(606\) | −7.17548 | −0.291484 | ||||||||
\(607\) | 7.57926 | 0.307633 | 0.153816 | − | 0.988099i | \(-0.450844\pi\) | ||||
0.153816 | + | 0.988099i | \(0.450844\pi\) | |||||||
\(608\) | 6.22982 | 0.252652 | ||||||||
\(609\) | −4.94567 | −0.200409 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | −2.86341 | −0.115841 | ||||||||
\(612\) | 4.22982 | 0.170980 | ||||||||
\(613\) | −2.75475 | −0.111263 | −0.0556316 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556316 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(614\) | −10.8106 | −0.436280 | ||||||||
\(615\) | 10.4596 | 0.421773 | ||||||||
\(616\) | −2.94567 | −0.118684 | ||||||||
\(617\) | −28.8106 | −1.15987 | −0.579935 | − | 0.814662i | \(-0.696922\pi\) | ||||
−0.579935 | + | 0.814662i | \(0.696922\pi\) | |||||||
\(618\) | −5.89134 | −0.236984 | ||||||||
\(619\) | −44.2857 | −1.77999 | −0.889996 | − | 0.455969i | \(-0.849293\pi\) | ||||
−0.889996 | + | 0.455969i | \(0.849293\pi\) | |||||||
\(620\) | −2.22982 | −0.0895515 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −7.74378 | −0.310497 | ||||||||
\(623\) | 3.17548 | 0.127223 | ||||||||
\(624\) | −1.28415 | −0.0514070 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.0668 | 0.682127 | ||||||||
\(627\) | 18.3510 | 0.732867 | ||||||||
\(628\) | −13.0279 | −0.519871 | ||||||||
\(629\) | −27.3230 | −1.08944 | ||||||||
\(630\) | 1.00000 | 0.0398410 | ||||||||
\(631\) | −3.78267 | −0.150586 | −0.0752929 | − | 0.997161i | \(-0.523989\pi\) | ||||
−0.0752929 | + | 0.997161i | \(0.523989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.00000 | −0.158986 | ||||||||
\(634\) | −8.56829 | −0.340290 | ||||||||
\(635\) | 13.5140 | 0.536285 | ||||||||
\(636\) | 6.45963 | 0.256141 | ||||||||
\(637\) | 1.28415 | 0.0508798 | ||||||||
\(638\) | −14.5683 | −0.576764 | ||||||||
\(639\) | 12.8370 | 0.507824 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.486038 | −0.0191973 | −0.00959867 | − | 0.999954i | \(-0.503055\pi\) | ||||
−0.00959867 | + | 0.999954i | \(0.503055\pi\) | |||||||
\(642\) | −4.00000 | −0.157867 | ||||||||
\(643\) | 16.0389 | 0.632512 | 0.316256 | − | 0.948674i | \(-0.397574\pi\) | ||||
0.316256 | + | 0.948674i | \(0.397574\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | −10.9457 | −0.430985 | ||||||||
\(646\) | 26.3510 | 1.03676 | ||||||||
\(647\) | −39.6087 | −1.55718 | −0.778589 | − | 0.627534i | \(-0.784064\pi\) | ||||
−0.778589 | + | 0.627534i | \(0.784064\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −24.9193 | −0.978167 | ||||||||
\(650\) | 1.28415 | 0.0503684 | ||||||||
\(651\) | 2.22982 | 0.0873933 | ||||||||
\(652\) | 10.5683 | 0.413886 | ||||||||
\(653\) | 11.8913 | 0.465344 | 0.232672 | − | 0.972555i | \(-0.425253\pi\) | ||||
0.232672 | + | 0.972555i | \(0.425253\pi\) | |||||||
\(654\) | −3.89134 | −0.152163 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | −10.4596 | −0.408380 | ||||||||
\(657\) | 3.43171 | 0.133884 | ||||||||
\(658\) | −2.22982 | −0.0869272 | ||||||||
\(659\) | −6.48604 | −0.252660 | −0.126330 | − | 0.991988i | \(-0.540320\pi\) | ||||
−0.126330 | + | 0.991988i | \(0.540320\pi\) | |||||||
\(660\) | 2.94567 | 0.114660 | ||||||||
\(661\) | −23.8913 | −0.929265 | −0.464633 | − | 0.885504i | \(-0.653814\pi\) | ||||
−0.464633 | + | 0.885504i | \(0.653814\pi\) | |||||||
\(662\) | 30.3510 | 1.17962 | ||||||||
\(663\) | −5.43171 | −0.210950 | ||||||||
\(664\) | −4.79811 | −0.186203 | ||||||||
\(665\) | 6.22982 | 0.241582 | ||||||||
\(666\) | −6.45963 | −0.250306 | ||||||||
\(667\) | −4.94567 | −0.191497 | ||||||||
\(668\) | 21.2577 | 0.822487 | ||||||||
\(669\) | 2.60719 | 0.100800 | ||||||||
\(670\) | 2.94567 | 0.113801 | ||||||||
\(671\) | 5.89134 | 0.227432 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 8.56829 | 0.330283 | 0.165142 | − | 0.986270i | \(-0.447192\pi\) | ||||
0.165142 | + | 0.986270i | \(0.447192\pi\) | |||||||
\(674\) | 27.2966 | 1.05143 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −11.3510 | −0.436576 | ||||||||
\(677\) | −18.9193 | −0.727126 | −0.363563 | − | 0.931570i | \(-0.618440\pi\) | ||||
−0.363563 | + | 0.931570i | \(0.618440\pi\) | |||||||
\(678\) | 2.45963 | 0.0944615 | ||||||||
\(679\) | 15.6351 | 0.600021 | ||||||||
\(680\) | 4.22982 | 0.162206 | ||||||||
\(681\) | 14.2298 | 0.545288 | ||||||||
\(682\) | 6.56829 | 0.251513 | ||||||||
\(683\) | −43.0529 | −1.64737 | −0.823687 | − | 0.567045i | \(-0.808086\pi\) | ||||
−0.823687 | + | 0.567045i | \(0.808086\pi\) | |||||||
\(684\) | 6.22982 | 0.238203 | ||||||||
\(685\) | −17.7827 | −0.679441 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −3.89134 | −0.148464 | ||||||||
\(688\) | 10.9457 | 0.417300 | ||||||||
\(689\) | −8.29512 | −0.316019 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | 26.1336 | 0.994170 | 0.497085 | − | 0.867702i | \(-0.334404\pi\) | ||||
0.497085 | + | 0.867702i | \(0.334404\pi\) | |||||||
\(692\) | −16.6894 | −0.634438 | ||||||||
\(693\) | −2.94567 | −0.111897 | ||||||||
\(694\) | 14.3510 | 0.544755 | ||||||||
\(695\) | −2.56829 | −0.0974210 | ||||||||
\(696\) | −4.94567 | −0.187465 | ||||||||
\(697\) | −44.2423 | −1.67580 | ||||||||
\(698\) | 4.01249 | 0.151875 | ||||||||
\(699\) | 10.4596 | 0.395620 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 21.4876 | 0.811574 | 0.405787 | − | 0.913968i | \(-0.366998\pi\) | ||||
0.405787 | + | 0.913968i | \(0.366998\pi\) | |||||||
\(702\) | −1.28415 | −0.0484670 | ||||||||
\(703\) | −40.2423 | −1.51777 | ||||||||
\(704\) | −2.94567 | −0.111019 | ||||||||
\(705\) | 2.22982 | 0.0839797 | ||||||||
\(706\) | 24.8106 | 0.933759 | ||||||||
\(707\) | 7.17548 | 0.269862 | ||||||||
\(708\) | −8.45963 | −0.317932 | ||||||||
\(709\) | −2.00000 | −0.0751116 | −0.0375558 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375558 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(710\) | 12.8370 | 0.481764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.17548 | 0.119006 | ||||||||
\(713\) | 2.22982 | 0.0835072 | ||||||||
\(714\) | −4.22982 | −0.158297 | ||||||||
\(715\) | −3.78267 | −0.141464 | ||||||||
\(716\) | −7.02792 | −0.262646 | ||||||||
\(717\) | −20.8370 | −0.778172 | ||||||||
\(718\) | −0.676959 | −0.0252639 | ||||||||
\(719\) | −31.2313 | −1.16473 | −0.582366 | − | 0.812927i | \(-0.697873\pi\) | ||||
−0.582366 | + | 0.812927i | \(0.697873\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 5.89134 | 0.219405 | ||||||||
\(722\) | 19.8106 | 0.737274 | ||||||||
\(723\) | 20.6894 | 0.769449 | ||||||||
\(724\) | 6.00000 | 0.222988 | ||||||||
\(725\) | 4.94567 | 0.183677 | ||||||||
\(726\) | 2.32304 | 0.0862161 | ||||||||
\(727\) | 39.4876 | 1.46451 | 0.732256 | − | 0.681029i | \(-0.238467\pi\) | ||||
0.732256 | + | 0.681029i | \(0.238467\pi\) | |||||||
\(728\) | 1.28415 | 0.0475937 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.43171 | 0.127013 | ||||||||
\(731\) | 46.2982 | 1.71240 | ||||||||
\(732\) | 2.00000 | 0.0739221 | ||||||||
\(733\) | 9.54037 | 0.352382 | 0.176191 | − | 0.984356i | \(-0.443622\pi\) | ||||
0.176191 | + | 0.984356i | \(0.443622\pi\) | |||||||
\(734\) | −0.754747 | −0.0278582 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −8.67696 | −0.319620 | ||||||||
\(738\) | −10.4596 | −0.385024 | ||||||||
\(739\) | −9.64903 | −0.354945 | −0.177473 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177473 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(740\) | −6.45963 | −0.237461 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | −6.45963 | −0.237140 | ||||||||
\(743\) | 38.9751 | 1.42986 | 0.714929 | − | 0.699197i | \(-0.246459\pi\) | ||||
0.714929 | + | 0.699197i | \(0.246459\pi\) | |||||||
\(744\) | 2.22982 | 0.0817490 | ||||||||
\(745\) | −9.32304 | −0.341570 | ||||||||
\(746\) | 6.67696 | 0.244461 | ||||||||
\(747\) | −4.79811 | −0.175554 | ||||||||
\(748\) | −12.4596 | −0.455569 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −33.8385 | −1.23479 | −0.617393 | − | 0.786655i | \(-0.711811\pi\) | ||||
−0.617393 | + | 0.786655i | \(0.711811\pi\) | |||||||
\(752\) | −2.22982 | −0.0813130 | ||||||||
\(753\) | −5.17548 | −0.188605 | ||||||||
\(754\) | 6.35097 | 0.231289 | ||||||||
\(755\) | −1.43171 | −0.0521051 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 14.7547 | 0.536270 | 0.268135 | − | 0.963381i | \(-0.413593\pi\) | ||||
0.268135 | + | 0.963381i | \(0.413593\pi\) | |||||||
\(758\) | −7.78267 | −0.282679 | ||||||||
\(759\) | −2.94567 | −0.106921 | ||||||||
\(760\) | 6.22982 | 0.225979 | ||||||||
\(761\) | −25.1057 | −0.910081 | −0.455041 | − | 0.890471i | \(-0.650375\pi\) | ||||
−0.455041 | + | 0.890471i | \(0.650375\pi\) | |||||||
\(762\) | −13.5140 | −0.489559 | ||||||||
\(763\) | 3.89134 | 0.140876 | ||||||||
\(764\) | 20.4596 | 0.740203 | ||||||||
\(765\) | 4.22982 | 0.152929 | ||||||||
\(766\) | −27.0279 | −0.976559 | ||||||||
\(767\) | 10.8634 | 0.392255 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −5.44419 | −0.196323 | −0.0981613 | − | 0.995171i | \(-0.531296\pi\) | ||||
−0.0981613 | + | 0.995171i | \(0.531296\pi\) | |||||||
\(770\) | −2.94567 | −0.106154 | ||||||||
\(771\) | 21.3230 | 0.767931 | ||||||||
\(772\) | 22.4596 | 0.808340 | ||||||||
\(773\) | 36.1336 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(774\) | 10.9457 | 0.393434 | ||||||||
\(775\) | −2.22982 | −0.0800973 | ||||||||
\(776\) | 15.6351 | 0.561268 | ||||||||
\(777\) | 6.45963 | 0.231738 | ||||||||
\(778\) | 4.81060 | 0.172468 | ||||||||
\(779\) | −65.1616 | −2.33466 | ||||||||
\(780\) | −1.28415 | −0.0459798 | ||||||||
\(781\) | −37.8135 | −1.35308 | ||||||||
\(782\) | −4.22982 | −0.151258 | ||||||||
\(783\) | −4.94567 | −0.176744 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −13.0279 | −0.464987 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | 29.1755 | 1.03999 | 0.519997 | − | 0.854168i | \(-0.325933\pi\) | ||||
0.519997 | + | 0.854168i | \(0.325933\pi\) | |||||||
\(788\) | 22.2423 | 0.792349 | ||||||||
\(789\) | −23.4876 | −0.836179 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.45963 | −0.0874544 | ||||||||
\(792\) | −2.94567 | −0.104670 | ||||||||
\(793\) | −2.56829 | −0.0912028 | ||||||||
\(794\) | 1.28415 | 0.0455727 | ||||||||
\(795\) | 6.45963 | 0.229099 | ||||||||
\(796\) | 12.4596 | 0.441620 | ||||||||
\(797\) | −19.5962 | −0.694134 | −0.347067 | − | 0.937840i | \(-0.612822\pi\) | ||||
−0.347067 | + | 0.937840i | \(0.612822\pi\) | |||||||
\(798\) | −6.22982 | −0.220533 | ||||||||
\(799\) | −9.43171 | −0.333670 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 3.17548 | 0.112200 | ||||||||
\(802\) | 1.62263 | 0.0572969 | ||||||||
\(803\) | −10.1087 | −0.356727 | ||||||||
\(804\) | −2.94567 | −0.103886 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | −2.86341 | −0.100859 | ||||||||
\(807\) | −10.2034 | −0.359177 | ||||||||
\(808\) | 7.17548 | 0.252433 | ||||||||
\(809\) | −5.75770 | −0.202430 | −0.101215 | − | 0.994865i | \(-0.532273\pi\) | ||||
−0.101215 | + | 0.994865i | \(0.532273\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 45.6740 | 1.60383 | 0.801916 | − | 0.597437i | \(-0.203814\pi\) | ||||
0.801916 | + | 0.597437i | \(0.203814\pi\) | |||||||
\(812\) | 4.94567 | 0.173559 | ||||||||
\(813\) | 14.0125 | 0.491439 | ||||||||
\(814\) | 19.0279 | 0.666928 | ||||||||
\(815\) | 10.5683 | 0.370191 | ||||||||
\(816\) | −4.22982 | −0.148073 | ||||||||
\(817\) | 68.1895 | 2.38565 | ||||||||
\(818\) | −8.10866 | −0.283513 | ||||||||
\(819\) | 1.28415 | 0.0448717 | ||||||||
\(820\) | −10.4596 | −0.365266 | ||||||||
\(821\) | 21.0235 | 0.733724 | 0.366862 | − | 0.930275i | \(-0.380432\pi\) | ||||
0.366862 | + | 0.930275i | \(0.380432\pi\) | |||||||
\(822\) | 17.7827 | 0.620242 | ||||||||
\(823\) | −44.3246 | −1.54506 | −0.772528 | − | 0.634980i | \(-0.781008\pi\) | ||||
−0.772528 | + | 0.634980i | \(0.781008\pi\) | |||||||
\(824\) | 5.89134 | 0.205234 | ||||||||
\(825\) | 2.94567 | 0.102555 | ||||||||
\(826\) | 8.45963 | 0.294348 | ||||||||
\(827\) | −20.9193 | −0.727434 | −0.363717 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363717 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 33.3914 | 1.15973 | 0.579865 | − | 0.814712i | \(-0.303105\pi\) | ||||
0.579865 | + | 0.814712i | \(0.303105\pi\) | |||||||
\(830\) | −4.79811 | −0.166545 | ||||||||
\(831\) | 7.51396 | 0.260656 | ||||||||
\(832\) | 1.28415 | 0.0445198 | ||||||||
\(833\) | 4.22982 | 0.146554 | ||||||||
\(834\) | 2.56829 | 0.0889328 | ||||||||
\(835\) | 21.2577 | 0.735654 | ||||||||
\(836\) | −18.3510 | −0.634681 | ||||||||
\(837\) | 2.22982 | 0.0770737 | ||||||||
\(838\) | −28.4985 | −0.984465 | ||||||||
\(839\) | −28.4596 | −0.982536 | −0.491268 | − | 0.871009i | \(-0.663466\pi\) | ||||
−0.491268 | + | 0.871009i | \(0.663466\pi\) | |||||||
\(840\) | −1.00000 | −0.0345033 | ||||||||
\(841\) | −4.54037 | −0.156564 | ||||||||
\(842\) | 20.5683 | 0.708830 | ||||||||
\(843\) | 1.40530 | 0.0484010 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | −11.3510 | −0.390485 | ||||||||
\(846\) | −2.22982 | −0.0766626 | ||||||||
\(847\) | −2.32304 | −0.0798206 | ||||||||
\(848\) | −6.45963 | −0.221825 | ||||||||
\(849\) | 8.20341 | 0.281540 | ||||||||
\(850\) | 4.22982 | 0.145081 | ||||||||
\(851\) | 6.45963 | 0.221433 | ||||||||
\(852\) | −12.8370 | −0.439788 | ||||||||
\(853\) | −27.4178 | −0.938767 | −0.469384 | − | 0.882994i | \(-0.655524\pi\) | ||||
−0.469384 | + | 0.882994i | \(0.655524\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | 6.22982 | 0.213055 | ||||||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | −30.1645 | −1.03040 | −0.515200 | − | 0.857070i | \(-0.672282\pi\) | ||||
−0.515200 | + | 0.857070i | \(0.672282\pi\) | |||||||
\(858\) | 3.78267 | 0.129138 | ||||||||
\(859\) | 23.7049 | 0.808800 | 0.404400 | − | 0.914582i | \(-0.367480\pi\) | ||||
0.404400 | + | 0.914582i | \(0.367480\pi\) | |||||||
\(860\) | 10.9457 | 0.373244 | ||||||||
\(861\) | 10.4596 | 0.356463 | ||||||||
\(862\) | −17.5962 | −0.599330 | ||||||||
\(863\) | −40.4068 | −1.37546 | −0.687732 | − | 0.725965i | \(-0.741394\pi\) | ||||
−0.687732 | + | 0.725965i | \(0.741394\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −16.6894 | −0.567458 | ||||||||
\(866\) | −9.28415 | −0.315488 | ||||||||
\(867\) | −0.891336 | −0.0302713 | ||||||||
\(868\) | −2.22982 | −0.0756849 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.94567 | −0.167674 | ||||||||
\(871\) | 3.78267 | 0.128171 | ||||||||
\(872\) | 3.89134 | 0.131777 | ||||||||
\(873\) | 15.6351 | 0.529168 | ||||||||
\(874\) | −6.22982 | −0.210727 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −3.43171 | −0.115947 | ||||||||
\(877\) | −18.6197 | −0.628742 | −0.314371 | − | 0.949300i | \(-0.601794\pi\) | ||||
−0.314371 | + | 0.949300i | \(0.601794\pi\) | |||||||
\(878\) | −19.6615 | −0.663544 | ||||||||
\(879\) | 7.89134 | 0.266168 | ||||||||
\(880\) | −2.94567 | −0.0992984 | ||||||||
\(881\) | −45.9861 | −1.54931 | −0.774655 | − | 0.632384i | \(-0.782077\pi\) | ||||
−0.774655 | + | 0.632384i | \(0.782077\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 4.51245 | 0.151856 | 0.0759279 | − | 0.997113i | \(-0.475808\pi\) | ||||
0.0759279 | + | 0.997113i | \(0.475808\pi\) | |||||||
\(884\) | 5.43171 | 0.182688 | ||||||||
\(885\) | −8.45963 | −0.284367 | ||||||||
\(886\) | 39.2702 | 1.31931 | ||||||||
\(887\) | −4.41627 | −0.148284 | −0.0741419 | − | 0.997248i | \(-0.523622\pi\) | ||||
−0.0741419 | + | 0.997248i | \(0.523622\pi\) | |||||||
\(888\) | 6.45963 | 0.216771 | ||||||||
\(889\) | 13.5140 | 0.453244 | ||||||||
\(890\) | 3.17548 | 0.106442 | ||||||||
\(891\) | −2.94567 | −0.0986836 | ||||||||
\(892\) | −2.60719 | −0.0872951 | ||||||||
\(893\) | −13.8913 | −0.464856 | ||||||||
\(894\) | 9.32304 | 0.311809 | ||||||||
\(895\) | −7.02792 | −0.234918 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 1.28415 | 0.0428764 | ||||||||
\(898\) | −13.4876 | −0.450086 | ||||||||
\(899\) | −11.0279 | −0.367802 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −27.3230 | −0.910262 | ||||||||
\(902\) | 30.8106 | 1.02588 | ||||||||
\(903\) | −10.9457 | −0.364249 | ||||||||
\(904\) | −2.45963 | −0.0818061 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 1.43171 | 0.0475652 | ||||||||
\(907\) | 22.4860 | 0.746637 | 0.373318 | − | 0.927703i | \(-0.378220\pi\) | ||||
0.373318 | + | 0.927703i | \(0.378220\pi\) | |||||||
\(908\) | −14.2298 | −0.472233 | ||||||||
\(909\) | 7.17548 | 0.237996 | ||||||||
\(910\) | 1.28415 | 0.0425691 | ||||||||
\(911\) | −15.4876 | −0.513126 | −0.256563 | − | 0.966528i | \(-0.582590\pi\) | ||||
−0.256563 | + | 0.966528i | \(0.582590\pi\) | |||||||
\(912\) | −6.22982 | −0.206290 | ||||||||
\(913\) | 14.1336 | 0.467755 | ||||||||
\(914\) | 40.5110 | 1.33999 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 3.89134 | 0.128573 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | −4.22982 | −0.139605 | ||||||||
\(919\) | −17.4317 | −0.575019 | −0.287509 | − | 0.957778i | \(-0.592827\pi\) | ||||
−0.287509 | + | 0.957778i | \(0.592827\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | 10.8106 | 0.356221 | ||||||||
\(922\) | −21.5264 | −0.708936 | ||||||||
\(923\) | 16.4846 | 0.542597 | ||||||||
\(924\) | 2.94567 | 0.0969054 | ||||||||
\(925\) | −6.45963 | −0.212391 | ||||||||
\(926\) | −13.7563 | −0.452059 | ||||||||
\(927\) | 5.89134 | 0.193497 | ||||||||
\(928\) | 4.94567 | 0.162349 | ||||||||
\(929\) | −2.97208 | −0.0975106 | −0.0487553 | − | 0.998811i | \(-0.515525\pi\) | ||||
−0.0487553 | + | 0.998811i | \(0.515525\pi\) | |||||||
\(930\) | 2.22982 | 0.0731185 | ||||||||
\(931\) | 6.22982 | 0.204174 | ||||||||
\(932\) | −10.4596 | −0.342617 | ||||||||
\(933\) | 7.74378 | 0.253520 | ||||||||
\(934\) | −0.338479 | −0.0110754 | ||||||||
\(935\) | −12.4596 | −0.407473 | ||||||||
\(936\) | 1.28415 | 0.0419737 | ||||||||
\(937\) | 55.8774 | 1.82544 | 0.912718 | − | 0.408591i | \(-0.133980\pi\) | ||||
0.912718 | + | 0.408591i | \(0.133980\pi\) | |||||||
\(938\) | 2.94567 | 0.0961795 | ||||||||
\(939\) | −17.0668 | −0.556955 | ||||||||
\(940\) | −2.22982 | −0.0727285 | ||||||||
\(941\) | −22.2173 | −0.724264 | −0.362132 | − | 0.932127i | \(-0.617951\pi\) | ||||
−0.362132 | + | 0.932127i | \(0.617951\pi\) | |||||||
\(942\) | 13.0279 | 0.424473 | ||||||||
\(943\) | 10.4596 | 0.340612 | ||||||||
\(944\) | 8.45963 | 0.275338 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −32.2423 | −1.04829 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.40682 | 0.143051 | ||||||||
\(950\) | 6.22982 | 0.202122 | ||||||||
\(951\) | 8.56829 | 0.277846 | ||||||||
\(952\) | 4.22982 | 0.137089 | ||||||||
\(953\) | −47.1616 | −1.52771 | −0.763856 | − | 0.645386i | \(-0.776696\pi\) | ||||
−0.763856 | + | 0.645386i | \(0.776696\pi\) | |||||||
\(954\) | −6.45963 | −0.209138 | ||||||||
\(955\) | 20.4596 | 0.662058 | ||||||||
\(956\) | 20.8370 | 0.673917 | ||||||||
\(957\) | 14.5683 | 0.470926 | ||||||||
\(958\) | −35.9472 | −1.16140 | ||||||||
\(959\) | −17.7827 | −0.574232 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −26.0279 | −0.839610 | ||||||||
\(962\) | −8.29512 | −0.267445 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | −20.6894 | −0.666362 | ||||||||
\(965\) | 22.4596 | 0.723001 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 0.299586 | 0.00963402 | 0.00481701 | − | 0.999988i | \(-0.498467\pi\) | ||||
0.00481701 | + | 0.999988i | \(0.498467\pi\) | |||||||
\(968\) | −2.32304 | −0.0746654 | ||||||||
\(969\) | −26.3510 | −0.846515 | ||||||||
\(970\) | 15.6351 | 0.502013 | ||||||||
\(971\) | −15.5264 | −0.498267 | −0.249134 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249134 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −2.56829 | −0.0823357 | ||||||||
\(974\) | −1.05433 | −0.0337830 | ||||||||
\(975\) | −1.28415 | −0.0411256 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 45.5125 | 1.45607 | 0.728037 | − | 0.685537i | \(-0.240433\pi\) | ||||
0.728037 | + | 0.685537i | \(0.240433\pi\) | |||||||
\(978\) | −10.5683 | −0.337937 | ||||||||
\(979\) | −9.35392 | −0.298953 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 3.89134 | 0.124241 | ||||||||
\(982\) | −12.9193 | −0.412270 | ||||||||
\(983\) | −11.6182 | −0.370562 | −0.185281 | − | 0.982686i | \(-0.559319\pi\) | ||||
−0.185281 | + | 0.982686i | \(0.559319\pi\) | |||||||
\(984\) | 10.4596 | 0.333441 | ||||||||
\(985\) | 22.2423 | 0.708699 | ||||||||
\(986\) | 20.9193 | 0.666205 | ||||||||
\(987\) | 2.22982 | 0.0709758 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | −10.9457 | −0.348052 | ||||||||
\(990\) | −2.94567 | −0.0936195 | ||||||||
\(991\) | −27.2702 | −0.866267 | −0.433134 | − | 0.901330i | \(-0.642592\pi\) | ||||
−0.433134 | + | 0.901330i | \(0.642592\pi\) | |||||||
\(992\) | −2.22982 | −0.0707967 | ||||||||
\(993\) | −30.3510 | −0.963159 | ||||||||
\(994\) | 12.8370 | 0.407165 | ||||||||
\(995\) | 12.4596 | 0.394997 | ||||||||
\(996\) | 4.79811 | 0.152034 | ||||||||
\(997\) | −14.1256 | −0.447363 | −0.223681 | − | 0.974662i | \(-0.571808\pi\) | ||||
−0.223681 | + | 0.974662i | \(0.571808\pi\) | |||||||
\(998\) | −29.8385 | −0.944522 | ||||||||
\(999\) | 6.45963 | 0.204374 |
(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 | 4830.2.a.cb.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.cb.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |