Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.04582 | −1.18116 | −0.590578 | − | 0.806980i | \(-0.701100\pi\) | ||||
−0.590578 | + | 0.806980i | \(0.701100\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.09434 | −1.83105 | −0.915523 | − | 0.402266i | \(-0.868223\pi\) | ||||
−0.915523 | + | 0.402266i | \(0.868223\pi\) | |||||||
\(6\) | 2.04582 | 0.835204 | ||||||||
\(7\) | 1.49846 | 0.566363 | 0.283182 | − | 0.959066i | \(-0.408610\pi\) | ||||
0.283182 | + | 0.959066i | \(0.408610\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.18539 | 0.395130 | ||||||||
\(10\) | 4.09434 | 1.29474 | ||||||||
\(11\) | 4.36668 | 1.31660 | 0.658302 | − | 0.752754i | \(-0.271275\pi\) | ||||
0.658302 | + | 0.752754i | \(0.271275\pi\) | |||||||
\(12\) | −2.04582 | −0.590578 | ||||||||
\(13\) | −2.07746 | −0.576182 | −0.288091 | − | 0.957603i | \(-0.593021\pi\) | ||||
−0.288091 | + | 0.957603i | \(0.593021\pi\) | |||||||
\(14\) | −1.49846 | −0.400479 | ||||||||
\(15\) | 8.37630 | 2.16275 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.71655 | 0.658861 | 0.329430 | − | 0.944180i | \(-0.393143\pi\) | ||||
0.329430 | + | 0.944180i | \(0.393143\pi\) | |||||||
\(18\) | −1.18539 | −0.279399 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.09434 | −0.915523 | ||||||||
\(21\) | −3.06558 | −0.668964 | ||||||||
\(22\) | −4.36668 | −0.930979 | ||||||||
\(23\) | −8.72662 | −1.81963 | −0.909813 | − | 0.415017i | \(-0.863776\pi\) | ||||
−0.909813 | + | 0.415017i | \(0.863776\pi\) | |||||||
\(24\) | 2.04582 | 0.417602 | ||||||||
\(25\) | 11.7636 | 2.35273 | ||||||||
\(26\) | 2.07746 | 0.407422 | ||||||||
\(27\) | 3.71237 | 0.714446 | ||||||||
\(28\) | 1.49846 | 0.283182 | ||||||||
\(29\) | 1.76891 | 0.328478 | 0.164239 | − | 0.986421i | \(-0.447483\pi\) | ||||
0.164239 | + | 0.986421i | \(0.447483\pi\) | |||||||
\(30\) | −8.37630 | −1.52930 | ||||||||
\(31\) | −3.93079 | −0.705991 | −0.352996 | − | 0.935625i | \(-0.614837\pi\) | ||||
−0.352996 | + | 0.935625i | \(0.614837\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.93345 | −1.55511 | ||||||||
\(34\) | −2.71655 | −0.465885 | ||||||||
\(35\) | −6.13520 | −1.03704 | ||||||||
\(36\) | 1.18539 | 0.197565 | ||||||||
\(37\) | −9.86688 | −1.62210 | −0.811052 | − | 0.584973i | \(-0.801105\pi\) | ||||
−0.811052 | + | 0.584973i | \(0.801105\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 4.25010 | 0.680561 | ||||||||
\(40\) | 4.09434 | 0.647372 | ||||||||
\(41\) | 5.20665 | 0.813142 | 0.406571 | − | 0.913619i | \(-0.366724\pi\) | ||||
0.406571 | + | 0.913619i | \(0.366724\pi\) | |||||||
\(42\) | 3.06558 | 0.473029 | ||||||||
\(43\) | 4.35112 | 0.663539 | 0.331769 | − | 0.943361i | \(-0.392354\pi\) | ||||
0.331769 | + | 0.943361i | \(0.392354\pi\) | |||||||
\(44\) | 4.36668 | 0.658302 | ||||||||
\(45\) | −4.85339 | −0.723501 | ||||||||
\(46\) | 8.72662 | 1.28667 | ||||||||
\(47\) | −5.27226 | −0.769039 | −0.384519 | − | 0.923117i | \(-0.625633\pi\) | ||||
−0.384519 | + | 0.923117i | \(0.625633\pi\) | |||||||
\(48\) | −2.04582 | −0.295289 | ||||||||
\(49\) | −4.75463 | −0.679232 | ||||||||
\(50\) | −11.7636 | −1.66363 | ||||||||
\(51\) | −5.55758 | −0.778218 | ||||||||
\(52\) | −2.07746 | −0.288091 | ||||||||
\(53\) | −2.90552 | −0.399104 | −0.199552 | − | 0.979887i | \(-0.563949\pi\) | ||||
−0.199552 | + | 0.979887i | \(0.563949\pi\) | |||||||
\(54\) | −3.71237 | −0.505190 | ||||||||
\(55\) | −17.8787 | −2.41076 | ||||||||
\(56\) | −1.49846 | −0.200240 | ||||||||
\(57\) | 2.04582 | 0.270976 | ||||||||
\(58\) | −1.76891 | −0.232269 | ||||||||
\(59\) | 7.50249 | 0.976741 | 0.488371 | − | 0.872636i | \(-0.337591\pi\) | ||||
0.488371 | + | 0.872636i | \(0.337591\pi\) | |||||||
\(60\) | 8.37630 | 1.08138 | ||||||||
\(61\) | −4.68551 | −0.599918 | −0.299959 | − | 0.953952i | \(-0.596973\pi\) | ||||
−0.299959 | + | 0.953952i | \(0.596973\pi\) | |||||||
\(62\) | 3.93079 | 0.499211 | ||||||||
\(63\) | 1.77626 | 0.223787 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.50581 | 1.05502 | ||||||||
\(66\) | 8.93345 | 1.09963 | ||||||||
\(67\) | −8.57101 | −1.04712 | −0.523558 | − | 0.851990i | \(-0.675396\pi\) | ||||
−0.523558 | + | 0.851990i | \(0.675396\pi\) | |||||||
\(68\) | 2.71655 | 0.329430 | ||||||||
\(69\) | 17.8531 | 2.14926 | ||||||||
\(70\) | 6.13520 | 0.733296 | ||||||||
\(71\) | 1.09328 | 0.129748 | 0.0648741 | − | 0.997893i | \(-0.479335\pi\) | ||||
0.0648741 | + | 0.997893i | \(0.479335\pi\) | |||||||
\(72\) | −1.18539 | −0.139700 | ||||||||
\(73\) | 11.3584 | 1.32940 | 0.664700 | − | 0.747111i | \(-0.268560\pi\) | ||||
0.664700 | + | 0.747111i | \(0.268560\pi\) | |||||||
\(74\) | 9.86688 | 1.14700 | ||||||||
\(75\) | −24.0663 | −2.77894 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 6.54328 | 0.745676 | ||||||||
\(78\) | −4.25010 | −0.481230 | ||||||||
\(79\) | 7.46127 | 0.839458 | 0.419729 | − | 0.907649i | \(-0.362125\pi\) | ||||
0.419729 | + | 0.907649i | \(0.362125\pi\) | |||||||
\(80\) | −4.09434 | −0.457761 | ||||||||
\(81\) | −11.1510 | −1.23900 | ||||||||
\(82\) | −5.20665 | −0.574978 | ||||||||
\(83\) | 15.3359 | 1.68333 | 0.841666 | − | 0.539999i | \(-0.181575\pi\) | ||||
0.841666 | + | 0.539999i | \(0.181575\pi\) | |||||||
\(84\) | −3.06558 | −0.334482 | ||||||||
\(85\) | −11.1225 | −1.20640 | ||||||||
\(86\) | −4.35112 | −0.469193 | ||||||||
\(87\) | −3.61887 | −0.387983 | ||||||||
\(88\) | −4.36668 | −0.465490 | ||||||||
\(89\) | 7.24142 | 0.767589 | 0.383795 | − | 0.923418i | \(-0.374617\pi\) | ||||
0.383795 | + | 0.923418i | \(0.374617\pi\) | |||||||
\(90\) | 4.85339 | 0.511593 | ||||||||
\(91\) | −3.11298 | −0.326329 | ||||||||
\(92\) | −8.72662 | −0.909813 | ||||||||
\(93\) | 8.04171 | 0.833886 | ||||||||
\(94\) | 5.27226 | 0.543792 | ||||||||
\(95\) | 4.09434 | 0.420071 | ||||||||
\(96\) | 2.04582 | 0.208801 | ||||||||
\(97\) | −16.3302 | −1.65808 | −0.829042 | − | 0.559186i | \(-0.811114\pi\) | ||||
−0.829042 | + | 0.559186i | \(0.811114\pi\) | |||||||
\(98\) | 4.75463 | 0.480290 | ||||||||
\(99\) | 5.17622 | 0.520230 | ||||||||
\(100\) | 11.7636 | 1.17636 | ||||||||
\(101\) | 1.31063 | 0.130413 | 0.0652063 | − | 0.997872i | \(-0.479229\pi\) | ||||
0.0652063 | + | 0.997872i | \(0.479229\pi\) | |||||||
\(102\) | 5.55758 | 0.550283 | ||||||||
\(103\) | −0.646222 | −0.0636742 | −0.0318371 | − | 0.999493i | \(-0.510136\pi\) | ||||
−0.0318371 | + | 0.999493i | \(0.510136\pi\) | |||||||
\(104\) | 2.07746 | 0.203711 | ||||||||
\(105\) | 12.5515 | 1.22490 | ||||||||
\(106\) | 2.90552 | 0.282209 | ||||||||
\(107\) | 17.4634 | 1.68825 | 0.844125 | − | 0.536147i | \(-0.180121\pi\) | ||||
0.844125 | + | 0.536147i | \(0.180121\pi\) | |||||||
\(108\) | 3.71237 | 0.357223 | ||||||||
\(109\) | 13.5424 | 1.29713 | 0.648565 | − | 0.761160i | \(-0.275370\pi\) | ||||
0.648565 | + | 0.761160i | \(0.275370\pi\) | |||||||
\(110\) | 17.8787 | 1.70467 | ||||||||
\(111\) | 20.1859 | 1.91596 | ||||||||
\(112\) | 1.49846 | 0.141591 | ||||||||
\(113\) | −10.1385 | −0.953747 | −0.476874 | − | 0.878972i | \(-0.658230\pi\) | ||||
−0.476874 | + | 0.878972i | \(0.658230\pi\) | |||||||
\(114\) | −2.04582 | −0.191609 | ||||||||
\(115\) | 35.7298 | 3.33182 | ||||||||
\(116\) | 1.76891 | 0.164239 | ||||||||
\(117\) | −2.46259 | −0.227667 | ||||||||
\(118\) | −7.50249 | −0.690660 | ||||||||
\(119\) | 4.07064 | 0.373155 | ||||||||
\(120\) | −8.37630 | −0.764648 | ||||||||
\(121\) | 8.06789 | 0.733445 | ||||||||
\(122\) | 4.68551 | 0.424206 | ||||||||
\(123\) | −10.6519 | −0.960447 | ||||||||
\(124\) | −3.93079 | −0.352996 | ||||||||
\(125\) | −27.6927 | −2.47691 | ||||||||
\(126\) | −1.77626 | −0.158241 | ||||||||
\(127\) | −11.5486 | −1.02477 | −0.512385 | − | 0.858756i | \(-0.671238\pi\) | ||||
−0.512385 | + | 0.858756i | \(0.671238\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.90161 | −0.783743 | ||||||||
\(130\) | −8.50581 | −0.746009 | ||||||||
\(131\) | −2.24440 | −0.196094 | −0.0980469 | − | 0.995182i | \(-0.531260\pi\) | ||||
−0.0980469 | + | 0.995182i | \(0.531260\pi\) | |||||||
\(132\) | −8.93345 | −0.777557 | ||||||||
\(133\) | −1.49846 | −0.129933 | ||||||||
\(134\) | 8.57101 | 0.740423 | ||||||||
\(135\) | −15.1997 | −1.30818 | ||||||||
\(136\) | −2.71655 | −0.232942 | ||||||||
\(137\) | 0.788239 | 0.0673438 | 0.0336719 | − | 0.999433i | \(-0.489280\pi\) | ||||
0.0336719 | + | 0.999433i | \(0.489280\pi\) | |||||||
\(138\) | −17.8531 | −1.51976 | ||||||||
\(139\) | 0.0659961 | 0.00559771 | 0.00279886 | − | 0.999996i | \(-0.499109\pi\) | ||||
0.00279886 | + | 0.999996i | \(0.499109\pi\) | |||||||
\(140\) | −6.13520 | −0.518519 | ||||||||
\(141\) | 10.7861 | 0.908355 | ||||||||
\(142\) | −1.09328 | −0.0917458 | ||||||||
\(143\) | −9.07158 | −0.758604 | ||||||||
\(144\) | 1.18539 | 0.0987825 | ||||||||
\(145\) | −7.24251 | −0.601458 | ||||||||
\(146\) | −11.3584 | −0.940027 | ||||||||
\(147\) | 9.72712 | 0.802280 | ||||||||
\(148\) | −9.86688 | −0.811052 | ||||||||
\(149\) | 21.7928 | 1.78533 | 0.892666 | − | 0.450718i | \(-0.148832\pi\) | ||||
0.892666 | + | 0.450718i | \(0.148832\pi\) | |||||||
\(150\) | 24.0663 | 1.96501 | ||||||||
\(151\) | 3.76642 | 0.306507 | 0.153254 | − | 0.988187i | \(-0.451025\pi\) | ||||
0.153254 | + | 0.988187i | \(0.451025\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 3.22017 | 0.260336 | ||||||||
\(154\) | −6.54328 | −0.527273 | ||||||||
\(155\) | 16.0940 | 1.29270 | ||||||||
\(156\) | 4.25010 | 0.340281 | ||||||||
\(157\) | 1.35547 | 0.108178 | 0.0540892 | − | 0.998536i | \(-0.482774\pi\) | ||||
0.0540892 | + | 0.998536i | \(0.482774\pi\) | |||||||
\(158\) | −7.46127 | −0.593586 | ||||||||
\(159\) | 5.94419 | 0.471405 | ||||||||
\(160\) | 4.09434 | 0.323686 | ||||||||
\(161\) | −13.0765 | −1.03057 | ||||||||
\(162\) | 11.1510 | 0.876107 | ||||||||
\(163\) | −3.10546 | −0.243238 | −0.121619 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121619 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(164\) | 5.20665 | 0.406571 | ||||||||
\(165\) | 36.5766 | 2.84749 | ||||||||
\(166\) | −15.3359 | −1.19029 | ||||||||
\(167\) | 20.7368 | 1.60466 | 0.802331 | − | 0.596879i | \(-0.203593\pi\) | ||||
0.802331 | + | 0.596879i | \(0.203593\pi\) | |||||||
\(168\) | 3.06558 | 0.236514 | ||||||||
\(169\) | −8.68418 | −0.668014 | ||||||||
\(170\) | 11.1225 | 0.853057 | ||||||||
\(171\) | −1.18539 | −0.0906490 | ||||||||
\(172\) | 4.35112 | 0.331769 | ||||||||
\(173\) | 15.9654 | 1.21382 | 0.606912 | − | 0.794769i | \(-0.292408\pi\) | ||||
0.606912 | + | 0.794769i | \(0.292408\pi\) | |||||||
\(174\) | 3.61887 | 0.274346 | ||||||||
\(175\) | 17.6273 | 1.33250 | ||||||||
\(176\) | 4.36668 | 0.329151 | ||||||||
\(177\) | −15.3488 | −1.15368 | ||||||||
\(178\) | −7.24142 | −0.542768 | ||||||||
\(179\) | 6.73294 | 0.503244 | 0.251622 | − | 0.967826i | \(-0.419036\pi\) | ||||
0.251622 | + | 0.967826i | \(0.419036\pi\) | |||||||
\(180\) | −4.85339 | −0.361751 | ||||||||
\(181\) | −11.4281 | −0.849445 | −0.424723 | − | 0.905323i | \(-0.639628\pi\) | ||||
−0.424723 | + | 0.905323i | \(0.639628\pi\) | |||||||
\(182\) | 3.11298 | 0.230749 | ||||||||
\(183\) | 9.58572 | 0.708596 | ||||||||
\(184\) | 8.72662 | 0.643335 | ||||||||
\(185\) | 40.3984 | 2.97015 | ||||||||
\(186\) | −8.04171 | −0.589646 | ||||||||
\(187\) | 11.8623 | 0.867458 | ||||||||
\(188\) | −5.27226 | −0.384519 | ||||||||
\(189\) | 5.56283 | 0.404636 | ||||||||
\(190\) | −4.09434 | −0.297035 | ||||||||
\(191\) | 22.8164 | 1.65093 | 0.825467 | − | 0.564450i | \(-0.190912\pi\) | ||||
0.825467 | + | 0.564450i | \(0.190912\pi\) | |||||||
\(192\) | −2.04582 | −0.147645 | ||||||||
\(193\) | −3.66905 | −0.264104 | −0.132052 | − | 0.991243i | \(-0.542157\pi\) | ||||
−0.132052 | + | 0.991243i | \(0.542157\pi\) | |||||||
\(194\) | 16.3302 | 1.17244 | ||||||||
\(195\) | −17.4014 | −1.24614 | ||||||||
\(196\) | −4.75463 | −0.339616 | ||||||||
\(197\) | −2.93118 | −0.208838 | −0.104419 | − | 0.994533i | \(-0.533298\pi\) | ||||
−0.104419 | + | 0.994533i | \(0.533298\pi\) | |||||||
\(198\) | −5.17622 | −0.367858 | ||||||||
\(199\) | 12.3039 | 0.872201 | 0.436100 | − | 0.899898i | \(-0.356359\pi\) | ||||
0.436100 | + | 0.899898i | \(0.356359\pi\) | |||||||
\(200\) | −11.7636 | −0.831815 | ||||||||
\(201\) | 17.5348 | 1.23681 | ||||||||
\(202\) | −1.31063 | −0.0922157 | ||||||||
\(203\) | 2.65063 | 0.186038 | ||||||||
\(204\) | −5.55758 | −0.389109 | ||||||||
\(205\) | −21.3178 | −1.48890 | ||||||||
\(206\) | 0.646222 | 0.0450244 | ||||||||
\(207\) | −10.3445 | −0.718989 | ||||||||
\(208\) | −2.07746 | −0.144046 | ||||||||
\(209\) | −4.36668 | −0.302050 | ||||||||
\(210\) | −12.5515 | −0.866137 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −2.90552 | −0.199552 | ||||||||
\(213\) | −2.23665 | −0.153253 | ||||||||
\(214\) | −17.4634 | −1.19377 | ||||||||
\(215\) | −17.8150 | −1.21497 | ||||||||
\(216\) | −3.71237 | −0.252595 | ||||||||
\(217\) | −5.89012 | −0.399848 | ||||||||
\(218\) | −13.5424 | −0.917209 | ||||||||
\(219\) | −23.2373 | −1.57023 | ||||||||
\(220\) | −17.8787 | −1.20538 | ||||||||
\(221\) | −5.64352 | −0.379624 | ||||||||
\(222\) | −20.1859 | −1.35479 | ||||||||
\(223\) | −15.1165 | −1.01228 | −0.506138 | − | 0.862453i | \(-0.668927\pi\) | ||||
−0.506138 | + | 0.862453i | \(0.668927\pi\) | |||||||
\(224\) | −1.49846 | −0.100120 | ||||||||
\(225\) | 13.9445 | 0.929634 | ||||||||
\(226\) | 10.1385 | 0.674401 | ||||||||
\(227\) | 5.52236 | 0.366532 | 0.183266 | − | 0.983063i | \(-0.441333\pi\) | ||||
0.183266 | + | 0.983063i | \(0.441333\pi\) | |||||||
\(228\) | 2.04582 | 0.135488 | ||||||||
\(229\) | 8.47458 | 0.560016 | 0.280008 | − | 0.959998i | \(-0.409663\pi\) | ||||
0.280008 | + | 0.959998i | \(0.409663\pi\) | |||||||
\(230\) | −35.7298 | −2.35595 | ||||||||
\(231\) | −13.3864 | −0.880760 | ||||||||
\(232\) | −1.76891 | −0.116134 | ||||||||
\(233\) | 11.7599 | 0.770415 | 0.385208 | − | 0.922830i | \(-0.374130\pi\) | ||||
0.385208 | + | 0.922830i | \(0.374130\pi\) | |||||||
\(234\) | 2.46259 | 0.160985 | ||||||||
\(235\) | 21.5865 | 1.40814 | ||||||||
\(236\) | 7.50249 | 0.488371 | ||||||||
\(237\) | −15.2644 | −0.991531 | ||||||||
\(238\) | −4.07064 | −0.263860 | ||||||||
\(239\) | −2.68897 | −0.173935 | −0.0869676 | − | 0.996211i | \(-0.527718\pi\) | ||||
−0.0869676 | + | 0.996211i | \(0.527718\pi\) | |||||||
\(240\) | 8.37630 | 0.540688 | ||||||||
\(241\) | 0.0708398 | 0.00456319 | 0.00228160 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228160 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(242\) | −8.06789 | −0.518624 | ||||||||
\(243\) | 11.6759 | 0.749009 | ||||||||
\(244\) | −4.68551 | −0.299959 | ||||||||
\(245\) | 19.4671 | 1.24371 | ||||||||
\(246\) | 10.6519 | 0.679139 | ||||||||
\(247\) | 2.07746 | 0.132185 | ||||||||
\(248\) | 3.93079 | 0.249606 | ||||||||
\(249\) | −31.3745 | −1.98828 | ||||||||
\(250\) | 27.6927 | 1.75144 | ||||||||
\(251\) | 28.0554 | 1.77084 | 0.885420 | − | 0.464792i | \(-0.153871\pi\) | ||||
0.885420 | + | 0.464792i | \(0.153871\pi\) | |||||||
\(252\) | 1.77626 | 0.111894 | ||||||||
\(253\) | −38.1064 | −2.39573 | ||||||||
\(254\) | 11.5486 | 0.724621 | ||||||||
\(255\) | 22.7547 | 1.42495 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4019 | −0.711230 | −0.355615 | − | 0.934633i | \(-0.615729\pi\) | ||||
−0.355615 | + | 0.934633i | \(0.615729\pi\) | |||||||
\(258\) | 8.90161 | 0.554190 | ||||||||
\(259\) | −14.7851 | −0.918701 | ||||||||
\(260\) | 8.50581 | 0.527508 | ||||||||
\(261\) | 2.09684 | 0.129791 | ||||||||
\(262\) | 2.24440 | 0.138659 | ||||||||
\(263\) | −32.2678 | −1.98972 | −0.994859 | − | 0.101272i | \(-0.967709\pi\) | ||||
−0.994859 | + | 0.101272i | \(0.967709\pi\) | |||||||
\(264\) | 8.93345 | 0.549816 | ||||||||
\(265\) | 11.8962 | 0.730779 | ||||||||
\(266\) | 1.49846 | 0.0918763 | ||||||||
\(267\) | −14.8147 | −0.906643 | ||||||||
\(268\) | −8.57101 | −0.523558 | ||||||||
\(269\) | −25.3155 | −1.54351 | −0.771756 | − | 0.635918i | \(-0.780621\pi\) | ||||
−0.771756 | + | 0.635918i | \(0.780621\pi\) | |||||||
\(270\) | 15.1997 | 0.925025 | ||||||||
\(271\) | −7.88294 | −0.478855 | −0.239427 | − | 0.970914i | \(-0.576960\pi\) | ||||
−0.239427 | + | 0.970914i | \(0.576960\pi\) | |||||||
\(272\) | 2.71655 | 0.164715 | ||||||||
\(273\) | 6.36860 | 0.385445 | ||||||||
\(274\) | −0.788239 | −0.0476193 | ||||||||
\(275\) | 51.3681 | 3.09761 | ||||||||
\(276\) | 17.8531 | 1.07463 | ||||||||
\(277\) | 6.05207 | 0.363634 | 0.181817 | − | 0.983332i | \(-0.441802\pi\) | ||||
0.181817 | + | 0.983332i | \(0.441802\pi\) | |||||||
\(278\) | −0.0659961 | −0.00395818 | ||||||||
\(279\) | −4.65952 | −0.278958 | ||||||||
\(280\) | 6.13520 | 0.366648 | ||||||||
\(281\) | −23.4655 | −1.39984 | −0.699918 | − | 0.714223i | \(-0.746780\pi\) | ||||
−0.699918 | + | 0.714223i | \(0.746780\pi\) | |||||||
\(282\) | −10.7861 | −0.642304 | ||||||||
\(283\) | 31.9526 | 1.89938 | 0.949691 | − | 0.313188i | \(-0.101397\pi\) | ||||
0.949691 | + | 0.313188i | \(0.101397\pi\) | |||||||
\(284\) | 1.09328 | 0.0648741 | ||||||||
\(285\) | −8.37630 | −0.496169 | ||||||||
\(286\) | 9.07158 | 0.536414 | ||||||||
\(287\) | 7.80193 | 0.460534 | ||||||||
\(288\) | −1.18539 | −0.0698498 | ||||||||
\(289\) | −9.62034 | −0.565902 | ||||||||
\(290\) | 7.24251 | 0.425295 | ||||||||
\(291\) | 33.4088 | 1.95846 | ||||||||
\(292\) | 11.3584 | 0.664700 | ||||||||
\(293\) | −0.530799 | −0.0310096 | −0.0155048 | − | 0.999880i | \(-0.504936\pi\) | ||||
−0.0155048 | + | 0.999880i | \(0.504936\pi\) | |||||||
\(294\) | −9.72712 | −0.567297 | ||||||||
\(295\) | −30.7178 | −1.78846 | ||||||||
\(296\) | 9.86688 | 0.573501 | ||||||||
\(297\) | 16.2107 | 0.940642 | ||||||||
\(298\) | −21.7928 | −1.26242 | ||||||||
\(299\) | 18.1292 | 1.04844 | ||||||||
\(300\) | −24.0663 | −1.38947 | ||||||||
\(301\) | 6.51996 | 0.375804 | ||||||||
\(302\) | −3.76642 | −0.216733 | ||||||||
\(303\) | −2.68132 | −0.154038 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 19.1841 | 1.09848 | ||||||||
\(306\) | −3.22017 | −0.184085 | ||||||||
\(307\) | 12.2045 | 0.696546 | 0.348273 | − | 0.937393i | \(-0.386768\pi\) | ||||
0.348273 | + | 0.937393i | \(0.386768\pi\) | |||||||
\(308\) | 6.54328 | 0.372838 | ||||||||
\(309\) | 1.32206 | 0.0752092 | ||||||||
\(310\) | −16.0940 | −0.914079 | ||||||||
\(311\) | 20.4475 | 1.15947 | 0.579736 | − | 0.814804i | \(-0.303156\pi\) | ||||
0.579736 | + | 0.814804i | \(0.303156\pi\) | |||||||
\(312\) | −4.25010 | −0.240615 | ||||||||
\(313\) | 32.5985 | 1.84258 | 0.921288 | − | 0.388881i | \(-0.127138\pi\) | ||||
0.921288 | + | 0.388881i | \(0.127138\pi\) | |||||||
\(314\) | −1.35547 | −0.0764937 | ||||||||
\(315\) | −7.27260 | −0.409765 | ||||||||
\(316\) | 7.46127 | 0.419729 | ||||||||
\(317\) | −26.8916 | −1.51038 | −0.755190 | − | 0.655505i | \(-0.772456\pi\) | ||||
−0.755190 | + | 0.655505i | \(0.772456\pi\) | |||||||
\(318\) | −5.94419 | −0.333333 | ||||||||
\(319\) | 7.72425 | 0.432475 | ||||||||
\(320\) | −4.09434 | −0.228881 | ||||||||
\(321\) | −35.7270 | −1.99409 | ||||||||
\(322\) | 13.0765 | 0.728723 | ||||||||
\(323\) | −2.71655 | −0.151153 | ||||||||
\(324\) | −11.1510 | −0.619501 | ||||||||
\(325\) | −24.4384 | −1.35560 | ||||||||
\(326\) | 3.10546 | 0.171996 | ||||||||
\(327\) | −27.7054 | −1.53211 | ||||||||
\(328\) | −5.20665 | −0.287489 | ||||||||
\(329\) | −7.90026 | −0.435555 | ||||||||
\(330\) | −36.5766 | −2.01348 | ||||||||
\(331\) | −28.2584 | −1.55322 | −0.776610 | − | 0.629982i | \(-0.783062\pi\) | ||||
−0.776610 | + | 0.629982i | \(0.783062\pi\) | |||||||
\(332\) | 15.3359 | 0.841666 | ||||||||
\(333\) | −11.6961 | −0.640942 | ||||||||
\(334\) | −20.7368 | −1.13467 | ||||||||
\(335\) | 35.0927 | 1.91732 | ||||||||
\(336\) | −3.06558 | −0.167241 | ||||||||
\(337\) | −19.2134 | −1.04662 | −0.523310 | − | 0.852142i | \(-0.675303\pi\) | ||||
−0.523310 | + | 0.852142i | \(0.675303\pi\) | |||||||
\(338\) | 8.68418 | 0.472357 | ||||||||
\(339\) | 20.7415 | 1.12652 | ||||||||
\(340\) | −11.1225 | −0.603202 | ||||||||
\(341\) | −17.1645 | −0.929511 | ||||||||
\(342\) | 1.18539 | 0.0640986 | ||||||||
\(343\) | −17.6138 | −0.951056 | ||||||||
\(344\) | −4.35112 | −0.234596 | ||||||||
\(345\) | −73.0968 | −3.93540 | ||||||||
\(346\) | −15.9654 | −0.858303 | ||||||||
\(347\) | −16.9938 | −0.912277 | −0.456139 | − | 0.889909i | \(-0.650768\pi\) | ||||
−0.456139 | + | 0.889909i | \(0.650768\pi\) | |||||||
\(348\) | −3.61887 | −0.193992 | ||||||||
\(349\) | −11.9704 | −0.640761 | −0.320381 | − | 0.947289i | \(-0.603811\pi\) | ||||
−0.320381 | + | 0.947289i | \(0.603811\pi\) | |||||||
\(350\) | −17.6273 | −0.942220 | ||||||||
\(351\) | −7.71228 | −0.411651 | ||||||||
\(352\) | −4.36668 | −0.232745 | ||||||||
\(353\) | 30.9605 | 1.64786 | 0.823931 | − | 0.566691i | \(-0.191777\pi\) | ||||
0.823931 | + | 0.566691i | \(0.191777\pi\) | |||||||
\(354\) | 15.3488 | 0.815778 | ||||||||
\(355\) | −4.47625 | −0.237575 | ||||||||
\(356\) | 7.24142 | 0.383795 | ||||||||
\(357\) | −8.32780 | −0.440754 | ||||||||
\(358\) | −6.73294 | −0.355847 | ||||||||
\(359\) | −30.9264 | −1.63223 | −0.816117 | − | 0.577887i | \(-0.803877\pi\) | ||||
−0.816117 | + | 0.577887i | \(0.803877\pi\) | |||||||
\(360\) | 4.85339 | 0.255796 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 11.4281 | 0.600649 | ||||||||
\(363\) | −16.5055 | −0.866313 | ||||||||
\(364\) | −3.11298 | −0.163164 | ||||||||
\(365\) | −46.5052 | −2.43419 | ||||||||
\(366\) | −9.58572 | −0.501053 | ||||||||
\(367\) | −36.5323 | −1.90697 | −0.953484 | − | 0.301443i | \(-0.902532\pi\) | ||||
−0.953484 | + | 0.301443i | \(0.902532\pi\) | |||||||
\(368\) | −8.72662 | −0.454907 | ||||||||
\(369\) | 6.17191 | 0.321297 | ||||||||
\(370\) | −40.3984 | −2.10021 | ||||||||
\(371\) | −4.35380 | −0.226038 | ||||||||
\(372\) | 8.04171 | 0.416943 | ||||||||
\(373\) | 14.1511 | 0.732718 | 0.366359 | − | 0.930474i | \(-0.380604\pi\) | ||||
0.366359 | + | 0.930474i | \(0.380604\pi\) | |||||||
\(374\) | −11.8623 | −0.613386 | ||||||||
\(375\) | 56.6543 | 2.92562 | ||||||||
\(376\) | 5.27226 | 0.271896 | ||||||||
\(377\) | −3.67482 | −0.189263 | ||||||||
\(378\) | −5.56283 | −0.286121 | ||||||||
\(379\) | 7.71892 | 0.396495 | 0.198247 | − | 0.980152i | \(-0.436475\pi\) | ||||
0.198247 | + | 0.980152i | \(0.436475\pi\) | |||||||
\(380\) | 4.09434 | 0.210035 | ||||||||
\(381\) | 23.6263 | 1.21041 | ||||||||
\(382\) | −22.8164 | −1.16739 | ||||||||
\(383\) | 12.3725 | 0.632207 | 0.316104 | − | 0.948725i | \(-0.397625\pi\) | ||||
0.316104 | + | 0.948725i | \(0.397625\pi\) | |||||||
\(384\) | 2.04582 | 0.104400 | ||||||||
\(385\) | −26.7904 | −1.36537 | ||||||||
\(386\) | 3.66905 | 0.186750 | ||||||||
\(387\) | 5.15777 | 0.262184 | ||||||||
\(388\) | −16.3302 | −0.829042 | ||||||||
\(389\) | −25.4546 | −1.29060 | −0.645299 | − | 0.763930i | \(-0.723267\pi\) | ||||
−0.645299 | + | 0.763930i | \(0.723267\pi\) | |||||||
\(390\) | 17.4014 | 0.881153 | ||||||||
\(391\) | −23.7063 | −1.19888 | ||||||||
\(392\) | 4.75463 | 0.240145 | ||||||||
\(393\) | 4.59163 | 0.231617 | ||||||||
\(394\) | 2.93118 | 0.147671 | ||||||||
\(395\) | −30.5490 | −1.53709 | ||||||||
\(396\) | 5.17622 | 0.260115 | ||||||||
\(397\) | 12.6444 | 0.634605 | 0.317302 | − | 0.948324i | \(-0.397223\pi\) | ||||
0.317302 | + | 0.948324i | \(0.397223\pi\) | |||||||
\(398\) | −12.3039 | −0.616739 | ||||||||
\(399\) | 3.06558 | 0.153471 | ||||||||
\(400\) | 11.7636 | 0.588182 | ||||||||
\(401\) | −14.7905 | −0.738605 | −0.369302 | − | 0.929309i | \(-0.620403\pi\) | ||||
−0.369302 | + | 0.929309i | \(0.620403\pi\) | |||||||
\(402\) | −17.5348 | −0.874555 | ||||||||
\(403\) | 8.16605 | 0.406780 | ||||||||
\(404\) | 1.31063 | 0.0652063 | ||||||||
\(405\) | 45.6561 | 2.26867 | ||||||||
\(406\) | −2.65063 | −0.131548 | ||||||||
\(407\) | −43.0855 | −2.13567 | ||||||||
\(408\) | 5.55758 | 0.275141 | ||||||||
\(409\) | −7.91564 | −0.391403 | −0.195702 | − | 0.980663i | \(-0.562698\pi\) | ||||
−0.195702 | + | 0.980663i | \(0.562698\pi\) | |||||||
\(410\) | 21.3178 | 1.05281 | ||||||||
\(411\) | −1.61260 | −0.0795436 | ||||||||
\(412\) | −0.646222 | −0.0318371 | ||||||||
\(413\) | 11.2422 | 0.553191 | ||||||||
\(414\) | 10.3445 | 0.508402 | ||||||||
\(415\) | −62.7903 | −3.08226 | ||||||||
\(416\) | 2.07746 | 0.101856 | ||||||||
\(417\) | −0.135016 | −0.00661177 | ||||||||
\(418\) | 4.36668 | 0.213581 | ||||||||
\(419\) | 3.22411 | 0.157508 | 0.0787540 | − | 0.996894i | \(-0.474906\pi\) | ||||
0.0787540 | + | 0.996894i | \(0.474906\pi\) | |||||||
\(420\) | 12.5515 | 0.612452 | ||||||||
\(421\) | 26.3204 | 1.28278 | 0.641389 | − | 0.767216i | \(-0.278358\pi\) | ||||
0.641389 | + | 0.767216i | \(0.278358\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −6.24969 | −0.303870 | ||||||||
\(424\) | 2.90552 | 0.141105 | ||||||||
\(425\) | 31.9566 | 1.55012 | ||||||||
\(426\) | 2.23665 | 0.108366 | ||||||||
\(427\) | −7.02103 | −0.339771 | ||||||||
\(428\) | 17.4634 | 0.844125 | ||||||||
\(429\) | 18.5588 | 0.896030 | ||||||||
\(430\) | 17.8150 | 0.859114 | ||||||||
\(431\) | −2.92758 | −0.141016 | −0.0705082 | − | 0.997511i | \(-0.522462\pi\) | ||||
−0.0705082 | + | 0.997511i | \(0.522462\pi\) | |||||||
\(432\) | 3.71237 | 0.178611 | ||||||||
\(433\) | −15.5142 | −0.745567 | −0.372784 | − | 0.927918i | \(-0.621597\pi\) | ||||
−0.372784 | + | 0.927918i | \(0.621597\pi\) | |||||||
\(434\) | 5.89012 | 0.282735 | ||||||||
\(435\) | 14.8169 | 0.710415 | ||||||||
\(436\) | 13.5424 | 0.648565 | ||||||||
\(437\) | 8.72662 | 0.417451 | ||||||||
\(438\) | 23.2373 | 1.11032 | ||||||||
\(439\) | 25.6971 | 1.22645 | 0.613227 | − | 0.789906i | \(-0.289871\pi\) | ||||
0.613227 | + | 0.789906i | \(0.289871\pi\) | |||||||
\(440\) | 17.8787 | 0.852333 | ||||||||
\(441\) | −5.63609 | −0.268385 | ||||||||
\(442\) | 5.64352 | 0.268435 | ||||||||
\(443\) | −4.35774 | −0.207042 | −0.103521 | − | 0.994627i | \(-0.533011\pi\) | ||||
−0.103521 | + | 0.994627i | \(0.533011\pi\) | |||||||
\(444\) | 20.1859 | 0.957980 | ||||||||
\(445\) | −29.6489 | −1.40549 | ||||||||
\(446\) | 15.1165 | 0.715787 | ||||||||
\(447\) | −44.5841 | −2.10876 | ||||||||
\(448\) | 1.49846 | 0.0707954 | ||||||||
\(449\) | −13.8264 | −0.652509 | −0.326254 | − | 0.945282i | \(-0.605787\pi\) | ||||
−0.326254 | + | 0.945282i | \(0.605787\pi\) | |||||||
\(450\) | −13.9445 | −0.657350 | ||||||||
\(451\) | 22.7358 | 1.07059 | ||||||||
\(452\) | −10.1385 | −0.476874 | ||||||||
\(453\) | −7.70544 | −0.362033 | ||||||||
\(454\) | −5.52236 | −0.259177 | ||||||||
\(455\) | 12.7456 | 0.597523 | ||||||||
\(456\) | −2.04582 | −0.0958044 | ||||||||
\(457\) | 11.6026 | 0.542748 | 0.271374 | − | 0.962474i | \(-0.412522\pi\) | ||||
0.271374 | + | 0.962474i | \(0.412522\pi\) | |||||||
\(458\) | −8.47458 | −0.395991 | ||||||||
\(459\) | 10.0848 | 0.470720 | ||||||||
\(460\) | 35.7298 | 1.66591 | ||||||||
\(461\) | 19.3868 | 0.902934 | 0.451467 | − | 0.892288i | \(-0.350901\pi\) | ||||
0.451467 | + | 0.892288i | \(0.350901\pi\) | |||||||
\(462\) | 13.3864 | 0.622791 | ||||||||
\(463\) | 30.5402 | 1.41932 | 0.709662 | − | 0.704543i | \(-0.248848\pi\) | ||||
0.709662 | + | 0.704543i | \(0.248848\pi\) | |||||||
\(464\) | 1.76891 | 0.0821194 | ||||||||
\(465\) | −32.9255 | −1.52688 | ||||||||
\(466\) | −11.7599 | −0.544766 | ||||||||
\(467\) | −23.8146 | −1.10201 | −0.551003 | − | 0.834503i | \(-0.685755\pi\) | ||||
−0.551003 | + | 0.834503i | \(0.685755\pi\) | |||||||
\(468\) | −2.46259 | −0.113833 | ||||||||
\(469\) | −12.8433 | −0.593048 | ||||||||
\(470\) | −21.5865 | −0.995709 | ||||||||
\(471\) | −2.77306 | −0.127776 | ||||||||
\(472\) | −7.50249 | −0.345330 | ||||||||
\(473\) | 18.9999 | 0.873618 | ||||||||
\(474\) | 15.2644 | 0.701118 | ||||||||
\(475\) | −11.7636 | −0.539753 | ||||||||
\(476\) | 4.07064 | 0.186577 | ||||||||
\(477\) | −3.44418 | −0.157698 | ||||||||
\(478\) | 2.68897 | 0.122991 | ||||||||
\(479\) | −31.5928 | −1.44351 | −0.721755 | − | 0.692148i | \(-0.756664\pi\) | ||||
−0.721755 | + | 0.692148i | \(0.756664\pi\) | |||||||
\(480\) | −8.37630 | −0.382324 | ||||||||
\(481\) | 20.4980 | 0.934628 | ||||||||
\(482\) | −0.0708398 | −0.00322667 | ||||||||
\(483\) | 26.7521 | 1.21726 | ||||||||
\(484\) | 8.06789 | 0.366722 | ||||||||
\(485\) | 66.8616 | 3.03603 | ||||||||
\(486\) | −11.6759 | −0.529630 | ||||||||
\(487\) | −43.3546 | −1.96459 | −0.982293 | − | 0.187351i | \(-0.940010\pi\) | ||||
−0.982293 | + | 0.187351i | \(0.940010\pi\) | |||||||
\(488\) | 4.68551 | 0.212103 | ||||||||
\(489\) | 6.35322 | 0.287303 | ||||||||
\(490\) | −19.4671 | −0.879433 | ||||||||
\(491\) | 11.7792 | 0.531589 | 0.265794 | − | 0.964030i | \(-0.414366\pi\) | ||||
0.265794 | + | 0.964030i | \(0.414366\pi\) | |||||||
\(492\) | −10.6519 | −0.480224 | ||||||||
\(493\) | 4.80533 | 0.216421 | ||||||||
\(494\) | −2.07746 | −0.0934691 | ||||||||
\(495\) | −21.1932 | −0.952564 | ||||||||
\(496\) | −3.93079 | −0.176498 | ||||||||
\(497\) | 1.63823 | 0.0734846 | ||||||||
\(498\) | 31.3745 | 1.40592 | ||||||||
\(499\) | −14.9516 | −0.669325 | −0.334663 | − | 0.942338i | \(-0.608622\pi\) | ||||
−0.334663 | + | 0.942338i | \(0.608622\pi\) | |||||||
\(500\) | −27.6927 | −1.23845 | ||||||||
\(501\) | −42.4238 | −1.89536 | ||||||||
\(502\) | −28.0554 | −1.25217 | ||||||||
\(503\) | −11.3813 | −0.507469 | −0.253734 | − | 0.967274i | \(-0.581659\pi\) | ||||
−0.253734 | + | 0.967274i | \(0.581659\pi\) | |||||||
\(504\) | −1.77626 | −0.0791207 | ||||||||
\(505\) | −5.36617 | −0.238792 | ||||||||
\(506\) | 38.1064 | 1.69404 | ||||||||
\(507\) | 17.7663 | 0.789029 | ||||||||
\(508\) | −11.5486 | −0.512385 | ||||||||
\(509\) | −8.22872 | −0.364732 | −0.182366 | − | 0.983231i | \(-0.558376\pi\) | ||||
−0.182366 | + | 0.983231i | \(0.558376\pi\) | |||||||
\(510\) | −22.7547 | −1.00759 | ||||||||
\(511\) | 17.0201 | 0.752923 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.71237 | −0.163905 | ||||||||
\(514\) | 11.4019 | 0.502915 | ||||||||
\(515\) | 2.64586 | 0.116590 | ||||||||
\(516\) | −8.90161 | −0.391872 | ||||||||
\(517\) | −23.0223 | −1.01252 | ||||||||
\(518\) | 14.7851 | 0.649620 | ||||||||
\(519\) | −32.6623 | −1.43371 | ||||||||
\(520\) | −8.50581 | −0.373005 | ||||||||
\(521\) | 14.5267 | 0.636428 | 0.318214 | − | 0.948019i | \(-0.396917\pi\) | ||||
0.318214 | + | 0.948019i | \(0.396917\pi\) | |||||||
\(522\) | −2.09684 | −0.0917763 | ||||||||
\(523\) | 43.6760 | 1.90982 | 0.954909 | − | 0.296898i | \(-0.0959521\pi\) | ||||
0.954909 | + | 0.296898i | \(0.0959521\pi\) | |||||||
\(524\) | −2.24440 | −0.0980469 | ||||||||
\(525\) | −36.0624 | −1.57389 | ||||||||
\(526\) | 32.2678 | 1.40694 | ||||||||
\(527\) | −10.6782 | −0.465150 | ||||||||
\(528\) | −8.93345 | −0.388779 | ||||||||
\(529\) | 53.1540 | 2.31104 | ||||||||
\(530\) | −11.8962 | −0.516738 | ||||||||
\(531\) | 8.89338 | 0.385940 | ||||||||
\(532\) | −1.49846 | −0.0649663 | ||||||||
\(533\) | −10.8166 | −0.468518 | ||||||||
\(534\) | 14.8147 | 0.641093 | ||||||||
\(535\) | −71.5011 | −3.09126 | ||||||||
\(536\) | 8.57101 | 0.370211 | ||||||||
\(537\) | −13.7744 | −0.594409 | ||||||||
\(538\) | 25.3155 | 1.09143 | ||||||||
\(539\) | −20.7619 | −0.894280 | ||||||||
\(540\) | −15.1997 | −0.654092 | ||||||||
\(541\) | −24.4618 | −1.05170 | −0.525848 | − | 0.850578i | \(-0.676252\pi\) | ||||
−0.525848 | + | 0.850578i | \(0.676252\pi\) | |||||||
\(542\) | 7.88294 | 0.338601 | ||||||||
\(543\) | 23.3799 | 1.00333 | ||||||||
\(544\) | −2.71655 | −0.116471 | ||||||||
\(545\) | −55.4473 | −2.37510 | ||||||||
\(546\) | −6.36860 | −0.272551 | ||||||||
\(547\) | −5.66493 | −0.242215 | −0.121107 | − | 0.992639i | \(-0.538645\pi\) | ||||
−0.121107 | + | 0.992639i | \(0.538645\pi\) | |||||||
\(548\) | 0.788239 | 0.0336719 | ||||||||
\(549\) | −5.55415 | −0.237045 | ||||||||
\(550\) | −51.3681 | −2.19034 | ||||||||
\(551\) | −1.76891 | −0.0753579 | ||||||||
\(552\) | −17.8531 | −0.759879 | ||||||||
\(553\) | 11.1804 | 0.475438 | ||||||||
\(554\) | −6.05207 | −0.257128 | ||||||||
\(555\) | −82.6479 | −3.50821 | ||||||||
\(556\) | 0.0659961 | 0.00279886 | ||||||||
\(557\) | 11.5574 | 0.489703 | 0.244852 | − | 0.969561i | \(-0.421261\pi\) | ||||
0.244852 | + | 0.969561i | \(0.421261\pi\) | |||||||
\(558\) | 4.65952 | 0.197253 | ||||||||
\(559\) | −9.03925 | −0.382319 | ||||||||
\(560\) | −6.13520 | −0.259259 | ||||||||
\(561\) | −24.2682 | −1.02460 | ||||||||
\(562\) | 23.4655 | 0.989833 | ||||||||
\(563\) | −10.8222 | −0.456100 | −0.228050 | − | 0.973649i | \(-0.573235\pi\) | ||||
−0.228050 | + | 0.973649i | \(0.573235\pi\) | |||||||
\(564\) | 10.7861 | 0.454177 | ||||||||
\(565\) | 41.5104 | 1.74635 | ||||||||
\(566\) | −31.9526 | −1.34307 | ||||||||
\(567\) | −16.7093 | −0.701726 | ||||||||
\(568\) | −1.09328 | −0.0458729 | ||||||||
\(569\) | 6.77462 | 0.284007 | 0.142003 | − | 0.989866i | \(-0.454646\pi\) | ||||
0.142003 | + | 0.989866i | \(0.454646\pi\) | |||||||
\(570\) | 8.37630 | 0.350845 | ||||||||
\(571\) | 2.24551 | 0.0939718 | 0.0469859 | − | 0.998896i | \(-0.485038\pi\) | ||||
0.0469859 | + | 0.998896i | \(0.485038\pi\) | |||||||
\(572\) | −9.07158 | −0.379302 | ||||||||
\(573\) | −46.6782 | −1.95001 | ||||||||
\(574\) | −7.80193 | −0.325646 | ||||||||
\(575\) | −102.657 | −4.28109 | ||||||||
\(576\) | 1.18539 | 0.0493913 | ||||||||
\(577\) | 0.473162 | 0.0196980 | 0.00984899 | − | 0.999951i | \(-0.496865\pi\) | ||||
0.00984899 | + | 0.999951i | \(0.496865\pi\) | |||||||
\(578\) | 9.62034 | 0.400153 | ||||||||
\(579\) | 7.50623 | 0.311948 | ||||||||
\(580\) | −7.24251 | −0.300729 | ||||||||
\(581\) | 22.9801 | 0.953377 | ||||||||
\(582\) | −33.4088 | −1.38484 | ||||||||
\(583\) | −12.6875 | −0.525462 | ||||||||
\(584\) | −11.3584 | −0.470014 | ||||||||
\(585\) | 10.0827 | 0.416869 | ||||||||
\(586\) | 0.530799 | 0.0219271 | ||||||||
\(587\) | 18.2336 | 0.752581 | 0.376291 | − | 0.926502i | \(-0.377199\pi\) | ||||
0.376291 | + | 0.926502i | \(0.377199\pi\) | |||||||
\(588\) | 9.72712 | 0.401140 | ||||||||
\(589\) | 3.93079 | 0.161966 | ||||||||
\(590\) | 30.7178 | 1.26463 | ||||||||
\(591\) | 5.99667 | 0.246670 | ||||||||
\(592\) | −9.86688 | −0.405526 | ||||||||
\(593\) | −32.4418 | −1.33223 | −0.666113 | − | 0.745850i | \(-0.732043\pi\) | ||||
−0.666113 | + | 0.745850i | \(0.732043\pi\) | |||||||
\(594\) | −16.2107 | −0.665134 | ||||||||
\(595\) | −16.6666 | −0.683263 | ||||||||
\(596\) | 21.7928 | 0.892666 | ||||||||
\(597\) | −25.1716 | −1.03021 | ||||||||
\(598\) | −18.1292 | −0.741357 | ||||||||
\(599\) | 1.69293 | 0.0691714 | 0.0345857 | − | 0.999402i | \(-0.488989\pi\) | ||||
0.0345857 | + | 0.999402i | \(0.488989\pi\) | |||||||
\(600\) | 24.0663 | 0.982504 | ||||||||
\(601\) | −36.2204 | −1.47746 | −0.738731 | − | 0.674000i | \(-0.764575\pi\) | ||||
−0.738731 | + | 0.674000i | \(0.764575\pi\) | |||||||
\(602\) | −6.51996 | −0.265734 | ||||||||
\(603\) | −10.1600 | −0.413747 | ||||||||
\(604\) | 3.76642 | 0.153254 | ||||||||
\(605\) | −33.0327 | −1.34297 | ||||||||
\(606\) | 2.68132 | 0.108921 | ||||||||
\(607\) | 22.6619 | 0.919819 | 0.459910 | − | 0.887966i | \(-0.347882\pi\) | ||||
0.459910 | + | 0.887966i | \(0.347882\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −5.42272 | −0.219740 | ||||||||
\(610\) | −19.1841 | −0.776740 | ||||||||
\(611\) | 10.9529 | 0.443106 | ||||||||
\(612\) | 3.22017 | 0.130168 | ||||||||
\(613\) | −33.5176 | −1.35376 | −0.676881 | − | 0.736092i | \(-0.736669\pi\) | ||||
−0.676881 | + | 0.736092i | \(0.736669\pi\) | |||||||
\(614\) | −12.2045 | −0.492532 | ||||||||
\(615\) | 43.6124 | 1.75862 | ||||||||
\(616\) | −6.54328 | −0.263636 | ||||||||
\(617\) | −41.9273 | −1.68793 | −0.843965 | − | 0.536399i | \(-0.819784\pi\) | ||||
−0.843965 | + | 0.536399i | \(0.819784\pi\) | |||||||
\(618\) | −1.32206 | −0.0531809 | ||||||||
\(619\) | 15.7090 | 0.631398 | 0.315699 | − | 0.948859i | \(-0.397761\pi\) | ||||
0.315699 | + | 0.948859i | \(0.397761\pi\) | |||||||
\(620\) | 16.0940 | 0.646351 | ||||||||
\(621\) | −32.3965 | −1.30003 | ||||||||
\(622\) | −20.4475 | −0.819871 | ||||||||
\(623\) | 10.8510 | 0.434734 | ||||||||
\(624\) | 4.25010 | 0.170140 | ||||||||
\(625\) | 54.5651 | 2.18261 | ||||||||
\(626\) | −32.5985 | −1.30290 | ||||||||
\(627\) | 8.93345 | 0.356768 | ||||||||
\(628\) | 1.35547 | 0.0540892 | ||||||||
\(629\) | −26.8039 | −1.06874 | ||||||||
\(630\) | 7.27260 | 0.289747 | ||||||||
\(631\) | 41.4461 | 1.64994 | 0.824972 | − | 0.565174i | \(-0.191191\pi\) | ||||
0.824972 | + | 0.565174i | \(0.191191\pi\) | |||||||
\(632\) | −7.46127 | −0.296793 | ||||||||
\(633\) | 2.04582 | 0.0813141 | ||||||||
\(634\) | 26.8916 | 1.06800 | ||||||||
\(635\) | 47.2838 | 1.87640 | ||||||||
\(636\) | 5.94419 | 0.235702 | ||||||||
\(637\) | 9.87753 | 0.391362 | ||||||||
\(638\) | −7.72425 | −0.305806 | ||||||||
\(639\) | 1.29596 | 0.0512674 | ||||||||
\(640\) | 4.09434 | 0.161843 | ||||||||
\(641\) | 38.9245 | 1.53742 | 0.768712 | − | 0.639595i | \(-0.220898\pi\) | ||||
0.768712 | + | 0.639595i | \(0.220898\pi\) | |||||||
\(642\) | 35.7270 | 1.41003 | ||||||||
\(643\) | −4.98299 | −0.196510 | −0.0982550 | − | 0.995161i | \(-0.531326\pi\) | ||||
−0.0982550 | + | 0.995161i | \(0.531326\pi\) | |||||||
\(644\) | −13.0765 | −0.515285 | ||||||||
\(645\) | 36.4462 | 1.43507 | ||||||||
\(646\) | 2.71655 | 0.106881 | ||||||||
\(647\) | −12.8205 | −0.504024 | −0.252012 | − | 0.967724i | \(-0.581092\pi\) | ||||
−0.252012 | + | 0.967724i | \(0.581092\pi\) | |||||||
\(648\) | 11.1510 | 0.438053 | ||||||||
\(649\) | 32.7610 | 1.28598 | ||||||||
\(650\) | 24.4384 | 0.958555 | ||||||||
\(651\) | 12.0501 | 0.472282 | ||||||||
\(652\) | −3.10546 | −0.121619 | ||||||||
\(653\) | 41.3605 | 1.61856 | 0.809281 | − | 0.587422i | \(-0.199857\pi\) | ||||
0.809281 | + | 0.587422i | \(0.199857\pi\) | |||||||
\(654\) | 27.7054 | 1.08337 | ||||||||
\(655\) | 9.18932 | 0.359057 | ||||||||
\(656\) | 5.20665 | 0.203285 | ||||||||
\(657\) | 13.4641 | 0.525286 | ||||||||
\(658\) | 7.90026 | 0.307984 | ||||||||
\(659\) | −23.9235 | −0.931926 | −0.465963 | − | 0.884804i | \(-0.654292\pi\) | ||||
−0.465963 | + | 0.884804i | \(0.654292\pi\) | |||||||
\(660\) | 36.5766 | 1.42374 | ||||||||
\(661\) | 48.5286 | 1.88754 | 0.943771 | − | 0.330599i | \(-0.107251\pi\) | ||||
0.943771 | + | 0.330599i | \(0.107251\pi\) | |||||||
\(662\) | 28.2584 | 1.09829 | ||||||||
\(663\) | 11.5456 | 0.448395 | ||||||||
\(664\) | −15.3359 | −0.595147 | ||||||||
\(665\) | 6.13520 | 0.237913 | ||||||||
\(666\) | 11.6961 | 0.453215 | ||||||||
\(667\) | −15.4366 | −0.597707 | ||||||||
\(668\) | 20.7368 | 0.802331 | ||||||||
\(669\) | 30.9257 | 1.19566 | ||||||||
\(670\) | −35.0927 | −1.35575 | ||||||||
\(671\) | −20.4601 | −0.789854 | ||||||||
\(672\) | 3.06558 | 0.118257 | ||||||||
\(673\) | −41.8990 | −1.61509 | −0.807545 | − | 0.589806i | \(-0.799204\pi\) | ||||
−0.807545 | + | 0.589806i | \(0.799204\pi\) | |||||||
\(674\) | 19.2134 | 0.740072 | ||||||||
\(675\) | 43.6710 | 1.68090 | ||||||||
\(676\) | −8.68418 | −0.334007 | ||||||||
\(677\) | −14.1658 | −0.544438 | −0.272219 | − | 0.962235i | \(-0.587757\pi\) | ||||
−0.272219 | + | 0.962235i | \(0.587757\pi\) | |||||||
\(678\) | −20.7415 | −0.796573 | ||||||||
\(679\) | −24.4701 | −0.939078 | ||||||||
\(680\) | 11.1225 | 0.426528 | ||||||||
\(681\) | −11.2978 | −0.432931 | ||||||||
\(682\) | 17.1645 | 0.657263 | ||||||||
\(683\) | −1.01076 | −0.0386757 | −0.0193378 | − | 0.999813i | \(-0.506156\pi\) | ||||
−0.0193378 | + | 0.999813i | \(0.506156\pi\) | |||||||
\(684\) | −1.18539 | −0.0453245 | ||||||||
\(685\) | −3.22732 | −0.123310 | ||||||||
\(686\) | 17.6138 | 0.672498 | ||||||||
\(687\) | −17.3375 | −0.661467 | ||||||||
\(688\) | 4.35112 | 0.165885 | ||||||||
\(689\) | 6.03610 | 0.229957 | ||||||||
\(690\) | 73.0968 | 2.78275 | ||||||||
\(691\) | 0.825563 | 0.0314059 | 0.0157030 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157030 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(692\) | 15.9654 | 0.606912 | ||||||||
\(693\) | 7.75634 | 0.294639 | ||||||||
\(694\) | 16.9938 | 0.645077 | ||||||||
\(695\) | −0.270211 | −0.0102497 | ||||||||
\(696\) | 3.61887 | 0.137173 | ||||||||
\(697\) | 14.1441 | 0.535747 | ||||||||
\(698\) | 11.9704 | 0.453087 | ||||||||
\(699\) | −24.0586 | −0.909981 | ||||||||
\(700\) | 17.6273 | 0.666250 | ||||||||
\(701\) | −38.0743 | −1.43805 | −0.719024 | − | 0.694985i | \(-0.755411\pi\) | ||||
−0.719024 | + | 0.694985i | \(0.755411\pi\) | |||||||
\(702\) | 7.71228 | 0.291081 | ||||||||
\(703\) | 9.86688 | 0.372136 | ||||||||
\(704\) | 4.36668 | 0.164575 | ||||||||
\(705\) | −44.1621 | −1.66324 | ||||||||
\(706\) | −30.9605 | −1.16521 | ||||||||
\(707\) | 1.96392 | 0.0738610 | ||||||||
\(708\) | −15.3488 | −0.576842 | ||||||||
\(709\) | −7.04075 | −0.264421 | −0.132211 | − | 0.991222i | \(-0.542207\pi\) | ||||
−0.132211 | + | 0.991222i | \(0.542207\pi\) | |||||||
\(710\) | 4.47625 | 0.167991 | ||||||||
\(711\) | 8.84451 | 0.331695 | ||||||||
\(712\) | −7.24142 | −0.271384 | ||||||||
\(713\) | 34.3026 | 1.28464 | ||||||||
\(714\) | 8.32780 | 0.311660 | ||||||||
\(715\) | 37.1422 | 1.38904 | ||||||||
\(716\) | 6.73294 | 0.251622 | ||||||||
\(717\) | 5.50116 | 0.205445 | ||||||||
\(718\) | 30.9264 | 1.15416 | ||||||||
\(719\) | −47.0755 | −1.75562 | −0.877810 | − | 0.479009i | \(-0.840996\pi\) | ||||
−0.877810 | + | 0.479009i | \(0.840996\pi\) | |||||||
\(720\) | −4.85339 | −0.180875 | ||||||||
\(721\) | −0.968336 | −0.0360627 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −0.144926 | −0.00538985 | ||||||||
\(724\) | −11.4281 | −0.424723 | ||||||||
\(725\) | 20.8088 | 0.772819 | ||||||||
\(726\) | 16.5055 | 0.612576 | ||||||||
\(727\) | −38.1337 | −1.41430 | −0.707151 | − | 0.707062i | \(-0.750020\pi\) | ||||
−0.707151 | + | 0.707062i | \(0.750020\pi\) | |||||||
\(728\) | 3.11298 | 0.115375 | ||||||||
\(729\) | 9.56624 | 0.354305 | ||||||||
\(730\) | 46.5052 | 1.72123 | ||||||||
\(731\) | 11.8200 | 0.437180 | ||||||||
\(732\) | 9.58572 | 0.354298 | ||||||||
\(733\) | −12.9104 | −0.476856 | −0.238428 | − | 0.971160i | \(-0.576632\pi\) | ||||
−0.238428 | + | 0.971160i | \(0.576632\pi\) | |||||||
\(734\) | 36.5323 | 1.34843 | ||||||||
\(735\) | −39.8262 | −1.46901 | ||||||||
\(736\) | 8.72662 | 0.321668 | ||||||||
\(737\) | −37.4269 | −1.37864 | ||||||||
\(738\) | −6.17191 | −0.227191 | ||||||||
\(739\) | 9.26237 | 0.340722 | 0.170361 | − | 0.985382i | \(-0.445507\pi\) | ||||
0.170361 | + | 0.985382i | \(0.445507\pi\) | |||||||
\(740\) | 40.3984 | 1.48507 | ||||||||
\(741\) | −4.25010 | −0.156131 | ||||||||
\(742\) | 4.35380 | 0.159833 | ||||||||
\(743\) | −8.65339 | −0.317462 | −0.158731 | − | 0.987322i | \(-0.550740\pi\) | ||||
−0.158731 | + | 0.987322i | \(0.550740\pi\) | |||||||
\(744\) | −8.04171 | −0.294823 | ||||||||
\(745\) | −89.2270 | −3.26903 | ||||||||
\(746\) | −14.1511 | −0.518110 | ||||||||
\(747\) | 18.1790 | 0.665135 | ||||||||
\(748\) | 11.8623 | 0.433729 | ||||||||
\(749\) | 26.1681 | 0.956162 | ||||||||
\(750\) | −56.6543 | −2.06872 | ||||||||
\(751\) | −39.3621 | −1.43634 | −0.718172 | − | 0.695865i | \(-0.755021\pi\) | ||||
−0.718172 | + | 0.695865i | \(0.755021\pi\) | |||||||
\(752\) | −5.27226 | −0.192260 | ||||||||
\(753\) | −57.3963 | −2.09164 | ||||||||
\(754\) | 3.67482 | 0.133829 | ||||||||
\(755\) | −15.4210 | −0.561229 | ||||||||
\(756\) | 5.56283 | 0.202318 | ||||||||
\(757\) | −30.3091 | −1.10160 | −0.550802 | − | 0.834636i | \(-0.685678\pi\) | ||||
−0.550802 | + | 0.834636i | \(0.685678\pi\) | |||||||
\(758\) | −7.71892 | −0.280364 | ||||||||
\(759\) | 77.9589 | 2.82973 | ||||||||
\(760\) | −4.09434 | −0.148517 | ||||||||
\(761\) | 16.7137 | 0.605871 | 0.302936 | − | 0.953011i | \(-0.402033\pi\) | ||||
0.302936 | + | 0.953011i | \(0.402033\pi\) | |||||||
\(762\) | −23.6263 | −0.855891 | ||||||||
\(763\) | 20.2927 | 0.734647 | ||||||||
\(764\) | 22.8164 | 0.825467 | ||||||||
\(765\) | −13.1845 | −0.476687 | ||||||||
\(766\) | −12.3725 | −0.447038 | ||||||||
\(767\) | −15.5861 | −0.562781 | ||||||||
\(768\) | −2.04582 | −0.0738223 | ||||||||
\(769\) | 37.2199 | 1.34218 | 0.671092 | − | 0.741374i | \(-0.265825\pi\) | ||||
0.671092 | + | 0.741374i | \(0.265825\pi\) | |||||||
\(770\) | 26.7904 | 0.965460 | ||||||||
\(771\) | 23.3262 | 0.840074 | ||||||||
\(772\) | −3.66905 | −0.132052 | ||||||||
\(773\) | −42.1269 | −1.51520 | −0.757599 | − | 0.652720i | \(-0.773628\pi\) | ||||
−0.757599 | + | 0.652720i | \(0.773628\pi\) | |||||||
\(774\) | −5.15777 | −0.185392 | ||||||||
\(775\) | −46.2405 | −1.66101 | ||||||||
\(776\) | 16.3302 | 0.586221 | ||||||||
\(777\) | 30.2477 | 1.08513 | ||||||||
\(778\) | 25.4546 | 0.912591 | ||||||||
\(779\) | −5.20665 | −0.186547 | ||||||||
\(780\) | −17.4014 | −0.623070 | ||||||||
\(781\) | 4.77399 | 0.170827 | ||||||||
\(782\) | 23.7063 | 0.847737 | ||||||||
\(783\) | 6.56683 | 0.234679 | ||||||||
\(784\) | −4.75463 | −0.169808 | ||||||||
\(785\) | −5.54977 | −0.198080 | ||||||||
\(786\) | −4.59163 | −0.163778 | ||||||||
\(787\) | −27.6128 | −0.984291 | −0.492146 | − | 0.870513i | \(-0.663787\pi\) | ||||
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(788\) | −2.93118 | −0.104419 | ||||||||
\(789\) | 66.0142 | 2.35017 | ||||||||
\(790\) | 30.5490 | 1.08688 | ||||||||
\(791\) | −15.1921 | −0.540168 | ||||||||
\(792\) | −5.17622 | −0.183929 | ||||||||
\(793\) | 9.73393 | 0.345662 | ||||||||
\(794\) | −12.6444 | −0.448733 | ||||||||
\(795\) | −24.3375 | −0.863164 | ||||||||
\(796\) | 12.3039 | 0.436100 | ||||||||
\(797\) | −44.7859 | −1.58640 | −0.793200 | − | 0.608962i | \(-0.791586\pi\) | ||||
−0.793200 | + | 0.608962i | \(0.791586\pi\) | |||||||
\(798\) | −3.06558 | −0.108520 | ||||||||
\(799\) | −14.3224 | −0.506689 | ||||||||
\(800\) | −11.7636 | −0.415908 | ||||||||
\(801\) | 8.58391 | 0.303298 | ||||||||
\(802\) | 14.7905 | 0.522272 | ||||||||
\(803\) | 49.5985 | 1.75029 | ||||||||
\(804\) | 17.5348 | 0.618404 | ||||||||
\(805\) | 53.5396 | 1.88702 | ||||||||
\(806\) | −8.16605 | −0.287637 | ||||||||
\(807\) | 51.7910 | 1.82313 | ||||||||
\(808\) | −1.31063 | −0.0461078 | ||||||||
\(809\) | 37.4511 | 1.31671 | 0.658355 | − | 0.752708i | \(-0.271253\pi\) | ||||
0.658355 | + | 0.752708i | \(0.271253\pi\) | |||||||
\(810\) | −45.6561 | −1.60419 | ||||||||
\(811\) | −38.7566 | −1.36093 | −0.680464 | − | 0.732782i | \(-0.738222\pi\) | ||||
−0.680464 | + | 0.732782i | \(0.738222\pi\) | |||||||
\(812\) | 2.65063 | 0.0930188 | ||||||||
\(813\) | 16.1271 | 0.565602 | ||||||||
\(814\) | 43.0855 | 1.51015 | ||||||||
\(815\) | 12.7148 | 0.445381 | ||||||||
\(816\) | −5.55758 | −0.194554 | ||||||||
\(817\) | −4.35112 | −0.152226 | ||||||||
\(818\) | 7.91564 | 0.276764 | ||||||||
\(819\) | −3.69009 | −0.128942 | ||||||||
\(820\) | −21.3178 | −0.744450 | ||||||||
\(821\) | 28.0920 | 0.980417 | 0.490208 | − | 0.871605i | \(-0.336921\pi\) | ||||
0.490208 | + | 0.871605i | \(0.336921\pi\) | |||||||
\(822\) | 1.61260 | 0.0562458 | ||||||||
\(823\) | 32.8455 | 1.14492 | 0.572461 | − | 0.819932i | \(-0.305989\pi\) | ||||
0.572461 | + | 0.819932i | \(0.305989\pi\) | |||||||
\(824\) | 0.646222 | 0.0225122 | ||||||||
\(825\) | −105.090 | −3.65876 | ||||||||
\(826\) | −11.2422 | −0.391165 | ||||||||
\(827\) | −7.59414 | −0.264074 | −0.132037 | − | 0.991245i | \(-0.542152\pi\) | ||||
−0.132037 | + | 0.991245i | \(0.542152\pi\) | |||||||
\(828\) | −10.3445 | −0.359495 | ||||||||
\(829\) | −24.7291 | −0.858878 | −0.429439 | − | 0.903096i | \(-0.641289\pi\) | ||||
−0.429439 | + | 0.903096i | \(0.641289\pi\) | |||||||
\(830\) | 62.7903 | 2.17948 | ||||||||
\(831\) | −12.3815 | −0.429508 | ||||||||
\(832\) | −2.07746 | −0.0720228 | ||||||||
\(833\) | −12.9162 | −0.447520 | ||||||||
\(834\) | 0.135016 | 0.00467523 | ||||||||
\(835\) | −84.9036 | −2.93821 | ||||||||
\(836\) | −4.36668 | −0.151025 | ||||||||
\(837\) | −14.5926 | −0.504393 | ||||||||
\(838\) | −3.22411 | −0.111375 | ||||||||
\(839\) | −14.8366 | −0.512215 | −0.256107 | − | 0.966648i | \(-0.582440\pi\) | ||||
−0.256107 | + | 0.966648i | \(0.582440\pi\) | |||||||
\(840\) | −12.5515 | −0.433069 | ||||||||
\(841\) | −25.8710 | −0.892102 | ||||||||
\(842\) | −26.3204 | −0.907061 | ||||||||
\(843\) | 48.0063 | 1.65342 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 35.5560 | 1.22316 | ||||||||
\(846\) | 6.24969 | 0.214869 | ||||||||
\(847\) | 12.0894 | 0.415396 | ||||||||
\(848\) | −2.90552 | −0.0997761 | ||||||||
\(849\) | −65.3693 | −2.24347 | ||||||||
\(850\) | −31.9566 | −1.09610 | ||||||||
\(851\) | 86.1045 | 2.95163 | ||||||||
\(852\) | −2.23665 | −0.0766264 | ||||||||
\(853\) | 46.3414 | 1.58670 | 0.793350 | − | 0.608766i | \(-0.208335\pi\) | ||||
0.793350 | + | 0.608766i | \(0.208335\pi\) | |||||||
\(854\) | 7.02103 | 0.240255 | ||||||||
\(855\) | 4.85339 | 0.165983 | ||||||||
\(856\) | −17.4634 | −0.596886 | ||||||||
\(857\) | 38.8509 | 1.32712 | 0.663561 | − | 0.748122i | \(-0.269044\pi\) | ||||
0.663561 | + | 0.748122i | \(0.269044\pi\) | |||||||
\(858\) | −18.5588 | −0.633589 | ||||||||
\(859\) | −9.96164 | −0.339887 | −0.169943 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169943 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(860\) | −17.8150 | −0.607485 | ||||||||
\(861\) | −15.9614 | −0.543962 | ||||||||
\(862\) | 2.92758 | 0.0997136 | ||||||||
\(863\) | −9.72885 | −0.331174 | −0.165587 | − | 0.986195i | \(-0.552952\pi\) | ||||
−0.165587 | + | 0.986195i | \(0.552952\pi\) | |||||||
\(864\) | −3.71237 | −0.126297 | ||||||||
\(865\) | −65.3676 | −2.22257 | ||||||||
\(866\) | 15.5142 | 0.527196 | ||||||||
\(867\) | 19.6815 | 0.668419 | ||||||||
\(868\) | −5.89012 | −0.199924 | ||||||||
\(869\) | 32.5810 | 1.10523 | ||||||||
\(870\) | −14.8169 | −0.502339 | ||||||||
\(871\) | 17.8059 | 0.603330 | ||||||||
\(872\) | −13.5424 | −0.458604 | ||||||||
\(873\) | −19.3577 | −0.655159 | ||||||||
\(874\) | −8.72662 | −0.295182 | ||||||||
\(875\) | −41.4963 | −1.40283 | ||||||||
\(876\) | −23.2373 | −0.785114 | ||||||||
\(877\) | −41.7847 | −1.41097 | −0.705484 | − | 0.708726i | \(-0.749270\pi\) | ||||
−0.705484 | + | 0.708726i | \(0.749270\pi\) | |||||||
\(878\) | −25.6971 | −0.867234 | ||||||||
\(879\) | 1.08592 | 0.0366272 | ||||||||
\(880\) | −17.8787 | −0.602690 | ||||||||
\(881\) | 36.0925 | 1.21599 | 0.607993 | − | 0.793942i | \(-0.291975\pi\) | ||||
0.607993 | + | 0.793942i | \(0.291975\pi\) | |||||||
\(882\) | 5.63609 | 0.189777 | ||||||||
\(883\) | 11.4951 | 0.386841 | 0.193421 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193421 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(884\) | −5.64352 | −0.189812 | ||||||||
\(885\) | 62.8431 | 2.11245 | ||||||||
\(886\) | 4.35774 | 0.146401 | ||||||||
\(887\) | 38.3961 | 1.28921 | 0.644607 | − | 0.764514i | \(-0.277021\pi\) | ||||
0.644607 | + | 0.764514i | \(0.277021\pi\) | |||||||
\(888\) | −20.1859 | −0.677394 | ||||||||
\(889\) | −17.3050 | −0.580392 | ||||||||
\(890\) | 29.6489 | 0.993832 | ||||||||
\(891\) | −48.6929 | −1.63127 | ||||||||
\(892\) | −15.1165 | −0.506138 | ||||||||
\(893\) | 5.27226 | 0.176430 | ||||||||
\(894\) | 44.5841 | 1.49112 | ||||||||
\(895\) | −27.5670 | −0.921462 | ||||||||
\(896\) | −1.49846 | −0.0500599 | ||||||||
\(897\) | −37.0891 | −1.23837 | ||||||||
\(898\) | 13.8264 | 0.461393 | ||||||||
\(899\) | −6.95320 | −0.231902 | ||||||||
\(900\) | 13.9445 | 0.464817 | ||||||||
\(901\) | −7.89301 | −0.262954 | ||||||||
\(902\) | −22.7358 | −0.757018 | ||||||||
\(903\) | −13.3387 | −0.443883 | ||||||||
\(904\) | 10.1385 | 0.337201 | ||||||||
\(905\) | 46.7906 | 1.55537 | ||||||||
\(906\) | 7.70544 | 0.255996 | ||||||||
\(907\) | −41.2826 | −1.37077 | −0.685383 | − | 0.728183i | \(-0.740365\pi\) | ||||
−0.685383 | + | 0.728183i | \(0.740365\pi\) | |||||||
\(908\) | 5.52236 | 0.183266 | ||||||||
\(909\) | 1.55361 | 0.0515300 | ||||||||
\(910\) | −12.7456 | −0.422512 | ||||||||
\(911\) | 22.5764 | 0.747991 | 0.373995 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373995 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(912\) | 2.04582 | 0.0677440 | ||||||||
\(913\) | 66.9669 | 2.21628 | ||||||||
\(914\) | −11.6026 | −0.383781 | ||||||||
\(915\) | −39.2472 | −1.29747 | ||||||||
\(916\) | 8.47458 | 0.280008 | ||||||||
\(917\) | −3.36313 | −0.111060 | ||||||||
\(918\) | −10.0848 | −0.332850 | ||||||||
\(919\) | −5.67769 | −0.187290 | −0.0936449 | − | 0.995606i | \(-0.529852\pi\) | ||||
−0.0936449 | + | 0.995606i | \(0.529852\pi\) | |||||||
\(920\) | −35.7298 | −1.17798 | ||||||||
\(921\) | −24.9682 | −0.822729 | ||||||||
\(922\) | −19.3868 | −0.638471 | ||||||||
\(923\) | −2.27124 | −0.0747586 | ||||||||
\(924\) | −13.3864 | −0.440380 | ||||||||
\(925\) | −116.070 | −3.81637 | ||||||||
\(926\) | −30.5402 | −1.00361 | ||||||||
\(927\) | −0.766026 | −0.0251596 | ||||||||
\(928\) | −1.76891 | −0.0580672 | ||||||||
\(929\) | −24.6134 | −0.807540 | −0.403770 | − | 0.914860i | \(-0.632300\pi\) | ||||
−0.403770 | + | 0.914860i | \(0.632300\pi\) | |||||||
\(930\) | 32.9255 | 1.07967 | ||||||||
\(931\) | 4.75463 | 0.155827 | ||||||||
\(932\) | 11.7599 | 0.385208 | ||||||||
\(933\) | −41.8320 | −1.36952 | ||||||||
\(934\) | 23.8146 | 0.779236 | ||||||||
\(935\) | −48.5684 | −1.58836 | ||||||||
\(936\) | 2.46259 | 0.0804924 | ||||||||
\(937\) | −20.7073 | −0.676477 | −0.338239 | − | 0.941060i | \(-0.609831\pi\) | ||||
−0.338239 | + | 0.941060i | \(0.609831\pi\) | |||||||
\(938\) | 12.8433 | 0.419348 | ||||||||
\(939\) | −66.6907 | −2.17637 | ||||||||
\(940\) | 21.5865 | 0.704072 | ||||||||
\(941\) | 7.68290 | 0.250455 | 0.125228 | − | 0.992128i | \(-0.460034\pi\) | ||||
0.125228 | + | 0.992128i | \(0.460034\pi\) | |||||||
\(942\) | 2.77306 | 0.0903510 | ||||||||
\(943\) | −45.4365 | −1.47961 | ||||||||
\(944\) | 7.50249 | 0.244185 | ||||||||
\(945\) | −22.7761 | −0.740907 | ||||||||
\(946\) | −18.9999 | −0.617741 | ||||||||
\(947\) | −30.5206 | −0.991787 | −0.495894 | − | 0.868383i | \(-0.665159\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665159\pi\) | |||||||
\(948\) | −15.2644 | −0.495766 | ||||||||
\(949\) | −23.5966 | −0.765976 | ||||||||
\(950\) | 11.7636 | 0.381663 | ||||||||
\(951\) | 55.0154 | 1.78400 | ||||||||
\(952\) | −4.07064 | −0.131930 | ||||||||
\(953\) | −7.70126 | −0.249468 | −0.124734 | − | 0.992190i | \(-0.539808\pi\) | ||||
−0.124734 | + | 0.992190i | \(0.539808\pi\) | |||||||
\(954\) | 3.44418 | 0.111509 | ||||||||
\(955\) | −93.4181 | −3.02294 | ||||||||
\(956\) | −2.68897 | −0.0869676 | ||||||||
\(957\) | −15.8024 | −0.510820 | ||||||||
\(958\) | 31.5928 | 1.02072 | ||||||||
\(959\) | 1.18114 | 0.0381411 | ||||||||
\(960\) | 8.37630 | 0.270344 | ||||||||
\(961\) | −15.5489 | −0.501576 | ||||||||
\(962\) | −20.4980 | −0.660882 | ||||||||
\(963\) | 20.7009 | 0.667078 | ||||||||
\(964\) | 0.0708398 | 0.00228160 | ||||||||
\(965\) | 15.0224 | 0.483587 | ||||||||
\(966\) | −26.7521 | −0.860736 | ||||||||
\(967\) | 10.0243 | 0.322358 | 0.161179 | − | 0.986925i | \(-0.448470\pi\) | ||||
0.161179 | + | 0.986925i | \(0.448470\pi\) | |||||||
\(968\) | −8.06789 | −0.259312 | ||||||||
\(969\) | 5.55758 | 0.178535 | ||||||||
\(970\) | −66.8616 | −2.14680 | ||||||||
\(971\) | 25.6509 | 0.823177 | 0.411589 | − | 0.911370i | \(-0.364974\pi\) | ||||
0.411589 | + | 0.911370i | \(0.364974\pi\) | |||||||
\(972\) | 11.6759 | 0.374505 | ||||||||
\(973\) | 0.0988922 | 0.00317034 | ||||||||
\(974\) | 43.3546 | 1.38917 | ||||||||
\(975\) | 49.9967 | 1.60118 | ||||||||
\(976\) | −4.68551 | −0.149979 | ||||||||
\(977\) | 35.3621 | 1.13133 | 0.565667 | − | 0.824634i | \(-0.308619\pi\) | ||||
0.565667 | + | 0.824634i | \(0.308619\pi\) | |||||||
\(978\) | −6.35322 | −0.203154 | ||||||||
\(979\) | 31.6210 | 1.01061 | ||||||||
\(980\) | 19.4671 | 0.621853 | ||||||||
\(981\) | 16.0531 | 0.512535 | ||||||||
\(982\) | −11.7792 | −0.375890 | ||||||||
\(983\) | −30.7198 | −0.979809 | −0.489904 | − | 0.871776i | \(-0.662968\pi\) | ||||
−0.489904 | + | 0.871776i | \(0.662968\pi\) | |||||||
\(984\) | 10.6519 | 0.339569 | ||||||||
\(985\) | 12.0013 | 0.382392 | ||||||||
\(986\) | −4.80533 | −0.153033 | ||||||||
\(987\) | 16.1625 | 0.514459 | ||||||||
\(988\) | 2.07746 | 0.0660927 | ||||||||
\(989\) | −37.9705 | −1.20739 | ||||||||
\(990\) | 21.1932 | 0.673565 | ||||||||
\(991\) | −22.4415 | −0.712877 | −0.356439 | − | 0.934319i | \(-0.616009\pi\) | ||||
−0.356439 | + | 0.934319i | \(0.616009\pi\) | |||||||
\(992\) | 3.93079 | 0.124803 | ||||||||
\(993\) | 57.8116 | 1.83460 | ||||||||
\(994\) | −1.63823 | −0.0519615 | ||||||||
\(995\) | −50.3764 | −1.59704 | ||||||||
\(996\) | −31.3745 | −0.994139 | ||||||||
\(997\) | −22.9174 | −0.725803 | −0.362901 | − | 0.931828i | \(-0.618214\pi\) | ||||
−0.362901 | + | 0.931828i | \(0.618214\pi\) | |||||||
\(998\) | 14.9516 | 0.473284 | ||||||||
\(999\) | −36.6295 | −1.15891 |
(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 | 8018.2.a.f.1.10 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.10 | ✓ | 34 | 1.1 | even | 1 | trivial |