Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.37720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37720 | 1.68094 | 0.840468 | − | 0.541861i | \(-0.182280\pi\) | ||||
0.840468 | + | 0.541861i | \(0.182280\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.65109 | 1.82555 | ||||||||
\(5\) | 4.02830 | 1.80151 | 0.900754 | − | 0.434329i | \(-0.143014\pi\) | ||||
0.900754 | + | 0.434329i | \(0.143014\pi\) | |||||||
\(6\) | −2.37720 | −0.970489 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.92498 | 1.38769 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.57608 | 3.02822 | ||||||||
\(11\) | 3.27389 | 0.987115 | 0.493558 | − | 0.869713i | \(-0.335696\pi\) | ||||
0.493558 | + | 0.869713i | \(0.335696\pi\) | |||||||
\(12\) | −3.65109 | −1.05398 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.37720 | 0.635334 | ||||||||
\(15\) | −4.02830 | −1.04010 | ||||||||
\(16\) | 2.02830 | 0.507074 | ||||||||
\(17\) | −0.377203 | −0.0914851 | −0.0457426 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457426 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(18\) | 2.37720 | 0.560312 | ||||||||
\(19\) | 3.54778 | 0.813917 | 0.406958 | − | 0.913447i | \(-0.366589\pi\) | ||||
0.406958 | + | 0.913447i | \(0.366589\pi\) | |||||||
\(20\) | 14.7077 | 3.28874 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 7.78270 | 1.65928 | ||||||||
\(23\) | 1.89669 | 0.395487 | 0.197743 | − | 0.980254i | \(-0.436639\pi\) | ||||
0.197743 | + | 0.980254i | \(0.436639\pi\) | |||||||
\(24\) | −3.92498 | −0.801184 | ||||||||
\(25\) | 11.2272 | 2.24543 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.65109 | 0.689992 | ||||||||
\(29\) | −8.67939 | −1.61172 | −0.805861 | − | 0.592105i | \(-0.798297\pi\) | ||||
−0.805861 | + | 0.592105i | \(0.798297\pi\) | |||||||
\(30\) | −9.57608 | −1.74834 | ||||||||
\(31\) | −6.33048 | −1.13699 | −0.568494 | − | 0.822687i | \(-0.692474\pi\) | ||||
−0.568494 | + | 0.822687i | \(0.692474\pi\) | |||||||
\(32\) | −3.02830 | −0.535332 | ||||||||
\(33\) | −3.27389 | −0.569911 | ||||||||
\(34\) | −0.896688 | −0.153781 | ||||||||
\(35\) | 4.02830 | 0.680906 | ||||||||
\(36\) | 3.65109 | 0.608516 | ||||||||
\(37\) | −4.02830 | −0.662248 | −0.331124 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331124 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(38\) | 8.43380 | 1.36814 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 15.8110 | 2.49994 | ||||||||
\(41\) | −7.50881 | −1.17268 | −0.586340 | − | 0.810065i | \(-0.699432\pi\) | ||||
−0.586340 | + | 0.810065i | \(0.699432\pi\) | |||||||
\(42\) | −2.37720 | −0.366810 | ||||||||
\(43\) | −8.65109 | −1.31928 | −0.659640 | − | 0.751582i | \(-0.729291\pi\) | ||||
−0.659640 | + | 0.751582i | \(0.729291\pi\) | |||||||
\(44\) | 11.9533 | 1.80202 | ||||||||
\(45\) | 4.02830 | 0.600503 | ||||||||
\(46\) | 4.50881 | 0.664788 | ||||||||
\(47\) | 12.1239 | 1.76845 | 0.884223 | − | 0.467064i | \(-0.154688\pi\) | ||||
0.884223 | + | 0.467064i | \(0.154688\pi\) | |||||||
\(48\) | −2.02830 | −0.292759 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 26.6893 | 3.77443 | ||||||||
\(51\) | 0.377203 | 0.0528190 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.75441 | 1.06515 | 0.532575 | − | 0.846383i | \(-0.321225\pi\) | ||||
0.532575 | + | 0.846383i | \(0.321225\pi\) | |||||||
\(54\) | −2.37720 | −0.323496 | ||||||||
\(55\) | 13.1882 | 1.77830 | ||||||||
\(56\) | 3.92498 | 0.524498 | ||||||||
\(57\) | −3.54778 | −0.469915 | ||||||||
\(58\) | −20.6327 | −2.70920 | ||||||||
\(59\) | 2.10331 | 0.273828 | 0.136914 | − | 0.990583i | \(-0.456282\pi\) | ||||
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(60\) | −14.7077 | −1.89875 | ||||||||
\(61\) | 7.75441 | 0.992850 | 0.496425 | − | 0.868080i | \(-0.334646\pi\) | ||||
0.496425 | + | 0.868080i | \(0.334646\pi\) | |||||||
\(62\) | −15.0488 | −1.91120 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −11.2555 | −1.40693 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.78270 | −0.957984 | ||||||||
\(67\) | −5.58383 | −0.682173 | −0.341087 | − | 0.940032i | \(-0.610795\pi\) | ||||
−0.341087 | + | 0.940032i | \(0.610795\pi\) | |||||||
\(68\) | −1.37720 | −0.167010 | ||||||||
\(69\) | −1.89669 | −0.228334 | ||||||||
\(70\) | 9.57608 | 1.14456 | ||||||||
\(71\) | −3.99225 | −0.473793 | −0.236896 | − | 0.971535i | \(-0.576130\pi\) | ||||
−0.236896 | + | 0.971535i | \(0.576130\pi\) | |||||||
\(72\) | 3.92498 | 0.462564 | ||||||||
\(73\) | −7.50106 | −0.877933 | −0.438966 | − | 0.898503i | \(-0.644655\pi\) | ||||
−0.438966 | + | 0.898503i | \(0.644655\pi\) | |||||||
\(74\) | −9.57608 | −1.11320 | ||||||||
\(75\) | −11.2272 | −1.29640 | ||||||||
\(76\) | 12.9533 | 1.48584 | ||||||||
\(77\) | 3.27389 | 0.373094 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.16283 | −0.130828 | −0.0654142 | − | 0.997858i | \(-0.520837\pi\) | ||||
−0.0654142 | + | 0.997858i | \(0.520837\pi\) | |||||||
\(80\) | 8.17058 | 0.913498 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.8500 | −1.97120 | ||||||||
\(83\) | −15.1805 | −1.66627 | −0.833135 | − | 0.553069i | \(-0.813457\pi\) | ||||
−0.833135 | + | 0.553069i | \(0.813457\pi\) | |||||||
\(84\) | −3.65109 | −0.398367 | ||||||||
\(85\) | −1.51948 | −0.164811 | ||||||||
\(86\) | −20.5654 | −2.21762 | ||||||||
\(87\) | 8.67939 | 0.930528 | ||||||||
\(88\) | 12.8500 | 1.36981 | ||||||||
\(89\) | −6.35878 | −0.674029 | −0.337015 | − | 0.941499i | \(-0.609417\pi\) | ||||
−0.337015 | + | 0.941499i | \(0.609417\pi\) | |||||||
\(90\) | 9.57608 | 1.00941 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.92498 | 0.721979 | ||||||||
\(93\) | 6.33048 | 0.656441 | ||||||||
\(94\) | 28.8209 | 2.97265 | ||||||||
\(95\) | 14.2915 | 1.46628 | ||||||||
\(96\) | 3.02830 | 0.309074 | ||||||||
\(97\) | −4.97170 | −0.504800 | −0.252400 | − | 0.967623i | \(-0.581220\pi\) | ||||
−0.252400 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(98\) | 2.37720 | 0.240134 | ||||||||
\(99\) | 3.27389 | 0.329038 | ||||||||
\(100\) | 40.9914 | 4.09914 | ||||||||
\(101\) | 5.89669 | 0.586742 | 0.293371 | − | 0.955999i | \(-0.405223\pi\) | ||||
0.293371 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(102\) | 0.896688 | 0.0887853 | ||||||||
\(103\) | 10.5654 | 1.04104 | 0.520520 | − | 0.853849i | \(-0.325738\pi\) | ||||
0.520520 | + | 0.853849i | \(0.325738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.02830 | −0.393121 | ||||||||
\(106\) | 18.4338 | 1.79045 | ||||||||
\(107\) | −12.4055 | −1.19928 | −0.599642 | − | 0.800268i | \(-0.704691\pi\) | ||||
−0.599642 | + | 0.800268i | \(0.704691\pi\) | |||||||
\(108\) | −3.65109 | −0.351327 | ||||||||
\(109\) | 12.1316 | 1.16200 | 0.580999 | − | 0.813905i | \(-0.302662\pi\) | ||||
0.580999 | + | 0.813905i | \(0.302662\pi\) | |||||||
\(110\) | 31.3510 | 2.98920 | ||||||||
\(111\) | 4.02830 | 0.382349 | ||||||||
\(112\) | 2.02830 | 0.191656 | ||||||||
\(113\) | −10.6716 | −1.00390 | −0.501952 | − | 0.864896i | \(-0.667384\pi\) | ||||
−0.501952 | + | 0.864896i | \(0.667384\pi\) | |||||||
\(114\) | −8.43380 | −0.789897 | ||||||||
\(115\) | 7.64042 | 0.712473 | ||||||||
\(116\) | −31.6893 | −2.94227 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.00000 | 0.460287 | ||||||||
\(119\) | −0.377203 | −0.0345781 | ||||||||
\(120\) | −15.8110 | −1.44334 | ||||||||
\(121\) | −0.281641 | −0.0256037 | ||||||||
\(122\) | 18.4338 | 1.66892 | ||||||||
\(123\) | 7.50881 | 0.677047 | ||||||||
\(124\) | −23.1132 | −2.07563 | ||||||||
\(125\) | 25.0849 | 2.24366 | ||||||||
\(126\) | 2.37720 | 0.211778 | ||||||||
\(127\) | 7.33048 | 0.650475 | 0.325238 | − | 0.945632i | \(-0.394556\pi\) | ||||
0.325238 | + | 0.945632i | \(0.394556\pi\) | |||||||
\(128\) | −20.6999 | −1.82963 | ||||||||
\(129\) | 8.65109 | 0.761686 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4239 | 0.998113 | 0.499056 | − | 0.866570i | \(-0.333680\pi\) | ||||
0.499056 | + | 0.866570i | \(0.333680\pi\) | |||||||
\(132\) | −11.9533 | −1.04040 | ||||||||
\(133\) | 3.54778 | 0.307632 | ||||||||
\(134\) | −13.2739 | −1.14669 | ||||||||
\(135\) | −4.02830 | −0.346701 | ||||||||
\(136\) | −1.48052 | −0.126953 | ||||||||
\(137\) | 3.19112 | 0.272636 | 0.136318 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136318 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(138\) | −4.50881 | −0.383816 | ||||||||
\(139\) | 5.37720 | 0.456088 | 0.228044 | − | 0.973651i | \(-0.426767\pi\) | ||||
0.228044 | + | 0.973651i | \(0.426767\pi\) | |||||||
\(140\) | 14.7077 | 1.24303 | ||||||||
\(141\) | −12.1239 | −1.02101 | ||||||||
\(142\) | −9.49039 | −0.796416 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.02830 | 0.169025 | ||||||||
\(145\) | −34.9632 | −2.90353 | ||||||||
\(146\) | −17.8315 | −1.47575 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −14.7077 | −1.20896 | ||||||||
\(149\) | 10.0283 | 0.821550 | 0.410775 | − | 0.911737i | \(-0.365258\pi\) | ||||
0.410775 | + | 0.911737i | \(0.365258\pi\) | |||||||
\(150\) | −26.6893 | −2.17917 | ||||||||
\(151\) | 9.71544 | 0.790631 | 0.395315 | − | 0.918545i | \(-0.370635\pi\) | ||||
0.395315 | + | 0.918545i | \(0.370635\pi\) | |||||||
\(152\) | 13.9250 | 1.12947 | ||||||||
\(153\) | −0.377203 | −0.0304950 | ||||||||
\(154\) | 7.78270 | 0.627148 | ||||||||
\(155\) | −25.5011 | −2.04829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5761 | 1.40272 | 0.701362 | − | 0.712805i | \(-0.252576\pi\) | ||||
0.701362 | + | 0.712805i | \(0.252576\pi\) | |||||||
\(158\) | −2.76428 | −0.219914 | ||||||||
\(159\) | −7.75441 | −0.614964 | ||||||||
\(160\) | −12.1989 | −0.964406 | ||||||||
\(161\) | 1.89669 | 0.149480 | ||||||||
\(162\) | 2.37720 | 0.186771 | ||||||||
\(163\) | 5.49119 | 0.430103 | 0.215052 | − | 0.976603i | \(-0.431008\pi\) | ||||
0.215052 | + | 0.976603i | \(0.431008\pi\) | |||||||
\(164\) | −27.4154 | −2.14078 | ||||||||
\(165\) | −13.1882 | −1.02670 | ||||||||
\(166\) | −36.0870 | −2.80090 | ||||||||
\(167\) | −4.43672 | −0.343324 | −0.171662 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171662 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(168\) | −3.92498 | −0.302819 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.61212 | −0.277037 | ||||||||
\(171\) | 3.54778 | 0.271306 | ||||||||
\(172\) | −31.5860 | −2.40841 | ||||||||
\(173\) | 22.1599 | 1.68479 | 0.842393 | − | 0.538863i | \(-0.181146\pi\) | ||||
0.842393 | + | 0.538863i | \(0.181146\pi\) | |||||||
\(174\) | 20.6327 | 1.56416 | ||||||||
\(175\) | 11.2272 | 0.848694 | ||||||||
\(176\) | 6.64042 | 0.500540 | ||||||||
\(177\) | −2.10331 | −0.158095 | ||||||||
\(178\) | −15.1161 | −1.13300 | ||||||||
\(179\) | −1.94048 | −0.145039 | −0.0725193 | − | 0.997367i | \(-0.523104\pi\) | ||||
−0.0725193 | + | 0.997367i | \(0.523104\pi\) | |||||||
\(180\) | 14.7077 | 1.09625 | ||||||||
\(181\) | −8.50106 | −0.631879 | −0.315939 | − | 0.948779i | \(-0.602320\pi\) | ||||
−0.315939 | + | 0.948779i | \(0.602320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.75441 | −0.573222 | ||||||||
\(184\) | 7.44447 | 0.548814 | ||||||||
\(185\) | −16.2272 | −1.19305 | ||||||||
\(186\) | 15.0488 | 1.10343 | ||||||||
\(187\) | −1.23492 | −0.0903064 | ||||||||
\(188\) | 44.2653 | 3.22838 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 33.9738 | 2.46472 | ||||||||
\(191\) | 0.651093 | 0.0471115 | 0.0235557 | − | 0.999723i | \(-0.492501\pi\) | ||||
0.0235557 | + | 0.999723i | \(0.492501\pi\) | |||||||
\(192\) | 11.2555 | 0.812293 | ||||||||
\(193\) | −19.0643 | −1.37228 | −0.686141 | − | 0.727469i | \(-0.740697\pi\) | ||||
−0.686141 | + | 0.727469i | \(0.740697\pi\) | |||||||
\(194\) | −11.8187 | −0.848537 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.65109 | 0.260792 | ||||||||
\(197\) | −24.7098 | −1.76050 | −0.880250 | − | 0.474509i | \(-0.842626\pi\) | ||||
−0.880250 | + | 0.474509i | \(0.842626\pi\) | |||||||
\(198\) | 7.78270 | 0.553093 | ||||||||
\(199\) | 13.1444 | 0.931782 | 0.465891 | − | 0.884842i | \(-0.345734\pi\) | ||||
0.465891 | + | 0.884842i | \(0.345734\pi\) | |||||||
\(200\) | 44.0665 | 3.11597 | ||||||||
\(201\) | 5.58383 | 0.393853 | ||||||||
\(202\) | 14.0176 | 0.986277 | ||||||||
\(203\) | −8.67939 | −0.609174 | ||||||||
\(204\) | 1.37720 | 0.0964235 | ||||||||
\(205\) | −30.2477 | −2.11259 | ||||||||
\(206\) | 25.1161 | 1.74992 | ||||||||
\(207\) | 1.89669 | 0.131829 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6150 | 0.803430 | ||||||||
\(210\) | −9.57608 | −0.660812 | ||||||||
\(211\) | −19.5966 | −1.34909 | −0.674544 | − | 0.738235i | \(-0.735660\pi\) | ||||
−0.674544 | + | 0.738235i | \(0.735660\pi\) | |||||||
\(212\) | 28.3121 | 1.94448 | ||||||||
\(213\) | 3.99225 | 0.273544 | ||||||||
\(214\) | −29.4904 | −2.01592 | ||||||||
\(215\) | −34.8492 | −2.37669 | ||||||||
\(216\) | −3.92498 | −0.267061 | ||||||||
\(217\) | −6.33048 | −0.429741 | ||||||||
\(218\) | 28.8393 | 1.95324 | ||||||||
\(219\) | 7.50106 | 0.506875 | ||||||||
\(220\) | 48.1514 | 3.24636 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.57608 | 0.642704 | ||||||||
\(223\) | 27.8676 | 1.86615 | 0.933076 | − | 0.359679i | \(-0.117114\pi\) | ||||
0.933076 | + | 0.359679i | \(0.117114\pi\) | |||||||
\(224\) | −3.02830 | −0.202337 | ||||||||
\(225\) | 11.2272 | 0.748478 | ||||||||
\(226\) | −25.3687 | −1.68750 | ||||||||
\(227\) | −12.0304 | −0.798487 | −0.399243 | − | 0.916845i | \(-0.630727\pi\) | ||||
−0.399243 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(228\) | −12.9533 | −0.857852 | ||||||||
\(229\) | 9.19887 | 0.607879 | 0.303939 | − | 0.952691i | \(-0.401698\pi\) | ||||
0.303939 | + | 0.952691i | \(0.401698\pi\) | |||||||
\(230\) | 18.1628 | 1.19762 | ||||||||
\(231\) | −3.27389 | −0.215406 | ||||||||
\(232\) | −34.0665 | −2.23657 | ||||||||
\(233\) | −12.4522 | −0.815772 | −0.407886 | − | 0.913033i | \(-0.633734\pi\) | ||||
−0.407886 | + | 0.913033i | \(0.633734\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 48.8385 | 3.18587 | ||||||||
\(236\) | 7.67939 | 0.499886 | ||||||||
\(237\) | 1.16283 | 0.0755338 | ||||||||
\(238\) | −0.896688 | −0.0581236 | ||||||||
\(239\) | 3.24559 | 0.209940 | 0.104970 | − | 0.994475i | \(-0.466525\pi\) | ||||
0.104970 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(240\) | −8.17058 | −0.527409 | ||||||||
\(241\) | −9.42605 | −0.607185 | −0.303592 | − | 0.952802i | \(-0.598186\pi\) | ||||
−0.303592 | + | 0.952802i | \(0.598186\pi\) | |||||||
\(242\) | −0.669517 | −0.0430382 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 28.3121 | 1.81249 | ||||||||
\(245\) | 4.02830 | 0.257358 | ||||||||
\(246\) | 17.8500 | 1.13807 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −24.8470 | −1.57779 | ||||||||
\(249\) | 15.1805 | 0.962022 | ||||||||
\(250\) | 59.6319 | 3.77145 | ||||||||
\(251\) | −11.9893 | −0.756760 | −0.378380 | − | 0.925650i | \(-0.623519\pi\) | ||||
−0.378380 | + | 0.925650i | \(0.623519\pi\) | |||||||
\(252\) | 3.65109 | 0.229997 | ||||||||
\(253\) | 6.20955 | 0.390391 | ||||||||
\(254\) | 17.4260 | 1.09341 | ||||||||
\(255\) | 1.51948 | 0.0951538 | ||||||||
\(256\) | −26.6970 | −1.66856 | ||||||||
\(257\) | 14.5966 | 0.910512 | 0.455256 | − | 0.890360i | \(-0.349548\pi\) | ||||
0.455256 | + | 0.890360i | \(0.349548\pi\) | |||||||
\(258\) | 20.5654 | 1.28035 | ||||||||
\(259\) | −4.02830 | −0.250306 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.67939 | −0.537241 | ||||||||
\(262\) | 27.1570 | 1.67776 | ||||||||
\(263\) | 22.6532 | 1.39686 | 0.698429 | − | 0.715680i | \(-0.253883\pi\) | ||||
0.698429 | + | 0.715680i | \(0.253883\pi\) | |||||||
\(264\) | −12.8500 | −0.790861 | ||||||||
\(265\) | 31.2370 | 1.91888 | ||||||||
\(266\) | 8.43380 | 0.517109 | ||||||||
\(267\) | 6.35878 | 0.389151 | ||||||||
\(268\) | −20.3871 | −1.24534 | ||||||||
\(269\) | −27.9893 | −1.70654 | −0.853270 | − | 0.521470i | \(-0.825384\pi\) | ||||
−0.853270 | + | 0.521470i | \(0.825384\pi\) | |||||||
\(270\) | −9.57608 | −0.582782 | ||||||||
\(271\) | 7.60730 | 0.462110 | 0.231055 | − | 0.972941i | \(-0.425782\pi\) | ||||
0.231055 | + | 0.972941i | \(0.425782\pi\) | |||||||
\(272\) | −0.765079 | −0.0463897 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.58595 | 0.458284 | ||||||||
\(275\) | 36.7565 | 2.21650 | ||||||||
\(276\) | −6.92498 | −0.416835 | ||||||||
\(277\) | −6.88894 | −0.413916 | −0.206958 | − | 0.978350i | \(-0.566356\pi\) | ||||
−0.206958 | + | 0.978350i | \(0.566356\pi\) | |||||||
\(278\) | 12.7827 | 0.766656 | ||||||||
\(279\) | −6.33048 | −0.378996 | ||||||||
\(280\) | 15.8110 | 0.944888 | ||||||||
\(281\) | −10.8062 | −0.644642 | −0.322321 | − | 0.946630i | \(-0.604463\pi\) | ||||
−0.322321 | + | 0.946630i | \(0.604463\pi\) | |||||||
\(282\) | −28.8209 | −1.71626 | ||||||||
\(283\) | −7.62492 | −0.453254 | −0.226627 | − | 0.973982i | \(-0.572770\pi\) | ||||
−0.226627 | + | 0.973982i | \(0.572770\pi\) | |||||||
\(284\) | −14.5761 | −0.864931 | ||||||||
\(285\) | −14.2915 | −0.846556 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.50881 | −0.443231 | ||||||||
\(288\) | −3.02830 | −0.178444 | ||||||||
\(289\) | −16.8577 | −0.991630 | ||||||||
\(290\) | −83.1145 | −4.88065 | ||||||||
\(291\) | 4.97170 | 0.291446 | ||||||||
\(292\) | −27.3871 | −1.60271 | ||||||||
\(293\) | 22.2915 | 1.30228 | 0.651142 | − | 0.758956i | \(-0.274290\pi\) | ||||
0.651142 | + | 0.758956i | \(0.274290\pi\) | |||||||
\(294\) | −2.37720 | −0.138641 | ||||||||
\(295\) | 8.47277 | 0.493303 | ||||||||
\(296\) | −15.8110 | −0.918996 | ||||||||
\(297\) | −3.27389 | −0.189970 | ||||||||
\(298\) | 23.8393 | 1.38097 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −40.9914 | −2.36664 | ||||||||
\(301\) | −8.65109 | −0.498641 | ||||||||
\(302\) | 23.0956 | 1.32900 | ||||||||
\(303\) | −5.89669 | −0.338756 | ||||||||
\(304\) | 7.19595 | 0.412716 | ||||||||
\(305\) | 31.2370 | 1.78863 | ||||||||
\(306\) | −0.896688 | −0.0512602 | ||||||||
\(307\) | 28.2448 | 1.61202 | 0.806008 | − | 0.591905i | \(-0.201624\pi\) | ||||
0.806008 | + | 0.591905i | \(0.201624\pi\) | |||||||
\(308\) | 11.9533 | 0.681101 | ||||||||
\(309\) | −10.5654 | −0.601045 | ||||||||
\(310\) | −60.6212 | −3.44305 | ||||||||
\(311\) | −2.66177 | −0.150935 | −0.0754675 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754675 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4826 | −1.27079 | −0.635397 | − | 0.772186i | \(-0.719163\pi\) | ||||
−0.635397 | + | 0.772186i | \(0.719163\pi\) | |||||||
\(314\) | 41.7819 | 2.35789 | ||||||||
\(315\) | 4.02830 | 0.226969 | ||||||||
\(316\) | −4.24559 | −0.238833 | ||||||||
\(317\) | −18.8315 | −1.05768 | −0.528842 | − | 0.848720i | \(-0.677374\pi\) | ||||
−0.528842 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(318\) | −18.4338 | −1.03372 | ||||||||
\(319\) | −28.4154 | −1.59096 | ||||||||
\(320\) | −45.3404 | −2.53460 | ||||||||
\(321\) | 12.4055 | 0.692407 | ||||||||
\(322\) | 4.50881 | 0.251266 | ||||||||
\(323\) | −1.33823 | −0.0744613 | ||||||||
\(324\) | 3.65109 | 0.202839 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.0537 | 0.722976 | ||||||||
\(327\) | −12.1316 | −0.670879 | ||||||||
\(328\) | −29.4720 | −1.62732 | ||||||||
\(329\) | 12.1239 | 0.668410 | ||||||||
\(330\) | −31.3510 | −1.72582 | ||||||||
\(331\) | 17.8315 | 0.980110 | 0.490055 | − | 0.871691i | \(-0.336977\pi\) | ||||
0.490055 | + | 0.871691i | \(0.336977\pi\) | |||||||
\(332\) | −55.4252 | −3.04186 | ||||||||
\(333\) | −4.02830 | −0.220749 | ||||||||
\(334\) | −10.5470 | −0.577105 | ||||||||
\(335\) | −22.4933 | −1.22894 | ||||||||
\(336\) | −2.02830 | −0.110653 | ||||||||
\(337\) | 7.57608 | 0.412695 | 0.206348 | − | 0.978479i | \(-0.433842\pi\) | ||||
0.206348 | + | 0.978479i | \(0.433842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6716 | 0.579604 | ||||||||
\(340\) | −5.54778 | −0.300871 | ||||||||
\(341\) | −20.7253 | −1.12234 | ||||||||
\(342\) | 8.43380 | 0.456047 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −33.9554 | −1.83075 | ||||||||
\(345\) | −7.64042 | −0.411346 | ||||||||
\(346\) | 52.6786 | 2.83202 | ||||||||
\(347\) | 7.88814 | 0.423457 | 0.211729 | − | 0.977328i | \(-0.432091\pi\) | ||||
0.211729 | + | 0.977328i | \(0.432091\pi\) | |||||||
\(348\) | 31.6893 | 1.69872 | ||||||||
\(349\) | 11.7339 | 0.628099 | 0.314050 | − | 0.949407i | \(-0.398314\pi\) | ||||
0.314050 | + | 0.949407i | \(0.398314\pi\) | |||||||
\(350\) | 26.6893 | 1.42660 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.91431 | −0.528435 | ||||||||
\(353\) | 12.5371 | 0.667283 | 0.333641 | − | 0.942700i | \(-0.391723\pi\) | ||||
0.333641 | + | 0.942700i | \(0.391723\pi\) | |||||||
\(354\) | −5.00000 | −0.265747 | ||||||||
\(355\) | −16.0820 | −0.853542 | ||||||||
\(356\) | −23.2165 | −1.23047 | ||||||||
\(357\) | 0.377203 | 0.0199637 | ||||||||
\(358\) | −4.61292 | −0.243801 | ||||||||
\(359\) | 5.01762 | 0.264820 | 0.132410 | − | 0.991195i | \(-0.457728\pi\) | ||||
0.132410 | + | 0.991195i | \(0.457728\pi\) | |||||||
\(360\) | 15.8110 | 0.833313 | ||||||||
\(361\) | −6.41325 | −0.337539 | ||||||||
\(362\) | −20.2087 | −1.06215 | ||||||||
\(363\) | 0.281641 | 0.0147823 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.2165 | −1.58160 | ||||||||
\(366\) | −18.4338 | −0.963550 | ||||||||
\(367\) | 23.7098 | 1.23764 | 0.618821 | − | 0.785532i | \(-0.287611\pi\) | ||||
0.618821 | + | 0.785532i | \(0.287611\pi\) | |||||||
\(368\) | 3.84704 | 0.200541 | ||||||||
\(369\) | −7.50881 | −0.390893 | ||||||||
\(370\) | −38.5753 | −2.00543 | ||||||||
\(371\) | 7.75441 | 0.402589 | ||||||||
\(372\) | 23.1132 | 1.19836 | ||||||||
\(373\) | −9.95328 | −0.515361 | −0.257681 | − | 0.966230i | \(-0.582958\pi\) | ||||
−0.257681 | + | 0.966230i | \(0.582958\pi\) | |||||||
\(374\) | −2.93566 | −0.151799 | ||||||||
\(375\) | −25.0849 | −1.29538 | ||||||||
\(376\) | 47.5860 | 2.45406 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.37720 | −0.122270 | ||||||||
\(379\) | 27.8500 | 1.43056 | 0.715278 | − | 0.698840i | \(-0.246300\pi\) | ||||
0.715278 | + | 0.698840i | \(0.246300\pi\) | |||||||
\(380\) | 52.1797 | 2.67676 | ||||||||
\(381\) | −7.33048 | −0.375552 | ||||||||
\(382\) | 1.54778 | 0.0791914 | ||||||||
\(383\) | 6.90444 | 0.352800 | 0.176400 | − | 0.984319i | \(-0.443555\pi\) | ||||
0.176400 | + | 0.984319i | \(0.443555\pi\) | |||||||
\(384\) | 20.6999 | 1.05634 | ||||||||
\(385\) | 13.1882 | 0.672133 | ||||||||
\(386\) | −45.3198 | −2.30672 | ||||||||
\(387\) | −8.65109 | −0.439760 | ||||||||
\(388\) | −18.1522 | −0.921536 | ||||||||
\(389\) | −28.3764 | −1.43874 | −0.719370 | − | 0.694627i | \(-0.755570\pi\) | ||||
−0.719370 | + | 0.694627i | \(0.755570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.715436 | −0.0361812 | ||||||||
\(392\) | 3.92498 | 0.198242 | ||||||||
\(393\) | −11.4239 | −0.576261 | ||||||||
\(394\) | −58.7402 | −2.95929 | ||||||||
\(395\) | −4.68422 | −0.235689 | ||||||||
\(396\) | 11.9533 | 0.600675 | ||||||||
\(397\) | 4.76720 | 0.239259 | 0.119630 | − | 0.992819i | \(-0.461829\pi\) | ||||
0.119630 | + | 0.992819i | \(0.461829\pi\) | |||||||
\(398\) | 31.2469 | 1.56627 | ||||||||
\(399\) | −3.54778 | −0.177611 | ||||||||
\(400\) | 22.7720 | 1.13860 | ||||||||
\(401\) | 8.26614 | 0.412791 | 0.206396 | − | 0.978469i | \(-0.433827\pi\) | ||||
0.206396 | + | 0.978469i | \(0.433827\pi\) | |||||||
\(402\) | 13.2739 | 0.662041 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 21.5294 | 1.07113 | ||||||||
\(405\) | 4.02830 | 0.200168 | ||||||||
\(406\) | −20.6327 | −1.02398 | ||||||||
\(407\) | −13.1882 | −0.653715 | ||||||||
\(408\) | 1.48052 | 0.0732964 | ||||||||
\(409\) | −21.4338 | −1.05983 | −0.529916 | − | 0.848050i | \(-0.677777\pi\) | ||||
−0.529916 | + | 0.848050i | \(0.677777\pi\) | |||||||
\(410\) | −71.9050 | −3.55113 | ||||||||
\(411\) | −3.19112 | −0.157407 | ||||||||
\(412\) | 38.5753 | 1.90047 | ||||||||
\(413\) | 2.10331 | 0.103497 | ||||||||
\(414\) | 4.50881 | 0.221596 | ||||||||
\(415\) | −61.1514 | −3.00180 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.37720 | −0.263323 | ||||||||
\(418\) | 27.6113 | 1.35051 | ||||||||
\(419\) | −2.29151 | −0.111948 | −0.0559739 | − | 0.998432i | \(-0.517826\pi\) | ||||
−0.0559739 | + | 0.998432i | \(0.517826\pi\) | |||||||
\(420\) | −14.7077 | −0.717662 | ||||||||
\(421\) | −7.61292 | −0.371031 | −0.185516 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185516 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(422\) | −46.5851 | −2.26773 | ||||||||
\(423\) | 12.1239 | 0.589482 | ||||||||
\(424\) | 30.4359 | 1.47810 | ||||||||
\(425\) | −4.23492 | −0.205424 | ||||||||
\(426\) | 9.49039 | 0.459811 | ||||||||
\(427\) | 7.75441 | 0.375262 | ||||||||
\(428\) | −45.2936 | −2.18935 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −82.8435 | −3.99507 | ||||||||
\(431\) | −20.8628 | −1.00492 | −0.502462 | − | 0.864599i | \(-0.667572\pi\) | ||||
−0.502462 | + | 0.864599i | \(0.667572\pi\) | |||||||
\(432\) | −2.02830 | −0.0975864 | ||||||||
\(433\) | −23.3764 | −1.12340 | −0.561699 | − | 0.827342i | \(-0.689852\pi\) | ||||
−0.561699 | + | 0.827342i | \(0.689852\pi\) | |||||||
\(434\) | −15.0488 | −0.722368 | ||||||||
\(435\) | 34.9632 | 1.67635 | ||||||||
\(436\) | 44.2936 | 2.12128 | ||||||||
\(437\) | 6.72903 | 0.321893 | ||||||||
\(438\) | 17.8315 | 0.852024 | ||||||||
\(439\) | 9.15508 | 0.436948 | 0.218474 | − | 0.975843i | \(-0.429892\pi\) | ||||
0.218474 | + | 0.975843i | \(0.429892\pi\) | |||||||
\(440\) | 51.7635 | 2.46773 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2632 | 0.535132 | 0.267566 | − | 0.963540i | \(-0.413781\pi\) | ||||
0.267566 | + | 0.963540i | \(0.413781\pi\) | |||||||
\(444\) | 14.7077 | 0.697996 | ||||||||
\(445\) | −25.6150 | −1.21427 | ||||||||
\(446\) | 66.2469 | 3.13688 | ||||||||
\(447\) | −10.0283 | −0.474322 | ||||||||
\(448\) | −11.2555 | −0.531771 | ||||||||
\(449\) | 33.7848 | 1.59440 | 0.797202 | − | 0.603712i | \(-0.206312\pi\) | ||||
0.797202 | + | 0.603712i | \(0.206312\pi\) | |||||||
\(450\) | 26.6893 | 1.25814 | ||||||||
\(451\) | −24.5830 | −1.15757 | ||||||||
\(452\) | −38.9632 | −1.83267 | ||||||||
\(453\) | −9.71544 | −0.456471 | ||||||||
\(454\) | −28.5987 | −1.34221 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.9250 | −0.652097 | ||||||||
\(457\) | −34.2944 | −1.60423 | −0.802113 | − | 0.597172i | \(-0.796291\pi\) | ||||
−0.802113 | + | 0.597172i | \(0.796291\pi\) | |||||||
\(458\) | 21.8676 | 1.02181 | ||||||||
\(459\) | 0.377203 | 0.0176063 | ||||||||
\(460\) | 27.8959 | 1.30065 | ||||||||
\(461\) | −19.3326 | −0.900409 | −0.450205 | − | 0.892925i | \(-0.648649\pi\) | ||||
−0.450205 | + | 0.892925i | \(0.648649\pi\) | |||||||
\(462\) | −7.78270 | −0.362084 | ||||||||
\(463\) | −6.29444 | −0.292527 | −0.146264 | − | 0.989246i | \(-0.546725\pi\) | ||||
−0.146264 | + | 0.989246i | \(0.546725\pi\) | |||||||
\(464\) | −17.6044 | −0.817263 | ||||||||
\(465\) | 25.5011 | 1.18258 | ||||||||
\(466\) | −29.6015 | −1.37126 | ||||||||
\(467\) | 24.2293 | 1.12120 | 0.560599 | − | 0.828087i | \(-0.310571\pi\) | ||||
0.560599 | + | 0.828087i | \(0.310571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.58383 | −0.257837 | ||||||||
\(470\) | 116.099 | 5.35525 | ||||||||
\(471\) | −17.5761 | −0.809863 | ||||||||
\(472\) | 8.25547 | 0.379989 | ||||||||
\(473\) | −28.3227 | −1.30228 | ||||||||
\(474\) | 2.76428 | 0.126968 | ||||||||
\(475\) | 39.8315 | 1.82760 | ||||||||
\(476\) | −1.37720 | −0.0631240 | ||||||||
\(477\) | 7.75441 | 0.355050 | ||||||||
\(478\) | 7.71544 | 0.352896 | ||||||||
\(479\) | 33.6297 | 1.53658 | 0.768291 | − | 0.640101i | \(-0.221107\pi\) | ||||
0.768291 | + | 0.640101i | \(0.221107\pi\) | |||||||
\(480\) | 12.1989 | 0.556800 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.4076 | −1.02064 | ||||||||
\(483\) | −1.89669 | −0.0863023 | ||||||||
\(484\) | −1.02830 | −0.0467407 | ||||||||
\(485\) | −20.0275 | −0.909402 | ||||||||
\(486\) | −2.37720 | −0.107832 | ||||||||
\(487\) | 7.92498 | 0.359115 | 0.179558 | − | 0.983747i | \(-0.442533\pi\) | ||||
0.179558 | + | 0.983747i | \(0.442533\pi\) | |||||||
\(488\) | 30.4359 | 1.37777 | ||||||||
\(489\) | −5.49119 | −0.248320 | ||||||||
\(490\) | 9.57608 | 0.432603 | ||||||||
\(491\) | 2.43167 | 0.109740 | 0.0548699 | − | 0.998494i | \(-0.482526\pi\) | ||||
0.0548699 | + | 0.998494i | \(0.482526\pi\) | |||||||
\(492\) | 27.4154 | 1.23598 | ||||||||
\(493\) | 3.27389 | 0.147449 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.1882 | 0.592766 | ||||||||
\(496\) | −12.8401 | −0.576537 | ||||||||
\(497\) | −3.99225 | −0.179077 | ||||||||
\(498\) | 36.0870 | 1.61710 | ||||||||
\(499\) | 18.5838 | 0.831926 | 0.415963 | − | 0.909381i | \(-0.363445\pi\) | ||||
0.415963 | + | 0.909381i | \(0.363445\pi\) | |||||||
\(500\) | 91.5873 | 4.09591 | ||||||||
\(501\) | 4.43672 | 0.198218 | ||||||||
\(502\) | −28.5011 | −1.27206 | ||||||||
\(503\) | −17.4543 | −0.778251 | −0.389125 | − | 0.921185i | \(-0.627223\pi\) | ||||
−0.389125 | + | 0.921185i | \(0.627223\pi\) | |||||||
\(504\) | 3.92498 | 0.174833 | ||||||||
\(505\) | 23.7536 | 1.05702 | ||||||||
\(506\) | 14.7614 | 0.656222 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.7643 | 1.18747 | ||||||||
\(509\) | −2.76991 | −0.122774 | −0.0613870 | − | 0.998114i | \(-0.519552\pi\) | ||||
−0.0613870 | + | 0.998114i | \(0.519552\pi\) | |||||||
\(510\) | 3.61212 | 0.159948 | ||||||||
\(511\) | −7.50106 | −0.331827 | ||||||||
\(512\) | −22.0643 | −0.975115 | ||||||||
\(513\) | −3.54778 | −0.156638 | ||||||||
\(514\) | 34.6991 | 1.53051 | ||||||||
\(515\) | 42.5606 | 1.87544 | ||||||||
\(516\) | 31.5860 | 1.39049 | ||||||||
\(517\) | 39.6922 | 1.74566 | ||||||||
\(518\) | −9.57608 | −0.420749 | ||||||||
\(519\) | −22.1599 | −0.972712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2816 | −1.15142 | −0.575710 | − | 0.817654i | \(-0.695274\pi\) | ||||
−0.575710 | + | 0.817654i | \(0.695274\pi\) | |||||||
\(522\) | −20.6327 | −0.903067 | ||||||||
\(523\) | 5.25042 | 0.229585 | 0.114792 | − | 0.993389i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993389i | \(0.463380\pi\) | |||||||
\(524\) | 41.7098 | 1.82210 | ||||||||
\(525\) | −11.2272 | −0.489994 | ||||||||
\(526\) | 53.8513 | 2.34803 | ||||||||
\(527\) | 2.38788 | 0.104018 | ||||||||
\(528\) | −6.64042 | −0.288987 | ||||||||
\(529\) | −19.4026 | −0.843590 | ||||||||
\(530\) | 74.2568 | 3.22551 | ||||||||
\(531\) | 2.10331 | 0.0912760 | ||||||||
\(532\) | 12.9533 | 0.561596 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15.1161 | 0.654138 | ||||||||
\(535\) | −49.9730 | −2.16052 | ||||||||
\(536\) | −21.9164 | −0.946646 | ||||||||
\(537\) | 1.94048 | 0.0837381 | ||||||||
\(538\) | −66.5363 | −2.86858 | ||||||||
\(539\) | 3.27389 | 0.141016 | ||||||||
\(540\) | −14.7077 | −0.632918 | ||||||||
\(541\) | 0.111863 | 0.00480937 | 0.00240468 | − | 0.999997i | \(-0.499235\pi\) | ||||
0.00240468 | + | 0.999997i | \(0.499235\pi\) | |||||||
\(542\) | 18.0841 | 0.776778 | ||||||||
\(543\) | 8.50106 | 0.364815 | ||||||||
\(544\) | 1.14228 | 0.0489749 | ||||||||
\(545\) | 48.8697 | 2.09335 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7515 | −1.44311 | −0.721555 | − | 0.692358i | \(-0.756572\pi\) | ||||
−0.721555 | + | 0.692358i | \(0.756572\pi\) | |||||||
\(548\) | 11.6511 | 0.497710 | ||||||||
\(549\) | 7.75441 | 0.330950 | ||||||||
\(550\) | 87.3777 | 3.72580 | ||||||||
\(551\) | −30.7926 | −1.31181 | ||||||||
\(552\) | −7.44447 | −0.316858 | ||||||||
\(553\) | −1.16283 | −0.0494485 | ||||||||
\(554\) | −16.3764 | −0.695767 | ||||||||
\(555\) | 16.2272 | 0.688805 | ||||||||
\(556\) | 19.6327 | 0.832611 | ||||||||
\(557\) | −29.0147 | −1.22939 | −0.614696 | − | 0.788764i | \(-0.710721\pi\) | ||||
−0.614696 | + | 0.788764i | \(0.710721\pi\) | |||||||
\(558\) | −15.0488 | −0.637068 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.17058 | 0.345270 | ||||||||
\(561\) | 1.23492 | 0.0521384 | ||||||||
\(562\) | −25.6885 | −1.08360 | ||||||||
\(563\) | 1.43167 | 0.0603378 | 0.0301689 | − | 0.999545i | \(-0.490395\pi\) | ||||
0.0301689 | + | 0.999545i | \(0.490395\pi\) | |||||||
\(564\) | −44.2653 | −1.86391 | ||||||||
\(565\) | −42.9885 | −1.80854 | ||||||||
\(566\) | −18.1260 | −0.761892 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −15.6695 | −0.657478 | ||||||||
\(569\) | −24.5011 | −1.02714 | −0.513569 | − | 0.858048i | \(-0.671677\pi\) | ||||
−0.513569 | + | 0.858048i | \(0.671677\pi\) | |||||||
\(570\) | −33.9738 | −1.42301 | ||||||||
\(571\) | −47.3735 | −1.98252 | −0.991259 | − | 0.131929i | \(-0.957883\pi\) | ||||
−0.991259 | + | 0.131929i | \(0.957883\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.651093 | −0.0271998 | ||||||||
\(574\) | −17.8500 | −0.745043 | ||||||||
\(575\) | 21.2944 | 0.888039 | ||||||||
\(576\) | −11.2555 | −0.468978 | ||||||||
\(577\) | −27.4055 | −1.14091 | −0.570453 | − | 0.821330i | \(-0.693232\pi\) | ||||
−0.570453 | + | 0.821330i | \(0.693232\pi\) | |||||||
\(578\) | −40.0742 | −1.66687 | ||||||||
\(579\) | 19.0643 | 0.792287 | ||||||||
\(580\) | −127.654 | −5.30053 | ||||||||
\(581\) | −15.1805 | −0.629791 | ||||||||
\(582\) | 11.8187 | 0.489903 | ||||||||
\(583\) | 25.3871 | 1.05143 | ||||||||
\(584\) | −29.4415 | −1.21830 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 52.9914 | 2.18906 | ||||||||
\(587\) | −27.8959 | −1.15139 | −0.575693 | − | 0.817666i | \(-0.695268\pi\) | ||||
−0.575693 | + | 0.817666i | \(0.695268\pi\) | |||||||
\(588\) | −3.65109 | −0.150569 | ||||||||
\(589\) | −22.4592 | −0.925414 | ||||||||
\(590\) | 20.1415 | 0.829212 | ||||||||
\(591\) | 24.7098 | 1.01643 | ||||||||
\(592\) | −8.17058 | −0.335809 | ||||||||
\(593\) | 16.6015 | 0.681740 | 0.340870 | − | 0.940110i | \(-0.389278\pi\) | ||||
0.340870 | + | 0.940110i | \(0.389278\pi\) | |||||||
\(594\) | −7.78270 | −0.319328 | ||||||||
\(595\) | −1.51948 | −0.0622928 | ||||||||
\(596\) | 36.6142 | 1.49978 | ||||||||
\(597\) | −13.1444 | −0.537965 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7913 | 0.481778 | 0.240889 | − | 0.970553i | \(-0.422561\pi\) | ||||
0.240889 | + | 0.970553i | \(0.422561\pi\) | |||||||
\(600\) | −44.0665 | −1.79901 | ||||||||
\(601\) | 13.8217 | 0.563798 | 0.281899 | − | 0.959444i | \(-0.409036\pi\) | ||||
0.281899 | + | 0.959444i | \(0.409036\pi\) | |||||||
\(602\) | −20.5654 | −0.838183 | ||||||||
\(603\) | −5.58383 | −0.227391 | ||||||||
\(604\) | 35.4720 | 1.44333 | ||||||||
\(605\) | −1.13453 | −0.0461253 | ||||||||
\(606\) | −14.0176 | −0.569427 | ||||||||
\(607\) | −21.0948 | −0.856210 | −0.428105 | − | 0.903729i | \(-0.640819\pi\) | ||||
−0.428105 | + | 0.903729i | \(0.640819\pi\) | |||||||
\(608\) | −10.7437 | −0.435716 | ||||||||
\(609\) | 8.67939 | 0.351707 | ||||||||
\(610\) | 74.2568 | 3.00657 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.37720 | −0.0556701 | ||||||||
\(613\) | −2.19383 | −0.0886079 | −0.0443039 | − | 0.999018i | \(-0.514107\pi\) | ||||
−0.0443039 | + | 0.999018i | \(0.514107\pi\) | |||||||
\(614\) | 67.1436 | 2.70970 | ||||||||
\(615\) | 30.2477 | 1.21971 | ||||||||
\(616\) | 12.8500 | 0.517740 | ||||||||
\(617\) | 6.34811 | 0.255565 | 0.127783 | − | 0.991802i | \(-0.459214\pi\) | ||||
0.127783 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(618\) | −25.1161 | −1.01032 | ||||||||
\(619\) | 7.77203 | 0.312384 | 0.156192 | − | 0.987727i | \(-0.450078\pi\) | ||||
0.156192 | + | 0.987727i | \(0.450078\pi\) | |||||||
\(620\) | −93.1068 | −3.73926 | ||||||||
\(621\) | −1.89669 | −0.0761115 | ||||||||
\(622\) | −6.32756 | −0.253712 | ||||||||
\(623\) | −6.35878 | −0.254759 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.9135 | 1.79654 | ||||||||
\(626\) | −53.4458 | −2.13612 | ||||||||
\(627\) | −11.6150 | −0.463860 | ||||||||
\(628\) | 64.1719 | 2.56074 | ||||||||
\(629\) | 1.51948 | 0.0605858 | ||||||||
\(630\) | 9.57608 | 0.381520 | ||||||||
\(631\) | −34.2624 | −1.36397 | −0.681983 | − | 0.731368i | \(-0.738882\pi\) | ||||
−0.681983 | + | 0.731368i | \(0.738882\pi\) | |||||||
\(632\) | −4.56408 | −0.181549 | ||||||||
\(633\) | 19.5966 | 0.778896 | ||||||||
\(634\) | −44.7664 | −1.77790 | ||||||||
\(635\) | 29.5294 | 1.17184 | ||||||||
\(636\) | −28.3121 | −1.12265 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −67.5491 | −2.67429 | ||||||||
\(639\) | −3.99225 | −0.157931 | ||||||||
\(640\) | −83.3855 | −3.29610 | ||||||||
\(641\) | −23.2186 | −0.917080 | −0.458540 | − | 0.888674i | \(-0.651627\pi\) | ||||
−0.458540 | + | 0.888674i | \(0.651627\pi\) | |||||||
\(642\) | 29.4904 | 1.16389 | ||||||||
\(643\) | −20.0801 | −0.791880 | −0.395940 | − | 0.918276i | \(-0.629581\pi\) | ||||
−0.395940 | + | 0.918276i | \(0.629581\pi\) | |||||||
\(644\) | 6.92498 | 0.272883 | ||||||||
\(645\) | 34.8492 | 1.37218 | ||||||||
\(646\) | −3.18125 | −0.125165 | ||||||||
\(647\) | −16.5294 | −0.649836 | −0.324918 | − | 0.945742i | \(-0.605337\pi\) | ||||
−0.324918 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(648\) | 3.92498 | 0.154188 | ||||||||
\(649\) | 6.88601 | 0.270300 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.33048 | 0.248111 | ||||||||
\(652\) | 20.0488 | 0.785173 | ||||||||
\(653\) | −0.927907 | −0.0363118 | −0.0181559 | − | 0.999835i | \(-0.505780\pi\) | ||||
−0.0181559 | + | 0.999835i | \(0.505780\pi\) | |||||||
\(654\) | −28.8393 | −1.12771 | ||||||||
\(655\) | 46.0189 | 1.79811 | ||||||||
\(656\) | −15.2301 | −0.594635 | ||||||||
\(657\) | −7.50106 | −0.292644 | ||||||||
\(658\) | 28.8209 | 1.12355 | ||||||||
\(659\) | 32.2568 | 1.25655 | 0.628273 | − | 0.777993i | \(-0.283762\pi\) | ||||
0.628273 | + | 0.777993i | \(0.283762\pi\) | |||||||
\(660\) | −48.1514 | −1.87429 | ||||||||
\(661\) | 22.8569 | 0.889031 | 0.444516 | − | 0.895771i | \(-0.353376\pi\) | ||||
0.444516 | + | 0.895771i | \(0.353376\pi\) | |||||||
\(662\) | 42.3892 | 1.64750 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.5830 | −2.31227 | ||||||||
\(665\) | 14.2915 | 0.554201 | ||||||||
\(666\) | −9.57608 | −0.371065 | ||||||||
\(667\) | −16.4621 | −0.637415 | ||||||||
\(668\) | −16.1989 | −0.626753 | ||||||||
\(669\) | −27.8676 | −1.07742 | ||||||||
\(670\) | −53.4712 | −2.06577 | ||||||||
\(671\) | 25.3871 | 0.980057 | ||||||||
\(672\) | 3.02830 | 0.116819 | ||||||||
\(673\) | 1.08569 | 0.0418503 | 0.0209251 | − | 0.999781i | \(-0.493339\pi\) | ||||
0.0209251 | + | 0.999781i | \(0.493339\pi\) | |||||||
\(674\) | 18.0099 | 0.693714 | ||||||||
\(675\) | −11.2272 | −0.432134 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.60730 | −0.330805 | −0.165403 | − | 0.986226i | \(-0.552892\pi\) | ||||
−0.165403 | + | 0.986226i | \(0.552892\pi\) | |||||||
\(678\) | 25.3687 | 0.974277 | ||||||||
\(679\) | −4.97170 | −0.190796 | ||||||||
\(680\) | −5.96395 | −0.228707 | ||||||||
\(681\) | 12.0304 | 0.461007 | ||||||||
\(682\) | −49.2683 | −1.88658 | ||||||||
\(683\) | −33.4621 | −1.28039 | −0.640196 | − | 0.768212i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768212i | \(0.721147\pi\) | |||||||
\(684\) | 12.9533 | 0.495281 | ||||||||
\(685\) | 12.8548 | 0.491156 | ||||||||
\(686\) | 2.37720 | 0.0907620 | ||||||||
\(687\) | −9.19887 | −0.350959 | ||||||||
\(688\) | −17.5470 | −0.668972 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −18.1628 | −0.691447 | ||||||||
\(691\) | 4.69219 | 0.178499 | 0.0892496 | − | 0.996009i | \(-0.471553\pi\) | ||||
0.0892496 | + | 0.996009i | \(0.471553\pi\) | |||||||
\(692\) | 80.9079 | 3.07566 | ||||||||
\(693\) | 3.27389 | 0.124365 | ||||||||
\(694\) | 18.7517 | 0.711805 | ||||||||
\(695\) | 21.6610 | 0.821647 | ||||||||
\(696\) | 34.0665 | 1.29129 | ||||||||
\(697\) | 2.83235 | 0.107283 | ||||||||
\(698\) | 27.8938 | 1.05579 | ||||||||
\(699\) | 12.4522 | 0.470986 | ||||||||
\(700\) | 40.9914 | 1.54933 | ||||||||
\(701\) | 41.4535 | 1.56568 | 0.782839 | − | 0.622224i | \(-0.213771\pi\) | ||||
0.782839 | + | 0.622224i | \(0.213771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2915 | −0.539015 | ||||||||
\(704\) | −36.8492 | −1.38881 | ||||||||
\(705\) | −48.8385 | −1.83936 | ||||||||
\(706\) | 29.8032 | 1.12166 | ||||||||
\(707\) | 5.89669 | 0.221768 | ||||||||
\(708\) | −7.67939 | −0.288609 | ||||||||
\(709\) | −3.84222 | −0.144298 | −0.0721488 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721488 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(710\) | −38.2301 | −1.43475 | ||||||||
\(711\) | −1.16283 | −0.0436095 | ||||||||
\(712\) | −24.9581 | −0.935345 | ||||||||
\(713\) | −12.0069 | −0.449664 | ||||||||
\(714\) | 0.896688 | 0.0335577 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.08489 | −0.264775 | ||||||||
\(717\) | −3.24559 | −0.121209 | ||||||||
\(718\) | 11.9279 | 0.445146 | ||||||||
\(719\) | 8.91219 | 0.332369 | 0.166184 | − | 0.986095i | \(-0.446855\pi\) | ||||
0.166184 | + | 0.986095i | \(0.446855\pi\) | |||||||
\(720\) | 8.17058 | 0.304499 | ||||||||
\(721\) | 10.5654 | 0.393476 | ||||||||
\(722\) | −15.2456 | −0.567382 | ||||||||
\(723\) | 9.42605 | 0.350558 | ||||||||
\(724\) | −31.0382 | −1.15352 | ||||||||
\(725\) | −97.4450 | −3.61902 | ||||||||
\(726\) | 0.669517 | 0.0248481 | ||||||||
\(727\) | 29.6815 | 1.10083 | 0.550413 | − | 0.834892i | \(-0.314470\pi\) | ||||
0.550413 | + | 0.834892i | \(0.314470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −71.8307 | −2.65858 | ||||||||
\(731\) | 3.26322 | 0.120694 | ||||||||
\(732\) | −28.3121 | −1.04644 | ||||||||
\(733\) | −5.30299 | −0.195870 | −0.0979352 | − | 0.995193i | \(-0.531224\pi\) | ||||
−0.0979352 | + | 0.995193i | \(0.531224\pi\) | |||||||
\(734\) | 56.3630 | 2.08040 | ||||||||
\(735\) | −4.02830 | −0.148586 | ||||||||
\(736\) | −5.74373 | −0.211717 | ||||||||
\(737\) | −18.2808 | −0.673383 | ||||||||
\(738\) | −17.8500 | −0.657066 | ||||||||
\(739\) | 20.9143 | 0.769345 | 0.384673 | − | 0.923053i | \(-0.374314\pi\) | ||||
0.384673 | + | 0.923053i | \(0.374314\pi\) | |||||||
\(740\) | −59.2469 | −2.17796 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.4338 | 0.676726 | ||||||||
\(743\) | 0.318488 | 0.0116842 | 0.00584209 | − | 0.999983i | \(-0.498140\pi\) | ||||
0.00584209 | + | 0.999983i | \(0.498140\pi\) | |||||||
\(744\) | 24.8470 | 0.910937 | ||||||||
\(745\) | 40.3969 | 1.48003 | ||||||||
\(746\) | −23.6610 | −0.866290 | ||||||||
\(747\) | −15.1805 | −0.555424 | ||||||||
\(748\) | −4.50881 | −0.164858 | ||||||||
\(749\) | −12.4055 | −0.453287 | ||||||||
\(750\) | −59.6319 | −2.17745 | ||||||||
\(751\) | 39.5881 | 1.44459 | 0.722295 | − | 0.691585i | \(-0.243087\pi\) | ||||
0.722295 | + | 0.691585i | \(0.243087\pi\) | |||||||
\(752\) | 24.5908 | 0.896733 | ||||||||
\(753\) | 11.9893 | 0.436915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.1367 | 1.42433 | ||||||||
\(756\) | −3.65109 | −0.132789 | ||||||||
\(757\) | −10.2533 | −0.372664 | −0.186332 | − | 0.982487i | \(-0.559660\pi\) | ||||
−0.186332 | + | 0.982487i | \(0.559660\pi\) | |||||||
\(758\) | 66.2050 | 2.40467 | ||||||||
\(759\) | −6.20955 | −0.225392 | ||||||||
\(760\) | 56.0940 | 2.03474 | ||||||||
\(761\) | 17.4784 | 0.633591 | 0.316796 | − | 0.948494i | \(-0.397393\pi\) | ||||
0.316796 | + | 0.948494i | \(0.397393\pi\) | |||||||
\(762\) | −17.4260 | −0.631279 | ||||||||
\(763\) | 12.1316 | 0.439194 | ||||||||
\(764\) | 2.37720 | 0.0860042 | ||||||||
\(765\) | −1.51948 | −0.0549371 | ||||||||
\(766\) | 16.4132 | 0.593035 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 26.6970 | 0.963345 | ||||||||
\(769\) | −36.0566 | −1.30023 | −0.650117 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(770\) | 31.3510 | 1.12981 | ||||||||
\(771\) | −14.5966 | −0.525685 | ||||||||
\(772\) | −69.6057 | −2.50516 | ||||||||
\(773\) | 10.7184 | 0.385513 | 0.192756 | − | 0.981247i | \(-0.438257\pi\) | ||||
0.192756 | + | 0.981247i | \(0.438257\pi\) | |||||||
\(774\) | −20.5654 | −0.739208 | ||||||||
\(775\) | −71.0734 | −2.55303 | ||||||||
\(776\) | −19.5139 | −0.700507 | ||||||||
\(777\) | 4.02830 | 0.144514 | ||||||||
\(778\) | −67.4565 | −2.41843 | ||||||||
\(779\) | −26.6396 | −0.954463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.0702 | −0.467688 | ||||||||
\(782\) | −1.70074 | −0.0608182 | ||||||||
\(783\) | 8.67939 | 0.310176 | ||||||||
\(784\) | 2.02830 | 0.0724392 | ||||||||
\(785\) | 70.8016 | 2.52702 | ||||||||
\(786\) | −27.1570 | −0.968657 | ||||||||
\(787\) | 8.95811 | 0.319322 | 0.159661 | − | 0.987172i | \(-0.448960\pi\) | ||||
0.159661 | + | 0.987172i | \(0.448960\pi\) | |||||||
\(788\) | −90.2178 | −3.21388 | ||||||||
\(789\) | −22.6532 | −0.806476 | ||||||||
\(790\) | −11.1353 | −0.396177 | ||||||||
\(791\) | −10.6716 | −0.379440 | ||||||||
\(792\) | 12.8500 | 0.456604 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.3326 | 0.402179 | ||||||||
\(795\) | −31.2370 | −1.10786 | ||||||||
\(796\) | 47.9914 | 1.70101 | ||||||||
\(797\) | −36.0686 | −1.27761 | −0.638807 | − | 0.769367i | \(-0.720572\pi\) | ||||
−0.638807 | + | 0.769367i | \(0.720572\pi\) | |||||||
\(798\) | −8.43380 | −0.298553 | ||||||||
\(799\) | −4.57315 | −0.161787 | ||||||||
\(800\) | −33.9992 | −1.20205 | ||||||||
\(801\) | −6.35878 | −0.224676 | ||||||||
\(802\) | 19.6503 | 0.693876 | ||||||||
\(803\) | −24.5577 | −0.866621 | ||||||||
\(804\) | 20.3871 | 0.718997 | ||||||||
\(805\) | 7.64042 | 0.269289 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.9893 | 0.985271 | ||||||||
\(808\) | 23.1444 | 0.814217 | ||||||||
\(809\) | 47.5294 | 1.67104 | 0.835522 | − | 0.549458i | \(-0.185166\pi\) | ||||
0.835522 | + | 0.549458i | \(0.185166\pi\) | |||||||
\(810\) | 9.57608 | 0.336469 | ||||||||
\(811\) | 5.34678 | 0.187751 | 0.0938755 | − | 0.995584i | \(-0.470074\pi\) | ||||
0.0938755 | + | 0.995584i | \(0.470074\pi\) | |||||||
\(812\) | −31.6893 | −1.11208 | ||||||||
\(813\) | −7.60730 | −0.266800 | ||||||||
\(814\) | −31.3510 | −1.09885 | ||||||||
\(815\) | 22.1201 | 0.774835 | ||||||||
\(816\) | 0.765079 | 0.0267831 | ||||||||
\(817\) | −30.6922 | −1.07378 | ||||||||
\(818\) | −50.9525 | −1.78151 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −110.437 | −3.85664 | ||||||||
\(821\) | 21.8697 | 0.763258 | 0.381629 | − | 0.924316i | \(-0.375363\pi\) | ||||
0.381629 | + | 0.924316i | \(0.375363\pi\) | |||||||
\(822\) | −7.58595 | −0.264590 | ||||||||
\(823\) | 22.9942 | 0.801526 | 0.400763 | − | 0.916182i | \(-0.368745\pi\) | ||||
0.400763 | + | 0.916182i | \(0.368745\pi\) | |||||||
\(824\) | 41.4690 | 1.44464 | ||||||||
\(825\) | −36.7565 | −1.27970 | ||||||||
\(826\) | 5.00000 | 0.173972 | ||||||||
\(827\) | −21.3425 | −0.742151 | −0.371075 | − | 0.928603i | \(-0.621011\pi\) | ||||
−0.371075 | + | 0.928603i | \(0.621011\pi\) | |||||||
\(828\) | 6.92498 | 0.240660 | ||||||||
\(829\) | 27.4309 | 0.952714 | 0.476357 | − | 0.879252i | \(-0.341957\pi\) | ||||
0.476357 | + | 0.879252i | \(0.341957\pi\) | |||||||
\(830\) | −145.369 | −5.04584 | ||||||||
\(831\) | 6.88894 | 0.238975 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.377203 | −0.0130693 | ||||||||
\(834\) | −12.7827 | −0.442629 | ||||||||
\(835\) | −17.8724 | −0.618501 | ||||||||
\(836\) | 42.4076 | 1.46670 | ||||||||
\(837\) | 6.33048 | 0.218814 | ||||||||
\(838\) | −5.44739 | −0.188177 | ||||||||
\(839\) | 4.43167 | 0.152998 | 0.0764992 | − | 0.997070i | \(-0.475626\pi\) | ||||
0.0764992 | + | 0.997070i | \(0.475626\pi\) | |||||||
\(840\) | −15.8110 | −0.545531 | ||||||||
\(841\) | 46.3318 | 1.59765 | ||||||||
\(842\) | −18.0975 | −0.623680 | ||||||||
\(843\) | 10.8062 | 0.372184 | ||||||||
\(844\) | −71.5491 | −2.46282 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28.8209 | 0.990882 | ||||||||
\(847\) | −0.281641 | −0.00967729 | ||||||||
\(848\) | 15.7282 | 0.540110 | ||||||||
\(849\) | 7.62492 | 0.261687 | ||||||||
\(850\) | −10.0673 | −0.345304 | ||||||||
\(851\) | −7.64042 | −0.261910 | ||||||||
\(852\) | 14.5761 | 0.499368 | ||||||||
\(853\) | −43.0040 | −1.47243 | −0.736215 | − | 0.676748i | \(-0.763389\pi\) | ||||
−0.736215 | + | 0.676748i | \(0.763389\pi\) | |||||||
\(854\) | 18.4338 | 0.630791 | ||||||||
\(855\) | 14.2915 | 0.488759 | ||||||||
\(856\) | −48.6914 | −1.66424 | ||||||||
\(857\) | 0.866269 | 0.0295912 | 0.0147956 | − | 0.999891i | \(-0.495290\pi\) | ||||
0.0147956 | + | 0.999891i | \(0.495290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.3481 | −0.523671 | −0.261835 | − | 0.965113i | \(-0.584328\pi\) | ||||
−0.261835 | + | 0.965113i | \(0.584328\pi\) | |||||||
\(860\) | −127.238 | −4.33876 | ||||||||
\(861\) | 7.50881 | 0.255900 | ||||||||
\(862\) | −49.5950 | −1.68921 | ||||||||
\(863\) | 37.0275 | 1.26043 | 0.630215 | − | 0.776420i | \(-0.282967\pi\) | ||||
0.630215 | + | 0.776420i | \(0.282967\pi\) | |||||||
\(864\) | 3.02830 | 0.103025 | ||||||||
\(865\) | 89.2667 | 3.03516 | ||||||||
\(866\) | −55.5704 | −1.88836 | ||||||||
\(867\) | 16.8577 | 0.572518 | ||||||||
\(868\) | −23.1132 | −0.784513 | ||||||||
\(869\) | −3.80697 | −0.129143 | ||||||||
\(870\) | 83.1145 | 2.81785 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 47.6164 | 1.61249 | ||||||||
\(873\) | −4.97170 | −0.168267 | ||||||||
\(874\) | 15.9963 | 0.541082 | ||||||||
\(875\) | 25.0849 | 0.848024 | ||||||||
\(876\) | 27.3871 | 0.925324 | ||||||||
\(877\) | −23.0205 | −0.777349 | −0.388674 | − | 0.921375i | \(-0.627067\pi\) | ||||
−0.388674 | + | 0.921375i | \(0.627067\pi\) | |||||||
\(878\) | 21.7635 | 0.734482 | ||||||||
\(879\) | −22.2915 | −0.751874 | ||||||||
\(880\) | 26.7496 | 0.901728 | ||||||||
\(881\) | 38.0168 | 1.28082 | 0.640410 | − | 0.768034i | \(-0.278765\pi\) | ||||
0.640410 | + | 0.768034i | \(0.278765\pi\) | |||||||
\(882\) | 2.37720 | 0.0800446 | ||||||||
\(883\) | −6.95620 | −0.234095 | −0.117047 | − | 0.993126i | \(-0.537343\pi\) | ||||
−0.117047 | + | 0.993126i | \(0.537343\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.47277 | −0.284809 | ||||||||
\(886\) | 26.7750 | 0.899522 | ||||||||
\(887\) | −25.8131 | −0.866720 | −0.433360 | − | 0.901221i | \(-0.642672\pi\) | ||||
−0.433360 | + | 0.901221i | \(0.642672\pi\) | |||||||
\(888\) | 15.8110 | 0.530582 | ||||||||
\(889\) | 7.33048 | 0.245857 | ||||||||
\(890\) | −60.8922 | −2.04111 | ||||||||
\(891\) | 3.27389 | 0.109679 | ||||||||
\(892\) | 101.747 | 3.40675 | ||||||||
\(893\) | 43.0128 | 1.43937 | ||||||||
\(894\) | −23.8393 | −0.797305 | ||||||||
\(895\) | −7.81684 | −0.261288 | ||||||||
\(896\) | −20.6999 | −0.691536 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 80.3134 | 2.68009 | ||||||||
\(899\) | 54.9447 | 1.83251 | ||||||||
\(900\) | 40.9914 | 1.36638 | ||||||||
\(901\) | −2.92498 | −0.0974453 | ||||||||
\(902\) | −58.4388 | −1.94580 | ||||||||
\(903\) | 8.65109 | 0.287890 | ||||||||
\(904\) | −41.8860 | −1.39311 | ||||||||
\(905\) | −34.2448 | −1.13834 | ||||||||
\(906\) | −23.0956 | −0.767299 | ||||||||
\(907\) | −2.59158 | −0.0860519 | −0.0430260 | − | 0.999074i | \(-0.513700\pi\) | ||||
−0.0430260 | + | 0.999074i | \(0.513700\pi\) | |||||||
\(908\) | −43.9242 | −1.45768 | ||||||||
\(909\) | 5.89669 | 0.195581 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.7507 | 1.21760 | 0.608802 | − | 0.793322i | \(-0.291650\pi\) | ||||
0.608802 | + | 0.793322i | \(0.291650\pi\) | |||||||
\(912\) | −7.19595 | −0.238282 | ||||||||
\(913\) | −49.6991 | −1.64480 | ||||||||
\(914\) | −81.5248 | −2.69660 | ||||||||
\(915\) | −31.2370 | −1.03266 | ||||||||
\(916\) | 33.5860 | 1.10971 | ||||||||
\(917\) | 11.4239 | 0.377251 | ||||||||
\(918\) | 0.896688 | 0.0295951 | ||||||||
\(919\) | −3.16283 | −0.104332 | −0.0521660 | − | 0.998638i | \(-0.516613\pi\) | ||||
−0.0521660 | + | 0.998638i | \(0.516613\pi\) | |||||||
\(920\) | 29.9885 | 0.988692 | ||||||||
\(921\) | −28.2448 | −0.930698 | ||||||||
\(922\) | −45.9575 | −1.51353 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −11.9533 | −0.393234 | ||||||||
\(925\) | −45.2264 | −1.48703 | ||||||||
\(926\) | −14.9632 | −0.491720 | ||||||||
\(927\) | 10.5654 | 0.347013 | ||||||||
\(928\) | 26.2838 | 0.862807 | ||||||||
\(929\) | −39.5929 | −1.29900 | −0.649500 | − | 0.760361i | \(-0.725022\pi\) | ||||
−0.649500 | + | 0.760361i | \(0.725022\pi\) | |||||||
\(930\) | 60.6212 | 1.98785 | ||||||||
\(931\) | 3.54778 | 0.116274 | ||||||||
\(932\) | −45.4642 | −1.48923 | ||||||||
\(933\) | 2.66177 | 0.0871423 | ||||||||
\(934\) | 57.5979 | 1.88466 | ||||||||
\(935\) | −4.97463 | −0.162688 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.94553 | 0.0962263 | 0.0481131 | − | 0.998842i | \(-0.484679\pi\) | ||||
0.0481131 | + | 0.998842i | \(0.484679\pi\) | |||||||
\(938\) | −13.2739 | −0.433408 | ||||||||
\(939\) | 22.4826 | 0.733693 | ||||||||
\(940\) | 178.314 | 5.81596 | ||||||||
\(941\) | −20.9893 | −0.684232 | −0.342116 | − | 0.939658i | \(-0.611144\pi\) | ||||
−0.342116 | + | 0.939658i | \(0.611144\pi\) | |||||||
\(942\) | −41.7819 | −1.36133 | ||||||||
\(943\) | −14.2419 | −0.463779 | ||||||||
\(944\) | 4.26614 | 0.138851 | ||||||||
\(945\) | −4.02830 | −0.131040 | ||||||||
\(946\) | −67.3289 | −2.18905 | ||||||||
\(947\) | 6.36733 | 0.206910 | 0.103455 | − | 0.994634i | \(-0.467010\pi\) | ||||
0.103455 | + | 0.994634i | \(0.467010\pi\) | |||||||
\(948\) | 4.24559 | 0.137890 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 94.6877 | 3.07207 | ||||||||
\(951\) | 18.8315 | 0.610655 | ||||||||
\(952\) | −1.48052 | −0.0479838 | ||||||||
\(953\) | 60.4535 | 1.95828 | 0.979141 | − | 0.203181i | \(-0.0651281\pi\) | ||||
0.979141 | + | 0.203181i | \(0.0651281\pi\) | |||||||
\(954\) | 18.4338 | 0.596816 | ||||||||
\(955\) | 2.62280 | 0.0848717 | ||||||||
\(956\) | 11.8500 | 0.383255 | ||||||||
\(957\) | 28.4154 | 0.918539 | ||||||||
\(958\) | 79.9447 | 2.58290 | ||||||||
\(959\) | 3.19112 | 0.103047 | ||||||||
\(960\) | 45.3404 | 1.46335 | ||||||||
\(961\) | 9.07502 | 0.292742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.4055 | −0.399762 | ||||||||
\(964\) | −34.4154 | −1.10844 | ||||||||
\(965\) | −76.7968 | −2.47218 | ||||||||
\(966\) | −4.50881 | −0.145069 | ||||||||
\(967\) | −48.1719 | −1.54910 | −0.774552 | − | 0.632510i | \(-0.782025\pi\) | ||||
−0.774552 | + | 0.632510i | \(0.782025\pi\) | |||||||
\(968\) | −1.10543 | −0.0355300 | ||||||||
\(969\) | 1.33823 | 0.0429902 | ||||||||
\(970\) | −47.6094 | −1.52865 | ||||||||
\(971\) | 17.9653 | 0.576533 | 0.288267 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288267 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(972\) | −3.65109 | −0.117109 | ||||||||
\(973\) | 5.37720 | 0.172385 | ||||||||
\(974\) | 18.8393 | 0.603650 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.7282 | 0.503448 | ||||||||
\(977\) | 2.82672 | 0.0904347 | 0.0452174 | − | 0.998977i | \(-0.485602\pi\) | ||||
0.0452174 | + | 0.998977i | \(0.485602\pi\) | |||||||
\(978\) | −13.0537 | −0.417410 | ||||||||
\(979\) | −20.8179 | −0.665344 | ||||||||
\(980\) | 14.7077 | 0.469820 | ||||||||
\(981\) | 12.1316 | 0.387332 | ||||||||
\(982\) | 5.78058 | 0.184466 | ||||||||
\(983\) | 29.8873 | 0.953258 | 0.476629 | − | 0.879105i | \(-0.341859\pi\) | ||||
0.476629 | + | 0.879105i | \(0.341859\pi\) | |||||||
\(984\) | 29.4720 | 0.939532 | ||||||||
\(985\) | −99.5384 | −3.17156 | ||||||||
\(986\) | 7.78270 | 0.247852 | ||||||||
\(987\) | −12.1239 | −0.385907 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4084 | −0.521757 | ||||||||
\(990\) | 31.3510 | 0.996401 | ||||||||
\(991\) | 36.9469 | 1.17366 | 0.586828 | − | 0.809712i | \(-0.300377\pi\) | ||||
0.586828 | + | 0.809712i | \(0.300377\pi\) | |||||||
\(992\) | 19.1706 | 0.608666 | ||||||||
\(993\) | −17.8315 | −0.565867 | ||||||||
\(994\) | −9.49039 | −0.301017 | ||||||||
\(995\) | 52.9496 | 1.67861 | ||||||||
\(996\) | 55.4252 | 1.75622 | ||||||||
\(997\) | 10.7176 | 0.339428 | 0.169714 | − | 0.985493i | \(-0.445716\pi\) | ||||
0.169714 | + | 0.985493i | \(0.445716\pi\) | |||||||
\(998\) | 44.1775 | 1.39842 | ||||||||
\(999\) | 4.02830 | 0.127450 |
(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 | 3549.2.a.s.1.3 | 3 | ||
13.4 | even | 6 | 273.2.k.d.211.3 | yes | 6 | ||
13.10 | even | 6 | 273.2.k.d.22.3 | ✓ | 6 | ||
13.12 | even | 2 | 3549.2.a.h.1.1 | 3 | |||
39.17 | odd | 6 | 819.2.o.d.757.1 | 6 | |||
39.23 | odd | 6 | 819.2.o.d.568.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.d.22.3 | ✓ | 6 | 13.10 | even | 6 | ||
273.2.k.d.211.3 | yes | 6 | 13.4 | even | 6 | ||
819.2.o.d.568.1 | 6 | 39.23 | odd | 6 | |||
819.2.o.d.757.1 | 6 | 39.17 | odd | 6 | |||
3549.2.a.h.1.1 | 3 | 13.12 | even | 2 | |||
3549.2.a.s.1.3 | 3 | 1.1 | even | 1 | trivial |