Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 6x - 2 \)
|
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 | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36333 | −0.515290 | −0.257645 | − | 0.966240i | \(-0.582946\pi\) | ||||
−0.257645 | + | 0.966240i | \(0.582946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.64600 | −1.70233 | −0.851167 | − | 0.524896i | \(-0.824104\pi\) | ||||
−0.851167 | + | 0.524896i | \(0.824104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.14134 | 0.519350 | 0.259675 | − | 0.965696i | \(-0.416385\pi\) | ||||
0.259675 | + | 0.965696i | \(0.416385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41468 | 0.553966 | 0.276983 | − | 0.960875i | \(-0.410666\pi\) | ||||
0.276983 | + | 0.960875i | \(0.410666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.36333 | −0.297503 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.72666 | −0.568547 | −0.284274 | − | 0.958743i | \(-0.591752\pi\) | ||||
−0.284274 | + | 0.958743i | \(0.591752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.28267 | −0.980968 | −0.490484 | − | 0.871450i | \(-0.663180\pi\) | ||||
−0.490484 | + | 0.871450i | \(0.663180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.64600 | −0.295630 | −0.147815 | − | 0.989015i | \(-0.547224\pi\) | ||||
−0.147815 | + | 0.989015i | \(0.547224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.64600 | −0.982843 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.86799 | 0.635894 | 0.317947 | − | 0.948108i | \(-0.397007\pi\) | ||||
0.317947 | + | 0.948108i | \(0.397007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.86799 | 0.916426 | 0.458213 | − | 0.888842i | \(-0.348490\pi\) | ||||
0.458213 | + | 0.888842i | \(0.348490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00933 | −1.37391 | −0.686955 | − | 0.726700i | \(-0.741053\pi\) | ||||
−0.686955 | + | 0.726700i | \(0.741053\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.77801 | 0.551079 | 0.275540 | − | 0.961290i | \(-0.411143\pi\) | ||||
0.275540 | + | 0.961290i | \(0.411143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.14134 | −0.734477 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.14134 | 0.299847 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0093 | 1.64961 | 0.824804 | − | 0.565419i | \(-0.191285\pi\) | ||||
0.824804 | + | 0.565419i | \(0.191285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.41468 | 0.319832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.19269 | 0.806219 | 0.403110 | − | 0.915152i | \(-0.367929\pi\) | ||||
0.403110 | + | 0.915152i | \(0.367929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5946 | 1.48454 | 0.742271 | − | 0.670099i | \(-0.233749\pi\) | ||||
0.742271 | + | 0.670099i | \(0.233749\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.36333 | −0.171763 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.324695 | −0.0396678 | −0.0198339 | − | 0.999803i | \(-0.506314\pi\) | ||||
−0.0198339 | + | 0.999803i | \(0.506314\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.72666 | −0.328251 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8680 | 1.40847 | 0.704236 | − | 0.709966i | \(-0.251290\pi\) | ||||
0.704236 | + | 0.709966i | \(0.251290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.28267 | 0.969413 | 0.484707 | − | 0.874677i | \(-0.338926\pi\) | ||||
0.484707 | + | 0.874677i | \(0.338926\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.69735 | 0.877195 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.31198 | 0.260118 | 0.130059 | − | 0.991506i | \(-0.458483\pi\) | ||||
0.130059 | + | 0.991506i | \(0.458483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.3727 | 1.13855 | 0.569274 | − | 0.822148i | \(-0.307225\pi\) | ||||
0.569274 | + | 0.822148i | \(0.307225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.28267 | −0.566362 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.73599 | 0.396014 | 0.198007 | − | 0.980201i | \(-0.436553\pi\) | ||||
0.198007 | + | 0.980201i | \(0.436553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.36333 | 0.142916 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.64600 | −0.170682 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.8480 | −1.71066 | −0.855328 | − | 0.518086i | \(-0.826645\pi\) | ||||
−0.855328 | + | 0.518086i | \(0.826645\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.64600 | −0.567444 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.87732 | −0.584815 | −0.292408 | − | 0.956294i | \(-0.594456\pi\) | ||||
−0.292408 | + | 0.956294i | \(0.594456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0187 | −1.38130 | −0.690650 | − | 0.723189i | \(-0.742675\pi\) | ||||
−0.690650 | + | 0.723189i | \(0.742675\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8773 | −1.05155 | −0.525775 | − | 0.850624i | \(-0.676225\pi\) | ||||
−0.525775 | + | 0.850624i | \(0.676225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.58532 | −0.343411 | −0.171706 | − | 0.985148i | \(-0.554928\pi\) | ||||
−0.171706 | + | 0.985148i | \(0.554928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.86799 | 0.367134 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.5653 | 1.74648 | 0.873240 | − | 0.487290i | \(-0.162014\pi\) | ||||
0.873240 | + | 0.487290i | \(0.162014\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.91934 | −0.267616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8773 | 1.89794 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.86799 | 0.529099 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.858664 | −0.0761941 | −0.0380970 | − | 0.999274i | \(-0.512130\pi\) | ||||
−0.0380970 | + | 0.999274i | \(0.512130\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.00933 | −0.793227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.86799 | −0.163207 | −0.0816036 | − | 0.996665i | \(-0.526004\pi\) | ||||
−0.0816036 | + | 0.996665i | \(0.526004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.29200 | −0.285453 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.24404 | −0.448028 | −0.224014 | − | 0.974586i | \(-0.571916\pi\) | ||||
−0.224014 | + | 0.974586i | \(0.571916\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.17997 | 0.693816 | 0.346908 | − | 0.937899i | \(-0.387232\pi\) | ||||
0.346908 | + | 0.937899i | \(0.387232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.77801 | 0.318166 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.64600 | 0.472142 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.14134 | −0.424050 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.73599 | 0.797603 | 0.398801 | − | 0.917037i | \(-0.369426\pi\) | ||||
0.398801 | + | 0.917037i | \(0.369426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.18336 | 0.0963004 | 0.0481502 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481502 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.14134 | 0.173117 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9800 | 1.43496 | 0.717481 | − | 0.696578i | \(-0.245295\pi\) | ||||
0.717481 | + | 0.696578i | \(0.245295\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0093 | 0.952402 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.71733 | 0.292966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.28267 | 0.335445 | 0.167722 | − | 0.985834i | \(-0.446359\pi\) | ||||
0.167722 | + | 0.985834i | \(0.446359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.41468 | −0.496383 | −0.248191 | − | 0.968711i | \(-0.579836\pi\) | ||||
−0.248191 | + | 0.968711i | \(0.579836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.41468 | 0.184655 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1800 | 1.30617 | 0.653084 | − | 0.757285i | \(-0.273475\pi\) | ||||
0.653084 | + | 0.757285i | \(0.273475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.19269 | 0.465471 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.11203 | 0.531578 | 0.265789 | − | 0.964031i | \(-0.414368\pi\) | ||||
0.265789 | + | 0.964031i | \(0.414368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.4333 | 1.89045 | 0.945223 | − | 0.326427i | \(-0.105845\pi\) | ||||
0.945223 | + | 0.326427i | \(0.105845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5946 | 0.857101 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0900 | −0.884107 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.36333 | −0.0991675 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1214 | 1.16650 | 0.583250 | − | 0.812292i | \(-0.301781\pi\) | ||||
0.583250 | + | 0.812292i | \(0.301781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0187 | 0.721159 | 0.360579 | − | 0.932729i | \(-0.382579\pi\) | ||||
0.360579 | + | 0.932729i | \(0.382579\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0187 | −0.713800 | −0.356900 | − | 0.934143i | \(-0.616166\pi\) | ||||
−0.356900 | + | 0.934143i | \(0.616166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4427 | −1.09470 | −0.547351 | − | 0.836903i | \(-0.684364\pi\) | ||||
−0.547351 | + | 0.836903i | \(0.684364\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.324695 | −0.0229022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.20202 | 0.505482 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.72666 | −0.189516 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6333 | −0.943034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8387 | 1.22807 | 0.614033 | − | 0.789280i | \(-0.289546\pi\) | ||||
0.614033 | + | 0.789280i | \(0.289546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8680 | 0.813181 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24404 | 0.152335 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.28267 | 0.559691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.14134 | −0.144042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.56534 | −0.439648 | −0.219824 | − | 0.975540i | \(-0.570548\pi\) | ||||
−0.219824 | + | 0.975540i | \(0.570548\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3820 | 0.888194 | 0.444097 | − | 0.895979i | \(-0.353525\pi\) | ||||
0.444097 | + | 0.895979i | \(0.353525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.88665 | 0.653328 | 0.326664 | − | 0.945140i | \(-0.394075\pi\) | ||||
0.326664 | + | 0.945140i | \(0.394075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.69735 | 0.506449 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.8667 | −1.76009 | −0.880047 | − | 0.474886i | \(-0.842489\pi\) | ||||
−0.880047 | + | 0.474886i | \(0.842489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.31198 | 0.150179 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.4847 | 1.77784 | 0.888918 | − | 0.458066i | \(-0.151458\pi\) | ||||
0.888918 | + | 0.458066i | \(0.151458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0187 | −0.645358 | −0.322679 | − | 0.946508i | \(-0.604584\pi\) | ||||
−0.322679 | + | 0.946508i | \(0.604584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.41468 | −0.153642 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.3727 | 0.657340 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1507 | −1.52438 | −0.762188 | − | 0.647355i | \(-0.775875\pi\) | ||||
−0.762188 | + | 0.647355i | \(0.775875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3947 | 0.967857 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.15066 | 0.0717765 | 0.0358882 | − | 0.999356i | \(-0.488574\pi\) | ||||
0.0358882 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.27334 | −0.327670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.28267 | −0.326989 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.28267 | −0.140756 | −0.0703778 | − | 0.997520i | \(-0.522420\pi\) | ||||
−0.0703778 | + | 0.997520i | \(0.522420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.73599 | 0.228639 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.17064 | 0.498173 | 0.249086 | − | 0.968481i | \(-0.419870\pi\) | ||||
0.249086 | + | 0.968481i | \(0.419870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5433 | 1.30866 | 0.654331 | − | 0.756208i | \(-0.272950\pi\) | ||||
0.654331 | + | 0.756208i | \(0.272950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.36333 | 0.0825124 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1307 | −1.38979 | −0.694894 | − | 0.719112i | \(-0.744549\pi\) | ||||
−0.694894 | + | 0.719112i | \(0.744549\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.64600 | −0.0985435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.96137 | 0.295970 | 0.147985 | − | 0.988990i | \(-0.452721\pi\) | ||||
0.147985 | + | 0.988990i | \(0.452721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74531 | 0.282080 | 0.141040 | − | 0.990004i | \(-0.454955\pi\) | ||||
0.141040 | + | 0.990004i | \(0.454955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4147 | −0.730275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.8480 | −0.987648 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.7360 | 1.73719 | 0.868597 | − | 0.495518i | \(-0.165022\pi\) | ||||
0.868597 | + | 0.495518i | \(0.165022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.64600 | −0.327614 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.72666 | 0.157687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2827 | 0.707961 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.87732 | −0.337643 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4520 | 1.05311 | 0.526555 | − | 0.850141i | \(-0.323483\pi\) | ||||
0.526555 | + | 0.850141i | \(0.323483\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0187 | −0.797494 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9160 | 0.902511 | 0.451255 | − | 0.892395i | \(-0.350976\pi\) | ||||
0.451255 | + | 0.892395i | \(0.350976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.99067 | −0.112519 | −0.0562597 | − | 0.998416i | \(-0.517917\pi\) | ||||
−0.0562597 | + | 0.998416i | \(0.517917\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.26401 | −0.127160 | −0.0635799 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635799 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.8260 | 1.66993 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.8773 | −0.607113 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.17064 | 0.287702 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.58532 | −0.198269 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.15066 | −0.283965 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.69867 | 0.0933674 | 0.0466837 | − | 0.998910i | \(-0.485135\pi\) | ||||
0.0466837 | + | 0.998910i | \(0.485135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.86799 | 0.211965 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7067 | −1.12796 | −0.563982 | − | 0.825787i | \(-0.690731\pi\) | ||||
−0.563982 | + | 0.825787i | \(0.690731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.5653 | 1.00833 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.29332 | 0.503261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5526 | 0.893758 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.97070 | 0.427889 | 0.213945 | − | 0.976846i | \(-0.431369\pi\) | ||||
0.213945 | + | 0.976846i | \(0.431369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.56534 | 0.351435 | 0.175717 | − | 0.984441i | \(-0.443776\pi\) | ||||
0.175717 | + | 0.984441i | \(0.443776\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.4520 | −1.08855 | −0.544275 | − | 0.838907i | \(-0.683195\pi\) | ||||
−0.544275 | + | 0.838907i | \(0.683195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.91934 | −0.154508 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8994 | −0.628025 | −0.314012 | − | 0.949419i | \(-0.601673\pi\) | ||||
−0.314012 | + | 0.949419i | \(0.601673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1693 | −0.693122 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.8773 | 1.09578 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5853 | −1.23114 | −0.615572 | − | 0.788081i | \(-0.711075\pi\) | ||||
−0.615572 | + | 0.788081i | \(0.711075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.86799 | 0.305475 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.3727 | −0.850026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.1693 | −1.30322 | −0.651609 | − | 0.758555i | \(-0.725906\pi\) | ||||
−0.651609 | + | 0.758555i | \(0.725906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.28267 | 0.272071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.83530 | −0.453839 | −0.226919 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226919 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.858664 | −0.0439907 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.9053 | −1.42589 | −0.712947 | − | 0.701218i | \(-0.752640\pi\) | ||||
−0.712947 | + | 0.701218i | \(0.752640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.00933 | −0.457970 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.697352 | −0.0353571 | −0.0176786 | − | 0.999844i | \(-0.505628\pi\) | ||||
−0.0176786 | + | 0.999844i | \(0.505628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.83869 | −0.295275 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.86799 | −0.0942278 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8867 | 0.897705 | 0.448853 | − | 0.893606i | \(-0.351833\pi\) | ||||
0.448853 | + | 0.893606i | \(0.351833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.29200 | −0.164806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.1120 | 1.25404 | 0.627018 | − | 0.779005i | \(-0.284275\pi\) | ||||
0.627018 | + | 0.779005i | \(0.284275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.64600 | 0.0819931 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.8387 | −1.08250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.6774 | −1.17077 | −0.585385 | − | 0.810755i | \(-0.699057\pi\) | ||||
−0.585385 | + | 0.810755i | \(0.699057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.24404 | −0.258669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.44267 | −0.415436 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.17997 | 0.400575 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7347 | −0.915248 | −0.457624 | − | 0.889146i | \(-0.651299\pi\) | ||||
−0.457624 | + | 0.889146i | \(0.651299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.26401 | 0.207815 | 0.103908 | − | 0.994587i | \(-0.466865\pi\) | ||||
0.103908 | + | 0.994587i | \(0.466865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.77801 | 0.183693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.8073 | −0.764969 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.64600 | 0.272591 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.1693 | 0.971522 | 0.485761 | − | 0.874092i | \(-0.338543\pi\) | ||||
0.485761 | + | 0.874092i | \(0.338543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6974 | −0.994651 | −0.497326 | − | 0.867564i | \(-0.665685\pi\) | ||||
−0.497326 | + | 0.867564i | \(0.665685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.58400 | −0.314956 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.31198 | −0.110345 | −0.0551723 | − | 0.998477i | \(-0.517571\pi\) | ||||
−0.0551723 | + | 0.998477i | \(0.517571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.14134 | −0.244826 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.25337 | 0.107061 | 0.0535304 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535304 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.73599 | 0.460496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.1693 | 1.04624 | 0.523118 | − | 0.852261i | \(-0.324769\pi\) | ||||
0.523118 | + | 0.852261i | \(0.324769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.1307 | −1.56006 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.18336 | 0.0555990 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4720 | 1.47220 | 0.736098 | − | 0.676875i | \(-0.236666\pi\) | ||||
0.736098 | + | 0.676875i | \(0.236666\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.14134 | 0.0999490 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7360 | 0.826047 | 0.413024 | − | 0.910720i | \(-0.364473\pi\) | ||||
0.413024 | + | 0.910720i | \(0.364473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.431266 | −0.0200426 | −0.0100213 | − | 0.999950i | \(-0.503190\pi\) | ||||
−0.0100213 | + | 0.999950i | \(0.503190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.30265 | −0.245377 | −0.122689 | − | 0.992445i | \(-0.539152\pi\) | ||||
−0.122689 | + | 0.992445i | \(0.539152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.442666 | 0.0204404 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.9800 | 0.828476 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.8667 | 2.33885 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0093 | 0.549869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.07934 | −0.0950074 | −0.0475037 | − | 0.998871i | \(-0.515127\pi\) | ||||
−0.0475037 | + | 0.998871i | \(0.515127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.86799 | −0.176365 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.71733 | 0.169144 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3633 | −0.696179 | −0.348089 | − | 0.937461i | \(-0.613169\pi\) | ||||
−0.348089 | + | 0.937461i | \(0.613169\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.28267 | 0.193669 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.2173 | 1.27343 | 0.636714 | − | 0.771100i | \(-0.280293\pi\) | ||||
0.636714 | + | 0.771100i | \(0.280293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3120 | −0.509466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.1800 | −0.725771 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.15405 | 0.320259 | 0.160130 | − | 0.987096i | \(-0.448809\pi\) | ||||
0.160130 | + | 0.987096i | \(0.448809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.41468 | −0.286587 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.09337 | 0.227102 | 0.113551 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113551 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.4906 | −0.952555 | −0.476278 | − | 0.879295i | \(-0.658014\pi\) | ||||
−0.476278 | + | 0.879295i | \(0.658014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2920 | −0.499529 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.41468 | 0.106611 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.3306 | −0.938120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1800 | 0.754117 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7360 | 1.12751 | 0.563757 | − | 0.825941i | \(-0.309355\pi\) | ||||
0.563757 | + | 0.825941i | \(0.309355\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.972014 | −0.0425032 | −0.0212516 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212516 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.52464 | −0.153536 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5653 | −0.676754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.19269 | 0.268740 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.86799 | −0.254171 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.11203 | 0.306907 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.0280 | 1.25032 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.6774 | 0.588036 | 0.294018 | − | 0.955800i | \(-0.405007\pi\) | ||||
0.294018 | + | 0.955800i | \(0.405007\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.4333 | 1.09145 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.7546 | −1.44324 | −0.721622 | − | 0.692287i | \(-0.756603\pi\) | ||||
−0.721622 | + | 0.692287i | \(0.756603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5946 | 0.494848 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7560 | −0.543422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.15198 | −0.134036 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2827 | 0.435691 | 0.217845 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217845 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.00933 | 0.381054 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0900 | −0.510440 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.3841 | −1.49126 | −0.745630 | − | 0.666360i | \(-0.767851\pi\) | ||||
−0.745630 | + | 0.666360i | \(0.767851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.36333 | −0.0572544 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.7160 | 0.910382 | 0.455191 | − | 0.890394i | \(-0.349571\pi\) | ||||
0.455191 | + | 0.890394i | \(0.349571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.9507 | 1.04416 | 0.522078 | − | 0.852898i | \(-0.325157\pi\) | ||||
0.522078 | + | 0.852898i | \(0.325157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1214 | 0.673479 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1893 | −1.13191 | −0.565953 | − | 0.824438i | \(-0.691492\pi\) | ||||
−0.565953 | + | 0.824438i | \(0.691492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.0187 | 0.416361 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.1413 | −0.586681 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −67.8047 | −2.80818 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −47.5220 | −1.96144 | −0.980721 | − | 0.195411i | \(-0.937396\pi\) | ||||
−0.980721 | + | 0.195411i | \(0.937396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.97456 | −0.163769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0187 | −0.412112 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.9453 | 0.736923 | 0.368462 | − | 0.929643i | \(-0.379885\pi\) | ||||
0.368462 | + | 0.929643i | \(0.379885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.4427 | −0.632026 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.4720 | 0.632168 | 0.316084 | − | 0.948731i | \(-0.397632\pi\) | ||||
0.316084 | + | 0.948731i | \(0.397632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.7453 | 1.86599 | 0.932995 | − | 0.359889i | \(-0.117185\pi\) | ||||
0.932995 | + | 0.359889i | \(0.117185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.324695 | −0.0132226 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.3467 | −0.622905 | −0.311453 | − | 0.950262i | \(-0.600815\pi\) | ||||
−0.311453 | + | 0.950262i | \(0.600815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.20202 | 0.291840 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.77801 | −0.152842 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.67738 | −0.229307 | −0.114654 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114654 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.8867 | 0.881123 | 0.440562 | − | 0.897722i | \(-0.354779\pi\) | ||||
0.440562 | + | 0.897722i | \(0.354779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.4134 | 0.860676 | 0.430338 | − | 0.902668i | \(-0.358394\pi\) | ||||
0.430338 | + | 0.902668i | \(0.358394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.72666 | −0.109417 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.09337 | −0.204062 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.6333 | −0.544461 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.28267 | 0.330252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.1893 | 1.40086 | 0.700432 | − | 0.713719i | \(-0.252991\pi\) | ||||
0.700432 | + | 0.713719i | \(0.252991\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8387 | 0.709024 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.14134 | 0.203707 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8680 | 0.469491 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5547 | 1.32533 | 0.662665 | − | 0.748916i | \(-0.269425\pi\) | ||||
0.662665 | + | 0.748916i | \(0.269425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.7160 | 0.738087 | 0.369044 | − | 0.929412i | \(-0.379685\pi\) | ||||
0.369044 | + | 0.929412i | \(0.379685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5653 | −0.651251 | −0.325625 | − | 0.945499i | \(-0.605575\pi\) | ||||
−0.325625 | + | 0.945499i | \(0.605575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.9639 | −1.37245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.24404 | 0.0879508 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.5454 | 1.03880 | 0.519400 | − | 0.854531i | \(-0.326155\pi\) | ||||
0.519400 | + | 0.854531i | \(0.326155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.28267 | 0.323138 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.3306 | 1.41524 | 0.707620 | − | 0.706593i | \(-0.249769\pi\) | ||||
0.707620 | + | 0.706593i | \(0.249769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.2279 | 0.864566 | 0.432283 | − | 0.901738i | \(-0.357708\pi\) | ||||
0.432283 | + | 0.901738i | \(0.357708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.14134 | −0.0831626 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.4040 | 0.557726 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.56534 | −0.253831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.4634 | −2.52719 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.46264 | 0.0563807 | 0.0281903 | − | 0.999603i | \(-0.491026\pi\) | ||||
0.0281903 | + | 0.999603i | \(0.491026\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5653 | 0.713524 | 0.356762 | − | 0.934195i | \(-0.383881\pi\) | ||||
0.356762 | + | 0.934195i | \(0.383881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.9694 | 0.881484 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3820 | 0.512799 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.03138 | 0.230784 | 0.115392 | − | 0.993320i | \(-0.463188\pi\) | ||||
0.115392 | + | 0.993320i | \(0.463188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.88665 | 0.377199 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0093 | −0.457519 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1566 | 0.538543 | 0.269271 | − | 0.963064i | \(-0.413217\pi\) | ||||
0.269271 | + | 0.963064i | \(0.413217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.69735 | 0.292398 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5653 | 0.475946 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.8667 | −1.01619 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.26270 | 0.236539 | 0.118269 | − | 0.992982i | \(-0.462265\pi\) | ||||
0.118269 | + | 0.992982i | \(0.462265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.33996 | 0.352263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.01272 | 0.301349 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.28267 | 0.235951 | 0.117975 | − | 0.993017i | \(-0.462360\pi\) | ||||
0.117975 | + | 0.993017i | \(0.462360\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.31198 | 0.0867059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.48808 | 0.168080 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.4847 | 1.02643 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.9253 | −1.07873 | −0.539366 | − | 0.842072i | \(-0.681336\pi\) | ||||
−0.539366 | + | 0.842072i | \(0.681336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.1120 | 0.711769 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0187 | −0.372598 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.2427 | −1.49252 | −0.746260 | − | 0.665655i | \(-0.768152\pi\) | ||||
−0.746260 | + | 0.665655i | \(0.768152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.2920 | −0.713540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7907 | 0.730987 | 0.365494 | − | 0.930814i | \(-0.380900\pi\) | ||||
0.365494 | + | 0.930814i | \(0.380900\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.83323 | 0.0675278 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.1634 | −0.668151 | −0.334075 | − | 0.942546i | \(-0.608424\pi\) | ||||
−0.334075 | + | 0.942546i | \(0.608424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.41468 | −0.0887055 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2661 | 0.890236 | 0.445118 | − | 0.895472i | \(-0.353162\pi\) | ||||
0.445118 | + | 0.895472i | \(0.353162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3727 | 0.379516 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.8294 | 0.541853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.2720 | 1.03166 | 0.515830 | − | 0.856691i | \(-0.327483\pi\) | ||||
0.515830 | + | 0.856691i | \(0.327483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.1507 | −0.880099 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.0853 | 1.34789 | 0.673944 | − | 0.738783i | \(-0.264599\pi\) | ||||
0.673944 | + | 0.738783i | \(0.264599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.3947 | 0.558792 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.4919 | 1.03283 | 0.516416 | − | 0.856338i | \(-0.327266\pi\) | ||||
0.516416 | + | 0.856338i | \(0.327266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.88797 | 0.176956 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.19269 | −0.223605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6774 | −0.998072 | −0.499036 | − | 0.866581i | \(-0.666312\pi\) | ||||
−0.499036 | + | 0.866581i | \(0.666312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.15066 | 0.0414402 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.6426 | 1.17407 | 0.587037 | − | 0.809560i | \(-0.300294\pi\) | ||||
0.587037 | + | 0.809560i | \(0.300294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.27334 | −0.189180 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.1693 | 0.507669 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67.0067 | −2.39769 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.28267 | −0.188787 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6740 | −1.80633 | −0.903166 | − | 0.429291i | \(-0.858764\pi\) | ||||
−0.903166 | + | 0.429291i | \(0.858764\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.28267 | −0.0812653 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.3107 | −0.899943 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5946 | −0.411738 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.3586 | −0.862827 | −0.431413 | − | 0.902154i | \(-0.641985\pi\) | ||||
−0.431413 | + | 0.902154i | \(0.641985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.08998 | 0.286203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.73599 | 0.132005 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.7640 | −1.65026 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.17064 | 0.287620 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.6027 | −1.77909 | −0.889547 | − | 0.456843i | \(-0.848980\pi\) | ||||
−0.889547 | + | 0.456843i | \(0.848980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4168 | 0.646700 | 0.323350 | − | 0.946280i | \(-0.395191\pi\) | ||||
0.323350 | + | 0.946280i | \(0.395191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.5433 | 0.755556 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.7546 | −0.761099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.36333 | 0.0476385 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.4906 | −1.09903 | −0.549515 | − | 0.835484i | \(-0.685188\pi\) | ||||
−0.549515 | + | 0.835484i | \(0.685188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.7347 | 0.653049 | 0.326525 | − | 0.945189i | \(-0.394122\pi\) | ||||
0.326525 | + | 0.945189i | \(0.394122\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7580 | −0.582734 | −0.291367 | − | 0.956611i | \(-0.594110\pi\) | ||||
−0.291367 | + | 0.956611i | \(0.594110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1014 | −0.698150 | −0.349075 | − | 0.937095i | \(-0.613504\pi\) | ||||
−0.349075 | + | 0.937095i | \(0.613504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.1307 | −0.802395 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.0093 | −0.381451 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.64600 | −0.0568941 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.82936 | −0.235776 | −0.117888 | − | 0.993027i | \(-0.537612\pi\) | ||||
−0.117888 | + | 0.993027i | \(0.537612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.09337 | −0.0377026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.96137 | 0.170879 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.4626 | −0.977988 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.74531 | 0.162859 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5467 | −0.361536 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2279 | 0.350198 | 0.175099 | − | 0.984551i | \(-0.443975\pi\) | ||||
0.175099 | + | 0.984551i | \(0.443975\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.1307 | 1.06340 | 0.531702 | − | 0.846931i | \(-0.321553\pi\) | ||||
0.531702 | + | 0.846931i | \(0.321553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0093 | −1.12626 | −0.563132 | − | 0.826367i | \(-0.690404\pi\) | ||||
−0.563132 | + | 0.826367i | \(0.690404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.4206 | 1.51210 | 0.756048 | − | 0.654516i | \(-0.227128\pi\) | ||||
0.756048 | + | 0.654516i | \(0.227128\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.4147 | −0.421625 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.0534 | −0.442807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.324695 | 0.0110019 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.8480 | −0.570219 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8867 | 0.536454 | 0.268227 | − | 0.963356i | \(-0.413562\pi\) | ||||
0.268227 | + | 0.963356i | \(0.413562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.7360 | 1.00297 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.13201 | 0.105520 | 0.0527600 | − | 0.998607i | \(-0.483198\pi\) | ||||
0.0527600 | + | 0.998607i | \(0.483198\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.1307 | −1.11494 | −0.557468 | − | 0.830198i | \(-0.688227\pi\) | ||||
−0.557468 | + | 0.830198i | \(0.688227\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.8200 | −0.665491 | −0.332746 | − | 0.943017i | \(-0.607975\pi\) | ||||
−0.332746 | + | 0.943017i | \(0.607975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.17064 | 0.0392620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.64600 | −0.189148 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.12268 | 0.305279 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.72666 | 0.0910404 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.69528 | 0.290004 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.7160 | 0.856724 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.2827 | 0.408742 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.6426 | −0.486200 | −0.243100 | − | 0.970001i | \(-0.578164\pi\) | ||||
−0.243100 | + | 0.970001i | \(0.578164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.87732 | −0.194938 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8973 | −1.25559 | −0.627797 | − | 0.778377i | \(-0.716043\pi\) | ||||
−0.627797 | + | 0.778377i | \(0.716043\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.5640 | −1.93819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.54669 | 0.0840990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.2534 | 0.866019 | 0.433009 | − | 0.901389i | \(-0.357452\pi\) | ||||
0.433009 | + | 0.901389i | \(0.357452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.4520 | 0.608014 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8680 | −0.390640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0187 | −0.460433 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.2066 | 1.71284 | 0.856422 | − | 0.516276i | \(-0.172682\pi\) | ||||
0.856422 | + | 0.516276i | \(0.172682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.4147 | −0.406875 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.9160 | 0.521065 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.3213 | −0.533194 | −0.266597 | − | 0.963808i | \(-0.585899\pi\) | ||||
−0.266597 | + | 0.963808i | \(0.585899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.99067 | −0.0649631 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.7546 | 1.16557 | 0.582784 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582784 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.73260 | 0.283771 | 0.141886 | − | 0.989883i | \(-0.454683\pi\) | ||||
0.141886 | + | 0.989883i | \(0.454683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.28267 | −0.268867 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.26401 | −0.0734157 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.8280 | 0.933832 | 0.466916 | − | 0.884302i | \(-0.345365\pi\) | ||||
0.466916 | + | 0.884302i | \(0.345365\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.8260 | 0.964137 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.14935 | 0.230864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2907 | −0.912603 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.8773 | −0.350517 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0687 | 1.22421 | 0.612103 | − | 0.790778i | \(-0.290324\pi\) | ||||
0.612103 | + | 0.790778i | \(0.290324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.17064 | 0.166105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.72534 | 0.0553687 | 0.0276844 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276844 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.1520 | −0.357516 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7173 | 0.694799 | 0.347399 | − | 0.937717i | \(-0.387065\pi\) | ||||
0.347399 | + | 0.937717i | \(0.387065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.0934 | −0.674147 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.58532 | −0.114470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0153 | 0.415123 | 0.207561 | − | 0.978222i | \(-0.433447\pi\) | ||||
0.207561 | + | 0.978222i | \(0.433447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.15066 | −0.163947 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.5653 | 0.781133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1413 | 0.735109 | 0.367554 | − | 0.930002i | \(-0.380195\pi\) | ||||
0.367554 | + | 0.930002i | \(0.380195\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.69867 | 0.0539057 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.9707 | 1.10753 | 0.553767 | − | 0.832672i | \(-0.313190\pi\) | ||||
0.553767 | + | 0.832672i | \(0.313190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.86799 | 0.122378 |
(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 | 7800.2.a.bn.1.2 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bm.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bm.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.bn.1.2 | yes | 3 | 1.1 | even | 1 | trivial |