Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.33655\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.33655 | −1.92636 | −0.963180 | − | 0.268858i | \(-0.913354\pi\) | ||||
−0.963180 | + | 0.268858i | \(0.913354\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35293 | 0.889324 | 0.444662 | − | 0.895698i | \(-0.353324\pi\) | ||||
0.444662 | + | 0.895698i | \(0.353324\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.13258 | 2.71086 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.41372 | −1.63230 | −0.816148 | − | 0.577842i | \(-0.803895\pi\) | ||||
−0.816148 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.10664 | 1.97103 | 0.985513 | − | 0.169599i | \(-0.0542472\pi\) | ||||
0.985513 | + | 0.169599i | \(0.0542472\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.33655 | −0.861494 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.30666 | −0.559446 | −0.279723 | − | 0.960081i | \(-0.590243\pi\) | ||||
−0.279723 | + | 0.960081i | \(0.590243\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.33812 | 0.765818 | 0.382909 | − | 0.923786i | \(-0.374922\pi\) | ||||
0.382909 | + | 0.923786i | \(0.374922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.85068 | −1.71316 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59719 | −0.541551 | −0.270775 | − | 0.962643i | \(-0.587280\pi\) | ||||
−0.270775 | + | 0.962643i | \(0.587280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.1251 | −3.29573 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45979 | −0.271077 | −0.135538 | − | 0.990772i | \(-0.543276\pi\) | ||||
−0.135538 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.14434 | 0.385135 | 0.192568 | − | 0.981284i | \(-0.438319\pi\) | ||||
0.192568 | + | 0.981284i | \(0.438319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.0631 | 3.14439 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.35293 | 0.397718 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.97284 | −1.47513 | −0.737563 | − | 0.675278i | \(-0.764024\pi\) | ||||
−0.737563 | + | 0.675278i | \(0.764024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −23.7117 | −3.79691 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.901406 | 0.140776 | 0.0703880 | − | 0.997520i | \(-0.477576\pi\) | ||||
0.0703880 | + | 0.997520i | \(0.477576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.97754 | −0.301572 | −0.150786 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150786 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.13258 | 1.21233 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7551 | −1.71466 | −0.857332 | − | 0.514764i | \(-0.827880\pi\) | ||||
−0.857332 | + | 0.514764i | \(0.827880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.46372 | −0.209103 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.69628 | 1.07769 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0416 | 1.37932 | 0.689658 | − | 0.724135i | \(-0.257761\pi\) | ||||
0.689658 | + | 0.724135i | \(0.257761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.41372 | −0.729985 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.1378 | −1.47524 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.21296 | −0.548480 | −0.274240 | − | 0.961661i | \(-0.588426\pi\) | ||||
−0.274240 | + | 0.961661i | \(0.588426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2881 | −1.57333 | −0.786664 | − | 0.617382i | \(-0.788193\pi\) | ||||
−0.786664 | + | 0.617382i | \(0.788193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.1354 | 2.41083 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.10664 | 0.881470 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.385186 | 0.0470579 | 0.0235290 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235290 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.66565 | 1.04322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4898 | −1.48226 | −0.741131 | − | 0.671361i | \(-0.765710\pi\) | ||||
−0.741131 | + | 0.671361i | \(0.765710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.72268 | −0.786830 | −0.393415 | − | 0.919361i | \(-0.628707\pi\) | ||||
−0.393415 | + | 0.919361i | \(0.628707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.33655 | −0.385272 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.7381 | −1.45164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.8609 | 1.44697 | 0.723484 | − | 0.690341i | \(-0.242540\pi\) | ||||
0.723484 | + | 0.690341i | \(0.242540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32.7411 | 3.63790 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.69229 | 0.295517 | 0.147759 | − | 0.989023i | \(-0.452794\pi\) | ||||
0.147759 | + | 0.989023i | \(0.452794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30666 | −0.250192 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.87068 | 0.522191 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4454 | 1.42521 | 0.712604 | − | 0.701567i | \(-0.247516\pi\) | ||||
0.712604 | + | 0.701567i | \(0.247516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.7214 | 1.75288 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.15471 | −0.741908 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.33812 | 0.342484 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.95427 | 0.604564 | 0.302282 | − | 0.953218i | \(-0.402251\pi\) | ||||
0.302282 | + | 0.953218i | \(0.402251\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −44.0275 | −4.42493 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.3540 | −1.62728 | −0.813642 | − | 0.581366i | \(-0.802519\pi\) | ||||
−0.813642 | + | 0.581366i | \(0.802519\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.41825 | 0.238277 | 0.119139 | − | 0.992878i | \(-0.461987\pi\) | ||||
0.119139 | + | 0.992878i | \(0.461987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.85068 | −0.766148 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.76217 | 0.750397 | 0.375198 | − | 0.926944i | \(-0.377575\pi\) | ||||
0.375198 | + | 0.926944i | \(0.377575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4274 | −1.57346 | −0.786728 | − | 0.617300i | \(-0.788226\pi\) | ||||
−0.786728 | + | 0.617300i | \(0.788226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29.9384 | 2.84162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.40511 | −0.790687 | −0.395343 | − | 0.918533i | \(-0.629374\pi\) | ||||
−0.395343 | + | 0.918533i | \(0.629374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.59719 | −0.242189 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 57.7953 | 5.34318 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.42740 | −0.497529 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3083 | 1.66439 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00759 | −0.271185 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.2710 | 1.71002 | 0.855010 | − | 0.518611i | \(-0.173551\pi\) | ||||
0.855010 | + | 0.518611i | \(0.173551\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.59818 | 0.580937 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.3384 | −1.07801 | −0.539006 | − | 0.842302i | \(-0.681200\pi\) | ||||
−0.539006 | + | 0.842302i | \(0.681200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.85437 | 0.681060 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.1251 | −1.47390 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.09541 | 0.179023 | 0.0895116 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895116 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5877 | −1.15249 | −0.576246 | − | 0.817276i | \(-0.695483\pi\) | ||||
−0.576246 | + | 0.817276i | \(0.695483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 39.2217 | 3.30306 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −38.4733 | −3.21730 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.45979 | −0.121229 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.88377 | 0.402807 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.63807 | 0.625735 | 0.312867 | − | 0.949797i | \(-0.398710\pi\) | ||||
0.312867 | + | 0.949797i | \(0.398710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.7591 | −1.51658 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.14434 | 0.172238 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.64551 | −0.290943 | −0.145472 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145472 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −33.5043 | −2.65706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.11100 | −0.481614 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2139 | 1.26997 | 0.634984 | − | 0.772525i | \(-0.281007\pi\) | ||||
0.634984 | + | 0.772525i | \(0.281007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.0631 | 1.40621 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.8658 | 1.84679 | 0.923396 | − | 0.383848i | \(-0.125401\pi\) | ||||
0.923396 | + | 0.383848i | \(0.125401\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.5043 | 2.88494 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.1475 | 2.07602 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4529 | −0.946773 | −0.473387 | − | 0.880855i | \(-0.656969\pi\) | ||||
−0.473387 | + | 0.880855i | \(0.656969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.35293 | 0.177865 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0567 | 1.05657 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8873 | −0.888498 | −0.444249 | − | 0.895903i | \(-0.646529\pi\) | ||||
−0.444249 | + | 0.895903i | \(0.646529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.53084 | −0.559763 | −0.279881 | − | 0.960035i | \(-0.590295\pi\) | ||||
−0.279881 | + | 0.960035i | \(0.590295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 40.9998 | 3.03079 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.97284 | −0.659696 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.4876 | 0.913183 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −40.2942 | −2.93097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.57380 | 0.330948 | 0.165474 | − | 0.986214i | \(-0.447085\pi\) | ||||
0.165474 | + | 0.986214i | \(0.447085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.68019 | 0.408869 | 0.204434 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204434 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −23.7117 | −1.69803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8905 | 0.918408 | 0.459204 | − | 0.888331i | \(-0.348135\pi\) | ||||
0.459204 | + | 0.888331i | \(0.348135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6389 | −0.966834 | −0.483417 | − | 0.875390i | \(-0.660605\pi\) | ||||
−0.483417 | + | 0.875390i | \(0.660605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28519 | −0.0906505 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.43479 | −0.241075 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.901406 | 0.0629569 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.1218 | −1.46807 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0716 | −1.25004 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.3880 | −1.74778 | −0.873891 | − | 0.486122i | \(-0.838411\pi\) | ||||
−0.873891 | + | 0.486122i | \(0.838411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.6727 | 2.85537 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.97754 | −0.134867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.04549 | 0.342510 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.4306 | 1.51572 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3926 | −1.10268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6645 | 1.51773 | 0.758864 | − | 0.651249i | \(-0.225755\pi\) | ||||
0.758864 | + | 0.651249i | \(0.225755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.13258 | 0.542172 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.5011 | −1.36071 | −0.680353 | − | 0.732885i | \(-0.738173\pi\) | ||||
−0.680353 | + | 0.732885i | \(0.738173\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.31552 | −0.483423 | −0.241712 | − | 0.970348i | \(-0.577709\pi\) | ||||
−0.241712 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 42.5013 | 2.79638 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.36300 | −0.613390 | −0.306695 | − | 0.951808i | \(-0.599223\pi\) | ||||
−0.306695 | + | 0.951808i | \(0.599223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.7551 | −0.766821 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −42.9112 | −2.78738 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1741 | −0.916847 | −0.458424 | − | 0.888734i | \(-0.651586\pi\) | ||||
−0.458424 | + | 0.888734i | \(0.651586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.16536 | −0.461561 | −0.230781 | − | 0.973006i | \(-0.574128\pi\) | ||||
−0.230781 | + | 0.973006i | \(0.574128\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −57.8671 | −3.71218 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.46372 | −0.0935135 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.7228 | 1.50945 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.98296 | −0.569272 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.50114 | −0.536587 | −0.268294 | − | 0.963337i | \(-0.586460\pi\) | ||||
−0.268294 | + | 0.963337i | \(0.586460\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0604 | 0.883972 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.69628 | 0.481960 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.65320 | 0.539772 | 0.269886 | − | 0.962892i | \(-0.413014\pi\) | ||||
0.269886 | + | 0.962892i | \(0.413014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.1125 | −1.31187 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.8719 | −0.734851 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.4377 | −0.890268 | −0.445134 | − | 0.895464i | \(-0.646844\pi\) | ||||
−0.445134 | + | 0.895464i | \(0.646844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0416 | 0.616849 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −44.8612 | −2.74546 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.3952 | −1.06061 | −0.530303 | − | 0.847808i | \(-0.677922\pi\) | ||||
−0.530303 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2168 | 1.83554 | 0.917770 | − | 0.397112i | \(-0.129987\pi\) | ||||
0.917770 | + | 0.397112i | \(0.129987\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55.7919 | −3.37668 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.41372 | −0.326459 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.14217 | 0.0686261 | 0.0343131 | − | 0.999411i | \(-0.489076\pi\) | ||||
0.0343131 | + | 0.999411i | \(0.489076\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.4390 | 1.04405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4049 | −0.978634 | −0.489317 | − | 0.872106i | \(-0.662754\pi\) | ||||
−0.489317 | + | 0.872106i | \(0.662754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6711 | −0.634328 | −0.317164 | − | 0.948371i | \(-0.602731\pi\) | ||||
−0.317164 | + | 0.948371i | \(0.602731\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1378 | −0.659747 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.12095 | 0.125195 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.6793 | −0.687020 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.8667 | −1.16461 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92639 | 0.404644 | 0.202322 | − | 0.979319i | \(-0.435151\pi\) | ||||
0.202322 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.21296 | −0.245288 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 92.7106 | 5.37961 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4573 | −1.06741 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.65302 | −0.268196 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 54.5660 | 3.13474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.2881 | −0.703613 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.20357 | 0.296984 | 0.148492 | − | 0.988914i | \(-0.452558\pi\) | ||||
0.148492 | + | 0.988914i | \(0.452558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.06862 | −0.459008 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.77414 | 0.384127 | 0.192063 | − | 0.981383i | \(-0.438482\pi\) | ||||
0.192063 | + | 0.981383i | \(0.438482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.80023 | 0.158278 | 0.0791391 | − | 0.996864i | \(-0.474783\pi\) | ||||
0.0791391 | + | 0.996864i | \(0.474783\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.1354 | 1.07816 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.7137 | −1.10723 | −0.553616 | − | 0.832772i | \(-0.686752\pi\) | ||||
−0.553616 | + | 0.832772i | \(0.686752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.90290 | 0.442478 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.8989 | −1.44553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.69990 | −0.428434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.10664 | 0.394205 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.8107 | 3.03104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.6590 | −1.52489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82468 | 0.155258 | 0.0776291 | − | 0.996982i | \(-0.475265\pi\) | ||||
0.0776291 | + | 0.996982i | \(0.475265\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −72.9724 | −3.99886 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.385186 | 0.0210449 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5951 | −1.44873 | −0.724363 | − | 0.689419i | \(-0.757866\pi\) | ||||
−0.724363 | + | 0.689419i | \(0.757866\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.0441 | 1.52315 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6089 | −0.628655 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9145 | −1.07528 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.66565 | 0.466543 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.89543 | 0.101752 | 0.0508760 | − | 0.998705i | \(-0.483799\pi\) | ||||
0.0508760 | + | 0.998705i | \(0.483799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5730 | 0.619487 | 0.309744 | − | 0.950820i | \(-0.399757\pi\) | ||||
0.309744 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −121.702 | −6.49598 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.5809 | −1.62766 | −0.813829 | − | 0.581105i | \(-0.802621\pi\) | ||||
−0.813829 | + | 0.581105i | \(0.802621\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4898 | −0.662888 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.1088 | 0.958420 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.93418 | −0.207638 | −0.103819 | − | 0.994596i | \(-0.533106\pi\) | ||||
−0.103819 | + | 0.994596i | \(0.533106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.85694 | −0.413523 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −61.0867 | −3.20622 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.72268 | −0.351881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.7904 | −1.18965 | −0.594824 | − | 0.803856i | \(-0.702778\pi\) | ||||
−0.594824 | + | 0.803856i | \(0.702778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.33076 | 0.381624 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.6271 | 1.22666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.2646 | −1.56704 | −0.783520 | − | 0.621367i | \(-0.786578\pi\) | ||||
−0.783520 | + | 0.621367i | \(0.786578\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.33655 | −0.172299 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3742 | −0.534299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9979 | 0.719025 | 0.359513 | − | 0.933140i | \(-0.382943\pi\) | ||||
0.359513 | + | 0.933140i | \(0.382943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −64.2985 | −3.29411 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6813 | 1.05677 | 0.528384 | − | 0.849006i | \(-0.322798\pi\) | ||||
0.528384 | + | 0.849006i | \(0.322798\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.7381 | −0.649194 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.0825 | −0.817521 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.90209 | −0.451354 | −0.225677 | − | 0.974202i | \(-0.572459\pi\) | ||||
−0.225677 | + | 0.974202i | \(0.572459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.99082 | 0.302969 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.1678 | 2.07664 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.8609 | 0.647104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.1091 | 1.61151 | 0.805756 | − | 0.592248i | \(-0.201759\pi\) | ||||
0.805756 | + | 0.592248i | \(0.201759\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −26.2065 | −1.31197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.7681 | 0.937234 | 0.468617 | − | 0.883401i | \(-0.344752\pi\) | ||||
0.468617 | + | 0.883401i | \(0.344752\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2391 | 0.759111 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.7411 | 1.62692 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.5764 | 2.40784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.6949 | −0.973849 | −0.486924 | − | 0.873444i | \(-0.661881\pi\) | ||||
−0.486924 | + | 0.873444i | \(0.661881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.99146 | −0.344863 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.91279 | −0.487777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.69229 | 0.132159 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 45.3360 | 2.22011 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.27818 | 0.111296 | 0.0556482 | − | 0.998450i | \(-0.482277\pi\) | ||||
0.0556482 | + | 0.998450i | \(0.482277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4056 | −0.507136 | −0.253568 | − | 0.967318i | \(-0.581604\pi\) | ||||
−0.253568 | + | 0.967318i | \(0.581604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −95.5997 | −4.64822 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.30666 | −0.111889 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.9130 | −1.39920 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 128.368 | 6.19768 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.99886 | −0.385291 | −0.192646 | − | 0.981268i | \(-0.561707\pi\) | ||||
−0.192646 | + | 0.981268i | \(0.561707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.5222 | 1.41875 | 0.709374 | − | 0.704832i | \(-0.248978\pi\) | ||||
0.709374 | + | 0.704832i | \(0.248978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.87068 | 0.233531 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.66972 | −0.414729 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.7474 | −0.512946 | −0.256473 | − | 0.966551i | \(-0.582560\pi\) | ||||
−0.256473 | + | 0.966551i | \(0.582560\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.9038 | −0.566848 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.61008 | −0.219031 | −0.109516 | − | 0.993985i | \(-0.534930\pi\) | ||||
−0.109516 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4454 | 0.637372 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.4848 | −1.20539 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.1548 | 1.94222 | 0.971109 | − | 0.238638i | \(-0.0767008\pi\) | ||||
0.971109 | + | 0.238638i | \(0.0767008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.87996 | −0.229788 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.33655 | −0.156765 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.7214 | 0.783912 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5181 | 0.772686 | 0.386343 | − | 0.922355i | \(-0.373738\pi\) | ||||
0.386343 | + | 0.922355i | \(0.373738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.5018 | 1.84379 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.908549 | 0.0423154 | 0.0211577 | − | 0.999776i | \(-0.493265\pi\) | ||||
0.0211577 | + | 0.999776i | \(0.493265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.7878 | −1.84910 | −0.924548 | − | 0.381066i | \(-0.875557\pi\) | ||||
−0.924548 | + | 0.381066i | \(0.875557\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.15471 | −0.331792 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.1345 | −0.654065 | −0.327032 | − | 0.945013i | \(-0.606049\pi\) | ||||
−0.327032 | + | 0.945013i | \(0.606049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.906315 | 0.0418498 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1634 | 0.560461 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7059 | 0.492256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.33812 | 0.153164 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 81.6640 | 3.73914 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.5386 | −1.71518 | −0.857592 | − | 0.514331i | \(-0.828040\pi\) | ||||
−0.857592 | + | 0.514331i | \(0.828040\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −63.7667 | −2.90751 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.3897 | 0.927762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.95427 | 0.270369 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.3571 | 0.695898 | 0.347949 | − | 0.937513i | \(-0.386878\pi\) | ||||
0.347949 | + | 0.937513i | \(0.386878\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −54.0984 | −2.44641 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8559 | −0.489918 | −0.244959 | − | 0.969533i | \(-0.578775\pi\) | ||||
−0.244959 | + | 0.969533i | \(0.578775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.36724 | 0.151653 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −44.0275 | −1.97889 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.3875 | −1.31821 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.90608 | −0.309159 | −0.154579 | − | 0.987980i | \(-0.549402\pi\) | ||||
−0.154579 | + | 0.987980i | \(0.549402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −79.6295 | −3.55759 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.2667 | −1.61705 | −0.808526 | − | 0.588461i | \(-0.799734\pi\) | ||||
−0.808526 | + | 0.588461i | \(0.799734\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.3540 | −0.727744 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −125.135 | −5.55744 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.83221 | −0.302833 | −0.151416 | − | 0.988470i | \(-0.548383\pi\) | ||||
−0.151416 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.8180 | −0.699747 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −57.1658 | −2.52393 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.41825 | 0.106561 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.6390 | 2.79884 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 41.5496 | 1.82383 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5686 | 0.857314 | 0.428657 | − | 0.903467i | \(-0.358987\pi\) | ||||
0.428657 | + | 0.903467i | \(0.358987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.236246 | 0.0103303 | 0.00516515 | − | 0.999987i | \(-0.498356\pi\) | ||||
0.00516515 | + | 0.999987i | \(0.498356\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.85068 | −0.342632 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.94626 | −0.215462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2546 | −0.706723 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.2622 | −1.48685 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.40597 | 0.277473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.76217 | 0.335588 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.6626 | 1.71157 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.92415 | 0.341317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1429 | −0.436078 | −0.218039 | − | 0.975940i | \(-0.569966\pi\) | ||||
−0.218039 | + | 0.975940i | \(0.569966\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.1270 | 1.07830 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4274 | −0.703671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.6631 | −1.18279 | −0.591394 | − | 0.806383i | \(-0.701422\pi\) | ||||
−0.591394 | + | 0.806383i | \(0.701422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −99.9338 | −4.26507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.87297 | −0.207595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.2609 | 1.28682 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.9384 | 1.27081 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.7970 | 1.68625 | 0.843127 | − | 0.537715i | \(-0.180712\pi\) | ||||
0.843127 | + | 0.537715i | \(0.180712\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.0537 | −0.594407 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.6655 | −1.75912 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.13579 | 0.342883 | 0.171441 | − | 0.985194i | \(-0.445158\pi\) | ||||
0.171441 | + | 0.985194i | \(0.445158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.40511 | −0.353606 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 77.0376 | 3.23528 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.78964 | −0.368481 | −0.184241 | − | 0.982881i | \(-0.558983\pi\) | ||||
−0.184241 | + | 0.982881i | \(0.558983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.4366 | 0.436760 | 0.218380 | − | 0.975864i | \(-0.429923\pi\) | ||||
0.218380 | + | 0.975864i | \(0.429923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2607 | −0.637525 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.59719 | −0.108310 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.4780 | −0.685988 | −0.342994 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342994 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.9523 | −0.787629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.33477 | 0.262810 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −54.3623 | −2.25145 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 57.7953 | 2.38954 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.32677 | 0.219859 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.15807 | 0.294943 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.0097 | −1.76918 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.2745 | 1.16109 | 0.580547 | − | 0.814227i | \(-0.302839\pi\) | ||||
0.580547 | + | 0.814227i | \(0.302839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.42740 | −0.222502 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 45.5068 | 1.86247 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.6103 | −0.842115 | −0.421057 | − | 0.907034i | \(-0.638341\pi\) | ||||
−0.421057 | + | 0.907034i | \(0.638341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.8576 | −1.38108 | −0.690541 | − | 0.723293i | \(-0.742627\pi\) | ||||
−0.690541 | + | 0.723293i | \(0.742627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.13255 | 0.127567 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.3083 | 0.744339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0293 | 0.731787 | 0.365893 | − | 0.930657i | \(-0.380764\pi\) | ||||
0.365893 | + | 0.930657i | \(0.380764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.4604 | 0.464397 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −83.5395 | −3.37965 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.1057 | 1.57946 | 0.789731 | − | 0.613453i | \(-0.210220\pi\) | ||||
0.789731 | + | 0.613453i | \(0.210220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.00759 | −0.121278 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0518 | −1.08907 | −0.544533 | − | 0.838740i | \(-0.683293\pi\) | ||||
−0.544533 | + | 0.838740i | \(0.683293\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.3853 | −0.618389 | −0.309194 | − | 0.950999i | \(-0.600059\pi\) | ||||
−0.309194 | + | 0.950999i | \(0.600059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.4771 | 1.78481 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.6360 | 1.26747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 60.2970 | 2.40803 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.6973 | 0.825254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.9743 | 1.27288 | 0.636439 | − | 0.771327i | \(-0.280407\pi\) | ||||
0.636439 | + | 0.771327i | \(0.280407\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 84.7084 | 3.36686 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.2710 | 0.764744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4021 | −0.412147 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −101.574 | −4.01820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2599 | −0.523736 | −0.261868 | − | 0.965104i | \(-0.584339\pi\) | ||||
−0.261868 | + | 0.965104i | \(0.584339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.66670 | 0.262909 | 0.131454 | − | 0.991322i | \(-0.458035\pi\) | ||||
0.131454 | + | 0.991322i | \(0.458035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.59818 | 0.259803 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.25281 | 0.285138 | 0.142569 | − | 0.989785i | \(-0.454464\pi\) | ||||
0.142569 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.8077 | 0.895282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8345 | −0.659797 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.3764 | 1.42352 | 0.711760 | − | 0.702423i | \(-0.247898\pi\) | ||||
0.711760 | + | 0.702423i | \(0.247898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.3384 | −0.482102 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −54.6728 | −2.13299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.2710 | −1.21815 | −0.609073 | − | 0.793114i | \(-0.708458\pi\) | ||||
−0.609073 | + | 0.793114i | \(0.708458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3459 | −0.908050 | −0.454025 | − | 0.890989i | \(-0.650012\pi\) | ||||
−0.454025 | + | 0.890989i | \(0.650012\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 54.6947 | 2.12416 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.85437 | 0.304579 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.79135 | 0.146802 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −75.6214 | −2.92369 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 66.5242 | 2.56814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23928 | −0.0477706 | −0.0238853 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238853 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.1251 | −0.659146 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5718 | 1.09810 | 0.549051 | − | 0.835789i | \(-0.314989\pi\) | ||||
0.549051 | + | 0.835789i | \(0.314989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0100 | 0.537654 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 68.4030 | 2.62121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.5979 | 0.711629 | 0.355814 | − | 0.934557i | \(-0.384204\pi\) | ||||
0.355814 | + | 0.934557i | \(0.384204\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.09541 | 0.0800616 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.4086 | 0.931247 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 71.3619 | 2.71867 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.8610 | 0.945759 | 0.472879 | − | 0.881127i | \(-0.343215\pi\) | ||||
0.472879 | + | 0.881127i | \(0.343215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −103.594 | −3.93520 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.5877 | −0.515410 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.07923 | −0.0787566 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.2401 | 1.18161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5861 | −1.45738 | −0.728689 | − | 0.684845i | \(-0.759870\pi\) | ||||
−0.728689 | + | 0.684845i | \(0.759870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.9524 | −1.12968 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.2217 | 1.47717 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.4799 | −1.44718 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.89928 | −0.371775 | −0.185888 | − | 0.982571i | \(-0.559516\pi\) | ||||
−0.185888 | + | 0.982571i | \(0.559516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 104.593 | 3.92253 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.56925 | −0.208570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.4733 | −1.43882 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.2927 | 1.76618 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.55542 | 0.356357 | 0.178179 | − | 0.983998i | \(-0.442980\pi\) | ||||
0.178179 | + | 0.983998i | \(0.442980\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.68998 | 0.211906 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.9076 | 0.889133 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.45979 | −0.0542153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.10017 | 0.0778911 | 0.0389455 | − | 0.999241i | \(-0.487600\pi\) | ||||
0.0389455 | + | 0.999241i | \(0.487600\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 94.8533 | 3.51309 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.56151 | 0.168714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.35961 | −0.124090 | −0.0620451 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620451 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.88377 | 0.180141 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.08529 | −0.0768125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1420 | −0.446652 | −0.223326 | − | 0.974744i | \(-0.571691\pi\) | ||||
−0.223326 | + | 0.974744i | \(0.571691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −79.1524 | −2.90774 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3929 | 0.674772 | 0.337386 | − | 0.941366i | \(-0.390457\pi\) | ||||
0.337386 | + | 0.941366i | \(0.390457\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.63807 | 0.279837 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.8953 | 0.801106 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.2638 | 0.667346 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.9814 | 1.13053 | 0.565264 | − | 0.824910i | \(-0.308774\pi\) | ||||
0.565264 | + | 0.824910i | \(0.308774\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.3645 | 1.03366 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.2346 | −1.64408 | −0.822040 | − | 0.569429i | \(-0.807164\pi\) | ||||
−0.822040 | + | 0.569429i | \(0.807164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −46.9134 | −1.70285 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.2717 | −0.771100 | −0.385550 | − | 0.922687i | \(-0.625988\pi\) | ||||
−0.385550 | + | 0.922687i | \(0.625988\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.6524 | −1.39931 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.7591 | −0.678236 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.9399 | −1.08107 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1576 | 0.366292 | 0.183146 | − | 0.983086i | \(-0.441372\pi\) | ||||
0.183146 | + | 0.983086i | \(0.441372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.8719 | −1.03980 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.4688 | 0.736210 | 0.368105 | − | 0.929784i | \(-0.380007\pi\) | ||||
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.14434 | 0.0770270 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 70.4429 | 2.52712 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.00900 | 0.107809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.6160 | 2.41949 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.9991 | 0.893396 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.64551 | −0.130114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.89209 | −0.174384 | −0.0871921 | − | 0.996192i | \(-0.527789\pi\) | ||||
−0.0871921 | + | 0.996192i | \(0.527789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.1722 | 1.71498 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.7766 | −0.703177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −87.3269 | −3.10107 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.5043 | −1.18827 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.0782 | −0.675784 | −0.337892 | − | 0.941185i | \(-0.609714\pi\) | ||||
−0.337892 | + | 0.941185i | \(0.609714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1151 | 0.959263 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 109.346 | 3.86354 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.3947 | 1.28434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.11100 | −0.215384 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 58.0401 | 2.04311 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.6655 | 1.18362 | 0.591809 | − | 0.806078i | \(-0.298414\pi\) | ||||
0.591809 | + | 0.806078i | \(0.298414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8424 | 0.802104 | 0.401052 | − | 0.916055i | \(-0.368645\pi\) | ||||
0.401052 | + | 0.916055i | \(0.368645\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −100.820 | −3.53591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.2139 | 0.567947 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.60128 | −0.230950 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 135.988 | 4.75182 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.517548 | 0.0180625 | 0.00903127 | − | 0.999959i | \(-0.497125\pi\) | ||||
0.00903127 | + | 0.999959i | \(0.497125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.91645 | 0.345666 | 0.172833 | − | 0.984951i | \(-0.444708\pi\) | ||||
0.172833 | + | 0.984951i | \(0.444708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.0631 | 0.628878 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.8207 | 1.83676 | 0.918378 | − | 0.395704i | \(-0.129499\pi\) | ||||
0.918378 | + | 0.395704i | \(0.129499\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5853 | 1.02754 | 0.513770 | − | 0.857928i | \(-0.328248\pi\) | ||||
0.513770 | + | 0.857928i | \(0.328248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.81090 | −0.132199 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.37629 | 0.116982 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.8658 | 0.825911 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.7221 | −1.26930 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.83903 | 0.339681 | 0.169840 | − | 0.985472i | \(-0.445675\pi\) | ||||
0.169840 | + | 0.985472i | \(0.445675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8690 | −0.926517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.7358 | 1.88520 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.5043 | 1.29019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.0782 | 1.48019 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.6045 | 1.22194 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.3041 | 0.798856 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.0584971 | −0.00200290 | −0.00100145 | − | 0.999999i | \(-0.500319\pi\) | ||||
−0.00100145 | + | 0.999999i | \(0.500319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.1475 | 0.928427 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.8637 | −1.83995 | −0.919974 | − | 0.391980i | \(-0.871790\pi\) | ||||
−0.919974 | + | 0.391980i | \(0.871790\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.7577 | −0.844721 | −0.422361 | − | 0.906428i | \(-0.638798\pi\) | ||||
−0.422361 | + | 0.906428i | \(0.638798\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.07665 | −0.241172 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.23688 | 0.212306 | 0.106153 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106153 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4529 | −0.423410 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.9687 | 1.32345 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −69.6254 | −2.36188 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.73738 | 0.0927524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.4236 | 1.63889 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.35293 | 0.0795436 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.8283 | −1.04100 | −0.520499 | − | 0.853862i | \(-0.674254\pi\) | ||||
−0.520499 | + | 0.853862i | \(0.674254\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.1103 | −0.779490 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.43062 | 0.250344 | 0.125172 | − | 0.992135i | \(-0.460052\pi\) | ||||
0.125172 | + | 0.992135i | \(0.460052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.2605 | −0.984695 | −0.492347 | − | 0.870399i | \(-0.663861\pi\) | ||||
−0.492347 | + | 0.870399i | \(0.663861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.0567 | 0.472512 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.9733 | 1.30860 | 0.654298 | − | 0.756237i | \(-0.272964\pi\) | ||||
0.654298 | + | 0.756237i | \(0.272964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.3432 | 1.52076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −177.251 | −5.93814 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.2401 | −1.31312 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.8873 | −0.397348 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 61.5836 | 2.05622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.13029 | −0.104401 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.1625 | −0.771654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5250 | 0.516641 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.53084 | −0.250334 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.5692 | 0.450557 | 0.225279 | − | 0.974294i | \(-0.427671\pi\) | ||||
0.225279 | + | 0.974294i | \(0.427671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −133.000 | −4.41134 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2093 | −0.735827 | −0.367913 | − | 0.929860i | \(-0.619928\pi\) | ||||
−0.367913 | + | 0.929860i | \(0.619928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.5753 | −0.482372 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.9998 | 1.35541 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.0314 | −0.958703 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.83245 | 0.225382 | 0.112691 | − | 0.993630i | \(-0.464053\pi\) | ||||
0.112691 | + | 0.993630i | \(0.464053\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3620 | −0.572097 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −88.7602 | −2.92158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.97284 | −0.295025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.6666 | 0.645937 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.6125 | −0.938745 | −0.469372 | − | 0.883000i | \(-0.655520\pi\) | ||||
−0.469372 | + | 0.883000i | \(0.655520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.88607 | −0.160134 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.6023 | −0.739966 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.4876 | 0.408388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.48793 | −0.146614 | −0.0733072 | − | 0.997309i | \(-0.523355\pi\) | ||||
−0.0733072 | + | 0.997309i | \(0.523355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.34311 | −0.304901 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.4634 | 1.77546 | 0.887728 | − | 0.460369i | \(-0.152283\pi\) | ||||
0.887728 | + | 0.460369i | \(0.152283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.34112 | −0.0762374 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40.2942 | −1.31077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.4643 | −1.15244 | −0.576218 | − | 0.817296i | \(-0.695472\pi\) | ||||
−0.576218 | + | 0.817296i | \(0.695472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.7757 | −1.55086 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65.7758 | 2.13293 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.68115 | −0.0868511 | −0.0434256 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434256 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.57380 | 0.148005 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26.3685 | −0.852371 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.93036 | 0.159210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4018 | −0.851671 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 63.1265 | 2.03422 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.68019 | 0.182852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1482 | −1.45187 | −0.725933 | − | 0.687765i | \(-0.758592\pi\) | ||||
−0.725933 | + | 0.687765i | \(0.758592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.6911 | 0.825318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8203 | −0.828614 | −0.414307 | − | 0.910137i | \(-0.635976\pi\) | ||||
−0.414307 | + | 0.910137i | \(0.635976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9709 | −1.02494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.7117 | −0.759381 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.5484 | 0.465445 | 0.232722 | − | 0.972543i | \(-0.425237\pi\) | ||||
0.232722 | + | 0.972543i | \(0.425237\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72.7895 | −2.32636 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −133.597 | −4.26542 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8003 | 1.07806 | 0.539032 | − | 0.842285i | \(-0.318790\pi\) | ||||
0.539032 | + | 0.842285i | \(0.318790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8905 | 0.410725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 92.2858 | 2.93749 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.13605 | 0.163317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5476 | 0.366822 | 0.183411 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183411 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.42468 | −0.299083 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.6389 | −0.432381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.0557 | 1.55361 | 0.776804 | − | 0.629742i | \(-0.216839\pi\) | ||||
0.776804 | + | 0.629742i | \(0.216839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 153.661 | 4.86162 |
(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 | 6040.2.a.p.1.1 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.1 | ✓ | 19 | 1.1 | even | 1 | trivial |