Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13968.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.386509\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | 3.05596 | 1.36667 | 0.683334 | − | 0.730106i | \(-0.260529\pi\) | ||||
0.683334 | + | 0.730106i | \(0.260529\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.05596 | 0.966380 | ||||||||
\(11\) | 3.44247 | 1.03794 | 0.518972 | − | 0.854791i | \(-0.326315\pi\) | ||||
0.518972 | + | 0.854791i | \(0.326315\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.05596 | −0.789046 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.82898 | −0.686129 | −0.343064 | − | 0.939312i | \(-0.611465\pi\) | ||||
−0.343064 | + | 0.939312i | \(0.611465\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.72542 | −0.395838 | −0.197919 | − | 0.980218i | \(-0.563418\pi\) | ||||
−0.197919 | + | 0.980218i | \(0.563418\pi\) | |||||||
\(20\) | 3.05596 | 0.683334 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.44247 | 0.733937 | ||||||||
\(23\) | 3.06260 | 0.638596 | 0.319298 | − | 0.947654i | \(-0.396553\pi\) | ||||
0.319298 | + | 0.947654i | \(0.396553\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.33891 | 0.867781 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.85061 | 0.715040 | 0.357520 | − | 0.933905i | \(-0.383622\pi\) | ||||
0.357520 | + | 0.933905i | \(0.383622\pi\) | |||||||
\(30\) | −3.05596 | −0.557940 | ||||||||
\(31\) | 0.978370 | 0.175720 | 0.0878602 | − | 0.996133i | \(-0.471997\pi\) | ||||
0.0878602 | + | 0.996133i | \(0.471997\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.44247 | −0.599257 | ||||||||
\(34\) | −2.82898 | −0.485166 | ||||||||
\(35\) | 3.05596 | 0.516552 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.29308 | −0.870177 | −0.435089 | − | 0.900388i | \(-0.643283\pi\) | ||||
−0.435089 | + | 0.900388i | \(0.643283\pi\) | |||||||
\(38\) | −1.72542 | −0.279899 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.05596 | 0.483190 | ||||||||
\(41\) | 9.96254 | 1.55589 | 0.777943 | − | 0.628334i | \(-0.216263\pi\) | ||||
0.777943 | + | 0.628334i | \(0.216263\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −3.02163 | −0.460794 | −0.230397 | − | 0.973097i | \(-0.574003\pi\) | ||||
−0.230397 | + | 0.973097i | \(0.574003\pi\) | |||||||
\(44\) | 3.44247 | 0.518972 | ||||||||
\(45\) | 3.05596 | 0.455556 | ||||||||
\(46\) | 3.06260 | 0.451555 | ||||||||
\(47\) | 8.04447 | 1.17341 | 0.586703 | − | 0.809802i | \(-0.300425\pi\) | ||||
0.586703 | + | 0.809802i | \(0.300425\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.33891 | 0.613614 | ||||||||
\(51\) | 2.82898 | 0.396137 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.33405 | −1.14477 | −0.572385 | − | 0.819985i | \(-0.693982\pi\) | ||||
−0.572385 | + | 0.819985i | \(0.693982\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 10.5201 | 1.41853 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.72542 | 0.228537 | ||||||||
\(58\) | 3.85061 | 0.505610 | ||||||||
\(59\) | 9.97753 | 1.29896 | 0.649482 | − | 0.760377i | \(-0.274986\pi\) | ||||
0.649482 | + | 0.760377i | \(0.274986\pi\) | |||||||
\(60\) | −3.05596 | −0.394523 | ||||||||
\(61\) | −11.5452 | −1.47821 | −0.739106 | − | 0.673590i | \(-0.764752\pi\) | ||||
−0.739106 | + | 0.673590i | \(0.764752\pi\) | |||||||
\(62\) | 0.978370 | 0.124253 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.44247 | −0.423739 | ||||||||
\(67\) | 4.75055 | 0.580372 | 0.290186 | − | 0.956970i | \(-0.406283\pi\) | ||||
0.290186 | + | 0.956970i | \(0.406283\pi\) | |||||||
\(68\) | −2.82898 | −0.343064 | ||||||||
\(69\) | −3.06260 | −0.368693 | ||||||||
\(70\) | 3.05596 | 0.365257 | ||||||||
\(71\) | 3.66945 | 0.435484 | 0.217742 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217742 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 10.1119 | 1.18351 | 0.591756 | − | 0.806117i | \(-0.298435\pi\) | ||||
0.591756 | + | 0.806117i | \(0.298435\pi\) | |||||||
\(74\) | −5.29308 | −0.615308 | ||||||||
\(75\) | −4.33891 | −0.501014 | ||||||||
\(76\) | −1.72542 | −0.197919 | ||||||||
\(77\) | 3.44247 | 0.392306 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.49843 | −0.506113 | −0.253057 | − | 0.967451i | \(-0.581436\pi\) | ||||
−0.253057 | + | 0.967451i | \(0.581436\pi\) | |||||||
\(80\) | 3.05596 | 0.341667 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.96254 | 1.10018 | ||||||||
\(83\) | −7.15869 | −0.785768 | −0.392884 | − | 0.919588i | \(-0.628523\pi\) | ||||
−0.392884 | + | 0.919588i | \(0.628523\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −8.64526 | −0.937710 | ||||||||
\(86\) | −3.02163 | −0.325831 | ||||||||
\(87\) | −3.85061 | −0.412829 | ||||||||
\(88\) | 3.44247 | 0.366969 | ||||||||
\(89\) | 7.90307 | 0.837724 | 0.418862 | − | 0.908050i | \(-0.362429\pi\) | ||||
0.418862 | + | 0.908050i | \(0.362429\pi\) | |||||||
\(90\) | 3.05596 | 0.322127 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.06260 | 0.319298 | ||||||||
\(93\) | −0.978370 | −0.101452 | ||||||||
\(94\) | 8.04447 | 0.829724 | ||||||||
\(95\) | −5.27281 | −0.540979 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 9.09922 | 0.923886 | 0.461943 | − | 0.886910i | \(-0.347152\pi\) | ||||
0.461943 | + | 0.886910i | \(0.347152\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 3.44247 | 0.345981 | ||||||||
\(100\) | 4.33891 | 0.433891 | ||||||||
\(101\) | 18.8533 | 1.87597 | 0.937985 | − | 0.346675i | \(-0.112689\pi\) | ||||
0.937985 | + | 0.346675i | \(0.112689\pi\) | |||||||
\(102\) | 2.82898 | 0.280111 | ||||||||
\(103\) | 13.7079 | 1.35068 | 0.675338 | − | 0.737509i | \(-0.263998\pi\) | ||||
0.675338 | + | 0.737509i | \(0.263998\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.05596 | −0.298231 | ||||||||
\(106\) | −8.33405 | −0.809474 | ||||||||
\(107\) | −3.31471 | −0.320445 | −0.160223 | − | 0.987081i | \(-0.551221\pi\) | ||||
−0.160223 | + | 0.987081i | \(0.551221\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −8.67525 | −0.830938 | −0.415469 | − | 0.909607i | \(-0.636383\pi\) | ||||
−0.415469 | + | 0.909607i | \(0.636383\pi\) | |||||||
\(110\) | 10.5201 | 1.00305 | ||||||||
\(111\) | 5.29308 | 0.502397 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −11.2111 | −1.05466 | −0.527328 | − | 0.849662i | \(-0.676806\pi\) | ||||
−0.527328 | + | 0.849662i | \(0.676806\pi\) | |||||||
\(114\) | 1.72542 | 0.161600 | ||||||||
\(115\) | 9.35918 | 0.872748 | ||||||||
\(116\) | 3.85061 | 0.357520 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.97753 | 0.918506 | ||||||||
\(119\) | −2.82898 | −0.259332 | ||||||||
\(120\) | −3.05596 | −0.278970 | ||||||||
\(121\) | 0.850611 | 0.0773282 | ||||||||
\(122\) | −11.5452 | −1.04525 | ||||||||
\(123\) | −9.96254 | −0.898292 | ||||||||
\(124\) | 0.978370 | 0.0878602 | ||||||||
\(125\) | −2.02028 | −0.180699 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 5.11506 | 0.453888 | 0.226944 | − | 0.973908i | \(-0.427127\pi\) | ||||
0.226944 | + | 0.973908i | \(0.427127\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.02163 | 0.266040 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7757 | −1.64044 | −0.820219 | − | 0.572049i | \(-0.806149\pi\) | ||||
−0.820219 | + | 0.572049i | \(0.806149\pi\) | |||||||
\(132\) | −3.44247 | −0.299629 | ||||||||
\(133\) | −1.72542 | −0.149613 | ||||||||
\(134\) | 4.75055 | 0.410385 | ||||||||
\(135\) | −3.05596 | −0.263015 | ||||||||
\(136\) | −2.82898 | −0.242583 | ||||||||
\(137\) | 2.66109 | 0.227353 | 0.113676 | − | 0.993518i | \(-0.463737\pi\) | ||||
0.113676 | + | 0.993518i | \(0.463737\pi\) | |||||||
\(138\) | −3.06260 | −0.260706 | ||||||||
\(139\) | −16.7064 | −1.41702 | −0.708511 | − | 0.705699i | \(-0.750633\pi\) | ||||
−0.708511 | + | 0.705699i | \(0.750633\pi\) | |||||||
\(140\) | 3.05596 | 0.258276 | ||||||||
\(141\) | −8.04447 | −0.677467 | ||||||||
\(142\) | 3.66945 | 0.307934 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.7673 | 0.977223 | ||||||||
\(146\) | 10.1119 | 0.836869 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −5.29308 | −0.435089 | ||||||||
\(149\) | −2.50157 | −0.204936 | −0.102468 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102468 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(150\) | −4.33891 | −0.354270 | ||||||||
\(151\) | −12.6465 | −1.02916 | −0.514578 | − | 0.857444i | \(-0.672051\pi\) | ||||
−0.514578 | + | 0.857444i | \(0.672051\pi\) | |||||||
\(152\) | −1.72542 | −0.139950 | ||||||||
\(153\) | −2.82898 | −0.228710 | ||||||||
\(154\) | 3.44247 | 0.277402 | ||||||||
\(155\) | 2.98986 | 0.240151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8131 | 1.42164 | 0.710822 | − | 0.703372i | \(-0.248323\pi\) | ||||
0.710822 | + | 0.703372i | \(0.248323\pi\) | |||||||
\(158\) | −4.49843 | −0.357876 | ||||||||
\(159\) | 8.33405 | 0.660933 | ||||||||
\(160\) | 3.05596 | 0.241595 | ||||||||
\(161\) | 3.06260 | 0.241366 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.87831 | −0.695403 | −0.347701 | − | 0.937605i | \(-0.613038\pi\) | ||||
−0.347701 | + | 0.937605i | \(0.613038\pi\) | |||||||
\(164\) | 9.96254 | 0.777943 | ||||||||
\(165\) | −10.5201 | −0.818986 | ||||||||
\(166\) | −7.15869 | −0.555622 | ||||||||
\(167\) | 9.76989 | 0.756017 | 0.378008 | − | 0.925802i | \(-0.376609\pi\) | ||||
0.378008 | + | 0.925802i | \(0.376609\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.64526 | −0.663061 | ||||||||
\(171\) | −1.72542 | −0.131946 | ||||||||
\(172\) | −3.02163 | −0.230397 | ||||||||
\(173\) | 8.67525 | 0.659567 | 0.329783 | − | 0.944057i | \(-0.393024\pi\) | ||||
0.329783 | + | 0.944057i | \(0.393024\pi\) | |||||||
\(174\) | −3.85061 | −0.291914 | ||||||||
\(175\) | 4.33891 | 0.327991 | ||||||||
\(176\) | 3.44247 | 0.259486 | ||||||||
\(177\) | −9.97753 | −0.749957 | ||||||||
\(178\) | 7.90307 | 0.592360 | ||||||||
\(179\) | −23.4278 | −1.75108 | −0.875540 | − | 0.483146i | \(-0.839494\pi\) | ||||
−0.875540 | + | 0.483146i | \(0.839494\pi\) | |||||||
\(180\) | 3.05596 | 0.227778 | ||||||||
\(181\) | −7.66632 | −0.569833 | −0.284917 | − | 0.958552i | \(-0.591966\pi\) | ||||
−0.284917 | + | 0.958552i | \(0.591966\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5452 | 0.853446 | ||||||||
\(184\) | 3.06260 | 0.225778 | ||||||||
\(185\) | −16.1755 | −1.18924 | ||||||||
\(186\) | −0.978370 | −0.0717376 | ||||||||
\(187\) | −9.73869 | −0.712163 | ||||||||
\(188\) | 8.04447 | 0.586703 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −5.27281 | −0.382530 | ||||||||
\(191\) | 25.4945 | 1.84471 | 0.922357 | − | 0.386338i | \(-0.126260\pi\) | ||||
0.922357 | + | 0.386338i | \(0.126260\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.52586 | 0.613705 | 0.306852 | − | 0.951757i | \(-0.400724\pi\) | ||||
0.306852 | + | 0.951757i | \(0.400724\pi\) | |||||||
\(194\) | 9.09922 | 0.653286 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 23.6823 | 1.68729 | 0.843645 | − | 0.536901i | \(-0.180405\pi\) | ||||
0.843645 | + | 0.536901i | \(0.180405\pi\) | |||||||
\(198\) | 3.44247 | 0.244646 | ||||||||
\(199\) | −24.8466 | −1.76133 | −0.880666 | − | 0.473738i | \(-0.842904\pi\) | ||||
−0.880666 | + | 0.473738i | \(0.842904\pi\) | |||||||
\(200\) | 4.33891 | 0.306807 | ||||||||
\(201\) | −4.75055 | −0.335078 | ||||||||
\(202\) | 18.8533 | 1.32651 | ||||||||
\(203\) | 3.85061 | 0.270260 | ||||||||
\(204\) | 2.82898 | 0.198068 | ||||||||
\(205\) | 30.4451 | 2.12638 | ||||||||
\(206\) | 13.7079 | 0.955072 | ||||||||
\(207\) | 3.06260 | 0.212865 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.93970 | −0.410857 | ||||||||
\(210\) | −3.05596 | −0.210881 | ||||||||
\(211\) | 0.773018 | 0.0532168 | 0.0266084 | − | 0.999646i | \(-0.491529\pi\) | ||||
0.0266084 | + | 0.999646i | \(0.491529\pi\) | |||||||
\(212\) | −8.33405 | −0.572385 | ||||||||
\(213\) | −3.66945 | −0.251427 | ||||||||
\(214\) | −3.31471 | −0.226589 | ||||||||
\(215\) | −9.23399 | −0.629753 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.978370 | 0.0664161 | ||||||||
\(218\) | −8.67525 | −0.587562 | ||||||||
\(219\) | −10.1119 | −0.683301 | ||||||||
\(220\) | 10.5201 | 0.709263 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.29308 | 0.355248 | ||||||||
\(223\) | −21.5354 | −1.44212 | −0.721060 | − | 0.692873i | \(-0.756345\pi\) | ||||
−0.721060 | + | 0.692873i | \(0.756345\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 4.33891 | 0.289260 | ||||||||
\(226\) | −11.2111 | −0.745754 | ||||||||
\(227\) | −17.5444 | −1.16446 | −0.582230 | − | 0.813024i | \(-0.697820\pi\) | ||||
−0.582230 | + | 0.813024i | \(0.697820\pi\) | |||||||
\(228\) | 1.72542 | 0.114268 | ||||||||
\(229\) | 10.3222 | 0.682109 | 0.341055 | − | 0.940043i | \(-0.389216\pi\) | ||||
0.341055 | + | 0.940043i | \(0.389216\pi\) | |||||||
\(230\) | 9.35918 | 0.617126 | ||||||||
\(231\) | −3.44247 | −0.226498 | ||||||||
\(232\) | 3.85061 | 0.252805 | ||||||||
\(233\) | 17.8290 | 1.16802 | 0.584008 | − | 0.811748i | \(-0.301484\pi\) | ||||
0.584008 | + | 0.811748i | \(0.301484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.5836 | 1.60366 | ||||||||
\(236\) | 9.97753 | 0.649482 | ||||||||
\(237\) | 4.49843 | 0.292205 | ||||||||
\(238\) | −2.82898 | −0.183376 | ||||||||
\(239\) | −5.71271 | −0.369525 | −0.184762 | − | 0.982783i | \(-0.559152\pi\) | ||||
−0.184762 | + | 0.982783i | \(0.559152\pi\) | |||||||
\(240\) | −3.05596 | −0.197262 | ||||||||
\(241\) | 1.00313 | 0.0646174 | 0.0323087 | − | 0.999478i | \(-0.489714\pi\) | ||||
0.0323087 | + | 0.999478i | \(0.489714\pi\) | |||||||
\(242\) | 0.850611 | 0.0546793 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.5452 | −0.739106 | ||||||||
\(245\) | 3.05596 | 0.195238 | ||||||||
\(246\) | −9.96254 | −0.635188 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.978370 | 0.0621266 | ||||||||
\(249\) | 7.15869 | 0.453663 | ||||||||
\(250\) | −2.02028 | −0.127773 | ||||||||
\(251\) | −0.672585 | −0.0424532 | −0.0212266 | − | 0.999775i | \(-0.506757\pi\) | ||||
−0.0212266 | + | 0.999775i | \(0.506757\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 10.5429 | 0.662827 | ||||||||
\(254\) | 5.11506 | 0.320947 | ||||||||
\(255\) | 8.64526 | 0.541387 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.3433 | 1.51850 | 0.759248 | − | 0.650801i | \(-0.225567\pi\) | ||||
0.759248 | + | 0.650801i | \(0.225567\pi\) | |||||||
\(258\) | 3.02163 | 0.188118 | ||||||||
\(259\) | −5.29308 | −0.328896 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85061 | 0.238347 | ||||||||
\(262\) | −18.7757 | −1.15997 | ||||||||
\(263\) | −17.0930 | −1.05400 | −0.526999 | − | 0.849866i | \(-0.676683\pi\) | ||||
−0.526999 | + | 0.849866i | \(0.676683\pi\) | |||||||
\(264\) | −3.44247 | −0.211869 | ||||||||
\(265\) | −25.4685 | −1.56452 | ||||||||
\(266\) | −1.72542 | −0.105792 | ||||||||
\(267\) | −7.90307 | −0.483660 | ||||||||
\(268\) | 4.75055 | 0.290186 | ||||||||
\(269\) | −26.6594 | −1.62545 | −0.812727 | − | 0.582645i | \(-0.802018\pi\) | ||||
−0.812727 | + | 0.582645i | \(0.802018\pi\) | |||||||
\(270\) | −3.05596 | −0.185980 | ||||||||
\(271\) | −24.4495 | −1.48520 | −0.742600 | − | 0.669735i | \(-0.766408\pi\) | ||||
−0.742600 | + | 0.669735i | \(0.766408\pi\) | |||||||
\(272\) | −2.82898 | −0.171532 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.66109 | 0.160763 | ||||||||
\(275\) | 14.9366 | 0.900709 | ||||||||
\(276\) | −3.06260 | −0.184347 | ||||||||
\(277\) | −28.4812 | −1.71127 | −0.855636 | − | 0.517578i | \(-0.826834\pi\) | ||||
−0.855636 | + | 0.517578i | \(0.826834\pi\) | |||||||
\(278\) | −16.7064 | −1.00199 | ||||||||
\(279\) | 0.978370 | 0.0585735 | ||||||||
\(280\) | 3.05596 | 0.182629 | ||||||||
\(281\) | 9.76032 | 0.582252 | 0.291126 | − | 0.956685i | \(-0.405970\pi\) | ||||
0.291126 | + | 0.956685i | \(0.405970\pi\) | |||||||
\(282\) | −8.04447 | −0.479041 | ||||||||
\(283\) | 11.6712 | 0.693783 | 0.346891 | − | 0.937905i | \(-0.387237\pi\) | ||||
0.346891 | + | 0.937905i | \(0.387237\pi\) | |||||||
\(284\) | 3.66945 | 0.217742 | ||||||||
\(285\) | 5.27281 | 0.312334 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.96254 | 0.588070 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −8.99687 | −0.529228 | ||||||||
\(290\) | 11.7673 | 0.691001 | ||||||||
\(291\) | −9.09922 | −0.533406 | ||||||||
\(292\) | 10.1119 | 0.591756 | ||||||||
\(293\) | 21.8202 | 1.27475 | 0.637373 | − | 0.770555i | \(-0.280021\pi\) | ||||
0.637373 | + | 0.770555i | \(0.280021\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 30.4910 | 1.77525 | ||||||||
\(296\) | −5.29308 | −0.307654 | ||||||||
\(297\) | −3.44247 | −0.199752 | ||||||||
\(298\) | −2.50157 | −0.144912 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.33891 | −0.250507 | ||||||||
\(301\) | −3.02163 | −0.174164 | ||||||||
\(302\) | −12.6465 | −0.727723 | ||||||||
\(303\) | −18.8533 | −1.08309 | ||||||||
\(304\) | −1.72542 | −0.0989594 | ||||||||
\(305\) | −35.2817 | −2.02022 | ||||||||
\(306\) | −2.82898 | −0.161722 | ||||||||
\(307\) | −4.87046 | −0.277972 | −0.138986 | − | 0.990294i | \(-0.544384\pi\) | ||||
−0.138986 | + | 0.990294i | \(0.544384\pi\) | |||||||
\(308\) | 3.44247 | 0.196153 | ||||||||
\(309\) | −13.7079 | −0.779813 | ||||||||
\(310\) | 2.98986 | 0.169813 | ||||||||
\(311\) | 3.90344 | 0.221344 | 0.110672 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110672 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0528 | 1.47259 | 0.736297 | − | 0.676659i | \(-0.236573\pi\) | ||||
0.736297 | + | 0.676659i | \(0.236573\pi\) | |||||||
\(314\) | 17.8131 | 1.00525 | ||||||||
\(315\) | 3.05596 | 0.172184 | ||||||||
\(316\) | −4.49843 | −0.253057 | ||||||||
\(317\) | −11.1107 | −0.624040 | −0.312020 | − | 0.950076i | \(-0.601006\pi\) | ||||
−0.312020 | + | 0.950076i | \(0.601006\pi\) | |||||||
\(318\) | 8.33405 | 0.467350 | ||||||||
\(319\) | 13.2556 | 0.742172 | ||||||||
\(320\) | 3.05596 | 0.170833 | ||||||||
\(321\) | 3.31471 | 0.185009 | ||||||||
\(322\) | 3.06260 | 0.170672 | ||||||||
\(323\) | 4.88117 | 0.271595 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.87831 | −0.491724 | ||||||||
\(327\) | 8.67525 | 0.479742 | ||||||||
\(328\) | 9.96254 | 0.550089 | ||||||||
\(329\) | 8.04447 | 0.443506 | ||||||||
\(330\) | −10.5201 | −0.579110 | ||||||||
\(331\) | −14.6478 | −0.805117 | −0.402559 | − | 0.915394i | \(-0.631879\pi\) | ||||
−0.402559 | + | 0.915394i | \(0.631879\pi\) | |||||||
\(332\) | −7.15869 | −0.392884 | ||||||||
\(333\) | −5.29308 | −0.290059 | ||||||||
\(334\) | 9.76989 | 0.534584 | ||||||||
\(335\) | 14.5175 | 0.793176 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 27.5456 | 1.50050 | 0.750251 | − | 0.661153i | \(-0.229932\pi\) | ||||
0.750251 | + | 0.661153i | \(0.229932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2111 | 0.608906 | ||||||||
\(340\) | −8.64526 | −0.468855 | ||||||||
\(341\) | 3.36801 | 0.182388 | ||||||||
\(342\) | −1.72542 | −0.0932998 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.02163 | −0.162915 | ||||||||
\(345\) | −9.35918 | −0.503881 | ||||||||
\(346\) | 8.67525 | 0.466384 | ||||||||
\(347\) | 5.24146 | 0.281376 | 0.140688 | − | 0.990054i | \(-0.455068\pi\) | ||||
0.140688 | + | 0.990054i | \(0.455068\pi\) | |||||||
\(348\) | −3.85061 | −0.206414 | ||||||||
\(349\) | 5.22965 | 0.279937 | 0.139968 | − | 0.990156i | \(-0.455300\pi\) | ||||
0.139968 | + | 0.990156i | \(0.455300\pi\) | |||||||
\(350\) | 4.33891 | 0.231924 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.44247 | 0.183484 | ||||||||
\(353\) | 3.76695 | 0.200495 | 0.100247 | − | 0.994963i | \(-0.468037\pi\) | ||||
0.100247 | + | 0.994963i | \(0.468037\pi\) | |||||||
\(354\) | −9.97753 | −0.530300 | ||||||||
\(355\) | 11.2137 | 0.595162 | ||||||||
\(356\) | 7.90307 | 0.418862 | ||||||||
\(357\) | 2.82898 | 0.149726 | ||||||||
\(358\) | −23.4278 | −1.23820 | ||||||||
\(359\) | 20.6003 | 1.08724 | 0.543622 | − | 0.839330i | \(-0.317053\pi\) | ||||
0.543622 | + | 0.839330i | \(0.317053\pi\) | |||||||
\(360\) | 3.05596 | 0.161063 | ||||||||
\(361\) | −16.0229 | −0.843313 | ||||||||
\(362\) | −7.66632 | −0.402933 | ||||||||
\(363\) | −0.850611 | −0.0446455 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9017 | 1.61747 | ||||||||
\(366\) | 11.5452 | 0.603477 | ||||||||
\(367\) | −27.9159 | −1.45720 | −0.728598 | − | 0.684941i | \(-0.759828\pi\) | ||||
−0.728598 | + | 0.684941i | \(0.759828\pi\) | |||||||
\(368\) | 3.06260 | 0.159649 | ||||||||
\(369\) | 9.96254 | 0.518629 | ||||||||
\(370\) | −16.1755 | −0.840922 | ||||||||
\(371\) | −8.33405 | −0.432682 | ||||||||
\(372\) | −0.978370 | −0.0507261 | ||||||||
\(373\) | 31.4183 | 1.62678 | 0.813388 | − | 0.581721i | \(-0.197620\pi\) | ||||
0.813388 | + | 0.581721i | \(0.197620\pi\) | |||||||
\(374\) | −9.73869 | −0.503575 | ||||||||
\(375\) | 2.02028 | 0.104327 | ||||||||
\(376\) | 8.04447 | 0.414862 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −31.8406 | −1.63554 | −0.817770 | − | 0.575545i | \(-0.804790\pi\) | ||||
−0.817770 | + | 0.575545i | \(0.804790\pi\) | |||||||
\(380\) | −5.27281 | −0.270489 | ||||||||
\(381\) | −5.11506 | −0.262052 | ||||||||
\(382\) | 25.4945 | 1.30441 | ||||||||
\(383\) | 4.72228 | 0.241297 | 0.120649 | − | 0.992695i | \(-0.461503\pi\) | ||||
0.120649 | + | 0.992695i | \(0.461503\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 10.5201 | 0.536152 | ||||||||
\(386\) | 8.52586 | 0.433955 | ||||||||
\(387\) | −3.02163 | −0.153598 | ||||||||
\(388\) | 9.09922 | 0.461943 | ||||||||
\(389\) | 30.5902 | 1.55099 | 0.775493 | − | 0.631356i | \(-0.217501\pi\) | ||||
0.775493 | + | 0.631356i | \(0.217501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.66403 | −0.438159 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 18.7757 | 0.947108 | ||||||||
\(394\) | 23.6823 | 1.19309 | ||||||||
\(395\) | −13.7470 | −0.691689 | ||||||||
\(396\) | 3.44247 | 0.172991 | ||||||||
\(397\) | 11.6778 | 0.586093 | 0.293046 | − | 0.956098i | \(-0.405331\pi\) | ||||
0.293046 | + | 0.956098i | \(0.405331\pi\) | |||||||
\(398\) | −24.8466 | −1.24545 | ||||||||
\(399\) | 1.72542 | 0.0863788 | ||||||||
\(400\) | 4.33891 | 0.216945 | ||||||||
\(401\) | −9.25697 | −0.462271 | −0.231136 | − | 0.972922i | \(-0.574244\pi\) | ||||
−0.231136 | + | 0.972922i | \(0.574244\pi\) | |||||||
\(402\) | −4.75055 | −0.236936 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.8533 | 0.937985 | ||||||||
\(405\) | 3.05596 | 0.151852 | ||||||||
\(406\) | 3.85061 | 0.191103 | ||||||||
\(407\) | −18.2213 | −0.903196 | ||||||||
\(408\) | 2.82898 | 0.140055 | ||||||||
\(409\) | 25.5989 | 1.26578 | 0.632891 | − | 0.774241i | \(-0.281868\pi\) | ||||
0.632891 | + | 0.774241i | \(0.281868\pi\) | |||||||
\(410\) | 30.4451 | 1.50358 | ||||||||
\(411\) | −2.66109 | −0.131262 | ||||||||
\(412\) | 13.7079 | 0.675338 | ||||||||
\(413\) | 9.97753 | 0.490962 | ||||||||
\(414\) | 3.06260 | 0.150518 | ||||||||
\(415\) | −21.8767 | −1.07388 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.7064 | 0.818118 | ||||||||
\(418\) | −5.93970 | −0.290520 | ||||||||
\(419\) | 28.2037 | 1.37784 | 0.688920 | − | 0.724838i | \(-0.258085\pi\) | ||||
0.688920 | + | 0.724838i | \(0.258085\pi\) | |||||||
\(420\) | −3.05596 | −0.149116 | ||||||||
\(421\) | −5.07012 | −0.247102 | −0.123551 | − | 0.992338i | \(-0.539428\pi\) | ||||
−0.123551 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(422\) | 0.773018 | 0.0376299 | ||||||||
\(423\) | 8.04447 | 0.391136 | ||||||||
\(424\) | −8.33405 | −0.404737 | ||||||||
\(425\) | −12.2747 | −0.595410 | ||||||||
\(426\) | −3.66945 | −0.177786 | ||||||||
\(427\) | −11.5452 | −0.558711 | ||||||||
\(428\) | −3.31471 | −0.160223 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.23399 | −0.445302 | ||||||||
\(431\) | −16.1437 | −0.777614 | −0.388807 | − | 0.921319i | \(-0.627113\pi\) | ||||
−0.388807 | + | 0.921319i | \(0.627113\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.6029 | −1.08623 | −0.543113 | − | 0.839660i | \(-0.682754\pi\) | ||||
−0.543113 | + | 0.839660i | \(0.682754\pi\) | |||||||
\(434\) | 0.978370 | 0.0469633 | ||||||||
\(435\) | −11.7673 | −0.564200 | ||||||||
\(436\) | −8.67525 | −0.415469 | ||||||||
\(437\) | −5.28425 | −0.252780 | ||||||||
\(438\) | −10.1119 | −0.483166 | ||||||||
\(439\) | 28.2971 | 1.35055 | 0.675273 | − | 0.737567i | \(-0.264026\pi\) | ||||
0.675273 | + | 0.737567i | \(0.264026\pi\) | |||||||
\(440\) | 10.5201 | 0.501524 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.38096 | −0.0656112 | −0.0328056 | − | 0.999462i | \(-0.510444\pi\) | ||||
−0.0328056 | + | 0.999462i | \(0.510444\pi\) | |||||||
\(444\) | 5.29308 | 0.251199 | ||||||||
\(445\) | 24.1515 | 1.14489 | ||||||||
\(446\) | −21.5354 | −1.01973 | ||||||||
\(447\) | 2.50157 | 0.118320 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −37.0059 | −1.74642 | −0.873208 | − | 0.487348i | \(-0.837964\pi\) | ||||
−0.873208 | + | 0.487348i | \(0.837964\pi\) | |||||||
\(450\) | 4.33891 | 0.204538 | ||||||||
\(451\) | 34.2957 | 1.61492 | ||||||||
\(452\) | −11.2111 | −0.527328 | ||||||||
\(453\) | 12.6465 | 0.594183 | ||||||||
\(454\) | −17.5444 | −0.823398 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.72542 | 0.0808000 | ||||||||
\(457\) | 13.9176 | 0.651036 | 0.325518 | − | 0.945536i | \(-0.394461\pi\) | ||||
0.325518 | + | 0.945536i | \(0.394461\pi\) | |||||||
\(458\) | 10.3222 | 0.482324 | ||||||||
\(459\) | 2.82898 | 0.132046 | ||||||||
\(460\) | 9.35918 | 0.436374 | ||||||||
\(461\) | −4.84795 | −0.225791 | −0.112896 | − | 0.993607i | \(-0.536013\pi\) | ||||
−0.112896 | + | 0.993607i | \(0.536013\pi\) | |||||||
\(462\) | −3.44247 | −0.160158 | ||||||||
\(463\) | 24.4377 | 1.13571 | 0.567857 | − | 0.823127i | \(-0.307773\pi\) | ||||
0.567857 | + | 0.823127i | \(0.307773\pi\) | |||||||
\(464\) | 3.85061 | 0.178760 | ||||||||
\(465\) | −2.98986 | −0.138652 | ||||||||
\(466\) | 17.8290 | 0.825912 | ||||||||
\(467\) | 36.0027 | 1.66600 | 0.833002 | − | 0.553270i | \(-0.186620\pi\) | ||||
0.833002 | + | 0.553270i | \(0.186620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.75055 | 0.219360 | ||||||||
\(470\) | 24.5836 | 1.13396 | ||||||||
\(471\) | −17.8131 | −0.820786 | ||||||||
\(472\) | 9.97753 | 0.459253 | ||||||||
\(473\) | −10.4019 | −0.478279 | ||||||||
\(474\) | 4.49843 | 0.206620 | ||||||||
\(475\) | −7.48642 | −0.343500 | ||||||||
\(476\) | −2.82898 | −0.129666 | ||||||||
\(477\) | −8.33405 | −0.381590 | ||||||||
\(478\) | −5.71271 | −0.261293 | ||||||||
\(479\) | 9.49288 | 0.433741 | 0.216870 | − | 0.976200i | \(-0.430415\pi\) | ||||
0.216870 | + | 0.976200i | \(0.430415\pi\) | |||||||
\(480\) | −3.05596 | −0.139485 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.00313 | 0.0456914 | ||||||||
\(483\) | −3.06260 | −0.139353 | ||||||||
\(484\) | 0.850611 | 0.0386641 | ||||||||
\(485\) | 27.8069 | 1.26265 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 40.9206 | 1.85429 | 0.927144 | − | 0.374704i | \(-0.122256\pi\) | ||||
0.927144 | + | 0.374704i | \(0.122256\pi\) | |||||||
\(488\) | −11.5452 | −0.522627 | ||||||||
\(489\) | 8.87831 | 0.401491 | ||||||||
\(490\) | 3.05596 | 0.138054 | ||||||||
\(491\) | −5.11506 | −0.230839 | −0.115420 | − | 0.993317i | \(-0.536821\pi\) | ||||
−0.115420 | + | 0.993317i | \(0.536821\pi\) | |||||||
\(492\) | −9.96254 | −0.449146 | ||||||||
\(493\) | −10.8933 | −0.490610 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.5201 | 0.472842 | ||||||||
\(496\) | 0.978370 | 0.0439301 | ||||||||
\(497\) | 3.66945 | 0.164597 | ||||||||
\(498\) | 7.15869 | 0.320788 | ||||||||
\(499\) | −19.5827 | −0.876640 | −0.438320 | − | 0.898819i | \(-0.644426\pi\) | ||||
−0.438320 | + | 0.898819i | \(0.644426\pi\) | |||||||
\(500\) | −2.02028 | −0.0903495 | ||||||||
\(501\) | −9.76989 | −0.436486 | ||||||||
\(502\) | −0.672585 | −0.0300189 | ||||||||
\(503\) | −29.0858 | −1.29687 | −0.648436 | − | 0.761269i | \(-0.724577\pi\) | ||||
−0.648436 | + | 0.761269i | \(0.724577\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 57.6149 | 2.56383 | ||||||||
\(506\) | 10.5429 | 0.468689 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.11506 | 0.226944 | ||||||||
\(509\) | −5.21983 | −0.231365 | −0.115682 | − | 0.993286i | \(-0.536906\pi\) | ||||
−0.115682 | + | 0.993286i | \(0.536906\pi\) | |||||||
\(510\) | 8.64526 | 0.382818 | ||||||||
\(511\) | 10.1119 | 0.447325 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.72542 | 0.0761790 | ||||||||
\(514\) | 24.3433 | 1.07374 | ||||||||
\(515\) | 41.8907 | 1.84592 | ||||||||
\(516\) | 3.02163 | 0.133020 | ||||||||
\(517\) | 27.6929 | 1.21793 | ||||||||
\(518\) | −5.29308 | −0.232565 | ||||||||
\(519\) | −8.67525 | −0.380801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.5259 | −0.636389 | −0.318195 | − | 0.948025i | \(-0.603077\pi\) | ||||
−0.318195 | + | 0.948025i | \(0.603077\pi\) | |||||||
\(522\) | 3.85061 | 0.168537 | ||||||||
\(523\) | 27.8735 | 1.21882 | 0.609410 | − | 0.792855i | \(-0.291406\pi\) | ||||
0.609410 | + | 0.792855i | \(0.291406\pi\) | |||||||
\(524\) | −18.7757 | −0.820219 | ||||||||
\(525\) | −4.33891 | −0.189365 | ||||||||
\(526\) | −17.0930 | −0.745288 | ||||||||
\(527\) | −2.76779 | −0.120567 | ||||||||
\(528\) | −3.44247 | −0.149814 | ||||||||
\(529\) | −13.6205 | −0.592196 | ||||||||
\(530\) | −25.4685 | −1.10628 | ||||||||
\(531\) | 9.97753 | 0.432988 | ||||||||
\(532\) | −1.72542 | −0.0748063 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.90307 | −0.341999 | ||||||||
\(535\) | −10.1296 | −0.437942 | ||||||||
\(536\) | 4.75055 | 0.205192 | ||||||||
\(537\) | 23.4278 | 1.01099 | ||||||||
\(538\) | −26.6594 | −1.14937 | ||||||||
\(539\) | 3.44247 | 0.148278 | ||||||||
\(540\) | −3.05596 | −0.131508 | ||||||||
\(541\) | −1.42341 | −0.0611970 | −0.0305985 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305985 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(542\) | −24.4495 | −1.05019 | ||||||||
\(543\) | 7.66632 | 0.328993 | ||||||||
\(544\) | −2.82898 | −0.121292 | ||||||||
\(545\) | −26.5112 | −1.13562 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.33008 | −0.398925 | −0.199463 | − | 0.979905i | \(-0.563920\pi\) | ||||
−0.199463 | + | 0.979905i | \(0.563920\pi\) | |||||||
\(548\) | 2.66109 | 0.113676 | ||||||||
\(549\) | −11.5452 | −0.492737 | ||||||||
\(550\) | 14.9366 | 0.636897 | ||||||||
\(551\) | −6.64390 | −0.283040 | ||||||||
\(552\) | −3.06260 | −0.130353 | ||||||||
\(553\) | −4.49843 | −0.191293 | ||||||||
\(554\) | −28.4812 | −1.21005 | ||||||||
\(555\) | 16.1755 | 0.686610 | ||||||||
\(556\) | −16.7064 | −0.708511 | ||||||||
\(557\) | −10.7857 | −0.457006 | −0.228503 | − | 0.973543i | \(-0.573383\pi\) | ||||
−0.228503 | + | 0.973543i | \(0.573383\pi\) | |||||||
\(558\) | 0.978370 | 0.0414177 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.05596 | 0.129138 | ||||||||
\(561\) | 9.73869 | 0.411168 | ||||||||
\(562\) | 9.76032 | 0.411714 | ||||||||
\(563\) | 25.5082 | 1.07504 | 0.537522 | − | 0.843250i | \(-0.319360\pi\) | ||||
0.537522 | + | 0.843250i | \(0.319360\pi\) | |||||||
\(564\) | −8.04447 | −0.338733 | ||||||||
\(565\) | −34.2608 | −1.44136 | ||||||||
\(566\) | 11.6712 | 0.490578 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 3.66945 | 0.153967 | ||||||||
\(569\) | −8.21670 | −0.344462 | −0.172231 | − | 0.985057i | \(-0.555098\pi\) | ||||
−0.172231 | + | 0.985057i | \(0.555098\pi\) | |||||||
\(570\) | 5.27281 | 0.220854 | ||||||||
\(571\) | −2.70500 | −0.113201 | −0.0566003 | − | 0.998397i | \(-0.518026\pi\) | ||||
−0.0566003 | + | 0.998397i | \(0.518026\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.4945 | −1.06505 | ||||||||
\(574\) | 9.96254 | 0.415828 | ||||||||
\(575\) | 13.2883 | 0.554161 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −21.4253 | −0.891946 | −0.445973 | − | 0.895046i | \(-0.647142\pi\) | ||||
−0.445973 | + | 0.895046i | \(0.647142\pi\) | |||||||
\(578\) | −8.99687 | −0.374220 | ||||||||
\(579\) | −8.52586 | −0.354323 | ||||||||
\(580\) | 11.7673 | 0.488611 | ||||||||
\(581\) | −7.15869 | −0.296992 | ||||||||
\(582\) | −9.09922 | −0.377175 | ||||||||
\(583\) | −28.6897 | −1.18821 | ||||||||
\(584\) | 10.1119 | 0.418434 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.8202 | 0.901382 | ||||||||
\(587\) | −5.73326 | −0.236637 | −0.118319 | − | 0.992976i | \(-0.537750\pi\) | ||||
−0.118319 | + | 0.992976i | \(0.537750\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −1.68810 | −0.0695567 | ||||||||
\(590\) | 30.4910 | 1.25529 | ||||||||
\(591\) | −23.6823 | −0.974158 | ||||||||
\(592\) | −5.29308 | −0.217544 | ||||||||
\(593\) | −17.3442 | −0.712240 | −0.356120 | − | 0.934440i | \(-0.615901\pi\) | ||||
−0.356120 | + | 0.934440i | \(0.615901\pi\) | |||||||
\(594\) | −3.44247 | −0.141246 | ||||||||
\(595\) | −8.64526 | −0.354421 | ||||||||
\(596\) | −2.50157 | −0.102468 | ||||||||
\(597\) | 24.8466 | 1.01691 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.5835 | −1.29047 | −0.645234 | − | 0.763985i | \(-0.723240\pi\) | ||||
−0.645234 | + | 0.763985i | \(0.723240\pi\) | |||||||
\(600\) | −4.33891 | −0.177135 | ||||||||
\(601\) | 24.8956 | 1.01551 | 0.507757 | − | 0.861500i | \(-0.330475\pi\) | ||||
0.507757 | + | 0.861500i | \(0.330475\pi\) | |||||||
\(602\) | −3.02163 | −0.123152 | ||||||||
\(603\) | 4.75055 | 0.193457 | ||||||||
\(604\) | −12.6465 | −0.514578 | ||||||||
\(605\) | 2.59943 | 0.105682 | ||||||||
\(606\) | −18.8533 | −0.765862 | ||||||||
\(607\) | 15.2590 | 0.619345 | 0.309672 | − | 0.950843i | \(-0.399781\pi\) | ||||
0.309672 | + | 0.950843i | \(0.399781\pi\) | |||||||
\(608\) | −1.72542 | −0.0699749 | ||||||||
\(609\) | −3.85061 | −0.156035 | ||||||||
\(610\) | −35.2817 | −1.42851 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.82898 | −0.114355 | ||||||||
\(613\) | −45.7515 | −1.84789 | −0.923943 | − | 0.382531i | \(-0.875052\pi\) | ||||
−0.923943 | + | 0.382531i | \(0.875052\pi\) | |||||||
\(614\) | −4.87046 | −0.196556 | ||||||||
\(615\) | −30.4451 | −1.22767 | ||||||||
\(616\) | 3.44247 | 0.138701 | ||||||||
\(617\) | −42.2813 | −1.70218 | −0.851090 | − | 0.525020i | \(-0.824058\pi\) | ||||
−0.851090 | + | 0.525020i | \(0.824058\pi\) | |||||||
\(618\) | −13.7079 | −0.551411 | ||||||||
\(619\) | 22.0261 | 0.885303 | 0.442651 | − | 0.896694i | \(-0.354038\pi\) | ||||
0.442651 | + | 0.896694i | \(0.354038\pi\) | |||||||
\(620\) | 2.98986 | 0.120076 | ||||||||
\(621\) | −3.06260 | −0.122898 | ||||||||
\(622\) | 3.90344 | 0.156514 | ||||||||
\(623\) | 7.90307 | 0.316630 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.8684 | −1.11474 | ||||||||
\(626\) | 26.0528 | 1.04128 | ||||||||
\(627\) | 5.93970 | 0.237209 | ||||||||
\(628\) | 17.8131 | 0.710822 | ||||||||
\(629\) | 14.9740 | 0.597054 | ||||||||
\(630\) | 3.05596 | 0.121752 | ||||||||
\(631\) | 20.8679 | 0.830738 | 0.415369 | − | 0.909653i | \(-0.363652\pi\) | ||||
0.415369 | + | 0.909653i | \(0.363652\pi\) | |||||||
\(632\) | −4.49843 | −0.178938 | ||||||||
\(633\) | −0.773018 | −0.0307247 | ||||||||
\(634\) | −11.1107 | −0.441263 | ||||||||
\(635\) | 15.6314 | 0.620314 | ||||||||
\(636\) | 8.33405 | 0.330467 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.2556 | 0.524795 | ||||||||
\(639\) | 3.66945 | 0.145161 | ||||||||
\(640\) | 3.05596 | 0.120798 | ||||||||
\(641\) | −20.9052 | −0.825707 | −0.412853 | − | 0.910798i | \(-0.635468\pi\) | ||||
−0.412853 | + | 0.910798i | \(0.635468\pi\) | |||||||
\(642\) | 3.31471 | 0.130821 | ||||||||
\(643\) | −39.1100 | −1.54235 | −0.771174 | − | 0.636624i | \(-0.780330\pi\) | ||||
−0.771174 | + | 0.636624i | \(0.780330\pi\) | |||||||
\(644\) | 3.06260 | 0.120683 | ||||||||
\(645\) | 9.23399 | 0.363588 | ||||||||
\(646\) | 4.88117 | 0.192047 | ||||||||
\(647\) | −7.93511 | −0.311961 | −0.155981 | − | 0.987760i | \(-0.549854\pi\) | ||||
−0.155981 | + | 0.987760i | \(0.549854\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 34.3474 | 1.34825 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.978370 | −0.0383453 | ||||||||
\(652\) | −8.87831 | −0.347701 | ||||||||
\(653\) | 42.7996 | 1.67488 | 0.837439 | − | 0.546531i | \(-0.184052\pi\) | ||||
0.837439 | + | 0.546531i | \(0.184052\pi\) | |||||||
\(654\) | 8.67525 | 0.339229 | ||||||||
\(655\) | −57.3778 | −2.24194 | ||||||||
\(656\) | 9.96254 | 0.388972 | ||||||||
\(657\) | 10.1119 | 0.394504 | ||||||||
\(658\) | 8.04447 | 0.313606 | ||||||||
\(659\) | 0.728548 | 0.0283802 | 0.0141901 | − | 0.999899i | \(-0.495483\pi\) | ||||
0.0141901 | + | 0.999899i | \(0.495483\pi\) | |||||||
\(660\) | −10.5201 | −0.409493 | ||||||||
\(661\) | 2.35965 | 0.0917798 | 0.0458899 | − | 0.998947i | \(-0.485388\pi\) | ||||
0.0458899 | + | 0.998947i | \(0.485388\pi\) | |||||||
\(662\) | −14.6478 | −0.569304 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.15869 | −0.277811 | ||||||||
\(665\) | −5.27281 | −0.204471 | ||||||||
\(666\) | −5.29308 | −0.205103 | ||||||||
\(667\) | 11.7929 | 0.456622 | ||||||||
\(668\) | 9.76989 | 0.378008 | ||||||||
\(669\) | 21.5354 | 0.832608 | ||||||||
\(670\) | 14.5175 | 0.560860 | ||||||||
\(671\) | −39.7440 | −1.53430 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 31.2557 | 1.20482 | 0.602410 | − | 0.798187i | \(-0.294207\pi\) | ||||
0.602410 | + | 0.798187i | \(0.294207\pi\) | |||||||
\(674\) | 27.5456 | 1.06102 | ||||||||
\(675\) | −4.33891 | −0.167005 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.7294 | −1.60379 | −0.801895 | − | 0.597464i | \(-0.796175\pi\) | ||||
−0.801895 | + | 0.597464i | \(0.796175\pi\) | |||||||
\(678\) | 11.2111 | 0.430562 | ||||||||
\(679\) | 9.09922 | 0.349196 | ||||||||
\(680\) | −8.64526 | −0.331531 | ||||||||
\(681\) | 17.5444 | 0.672301 | ||||||||
\(682\) | 3.36801 | 0.128968 | ||||||||
\(683\) | −9.21998 | −0.352793 | −0.176396 | − | 0.984319i | \(-0.556444\pi\) | ||||
−0.176396 | + | 0.984319i | \(0.556444\pi\) | |||||||
\(684\) | −1.72542 | −0.0659729 | ||||||||
\(685\) | 8.13220 | 0.310715 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −10.3222 | −0.393816 | ||||||||
\(688\) | −3.02163 | −0.115199 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −9.35918 | −0.356298 | ||||||||
\(691\) | −9.20858 | −0.350311 | −0.175156 | − | 0.984541i | \(-0.556043\pi\) | ||||
−0.175156 | + | 0.984541i | \(0.556043\pi\) | |||||||
\(692\) | 8.67525 | 0.329783 | ||||||||
\(693\) | 3.44247 | 0.130769 | ||||||||
\(694\) | 5.24146 | 0.198963 | ||||||||
\(695\) | −51.0543 | −1.93660 | ||||||||
\(696\) | −3.85061 | −0.145957 | ||||||||
\(697\) | −28.1838 | −1.06754 | ||||||||
\(698\) | 5.22965 | 0.197945 | ||||||||
\(699\) | −17.8290 | −0.674354 | ||||||||
\(700\) | 4.33891 | 0.163995 | ||||||||
\(701\) | −20.8683 | −0.788184 | −0.394092 | − | 0.919071i | \(-0.628941\pi\) | ||||
−0.394092 | + | 0.919071i | \(0.628941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.13277 | 0.344449 | ||||||||
\(704\) | 3.44247 | 0.129743 | ||||||||
\(705\) | −24.5836 | −0.925872 | ||||||||
\(706\) | 3.76695 | 0.141771 | ||||||||
\(707\) | 18.8533 | 0.709050 | ||||||||
\(708\) | −9.97753 | −0.374979 | ||||||||
\(709\) | −14.8645 | −0.558249 | −0.279124 | − | 0.960255i | \(-0.590044\pi\) | ||||
−0.279124 | + | 0.960255i | \(0.590044\pi\) | |||||||
\(710\) | 11.2137 | 0.420843 | ||||||||
\(711\) | −4.49843 | −0.168704 | ||||||||
\(712\) | 7.90307 | 0.296180 | ||||||||
\(713\) | 2.99635 | 0.112214 | ||||||||
\(714\) | 2.82898 | 0.105872 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.4278 | −0.875540 | ||||||||
\(717\) | 5.71271 | 0.213345 | ||||||||
\(718\) | 20.6003 | 0.768797 | ||||||||
\(719\) | −25.6531 | −0.956697 | −0.478349 | − | 0.878170i | \(-0.658764\pi\) | ||||
−0.478349 | + | 0.878170i | \(0.658764\pi\) | |||||||
\(720\) | 3.05596 | 0.113889 | ||||||||
\(721\) | 13.7079 | 0.510507 | ||||||||
\(722\) | −16.0229 | −0.596312 | ||||||||
\(723\) | −1.00313 | −0.0373069 | ||||||||
\(724\) | −7.66632 | −0.284917 | ||||||||
\(725\) | 16.7074 | 0.620499 | ||||||||
\(726\) | −0.850611 | −0.0315691 | ||||||||
\(727\) | −41.6568 | −1.54497 | −0.772483 | − | 0.635036i | \(-0.780985\pi\) | ||||
−0.772483 | + | 0.635036i | \(0.780985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.9017 | 1.14372 | ||||||||
\(731\) | 8.54813 | 0.316164 | ||||||||
\(732\) | 11.5452 | 0.426723 | ||||||||
\(733\) | 26.4965 | 0.978671 | 0.489336 | − | 0.872096i | \(-0.337239\pi\) | ||||
0.489336 | + | 0.872096i | \(0.337239\pi\) | |||||||
\(734\) | −27.9159 | −1.03039 | ||||||||
\(735\) | −3.05596 | −0.112721 | ||||||||
\(736\) | 3.06260 | 0.112889 | ||||||||
\(737\) | 16.3536 | 0.602394 | ||||||||
\(738\) | 9.96254 | 0.366726 | ||||||||
\(739\) | −20.9011 | −0.768861 | −0.384431 | − | 0.923154i | \(-0.625602\pi\) | ||||
−0.384431 | + | 0.923154i | \(0.625602\pi\) | |||||||
\(740\) | −16.1755 | −0.594622 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.33405 | −0.305953 | ||||||||
\(743\) | 5.64647 | 0.207149 | 0.103574 | − | 0.994622i | \(-0.466972\pi\) | ||||
0.103574 | + | 0.994622i | \(0.466972\pi\) | |||||||
\(744\) | −0.978370 | −0.0358688 | ||||||||
\(745\) | −7.64469 | −0.280080 | ||||||||
\(746\) | 31.4183 | 1.15030 | ||||||||
\(747\) | −7.15869 | −0.261923 | ||||||||
\(748\) | −9.73869 | −0.356082 | ||||||||
\(749\) | −3.31471 | −0.121117 | ||||||||
\(750\) | 2.02028 | 0.0737701 | ||||||||
\(751\) | 15.4088 | 0.562274 | 0.281137 | − | 0.959668i | \(-0.409288\pi\) | ||||
0.281137 | + | 0.959668i | \(0.409288\pi\) | |||||||
\(752\) | 8.04447 | 0.293352 | ||||||||
\(753\) | 0.672585 | 0.0245104 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.6471 | −1.40651 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −35.5372 | −1.29162 | −0.645811 | − | 0.763497i | \(-0.723481\pi\) | ||||
−0.645811 | + | 0.763497i | \(0.723481\pi\) | |||||||
\(758\) | −31.8406 | −1.15650 | ||||||||
\(759\) | −10.5429 | −0.382683 | ||||||||
\(760\) | −5.27281 | −0.191265 | ||||||||
\(761\) | 41.8247 | 1.51615 | 0.758073 | − | 0.652170i | \(-0.226141\pi\) | ||||
0.758073 | + | 0.652170i | \(0.226141\pi\) | |||||||
\(762\) | −5.11506 | −0.185299 | ||||||||
\(763\) | −8.67525 | −0.314065 | ||||||||
\(764\) | 25.4945 | 0.922357 | ||||||||
\(765\) | −8.64526 | −0.312570 | ||||||||
\(766\) | 4.72228 | 0.170623 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 17.8527 | 0.643785 | 0.321893 | − | 0.946776i | \(-0.395681\pi\) | ||||
0.321893 | + | 0.946776i | \(0.395681\pi\) | |||||||
\(770\) | 10.5201 | 0.379117 | ||||||||
\(771\) | −24.3433 | −0.876704 | ||||||||
\(772\) | 8.52586 | 0.306852 | ||||||||
\(773\) | −12.1119 | −0.435636 | −0.217818 | − | 0.975989i | \(-0.569894\pi\) | ||||
−0.217818 | + | 0.975989i | \(0.569894\pi\) | |||||||
\(774\) | −3.02163 | −0.108610 | ||||||||
\(775\) | 4.24506 | 0.152487 | ||||||||
\(776\) | 9.09922 | 0.326643 | ||||||||
\(777\) | 5.29308 | 0.189888 | ||||||||
\(778\) | 30.5902 | 1.09671 | ||||||||
\(779\) | −17.1895 | −0.615878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6320 | 0.452008 | ||||||||
\(782\) | −8.66403 | −0.309825 | ||||||||
\(783\) | −3.85061 | −0.137610 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 54.4363 | 1.94292 | ||||||||
\(786\) | 18.7757 | 0.669706 | ||||||||
\(787\) | 32.0549 | 1.14263 | 0.571317 | − | 0.820729i | \(-0.306433\pi\) | ||||
0.571317 | + | 0.820729i | \(0.306433\pi\) | |||||||
\(788\) | 23.6823 | 0.843645 | ||||||||
\(789\) | 17.0930 | 0.608525 | ||||||||
\(790\) | −13.7470 | −0.489098 | ||||||||
\(791\) | −11.2111 | −0.398623 | ||||||||
\(792\) | 3.44247 | 0.122323 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.6778 | 0.414430 | ||||||||
\(795\) | 25.4685 | 0.903276 | ||||||||
\(796\) | −24.8466 | −0.880666 | ||||||||
\(797\) | 9.13089 | 0.323433 | 0.161716 | − | 0.986837i | \(-0.448297\pi\) | ||||
0.161716 | + | 0.986837i | \(0.448297\pi\) | |||||||
\(798\) | 1.72542 | 0.0610791 | ||||||||
\(799\) | −22.7577 | −0.805108 | ||||||||
\(800\) | 4.33891 | 0.153404 | ||||||||
\(801\) | 7.90307 | 0.279241 | ||||||||
\(802\) | −9.25697 | −0.326875 | ||||||||
\(803\) | 34.8100 | 1.22842 | ||||||||
\(804\) | −4.75055 | −0.167539 | ||||||||
\(805\) | 9.35918 | 0.329868 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.6594 | 0.938456 | ||||||||
\(808\) | 18.8533 | 0.663256 | ||||||||
\(809\) | 21.4623 | 0.754574 | 0.377287 | − | 0.926096i | \(-0.376857\pi\) | ||||
0.377287 | + | 0.926096i | \(0.376857\pi\) | |||||||
\(810\) | 3.05596 | 0.107376 | ||||||||
\(811\) | −44.2671 | −1.55443 | −0.777214 | − | 0.629236i | \(-0.783368\pi\) | ||||
−0.777214 | + | 0.629236i | \(0.783368\pi\) | |||||||
\(812\) | 3.85061 | 0.135130 | ||||||||
\(813\) | 24.4495 | 0.857481 | ||||||||
\(814\) | −18.2213 | −0.638656 | ||||||||
\(815\) | −27.1318 | −0.950385 | ||||||||
\(816\) | 2.82898 | 0.0990341 | ||||||||
\(817\) | 5.21357 | 0.182400 | ||||||||
\(818\) | 25.5989 | 0.895043 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.4451 | 1.06319 | ||||||||
\(821\) | −9.31994 | −0.325268 | −0.162634 | − | 0.986686i | \(-0.551999\pi\) | ||||
−0.162634 | + | 0.986686i | \(0.551999\pi\) | |||||||
\(822\) | −2.66109 | −0.0928163 | ||||||||
\(823\) | 29.6852 | 1.03476 | 0.517381 | − | 0.855755i | \(-0.326907\pi\) | ||||
0.517381 | + | 0.855755i | \(0.326907\pi\) | |||||||
\(824\) | 13.7079 | 0.477536 | ||||||||
\(825\) | −14.9366 | −0.520024 | ||||||||
\(826\) | 9.97753 | 0.347163 | ||||||||
\(827\) | 22.6364 | 0.787146 | 0.393573 | − | 0.919293i | \(-0.371239\pi\) | ||||
0.393573 | + | 0.919293i | \(0.371239\pi\) | |||||||
\(828\) | 3.06260 | 0.106433 | ||||||||
\(829\) | −9.64334 | −0.334927 | −0.167463 | − | 0.985878i | \(-0.553558\pi\) | ||||
−0.167463 | + | 0.985878i | \(0.553558\pi\) | |||||||
\(830\) | −21.8767 | −0.759351 | ||||||||
\(831\) | 28.4812 | 0.988003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.82898 | −0.0980184 | ||||||||
\(834\) | 16.7064 | 0.578497 | ||||||||
\(835\) | 29.8564 | 1.03322 | ||||||||
\(836\) | −5.93970 | −0.205429 | ||||||||
\(837\) | −0.978370 | −0.0338174 | ||||||||
\(838\) | 28.2037 | 0.974280 | ||||||||
\(839\) | −33.4844 | −1.15601 | −0.578005 | − | 0.816034i | \(-0.696168\pi\) | ||||
−0.578005 | + | 0.816034i | \(0.696168\pi\) | |||||||
\(840\) | −3.05596 | −0.105441 | ||||||||
\(841\) | −14.1728 | −0.488717 | ||||||||
\(842\) | −5.07012 | −0.174728 | ||||||||
\(843\) | −9.76032 | −0.336163 | ||||||||
\(844\) | 0.773018 | 0.0266084 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.04447 | 0.276575 | ||||||||
\(847\) | 0.850611 | 0.0292273 | ||||||||
\(848\) | −8.33405 | −0.286192 | ||||||||
\(849\) | −11.6712 | −0.400556 | ||||||||
\(850\) | −12.2747 | −0.421018 | ||||||||
\(851\) | −16.2106 | −0.555692 | ||||||||
\(852\) | −3.66945 | −0.125713 | ||||||||
\(853\) | −23.7246 | −0.812316 | −0.406158 | − | 0.913803i | \(-0.633132\pi\) | ||||
−0.406158 | + | 0.913803i | \(0.633132\pi\) | |||||||
\(854\) | −11.5452 | −0.395069 | ||||||||
\(855\) | −5.27281 | −0.180326 | ||||||||
\(856\) | −3.31471 | −0.113295 | ||||||||
\(857\) | 24.4823 | 0.836299 | 0.418149 | − | 0.908378i | \(-0.362679\pi\) | ||||
0.418149 | + | 0.908378i | \(0.362679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.7787 | −0.913676 | −0.456838 | − | 0.889550i | \(-0.651018\pi\) | ||||
−0.456838 | + | 0.889550i | \(0.651018\pi\) | |||||||
\(860\) | −9.23399 | −0.314876 | ||||||||
\(861\) | −9.96254 | −0.339522 | ||||||||
\(862\) | −16.1437 | −0.549856 | ||||||||
\(863\) | −54.8533 | −1.86723 | −0.933614 | − | 0.358282i | \(-0.883363\pi\) | ||||
−0.933614 | + | 0.358282i | \(0.883363\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 26.5112 | 0.901409 | ||||||||
\(866\) | −22.6029 | −0.768077 | ||||||||
\(867\) | 8.99687 | 0.305550 | ||||||||
\(868\) | 0.978370 | 0.0332080 | ||||||||
\(869\) | −15.4857 | −0.525317 | ||||||||
\(870\) | −11.7673 | −0.398950 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.67525 | −0.293781 | ||||||||
\(873\) | 9.09922 | 0.307962 | ||||||||
\(874\) | −5.28425 | −0.178743 | ||||||||
\(875\) | −2.02028 | −0.0682978 | ||||||||
\(876\) | −10.1119 | −0.341650 | ||||||||
\(877\) | −5.39968 | −0.182334 | −0.0911671 | − | 0.995836i | \(-0.529060\pi\) | ||||
−0.0911671 | + | 0.995836i | \(0.529060\pi\) | |||||||
\(878\) | 28.2971 | 0.954981 | ||||||||
\(879\) | −21.8202 | −0.735975 | ||||||||
\(880\) | 10.5201 | 0.354631 | ||||||||
\(881\) | −16.3667 | −0.551407 | −0.275703 | − | 0.961243i | \(-0.588911\pi\) | ||||
−0.275703 | + | 0.961243i | \(0.588911\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −10.8294 | −0.364440 | −0.182220 | − | 0.983258i | \(-0.558328\pi\) | ||||
−0.182220 | + | 0.983258i | \(0.558328\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.4910 | −1.02494 | ||||||||
\(886\) | −1.38096 | −0.0463941 | ||||||||
\(887\) | −33.1553 | −1.11325 | −0.556623 | − | 0.830765i | \(-0.687903\pi\) | ||||
−0.556623 | + | 0.830765i | \(0.687903\pi\) | |||||||
\(888\) | 5.29308 | 0.177624 | ||||||||
\(889\) | 5.11506 | 0.171553 | ||||||||
\(890\) | 24.1515 | 0.809560 | ||||||||
\(891\) | 3.44247 | 0.115327 | ||||||||
\(892\) | −21.5354 | −0.721060 | ||||||||
\(893\) | −13.8801 | −0.464478 | ||||||||
\(894\) | 2.50157 | 0.0836649 | ||||||||
\(895\) | −71.5946 | −2.39314 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.0059 | −1.23490 | ||||||||
\(899\) | 3.76732 | 0.125647 | ||||||||
\(900\) | 4.33891 | 0.144630 | ||||||||
\(901\) | 23.5769 | 0.785459 | ||||||||
\(902\) | 34.2957 | 1.14192 | ||||||||
\(903\) | 3.02163 | 0.100554 | ||||||||
\(904\) | −11.2111 | −0.372877 | ||||||||
\(905\) | −23.4280 | −0.778773 | ||||||||
\(906\) | 12.6465 | 0.420151 | ||||||||
\(907\) | 31.0699 | 1.03166 | 0.515829 | − | 0.856691i | \(-0.327484\pi\) | ||||
0.515829 | + | 0.856691i | \(0.327484\pi\) | |||||||
\(908\) | −17.5444 | −0.582230 | ||||||||
\(909\) | 18.8533 | 0.625324 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.26309 | −0.240637 | −0.120318 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(912\) | 1.72542 | 0.0571342 | ||||||||
\(913\) | −24.6436 | −0.815583 | ||||||||
\(914\) | 13.9176 | 0.460352 | ||||||||
\(915\) | 35.2817 | 1.16638 | ||||||||
\(916\) | 10.3222 | 0.341055 | ||||||||
\(917\) | −18.7757 | −0.620028 | ||||||||
\(918\) | 2.82898 | 0.0933703 | ||||||||
\(919\) | 34.1726 | 1.12725 | 0.563625 | − | 0.826031i | \(-0.309406\pi\) | ||||
0.563625 | + | 0.826031i | \(0.309406\pi\) | |||||||
\(920\) | 9.35918 | 0.308563 | ||||||||
\(921\) | 4.87046 | 0.160487 | ||||||||
\(922\) | −4.84795 | −0.159659 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.44247 | −0.113249 | ||||||||
\(925\) | −22.9662 | −0.755124 | ||||||||
\(926\) | 24.4377 | 0.803071 | ||||||||
\(927\) | 13.7079 | 0.450225 | ||||||||
\(928\) | 3.85061 | 0.126402 | ||||||||
\(929\) | 13.6546 | 0.447992 | 0.223996 | − | 0.974590i | \(-0.428090\pi\) | ||||
0.223996 | + | 0.974590i | \(0.428090\pi\) | |||||||
\(930\) | −2.98986 | −0.0980414 | ||||||||
\(931\) | −1.72542 | −0.0565482 | ||||||||
\(932\) | 17.8290 | 0.584008 | ||||||||
\(933\) | −3.90344 | −0.127793 | ||||||||
\(934\) | 36.0027 | 1.17804 | ||||||||
\(935\) | −29.7611 | −0.973291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5716 | 1.42342 | 0.711712 | − | 0.702472i | \(-0.247920\pi\) | ||||
0.711712 | + | 0.702472i | \(0.247920\pi\) | |||||||
\(938\) | 4.75055 | 0.155111 | ||||||||
\(939\) | −26.0528 | −0.850202 | ||||||||
\(940\) | 24.5836 | 0.801829 | ||||||||
\(941\) | 55.8282 | 1.81995 | 0.909973 | − | 0.414666i | \(-0.136102\pi\) | ||||
0.909973 | + | 0.414666i | \(0.136102\pi\) | |||||||
\(942\) | −17.8131 | −0.580384 | ||||||||
\(943\) | 30.5112 | 0.993583 | ||||||||
\(944\) | 9.97753 | 0.324741 | ||||||||
\(945\) | −3.05596 | −0.0994105 | ||||||||
\(946\) | −10.4019 | −0.338194 | ||||||||
\(947\) | −52.4896 | −1.70568 | −0.852842 | − | 0.522170i | \(-0.825123\pi\) | ||||
−0.852842 | + | 0.522170i | \(0.825123\pi\) | |||||||
\(948\) | 4.49843 | 0.146102 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −7.48642 | −0.242891 | ||||||||
\(951\) | 11.1107 | 0.360290 | ||||||||
\(952\) | −2.82898 | −0.0916878 | ||||||||
\(953\) | −7.01971 | −0.227391 | −0.113695 | − | 0.993516i | \(-0.536269\pi\) | ||||
−0.113695 | + | 0.993516i | \(0.536269\pi\) | |||||||
\(954\) | −8.33405 | −0.269825 | ||||||||
\(955\) | 77.9101 | 2.52111 | ||||||||
\(956\) | −5.71271 | −0.184762 | ||||||||
\(957\) | −13.2556 | −0.428493 | ||||||||
\(958\) | 9.49288 | 0.306701 | ||||||||
\(959\) | 2.66109 | 0.0859312 | ||||||||
\(960\) | −3.05596 | −0.0986308 | ||||||||
\(961\) | −30.0428 | −0.969122 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.31471 | −0.106815 | ||||||||
\(964\) | 1.00313 | 0.0323087 | ||||||||
\(965\) | 26.0547 | 0.838731 | ||||||||
\(966\) | −3.06260 | −0.0985375 | ||||||||
\(967\) | 36.8770 | 1.18588 | 0.592942 | − | 0.805245i | \(-0.297966\pi\) | ||||
0.592942 | + | 0.805245i | \(0.297966\pi\) | |||||||
\(968\) | 0.850611 | 0.0273397 | ||||||||
\(969\) | −4.88117 | −0.156806 | ||||||||
\(970\) | 27.8069 | 0.892825 | ||||||||
\(971\) | 27.6403 | 0.887021 | 0.443511 | − | 0.896269i | \(-0.353733\pi\) | ||||
0.443511 | + | 0.896269i | \(0.353733\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −16.7064 | −0.535584 | ||||||||
\(974\) | 40.9206 | 1.31118 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.5452 | −0.369553 | ||||||||
\(977\) | −55.6454 | −1.78026 | −0.890128 | − | 0.455711i | \(-0.849385\pi\) | ||||
−0.890128 | + | 0.455711i | \(0.849385\pi\) | |||||||
\(978\) | 8.87831 | 0.283897 | ||||||||
\(979\) | 27.2061 | 0.869511 | ||||||||
\(980\) | 3.05596 | 0.0976191 | ||||||||
\(981\) | −8.67525 | −0.276979 | ||||||||
\(982\) | −5.11506 | −0.163228 | ||||||||
\(983\) | −25.0022 | −0.797446 | −0.398723 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398723 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(984\) | −9.96254 | −0.317594 | ||||||||
\(985\) | 72.3721 | 2.30597 | ||||||||
\(986\) | −10.8933 | −0.346913 | ||||||||
\(987\) | −8.04447 | −0.256058 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.25404 | −0.294261 | ||||||||
\(990\) | 10.5201 | 0.334350 | ||||||||
\(991\) | −27.2151 | −0.864517 | −0.432258 | − | 0.901750i | \(-0.642283\pi\) | ||||
−0.432258 | + | 0.901750i | \(0.642283\pi\) | |||||||
\(992\) | 0.978370 | 0.0310633 | ||||||||
\(993\) | 14.6478 | 0.464835 | ||||||||
\(994\) | 3.66945 | 0.116388 | ||||||||
\(995\) | −75.9304 | −2.40716 | ||||||||
\(996\) | 7.15869 | 0.226832 | ||||||||
\(997\) | −16.8541 | −0.533775 | −0.266888 | − | 0.963728i | \(-0.585995\pi\) | ||||
−0.266888 | + | 0.963728i | \(0.585995\pi\) | |||||||
\(998\) | −19.5827 | −0.619878 | ||||||||
\(999\) | 5.29308 | 0.167466 |
(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 | 7098.2.a.co.1.3 | 4 | ||
13.2 | odd | 12 | 546.2.s.e.43.3 | ✓ | 8 | ||
13.7 | odd | 12 | 546.2.s.e.127.4 | yes | 8 | ||
13.12 | even | 2 | 7098.2.a.cn.1.2 | 4 | |||
39.2 | even | 12 | 1638.2.bj.f.1135.2 | 8 | |||
39.20 | even | 12 | 1638.2.bj.f.127.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.e.43.3 | ✓ | 8 | 13.2 | odd | 12 | ||
546.2.s.e.127.4 | yes | 8 | 13.7 | odd | 12 | ||
1638.2.bj.f.127.1 | 8 | 39.20 | even | 12 | |||
1638.2.bj.f.1135.2 | 8 | 39.2 | even | 12 | |||
7098.2.a.cn.1.2 | 4 | 13.12 | even | 2 | |||
7098.2.a.co.1.3 | 4 | 1.1 | even | 1 | trivial |