Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.83715 | −1.71602 | −0.858012 | − | 0.513630i | \(-0.828301\pi\) | ||||
−0.858012 | + | 0.513630i | \(0.828301\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0390685 | 0.0147665 | 0.00738326 | − | 0.999973i | \(-0.497650\pi\) | ||||
0.00738326 | + | 0.999973i | \(0.497650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.02930 | −0.913368 | −0.456684 | − | 0.889629i | \(-0.650963\pi\) | ||||
−0.456684 | + | 0.889629i | \(0.650963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65520 | 0.736421 | 0.368210 | − | 0.929743i | \(-0.379971\pi\) | ||||
0.368210 | + | 0.929743i | \(0.379971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.83715 | 0.990747 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.40342 | −0.340379 | −0.170189 | − | 0.985411i | \(-0.554438\pi\) | ||||
−0.170189 | + | 0.985411i | \(0.554438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.22877 | −1.42898 | −0.714489 | − | 0.699646i | \(-0.753341\pi\) | ||||
−0.714489 | + | 0.699646i | \(0.753341\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0390685 | −0.00852545 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.84008 | −1.42626 | −0.713128 | − | 0.701034i | \(-0.752722\pi\) | ||||
−0.713128 | + | 0.701034i | \(0.752722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.72369 | 1.94474 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.49534 | −1.20615 | −0.603077 | − | 0.797683i | \(-0.706059\pi\) | ||||
−0.603077 | + | 0.797683i | \(0.706059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46543 | 0.981620 | 0.490810 | − | 0.871267i | \(-0.336701\pi\) | ||||
0.490810 | + | 0.871267i | \(0.336701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.02930 | 0.527333 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.149912 | −0.0253397 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.51070 | 0.905953 | 0.452977 | − | 0.891522i | \(-0.350362\pi\) | ||||
0.452977 | + | 0.891522i | \(0.350362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.65520 | −0.425173 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.57053 | 0.245275 | 0.122638 | − | 0.992452i | \(-0.460865\pi\) | ||||
0.122638 | + | 0.992452i | \(0.460865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27143 | −1.10888 | −0.554442 | − | 0.832223i | \(-0.687068\pi\) | ||||
−0.554442 | + | 0.832223i | \(0.687068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.83715 | −0.572008 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.27547 | −1.20710 | −0.603551 | − | 0.797325i | \(-0.706248\pi\) | ||||
−0.603551 | + | 0.797325i | \(0.706248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99847 | −0.999782 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.40342 | 0.196518 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.95739 | 0.268869 | 0.134434 | − | 0.990923i | \(-0.457078\pi\) | ||||
0.134434 | + | 0.990923i | \(0.457078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.6239 | 1.56736 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.22877 | 0.825021 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.20540 | −0.938063 | −0.469031 | − | 0.883182i | \(-0.655397\pi\) | ||||
−0.469031 | + | 0.883182i | \(0.655397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8372 | −1.51559 | −0.757797 | − | 0.652491i | \(-0.773724\pi\) | ||||
−0.757797 | + | 0.652491i | \(0.773724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0390685 | 0.00492217 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.1884 | −1.26372 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.49442 | −0.549081 | −0.274541 | − | 0.961576i | \(-0.588526\pi\) | ||||
−0.274541 | + | 0.961576i | \(0.588526\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.84008 | 0.823449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1096 | −1.67450 | −0.837252 | − | 0.546817i | \(-0.815840\pi\) | ||||
−0.837252 | + | 0.546817i | \(0.815840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5600 | 1.23595 | 0.617976 | − | 0.786197i | \(-0.287953\pi\) | ||||
0.617976 | + | 0.786197i | \(0.287953\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.72369 | −1.12279 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.118350 | −0.0134873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1134 | 1.58788 | 0.793940 | − | 0.607997i | \(-0.208027\pi\) | ||||
0.793940 | + | 0.607997i | \(0.208027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.15120 | −0.236125 | −0.118062 | − | 0.993006i | \(-0.537668\pi\) | ||||
−0.118062 | + | 0.993006i | \(0.537668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.38512 | 0.584098 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.49534 | 0.696373 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6325 | 1.55104 | 0.775521 | − | 0.631322i | \(-0.217487\pi\) | ||||
0.775521 | + | 0.631322i | \(0.217487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.103735 | 0.0108744 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.46543 | −0.566738 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.9007 | 2.45216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8990 | −1.10663 | −0.553314 | − | 0.832973i | \(-0.686637\pi\) | ||||
−0.553314 | + | 0.832973i | \(0.686637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.02930 | −0.304456 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.205647 | 0.0204626 | 0.0102313 | − | 0.999948i | \(-0.496743\pi\) | ||||
0.0102313 | + | 0.999948i | \(0.496743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4002 | −1.22183 | −0.610916 | − | 0.791696i | \(-0.709199\pi\) | ||||
−0.610916 | + | 0.791696i | \(0.709199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.149912 | 0.0146299 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.40725 | −0.232718 | −0.116359 | − | 0.993207i | \(-0.537122\pi\) | ||||
−0.116359 | + | 0.993207i | \(0.537122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.79279 | −0.746414 | −0.373207 | − | 0.927748i | \(-0.621742\pi\) | ||||
−0.373207 | + | 0.927748i | \(0.621742\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.51070 | −0.523052 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.79544 | 0.262973 | 0.131487 | − | 0.991318i | \(-0.458025\pi\) | ||||
0.131487 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.2464 | 2.44749 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.65520 | 0.245474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0548295 | −0.00502621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82335 | −0.165759 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.57053 | −0.141610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.1255 | −1.62119 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.615625 | 0.0546279 | 0.0273139 | − | 0.999627i | \(-0.491305\pi\) | ||||
0.0273139 | + | 0.999627i | \(0.491305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.27143 | 0.640214 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.72461 | 0.150680 | 0.0753398 | − | 0.997158i | \(-0.475996\pi\) | ||||
0.0753398 | + | 0.997158i | \(0.475996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.243349 | −0.0211010 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.83715 | 0.330249 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.88340 | 0.502653 | 0.251326 | − | 0.967902i | \(-0.419133\pi\) | ||||
0.251326 | + | 0.967902i | \(0.419133\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.606430 | 0.0514367 | 0.0257184 | − | 0.999669i | \(-0.491813\pi\) | ||||
0.0257184 | + | 0.999669i | \(0.491813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.27547 | 0.696920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.04340 | −0.672623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.9236 | 2.06979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.99847 | 0.577224 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.74814 | −0.716676 | −0.358338 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358338 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.73638 | −0.466820 | −0.233410 | − | 0.972378i | \(-0.574988\pi\) | ||||
−0.233410 | + | 0.972378i | \(0.574988\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.40342 | −0.113460 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.9716 | −1.68448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.84099 | −0.545970 | −0.272985 | − | 0.962018i | \(-0.588011\pi\) | ||||
−0.272985 | + | 0.962018i | \(0.588011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.95739 | −0.155231 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.267232 | −0.0210608 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.56041 | 0.748829 | 0.374414 | − | 0.927261i | \(-0.377844\pi\) | ||||
0.374414 | + | 0.927261i | \(0.377844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.6239 | −0.904916 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.47894 | 0.501355 | 0.250678 | − | 0.968071i | \(-0.419347\pi\) | ||||
0.250678 | + | 0.968071i | \(0.419347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.94990 | −0.457684 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.22877 | −0.476326 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7896 | 1.42855 | 0.714274 | − | 0.699866i | \(-0.246757\pi\) | ||||
0.714274 | + | 0.699866i | \(0.246757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.379890 | 0.0287170 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.20540 | 0.541591 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.42836 | −0.256248 | −0.128124 | − | 0.991758i | \(-0.540896\pi\) | ||||
−0.128124 | + | 0.991758i | \(0.540896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.1458 | −1.79474 | −0.897370 | − | 0.441279i | \(-0.854525\pi\) | ||||
−0.897370 | + | 0.441279i | \(0.854525\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8372 | 0.875028 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.1454 | −1.55464 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.25137 | 0.310891 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0390685 | −0.00284182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.90983 | 0.138191 | 0.0690953 | − | 0.997610i | \(-0.477989\pi\) | ||||
0.0690953 | + | 0.997610i | \(0.477989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8675 | 0.854243 | 0.427121 | − | 0.904194i | \(-0.359528\pi\) | ||||
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.1884 | 0.729607 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4184 | 0.884775 | 0.442387 | − | 0.896824i | \(-0.354132\pi\) | ||||
0.442387 | + | 0.896824i | \(0.354132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2061 | 1.64504 | 0.822519 | − | 0.568737i | \(-0.192568\pi\) | ||||
0.822519 | + | 0.568737i | \(0.192568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.49442 | 0.317012 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.253763 | −0.0178107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.02634 | −0.420898 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.84008 | −0.475418 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.8688 | 1.30518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9393 | 1.71689 | 0.858446 | − | 0.512904i | \(-0.171430\pi\) | ||||
0.858446 | + | 0.512904i | \(0.171430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1096 | 0.966776 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.9015 | 1.90287 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.213526 | 0.0144951 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5600 | −0.713577 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.72636 | −0.250662 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.56656 | 0.238834 | 0.119417 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119417 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.72369 | 0.648246 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.7918 | −1.24726 | −0.623629 | − | 0.781721i | \(-0.714342\pi\) | ||||
−0.623629 | + | 0.781721i | \(0.714342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.8157 | 1.83811 | 0.919057 | − | 0.394124i | \(-0.128952\pi\) | ||||
0.919057 | + | 0.394124i | \(0.128952\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.118350 | 0.00778687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.3547 | −1.33348 | −0.666741 | − | 0.745290i | \(-0.732311\pi\) | ||||
−0.666741 | + | 0.745290i | \(0.732311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.7542 | 2.07142 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1134 | −0.916763 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.41325 | 0.350154 | 0.175077 | − | 0.984555i | \(-0.443983\pi\) | ||||
0.175077 | + | 0.984555i | \(0.443983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0541 | −0.647643 | −0.323821 | − | 0.946118i | \(-0.604968\pi\) | ||||
−0.323821 | + | 0.946118i | \(0.604968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.8542 | 1.71565 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.5387 | −1.05233 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.15120 | 0.136327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.24106 | 0.393932 | 0.196966 | − | 0.980410i | \(-0.436891\pi\) | ||||
0.196966 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7206 | 1.30270 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.38512 | −0.337229 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.4905 | 1.27817 | 0.639083 | − | 0.769138i | \(-0.279314\pi\) | ||||
0.639083 | + | 0.769138i | \(0.279314\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.215295 | 0.0133778 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.49534 | −0.402051 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.3112 | 1.49909 | 0.749547 | − | 0.661951i | \(-0.230271\pi\) | ||||
0.749547 | + | 0.661951i | \(0.230271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.51080 | −0.461385 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6325 | −0.895494 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.374620 | 0.0228410 | 0.0114205 | − | 0.999935i | \(-0.496365\pi\) | ||||
0.0114205 | + | 0.999935i | \(0.496365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.25550 | 0.258503 | 0.129252 | − | 0.991612i | \(-0.458742\pi\) | ||||
0.129252 | + | 0.991612i | \(0.458742\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.103735 | −0.00627832 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.4560 | −1.77626 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.55446 | −0.273651 | −0.136826 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136826 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.46543 | 0.327207 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.1317 | 1.73785 | 0.868924 | − | 0.494945i | \(-0.164812\pi\) | ||||
0.868924 | + | 0.494945i | \(0.164812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7994 | 1.35529 | 0.677643 | − | 0.735391i | \(-0.263001\pi\) | ||||
0.677643 | + | 0.735391i | \(0.263001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.9007 | −1.41576 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0613582 | 0.00362186 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0304 | −0.884142 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8990 | 0.638912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.1807 | 1.29581 | 0.647906 | − | 0.761720i | \(-0.275645\pi\) | ||||
0.647906 | + | 0.761720i | \(0.275645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6482 | 1.60974 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.02930 | 0.175778 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1618 | −1.05032 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.284084 | −0.0163743 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.205647 | −0.0118141 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 45.4209 | 2.60079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.2511 | 0.984570 | 0.492285 | − | 0.870434i | \(-0.336162\pi\) | ||||
0.492285 | + | 0.870434i | \(0.336162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.4002 | 0.705425 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.72157 | 0.381145 | 0.190573 | − | 0.981673i | \(-0.438966\pi\) | ||||
0.190573 | + | 0.981673i | \(0.438966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7539 | −1.00351 | −0.501756 | − | 0.865009i | \(-0.667312\pi\) | ||||
−0.501756 | + | 0.865009i | \(0.667312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.149912 | −0.00844656 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.9958 | −1.40390 | −0.701951 | − | 0.712225i | \(-0.747687\pi\) | ||||
−0.701951 | + | 0.712225i | \(0.747687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.6763 | 1.10166 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.40725 | 0.134360 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.74157 | 0.486394 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.8184 | 1.43215 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.79279 | 0.430942 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.323310 | −0.0178247 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.54725 | 0.469799 | 0.234900 | − | 0.972020i | \(-0.424524\pi\) | ||||
0.234900 | + | 0.972020i | \(0.424524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.51070 | 0.301984 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2458 | 0.942236 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.7198 | 1.67342 | 0.836708 | − | 0.547649i | \(-0.184477\pi\) | ||||
0.836708 | + | 0.547649i | \(0.184477\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.79544 | −0.151828 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.5564 | −0.896580 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.546900 | −0.0295298 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.2464 | −1.41306 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.299088 | 0.0160559 | 0.00802795 | − | 0.999968i | \(-0.497445\pi\) | ||||
0.00802795 | + | 0.999968i | \(0.497445\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.665481 | −0.0356224 | −0.0178112 | − | 0.999841i | \(-0.505670\pi\) | ||||
−0.0178112 | + | 0.999841i | \(0.505670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65520 | −0.141724 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.411030 | 0.0218769 | 0.0109385 | − | 0.999940i | \(-0.496518\pi\) | ||||
0.0109385 | + | 0.999940i | \(0.496518\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.1407 | 2.87349 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0548295 | 0.00290188 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.60341 | 0.401293 | 0.200646 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200646 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.7976 | 1.04198 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.82335 | 0.0957011 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.5202 | −2.12092 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9614 | −1.61617 | −0.808085 | − | 0.589066i | \(-0.799496\pi\) | ||||
−0.808085 | + | 0.589066i | \(0.799496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.57053 | 0.0817584 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0764724 | 0.00397025 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.33616 | 0.172740 | 0.0863699 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863699 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.1255 | 0.935996 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.2464 | −0.888237 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6981 | −1.42276 | −0.711379 | − | 0.702809i | \(-0.751929\pi\) | ||||
−0.711379 | + | 0.702809i | \(0.751929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.615625 | −0.0315394 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3897 | 0.530890 | 0.265445 | − | 0.964126i | \(-0.414481\pi\) | ||||
0.265445 | + | 0.964126i | \(0.414481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.454127 | 0.0231445 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.27143 | −0.369628 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8787 | 1.26140 | 0.630701 | − | 0.776026i | \(-0.282767\pi\) | ||||
0.630701 | + | 0.776026i | \(0.282767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.59949 | 0.485467 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.72461 | −0.0869949 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −54.1551 | −2.72484 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6566 | 0.936348 | 0.468174 | − | 0.883636i | \(-0.344912\pi\) | ||||
0.468174 | + | 0.883636i | \(0.344912\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.243349 | 0.0121827 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.3355 | −1.91439 | −0.957193 | − | 0.289451i | \(-0.906527\pi\) | ||||
−0.957193 | + | 0.289451i | \(0.906527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5118 | 0.722885 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.83715 | −0.190669 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.6936 | −0.827469 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.5485 | 1.55997 | 0.779986 | − | 0.625797i | \(-0.215226\pi\) | ||||
0.779986 | + | 0.625797i | \(0.215226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.88340 | −0.290207 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.281504 | −0.0138519 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.25446 | 0.405195 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.606430 | −0.0296970 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.9946 | −1.85616 | −0.928078 | − | 0.372386i | \(-0.878540\pi\) | ||||
−0.928078 | + | 0.372386i | \(0.878540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.56960 | −0.173972 | −0.0869858 | − | 0.996210i | \(-0.527723\pi\) | ||||
−0.0869858 | + | 0.996210i | \(0.527723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.27547 | −0.402367 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.6464 | −0.661948 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.462460 | −0.0223800 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.04340 | 0.388339 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.73333 | −0.420670 | −0.210335 | − | 0.977629i | \(-0.567455\pi\) | ||||
−0.210335 | + | 0.977629i | \(0.567455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.385145 | −0.0185089 | −0.00925443 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925443 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −24.9236 | −1.19499 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 42.6053 | 2.03809 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5407 | 0.598534 | 0.299267 | − | 0.954169i | \(-0.403258\pi\) | ||||
0.299267 | + | 0.954169i | \(0.403258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99847 | −0.333261 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.95596 | 0.187953 | 0.0939766 | − | 0.995574i | \(-0.470042\pi\) | ||||
0.0939766 | + | 0.995574i | \(0.470042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −56.1470 | −2.66162 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.74814 | 0.413773 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.8450 | −1.36128 | −0.680639 | − | 0.732619i | \(-0.738298\pi\) | ||||
−0.680639 | + | 0.732619i | \(0.738298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.75760 | −0.224026 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.73638 | 0.269519 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.398046 | −0.0186607 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9524 | 0.559112 | 0.279556 | − | 0.960129i | \(-0.409813\pi\) | ||||
0.279556 | + | 0.960129i | \(0.409813\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.40342 | 0.0655059 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.157915 | 0.00735484 | 0.00367742 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367742 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.9683 | −1.20685 | −0.603424 | − | 0.797421i | \(-0.706197\pi\) | ||||
−0.603424 | + | 0.797421i | \(0.706197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9716 | 0.972537 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.43023 | −0.390104 | −0.195052 | − | 0.980793i | \(-0.562488\pi\) | ||||
−0.195052 | + | 0.980793i | \(0.562488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.175590 | −0.00810801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.84099 | 0.315216 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0273 | 1.01282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −60.5667 | −2.77899 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.95739 | 0.0896228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2764 | 0.606615 | 0.303307 | − | 0.952893i | \(-0.401909\pi\) | ||||
0.303307 | + | 0.952893i | \(0.401909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6320 | 0.667163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.267232 | 0.0121595 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.8212 | 1.89900 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0896 | −0.819718 | −0.409859 | − | 0.912149i | \(-0.634422\pi\) | ||||
−0.409859 | + | 0.912149i | \(0.634422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.56041 | −0.432337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.7182 | −1.25091 | −0.625453 | − | 0.780262i | \(-0.715086\pi\) | ||||
−0.625453 | + | 0.780262i | \(0.715086\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.11567 | 0.410549 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.6239 | 0.522454 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.551242 | −0.0247266 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.6472 | 0.969064 | 0.484532 | − | 0.874774i | \(-0.338990\pi\) | ||||
0.484532 | + | 0.874774i | \(0.338990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.47894 | −0.289458 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.789097 | −0.0351144 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.94990 | 0.264244 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9445 | 0.662402 | 0.331201 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331201 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.412563 | 0.0182507 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.22877 | 0.275007 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 47.5815 | 2.09669 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.0689 | 1.10253 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.7896 | −0.824772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0317 | 1.40334 | 0.701668 | − | 0.712504i | \(-0.252439\pi\) | ||||
0.701668 | + | 0.712504i | \(0.252439\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.7550 | −1.95700 | −0.978500 | − | 0.206245i | \(-0.933876\pi\) | ||||
−0.978500 | + | 0.206245i | \(0.933876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.379890 | −0.0165798 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.67028 | −0.334123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.7867 | 1.03420 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.20540 | −0.312688 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.17007 | 0.180626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.23698 | 0.399349 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.42836 | 0.147945 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.2005 | 0.913169 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.9371 | −1.33009 | −0.665046 | − | 0.746802i | \(-0.731588\pi\) | ||||
−0.665046 | + | 0.746802i | \(0.731588\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.1458 | 1.03619 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.9021 | 1.28086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9499 | −1.06678 | −0.533390 | − | 0.845869i | \(-0.679082\pi\) | ||||
−0.533390 | + | 0.845869i | \(0.679082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.8372 | −0.505198 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.4580 | 1.72357 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.551389 | 0.0234474 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.1454 | 0.897570 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.82451 | 0.204421 | 0.102210 | − | 0.994763i | \(-0.467408\pi\) | ||||
0.102210 | + | 0.994763i | \(0.467408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3071 | −0.816604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.25137 | −0.179493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.5910 | 1.54213 | 0.771063 | − | 0.636759i | \(-0.219725\pi\) | ||||
0.771063 | + | 0.636759i | \(0.219725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7265 | −0.451268 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0390685 | 0.00164072 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.7838 | 0.955148 | 0.477574 | − | 0.878592i | \(-0.341516\pi\) | ||||
0.477574 | + | 0.878592i | \(0.341516\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9495 | 0.625616 | 0.312808 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312808 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.90983 | −0.0797844 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −66.5108 | −2.77369 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.1589 | 1.04738 | 0.523690 | − | 0.851909i | \(-0.324555\pi\) | ||||
0.523690 | + | 0.851909i | \(0.324555\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.8675 | −0.493197 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0840441 | −0.00348674 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.92953 | −0.245576 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.1884 | −0.421239 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.76003 | 0.279016 | 0.139508 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139508 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.0429 | −1.40271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4184 | −0.510825 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.25925 | −0.257037 | −0.128518 | − | 0.991707i | \(-0.541022\pi\) | ||||
−0.128518 | + | 0.991707i | \(0.541022\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.210389 | 0.00862509 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.2061 | −0.949763 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4362 | 0.426413 | 0.213207 | − | 0.977007i | \(-0.431609\pi\) | ||||
0.213207 | + | 0.977007i | \(0.431609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3706 | −1.19805 | −0.599026 | − | 0.800730i | \(-0.704445\pi\) | ||||
−0.599026 | + | 0.800730i | \(0.704445\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.49442 | −0.183027 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.99646 | 0.284447 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4328 | 1.15405 | 0.577026 | − | 0.816726i | \(-0.304213\pi\) | ||||
0.577026 | + | 0.816726i | \(0.304213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.253763 | 0.0102830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.9731 | −0.888935 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.1123 | 1.05467 | 0.527333 | − | 0.849659i | \(-0.323192\pi\) | ||||
0.527333 | + | 0.849659i | \(0.323192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.02634 | 0.243006 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.73815 | −0.311526 | −0.155763 | − | 0.987794i | \(-0.549784\pi\) | ||||
−0.155763 | + | 0.987794i | \(0.549784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.1463 | 1.69400 | 0.847002 | − | 0.531590i | \(-0.178405\pi\) | ||||
0.847002 | + | 0.531590i | \(0.178405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.84008 | 0.274483 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.571670 | 0.0229035 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.9317 | 0.837268 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.8688 | −0.753548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.73381 | −0.308367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0497 | −1.67397 | −0.836986 | − | 0.547224i | \(-0.815685\pi\) | ||||
−0.836986 | + | 0.547224i | \(0.815685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.9393 | −0.991248 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.36224 | −0.0937427 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.5824 | −0.736260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1096 | −0.558168 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.13011 | 0.242125 | 0.121062 | − | 0.992645i | \(-0.461370\pi\) | ||||
0.121062 | + | 0.992645i | \(0.461370\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.9585 | −1.41807 | −0.709033 | − | 0.705176i | \(-0.750868\pi\) | ||||
−0.709033 | + | 0.705176i | \(0.750868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.9015 | −1.09862 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.1620 | −0.596080 | −0.298040 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298040 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.8273 | 0.856796 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.213526 | −0.00836875 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.79559 | −0.265932 | −0.132966 | − | 0.991121i | \(-0.542450\pi\) | ||||
−0.132966 | + | 0.991121i | \(0.542450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.61757 | −0.258570 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5600 | 0.411984 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.81047 | 0.265298 | 0.132649 | − | 0.991163i | \(-0.457652\pi\) | ||||
0.132649 | + | 0.991163i | \(0.457652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7175 | −0.728026 | −0.364013 | − | 0.931394i | \(-0.618594\pi\) | ||||
−0.364013 | + | 0.931394i | \(0.618594\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.72636 | 0.144720 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.933766 | 0.0362099 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.4286 | 1.72028 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.56656 | −0.137891 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.8583 | 1.38429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.3181 | 0.860298 | 0.430149 | − | 0.902758i | \(-0.358461\pi\) | ||||
0.430149 | + | 0.902758i | \(0.358461\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.72369 | −0.374265 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.8892 | −0.418504 | −0.209252 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209252 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.425809 | −0.0163410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7918 | 0.720105 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.9652 | −1.64402 | −0.822009 | − | 0.569475i | \(-0.807147\pi\) | ||||
−0.822009 | + | 0.569475i | \(0.807147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5755 | −0.862564 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.8157 | −1.06124 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.19727 | 0.198000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.1065 | −1.44964 | −0.724819 | − | 0.688939i | \(-0.758077\pi\) | ||||
−0.724819 | + | 0.688939i | \(0.758077\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.118350 | −0.00449575 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.32696 | −0.0882666 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20411 | −0.0834865 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.3547 | 0.769886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6026 | 0.589303 | 0.294652 | − | 0.955605i | \(-0.404796\pi\) | ||||
0.294652 | + | 0.955605i | \(0.404796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.3249 | −1.29459 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.7542 | −1.19593 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.00803432 | 0.000302162 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.2373 | 0.647362 | 0.323681 | − | 0.946166i | \(-0.395080\pi\) | ||||
0.323681 | + | 0.946166i | \(0.395080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1134 | 0.529293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.3840 | −1.40004 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.8637 | 1.15424 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.41325 | −0.202161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.81684 | −0.328813 | −0.164406 | − | 0.986393i | \(-0.552571\pi\) | ||||
−0.164406 | + | 0.986393i | \(0.552571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.484459 | −0.0180422 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0541 | 0.373917 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −63.1586 | −2.34565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.0589 | −1.26317 | −0.631587 | − | 0.775305i | \(-0.717596\pi\) | ||||
−0.631587 | + | 0.775305i | \(0.717596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2049 | 0.377440 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.26116 | 0.194325 | 0.0971627 | − | 0.995269i | \(-0.469023\pi\) | ||||
0.0971627 | + | 0.995269i | \(0.469023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.8542 | −0.990531 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6149 | 0.501513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.79365 | −0.249909 | −0.124954 | − | 0.992162i | \(-0.539878\pi\) | ||||
−0.124954 | + | 0.992162i | \(0.539878\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5387 | 0.607563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8291 | 0.837520 | 0.418760 | − | 0.908097i | \(-0.362465\pi\) | ||||
0.418760 | + | 0.908097i | \(0.362465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.5679 | 1.22983 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.15120 | −0.0787082 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.0940478 | −0.00343643 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.3210 | 1.10643 | 0.553214 | − | 0.833039i | \(-0.313401\pi\) | ||||
0.553214 | + | 0.833039i | \(0.313401\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.24106 | −0.227437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.0113 | 0.801075 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2068 | 1.13423 | 0.567115 | − | 0.823639i | \(-0.308059\pi\) | ||||
0.567115 | + | 0.823639i | \(0.308059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.7206 | −0.752112 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9250 | 0.686031 | 0.343015 | − | 0.939330i | \(-0.388552\pi\) | ||||
0.343015 | + | 0.939330i | \(0.388552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.304453 | −0.0110219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.38512 | 0.194699 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.1318 | −0.690809 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8294 | −0.606884 | −0.303442 | − | 0.952850i | \(-0.598136\pi\) | ||||
−0.303442 | + | 0.952850i | \(0.598136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4905 | −0.737949 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.45996 | 0.124446 | 0.0622230 | − | 0.998062i | \(-0.480181\pi\) | ||||
0.0622230 | + | 0.998062i | \(0.480181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 53.1441 | 1.90899 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.215295 | −0.00772366 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.78246 | −0.350493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.7423 | 1.52944 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.49534 | 0.232124 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.2499 | 0.936898 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5238 | −0.909823 | −0.454912 | − | 0.890537i | \(-0.650329\pi\) | ||||
−0.454912 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.3112 | −0.865503 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.109214 | 0.00388319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.4301 | −1.11611 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.51080 | 0.266381 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.6053 | −0.446503 | −0.223251 | − | 0.974761i | \(-0.571667\pi\) | ||||
−0.223251 | + | 0.974761i | \(0.571667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6139 | 0.410872 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.6325 | 0.517014 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.9893 | −1.12888 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.02541 | 0.0361409 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.374620 | −0.0131873 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.50905 | 0.264004 | 0.132002 | − | 0.991249i | \(-0.457859\pi\) | ||||
0.132002 | + | 0.991249i | \(0.457859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.46364 | 0.121625 | 0.0608125 | − | 0.998149i | \(-0.480631\pi\) | ||||
0.0608125 | + | 0.998149i | \(0.480631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.25550 | −0.149247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.6847 | −1.28501 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.2921 | 1.58457 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.103735 | 0.00362479 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7887 | −0.516130 | −0.258065 | − | 0.966128i | \(-0.583085\pi\) | ||||
−0.258065 | + | 0.966128i | \(0.583085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.8351 | −0.726265 | −0.363133 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363133 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.4560 | 1.02552 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.1692 | −1.32727 | −0.663637 | − | 0.748055i | \(-0.730988\pi\) | ||||
−0.663637 | + | 0.748055i | \(0.730988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.9228 | 1.59497 | 0.797483 | − | 0.603342i | \(-0.206165\pi\) | ||||
0.797483 | + | 0.603342i | \(0.206165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.55446 | 0.157993 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.82178 | 0.340305 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.8606 | −0.860338 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.46543 | −0.188913 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.7693 | −0.751561 | −0.375781 | − | 0.926709i | \(-0.622625\pi\) | ||||
−0.375781 | + | 0.926709i | \(0.622625\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1894 | 0.454807 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.1317 | −1.00335 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.8306 | 0.785397 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0712356 | −0.00244768 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.7994 | −0.782475 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6936 | −1.29212 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0715 | 0.516037 | 0.258019 | − | 0.966140i | \(-0.416930\pi\) | ||||
0.258019 | + | 0.966140i | \(0.416930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.9007 | 0.817387 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.6455 | 0.671077 | 0.335539 | − | 0.942026i | \(-0.391082\pi\) | ||||
0.335539 | + | 0.942026i | \(0.391082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.56535 | −0.121648 | −0.0608241 | − | 0.998149i | \(-0.519373\pi\) | ||||
−0.0608241 | + | 0.998149i | \(0.519373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0613582 | −0.00209108 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.1135 | −1.02508 | −0.512538 | − | 0.858665i | \(-0.671294\pi\) | ||||
−0.512538 | + | 0.858665i | \(0.671294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.0985 | −2.45142 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.0304 | 0.510460 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.7536 | −1.45032 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9336 | −0.404355 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.8990 | −0.368876 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.708136 | −0.0239394 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5131 | −1.40180 | −0.700899 | − | 0.713260i | \(-0.747218\pi\) | ||||
−0.700899 | + | 0.713260i | \(0.747218\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.1807 | −0.748138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.2698 | −1.52518 | −0.762590 | − | 0.646883i | \(-0.776072\pi\) | ||||
−0.762590 | + | 0.646883i | \(0.776072\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5916 | −0.995836 | −0.497918 | − | 0.867224i | \(-0.665902\pi\) | ||||
−0.497918 | + | 0.867224i | \(0.665902\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.6482 | −0.929383 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.6404 | 1.46530 | 0.732650 | − | 0.680606i | \(-0.238283\pi\) | ||||
0.732650 | + | 0.680606i | \(0.238283\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0240516 | 0.000806663 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.02930 | −0.101485 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.5460 | 1.72492 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1551 | 0.439727 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.1618 | 0.606405 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35.4998 | −1.18398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.74704 | −0.0915172 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.284084 | 0.00945373 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 92.6508 | 3.07982 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.6209 | −1.34879 | −0.674397 | − | 0.738369i | \(-0.735596\pi\) | ||||
−0.674397 | + | 0.738369i | \(0.735596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.205647 | 0.00682088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.9835 | 1.02653 | 0.513264 | − | 0.858231i | \(-0.328436\pi\) | ||||
0.513264 | + | 0.858231i | \(0.328436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.51662 | 0.215669 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45.4209 | −1.50157 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0673779 | 0.00222501 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8095 | −0.554494 | −0.277247 | − | 0.960799i | \(-0.589422\pi\) | ||||
−0.277247 | + | 0.960799i | \(0.589422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.2511 | −0.568442 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.4639 | −1.23314 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.5843 | 1.76184 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4002 | −0.407277 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3104 | −0.633554 | −0.316777 | − | 0.948500i | \(-0.602601\pi\) | ||||
−0.316777 | + | 0.948500i | \(0.602601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.5919 | 1.42867 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.72157 | −0.220054 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.3131 | −0.533497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.83866 | −0.0600665 | −0.0300332 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300332 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.7539 | 0.579378 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.94424 | 0.258975 | 0.129487 | − | 0.991581i | \(-0.458667\pi\) | ||||
0.129487 | + | 0.991581i | \(0.458667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.7425 | −0.349825 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.149912 | 0.00487663 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4344 | 0.696525 | 0.348262 | − | 0.937397i | \(-0.386772\pi\) | ||||
0.348262 | + | 0.937397i | \(0.386772\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0389 | 0.910181 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.9958 | 0.810543 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.9229 | −1.35802 | −0.679009 | − | 0.734130i | \(-0.737590\pi\) | ||||
−0.679009 | + | 0.734130i | \(0.737590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.32830 | −0.237138 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.6763 | −0.636045 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.229856 | 0.00742243 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.12911 | −0.0364229 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.40725 | −0.0775726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.5374 | −1.46590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0934 | 1.38579 | 0.692896 | − | 0.721038i | \(-0.256335\pi\) | ||||
0.692896 | + | 0.721038i | \(0.256335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.74157 | −0.280820 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0155 | 0.417688 | 0.208844 | − | 0.977949i | \(-0.433030\pi\) | ||||
0.208844 | + | 0.977949i | \(0.433030\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0236923 | 0.000759541 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.8184 | −0.826849 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.7460 | −0.375789 | −0.187895 | − | 0.982189i | \(-0.560166\pi\) | ||||
−0.187895 | + | 0.982189i | \(0.560166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.3262 | −1.41667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.79279 | −0.248805 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.5071 | −1.13250 | −0.566250 | − | 0.824233i | \(-0.691606\pi\) | ||||
−0.566250 | + | 0.824233i | \(0.691606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.6512 | −1.51829 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.323310 | 0.0102911 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.7372 | 1.58155 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.6990 | 1.64227 | 0.821136 | − | 0.570733i | \(-0.193341\pi\) | ||||
0.821136 | + | 0.570733i | \(0.193341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.54725 | −0.271239 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −89.0453 | −2.82293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.0780 | −1.71267 | −0.856333 | − | 0.516423i | \(-0.827263\pi\) | ||||
−0.856333 | + | 0.516423i | \(0.827263\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.51070 | −0.174351 |
(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 | 6036.2.a.i.1.2 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.2 | ✓ | 26 | 1.1 | even | 1 | trivial |