Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.37784 | 0.795495 | 0.397747 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397747 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.53697 | 1.58178 | 0.790891 | − | 0.611957i | \(-0.209617\pi\) | ||||
0.790891 | + | 0.611957i | \(0.209617\pi\) | |||||||
\(6\) | 1.37784 | 0.562500 | ||||||||
\(7\) | −2.08526 | −0.788153 | −0.394076 | − | 0.919078i | \(-0.628935\pi\) | ||||
−0.394076 | + | 0.919078i | \(0.628935\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.10156 | −0.367188 | ||||||||
\(10\) | 3.53697 | 1.11849 | ||||||||
\(11\) | −3.14295 | −0.947636 | −0.473818 | − | 0.880623i | \(-0.657125\pi\) | ||||
−0.473818 | + | 0.880623i | \(0.657125\pi\) | |||||||
\(12\) | 1.37784 | 0.397747 | ||||||||
\(13\) | −3.99759 | −1.10873 | −0.554366 | − | 0.832273i | \(-0.687039\pi\) | ||||
−0.554366 | + | 0.832273i | \(0.687039\pi\) | |||||||
\(14\) | −2.08526 | −0.557308 | ||||||||
\(15\) | 4.87337 | 1.25830 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.01813 | −1.45961 | −0.729805 | − | 0.683655i | \(-0.760389\pi\) | ||||
−0.729805 | + | 0.683655i | \(0.760389\pi\) | |||||||
\(18\) | −1.10156 | −0.259641 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.53697 | 0.790891 | ||||||||
\(21\) | −2.87314 | −0.626971 | ||||||||
\(22\) | −3.14295 | −0.670080 | ||||||||
\(23\) | −6.22231 | −1.29744 | −0.648721 | − | 0.761026i | \(-0.724696\pi\) | ||||
−0.648721 | + | 0.761026i | \(0.724696\pi\) | |||||||
\(24\) | 1.37784 | 0.281250 | ||||||||
\(25\) | 7.51017 | 1.50203 | ||||||||
\(26\) | −3.99759 | −0.783991 | ||||||||
\(27\) | −5.65129 | −1.08759 | ||||||||
\(28\) | −2.08526 | −0.394076 | ||||||||
\(29\) | −6.86242 | −1.27432 | −0.637160 | − | 0.770732i | \(-0.719891\pi\) | ||||
−0.637160 | + | 0.770732i | \(0.719891\pi\) | |||||||
\(30\) | 4.87337 | 0.889752 | ||||||||
\(31\) | 6.59507 | 1.18451 | 0.592255 | − | 0.805751i | \(-0.298238\pi\) | ||||
0.592255 | + | 0.805751i | \(0.298238\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.33048 | −0.753840 | ||||||||
\(34\) | −6.01813 | −1.03210 | ||||||||
\(35\) | −7.37550 | −1.24669 | ||||||||
\(36\) | −1.10156 | −0.183594 | ||||||||
\(37\) | −3.67195 | −0.603665 | −0.301833 | − | 0.953361i | \(-0.597598\pi\) | ||||
−0.301833 | + | 0.953361i | \(0.597598\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −5.50802 | −0.881990 | ||||||||
\(40\) | 3.53697 | 0.559244 | ||||||||
\(41\) | 8.95892 | 1.39915 | 0.699574 | − | 0.714560i | \(-0.253373\pi\) | ||||
0.699574 | + | 0.714560i | \(0.253373\pi\) | |||||||
\(42\) | −2.87314 | −0.443336 | ||||||||
\(43\) | 0.304255 | 0.0463985 | 0.0231993 | − | 0.999731i | \(-0.492615\pi\) | ||||
0.0231993 | + | 0.999731i | \(0.492615\pi\) | |||||||
\(44\) | −3.14295 | −0.473818 | ||||||||
\(45\) | −3.89620 | −0.580812 | ||||||||
\(46\) | −6.22231 | −0.917430 | ||||||||
\(47\) | 0.829211 | 0.120953 | 0.0604764 | − | 0.998170i | \(-0.480738\pi\) | ||||
0.0604764 | + | 0.998170i | \(0.480738\pi\) | |||||||
\(48\) | 1.37784 | 0.198874 | ||||||||
\(49\) | −2.65170 | −0.378815 | ||||||||
\(50\) | 7.51017 | 1.06210 | ||||||||
\(51\) | −8.29200 | −1.16111 | ||||||||
\(52\) | −3.99759 | −0.554366 | ||||||||
\(53\) | 3.90013 | 0.535724 | 0.267862 | − | 0.963457i | \(-0.413683\pi\) | ||||
0.267862 | + | 0.963457i | \(0.413683\pi\) | |||||||
\(54\) | −5.65129 | −0.769043 | ||||||||
\(55\) | −11.1165 | −1.49895 | ||||||||
\(56\) | −2.08526 | −0.278654 | ||||||||
\(57\) | 1.37784 | 0.182499 | ||||||||
\(58\) | −6.86242 | −0.901080 | ||||||||
\(59\) | −10.5452 | −1.37287 | −0.686434 | − | 0.727192i | \(-0.740825\pi\) | ||||
−0.686434 | + | 0.727192i | \(0.740825\pi\) | |||||||
\(60\) | 4.87337 | 0.629150 | ||||||||
\(61\) | 2.06867 | 0.264866 | 0.132433 | − | 0.991192i | \(-0.457721\pi\) | ||||
0.132433 | + | 0.991192i | \(0.457721\pi\) | |||||||
\(62\) | 6.59507 | 0.837575 | ||||||||
\(63\) | 2.29705 | 0.289401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.1394 | −1.75377 | ||||||||
\(66\) | −4.33048 | −0.533045 | ||||||||
\(67\) | 4.91181 | 0.600073 | 0.300037 | − | 0.953928i | \(-0.403001\pi\) | ||||
0.300037 | + | 0.953928i | \(0.403001\pi\) | |||||||
\(68\) | −6.01813 | −0.729805 | ||||||||
\(69\) | −8.57334 | −1.03211 | ||||||||
\(70\) | −7.37550 | −0.881540 | ||||||||
\(71\) | −1.61616 | −0.191803 | −0.0959016 | − | 0.995391i | \(-0.530573\pi\) | ||||
−0.0959016 | + | 0.995391i | \(0.530573\pi\) | |||||||
\(72\) | −1.10156 | −0.129821 | ||||||||
\(73\) | −2.42349 | −0.283648 | −0.141824 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141824 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(74\) | −3.67195 | −0.426856 | ||||||||
\(75\) | 10.3478 | 1.19486 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 6.55387 | 0.746883 | ||||||||
\(78\) | −5.50802 | −0.623661 | ||||||||
\(79\) | −2.78453 | −0.313284 | −0.156642 | − | 0.987655i | \(-0.550067\pi\) | ||||
−0.156642 | + | 0.987655i | \(0.550067\pi\) | |||||||
\(80\) | 3.53697 | 0.395446 | ||||||||
\(81\) | −4.48186 | −0.497985 | ||||||||
\(82\) | 8.95892 | 0.989347 | ||||||||
\(83\) | 12.8628 | 1.41187 | 0.705937 | − | 0.708275i | \(-0.250526\pi\) | ||||
0.705937 | + | 0.708275i | \(0.250526\pi\) | |||||||
\(84\) | −2.87314 | −0.313486 | ||||||||
\(85\) | −21.2859 | −2.30878 | ||||||||
\(86\) | 0.304255 | 0.0328087 | ||||||||
\(87\) | −9.45530 | −1.01371 | ||||||||
\(88\) | −3.14295 | −0.335040 | ||||||||
\(89\) | −3.09295 | −0.327852 | −0.163926 | − | 0.986473i | \(-0.552416\pi\) | ||||
−0.163926 | + | 0.986473i | \(0.552416\pi\) | |||||||
\(90\) | −3.89620 | −0.410696 | ||||||||
\(91\) | 8.33600 | 0.873850 | ||||||||
\(92\) | −6.22231 | −0.648721 | ||||||||
\(93\) | 9.08693 | 0.942271 | ||||||||
\(94\) | 0.829211 | 0.0855266 | ||||||||
\(95\) | 3.53697 | 0.362886 | ||||||||
\(96\) | 1.37784 | 0.140625 | ||||||||
\(97\) | 2.90999 | 0.295465 | 0.147732 | − | 0.989027i | \(-0.452803\pi\) | ||||
0.147732 | + | 0.989027i | \(0.452803\pi\) | |||||||
\(98\) | −2.65170 | −0.267863 | ||||||||
\(99\) | 3.46217 | 0.347961 | ||||||||
\(100\) | 7.51017 | 0.751017 | ||||||||
\(101\) | −1.30507 | −0.129859 | −0.0649296 | − | 0.997890i | \(-0.520682\pi\) | ||||
−0.0649296 | + | 0.997890i | \(0.520682\pi\) | |||||||
\(102\) | −8.29200 | −0.821030 | ||||||||
\(103\) | −12.3411 | −1.21601 | −0.608003 | − | 0.793935i | \(-0.708029\pi\) | ||||
−0.608003 | + | 0.793935i | \(0.708029\pi\) | |||||||
\(104\) | −3.99759 | −0.391996 | ||||||||
\(105\) | −10.1622 | −0.991732 | ||||||||
\(106\) | 3.90013 | 0.378814 | ||||||||
\(107\) | 1.14970 | 0.111146 | 0.0555729 | − | 0.998455i | \(-0.482301\pi\) | ||||
0.0555729 | + | 0.998455i | \(0.482301\pi\) | |||||||
\(108\) | −5.65129 | −0.543795 | ||||||||
\(109\) | 4.57273 | 0.437988 | 0.218994 | − | 0.975726i | \(-0.429722\pi\) | ||||
0.218994 | + | 0.975726i | \(0.429722\pi\) | |||||||
\(110\) | −11.1165 | −1.05992 | ||||||||
\(111\) | −5.05935 | −0.480212 | ||||||||
\(112\) | −2.08526 | −0.197038 | ||||||||
\(113\) | −1.47352 | −0.138617 | −0.0693087 | − | 0.997595i | \(-0.522079\pi\) | ||||
−0.0693087 | + | 0.997595i | \(0.522079\pi\) | |||||||
\(114\) | 1.37784 | 0.129046 | ||||||||
\(115\) | −22.0082 | −2.05227 | ||||||||
\(116\) | −6.86242 | −0.637160 | ||||||||
\(117\) | 4.40360 | 0.407113 | ||||||||
\(118\) | −10.5452 | −0.970764 | ||||||||
\(119\) | 12.5493 | 1.15040 | ||||||||
\(120\) | 4.87337 | 0.444876 | ||||||||
\(121\) | −1.12184 | −0.101985 | ||||||||
\(122\) | 2.06867 | 0.187288 | ||||||||
\(123\) | 12.3439 | 1.11301 | ||||||||
\(124\) | 6.59507 | 0.592255 | ||||||||
\(125\) | 8.87841 | 0.794109 | ||||||||
\(126\) | 2.29705 | 0.204637 | ||||||||
\(127\) | −12.0006 | −1.06488 | −0.532442 | − | 0.846467i | \(-0.678725\pi\) | ||||
−0.532442 | + | 0.846467i | \(0.678725\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.419215 | 0.0369098 | ||||||||
\(130\) | −14.1394 | −1.24010 | ||||||||
\(131\) | −8.37543 | −0.731765 | −0.365882 | − | 0.930661i | \(-0.619233\pi\) | ||||
−0.365882 | + | 0.930661i | \(0.619233\pi\) | |||||||
\(132\) | −4.33048 | −0.376920 | ||||||||
\(133\) | −2.08526 | −0.180815 | ||||||||
\(134\) | 4.91181 | 0.424316 | ||||||||
\(135\) | −19.9885 | −1.72033 | ||||||||
\(136\) | −6.01813 | −0.516050 | ||||||||
\(137\) | −10.7677 | −0.919944 | −0.459972 | − | 0.887933i | \(-0.652141\pi\) | ||||
−0.459972 | + | 0.887933i | \(0.652141\pi\) | |||||||
\(138\) | −8.57334 | −0.729811 | ||||||||
\(139\) | 1.42665 | 0.121007 | 0.0605035 | − | 0.998168i | \(-0.480729\pi\) | ||||
0.0605035 | + | 0.998168i | \(0.480729\pi\) | |||||||
\(140\) | −7.37550 | −0.623343 | ||||||||
\(141\) | 1.14252 | 0.0962174 | ||||||||
\(142\) | −1.61616 | −0.135625 | ||||||||
\(143\) | 12.5642 | 1.05067 | ||||||||
\(144\) | −1.10156 | −0.0917971 | ||||||||
\(145\) | −24.2722 | −2.01570 | ||||||||
\(146\) | −2.42349 | −0.200569 | ||||||||
\(147\) | −3.65362 | −0.301345 | ||||||||
\(148\) | −3.67195 | −0.301833 | ||||||||
\(149\) | −1.66215 | −0.136169 | −0.0680843 | − | 0.997680i | \(-0.521689\pi\) | ||||
−0.0680843 | + | 0.997680i | \(0.521689\pi\) | |||||||
\(150\) | 10.3478 | 0.844894 | ||||||||
\(151\) | 5.77068 | 0.469611 | 0.234806 | − | 0.972042i | \(-0.424555\pi\) | ||||
0.234806 | + | 0.972042i | \(0.424555\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 6.62935 | 0.535952 | ||||||||
\(154\) | 6.55387 | 0.528126 | ||||||||
\(155\) | 23.3266 | 1.87364 | ||||||||
\(156\) | −5.50802 | −0.440995 | ||||||||
\(157\) | −7.85464 | −0.626869 | −0.313434 | − | 0.949610i | \(-0.601480\pi\) | ||||
−0.313434 | + | 0.949610i | \(0.601480\pi\) | |||||||
\(158\) | −2.78453 | −0.221526 | ||||||||
\(159\) | 5.37374 | 0.426166 | ||||||||
\(160\) | 3.53697 | 0.279622 | ||||||||
\(161\) | 12.9751 | 1.02258 | ||||||||
\(162\) | −4.48186 | −0.352128 | ||||||||
\(163\) | −4.10851 | −0.321803 | −0.160902 | − | 0.986970i | \(-0.551440\pi\) | ||||
−0.160902 | + | 0.986970i | \(0.551440\pi\) | |||||||
\(164\) | 8.95892 | 0.699574 | ||||||||
\(165\) | −15.3168 | −1.19241 | ||||||||
\(166\) | 12.8628 | 0.998345 | ||||||||
\(167\) | 7.06678 | 0.546844 | 0.273422 | − | 0.961894i | \(-0.411845\pi\) | ||||
0.273422 | + | 0.961894i | \(0.411845\pi\) | |||||||
\(168\) | −2.87314 | −0.221668 | ||||||||
\(169\) | 2.98071 | 0.229285 | ||||||||
\(170\) | −21.2859 | −1.63256 | ||||||||
\(171\) | −1.10156 | −0.0842388 | ||||||||
\(172\) | 0.304255 | 0.0231993 | ||||||||
\(173\) | 9.71788 | 0.738837 | 0.369418 | − | 0.929263i | \(-0.379557\pi\) | ||||
0.369418 | + | 0.929263i | \(0.379557\pi\) | |||||||
\(174\) | −9.45530 | −0.716804 | ||||||||
\(175\) | −15.6606 | −1.18383 | ||||||||
\(176\) | −3.14295 | −0.236909 | ||||||||
\(177\) | −14.5296 | −1.09211 | ||||||||
\(178\) | −3.09295 | −0.231826 | ||||||||
\(179\) | −24.7875 | −1.85270 | −0.926352 | − | 0.376659i | \(-0.877073\pi\) | ||||
−0.926352 | + | 0.376659i | \(0.877073\pi\) | |||||||
\(180\) | −3.89620 | −0.290406 | ||||||||
\(181\) | −2.42472 | −0.180228 | −0.0901142 | − | 0.995931i | \(-0.528723\pi\) | ||||
−0.0901142 | + | 0.995931i | \(0.528723\pi\) | |||||||
\(182\) | 8.33600 | 0.617905 | ||||||||
\(183\) | 2.85029 | 0.210699 | ||||||||
\(184\) | −6.22231 | −0.458715 | ||||||||
\(185\) | −12.9876 | −0.954867 | ||||||||
\(186\) | 9.08693 | 0.666286 | ||||||||
\(187\) | 18.9147 | 1.38318 | ||||||||
\(188\) | 0.829211 | 0.0604764 | ||||||||
\(189\) | 11.7844 | 0.857188 | ||||||||
\(190\) | 3.53697 | 0.256599 | ||||||||
\(191\) | 19.0532 | 1.37864 | 0.689322 | − | 0.724455i | \(-0.257909\pi\) | ||||
0.689322 | + | 0.724455i | \(0.257909\pi\) | |||||||
\(192\) | 1.37784 | 0.0994368 | ||||||||
\(193\) | −6.16409 | −0.443701 | −0.221850 | − | 0.975081i | \(-0.571210\pi\) | ||||
−0.221850 | + | 0.975081i | \(0.571210\pi\) | |||||||
\(194\) | 2.90999 | 0.208925 | ||||||||
\(195\) | −19.4817 | −1.39512 | ||||||||
\(196\) | −2.65170 | −0.189407 | ||||||||
\(197\) | 3.38890 | 0.241449 | 0.120725 | − | 0.992686i | \(-0.461478\pi\) | ||||
0.120725 | + | 0.992686i | \(0.461478\pi\) | |||||||
\(198\) | 3.46217 | 0.246046 | ||||||||
\(199\) | 7.72991 | 0.547959 | 0.273979 | − | 0.961736i | \(-0.411660\pi\) | ||||
0.273979 | + | 0.961736i | \(0.411660\pi\) | |||||||
\(200\) | 7.51017 | 0.531049 | ||||||||
\(201\) | 6.76768 | 0.477355 | ||||||||
\(202\) | −1.30507 | −0.0918243 | ||||||||
\(203\) | 14.3099 | 1.00436 | ||||||||
\(204\) | −8.29200 | −0.580556 | ||||||||
\(205\) | 31.6874 | 2.21315 | ||||||||
\(206\) | −12.3411 | −0.859846 | ||||||||
\(207\) | 6.85428 | 0.476406 | ||||||||
\(208\) | −3.99759 | −0.277183 | ||||||||
\(209\) | −3.14295 | −0.217403 | ||||||||
\(210\) | −10.1622 | −0.701261 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 3.90013 | 0.267862 | ||||||||
\(213\) | −2.22681 | −0.152578 | ||||||||
\(214\) | 1.14970 | 0.0785920 | ||||||||
\(215\) | 1.07614 | 0.0733924 | ||||||||
\(216\) | −5.65129 | −0.384521 | ||||||||
\(217\) | −13.7524 | −0.933575 | ||||||||
\(218\) | 4.57273 | 0.309704 | ||||||||
\(219\) | −3.33917 | −0.225640 | ||||||||
\(220\) | −11.1165 | −0.749477 | ||||||||
\(221\) | 24.0580 | 1.61832 | ||||||||
\(222\) | −5.05935 | −0.339562 | ||||||||
\(223\) | −4.53033 | −0.303373 | −0.151687 | − | 0.988429i | \(-0.548470\pi\) | ||||
−0.151687 | + | 0.988429i | \(0.548470\pi\) | |||||||
\(224\) | −2.08526 | −0.139327 | ||||||||
\(225\) | −8.27294 | −0.551529 | ||||||||
\(226\) | −1.47352 | −0.0980173 | ||||||||
\(227\) | −4.60548 | −0.305676 | −0.152838 | − | 0.988251i | \(-0.548841\pi\) | ||||
−0.152838 | + | 0.988251i | \(0.548841\pi\) | |||||||
\(228\) | 1.37784 | 0.0912495 | ||||||||
\(229\) | −18.8360 | −1.24472 | −0.622359 | − | 0.782732i | \(-0.713826\pi\) | ||||
−0.622359 | + | 0.782732i | \(0.713826\pi\) | |||||||
\(230\) | −22.0082 | −1.45117 | ||||||||
\(231\) | 9.03016 | 0.594141 | ||||||||
\(232\) | −6.86242 | −0.450540 | ||||||||
\(233\) | 13.9203 | 0.911951 | 0.455976 | − | 0.889992i | \(-0.349290\pi\) | ||||
0.455976 | + | 0.889992i | \(0.349290\pi\) | |||||||
\(234\) | 4.40360 | 0.287872 | ||||||||
\(235\) | 2.93290 | 0.191321 | ||||||||
\(236\) | −10.5452 | −0.686434 | ||||||||
\(237\) | −3.83663 | −0.249216 | ||||||||
\(238\) | 12.5493 | 0.813453 | ||||||||
\(239\) | −1.61370 | −0.104382 | −0.0521909 | − | 0.998637i | \(-0.516620\pi\) | ||||
−0.0521909 | + | 0.998637i | \(0.516620\pi\) | |||||||
\(240\) | 4.87337 | 0.314575 | ||||||||
\(241\) | −5.33913 | −0.343924 | −0.171962 | − | 0.985104i | \(-0.555011\pi\) | ||||
−0.171962 | + | 0.985104i | \(0.555011\pi\) | |||||||
\(242\) | −1.12184 | −0.0721143 | ||||||||
\(243\) | 10.7786 | 0.691447 | ||||||||
\(244\) | 2.06867 | 0.132433 | ||||||||
\(245\) | −9.37900 | −0.599203 | ||||||||
\(246\) | 12.3439 | 0.787020 | ||||||||
\(247\) | −3.99759 | −0.254360 | ||||||||
\(248\) | 6.59507 | 0.418787 | ||||||||
\(249\) | 17.7228 | 1.12314 | ||||||||
\(250\) | 8.87841 | 0.561520 | ||||||||
\(251\) | −15.5928 | −0.984208 | −0.492104 | − | 0.870536i | \(-0.663772\pi\) | ||||
−0.492104 | + | 0.870536i | \(0.663772\pi\) | |||||||
\(252\) | 2.29705 | 0.144700 | ||||||||
\(253\) | 19.5565 | 1.22950 | ||||||||
\(254\) | −12.0006 | −0.752986 | ||||||||
\(255\) | −29.3286 | −1.83663 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.7444 | 1.04449 | 0.522244 | − | 0.852796i | \(-0.325095\pi\) | ||||
0.522244 | + | 0.852796i | \(0.325095\pi\) | |||||||
\(258\) | 0.419215 | 0.0260992 | ||||||||
\(259\) | 7.65696 | 0.475781 | ||||||||
\(260\) | −14.1394 | −0.876886 | ||||||||
\(261\) | 7.55940 | 0.467915 | ||||||||
\(262\) | −8.37543 | −0.517436 | ||||||||
\(263\) | 16.0204 | 0.987858 | 0.493929 | − | 0.869502i | \(-0.335560\pi\) | ||||
0.493929 | + | 0.869502i | \(0.335560\pi\) | |||||||
\(264\) | −4.33048 | −0.266523 | ||||||||
\(265\) | 13.7947 | 0.847399 | ||||||||
\(266\) | −2.08526 | −0.127855 | ||||||||
\(267\) | −4.26158 | −0.260804 | ||||||||
\(268\) | 4.91181 | 0.300037 | ||||||||
\(269\) | −18.2562 | −1.11310 | −0.556551 | − | 0.830813i | \(-0.687876\pi\) | ||||
−0.556551 | + | 0.830813i | \(0.687876\pi\) | |||||||
\(270\) | −19.9885 | −1.21646 | ||||||||
\(271\) | 19.6564 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296351\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296351\pi\) | |||||||
\(272\) | −6.01813 | −0.364902 | ||||||||
\(273\) | 11.4856 | 0.695143 | ||||||||
\(274\) | −10.7677 | −0.650499 | ||||||||
\(275\) | −23.6041 | −1.42338 | ||||||||
\(276\) | −8.57334 | −0.516054 | ||||||||
\(277\) | −20.4390 | −1.22806 | −0.614030 | − | 0.789283i | \(-0.710452\pi\) | ||||
−0.614030 | + | 0.789283i | \(0.710452\pi\) | |||||||
\(278\) | 1.42665 | 0.0855649 | ||||||||
\(279\) | −7.26490 | −0.434938 | ||||||||
\(280\) | −7.37550 | −0.440770 | ||||||||
\(281\) | 6.65167 | 0.396805 | 0.198403 | − | 0.980121i | \(-0.436425\pi\) | ||||
0.198403 | + | 0.980121i | \(0.436425\pi\) | |||||||
\(282\) | 1.14252 | 0.0680360 | ||||||||
\(283\) | −9.99361 | −0.594058 | −0.297029 | − | 0.954868i | \(-0.595996\pi\) | ||||
−0.297029 | + | 0.954868i | \(0.595996\pi\) | |||||||
\(284\) | −1.61616 | −0.0959016 | ||||||||
\(285\) | 4.87337 | 0.288674 | ||||||||
\(286\) | 12.5642 | 0.742939 | ||||||||
\(287\) | −18.6816 | −1.10274 | ||||||||
\(288\) | −1.10156 | −0.0649103 | ||||||||
\(289\) | 19.2178 | 1.13046 | ||||||||
\(290\) | −24.2722 | −1.42531 | ||||||||
\(291\) | 4.00949 | 0.235041 | ||||||||
\(292\) | −2.42349 | −0.141824 | ||||||||
\(293\) | 11.8689 | 0.693387 | 0.346694 | − | 0.937978i | \(-0.387304\pi\) | ||||
0.346694 | + | 0.937978i | \(0.387304\pi\) | |||||||
\(294\) | −3.65362 | −0.213083 | ||||||||
\(295\) | −37.2981 | −2.17158 | ||||||||
\(296\) | −3.67195 | −0.213428 | ||||||||
\(297\) | 17.7617 | 1.03064 | ||||||||
\(298\) | −1.66215 | −0.0962858 | ||||||||
\(299\) | 24.8742 | 1.43851 | ||||||||
\(300\) | 10.3478 | 0.597430 | ||||||||
\(301\) | −0.634451 | −0.0365691 | ||||||||
\(302\) | 5.77068 | 0.332065 | ||||||||
\(303\) | −1.79817 | −0.103302 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 7.31682 | 0.418960 | ||||||||
\(306\) | 6.62935 | 0.378975 | ||||||||
\(307\) | 0.203433 | 0.0116105 | 0.00580526 | − | 0.999983i | \(-0.498152\pi\) | ||||
0.00580526 | + | 0.999983i | \(0.498152\pi\) | |||||||
\(308\) | 6.55387 | 0.373441 | ||||||||
\(309\) | −17.0040 | −0.967326 | ||||||||
\(310\) | 23.3266 | 1.32486 | ||||||||
\(311\) | 6.86918 | 0.389515 | 0.194758 | − | 0.980851i | \(-0.437608\pi\) | ||||
0.194758 | + | 0.980851i | \(0.437608\pi\) | |||||||
\(312\) | −5.50802 | −0.311830 | ||||||||
\(313\) | 13.2839 | 0.750852 | 0.375426 | − | 0.926852i | \(-0.377496\pi\) | ||||
0.375426 | + | 0.926852i | \(0.377496\pi\) | |||||||
\(314\) | −7.85464 | −0.443263 | ||||||||
\(315\) | 8.12459 | 0.457769 | ||||||||
\(316\) | −2.78453 | −0.156642 | ||||||||
\(317\) | 2.61783 | 0.147032 | 0.0735161 | − | 0.997294i | \(-0.476578\pi\) | ||||
0.0735161 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(318\) | 5.37374 | 0.301345 | ||||||||
\(319\) | 21.5683 | 1.20759 | ||||||||
\(320\) | 3.53697 | 0.197723 | ||||||||
\(321\) | 1.58410 | 0.0884159 | ||||||||
\(322\) | 12.9751 | 0.723075 | ||||||||
\(323\) | −6.01813 | −0.334857 | ||||||||
\(324\) | −4.48186 | −0.248992 | ||||||||
\(325\) | −30.0226 | −1.66535 | ||||||||
\(326\) | −4.10851 | −0.227549 | ||||||||
\(327\) | 6.30048 | 0.348417 | ||||||||
\(328\) | 8.95892 | 0.494674 | ||||||||
\(329\) | −1.72912 | −0.0953294 | ||||||||
\(330\) | −15.3168 | −0.843161 | ||||||||
\(331\) | 1.55037 | 0.0852161 | 0.0426081 | − | 0.999092i | \(-0.486433\pi\) | ||||
0.0426081 | + | 0.999092i | \(0.486433\pi\) | |||||||
\(332\) | 12.8628 | 0.705937 | ||||||||
\(333\) | 4.04489 | 0.221659 | ||||||||
\(334\) | 7.06678 | 0.386677 | ||||||||
\(335\) | 17.3729 | 0.949185 | ||||||||
\(336\) | −2.87314 | −0.156743 | ||||||||
\(337\) | −2.68537 | −0.146281 | −0.0731406 | − | 0.997322i | \(-0.523302\pi\) | ||||
−0.0731406 | + | 0.997322i | \(0.523302\pi\) | |||||||
\(338\) | 2.98071 | 0.162129 | ||||||||
\(339\) | −2.03028 | −0.110269 | ||||||||
\(340\) | −21.2859 | −1.15439 | ||||||||
\(341\) | −20.7280 | −1.12248 | ||||||||
\(342\) | −1.10156 | −0.0595658 | ||||||||
\(343\) | 20.1263 | 1.08672 | ||||||||
\(344\) | 0.304255 | 0.0164044 | ||||||||
\(345\) | −30.3237 | −1.63257 | ||||||||
\(346\) | 9.71788 | 0.522436 | ||||||||
\(347\) | 31.9733 | 1.71642 | 0.858209 | − | 0.513300i | \(-0.171577\pi\) | ||||
0.858209 | + | 0.513300i | \(0.171577\pi\) | |||||||
\(348\) | −9.45530 | −0.506857 | ||||||||
\(349\) | −10.4598 | −0.559899 | −0.279949 | − | 0.960015i | \(-0.590318\pi\) | ||||
−0.279949 | + | 0.960015i | \(0.590318\pi\) | |||||||
\(350\) | −15.6606 | −0.837096 | ||||||||
\(351\) | 22.5915 | 1.20585 | ||||||||
\(352\) | −3.14295 | −0.167520 | ||||||||
\(353\) | 16.4897 | 0.877659 | 0.438829 | − | 0.898570i | \(-0.355393\pi\) | ||||
0.438829 | + | 0.898570i | \(0.355393\pi\) | |||||||
\(354\) | −14.5296 | −0.772238 | ||||||||
\(355\) | −5.71632 | −0.303391 | ||||||||
\(356\) | −3.09295 | −0.163926 | ||||||||
\(357\) | 17.2909 | 0.915134 | ||||||||
\(358\) | −24.7875 | −1.31006 | ||||||||
\(359\) | 22.9622 | 1.21190 | 0.605949 | − | 0.795504i | \(-0.292794\pi\) | ||||
0.605949 | + | 0.795504i | \(0.292794\pi\) | |||||||
\(360\) | −3.89620 | −0.205348 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −2.42472 | −0.127441 | ||||||||
\(363\) | −1.54571 | −0.0811286 | ||||||||
\(364\) | 8.33600 | 0.436925 | ||||||||
\(365\) | −8.57180 | −0.448669 | ||||||||
\(366\) | 2.85029 | 0.148987 | ||||||||
\(367\) | 11.1602 | 0.582558 | 0.291279 | − | 0.956638i | \(-0.405919\pi\) | ||||
0.291279 | + | 0.956638i | \(0.405919\pi\) | |||||||
\(368\) | −6.22231 | −0.324361 | ||||||||
\(369\) | −9.86883 | −0.513751 | ||||||||
\(370\) | −12.9876 | −0.675193 | ||||||||
\(371\) | −8.13277 | −0.422233 | ||||||||
\(372\) | 9.08693 | 0.471135 | ||||||||
\(373\) | −22.3744 | −1.15850 | −0.579250 | − | 0.815150i | \(-0.696655\pi\) | ||||
−0.579250 | + | 0.815150i | \(0.696655\pi\) | |||||||
\(374\) | 18.9147 | 0.978056 | ||||||||
\(375\) | 12.2330 | 0.631710 | ||||||||
\(376\) | 0.829211 | 0.0427633 | ||||||||
\(377\) | 27.4331 | 1.41288 | ||||||||
\(378\) | 11.7844 | 0.606123 | ||||||||
\(379\) | −24.4532 | −1.25608 | −0.628039 | − | 0.778182i | \(-0.716142\pi\) | ||||
−0.628039 | + | 0.778182i | \(0.716142\pi\) | |||||||
\(380\) | 3.53697 | 0.181443 | ||||||||
\(381\) | −16.5349 | −0.847109 | ||||||||
\(382\) | 19.0532 | 0.974849 | ||||||||
\(383\) | −25.9429 | −1.32562 | −0.662811 | − | 0.748787i | \(-0.730637\pi\) | ||||
−0.662811 | + | 0.748787i | \(0.730637\pi\) | |||||||
\(384\) | 1.37784 | 0.0703125 | ||||||||
\(385\) | 23.1808 | 1.18141 | ||||||||
\(386\) | −6.16409 | −0.313744 | ||||||||
\(387\) | −0.335157 | −0.0170370 | ||||||||
\(388\) | 2.90999 | 0.147732 | ||||||||
\(389\) | 24.6340 | 1.24899 | 0.624497 | − | 0.781028i | \(-0.285304\pi\) | ||||
0.624497 | + | 0.781028i | \(0.285304\pi\) | |||||||
\(390\) | −19.4817 | −0.986496 | ||||||||
\(391\) | 37.4467 | 1.89376 | ||||||||
\(392\) | −2.65170 | −0.133931 | ||||||||
\(393\) | −11.5400 | −0.582115 | ||||||||
\(394\) | 3.38890 | 0.170730 | ||||||||
\(395\) | −9.84882 | −0.495548 | ||||||||
\(396\) | 3.46217 | 0.173980 | ||||||||
\(397\) | 13.3044 | 0.667728 | 0.333864 | − | 0.942621i | \(-0.391647\pi\) | ||||
0.333864 | + | 0.942621i | \(0.391647\pi\) | |||||||
\(398\) | 7.72991 | 0.387465 | ||||||||
\(399\) | −2.87314 | −0.143837 | ||||||||
\(400\) | 7.51017 | 0.375509 | ||||||||
\(401\) | 16.5602 | 0.826977 | 0.413489 | − | 0.910509i | \(-0.364310\pi\) | ||||
0.413489 | + | 0.910509i | \(0.364310\pi\) | |||||||
\(402\) | 6.76768 | 0.337541 | ||||||||
\(403\) | −26.3644 | −1.31330 | ||||||||
\(404\) | −1.30507 | −0.0649296 | ||||||||
\(405\) | −15.8522 | −0.787703 | ||||||||
\(406\) | 14.3099 | 0.710189 | ||||||||
\(407\) | 11.5408 | 0.572055 | ||||||||
\(408\) | −8.29200 | −0.410515 | ||||||||
\(409\) | 26.6765 | 1.31907 | 0.659534 | − | 0.751675i | \(-0.270754\pi\) | ||||
0.659534 | + | 0.751675i | \(0.270754\pi\) | |||||||
\(410\) | 31.6874 | 1.56493 | ||||||||
\(411\) | −14.8361 | −0.731811 | ||||||||
\(412\) | −12.3411 | −0.608003 | ||||||||
\(413\) | 21.9894 | 1.08203 | ||||||||
\(414\) | 6.85428 | 0.336870 | ||||||||
\(415\) | 45.4953 | 2.23328 | ||||||||
\(416\) | −3.99759 | −0.195998 | ||||||||
\(417\) | 1.96569 | 0.0962604 | ||||||||
\(418\) | −3.14295 | −0.153727 | ||||||||
\(419\) | −27.4551 | −1.34127 | −0.670635 | − | 0.741788i | \(-0.733978\pi\) | ||||
−0.670635 | + | 0.741788i | \(0.733978\pi\) | |||||||
\(420\) | −10.1622 | −0.495866 | ||||||||
\(421\) | 11.2610 | 0.548828 | 0.274414 | − | 0.961612i | \(-0.411516\pi\) | ||||
0.274414 | + | 0.961612i | \(0.411516\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −0.913430 | −0.0444125 | ||||||||
\(424\) | 3.90013 | 0.189407 | ||||||||
\(425\) | −45.1972 | −2.19238 | ||||||||
\(426\) | −2.22681 | −0.107889 | ||||||||
\(427\) | −4.31370 | −0.208755 | ||||||||
\(428\) | 1.14970 | 0.0555729 | ||||||||
\(429\) | 17.3115 | 0.835806 | ||||||||
\(430\) | 1.07614 | 0.0518962 | ||||||||
\(431\) | 18.3117 | 0.882041 | 0.441021 | − | 0.897497i | \(-0.354617\pi\) | ||||
0.441021 | + | 0.897497i | \(0.354617\pi\) | |||||||
\(432\) | −5.65129 | −0.271898 | ||||||||
\(433\) | −17.6693 | −0.849134 | −0.424567 | − | 0.905396i | \(-0.639574\pi\) | ||||
−0.424567 | + | 0.905396i | \(0.639574\pi\) | |||||||
\(434\) | −13.7524 | −0.660137 | ||||||||
\(435\) | −33.4431 | −1.60348 | ||||||||
\(436\) | 4.57273 | 0.218994 | ||||||||
\(437\) | −6.22231 | −0.297654 | ||||||||
\(438\) | −3.33917 | −0.159552 | ||||||||
\(439\) | 13.3069 | 0.635106 | 0.317553 | − | 0.948241i | \(-0.397139\pi\) | ||||
0.317553 | + | 0.948241i | \(0.397139\pi\) | |||||||
\(440\) | −11.1165 | −0.529960 | ||||||||
\(441\) | 2.92102 | 0.139096 | ||||||||
\(442\) | 24.0580 | 1.14432 | ||||||||
\(443\) | 15.0992 | 0.717385 | 0.358693 | − | 0.933456i | \(-0.383223\pi\) | ||||
0.358693 | + | 0.933456i | \(0.383223\pi\) | |||||||
\(444\) | −5.05935 | −0.240106 | ||||||||
\(445\) | −10.9397 | −0.518590 | ||||||||
\(446\) | −4.53033 | −0.214517 | ||||||||
\(447\) | −2.29017 | −0.108321 | ||||||||
\(448\) | −2.08526 | −0.0985191 | ||||||||
\(449\) | 7.48980 | 0.353465 | 0.176733 | − | 0.984259i | \(-0.443447\pi\) | ||||
0.176733 | + | 0.984259i | \(0.443447\pi\) | |||||||
\(450\) | −8.27294 | −0.389990 | ||||||||
\(451\) | −28.1575 | −1.32588 | ||||||||
\(452\) | −1.47352 | −0.0693087 | ||||||||
\(453\) | 7.95106 | 0.373573 | ||||||||
\(454\) | −4.60548 | −0.216146 | ||||||||
\(455\) | 29.4842 | 1.38224 | ||||||||
\(456\) | 1.37784 | 0.0645231 | ||||||||
\(457\) | −13.3573 | −0.624827 | −0.312413 | − | 0.949946i | \(-0.601137\pi\) | ||||
−0.312413 | + | 0.949946i | \(0.601137\pi\) | |||||||
\(458\) | −18.8360 | −0.880149 | ||||||||
\(459\) | 34.0102 | 1.58746 | ||||||||
\(460\) | −22.0082 | −1.02614 | ||||||||
\(461\) | −29.7300 | −1.38467 | −0.692333 | − | 0.721578i | \(-0.743417\pi\) | ||||
−0.692333 | + | 0.721578i | \(0.743417\pi\) | |||||||
\(462\) | 9.03016 | 0.420121 | ||||||||
\(463\) | −15.9808 | −0.742691 | −0.371345 | − | 0.928495i | \(-0.621103\pi\) | ||||
−0.371345 | + | 0.928495i | \(0.621103\pi\) | |||||||
\(464\) | −6.86242 | −0.318580 | ||||||||
\(465\) | 32.1402 | 1.49047 | ||||||||
\(466\) | 13.9203 | 0.644847 | ||||||||
\(467\) | 10.1118 | 0.467920 | 0.233960 | − | 0.972246i | \(-0.424832\pi\) | ||||
0.233960 | + | 0.972246i | \(0.424832\pi\) | |||||||
\(468\) | 4.40360 | 0.203557 | ||||||||
\(469\) | −10.2424 | −0.472950 | ||||||||
\(470\) | 2.93290 | 0.135284 | ||||||||
\(471\) | −10.8224 | −0.498671 | ||||||||
\(472\) | −10.5452 | −0.485382 | ||||||||
\(473\) | −0.956261 | −0.0439689 | ||||||||
\(474\) | −3.83663 | −0.176222 | ||||||||
\(475\) | 7.51017 | 0.344590 | ||||||||
\(476\) | 12.5493 | 0.575198 | ||||||||
\(477\) | −4.29625 | −0.196712 | ||||||||
\(478\) | −1.61370 | −0.0738091 | ||||||||
\(479\) | −18.6733 | −0.853203 | −0.426602 | − | 0.904440i | \(-0.640289\pi\) | ||||
−0.426602 | + | 0.904440i | \(0.640289\pi\) | |||||||
\(480\) | 4.87337 | 0.222438 | ||||||||
\(481\) | 14.6790 | 0.669303 | ||||||||
\(482\) | −5.33913 | −0.243191 | ||||||||
\(483\) | 17.8776 | 0.813459 | ||||||||
\(484\) | −1.12184 | −0.0509925 | ||||||||
\(485\) | 10.2926 | 0.467361 | ||||||||
\(486\) | 10.7786 | 0.488927 | ||||||||
\(487\) | 7.80494 | 0.353676 | 0.176838 | − | 0.984240i | \(-0.443413\pi\) | ||||
0.176838 | + | 0.984240i | \(0.443413\pi\) | |||||||
\(488\) | 2.06867 | 0.0936442 | ||||||||
\(489\) | −5.66085 | −0.255993 | ||||||||
\(490\) | −9.37900 | −0.423700 | ||||||||
\(491\) | 30.4261 | 1.37311 | 0.686556 | − | 0.727077i | \(-0.259122\pi\) | ||||
0.686556 | + | 0.727077i | \(0.259122\pi\) | |||||||
\(492\) | 12.3439 | 0.556507 | ||||||||
\(493\) | 41.2989 | 1.86001 | ||||||||
\(494\) | −3.99759 | −0.179860 | ||||||||
\(495\) | 12.2456 | 0.550398 | ||||||||
\(496\) | 6.59507 | 0.296127 | ||||||||
\(497\) | 3.37011 | 0.151170 | ||||||||
\(498\) | 17.7228 | 0.794178 | ||||||||
\(499\) | −27.5678 | −1.23411 | −0.617053 | − | 0.786922i | \(-0.711673\pi\) | ||||
−0.617053 | + | 0.786922i | \(0.711673\pi\) | |||||||
\(500\) | 8.87841 | 0.397055 | ||||||||
\(501\) | 9.73687 | 0.435011 | ||||||||
\(502\) | −15.5928 | −0.695940 | ||||||||
\(503\) | −21.2454 | −0.947283 | −0.473642 | − | 0.880718i | \(-0.657061\pi\) | ||||
−0.473642 | + | 0.880718i | \(0.657061\pi\) | |||||||
\(504\) | 2.29705 | 0.102319 | ||||||||
\(505\) | −4.61599 | −0.205409 | ||||||||
\(506\) | 19.5565 | 0.869390 | ||||||||
\(507\) | 4.10693 | 0.182395 | ||||||||
\(508\) | −12.0006 | −0.532442 | ||||||||
\(509\) | −8.63307 | −0.382654 | −0.191327 | − | 0.981526i | \(-0.561279\pi\) | ||||
−0.191327 | + | 0.981526i | \(0.561279\pi\) | |||||||
\(510\) | −29.3286 | −1.29869 | ||||||||
\(511\) | 5.05359 | 0.223558 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.65129 | −0.249510 | ||||||||
\(514\) | 16.7444 | 0.738564 | ||||||||
\(515\) | −43.6502 | −1.92346 | ||||||||
\(516\) | 0.419215 | 0.0184549 | ||||||||
\(517\) | −2.60617 | −0.114619 | ||||||||
\(518\) | 7.65696 | 0.336428 | ||||||||
\(519\) | 13.3897 | 0.587741 | ||||||||
\(520\) | −14.1394 | −0.620052 | ||||||||
\(521\) | 39.7373 | 1.74092 | 0.870461 | − | 0.492237i | \(-0.163821\pi\) | ||||
0.870461 | + | 0.492237i | \(0.163821\pi\) | |||||||
\(522\) | 7.55940 | 0.330866 | ||||||||
\(523\) | −12.5368 | −0.548196 | −0.274098 | − | 0.961702i | \(-0.588379\pi\) | ||||
−0.274098 | + | 0.961702i | \(0.588379\pi\) | |||||||
\(524\) | −8.37543 | −0.365882 | ||||||||
\(525\) | −21.5778 | −0.941733 | ||||||||
\(526\) | 16.0204 | 0.698521 | ||||||||
\(527\) | −39.6900 | −1.72892 | ||||||||
\(528\) | −4.33048 | −0.188460 | ||||||||
\(529\) | 15.7172 | 0.683357 | ||||||||
\(530\) | 13.7947 | 0.599201 | ||||||||
\(531\) | 11.6162 | 0.504101 | ||||||||
\(532\) | −2.08526 | −0.0904073 | ||||||||
\(533\) | −35.8141 | −1.55128 | ||||||||
\(534\) | −4.26158 | −0.184417 | ||||||||
\(535\) | 4.06646 | 0.175809 | ||||||||
\(536\) | 4.91181 | 0.212158 | ||||||||
\(537\) | −34.1531 | −1.47382 | ||||||||
\(538\) | −18.2562 | −0.787082 | ||||||||
\(539\) | 8.33419 | 0.358979 | ||||||||
\(540\) | −19.9885 | −0.860166 | ||||||||
\(541\) | 29.9048 | 1.28571 | 0.642855 | − | 0.765988i | \(-0.277750\pi\) | ||||
0.642855 | + | 0.765988i | \(0.277750\pi\) | |||||||
\(542\) | 19.6564 | 0.844317 | ||||||||
\(543\) | −3.34087 | −0.143371 | ||||||||
\(544\) | −6.01813 | −0.258025 | ||||||||
\(545\) | 16.1736 | 0.692802 | ||||||||
\(546\) | 11.4856 | 0.491540 | ||||||||
\(547\) | 17.3234 | 0.740696 | 0.370348 | − | 0.928893i | \(-0.379238\pi\) | ||||
0.370348 | + | 0.928893i | \(0.379238\pi\) | |||||||
\(548\) | −10.7677 | −0.459972 | ||||||||
\(549\) | −2.27877 | −0.0972556 | ||||||||
\(550\) | −23.6041 | −1.00648 | ||||||||
\(551\) | −6.86242 | −0.292349 | ||||||||
\(552\) | −8.57334 | −0.364905 | ||||||||
\(553\) | 5.80647 | 0.246916 | ||||||||
\(554\) | −20.4390 | −0.868369 | ||||||||
\(555\) | −17.8948 | −0.759592 | ||||||||
\(556\) | 1.42665 | 0.0605035 | ||||||||
\(557\) | −29.8705 | −1.26565 | −0.632827 | − | 0.774293i | \(-0.718106\pi\) | ||||
−0.632827 | + | 0.774293i | \(0.718106\pi\) | |||||||
\(558\) | −7.26490 | −0.307548 | ||||||||
\(559\) | −1.21629 | −0.0514435 | ||||||||
\(560\) | −7.37550 | −0.311672 | ||||||||
\(561\) | 26.0614 | 1.10031 | ||||||||
\(562\) | 6.65167 | 0.280584 | ||||||||
\(563\) | 21.5489 | 0.908178 | 0.454089 | − | 0.890956i | \(-0.349965\pi\) | ||||
0.454089 | + | 0.890956i | \(0.349965\pi\) | |||||||
\(564\) | 1.14252 | 0.0481087 | ||||||||
\(565\) | −5.21181 | −0.219263 | ||||||||
\(566\) | −9.99361 | −0.420063 | ||||||||
\(567\) | 9.34583 | 0.392488 | ||||||||
\(568\) | −1.61616 | −0.0678126 | ||||||||
\(569\) | −27.9037 | −1.16979 | −0.584893 | − | 0.811111i | \(-0.698863\pi\) | ||||
−0.584893 | + | 0.811111i | \(0.698863\pi\) | |||||||
\(570\) | 4.87337 | 0.204123 | ||||||||
\(571\) | 32.8503 | 1.37474 | 0.687371 | − | 0.726307i | \(-0.258765\pi\) | ||||
0.687371 | + | 0.726307i | \(0.258765\pi\) | |||||||
\(572\) | 12.5642 | 0.525337 | ||||||||
\(573\) | 26.2523 | 1.09670 | ||||||||
\(574\) | −18.6816 | −0.779757 | ||||||||
\(575\) | −46.7307 | −1.94880 | ||||||||
\(576\) | −1.10156 | −0.0458985 | ||||||||
\(577\) | −5.47732 | −0.228024 | −0.114012 | − | 0.993479i | \(-0.536370\pi\) | ||||
−0.114012 | + | 0.993479i | \(0.536370\pi\) | |||||||
\(578\) | 19.2178 | 0.799356 | ||||||||
\(579\) | −8.49311 | −0.352962 | ||||||||
\(580\) | −24.2722 | −1.00785 | ||||||||
\(581\) | −26.8222 | −1.11277 | ||||||||
\(582\) | 4.00949 | 0.166199 | ||||||||
\(583\) | −12.2579 | −0.507672 | ||||||||
\(584\) | −2.42349 | −0.100285 | ||||||||
\(585\) | 15.5754 | 0.643964 | ||||||||
\(586\) | 11.8689 | 0.490299 | ||||||||
\(587\) | −11.0692 | −0.456873 | −0.228437 | − | 0.973559i | \(-0.573361\pi\) | ||||
−0.228437 | + | 0.973559i | \(0.573361\pi\) | |||||||
\(588\) | −3.65362 | −0.150673 | ||||||||
\(589\) | 6.59507 | 0.271745 | ||||||||
\(590\) | −37.2981 | −1.53554 | ||||||||
\(591\) | 4.66935 | 0.192071 | ||||||||
\(592\) | −3.67195 | −0.150916 | ||||||||
\(593\) | −14.4974 | −0.595337 | −0.297669 | − | 0.954669i | \(-0.596209\pi\) | ||||
−0.297669 | + | 0.954669i | \(0.596209\pi\) | |||||||
\(594\) | 17.7617 | 0.728773 | ||||||||
\(595\) | 44.3867 | 1.81968 | ||||||||
\(596\) | −1.66215 | −0.0680843 | ||||||||
\(597\) | 10.6506 | 0.435898 | ||||||||
\(598\) | 24.8742 | 1.01718 | ||||||||
\(599\) | 17.2497 | 0.704802 | 0.352401 | − | 0.935849i | \(-0.385365\pi\) | ||||
0.352401 | + | 0.935849i | \(0.385365\pi\) | |||||||
\(600\) | 10.3478 | 0.422447 | ||||||||
\(601\) | −27.1951 | −1.10931 | −0.554655 | − | 0.832081i | \(-0.687150\pi\) | ||||
−0.554655 | + | 0.832081i | \(0.687150\pi\) | |||||||
\(602\) | −0.634451 | −0.0258583 | ||||||||
\(603\) | −5.41068 | −0.220340 | ||||||||
\(604\) | 5.77068 | 0.234806 | ||||||||
\(605\) | −3.96790 | −0.161318 | ||||||||
\(606\) | −1.79817 | −0.0730458 | ||||||||
\(607\) | 29.3930 | 1.19303 | 0.596513 | − | 0.802604i | \(-0.296553\pi\) | ||||
0.596513 | + | 0.802604i | \(0.296553\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 19.7167 | 0.798962 | ||||||||
\(610\) | 7.31682 | 0.296250 | ||||||||
\(611\) | −3.31484 | −0.134104 | ||||||||
\(612\) | 6.62935 | 0.267976 | ||||||||
\(613\) | −26.7405 | −1.08004 | −0.540020 | − | 0.841652i | \(-0.681583\pi\) | ||||
−0.540020 | + | 0.841652i | \(0.681583\pi\) | |||||||
\(614\) | 0.203433 | 0.00820988 | ||||||||
\(615\) | 43.6601 | 1.76055 | ||||||||
\(616\) | 6.55387 | 0.264063 | ||||||||
\(617\) | −2.53854 | −0.102198 | −0.0510989 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510989 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(618\) | −17.0040 | −0.684003 | ||||||||
\(619\) | 4.50555 | 0.181093 | 0.0905467 | − | 0.995892i | \(-0.471139\pi\) | ||||
0.0905467 | + | 0.995892i | \(0.471139\pi\) | |||||||
\(620\) | 23.3266 | 0.936818 | ||||||||
\(621\) | 35.1641 | 1.41109 | ||||||||
\(622\) | 6.86918 | 0.275429 | ||||||||
\(623\) | 6.44959 | 0.258398 | ||||||||
\(624\) | −5.50802 | −0.220497 | ||||||||
\(625\) | −6.14817 | −0.245927 | ||||||||
\(626\) | 13.2839 | 0.530933 | ||||||||
\(627\) | −4.33048 | −0.172943 | ||||||||
\(628\) | −7.85464 | −0.313434 | ||||||||
\(629\) | 22.0983 | 0.881116 | ||||||||
\(630\) | 8.12459 | 0.323691 | ||||||||
\(631\) | 14.0791 | 0.560478 | 0.280239 | − | 0.959930i | \(-0.409586\pi\) | ||||
0.280239 | + | 0.959930i | \(0.409586\pi\) | |||||||
\(632\) | −2.78453 | −0.110763 | ||||||||
\(633\) | −1.37784 | −0.0547641 | ||||||||
\(634\) | 2.61783 | 0.103967 | ||||||||
\(635\) | −42.4459 | −1.68441 | ||||||||
\(636\) | 5.37374 | 0.213083 | ||||||||
\(637\) | 10.6004 | 0.420004 | ||||||||
\(638\) | 21.5683 | 0.853896 | ||||||||
\(639\) | 1.78031 | 0.0704278 | ||||||||
\(640\) | 3.53697 | 0.139811 | ||||||||
\(641\) | −24.3660 | −0.962399 | −0.481199 | − | 0.876611i | \(-0.659799\pi\) | ||||
−0.481199 | + | 0.876611i | \(0.659799\pi\) | |||||||
\(642\) | 1.58410 | 0.0625195 | ||||||||
\(643\) | 45.0314 | 1.77586 | 0.887932 | − | 0.459975i | \(-0.152142\pi\) | ||||
0.887932 | + | 0.459975i | \(0.152142\pi\) | |||||||
\(644\) | 12.9751 | 0.511292 | ||||||||
\(645\) | 1.48275 | 0.0583832 | ||||||||
\(646\) | −6.01813 | −0.236780 | ||||||||
\(647\) | −7.60264 | −0.298891 | −0.149445 | − | 0.988770i | \(-0.547749\pi\) | ||||
−0.149445 | + | 0.988770i | \(0.547749\pi\) | |||||||
\(648\) | −4.48186 | −0.176064 | ||||||||
\(649\) | 33.1431 | 1.30098 | ||||||||
\(650\) | −30.0226 | −1.17758 | ||||||||
\(651\) | −18.9486 | −0.742654 | ||||||||
\(652\) | −4.10851 | −0.160902 | ||||||||
\(653\) | −21.0806 | −0.824948 | −0.412474 | − | 0.910969i | \(-0.635335\pi\) | ||||
−0.412474 | + | 0.910969i | \(0.635335\pi\) | |||||||
\(654\) | 6.30048 | 0.246368 | ||||||||
\(655\) | −29.6237 | −1.15749 | ||||||||
\(656\) | 8.95892 | 0.349787 | ||||||||
\(657\) | 2.66963 | 0.104152 | ||||||||
\(658\) | −1.72912 | −0.0674081 | ||||||||
\(659\) | 28.7679 | 1.12064 | 0.560320 | − | 0.828276i | \(-0.310678\pi\) | ||||
0.560320 | + | 0.828276i | \(0.310678\pi\) | |||||||
\(660\) | −15.3168 | −0.596205 | ||||||||
\(661\) | −29.5633 | −1.14988 | −0.574940 | − | 0.818196i | \(-0.694975\pi\) | ||||
−0.574940 | + | 0.818196i | \(0.694975\pi\) | |||||||
\(662\) | 1.55037 | 0.0602569 | ||||||||
\(663\) | 33.1480 | 1.28736 | ||||||||
\(664\) | 12.8628 | 0.499173 | ||||||||
\(665\) | −7.37550 | −0.286009 | ||||||||
\(666\) | 4.04489 | 0.156736 | ||||||||
\(667\) | 42.7001 | 1.65336 | ||||||||
\(668\) | 7.06678 | 0.273422 | ||||||||
\(669\) | −6.24206 | −0.241332 | ||||||||
\(670\) | 17.3729 | 0.671175 | ||||||||
\(671\) | −6.50173 | −0.250997 | ||||||||
\(672\) | −2.87314 | −0.110834 | ||||||||
\(673\) | −19.2315 | −0.741318 | −0.370659 | − | 0.928769i | \(-0.620868\pi\) | ||||
−0.370659 | + | 0.928769i | \(0.620868\pi\) | |||||||
\(674\) | −2.68537 | −0.103436 | ||||||||
\(675\) | −42.4422 | −1.63360 | ||||||||
\(676\) | 2.98071 | 0.114643 | ||||||||
\(677\) | 13.8011 | 0.530421 | 0.265210 | − | 0.964191i | \(-0.414559\pi\) | ||||
0.265210 | + | 0.964191i | \(0.414559\pi\) | |||||||
\(678\) | −2.03028 | −0.0779723 | ||||||||
\(679\) | −6.06808 | −0.232871 | ||||||||
\(680\) | −21.2859 | −0.816279 | ||||||||
\(681\) | −6.34560 | −0.243164 | ||||||||
\(682\) | −20.7280 | −0.793716 | ||||||||
\(683\) | −19.4834 | −0.745511 | −0.372756 | − | 0.927930i | \(-0.621587\pi\) | ||||
−0.372756 | + | 0.927930i | \(0.621587\pi\) | |||||||
\(684\) | −1.10156 | −0.0421194 | ||||||||
\(685\) | −38.0850 | −1.45515 | ||||||||
\(686\) | 20.1263 | 0.768425 | ||||||||
\(687\) | −25.9529 | −0.990167 | ||||||||
\(688\) | 0.304255 | 0.0115996 | ||||||||
\(689\) | −15.5911 | −0.593974 | ||||||||
\(690\) | −30.3237 | −1.15440 | ||||||||
\(691\) | 37.7494 | 1.43605 | 0.718027 | − | 0.696015i | \(-0.245045\pi\) | ||||
0.718027 | + | 0.696015i | \(0.245045\pi\) | |||||||
\(692\) | 9.71788 | 0.369418 | ||||||||
\(693\) | −7.21951 | −0.274246 | ||||||||
\(694\) | 31.9733 | 1.21369 | ||||||||
\(695\) | 5.04603 | 0.191407 | ||||||||
\(696\) | −9.45530 | −0.358402 | ||||||||
\(697\) | −53.9159 | −2.04221 | ||||||||
\(698\) | −10.4598 | −0.395908 | ||||||||
\(699\) | 19.1799 | 0.725452 | ||||||||
\(700\) | −15.6606 | −0.591917 | ||||||||
\(701\) | −28.1212 | −1.06212 | −0.531061 | − | 0.847334i | \(-0.678206\pi\) | ||||
−0.531061 | + | 0.847334i | \(0.678206\pi\) | |||||||
\(702\) | 22.5915 | 0.852662 | ||||||||
\(703\) | −3.67195 | −0.138490 | ||||||||
\(704\) | −3.14295 | −0.118455 | ||||||||
\(705\) | 4.04105 | 0.152195 | ||||||||
\(706\) | 16.4897 | 0.620598 | ||||||||
\(707\) | 2.72140 | 0.102349 | ||||||||
\(708\) | −14.5296 | −0.546054 | ||||||||
\(709\) | −8.69213 | −0.326440 | −0.163220 | − | 0.986590i | \(-0.552188\pi\) | ||||
−0.163220 | + | 0.986590i | \(0.552188\pi\) | |||||||
\(710\) | −5.71632 | −0.214530 | ||||||||
\(711\) | 3.06734 | 0.115034 | ||||||||
\(712\) | −3.09295 | −0.115913 | ||||||||
\(713\) | −41.0366 | −1.53683 | ||||||||
\(714\) | 17.2909 | 0.647097 | ||||||||
\(715\) | 44.4394 | 1.66194 | ||||||||
\(716\) | −24.7875 | −0.926352 | ||||||||
\(717\) | −2.22342 | −0.0830352 | ||||||||
\(718\) | 22.9622 | 0.856941 | ||||||||
\(719\) | 18.3861 | 0.685686 | 0.342843 | − | 0.939393i | \(-0.388610\pi\) | ||||
0.342843 | + | 0.939393i | \(0.388610\pi\) | |||||||
\(720\) | −3.89620 | −0.145203 | ||||||||
\(721\) | 25.7344 | 0.958399 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −7.35646 | −0.273590 | ||||||||
\(724\) | −2.42472 | −0.0901142 | ||||||||
\(725\) | −51.5380 | −1.91407 | ||||||||
\(726\) | −1.54571 | −0.0573666 | ||||||||
\(727\) | 17.5555 | 0.651097 | 0.325548 | − | 0.945525i | \(-0.394451\pi\) | ||||
0.325548 | + | 0.945525i | \(0.394451\pi\) | |||||||
\(728\) | 8.33600 | 0.308953 | ||||||||
\(729\) | 28.2967 | 1.04803 | ||||||||
\(730\) | −8.57180 | −0.317257 | ||||||||
\(731\) | −1.83105 | −0.0677237 | ||||||||
\(732\) | 2.85029 | 0.105350 | ||||||||
\(733\) | −46.1061 | −1.70297 | −0.851483 | − | 0.524382i | \(-0.824296\pi\) | ||||
−0.851483 | + | 0.524382i | \(0.824296\pi\) | |||||||
\(734\) | 11.1602 | 0.411931 | ||||||||
\(735\) | −12.9227 | −0.476662 | ||||||||
\(736\) | −6.22231 | −0.229358 | ||||||||
\(737\) | −15.4376 | −0.568651 | ||||||||
\(738\) | −9.86883 | −0.363277 | ||||||||
\(739\) | 22.4589 | 0.826162 | 0.413081 | − | 0.910694i | \(-0.364453\pi\) | ||||
0.413081 | + | 0.910694i | \(0.364453\pi\) | |||||||
\(740\) | −12.9876 | −0.477433 | ||||||||
\(741\) | −5.50802 | −0.202342 | ||||||||
\(742\) | −8.13277 | −0.298564 | ||||||||
\(743\) | −49.4864 | −1.81548 | −0.907741 | − | 0.419531i | \(-0.862194\pi\) | ||||
−0.907741 | + | 0.419531i | \(0.862194\pi\) | |||||||
\(744\) | 9.08693 | 0.333143 | ||||||||
\(745\) | −5.87898 | −0.215389 | ||||||||
\(746\) | −22.3744 | −0.819183 | ||||||||
\(747\) | −14.1692 | −0.518423 | ||||||||
\(748\) | 18.9147 | 0.691590 | ||||||||
\(749\) | −2.39742 | −0.0875999 | ||||||||
\(750\) | 12.2330 | 0.446686 | ||||||||
\(751\) | −20.0847 | −0.732900 | −0.366450 | − | 0.930438i | \(-0.619427\pi\) | ||||
−0.366450 | + | 0.930438i | \(0.619427\pi\) | |||||||
\(752\) | 0.829211 | 0.0302382 | ||||||||
\(753\) | −21.4843 | −0.782932 | ||||||||
\(754\) | 27.4331 | 0.999056 | ||||||||
\(755\) | 20.4107 | 0.742823 | ||||||||
\(756\) | 11.7844 | 0.428594 | ||||||||
\(757\) | −26.3031 | −0.956003 | −0.478002 | − | 0.878359i | \(-0.658639\pi\) | ||||
−0.478002 | + | 0.878359i | \(0.658639\pi\) | |||||||
\(758\) | −24.4532 | −0.888181 | ||||||||
\(759\) | 26.9456 | 0.978064 | ||||||||
\(760\) | 3.53697 | 0.128299 | ||||||||
\(761\) | −28.8315 | −1.04514 | −0.522570 | − | 0.852597i | \(-0.675027\pi\) | ||||
−0.522570 | + | 0.852597i | \(0.675027\pi\) | |||||||
\(762\) | −16.5349 | −0.598997 | ||||||||
\(763\) | −9.53532 | −0.345202 | ||||||||
\(764\) | 19.0532 | 0.689322 | ||||||||
\(765\) | 23.4478 | 0.847759 | ||||||||
\(766\) | −25.9429 | −0.937356 | ||||||||
\(767\) | 42.1553 | 1.52214 | ||||||||
\(768\) | 1.37784 | 0.0497184 | ||||||||
\(769\) | 17.7757 | 0.641007 | 0.320503 | − | 0.947247i | \(-0.396148\pi\) | ||||
0.320503 | + | 0.947247i | \(0.396148\pi\) | |||||||
\(770\) | 23.1808 | 0.835380 | ||||||||
\(771\) | 23.0711 | 0.830884 | ||||||||
\(772\) | −6.16409 | −0.221850 | ||||||||
\(773\) | −1.54444 | −0.0555497 | −0.0277749 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277749 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(774\) | −0.335157 | −0.0120470 | ||||||||
\(775\) | 49.5301 | 1.77917 | ||||||||
\(776\) | 2.90999 | 0.104463 | ||||||||
\(777\) | 10.5500 | 0.378481 | ||||||||
\(778\) | 24.6340 | 0.883171 | ||||||||
\(779\) | 8.95892 | 0.320987 | ||||||||
\(780\) | −19.4817 | −0.697558 | ||||||||
\(781\) | 5.07952 | 0.181760 | ||||||||
\(782\) | 37.4467 | 1.33909 | ||||||||
\(783\) | 38.7815 | 1.38594 | ||||||||
\(784\) | −2.65170 | −0.0947037 | ||||||||
\(785\) | −27.7817 | −0.991570 | ||||||||
\(786\) | −11.5400 | −0.411617 | ||||||||
\(787\) | −14.7378 | −0.525345 | −0.262673 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262673 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(788\) | 3.38890 | 0.120725 | ||||||||
\(789\) | 22.0734 | 0.785835 | ||||||||
\(790\) | −9.84882 | −0.350405 | ||||||||
\(791\) | 3.07267 | 0.109252 | ||||||||
\(792\) | 3.46217 | 0.123023 | ||||||||
\(793\) | −8.26968 | −0.293665 | ||||||||
\(794\) | 13.3044 | 0.472155 | ||||||||
\(795\) | 19.0068 | 0.674101 | ||||||||
\(796\) | 7.72991 | 0.273979 | ||||||||
\(797\) | −14.7054 | −0.520892 | −0.260446 | − | 0.965488i | \(-0.583870\pi\) | ||||
−0.260446 | + | 0.965488i | \(0.583870\pi\) | |||||||
\(798\) | −2.87314 | −0.101708 | ||||||||
\(799\) | −4.99030 | −0.176544 | ||||||||
\(800\) | 7.51017 | 0.265525 | ||||||||
\(801\) | 3.40708 | 0.120383 | ||||||||
\(802\) | 16.5602 | 0.584761 | ||||||||
\(803\) | 7.61691 | 0.268795 | ||||||||
\(804\) | 6.76768 | 0.238678 | ||||||||
\(805\) | 45.8927 | 1.61750 | ||||||||
\(806\) | −26.3644 | −0.928645 | ||||||||
\(807\) | −25.1541 | −0.885467 | ||||||||
\(808\) | −1.30507 | −0.0459122 | ||||||||
\(809\) | 21.3092 | 0.749191 | 0.374596 | − | 0.927188i | \(-0.377782\pi\) | ||||
0.374596 | + | 0.927188i | \(0.377782\pi\) | |||||||
\(810\) | −15.8522 | −0.556990 | ||||||||
\(811\) | 55.7967 | 1.95929 | 0.979644 | − | 0.200745i | \(-0.0643363\pi\) | ||||
0.979644 | + | 0.200745i | \(0.0643363\pi\) | |||||||
\(812\) | 14.3099 | 0.502179 | ||||||||
\(813\) | 27.0834 | 0.949856 | ||||||||
\(814\) | 11.5408 | 0.404504 | ||||||||
\(815\) | −14.5317 | −0.509022 | ||||||||
\(816\) | −8.29200 | −0.290278 | ||||||||
\(817\) | 0.304255 | 0.0106446 | ||||||||
\(818\) | 26.6765 | 0.932721 | ||||||||
\(819\) | −9.18264 | −0.320867 | ||||||||
\(820\) | 31.6874 | 1.10657 | ||||||||
\(821\) | −36.2826 | −1.26627 | −0.633136 | − | 0.774041i | \(-0.718232\pi\) | ||||
−0.633136 | + | 0.774041i | \(0.718232\pi\) | |||||||
\(822\) | −14.8361 | −0.517468 | ||||||||
\(823\) | 40.4131 | 1.40871 | 0.704356 | − | 0.709847i | \(-0.251236\pi\) | ||||
0.704356 | + | 0.709847i | \(0.251236\pi\) | |||||||
\(824\) | −12.3411 | −0.429923 | ||||||||
\(825\) | −32.5227 | −1.13229 | ||||||||
\(826\) | 21.9894 | 0.765110 | ||||||||
\(827\) | −14.6019 | −0.507759 | −0.253879 | − | 0.967236i | \(-0.581707\pi\) | ||||
−0.253879 | + | 0.967236i | \(0.581707\pi\) | |||||||
\(828\) | 6.85428 | 0.238203 | ||||||||
\(829\) | −47.6614 | −1.65535 | −0.827674 | − | 0.561209i | \(-0.810336\pi\) | ||||
−0.827674 | + | 0.561209i | \(0.810336\pi\) | |||||||
\(830\) | 45.4953 | 1.57916 | ||||||||
\(831\) | −28.1616 | −0.976915 | ||||||||
\(832\) | −3.99759 | −0.138591 | ||||||||
\(833\) | 15.9583 | 0.552922 | ||||||||
\(834\) | 1.96569 | 0.0680664 | ||||||||
\(835\) | 24.9950 | 0.864987 | ||||||||
\(836\) | −3.14295 | −0.108701 | ||||||||
\(837\) | −37.2706 | −1.28826 | ||||||||
\(838\) | −27.4551 | −0.948421 | ||||||||
\(839\) | 30.1178 | 1.03978 | 0.519890 | − | 0.854233i | \(-0.325973\pi\) | ||||
0.519890 | + | 0.854233i | \(0.325973\pi\) | |||||||
\(840\) | −10.1622 | −0.350630 | ||||||||
\(841\) | 18.0928 | 0.623891 | ||||||||
\(842\) | 11.2610 | 0.388080 | ||||||||
\(843\) | 9.16491 | 0.315656 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 10.5427 | 0.362679 | ||||||||
\(846\) | −0.913430 | −0.0314044 | ||||||||
\(847\) | 2.33932 | 0.0803798 | ||||||||
\(848\) | 3.90013 | 0.133931 | ||||||||
\(849\) | −13.7696 | −0.472570 | ||||||||
\(850\) | −45.1972 | −1.55025 | ||||||||
\(851\) | 22.8480 | 0.783221 | ||||||||
\(852\) | −2.22681 | −0.0762892 | ||||||||
\(853\) | −33.0738 | −1.13243 | −0.566213 | − | 0.824259i | \(-0.691592\pi\) | ||||
−0.566213 | + | 0.824259i | \(0.691592\pi\) | |||||||
\(854\) | −4.31370 | −0.147612 | ||||||||
\(855\) | −3.89620 | −0.133247 | ||||||||
\(856\) | 1.14970 | 0.0392960 | ||||||||
\(857\) | −42.3024 | −1.44502 | −0.722512 | − | 0.691358i | \(-0.757013\pi\) | ||||
−0.722512 | + | 0.691358i | \(0.757013\pi\) | |||||||
\(858\) | 17.3115 | 0.591004 | ||||||||
\(859\) | −21.3341 | −0.727909 | −0.363955 | − | 0.931417i | \(-0.618574\pi\) | ||||
−0.363955 | + | 0.931417i | \(0.618574\pi\) | |||||||
\(860\) | 1.07614 | 0.0366962 | ||||||||
\(861\) | −25.7403 | −0.877226 | ||||||||
\(862\) | 18.3117 | 0.623697 | ||||||||
\(863\) | −32.4571 | −1.10485 | −0.552427 | − | 0.833561i | \(-0.686298\pi\) | ||||
−0.552427 | + | 0.833561i | \(0.686298\pi\) | |||||||
\(864\) | −5.65129 | −0.192261 | ||||||||
\(865\) | 34.3719 | 1.16868 | ||||||||
\(866\) | −17.6693 | −0.600429 | ||||||||
\(867\) | 26.4790 | 0.899276 | ||||||||
\(868\) | −13.7524 | −0.466787 | ||||||||
\(869\) | 8.75166 | 0.296880 | ||||||||
\(870\) | −33.4431 | −1.13383 | ||||||||
\(871\) | −19.6354 | −0.665320 | ||||||||
\(872\) | 4.57273 | 0.154852 | ||||||||
\(873\) | −3.20554 | −0.108491 | ||||||||
\(874\) | −6.22231 | −0.210473 | ||||||||
\(875\) | −18.5138 | −0.625880 | ||||||||
\(876\) | −3.33917 | −0.112820 | ||||||||
\(877\) | 0.468896 | 0.0158335 | 0.00791675 | − | 0.999969i | \(-0.497480\pi\) | ||||
0.00791675 | + | 0.999969i | \(0.497480\pi\) | |||||||
\(878\) | 13.3069 | 0.449087 | ||||||||
\(879\) | 16.3534 | 0.551586 | ||||||||
\(880\) | −11.1165 | −0.374739 | ||||||||
\(881\) | −36.5735 | −1.23219 | −0.616096 | − | 0.787671i | \(-0.711287\pi\) | ||||
−0.616096 | + | 0.787671i | \(0.711287\pi\) | |||||||
\(882\) | 2.92102 | 0.0983560 | ||||||||
\(883\) | −34.1591 | −1.14954 | −0.574772 | − | 0.818313i | \(-0.694909\pi\) | ||||
−0.574772 | + | 0.818313i | \(0.694909\pi\) | |||||||
\(884\) | 24.0580 | 0.809158 | ||||||||
\(885\) | −51.3907 | −1.72748 | ||||||||
\(886\) | 15.0992 | 0.507268 | ||||||||
\(887\) | −48.8571 | −1.64046 | −0.820230 | − | 0.572034i | \(-0.806155\pi\) | ||||
−0.820230 | + | 0.572034i | \(0.806155\pi\) | |||||||
\(888\) | −5.05935 | −0.169781 | ||||||||
\(889\) | 25.0244 | 0.839291 | ||||||||
\(890\) | −10.9397 | −0.366699 | ||||||||
\(891\) | 14.0863 | 0.471908 | ||||||||
\(892\) | −4.53033 | −0.151687 | ||||||||
\(893\) | 0.829211 | 0.0277485 | ||||||||
\(894\) | −2.29017 | −0.0765948 | ||||||||
\(895\) | −87.6727 | −2.93057 | ||||||||
\(896\) | −2.08526 | −0.0696635 | ||||||||
\(897\) | 34.2727 | 1.14433 | ||||||||
\(898\) | 7.48980 | 0.249938 | ||||||||
\(899\) | −45.2581 | −1.50944 | ||||||||
\(900\) | −8.27294 | −0.275765 | ||||||||
\(901\) | −23.4715 | −0.781948 | ||||||||
\(902\) | −28.1575 | −0.937541 | ||||||||
\(903\) | −0.874170 | −0.0290906 | ||||||||
\(904\) | −1.47352 | −0.0490087 | ||||||||
\(905\) | −8.57618 | −0.285082 | ||||||||
\(906\) | 7.95106 | 0.264156 | ||||||||
\(907\) | −0.521839 | −0.0173274 | −0.00866370 | − | 0.999962i | \(-0.502758\pi\) | ||||
−0.00866370 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(908\) | −4.60548 | −0.152838 | ||||||||
\(909\) | 1.43762 | 0.0476828 | ||||||||
\(910\) | 29.4842 | 0.977391 | ||||||||
\(911\) | −12.0419 | −0.398967 | −0.199484 | − | 0.979901i | \(-0.563926\pi\) | ||||
−0.199484 | + | 0.979901i | \(0.563926\pi\) | |||||||
\(912\) | 1.37784 | 0.0456247 | ||||||||
\(913\) | −40.4271 | −1.33794 | ||||||||
\(914\) | −13.3573 | −0.441819 | ||||||||
\(915\) | 10.0814 | 0.333280 | ||||||||
\(916\) | −18.8360 | −0.622359 | ||||||||
\(917\) | 17.4649 | 0.576743 | ||||||||
\(918\) | 34.0102 | 1.12250 | ||||||||
\(919\) | 45.3593 | 1.49626 | 0.748132 | − | 0.663550i | \(-0.230951\pi\) | ||||
0.748132 | + | 0.663550i | \(0.230951\pi\) | |||||||
\(920\) | −22.0082 | −0.725587 | ||||||||
\(921\) | 0.280297 | 0.00923611 | ||||||||
\(922\) | −29.7300 | −0.979106 | ||||||||
\(923\) | 6.46075 | 0.212658 | ||||||||
\(924\) | 9.03016 | 0.297071 | ||||||||
\(925\) | −27.5770 | −0.906726 | ||||||||
\(926\) | −15.9808 | −0.525162 | ||||||||
\(927\) | 13.5945 | 0.446503 | ||||||||
\(928\) | −6.86242 | −0.225270 | ||||||||
\(929\) | −21.1047 | −0.692421 | −0.346211 | − | 0.938157i | \(-0.612532\pi\) | ||||
−0.346211 | + | 0.938157i | \(0.612532\pi\) | |||||||
\(930\) | 32.1402 | 1.05392 | ||||||||
\(931\) | −2.65170 | −0.0869061 | ||||||||
\(932\) | 13.9203 | 0.455976 | ||||||||
\(933\) | 9.46461 | 0.309857 | ||||||||
\(934\) | 10.1118 | 0.330869 | ||||||||
\(935\) | 66.9008 | 2.18789 | ||||||||
\(936\) | 4.40360 | 0.143936 | ||||||||
\(937\) | 21.8671 | 0.714368 | 0.357184 | − | 0.934034i | \(-0.383737\pi\) | ||||
0.357184 | + | 0.934034i | \(0.383737\pi\) | |||||||
\(938\) | −10.2424 | −0.334426 | ||||||||
\(939\) | 18.3031 | 0.597299 | ||||||||
\(940\) | 2.93290 | 0.0956606 | ||||||||
\(941\) | 9.59255 | 0.312708 | 0.156354 | − | 0.987701i | \(-0.450026\pi\) | ||||
0.156354 | + | 0.987701i | \(0.450026\pi\) | |||||||
\(942\) | −10.8224 | −0.352614 | ||||||||
\(943\) | −55.7452 | −1.81531 | ||||||||
\(944\) | −10.5452 | −0.343217 | ||||||||
\(945\) | 41.6811 | 1.35588 | ||||||||
\(946\) | −0.956261 | −0.0310907 | ||||||||
\(947\) | −34.1196 | −1.10874 | −0.554368 | − | 0.832271i | \(-0.687040\pi\) | ||||
−0.554368 | + | 0.832271i | \(0.687040\pi\) | |||||||
\(948\) | −3.83663 | −0.124608 | ||||||||
\(949\) | 9.68810 | 0.314489 | ||||||||
\(950\) | 7.51017 | 0.243662 | ||||||||
\(951\) | 3.60695 | 0.116963 | ||||||||
\(952\) | 12.5493 | 0.406726 | ||||||||
\(953\) | −41.1267 | −1.33223 | −0.666113 | − | 0.745851i | \(-0.732043\pi\) | ||||
−0.666113 | + | 0.745851i | \(0.732043\pi\) | |||||||
\(954\) | −4.29625 | −0.139096 | ||||||||
\(955\) | 67.3908 | 2.18071 | ||||||||
\(956\) | −1.61370 | −0.0521909 | ||||||||
\(957\) | 29.7176 | 0.960633 | ||||||||
\(958\) | −18.6733 | −0.603306 | ||||||||
\(959\) | 22.4534 | 0.725057 | ||||||||
\(960\) | 4.87337 | 0.157287 | ||||||||
\(961\) | 12.4949 | 0.403062 | ||||||||
\(962\) | 14.6790 | 0.473268 | ||||||||
\(963\) | −1.26647 | −0.0408115 | ||||||||
\(964\) | −5.33913 | −0.171962 | ||||||||
\(965\) | −21.8022 | −0.701838 | ||||||||
\(966\) | 17.8776 | 0.575203 | ||||||||
\(967\) | −48.9448 | −1.57396 | −0.786980 | − | 0.616979i | \(-0.788357\pi\) | ||||
−0.786980 | + | 0.616979i | \(0.788357\pi\) | |||||||
\(968\) | −1.12184 | −0.0360572 | ||||||||
\(969\) | −8.29200 | −0.266377 | ||||||||
\(970\) | 10.2926 | 0.330474 | ||||||||
\(971\) | −51.4521 | −1.65118 | −0.825589 | − | 0.564272i | \(-0.809157\pi\) | ||||
−0.825589 | + | 0.564272i | \(0.809157\pi\) | |||||||
\(972\) | 10.7786 | 0.345723 | ||||||||
\(973\) | −2.97494 | −0.0953720 | ||||||||
\(974\) | 7.80494 | 0.250087 | ||||||||
\(975\) | −41.3662 | −1.32478 | ||||||||
\(976\) | 2.06867 | 0.0662165 | ||||||||
\(977\) | −16.1395 | −0.516349 | −0.258175 | − | 0.966098i | \(-0.583121\pi\) | ||||
−0.258175 | + | 0.966098i | \(0.583121\pi\) | |||||||
\(978\) | −5.66085 | −0.181014 | ||||||||
\(979\) | 9.72100 | 0.310684 | ||||||||
\(980\) | −9.37900 | −0.299601 | ||||||||
\(981\) | −5.03716 | −0.160824 | ||||||||
\(982\) | 30.4261 | 0.970937 | ||||||||
\(983\) | −17.2121 | −0.548981 | −0.274490 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274490 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(984\) | 12.3439 | 0.393510 | ||||||||
\(985\) | 11.9864 | 0.381920 | ||||||||
\(986\) | 41.2989 | 1.31523 | ||||||||
\(987\) | −2.38244 | −0.0758340 | ||||||||
\(988\) | −3.99759 | −0.127180 | ||||||||
\(989\) | −1.89317 | −0.0601994 | ||||||||
\(990\) | 12.2456 | 0.389190 | ||||||||
\(991\) | −6.25321 | −0.198640 | −0.0993198 | − | 0.995056i | \(-0.531667\pi\) | ||||
−0.0993198 | + | 0.995056i | \(0.531667\pi\) | |||||||
\(992\) | 6.59507 | 0.209394 | ||||||||
\(993\) | 2.13616 | 0.0677890 | ||||||||
\(994\) | 3.37011 | 0.106893 | ||||||||
\(995\) | 27.3405 | 0.866751 | ||||||||
\(996\) | 17.7228 | 0.561569 | ||||||||
\(997\) | −10.4092 | −0.329663 | −0.164832 | − | 0.986322i | \(-0.552708\pi\) | ||||
−0.164832 | + | 0.986322i | \(0.552708\pi\) | |||||||
\(998\) | −27.5678 | −0.872644 | ||||||||
\(999\) | 20.7513 | 0.656541 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.d.1.23 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.23 | ✓ | 30 | 1.1 | even | 1 | trivial |