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: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.118870813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 \) |
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 | 1.7 | ||
Root | \(1.13462\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48001 | 1.75363 | 0.876814 | − | 0.480829i | \(-0.159664\pi\) | ||||
0.876814 | + | 0.480829i | \(0.159664\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.15043 | 2.07521 | ||||||||
\(5\) | 0.783950 | 0.350593 | 0.175297 | − | 0.984516i | \(-0.443912\pi\) | ||||
0.175297 | + | 0.984516i | \(0.443912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 5.33307 | 1.88553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.94420 | 0.614810 | ||||||||
\(11\) | −4.88599 | −1.47318 | −0.736590 | − | 0.676340i | \(-0.763565\pi\) | ||||
−0.736590 | + | 0.676340i | \(0.763565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.65543 | −1.84589 | −0.922943 | − | 0.384937i | \(-0.874223\pi\) | ||||
−0.922943 | + | 0.384937i | \(0.874223\pi\) | |||||||
\(14\) | 2.48001 | 0.662809 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.92520 | 1.23130 | ||||||||
\(17\) | −1.25567 | −0.304544 | −0.152272 | − | 0.988339i | \(-0.548659\pi\) | ||||
−0.152272 | + | 0.988339i | \(0.548659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.07830 | −0.476795 | −0.238397 | − | 0.971168i | \(-0.576622\pi\) | ||||
−0.238397 | + | 0.971168i | \(0.576622\pi\) | |||||||
\(20\) | 3.25373 | 0.727556 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.1173 | −2.58341 | ||||||||
\(23\) | −6.86976 | −1.43244 | −0.716222 | − | 0.697872i | \(-0.754130\pi\) | ||||
−0.716222 | + | 0.697872i | \(0.754130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.38542 | −0.877084 | ||||||||
\(26\) | −16.5055 | −3.23700 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.15043 | 0.784357 | ||||||||
\(29\) | 9.79804 | 1.81945 | 0.909726 | − | 0.415210i | \(-0.136292\pi\) | ||||
0.909726 | + | 0.415210i | \(0.136292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.45591 | −0.620699 | −0.310349 | − | 0.950623i | \(-0.600446\pi\) | ||||
−0.310349 | + | 0.950623i | \(0.600446\pi\) | |||||||
\(32\) | 1.54837 | 0.273715 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.11406 | −0.534057 | ||||||||
\(35\) | 0.783950 | 0.132512 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.67789 | −0.440242 | −0.220121 | − | 0.975473i | \(-0.570645\pi\) | ||||
−0.220121 | + | 0.975473i | \(0.570645\pi\) | |||||||
\(38\) | −5.15419 | −0.836121 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.18086 | 0.661052 | ||||||||
\(41\) | 4.19977 | 0.655893 | 0.327947 | − | 0.944696i | \(-0.393643\pi\) | ||||
0.327947 | + | 0.944696i | \(0.393643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.11683 | −0.627811 | −0.313906 | − | 0.949454i | \(-0.601638\pi\) | ||||
−0.313906 | + | 0.949454i | \(0.601638\pi\) | |||||||
\(44\) | −20.2789 | −3.05716 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.0370 | −2.51198 | ||||||||
\(47\) | 6.51041 | 0.949640 | 0.474820 | − | 0.880083i | \(-0.342513\pi\) | ||||
0.474820 | + | 0.880083i | \(0.342513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −10.8759 | −1.53808 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −27.6229 | −3.83061 | ||||||||
\(53\) | −3.48731 | −0.479019 | −0.239510 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239510 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.83037 | −0.516487 | ||||||||
\(56\) | 5.33307 | 0.712662 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.2992 | 3.19064 | ||||||||
\(59\) | −12.2268 | −1.59180 | −0.795899 | − | 0.605430i | \(-0.793001\pi\) | ||||
−0.795899 | + | 0.605430i | \(0.793001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.13863 | 0.785971 | 0.392986 | − | 0.919545i | \(-0.371442\pi\) | ||||
0.392986 | + | 0.919545i | \(0.371442\pi\) | |||||||
\(62\) | −8.57067 | −1.08848 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.01043 | −0.751304 | ||||||||
\(65\) | −5.21753 | −0.647155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.0576 | −1.83958 | −0.919790 | − | 0.392412i | \(-0.871641\pi\) | ||||
−0.919790 | + | 0.392412i | \(0.871641\pi\) | |||||||
\(68\) | −5.21155 | −0.631994 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.94420 | 0.232376 | ||||||||
\(71\) | 7.18924 | 0.853206 | 0.426603 | − | 0.904439i | \(-0.359710\pi\) | ||||
0.426603 | + | 0.904439i | \(0.359710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.24951 | 0.263285 | 0.131643 | − | 0.991297i | \(-0.457975\pi\) | ||||
0.131643 | + | 0.991297i | \(0.457975\pi\) | |||||||
\(74\) | −6.64118 | −0.772021 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.62583 | −0.989451 | ||||||||
\(77\) | −4.88599 | −0.556810 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.38716 | −0.831120 | −0.415560 | − | 0.909566i | \(-0.636414\pi\) | ||||
−0.415560 | + | 0.909566i | \(0.636414\pi\) | |||||||
\(80\) | 3.86111 | 0.431685 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.4154 | 1.15019 | ||||||||
\(83\) | 3.82920 | 0.420310 | 0.210155 | − | 0.977668i | \(-0.432603\pi\) | ||||
0.210155 | + | 0.977668i | \(0.432603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.984380 | −0.106771 | ||||||||
\(86\) | −10.2098 | −1.10095 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −26.0573 | −2.77772 | ||||||||
\(89\) | 16.4372 | 1.74234 | 0.871171 | − | 0.490980i | \(-0.163361\pi\) | ||||
0.871171 | + | 0.490980i | \(0.163361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.65543 | −0.697679 | ||||||||
\(92\) | −28.5124 | −2.97263 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.1458 | 1.66532 | ||||||||
\(95\) | −1.62928 | −0.167161 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8967 | 1.71560 | 0.857798 | − | 0.513987i | \(-0.171832\pi\) | ||||
0.857798 | + | 0.513987i | \(0.171832\pi\) | |||||||
\(98\) | 2.48001 | 0.250518 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.2014 | −1.82014 | ||||||||
\(101\) | −0.691702 | −0.0688269 | −0.0344134 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344134 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5225 | −1.62801 | −0.814003 | − | 0.580861i | \(-0.802716\pi\) | ||||
−0.814003 | + | 0.580861i | \(0.802716\pi\) | |||||||
\(104\) | −35.4939 | −3.48047 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.64855 | −0.840022 | ||||||||
\(107\) | 19.1211 | 1.84851 | 0.924255 | − | 0.381776i | \(-0.124687\pi\) | ||||
0.924255 | + | 0.381776i | \(0.124687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7383 | 1.41167 | 0.705837 | − | 0.708374i | \(-0.250571\pi\) | ||||
0.705837 | + | 0.708374i | \(0.250571\pi\) | |||||||
\(110\) | −9.49933 | −0.905726 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.92520 | 0.465387 | ||||||||
\(113\) | −12.5353 | −1.17922 | −0.589612 | − | 0.807686i | \(-0.700719\pi\) | ||||
−0.589612 | + | 0.807686i | \(0.700719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.38555 | −0.502205 | ||||||||
\(116\) | 40.6661 | 3.77575 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −30.3226 | −2.79142 | ||||||||
\(119\) | −1.25567 | −0.115107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.8729 | 1.17026 | ||||||||
\(122\) | 15.2238 | 1.37830 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.3435 | −1.28808 | ||||||||
\(125\) | −7.35770 | −0.658093 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −18.0026 | −1.59122 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.9395 | −1.13487 | ||||||||
\(131\) | 0.687639 | 0.0600793 | 0.0300397 | − | 0.999549i | \(-0.490437\pi\) | ||||
0.0300397 | + | 0.999549i | \(0.490437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.07830 | −0.180211 | ||||||||
\(134\) | −37.3429 | −3.22594 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.69656 | −0.574225 | ||||||||
\(137\) | 7.96226 | 0.680262 | 0.340131 | − | 0.940378i | \(-0.389529\pi\) | ||||
0.340131 | + | 0.940378i | \(0.389529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.410908 | −0.0348528 | −0.0174264 | − | 0.999848i | \(-0.505547\pi\) | ||||
−0.0174264 | + | 0.999848i | \(0.505547\pi\) | |||||||
\(140\) | 3.25373 | 0.274990 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 17.8294 | 1.49621 | ||||||||
\(143\) | 32.5184 | 2.71932 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.68118 | 0.637887 | ||||||||
\(146\) | 5.57880 | 0.461705 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.1144 | −0.913597 | ||||||||
\(149\) | −23.6085 | −1.93408 | −0.967041 | − | 0.254620i | \(-0.918050\pi\) | ||||
−0.967041 | + | 0.254620i | \(0.918050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.43593 | −0.523748 | −0.261874 | − | 0.965102i | \(-0.584341\pi\) | ||||
−0.261874 | + | 0.965102i | \(0.584341\pi\) | |||||||
\(152\) | −11.0837 | −0.899009 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.1173 | −0.976438 | ||||||||
\(155\) | −2.70926 | −0.217613 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.4987 | −1.15712 | −0.578561 | − | 0.815639i | \(-0.696385\pi\) | ||||
−0.578561 | + | 0.815639i | \(0.696385\pi\) | |||||||
\(158\) | −18.3202 | −1.45748 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.21384 | 0.0959627 | ||||||||
\(161\) | −6.86976 | −0.541413 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.06383 | 0.631608 | 0.315804 | − | 0.948824i | \(-0.397726\pi\) | ||||
0.315804 | + | 0.948824i | \(0.397726\pi\) | |||||||
\(164\) | 17.4308 | 1.36112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.49645 | 0.737067 | ||||||||
\(167\) | −4.60533 | −0.356371 | −0.178186 | − | 0.983997i | \(-0.557023\pi\) | ||||
−0.178186 | + | 0.983997i | \(0.557023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.2948 | 2.40729 | ||||||||
\(170\) | −2.44127 | −0.187237 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.0866 | −1.30284 | ||||||||
\(173\) | 11.5019 | 0.874475 | 0.437237 | − | 0.899346i | \(-0.355957\pi\) | ||||
0.437237 | + | 0.899346i | \(0.355957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.38542 | −0.331507 | ||||||||
\(176\) | −24.0644 | −1.81393 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 40.7644 | 3.05542 | ||||||||
\(179\) | −22.8385 | −1.70703 | −0.853515 | − | 0.521068i | \(-0.825534\pi\) | ||||
−0.853515 | + | 0.521068i | \(0.825534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.40434 | 0.327372 | 0.163686 | − | 0.986512i | \(-0.447662\pi\) | ||||
0.163686 | + | 0.986512i | \(0.447662\pi\) | |||||||
\(182\) | −16.5055 | −1.22347 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.6369 | −2.70091 | ||||||||
\(185\) | −2.09933 | −0.154346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.13517 | 0.448648 | ||||||||
\(188\) | 27.0210 | 1.97071 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.04063 | −0.293138 | ||||||||
\(191\) | −20.5561 | −1.48739 | −0.743695 | − | 0.668520i | \(-0.766928\pi\) | ||||
−0.743695 | + | 0.668520i | \(0.766928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0715 | −1.30082 | −0.650409 | − | 0.759584i | \(-0.725402\pi\) | ||||
−0.650409 | + | 0.759584i | \(0.725402\pi\) | |||||||
\(194\) | 41.9038 | 3.00852 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.15043 | 0.296459 | ||||||||
\(197\) | 24.7109 | 1.76058 | 0.880291 | − | 0.474434i | \(-0.157347\pi\) | ||||
0.880291 | + | 0.474434i | \(0.157347\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.6604 | 1.18102 | 0.590511 | − | 0.807030i | \(-0.298926\pi\) | ||||
0.590511 | + | 0.807030i | \(0.298926\pi\) | |||||||
\(200\) | −23.3878 | −1.65377 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.71542 | −0.120697 | ||||||||
\(203\) | 9.79804 | 0.687688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29241 | 0.229952 | ||||||||
\(206\) | −40.9758 | −2.85492 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −32.7793 | −2.27284 | ||||||||
\(209\) | 10.1545 | 0.702404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5672 | 1.00284 | 0.501422 | − | 0.865203i | \(-0.332810\pi\) | ||||
0.501422 | + | 0.865203i | \(0.332810\pi\) | |||||||
\(212\) | −14.4738 | −0.994067 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 47.4205 | 3.24160 | ||||||||
\(215\) | −3.22739 | −0.220106 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.45591 | −0.234602 | ||||||||
\(218\) | 36.5511 | 2.47555 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.8977 | −1.07182 | ||||||||
\(221\) | 8.35701 | 0.562153 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.76267 | −0.653757 | −0.326878 | − | 0.945066i | \(-0.605997\pi\) | ||||
−0.326878 | + | 0.945066i | \(0.605997\pi\) | |||||||
\(224\) | 1.54837 | 0.103455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.0877 | −2.06792 | ||||||||
\(227\) | 26.0747 | 1.73064 | 0.865321 | − | 0.501219i | \(-0.167115\pi\) | ||||
0.865321 | + | 0.501219i | \(0.167115\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.24716 | 0.412824 | 0.206412 | − | 0.978465i | \(-0.433821\pi\) | ||||
0.206412 | + | 0.978465i | \(0.433821\pi\) | |||||||
\(230\) | −13.3562 | −0.880681 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 52.2537 | 3.43062 | ||||||||
\(233\) | −6.77809 | −0.444047 | −0.222024 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222024 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.10383 | 0.332937 | ||||||||
\(236\) | −50.7466 | −3.30332 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.11406 | −0.201855 | ||||||||
\(239\) | 23.7065 | 1.53345 | 0.766724 | − | 0.641977i | \(-0.221885\pi\) | ||||
0.766724 | + | 0.641977i | \(0.221885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.28434 | −0.598057 | −0.299028 | − | 0.954244i | \(-0.596663\pi\) | ||||
−0.299028 | + | 0.954244i | \(0.596663\pi\) | |||||||
\(242\) | 31.9247 | 2.05220 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25.4779 | 1.63106 | ||||||||
\(245\) | 0.783950 | 0.0500847 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8320 | 0.880108 | ||||||||
\(248\) | −18.4306 | −1.17034 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.2471 | −1.15405 | ||||||||
\(251\) | −0.539366 | −0.0340445 | −0.0170222 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170222 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.5656 | 2.11025 | ||||||||
\(254\) | −2.48001 | −0.155609 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.6258 | −2.03911 | ||||||||
\(257\) | 4.16847 | 0.260022 | 0.130011 | − | 0.991513i | \(-0.458499\pi\) | ||||
0.130011 | + | 0.991513i | \(0.458499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.67789 | −0.166396 | ||||||||
\(260\) | −21.6550 | −1.34298 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.70535 | 0.105357 | ||||||||
\(263\) | 23.9281 | 1.47547 | 0.737734 | − | 0.675092i | \(-0.235896\pi\) | ||||
0.737734 | + | 0.675092i | \(0.235896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.73388 | −0.167941 | ||||||||
\(266\) | −5.15419 | −0.316024 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −62.4955 | −3.81752 | ||||||||
\(269\) | 30.9708 | 1.88832 | 0.944160 | − | 0.329487i | \(-0.106876\pi\) | ||||
0.944160 | + | 0.329487i | \(0.106876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8214 | −1.44705 | −0.723523 | − | 0.690300i | \(-0.757478\pi\) | ||||
−0.723523 | + | 0.690300i | \(0.757478\pi\) | |||||||
\(272\) | −6.18440 | −0.374985 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.7465 | 1.19293 | ||||||||
\(275\) | 21.4271 | 1.29210 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3357 | −0.861351 | −0.430675 | − | 0.902507i | \(-0.641725\pi\) | ||||
−0.430675 | + | 0.902507i | \(0.641725\pi\) | |||||||
\(278\) | −1.01905 | −0.0611188 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.18086 | 0.249854 | ||||||||
\(281\) | −20.6212 | −1.23016 | −0.615079 | − | 0.788466i | \(-0.710876\pi\) | ||||
−0.615079 | + | 0.788466i | \(0.710876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.77609 | 0.224465 | 0.112233 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112233 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(284\) | 29.8384 | 1.77058 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 80.6457 | 4.76868 | ||||||||
\(287\) | 4.19977 | 0.247904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4233 | −0.907253 | ||||||||
\(290\) | 19.0494 | 1.11862 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.33644 | 0.546374 | ||||||||
\(293\) | 24.2919 | 1.41915 | 0.709573 | − | 0.704632i | \(-0.248888\pi\) | ||||
0.709573 | + | 0.704632i | \(0.248888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.58522 | −0.558073 | ||||||||
\(296\) | −14.2814 | −0.830088 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −58.5492 | −3.39166 | ||||||||
\(299\) | 45.7212 | 2.64413 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.11683 | −0.237290 | ||||||||
\(302\) | −15.9611 | −0.918460 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.2360 | −0.587077 | ||||||||
\(305\) | 4.81238 | 0.275556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6482 | −1.06431 | −0.532153 | − | 0.846648i | \(-0.678617\pi\) | ||||
−0.532153 | + | 0.846648i | \(0.678617\pi\) | |||||||
\(308\) | −20.2789 | −1.15550 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.71897 | −0.381612 | ||||||||
\(311\) | −20.8747 | −1.18370 | −0.591848 | − | 0.806050i | \(-0.701601\pi\) | ||||
−0.591848 | + | 0.806050i | \(0.701601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.93347 | −0.448426 | −0.224213 | − | 0.974540i | \(-0.571981\pi\) | ||||
−0.224213 | + | 0.974540i | \(0.571981\pi\) | |||||||
\(314\) | −35.9568 | −2.02916 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −30.6599 | −1.72475 | ||||||||
\(317\) | −11.3644 | −0.638290 | −0.319145 | − | 0.947706i | \(-0.603396\pi\) | ||||
−0.319145 | + | 0.947706i | \(0.603396\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.8731 | −2.68038 | ||||||||
\(320\) | −4.71188 | −0.263402 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.0370 | −0.949437 | ||||||||
\(323\) | 2.60965 | 0.145205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.1869 | 1.61900 | ||||||||
\(326\) | 19.9983 | 1.10761 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.3977 | 1.23670 | ||||||||
\(329\) | 6.51041 | 0.358930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1983 | −1.05523 | −0.527616 | − | 0.849483i | \(-0.676914\pi\) | ||||
−0.527616 | + | 0.849483i | \(0.676914\pi\) | |||||||
\(332\) | 15.8928 | 0.872233 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.4213 | −0.624943 | ||||||||
\(335\) | −11.8044 | −0.644944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.90770 | 0.485234 | 0.242617 | − | 0.970122i | \(-0.421994\pi\) | ||||
0.242617 | + | 0.970122i | \(0.421994\pi\) | |||||||
\(338\) | 77.6113 | 4.22150 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.08560 | −0.221573 | ||||||||
\(341\) | 16.8855 | 0.914401 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −21.9554 | −1.18375 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.5248 | 1.53350 | ||||||||
\(347\) | 1.17952 | 0.0633201 | 0.0316601 | − | 0.999499i | \(-0.489921\pi\) | ||||
0.0316601 | + | 0.999499i | \(0.489921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.5422 | −1.58136 | −0.790679 | − | 0.612231i | \(-0.790272\pi\) | ||||
−0.790679 | + | 0.612231i | \(0.790272\pi\) | |||||||
\(350\) | −10.8759 | −0.581340 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.56530 | −0.403232 | ||||||||
\(353\) | −10.1955 | −0.542653 | −0.271327 | − | 0.962487i | \(-0.587462\pi\) | ||||
−0.271327 | + | 0.962487i | \(0.587462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.63601 | 0.299128 | ||||||||
\(356\) | 68.2215 | 3.61573 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −56.6396 | −2.99350 | ||||||||
\(359\) | −30.6151 | −1.61580 | −0.807900 | − | 0.589319i | \(-0.799396\pi\) | ||||
−0.807900 | + | 0.589319i | \(0.799396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6807 | −0.772667 | ||||||||
\(362\) | 10.9228 | 0.574089 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −27.6229 | −1.44783 | ||||||||
\(365\) | 1.76350 | 0.0923061 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8181 | −0.564702 | −0.282351 | − | 0.959311i | \(-0.591114\pi\) | ||||
−0.282351 | + | 0.959311i | \(0.591114\pi\) | |||||||
\(368\) | −33.8349 | −1.76377 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.20635 | −0.270665 | ||||||||
\(371\) | −3.48731 | −0.181052 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2006 | 0.528169 | 0.264085 | − | 0.964499i | \(-0.414930\pi\) | ||||
0.264085 | + | 0.964499i | \(0.414930\pi\) | |||||||
\(374\) | 15.2153 | 0.786762 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.7205 | 1.79057 | ||||||||
\(377\) | −65.2102 | −3.35850 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.58231 | 0.338110 | 0.169055 | − | 0.985607i | \(-0.445928\pi\) | ||||
0.169055 | + | 0.985607i | \(0.445928\pi\) | |||||||
\(380\) | −6.76222 | −0.346895 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −50.9793 | −2.60833 | ||||||||
\(383\) | 20.2431 | 1.03438 | 0.517188 | − | 0.855872i | \(-0.326979\pi\) | ||||
0.517188 | + | 0.855872i | \(0.326979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.83037 | −0.195214 | ||||||||
\(386\) | −44.8175 | −2.28115 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 70.1283 | 3.56023 | ||||||||
\(389\) | −8.10612 | −0.410997 | −0.205498 | − | 0.978657i | \(-0.565882\pi\) | ||||
−0.205498 | + | 0.978657i | \(0.565882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.62613 | 0.436242 | ||||||||
\(392\) | 5.33307 | 0.269361 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 61.2833 | 3.08741 | ||||||||
\(395\) | −5.79116 | −0.291385 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.9348 | −0.799745 | −0.399872 | − | 0.916571i | \(-0.630946\pi\) | ||||
−0.399872 | + | 0.916571i | \(0.630946\pi\) | |||||||
\(398\) | 41.3178 | 2.07107 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −21.5991 | −1.07995 | ||||||||
\(401\) | −35.9972 | −1.79761 | −0.898807 | − | 0.438344i | \(-0.855565\pi\) | ||||
−0.898807 | + | 0.438344i | \(0.855565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.0006 | 1.14574 | ||||||||
\(404\) | −2.87086 | −0.142831 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.2992 | 1.20595 | ||||||||
\(407\) | 13.0841 | 0.648556 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3091 | −1.05367 | −0.526833 | − | 0.849969i | \(-0.676621\pi\) | ||||
−0.526833 | + | 0.849969i | \(0.676621\pi\) | |||||||
\(410\) | 8.16519 | 0.403250 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −68.5752 | −3.37846 | ||||||||
\(413\) | −12.2268 | −0.601643 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.00190 | 0.147358 | ||||||||
\(416\) | −10.3051 | −0.505247 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.1833 | 1.23176 | ||||||||
\(419\) | 26.8399 | 1.31122 | 0.655608 | − | 0.755101i | \(-0.272412\pi\) | ||||
0.655608 | + | 0.755101i | \(0.272412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.71312 | 0.0834923 | 0.0417462 | − | 0.999128i | \(-0.486708\pi\) | ||||
0.0417462 | + | 0.999128i | \(0.486708\pi\) | |||||||
\(422\) | 36.1266 | 1.75862 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.5981 | −0.903203 | ||||||||
\(425\) | 5.50663 | 0.267111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.13863 | 0.297069 | ||||||||
\(428\) | 79.3609 | 3.83605 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00395 | −0.385985 | ||||||||
\(431\) | −29.8518 | −1.43791 | −0.718954 | − | 0.695057i | \(-0.755379\pi\) | ||||
−0.718954 | + | 0.695057i | \(0.755379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.53077 | −0.313849 | −0.156924 | − | 0.987611i | \(-0.550158\pi\) | ||||
−0.156924 | + | 0.987611i | \(0.550158\pi\) | |||||||
\(434\) | −8.57067 | −0.411405 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 61.1703 | 2.92953 | ||||||||
\(437\) | 14.2774 | 0.682982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9276 | −0.712457 | −0.356228 | − | 0.934399i | \(-0.615938\pi\) | ||||
−0.356228 | + | 0.934399i | \(0.615938\pi\) | |||||||
\(440\) | −20.4276 | −0.973849 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.7254 | 0.985808 | ||||||||
\(443\) | 4.63421 | 0.220178 | 0.110089 | − | 0.993922i | \(-0.464886\pi\) | ||||
0.110089 | + | 0.993922i | \(0.464886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8860 | 0.610853 | ||||||||
\(446\) | −24.2115 | −1.14645 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.01043 | −0.283966 | ||||||||
\(449\) | 6.63579 | 0.313162 | 0.156581 | − | 0.987665i | \(-0.449953\pi\) | ||||
0.156581 | + | 0.987665i | \(0.449953\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.5200 | −0.966249 | ||||||||
\(452\) | −52.0270 | −2.44714 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 64.6655 | 3.03490 | ||||||||
\(455\) | −5.21753 | −0.244601 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6826 | −0.827157 | −0.413578 | − | 0.910468i | \(-0.635721\pi\) | ||||
−0.413578 | + | 0.910468i | \(0.635721\pi\) | |||||||
\(458\) | 15.4930 | 0.723940 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.3523 | −1.04218 | ||||||||
\(461\) | 40.2668 | 1.87541 | 0.937706 | − | 0.347431i | \(-0.112946\pi\) | ||||
0.937706 | + | 0.347431i | \(0.112946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.88536 | −0.180568 | −0.0902841 | − | 0.995916i | \(-0.528777\pi\) | ||||
−0.0902841 | + | 0.995916i | \(0.528777\pi\) | |||||||
\(464\) | 48.2573 | 2.24029 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.8097 | −0.778694 | ||||||||
\(467\) | 1.32929 | 0.0615123 | 0.0307561 | − | 0.999527i | \(-0.490208\pi\) | ||||
0.0307561 | + | 0.999527i | \(0.490208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0576 | −0.695296 | ||||||||
\(470\) | 12.6575 | 0.583849 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −65.2066 | −3.00138 | ||||||||
\(473\) | 20.1148 | 0.924879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.11422 | 0.418189 | ||||||||
\(476\) | −5.21155 | −0.238871 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 58.7923 | 2.68910 | ||||||||
\(479\) | 10.9654 | 0.501022 | 0.250511 | − | 0.968114i | \(-0.419401\pi\) | ||||
0.250511 | + | 0.968114i | \(0.419401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8225 | 0.812637 | ||||||||
\(482\) | −23.0252 | −1.04877 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 53.4278 | 2.42854 | ||||||||
\(485\) | 13.2461 | 0.601476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.42363 | 0.336397 | 0.168198 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168198 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(488\) | 32.7378 | 1.48197 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.94420 | 0.0878300 | ||||||||
\(491\) | −10.4742 | −0.472694 | −0.236347 | − | 0.971669i | \(-0.575950\pi\) | ||||
−0.236347 | + | 0.971669i | \(0.575950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3031 | −0.554103 | ||||||||
\(494\) | 34.3034 | 1.54338 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.0210 | −0.764266 | ||||||||
\(497\) | 7.18924 | 0.322482 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.6794 | 1.19433 | 0.597167 | − | 0.802117i | \(-0.296293\pi\) | ||||
0.597167 | + | 0.802117i | \(0.296293\pi\) | |||||||
\(500\) | −30.5376 | −1.36568 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.33763 | −0.0597013 | ||||||||
\(503\) | −27.1665 | −1.21129 | −0.605646 | − | 0.795734i | \(-0.707085\pi\) | ||||
−0.605646 | + | 0.795734i | \(0.707085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.542259 | −0.0241302 | ||||||||
\(506\) | 83.2428 | 3.70059 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.15043 | −0.184145 | ||||||||
\(509\) | 5.67100 | 0.251363 | 0.125681 | − | 0.992071i | \(-0.459888\pi\) | ||||
0.125681 | + | 0.992071i | \(0.459888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.24951 | 0.0995126 | ||||||||
\(512\) | −44.9069 | −1.98462 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.3378 | 0.455982 | ||||||||
\(515\) | −12.9528 | −0.570767 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.8098 | −1.39899 | ||||||||
\(518\) | −6.64118 | −0.291797 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −27.8255 | −1.22023 | ||||||||
\(521\) | −32.7163 | −1.43333 | −0.716664 | − | 0.697419i | \(-0.754332\pi\) | ||||
−0.716664 | + | 0.697419i | \(0.754332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.8450 | 0.911486 | 0.455743 | − | 0.890111i | \(-0.349374\pi\) | ||||
0.455743 | + | 0.890111i | \(0.349374\pi\) | |||||||
\(524\) | 2.85400 | 0.124677 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 59.3417 | 2.58742 | ||||||||
\(527\) | 4.33946 | 0.189030 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.1936 | 1.05190 | ||||||||
\(530\) | −6.78003 | −0.294506 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.62583 | −0.373977 | ||||||||
\(533\) | −27.9513 | −1.21070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9900 | 0.648075 | ||||||||
\(536\) | −80.3033 | −3.46857 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 76.8077 | 3.31141 | ||||||||
\(539\) | −4.88599 | −0.210454 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.1270 | −0.908319 | −0.454159 | − | 0.890920i | \(-0.650060\pi\) | ||||
−0.454159 | + | 0.890920i | \(0.650060\pi\) | |||||||
\(542\) | −59.0772 | −2.53758 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.94423 | −0.0833583 | ||||||||
\(545\) | 11.5541 | 0.494923 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1713 | 0.434895 | 0.217448 | − | 0.976072i | \(-0.430227\pi\) | ||||
0.217448 | + | 0.976072i | \(0.430227\pi\) | |||||||
\(548\) | 33.0468 | 1.41169 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 53.1394 | 2.26587 | ||||||||
\(551\) | −20.3633 | −0.867504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.38716 | −0.314134 | ||||||||
\(554\) | −35.5527 | −1.51049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.70544 | −0.0723270 | ||||||||
\(557\) | 29.5187 | 1.25075 | 0.625373 | − | 0.780326i | \(-0.284947\pi\) | ||||
0.625373 | + | 0.780326i | \(0.284947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.3993 | 1.15887 | ||||||||
\(560\) | 3.86111 | 0.163162 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −51.1407 | −2.15724 | ||||||||
\(563\) | −29.4720 | −1.24210 | −0.621049 | − | 0.783772i | \(-0.713293\pi\) | ||||
−0.621049 | + | 0.783772i | \(0.713293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.82707 | −0.413428 | ||||||||
\(566\) | 9.36473 | 0.393629 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.3408 | 1.60874 | ||||||||
\(569\) | −18.1639 | −0.761471 | −0.380735 | − | 0.924684i | \(-0.624329\pi\) | ||||
−0.380735 | + | 0.924684i | \(0.624329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.20524 | −0.217832 | −0.108916 | − | 0.994051i | \(-0.534738\pi\) | ||||
−0.108916 | + | 0.994051i | \(0.534738\pi\) | |||||||
\(572\) | 134.965 | 5.64317 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.4154 | 0.434732 | ||||||||
\(575\) | 30.1268 | 1.25637 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5036 | 0.936835 | 0.468418 | − | 0.883507i | \(-0.344824\pi\) | ||||
0.468418 | + | 0.883507i | \(0.344824\pi\) | |||||||
\(578\) | −38.2499 | −1.59099 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 31.8802 | 1.32375 | ||||||||
\(581\) | 3.82920 | 0.158862 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.0390 | 0.705681 | ||||||||
\(584\) | 11.9968 | 0.496432 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 60.2440 | 2.48866 | ||||||||
\(587\) | 11.1742 | 0.461208 | 0.230604 | − | 0.973048i | \(-0.425930\pi\) | ||||
0.230604 | + | 0.973048i | \(0.425930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.18241 | 0.295946 | ||||||||
\(590\) | −23.7714 | −0.978653 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.1891 | −0.542070 | ||||||||
\(593\) | −10.7553 | −0.441669 | −0.220835 | − | 0.975311i | \(-0.570878\pi\) | ||||
−0.220835 | + | 0.975311i | \(0.570878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.984380 | −0.0403556 | ||||||||
\(596\) | −97.9853 | −4.01364 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 113.389 | 4.63682 | ||||||||
\(599\) | −16.4493 | −0.672099 | −0.336049 | − | 0.941844i | \(-0.609091\pi\) | ||||
−0.336049 | + | 0.941844i | \(0.609091\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6614 | 1.00596 | 0.502979 | − | 0.864298i | \(-0.332237\pi\) | ||||
0.502979 | + | 0.864298i | \(0.332237\pi\) | |||||||
\(602\) | −10.2098 | −0.416119 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.7118 | −1.08689 | ||||||||
\(605\) | 10.0917 | 0.410285 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.40510 | −0.259975 | −0.129988 | − | 0.991516i | \(-0.541494\pi\) | ||||
−0.129988 | + | 0.991516i | \(0.541494\pi\) | |||||||
\(608\) | −3.21797 | −0.130506 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.9347 | 0.483223 | ||||||||
\(611\) | −43.3296 | −1.75293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.77647 | 0.394868 | 0.197434 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197434 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(614\) | −46.2475 | −1.86640 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.0573 | −1.04988 | ||||||||
\(617\) | −36.0074 | −1.44960 | −0.724802 | − | 0.688958i | \(-0.758069\pi\) | ||||
−0.724802 | + | 0.688958i | \(0.758069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4220 | −0.740441 | −0.370220 | − | 0.928944i | \(-0.620718\pi\) | ||||
−0.370220 | + | 0.928944i | \(0.620718\pi\) | |||||||
\(620\) | −11.2446 | −0.451593 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −51.7694 | −2.07576 | ||||||||
\(623\) | 16.4372 | 0.658543 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.1590 | 0.646362 | ||||||||
\(626\) | −19.6750 | −0.786373 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −60.1758 | −2.40127 | ||||||||
\(629\) | 3.36254 | 0.134073 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.8713 | −0.870682 | −0.435341 | − | 0.900266i | \(-0.643372\pi\) | ||||
−0.435341 | + | 0.900266i | \(0.643372\pi\) | |||||||
\(632\) | −39.3962 | −1.56710 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.1838 | −1.11932 | ||||||||
\(635\) | −0.783950 | −0.0311101 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.65543 | −0.263698 | ||||||||
\(638\) | −118.726 | −4.70039 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.1132 | −0.557872 | ||||||||
\(641\) | 5.35545 | 0.211527 | 0.105764 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.1586 | 0.479488 | 0.239744 | − | 0.970836i | \(-0.422936\pi\) | ||||
0.239744 | + | 0.970836i | \(0.422936\pi\) | |||||||
\(644\) | −28.5124 | −1.12355 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.47195 | 0.254635 | ||||||||
\(647\) | 3.92615 | 0.154353 | 0.0771764 | − | 0.997017i | \(-0.475410\pi\) | ||||
0.0771764 | + | 0.997017i | \(0.475410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 59.7401 | 2.34500 | ||||||||
\(650\) | 72.3837 | 2.83912 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.4683 | 1.31072 | ||||||||
\(653\) | −3.49414 | −0.136736 | −0.0683681 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683681 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.539075 | 0.0210634 | ||||||||
\(656\) | 20.6847 | 0.807601 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.1458 | 0.629431 | ||||||||
\(659\) | −26.1167 | −1.01736 | −0.508682 | − | 0.860955i | \(-0.669867\pi\) | ||||
−0.508682 | + | 0.860955i | \(0.669867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.1023 | −1.32643 | −0.663213 | − | 0.748431i | \(-0.730808\pi\) | ||||
−0.663213 | + | 0.748431i | \(0.730808\pi\) | |||||||
\(662\) | −47.6118 | −1.85049 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.4214 | 0.792505 | ||||||||
\(665\) | −1.62928 | −0.0631809 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −67.3102 | −2.60626 | ||||||||
\(668\) | −19.1141 | −0.739547 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.2750 | −1.13099 | ||||||||
\(671\) | −29.9933 | −1.15788 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3642 | −0.438058 | −0.219029 | − | 0.975718i | \(-0.570289\pi\) | ||||
−0.219029 | + | 0.975718i | \(0.570289\pi\) | |||||||
\(674\) | 22.0912 | 0.850920 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 129.887 | 4.99565 | ||||||||
\(677\) | 8.47890 | 0.325870 | 0.162935 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162935 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8967 | 0.648434 | ||||||||
\(680\) | −5.24977 | −0.201319 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 41.8761 | 1.60352 | ||||||||
\(683\) | −13.5516 | −0.518537 | −0.259269 | − | 0.965805i | \(-0.583482\pi\) | ||||
−0.259269 | + | 0.965805i | \(0.583482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.24201 | 0.238495 | ||||||||
\(686\) | 2.48001 | 0.0946871 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.2762 | −0.773023 | ||||||||
\(689\) | 23.2096 | 0.884214 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.4677 | −1.65359 | −0.826794 | − | 0.562505i | \(-0.809838\pi\) | ||||
−0.826794 | + | 0.562505i | \(0.809838\pi\) | |||||||
\(692\) | 47.7379 | 1.81472 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.92522 | 0.111040 | ||||||||
\(695\) | −0.322131 | −0.0122191 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.27351 | −0.199748 | ||||||||
\(698\) | −73.2649 | −2.77312 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.2014 | −0.687947 | ||||||||
\(701\) | −28.8144 | −1.08831 | −0.544153 | − | 0.838986i | \(-0.683149\pi\) | ||||
−0.544153 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.56545 | 0.209905 | ||||||||
\(704\) | 29.3669 | 1.10681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.2850 | −0.951612 | ||||||||
\(707\) | −0.691702 | −0.0260141 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9862 | −0.788154 | −0.394077 | − | 0.919077i | \(-0.628936\pi\) | ||||
−0.394077 | + | 0.919077i | \(0.628936\pi\) | |||||||
\(710\) | 13.9773 | 0.524560 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 87.6609 | 3.28523 | ||||||||
\(713\) | 23.7412 | 0.889117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.4928 | 0.953375 | ||||||||
\(716\) | −94.7896 | −3.54245 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −75.9255 | −2.83351 | ||||||||
\(719\) | 4.40085 | 0.164124 | 0.0820620 | − | 0.996627i | \(-0.473849\pi\) | ||||
0.0820620 | + | 0.996627i | \(0.473849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5225 | −0.615328 | ||||||||
\(722\) | −36.4081 | −1.35497 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.2799 | 0.679368 | ||||||||
\(725\) | −42.9686 | −1.59581 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6396 | 0.802568 | 0.401284 | − | 0.915954i | \(-0.368564\pi\) | ||||
0.401284 | + | 0.915954i | \(0.368564\pi\) | |||||||
\(728\) | −35.4939 | −1.31549 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.37350 | 0.161871 | ||||||||
\(731\) | 5.16937 | 0.191196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.9010 | 1.14136 | 0.570678 | − | 0.821174i | \(-0.306680\pi\) | ||||
0.570678 | + | 0.821174i | \(0.306680\pi\) | |||||||
\(734\) | −26.8291 | −0.990279 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.6369 | −0.392082 | ||||||||
\(737\) | 73.5712 | 2.71003 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.2746 | −1.18724 | −0.593620 | − | 0.804745i | \(-0.702302\pi\) | ||||
−0.593620 | + | 0.804745i | \(0.702302\pi\) | |||||||
\(740\) | −8.71312 | −0.320301 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.64855 | −0.317498 | ||||||||
\(743\) | −28.5122 | −1.04601 | −0.523006 | − | 0.852329i | \(-0.675190\pi\) | ||||
−0.523006 | + | 0.852329i | \(0.675190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.5079 | −0.678076 | ||||||||
\(746\) | 25.2977 | 0.926213 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 25.4636 | 0.931040 | ||||||||
\(749\) | 19.1211 | 0.698671 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0517 | −0.877659 | −0.438829 | − | 0.898570i | \(-0.644607\pi\) | ||||
−0.438829 | + | 0.898570i | \(0.644607\pi\) | |||||||
\(752\) | 32.0650 | 1.16929 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −161.722 | −5.88956 | ||||||||
\(755\) | −5.04544 | −0.183623 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.1952 | −1.20650 | −0.603249 | − | 0.797553i | \(-0.706128\pi\) | ||||
−0.603249 | + | 0.797553i | \(0.706128\pi\) | |||||||
\(758\) | 16.3242 | 0.592920 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.68908 | −0.315186 | ||||||||
\(761\) | −27.5176 | −0.997511 | −0.498755 | − | 0.866743i | \(-0.666209\pi\) | ||||
−0.498755 | + | 0.866743i | \(0.666209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.7383 | 0.533563 | ||||||||
\(764\) | −85.3167 | −3.08665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.2031 | 1.81391 | ||||||||
\(767\) | 81.3748 | 2.93828 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6074 | −0.526757 | −0.263378 | − | 0.964693i | \(-0.584837\pi\) | ||||
−0.263378 | + | 0.964693i | \(0.584837\pi\) | |||||||
\(770\) | −9.49933 | −0.342332 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −75.0046 | −2.69948 | ||||||||
\(773\) | −4.97622 | −0.178982 | −0.0894912 | − | 0.995988i | \(-0.528524\pi\) | ||||
−0.0894912 | + | 0.995988i | \(0.528524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.1556 | 0.544405 | ||||||||
\(776\) | 90.1111 | 3.23480 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.1032 | −0.720736 | ||||||||
\(779\) | −8.72837 | −0.312726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.1265 | −1.25693 | ||||||||
\(782\) | 21.3928 | 0.765007 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.92520 | 0.175900 | ||||||||
\(785\) | −11.3662 | −0.405679 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.1321 | 0.717633 | 0.358816 | − | 0.933408i | \(-0.383180\pi\) | ||||
0.358816 | + | 0.933408i | \(0.383180\pi\) | |||||||
\(788\) | 102.561 | 3.65358 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.3621 | −0.510981 | ||||||||
\(791\) | −12.5353 | −0.445705 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.8553 | −1.45081 | ||||||||
\(794\) | −39.5184 | −1.40246 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 69.1476 | 2.45087 | ||||||||
\(797\) | 35.3654 | 1.25271 | 0.626354 | − | 0.779539i | \(-0.284546\pi\) | ||||
0.626354 | + | 0.779539i | \(0.284546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.17490 | −0.289207 | ||||||||
\(800\) | −6.79025 | −0.240071 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −89.2733 | −3.15235 | ||||||||
\(803\) | −10.9911 | −0.387867 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.38555 | −0.189816 | ||||||||
\(806\) | 57.0415 | 2.00920 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.68890 | −0.129775 | ||||||||
\(809\) | −9.88279 | −0.347460 | −0.173730 | − | 0.984793i | \(-0.555582\pi\) | ||||
−0.173730 | + | 0.984793i | \(0.555582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.3646 | 1.03113 | 0.515566 | − | 0.856850i | \(-0.327582\pi\) | ||||
0.515566 | + | 0.856850i | \(0.327582\pi\) | |||||||
\(812\) | 40.6661 | 1.42710 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.4487 | 1.13733 | ||||||||
\(815\) | 6.32164 | 0.221437 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.55601 | 0.299337 | ||||||||
\(818\) | −52.8466 | −1.84774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.6649 | 0.477199 | ||||||||
\(821\) | 11.5855 | 0.404338 | 0.202169 | − | 0.979351i | \(-0.435201\pi\) | ||||
0.202169 | + | 0.979351i | \(0.435201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4979 | 1.13281 | 0.566404 | − | 0.824128i | \(-0.308334\pi\) | ||||
0.566404 | + | 0.824128i | \(0.308334\pi\) | |||||||
\(824\) | −88.1154 | −3.06965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.3226 | −1.05506 | ||||||||
\(827\) | 34.8327 | 1.21125 | 0.605626 | − | 0.795749i | \(-0.292923\pi\) | ||||
0.605626 | + | 0.795749i | \(0.292923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0563 | 0.870241 | 0.435120 | − | 0.900372i | \(-0.356706\pi\) | ||||
0.435120 | + | 0.900372i | \(0.356706\pi\) | |||||||
\(830\) | 7.44474 | 0.258411 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 40.0020 | 1.38682 | ||||||||
\(833\) | −1.25567 | −0.0435063 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.61035 | −0.124941 | ||||||||
\(836\) | 42.1457 | 1.45764 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 66.5632 | 2.29939 | ||||||||
\(839\) | 16.0782 | 0.555082 | 0.277541 | − | 0.960714i | \(-0.410481\pi\) | ||||
0.277541 | + | 0.960714i | \(0.410481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67.0017 | 2.31040 | ||||||||
\(842\) | 4.24855 | 0.146415 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 60.4599 | 2.08112 | ||||||||
\(845\) | 24.5336 | 0.843980 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8729 | 0.442316 | ||||||||
\(848\) | −17.1757 | −0.589816 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.6565 | 0.468413 | ||||||||
\(851\) | 18.3965 | 0.630622 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.71995 | 0.332805 | 0.166402 | − | 0.986058i | \(-0.446785\pi\) | ||||
0.166402 | + | 0.986058i | \(0.446785\pi\) | |||||||
\(854\) | 15.2238 | 0.520949 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 101.974 | 3.48541 | ||||||||
\(857\) | −41.2846 | −1.41025 | −0.705127 | − | 0.709081i | \(-0.749110\pi\) | ||||
−0.705127 | + | 0.709081i | \(0.749110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.05236 | −0.0359061 | −0.0179531 | − | 0.999839i | \(-0.505715\pi\) | ||||
−0.0179531 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(860\) | −13.3951 | −0.456768 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −74.0325 | −2.52156 | ||||||||
\(863\) | −34.4783 | −1.17365 | −0.586827 | − | 0.809712i | \(-0.699623\pi\) | ||||
−0.586827 | + | 0.809712i | \(0.699623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.01693 | 0.306585 | ||||||||
\(866\) | −16.1963 | −0.550374 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.3435 | −0.486850 | ||||||||
\(869\) | 36.0935 | 1.22439 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 100.215 | 3.39565 | ||||||||
\(872\) | 78.6005 | 2.66175 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.4081 | 1.19770 | ||||||||
\(875\) | −7.35770 | −0.248736 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.2483 | 1.39285 | 0.696427 | − | 0.717627i | \(-0.254772\pi\) | ||||
0.696427 | + | 0.717627i | \(0.254772\pi\) | |||||||
\(878\) | −37.0206 | −1.24939 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.8653 | −0.635950 | ||||||||
\(881\) | −16.3701 | −0.551523 | −0.275761 | − | 0.961226i | \(-0.588930\pi\) | ||||
−0.275761 | + | 0.961226i | \(0.588930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.4843 | 1.32875 | 0.664376 | − | 0.747398i | \(-0.268697\pi\) | ||||
0.664376 | + | 0.747398i | \(0.268697\pi\) | |||||||
\(884\) | 34.6851 | 1.16659 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.4929 | 0.386110 | ||||||||
\(887\) | 14.0226 | 0.470831 | 0.235416 | − | 0.971895i | \(-0.424355\pi\) | ||||
0.235416 | + | 0.971895i | \(0.424355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 31.9572 | 1.07121 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.5193 | −1.35669 | ||||||||
\(893\) | −13.5306 | −0.452783 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.9042 | −0.598473 | ||||||||
\(896\) | −18.0026 | −0.601426 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.4568 | 0.549171 | ||||||||
\(899\) | −33.8611 | −1.12933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.37890 | 0.145882 | ||||||||
\(902\) | −50.8897 | −1.69444 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −66.8518 | −2.22346 | ||||||||
\(905\) | 3.45278 | 0.114774 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.6241 | −1.18288 | −0.591440 | − | 0.806349i | \(-0.701440\pi\) | ||||
−0.591440 | + | 0.806349i | \(0.701440\pi\) | |||||||
\(908\) | 108.221 | 3.59145 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.9395 | −0.428940 | ||||||||
\(911\) | −4.45318 | −0.147541 | −0.0737703 | − | 0.997275i | \(-0.523503\pi\) | ||||
−0.0737703 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.7094 | −0.619192 | ||||||||
\(914\) | −43.8529 | −1.45053 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.9284 | 0.856698 | ||||||||
\(917\) | 0.687639 | 0.0227078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4633 | 1.26879 | 0.634394 | − | 0.773010i | \(-0.281250\pi\) | ||||
0.634394 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(920\) | −28.7215 | −0.946921 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 99.8618 | 3.28877 | ||||||||
\(923\) | −47.8475 | −1.57492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7437 | 0.386130 | ||||||||
\(926\) | −9.63572 | −0.316649 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.1710 | 0.498012 | ||||||||
\(929\) | −41.8359 | −1.37259 | −0.686295 | − | 0.727323i | \(-0.740764\pi\) | ||||
−0.686295 | + | 0.727323i | \(0.740764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.07830 | −0.0681135 | ||||||||
\(932\) | −28.1320 | −0.921493 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.29665 | 0.107870 | ||||||||
\(935\) | 4.80966 | 0.157293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1190 | 0.885938 | 0.442969 | − | 0.896537i | \(-0.353925\pi\) | ||||
0.442969 | + | 0.896537i | \(0.353925\pi\) | |||||||
\(938\) | −37.3429 | −1.21929 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.1831 | 0.690916 | ||||||||
\(941\) | 28.1483 | 0.917608 | 0.458804 | − | 0.888538i | \(-0.348278\pi\) | ||||
0.458804 | + | 0.888538i | \(0.348278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.8514 | −0.939531 | ||||||||
\(944\) | −60.2195 | −1.95998 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.8848 | 1.62189 | ||||||||
\(947\) | −26.7498 | −0.869251 | −0.434625 | − | 0.900611i | \(-0.643119\pi\) | ||||
−0.434625 | + | 0.900611i | \(0.643119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9715 | −0.485995 | ||||||||
\(950\) | 22.6033 | 0.733349 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.69656 | −0.217037 | ||||||||
\(953\) | 59.4329 | 1.92522 | 0.962611 | − | 0.270888i | \(-0.0873174\pi\) | ||||
0.962611 | + | 0.270888i | \(0.0873174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.1150 | −0.521468 | ||||||||
\(956\) | 98.3923 | 3.18223 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.1943 | 0.878607 | ||||||||
\(959\) | 7.96226 | 0.257115 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0567 | −0.614733 | ||||||||
\(962\) | 44.1999 | 1.42506 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −38.5340 | −1.24110 | ||||||||
\(965\) | −14.1672 | −0.456058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.26909 | −0.137285 | −0.0686424 | − | 0.997641i | \(-0.521867\pi\) | ||||
−0.0686424 | + | 0.997641i | \(0.521867\pi\) | |||||||
\(968\) | 68.6519 | 2.20655 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.8505 | 1.05477 | ||||||||
\(971\) | −53.2969 | −1.71038 | −0.855190 | − | 0.518315i | \(-0.826559\pi\) | ||||
−0.855190 | + | 0.518315i | \(0.826559\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.410908 | −0.0131731 | ||||||||
\(974\) | 18.4106 | 0.589915 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.2340 | 0.967766 | ||||||||
\(977\) | −19.3371 | −0.618647 | −0.309324 | − | 0.950957i | \(-0.600103\pi\) | ||||
−0.309324 | + | 0.950957i | \(0.600103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.3120 | −2.56678 | ||||||||
\(980\) | 3.25373 | 0.103937 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.9761 | −0.828930 | ||||||||
\(983\) | 38.4570 | 1.22659 | 0.613294 | − | 0.789855i | \(-0.289844\pi\) | ||||
0.613294 | + | 0.789855i | \(0.289844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.3721 | 0.617248 | ||||||||
\(986\) | −30.5117 | −0.971690 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57.4087 | 1.82641 | ||||||||
\(989\) | 28.2817 | 0.899305 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.2038 | 0.800626 | 0.400313 | − | 0.916379i | \(-0.368901\pi\) | ||||
0.400313 | + | 0.916379i | \(0.368901\pi\) | |||||||
\(992\) | −5.35101 | −0.169895 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.8294 | 0.565513 | ||||||||
\(995\) | 13.0609 | 0.414058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0562 | 1.33193 | 0.665966 | − | 0.745982i | \(-0.268019\pi\) | ||||
0.665966 | + | 0.745982i | \(0.268019\pi\) | |||||||
\(998\) | 66.1651 | 2.09442 | ||||||||
\(999\) | 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.l.1.7 | 7 | ||
3.2 | odd | 2 | 2667.2.a.j.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.j.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
8001.2.a.l.1.7 | 7 | 1.1 | even | 1 | trivial |