Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44949 | −1.73205 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 2.00000 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −4.89898 | −1.73205 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | 1.89737 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.89898 | −0.804032 | −0.402016 | − | 0.915633i | \(-0.631690\pi\) | ||||
−0.402016 | + | 0.915633i | \(0.631690\pi\) | |||||||
\(14\) | −2.44949 | −0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 5.44949 | 1.32170 | 0.660848 | − | 0.750520i | \(-0.270197\pi\) | ||||
0.660848 | + | 0.750520i | \(0.270197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.44949 | 1.02078 | 0.510391 | − | 0.859942i | \(-0.329501\pi\) | ||||
0.510391 | + | 0.859942i | \(0.329501\pi\) | |||||||
\(20\) | −9.79796 | −2.19089 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.10102 | 1.39262 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 7.89898 | 1.46680 | 0.733402 | − | 0.679795i | \(-0.237931\pi\) | ||||
0.733402 | + | 0.679795i | \(0.237931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.3485 | −2.28924 | ||||||||
\(35\) | −2.44949 | −0.414039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | −10.8990 | −1.76805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.0000 | 1.89737 | ||||||||
\(41\) | −5.44949 | −0.851067 | −0.425534 | − | 0.904943i | \(-0.639914\pi\) | ||||
−0.425534 | + | 0.904943i | \(0.639914\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.6969 | 2.16695 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.44949 | −0.346410 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.5959 | −1.60806 | ||||||||
\(53\) | −1.89898 | −0.260845 | −0.130422 | − | 0.991459i | \(-0.541633\pi\) | ||||
−0.130422 | + | 0.991459i | \(0.541633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.89898 | −0.654654 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.3485 | −2.54058 | ||||||||
\(59\) | 2.44949 | 0.318896 | 0.159448 | − | 0.987206i | \(-0.449029\pi\) | ||||
0.159448 | + | 0.987206i | \(0.449029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.44949 | 0.569699 | 0.284849 | − | 0.958572i | \(-0.408056\pi\) | ||||
0.284849 | + | 0.958572i | \(0.408056\pi\) | |||||||
\(62\) | −19.5959 | −2.48868 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 7.10102 | 0.880773 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2474 | −1.25193 | −0.625963 | − | 0.779853i | \(-0.715294\pi\) | ||||
−0.625963 | + | 0.779853i | \(0.715294\pi\) | |||||||
\(68\) | 21.7980 | 2.64339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | 0.717137 | ||||||||
\(71\) | −3.55051 | −0.421368 | −0.210684 | − | 0.977554i | \(-0.567569\pi\) | ||||
−0.210684 | + | 0.977554i | \(0.567569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.34847 | 0.391909 | 0.195954 | − | 0.980613i | \(-0.437220\pi\) | ||||
0.195954 | + | 0.980613i | \(0.437220\pi\) | |||||||
\(74\) | 17.1464 | 1.99323 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.7980 | 2.04157 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.89898 | 0.438669 | 0.219335 | − | 0.975650i | \(-0.429611\pi\) | ||||
0.219335 | + | 0.975650i | \(0.429611\pi\) | |||||||
\(80\) | −9.79796 | −1.09545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.3485 | 1.47409 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3485 | −1.44784 | ||||||||
\(86\) | −4.89898 | −0.528271 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.79796 | 1.03858 | 0.519291 | − | 0.854598i | \(-0.326196\pi\) | ||||
0.519291 | + | 0.854598i | \(0.326196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.89898 | −0.303896 | ||||||||
\(92\) | −24.0000 | −2.50217 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29.3939 | −3.03175 | ||||||||
\(95\) | −10.8990 | −1.11821 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.34847 | −0.238451 | −0.119225 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119225 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(98\) | −2.44949 | −0.247436 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 14.2020 | 1.39262 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.65153 | 0.451797 | ||||||||
\(107\) | −7.34847 | −0.710403 | −0.355202 | − | 0.934790i | \(-0.615588\pi\) | ||||
−0.355202 | + | 0.934790i | \(0.615588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.34847 | −0.512290 | −0.256145 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256145 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.6969 | 1.37050 | ||||||||
\(116\) | 31.5959 | 2.93361 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 5.44949 | 0.499554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −10.8990 | −0.986747 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 32.0000 | 2.87368 | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 19.5959 | 1.73205 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.3939 | −1.52554 | ||||||||
\(131\) | 4.34847 | 0.379928 | 0.189964 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189964 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.44949 | 0.385820 | ||||||||
\(134\) | 25.1010 | 2.16840 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26.6969 | −2.28924 | ||||||||
\(137\) | −2.20204 | −0.188133 | −0.0940665 | − | 0.995566i | \(-0.529987\pi\) | ||||
−0.0940665 | + | 0.995566i | \(0.529987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.65153 | −0.479357 | −0.239678 | − | 0.970852i | \(-0.577042\pi\) | ||||
−0.239678 | + | 0.970852i | \(0.577042\pi\) | |||||||
\(140\) | −9.79796 | −0.828079 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.69694 | 0.729831 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.3485 | −1.60680 | ||||||||
\(146\) | −8.20204 | −0.678806 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.0000 | −2.30159 | ||||||||
\(149\) | 20.6969 | 1.69556 | 0.847780 | − | 0.530349i | \(-0.177939\pi\) | ||||
0.847780 | + | 0.530349i | \(0.177939\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.34847 | 0.760768 | 0.380384 | − | 0.924829i | \(-0.375792\pi\) | ||||
0.380384 | + | 0.924829i | \(0.375792\pi\) | |||||||
\(152\) | −21.7980 | −1.76805 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.5959 | −1.57398 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.55051 | −0.123744 | −0.0618721 | − | 0.998084i | \(-0.519707\pi\) | ||||
−0.0618721 | + | 0.998084i | \(0.519707\pi\) | |||||||
\(158\) | −9.55051 | −0.759798 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | 1.33154 | 0.665771 | − | 0.746156i | \(-0.268103\pi\) | ||||
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | −21.7980 | −1.70213 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.6969 | 1.14070 | ||||||||
\(167\) | −23.1464 | −1.79112 | −0.895562 | − | 0.444936i | \(-0.853226\pi\) | ||||
−0.895562 | + | 0.444936i | \(0.853226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59592 | −0.353532 | ||||||||
\(170\) | 32.6969 | 2.50774 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −18.2474 | −1.38733 | −0.693664 | − | 0.720299i | \(-0.744005\pi\) | ||||
−0.693664 | + | 0.720299i | \(0.744005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.0000 | −1.79888 | ||||||||
\(179\) | −15.7980 | −1.18079 | −0.590397 | − | 0.807113i | \(-0.701029\pi\) | ||||
−0.590397 | + | 0.807113i | \(0.701029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1464 | 0.754178 | 0.377089 | − | 0.926177i | \(-0.376925\pi\) | ||||
0.377089 | + | 0.926177i | \(0.376925\pi\) | |||||||
\(182\) | 7.10102 | 0.526363 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 29.3939 | 2.16695 | ||||||||
\(185\) | 17.1464 | 1.26063 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 48.0000 | 3.50076 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.6969 | 1.93680 | ||||||||
\(191\) | 13.3485 | 0.965861 | 0.482931 | − | 0.875659i | \(-0.339572\pi\) | ||||
0.482931 | + | 0.875659i | \(0.339572\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.55051 | 0.399534 | 0.199767 | − | 0.979843i | \(-0.435981\pi\) | ||||
0.199767 | + | 0.979843i | \(0.435981\pi\) | |||||||
\(194\) | 5.75255 | 0.413009 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | −8.44949 | −0.602001 | −0.301001 | − | 0.953624i | \(-0.597321\pi\) | ||||
−0.301001 | + | 0.953624i | \(0.597321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | −4.89898 | −0.346410 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.89898 | 0.554400 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.3485 | 0.932298 | ||||||||
\(206\) | 9.79796 | 0.682656 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.5959 | −0.804032 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.6969 | −1.70021 | −0.850104 | − | 0.526615i | \(-0.823461\pi\) | ||||
−0.850104 | + | 0.526615i | \(0.823461\pi\) | |||||||
\(212\) | −7.59592 | −0.521690 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | −4.89898 | −0.334108 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 13.1010 | 0.887313 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7980 | −1.06269 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.55051 | 0.170795 | 0.0853974 | − | 0.996347i | \(-0.472784\pi\) | ||||
0.0853974 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.6969 | −0.977626 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.44949 | 0.492276 | 0.246138 | − | 0.969235i | \(-0.420838\pi\) | ||||
0.246138 | + | 0.969235i | \(0.420838\pi\) | |||||||
\(230\) | −36.0000 | −2.37377 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −38.6969 | −2.54058 | ||||||||
\(233\) | 7.89898 | 0.517479 | 0.258740 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258740 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.3939 | −1.91745 | ||||||||
\(236\) | 9.79796 | 0.637793 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −13.3485 | −0.865253 | ||||||||
\(239\) | −3.00000 | −0.194054 | −0.0970269 | − | 0.995282i | \(-0.530933\pi\) | ||||
−0.0970269 | + | 0.995282i | \(0.530933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.24745 | 0.338018 | 0.169009 | − | 0.985615i | \(-0.445943\pi\) | ||||
0.169009 | + | 0.985615i | \(0.445943\pi\) | |||||||
\(242\) | 26.9444 | 1.73205 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 17.7980 | 1.13940 | ||||||||
\(245\) | −2.44949 | −0.156492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.8990 | −0.820742 | ||||||||
\(248\) | −39.1918 | −2.48868 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24.0000 | −1.51789 | ||||||||
\(251\) | −4.34847 | −0.274473 | −0.137236 | − | 0.990538i | \(-0.543822\pi\) | ||||
−0.137236 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.44949 | −0.153695 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | 11.1464 | 0.695295 | 0.347648 | − | 0.937625i | \(-0.386981\pi\) | ||||
0.347648 | + | 0.937625i | \(0.386981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 28.4041 | 1.76155 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.6515 | −0.658054 | ||||||||
\(263\) | 23.1464 | 1.42727 | 0.713635 | − | 0.700518i | \(-0.247048\pi\) | ||||
0.713635 | + | 0.700518i | \(0.247048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.65153 | 0.285741 | ||||||||
\(266\) | −10.8990 | −0.668259 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.9898 | −2.50385 | ||||||||
\(269\) | −27.2474 | −1.66131 | −0.830653 | − | 0.556790i | \(-0.812033\pi\) | ||||
−0.830653 | + | 0.556790i | \(0.812033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9444 | −1.87974 | −0.939869 | − | 0.341536i | \(-0.889053\pi\) | ||||
−0.939869 | + | 0.341536i | \(0.889053\pi\) | |||||||
\(272\) | 21.7980 | 1.32170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.39388 | 0.325856 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2020 | 0.612981 | 0.306491 | − | 0.951874i | \(-0.400845\pi\) | ||||
0.306491 | + | 0.951874i | \(0.400845\pi\) | |||||||
\(278\) | 13.8434 | 0.830270 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0000 | 0.717137 | ||||||||
\(281\) | 5.20204 | 0.310328 | 0.155164 | − | 0.987889i | \(-0.450409\pi\) | ||||
0.155164 | + | 0.987889i | \(0.450409\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3485 | 1.44737 | 0.723683 | − | 0.690132i | \(-0.242448\pi\) | ||||
0.723683 | + | 0.690132i | \(0.242448\pi\) | |||||||
\(284\) | −14.2020 | −0.842736 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.44949 | −0.321673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6969 | 0.746879 | ||||||||
\(290\) | 47.3939 | 2.78306 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.3939 | 0.783817 | ||||||||
\(293\) | −26.4495 | −1.54520 | −0.772598 | − | 0.634896i | \(-0.781043\pi\) | ||||
−0.772598 | + | 0.634896i | \(0.781043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 34.2929 | 1.99323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −50.6969 | −2.93679 | ||||||||
\(299\) | 17.3939 | 1.00591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | −22.8990 | −1.31769 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.7980 | 1.02078 | ||||||||
\(305\) | −10.8990 | −0.624074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.5505 | 1.17288 | 0.586440 | − | 0.809993i | \(-0.300529\pi\) | ||||
0.586440 | + | 0.809993i | \(0.300529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 48.0000 | 2.72622 | ||||||||
\(311\) | 17.1464 | 0.972285 | 0.486142 | − | 0.873880i | \(-0.338404\pi\) | ||||
0.486142 | + | 0.873880i | \(0.338404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4495 | 1.43849 | 0.719245 | − | 0.694756i | \(-0.244488\pi\) | ||||
0.719245 | + | 0.694756i | \(0.244488\pi\) | |||||||
\(314\) | 3.79796 | 0.214331 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5959 | 0.877339 | ||||||||
\(317\) | 19.1010 | 1.07282 | 0.536410 | − | 0.843957i | \(-0.319780\pi\) | ||||
0.536410 | + | 0.843957i | \(0.319780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 19.5959 | 1.09545 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.6969 | 0.819028 | ||||||||
\(323\) | 24.2474 | 1.34916 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.89898 | −0.160806 | ||||||||
\(326\) | −41.6413 | −2.30630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 26.6969 | 1.47409 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4495 | −1.01408 | −0.507038 | − | 0.861924i | \(-0.669260\pi\) | ||||
−0.507038 | + | 0.861924i | \(0.669260\pi\) | |||||||
\(332\) | −24.0000 | −1.31717 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 56.6969 | 3.10232 | ||||||||
\(335\) | 25.1010 | 1.37142 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.3485 | −1.27187 | −0.635936 | − | 0.771742i | \(-0.719386\pi\) | ||||
−0.635936 | + | 0.771742i | \(0.719386\pi\) | |||||||
\(338\) | 11.2577 | 0.612336 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −53.3939 | −2.89569 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −9.79796 | −0.528271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 44.6969 | 2.40292 | ||||||||
\(347\) | 17.6969 | 0.950021 | 0.475011 | − | 0.879980i | \(-0.342444\pi\) | ||||
0.475011 | + | 0.879980i | \(0.342444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0454 | −0.912420 | −0.456210 | − | 0.889872i | \(-0.650793\pi\) | ||||
−0.456210 | + | 0.889872i | \(0.650793\pi\) | |||||||
\(350\) | −2.44949 | −0.130931 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.8990 | −0.899442 | −0.449721 | − | 0.893169i | \(-0.648477\pi\) | ||||
−0.449721 | + | 0.893169i | \(0.648477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.69694 | 0.461586 | ||||||||
\(356\) | 39.1918 | 2.07716 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.6969 | 2.04520 | ||||||||
\(359\) | −15.0000 | −0.791670 | −0.395835 | − | 0.918322i | \(-0.629545\pi\) | ||||
−0.395835 | + | 0.918322i | \(0.629545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.797959 | 0.0419978 | ||||||||
\(362\) | −24.8536 | −1.30627 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.5959 | −0.607791 | ||||||||
\(365\) | −8.20204 | −0.429314 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | 0.104399 | 0.0521996 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521996 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(368\) | −24.0000 | −1.25109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −42.0000 | −2.18348 | ||||||||
\(371\) | −1.89898 | −0.0985901 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.1010 | 0.781901 | 0.390951 | − | 0.920412i | \(-0.372146\pi\) | ||||
0.390951 | + | 0.920412i | \(0.372146\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −58.7878 | −3.03175 | ||||||||
\(377\) | −22.8990 | −1.17936 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −43.5959 | −2.23642 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.6969 | −1.67292 | ||||||||
\(383\) | 21.2474 | 1.08569 | 0.542847 | − | 0.839832i | \(-0.317346\pi\) | ||||
0.542847 | + | 0.839832i | \(0.317346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5959 | −0.692014 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.39388 | −0.476902 | ||||||||
\(389\) | 34.0454 | 1.72617 | 0.863085 | − | 0.505058i | \(-0.168529\pi\) | ||||
0.863085 | + | 0.505058i | \(0.168529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.6969 | −1.65356 | ||||||||
\(392\) | −4.89898 | −0.247436 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.6969 | 1.04270 | ||||||||
\(395\) | −9.55051 | −0.480538 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.69694 | −0.336110 | −0.168055 | − | 0.985778i | \(-0.553749\pi\) | ||||
−0.168055 | + | 0.985778i | \(0.553749\pi\) | |||||||
\(398\) | −48.9898 | −2.45564 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 0.303062 | 0.0151342 | 0.00756709 | − | 0.999971i | \(-0.497591\pi\) | ||||
0.00756709 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.1918 | −1.15527 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.3485 | −0.960248 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6969 | 0.825610 | 0.412805 | − | 0.910819i | \(-0.364549\pi\) | ||||
0.412805 | + | 0.910819i | \(0.364549\pi\) | |||||||
\(410\) | −32.6969 | −1.61479 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.0000 | −0.788263 | ||||||||
\(413\) | 2.44949 | 0.120532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.6969 | 0.721444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.5959 | 1.54356 | 0.771781 | − | 0.635889i | \(-0.219366\pi\) | ||||
0.771781 | + | 0.635889i | \(0.219366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.04541 | 0.294635 | 0.147318 | − | 0.989089i | \(-0.452936\pi\) | ||||
0.147318 | + | 0.989089i | \(0.452936\pi\) | |||||||
\(422\) | 60.4949 | 2.94485 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.30306 | 0.451797 | ||||||||
\(425\) | 5.44949 | 0.264339 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.44949 | 0.215326 | ||||||||
\(428\) | −29.3939 | −1.42081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | −1.34847 | −0.0649535 | −0.0324767 | − | 0.999472i | \(-0.510339\pi\) | ||||
−0.0324767 | + | 0.999472i | \(0.510339\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.651531 | 0.0313106 | 0.0156553 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156553 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(434\) | −19.5959 | −0.940634 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.3939 | −1.02458 | ||||||||
\(437\) | −26.6969 | −1.27709 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.3485 | −0.684815 | −0.342408 | − | 0.939552i | \(-0.611242\pi\) | ||||
−0.342408 | + | 0.939552i | \(0.611242\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 38.6969 | 1.84063 | ||||||||
\(443\) | −21.5505 | −1.02390 | −0.511948 | − | 0.859017i | \(-0.671076\pi\) | ||||
−0.511948 | + | 0.859017i | \(0.671076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | −1.13771 | ||||||||
\(446\) | −6.24745 | −0.295825 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | −19.1010 | −0.901433 | −0.450716 | − | 0.892667i | \(-0.648831\pi\) | ||||
−0.450716 | + | 0.892667i | \(0.648831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 24.0000 | 1.12887 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 29.3939 | 1.37952 | ||||||||
\(455\) | 7.10102 | 0.332901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4949 | 1.37971 | 0.689857 | − | 0.723946i | \(-0.257674\pi\) | ||||
0.689857 | + | 0.723946i | \(0.257674\pi\) | |||||||
\(458\) | −18.2474 | −0.852647 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 58.7878 | 2.74099 | ||||||||
\(461\) | 5.14643 | 0.239693 | 0.119847 | − | 0.992792i | \(-0.461760\pi\) | ||||
0.119847 | + | 0.992792i | \(0.461760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.202041 | −0.00938964 | −0.00469482 | − | 0.999989i | \(-0.501494\pi\) | ||||
−0.00469482 | + | 0.999989i | \(0.501494\pi\) | |||||||
\(464\) | 31.5959 | 1.46680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.3485 | −0.896301 | ||||||||
\(467\) | −31.5959 | −1.46208 | −0.731042 | − | 0.682332i | \(-0.760966\pi\) | ||||
−0.731042 | + | 0.682332i | \(0.760966\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2474 | −0.473183 | ||||||||
\(470\) | 72.0000 | 3.32111 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.44949 | 0.204157 | ||||||||
\(476\) | 21.7980 | 0.999108 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.34847 | 0.336111 | ||||||||
\(479\) | −3.24745 | −0.148380 | −0.0741899 | − | 0.997244i | \(-0.523637\pi\) | ||||
−0.0741899 | + | 0.997244i | \(0.523637\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2929 | 0.925275 | ||||||||
\(482\) | −12.8536 | −0.585464 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −44.0000 | −2.00000 | ||||||||
\(485\) | 5.75255 | 0.261210 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.9444 | −1.40222 | −0.701112 | − | 0.713051i | \(-0.747313\pi\) | ||||
−0.701112 | + | 0.713051i | \(0.747313\pi\) | |||||||
\(488\) | −21.7980 | −0.986747 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000 | 0.271052 | ||||||||
\(491\) | 13.1010 | 0.591241 | 0.295620 | − | 0.955305i | \(-0.404474\pi\) | ||||
0.295620 | + | 0.955305i | \(0.404474\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.0454 | 1.93867 | ||||||||
\(494\) | 31.5959 | 1.42157 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | −3.55051 | −0.159262 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04541 | 0.270630 | 0.135315 | − | 0.990803i | \(-0.456795\pi\) | ||||
0.135315 | + | 0.990803i | \(0.456795\pi\) | |||||||
\(500\) | 39.1918 | 1.75271 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.6515 | 0.475401 | ||||||||
\(503\) | −29.4495 | −1.31309 | −0.656544 | − | 0.754288i | \(-0.727982\pi\) | ||||
−0.656544 | + | 0.754288i | \(0.727982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | 7.04541 | 0.312282 | 0.156141 | − | 0.987735i | \(-0.450095\pi\) | ||||
0.156141 | + | 0.987735i | \(0.450095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.34847 | 0.148128 | ||||||||
\(512\) | 39.1918 | 1.73205 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.3031 | −1.20429 | ||||||||
\(515\) | 9.79796 | 0.431750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 17.1464 | 0.753371 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −34.7878 | −1.52554 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.2474 | −1.23517 | −0.617587 | − | 0.786502i | \(-0.711890\pi\) | ||||
−0.617587 | + | 0.786502i | \(0.711890\pi\) | |||||||
\(524\) | 17.3939 | 0.759855 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.6969 | −2.47210 | ||||||||
\(527\) | 43.5959 | 1.89907 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −11.3939 | −0.494918 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.7980 | 0.771639 | ||||||||
\(533\) | 15.7980 | 0.684286 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | 0.778208 | ||||||||
\(536\) | 50.2020 | 2.16840 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 66.7423 | 2.87747 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.89898 | −0.382597 | −0.191299 | − | 0.981532i | \(-0.561270\pi\) | ||||
−0.191299 | + | 0.981532i | \(0.561270\pi\) | |||||||
\(542\) | 75.7980 | 3.25580 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.1010 | 0.561186 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.79796 | −0.0768752 | −0.0384376 | − | 0.999261i | \(-0.512238\pi\) | ||||
−0.0384376 | + | 0.999261i | \(0.512238\pi\) | |||||||
\(548\) | −8.80816 | −0.376266 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.1464 | 1.49729 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.89898 | 0.165801 | ||||||||
\(554\) | −24.9898 | −1.06171 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.6061 | −0.958713 | ||||||||
\(557\) | −21.7980 | −0.923609 | −0.461805 | − | 0.886982i | \(-0.652798\pi\) | ||||
−0.461805 | + | 0.886982i | \(0.652798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.79796 | −0.245228 | ||||||||
\(560\) | −9.79796 | −0.414039 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7423 | −0.537503 | ||||||||
\(563\) | −34.2929 | −1.44527 | −0.722636 | − | 0.691229i | \(-0.757070\pi\) | ||||
−0.722636 | + | 0.691229i | \(0.757070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.6969 | −0.618305 | ||||||||
\(566\) | −59.6413 | −2.50691 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.3939 | 0.729831 | ||||||||
\(569\) | 30.4949 | 1.27841 | 0.639206 | − | 0.769035i | \(-0.279263\pi\) | ||||
0.639206 | + | 0.769035i | \(0.279263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.1464 | −1.88932 | −0.944660 | − | 0.328052i | \(-0.893608\pi\) | ||||
−0.944660 | + | 0.328052i | \(0.893608\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.3485 | 0.557154 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6515 | −0.859734 | −0.429867 | − | 0.902892i | \(-0.641440\pi\) | ||||
−0.429867 | + | 0.902892i | \(0.641440\pi\) | |||||||
\(578\) | −31.1010 | −1.29363 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −77.3939 | −3.21361 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −16.4041 | −0.678806 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 64.7878 | 2.67636 | ||||||||
\(587\) | 5.44949 | 0.224925 | 0.112462 | − | 0.993656i | \(-0.464126\pi\) | ||||
0.112462 | + | 0.993656i | \(0.464126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.5959 | 1.46670 | ||||||||
\(590\) | 14.6969 | 0.605063 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.0000 | −1.15079 | ||||||||
\(593\) | 9.79796 | 0.402354 | 0.201177 | − | 0.979555i | \(-0.435523\pi\) | ||||
0.201177 | + | 0.979555i | \(0.435523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.3485 | −0.547234 | ||||||||
\(596\) | 82.7878 | 3.39112 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −42.6061 | −1.74229 | ||||||||
\(599\) | 33.0000 | 1.34834 | 0.674172 | − | 0.738575i | \(-0.264501\pi\) | ||||
0.674172 | + | 0.738575i | \(0.264501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.65153 | −0.230531 | −0.115265 | − | 0.993335i | \(-0.536772\pi\) | ||||
−0.115265 | + | 0.993335i | \(0.536772\pi\) | |||||||
\(602\) | −4.89898 | −0.199667 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 37.3939 | 1.52154 | ||||||||
\(605\) | 26.9444 | 1.09545 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.34847 | 0.379443 | 0.189721 | − | 0.981838i | \(-0.439242\pi\) | ||||
0.189721 | + | 0.981838i | \(0.439242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.6969 | 1.08093 | ||||||||
\(611\) | −34.7878 | −1.40736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.4949 | 1.55479 | 0.777397 | − | 0.629010i | \(-0.216540\pi\) | ||||
0.777397 | + | 0.629010i | \(0.216540\pi\) | |||||||
\(614\) | −50.3383 | −2.03149 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0000 | −1.08698 | −0.543490 | − | 0.839416i | \(-0.682897\pi\) | ||||
−0.543490 | + | 0.839416i | \(0.682897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.3485 | 0.737487 | 0.368744 | − | 0.929531i | \(-0.379788\pi\) | ||||
0.368744 | + | 0.929531i | \(0.379788\pi\) | |||||||
\(620\) | −78.3837 | −3.14796 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42.0000 | −1.68405 | ||||||||
\(623\) | 9.79796 | 0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −62.3383 | −2.49154 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.20204 | −0.247488 | ||||||||
\(629\) | −38.1464 | −1.52100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.7980 | 1.90281 | 0.951403 | − | 0.307948i | \(-0.0996421\pi\) | ||||
0.951403 | + | 0.307948i | \(0.0996421\pi\) | |||||||
\(632\) | −19.1010 | −0.759798 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −46.7878 | −1.85818 | ||||||||
\(635\) | −2.44949 | −0.0972050 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.89898 | −0.114862 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −48.0000 | −1.89737 | ||||||||
\(641\) | −1.89898 | −0.0750052 | −0.0375026 | − | 0.999297i | \(-0.511940\pi\) | ||||
−0.0375026 | + | 0.999297i | \(0.511940\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.34847 | 0.368668 | 0.184334 | − | 0.982864i | \(-0.440987\pi\) | ||||
0.184334 | + | 0.982864i | \(0.440987\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −59.3939 | −2.33682 | ||||||||
\(647\) | −44.6969 | −1.75722 | −0.878609 | − | 0.477542i | \(-0.841528\pi\) | ||||
−0.878609 | + | 0.477542i | \(0.841528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.10102 | 0.278525 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 68.0000 | 2.66309 | ||||||||
\(653\) | −26.4495 | −1.03505 | −0.517524 | − | 0.855669i | \(-0.673146\pi\) | ||||
−0.517524 | + | 0.855669i | \(0.673146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6515 | −0.416190 | ||||||||
\(656\) | −21.7980 | −0.851067 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.3939 | −1.14589 | ||||||||
\(659\) | 13.1010 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.6515 | −0.803251 | −0.401626 | − | 0.915804i | \(-0.631555\pi\) | ||||
−0.401626 | + | 0.915804i | \(0.631555\pi\) | |||||||
\(662\) | 45.1918 | 1.75643 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.3939 | 1.14070 | ||||||||
\(665\) | −10.8990 | −0.422644 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47.3939 | −1.83510 | ||||||||
\(668\) | −92.5857 | −3.58225 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −61.4847 | −2.37536 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.6969 | 1.68439 | 0.842197 | − | 0.539171i | \(-0.181262\pi\) | ||||
0.842197 | + | 0.539171i | \(0.181262\pi\) | |||||||
\(674\) | 57.1918 | 2.20295 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3837 | −0.707064 | ||||||||
\(677\) | 23.4495 | 0.901237 | 0.450619 | − | 0.892717i | \(-0.351203\pi\) | ||||
0.450619 | + | 0.892717i | \(0.351203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.34847 | −0.0901260 | ||||||||
\(680\) | 65.3939 | 2.50774 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.5959 | 0.979401 | 0.489700 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489700 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.39388 | 0.206089 | ||||||||
\(686\) | −2.44949 | −0.0935220 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 5.50510 | 0.209728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.5505 | 1.23828 | 0.619140 | − | 0.785281i | \(-0.287481\pi\) | ||||
0.619140 | + | 0.785281i | \(0.287481\pi\) | |||||||
\(692\) | −72.9898 | −2.77466 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.3485 | −1.64549 | ||||||||
\(695\) | 13.8434 | 0.525109 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.6969 | −1.12485 | ||||||||
\(698\) | 41.7526 | 1.58036 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | 0.151186 | ||||||||
\(701\) | 24.4949 | 0.925160 | 0.462580 | − | 0.886578i | \(-0.346924\pi\) | ||||
0.462580 | + | 0.886578i | \(0.346924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.1464 | −1.17471 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41.3939 | 1.55788 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3939 | 0.615685 | 0.307842 | − | 0.951437i | \(-0.400393\pi\) | ||||
0.307842 | + | 0.951437i | \(0.400393\pi\) | |||||||
\(710\) | −21.3031 | −0.799490 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −48.0000 | −1.79888 | ||||||||
\(713\) | −48.0000 | −1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −63.1918 | −2.36159 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 36.7423 | 1.37121 | ||||||||
\(719\) | 38.1464 | 1.42262 | 0.711311 | − | 0.702878i | \(-0.248102\pi\) | ||||
0.711311 | + | 0.702878i | \(0.248102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | −1.95459 | −0.0727424 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.5857 | 1.50836 | ||||||||
\(725\) | 7.89898 | 0.293361 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.6413 | 1.95236 | 0.976179 | − | 0.216965i | \(-0.0696158\pi\) | ||||
0.976179 | + | 0.216965i | \(0.0696158\pi\) | |||||||
\(728\) | 14.2020 | 0.526363 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.0908 | 0.743594 | ||||||||
\(731\) | 10.8990 | 0.403113 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.3485 | −1.08401 | −0.542005 | − | 0.840375i | \(-0.682335\pi\) | ||||
−0.542005 | + | 0.840375i | \(0.682335\pi\) | |||||||
\(734\) | −4.89898 | −0.180825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.30306 | −0.158291 | −0.0791453 | − | 0.996863i | \(-0.525219\pi\) | ||||
−0.0791453 | + | 0.996863i | \(0.525219\pi\) | |||||||
\(740\) | 68.5857 | 2.52126 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.65153 | 0.170763 | ||||||||
\(743\) | 23.6969 | 0.869356 | 0.434678 | − | 0.900586i | \(-0.356862\pi\) | ||||
0.434678 | + | 0.900586i | \(0.356862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.6969 | −1.85739 | ||||||||
\(746\) | −36.9898 | −1.35429 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.34847 | −0.268507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.6413 | 1.59249 | 0.796247 | − | 0.604971i | \(-0.206815\pi\) | ||||
0.796247 | + | 0.604971i | \(0.206815\pi\) | |||||||
\(752\) | 48.0000 | 1.75038 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 56.0908 | 2.04271 | ||||||||
\(755\) | −22.8990 | −0.833379 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.0908 | 1.56616 | 0.783081 | − | 0.621920i | \(-0.213647\pi\) | ||||
0.783081 | + | 0.621920i | \(0.213647\pi\) | |||||||
\(758\) | −48.9898 | −1.77939 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 53.3939 | 1.93680 | ||||||||
\(761\) | 53.6413 | 1.94450 | 0.972248 | − | 0.233952i | \(-0.0751657\pi\) | ||||
0.972248 | + | 0.233952i | \(0.0751657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.34847 | −0.193628 | ||||||||
\(764\) | 53.3939 | 1.93172 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −52.0454 | −1.88048 | ||||||||
\(767\) | −7.10102 | −0.256403 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.5505 | 1.17380 | 0.586901 | − | 0.809659i | \(-0.300348\pi\) | ||||
0.586901 | + | 0.809659i | \(0.300348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.2020 | 0.799069 | ||||||||
\(773\) | 51.2474 | 1.84324 | 0.921621 | − | 0.388090i | \(-0.126865\pi\) | ||||
0.921621 | + | 0.388090i | \(0.126865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 11.5051 | 0.413009 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −83.3939 | −2.98982 | ||||||||
\(779\) | −24.2474 | −0.868755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 80.0908 | 2.86404 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | 3.79796 | 0.135555 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 55.1464 | 1.96576 | 0.982879 | − | 0.184253i | \(-0.0589864\pi\) | ||||
0.982879 | + | 0.184253i | \(0.0589864\pi\) | |||||||
\(788\) | −33.7980 | −1.20400 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.3939 | 0.832317 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.8990 | −0.458056 | ||||||||
\(794\) | 16.4041 | 0.582159 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 80.0000 | 2.83552 | ||||||||
\(797\) | −8.20204 | −0.290531 | −0.145266 | − | 0.989393i | \(-0.546404\pi\) | ||||
−0.145266 | + | 0.989393i | \(0.546404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.3939 | 2.31347 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.742346 | −0.0262132 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6969 | 0.517999 | ||||||||
\(806\) | 56.8082 | 2.00098 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1464 | −0.391888 | −0.195944 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195944 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.4949 | 1.56243 | 0.781214 | − | 0.624264i | \(-0.214601\pi\) | ||||
0.781214 | + | 0.624264i | \(0.214601\pi\) | |||||||
\(812\) | 31.5959 | 1.10880 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.6413 | −1.45863 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.89898 | 0.311336 | ||||||||
\(818\) | −40.8990 | −1.43000 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 53.3939 | 1.86460 | ||||||||
\(821\) | −6.79796 | −0.237250 | −0.118625 | − | 0.992939i | \(-0.537849\pi\) | ||||
−0.118625 | + | 0.992939i | \(0.537849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0000 | −0.662298 | −0.331149 | − | 0.943578i | \(-0.607436\pi\) | ||||
−0.331149 | + | 0.943578i | \(0.607436\pi\) | |||||||
\(824\) | 19.5959 | 0.682656 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 24.7980 | 0.862310 | 0.431155 | − | 0.902278i | \(-0.358106\pi\) | ||||
0.431155 | + | 0.902278i | \(0.358106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.4949 | 1.12859 | 0.564297 | − | 0.825572i | \(-0.309147\pi\) | ||||
0.564297 | + | 0.825572i | \(0.309147\pi\) | |||||||
\(830\) | −36.0000 | −1.24958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23.1918 | 0.804032 | ||||||||
\(833\) | 5.44949 | 0.188814 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 56.6969 | 1.96208 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −77.3939 | −2.67353 | ||||||||
\(839\) | 37.8434 | 1.30650 | 0.653249 | − | 0.757143i | \(-0.273405\pi\) | ||||
0.653249 | + | 0.757143i | \(0.273405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.3939 | 1.15151 | ||||||||
\(842\) | −14.8082 | −0.510323 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −98.7878 | −3.40041 | ||||||||
\(845\) | 11.2577 | 0.387275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0000 | −0.377964 | ||||||||
\(848\) | −7.59592 | −0.260845 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.3485 | −0.457849 | ||||||||
\(851\) | 42.0000 | 1.43974 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.7423 | 0.607486 | 0.303743 | − | 0.952754i | \(-0.401764\pi\) | ||||
0.303743 | + | 0.952754i | \(0.401764\pi\) | |||||||
\(854\) | −10.8990 | −0.372955 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0000 | 1.23045 | ||||||||
\(857\) | −32.6969 | −1.11691 | −0.558453 | − | 0.829536i | \(-0.688605\pi\) | ||||
−0.558453 | + | 0.829536i | \(0.688605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.1464 | −1.23330 | −0.616650 | − | 0.787237i | \(-0.711511\pi\) | ||||
−0.616650 | + | 0.787237i | \(0.711511\pi\) | |||||||
\(860\) | −19.5959 | −0.668215 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.30306 | 0.112503 | ||||||||
\(863\) | 37.8990 | 1.29010 | 0.645048 | − | 0.764142i | \(-0.276837\pi\) | ||||
0.645048 | + | 0.764142i | \(0.276837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.6969 | 1.51974 | ||||||||
\(866\) | −1.59592 | −0.0542315 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.0000 | 1.08615 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.7071 | 1.00659 | ||||||||
\(872\) | 26.2020 | 0.887313 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 65.3939 | 2.21198 | ||||||||
\(875\) | 9.79796 | 0.331231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3031 | 0.482980 | 0.241490 | − | 0.970403i | \(-0.422364\pi\) | ||||
0.241490 | + | 0.970403i | \(0.422364\pi\) | |||||||
\(878\) | 35.1464 | 1.18613 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7526 | 0.598099 | 0.299049 | − | 0.954238i | \(-0.403330\pi\) | ||||
0.299049 | + | 0.954238i | \(0.403330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.202041 | −0.00679922 | −0.00339961 | − | 0.999994i | \(-0.501082\pi\) | ||||
−0.00339961 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(884\) | −63.1918 | −2.12537 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.7878 | 1.77344 | ||||||||
\(887\) | −4.89898 | −0.164492 | −0.0822458 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822458 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 58.7878 | 1.97057 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.2020 | 0.341590 | ||||||||
\(893\) | 53.3939 | 1.78676 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.6969 | 1.29350 | ||||||||
\(896\) | 19.5959 | 0.654654 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.7878 | 1.56133 | ||||||||
\(899\) | 63.1918 | 2.10757 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.3485 | −0.344757 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.3939 | −0.977626 | ||||||||
\(905\) | −24.8536 | −0.826161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.7980 | 1.08904 | 0.544519 | − | 0.838748i | \(-0.316712\pi\) | ||||
0.544519 | + | 0.838748i | \(0.316712\pi\) | |||||||
\(908\) | −48.0000 | −1.59294 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.3939 | −0.576601 | ||||||||
\(911\) | 20.6969 | 0.685720 | 0.342860 | − | 0.939386i | \(-0.388604\pi\) | ||||
0.342860 | + | 0.939386i | \(0.388604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −72.2474 | −2.38973 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.7980 | 0.984552 | ||||||||
\(917\) | 4.34847 | 0.143599 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7980 | 0.488140 | 0.244070 | − | 0.969758i | \(-0.421517\pi\) | ||||
0.244070 | + | 0.969758i | \(0.421517\pi\) | |||||||
\(920\) | −72.0000 | −2.37377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.6061 | −0.415161 | ||||||||
\(923\) | 10.2929 | 0.338793 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0.494897 | 0.0162633 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.2929 | −1.51882 | −0.759410 | − | 0.650613i | \(-0.774512\pi\) | ||||
−0.759410 | + | 0.650613i | \(0.774512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.44949 | 0.145826 | ||||||||
\(932\) | 31.5959 | 1.03496 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 77.3939 | 2.53241 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.3031 | −0.434592 | −0.217296 | − | 0.976106i | \(-0.569724\pi\) | ||||
−0.217296 | + | 0.976106i | \(0.569724\pi\) | |||||||
\(938\) | 25.1010 | 0.819577 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −117.576 | −3.83489 | ||||||||
\(941\) | −34.8434 | −1.13586 | −0.567931 | − | 0.823076i | \(-0.692256\pi\) | ||||
−0.567931 | + | 0.823076i | \(0.692256\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.6969 | 1.06476 | ||||||||
\(944\) | 9.79796 | 0.318896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.9898 | −1.49447 | −0.747234 | − | 0.664561i | \(-0.768618\pi\) | ||||
−0.747234 | + | 0.664561i | \(0.768618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.70714 | −0.315107 | ||||||||
\(950\) | −10.8990 | −0.353610 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.6969 | −0.865253 | ||||||||
\(953\) | 1.34847 | 0.0436812 | 0.0218406 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218406 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.6969 | −1.05805 | ||||||||
\(956\) | −12.0000 | −0.388108 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.95459 | 0.257001 | ||||||||
\(959\) | −2.20204 | −0.0711076 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −49.7071 | −1.60262 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.9898 | 0.676036 | ||||||||
\(965\) | −13.5959 | −0.437668 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9444 | 0.351948 | 0.175974 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175974 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(968\) | 53.8888 | 1.73205 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0908 | −0.452429 | ||||||||
\(971\) | −37.5959 | −1.20651 | −0.603255 | − | 0.797548i | \(-0.706130\pi\) | ||||
−0.603255 | + | 0.797548i | \(0.706130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.65153 | −0.181180 | ||||||||
\(974\) | 75.7980 | 2.42872 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.7980 | 0.569699 | ||||||||
\(977\) | 57.7980 | 1.84912 | 0.924560 | − | 0.381036i | \(-0.124433\pi\) | ||||
0.924560 | + | 0.381036i | \(0.124433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −9.79796 | −0.312984 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32.0908 | −1.02406 | ||||||||
\(983\) | −11.9444 | −0.380967 | −0.190483 | − | 0.981690i | \(-0.561006\pi\) | ||||
−0.190483 | + | 0.981690i | \(0.561006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.6969 | 0.659459 | ||||||||
\(986\) | −105.439 | −3.35787 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −51.5959 | −1.64148 | ||||||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4495 | 0.331939 | 0.165969 | − | 0.986131i | \(-0.446925\pi\) | ||||
0.165969 | + | 0.986131i | \(0.446925\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.69694 | 0.275850 | ||||||||
\(995\) | −48.9898 | −1.55308 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.50510 | 0.237689 | 0.118844 | − | 0.992913i | \(-0.462081\pi\) | ||||
0.118844 | + | 0.992913i | \(0.462081\pi\) | |||||||
\(998\) | −14.8082 | −0.468744 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.k.1.1 | 2 | ||
3.2 | odd | 2 | 2667.2.a.h.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.h.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
8001.2.a.k.1.1 | 2 | 1.1 | even | 1 | trivial |