Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.46524\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.46524 | 0.655276 | 0.327638 | − | 0.944803i | \(-0.393747\pi\) | ||||
0.327638 | + | 0.944803i | \(0.393747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.53999 | −1.33799 | −0.668995 | − | 0.743267i | \(-0.733275\pi\) | ||||
−0.668995 | + | 0.743267i | \(0.733275\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.46524 | −0.463350 | ||||||||
\(11\) | −4.22810 | −1.27482 | −0.637410 | − | 0.770525i | \(-0.719994\pi\) | ||||
−0.637410 | + | 0.770525i | \(0.719994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.227772 | −0.0631727 | −0.0315863 | − | 0.999501i | \(-0.510056\pi\) | ||||
−0.0315863 | + | 0.999501i | \(0.510056\pi\) | |||||||
\(14\) | 3.53999 | 0.946102 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.27991 | 1.52310 | 0.761551 | − | 0.648105i | \(-0.224438\pi\) | ||||
0.761551 | + | 0.648105i | \(0.224438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57419 | 0.590560 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(20\) | 1.46524 | 0.327638 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.22810 | 0.901433 | ||||||||
\(23\) | 3.30009 | 0.688116 | 0.344058 | − | 0.938948i | \(-0.388198\pi\) | ||||
0.344058 | + | 0.938948i | \(0.388198\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.85307 | −0.570614 | ||||||||
\(26\) | 0.227772 | 0.0446698 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.53999 | −0.668995 | ||||||||
\(29\) | −3.57821 | −0.664456 | −0.332228 | − | 0.943199i | \(-0.607800\pi\) | ||||
−0.332228 | + | 0.943199i | \(0.607800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.37510 | 1.32461 | 0.662304 | − | 0.749236i | \(-0.269579\pi\) | ||||
0.662304 | + | 0.749236i | \(0.269579\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.27991 | −1.07700 | ||||||||
\(35\) | −5.18694 | −0.876753 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.39823 | −0.723065 | −0.361532 | − | 0.932360i | \(-0.617746\pi\) | ||||
−0.361532 | + | 0.932360i | \(0.617746\pi\) | |||||||
\(38\) | −2.57419 | −0.417589 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.46524 | −0.231675 | ||||||||
\(41\) | −4.53941 | −0.708937 | −0.354469 | − | 0.935068i | \(-0.615338\pi\) | ||||
−0.354469 | + | 0.935068i | \(0.615338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36273 | −0.207814 | −0.103907 | − | 0.994587i | \(-0.533135\pi\) | ||||
−0.103907 | + | 0.994587i | \(0.533135\pi\) | |||||||
\(44\) | −4.22810 | −0.637410 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.30009 | −0.486572 | ||||||||
\(47\) | 7.53590 | 1.09922 | 0.549612 | − | 0.835420i | \(-0.314776\pi\) | ||||
0.549612 | + | 0.835420i | \(0.314776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.53153 | 0.790219 | ||||||||
\(50\) | 2.85307 | 0.403485 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.227772 | −0.0315863 | ||||||||
\(53\) | −10.3373 | −1.41994 | −0.709972 | − | 0.704230i | \(-0.751292\pi\) | ||||
−0.709972 | + | 0.704230i | \(0.751292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.19518 | −0.835358 | ||||||||
\(56\) | 3.53999 | 0.473051 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.57821 | 0.469842 | ||||||||
\(59\) | −1.84299 | −0.239937 | −0.119968 | − | 0.992778i | \(-0.538279\pi\) | ||||
−0.119968 | + | 0.992778i | \(0.538279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0848386 | −0.0108625 | −0.00543123 | − | 0.999985i | \(-0.501729\pi\) | ||||
−0.00543123 | + | 0.999985i | \(0.501729\pi\) | |||||||
\(62\) | −7.37510 | −0.936639 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.333741 | −0.0413955 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.55903 | 0.556974 | 0.278487 | − | 0.960440i | \(-0.410167\pi\) | ||||
0.278487 | + | 0.960440i | \(0.410167\pi\) | |||||||
\(68\) | 6.27991 | 0.761551 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.18694 | 0.619958 | ||||||||
\(71\) | 2.24203 | 0.266080 | 0.133040 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133040 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.79670 | −0.795494 | −0.397747 | − | 0.917495i | \(-0.630208\pi\) | ||||
−0.397747 | + | 0.917495i | \(0.630208\pi\) | |||||||
\(74\) | 4.39823 | 0.511284 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.57419 | 0.295280 | ||||||||
\(77\) | 14.9674 | 1.70570 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.14110 | 0.353401 | 0.176701 | − | 0.984265i | \(-0.443458\pi\) | ||||
0.176701 | + | 0.984265i | \(0.443458\pi\) | |||||||
\(80\) | 1.46524 | 0.163819 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.53941 | 0.501294 | ||||||||
\(83\) | 1.74078 | 0.191076 | 0.0955378 | − | 0.995426i | \(-0.469543\pi\) | ||||
0.0955378 | + | 0.995426i | \(0.469543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.20158 | 0.998051 | ||||||||
\(86\) | 1.36273 | 0.146947 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.22810 | 0.450717 | ||||||||
\(89\) | −5.71960 | −0.606276 | −0.303138 | − | 0.952947i | \(-0.598034\pi\) | ||||
−0.303138 | + | 0.952947i | \(0.598034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.806312 | 0.0845245 | ||||||||
\(92\) | 3.30009 | 0.344058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.53590 | −0.777268 | ||||||||
\(95\) | 3.77181 | 0.386980 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.1029 | 1.93961 | 0.969804 | − | 0.243884i | \(-0.0784217\pi\) | ||||
0.969804 | + | 0.243884i | \(0.0784217\pi\) | |||||||
\(98\) | −5.53153 | −0.558769 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.85307 | −0.285307 | ||||||||
\(101\) | −3.67787 | −0.365962 | −0.182981 | − | 0.983116i | \(-0.558575\pi\) | ||||
−0.182981 | + | 0.983116i | \(0.558575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13416 | 0.111752 | 0.0558759 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558759 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(104\) | 0.227772 | 0.0223349 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3373 | 1.00405 | ||||||||
\(107\) | −7.11155 | −0.687500 | −0.343750 | − | 0.939061i | \(-0.611697\pi\) | ||||
−0.343750 | + | 0.939061i | \(0.611697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.1888 | 1.55061 | 0.775305 | − | 0.631587i | \(-0.217596\pi\) | ||||
0.775305 | + | 0.631587i | \(0.217596\pi\) | |||||||
\(110\) | 6.19518 | 0.590687 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.53999 | −0.334498 | ||||||||
\(113\) | −1.96757 | −0.185093 | −0.0925466 | − | 0.995708i | \(-0.529501\pi\) | ||||
−0.0925466 | + | 0.995708i | \(0.529501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.83543 | 0.450906 | ||||||||
\(116\) | −3.57821 | −0.332228 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.84299 | 0.169661 | ||||||||
\(119\) | −22.2308 | −2.03790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.87680 | 0.625164 | ||||||||
\(122\) | 0.0848386 | 0.00768092 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.37510 | 0.662304 | ||||||||
\(125\) | −11.5066 | −1.02919 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.56617 | 0.227710 | 0.113855 | − | 0.993497i | \(-0.463680\pi\) | ||||
0.113855 | + | 0.993497i | \(0.463680\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.333741 | 0.0292711 | ||||||||
\(131\) | 21.1716 | 1.84978 | 0.924888 | − | 0.380240i | \(-0.124159\pi\) | ||||
0.924888 | + | 0.380240i | \(0.124159\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.11262 | −0.790164 | ||||||||
\(134\) | −4.55903 | −0.393840 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.27991 | −0.538498 | ||||||||
\(137\) | −17.0465 | −1.45638 | −0.728192 | − | 0.685373i | \(-0.759639\pi\) | ||||
−0.728192 | + | 0.685373i | \(0.759639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5556 | −0.980132 | −0.490066 | − | 0.871685i | \(-0.663027\pi\) | ||||
−0.490066 | + | 0.871685i | \(0.663027\pi\) | |||||||
\(140\) | −5.18694 | −0.438376 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.24203 | −0.188147 | ||||||||
\(143\) | 0.963044 | 0.0805337 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.24293 | −0.435402 | ||||||||
\(146\) | 6.79670 | 0.562499 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.39823 | −0.361532 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.85207 | 0.476235 | 0.238117 | − | 0.971236i | \(-0.423470\pi\) | ||||
0.238117 | + | 0.971236i | \(0.423470\pi\) | |||||||
\(152\) | −2.57419 | −0.208795 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.9674 | −1.20611 | ||||||||
\(155\) | 10.8063 | 0.867983 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.89904 | −0.630412 | −0.315206 | − | 0.949023i | \(-0.602074\pi\) | ||||
−0.315206 | + | 0.949023i | \(0.602074\pi\) | |||||||
\(158\) | −3.14110 | −0.249892 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.46524 | −0.115837 | ||||||||
\(161\) | −11.6823 | −0.920693 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.40642 | 0.188485 | 0.0942427 | − | 0.995549i | \(-0.469957\pi\) | ||||
0.0942427 | + | 0.995549i | \(0.469957\pi\) | |||||||
\(164\) | −4.53941 | −0.354469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.74078 | −0.135111 | ||||||||
\(167\) | −4.87364 | −0.377133 | −0.188567 | − | 0.982060i | \(-0.560384\pi\) | ||||
−0.188567 | + | 0.982060i | \(0.560384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9481 | −0.996009 | ||||||||
\(170\) | −9.20158 | −0.705729 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.36273 | −0.103907 | ||||||||
\(173\) | −12.8982 | −0.980633 | −0.490317 | − | 0.871544i | \(-0.663119\pi\) | ||||
−0.490317 | + | 0.871544i | \(0.663119\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0998 | 0.763476 | ||||||||
\(176\) | −4.22810 | −0.318705 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.71960 | 0.428702 | ||||||||
\(179\) | 8.33812 | 0.623221 | 0.311610 | − | 0.950210i | \(-0.399132\pi\) | ||||
0.311610 | + | 0.950210i | \(0.399132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.7248 | 1.91211 | 0.956055 | − | 0.293187i | \(-0.0947158\pi\) | ||||
0.956055 | + | 0.293187i | \(0.0947158\pi\) | |||||||
\(182\) | −0.806312 | −0.0597678 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.30009 | −0.243286 | ||||||||
\(185\) | −6.44447 | −0.473807 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5521 | −1.94168 | ||||||||
\(188\) | 7.53590 | 0.549612 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.77181 | −0.273636 | ||||||||
\(191\) | −21.3232 | −1.54289 | −0.771446 | − | 0.636295i | \(-0.780466\pi\) | ||||
−0.771446 | + | 0.636295i | \(0.780466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.44168 | 0.679627 | 0.339813 | − | 0.940493i | \(-0.389636\pi\) | ||||
0.339813 | + | 0.940493i | \(0.389636\pi\) | |||||||
\(194\) | −19.1029 | −1.37151 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.53153 | 0.395110 | ||||||||
\(197\) | −13.7269 | −0.978004 | −0.489002 | − | 0.872283i | \(-0.662639\pi\) | ||||
−0.489002 | + | 0.872283i | \(0.662639\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9142 | −1.83701 | −0.918504 | − | 0.395412i | \(-0.870602\pi\) | ||||
−0.918504 | + | 0.395412i | \(0.870602\pi\) | |||||||
\(200\) | 2.85307 | 0.201742 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.67787 | 0.258774 | ||||||||
\(203\) | 12.6668 | 0.889036 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.65134 | −0.464549 | ||||||||
\(206\) | −1.13416 | −0.0790204 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.227772 | −0.0157932 | ||||||||
\(209\) | −10.8839 | −0.752858 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.68939 | 0.322831 | 0.161416 | − | 0.986887i | \(-0.448394\pi\) | ||||
0.161416 | + | 0.986887i | \(0.448394\pi\) | |||||||
\(212\) | −10.3373 | −0.709972 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.11155 | 0.486136 | ||||||||
\(215\) | −1.99673 | −0.136176 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.1078 | −1.77231 | ||||||||
\(218\) | −16.1888 | −1.09645 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.19518 | −0.417679 | ||||||||
\(221\) | −1.43039 | −0.0962184 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.3356 | 1.42874 | 0.714369 | − | 0.699769i | \(-0.246714\pi\) | ||||
0.714369 | + | 0.699769i | \(0.246714\pi\) | |||||||
\(224\) | 3.53999 | 0.236526 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.96757 | 0.130881 | ||||||||
\(227\) | −14.9565 | −0.992696 | −0.496348 | − | 0.868124i | \(-0.665326\pi\) | ||||
−0.496348 | + | 0.868124i | \(0.665326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3500 | −0.683945 | −0.341973 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341973 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(230\) | −4.83543 | −0.318839 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.57821 | 0.234921 | ||||||||
\(233\) | −3.89733 | −0.255323 | −0.127661 | − | 0.991818i | \(-0.540747\pi\) | ||||
−0.127661 | + | 0.991818i | \(0.540747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0419 | 0.720294 | ||||||||
\(236\) | −1.84299 | −0.119968 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.2308 | 1.44101 | ||||||||
\(239\) | −28.9563 | −1.87303 | −0.936515 | − | 0.350628i | \(-0.885968\pi\) | ||||
−0.936515 | + | 0.350628i | \(0.885968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6773 | −0.945449 | −0.472725 | − | 0.881210i | \(-0.656729\pi\) | ||||
−0.472725 | + | 0.881210i | \(0.656729\pi\) | |||||||
\(242\) | −6.87680 | −0.442057 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0848386 | −0.00543123 | ||||||||
\(245\) | 8.10503 | 0.517811 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.586330 | −0.0373073 | ||||||||
\(248\) | −7.37510 | −0.468319 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5066 | 0.727744 | ||||||||
\(251\) | −1.07802 | −0.0680438 | −0.0340219 | − | 0.999421i | \(-0.510832\pi\) | ||||
−0.0340219 | + | 0.999421i | \(0.510832\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.9531 | −0.877224 | ||||||||
\(254\) | −2.56617 | −0.161016 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6721 | 0.852839 | 0.426420 | − | 0.904525i | \(-0.359775\pi\) | ||||
0.426420 | + | 0.904525i | \(0.359775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.5697 | 0.967454 | ||||||||
\(260\) | −0.333741 | −0.0206978 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.1716 | −1.30799 | ||||||||
\(263\) | −11.7549 | −0.724839 | −0.362419 | − | 0.932015i | \(-0.618049\pi\) | ||||
−0.362419 | + | 0.932015i | \(0.618049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.1467 | −0.930455 | ||||||||
\(266\) | 9.11262 | 0.558730 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.55903 | 0.278487 | ||||||||
\(269\) | −18.2194 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687446\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687446\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5134 | −0.942372 | −0.471186 | − | 0.882034i | \(-0.656174\pi\) | ||||
−0.471186 | + | 0.882034i | \(0.656174\pi\) | |||||||
\(272\) | 6.27991 | 0.380775 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0465 | 1.02982 | ||||||||
\(275\) | 12.0630 | 0.727429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.5931 | −1.95833 | −0.979164 | − | 0.203073i | \(-0.934907\pi\) | ||||
−0.979164 | + | 0.203073i | \(0.934907\pi\) | |||||||
\(278\) | 11.5556 | 0.693058 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.18694 | 0.309979 | ||||||||
\(281\) | −27.5743 | −1.64495 | −0.822473 | − | 0.568805i | \(-0.807406\pi\) | ||||
−0.822473 | + | 0.568805i | \(0.807406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.606670 | −0.0360628 | −0.0180314 | − | 0.999837i | \(-0.505740\pi\) | ||||
−0.0180314 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(284\) | 2.24203 | 0.133040 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.963044 | −0.0569460 | ||||||||
\(287\) | 16.0695 | 0.948552 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.4373 | 1.31984 | ||||||||
\(290\) | 5.24293 | 0.307876 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.79670 | −0.397747 | ||||||||
\(293\) | 9.36340 | 0.547016 | 0.273508 | − | 0.961870i | \(-0.411816\pi\) | ||||
0.273508 | + | 0.961870i | \(0.411816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.70042 | −0.157225 | ||||||||
\(296\) | 4.39823 | 0.255642 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −0.751669 | −0.0434702 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.82405 | 0.278054 | ||||||||
\(302\) | −5.85207 | −0.336749 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.57419 | 0.147640 | ||||||||
\(305\) | −0.124309 | −0.00711791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5000 | 0.770486 | 0.385243 | − | 0.922815i | \(-0.374118\pi\) | ||||
0.385243 | + | 0.922815i | \(0.374118\pi\) | |||||||
\(308\) | 14.9674 | 0.852848 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.8063 | −0.613757 | ||||||||
\(311\) | −27.1871 | −1.54164 | −0.770821 | − | 0.637052i | \(-0.780153\pi\) | ||||
−0.770821 | + | 0.637052i | \(0.780153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7246 | −0.662711 | −0.331356 | − | 0.943506i | \(-0.607506\pi\) | ||||
−0.331356 | + | 0.943506i | \(0.607506\pi\) | |||||||
\(314\) | 7.89904 | 0.445769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.14110 | 0.176701 | ||||||||
\(317\) | −13.8607 | −0.778493 | −0.389247 | − | 0.921134i | \(-0.627265\pi\) | ||||
−0.389247 | + | 0.921134i | \(0.627265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.1290 | 0.847061 | ||||||||
\(320\) | 1.46524 | 0.0819095 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.6823 | 0.651028 | ||||||||
\(323\) | 16.1657 | 0.899483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.649850 | 0.0360472 | ||||||||
\(326\) | −2.40642 | −0.133279 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.53941 | 0.250647 | ||||||||
\(329\) | −26.6770 | −1.47075 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.46657 | 0.520330 | 0.260165 | − | 0.965564i | \(-0.416223\pi\) | ||||
0.260165 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(332\) | 1.74078 | 0.0955378 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.87364 | 0.266674 | ||||||||
\(335\) | 6.68007 | 0.364971 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.81960 | −0.208067 | −0.104033 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104033 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(338\) | 12.9481 | 0.704285 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.20158 | 0.499026 | ||||||||
\(341\) | −31.1826 | −1.68863 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.19836 | 0.280685 | ||||||||
\(344\) | 1.36273 | 0.0734735 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.8982 | 0.693413 | ||||||||
\(347\) | 23.0564 | 1.23773 | 0.618866 | − | 0.785497i | \(-0.287592\pi\) | ||||
0.618866 | + | 0.785497i | \(0.287592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8302 | 1.70383 | 0.851916 | − | 0.523678i | \(-0.175441\pi\) | ||||
0.851916 | + | 0.523678i | \(0.175441\pi\) | |||||||
\(350\) | −10.0998 | −0.539859 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.22810 | 0.225358 | ||||||||
\(353\) | −18.8310 | −1.00227 | −0.501137 | − | 0.865368i | \(-0.667085\pi\) | ||||
−0.501137 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.28511 | 0.174355 | ||||||||
\(356\) | −5.71960 | −0.303138 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.33812 | −0.440684 | ||||||||
\(359\) | −7.29303 | −0.384911 | −0.192456 | − | 0.981306i | \(-0.561645\pi\) | ||||
−0.192456 | + | 0.981306i | \(0.561645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3735 | −0.651239 | ||||||||
\(362\) | −25.7248 | −1.35207 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.806312 | 0.0422622 | ||||||||
\(365\) | −9.95881 | −0.521268 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.6833 | 1.28846 | 0.644229 | − | 0.764833i | \(-0.277178\pi\) | ||||
0.644229 | + | 0.764833i | \(0.277178\pi\) | |||||||
\(368\) | 3.30009 | 0.172029 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.44447 | 0.335032 | ||||||||
\(371\) | 36.5941 | 1.89987 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.75225 | 0.504952 | 0.252476 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252476 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(374\) | 26.5521 | 1.37297 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.53590 | −0.388634 | ||||||||
\(377\) | 0.815017 | 0.0419755 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0298 | −0.566565 | −0.283282 | − | 0.959037i | \(-0.591423\pi\) | ||||
−0.283282 | + | 0.959037i | \(0.591423\pi\) | |||||||
\(380\) | 3.77181 | 0.193490 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.3232 | 1.09099 | ||||||||
\(383\) | −12.3380 | −0.630441 | −0.315220 | − | 0.949018i | \(-0.602078\pi\) | ||||
−0.315220 | + | 0.949018i | \(0.602078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.9309 | 1.11770 | ||||||||
\(386\) | −9.44168 | −0.480569 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.1029 | 0.969804 | ||||||||
\(389\) | 8.33709 | 0.422707 | 0.211354 | − | 0.977410i | \(-0.432213\pi\) | ||||
0.211354 | + | 0.977410i | \(0.432213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7243 | 1.04807 | ||||||||
\(392\) | −5.53153 | −0.279385 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.7269 | 0.691553 | ||||||||
\(395\) | 4.60246 | 0.231575 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3671 | −1.17276 | −0.586382 | − | 0.810035i | \(-0.699448\pi\) | ||||
−0.586382 | + | 0.810035i | \(0.699448\pi\) | |||||||
\(398\) | 25.9142 | 1.29896 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.85307 | −0.142653 | ||||||||
\(401\) | −21.0592 | −1.05165 | −0.525824 | − | 0.850593i | \(-0.676243\pi\) | ||||
−0.525824 | + | 0.850593i | \(0.676243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.67984 | −0.0836790 | ||||||||
\(404\) | −3.67787 | −0.182981 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.6668 | −0.628644 | ||||||||
\(407\) | 18.5962 | 0.921777 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.26707 | −0.112099 | −0.0560497 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560497 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(410\) | 6.65134 | 0.328486 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.13416 | 0.0558759 | ||||||||
\(413\) | 6.52416 | 0.321033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.55066 | 0.125207 | ||||||||
\(416\) | 0.227772 | 0.0111675 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.8839 | 0.532351 | ||||||||
\(419\) | 34.4011 | 1.68060 | 0.840302 | − | 0.542119i | \(-0.182378\pi\) | ||||
0.840302 | + | 0.542119i | \(0.182378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5050 | 0.999355 | 0.499677 | − | 0.866212i | \(-0.333452\pi\) | ||||
0.499677 | + | 0.866212i | \(0.333452\pi\) | |||||||
\(422\) | −4.68939 | −0.228276 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.3373 | 0.502026 | ||||||||
\(425\) | −17.9170 | −0.869103 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.300328 | 0.0145339 | ||||||||
\(428\) | −7.11155 | −0.343750 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.99673 | 0.0962908 | ||||||||
\(431\) | 15.7752 | 0.759864 | 0.379932 | − | 0.925014i | \(-0.375947\pi\) | ||||
0.379932 | + | 0.925014i | \(0.375947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.9521 | −1.10301 | −0.551504 | − | 0.834172i | \(-0.685946\pi\) | ||||
−0.551504 | + | 0.834172i | \(0.685946\pi\) | |||||||
\(434\) | 26.1078 | 1.25321 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.1888 | 0.775305 | ||||||||
\(437\) | 8.49507 | 0.406374 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0417 | 0.717899 | 0.358950 | − | 0.933357i | \(-0.383135\pi\) | ||||
0.358950 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(440\) | 6.19518 | 0.295344 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.43039 | 0.0680367 | ||||||||
\(443\) | −11.3602 | −0.539738 | −0.269869 | − | 0.962897i | \(-0.586980\pi\) | ||||
−0.269869 | + | 0.962897i | \(0.586980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.38059 | −0.397278 | ||||||||
\(446\) | −21.3356 | −1.01027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.53999 | −0.167249 | ||||||||
\(449\) | −14.1274 | −0.666712 | −0.333356 | − | 0.942801i | \(-0.608181\pi\) | ||||
−0.333356 | + | 0.942801i | \(0.608181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1931 | 0.903767 | ||||||||
\(452\) | −1.96757 | −0.0925466 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.9565 | 0.701942 | ||||||||
\(455\) | 1.18144 | 0.0553868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.3781 | −1.37425 | −0.687124 | − | 0.726540i | \(-0.741127\pi\) | ||||
−0.687124 | + | 0.726540i | \(0.741127\pi\) | |||||||
\(458\) | 10.3500 | 0.483622 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.83543 | 0.225453 | ||||||||
\(461\) | −14.3347 | −0.667632 | −0.333816 | − | 0.942638i | \(-0.608336\pi\) | ||||
−0.333816 | + | 0.942638i | \(0.608336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6011 | 0.492675 | 0.246338 | − | 0.969184i | \(-0.420773\pi\) | ||||
0.246338 | + | 0.969184i | \(0.420773\pi\) | |||||||
\(464\) | −3.57821 | −0.166114 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.89733 | 0.180540 | ||||||||
\(467\) | 6.22349 | 0.287989 | 0.143994 | − | 0.989579i | \(-0.454005\pi\) | ||||
0.143994 | + | 0.989579i | \(0.454005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1389 | −0.745226 | ||||||||
\(470\) | −11.0419 | −0.509325 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.84299 | 0.0848305 | ||||||||
\(473\) | 5.76176 | 0.264926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.34435 | −0.336982 | ||||||||
\(476\) | −22.2308 | −1.01895 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.9563 | 1.32443 | ||||||||
\(479\) | −20.7476 | −0.947983 | −0.473991 | − | 0.880529i | \(-0.657187\pi\) | ||||
−0.473991 | + | 0.880529i | \(0.657187\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00180 | 0.0456780 | ||||||||
\(482\) | 14.6773 | 0.668534 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.87680 | 0.312582 | ||||||||
\(485\) | 27.9904 | 1.27098 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.42424 | 0.336425 | 0.168212 | − | 0.985751i | \(-0.446201\pi\) | ||||
0.168212 | + | 0.985751i | \(0.446201\pi\) | |||||||
\(488\) | 0.0848386 | 0.00384046 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.10503 | −0.366148 | ||||||||
\(491\) | −11.2139 | −0.506078 | −0.253039 | − | 0.967456i | \(-0.581430\pi\) | ||||
−0.253039 | + | 0.967456i | \(0.581430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.4708 | −1.01203 | ||||||||
\(494\) | 0.586330 | 0.0263802 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.37510 | 0.331152 | ||||||||
\(497\) | −7.93675 | −0.356012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.6372 | −1.19244 | −0.596222 | − | 0.802820i | \(-0.703332\pi\) | ||||
−0.596222 | + | 0.802820i | \(0.703332\pi\) | |||||||
\(500\) | −11.5066 | −0.514593 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.07802 | 0.0481143 | ||||||||
\(503\) | −43.8172 | −1.95371 | −0.976856 | − | 0.213896i | \(-0.931385\pi\) | ||||
−0.976856 | + | 0.213896i | \(0.931385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.38897 | −0.239806 | ||||||||
\(506\) | 13.9531 | 0.620291 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.56617 | 0.113855 | ||||||||
\(509\) | 12.7752 | 0.566252 | 0.283126 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283126 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0603 | 1.06436 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.6721 | −0.603048 | ||||||||
\(515\) | 1.66181 | 0.0732282 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.8625 | −1.40131 | ||||||||
\(518\) | −15.5697 | −0.684093 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.333741 | 0.0146355 | ||||||||
\(521\) | −10.0510 | −0.440341 | −0.220171 | − | 0.975461i | \(-0.570661\pi\) | ||||
−0.220171 | + | 0.975461i | \(0.570661\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.79781 | −0.253521 | −0.126760 | − | 0.991933i | \(-0.540458\pi\) | ||||
−0.126760 | + | 0.991933i | \(0.540458\pi\) | |||||||
\(524\) | 21.1716 | 0.924888 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.7549 | 0.512539 | ||||||||
\(527\) | 46.3150 | 2.01751 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.1094 | −0.526496 | ||||||||
\(530\) | 15.1467 | 0.657931 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.11262 | −0.395082 | ||||||||
\(533\) | 1.03395 | 0.0447855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.4201 | −0.450502 | ||||||||
\(536\) | −4.55903 | −0.196920 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.2194 | 0.785494 | ||||||||
\(539\) | −23.3879 | −1.00739 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.8299 | −0.637586 | −0.318793 | − | 0.947824i | \(-0.603277\pi\) | ||||
−0.318793 | + | 0.947824i | \(0.603277\pi\) | |||||||
\(542\) | 15.5134 | 0.666358 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.27991 | −0.269249 | ||||||||
\(545\) | 23.7205 | 1.01608 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80078 | −0.0769958 | −0.0384979 | − | 0.999259i | \(-0.512257\pi\) | ||||
−0.0384979 | + | 0.999259i | \(0.512257\pi\) | |||||||
\(548\) | −17.0465 | −0.728192 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.0630 | −0.514370 | ||||||||
\(551\) | −9.21099 | −0.392401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1195 | −0.472847 | ||||||||
\(554\) | 32.5931 | 1.38475 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.5556 | −0.490066 | ||||||||
\(557\) | 17.8340 | 0.755651 | 0.377825 | − | 0.925877i | \(-0.376672\pi\) | ||||
0.377825 | + | 0.925877i | \(0.376672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.310392 | 0.0131282 | ||||||||
\(560\) | −5.18694 | −0.219188 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.5743 | 1.16315 | ||||||||
\(563\) | −43.5290 | −1.83453 | −0.917264 | − | 0.398279i | \(-0.869607\pi\) | ||||
−0.917264 | + | 0.398279i | \(0.869607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.88296 | −0.121287 | ||||||||
\(566\) | 0.606670 | 0.0255002 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.24203 | −0.0940733 | ||||||||
\(569\) | 23.8279 | 0.998919 | 0.499460 | − | 0.866337i | \(-0.333532\pi\) | ||||
0.499460 | + | 0.866337i | \(0.333532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8475 | −0.705044 | −0.352522 | − | 0.935804i | \(-0.614676\pi\) | ||||
−0.352522 | + | 0.935804i | \(0.614676\pi\) | |||||||
\(572\) | 0.963044 | 0.0402669 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.0695 | −0.670727 | ||||||||
\(575\) | −9.41538 | −0.392649 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.9952 | −0.624260 | −0.312130 | − | 0.950039i | \(-0.601042\pi\) | ||||
−0.312130 | + | 0.950039i | \(0.601042\pi\) | |||||||
\(578\) | −22.4373 | −0.933267 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.24293 | −0.217701 | ||||||||
\(581\) | −6.16235 | −0.255657 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.7073 | 1.81017 | ||||||||
\(584\) | 6.79670 | 0.281249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.36340 | −0.386799 | ||||||||
\(587\) | 33.7563 | 1.39327 | 0.696636 | − | 0.717425i | \(-0.254679\pi\) | ||||
0.696636 | + | 0.717425i | \(0.254679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9849 | 0.782260 | ||||||||
\(590\) | 2.70042 | 0.111175 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.39823 | −0.180766 | ||||||||
\(593\) | −8.47497 | −0.348025 | −0.174013 | − | 0.984743i | \(-0.555673\pi\) | ||||
−0.174013 | + | 0.984743i | \(0.555673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.5735 | −1.33538 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.751669 | 0.0307380 | ||||||||
\(599\) | −28.5142 | −1.16506 | −0.582530 | − | 0.812809i | \(-0.697937\pi\) | ||||
−0.582530 | + | 0.812809i | \(0.697937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.4417 | −1.85361 | −0.926803 | − | 0.375549i | \(-0.877454\pi\) | ||||
−0.926803 | + | 0.375549i | \(0.877454\pi\) | |||||||
\(602\) | −4.82405 | −0.196614 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.85207 | 0.238117 | ||||||||
\(605\) | 10.0762 | 0.409654 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2507 | −0.862541 | −0.431270 | − | 0.902223i | \(-0.641934\pi\) | ||||
−0.431270 | + | 0.902223i | \(0.641934\pi\) | |||||||
\(608\) | −2.57419 | −0.104397 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.124309 | 0.00503312 | ||||||||
\(611\) | −1.71647 | −0.0694409 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6344 | −0.469909 | −0.234955 | − | 0.972006i | \(-0.575494\pi\) | ||||
−0.234955 | + | 0.972006i | \(0.575494\pi\) | |||||||
\(614\) | −13.5000 | −0.544816 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.9674 | −0.603055 | ||||||||
\(617\) | 22.9162 | 0.922571 | 0.461286 | − | 0.887252i | \(-0.347388\pi\) | ||||
0.461286 | + | 0.887252i | \(0.347388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.4773 | 1.86808 | 0.934041 | − | 0.357167i | \(-0.116257\pi\) | ||||
0.934041 | + | 0.357167i | \(0.116257\pi\) | |||||||
\(620\) | 10.8063 | 0.433991 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.1871 | 1.09010 | ||||||||
\(623\) | 20.2473 | 0.811191 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.59465 | −0.103786 | ||||||||
\(626\) | 11.7246 | 0.468608 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.89904 | −0.315206 | ||||||||
\(629\) | −27.6205 | −1.10130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.74494 | −0.268512 | −0.134256 | − | 0.990947i | \(-0.542864\pi\) | ||||
−0.134256 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(632\) | −3.14110 | −0.124946 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.8607 | 0.550478 | ||||||||
\(635\) | 3.76005 | 0.149213 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.25993 | −0.0499203 | ||||||||
\(638\) | −15.1290 | −0.598963 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.46524 | −0.0579187 | ||||||||
\(641\) | 3.15648 | 0.124673 | 0.0623367 | − | 0.998055i | \(-0.480145\pi\) | ||||
0.0623367 | + | 0.998055i | \(0.480145\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0283 | 0.434913 | 0.217457 | − | 0.976070i | \(-0.430224\pi\) | ||||
0.217457 | + | 0.976070i | \(0.430224\pi\) | |||||||
\(644\) | −11.6823 | −0.460347 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.1657 | −0.636031 | ||||||||
\(647\) | 17.4386 | 0.685584 | 0.342792 | − | 0.939411i | \(-0.388627\pi\) | ||||
0.342792 | + | 0.939411i | \(0.388627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.79234 | 0.305876 | ||||||||
\(650\) | −0.649850 | −0.0254892 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.40642 | 0.0942427 | ||||||||
\(653\) | 13.2528 | 0.518621 | 0.259310 | − | 0.965794i | \(-0.416505\pi\) | ||||
0.259310 | + | 0.965794i | \(0.416505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.0216 | 1.21211 | ||||||||
\(656\) | −4.53941 | −0.177234 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.6770 | 1.03998 | ||||||||
\(659\) | −34.7215 | −1.35256 | −0.676279 | − | 0.736646i | \(-0.736409\pi\) | ||||
−0.676279 | + | 0.736646i | \(0.736409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8202 | −1.31545 | −0.657726 | − | 0.753257i | \(-0.728482\pi\) | ||||
−0.657726 | + | 0.753257i | \(0.728482\pi\) | |||||||
\(662\) | −9.46657 | −0.367929 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.74078 | −0.0675554 | ||||||||
\(665\) | −13.3522 | −0.517775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8084 | −0.457223 | ||||||||
\(668\) | −4.87364 | −0.188567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.68007 | −0.258074 | ||||||||
\(671\) | 0.358706 | 0.0138477 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3295 | 1.01493 | 0.507464 | − | 0.861673i | \(-0.330583\pi\) | ||||
0.507464 | + | 0.861673i | \(0.330583\pi\) | |||||||
\(674\) | 3.81960 | 0.147125 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9481 | −0.498005 | ||||||||
\(677\) | 16.3556 | 0.628596 | 0.314298 | − | 0.949324i | \(-0.398231\pi\) | ||||
0.314298 | + | 0.949324i | \(0.398231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −67.6242 | −2.59518 | ||||||||
\(680\) | −9.20158 | −0.352864 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.1826 | 1.19404 | ||||||||
\(683\) | 45.4585 | 1.73942 | 0.869711 | − | 0.493561i | \(-0.164305\pi\) | ||||
0.869711 | + | 0.493561i | \(0.164305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.9773 | −0.954333 | ||||||||
\(686\) | −5.19836 | −0.198474 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.36273 | −0.0519536 | ||||||||
\(689\) | 2.35456 | 0.0897017 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.61901 | −0.251799 | −0.125899 | − | 0.992043i | \(-0.540182\pi\) | ||||
−0.125899 | + | 0.992043i | \(0.540182\pi\) | |||||||
\(692\) | −12.8982 | −0.490317 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.0564 | −0.875208 | ||||||||
\(695\) | −16.9317 | −0.642257 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.5071 | −1.07978 | ||||||||
\(698\) | −31.8302 | −1.20479 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0998 | 0.381738 | ||||||||
\(701\) | 35.8627 | 1.35452 | 0.677258 | − | 0.735745i | \(-0.263168\pi\) | ||||
0.677258 | + | 0.735745i | \(0.263168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3219 | −0.427013 | ||||||||
\(704\) | −4.22810 | −0.159352 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.8310 | 0.708714 | ||||||||
\(707\) | 13.0196 | 0.489653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.55359 | −0.0583463 | −0.0291732 | − | 0.999574i | \(-0.509287\pi\) | ||||
−0.0291732 | + | 0.999574i | \(0.509287\pi\) | |||||||
\(710\) | −3.28511 | −0.123288 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.71960 | 0.214351 | ||||||||
\(713\) | 24.3385 | 0.911484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.41109 | 0.0527718 | ||||||||
\(716\) | 8.33812 | 0.311610 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.29303 | 0.272173 | ||||||||
\(719\) | −2.47572 | −0.0923288 | −0.0461644 | − | 0.998934i | \(-0.514700\pi\) | ||||
−0.0461644 | + | 0.998934i | \(0.514700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.01490 | −0.149523 | ||||||||
\(722\) | 12.3735 | 0.460495 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.7248 | 0.956055 | ||||||||
\(725\) | 10.2089 | 0.379148 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.0691 | −0.558884 | −0.279442 | − | 0.960163i | \(-0.590149\pi\) | ||||
−0.279442 | + | 0.960163i | \(0.590149\pi\) | |||||||
\(728\) | −0.806312 | −0.0298839 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.95881 | 0.368592 | ||||||||
\(731\) | −8.55782 | −0.316523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.22863 | 0.0453805 | 0.0226902 | − | 0.999743i | \(-0.492777\pi\) | ||||
0.0226902 | + | 0.999743i | \(0.492777\pi\) | |||||||
\(734\) | −24.6833 | −0.911077 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.30009 | −0.121643 | ||||||||
\(737\) | −19.2760 | −0.710041 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7074 | 0.872090 | 0.436045 | − | 0.899925i | \(-0.356379\pi\) | ||||
0.436045 | + | 0.899925i | \(0.356379\pi\) | |||||||
\(740\) | −6.44447 | −0.236903 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.5941 | −1.34341 | ||||||||
\(743\) | −47.1223 | −1.72875 | −0.864375 | − | 0.502848i | \(-0.832286\pi\) | ||||
−0.864375 | + | 0.502848i | \(0.832286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.46524 | −0.0536823 | ||||||||
\(746\) | −9.75225 | −0.357055 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −26.5521 | −0.970839 | ||||||||
\(749\) | 25.1748 | 0.919868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.3517 | −1.39947 | −0.699737 | − | 0.714401i | \(-0.746699\pi\) | ||||
−0.699737 | + | 0.714401i | \(0.746699\pi\) | |||||||
\(752\) | 7.53590 | 0.274806 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.815017 | −0.0296812 | ||||||||
\(755\) | 8.57469 | 0.312065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.13944 | 0.0777591 | 0.0388796 | − | 0.999244i | \(-0.487621\pi\) | ||||
0.0388796 | + | 0.999244i | \(0.487621\pi\) | |||||||
\(758\) | 11.0298 | 0.400622 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.77181 | −0.136818 | ||||||||
\(761\) | −24.7239 | −0.896241 | −0.448121 | − | 0.893973i | \(-0.647906\pi\) | ||||
−0.448121 | + | 0.893973i | \(0.647906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.3083 | −2.07470 | ||||||||
\(764\) | −21.3232 | −0.771446 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.3380 | 0.445789 | ||||||||
\(767\) | 0.419782 | 0.0151575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4880 | −1.53216 | −0.766079 | − | 0.642746i | \(-0.777795\pi\) | ||||
−0.766079 | + | 0.642746i | \(0.777795\pi\) | |||||||
\(770\) | −21.9309 | −0.790334 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.44168 | 0.339813 | ||||||||
\(773\) | 32.6589 | 1.17466 | 0.587330 | − | 0.809348i | \(-0.300179\pi\) | ||||
0.587330 | + | 0.809348i | \(0.300179\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.0417 | −0.755839 | ||||||||
\(776\) | −19.1029 | −0.685755 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.33709 | −0.298899 | ||||||||
\(779\) | −11.6853 | −0.418670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.47950 | −0.339203 | ||||||||
\(782\) | −20.7243 | −0.741098 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.53153 | 0.197555 | ||||||||
\(785\) | −11.5740 | −0.413094 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.4554 | −1.76289 | −0.881446 | − | 0.472284i | \(-0.843430\pi\) | ||||
−0.881446 | + | 0.472284i | \(0.843430\pi\) | |||||||
\(788\) | −13.7269 | −0.489002 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.60246 | −0.163748 | ||||||||
\(791\) | 6.96517 | 0.247653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0193239 | 0.000686211 0 | ||||||||
\(794\) | 23.3671 | 0.829269 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.9142 | −0.918504 | ||||||||
\(797\) | 32.3598 | 1.14624 | 0.573121 | − | 0.819471i | \(-0.305733\pi\) | ||||
0.573121 | + | 0.819471i | \(0.305733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.3247 | 1.67423 | ||||||||
\(800\) | 2.85307 | 0.100871 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.0592 | 0.743627 | ||||||||
\(803\) | 28.7371 | 1.01411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.1174 | −0.603308 | ||||||||
\(806\) | 1.67984 | 0.0591700 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.67787 | 0.129387 | ||||||||
\(809\) | −24.6466 | −0.866528 | −0.433264 | − | 0.901267i | \(-0.642638\pi\) | ||||
−0.433264 | + | 0.901267i | \(0.642638\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9169 | 1.05052 | 0.525262 | − | 0.850941i | \(-0.323967\pi\) | ||||
0.525262 | + | 0.850941i | \(0.323967\pi\) | |||||||
\(812\) | 12.6668 | 0.444518 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.5962 | −0.651795 | ||||||||
\(815\) | 3.52599 | 0.123510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50793 | −0.122727 | ||||||||
\(818\) | 2.26707 | 0.0792662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.65134 | −0.232275 | ||||||||
\(821\) | 4.48913 | 0.156672 | 0.0783359 | − | 0.996927i | \(-0.475039\pi\) | ||||
0.0783359 | + | 0.996927i | \(0.475039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.3547 | −0.674664 | −0.337332 | − | 0.941386i | \(-0.609524\pi\) | ||||
−0.337332 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(824\) | −1.13416 | −0.0395102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.52416 | −0.227005 | ||||||||
\(827\) | 18.4040 | 0.639970 | 0.319985 | − | 0.947423i | \(-0.396322\pi\) | ||||
0.319985 | + | 0.947423i | \(0.396322\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.2823 | −0.843361 | −0.421680 | − | 0.906745i | \(-0.638560\pi\) | ||||
−0.421680 | + | 0.906745i | \(0.638560\pi\) | |||||||
\(830\) | −2.55066 | −0.0885348 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.227772 | −0.00789659 | ||||||||
\(833\) | 34.7375 | 1.20358 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.14105 | −0.247126 | ||||||||
\(836\) | −10.8839 | −0.376429 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −34.4011 | −1.18837 | ||||||||
\(839\) | −34.6031 | −1.19463 | −0.597316 | − | 0.802006i | \(-0.703766\pi\) | ||||
−0.597316 | + | 0.802006i | \(0.703766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1964 | −0.558498 | ||||||||
\(842\) | −20.5050 | −0.706650 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.68939 | 0.161416 | ||||||||
\(845\) | −18.9721 | −0.652661 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.3438 | −0.836463 | ||||||||
\(848\) | −10.3373 | −0.354986 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.9170 | 0.614548 | ||||||||
\(851\) | −14.5146 | −0.497553 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.09858 | 0.0718541 | 0.0359271 | − | 0.999354i | \(-0.488562\pi\) | ||||
0.0359271 | + | 0.999354i | \(0.488562\pi\) | |||||||
\(854\) | −0.300328 | −0.0102770 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.11155 | 0.243068 | ||||||||
\(857\) | −34.2049 | −1.16842 | −0.584209 | − | 0.811603i | \(-0.698595\pi\) | ||||
−0.584209 | + | 0.811603i | \(0.698595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.92208 | 0.202059 | 0.101029 | − | 0.994883i | \(-0.467786\pi\) | ||||
0.101029 | + | 0.994883i | \(0.467786\pi\) | |||||||
\(860\) | −1.99673 | −0.0680879 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.7752 | −0.537305 | ||||||||
\(863\) | −7.96972 | −0.271292 | −0.135646 | − | 0.990757i | \(-0.543311\pi\) | ||||
−0.135646 | + | 0.990757i | \(0.543311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.8990 | −0.642585 | ||||||||
\(866\) | 22.9521 | 0.779944 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.1078 | −0.886156 | ||||||||
\(869\) | −13.2809 | −0.450522 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.03842 | −0.0351855 | ||||||||
\(872\) | −16.1888 | −0.548223 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.49507 | −0.287350 | ||||||||
\(875\) | 40.7334 | 1.37704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.249393 | 0.00842141 | 0.00421071 | − | 0.999991i | \(-0.498660\pi\) | ||||
0.00421071 | + | 0.999991i | \(0.498660\pi\) | |||||||
\(878\) | −15.0417 | −0.507631 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.19518 | −0.208839 | ||||||||
\(881\) | 44.4729 | 1.49833 | 0.749165 | − | 0.662383i | \(-0.230455\pi\) | ||||
0.749165 | + | 0.662383i | \(0.230455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.3933 | 1.22473 | 0.612366 | − | 0.790575i | \(-0.290218\pi\) | ||||
0.612366 | + | 0.790575i | \(0.290218\pi\) | |||||||
\(884\) | −1.43039 | −0.0481092 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.3602 | 0.381653 | ||||||||
\(887\) | 57.1344 | 1.91838 | 0.959192 | − | 0.282756i | \(-0.0912486\pi\) | ||||
0.959192 | + | 0.282756i | \(0.0912486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.08420 | −0.304674 | ||||||||
\(890\) | 8.38059 | 0.280918 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.3356 | 0.714369 | ||||||||
\(893\) | 19.3988 | 0.649158 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2174 | 0.408381 | ||||||||
\(896\) | 3.53999 | 0.118263 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.1274 | 0.471437 | ||||||||
\(899\) | −26.3896 | −0.880143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.9176 | −2.16272 | ||||||||
\(902\) | −19.1931 | −0.639060 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.96757 | 0.0654404 | ||||||||
\(905\) | 37.6931 | 1.25296 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.9692 | 1.09472 | 0.547362 | − | 0.836896i | \(-0.315632\pi\) | ||||
0.547362 | + | 0.836896i | \(0.315632\pi\) | |||||||
\(908\) | −14.9565 | −0.496348 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.18144 | −0.0391644 | ||||||||
\(911\) | 17.3024 | 0.573254 | 0.286627 | − | 0.958042i | \(-0.407466\pi\) | ||||
0.286627 | + | 0.958042i | \(0.407466\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.36019 | −0.243587 | ||||||||
\(914\) | 29.3781 | 0.971741 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.3500 | −0.341973 | ||||||||
\(917\) | −74.9474 | −2.47498 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.5986 | 1.27325 | 0.636626 | − | 0.771173i | \(-0.280330\pi\) | ||||
0.636626 | + | 0.771173i | \(0.280330\pi\) | |||||||
\(920\) | −4.83543 | −0.159419 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.3347 | 0.472087 | ||||||||
\(923\) | −0.510672 | −0.0168090 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5485 | 0.412591 | ||||||||
\(926\) | −10.6011 | −0.348374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.57821 | 0.117460 | ||||||||
\(929\) | −7.90865 | −0.259474 | −0.129737 | − | 0.991548i | \(-0.541413\pi\) | ||||
−0.129737 | + | 0.991548i | \(0.541413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.2392 | 0.466672 | ||||||||
\(932\) | −3.89733 | −0.127661 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.22349 | −0.203639 | ||||||||
\(935\) | −38.9052 | −1.27233 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.8586 | −0.746759 | −0.373379 | − | 0.927679i | \(-0.621801\pi\) | ||||
−0.373379 | + | 0.927679i | \(0.621801\pi\) | |||||||
\(938\) | 16.1389 | 0.526954 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.0419 | 0.360147 | ||||||||
\(941\) | −37.2088 | −1.21297 | −0.606486 | − | 0.795094i | \(-0.707421\pi\) | ||||
−0.606486 | + | 0.795094i | \(0.707421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.9805 | −0.487831 | ||||||||
\(944\) | −1.84299 | −0.0599842 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.76176 | −0.187331 | ||||||||
\(947\) | −29.8932 | −0.971397 | −0.485699 | − | 0.874126i | \(-0.661435\pi\) | ||||
−0.485699 | + | 0.874126i | \(0.661435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.54810 | 0.0502535 | ||||||||
\(950\) | 7.34435 | 0.238282 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.2308 | 0.720505 | ||||||||
\(953\) | 18.1015 | 0.586364 | 0.293182 | − | 0.956057i | \(-0.405286\pi\) | ||||
0.293182 | + | 0.956057i | \(0.405286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.2436 | −1.01102 | ||||||||
\(956\) | −28.9563 | −0.936515 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.7476 | 0.670325 | ||||||||
\(959\) | 60.3446 | 1.94863 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3921 | 0.754584 | ||||||||
\(962\) | −1.00180 | −0.0322992 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.6773 | −0.472725 | ||||||||
\(965\) | 13.8343 | 0.445343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.95620 | 0.288012 | 0.144006 | − | 0.989577i | \(-0.454002\pi\) | ||||
0.144006 | + | 0.989577i | \(0.454002\pi\) | |||||||
\(968\) | −6.87680 | −0.221029 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.9904 | −0.898718 | ||||||||
\(971\) | −56.3517 | −1.80841 | −0.904206 | − | 0.427096i | \(-0.859537\pi\) | ||||
−0.904206 | + | 0.427096i | \(0.859537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.9067 | 1.31141 | ||||||||
\(974\) | −7.42424 | −0.237888 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0848386 | −0.00271562 | ||||||||
\(977\) | 36.6371 | 1.17213 | 0.586063 | − | 0.810266i | \(-0.300677\pi\) | ||||
0.586063 | + | 0.810266i | \(0.300677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.1830 | 0.772892 | ||||||||
\(980\) | 8.10503 | 0.258906 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.2139 | 0.357851 | ||||||||
\(983\) | 48.0649 | 1.53303 | 0.766516 | − | 0.642225i | \(-0.221989\pi\) | ||||
0.766516 | + | 0.642225i | \(0.221989\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.1133 | −0.640862 | ||||||||
\(986\) | 22.4708 | 0.715616 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.586330 | −0.0186536 | ||||||||
\(989\) | −4.49713 | −0.143001 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.53139 | −0.175710 | −0.0878552 | − | 0.996133i | \(-0.528001\pi\) | ||||
−0.0878552 | + | 0.996133i | \(0.528001\pi\) | |||||||
\(992\) | −7.37510 | −0.234160 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.93675 | 0.251738 | ||||||||
\(995\) | −37.9705 | −1.20375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.3951 | −1.18431 | −0.592157 | − | 0.805823i | \(-0.701723\pi\) | ||||
−0.592157 | + | 0.805823i | \(0.701723\pi\) | |||||||
\(998\) | 26.6372 | 0.843185 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.j.1.8 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.o.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.o.1.5 | yes | 12 | 3.2 | odd | 2 |