Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.13381\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | −2.24210 | −1.00270 | −0.501350 | − | 0.865245i | \(-0.667163\pi\) | ||||
−0.501350 | + | 0.865245i | \(0.667163\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.80624 | −1.81659 | −0.908294 | − | 0.418332i | \(-0.862615\pi\) | ||||
−0.908294 | + | 0.418332i | \(0.862615\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.24210 | 0.709015 | ||||||||
\(11\) | −5.91070 | −1.78214 | −0.891071 | − | 0.453864i | \(-0.850045\pi\) | ||||
−0.891071 | + | 0.453864i | \(0.850045\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.80624 | 1.28452 | ||||||||
\(15\) | 2.24210 | 0.578909 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.672431 | 0.163088 | 0.0815442 | − | 0.996670i | \(-0.474015\pi\) | ||||
0.0815442 | + | 0.996670i | \(0.474015\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.07560 | −1.39384 | −0.696919 | − | 0.717150i | \(-0.745446\pi\) | ||||
−0.696919 | + | 0.717150i | \(0.745446\pi\) | |||||||
\(20\) | −2.24210 | −0.501350 | ||||||||
\(21\) | 4.80624 | 1.04881 | ||||||||
\(22\) | 5.91070 | 1.26016 | ||||||||
\(23\) | −1.49584 | −0.311903 | −0.155952 | − | 0.987765i | \(-0.549844\pi\) | ||||
−0.155952 | + | 0.987765i | \(0.549844\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.0270290 | 0.00540581 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.80624 | −0.908294 | ||||||||
\(29\) | 4.90360 | 0.910575 | 0.455288 | − | 0.890344i | \(-0.349536\pi\) | ||||
0.455288 | + | 0.890344i | \(0.349536\pi\) | |||||||
\(30\) | −2.24210 | −0.409350 | ||||||||
\(31\) | −0.627355 | −0.112676 | −0.0563381 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563381 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.91070 | 1.02892 | ||||||||
\(34\) | −0.672431 | −0.115321 | ||||||||
\(35\) | 10.7761 | 1.82149 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.51867 | 1.56486 | 0.782430 | − | 0.622739i | \(-0.213980\pi\) | ||||
0.782430 | + | 0.622739i | \(0.213980\pi\) | |||||||
\(38\) | 6.07560 | 0.985592 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.24210 | 0.354508 | ||||||||
\(41\) | 4.06918 | 0.635500 | 0.317750 | − | 0.948175i | \(-0.397073\pi\) | ||||
0.317750 | + | 0.948175i | \(0.397073\pi\) | |||||||
\(42\) | −4.80624 | −0.741619 | ||||||||
\(43\) | 8.49168 | 1.29497 | 0.647484 | − | 0.762079i | \(-0.275821\pi\) | ||||
0.647484 | + | 0.762079i | \(0.275821\pi\) | |||||||
\(44\) | −5.91070 | −0.891071 | ||||||||
\(45\) | −2.24210 | −0.334233 | ||||||||
\(46\) | 1.49584 | 0.220549 | ||||||||
\(47\) | 3.45713 | 0.504275 | 0.252137 | − | 0.967691i | \(-0.418867\pi\) | ||||
0.252137 | + | 0.967691i | \(0.418867\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 16.0999 | 2.29999 | ||||||||
\(50\) | −0.0270290 | −0.00382248 | ||||||||
\(51\) | −0.672431 | −0.0941591 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 7.99289 | 1.09791 | 0.548954 | − | 0.835853i | \(-0.315026\pi\) | ||||
0.548954 | + | 0.835853i | \(0.315026\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 13.2524 | 1.78695 | ||||||||
\(56\) | 4.80624 | 0.642261 | ||||||||
\(57\) | 6.07560 | 0.804733 | ||||||||
\(58\) | −4.90360 | −0.643874 | ||||||||
\(59\) | 4.41705 | 0.575052 | 0.287526 | − | 0.957773i | \(-0.407167\pi\) | ||||
0.287526 | + | 0.957773i | \(0.407167\pi\) | |||||||
\(60\) | 2.24210 | 0.289454 | ||||||||
\(61\) | −5.58215 | −0.714721 | −0.357360 | − | 0.933967i | \(-0.616323\pi\) | ||||
−0.357360 | + | 0.933967i | \(0.616323\pi\) | |||||||
\(62\) | 0.627355 | 0.0796741 | ||||||||
\(63\) | −4.80624 | −0.605529 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.24210 | 0.278099 | ||||||||
\(66\) | −5.91070 | −0.727556 | ||||||||
\(67\) | −0.920585 | −0.112467 | −0.0562337 | − | 0.998418i | \(-0.517909\pi\) | ||||
−0.0562337 | + | 0.998418i | \(0.517909\pi\) | |||||||
\(68\) | 0.672431 | 0.0815442 | ||||||||
\(69\) | 1.49584 | 0.180077 | ||||||||
\(70\) | −10.7761 | −1.28799 | ||||||||
\(71\) | −1.63814 | −0.194411 | −0.0972057 | − | 0.995264i | \(-0.530990\pi\) | ||||
−0.0972057 | + | 0.995264i | \(0.530990\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.4188 | −1.57055 | −0.785276 | − | 0.619146i | \(-0.787479\pi\) | ||||
−0.785276 | + | 0.619146i | \(0.787479\pi\) | |||||||
\(74\) | −9.51867 | −1.10652 | ||||||||
\(75\) | −0.0270290 | −0.00312104 | ||||||||
\(76\) | −6.07560 | −0.696919 | ||||||||
\(77\) | 28.4082 | 3.23742 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −6.26995 | −0.705425 | −0.352712 | − | 0.935732i | \(-0.614741\pi\) | ||||
−0.352712 | + | 0.935732i | \(0.614741\pi\) | |||||||
\(80\) | −2.24210 | −0.250675 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.06918 | −0.449366 | ||||||||
\(83\) | −5.91252 | −0.648983 | −0.324492 | − | 0.945889i | \(-0.605193\pi\) | ||||
−0.324492 | + | 0.945889i | \(0.605193\pi\) | |||||||
\(84\) | 4.80624 | 0.524404 | ||||||||
\(85\) | −1.50766 | −0.163529 | ||||||||
\(86\) | −8.49168 | −0.915681 | ||||||||
\(87\) | −4.90360 | −0.525721 | ||||||||
\(88\) | 5.91070 | 0.630082 | ||||||||
\(89\) | 8.71748 | 0.924051 | 0.462025 | − | 0.886867i | \(-0.347123\pi\) | ||||
0.462025 | + | 0.886867i | \(0.347123\pi\) | |||||||
\(90\) | 2.24210 | 0.236338 | ||||||||
\(91\) | 4.80624 | 0.503831 | ||||||||
\(92\) | −1.49584 | −0.155952 | ||||||||
\(93\) | 0.627355 | 0.0650537 | ||||||||
\(94\) | −3.45713 | −0.356576 | ||||||||
\(95\) | 13.6221 | 1.39760 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.09607 | −0.415893 | −0.207947 | − | 0.978140i | \(-0.566678\pi\) | ||||
−0.207947 | + | 0.978140i | \(0.566678\pi\) | |||||||
\(98\) | −16.0999 | −1.62634 | ||||||||
\(99\) | −5.91070 | −0.594047 | ||||||||
\(100\) | 0.0270290 | 0.00270290 | ||||||||
\(101\) | −3.14660 | −0.313099 | −0.156549 | − | 0.987670i | \(-0.550037\pi\) | ||||
−0.156549 | + | 0.987670i | \(0.550037\pi\) | |||||||
\(102\) | 0.672431 | 0.0665805 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −10.7761 | −1.05164 | ||||||||
\(106\) | −7.99289 | −0.776338 | ||||||||
\(107\) | −11.6094 | −1.12232 | −0.561161 | − | 0.827707i | \(-0.689645\pi\) | ||||
−0.561161 | + | 0.827707i | \(0.689645\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.42987 | 0.136957 | 0.0684785 | − | 0.997653i | \(-0.478186\pi\) | ||||
0.0684785 | + | 0.997653i | \(0.478186\pi\) | |||||||
\(110\) | −13.2524 | −1.26357 | ||||||||
\(111\) | −9.51867 | −0.903472 | ||||||||
\(112\) | −4.80624 | −0.454147 | ||||||||
\(113\) | −4.63061 | −0.435611 | −0.217805 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217805 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(114\) | −6.07560 | −0.569032 | ||||||||
\(115\) | 3.35382 | 0.312745 | ||||||||
\(116\) | 4.90360 | 0.455288 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −4.41705 | −0.406623 | ||||||||
\(119\) | −3.23186 | −0.296264 | ||||||||
\(120\) | −2.24210 | −0.204675 | ||||||||
\(121\) | 23.9363 | 2.17603 | ||||||||
\(122\) | 5.58215 | 0.505384 | ||||||||
\(123\) | −4.06918 | −0.366906 | ||||||||
\(124\) | −0.627355 | −0.0563381 | ||||||||
\(125\) | 11.1499 | 0.997279 | ||||||||
\(126\) | 4.80624 | 0.428174 | ||||||||
\(127\) | 7.80292 | 0.692397 | 0.346198 | − | 0.938161i | \(-0.387472\pi\) | ||||
0.346198 | + | 0.938161i | \(0.387472\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.49168 | −0.747650 | ||||||||
\(130\) | −2.24210 | −0.196646 | ||||||||
\(131\) | 12.7886 | 1.11734 | 0.558671 | − | 0.829389i | \(-0.311311\pi\) | ||||
0.558671 | + | 0.829389i | \(0.311311\pi\) | |||||||
\(132\) | 5.91070 | 0.514460 | ||||||||
\(133\) | 29.2008 | 2.53203 | ||||||||
\(134\) | 0.920585 | 0.0795264 | ||||||||
\(135\) | 2.24210 | 0.192970 | ||||||||
\(136\) | −0.672431 | −0.0576604 | ||||||||
\(137\) | 7.33630 | 0.626782 | 0.313391 | − | 0.949624i | \(-0.398535\pi\) | ||||
0.313391 | + | 0.949624i | \(0.398535\pi\) | |||||||
\(138\) | −1.49584 | −0.127334 | ||||||||
\(139\) | 13.9536 | 1.18353 | 0.591763 | − | 0.806112i | \(-0.298432\pi\) | ||||
0.591763 | + | 0.806112i | \(0.298432\pi\) | |||||||
\(140\) | 10.7761 | 0.910746 | ||||||||
\(141\) | −3.45713 | −0.291143 | ||||||||
\(142\) | 1.63814 | 0.137470 | ||||||||
\(143\) | 5.91070 | 0.494277 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.9944 | −0.913033 | ||||||||
\(146\) | 13.4188 | 1.11055 | ||||||||
\(147\) | −16.0999 | −1.32790 | ||||||||
\(148\) | 9.51867 | 0.782430 | ||||||||
\(149\) | 7.46230 | 0.611335 | 0.305668 | − | 0.952138i | \(-0.401120\pi\) | ||||
0.305668 | + | 0.952138i | \(0.401120\pi\) | |||||||
\(150\) | 0.0270290 | 0.00220691 | ||||||||
\(151\) | −22.9189 | −1.86512 | −0.932558 | − | 0.361020i | \(-0.882429\pi\) | ||||
−0.932558 | + | 0.361020i | \(0.882429\pi\) | |||||||
\(152\) | 6.07560 | 0.492796 | ||||||||
\(153\) | 0.672431 | 0.0543628 | ||||||||
\(154\) | −28.4082 | −2.28920 | ||||||||
\(155\) | 1.40659 | 0.112980 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −1.63459 | −0.130454 | −0.0652272 | − | 0.997870i | \(-0.520777\pi\) | ||||
−0.0652272 | + | 0.997870i | \(0.520777\pi\) | |||||||
\(158\) | 6.26995 | 0.498811 | ||||||||
\(159\) | −7.99289 | −0.633877 | ||||||||
\(160\) | 2.24210 | 0.177254 | ||||||||
\(161\) | 7.18935 | 0.566600 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.6719 | −0.914212 | −0.457106 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457106 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(164\) | 4.06918 | 0.317750 | ||||||||
\(165\) | −13.2524 | −1.03170 | ||||||||
\(166\) | 5.91252 | 0.458901 | ||||||||
\(167\) | 16.4960 | 1.27650 | 0.638249 | − | 0.769830i | \(-0.279659\pi\) | ||||
0.638249 | + | 0.769830i | \(0.279659\pi\) | |||||||
\(168\) | −4.80624 | −0.370810 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.50766 | 0.115632 | ||||||||
\(171\) | −6.07560 | −0.464613 | ||||||||
\(172\) | 8.49168 | 0.647484 | ||||||||
\(173\) | 3.96489 | 0.301445 | 0.150722 | − | 0.988576i | \(-0.451840\pi\) | ||||
0.150722 | + | 0.988576i | \(0.451840\pi\) | |||||||
\(174\) | 4.90360 | 0.371741 | ||||||||
\(175\) | −0.129908 | −0.00982012 | ||||||||
\(176\) | −5.91070 | −0.445535 | ||||||||
\(177\) | −4.41705 | −0.332006 | ||||||||
\(178\) | −8.71748 | −0.653402 | ||||||||
\(179\) | −24.2136 | −1.80981 | −0.904904 | − | 0.425616i | \(-0.860057\pi\) | ||||
−0.904904 | + | 0.425616i | \(0.860057\pi\) | |||||||
\(180\) | −2.24210 | −0.167117 | ||||||||
\(181\) | −22.6425 | −1.68301 | −0.841503 | − | 0.540252i | \(-0.818329\pi\) | ||||
−0.841503 | + | 0.540252i | \(0.818329\pi\) | |||||||
\(182\) | −4.80624 | −0.356262 | ||||||||
\(183\) | 5.58215 | 0.412644 | ||||||||
\(184\) | 1.49584 | 0.110274 | ||||||||
\(185\) | −21.3418 | −1.56908 | ||||||||
\(186\) | −0.627355 | −0.0459999 | ||||||||
\(187\) | −3.97453 | −0.290647 | ||||||||
\(188\) | 3.45713 | 0.252137 | ||||||||
\(189\) | 4.80624 | 0.349603 | ||||||||
\(190\) | −13.6221 | −0.988253 | ||||||||
\(191\) | −9.27186 | −0.670888 | −0.335444 | − | 0.942060i | \(-0.608886\pi\) | ||||
−0.335444 | + | 0.942060i | \(0.608886\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.75521 | −0.270306 | −0.135153 | − | 0.990825i | \(-0.543153\pi\) | ||||
−0.135153 | + | 0.990825i | \(0.543153\pi\) | |||||||
\(194\) | 4.09607 | 0.294081 | ||||||||
\(195\) | −2.24210 | −0.160560 | ||||||||
\(196\) | 16.0999 | 1.15000 | ||||||||
\(197\) | −0.598107 | −0.0426133 | −0.0213067 | − | 0.999773i | \(-0.506783\pi\) | ||||
−0.0213067 | + | 0.999773i | \(0.506783\pi\) | |||||||
\(198\) | 5.91070 | 0.420055 | ||||||||
\(199\) | 14.1966 | 1.00637 | 0.503185 | − | 0.864179i | \(-0.332161\pi\) | ||||
0.503185 | + | 0.864179i | \(0.332161\pi\) | |||||||
\(200\) | −0.0270290 | −0.00191124 | ||||||||
\(201\) | 0.920585 | 0.0649331 | ||||||||
\(202\) | 3.14660 | 0.221394 | ||||||||
\(203\) | −23.5679 | −1.65414 | ||||||||
\(204\) | −0.672431 | −0.0470796 | ||||||||
\(205\) | −9.12353 | −0.637215 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −1.49584 | −0.103968 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 35.9110 | 2.48402 | ||||||||
\(210\) | 10.7761 | 0.743621 | ||||||||
\(211\) | −18.6089 | −1.28109 | −0.640544 | − | 0.767922i | \(-0.721291\pi\) | ||||
−0.640544 | + | 0.767922i | \(0.721291\pi\) | |||||||
\(212\) | 7.99289 | 0.548954 | ||||||||
\(213\) | 1.63814 | 0.112243 | ||||||||
\(214\) | 11.6094 | 0.793601 | ||||||||
\(215\) | −19.0392 | −1.29846 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.01522 | 0.204686 | ||||||||
\(218\) | −1.42987 | −0.0968433 | ||||||||
\(219\) | 13.4188 | 0.906758 | ||||||||
\(220\) | 13.2524 | 0.893476 | ||||||||
\(221\) | −0.672431 | −0.0452326 | ||||||||
\(222\) | 9.51867 | 0.638851 | ||||||||
\(223\) | 10.3883 | 0.695655 | 0.347827 | − | 0.937559i | \(-0.386919\pi\) | ||||
0.347827 | + | 0.937559i | \(0.386919\pi\) | |||||||
\(224\) | 4.80624 | 0.321130 | ||||||||
\(225\) | 0.0270290 | 0.00180194 | ||||||||
\(226\) | 4.63061 | 0.308023 | ||||||||
\(227\) | 16.8032 | 1.11527 | 0.557635 | − | 0.830087i | \(-0.311709\pi\) | ||||
0.557635 | + | 0.830087i | \(0.311709\pi\) | |||||||
\(228\) | 6.07560 | 0.402366 | ||||||||
\(229\) | 9.48249 | 0.626621 | 0.313310 | − | 0.949651i | \(-0.398562\pi\) | ||||
0.313310 | + | 0.949651i | \(0.398562\pi\) | |||||||
\(230\) | −3.35382 | −0.221144 | ||||||||
\(231\) | −28.4082 | −1.86912 | ||||||||
\(232\) | −4.90360 | −0.321937 | ||||||||
\(233\) | −12.4591 | −0.816221 | −0.408111 | − | 0.912932i | \(-0.633812\pi\) | ||||
−0.408111 | + | 0.912932i | \(0.633812\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −7.75125 | −0.505636 | ||||||||
\(236\) | 4.41705 | 0.287526 | ||||||||
\(237\) | 6.26995 | 0.407277 | ||||||||
\(238\) | 3.23186 | 0.209491 | ||||||||
\(239\) | 2.52514 | 0.163338 | 0.0816688 | − | 0.996660i | \(-0.473975\pi\) | ||||
0.0816688 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(240\) | 2.24210 | 0.144727 | ||||||||
\(241\) | −1.47817 | −0.0952174 | −0.0476087 | − | 0.998866i | \(-0.515160\pi\) | ||||
−0.0476087 | + | 0.998866i | \(0.515160\pi\) | |||||||
\(242\) | −23.9363 | −1.53869 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.58215 | −0.357360 | ||||||||
\(245\) | −36.0978 | −2.30620 | ||||||||
\(246\) | 4.06918 | 0.259442 | ||||||||
\(247\) | 6.07560 | 0.386581 | ||||||||
\(248\) | 0.627355 | 0.0398371 | ||||||||
\(249\) | 5.91252 | 0.374691 | ||||||||
\(250\) | −11.1499 | −0.705183 | ||||||||
\(251\) | 26.9090 | 1.69848 | 0.849240 | − | 0.528008i | \(-0.177061\pi\) | ||||
0.849240 | + | 0.528008i | \(0.177061\pi\) | |||||||
\(252\) | −4.80624 | −0.302765 | ||||||||
\(253\) | 8.84143 | 0.555856 | ||||||||
\(254\) | −7.80292 | −0.489599 | ||||||||
\(255\) | 1.50766 | 0.0944133 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.78562 | −0.236141 | −0.118070 | − | 0.993005i | \(-0.537671\pi\) | ||||
−0.118070 | + | 0.993005i | \(0.537671\pi\) | |||||||
\(258\) | 8.49168 | 0.528669 | ||||||||
\(259\) | −45.7490 | −2.84271 | ||||||||
\(260\) | 2.24210 | 0.139049 | ||||||||
\(261\) | 4.90360 | 0.303525 | ||||||||
\(262\) | −12.7886 | −0.790081 | ||||||||
\(263\) | 0.134193 | 0.00827467 | 0.00413734 | − | 0.999991i | \(-0.498683\pi\) | ||||
0.00413734 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(264\) | −5.91070 | −0.363778 | ||||||||
\(265\) | −17.9209 | −1.10087 | ||||||||
\(266\) | −29.2008 | −1.79042 | ||||||||
\(267\) | −8.71748 | −0.533501 | ||||||||
\(268\) | −0.920585 | −0.0562337 | ||||||||
\(269\) | −2.04038 | −0.124404 | −0.0622021 | − | 0.998064i | \(-0.519812\pi\) | ||||
−0.0622021 | + | 0.998064i | \(0.519812\pi\) | |||||||
\(270\) | −2.24210 | −0.136450 | ||||||||
\(271\) | −12.6125 | −0.766153 | −0.383077 | − | 0.923717i | \(-0.625136\pi\) | ||||
−0.383077 | + | 0.923717i | \(0.625136\pi\) | |||||||
\(272\) | 0.672431 | 0.0407721 | ||||||||
\(273\) | −4.80624 | −0.290887 | ||||||||
\(274\) | −7.33630 | −0.443202 | ||||||||
\(275\) | −0.159760 | −0.00963391 | ||||||||
\(276\) | 1.49584 | 0.0900387 | ||||||||
\(277\) | 6.51103 | 0.391210 | 0.195605 | − | 0.980683i | \(-0.437333\pi\) | ||||
0.195605 | + | 0.980683i | \(0.437333\pi\) | |||||||
\(278\) | −13.9536 | −0.836879 | ||||||||
\(279\) | −0.627355 | −0.0375588 | ||||||||
\(280\) | −10.7761 | −0.643995 | ||||||||
\(281\) | 32.0118 | 1.90967 | 0.954833 | − | 0.297142i | \(-0.0960334\pi\) | ||||
0.954833 | + | 0.297142i | \(0.0960334\pi\) | |||||||
\(282\) | 3.45713 | 0.205869 | ||||||||
\(283\) | −23.0851 | −1.37227 | −0.686133 | − | 0.727476i | \(-0.740693\pi\) | ||||
−0.686133 | + | 0.727476i | \(0.740693\pi\) | |||||||
\(284\) | −1.63814 | −0.0972057 | ||||||||
\(285\) | −13.6221 | −0.806905 | ||||||||
\(286\) | −5.91070 | −0.349507 | ||||||||
\(287\) | −19.5575 | −1.15444 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.5478 | −0.973402 | ||||||||
\(290\) | 10.9944 | 0.645612 | ||||||||
\(291\) | 4.09607 | 0.240116 | ||||||||
\(292\) | −13.4188 | −0.785276 | ||||||||
\(293\) | −5.80059 | −0.338874 | −0.169437 | − | 0.985541i | \(-0.554195\pi\) | ||||
−0.169437 | + | 0.985541i | \(0.554195\pi\) | |||||||
\(294\) | 16.0999 | 0.938968 | ||||||||
\(295\) | −9.90350 | −0.576604 | ||||||||
\(296\) | −9.51867 | −0.553262 | ||||||||
\(297\) | 5.91070 | 0.342973 | ||||||||
\(298\) | −7.46230 | −0.432279 | ||||||||
\(299\) | 1.49584 | 0.0865064 | ||||||||
\(300\) | −0.0270290 | −0.00156052 | ||||||||
\(301\) | −40.8130 | −2.35242 | ||||||||
\(302\) | 22.9189 | 1.31884 | ||||||||
\(303\) | 3.14660 | 0.180768 | ||||||||
\(304\) | −6.07560 | −0.348460 | ||||||||
\(305\) | 12.5158 | 0.716650 | ||||||||
\(306\) | −0.672431 | −0.0384403 | ||||||||
\(307\) | −23.0901 | −1.31782 | −0.658911 | − | 0.752221i | \(-0.728983\pi\) | ||||
−0.658911 | + | 0.752221i | \(0.728983\pi\) | |||||||
\(308\) | 28.4082 | 1.61871 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −1.40659 | −0.0798892 | ||||||||
\(311\) | 19.8514 | 1.12567 | 0.562836 | − | 0.826569i | \(-0.309710\pi\) | ||||
0.562836 | + | 0.826569i | \(0.309710\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 18.6054 | 1.05164 | 0.525820 | − | 0.850596i | \(-0.323759\pi\) | ||||
0.525820 | + | 0.850596i | \(0.323759\pi\) | |||||||
\(314\) | 1.63459 | 0.0922451 | ||||||||
\(315\) | 10.7761 | 0.607164 | ||||||||
\(316\) | −6.26995 | −0.352712 | ||||||||
\(317\) | −16.6967 | −0.937783 | −0.468891 | − | 0.883256i | \(-0.655346\pi\) | ||||
−0.468891 | + | 0.883256i | \(0.655346\pi\) | |||||||
\(318\) | 7.99289 | 0.448219 | ||||||||
\(319\) | −28.9837 | −1.62277 | ||||||||
\(320\) | −2.24210 | −0.125337 | ||||||||
\(321\) | 11.6094 | 0.647973 | ||||||||
\(322\) | −7.18935 | −0.400647 | ||||||||
\(323\) | −4.08542 | −0.227319 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.0270290 | −0.00149930 | ||||||||
\(326\) | 11.6719 | 0.646446 | ||||||||
\(327\) | −1.42987 | −0.0790722 | ||||||||
\(328\) | −4.06918 | −0.224683 | ||||||||
\(329\) | −16.6158 | −0.916060 | ||||||||
\(330\) | 13.2524 | 0.729520 | ||||||||
\(331\) | 4.68546 | 0.257536 | 0.128768 | − | 0.991675i | \(-0.458898\pi\) | ||||
0.128768 | + | 0.991675i | \(0.458898\pi\) | |||||||
\(332\) | −5.91252 | −0.324492 | ||||||||
\(333\) | 9.51867 | 0.521620 | ||||||||
\(334\) | −16.4960 | −0.902620 | ||||||||
\(335\) | 2.06405 | 0.112771 | ||||||||
\(336\) | 4.80624 | 0.262202 | ||||||||
\(337\) | 11.0153 | 0.600040 | 0.300020 | − | 0.953933i | \(-0.403007\pi\) | ||||
0.300020 | + | 0.953933i | \(0.403007\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 4.63061 | 0.251500 | ||||||||
\(340\) | −1.50766 | −0.0817643 | ||||||||
\(341\) | 3.70810 | 0.200805 | ||||||||
\(342\) | 6.07560 | 0.328531 | ||||||||
\(343\) | −43.7365 | −2.36155 | ||||||||
\(344\) | −8.49168 | −0.457841 | ||||||||
\(345\) | −3.35382 | −0.180564 | ||||||||
\(346\) | −3.96489 | −0.213154 | ||||||||
\(347\) | 29.7512 | 1.59713 | 0.798563 | − | 0.601911i | \(-0.205594\pi\) | ||||
0.798563 | + | 0.601911i | \(0.205594\pi\) | |||||||
\(348\) | −4.90360 | −0.262860 | ||||||||
\(349\) | 1.29640 | 0.0693945 | 0.0346973 | − | 0.999398i | \(-0.488953\pi\) | ||||
0.0346973 | + | 0.999398i | \(0.488953\pi\) | |||||||
\(350\) | 0.129908 | 0.00694388 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 5.91070 | 0.315041 | ||||||||
\(353\) | 32.1071 | 1.70889 | 0.854443 | − | 0.519545i | \(-0.173898\pi\) | ||||
0.854443 | + | 0.519545i | \(0.173898\pi\) | |||||||
\(354\) | 4.41705 | 0.234764 | ||||||||
\(355\) | 3.67288 | 0.194936 | ||||||||
\(356\) | 8.71748 | 0.462025 | ||||||||
\(357\) | 3.23186 | 0.171048 | ||||||||
\(358\) | 24.2136 | 1.27973 | ||||||||
\(359\) | 6.85815 | 0.361959 | 0.180980 | − | 0.983487i | \(-0.442073\pi\) | ||||
0.180980 | + | 0.983487i | \(0.442073\pi\) | |||||||
\(360\) | 2.24210 | 0.118169 | ||||||||
\(361\) | 17.9129 | 0.942785 | ||||||||
\(362\) | 22.6425 | 1.19007 | ||||||||
\(363\) | −23.9363 | −1.25633 | ||||||||
\(364\) | 4.80624 | 0.251915 | ||||||||
\(365\) | 30.0863 | 1.57479 | ||||||||
\(366\) | −5.58215 | −0.291784 | ||||||||
\(367\) | 0.851961 | 0.0444720 | 0.0222360 | − | 0.999753i | \(-0.492921\pi\) | ||||
0.0222360 | + | 0.999753i | \(0.492921\pi\) | |||||||
\(368\) | −1.49584 | −0.0779758 | ||||||||
\(369\) | 4.06918 | 0.211833 | ||||||||
\(370\) | 21.3418 | 1.10951 | ||||||||
\(371\) | −38.4157 | −1.99445 | ||||||||
\(372\) | 0.627355 | 0.0325268 | ||||||||
\(373\) | 23.4478 | 1.21408 | 0.607039 | − | 0.794672i | \(-0.292357\pi\) | ||||
0.607039 | + | 0.794672i | \(0.292357\pi\) | |||||||
\(374\) | 3.97453 | 0.205518 | ||||||||
\(375\) | −11.1499 | −0.575779 | ||||||||
\(376\) | −3.45713 | −0.178288 | ||||||||
\(377\) | −4.90360 | −0.252548 | ||||||||
\(378\) | −4.80624 | −0.247206 | ||||||||
\(379\) | 14.6048 | 0.750198 | 0.375099 | − | 0.926985i | \(-0.377609\pi\) | ||||
0.375099 | + | 0.926985i | \(0.377609\pi\) | |||||||
\(380\) | 13.6221 | 0.698800 | ||||||||
\(381\) | −7.80292 | −0.399756 | ||||||||
\(382\) | 9.27186 | 0.474390 | ||||||||
\(383\) | 24.8699 | 1.27079 | 0.635395 | − | 0.772187i | \(-0.280837\pi\) | ||||
0.635395 | + | 0.772187i | \(0.280837\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −63.6942 | −3.24616 | ||||||||
\(386\) | 3.75521 | 0.191135 | ||||||||
\(387\) | 8.49168 | 0.431656 | ||||||||
\(388\) | −4.09607 | −0.207947 | ||||||||
\(389\) | −29.8539 | −1.51365 | −0.756826 | − | 0.653616i | \(-0.773251\pi\) | ||||
−0.756826 | + | 0.653616i | \(0.773251\pi\) | |||||||
\(390\) | 2.24210 | 0.113533 | ||||||||
\(391\) | −1.00585 | −0.0508678 | ||||||||
\(392\) | −16.0999 | −0.813170 | ||||||||
\(393\) | −12.7886 | −0.645098 | ||||||||
\(394\) | 0.598107 | 0.0301322 | ||||||||
\(395\) | 14.0579 | 0.707329 | ||||||||
\(396\) | −5.91070 | −0.297024 | ||||||||
\(397\) | 32.7033 | 1.64133 | 0.820666 | − | 0.571408i | \(-0.193603\pi\) | ||||
0.820666 | + | 0.571408i | \(0.193603\pi\) | |||||||
\(398\) | −14.1966 | −0.711611 | ||||||||
\(399\) | −29.2008 | −1.46187 | ||||||||
\(400\) | 0.0270290 | 0.00135145 | ||||||||
\(401\) | −21.0049 | −1.04893 | −0.524467 | − | 0.851431i | \(-0.675735\pi\) | ||||
−0.524467 | + | 0.851431i | \(0.675735\pi\) | |||||||
\(402\) | −0.920585 | −0.0459146 | ||||||||
\(403\) | 0.627355 | 0.0312508 | ||||||||
\(404\) | −3.14660 | −0.156549 | ||||||||
\(405\) | −2.24210 | −0.111411 | ||||||||
\(406\) | 23.5679 | 1.16965 | ||||||||
\(407\) | −56.2620 | −2.78880 | ||||||||
\(408\) | 0.672431 | 0.0332903 | ||||||||
\(409\) | 0.600833 | 0.0297093 | 0.0148546 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148546 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(410\) | 9.12353 | 0.450579 | ||||||||
\(411\) | −7.33630 | −0.361873 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −21.2294 | −1.04463 | ||||||||
\(414\) | 1.49584 | 0.0735163 | ||||||||
\(415\) | 13.2565 | 0.650735 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −13.9536 | −0.683309 | ||||||||
\(418\) | −35.9110 | −1.75647 | ||||||||
\(419\) | 17.3081 | 0.845556 | 0.422778 | − | 0.906233i | \(-0.361055\pi\) | ||||
0.422778 | + | 0.906233i | \(0.361055\pi\) | |||||||
\(420\) | −10.7761 | −0.525819 | ||||||||
\(421\) | 25.2015 | 1.22825 | 0.614123 | − | 0.789210i | \(-0.289510\pi\) | ||||
0.614123 | + | 0.789210i | \(0.289510\pi\) | |||||||
\(422\) | 18.6089 | 0.905866 | ||||||||
\(423\) | 3.45713 | 0.168092 | ||||||||
\(424\) | −7.99289 | −0.388169 | ||||||||
\(425\) | 0.0181751 | 0.000881624 0 | ||||||||
\(426\) | −1.63814 | −0.0793681 | ||||||||
\(427\) | 26.8291 | 1.29835 | ||||||||
\(428\) | −11.6094 | −0.561161 | ||||||||
\(429\) | −5.91070 | −0.285371 | ||||||||
\(430\) | 19.0392 | 0.918153 | ||||||||
\(431\) | 0.589597 | 0.0283999 | 0.0141999 | − | 0.999899i | \(-0.495480\pi\) | ||||
0.0141999 | + | 0.999899i | \(0.495480\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 24.6034 | 1.18236 | 0.591182 | − | 0.806538i | \(-0.298662\pi\) | ||||
0.591182 | + | 0.806538i | \(0.298662\pi\) | |||||||
\(434\) | −3.01522 | −0.144735 | ||||||||
\(435\) | 10.9944 | 0.527140 | ||||||||
\(436\) | 1.42987 | 0.0684785 | ||||||||
\(437\) | 9.08810 | 0.434743 | ||||||||
\(438\) | −13.4188 | −0.641175 | ||||||||
\(439\) | 15.3763 | 0.733873 | 0.366936 | − | 0.930246i | \(-0.380407\pi\) | ||||
0.366936 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(440\) | −13.2524 | −0.631783 | ||||||||
\(441\) | 16.0999 | 0.766664 | ||||||||
\(442\) | 0.672431 | 0.0319843 | ||||||||
\(443\) | 26.8246 | 1.27448 | 0.637238 | − | 0.770667i | \(-0.280077\pi\) | ||||
0.637238 | + | 0.770667i | \(0.280077\pi\) | |||||||
\(444\) | −9.51867 | −0.451736 | ||||||||
\(445\) | −19.5455 | −0.926545 | ||||||||
\(446\) | −10.3883 | −0.491902 | ||||||||
\(447\) | −7.46230 | −0.352955 | ||||||||
\(448\) | −4.80624 | −0.227074 | ||||||||
\(449\) | −33.0054 | −1.55762 | −0.778810 | − | 0.627260i | \(-0.784176\pi\) | ||||
−0.778810 | + | 0.627260i | \(0.784176\pi\) | |||||||
\(450\) | −0.0270290 | −0.00127416 | ||||||||
\(451\) | −24.0517 | −1.13255 | ||||||||
\(452\) | −4.63061 | −0.217805 | ||||||||
\(453\) | 22.9189 | 1.07683 | ||||||||
\(454\) | −16.8032 | −0.788614 | ||||||||
\(455\) | −10.7761 | −0.505191 | ||||||||
\(456\) | −6.07560 | −0.284516 | ||||||||
\(457\) | −15.6619 | −0.732631 | −0.366315 | − | 0.930491i | \(-0.619381\pi\) | ||||
−0.366315 | + | 0.930491i | \(0.619381\pi\) | |||||||
\(458\) | −9.48249 | −0.443088 | ||||||||
\(459\) | −0.672431 | −0.0313864 | ||||||||
\(460\) | 3.35382 | 0.156373 | ||||||||
\(461\) | −20.5765 | −0.958342 | −0.479171 | − | 0.877722i | \(-0.659063\pi\) | ||||
−0.479171 | + | 0.877722i | \(0.659063\pi\) | |||||||
\(462\) | 28.4082 | 1.32167 | ||||||||
\(463\) | −24.3204 | −1.13026 | −0.565132 | − | 0.825000i | \(-0.691175\pi\) | ||||
−0.565132 | + | 0.825000i | \(0.691175\pi\) | |||||||
\(464\) | 4.90360 | 0.227644 | ||||||||
\(465\) | −1.40659 | −0.0652293 | ||||||||
\(466\) | 12.4591 | 0.577156 | ||||||||
\(467\) | 28.9855 | 1.34129 | 0.670643 | − | 0.741780i | \(-0.266018\pi\) | ||||
0.670643 | + | 0.741780i | \(0.266018\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 4.42455 | 0.204307 | ||||||||
\(470\) | 7.75125 | 0.357539 | ||||||||
\(471\) | 1.63459 | 0.0753178 | ||||||||
\(472\) | −4.41705 | −0.203311 | ||||||||
\(473\) | −50.1917 | −2.30782 | ||||||||
\(474\) | −6.26995 | −0.287988 | ||||||||
\(475\) | −0.164218 | −0.00753482 | ||||||||
\(476\) | −3.23186 | −0.148132 | ||||||||
\(477\) | 7.99289 | 0.365969 | ||||||||
\(478\) | −2.52514 | −0.115497 | ||||||||
\(479\) | −22.8890 | −1.04582 | −0.522912 | − | 0.852387i | \(-0.675154\pi\) | ||||
−0.522912 | + | 0.852387i | \(0.675154\pi\) | |||||||
\(480\) | −2.24210 | −0.102338 | ||||||||
\(481\) | −9.51867 | −0.434014 | ||||||||
\(482\) | 1.47817 | 0.0673288 | ||||||||
\(483\) | −7.18935 | −0.327127 | ||||||||
\(484\) | 23.9363 | 1.08801 | ||||||||
\(485\) | 9.18382 | 0.417016 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −42.1614 | −1.91052 | −0.955258 | − | 0.295775i | \(-0.904422\pi\) | ||||
−0.955258 | + | 0.295775i | \(0.904422\pi\) | |||||||
\(488\) | 5.58215 | 0.252692 | ||||||||
\(489\) | 11.6719 | 0.527821 | ||||||||
\(490\) | 36.0978 | 1.63073 | ||||||||
\(491\) | −18.3178 | −0.826671 | −0.413335 | − | 0.910579i | \(-0.635636\pi\) | ||||
−0.413335 | + | 0.910579i | \(0.635636\pi\) | |||||||
\(492\) | −4.06918 | −0.183453 | ||||||||
\(493\) | 3.29733 | 0.148504 | ||||||||
\(494\) | −6.07560 | −0.273354 | ||||||||
\(495\) | 13.2524 | 0.595651 | ||||||||
\(496\) | −0.627355 | −0.0281691 | ||||||||
\(497\) | 7.87329 | 0.353165 | ||||||||
\(498\) | −5.91252 | −0.264946 | ||||||||
\(499\) | −12.0980 | −0.541580 | −0.270790 | − | 0.962639i | \(-0.587285\pi\) | ||||
−0.270790 | + | 0.962639i | \(0.587285\pi\) | |||||||
\(500\) | 11.1499 | 0.498639 | ||||||||
\(501\) | −16.4960 | −0.736987 | ||||||||
\(502\) | −26.9090 | −1.20101 | ||||||||
\(503\) | 14.4300 | 0.643404 | 0.321702 | − | 0.946841i | \(-0.395745\pi\) | ||||
0.321702 | + | 0.946841i | \(0.395745\pi\) | |||||||
\(504\) | 4.80624 | 0.214087 | ||||||||
\(505\) | 7.05501 | 0.313944 | ||||||||
\(506\) | −8.84143 | −0.393049 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 7.80292 | 0.346198 | ||||||||
\(509\) | −25.7790 | −1.14263 | −0.571317 | − | 0.820730i | \(-0.693567\pi\) | ||||
−0.571317 | + | 0.820730i | \(0.693567\pi\) | |||||||
\(510\) | −1.50766 | −0.0667603 | ||||||||
\(511\) | 64.4940 | 2.85305 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.07560 | 0.268244 | ||||||||
\(514\) | 3.78562 | 0.166977 | ||||||||
\(515\) | 2.24210 | 0.0987989 | ||||||||
\(516\) | −8.49168 | −0.373825 | ||||||||
\(517\) | −20.4341 | −0.898689 | ||||||||
\(518\) | 45.7490 | 2.01010 | ||||||||
\(519\) | −3.96489 | −0.174039 | ||||||||
\(520\) | −2.24210 | −0.0983228 | ||||||||
\(521\) | 20.1761 | 0.883930 | 0.441965 | − | 0.897032i | \(-0.354282\pi\) | ||||
0.441965 | + | 0.897032i | \(0.354282\pi\) | |||||||
\(522\) | −4.90360 | −0.214625 | ||||||||
\(523\) | −21.5296 | −0.941424 | −0.470712 | − | 0.882287i | \(-0.656003\pi\) | ||||
−0.470712 | + | 0.882287i | \(0.656003\pi\) | |||||||
\(524\) | 12.7886 | 0.558671 | ||||||||
\(525\) | 0.129908 | 0.00566965 | ||||||||
\(526\) | −0.134193 | −0.00585108 | ||||||||
\(527\) | −0.421853 | −0.0183762 | ||||||||
\(528\) | 5.91070 | 0.257230 | ||||||||
\(529\) | −20.7625 | −0.902716 | ||||||||
\(530\) | 17.9209 | 0.778434 | ||||||||
\(531\) | 4.41705 | 0.191684 | ||||||||
\(532\) | 29.2008 | 1.26601 | ||||||||
\(533\) | −4.06918 | −0.176256 | ||||||||
\(534\) | 8.71748 | 0.377242 | ||||||||
\(535\) | 26.0294 | 1.12535 | ||||||||
\(536\) | 0.920585 | 0.0397632 | ||||||||
\(537\) | 24.2136 | 1.04489 | ||||||||
\(538\) | 2.04038 | 0.0879670 | ||||||||
\(539\) | −95.1619 | −4.09891 | ||||||||
\(540\) | 2.24210 | 0.0964848 | ||||||||
\(541\) | 30.1218 | 1.29504 | 0.647518 | − | 0.762050i | \(-0.275807\pi\) | ||||
0.647518 | + | 0.762050i | \(0.275807\pi\) | |||||||
\(542\) | 12.6125 | 0.541752 | ||||||||
\(543\) | 22.6425 | 0.971684 | ||||||||
\(544\) | −0.672431 | −0.0288302 | ||||||||
\(545\) | −3.20592 | −0.137327 | ||||||||
\(546\) | 4.80624 | 0.205688 | ||||||||
\(547\) | 34.1821 | 1.46152 | 0.730760 | − | 0.682634i | \(-0.239166\pi\) | ||||
0.730760 | + | 0.682634i | \(0.239166\pi\) | |||||||
\(548\) | 7.33630 | 0.313391 | ||||||||
\(549\) | −5.58215 | −0.238240 | ||||||||
\(550\) | 0.159760 | 0.00681220 | ||||||||
\(551\) | −29.7923 | −1.26919 | ||||||||
\(552\) | −1.49584 | −0.0636670 | ||||||||
\(553\) | 30.1349 | 1.28147 | ||||||||
\(554\) | −6.51103 | −0.276627 | ||||||||
\(555\) | 21.3418 | 0.905911 | ||||||||
\(556\) | 13.9536 | 0.591763 | ||||||||
\(557\) | 15.0510 | 0.637731 | 0.318866 | − | 0.947800i | \(-0.396698\pi\) | ||||
0.318866 | + | 0.947800i | \(0.396698\pi\) | |||||||
\(558\) | 0.627355 | 0.0265580 | ||||||||
\(559\) | −8.49168 | −0.359160 | ||||||||
\(560\) | 10.7761 | 0.455373 | ||||||||
\(561\) | 3.97453 | 0.167805 | ||||||||
\(562\) | −32.0118 | −1.35034 | ||||||||
\(563\) | 44.8939 | 1.89205 | 0.946026 | − | 0.324092i | \(-0.105059\pi\) | ||||
0.946026 | + | 0.324092i | \(0.105059\pi\) | |||||||
\(564\) | −3.45713 | −0.145572 | ||||||||
\(565\) | 10.3823 | 0.436787 | ||||||||
\(566\) | 23.0851 | 0.970339 | ||||||||
\(567\) | −4.80624 | −0.201843 | ||||||||
\(568\) | 1.63814 | 0.0687348 | ||||||||
\(569\) | 11.8787 | 0.497981 | 0.248991 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248991 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(570\) | 13.6221 | 0.570568 | ||||||||
\(571\) | −19.3920 | −0.811529 | −0.405765 | − | 0.913978i | \(-0.632995\pi\) | ||||
−0.405765 | + | 0.913978i | \(0.632995\pi\) | |||||||
\(572\) | 5.91070 | 0.247139 | ||||||||
\(573\) | 9.27186 | 0.387337 | ||||||||
\(574\) | 19.5575 | 0.816313 | ||||||||
\(575\) | −0.0404310 | −0.00168609 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 29.9292 | 1.24597 | 0.622985 | − | 0.782234i | \(-0.285920\pi\) | ||||
0.622985 | + | 0.782234i | \(0.285920\pi\) | |||||||
\(578\) | 16.5478 | 0.688299 | ||||||||
\(579\) | 3.75521 | 0.156061 | ||||||||
\(580\) | −10.9944 | −0.456517 | ||||||||
\(581\) | 28.4170 | 1.17894 | ||||||||
\(582\) | −4.09607 | −0.169788 | ||||||||
\(583\) | −47.2435 | −1.95663 | ||||||||
\(584\) | 13.4188 | 0.555274 | ||||||||
\(585\) | 2.24210 | 0.0926996 | ||||||||
\(586\) | 5.80059 | 0.239620 | ||||||||
\(587\) | 13.4709 | 0.556001 | 0.278001 | − | 0.960581i | \(-0.410328\pi\) | ||||
0.278001 | + | 0.960581i | \(0.410328\pi\) | |||||||
\(588\) | −16.0999 | −0.663951 | ||||||||
\(589\) | 3.81156 | 0.157052 | ||||||||
\(590\) | 9.90350 | 0.407720 | ||||||||
\(591\) | 0.598107 | 0.0246028 | ||||||||
\(592\) | 9.51867 | 0.391215 | ||||||||
\(593\) | −8.39829 | −0.344876 | −0.172438 | − | 0.985020i | \(-0.555164\pi\) | ||||
−0.172438 | + | 0.985020i | \(0.555164\pi\) | |||||||
\(594\) | −5.91070 | −0.242519 | ||||||||
\(595\) | 7.24617 | 0.297064 | ||||||||
\(596\) | 7.46230 | 0.305668 | ||||||||
\(597\) | −14.1966 | −0.581028 | ||||||||
\(598\) | −1.49584 | −0.0611693 | ||||||||
\(599\) | −17.1173 | −0.699395 | −0.349697 | − | 0.936863i | \(-0.613716\pi\) | ||||
−0.349697 | + | 0.936863i | \(0.613716\pi\) | |||||||
\(600\) | 0.0270290 | 0.00110346 | ||||||||
\(601\) | −35.4088 | −1.44436 | −0.722178 | − | 0.691708i | \(-0.756859\pi\) | ||||
−0.722178 | + | 0.691708i | \(0.756859\pi\) | |||||||
\(602\) | 40.8130 | 1.66342 | ||||||||
\(603\) | −0.920585 | −0.0374891 | ||||||||
\(604\) | −22.9189 | −0.932558 | ||||||||
\(605\) | −53.6677 | −2.18190 | ||||||||
\(606\) | −3.14660 | −0.127822 | ||||||||
\(607\) | −43.5045 | −1.76579 | −0.882896 | − | 0.469569i | \(-0.844409\pi\) | ||||
−0.882896 | + | 0.469569i | \(0.844409\pi\) | |||||||
\(608\) | 6.07560 | 0.246398 | ||||||||
\(609\) | 23.5679 | 0.955018 | ||||||||
\(610\) | −12.5158 | −0.506748 | ||||||||
\(611\) | −3.45713 | −0.139861 | ||||||||
\(612\) | 0.672431 | 0.0271814 | ||||||||
\(613\) | −36.0677 | −1.45676 | −0.728381 | − | 0.685173i | \(-0.759727\pi\) | ||||
−0.728381 | + | 0.685173i | \(0.759727\pi\) | |||||||
\(614\) | 23.0901 | 0.931841 | ||||||||
\(615\) | 9.12353 | 0.367896 | ||||||||
\(616\) | −28.4082 | −1.14460 | ||||||||
\(617\) | 14.7141 | 0.592366 | 0.296183 | − | 0.955131i | \(-0.404286\pi\) | ||||
0.296183 | + | 0.955131i | \(0.404286\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 21.8863 | 0.879683 | 0.439842 | − | 0.898075i | \(-0.355035\pi\) | ||||
0.439842 | + | 0.898075i | \(0.355035\pi\) | |||||||
\(620\) | 1.40659 | 0.0564902 | ||||||||
\(621\) | 1.49584 | 0.0600258 | ||||||||
\(622\) | −19.8514 | −0.795970 | ||||||||
\(623\) | −41.8983 | −1.67862 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −25.1344 | −1.00538 | ||||||||
\(626\) | −18.6054 | −0.743621 | ||||||||
\(627\) | −35.9110 | −1.43415 | ||||||||
\(628\) | −1.63459 | −0.0652272 | ||||||||
\(629\) | 6.40065 | 0.255210 | ||||||||
\(630\) | −10.7761 | −0.429330 | ||||||||
\(631\) | −9.28318 | −0.369558 | −0.184779 | − | 0.982780i | \(-0.559157\pi\) | ||||
−0.184779 | + | 0.982780i | \(0.559157\pi\) | |||||||
\(632\) | 6.26995 | 0.249405 | ||||||||
\(633\) | 18.6089 | 0.739636 | ||||||||
\(634\) | 16.6967 | 0.663113 | ||||||||
\(635\) | −17.4950 | −0.694266 | ||||||||
\(636\) | −7.99289 | −0.316939 | ||||||||
\(637\) | −16.0999 | −0.637903 | ||||||||
\(638\) | 28.9837 | 1.14747 | ||||||||
\(639\) | −1.63814 | −0.0648038 | ||||||||
\(640\) | 2.24210 | 0.0886269 | ||||||||
\(641\) | −30.2790 | −1.19595 | −0.597974 | − | 0.801515i | \(-0.704027\pi\) | ||||
−0.597974 | + | 0.801515i | \(0.704027\pi\) | |||||||
\(642\) | −11.6094 | −0.458186 | ||||||||
\(643\) | −2.69109 | −0.106126 | −0.0530631 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530631 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(644\) | 7.18935 | 0.283300 | ||||||||
\(645\) | 19.0392 | 0.749669 | ||||||||
\(646\) | 4.08542 | 0.160739 | ||||||||
\(647\) | 14.3648 | 0.564738 | 0.282369 | − | 0.959306i | \(-0.408880\pi\) | ||||
0.282369 | + | 0.959306i | \(0.408880\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −26.1079 | −1.02482 | ||||||||
\(650\) | 0.0270290 | 0.00106017 | ||||||||
\(651\) | −3.01522 | −0.118176 | ||||||||
\(652\) | −11.6719 | −0.457106 | ||||||||
\(653\) | 19.1973 | 0.751250 | 0.375625 | − | 0.926772i | \(-0.377428\pi\) | ||||
0.375625 | + | 0.926772i | \(0.377428\pi\) | |||||||
\(654\) | 1.42987 | 0.0559125 | ||||||||
\(655\) | −28.6733 | −1.12036 | ||||||||
\(656\) | 4.06918 | 0.158875 | ||||||||
\(657\) | −13.4188 | −0.523517 | ||||||||
\(658\) | 16.6158 | 0.647752 | ||||||||
\(659\) | 30.7471 | 1.19774 | 0.598869 | − | 0.800847i | \(-0.295617\pi\) | ||||
0.598869 | + | 0.800847i | \(0.295617\pi\) | |||||||
\(660\) | −13.2524 | −0.515849 | ||||||||
\(661\) | −13.2678 | −0.516059 | −0.258030 | − | 0.966137i | \(-0.583073\pi\) | ||||
−0.258030 | + | 0.966137i | \(0.583073\pi\) | |||||||
\(662\) | −4.68546 | −0.182105 | ||||||||
\(663\) | 0.672431 | 0.0261150 | ||||||||
\(664\) | 5.91252 | 0.229450 | ||||||||
\(665\) | −65.4712 | −2.53886 | ||||||||
\(666\) | −9.51867 | −0.368841 | ||||||||
\(667\) | −7.33498 | −0.284011 | ||||||||
\(668\) | 16.4960 | 0.638249 | ||||||||
\(669\) | −10.3883 | −0.401637 | ||||||||
\(670\) | −2.06405 | −0.0797411 | ||||||||
\(671\) | 32.9944 | 1.27373 | ||||||||
\(672\) | −4.80624 | −0.185405 | ||||||||
\(673\) | −44.4192 | −1.71223 | −0.856116 | − | 0.516783i | \(-0.827129\pi\) | ||||
−0.856116 | + | 0.516783i | \(0.827129\pi\) | |||||||
\(674\) | −11.0153 | −0.424293 | ||||||||
\(675\) | −0.0270290 | −0.00104035 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −35.7710 | −1.37479 | −0.687396 | − | 0.726282i | \(-0.741247\pi\) | ||||
−0.687396 | + | 0.726282i | \(0.741247\pi\) | |||||||
\(678\) | −4.63061 | −0.177837 | ||||||||
\(679\) | 19.6867 | 0.755506 | ||||||||
\(680\) | 1.50766 | 0.0578161 | ||||||||
\(681\) | −16.8032 | −0.643901 | ||||||||
\(682\) | −3.70810 | −0.141991 | ||||||||
\(683\) | 31.2452 | 1.19556 | 0.597782 | − | 0.801658i | \(-0.296049\pi\) | ||||
0.597782 | + | 0.801658i | \(0.296049\pi\) | |||||||
\(684\) | −6.07560 | −0.232306 | ||||||||
\(685\) | −16.4487 | −0.628474 | ||||||||
\(686\) | 43.7365 | 1.66987 | ||||||||
\(687\) | −9.48249 | −0.361780 | ||||||||
\(688\) | 8.49168 | 0.323742 | ||||||||
\(689\) | −7.99289 | −0.304505 | ||||||||
\(690\) | 3.35382 | 0.127678 | ||||||||
\(691\) | 6.47846 | 0.246452 | 0.123226 | − | 0.992379i | \(-0.460676\pi\) | ||||
0.123226 | + | 0.992379i | \(0.460676\pi\) | |||||||
\(692\) | 3.96489 | 0.150722 | ||||||||
\(693\) | 28.4082 | 1.07914 | ||||||||
\(694\) | −29.7512 | −1.12934 | ||||||||
\(695\) | −31.2853 | −1.18672 | ||||||||
\(696\) | 4.90360 | 0.185870 | ||||||||
\(697\) | 2.73624 | 0.103643 | ||||||||
\(698\) | −1.29640 | −0.0490693 | ||||||||
\(699\) | 12.4591 | 0.471246 | ||||||||
\(700\) | −0.129908 | −0.00491006 | ||||||||
\(701\) | −27.2691 | −1.02994 | −0.514970 | − | 0.857208i | \(-0.672197\pi\) | ||||
−0.514970 | + | 0.857208i | \(0.672197\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −57.8316 | −2.18116 | ||||||||
\(704\) | −5.91070 | −0.222768 | ||||||||
\(705\) | 7.75125 | 0.291929 | ||||||||
\(706\) | −32.1071 | −1.20837 | ||||||||
\(707\) | 15.1233 | 0.568771 | ||||||||
\(708\) | −4.41705 | −0.166003 | ||||||||
\(709\) | 19.7022 | 0.739930 | 0.369965 | − | 0.929046i | \(-0.379370\pi\) | ||||
0.369965 | + | 0.929046i | \(0.379370\pi\) | |||||||
\(710\) | −3.67288 | −0.137841 | ||||||||
\(711\) | −6.26995 | −0.235142 | ||||||||
\(712\) | −8.71748 | −0.326701 | ||||||||
\(713\) | 0.938420 | 0.0351441 | ||||||||
\(714\) | −3.23186 | −0.120949 | ||||||||
\(715\) | −13.2524 | −0.495611 | ||||||||
\(716\) | −24.2136 | −0.904904 | ||||||||
\(717\) | −2.52514 | −0.0943030 | ||||||||
\(718\) | −6.85815 | −0.255944 | ||||||||
\(719\) | −28.8578 | −1.07622 | −0.538108 | − | 0.842876i | \(-0.680861\pi\) | ||||
−0.538108 | + | 0.842876i | \(0.680861\pi\) | |||||||
\(720\) | −2.24210 | −0.0835583 | ||||||||
\(721\) | 4.80624 | 0.178994 | ||||||||
\(722\) | −17.9129 | −0.666649 | ||||||||
\(723\) | 1.47817 | 0.0549738 | ||||||||
\(724\) | −22.6425 | −0.841503 | ||||||||
\(725\) | 0.132539 | 0.00492239 | ||||||||
\(726\) | 23.9363 | 0.888360 | ||||||||
\(727\) | 22.9904 | 0.852667 | 0.426334 | − | 0.904566i | \(-0.359805\pi\) | ||||
0.426334 | + | 0.904566i | \(0.359805\pi\) | |||||||
\(728\) | −4.80624 | −0.178131 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −30.0863 | −1.11355 | ||||||||
\(731\) | 5.71006 | 0.211194 | ||||||||
\(732\) | 5.58215 | 0.206322 | ||||||||
\(733\) | 33.3950 | 1.23347 | 0.616736 | − | 0.787170i | \(-0.288455\pi\) | ||||
0.616736 | + | 0.787170i | \(0.288455\pi\) | |||||||
\(734\) | −0.851961 | −0.0314465 | ||||||||
\(735\) | 36.0978 | 1.33149 | ||||||||
\(736\) | 1.49584 | 0.0551372 | ||||||||
\(737\) | 5.44130 | 0.200433 | ||||||||
\(738\) | −4.06918 | −0.149789 | ||||||||
\(739\) | −34.8698 | −1.28271 | −0.641354 | − | 0.767245i | \(-0.721627\pi\) | ||||
−0.641354 | + | 0.767245i | \(0.721627\pi\) | |||||||
\(740\) | −21.3418 | −0.784542 | ||||||||
\(741\) | −6.07560 | −0.223193 | ||||||||
\(742\) | 38.4157 | 1.41029 | ||||||||
\(743\) | 29.2172 | 1.07188 | 0.535938 | − | 0.844257i | \(-0.319958\pi\) | ||||
0.535938 | + | 0.844257i | \(0.319958\pi\) | |||||||
\(744\) | −0.627355 | −0.0229999 | ||||||||
\(745\) | −16.7312 | −0.612985 | ||||||||
\(746\) | −23.4478 | −0.858483 | ||||||||
\(747\) | −5.91252 | −0.216328 | ||||||||
\(748\) | −3.97453 | −0.145323 | ||||||||
\(749\) | 55.7975 | 2.03880 | ||||||||
\(750\) | 11.1499 | 0.407137 | ||||||||
\(751\) | −8.14976 | −0.297389 | −0.148695 | − | 0.988883i | \(-0.547507\pi\) | ||||
−0.148695 | + | 0.988883i | \(0.547507\pi\) | |||||||
\(752\) | 3.45713 | 0.126069 | ||||||||
\(753\) | −26.9090 | −0.980617 | ||||||||
\(754\) | 4.90360 | 0.178579 | ||||||||
\(755\) | 51.3866 | 1.87015 | ||||||||
\(756\) | 4.80624 | 0.174801 | ||||||||
\(757\) | 42.6983 | 1.55190 | 0.775948 | − | 0.630797i | \(-0.217272\pi\) | ||||
0.775948 | + | 0.630797i | \(0.217272\pi\) | |||||||
\(758\) | −14.6048 | −0.530470 | ||||||||
\(759\) | −8.84143 | −0.320924 | ||||||||
\(760\) | −13.6221 | −0.494126 | ||||||||
\(761\) | −17.2520 | −0.625384 | −0.312692 | − | 0.949855i | \(-0.601231\pi\) | ||||
−0.312692 | + | 0.949855i | \(0.601231\pi\) | |||||||
\(762\) | 7.80292 | 0.282670 | ||||||||
\(763\) | −6.87232 | −0.248795 | ||||||||
\(764\) | −9.27186 | −0.335444 | ||||||||
\(765\) | −1.50766 | −0.0545095 | ||||||||
\(766\) | −24.8699 | −0.898585 | ||||||||
\(767\) | −4.41705 | −0.159491 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −27.8000 | −1.00249 | −0.501246 | − | 0.865305i | \(-0.667125\pi\) | ||||
−0.501246 | + | 0.865305i | \(0.667125\pi\) | |||||||
\(770\) | 63.6942 | 2.29538 | ||||||||
\(771\) | 3.78562 | 0.136336 | ||||||||
\(772\) | −3.75521 | −0.135153 | ||||||||
\(773\) | 10.9435 | 0.393609 | 0.196805 | − | 0.980443i | \(-0.436944\pi\) | ||||
0.196805 | + | 0.980443i | \(0.436944\pi\) | |||||||
\(774\) | −8.49168 | −0.305227 | ||||||||
\(775\) | −0.0169568 | −0.000609106 0 | ||||||||
\(776\) | 4.09607 | 0.147040 | ||||||||
\(777\) | 45.7490 | 1.64124 | ||||||||
\(778\) | 29.8539 | 1.07031 | ||||||||
\(779\) | −24.7227 | −0.885783 | ||||||||
\(780\) | −2.24210 | −0.0802802 | ||||||||
\(781\) | 9.68254 | 0.346469 | ||||||||
\(782\) | 1.00585 | 0.0359690 | ||||||||
\(783\) | −4.90360 | −0.175240 | ||||||||
\(784\) | 16.0999 | 0.574998 | ||||||||
\(785\) | 3.66492 | 0.130806 | ||||||||
\(786\) | 12.7886 | 0.456153 | ||||||||
\(787\) | 28.9550 | 1.03213 | 0.516067 | − | 0.856548i | \(-0.327396\pi\) | ||||
0.516067 | + | 0.856548i | \(0.327396\pi\) | |||||||
\(788\) | −0.598107 | −0.0213067 | ||||||||
\(789\) | −0.134193 | −0.00477738 | ||||||||
\(790\) | −14.0579 | −0.500157 | ||||||||
\(791\) | 22.2558 | 0.791326 | ||||||||
\(792\) | 5.91070 | 0.210027 | ||||||||
\(793\) | 5.58215 | 0.198228 | ||||||||
\(794\) | −32.7033 | −1.16060 | ||||||||
\(795\) | 17.9209 | 0.635588 | ||||||||
\(796\) | 14.1966 | 0.503185 | ||||||||
\(797\) | 0.627633 | 0.0222319 | 0.0111159 | − | 0.999938i | \(-0.496462\pi\) | ||||
0.0111159 | + | 0.999938i | \(0.496462\pi\) | |||||||
\(798\) | 29.2008 | 1.03370 | ||||||||
\(799\) | 2.32468 | 0.0822414 | ||||||||
\(800\) | −0.0270290 | −0.000955620 0 | ||||||||
\(801\) | 8.71748 | 0.308017 | ||||||||
\(802\) | 21.0049 | 0.741708 | ||||||||
\(803\) | 79.3144 | 2.79895 | ||||||||
\(804\) | 0.920585 | 0.0324665 | ||||||||
\(805\) | −16.1193 | −0.568129 | ||||||||
\(806\) | −0.627355 | −0.0220976 | ||||||||
\(807\) | 2.04038 | 0.0718248 | ||||||||
\(808\) | 3.14660 | 0.110697 | ||||||||
\(809\) | −27.9461 | −0.982533 | −0.491266 | − | 0.871009i | \(-0.663466\pi\) | ||||
−0.491266 | + | 0.871009i | \(0.663466\pi\) | |||||||
\(810\) | 2.24210 | 0.0787795 | ||||||||
\(811\) | −37.0432 | −1.30076 | −0.650381 | − | 0.759609i | \(-0.725391\pi\) | ||||
−0.650381 | + | 0.759609i | \(0.725391\pi\) | |||||||
\(812\) | −23.5679 | −0.827070 | ||||||||
\(813\) | 12.6125 | 0.442339 | ||||||||
\(814\) | 56.2620 | 1.97198 | ||||||||
\(815\) | 26.1696 | 0.916680 | ||||||||
\(816\) | −0.672431 | −0.0235398 | ||||||||
\(817\) | −51.5920 | −1.80498 | ||||||||
\(818\) | −0.600833 | −0.0210076 | ||||||||
\(819\) | 4.80624 | 0.167944 | ||||||||
\(820\) | −9.12353 | −0.318607 | ||||||||
\(821\) | −31.6811 | −1.10568 | −0.552840 | − | 0.833288i | \(-0.686456\pi\) | ||||
−0.552840 | + | 0.833288i | \(0.686456\pi\) | |||||||
\(822\) | 7.33630 | 0.255883 | ||||||||
\(823\) | −32.1436 | −1.12046 | −0.560228 | − | 0.828339i | \(-0.689286\pi\) | ||||
−0.560228 | + | 0.828339i | \(0.689286\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 0.159760 | 0.00556214 | ||||||||
\(826\) | 21.2294 | 0.738666 | ||||||||
\(827\) | 1.67948 | 0.0584012 | 0.0292006 | − | 0.999574i | \(-0.490704\pi\) | ||||
0.0292006 | + | 0.999574i | \(0.490704\pi\) | |||||||
\(828\) | −1.49584 | −0.0519839 | ||||||||
\(829\) | −16.0453 | −0.557276 | −0.278638 | − | 0.960396i | \(-0.589883\pi\) | ||||
−0.278638 | + | 0.960396i | \(0.589883\pi\) | |||||||
\(830\) | −13.2565 | −0.460139 | ||||||||
\(831\) | −6.51103 | −0.225865 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 10.8261 | 0.375102 | ||||||||
\(834\) | 13.9536 | 0.483172 | ||||||||
\(835\) | −36.9857 | −1.27994 | ||||||||
\(836\) | 35.9110 | 1.24201 | ||||||||
\(837\) | 0.627355 | 0.0216846 | ||||||||
\(838\) | −17.3081 | −0.597899 | ||||||||
\(839\) | −17.5745 | −0.606740 | −0.303370 | − | 0.952873i | \(-0.598112\pi\) | ||||
−0.303370 | + | 0.952873i | \(0.598112\pi\) | |||||||
\(840\) | 10.7761 | 0.371810 | ||||||||
\(841\) | −4.95473 | −0.170853 | ||||||||
\(842\) | −25.2015 | −0.868501 | ||||||||
\(843\) | −32.0118 | −1.10255 | ||||||||
\(844\) | −18.6089 | −0.640544 | ||||||||
\(845\) | −2.24210 | −0.0771307 | ||||||||
\(846\) | −3.45713 | −0.118859 | ||||||||
\(847\) | −115.044 | −3.95295 | ||||||||
\(848\) | 7.99289 | 0.274477 | ||||||||
\(849\) | 23.0851 | 0.792278 | ||||||||
\(850\) | −0.0181751 | −0.000623402 0 | ||||||||
\(851\) | −14.2384 | −0.488085 | ||||||||
\(852\) | 1.63814 | 0.0561217 | ||||||||
\(853\) | 32.2588 | 1.10452 | 0.552260 | − | 0.833672i | \(-0.313766\pi\) | ||||
0.552260 | + | 0.833672i | \(0.313766\pi\) | |||||||
\(854\) | −26.8291 | −0.918074 | ||||||||
\(855\) | 13.6221 | 0.465867 | ||||||||
\(856\) | 11.6094 | 0.396801 | ||||||||
\(857\) | −42.5618 | −1.45388 | −0.726941 | − | 0.686700i | \(-0.759059\pi\) | ||||
−0.726941 | + | 0.686700i | \(0.759059\pi\) | |||||||
\(858\) | 5.91070 | 0.201788 | ||||||||
\(859\) | 30.9532 | 1.05611 | 0.528055 | − | 0.849210i | \(-0.322921\pi\) | ||||
0.528055 | + | 0.849210i | \(0.322921\pi\) | |||||||
\(860\) | −19.0392 | −0.649232 | ||||||||
\(861\) | 19.5575 | 0.666517 | ||||||||
\(862\) | −0.589597 | −0.0200818 | ||||||||
\(863\) | −9.44732 | −0.321591 | −0.160795 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160795 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −8.88969 | −0.302259 | ||||||||
\(866\) | −24.6034 | −0.836057 | ||||||||
\(867\) | 16.5478 | 0.561994 | ||||||||
\(868\) | 3.01522 | 0.102343 | ||||||||
\(869\) | 37.0598 | 1.25717 | ||||||||
\(870\) | −10.9944 | −0.372744 | ||||||||
\(871\) | 0.920585 | 0.0311928 | ||||||||
\(872\) | −1.42987 | −0.0484216 | ||||||||
\(873\) | −4.09607 | −0.138631 | ||||||||
\(874\) | −9.08810 | −0.307409 | ||||||||
\(875\) | −53.5892 | −1.81164 | ||||||||
\(876\) | 13.4188 | 0.453379 | ||||||||
\(877\) | 41.0730 | 1.38694 | 0.693468 | − | 0.720487i | \(-0.256082\pi\) | ||||
0.693468 | + | 0.720487i | \(0.256082\pi\) | |||||||
\(878\) | −15.3763 | −0.518926 | ||||||||
\(879\) | 5.80059 | 0.195649 | ||||||||
\(880\) | 13.2524 | 0.446738 | ||||||||
\(881\) | −11.9675 | −0.403196 | −0.201598 | − | 0.979468i | \(-0.564613\pi\) | ||||
−0.201598 | + | 0.979468i | \(0.564613\pi\) | |||||||
\(882\) | −16.0999 | −0.542113 | ||||||||
\(883\) | −19.3334 | −0.650619 | −0.325310 | − | 0.945608i | \(-0.605469\pi\) | ||||
−0.325310 | + | 0.945608i | \(0.605469\pi\) | |||||||
\(884\) | −0.672431 | −0.0226163 | ||||||||
\(885\) | 9.90350 | 0.332902 | ||||||||
\(886\) | −26.8246 | −0.901191 | ||||||||
\(887\) | 0.196098 | 0.00658433 | 0.00329217 | − | 0.999995i | \(-0.498952\pi\) | ||||
0.00329217 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(888\) | 9.51867 | 0.319426 | ||||||||
\(889\) | −37.5027 | −1.25780 | ||||||||
\(890\) | 19.5455 | 0.655166 | ||||||||
\(891\) | −5.91070 | −0.198016 | ||||||||
\(892\) | 10.3883 | 0.347827 | ||||||||
\(893\) | −21.0042 | −0.702877 | ||||||||
\(894\) | 7.46230 | 0.249577 | ||||||||
\(895\) | 54.2893 | 1.81469 | ||||||||
\(896\) | 4.80624 | 0.160565 | ||||||||
\(897\) | −1.49584 | −0.0499445 | ||||||||
\(898\) | 33.0054 | 1.10140 | ||||||||
\(899\) | −3.07630 | −0.102600 | ||||||||
\(900\) | 0.0270290 | 0.000900968 0 | ||||||||
\(901\) | 5.37466 | 0.179056 | ||||||||
\(902\) | 24.0517 | 0.800834 | ||||||||
\(903\) | 40.8130 | 1.35817 | ||||||||
\(904\) | 4.63061 | 0.154012 | ||||||||
\(905\) | 50.7669 | 1.68755 | ||||||||
\(906\) | −22.9189 | −0.761430 | ||||||||
\(907\) | 32.7930 | 1.08888 | 0.544438 | − | 0.838801i | \(-0.316743\pi\) | ||||
0.544438 | + | 0.838801i | \(0.316743\pi\) | |||||||
\(908\) | 16.8032 | 0.557635 | ||||||||
\(909\) | −3.14660 | −0.104366 | ||||||||
\(910\) | 10.7761 | 0.357224 | ||||||||
\(911\) | 50.8143 | 1.68355 | 0.841777 | − | 0.539825i | \(-0.181510\pi\) | ||||
0.841777 | + | 0.539825i | \(0.181510\pi\) | |||||||
\(912\) | 6.07560 | 0.201183 | ||||||||
\(913\) | 34.9471 | 1.15658 | ||||||||
\(914\) | 15.6619 | 0.518048 | ||||||||
\(915\) | −12.5158 | −0.413758 | ||||||||
\(916\) | 9.48249 | 0.313310 | ||||||||
\(917\) | −61.4650 | −2.02975 | ||||||||
\(918\) | 0.672431 | 0.0221935 | ||||||||
\(919\) | −6.78086 | −0.223680 | −0.111840 | − | 0.993726i | \(-0.535674\pi\) | ||||
−0.111840 | + | 0.993726i | \(0.535674\pi\) | |||||||
\(920\) | −3.35382 | −0.110572 | ||||||||
\(921\) | 23.0901 | 0.760845 | ||||||||
\(922\) | 20.5765 | 0.677650 | ||||||||
\(923\) | 1.63814 | 0.0539200 | ||||||||
\(924\) | −28.4082 | −0.934562 | ||||||||
\(925\) | 0.257280 | 0.00845933 | ||||||||
\(926\) | 24.3204 | 0.799218 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −4.90360 | −0.160968 | ||||||||
\(929\) | 23.4158 | 0.768249 | 0.384125 | − | 0.923281i | \(-0.374503\pi\) | ||||
0.384125 | + | 0.923281i | \(0.374503\pi\) | |||||||
\(930\) | 1.40659 | 0.0461241 | ||||||||
\(931\) | −97.8168 | −3.20582 | ||||||||
\(932\) | −12.4591 | −0.408111 | ||||||||
\(933\) | −19.8514 | −0.649907 | ||||||||
\(934\) | −28.9855 | −0.948433 | ||||||||
\(935\) | 8.91131 | 0.291431 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −39.2385 | −1.28187 | −0.640933 | − | 0.767597i | \(-0.721452\pi\) | ||||
−0.640933 | + | 0.767597i | \(0.721452\pi\) | |||||||
\(938\) | −4.42455 | −0.144467 | ||||||||
\(939\) | −18.6054 | −0.607164 | ||||||||
\(940\) | −7.75125 | −0.252818 | ||||||||
\(941\) | 3.60297 | 0.117453 | 0.0587267 | − | 0.998274i | \(-0.481296\pi\) | ||||
0.0587267 | + | 0.998274i | \(0.481296\pi\) | |||||||
\(942\) | −1.63459 | −0.0532578 | ||||||||
\(943\) | −6.08683 | −0.198214 | ||||||||
\(944\) | 4.41705 | 0.143763 | ||||||||
\(945\) | −10.7761 | −0.350546 | ||||||||
\(946\) | 50.1917 | 1.63187 | ||||||||
\(947\) | 6.55134 | 0.212890 | 0.106445 | − | 0.994319i | \(-0.466053\pi\) | ||||
0.106445 | + | 0.994319i | \(0.466053\pi\) | |||||||
\(948\) | 6.26995 | 0.203639 | ||||||||
\(949\) | 13.4188 | 0.435593 | ||||||||
\(950\) | 0.164218 | 0.00532792 | ||||||||
\(951\) | 16.6967 | 0.541429 | ||||||||
\(952\) | 3.23186 | 0.104745 | ||||||||
\(953\) | 51.6736 | 1.67387 | 0.836937 | − | 0.547300i | \(-0.184344\pi\) | ||||
0.836937 | + | 0.547300i | \(0.184344\pi\) | |||||||
\(954\) | −7.99289 | −0.258779 | ||||||||
\(955\) | 20.7885 | 0.672699 | ||||||||
\(956\) | 2.52514 | 0.0816688 | ||||||||
\(957\) | 28.9837 | 0.936909 | ||||||||
\(958\) | 22.8890 | 0.739509 | ||||||||
\(959\) | −35.2600 | −1.13861 | ||||||||
\(960\) | 2.24210 | 0.0723636 | ||||||||
\(961\) | −30.6064 | −0.987304 | ||||||||
\(962\) | 9.51867 | 0.306894 | ||||||||
\(963\) | −11.6094 | −0.374107 | ||||||||
\(964\) | −1.47817 | −0.0476087 | ||||||||
\(965\) | 8.41956 | 0.271035 | ||||||||
\(966\) | 7.18935 | 0.231313 | ||||||||
\(967\) | 56.8604 | 1.82851 | 0.914254 | − | 0.405142i | \(-0.132778\pi\) | ||||
0.914254 | + | 0.405142i | \(0.132778\pi\) | |||||||
\(968\) | −23.9363 | −0.769343 | ||||||||
\(969\) | 4.08542 | 0.131243 | ||||||||
\(970\) | −9.18382 | −0.294875 | ||||||||
\(971\) | 0.120634 | 0.00387133 | 0.00193566 | − | 0.999998i | \(-0.499384\pi\) | ||||
0.00193566 | + | 0.999998i | \(0.499384\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −67.0642 | −2.14998 | ||||||||
\(974\) | 42.1614 | 1.35094 | ||||||||
\(975\) | 0.0270290 | 0.000865622 0 | ||||||||
\(976\) | −5.58215 | −0.178680 | ||||||||
\(977\) | 21.8504 | 0.699055 | 0.349528 | − | 0.936926i | \(-0.386342\pi\) | ||||
0.349528 | + | 0.936926i | \(0.386342\pi\) | |||||||
\(978\) | −11.6719 | −0.373225 | ||||||||
\(979\) | −51.5263 | −1.64679 | ||||||||
\(980\) | −36.0978 | −1.15310 | ||||||||
\(981\) | 1.42987 | 0.0456524 | ||||||||
\(982\) | 18.3178 | 0.584544 | ||||||||
\(983\) | 0.160929 | 0.00513283 | 0.00256641 | − | 0.999997i | \(-0.499183\pi\) | ||||
0.00256641 | + | 0.999997i | \(0.499183\pi\) | |||||||
\(984\) | 4.06918 | 0.129721 | ||||||||
\(985\) | 1.34102 | 0.0427284 | ||||||||
\(986\) | −3.29733 | −0.105008 | ||||||||
\(987\) | 16.6158 | 0.528887 | ||||||||
\(988\) | 6.07560 | 0.193291 | ||||||||
\(989\) | −12.7022 | −0.403905 | ||||||||
\(990\) | −13.2524 | −0.421189 | ||||||||
\(991\) | 50.8920 | 1.61664 | 0.808319 | − | 0.588744i | \(-0.200377\pi\) | ||||
0.808319 | + | 0.588744i | \(0.200377\pi\) | |||||||
\(992\) | 0.627355 | 0.0199185 | ||||||||
\(993\) | −4.68546 | −0.148688 | ||||||||
\(994\) | −7.87329 | −0.249726 | ||||||||
\(995\) | −31.8302 | −1.00909 | ||||||||
\(996\) | 5.91252 | 0.187345 | ||||||||
\(997\) | −25.4849 | −0.807116 | −0.403558 | − | 0.914954i | \(-0.632227\pi\) | ||||
−0.403558 | + | 0.914954i | \(0.632227\pi\) | |||||||
\(998\) | 12.0980 | 0.382955 | ||||||||
\(999\) | −9.51867 | −0.301157 |
(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 | 8034.2.a.s.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.s.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial |