Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.48689336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 7x^{3} + 9x^{2} - 5x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.51181\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.51181 | −1.12332 | −0.561659 | − | 0.827369i | \(-0.689837\pi\) | ||||
−0.561659 | + | 0.827369i | \(0.689837\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.73805 | 0.656919 | 0.328460 | − | 0.944518i | \(-0.393470\pi\) | ||||
0.328460 | + | 0.944518i | \(0.393470\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.51181 | −0.794306 | ||||||||
\(11\) | −0.642525 | −0.193729 | −0.0968643 | − | 0.995298i | \(-0.530881\pi\) | ||||
−0.0968643 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.58371 | −0.716591 | −0.358295 | − | 0.933608i | \(-0.616642\pi\) | ||||
−0.358295 | + | 0.933608i | \(0.616642\pi\) | |||||||
\(14\) | 1.73805 | 0.464512 | ||||||||
\(15\) | −2.51181 | −0.648548 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.71760 | −1.87179 | −0.935896 | − | 0.352276i | \(-0.885408\pi\) | ||||
−0.935896 | + | 0.352276i | \(0.885408\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.51181 | −0.561659 | ||||||||
\(21\) | 1.73805 | 0.379273 | ||||||||
\(22\) | −0.642525 | −0.136987 | ||||||||
\(23\) | 5.46221 | 1.13895 | 0.569475 | − | 0.822009i | \(-0.307147\pi\) | ||||
0.569475 | + | 0.822009i | \(0.307147\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.30921 | 0.261843 | ||||||||
\(26\) | −2.58371 | −0.506706 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.73805 | 0.328460 | ||||||||
\(29\) | 8.07071 | 1.49869 | 0.749347 | − | 0.662178i | \(-0.230368\pi\) | ||||
0.749347 | + | 0.662178i | \(0.230368\pi\) | |||||||
\(30\) | −2.51181 | −0.458593 | ||||||||
\(31\) | −0.677087 | −0.121608 | −0.0608042 | − | 0.998150i | \(-0.519367\pi\) | ||||
−0.0608042 | + | 0.998150i | \(0.519367\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.642525 | −0.111849 | ||||||||
\(34\) | −7.71760 | −1.32356 | ||||||||
\(35\) | −4.36565 | −0.737929 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.32238 | −1.20379 | −0.601896 | − | 0.798575i | \(-0.705588\pi\) | ||||
−0.601896 | + | 0.798575i | \(0.705588\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −2.58371 | −0.413724 | ||||||||
\(40\) | −2.51181 | −0.397153 | ||||||||
\(41\) | −6.11026 | −0.954263 | −0.477131 | − | 0.878832i | \(-0.658323\pi\) | ||||
−0.477131 | + | 0.878832i | \(0.658323\pi\) | |||||||
\(42\) | 1.73805 | 0.268186 | ||||||||
\(43\) | −1.89833 | −0.289492 | −0.144746 | − | 0.989469i | \(-0.546237\pi\) | ||||
−0.144746 | + | 0.989469i | \(0.546237\pi\) | |||||||
\(44\) | −0.642525 | −0.0968643 | ||||||||
\(45\) | −2.51181 | −0.374439 | ||||||||
\(46\) | 5.46221 | 0.805359 | ||||||||
\(47\) | −10.5353 | −1.53673 | −0.768363 | − | 0.640014i | \(-0.778929\pi\) | ||||
−0.768363 | + | 0.640014i | \(0.778929\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.97920 | −0.568457 | ||||||||
\(50\) | 1.30921 | 0.185151 | ||||||||
\(51\) | −7.71760 | −1.08068 | ||||||||
\(52\) | −2.58371 | −0.358295 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.61390 | 0.217619 | ||||||||
\(56\) | 1.73805 | 0.232256 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 8.07071 | 1.05974 | ||||||||
\(59\) | 6.39044 | 0.831965 | 0.415982 | − | 0.909373i | \(-0.363438\pi\) | ||||
0.415982 | + | 0.909373i | \(0.363438\pi\) | |||||||
\(60\) | −2.51181 | −0.324274 | ||||||||
\(61\) | −4.23726 | −0.542526 | −0.271263 | − | 0.962505i | \(-0.587441\pi\) | ||||
−0.271263 | + | 0.962505i | \(0.587441\pi\) | |||||||
\(62\) | −0.677087 | −0.0859901 | ||||||||
\(63\) | 1.73805 | 0.218973 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.48979 | 0.804959 | ||||||||
\(66\) | −0.642525 | −0.0790894 | ||||||||
\(67\) | −12.8611 | −1.57124 | −0.785618 | − | 0.618712i | \(-0.787655\pi\) | ||||
−0.785618 | + | 0.618712i | \(0.787655\pi\) | |||||||
\(68\) | −7.71760 | −0.935896 | ||||||||
\(69\) | 5.46221 | 0.657573 | ||||||||
\(70\) | −4.36565 | −0.521795 | ||||||||
\(71\) | 13.8022 | 1.63802 | 0.819009 | − | 0.573781i | \(-0.194524\pi\) | ||||
0.819009 | + | 0.573781i | \(0.194524\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.86264 | 0.686170 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(74\) | −7.32238 | −0.851209 | ||||||||
\(75\) | 1.30921 | 0.151175 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.11674 | −0.127264 | ||||||||
\(78\) | −2.58371 | −0.292547 | ||||||||
\(79\) | −9.67603 | −1.08864 | −0.544319 | − | 0.838878i | \(-0.683212\pi\) | ||||
−0.544319 | + | 0.838878i | \(0.683212\pi\) | |||||||
\(80\) | −2.51181 | −0.280829 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.11026 | −0.674766 | ||||||||
\(83\) | −0.708381 | −0.0777549 | −0.0388774 | − | 0.999244i | \(-0.512378\pi\) | ||||
−0.0388774 | + | 0.999244i | \(0.512378\pi\) | |||||||
\(84\) | 1.73805 | 0.189636 | ||||||||
\(85\) | 19.3852 | 2.10262 | ||||||||
\(86\) | −1.89833 | −0.204702 | ||||||||
\(87\) | 8.07071 | 0.865271 | ||||||||
\(88\) | −0.642525 | −0.0684934 | ||||||||
\(89\) | 9.33097 | 0.989081 | 0.494540 | − | 0.869155i | \(-0.335336\pi\) | ||||
0.494540 | + | 0.869155i | \(0.335336\pi\) | |||||||
\(90\) | −2.51181 | −0.264769 | ||||||||
\(91\) | −4.49060 | −0.470743 | ||||||||
\(92\) | 5.46221 | 0.569475 | ||||||||
\(93\) | −0.677087 | −0.0702106 | ||||||||
\(94\) | −10.5353 | −1.08663 | ||||||||
\(95\) | 2.51181 | 0.257707 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −13.5187 | −1.37262 | −0.686310 | − | 0.727309i | \(-0.740771\pi\) | ||||
−0.686310 | + | 0.727309i | \(0.740771\pi\) | |||||||
\(98\) | −3.97920 | −0.401960 | ||||||||
\(99\) | −0.642525 | −0.0645762 | ||||||||
\(100\) | 1.30921 | 0.130921 | ||||||||
\(101\) | −13.1581 | −1.30928 | −0.654639 | − | 0.755941i | \(-0.727180\pi\) | ||||
−0.654639 | + | 0.755941i | \(0.727180\pi\) | |||||||
\(102\) | −7.71760 | −0.764156 | ||||||||
\(103\) | −6.90709 | −0.680576 | −0.340288 | − | 0.940321i | \(-0.610525\pi\) | ||||
−0.340288 | + | 0.940321i | \(0.610525\pi\) | |||||||
\(104\) | −2.58371 | −0.253353 | ||||||||
\(105\) | −4.36565 | −0.426044 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −8.90249 | −0.860636 | −0.430318 | − | 0.902677i | \(-0.641599\pi\) | ||||
−0.430318 | + | 0.902677i | \(0.641599\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 5.61503 | 0.537823 | 0.268911 | − | 0.963165i | \(-0.413336\pi\) | ||||
0.268911 | + | 0.963165i | \(0.413336\pi\) | |||||||
\(110\) | 1.61390 | 0.153880 | ||||||||
\(111\) | −7.32238 | −0.695009 | ||||||||
\(112\) | 1.73805 | 0.164230 | ||||||||
\(113\) | −2.37558 | −0.223476 | −0.111738 | − | 0.993738i | \(-0.535642\pi\) | ||||
−0.111738 | + | 0.993738i | \(0.535642\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −13.7201 | −1.27940 | ||||||||
\(116\) | 8.07071 | 0.749347 | ||||||||
\(117\) | −2.58371 | −0.238864 | ||||||||
\(118\) | 6.39044 | 0.588288 | ||||||||
\(119\) | −13.4135 | −1.22962 | ||||||||
\(120\) | −2.51181 | −0.229296 | ||||||||
\(121\) | −10.5872 | −0.962469 | ||||||||
\(122\) | −4.23726 | −0.383624 | ||||||||
\(123\) | −6.11026 | −0.550944 | ||||||||
\(124\) | −0.677087 | −0.0608042 | ||||||||
\(125\) | 9.27057 | 0.829185 | ||||||||
\(126\) | 1.73805 | 0.154837 | ||||||||
\(127\) | −15.6681 | −1.39032 | −0.695160 | − | 0.718855i | \(-0.744667\pi\) | ||||
−0.695160 | + | 0.718855i | \(0.744667\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.89833 | −0.167138 | ||||||||
\(130\) | 6.48979 | 0.569192 | ||||||||
\(131\) | −18.4589 | −1.61276 | −0.806380 | − | 0.591397i | \(-0.798576\pi\) | ||||
−0.806380 | + | 0.591397i | \(0.798576\pi\) | |||||||
\(132\) | −0.642525 | −0.0559246 | ||||||||
\(133\) | −1.73805 | −0.150708 | ||||||||
\(134\) | −12.8611 | −1.11103 | ||||||||
\(135\) | −2.51181 | −0.216183 | ||||||||
\(136\) | −7.71760 | −0.661779 | ||||||||
\(137\) | 3.80218 | 0.324842 | 0.162421 | − | 0.986722i | \(-0.448070\pi\) | ||||
0.162421 | + | 0.986722i | \(0.448070\pi\) | |||||||
\(138\) | 5.46221 | 0.464974 | ||||||||
\(139\) | 16.4985 | 1.39938 | 0.699691 | − | 0.714445i | \(-0.253321\pi\) | ||||
0.699691 | + | 0.714445i | \(0.253321\pi\) | |||||||
\(140\) | −4.36565 | −0.368965 | ||||||||
\(141\) | −10.5353 | −0.887229 | ||||||||
\(142\) | 13.8022 | 1.15825 | ||||||||
\(143\) | 1.66010 | 0.138824 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −20.2721 | −1.68351 | ||||||||
\(146\) | 5.86264 | 0.485195 | ||||||||
\(147\) | −3.97920 | −0.328199 | ||||||||
\(148\) | −7.32238 | −0.601896 | ||||||||
\(149\) | 17.3379 | 1.42037 | 0.710187 | − | 0.704013i | \(-0.248610\pi\) | ||||
0.710187 | + | 0.704013i | \(0.248610\pi\) | |||||||
\(150\) | 1.30921 | 0.106897 | ||||||||
\(151\) | 17.8421 | 1.45197 | 0.725986 | − | 0.687709i | \(-0.241384\pi\) | ||||
0.725986 | + | 0.687709i | \(0.241384\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −7.71760 | −0.623931 | ||||||||
\(154\) | −1.11674 | −0.0899893 | ||||||||
\(155\) | 1.70072 | 0.136605 | ||||||||
\(156\) | −2.58371 | −0.206862 | ||||||||
\(157\) | −0.480011 | −0.0383091 | −0.0191545 | − | 0.999817i | \(-0.506097\pi\) | ||||
−0.0191545 | + | 0.999817i | \(0.506097\pi\) | |||||||
\(158\) | −9.67603 | −0.769783 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | −2.51181 | −0.198576 | ||||||||
\(161\) | 9.49357 | 0.748198 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −23.0963 | −1.80904 | −0.904520 | − | 0.426431i | \(-0.859771\pi\) | ||||
−0.904520 | + | 0.426431i | \(0.859771\pi\) | |||||||
\(164\) | −6.11026 | −0.477131 | ||||||||
\(165\) | 1.61390 | 0.125642 | ||||||||
\(166\) | −0.708381 | −0.0549810 | ||||||||
\(167\) | −14.1792 | −1.09722 | −0.548609 | − | 0.836079i | \(-0.684842\pi\) | ||||
−0.548609 | + | 0.836079i | \(0.684842\pi\) | |||||||
\(168\) | 1.73805 | 0.134093 | ||||||||
\(169\) | −6.32447 | −0.486497 | ||||||||
\(170\) | 19.3852 | 1.48678 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −1.89833 | −0.144746 | ||||||||
\(173\) | 19.5868 | 1.48915 | 0.744577 | − | 0.667537i | \(-0.232651\pi\) | ||||
0.744577 | + | 0.667537i | \(0.232651\pi\) | |||||||
\(174\) | 8.07071 | 0.611839 | ||||||||
\(175\) | 2.27547 | 0.172010 | ||||||||
\(176\) | −0.642525 | −0.0484322 | ||||||||
\(177\) | 6.39044 | 0.480335 | ||||||||
\(178\) | 9.33097 | 0.699386 | ||||||||
\(179\) | −2.28116 | −0.170502 | −0.0852510 | − | 0.996360i | \(-0.527169\pi\) | ||||
−0.0852510 | + | 0.996360i | \(0.527169\pi\) | |||||||
\(180\) | −2.51181 | −0.187220 | ||||||||
\(181\) | −20.3337 | −1.51139 | −0.755696 | − | 0.654922i | \(-0.772701\pi\) | ||||
−0.755696 | + | 0.654922i | \(0.772701\pi\) | |||||||
\(182\) | −4.49060 | −0.332865 | ||||||||
\(183\) | −4.23726 | −0.313228 | ||||||||
\(184\) | 5.46221 | 0.402680 | ||||||||
\(185\) | 18.3925 | 1.35224 | ||||||||
\(186\) | −0.677087 | −0.0496464 | ||||||||
\(187\) | 4.95875 | 0.362620 | ||||||||
\(188\) | −10.5353 | −0.768363 | ||||||||
\(189\) | 1.73805 | 0.126424 | ||||||||
\(190\) | 2.51181 | 0.182226 | ||||||||
\(191\) | 8.19066 | 0.592655 | 0.296328 | − | 0.955086i | \(-0.404238\pi\) | ||||
0.296328 | + | 0.955086i | \(0.404238\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 5.39374 | 0.388250 | 0.194125 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194125 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(194\) | −13.5187 | −0.970590 | ||||||||
\(195\) | 6.48979 | 0.464744 | ||||||||
\(196\) | −3.97920 | −0.284228 | ||||||||
\(197\) | −0.633256 | −0.0451176 | −0.0225588 | − | 0.999746i | \(-0.507181\pi\) | ||||
−0.0225588 | + | 0.999746i | \(0.507181\pi\) | |||||||
\(198\) | −0.642525 | −0.0456623 | ||||||||
\(199\) | 14.4610 | 1.02511 | 0.512557 | − | 0.858653i | \(-0.328699\pi\) | ||||
0.512557 | + | 0.858653i | \(0.328699\pi\) | |||||||
\(200\) | 1.30921 | 0.0925754 | ||||||||
\(201\) | −12.8611 | −0.907154 | ||||||||
\(202\) | −13.1581 | −0.925800 | ||||||||
\(203\) | 14.0273 | 0.984521 | ||||||||
\(204\) | −7.71760 | −0.540340 | ||||||||
\(205\) | 15.3478 | 1.07194 | ||||||||
\(206\) | −6.90709 | −0.481240 | ||||||||
\(207\) | 5.46221 | 0.379650 | ||||||||
\(208\) | −2.58371 | −0.179148 | ||||||||
\(209\) | 0.642525 | 0.0444444 | ||||||||
\(210\) | −4.36565 | −0.301258 | ||||||||
\(211\) | 15.5116 | 1.06786 | 0.533931 | − | 0.845528i | \(-0.320714\pi\) | ||||
0.533931 | + | 0.845528i | \(0.320714\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 13.8022 | 0.945710 | ||||||||
\(214\) | −8.90249 | −0.608562 | ||||||||
\(215\) | 4.76824 | 0.325192 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.17681 | −0.0798869 | ||||||||
\(218\) | 5.61503 | 0.380298 | ||||||||
\(219\) | 5.86264 | 0.396160 | ||||||||
\(220\) | 1.61390 | 0.108809 | ||||||||
\(221\) | 19.9400 | 1.34131 | ||||||||
\(222\) | −7.32238 | −0.491446 | ||||||||
\(223\) | −15.6842 | −1.05029 | −0.525147 | − | 0.851012i | \(-0.675990\pi\) | ||||
−0.525147 | + | 0.851012i | \(0.675990\pi\) | |||||||
\(224\) | 1.73805 | 0.116128 | ||||||||
\(225\) | 1.30921 | 0.0872810 | ||||||||
\(226\) | −2.37558 | −0.158021 | ||||||||
\(227\) | −4.07495 | −0.270464 | −0.135232 | − | 0.990814i | \(-0.543178\pi\) | ||||
−0.135232 | + | 0.990814i | \(0.543178\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | −14.8872 | −0.983777 | −0.491889 | − | 0.870658i | \(-0.663693\pi\) | ||||
−0.491889 | + | 0.870658i | \(0.663693\pi\) | |||||||
\(230\) | −13.7201 | −0.904674 | ||||||||
\(231\) | −1.11674 | −0.0734760 | ||||||||
\(232\) | 8.07071 | 0.529868 | ||||||||
\(233\) | 15.0002 | 0.982697 | 0.491348 | − | 0.870963i | \(-0.336504\pi\) | ||||
0.491348 | + | 0.870963i | \(0.336504\pi\) | |||||||
\(234\) | −2.58371 | −0.168902 | ||||||||
\(235\) | 26.4626 | 1.72623 | ||||||||
\(236\) | 6.39044 | 0.415982 | ||||||||
\(237\) | −9.67603 | −0.628525 | ||||||||
\(238\) | −13.4135 | −0.869470 | ||||||||
\(239\) | −5.82577 | −0.376838 | −0.188419 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188419 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(240\) | −2.51181 | −0.162137 | ||||||||
\(241\) | 6.25361 | 0.402830 | 0.201415 | − | 0.979506i | \(-0.435446\pi\) | ||||
0.201415 | + | 0.979506i | \(0.435446\pi\) | |||||||
\(242\) | −10.5872 | −0.680569 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.23726 | −0.271263 | ||||||||
\(245\) | 9.99501 | 0.638558 | ||||||||
\(246\) | −6.11026 | −0.389576 | ||||||||
\(247\) | 2.58371 | 0.164397 | ||||||||
\(248\) | −0.677087 | −0.0429951 | ||||||||
\(249\) | −0.708381 | −0.0448918 | ||||||||
\(250\) | 9.27057 | 0.586322 | ||||||||
\(251\) | 15.9849 | 1.00896 | 0.504480 | − | 0.863423i | \(-0.331684\pi\) | ||||
0.504480 | + | 0.863423i | \(0.331684\pi\) | |||||||
\(252\) | 1.73805 | 0.109487 | ||||||||
\(253\) | −3.50961 | −0.220647 | ||||||||
\(254\) | −15.6681 | −0.983105 | ||||||||
\(255\) | 19.3852 | 1.21395 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.64274 | 0.476741 | 0.238370 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238370 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(258\) | −1.89833 | −0.118185 | ||||||||
\(259\) | −12.7266 | −0.790794 | ||||||||
\(260\) | 6.48979 | 0.402480 | ||||||||
\(261\) | 8.07071 | 0.499564 | ||||||||
\(262\) | −18.4589 | −1.14039 | ||||||||
\(263\) | 7.70372 | 0.475032 | 0.237516 | − | 0.971384i | \(-0.423667\pi\) | ||||
0.237516 | + | 0.971384i | \(0.423667\pi\) | |||||||
\(264\) | −0.642525 | −0.0395447 | ||||||||
\(265\) | 2.51181 | 0.154300 | ||||||||
\(266\) | −1.73805 | −0.106566 | ||||||||
\(267\) | 9.33097 | 0.571046 | ||||||||
\(268\) | −12.8611 | −0.785618 | ||||||||
\(269\) | 18.4670 | 1.12595 | 0.562977 | − | 0.826473i | \(-0.309656\pi\) | ||||
0.562977 | + | 0.826473i | \(0.309656\pi\) | |||||||
\(270\) | −2.51181 | −0.152864 | ||||||||
\(271\) | −6.67605 | −0.405541 | −0.202771 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202771 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(272\) | −7.71760 | −0.467948 | ||||||||
\(273\) | −4.49060 | −0.271783 | ||||||||
\(274\) | 3.80218 | 0.229698 | ||||||||
\(275\) | −0.841203 | −0.0507265 | ||||||||
\(276\) | 5.46221 | 0.328787 | ||||||||
\(277\) | −7.19303 | −0.432188 | −0.216094 | − | 0.976373i | \(-0.569332\pi\) | ||||
−0.216094 | + | 0.976373i | \(0.569332\pi\) | |||||||
\(278\) | 16.4985 | 0.989513 | ||||||||
\(279\) | −0.677087 | −0.0405361 | ||||||||
\(280\) | −4.36565 | −0.260897 | ||||||||
\(281\) | −20.6372 | −1.23111 | −0.615557 | − | 0.788092i | \(-0.711069\pi\) | ||||
−0.615557 | + | 0.788092i | \(0.711069\pi\) | |||||||
\(282\) | −10.5353 | −0.627366 | ||||||||
\(283\) | 10.1190 | 0.601512 | 0.300756 | − | 0.953701i | \(-0.402761\pi\) | ||||
0.300756 | + | 0.953701i | \(0.402761\pi\) | |||||||
\(284\) | 13.8022 | 0.819009 | ||||||||
\(285\) | 2.51181 | 0.148787 | ||||||||
\(286\) | 1.66010 | 0.0981635 | ||||||||
\(287\) | −10.6199 | −0.626874 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 42.5613 | 2.50361 | ||||||||
\(290\) | −20.2721 | −1.19042 | ||||||||
\(291\) | −13.5187 | −0.792483 | ||||||||
\(292\) | 5.86264 | 0.343085 | ||||||||
\(293\) | −11.1099 | −0.649050 | −0.324525 | − | 0.945877i | \(-0.605204\pi\) | ||||
−0.324525 | + | 0.945877i | \(0.605204\pi\) | |||||||
\(294\) | −3.97920 | −0.232072 | ||||||||
\(295\) | −16.0516 | −0.934561 | ||||||||
\(296\) | −7.32238 | −0.425605 | ||||||||
\(297\) | −0.642525 | −0.0372831 | ||||||||
\(298\) | 17.3379 | 1.00436 | ||||||||
\(299\) | −14.1127 | −0.816161 | ||||||||
\(300\) | 1.30921 | 0.0755875 | ||||||||
\(301\) | −3.29938 | −0.190173 | ||||||||
\(302\) | 17.8421 | 1.02670 | ||||||||
\(303\) | −13.1581 | −0.755913 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 10.6432 | 0.609429 | ||||||||
\(306\) | −7.71760 | −0.441186 | ||||||||
\(307\) | −29.0392 | −1.65735 | −0.828677 | − | 0.559727i | \(-0.810906\pi\) | ||||
−0.828677 | + | 0.559727i | \(0.810906\pi\) | |||||||
\(308\) | −1.11674 | −0.0636320 | ||||||||
\(309\) | −6.90709 | −0.392931 | ||||||||
\(310\) | 1.70072 | 0.0965942 | ||||||||
\(311\) | −30.7392 | −1.74306 | −0.871530 | − | 0.490343i | \(-0.836872\pi\) | ||||
−0.871530 | + | 0.490343i | \(0.836872\pi\) | |||||||
\(312\) | −2.58371 | −0.146274 | ||||||||
\(313\) | −2.12783 | −0.120272 | −0.0601361 | − | 0.998190i | \(-0.519153\pi\) | ||||
−0.0601361 | + | 0.998190i | \(0.519153\pi\) | |||||||
\(314\) | −0.480011 | −0.0270886 | ||||||||
\(315\) | −4.36565 | −0.245976 | ||||||||
\(316\) | −9.67603 | −0.544319 | ||||||||
\(317\) | −27.0644 | −1.52009 | −0.760043 | − | 0.649873i | \(-0.774822\pi\) | ||||
−0.760043 | + | 0.649873i | \(0.774822\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −5.18563 | −0.290340 | ||||||||
\(320\) | −2.51181 | −0.140415 | ||||||||
\(321\) | −8.90249 | −0.496889 | ||||||||
\(322\) | 9.49357 | 0.529056 | ||||||||
\(323\) | 7.71760 | 0.429419 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.38262 | −0.187634 | ||||||||
\(326\) | −23.0963 | −1.27918 | ||||||||
\(327\) | 5.61503 | 0.310512 | ||||||||
\(328\) | −6.11026 | −0.337383 | ||||||||
\(329\) | −18.3108 | −1.00951 | ||||||||
\(330\) | 1.61390 | 0.0888425 | ||||||||
\(331\) | 2.20656 | 0.121284 | 0.0606419 | − | 0.998160i | \(-0.480685\pi\) | ||||
0.0606419 | + | 0.998160i | \(0.480685\pi\) | |||||||
\(332\) | −0.708381 | −0.0388774 | ||||||||
\(333\) | −7.32238 | −0.401264 | ||||||||
\(334\) | −14.1792 | −0.775850 | ||||||||
\(335\) | 32.3048 | 1.76500 | ||||||||
\(336\) | 1.73805 | 0.0948182 | ||||||||
\(337\) | −22.5004 | −1.22568 | −0.612838 | − | 0.790209i | \(-0.709972\pi\) | ||||
−0.612838 | + | 0.790209i | \(0.709972\pi\) | |||||||
\(338\) | −6.32447 | −0.344006 | ||||||||
\(339\) | −2.37558 | −0.129024 | ||||||||
\(340\) | 19.3852 | 1.05131 | ||||||||
\(341\) | 0.435045 | 0.0235590 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −19.0823 | −1.03035 | ||||||||
\(344\) | −1.89833 | −0.102351 | ||||||||
\(345\) | −13.7201 | −0.738664 | ||||||||
\(346\) | 19.5868 | 1.05299 | ||||||||
\(347\) | 5.83468 | 0.313222 | 0.156611 | − | 0.987660i | \(-0.449943\pi\) | ||||
0.156611 | + | 0.987660i | \(0.449943\pi\) | |||||||
\(348\) | 8.07071 | 0.432635 | ||||||||
\(349\) | 15.7691 | 0.844103 | 0.422052 | − | 0.906572i | \(-0.361310\pi\) | ||||
0.422052 | + | 0.906572i | \(0.361310\pi\) | |||||||
\(350\) | 2.27547 | 0.121629 | ||||||||
\(351\) | −2.58371 | −0.137908 | ||||||||
\(352\) | −0.642525 | −0.0342467 | ||||||||
\(353\) | 18.4969 | 0.984491 | 0.492245 | − | 0.870456i | \(-0.336176\pi\) | ||||
0.492245 | + | 0.870456i | \(0.336176\pi\) | |||||||
\(354\) | 6.39044 | 0.339648 | ||||||||
\(355\) | −34.6685 | −1.84002 | ||||||||
\(356\) | 9.33097 | 0.494540 | ||||||||
\(357\) | −13.4135 | −0.709920 | ||||||||
\(358\) | −2.28116 | −0.120563 | ||||||||
\(359\) | −3.10195 | −0.163715 | −0.0818574 | − | 0.996644i | \(-0.526085\pi\) | ||||
−0.0818574 | + | 0.996644i | \(0.526085\pi\) | |||||||
\(360\) | −2.51181 | −0.132384 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −20.3337 | −1.06872 | ||||||||
\(363\) | −10.5872 | −0.555682 | ||||||||
\(364\) | −4.49060 | −0.235371 | ||||||||
\(365\) | −14.7259 | −0.770787 | ||||||||
\(366\) | −4.23726 | −0.221485 | ||||||||
\(367\) | 12.3041 | 0.642268 | 0.321134 | − | 0.947034i | \(-0.395936\pi\) | ||||
0.321134 | + | 0.947034i | \(0.395936\pi\) | |||||||
\(368\) | 5.46221 | 0.284738 | ||||||||
\(369\) | −6.11026 | −0.318088 | ||||||||
\(370\) | 18.3925 | 0.956179 | ||||||||
\(371\) | −1.73805 | −0.0902348 | ||||||||
\(372\) | −0.677087 | −0.0351053 | ||||||||
\(373\) | 10.1898 | 0.527606 | 0.263803 | − | 0.964577i | \(-0.415023\pi\) | ||||
0.263803 | + | 0.964577i | \(0.415023\pi\) | |||||||
\(374\) | 4.95875 | 0.256411 | ||||||||
\(375\) | 9.27057 | 0.478730 | ||||||||
\(376\) | −10.5353 | −0.543315 | ||||||||
\(377\) | −20.8523 | −1.07395 | ||||||||
\(378\) | 1.73805 | 0.0893954 | ||||||||
\(379\) | 6.85298 | 0.352014 | 0.176007 | − | 0.984389i | \(-0.443682\pi\) | ||||
0.176007 | + | 0.984389i | \(0.443682\pi\) | |||||||
\(380\) | 2.51181 | 0.128853 | ||||||||
\(381\) | −15.6681 | −0.802702 | ||||||||
\(382\) | 8.19066 | 0.419071 | ||||||||
\(383\) | −20.4129 | −1.04305 | −0.521524 | − | 0.853237i | \(-0.674636\pi\) | ||||
−0.521524 | + | 0.853237i | \(0.674636\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.80504 | 0.142958 | ||||||||
\(386\) | 5.39374 | 0.274534 | ||||||||
\(387\) | −1.89833 | −0.0964973 | ||||||||
\(388\) | −13.5187 | −0.686310 | ||||||||
\(389\) | −3.44093 | −0.174462 | −0.0872310 | − | 0.996188i | \(-0.527802\pi\) | ||||
−0.0872310 | + | 0.996188i | \(0.527802\pi\) | |||||||
\(390\) | 6.48979 | 0.328623 | ||||||||
\(391\) | −42.1552 | −2.13188 | ||||||||
\(392\) | −3.97920 | −0.200980 | ||||||||
\(393\) | −18.4589 | −0.931128 | ||||||||
\(394\) | −0.633256 | −0.0319030 | ||||||||
\(395\) | 24.3044 | 1.22289 | ||||||||
\(396\) | −0.642525 | −0.0322881 | ||||||||
\(397\) | 20.7359 | 1.04071 | 0.520353 | − | 0.853951i | \(-0.325800\pi\) | ||||
0.520353 | + | 0.853951i | \(0.325800\pi\) | |||||||
\(398\) | 14.4610 | 0.724864 | ||||||||
\(399\) | −1.73805 | −0.0870111 | ||||||||
\(400\) | 1.30921 | 0.0654607 | ||||||||
\(401\) | 5.53945 | 0.276627 | 0.138314 | − | 0.990388i | \(-0.455832\pi\) | ||||
0.138314 | + | 0.990388i | \(0.455832\pi\) | |||||||
\(402\) | −12.8611 | −0.641455 | ||||||||
\(403\) | 1.74939 | 0.0871435 | ||||||||
\(404\) | −13.1581 | −0.654639 | ||||||||
\(405\) | −2.51181 | −0.124813 | ||||||||
\(406\) | 14.0273 | 0.696161 | ||||||||
\(407\) | 4.70481 | 0.233209 | ||||||||
\(408\) | −7.71760 | −0.382078 | ||||||||
\(409\) | 10.6100 | 0.524631 | 0.262315 | − | 0.964982i | \(-0.415514\pi\) | ||||
0.262315 | + | 0.964982i | \(0.415514\pi\) | |||||||
\(410\) | 15.3478 | 0.757976 | ||||||||
\(411\) | 3.80218 | 0.187548 | ||||||||
\(412\) | −6.90709 | −0.340288 | ||||||||
\(413\) | 11.1069 | 0.546534 | ||||||||
\(414\) | 5.46221 | 0.268453 | ||||||||
\(415\) | 1.77932 | 0.0873435 | ||||||||
\(416\) | −2.58371 | −0.126677 | ||||||||
\(417\) | 16.4985 | 0.807934 | ||||||||
\(418\) | 0.642525 | 0.0314269 | ||||||||
\(419\) | −2.58451 | −0.126262 | −0.0631309 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631309 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(420\) | −4.36565 | −0.213022 | ||||||||
\(421\) | 29.8910 | 1.45680 | 0.728399 | − | 0.685153i | \(-0.240265\pi\) | ||||
0.728399 | + | 0.685153i | \(0.240265\pi\) | |||||||
\(422\) | 15.5116 | 0.755092 | ||||||||
\(423\) | −10.5353 | −0.512242 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | −10.1040 | −0.490116 | ||||||||
\(426\) | 13.8022 | 0.668718 | ||||||||
\(427\) | −7.36456 | −0.356396 | ||||||||
\(428\) | −8.90249 | −0.430318 | ||||||||
\(429\) | 1.66010 | 0.0801502 | ||||||||
\(430\) | 4.76824 | 0.229945 | ||||||||
\(431\) | 15.2898 | 0.736486 | 0.368243 | − | 0.929730i | \(-0.379959\pi\) | ||||
0.368243 | + | 0.929730i | \(0.379959\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.06601 | −0.0512292 | −0.0256146 | − | 0.999672i | \(-0.508154\pi\) | ||||
−0.0256146 | + | 0.999672i | \(0.508154\pi\) | |||||||
\(434\) | −1.17681 | −0.0564886 | ||||||||
\(435\) | −20.2721 | −0.971974 | ||||||||
\(436\) | 5.61503 | 0.268911 | ||||||||
\(437\) | −5.46221 | −0.261293 | ||||||||
\(438\) | 5.86264 | 0.280128 | ||||||||
\(439\) | −13.9808 | −0.667265 | −0.333632 | − | 0.942703i | \(-0.608274\pi\) | ||||
−0.333632 | + | 0.942703i | \(0.608274\pi\) | |||||||
\(440\) | 1.61390 | 0.0769399 | ||||||||
\(441\) | −3.97920 | −0.189486 | ||||||||
\(442\) | 19.9400 | 0.948449 | ||||||||
\(443\) | 24.7683 | 1.17678 | 0.588388 | − | 0.808579i | \(-0.299763\pi\) | ||||
0.588388 | + | 0.808579i | \(0.299763\pi\) | |||||||
\(444\) | −7.32238 | −0.347505 | ||||||||
\(445\) | −23.4377 | −1.11105 | ||||||||
\(446\) | −15.6842 | −0.742670 | ||||||||
\(447\) | 17.3379 | 0.820053 | ||||||||
\(448\) | 1.73805 | 0.0821149 | ||||||||
\(449\) | 38.3823 | 1.81137 | 0.905687 | − | 0.423948i | \(-0.139356\pi\) | ||||
0.905687 | + | 0.423948i | \(0.139356\pi\) | |||||||
\(450\) | 1.30921 | 0.0617170 | ||||||||
\(451\) | 3.92600 | 0.184868 | ||||||||
\(452\) | −2.37558 | −0.111738 | ||||||||
\(453\) | 17.8421 | 0.838297 | ||||||||
\(454\) | −4.07495 | −0.191247 | ||||||||
\(455\) | 11.2795 | 0.528793 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 7.38642 | 0.345522 | 0.172761 | − | 0.984964i | \(-0.444731\pi\) | ||||
0.172761 | + | 0.984964i | \(0.444731\pi\) | |||||||
\(458\) | −14.8872 | −0.695635 | ||||||||
\(459\) | −7.71760 | −0.360227 | ||||||||
\(460\) | −13.7201 | −0.639701 | ||||||||
\(461\) | 15.1036 | 0.703444 | 0.351722 | − | 0.936104i | \(-0.385596\pi\) | ||||
0.351722 | + | 0.936104i | \(0.385596\pi\) | |||||||
\(462\) | −1.11674 | −0.0519553 | ||||||||
\(463\) | −36.1124 | −1.67829 | −0.839143 | − | 0.543911i | \(-0.816943\pi\) | ||||
−0.839143 | + | 0.543911i | \(0.816943\pi\) | |||||||
\(464\) | 8.07071 | 0.374673 | ||||||||
\(465\) | 1.70072 | 0.0788688 | ||||||||
\(466\) | 15.0002 | 0.694871 | ||||||||
\(467\) | 0.364195 | 0.0168529 | 0.00842647 | − | 0.999964i | \(-0.497318\pi\) | ||||
0.00842647 | + | 0.999964i | \(0.497318\pi\) | |||||||
\(468\) | −2.58371 | −0.119432 | ||||||||
\(469\) | −22.3532 | −1.03218 | ||||||||
\(470\) | 26.4626 | 1.22063 | ||||||||
\(471\) | −0.480011 | −0.0221178 | ||||||||
\(472\) | 6.39044 | 0.294144 | ||||||||
\(473\) | 1.21972 | 0.0560829 | ||||||||
\(474\) | −9.67603 | −0.444435 | ||||||||
\(475\) | −1.30921 | −0.0600709 | ||||||||
\(476\) | −13.4135 | −0.614808 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | −5.82577 | −0.266465 | ||||||||
\(479\) | 30.1157 | 1.37602 | 0.688011 | − | 0.725701i | \(-0.258484\pi\) | ||||
0.688011 | + | 0.725701i | \(0.258484\pi\) | |||||||
\(480\) | −2.51181 | −0.114648 | ||||||||
\(481\) | 18.9189 | 0.862626 | ||||||||
\(482\) | 6.25361 | 0.284844 | ||||||||
\(483\) | 9.49357 | 0.431973 | ||||||||
\(484\) | −10.5872 | −0.481235 | ||||||||
\(485\) | 33.9566 | 1.54189 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 29.7321 | 1.34729 | 0.673646 | − | 0.739054i | \(-0.264727\pi\) | ||||
0.673646 | + | 0.739054i | \(0.264727\pi\) | |||||||
\(488\) | −4.23726 | −0.191812 | ||||||||
\(489\) | −23.0963 | −1.04445 | ||||||||
\(490\) | 9.99501 | 0.451528 | ||||||||
\(491\) | −0.905199 | −0.0408511 | −0.0204255 | − | 0.999791i | \(-0.506502\pi\) | ||||
−0.0204255 | + | 0.999791i | \(0.506502\pi\) | |||||||
\(492\) | −6.11026 | −0.275472 | ||||||||
\(493\) | −62.2865 | −2.80524 | ||||||||
\(494\) | 2.58371 | 0.116246 | ||||||||
\(495\) | 1.61390 | 0.0725396 | ||||||||
\(496\) | −0.677087 | −0.0304021 | ||||||||
\(497\) | 23.9888 | 1.07605 | ||||||||
\(498\) | −0.708381 | −0.0317433 | ||||||||
\(499\) | −28.5614 | −1.27859 | −0.639293 | − | 0.768964i | \(-0.720773\pi\) | ||||
−0.639293 | + | 0.768964i | \(0.720773\pi\) | |||||||
\(500\) | 9.27057 | 0.414593 | ||||||||
\(501\) | −14.1792 | −0.633479 | ||||||||
\(502\) | 15.9849 | 0.713443 | ||||||||
\(503\) | −12.3975 | −0.552775 | −0.276388 | − | 0.961046i | \(-0.589137\pi\) | ||||
−0.276388 | + | 0.961046i | \(0.589137\pi\) | |||||||
\(504\) | 1.73805 | 0.0774187 | ||||||||
\(505\) | 33.0507 | 1.47074 | ||||||||
\(506\) | −3.50961 | −0.156021 | ||||||||
\(507\) | −6.32447 | −0.280879 | ||||||||
\(508\) | −15.6681 | −0.695160 | ||||||||
\(509\) | −30.7216 | −1.36171 | −0.680855 | − | 0.732419i | \(-0.738391\pi\) | ||||
−0.680855 | + | 0.732419i | \(0.738391\pi\) | |||||||
\(510\) | 19.3852 | 0.858390 | ||||||||
\(511\) | 10.1895 | 0.450758 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 7.64274 | 0.337107 | ||||||||
\(515\) | 17.3493 | 0.764503 | ||||||||
\(516\) | −1.89833 | −0.0835692 | ||||||||
\(517\) | 6.76917 | 0.297708 | ||||||||
\(518\) | −12.7266 | −0.559176 | ||||||||
\(519\) | 19.5868 | 0.859763 | ||||||||
\(520\) | 6.48979 | 0.284596 | ||||||||
\(521\) | −6.28277 | −0.275253 | −0.137627 | − | 0.990484i | \(-0.543947\pi\) | ||||
−0.137627 | + | 0.990484i | \(0.543947\pi\) | |||||||
\(522\) | 8.07071 | 0.353245 | ||||||||
\(523\) | 10.3593 | 0.452979 | 0.226490 | − | 0.974014i | \(-0.427275\pi\) | ||||
0.226490 | + | 0.974014i | \(0.427275\pi\) | |||||||
\(524\) | −18.4589 | −0.806380 | ||||||||
\(525\) | 2.27547 | 0.0993098 | ||||||||
\(526\) | 7.70372 | 0.335898 | ||||||||
\(527\) | 5.22548 | 0.227626 | ||||||||
\(528\) | −0.642525 | −0.0279623 | ||||||||
\(529\) | 6.83577 | 0.297207 | ||||||||
\(530\) | 2.51181 | 0.109106 | ||||||||
\(531\) | 6.39044 | 0.277322 | ||||||||
\(532\) | −1.73805 | −0.0753538 | ||||||||
\(533\) | 15.7871 | 0.683816 | ||||||||
\(534\) | 9.33097 | 0.403790 | ||||||||
\(535\) | 22.3614 | 0.966768 | ||||||||
\(536\) | −12.8611 | −0.555516 | ||||||||
\(537\) | −2.28116 | −0.0984394 | ||||||||
\(538\) | 18.4670 | 0.796170 | ||||||||
\(539\) | 2.55673 | 0.110126 | ||||||||
\(540\) | −2.51181 | −0.108091 | ||||||||
\(541\) | 14.8604 | 0.638897 | 0.319449 | − | 0.947604i | \(-0.396502\pi\) | ||||
0.319449 | + | 0.947604i | \(0.396502\pi\) | |||||||
\(542\) | −6.67605 | −0.286761 | ||||||||
\(543\) | −20.3337 | −0.872603 | ||||||||
\(544\) | −7.71760 | −0.330889 | ||||||||
\(545\) | −14.1039 | −0.604146 | ||||||||
\(546\) | −4.49060 | −0.192180 | ||||||||
\(547\) | 35.3324 | 1.51071 | 0.755353 | − | 0.655318i | \(-0.227466\pi\) | ||||
0.755353 | + | 0.655318i | \(0.227466\pi\) | |||||||
\(548\) | 3.80218 | 0.162421 | ||||||||
\(549\) | −4.23726 | −0.180842 | ||||||||
\(550\) | −0.841203 | −0.0358690 | ||||||||
\(551\) | −8.07071 | −0.343824 | ||||||||
\(552\) | 5.46221 | 0.232487 | ||||||||
\(553\) | −16.8174 | −0.715147 | ||||||||
\(554\) | −7.19303 | −0.305603 | ||||||||
\(555\) | 18.3925 | 0.780716 | ||||||||
\(556\) | 16.4985 | 0.699691 | ||||||||
\(557\) | −38.4565 | −1.62946 | −0.814728 | − | 0.579843i | \(-0.803114\pi\) | ||||
−0.814728 | + | 0.579843i | \(0.803114\pi\) | |||||||
\(558\) | −0.677087 | −0.0286634 | ||||||||
\(559\) | 4.90472 | 0.207447 | ||||||||
\(560\) | −4.36565 | −0.184482 | ||||||||
\(561\) | 4.95875 | 0.209359 | ||||||||
\(562\) | −20.6372 | −0.870530 | ||||||||
\(563\) | −14.2639 | −0.601153 | −0.300577 | − | 0.953758i | \(-0.597179\pi\) | ||||
−0.300577 | + | 0.953758i | \(0.597179\pi\) | |||||||
\(564\) | −10.5353 | −0.443615 | ||||||||
\(565\) | 5.96702 | 0.251034 | ||||||||
\(566\) | 10.1190 | 0.425333 | ||||||||
\(567\) | 1.73805 | 0.0729910 | ||||||||
\(568\) | 13.8022 | 0.579127 | ||||||||
\(569\) | 36.6158 | 1.53501 | 0.767507 | − | 0.641041i | \(-0.221497\pi\) | ||||
0.767507 | + | 0.641041i | \(0.221497\pi\) | |||||||
\(570\) | 2.51181 | 0.105208 | ||||||||
\(571\) | −21.1733 | −0.886077 | −0.443038 | − | 0.896503i | \(-0.646099\pi\) | ||||
−0.443038 | + | 0.896503i | \(0.646099\pi\) | |||||||
\(572\) | 1.66010 | 0.0694121 | ||||||||
\(573\) | 8.19066 | 0.342170 | ||||||||
\(574\) | −10.6199 | −0.443267 | ||||||||
\(575\) | 7.15121 | 0.298226 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.8741 | −1.82650 | −0.913252 | − | 0.407396i | \(-0.866437\pi\) | ||||
−0.913252 | + | 0.407396i | \(0.866437\pi\) | |||||||
\(578\) | 42.5613 | 1.77032 | ||||||||
\(579\) | 5.39374 | 0.224156 | ||||||||
\(580\) | −20.2721 | −0.841754 | ||||||||
\(581\) | −1.23120 | −0.0510787 | ||||||||
\(582\) | −13.5187 | −0.560370 | ||||||||
\(583\) | 0.642525 | 0.0266107 | ||||||||
\(584\) | 5.86264 | 0.242598 | ||||||||
\(585\) | 6.48979 | 0.268320 | ||||||||
\(586\) | −11.1099 | −0.458947 | ||||||||
\(587\) | 15.0810 | 0.622460 | 0.311230 | − | 0.950335i | \(-0.399259\pi\) | ||||
0.311230 | + | 0.950335i | \(0.399259\pi\) | |||||||
\(588\) | −3.97920 | −0.164099 | ||||||||
\(589\) | 0.677087 | 0.0278989 | ||||||||
\(590\) | −16.0516 | −0.660834 | ||||||||
\(591\) | −0.633256 | −0.0260487 | ||||||||
\(592\) | −7.32238 | −0.300948 | ||||||||
\(593\) | 28.6154 | 1.17509 | 0.587546 | − | 0.809191i | \(-0.300094\pi\) | ||||
0.587546 | + | 0.809191i | \(0.300094\pi\) | |||||||
\(594\) | −0.642525 | −0.0263631 | ||||||||
\(595\) | 33.6923 | 1.38125 | ||||||||
\(596\) | 17.3379 | 0.710187 | ||||||||
\(597\) | 14.4610 | 0.591849 | ||||||||
\(598\) | −14.1127 | −0.577113 | ||||||||
\(599\) | −24.1821 | −0.988055 | −0.494027 | − | 0.869446i | \(-0.664476\pi\) | ||||
−0.494027 | + | 0.869446i | \(0.664476\pi\) | |||||||
\(600\) | 1.30921 | 0.0534485 | ||||||||
\(601\) | 8.69776 | 0.354789 | 0.177394 | − | 0.984140i | \(-0.443233\pi\) | ||||
0.177394 | + | 0.984140i | \(0.443233\pi\) | |||||||
\(602\) | −3.29938 | −0.134473 | ||||||||
\(603\) | −12.8611 | −0.523746 | ||||||||
\(604\) | 17.8421 | 0.725986 | ||||||||
\(605\) | 26.5930 | 1.08116 | ||||||||
\(606\) | −13.1581 | −0.534511 | ||||||||
\(607\) | 0.653287 | 0.0265161 | 0.0132581 | − | 0.999912i | \(-0.495780\pi\) | ||||
0.0132581 | + | 0.999912i | \(0.495780\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 14.0273 | 0.568413 | ||||||||
\(610\) | 10.6432 | 0.430931 | ||||||||
\(611\) | 27.2200 | 1.10120 | ||||||||
\(612\) | −7.71760 | −0.311965 | ||||||||
\(613\) | 29.4154 | 1.18808 | 0.594038 | − | 0.804437i | \(-0.297533\pi\) | ||||
0.594038 | + | 0.804437i | \(0.297533\pi\) | |||||||
\(614\) | −29.0392 | −1.17193 | ||||||||
\(615\) | 15.3478 | 0.618885 | ||||||||
\(616\) | −1.11674 | −0.0449947 | ||||||||
\(617\) | 13.0372 | 0.524856 | 0.262428 | − | 0.964952i | \(-0.415477\pi\) | ||||
0.262428 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(618\) | −6.90709 | −0.277844 | ||||||||
\(619\) | −13.9812 | −0.561954 | −0.280977 | − | 0.959715i | \(-0.590658\pi\) | ||||
−0.280977 | + | 0.959715i | \(0.590658\pi\) | |||||||
\(620\) | 1.70072 | 0.0683024 | ||||||||
\(621\) | 5.46221 | 0.219191 | ||||||||
\(622\) | −30.7392 | −1.23253 | ||||||||
\(623\) | 16.2176 | 0.649746 | ||||||||
\(624\) | −2.58371 | −0.103431 | ||||||||
\(625\) | −29.8320 | −1.19328 | ||||||||
\(626\) | −2.12783 | −0.0850452 | ||||||||
\(627\) | 0.642525 | 0.0256600 | ||||||||
\(628\) | −0.480011 | −0.0191545 | ||||||||
\(629\) | 56.5112 | 2.25325 | ||||||||
\(630\) | −4.36565 | −0.173932 | ||||||||
\(631\) | 3.45346 | 0.137480 | 0.0687399 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687399 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(632\) | −9.67603 | −0.384892 | ||||||||
\(633\) | 15.5116 | 0.616530 | ||||||||
\(634\) | −27.0644 | −1.07486 | ||||||||
\(635\) | 39.3554 | 1.56177 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 10.2811 | 0.407351 | ||||||||
\(638\) | −5.18563 | −0.205301 | ||||||||
\(639\) | 13.8022 | 0.546006 | ||||||||
\(640\) | −2.51181 | −0.0992882 | ||||||||
\(641\) | −1.22750 | −0.0484834 | −0.0242417 | − | 0.999706i | \(-0.507717\pi\) | ||||
−0.0242417 | + | 0.999706i | \(0.507717\pi\) | |||||||
\(642\) | −8.90249 | −0.351353 | ||||||||
\(643\) | −6.02283 | −0.237517 | −0.118759 | − | 0.992923i | \(-0.537891\pi\) | ||||
−0.118759 | + | 0.992923i | \(0.537891\pi\) | |||||||
\(644\) | 9.49357 | 0.374099 | ||||||||
\(645\) | 4.76824 | 0.187749 | ||||||||
\(646\) | 7.71760 | 0.303645 | ||||||||
\(647\) | 1.59626 | 0.0627553 | 0.0313776 | − | 0.999508i | \(-0.490011\pi\) | ||||
0.0313776 | + | 0.999508i | \(0.490011\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −4.10602 | −0.161175 | ||||||||
\(650\) | −3.38262 | −0.132677 | ||||||||
\(651\) | −1.17681 | −0.0461227 | ||||||||
\(652\) | −23.0963 | −0.904520 | ||||||||
\(653\) | 15.8783 | 0.621367 | 0.310683 | − | 0.950513i | \(-0.399442\pi\) | ||||
0.310683 | + | 0.950513i | \(0.399442\pi\) | |||||||
\(654\) | 5.61503 | 0.219565 | ||||||||
\(655\) | 46.3653 | 1.81164 | ||||||||
\(656\) | −6.11026 | −0.238566 | ||||||||
\(657\) | 5.86264 | 0.228723 | ||||||||
\(658\) | −18.3108 | −0.713828 | ||||||||
\(659\) | −45.7024 | −1.78031 | −0.890157 | − | 0.455655i | \(-0.849405\pi\) | ||||
−0.890157 | + | 0.455655i | \(0.849405\pi\) | |||||||
\(660\) | 1.61390 | 0.0628211 | ||||||||
\(661\) | 28.9964 | 1.12783 | 0.563914 | − | 0.825833i | \(-0.309295\pi\) | ||||
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(662\) | 2.20656 | 0.0857605 | ||||||||
\(663\) | 19.9400 | 0.774405 | ||||||||
\(664\) | −0.708381 | −0.0274905 | ||||||||
\(665\) | 4.36565 | 0.169293 | ||||||||
\(666\) | −7.32238 | −0.283736 | ||||||||
\(667\) | 44.0839 | 1.70694 | ||||||||
\(668\) | −14.1792 | −0.548609 | ||||||||
\(669\) | −15.6842 | −0.606387 | ||||||||
\(670\) | 32.3048 | 1.24804 | ||||||||
\(671\) | 2.72255 | 0.105103 | ||||||||
\(672\) | 1.73805 | 0.0670466 | ||||||||
\(673\) | −41.9506 | −1.61708 | −0.808539 | − | 0.588443i | \(-0.799741\pi\) | ||||
−0.808539 | + | 0.588443i | \(0.799741\pi\) | |||||||
\(674\) | −22.5004 | −0.866684 | ||||||||
\(675\) | 1.30921 | 0.0503917 | ||||||||
\(676\) | −6.32447 | −0.243249 | ||||||||
\(677\) | −8.85102 | −0.340172 | −0.170086 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170086 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(678\) | −2.37558 | −0.0912336 | ||||||||
\(679\) | −23.4962 | −0.901701 | ||||||||
\(680\) | 19.3852 | 0.743388 | ||||||||
\(681\) | −4.07495 | −0.156153 | ||||||||
\(682\) | 0.435045 | 0.0166587 | ||||||||
\(683\) | −22.2419 | −0.851064 | −0.425532 | − | 0.904943i | \(-0.639913\pi\) | ||||
−0.425532 | + | 0.904943i | \(0.639913\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | −9.55037 | −0.364901 | ||||||||
\(686\) | −19.0823 | −0.728567 | ||||||||
\(687\) | −14.8872 | −0.567984 | ||||||||
\(688\) | −1.89833 | −0.0723730 | ||||||||
\(689\) | 2.58371 | 0.0984313 | ||||||||
\(690\) | −13.7201 | −0.522314 | ||||||||
\(691\) | 12.5452 | 0.477241 | 0.238621 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238621 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(692\) | 19.5868 | 0.744577 | ||||||||
\(693\) | −1.11674 | −0.0424214 | ||||||||
\(694\) | 5.83468 | 0.221481 | ||||||||
\(695\) | −41.4411 | −1.57195 | ||||||||
\(696\) | 8.07071 | 0.305919 | ||||||||
\(697\) | 47.1566 | 1.78618 | ||||||||
\(698\) | 15.7691 | 0.596871 | ||||||||
\(699\) | 15.0002 | 0.567360 | ||||||||
\(700\) | 2.27547 | 0.0860048 | ||||||||
\(701\) | −12.9068 | −0.487484 | −0.243742 | − | 0.969840i | \(-0.578375\pi\) | ||||
−0.243742 | + | 0.969840i | \(0.578375\pi\) | |||||||
\(702\) | −2.58371 | −0.0975157 | ||||||||
\(703\) | 7.32238 | 0.276169 | ||||||||
\(704\) | −0.642525 | −0.0242161 | ||||||||
\(705\) | 26.4626 | 0.996641 | ||||||||
\(706\) | 18.4969 | 0.696140 | ||||||||
\(707\) | −22.8694 | −0.860091 | ||||||||
\(708\) | 6.39044 | 0.240167 | ||||||||
\(709\) | −13.8019 | −0.518340 | −0.259170 | − | 0.965832i | \(-0.583449\pi\) | ||||
−0.259170 | + | 0.965832i | \(0.583449\pi\) | |||||||
\(710\) | −34.6685 | −1.30109 | ||||||||
\(711\) | −9.67603 | −0.362879 | ||||||||
\(712\) | 9.33097 | 0.349693 | ||||||||
\(713\) | −3.69839 | −0.138506 | ||||||||
\(714\) | −13.4135 | −0.501989 | ||||||||
\(715\) | −4.16985 | −0.155944 | ||||||||
\(716\) | −2.28116 | −0.0852510 | ||||||||
\(717\) | −5.82577 | −0.217568 | ||||||||
\(718\) | −3.10195 | −0.115764 | ||||||||
\(719\) | 14.7191 | 0.548928 | 0.274464 | − | 0.961597i | \(-0.411500\pi\) | ||||
0.274464 | + | 0.961597i | \(0.411500\pi\) | |||||||
\(720\) | −2.51181 | −0.0936098 | ||||||||
\(721\) | −12.0048 | −0.447084 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 6.25361 | 0.232574 | ||||||||
\(724\) | −20.3337 | −0.755696 | ||||||||
\(725\) | 10.5663 | 0.392422 | ||||||||
\(726\) | −10.5872 | −0.392926 | ||||||||
\(727\) | −38.5602 | −1.43012 | −0.715059 | − | 0.699064i | \(-0.753600\pi\) | ||||
−0.715059 | + | 0.699064i | \(0.753600\pi\) | |||||||
\(728\) | −4.49060 | −0.166433 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.7259 | −0.545028 | ||||||||
\(731\) | 14.6505 | 0.541869 | ||||||||
\(732\) | −4.23726 | −0.156614 | ||||||||
\(733\) | 13.4126 | 0.495407 | 0.247704 | − | 0.968836i | \(-0.420324\pi\) | ||||
0.247704 | + | 0.968836i | \(0.420324\pi\) | |||||||
\(734\) | 12.3041 | 0.454152 | ||||||||
\(735\) | 9.99501 | 0.368671 | ||||||||
\(736\) | 5.46221 | 0.201340 | ||||||||
\(737\) | 8.26360 | 0.304393 | ||||||||
\(738\) | −6.11026 | −0.224922 | ||||||||
\(739\) | 26.2170 | 0.964408 | 0.482204 | − | 0.876059i | \(-0.339836\pi\) | ||||
0.482204 | + | 0.876059i | \(0.339836\pi\) | |||||||
\(740\) | 18.3925 | 0.676120 | ||||||||
\(741\) | 2.58371 | 0.0949148 | ||||||||
\(742\) | −1.73805 | −0.0638057 | ||||||||
\(743\) | 15.7061 | 0.576202 | 0.288101 | − | 0.957600i | \(-0.406976\pi\) | ||||
0.288101 | + | 0.957600i | \(0.406976\pi\) | |||||||
\(744\) | −0.677087 | −0.0248232 | ||||||||
\(745\) | −43.5495 | −1.59553 | ||||||||
\(746\) | 10.1898 | 0.373074 | ||||||||
\(747\) | −0.708381 | −0.0259183 | ||||||||
\(748\) | 4.95875 | 0.181310 | ||||||||
\(749\) | −15.4729 | −0.565369 | ||||||||
\(750\) | 9.27057 | 0.338513 | ||||||||
\(751\) | 6.45204 | 0.235438 | 0.117719 | − | 0.993047i | \(-0.462442\pi\) | ||||
0.117719 | + | 0.993047i | \(0.462442\pi\) | |||||||
\(752\) | −10.5353 | −0.384182 | ||||||||
\(753\) | 15.9849 | 0.582523 | ||||||||
\(754\) | −20.8523 | −0.759397 | ||||||||
\(755\) | −44.8161 | −1.63103 | ||||||||
\(756\) | 1.73805 | 0.0632121 | ||||||||
\(757\) | 49.6307 | 1.80386 | 0.901930 | − | 0.431883i | \(-0.142151\pi\) | ||||
0.901930 | + | 0.431883i | \(0.142151\pi\) | |||||||
\(758\) | 6.85298 | 0.248912 | ||||||||
\(759\) | −3.50961 | −0.127391 | ||||||||
\(760\) | 2.51181 | 0.0911131 | ||||||||
\(761\) | −7.00710 | −0.254007 | −0.127004 | − | 0.991902i | \(-0.540536\pi\) | ||||
−0.127004 | + | 0.991902i | \(0.540536\pi\) | |||||||
\(762\) | −15.6681 | −0.567596 | ||||||||
\(763\) | 9.75918 | 0.353306 | ||||||||
\(764\) | 8.19066 | 0.296328 | ||||||||
\(765\) | 19.3852 | 0.700873 | ||||||||
\(766\) | −20.4129 | −0.737546 | ||||||||
\(767\) | −16.5110 | −0.596178 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −24.1923 | −0.872397 | −0.436198 | − | 0.899851i | \(-0.643675\pi\) | ||||
−0.436198 | + | 0.899851i | \(0.643675\pi\) | |||||||
\(770\) | 2.80504 | 0.101087 | ||||||||
\(771\) | 7.64274 | 0.275246 | ||||||||
\(772\) | 5.39374 | 0.194125 | ||||||||
\(773\) | −51.2203 | −1.84227 | −0.921134 | − | 0.389246i | \(-0.872736\pi\) | ||||
−0.921134 | + | 0.389246i | \(0.872736\pi\) | |||||||
\(774\) | −1.89833 | −0.0682339 | ||||||||
\(775\) | −0.886452 | −0.0318423 | ||||||||
\(776\) | −13.5187 | −0.485295 | ||||||||
\(777\) | −12.7266 | −0.456565 | ||||||||
\(778\) | −3.44093 | −0.123363 | ||||||||
\(779\) | 6.11026 | 0.218923 | ||||||||
\(780\) | 6.48979 | 0.232372 | ||||||||
\(781\) | −8.86825 | −0.317331 | ||||||||
\(782\) | −42.1552 | −1.50747 | ||||||||
\(783\) | 8.07071 | 0.288424 | ||||||||
\(784\) | −3.97920 | −0.142114 | ||||||||
\(785\) | 1.20570 | 0.0430333 | ||||||||
\(786\) | −18.4589 | −0.658407 | ||||||||
\(787\) | 8.50365 | 0.303122 | 0.151561 | − | 0.988448i | \(-0.451570\pi\) | ||||
0.151561 | + | 0.988448i | \(0.451570\pi\) | |||||||
\(788\) | −0.633256 | −0.0225588 | ||||||||
\(789\) | 7.70372 | 0.274260 | ||||||||
\(790\) | 24.3044 | 0.864711 | ||||||||
\(791\) | −4.12887 | −0.146806 | ||||||||
\(792\) | −0.642525 | −0.0228311 | ||||||||
\(793\) | 10.9478 | 0.388769 | ||||||||
\(794\) | 20.7359 | 0.735891 | ||||||||
\(795\) | 2.51181 | 0.0890849 | ||||||||
\(796\) | 14.4610 | 0.512557 | ||||||||
\(797\) | −44.4551 | −1.57468 | −0.787340 | − | 0.616519i | \(-0.788542\pi\) | ||||
−0.787340 | + | 0.616519i | \(0.788542\pi\) | |||||||
\(798\) | −1.73805 | −0.0615261 | ||||||||
\(799\) | 81.3069 | 2.87643 | ||||||||
\(800\) | 1.30921 | 0.0462877 | ||||||||
\(801\) | 9.33097 | 0.329694 | ||||||||
\(802\) | 5.53945 | 0.195605 | ||||||||
\(803\) | −3.76689 | −0.132931 | ||||||||
\(804\) | −12.8611 | −0.453577 | ||||||||
\(805\) | −23.8461 | −0.840465 | ||||||||
\(806\) | 1.74939 | 0.0616197 | ||||||||
\(807\) | 18.4670 | 0.650070 | ||||||||
\(808\) | −13.1581 | −0.462900 | ||||||||
\(809\) | −20.7555 | −0.729726 | −0.364863 | − | 0.931061i | \(-0.618884\pi\) | ||||
−0.364863 | + | 0.931061i | \(0.618884\pi\) | |||||||
\(810\) | −2.51181 | −0.0882562 | ||||||||
\(811\) | 47.7569 | 1.67697 | 0.838486 | − | 0.544922i | \(-0.183441\pi\) | ||||
0.838486 | + | 0.544922i | \(0.183441\pi\) | |||||||
\(812\) | 14.0273 | 0.492260 | ||||||||
\(813\) | −6.67605 | −0.234139 | ||||||||
\(814\) | 4.70481 | 0.164904 | ||||||||
\(815\) | 58.0136 | 2.03213 | ||||||||
\(816\) | −7.71760 | −0.270170 | ||||||||
\(817\) | 1.89833 | 0.0664140 | ||||||||
\(818\) | 10.6100 | 0.370970 | ||||||||
\(819\) | −4.49060 | −0.156914 | ||||||||
\(820\) | 15.3478 | 0.535970 | ||||||||
\(821\) | 30.4050 | 1.06114 | 0.530570 | − | 0.847641i | \(-0.321978\pi\) | ||||
0.530570 | + | 0.847641i | \(0.321978\pi\) | |||||||
\(822\) | 3.80218 | 0.132616 | ||||||||
\(823\) | 53.9357 | 1.88008 | 0.940039 | − | 0.341066i | \(-0.110788\pi\) | ||||
0.940039 | + | 0.341066i | \(0.110788\pi\) | |||||||
\(824\) | −6.90709 | −0.240620 | ||||||||
\(825\) | −0.841203 | −0.0292869 | ||||||||
\(826\) | 11.1069 | 0.386458 | ||||||||
\(827\) | −11.4537 | −0.398286 | −0.199143 | − | 0.979970i | \(-0.563816\pi\) | ||||
−0.199143 | + | 0.979970i | \(0.563816\pi\) | |||||||
\(828\) | 5.46221 | 0.189825 | ||||||||
\(829\) | 24.2545 | 0.842394 | 0.421197 | − | 0.906969i | \(-0.361610\pi\) | ||||
0.421197 | + | 0.906969i | \(0.361610\pi\) | |||||||
\(830\) | 1.77932 | 0.0617612 | ||||||||
\(831\) | −7.19303 | −0.249524 | ||||||||
\(832\) | −2.58371 | −0.0895739 | ||||||||
\(833\) | 30.7099 | 1.06403 | ||||||||
\(834\) | 16.4985 | 0.571296 | ||||||||
\(835\) | 35.6155 | 1.23252 | ||||||||
\(836\) | 0.642525 | 0.0222222 | ||||||||
\(837\) | −0.677087 | −0.0234035 | ||||||||
\(838\) | −2.58451 | −0.0892805 | ||||||||
\(839\) | −9.88122 | −0.341138 | −0.170569 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170569 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(840\) | −4.36565 | −0.150629 | ||||||||
\(841\) | 36.1364 | 1.24608 | ||||||||
\(842\) | 29.8910 | 1.03011 | ||||||||
\(843\) | −20.6372 | −0.710784 | ||||||||
\(844\) | 15.5116 | 0.533931 | ||||||||
\(845\) | 15.8859 | 0.546491 | ||||||||
\(846\) | −10.5353 | −0.362210 | ||||||||
\(847\) | −18.4010 | −0.632265 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 10.1190 | 0.347283 | ||||||||
\(850\) | −10.1040 | −0.346564 | ||||||||
\(851\) | −39.9964 | −1.37106 | ||||||||
\(852\) | 13.8022 | 0.472855 | ||||||||
\(853\) | 13.1067 | 0.448766 | 0.224383 | − | 0.974501i | \(-0.427963\pi\) | ||||
0.224383 | + | 0.974501i | \(0.427963\pi\) | |||||||
\(854\) | −7.36456 | −0.252010 | ||||||||
\(855\) | 2.51181 | 0.0859023 | ||||||||
\(856\) | −8.90249 | −0.304281 | ||||||||
\(857\) | 20.4708 | 0.699270 | 0.349635 | − | 0.936886i | \(-0.386306\pi\) | ||||
0.349635 | + | 0.936886i | \(0.386306\pi\) | |||||||
\(858\) | 1.66010 | 0.0566747 | ||||||||
\(859\) | 3.36408 | 0.114781 | 0.0573905 | − | 0.998352i | \(-0.481722\pi\) | ||||
0.0573905 | + | 0.998352i | \(0.481722\pi\) | |||||||
\(860\) | 4.76824 | 0.162596 | ||||||||
\(861\) | −10.6199 | −0.361926 | ||||||||
\(862\) | 15.2898 | 0.520774 | ||||||||
\(863\) | −41.1059 | −1.39926 | −0.699630 | − | 0.714505i | \(-0.746652\pi\) | ||||
−0.699630 | + | 0.714505i | \(0.746652\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −49.1983 | −1.67279 | ||||||||
\(866\) | −1.06601 | −0.0362245 | ||||||||
\(867\) | 42.5613 | 1.44546 | ||||||||
\(868\) | −1.17681 | −0.0399435 | ||||||||
\(869\) | 6.21709 | 0.210900 | ||||||||
\(870\) | −20.2721 | −0.687290 | ||||||||
\(871\) | 33.2294 | 1.12593 | ||||||||
\(872\) | 5.61503 | 0.190149 | ||||||||
\(873\) | −13.5187 | −0.457540 | ||||||||
\(874\) | −5.46221 | −0.184762 | ||||||||
\(875\) | 16.1127 | 0.544708 | ||||||||
\(876\) | 5.86264 | 0.198080 | ||||||||
\(877\) | 48.1675 | 1.62650 | 0.813250 | − | 0.581914i | \(-0.197696\pi\) | ||||
0.813250 | + | 0.581914i | \(0.197696\pi\) | |||||||
\(878\) | −13.9808 | −0.471828 | ||||||||
\(879\) | −11.1099 | −0.374729 | ||||||||
\(880\) | 1.61390 | 0.0544047 | ||||||||
\(881\) | 12.8868 | 0.434169 | 0.217084 | − | 0.976153i | \(-0.430345\pi\) | ||||
0.217084 | + | 0.976153i | \(0.430345\pi\) | |||||||
\(882\) | −3.97920 | −0.133987 | ||||||||
\(883\) | 5.85298 | 0.196968 | 0.0984842 | − | 0.995139i | \(-0.468601\pi\) | ||||
0.0984842 | + | 0.995139i | \(0.468601\pi\) | |||||||
\(884\) | 19.9400 | 0.670655 | ||||||||
\(885\) | −16.0516 | −0.539569 | ||||||||
\(886\) | 24.7683 | 0.832106 | ||||||||
\(887\) | 28.8274 | 0.967929 | 0.483965 | − | 0.875088i | \(-0.339196\pi\) | ||||
0.483965 | + | 0.875088i | \(0.339196\pi\) | |||||||
\(888\) | −7.32238 | −0.245723 | ||||||||
\(889\) | −27.2319 | −0.913328 | ||||||||
\(890\) | −23.4377 | −0.785632 | ||||||||
\(891\) | −0.642525 | −0.0215254 | ||||||||
\(892\) | −15.6842 | −0.525147 | ||||||||
\(893\) | 10.5353 | 0.352549 | ||||||||
\(894\) | 17.3379 | 0.579865 | ||||||||
\(895\) | 5.72985 | 0.191528 | ||||||||
\(896\) | 1.73805 | 0.0580640 | ||||||||
\(897\) | −14.1127 | −0.471211 | ||||||||
\(898\) | 38.3823 | 1.28083 | ||||||||
\(899\) | −5.46457 | −0.182254 | ||||||||
\(900\) | 1.30921 | 0.0436405 | ||||||||
\(901\) | 7.71760 | 0.257110 | ||||||||
\(902\) | 3.92600 | 0.130721 | ||||||||
\(903\) | −3.29938 | −0.109796 | ||||||||
\(904\) | −2.37558 | −0.0790106 | ||||||||
\(905\) | 51.0745 | 1.69777 | ||||||||
\(906\) | 17.8421 | 0.592765 | ||||||||
\(907\) | 17.9831 | 0.597120 | 0.298560 | − | 0.954391i | \(-0.403494\pi\) | ||||
0.298560 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(908\) | −4.07495 | −0.135232 | ||||||||
\(909\) | −13.1581 | −0.436426 | ||||||||
\(910\) | 11.2795 | 0.373913 | ||||||||
\(911\) | 1.05981 | 0.0351130 | 0.0175565 | − | 0.999846i | \(-0.494411\pi\) | ||||
0.0175565 | + | 0.999846i | \(0.494411\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | 0.455152 | 0.0150633 | ||||||||
\(914\) | 7.38642 | 0.244321 | ||||||||
\(915\) | 10.6432 | 0.351854 | ||||||||
\(916\) | −14.8872 | −0.491889 | ||||||||
\(917\) | −32.0824 | −1.05945 | ||||||||
\(918\) | −7.71760 | −0.254719 | ||||||||
\(919\) | −16.3849 | −0.540489 | −0.270245 | − | 0.962792i | \(-0.587105\pi\) | ||||
−0.270245 | + | 0.962792i | \(0.587105\pi\) | |||||||
\(920\) | −13.7201 | −0.452337 | ||||||||
\(921\) | −29.0392 | −0.956873 | ||||||||
\(922\) | 15.1036 | 0.497410 | ||||||||
\(923\) | −35.6608 | −1.17379 | ||||||||
\(924\) | −1.11674 | −0.0367380 | ||||||||
\(925\) | −9.58656 | −0.315204 | ||||||||
\(926\) | −36.1124 | −1.18673 | ||||||||
\(927\) | −6.90709 | −0.226859 | ||||||||
\(928\) | 8.07071 | 0.264934 | ||||||||
\(929\) | 13.7195 | 0.450122 | 0.225061 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225061 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(930\) | 1.70072 | 0.0557687 | ||||||||
\(931\) | 3.97920 | 0.130413 | ||||||||
\(932\) | 15.0002 | 0.491348 | ||||||||
\(933\) | −30.7392 | −1.00636 | ||||||||
\(934\) | 0.364195 | 0.0119168 | ||||||||
\(935\) | −12.4555 | −0.407337 | ||||||||
\(936\) | −2.58371 | −0.0844511 | ||||||||
\(937\) | −41.5301 | −1.35673 | −0.678364 | − | 0.734726i | \(-0.737311\pi\) | ||||
−0.678364 | + | 0.734726i | \(0.737311\pi\) | |||||||
\(938\) | −22.3532 | −0.729859 | ||||||||
\(939\) | −2.12783 | −0.0694391 | ||||||||
\(940\) | 26.4626 | 0.863116 | ||||||||
\(941\) | −52.3744 | −1.70736 | −0.853678 | − | 0.520801i | \(-0.825633\pi\) | ||||
−0.853678 | + | 0.520801i | \(0.825633\pi\) | |||||||
\(942\) | −0.480011 | −0.0156396 | ||||||||
\(943\) | −33.3756 | −1.08686 | ||||||||
\(944\) | 6.39044 | 0.207991 | ||||||||
\(945\) | −4.36565 | −0.142015 | ||||||||
\(946\) | 1.21972 | 0.0396566 | ||||||||
\(947\) | 6.89857 | 0.224173 | 0.112087 | − | 0.993698i | \(-0.464247\pi\) | ||||
0.112087 | + | 0.993698i | \(0.464247\pi\) | |||||||
\(948\) | −9.67603 | −0.314263 | ||||||||
\(949\) | −15.1473 | −0.491703 | ||||||||
\(950\) | −1.30921 | −0.0424765 | ||||||||
\(951\) | −27.0644 | −0.877622 | ||||||||
\(952\) | −13.4135 | −0.434735 | ||||||||
\(953\) | 47.4542 | 1.53719 | 0.768596 | − | 0.639734i | \(-0.220955\pi\) | ||||
0.768596 | + | 0.639734i | \(0.220955\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −20.5734 | −0.665740 | ||||||||
\(956\) | −5.82577 | −0.188419 | ||||||||
\(957\) | −5.18563 | −0.167628 | ||||||||
\(958\) | 30.1157 | 0.972994 | ||||||||
\(959\) | 6.60836 | 0.213395 | ||||||||
\(960\) | −2.51181 | −0.0810685 | ||||||||
\(961\) | −30.5416 | −0.985211 | ||||||||
\(962\) | 18.9189 | 0.609969 | ||||||||
\(963\) | −8.90249 | −0.286879 | ||||||||
\(964\) | 6.25361 | 0.201415 | ||||||||
\(965\) | −13.5481 | −0.436128 | ||||||||
\(966\) | 9.49357 | 0.305451 | ||||||||
\(967\) | 36.9667 | 1.18877 | 0.594384 | − | 0.804181i | \(-0.297396\pi\) | ||||
0.594384 | + | 0.804181i | \(0.297396\pi\) | |||||||
\(968\) | −10.5872 | −0.340284 | ||||||||
\(969\) | 7.71760 | 0.247925 | ||||||||
\(970\) | 33.9566 | 1.09028 | ||||||||
\(971\) | 62.1228 | 1.99362 | 0.996808 | − | 0.0798339i | \(-0.0254390\pi\) | ||||
0.996808 | + | 0.0798339i | \(0.0254390\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 28.6751 | 0.919282 | ||||||||
\(974\) | 29.7321 | 0.952679 | ||||||||
\(975\) | −3.38262 | −0.108331 | ||||||||
\(976\) | −4.23726 | −0.135631 | ||||||||
\(977\) | 15.0045 | 0.480038 | 0.240019 | − | 0.970768i | \(-0.422846\pi\) | ||||
0.240019 | + | 0.970768i | \(0.422846\pi\) | |||||||
\(978\) | −23.0963 | −0.738537 | ||||||||
\(979\) | −5.99538 | −0.191613 | ||||||||
\(980\) | 9.99501 | 0.319279 | ||||||||
\(981\) | 5.61503 | 0.179274 | ||||||||
\(982\) | −0.905199 | −0.0288861 | ||||||||
\(983\) | −16.0226 | −0.511042 | −0.255521 | − | 0.966803i | \(-0.582247\pi\) | ||||
−0.255521 | + | 0.966803i | \(0.582247\pi\) | |||||||
\(984\) | −6.11026 | −0.194788 | ||||||||
\(985\) | 1.59062 | 0.0506814 | ||||||||
\(986\) | −62.2865 | −1.98361 | ||||||||
\(987\) | −18.3108 | −0.582838 | ||||||||
\(988\) | 2.58371 | 0.0821986 | ||||||||
\(989\) | −10.3691 | −0.329717 | ||||||||
\(990\) | 1.61390 | 0.0512932 | ||||||||
\(991\) | 31.5170 | 1.00117 | 0.500585 | − | 0.865688i | \(-0.333118\pi\) | ||||
0.500585 | + | 0.865688i | \(0.333118\pi\) | |||||||
\(992\) | −0.677087 | −0.0214975 | ||||||||
\(993\) | 2.20656 | 0.0700232 | ||||||||
\(994\) | 23.9888 | 0.760879 | ||||||||
\(995\) | −36.3234 | −1.15153 | ||||||||
\(996\) | −0.708381 | −0.0224459 | ||||||||
\(997\) | 4.06176 | 0.128637 | 0.0643185 | − | 0.997929i | \(-0.479513\pi\) | ||||
0.0643185 | + | 0.997929i | \(0.479513\pi\) | |||||||
\(998\) | −28.5614 | −0.904096 | ||||||||
\(999\) | −7.32238 | −0.231670 |
(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 | 6042.2.a.x.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.x.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |