Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(1,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, 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("416.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.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: | \(3.32177672409\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 416.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56155 | 0.901563 | 0.450781 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.56155 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.56155 | −1.34614 | −0.673070 | − | 0.739579i | \(-0.735025\pi\) | ||||
−0.673070 | + | 0.739579i | \(0.735025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.56155 | −1.43599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56155 | 0.863803 | 0.431902 | − | 0.901921i | \(-0.357843\pi\) | ||||
0.431902 | + | 0.901921i | \(0.357843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.56155 | −1.21363 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24621 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12311 | 0.201716 | 0.100858 | − | 0.994901i | \(-0.467841\pi\) | ||||
0.100858 | + | 0.994901i | \(0.467841\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12311 | −0.543663 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6847 | 2.14410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.68466 | 0.441355 | 0.220678 | − | 0.975347i | \(-0.429173\pi\) | ||||
0.220678 | + | 0.975347i | \(0.429173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.56155 | −0.250049 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.8078 | −1.80067 | −0.900334 | − | 0.435200i | \(-0.856677\pi\) | ||||
−0.900334 | + | 0.435200i | \(0.856677\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.6847 | 1.55852 | 0.779259 | − | 0.626702i | \(-0.215596\pi\) | ||||
0.779259 | + | 0.626702i | \(0.215596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.68466 | 0.812094 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.56155 | 0.778773 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.1231 | −1.80260 | −0.901299 | − | 0.433198i | \(-0.857385\pi\) | ||||
−0.901299 | + | 0.433198i | \(0.857385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.12311 | 0.960479 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.36932 | −1.24100 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3693 | −1.45569 | −0.727846 | − | 0.685741i | \(-0.759478\pi\) | ||||
−0.727846 | + | 0.685741i | \(0.759478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56155 | 0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | −0.733017 | −0.366508 | − | 0.930415i | \(-0.619447\pi\) | ||||
−0.366508 | + | 0.930415i | \(0.619447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6847 | −1.26804 | −0.634018 | − | 0.773318i | \(-0.718595\pi\) | ||||
−0.634018 | + | 0.773318i | \(0.718595\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000 | 1.17041 | 0.585206 | − | 0.810885i | \(-0.301014\pi\) | ||||
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.0000 | 1.38564 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.12311 | 0.811753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.36932 | −0.808888 | −0.404444 | − | 0.914563i | \(-0.632535\pi\) | ||||
−0.404444 | + | 0.914563i | \(0.632535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.6847 | −1.37584 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.8769 | 1.38055 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.24621 | 0.874097 | 0.437048 | − | 0.899438i | \(-0.356024\pi\) | ||||
0.437048 | + | 0.899438i | \(0.356024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56155 | 0.373352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.75379 | 0.181859 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.3693 | 2.19245 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.12311 | 0.112876 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.12311 | 0.111753 | 0.0558766 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558766 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.8078 | 1.93304 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6847 | 1.02340 | 0.511702 | − | 0.859163i | \(-0.329015\pi\) | ||||
0.511702 | + | 0.859163i | \(0.329015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.19224 | 0.397909 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24621 | −0.775738 | −0.387869 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387869 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.561553 | 0.0519156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.6847 | −1.16280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75379 | −0.158134 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.56155 | −0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2462 | 1.26415 | 0.632073 | − | 0.774909i | \(-0.282204\pi\) | ||||
0.632073 | + | 0.774909i | \(0.282204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.4384 | −1.62341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31534 | −0.289663 | −0.144831 | − | 0.989456i | \(-0.546264\pi\) | ||||
−0.144831 | + | 0.989456i | \(0.546264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.3693 | 1.85295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.8078 | 1.70478 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1231 | 1.12118 | 0.560591 | − | 0.828093i | \(-0.310574\pi\) | ||||
0.560591 | + | 0.828093i | \(0.310574\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.68466 | 0.397348 | 0.198674 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198674 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.6847 | 1.40510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29.3693 | −2.43899 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.87689 | 0.732154 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.24621 | 0.675556 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6847 | −1.84605 | −0.923026 | − | 0.384738i | \(-0.874292\pi\) | ||||
−0.923026 | + | 0.384738i | \(0.874292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.4924 | −1.62515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3693 | 1.20382 | 0.601909 | − | 0.798565i | \(-0.294407\pi\) | ||||
0.601909 | + | 0.798565i | \(0.294407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1231 | 0.865933 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3693 | −1.18931 | −0.594657 | − | 0.803980i | \(-0.702712\pi\) | ||||
−0.594657 | + | 0.803980i | \(0.702712\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.36932 | 0.257658 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.36932 | −0.256164 | −0.128082 | − | 0.991764i | \(-0.540882\pi\) | ||||
−0.128082 | + | 0.991764i | \(0.540882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.3693 | −2.06893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.36932 | 0.704241 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0540 | −1.34942 | −0.674709 | − | 0.738084i | \(-0.735731\pi\) | ||||
−0.674709 | + | 0.738084i | \(0.735731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.36932 | −0.547757 | −0.273879 | − | 0.961764i | \(-0.588307\pi\) | ||||
−0.273879 | + | 0.961764i | \(0.588307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.7538 | −1.31240 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.56155 | −0.702979 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.12311 | −0.520893 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.8078 | 1.44080 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.36932 | −0.388510 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3693 | −1.68216 | −0.841080 | − | 0.540911i | \(-0.818080\pi\) | ||||
−0.841080 | + | 0.540911i | \(0.818080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.56155 | 0.398271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.31534 | 0.0937142 | 0.0468571 | − | 0.998902i | \(-0.485079\pi\) | ||||
0.0468571 | + | 0.998902i | \(0.485079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.36932 | 0.664173 | 0.332087 | − | 0.943249i | \(-0.392247\pi\) | ||||
0.332087 | + | 0.943249i | \(0.392247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.36932 | −0.660861 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.3693 | −2.06132 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8078 | −1.63899 | −0.819497 | − | 0.573083i | \(-0.805747\pi\) | ||||
−0.819497 | + | 0.573083i | \(0.805747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.6847 | −1.14321 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.0540 | 2.86806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.6155 | 1.05520 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.56155 | −0.239576 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.19224 | −0.414663 | −0.207331 | − | 0.978271i | \(-0.566478\pi\) | ||||
−0.207331 | + | 0.978271i | \(0.566478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.31534 | −0.287689 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.36932 | 0.223629 | 0.111815 | − | 0.993729i | \(-0.464334\pi\) | ||||
0.111815 | + | 0.993729i | \(0.464334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31534 | 0.0869202 | 0.0434601 | − | 0.999055i | \(-0.486162\pi\) | ||||
0.0434601 | + | 0.999055i | \(0.486162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1231 | 0.731847 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.31534 | 0.0861709 | 0.0430854 | − | 0.999071i | \(-0.486281\pi\) | ||||
0.0430854 | + | 0.999071i | \(0.486281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38.0540 | −2.48237 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.7386 | −1.21721 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.31534 | −0.602559 | −0.301280 | − | 0.953536i | \(-0.597414\pi\) | ||||
−0.301280 | + | 0.953536i | \(0.597414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.2462 | −1.29348 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.5076 | −0.729263 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.8078 | −1.24041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.9309 | −0.806605 | −0.403303 | − | 0.915067i | \(-0.632138\pi\) | ||||
−0.403303 | + | 0.915067i | \(0.632138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.56155 | −0.594126 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.63068 | −0.286632 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7386 | 1.40212 | 0.701062 | − | 0.713100i | \(-0.252710\pi\) | ||||
0.701062 | + | 0.713100i | \(0.252710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 46.7386 | 2.87113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8769 | 0.788053 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.36932 | 0.205431 | 0.102715 | − | 0.994711i | \(-0.467247\pi\) | ||||
0.102715 | + | 0.994711i | \(0.467247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6847 | 0.649047 | 0.324523 | − | 0.945878i | \(-0.394796\pi\) | ||||
0.324523 | + | 0.945878i | \(0.394796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.56155 | 0.336600 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.3693 | −0.926805 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3693 | 1.40413 | 0.702063 | − | 0.712115i | \(-0.252262\pi\) | ||||
0.702063 | + | 0.712115i | \(0.252262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.630683 | −0.0377580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.75379 | 0.223932 | 0.111966 | − | 0.993712i | \(-0.464285\pi\) | ||||
0.111966 | + | 0.993712i | \(0.464285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2462 | 0.846849 | 0.423425 | − | 0.905931i | \(-0.360828\pi\) | ||||
0.423425 | + | 0.905931i | \(0.360828\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.3693 | 1.97663 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.31534 | −0.253844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.36932 | −0.549239 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.5616 | −1.61016 | −0.805082 | − | 0.593164i | \(-0.797879\pi\) | ||||
−0.805082 | + | 0.593164i | \(0.797879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.3693 | −1.24417 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1231 | 0.645428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.0540 | 2.42395 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.75379 | 0.100753 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 40.4924 | 2.31859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000 | 0.342438 | 0.171219 | − | 0.985233i | \(-0.445229\pi\) | ||||
0.171219 | + | 0.985233i | \(0.445229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.36932 | −0.531285 | −0.265643 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.0540 | −1.13352 | −0.566759 | − | 0.823884i | \(-0.691803\pi\) | ||||
−0.566759 | + | 0.823884i | \(0.691803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.12311 | −0.401342 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.7538 | −0.884821 | −0.442410 | − | 0.896813i | \(-0.645877\pi\) | ||||
−0.442410 | + | 0.896813i | \(0.645877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.4924 | −0.923398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7386 | 1.04589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.3693 | −1.18902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.68466 | −0.426268 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.6847 | 0.922664 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −38.0540 | −2.09798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.36932 | 0.185194 | 0.0925972 | − | 0.995704i | \(-0.470483\pi\) | ||||
0.0925972 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.50758 | −0.0826147 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.3693 | 1.16753 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.0540 | −1.96399 | −0.981993 | − | 0.188919i | \(-0.939501\pi\) | ||||
−0.981993 | + | 0.188919i | \(0.939501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.8769 | −0.699377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.24621 | −0.121639 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.68466 | 0.252948 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.6847 | 1.53987 | 0.769937 | − | 0.638120i | \(-0.220288\pi\) | ||||
0.769937 | + | 0.638120i | \(0.220288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.05398 | −0.431119 | −0.215560 | − | 0.976491i | \(-0.569158\pi\) | ||||
−0.215560 | + | 0.976491i | \(0.569158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.56155 | 0.296854 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.8617 | 1.69583 | 0.847915 | − | 0.530133i | \(-0.177858\pi\) | ||||
0.847915 | + | 0.530133i | \(0.177858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.0540 | 2.01970 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.8078 | −1.04834 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.36932 | −0.388938 | −0.194469 | − | 0.980909i | \(-0.562298\pi\) | ||||
−0.194469 | + | 0.980909i | \(0.562298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9309 | −0.573722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.6155 | −1.86420 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.63068 | 0.137321 | 0.0686603 | − | 0.997640i | \(-0.478128\pi\) | ||||
0.0686603 | + | 0.997640i | \(0.478128\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.630683 | 0.0328321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.7386 | 2.42655 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3693 | 0.588681 | 0.294340 | − | 0.955701i | \(-0.404900\pi\) | ||||
0.294340 | + | 0.955701i | \(0.404900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.9309 | −0.771027 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.24621 | −0.424701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1231 | −1.29049 | −0.645244 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2462 | 1.13971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6847 | −0.545961 | −0.272980 | − | 0.962020i | \(-0.588009\pi\) | ||||
−0.272980 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.3693 | −1.29294 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.63068 | 0.337057 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.75379 | 0.190325 | 0.0951623 | − | 0.995462i | \(-0.469663\pi\) | ||||
0.0951623 | + | 0.995462i | \(0.469663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.17708 | −0.261149 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 42.7386 | 2.15041 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.00000 | −0.301131 | −0.150566 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150566 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.3693 | 1.67056 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.8769 | 1.14242 | 0.571209 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571209 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.12311 | −0.0559459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.9309 | 1.23882 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.36932 | −0.266147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.3693 | −1.55111 | −0.775556 | − | 0.631278i | \(-0.782531\pi\) | ||||
−0.775556 | + | 0.631278i | \(0.782531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4924 | 1.01082 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.3693 | −1.05152 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.2462 | 1.28838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.31534 | 0.358234 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0540 | 1.07741 | 0.538704 | − | 0.842495i | \(-0.318914\pi\) | ||||
0.538704 | + | 0.842495i | \(0.318914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3153 | −1.03885 | −0.519423 | − | 0.854517i | \(-0.673853\pi\) | ||||
−0.519423 | + | 0.854517i | \(0.673853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.3693 | 1.32761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.4924 | 1.95957 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.12311 | 0.150785 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.68466 | 0.321989 | 0.160994 | − | 0.986955i | \(-0.448530\pi\) | ||||
0.160994 | + | 0.986955i | \(0.448530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6847 | 1.28238 | 0.641191 | − | 0.767381i | \(-0.278440\pi\) | ||||
0.641191 | + | 0.767381i | \(0.278440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −45.8617 | −2.19890 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.384472 | 0.0183498 | 0.00917492 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917492 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.19224 | −0.152011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.68466 | −0.222575 | −0.111287 | − | 0.993788i | \(-0.535497\pi\) | ||||
−0.111287 | + | 0.993788i | \(0.535497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.3693 | −1.39224 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.8769 | 0.609056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24621 | 0.105770 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.4233 | −1.66433 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.6847 | −0.594666 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | −0.654892 | −0.327446 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327446 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.8078 | −0.924547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.8078 | −1.94718 | −0.973591 | − | 0.228300i | \(-0.926683\pi\) | ||||
−0.973591 | + | 0.228300i | \(0.926683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6155 | 0.818663 | 0.409332 | − | 0.912386i | \(-0.365762\pi\) | ||||
0.409332 | + | 0.912386i | \(0.365762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.24621 | −0.289661 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.7386 | 1.60751 | 0.803756 | − | 0.594959i | \(-0.202832\pi\) | ||||
0.803756 | + | 0.594959i | \(0.202832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3693 | 0.986743 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12311 | 0.143905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.6155 | 1.08584 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −46.1080 | −2.11558 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.36932 | 0.337418 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.3153 | −0.973923 | −0.486961 | − | 0.873423i | \(-0.661895\pi\) | ||||
−0.486961 | + | 0.873423i | \(0.661895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.68466 | −0.122410 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3693 | 0.970331 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.8769 | 0.492879 | 0.246440 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246440 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3153 | −1.05221 | −0.526103 | − | 0.850421i | \(-0.676347\pi\) | ||||
−0.526103 | + | 0.850421i | \(0.676347\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.3693 | 1.32273 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 38.0540 | 1.70695 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.1231 | −1.12466 | −0.562332 | − | 0.826911i | \(-0.690096\pi\) | ||||
−0.562332 | + | 0.826911i | \(0.690096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0000 | −1.07224 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.3693 | 1.30951 | 0.654757 | − | 0.755840i | \(-0.272771\pi\) | ||||
0.654757 | + | 0.755840i | \(0.272771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | −0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.56155 | 0.0693510 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.4924 | 0.996959 | 0.498480 | − | 0.866901i | \(-0.333892\pi\) | ||||
0.498480 | + | 0.866901i | \(0.333892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.6155 | −1.57554 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.3693 | 1.47329 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.3693 | −0.939821 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.26137 | −0.230948 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.43845 | 0.369695 | 0.184848 | − | 0.982767i | \(-0.440821\pi\) | ||||
0.184848 | + | 0.982767i | \(0.440821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.50758 | 0.328283 | 0.164142 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164142 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −42.7386 | −1.86527 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.36932 | −0.146216 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.12311 | 0.0486471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.7386 | −1.84775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.1922 | −1.21658 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.3693 | −0.489711 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6847 | −1.31924 | −0.659618 | − | 0.751601i | \(-0.729282\pi\) | ||||
−0.659618 | + | 0.751601i | \(0.729282\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.5076 | −0.493837 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.0540 | −1.63005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0540 | 0.600905 | 0.300452 | − | 0.953797i | \(-0.402862\pi\) | ||||
0.300452 | + | 0.953797i | \(0.402862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.38447 | 0.272483 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.4773 | −2.10780 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.7386 | 1.81743 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.9309 | −0.633780 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3002 | 0.436433 | 0.218216 | − | 0.975900i | \(-0.429976\pi\) | ||||
0.218216 | + | 0.975900i | \(0.429976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8078 | 0.499415 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.1231 | −0.469618 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.3153 | −1.31978 | −0.659892 | − | 0.751360i | \(-0.729398\pi\) | ||||
−0.659892 | + | 0.751360i | \(0.729398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.3693 | 1.23558 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.9309 | 1.04700 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3153 | −0.558208 | −0.279104 | − | 0.960261i | \(-0.590037\pi\) | ||||
−0.279104 | + | 0.960261i | \(0.590037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5616 | 0.902323 | 0.451161 | − | 0.892442i | \(-0.351010\pi\) | ||||
0.451161 | + | 0.892442i | \(0.351010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.38447 | −0.350266 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.7386 | 1.86249 | 0.931247 | − | 0.364389i | \(-0.118722\pi\) | ||||
0.931247 | + | 0.364389i | \(0.118722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.4924 | −1.51657 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.2462 | 1.08888 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.2462 | 1.08701 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.3693 | −0.634360 | −0.317180 | − | 0.948365i | \(-0.602736\pi\) | ||||
−0.317180 | + | 0.948365i | \(0.602736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.73863 | −0.277661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.05398 | 0.0844893 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.75379 | 0.154150 | 0.0770748 | − | 0.997025i | \(-0.475442\pi\) | ||||
0.0770748 | + | 0.997025i | \(0.475442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.1771 | 1.85208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.6307 | 0.598794 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.6307 | −0.434358 | −0.217179 | − | 0.976132i | \(-0.569686\pi\) | ||||
−0.217179 | + | 0.976132i | \(0.569686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0540 | 0.654855 | 0.327428 | − | 0.944876i | \(-0.393818\pi\) | ||||
0.327428 | + | 0.944876i | \(0.393818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.36932 | 0.137209 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.9309 | 1.01358 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8617 | 1.04970 | 0.524848 | − | 0.851196i | \(-0.324122\pi\) | ||||
0.524848 | + | 0.851196i | \(0.324122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.8617 | −1.85841 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.6847 | −0.432255 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.24621 | 0.251872 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6155 | 0.709174 | 0.354587 | − | 0.935023i | \(-0.384621\pi\) | ||||
0.354587 | + | 0.935023i | \(0.384621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3693 | 0.617745 | 0.308873 | − | 0.951103i | \(-0.400048\pi\) | ||||
0.308873 | + | 0.951103i | \(0.400048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.3693 | −1.17666 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7386 | 0.748349 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.56155 | 0.381244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.94602 | −0.157089 | −0.0785444 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785444 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.1771 | −1.47766 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −50.7386 | −2.01350 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.68466 | −0.225234 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4924 | −0.888397 | −0.444199 | − | 0.895928i | \(-0.646512\pi\) | ||||
−0.444199 | + | 0.895928i | \(0.646512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | 0.709851 | 0.354925 | − | 0.934895i | \(-0.384506\pi\) | ||||
0.354925 | + | 0.934895i | \(0.384506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 65.6695 | 2.58573 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.1080 | −1.73406 | −0.867031 | − | 0.498254i | \(-0.833975\pi\) | ||||
−0.867031 | + | 0.498254i | \(0.833975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.24621 | −0.244808 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.38447 | −0.249844 | −0.124922 | − | 0.992167i | \(-0.539868\pi\) | ||||
−0.124922 | + | 0.992167i | \(0.539868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8078 | 0.461368 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.61553 | −0.219083 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7386 | 1.11780 | 0.558902 | − | 0.829234i | \(-0.311223\pi\) | ||||
0.558902 | + | 0.829234i | \(0.311223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.56155 | −0.215993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −76.1080 | −2.95134 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.66950 | −0.373845 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.7386 | 0.877815 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0540 | 0.618835 | 0.309418 | − | 0.950926i | \(-0.399866\pi\) | ||||
0.309418 | + | 0.950926i | \(0.399866\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.7386 | −1.64501 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.36932 | −0.129493 | −0.0647467 | − | 0.997902i | \(-0.520624\pi\) | ||||
−0.0647467 | + | 0.997902i | \(0.520624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3693 | 0.820079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.26137 | 0.201616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.3693 | −0.741146 | −0.370573 | − | 0.928803i | \(-0.620839\pi\) | ||||
−0.370573 | + | 0.928803i | \(0.620839\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.7386 | −1.78579 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.05398 | 0.0783640 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.1231 | 0.499951 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.1231 | 0.499226 | 0.249613 | − | 0.968346i | \(-0.419697\pi\) | ||||
0.249613 | + | 0.968346i | \(0.419697\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.6847 | −0.632885 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.05398 | 0.0776885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.3693 | −0.580491 | −0.290246 | − | 0.956952i | \(-0.593737\pi\) | ||||
−0.290246 | + | 0.956952i | \(0.593737\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1080 | −0.607523 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −59.4233 | −2.23801 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00000 | −0.150435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.7386 | −1.22953 | −0.614763 | − | 0.788712i | \(-0.710748\pi\) | ||||
−0.614763 | + | 0.788712i | \(0.710748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.73863 | 0.252719 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.12311 | −0.266389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.5464 | −0.543245 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.36932 | −0.349417 | −0.174708 | − | 0.984620i | \(-0.555898\pi\) | ||||
−0.174708 | + | 0.984620i | \(0.555898\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.12311 | 0.116150 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 63.3693 | 2.35348 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.384472 | 0.0142593 | 0.00712964 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712964 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.0540 | −1.55542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0540 | 0.445224 | 0.222612 | − | 0.974907i | \(-0.428542\pi\) | ||||
0.222612 | + | 0.974907i | \(0.428542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −31.6155 | −1.16616 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0000 | 0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.1080 | −0.813254 | −0.406627 | − | 0.913594i | \(-0.633295\pi\) | ||||
−0.406627 | + | 0.913594i | \(0.633295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.36932 | 0.344190 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.31534 | −0.0482552 | −0.0241276 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241276 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.3693 | −1.07601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.13826 | 0.151411 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.7386 | −1.56164 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.75379 | 0.355921 | 0.177960 | − | 0.984038i | \(-0.443050\pi\) | ||||
0.177960 | + | 0.984038i | \(0.443050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9848 | 0.910498 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 80.7926 | 2.94034 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3693 | 0.558607 | 0.279304 | − | 0.960203i | \(-0.409896\pi\) | ||||
0.279304 | + | 0.960203i | \(0.409896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0540 | −1.37765 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.12311 | 0.257536 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.3693 | −0.554232 | −0.277116 | − | 0.960837i | \(-0.589379\pi\) | ||||
−0.277116 | + | 0.960837i | \(0.589379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1922 | −0.727206 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.3153 | −0.478920 | −0.239460 | − | 0.970906i | \(-0.576970\pi\) | ||||
−0.239460 | + | 0.970906i | \(0.576970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.63068 | 0.310023 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.9309 | −0.535642 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.73863 | 0.241437 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3693 | 0.764654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.8617 | −1.63896 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.12311 | −0.254235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.61553 | 0.200172 | 0.100086 | − | 0.994979i | \(-0.468088\pi\) | ||||
0.100086 | + | 0.994979i | \(0.468088\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.5076 | 1.26410 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.3693 | 1.04425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3693 | 0.403736 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.9848 | 2.58851 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7386 | 1.30135 | 0.650675 | − | 0.759357i | \(-0.274486\pi\) | ||||
0.650675 | + | 0.759357i | \(0.274486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.0540 | 1.34625 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.63068 | −0.163617 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.0000 | −0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.26137 | 0.185209 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0691 | −0.389170 | −0.194585 | − | 0.980886i | \(-0.562336\pi\) | ||||
−0.194585 | + | 0.980886i | \(0.562336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8617 | 1.11882 | 0.559408 | − | 0.828892i | \(-0.311028\pi\) | ||||
0.559408 | + | 0.828892i | \(0.311028\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.6847 | 0.585157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −54.7386 | −1.91741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 70.8466 | 2.47861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.0540 | −1.11869 | −0.559346 | − | 0.828934i | \(-0.688948\pi\) | ||||
−0.559346 | + | 0.828934i | \(0.688948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6307 | 0.509994 | 0.254997 | − | 0.966942i | \(-0.417926\pi\) | ||||
0.254997 | + | 0.966942i | \(0.417926\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.0000 | −0.835573 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.7386 | −0.442966 | −0.221483 | − | 0.975164i | \(-0.571090\pi\) | ||||
−0.221483 | + | 0.975164i | \(0.571090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.7386 | 0.581357 | 0.290678 | − | 0.956821i | \(-0.406119\pi\) | ||||
0.290678 | + | 0.956821i | \(0.406119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.4924 | 1.26591 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2462 | 0.701490 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.7386 | 1.89431 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.24621 | −0.215901 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.1080 | 1.31563 | 0.657816 | − | 0.753178i | \(-0.271480\pi\) | ||||
0.657816 | + | 0.753178i | \(0.271480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.86174 | 0.201889 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.56155 | −0.122521 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.9309 | 0.856635 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.2462 | 0.763488 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.31534 | 0.318951 | 0.159476 | − | 0.987202i | \(-0.449020\pi\) | ||||
0.159476 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | −0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.7538 | −0.538139 | −0.269070 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269070 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.0000 | 1.22830 | 0.614152 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614152 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.24621 | 0.212870 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0540 | −0.410322 | −0.205161 | − | 0.978728i | \(-0.565772\pi\) | ||||
−0.205161 | + | 0.978728i | \(0.565772\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.73863 | −0.228856 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | 0.203302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.36932 | 0.114034 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.0540 | 1.15123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.7926 | 1.85021 | 0.925107 | − | 0.379705i | \(-0.123975\pi\) | ||||
0.925107 | + | 0.379705i | \(0.123975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.0388 | −1.45166 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3002 | 1.15560 | 0.577801 | − | 0.816177i | \(-0.303911\pi\) | ||||
0.577801 | + | 0.816177i | \(0.303911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5616 | 0.725604 | 0.362802 | − | 0.931866i | \(-0.381820\pi\) | ||||
0.362802 | + | 0.931866i | \(0.381820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.3693 | −1.12170 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.7386 | −1.70172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0000 | 0.469018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −64.1080 | −2.14529 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.3002 | 2.14932 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.26137 | 0.308884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.7386 | −1.55709 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.6695 | 2.18534 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.2462 | 0.872454 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.4233 | 1.17621 | 0.588106 | − | 0.808784i | \(-0.299874\pi\) | ||||
0.588106 | + | 0.808784i | \(0.299874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.630683 | −0.0209184 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.63068 | 0.0871584 | 0.0435792 | − | 0.999050i | \(-0.486124\pi\) | ||||
0.0435792 | + | 0.999050i | \(0.486124\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.7386 | 0.487778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.2311 | 2.09035 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.8078 | 0.389927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.2462 | −1.65747 | −0.828735 | − | 0.559642i | \(-0.810939\pi\) | ||||
−0.828735 | + | 0.559642i | \(0.810939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.36932 | 0.308729 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6847 | 0.351690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.6307 | 0.678333 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.61553 | −0.184240 | −0.0921198 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921198 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.1080 | −1.11784 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6307 | −0.478987 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.3693 | 0.829665 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.73863 | −0.285479 | −0.142739 | − | 0.989760i | \(-0.545591\pi\) | ||||
−0.142739 | + | 0.989760i | \(0.545591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3153 | −1.02194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.3153 | 0.825257 | 0.412628 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412628 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70.5464 | −2.29487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.00000 | −0.0649913 | −0.0324956 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324956 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.0000 | −0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6004 | −0.797722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.8078 | −1.35429 | −0.677143 | − | 0.735851i | \(-0.736782\pi\) | ||||
−0.677143 | + | 0.735851i | \(0.736782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1231 | 0.618809 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.7538 | −0.832502 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.7386 | −1.50927 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7386 | −0.959311 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.73863 | −0.217149 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 83.2311 | 2.67930 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.4233 | −1.71798 | −0.858989 | − | 0.511995i | \(-0.828907\pi\) | ||||
−0.858989 | + | 0.511995i | \(0.828907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.3693 | −1.07198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.31534 | 0.106394 | 0.0531972 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531972 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6847 | −0.534886 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0000 | −0.384308 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.9848 | −0.479408 | −0.239704 | − | 0.970846i | \(-0.577050\pi\) | ||||
−0.239704 | + | 0.970846i | \(0.577050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.4924 | −0.527100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.4233 | 0.683297 | 0.341648 | − | 0.939828i | \(-0.389015\pi\) | ||||
0.341648 | + | 0.939828i | \(0.389015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.68466 | −0.149266 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −59.4233 | −1.89146 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3693 | 0.678819 | 0.339409 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339409 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.26137 | 0.166964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.3693 | −1.05788 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.73863 | −0.150074 | −0.0750370 | − | 0.997181i | \(-0.523907\pi\) | ||||
−0.0750370 | + | 0.997181i | \(0.523907\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.9309 | −0.472392 |
(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 | 416.2.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3744.2.a.x.1.2 | 2 | |||
4.3 | odd | 2 | 416.2.a.e.1.1 | yes | 2 | ||
8.3 | odd | 2 | 832.2.a.l.1.2 | 2 | |||
8.5 | even | 2 | 832.2.a.o.1.1 | 2 | |||
12.11 | even | 2 | 3744.2.a.y.1.2 | 2 | |||
13.12 | even | 2 | 5408.2.a.p.1.2 | 2 | |||
16.3 | odd | 4 | 3328.2.b.u.1665.2 | 4 | |||
16.5 | even | 4 | 3328.2.b.ba.1665.2 | 4 | |||
16.11 | odd | 4 | 3328.2.b.u.1665.3 | 4 | |||
16.13 | even | 4 | 3328.2.b.ba.1665.3 | 4 | |||
24.5 | odd | 2 | 7488.2.a.ce.1.1 | 2 | |||
24.11 | even | 2 | 7488.2.a.cf.1.1 | 2 | |||
52.51 | odd | 2 | 5408.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
416.2.a.e.1.1 | yes | 2 | 4.3 | odd | 2 | ||
832.2.a.l.1.2 | 2 | 8.3 | odd | 2 | |||
832.2.a.o.1.1 | 2 | 8.5 | even | 2 | |||
3328.2.b.u.1665.2 | 4 | 16.3 | odd | 4 | |||
3328.2.b.u.1665.3 | 4 | 16.11 | odd | 4 | |||
3328.2.b.ba.1665.2 | 4 | 16.5 | even | 4 | |||
3328.2.b.ba.1665.3 | 4 | 16.13 | even | 4 | |||
3744.2.a.x.1.2 | 2 | 3.2 | odd | 2 | |||
3744.2.a.y.1.2 | 2 | 12.11 | even | 2 | |||
5408.2.a.p.1.2 | 2 | 13.12 | even | 2 | |||
5408.2.a.bd.1.1 | 2 | 52.51 | odd | 2 | |||
7488.2.a.ce.1.1 | 2 | 24.5 | odd | 2 | |||
7488.2.a.cf.1.1 | 2 | 24.11 | even | 2 |