Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8025,2,Mod(1,8025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8025, 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("8025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8025 = 3 \cdot 5^{2} \cdot 107 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0799476221\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 9x^{5} + 24x^{4} + 13x^{3} - 47x^{2} + 19x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 321) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.67795\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39839 | 1.69592 | 0.847958 | − | 0.530063i | \(-0.177832\pi\) | ||||
0.847958 | + | 0.530063i | \(0.177832\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.75227 | 1.87613 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.39839 | 0.979138 | ||||||||
\(7\) | −2.59863 | −0.982188 | −0.491094 | − | 0.871107i | \(-0.663403\pi\) | ||||
−0.491094 | + | 0.871107i | \(0.663403\pi\) | |||||||
\(8\) | 4.20262 | 1.48585 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.31906 | −0.699224 | −0.349612 | − | 0.936895i | \(-0.613687\pi\) | ||||
−0.349612 | + | 0.936895i | \(0.613687\pi\) | |||||||
\(12\) | 3.75227 | 1.08319 | ||||||||
\(13\) | 0.510992 | 0.141724 | 0.0708618 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708618 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(14\) | −6.23251 | −1.66571 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.57497 | 0.643743 | ||||||||
\(17\) | 1.70532 | 0.413600 | 0.206800 | − | 0.978383i | \(-0.433695\pi\) | ||||
0.206800 | + | 0.978383i | \(0.433695\pi\) | |||||||
\(18\) | 2.39839 | 0.565306 | ||||||||
\(19\) | 7.72152 | 1.77144 | 0.885719 | − | 0.464221i | \(-0.153666\pi\) | ||||
0.885719 | + | 0.464221i | \(0.153666\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.59863 | −0.567067 | ||||||||
\(22\) | −5.56201 | −1.18582 | ||||||||
\(23\) | −0.207050 | −0.0431728 | −0.0215864 | − | 0.999767i | \(-0.506872\pi\) | ||||
−0.0215864 | + | 0.999767i | \(0.506872\pi\) | |||||||
\(24\) | 4.20262 | 0.857855 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.22556 | 0.240351 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −9.75073 | −1.84272 | ||||||||
\(29\) | 4.79678 | 0.890739 | 0.445370 | − | 0.895347i | \(-0.353072\pi\) | ||||
0.445370 | + | 0.895347i | \(0.353072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.71600 | 1.56544 | 0.782720 | − | 0.622374i | \(-0.213832\pi\) | ||||
0.782720 | + | 0.622374i | \(0.213832\pi\) | |||||||
\(32\) | −2.22945 | −0.394115 | ||||||||
\(33\) | −2.31906 | −0.403697 | ||||||||
\(34\) | 4.09001 | 0.701431 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.75227 | 0.625378 | ||||||||
\(37\) | 5.97891 | 0.982926 | 0.491463 | − | 0.870898i | \(-0.336462\pi\) | ||||
0.491463 | + | 0.870898i | \(0.336462\pi\) | |||||||
\(38\) | 18.5192 | 3.00421 | ||||||||
\(39\) | 0.510992 | 0.0818242 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.04876 | 0.944657 | 0.472329 | − | 0.881423i | \(-0.343414\pi\) | ||||
0.472329 | + | 0.881423i | \(0.343414\pi\) | |||||||
\(42\) | −6.23251 | −0.961698 | ||||||||
\(43\) | −3.98090 | −0.607082 | −0.303541 | − | 0.952818i | \(-0.598169\pi\) | ||||
−0.303541 | + | 0.952818i | \(0.598169\pi\) | |||||||
\(44\) | −8.70174 | −1.31184 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.496586 | −0.0732176 | ||||||||
\(47\) | −4.96026 | −0.723529 | −0.361764 | − | 0.932270i | \(-0.617826\pi\) | ||||
−0.361764 | + | 0.932270i | \(0.617826\pi\) | |||||||
\(48\) | 2.57497 | 0.371665 | ||||||||
\(49\) | −0.247147 | −0.0353067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.70532 | 0.238792 | ||||||||
\(52\) | 1.91738 | 0.265892 | ||||||||
\(53\) | −0.544225 | −0.0747551 | −0.0373775 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373775 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(54\) | 2.39839 | 0.326379 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.9210 | −1.45938 | ||||||||
\(57\) | 7.72152 | 1.02274 | ||||||||
\(58\) | 11.5045 | 1.51062 | ||||||||
\(59\) | 11.6915 | 1.52211 | 0.761055 | − | 0.648688i | \(-0.224682\pi\) | ||||
0.761055 | + | 0.648688i | \(0.224682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.943204 | 0.120765 | 0.0603825 | − | 0.998175i | \(-0.480768\pi\) | ||||
0.0603825 | + | 0.998175i | \(0.480768\pi\) | |||||||
\(62\) | 20.9044 | 2.65486 | ||||||||
\(63\) | −2.59863 | −0.327396 | ||||||||
\(64\) | −10.4970 | −1.31213 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.56201 | −0.684636 | ||||||||
\(67\) | 0.605901 | 0.0740226 | 0.0370113 | − | 0.999315i | \(-0.488216\pi\) | ||||
0.0370113 | + | 0.999315i | \(0.488216\pi\) | |||||||
\(68\) | 6.39880 | 0.775969 | ||||||||
\(69\) | −0.207050 | −0.0249259 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.91240 | −0.226960 | −0.113480 | − | 0.993540i | \(-0.536200\pi\) | ||||
−0.113480 | + | 0.993540i | \(0.536200\pi\) | |||||||
\(72\) | 4.20262 | 0.495283 | ||||||||
\(73\) | 13.0474 | 1.52709 | 0.763544 | − | 0.645756i | \(-0.223458\pi\) | ||||
0.763544 | + | 0.645756i | \(0.223458\pi\) | |||||||
\(74\) | 14.3397 | 1.66696 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.9732 | 3.32345 | ||||||||
\(77\) | 6.02637 | 0.686769 | ||||||||
\(78\) | 1.22556 | 0.138767 | ||||||||
\(79\) | 1.42355 | 0.160162 | 0.0800810 | − | 0.996788i | \(-0.474482\pi\) | ||||
0.0800810 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.5073 | 1.60206 | ||||||||
\(83\) | 12.5487 | 1.37740 | 0.688701 | − | 0.725046i | \(-0.258181\pi\) | ||||
0.688701 | + | 0.725046i | \(0.258181\pi\) | |||||||
\(84\) | −9.75073 | −1.06389 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.54775 | −1.02956 | ||||||||
\(87\) | 4.79678 | 0.514268 | ||||||||
\(88\) | −9.74613 | −1.03894 | ||||||||
\(89\) | 13.4753 | 1.42838 | 0.714188 | − | 0.699954i | \(-0.246796\pi\) | ||||
0.714188 | + | 0.699954i | \(0.246796\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32788 | −0.139199 | ||||||||
\(92\) | −0.776906 | −0.0809980 | ||||||||
\(93\) | 8.71600 | 0.903807 | ||||||||
\(94\) | −11.8966 | −1.22704 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.22945 | −0.227542 | ||||||||
\(97\) | −12.7949 | −1.29912 | −0.649562 | − | 0.760308i | \(-0.725048\pi\) | ||||
−0.649562 | + | 0.760308i | \(0.725048\pi\) | |||||||
\(98\) | −0.592753 | −0.0598771 | ||||||||
\(99\) | −2.31906 | −0.233075 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.38268 | −0.834108 | −0.417054 | − | 0.908882i | \(-0.636937\pi\) | ||||
−0.417054 | + | 0.908882i | \(0.636937\pi\) | |||||||
\(102\) | 4.09001 | 0.404972 | ||||||||
\(103\) | −15.1868 | −1.49640 | −0.748201 | − | 0.663472i | \(-0.769082\pi\) | ||||
−0.748201 | + | 0.663472i | \(0.769082\pi\) | |||||||
\(104\) | 2.14750 | 0.210580 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.30526 | −0.126778 | ||||||||
\(107\) | −1.00000 | −0.0966736 | ||||||||
\(108\) | 3.75227 | 0.361062 | ||||||||
\(109\) | −7.45820 | −0.714366 | −0.357183 | − | 0.934034i | \(-0.616263\pi\) | ||||
−0.357183 | + | 0.934034i | \(0.616263\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.97891 | 0.567493 | ||||||||
\(112\) | −6.69138 | −0.632276 | ||||||||
\(113\) | −9.64461 | −0.907289 | −0.453644 | − | 0.891183i | \(-0.649876\pi\) | ||||
−0.453644 | + | 0.891183i | \(0.649876\pi\) | |||||||
\(114\) | 18.5192 | 1.73448 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 17.9988 | 1.67115 | ||||||||
\(117\) | 0.510992 | 0.0472412 | ||||||||
\(118\) | 28.0409 | 2.58137 | ||||||||
\(119\) | −4.43148 | −0.406233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.62195 | −0.511086 | ||||||||
\(122\) | 2.26217 | 0.204807 | ||||||||
\(123\) | 6.04876 | 0.545398 | ||||||||
\(124\) | 32.7048 | 2.93697 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.23251 | −0.555236 | ||||||||
\(127\) | 18.9347 | 1.68018 | 0.840090 | − | 0.542448i | \(-0.182502\pi\) | ||||
0.840090 | + | 0.542448i | \(0.182502\pi\) | |||||||
\(128\) | −20.7171 | −1.83115 | ||||||||
\(129\) | −3.98090 | −0.350499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7388 | 1.20037 | 0.600184 | − | 0.799862i | \(-0.295094\pi\) | ||||
0.600184 | + | 0.799862i | \(0.295094\pi\) | |||||||
\(132\) | −8.70174 | −0.757389 | ||||||||
\(133\) | −20.0653 | −1.73989 | ||||||||
\(134\) | 1.45319 | 0.125536 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.16679 | 0.614547 | ||||||||
\(137\) | −7.93715 | −0.678117 | −0.339058 | − | 0.940765i | \(-0.610108\pi\) | ||||
−0.339058 | + | 0.940765i | \(0.610108\pi\) | |||||||
\(138\) | −0.496586 | −0.0422722 | ||||||||
\(139\) | −18.0551 | −1.53142 | −0.765708 | − | 0.643189i | \(-0.777611\pi\) | ||||
−0.765708 | + | 0.643189i | \(0.777611\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.96026 | −0.417730 | ||||||||
\(142\) | −4.58667 | −0.384905 | ||||||||
\(143\) | −1.18502 | −0.0990965 | ||||||||
\(144\) | 2.57497 | 0.214581 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 31.2928 | 2.58981 | ||||||||
\(147\) | −0.247147 | −0.0203843 | ||||||||
\(148\) | 22.4345 | 1.84410 | ||||||||
\(149\) | −7.28825 | −0.597077 | −0.298539 | − | 0.954398i | \(-0.596499\pi\) | ||||
−0.298539 | + | 0.954398i | \(0.596499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7419 | 0.955544 | 0.477772 | − | 0.878484i | \(-0.341445\pi\) | ||||
0.477772 | + | 0.878484i | \(0.341445\pi\) | |||||||
\(152\) | 32.4506 | 2.63209 | ||||||||
\(153\) | 1.70532 | 0.137867 | ||||||||
\(154\) | 14.4536 | 1.16470 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.91738 | 0.153513 | ||||||||
\(157\) | 9.56141 | 0.763084 | 0.381542 | − | 0.924352i | \(-0.375393\pi\) | ||||
0.381542 | + | 0.924352i | \(0.375393\pi\) | |||||||
\(158\) | 3.41423 | 0.271621 | ||||||||
\(159\) | −0.544225 | −0.0431599 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.538045 | 0.0424039 | ||||||||
\(162\) | 2.39839 | 0.188435 | ||||||||
\(163\) | −11.2774 | −0.883318 | −0.441659 | − | 0.897183i | \(-0.645610\pi\) | ||||
−0.441659 | + | 0.897183i | \(0.645610\pi\) | |||||||
\(164\) | 22.6966 | 1.77230 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 30.0967 | 2.33596 | ||||||||
\(167\) | 21.3638 | 1.65318 | 0.826591 | − | 0.562802i | \(-0.190277\pi\) | ||||
0.826591 | + | 0.562802i | \(0.190277\pi\) | |||||||
\(168\) | −10.9210 | −0.842575 | ||||||||
\(169\) | −12.7389 | −0.979914 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.72152 | 0.590479 | ||||||||
\(172\) | −14.9374 | −1.13897 | ||||||||
\(173\) | 18.3110 | 1.39216 | 0.696079 | − | 0.717965i | \(-0.254926\pi\) | ||||
0.696079 | + | 0.717965i | \(0.254926\pi\) | |||||||
\(174\) | 11.5045 | 0.872156 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.97152 | −0.450120 | ||||||||
\(177\) | 11.6915 | 0.878790 | ||||||||
\(178\) | 32.3189 | 2.42241 | ||||||||
\(179\) | −18.3871 | −1.37432 | −0.687158 | − | 0.726508i | \(-0.741142\pi\) | ||||
−0.687158 | + | 0.726508i | \(0.741142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.36497 | 0.621763 | 0.310882 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310882 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(182\) | −3.18476 | −0.236070 | ||||||||
\(183\) | 0.943204 | 0.0697237 | ||||||||
\(184\) | −0.870150 | −0.0641483 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 20.9044 | 1.53278 | ||||||||
\(187\) | −3.95474 | −0.289199 | ||||||||
\(188\) | −18.6122 | −1.35744 | ||||||||
\(189\) | −2.59863 | −0.189022 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4092 | 0.970254 | 0.485127 | − | 0.874444i | \(-0.338773\pi\) | ||||
0.485127 | + | 0.874444i | \(0.338773\pi\) | |||||||
\(192\) | −10.4970 | −0.757558 | ||||||||
\(193\) | 10.1874 | 0.733303 | 0.366652 | − | 0.930358i | \(-0.380504\pi\) | ||||
0.366652 | + | 0.930358i | \(0.380504\pi\) | |||||||
\(194\) | −30.6871 | −2.20321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.927360 | −0.0662400 | ||||||||
\(197\) | 9.51148 | 0.677665 | 0.338832 | − | 0.940847i | \(-0.389968\pi\) | ||||
0.338832 | + | 0.940847i | \(0.389968\pi\) | |||||||
\(198\) | −5.56201 | −0.395275 | ||||||||
\(199\) | −8.83850 | −0.626544 | −0.313272 | − | 0.949663i | \(-0.601425\pi\) | ||||
−0.313272 | + | 0.949663i | \(0.601425\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.605901 | 0.0427370 | ||||||||
\(202\) | −20.1049 | −1.41458 | ||||||||
\(203\) | −12.4650 | −0.874873 | ||||||||
\(204\) | 6.39880 | 0.448006 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −36.4239 | −2.53777 | ||||||||
\(207\) | −0.207050 | −0.0143909 | ||||||||
\(208\) | 1.31579 | 0.0912336 | ||||||||
\(209\) | −17.9067 | −1.23863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.98608 | 0.205570 | 0.102785 | − | 0.994704i | \(-0.467225\pi\) | ||||
0.102785 | + | 0.994704i | \(0.467225\pi\) | |||||||
\(212\) | −2.04208 | −0.140250 | ||||||||
\(213\) | −1.91240 | −0.131035 | ||||||||
\(214\) | −2.39839 | −0.163950 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.20262 | 0.285952 | ||||||||
\(217\) | −22.6496 | −1.53756 | ||||||||
\(218\) | −17.8877 | −1.21150 | ||||||||
\(219\) | 13.0474 | 0.881665 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.871403 | 0.0586169 | ||||||||
\(222\) | 14.3397 | 0.962420 | ||||||||
\(223\) | −12.6326 | −0.845941 | −0.422971 | − | 0.906143i | \(-0.639013\pi\) | ||||
−0.422971 | + | 0.906143i | \(0.639013\pi\) | |||||||
\(224\) | 5.79351 | 0.387095 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.1315 | −1.53869 | ||||||||
\(227\) | 29.4478 | 1.95452 | 0.977260 | − | 0.212046i | \(-0.0680125\pi\) | ||||
0.977260 | + | 0.212046i | \(0.0680125\pi\) | |||||||
\(228\) | 28.9732 | 1.91880 | ||||||||
\(229\) | −25.3001 | −1.67187 | −0.835937 | − | 0.548825i | \(-0.815075\pi\) | ||||
−0.835937 | + | 0.548825i | \(0.815075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.02637 | 0.396506 | ||||||||
\(232\) | 20.1590 | 1.32350 | ||||||||
\(233\) | −8.78721 | −0.575669 | −0.287835 | − | 0.957680i | \(-0.592935\pi\) | ||||
−0.287835 | + | 0.957680i | \(0.592935\pi\) | |||||||
\(234\) | 1.22556 | 0.0801172 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.8698 | 2.85568 | ||||||||
\(237\) | 1.42355 | 0.0924696 | ||||||||
\(238\) | −10.6284 | −0.688937 | ||||||||
\(239\) | −15.3859 | −0.995229 | −0.497614 | − | 0.867398i | \(-0.665791\pi\) | ||||
−0.497614 | + | 0.867398i | \(0.665791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.74583 | 0.176874 | 0.0884371 | − | 0.996082i | \(-0.471813\pi\) | ||||
0.0884371 | + | 0.996082i | \(0.471813\pi\) | |||||||
\(242\) | −13.4836 | −0.866760 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.53915 | 0.226571 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.5073 | 0.924950 | ||||||||
\(247\) | 3.94563 | 0.251055 | ||||||||
\(248\) | 36.6300 | 2.32601 | ||||||||
\(249\) | 12.5487 | 0.795243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.51184 | −0.600382 | −0.300191 | − | 0.953879i | \(-0.597050\pi\) | ||||
−0.300191 | + | 0.953879i | \(0.597050\pi\) | |||||||
\(252\) | −9.75073 | −0.614239 | ||||||||
\(253\) | 0.480161 | 0.0301875 | ||||||||
\(254\) | 45.4127 | 2.84944 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.6935 | −1.79334 | ||||||||
\(257\) | −9.59376 | −0.598442 | −0.299221 | − | 0.954184i | \(-0.596727\pi\) | ||||
−0.299221 | + | 0.954184i | \(0.596727\pi\) | |||||||
\(258\) | −9.54775 | −0.594417 | ||||||||
\(259\) | −15.5369 | −0.965418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.79678 | 0.296913 | ||||||||
\(262\) | 32.9511 | 2.03572 | ||||||||
\(263\) | −6.68810 | −0.412406 | −0.206203 | − | 0.978509i | \(-0.566111\pi\) | ||||
−0.206203 | + | 0.978509i | \(0.566111\pi\) | |||||||
\(264\) | −9.74613 | −0.599833 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −48.1245 | −2.95070 | ||||||||
\(267\) | 13.4753 | 0.824673 | ||||||||
\(268\) | 2.27350 | 0.138876 | ||||||||
\(269\) | −12.7174 | −0.775391 | −0.387696 | − | 0.921787i | \(-0.626729\pi\) | ||||
−0.387696 | + | 0.921787i | \(0.626729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0805 | 0.855327 | 0.427663 | − | 0.903938i | \(-0.359337\pi\) | ||||
0.427663 | + | 0.903938i | \(0.359337\pi\) | |||||||
\(272\) | 4.39114 | 0.266252 | ||||||||
\(273\) | −1.32788 | −0.0803667 | ||||||||
\(274\) | −19.0364 | −1.15003 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.776906 | −0.0467642 | ||||||||
\(277\) | 25.7886 | 1.54949 | 0.774743 | − | 0.632277i | \(-0.217879\pi\) | ||||
0.774743 | + | 0.632277i | \(0.217879\pi\) | |||||||
\(278\) | −43.3032 | −2.59715 | ||||||||
\(279\) | 8.71600 | 0.521813 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9704 | −1.19133 | −0.595667 | − | 0.803231i | \(-0.703112\pi\) | ||||
−0.595667 | + | 0.803231i | \(0.703112\pi\) | |||||||
\(282\) | −11.8966 | −0.708435 | ||||||||
\(283\) | −29.5986 | −1.75945 | −0.879727 | − | 0.475480i | \(-0.842275\pi\) | ||||
−0.879727 | + | 0.475480i | \(0.842275\pi\) | |||||||
\(284\) | −7.17582 | −0.425807 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.84214 | −0.168059 | ||||||||
\(287\) | −15.7185 | −0.927831 | ||||||||
\(288\) | −2.22945 | −0.131372 | ||||||||
\(289\) | −14.0919 | −0.828935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.7949 | −0.750050 | ||||||||
\(292\) | 48.9575 | 2.86502 | ||||||||
\(293\) | 6.23225 | 0.364092 | 0.182046 | − | 0.983290i | \(-0.441728\pi\) | ||||
0.182046 | + | 0.983290i | \(0.441728\pi\) | |||||||
\(294\) | −0.592753 | −0.0345701 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 25.1270 | 1.46048 | ||||||||
\(297\) | −2.31906 | −0.134566 | ||||||||
\(298\) | −17.4801 | −1.01259 | ||||||||
\(299\) | −0.105801 | −0.00611861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3449 | 0.596269 | ||||||||
\(302\) | 28.1617 | 1.62052 | ||||||||
\(303\) | −8.38268 | −0.481572 | ||||||||
\(304\) | 19.8827 | 1.14035 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.09001 | 0.233810 | ||||||||
\(307\) | 27.6374 | 1.57735 | 0.788674 | − | 0.614812i | \(-0.210768\pi\) | ||||
0.788674 | + | 0.614812i | \(0.210768\pi\) | |||||||
\(308\) | 22.6126 | 1.28847 | ||||||||
\(309\) | −15.1868 | −0.863948 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7005 | −0.833590 | −0.416795 | − | 0.909001i | \(-0.636847\pi\) | ||||
−0.416795 | + | 0.909001i | \(0.636847\pi\) | |||||||
\(312\) | 2.14750 | 0.121578 | ||||||||
\(313\) | −12.6308 | −0.713933 | −0.356966 | − | 0.934117i | \(-0.616189\pi\) | ||||
−0.356966 | + | 0.934117i | \(0.616189\pi\) | |||||||
\(314\) | 22.9320 | 1.29413 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.34154 | 0.300485 | ||||||||
\(317\) | −3.42979 | −0.192636 | −0.0963182 | − | 0.995351i | \(-0.530707\pi\) | ||||
−0.0963182 | + | 0.995351i | \(0.530707\pi\) | |||||||
\(318\) | −1.30526 | −0.0731955 | ||||||||
\(319\) | −11.1240 | −0.622826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | −0.0558146 | ||||||||
\(322\) | 1.29044 | 0.0719134 | ||||||||
\(323\) | 13.1676 | 0.732667 | ||||||||
\(324\) | 3.75227 | 0.208459 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.0477 | −1.49803 | ||||||||
\(327\) | −7.45820 | −0.412439 | ||||||||
\(328\) | 25.4206 | 1.40362 | ||||||||
\(329\) | 12.8899 | 0.710641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.45780 | 0.135093 | 0.0675466 | − | 0.997716i | \(-0.478483\pi\) | ||||
0.0675466 | + | 0.997716i | \(0.478483\pi\) | |||||||
\(332\) | 47.0862 | 2.58419 | ||||||||
\(333\) | 5.97891 | 0.327642 | ||||||||
\(334\) | 51.2388 | 2.80366 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.69138 | −0.365045 | ||||||||
\(337\) | −18.2240 | −0.992726 | −0.496363 | − | 0.868115i | \(-0.665332\pi\) | ||||
−0.496363 | + | 0.868115i | \(0.665332\pi\) | |||||||
\(338\) | −30.5528 | −1.66185 | ||||||||
\(339\) | −9.64461 | −0.523823 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.2130 | −1.09459 | ||||||||
\(342\) | 18.5192 | 1.00140 | ||||||||
\(343\) | 18.8326 | 1.01687 | ||||||||
\(344\) | −16.7302 | −0.902032 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 43.9169 | 2.36099 | ||||||||
\(347\) | −24.3524 | −1.30731 | −0.653653 | − | 0.756794i | \(-0.726764\pi\) | ||||
−0.653653 | + | 0.756794i | \(0.726764\pi\) | |||||||
\(348\) | 17.9988 | 0.964836 | ||||||||
\(349\) | 33.5583 | 1.79634 | 0.898168 | − | 0.439653i | \(-0.144899\pi\) | ||||
0.898168 | + | 0.439653i | \(0.144899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.510992 | 0.0272747 | ||||||||
\(352\) | 5.17024 | 0.275574 | ||||||||
\(353\) | −20.2678 | −1.07874 | −0.539372 | − | 0.842068i | \(-0.681338\pi\) | ||||
−0.539372 | + | 0.842068i | \(0.681338\pi\) | |||||||
\(354\) | 28.0409 | 1.49035 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 50.5628 | 2.67982 | ||||||||
\(357\) | −4.43148 | −0.234539 | ||||||||
\(358\) | −44.0994 | −2.33072 | ||||||||
\(359\) | 16.9473 | 0.894444 | 0.447222 | − | 0.894423i | \(-0.352413\pi\) | ||||
0.447222 | + | 0.894423i | \(0.352413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.6219 | 2.13799 | ||||||||
\(362\) | 20.0624 | 1.05446 | ||||||||
\(363\) | −5.62195 | −0.295076 | ||||||||
\(364\) | −4.98255 | −0.261156 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.26217 | 0.118246 | ||||||||
\(367\) | −28.3838 | −1.48162 | −0.740811 | − | 0.671714i | \(-0.765558\pi\) | ||||
−0.740811 | + | 0.671714i | \(0.765558\pi\) | |||||||
\(368\) | −0.533147 | −0.0277922 | ||||||||
\(369\) | 6.04876 | 0.314886 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.41424 | 0.0734235 | ||||||||
\(372\) | 32.7048 | 1.69566 | ||||||||
\(373\) | −33.0422 | −1.71086 | −0.855431 | − | 0.517917i | \(-0.826708\pi\) | ||||
−0.855431 | + | 0.517917i | \(0.826708\pi\) | |||||||
\(374\) | −9.48499 | −0.490457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.8461 | −1.07505 | ||||||||
\(377\) | 2.45111 | 0.126239 | ||||||||
\(378\) | −6.23251 | −0.320566 | ||||||||
\(379\) | −25.7958 | −1.32504 | −0.662519 | − | 0.749045i | \(-0.730513\pi\) | ||||
−0.662519 | + | 0.749045i | \(0.730513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9347 | 0.970052 | ||||||||
\(382\) | 32.1604 | 1.64547 | ||||||||
\(383\) | 23.4961 | 1.20059 | 0.600297 | − | 0.799777i | \(-0.295049\pi\) | ||||
0.600297 | + | 0.799777i | \(0.295049\pi\) | |||||||
\(384\) | −20.7171 | −1.05721 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.4333 | 1.24362 | ||||||||
\(387\) | −3.98090 | −0.202361 | ||||||||
\(388\) | −48.0099 | −2.43733 | ||||||||
\(389\) | −23.7803 | −1.20571 | −0.602853 | − | 0.797852i | \(-0.705970\pi\) | ||||
−0.602853 | + | 0.797852i | \(0.705970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.353085 | −0.0178563 | ||||||||
\(392\) | −1.03866 | −0.0524603 | ||||||||
\(393\) | 13.7388 | 0.693033 | ||||||||
\(394\) | 22.8122 | 1.14926 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.70174 | −0.437279 | ||||||||
\(397\) | −17.3777 | −0.872163 | −0.436081 | − | 0.899907i | \(-0.643634\pi\) | ||||
−0.436081 | + | 0.899907i | \(0.643634\pi\) | |||||||
\(398\) | −21.1981 | −1.06257 | ||||||||
\(399\) | −20.0653 | −1.00452 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.79926 | −0.439414 | −0.219707 | − | 0.975566i | \(-0.570510\pi\) | ||||
−0.219707 | + | 0.975566i | \(0.570510\pi\) | |||||||
\(402\) | 1.45319 | 0.0724783 | ||||||||
\(403\) | 4.45381 | 0.221860 | ||||||||
\(404\) | −31.4540 | −1.56490 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.8960 | −1.48371 | ||||||||
\(407\) | −13.8655 | −0.687285 | ||||||||
\(408\) | 7.16679 | 0.354809 | ||||||||
\(409\) | −0.340432 | −0.0168333 | −0.00841663 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841663 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.93715 | −0.391511 | ||||||||
\(412\) | −56.9850 | −2.80745 | ||||||||
\(413\) | −30.3819 | −1.49500 | ||||||||
\(414\) | −0.496586 | −0.0244059 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.13923 | −0.0558554 | ||||||||
\(417\) | −18.0551 | −0.884163 | ||||||||
\(418\) | −42.9472 | −2.10062 | ||||||||
\(419\) | −1.81254 | −0.0885486 | −0.0442743 | − | 0.999019i | \(-0.514098\pi\) | ||||
−0.0442743 | + | 0.999019i | \(0.514098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.91272 | −0.434379 | −0.217190 | − | 0.976129i | \(-0.569689\pi\) | ||||
−0.217190 | + | 0.976129i | \(0.569689\pi\) | |||||||
\(422\) | 7.16178 | 0.348630 | ||||||||
\(423\) | −4.96026 | −0.241176 | ||||||||
\(424\) | −2.28717 | −0.111075 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.58667 | −0.222225 | ||||||||
\(427\) | −2.45103 | −0.118614 | ||||||||
\(428\) | −3.75227 | −0.181373 | ||||||||
\(429\) | −1.18502 | −0.0572134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.1473 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(432\) | 2.57497 | 0.123888 | ||||||||
\(433\) | 34.4959 | 1.65777 | 0.828883 | − | 0.559422i | \(-0.188977\pi\) | ||||
0.828883 | + | 0.559422i | \(0.188977\pi\) | |||||||
\(434\) | −54.3226 | −2.60757 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.9851 | −1.34025 | ||||||||
\(437\) | −1.59874 | −0.0764780 | ||||||||
\(438\) | 31.2928 | 1.49523 | ||||||||
\(439\) | −13.4740 | −0.643080 | −0.321540 | − | 0.946896i | \(-0.604200\pi\) | ||||
−0.321540 | + | 0.946896i | \(0.604200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.247147 | −0.0117689 | ||||||||
\(442\) | 2.08996 | 0.0994094 | ||||||||
\(443\) | −35.3480 | −1.67944 | −0.839718 | − | 0.543023i | \(-0.817279\pi\) | ||||
−0.839718 | + | 0.543023i | \(0.817279\pi\) | |||||||
\(444\) | 22.4345 | 1.06469 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.2979 | −1.43465 | ||||||||
\(447\) | −7.28825 | −0.344723 | ||||||||
\(448\) | 27.2778 | 1.28876 | ||||||||
\(449\) | 9.63784 | 0.454838 | 0.227419 | − | 0.973797i | \(-0.426971\pi\) | ||||
0.227419 | + | 0.973797i | \(0.426971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0274 | −0.660527 | ||||||||
\(452\) | −36.1892 | −1.70219 | ||||||||
\(453\) | 11.7419 | 0.551684 | ||||||||
\(454\) | 70.6273 | 3.31470 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 32.4506 | 1.51964 | ||||||||
\(457\) | −11.8024 | −0.552091 | −0.276045 | − | 0.961145i | \(-0.589024\pi\) | ||||
−0.276045 | + | 0.961145i | \(0.589024\pi\) | |||||||
\(458\) | −60.6794 | −2.83536 | ||||||||
\(459\) | 1.70532 | 0.0795974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3134 | 0.480345 | 0.240172 | − | 0.970730i | \(-0.422796\pi\) | ||||
0.240172 | + | 0.970730i | \(0.422796\pi\) | |||||||
\(462\) | 14.4536 | 0.672442 | ||||||||
\(463\) | 5.32448 | 0.247450 | 0.123725 | − | 0.992317i | \(-0.460516\pi\) | ||||
0.123725 | + | 0.992317i | \(0.460516\pi\) | |||||||
\(464\) | 12.3516 | 0.573407 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.0751 | −0.976287 | ||||||||
\(467\) | −5.00072 | −0.231406 | −0.115703 | − | 0.993284i | \(-0.536912\pi\) | ||||
−0.115703 | + | 0.993284i | \(0.536912\pi\) | |||||||
\(468\) | 1.91738 | 0.0886308 | ||||||||
\(469\) | −1.57451 | −0.0727041 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.56141 | 0.440567 | ||||||||
\(472\) | 49.1351 | 2.26162 | ||||||||
\(473\) | 9.23196 | 0.424486 | ||||||||
\(474\) | 3.41423 | 0.156821 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.6281 | −0.762147 | ||||||||
\(477\) | −0.544225 | −0.0249184 | ||||||||
\(478\) | −36.9013 | −1.68783 | ||||||||
\(479\) | −25.5519 | −1.16750 | −0.583749 | − | 0.811934i | \(-0.698415\pi\) | ||||
−0.583749 | + | 0.811934i | \(0.698415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.05517 | 0.139304 | ||||||||
\(482\) | 6.58556 | 0.299964 | ||||||||
\(483\) | 0.538045 | 0.0244819 | ||||||||
\(484\) | −21.0951 | −0.958866 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.39839 | 0.108793 | ||||||||
\(487\) | 17.7207 | 0.803002 | 0.401501 | − | 0.915859i | \(-0.368489\pi\) | ||||
0.401501 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(488\) | 3.96393 | 0.179438 | ||||||||
\(489\) | −11.2774 | −0.509984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.14679 | −0.322530 | −0.161265 | − | 0.986911i | \(-0.551557\pi\) | ||||
−0.161265 | + | 0.986911i | \(0.551557\pi\) | |||||||
\(492\) | 22.6966 | 1.02324 | ||||||||
\(493\) | 8.18002 | 0.368410 | ||||||||
\(494\) | 9.46316 | 0.425768 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.4435 | 1.00774 | ||||||||
\(497\) | 4.96960 | 0.222917 | ||||||||
\(498\) | 30.0967 | 1.34867 | ||||||||
\(499\) | 15.0773 | 0.674951 | 0.337476 | − | 0.941334i | \(-0.390427\pi\) | ||||
0.337476 | + | 0.941334i | \(0.390427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.3638 | 0.954466 | ||||||||
\(502\) | −22.8131 | −1.01820 | ||||||||
\(503\) | −12.2097 | −0.544402 | −0.272201 | − | 0.962240i | \(-0.587752\pi\) | ||||
−0.272201 | + | 0.962240i | \(0.587752\pi\) | |||||||
\(504\) | −10.9210 | −0.486461 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.15161 | 0.0511954 | ||||||||
\(507\) | −12.7389 | −0.565754 | ||||||||
\(508\) | 71.0479 | 3.15224 | ||||||||
\(509\) | 29.1949 | 1.29404 | 0.647020 | − | 0.762473i | \(-0.276015\pi\) | ||||
0.647020 | + | 0.762473i | \(0.276015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.9054 | −1.49989 | ||||||||
\(512\) | −27.3840 | −1.21021 | ||||||||
\(513\) | 7.72152 | 0.340913 | ||||||||
\(514\) | −23.0096 | −1.01491 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −14.9374 | −0.657583 | ||||||||
\(517\) | 11.5032 | 0.505908 | ||||||||
\(518\) | −37.2636 | −1.63727 | ||||||||
\(519\) | 18.3110 | 0.803763 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.9233 | −1.79288 | −0.896441 | − | 0.443163i | \(-0.853856\pi\) | ||||
−0.896441 | + | 0.443163i | \(0.853856\pi\) | |||||||
\(522\) | 11.5045 | 0.503540 | ||||||||
\(523\) | 30.1119 | 1.31670 | 0.658350 | − | 0.752712i | \(-0.271255\pi\) | ||||
0.658350 | + | 0.752712i | \(0.271255\pi\) | |||||||
\(524\) | 51.5518 | 2.25205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0407 | −0.699406 | ||||||||
\(527\) | 14.8635 | 0.647466 | ||||||||
\(528\) | −5.97152 | −0.259877 | ||||||||
\(529\) | −22.9571 | −0.998136 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6915 | 0.507370 | ||||||||
\(532\) | −75.2905 | −3.26426 | ||||||||
\(533\) | 3.09087 | 0.133880 | ||||||||
\(534\) | 32.3189 | 1.39858 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.54637 | 0.109986 | ||||||||
\(537\) | −18.3871 | −0.793462 | ||||||||
\(538\) | −30.5012 | −1.31500 | ||||||||
\(539\) | 0.573148 | 0.0246872 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.9471 | −0.900586 | −0.450293 | − | 0.892881i | \(-0.648680\pi\) | ||||
−0.450293 | + | 0.892881i | \(0.648680\pi\) | |||||||
\(542\) | 33.7704 | 1.45056 | ||||||||
\(543\) | 8.36497 | 0.358975 | ||||||||
\(544\) | −3.80192 | −0.163006 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.18476 | −0.136295 | ||||||||
\(547\) | −14.2139 | −0.607744 | −0.303872 | − | 0.952713i | \(-0.598279\pi\) | ||||
−0.303872 | + | 0.952713i | \(0.598279\pi\) | |||||||
\(548\) | −29.7823 | −1.27224 | ||||||||
\(549\) | 0.943204 | 0.0402550 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.0384 | 1.57789 | ||||||||
\(552\) | −0.870150 | −0.0370361 | ||||||||
\(553\) | −3.69928 | −0.157309 | ||||||||
\(554\) | 61.8510 | 2.62780 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −67.7476 | −2.87314 | ||||||||
\(557\) | 43.5974 | 1.84728 | 0.923640 | − | 0.383261i | \(-0.125199\pi\) | ||||
0.923640 | + | 0.383261i | \(0.125199\pi\) | |||||||
\(558\) | 20.9044 | 0.884952 | ||||||||
\(559\) | −2.03421 | −0.0860378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.95474 | −0.166969 | ||||||||
\(562\) | −47.8968 | −2.02040 | ||||||||
\(563\) | 14.2699 | 0.601404 | 0.300702 | − | 0.953718i | \(-0.402779\pi\) | ||||
0.300702 | + | 0.953718i | \(0.402779\pi\) | |||||||
\(564\) | −18.6122 | −0.783716 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −70.9889 | −2.98389 | ||||||||
\(567\) | −2.59863 | −0.109132 | ||||||||
\(568\) | −8.03707 | −0.337228 | ||||||||
\(569\) | −24.8762 | −1.04287 | −0.521433 | − | 0.853292i | \(-0.674602\pi\) | ||||
−0.521433 | + | 0.853292i | \(0.674602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.4791 | 1.06627 | 0.533135 | − | 0.846030i | \(-0.321014\pi\) | ||||
0.533135 | + | 0.846030i | \(0.321014\pi\) | |||||||
\(572\) | −4.44652 | −0.185918 | ||||||||
\(573\) | 13.4092 | 0.560176 | ||||||||
\(574\) | −37.6990 | −1.57352 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.4970 | −0.437376 | ||||||||
\(577\) | −12.7043 | −0.528888 | −0.264444 | − | 0.964401i | \(-0.585188\pi\) | ||||
−0.264444 | + | 0.964401i | \(0.585188\pi\) | |||||||
\(578\) | −33.7978 | −1.40580 | ||||||||
\(579\) | 10.1874 | 0.423373 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.6094 | −1.35287 | ||||||||
\(582\) | −30.6871 | −1.27202 | ||||||||
\(583\) | 1.26209 | 0.0522705 | ||||||||
\(584\) | 54.8334 | 2.26902 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.9474 | 0.617470 | ||||||||
\(587\) | 46.5082 | 1.91960 | 0.959800 | − | 0.280686i | \(-0.0905618\pi\) | ||||
0.959800 | + | 0.280686i | \(0.0905618\pi\) | |||||||
\(588\) | −0.927360 | −0.0382437 | ||||||||
\(589\) | 67.3008 | 2.77308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.51148 | 0.391250 | ||||||||
\(592\) | 15.3955 | 0.632752 | ||||||||
\(593\) | 18.6267 | 0.764908 | 0.382454 | − | 0.923975i | \(-0.375079\pi\) | ||||
0.382454 | + | 0.923975i | \(0.375079\pi\) | |||||||
\(594\) | −5.56201 | −0.228212 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.3475 | −1.12020 | ||||||||
\(597\) | −8.83850 | −0.361736 | ||||||||
\(598\) | −0.253751 | −0.0103767 | ||||||||
\(599\) | 29.4150 | 1.20186 | 0.600931 | − | 0.799301i | \(-0.294797\pi\) | ||||
0.600931 | + | 0.799301i | \(0.294797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.71448 | −0.314680 | −0.157340 | − | 0.987544i | \(-0.550292\pi\) | ||||
−0.157340 | + | 0.987544i | \(0.550292\pi\) | |||||||
\(602\) | 24.8110 | 1.01122 | ||||||||
\(603\) | 0.605901 | 0.0246742 | ||||||||
\(604\) | 44.0588 | 1.79273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −20.1049 | −0.816706 | ||||||||
\(607\) | −11.5194 | −0.467556 | −0.233778 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233778 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(608\) | −17.2148 | −0.698150 | ||||||||
\(609\) | −12.4650 | −0.505108 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.53465 | −0.102541 | ||||||||
\(612\) | 6.39880 | 0.258656 | ||||||||
\(613\) | −4.93728 | −0.199415 | −0.0997074 | − | 0.995017i | \(-0.531791\pi\) | ||||
−0.0997074 | + | 0.995017i | \(0.531791\pi\) | |||||||
\(614\) | 66.2851 | 2.67505 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.3265 | 1.02044 | ||||||||
\(617\) | 2.49009 | 0.100247 | 0.0501236 | − | 0.998743i | \(-0.484038\pi\) | ||||
0.0501236 | + | 0.998743i | \(0.484038\pi\) | |||||||
\(618\) | −36.4239 | −1.46518 | ||||||||
\(619\) | −34.4243 | −1.38363 | −0.691815 | − | 0.722075i | \(-0.743189\pi\) | ||||
−0.691815 | + | 0.722075i | \(0.743189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.207050 | −0.00830862 | ||||||||
\(622\) | −35.2575 | −1.41370 | ||||||||
\(623\) | −35.0172 | −1.40293 | ||||||||
\(624\) | 1.31579 | 0.0526737 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.2935 | −1.21077 | ||||||||
\(627\) | −17.9067 | −0.715124 | ||||||||
\(628\) | 35.8770 | 1.43165 | ||||||||
\(629\) | 10.1959 | 0.406538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0793 | 1.79458 | 0.897288 | − | 0.441445i | \(-0.145534\pi\) | ||||
0.897288 | + | 0.441445i | \(0.145534\pi\) | |||||||
\(632\) | 5.98264 | 0.237977 | ||||||||
\(633\) | 2.98608 | 0.118686 | ||||||||
\(634\) | −8.22598 | −0.326695 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.04208 | −0.0809736 | ||||||||
\(637\) | −0.126290 | −0.00500379 | ||||||||
\(638\) | −26.6797 | −1.05626 | ||||||||
\(639\) | −1.91240 | −0.0756532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.39775 | −0.213198 | −0.106599 | − | 0.994302i | \(-0.533996\pi\) | ||||
−0.106599 | + | 0.994302i | \(0.533996\pi\) | |||||||
\(642\) | −2.39839 | −0.0946568 | ||||||||
\(643\) | −36.7733 | −1.45020 | −0.725099 | − | 0.688644i | \(-0.758206\pi\) | ||||
−0.725099 | + | 0.688644i | \(0.758206\pi\) | |||||||
\(644\) | 2.01889 | 0.0795553 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 31.5811 | 1.24254 | ||||||||
\(647\) | −40.2852 | −1.58378 | −0.791888 | − | 0.610667i | \(-0.790902\pi\) | ||||
−0.791888 | + | 0.610667i | \(0.790902\pi\) | |||||||
\(648\) | 4.20262 | 0.165094 | ||||||||
\(649\) | −27.1134 | −1.06429 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.6496 | −0.887709 | ||||||||
\(652\) | −42.3160 | −1.65722 | ||||||||
\(653\) | 7.09277 | 0.277562 | 0.138781 | − | 0.990323i | \(-0.455682\pi\) | ||||
0.138781 | + | 0.990323i | \(0.455682\pi\) | |||||||
\(654\) | −17.8877 | −0.699462 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.5754 | 0.608116 | ||||||||
\(657\) | 13.0474 | 0.509029 | ||||||||
\(658\) | 30.9149 | 1.20519 | ||||||||
\(659\) | −33.1662 | −1.29197 | −0.645985 | − | 0.763350i | \(-0.723553\pi\) | ||||
−0.645985 | + | 0.763350i | \(0.723553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.62018 | −0.257495 | −0.128748 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128748 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(662\) | 5.89477 | 0.229107 | ||||||||
\(663\) | 0.871403 | 0.0338425 | ||||||||
\(664\) | 52.7375 | 2.04661 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.3397 | 0.555654 | ||||||||
\(667\) | −0.993171 | −0.0384557 | ||||||||
\(668\) | 80.1628 | 3.10159 | ||||||||
\(669\) | −12.6326 | −0.488404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.18735 | −0.0844417 | ||||||||
\(672\) | 5.79351 | 0.223489 | ||||||||
\(673\) | 4.50311 | 0.173582 | 0.0867911 | − | 0.996227i | \(-0.472339\pi\) | ||||
0.0867911 | + | 0.996227i | \(0.472339\pi\) | |||||||
\(674\) | −43.7083 | −1.68358 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −47.7997 | −1.83845 | ||||||||
\(677\) | 12.3244 | 0.473663 | 0.236832 | − | 0.971551i | \(-0.423891\pi\) | ||||
0.236832 | + | 0.971551i | \(0.423891\pi\) | |||||||
\(678\) | −23.1315 | −0.888361 | ||||||||
\(679\) | 33.2491 | 1.27598 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.4478 | 1.12844 | ||||||||
\(682\) | −48.4785 | −1.85634 | ||||||||
\(683\) | 28.0420 | 1.07300 | 0.536499 | − | 0.843901i | \(-0.319747\pi\) | ||||
0.536499 | + | 0.843901i | \(0.319747\pi\) | |||||||
\(684\) | 28.9732 | 1.10782 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 45.1679 | 1.72452 | ||||||||
\(687\) | −25.3001 | −0.965257 | ||||||||
\(688\) | −10.2507 | −0.390805 | ||||||||
\(689\) | −0.278095 | −0.0105946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8054 | −0.981684 | −0.490842 | − | 0.871249i | \(-0.663311\pi\) | ||||
−0.490842 | + | 0.871249i | \(0.663311\pi\) | |||||||
\(692\) | 68.7077 | 2.61188 | ||||||||
\(693\) | 6.02637 | 0.228923 | ||||||||
\(694\) | −58.4065 | −2.21708 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.1590 | 0.764125 | ||||||||
\(697\) | 10.3150 | 0.390710 | ||||||||
\(698\) | 80.4859 | 3.04643 | ||||||||
\(699\) | −8.78721 | −0.332363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9498 | 1.62219 | 0.811095 | − | 0.584915i | \(-0.198872\pi\) | ||||
0.811095 | + | 0.584915i | \(0.198872\pi\) | |||||||
\(702\) | 1.22556 | 0.0462557 | ||||||||
\(703\) | 46.1663 | 1.74119 | ||||||||
\(704\) | 24.3433 | 0.917471 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −48.6100 | −1.82946 | ||||||||
\(707\) | 21.7834 | 0.819250 | ||||||||
\(708\) | 43.8698 | 1.64873 | ||||||||
\(709\) | 8.78803 | 0.330041 | 0.165021 | − | 0.986290i | \(-0.447231\pi\) | ||||
0.165021 | + | 0.986290i | \(0.447231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.42355 | 0.0533873 | ||||||||
\(712\) | 56.6314 | 2.12235 | ||||||||
\(713\) | −1.80465 | −0.0675845 | ||||||||
\(714\) | −10.6284 | −0.397758 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −68.9933 | −2.57840 | ||||||||
\(717\) | −15.3859 | −0.574596 | ||||||||
\(718\) | 40.6462 | 1.51690 | ||||||||
\(719\) | 13.3007 | 0.496034 | 0.248017 | − | 0.968756i | \(-0.420221\pi\) | ||||
0.248017 | + | 0.968756i | \(0.420221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.4648 | 1.46975 | ||||||||
\(722\) | 97.4270 | 3.62586 | ||||||||
\(723\) | 2.74583 | 0.102118 | ||||||||
\(724\) | 31.3876 | 1.16651 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13.4836 | −0.500424 | ||||||||
\(727\) | 16.7795 | 0.622317 | 0.311159 | − | 0.950358i | \(-0.399283\pi\) | ||||
0.311159 | + | 0.950358i | \(0.399283\pi\) | |||||||
\(728\) | −5.58055 | −0.206829 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.78870 | −0.251089 | ||||||||
\(732\) | 3.53915 | 0.130811 | ||||||||
\(733\) | −14.8741 | −0.549389 | −0.274694 | − | 0.961532i | \(-0.588577\pi\) | ||||
−0.274694 | + | 0.961532i | \(0.588577\pi\) | |||||||
\(734\) | −68.0753 | −2.51271 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.461607 | 0.0170151 | ||||||||
\(737\) | −1.40512 | −0.0517583 | ||||||||
\(738\) | 14.5073 | 0.534020 | ||||||||
\(739\) | 0.303603 | 0.0111682 | 0.00558412 | − | 0.999984i | \(-0.498223\pi\) | ||||
0.00558412 | + | 0.999984i | \(0.498223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.94563 | 0.144946 | ||||||||
\(742\) | 3.39189 | 0.124520 | ||||||||
\(743\) | −46.5691 | −1.70846 | −0.854228 | − | 0.519899i | \(-0.825969\pi\) | ||||
−0.854228 | + | 0.519899i | \(0.825969\pi\) | |||||||
\(744\) | 36.6300 | 1.34292 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −79.2481 | −2.90148 | ||||||||
\(747\) | 12.5487 | 0.459134 | ||||||||
\(748\) | −14.8392 | −0.542576 | ||||||||
\(749\) | 2.59863 | 0.0949517 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.3917 | −0.963047 | −0.481523 | − | 0.876433i | \(-0.659916\pi\) | ||||
−0.481523 | + | 0.876433i | \(0.659916\pi\) | |||||||
\(752\) | −12.7725 | −0.465766 | ||||||||
\(753\) | −9.51184 | −0.346631 | ||||||||
\(754\) | 5.87872 | 0.214090 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.75073 | −0.354631 | ||||||||
\(757\) | 13.9095 | 0.505551 | 0.252775 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252775 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(758\) | −61.8682 | −2.24716 | ||||||||
\(759\) | 0.480161 | 0.0174287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1860 | 0.441742 | 0.220871 | − | 0.975303i | \(-0.429110\pi\) | ||||
0.220871 | + | 0.975303i | \(0.429110\pi\) | |||||||
\(762\) | 45.4127 | 1.64513 | ||||||||
\(763\) | 19.3811 | 0.701641 | ||||||||
\(764\) | 50.3148 | 1.82033 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 56.3528 | 2.03611 | ||||||||
\(767\) | 5.97428 | 0.215719 | ||||||||
\(768\) | −28.6935 | −1.03539 | ||||||||
\(769\) | −18.1664 | −0.655097 | −0.327548 | − | 0.944834i | \(-0.606222\pi\) | ||||
−0.327548 | + | 0.944834i | \(0.606222\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.59376 | −0.345511 | ||||||||
\(772\) | 38.2257 | 1.37577 | ||||||||
\(773\) | 9.81626 | 0.353066 | 0.176533 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176533 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(774\) | −9.54775 | −0.343187 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −53.7720 | −1.93030 | ||||||||
\(777\) | −15.5369 | −0.557385 | ||||||||
\(778\) | −57.0343 | −2.04478 | ||||||||
\(779\) | 46.7056 | 1.67340 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.43497 | 0.158696 | ||||||||
\(782\) | −0.846836 | −0.0302828 | ||||||||
\(783\) | 4.79678 | 0.171423 | ||||||||
\(784\) | −0.636395 | −0.0227284 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.9511 | 1.17533 | ||||||||
\(787\) | 29.7235 | 1.05953 | 0.529765 | − | 0.848145i | \(-0.322280\pi\) | ||||
0.529765 | + | 0.848145i | \(0.322280\pi\) | |||||||
\(788\) | 35.6896 | 1.27139 | ||||||||
\(789\) | −6.68810 | −0.238103 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.0627 | 0.891128 | ||||||||
\(792\) | −9.74613 | −0.346314 | ||||||||
\(793\) | 0.481970 | 0.0171152 | ||||||||
\(794\) | −41.6785 | −1.47912 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.1644 | −1.17548 | ||||||||
\(797\) | −32.5535 | −1.15310 | −0.576552 | − | 0.817061i | \(-0.695602\pi\) | ||||
−0.576552 | + | 0.817061i | \(0.695602\pi\) | |||||||
\(798\) | −48.1245 | −1.70359 | ||||||||
\(799\) | −8.45882 | −0.299252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4753 | 0.476125 | ||||||||
\(802\) | −21.1040 | −0.745210 | ||||||||
\(803\) | −30.2578 | −1.06778 | ||||||||
\(804\) | 2.27350 | 0.0801802 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.6820 | 0.376256 | ||||||||
\(807\) | −12.7174 | −0.447672 | ||||||||
\(808\) | −35.2292 | −1.23936 | ||||||||
\(809\) | −21.7347 | −0.764153 | −0.382077 | − | 0.924131i | \(-0.624791\pi\) | ||||
−0.382077 | + | 0.924131i | \(0.624791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.98018 | −0.245107 | −0.122554 | − | 0.992462i | \(-0.539108\pi\) | ||||
−0.122554 | + | 0.992462i | \(0.539108\pi\) | |||||||
\(812\) | −46.7721 | −1.64138 | ||||||||
\(813\) | 14.0805 | 0.493823 | ||||||||
\(814\) | −33.2548 | −1.16558 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.39114 | 0.153721 | ||||||||
\(817\) | −30.7386 | −1.07541 | ||||||||
\(818\) | −0.816487 | −0.0285478 | ||||||||
\(819\) | −1.32788 | −0.0463998 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0515 | −0.839403 | −0.419702 | − | 0.907662i | \(-0.637865\pi\) | ||||
−0.419702 | + | 0.907662i | \(0.637865\pi\) | |||||||
\(822\) | −19.0364 | −0.663970 | ||||||||
\(823\) | 4.37135 | 0.152376 | 0.0761879 | − | 0.997093i | \(-0.475725\pi\) | ||||
0.0761879 | + | 0.997093i | \(0.475725\pi\) | |||||||
\(824\) | −63.8244 | −2.22343 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −72.8677 | −2.53539 | ||||||||
\(827\) | 35.9008 | 1.24839 | 0.624197 | − | 0.781267i | \(-0.285426\pi\) | ||||
0.624197 | + | 0.781267i | \(0.285426\pi\) | |||||||
\(828\) | −0.776906 | −0.0269993 | ||||||||
\(829\) | 51.9960 | 1.80590 | 0.902948 | − | 0.429749i | \(-0.141398\pi\) | ||||
0.902948 | + | 0.429749i | \(0.141398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.7886 | 0.894596 | ||||||||
\(832\) | −5.36390 | −0.185960 | ||||||||
\(833\) | −0.421463 | −0.0146028 | ||||||||
\(834\) | −43.3032 | −1.49947 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −67.1907 | −2.32384 | ||||||||
\(837\) | 8.71600 | 0.301269 | ||||||||
\(838\) | −4.34719 | −0.150171 | ||||||||
\(839\) | 43.5905 | 1.50491 | 0.752455 | − | 0.658644i | \(-0.228869\pi\) | ||||
0.752455 | + | 0.658644i | \(0.228869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.99093 | −0.206584 | ||||||||
\(842\) | −21.3762 | −0.736671 | ||||||||
\(843\) | −19.9704 | −0.687817 | ||||||||
\(844\) | 11.2046 | 0.385677 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.8966 | −0.409015 | ||||||||
\(847\) | 14.6093 | 0.501983 | ||||||||
\(848\) | −1.40136 | −0.0481230 | ||||||||
\(849\) | −29.5986 | −1.01582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.23793 | −0.0424357 | ||||||||
\(852\) | −7.17582 | −0.245840 | ||||||||
\(853\) | −26.4502 | −0.905638 | −0.452819 | − | 0.891603i | \(-0.649582\pi\) | ||||
−0.452819 | + | 0.891603i | \(0.649582\pi\) | |||||||
\(854\) | −5.87853 | −0.201159 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.20262 | −0.143642 | ||||||||
\(857\) | −44.3271 | −1.51419 | −0.757093 | − | 0.653307i | \(-0.773381\pi\) | ||||
−0.757093 | + | 0.653307i | \(0.773381\pi\) | |||||||
\(858\) | −2.84214 | −0.0970291 | ||||||||
\(859\) | −38.2891 | −1.30641 | −0.653204 | − | 0.757182i | \(-0.726576\pi\) | ||||
−0.653204 | + | 0.757182i | \(0.726576\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.7185 | −0.535684 | ||||||||
\(862\) | 50.7195 | 1.72751 | ||||||||
\(863\) | 1.76848 | 0.0601997 | 0.0300998 | − | 0.999547i | \(-0.490417\pi\) | ||||
0.0300998 | + | 0.999547i | \(0.490417\pi\) | |||||||
\(864\) | −2.22945 | −0.0758475 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 82.7345 | 2.81143 | ||||||||
\(867\) | −14.0919 | −0.478586 | ||||||||
\(868\) | −84.9874 | −2.88466 | ||||||||
\(869\) | −3.30130 | −0.111989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.309610 | 0.0104907 | ||||||||
\(872\) | −31.3439 | −1.06144 | ||||||||
\(873\) | −12.7949 | −0.433042 | ||||||||
\(874\) | −3.83440 | −0.129700 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 48.9575 | 1.65412 | ||||||||
\(877\) | −37.2241 | −1.25697 | −0.628484 | − | 0.777822i | \(-0.716324\pi\) | ||||
−0.628484 | + | 0.777822i | \(0.716324\pi\) | |||||||
\(878\) | −32.3159 | −1.09061 | ||||||||
\(879\) | 6.23225 | 0.210209 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.4231 | 1.15974 | 0.579872 | − | 0.814708i | \(-0.303103\pi\) | ||||
0.579872 | + | 0.814708i | \(0.303103\pi\) | |||||||
\(882\) | −0.592753 | −0.0199590 | ||||||||
\(883\) | −12.4548 | −0.419139 | −0.209569 | − | 0.977794i | \(-0.567206\pi\) | ||||
−0.209569 | + | 0.977794i | \(0.567206\pi\) | |||||||
\(884\) | 3.26974 | 0.109973 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −84.7783 | −2.84818 | ||||||||
\(887\) | 48.0530 | 1.61346 | 0.806731 | − | 0.590918i | \(-0.201235\pi\) | ||||
0.806731 | + | 0.590918i | \(0.201235\pi\) | |||||||
\(888\) | 25.1270 | 0.843209 | ||||||||
\(889\) | −49.2041 | −1.65025 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.31906 | −0.0776915 | ||||||||
\(892\) | −47.4009 | −1.58710 | ||||||||
\(893\) | −38.3008 | −1.28169 | ||||||||
\(894\) | −17.4801 | −0.584621 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 53.8359 | 1.79853 | ||||||||
\(897\) | −0.105801 | −0.00353258 | ||||||||
\(898\) | 23.1153 | 0.771367 | ||||||||
\(899\) | 41.8087 | 1.39440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.928076 | −0.0309187 | ||||||||
\(902\) | −33.6433 | −1.12020 | ||||||||
\(903\) | 10.3449 | 0.344256 | ||||||||
\(904\) | −40.5326 | −1.34809 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 28.1617 | 0.935609 | ||||||||
\(907\) | −28.7360 | −0.954164 | −0.477082 | − | 0.878859i | \(-0.658306\pi\) | ||||
−0.477082 | + | 0.878859i | \(0.658306\pi\) | |||||||
\(908\) | 110.496 | 3.66694 | ||||||||
\(909\) | −8.38268 | −0.278036 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.1645 | 0.436160 | 0.218080 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218080 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(912\) | 19.8827 | 0.658382 | ||||||||
\(913\) | −29.1013 | −0.963111 | ||||||||
\(914\) | −28.3066 | −0.936300 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −94.9326 | −3.13666 | ||||||||
\(917\) | −35.7021 | −1.17899 | ||||||||
\(918\) | 4.09001 | 0.134991 | ||||||||
\(919\) | 25.2878 | 0.834167 | 0.417084 | − | 0.908868i | \(-0.363052\pi\) | ||||
0.417084 | + | 0.908868i | \(0.363052\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.6374 | 0.910682 | ||||||||
\(922\) | 24.7356 | 0.814625 | ||||||||
\(923\) | −0.977219 | −0.0321656 | ||||||||
\(924\) | 22.6126 | 0.743899 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.7702 | 0.419654 | ||||||||
\(927\) | −15.1868 | −0.498801 | ||||||||
\(928\) | −10.6942 | −0.351054 | ||||||||
\(929\) | 22.5813 | 0.740869 | 0.370435 | − | 0.928859i | \(-0.379209\pi\) | ||||
0.370435 | + | 0.928859i | \(0.379209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90835 | −0.0625436 | ||||||||
\(932\) | −32.9719 | −1.08003 | ||||||||
\(933\) | −14.7005 | −0.481273 | ||||||||
\(934\) | −11.9937 | −0.392445 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.14750 | 0.0701933 | ||||||||
\(937\) | −0.720844 | −0.0235489 | −0.0117745 | − | 0.999931i | \(-0.503748\pi\) | ||||
−0.0117745 | + | 0.999931i | \(0.503748\pi\) | |||||||
\(938\) | −3.77628 | −0.123300 | ||||||||
\(939\) | −12.6308 | −0.412189 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4512 | 0.340699 | 0.170350 | − | 0.985384i | \(-0.445510\pi\) | ||||
0.170350 | + | 0.985384i | \(0.445510\pi\) | |||||||
\(942\) | 22.9320 | 0.747164 | ||||||||
\(943\) | −1.25239 | −0.0407835 | ||||||||
\(944\) | 30.1054 | 0.979847 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.1418 | 0.719893 | ||||||||
\(947\) | 51.3114 | 1.66740 | 0.833698 | − | 0.552220i | \(-0.186219\pi\) | ||||
0.833698 | + | 0.552220i | \(0.186219\pi\) | |||||||
\(948\) | 5.34154 | 0.173485 | ||||||||
\(949\) | 6.66714 | 0.216424 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.42979 | −0.111219 | ||||||||
\(952\) | −18.6238 | −0.603601 | ||||||||
\(953\) | −41.2436 | −1.33601 | −0.668006 | − | 0.744156i | \(-0.732852\pi\) | ||||
−0.668006 | + | 0.744156i | \(0.732852\pi\) | |||||||
\(954\) | −1.30526 | −0.0422595 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −57.7319 | −1.86718 | ||||||||
\(957\) | −11.1240 | −0.359589 | ||||||||
\(958\) | −61.2835 | −1.97998 | ||||||||
\(959\) | 20.6257 | 0.666038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.9687 | 1.45060 | ||||||||
\(962\) | 7.32749 | 0.236248 | ||||||||
\(963\) | −1.00000 | −0.0322245 | ||||||||
\(964\) | 10.3031 | 0.331840 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.29044 | 0.0415192 | ||||||||
\(967\) | −27.7604 | −0.892716 | −0.446358 | − | 0.894855i | \(-0.647279\pi\) | ||||
−0.446358 | + | 0.894855i | \(0.647279\pi\) | |||||||
\(968\) | −23.6269 | −0.759397 | ||||||||
\(969\) | 13.1676 | 0.423006 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.2741 | 1.67756 | 0.838778 | − | 0.544474i | \(-0.183271\pi\) | ||||
0.838778 | + | 0.544474i | \(0.183271\pi\) | |||||||
\(972\) | 3.75227 | 0.120354 | ||||||||
\(973\) | 46.9185 | 1.50414 | ||||||||
\(974\) | 42.5011 | 1.36182 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.42872 | 0.0777416 | ||||||||
\(977\) | −45.2329 | −1.44713 | −0.723565 | − | 0.690256i | \(-0.757498\pi\) | ||||
−0.723565 | + | 0.690256i | \(0.757498\pi\) | |||||||
\(978\) | −27.0477 | −0.864890 | ||||||||
\(979\) | −31.2500 | −0.998754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.45820 | −0.238122 | ||||||||
\(982\) | −17.1408 | −0.546984 | ||||||||
\(983\) | −14.3566 | −0.457906 | −0.228953 | − | 0.973437i | \(-0.573530\pi\) | ||||
−0.228953 | + | 0.973437i | \(0.573530\pi\) | |||||||
\(984\) | 25.4206 | 0.810379 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.6189 | 0.624792 | ||||||||
\(987\) | 12.8899 | 0.410289 | ||||||||
\(988\) | 14.8051 | 0.471012 | ||||||||
\(989\) | 0.824245 | 0.0262095 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.4840 | 0.968357 | 0.484179 | − | 0.874969i | \(-0.339118\pi\) | ||||
0.484179 | + | 0.874969i | \(0.339118\pi\) | |||||||
\(992\) | −19.4319 | −0.616963 | ||||||||
\(993\) | 2.45780 | 0.0779960 | ||||||||
\(994\) | 11.9190 | 0.378049 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 47.0862 | 1.49198 | ||||||||
\(997\) | −7.85984 | −0.248924 | −0.124462 | − | 0.992224i | \(-0.539720\pi\) | ||||
−0.124462 | + | 0.992224i | \(0.539720\pi\) | |||||||
\(998\) | 36.1611 | 1.14466 | ||||||||
\(999\) | 5.97891 | 0.189164 |
(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 | 8025.2.a.bb.1.6 | 7 | ||
5.4 | even | 2 | 321.2.a.d.1.2 | ✓ | 7 | ||
15.14 | odd | 2 | 963.2.a.e.1.6 | 7 | |||
20.19 | odd | 2 | 5136.2.a.bi.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
321.2.a.d.1.2 | ✓ | 7 | 5.4 | even | 2 | ||
963.2.a.e.1.6 | 7 | 15.14 | odd | 2 | |||
5136.2.a.bi.1.6 | 7 | 20.19 | odd | 2 | |||
8025.2.a.bb.1.6 | 7 | 1.1 | even | 1 | trivial |