Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 740) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-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 | ||||||||
\(3\) | −2.21432 | −1.27844 | −0.639219 | − | 0.769025i | \(-0.720742\pi\) | ||||
−0.639219 | + | 0.769025i | \(0.720742\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.83654 | −1.07211 | −0.536055 | − | 0.844183i | \(-0.680086\pi\) | ||||
−0.536055 | + | 0.844183i | \(0.680086\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.90321 | 0.634404 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37778 | 0.415418 | 0.207709 | − | 0.978191i | \(-0.433399\pi\) | ||||
0.207709 | + | 0.978191i | \(0.433399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.28100 | 1.18733 | 0.593667 | − | 0.804711i | \(-0.297679\pi\) | ||||
0.593667 | + | 0.804711i | \(0.297679\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21432 | 0.571735 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.33185 | −0.808093 | −0.404046 | − | 0.914739i | \(-0.632397\pi\) | ||||
−0.404046 | + | 0.914739i | \(0.632397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.21432 | −1.88449 | −0.942247 | − | 0.334919i | \(-0.891291\pi\) | ||||
−0.942247 | + | 0.334919i | \(0.891291\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.28100 | 1.37063 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.622216 | 0.129741 | 0.0648705 | − | 0.997894i | \(-0.479337\pi\) | ||||
0.0648705 | + | 0.997894i | \(0.479337\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.42864 | 0.467392 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.18421 | −0.962683 | −0.481342 | − | 0.876533i | \(-0.659850\pi\) | ||||
−0.481342 | + | 0.876533i | \(0.659850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64296 | −1.19311 | −0.596555 | − | 0.802572i | \(-0.703464\pi\) | ||||
−0.596555 | + | 0.802572i | \(0.703464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.05086 | −0.531086 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.83654 | 0.479462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.47949 | −1.51793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.42864 | 0.379290 | 0.189645 | − | 0.981853i | \(-0.439266\pi\) | ||||
0.189645 | + | 0.981853i | \(0.439266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.18421 | 0.180590 | 0.0902950 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902950 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.90321 | −0.283714 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.54125 | −0.370679 | −0.185340 | − | 0.982675i | \(-0.559339\pi\) | ||||
−0.185340 | + | 0.982675i | \(0.559339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.04593 | 0.149419 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.37778 | 1.03310 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.56199 | −0.351917 | −0.175958 | − | 0.984398i | \(-0.556302\pi\) | ||||
−0.175958 | + | 0.984398i | \(0.556302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.37778 | −0.185780 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.1891 | 2.40921 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.8272 | −1.80014 | −0.900072 | − | 0.435741i | \(-0.856486\pi\) | ||||
−0.900072 | + | 0.435741i | \(0.856486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4701 | −1.85271 | −0.926355 | − | 0.376652i | \(-0.877075\pi\) | ||||
−0.926355 | + | 0.376652i | \(0.877075\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.39853 | −0.680151 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.28100 | −0.530992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.87802 | 1.08462 | 0.542312 | − | 0.840177i | \(-0.317549\pi\) | ||||
0.542312 | + | 0.840177i | \(0.317549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.37778 | −0.165866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0509 | 1.78621 | 0.893104 | − | 0.449850i | \(-0.148523\pi\) | ||||
0.893104 | + | 0.449850i | \(0.148523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.622216 | 0.0728248 | 0.0364124 | − | 0.999337i | \(-0.488407\pi\) | ||||
0.0364124 | + | 0.999337i | \(0.488407\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.21432 | −0.255688 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.90813 | −0.445373 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.26517 | 1.04241 | 0.521207 | − | 0.853430i | \(-0.325482\pi\) | ||||
0.521207 | + | 0.853430i | \(0.325482\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0874 | −1.23194 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16346 | 0.347235 | 0.173618 | − | 0.984813i | \(-0.444454\pi\) | ||||
0.173618 | + | 0.984813i | \(0.444454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.33185 | 0.361390 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.4795 | 1.23073 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4193 | 1.21044 | 0.605220 | − | 0.796058i | \(-0.293085\pi\) | ||||
0.605220 | + | 0.796058i | \(0.293085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.1432 | −1.27295 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.7096 | 1.52532 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.21432 | 0.842771 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4286 | 1.05887 | 0.529434 | − | 0.848351i | \(-0.322404\pi\) | ||||
0.529434 | + | 0.848351i | \(0.322404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.62222 | 0.263543 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.39207 | −0.536531 | −0.268266 | − | 0.963345i | \(-0.586451\pi\) | ||||
−0.268266 | + | 0.963345i | \(0.586451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5620 | 1.04070 | 0.520352 | − | 0.853952i | \(-0.325801\pi\) | ||||
0.520352 | + | 0.853952i | \(0.325801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.28100 | −0.612962 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.53188 | −0.728134 | −0.364067 | − | 0.931373i | \(-0.618612\pi\) | ||||
−0.364067 | + | 0.931373i | \(0.618612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.80642 | 0.364589 | 0.182295 | − | 0.983244i | \(-0.441648\pi\) | ||||
0.182295 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.21432 | 0.210174 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1383 | 1.23594 | 0.617972 | − | 0.786200i | \(-0.287954\pi\) | ||||
0.617972 | + | 0.786200i | \(0.287954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.622216 | −0.0580219 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.14764 | 0.753250 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.45091 | 0.866364 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.10171 | −0.827428 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.37778 | −0.484898 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.16346 | 0.635655 | 0.317827 | − | 0.948149i | \(-0.397047\pi\) | ||||
0.317827 | + | 0.948149i | \(0.397047\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.62222 | −0.230873 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.6938 | 1.37117 | 0.685587 | − | 0.727990i | \(-0.259545\pi\) | ||||
0.685587 | + | 0.727990i | \(0.259545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.3002 | 2.02038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.42864 | −0.209024 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9906 | −0.938993 | −0.469497 | − | 0.882934i | \(-0.655565\pi\) | ||||
−0.469497 | + | 0.882934i | \(0.655565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8064 | −1.17105 | −0.585523 | − | 0.810656i | \(-0.699111\pi\) | ||||
−0.585523 | + | 0.810656i | \(0.699111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.62714 | 0.473890 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.89829 | 0.493240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.18421 | 0.430525 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.31603 | −0.191023 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.60793 | 0.213650 | 0.106825 | − | 0.994278i | \(-0.465932\pi\) | ||||
0.106825 | + | 0.994278i | \(0.465932\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.7239 | 1.36097 | 0.680487 | − | 0.732760i | \(-0.261768\pi\) | ||||
0.680487 | + | 0.732760i | \(0.261768\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.34122 | −0.512657 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.64296 | 0.533575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.235063 | −0.0187601 | −0.00938005 | − | 0.999956i | \(-0.502986\pi\) | ||||
−0.00938005 | + | 0.999956i | \(0.502986\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.67307 | 0.449904 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.76494 | −0.139096 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9590 | 1.32833 | 0.664165 | − | 0.747586i | \(-0.268787\pi\) | ||||
0.664165 | + | 0.747586i | \(0.268787\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.05086 | 0.237509 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.75557 | 0.367997 | 0.183998 | − | 0.982927i | \(-0.441096\pi\) | ||||
0.183998 | + | 0.982927i | \(0.441096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.32693 | 0.409764 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.6336 | −1.19553 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.2859 | 1.77040 | 0.885198 | − | 0.465215i | \(-0.154023\pi\) | ||||
0.885198 | + | 0.465215i | \(0.154023\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.83654 | −0.214422 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.6178 | 2.30137 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.64296 | −0.646005 | −0.323003 | − | 0.946398i | \(-0.604692\pi\) | ||||
−0.323003 | + | 0.946398i | \(0.604692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.09679 | −0.378841 | −0.189421 | − | 0.981896i | \(-0.560661\pi\) | ||||
−0.189421 | + | 0.981896i | \(0.560661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.0415 | 2.36857 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.59057 | −0.335696 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.88892 | −0.501095 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.26517 | −0.380975 | −0.190487 | − | 0.981690i | \(-0.561007\pi\) | ||||
−0.190487 | + | 0.981690i | \(0.561007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.488863 | −0.0351891 | −0.0175945 | − | 0.999845i | \(-0.505601\pi\) | ||||
−0.0175945 | + | 0.999845i | \(0.505601\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.47949 | 0.678841 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.4286 | −1.02800 | −0.513999 | − | 0.857791i | \(-0.671837\pi\) | ||||
−0.513999 | + | 0.857791i | \(0.671837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0622 | 0.996845 | 0.498423 | − | 0.866934i | \(-0.333913\pi\) | ||||
0.498423 | + | 0.866934i | \(0.333913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.6588 | −1.38662 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.7052 | 1.03210 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.42864 | −0.169624 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.18421 | 0.0823082 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3176 | −0.782852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7146 | 1.21952 | 0.609760 | − | 0.792586i | \(-0.291266\pi\) | ||||
0.609760 | + | 0.792586i | \(0.291266\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −33.3274 | −2.28356 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.18421 | −0.0807623 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8430 | 1.27915 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.37778 | −0.0931020 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2636 | −0.959476 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.28745 | −0.554969 | −0.277484 | − | 0.960730i | \(-0.589501\pi\) | ||||
−0.277484 | + | 0.960730i | \(0.589501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.90321 | 0.126881 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.31756 | −0.0874496 | −0.0437248 | − | 0.999044i | \(-0.513922\pi\) | ||||
−0.0437248 | + | 0.999044i | \(0.513922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.69535 | 0.178113 | 0.0890567 | − | 0.996027i | \(-0.471615\pi\) | ||||
0.0890567 | + | 0.996027i | \(0.471615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.65386 | 0.569382 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9906 | −0.982069 | −0.491034 | − | 0.871140i | \(-0.663381\pi\) | ||||
−0.491034 | + | 0.871140i | \(0.663381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.54125 | 0.165773 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.5161 | −1.33266 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.4909 | 1.97229 | 0.986145 | − | 0.165884i | \(-0.0530478\pi\) | ||||
0.986145 | + | 0.165884i | \(0.0530478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.74620 | −0.112483 | −0.0562413 | − | 0.998417i | \(-0.517912\pi\) | ||||
−0.0562413 | + | 0.998417i | \(0.517912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.2652 | 1.10756 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.04593 | −0.0668222 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.1655 | −2.23753 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.00492 | −0.443919 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5096 | −1.29455 | −0.647277 | − | 0.762255i | \(-0.724092\pi\) | ||||
−0.647277 | + | 0.762255i | \(0.724092\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.857279 | 0.0538967 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.37778 | −0.462015 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2810 | 0.766068 | 0.383034 | − | 0.923734i | \(-0.374879\pi\) | ||||
0.383034 | + | 0.923734i | \(0.374879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.83654 | 0.176254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.86665 | −0.610730 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3985 | −0.826189 | −0.413094 | − | 0.910688i | \(-0.635552\pi\) | ||||
−0.413094 | + | 0.910688i | \(0.635552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.56199 | 0.157382 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.2859 | −1.54747 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6588 | −1.07667 | −0.538337 | − | 0.842729i | \(-0.680947\pi\) | ||||
−0.538337 | + | 0.842729i | \(0.680947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9491 | 0.786605 | 0.393302 | − | 0.919409i | \(-0.371333\pi\) | ||||
0.393302 | + | 0.919409i | \(0.371333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.8889 | 1.62739 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.37778 | 0.0830835 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2810 | 1.45890 | 0.729452 | − | 0.684032i | \(-0.239775\pi\) | ||||
0.729452 | + | 0.684032i | \(0.239775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.6430 | −0.756914 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2128 | 0.788209 | 0.394104 | − | 0.919066i | \(-0.371055\pi\) | ||||
0.394104 | + | 0.919066i | \(0.371055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.07313 | −0.479898 | −0.239949 | − | 0.970786i | \(-0.577131\pi\) | ||||
−0.239949 | + | 0.970786i | \(0.577131\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.1891 | −1.07743 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.88892 | −0.406640 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.89877 | −0.346986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.0923 | −1.35370 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.7146 | 1.38542 | 0.692710 | − | 0.721217i | \(-0.256417\pi\) | ||||
0.692710 | + | 0.721217i | \(0.256417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.8272 | 0.805049 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.34614 | 0.194163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.66370 | 0.154046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.35905 | −0.193612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.9398 | 0.685922 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4701 | 0.828557 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8874 | −0.792595 | −0.396298 | − | 0.918122i | \(-0.629705\pi\) | ||||
−0.396298 | + | 0.918122i | \(0.629705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.3876 | −1.33048 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.69381 | −0.0960474 | −0.0480237 | − | 0.998846i | \(-0.515292\pi\) | ||||
−0.0480237 | + | 0.998846i | \(0.515292\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7971 | 1.40161 | 0.700806 | − | 0.713352i | \(-0.252824\pi\) | ||||
0.700806 | + | 0.713352i | \(0.252824\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.39853 | 0.304173 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.21279 | 0.292779 | 0.146390 | − | 0.989227i | \(-0.453235\pi\) | ||||
0.146390 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.14272 | −0.399916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.6780 | 0.930875 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.3689 | 1.52285 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.28100 | 0.237467 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.42864 | −0.466105 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.20834 | 0.397409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7763 | 0.702250 | 0.351125 | − | 0.936329i | \(-0.385799\pi\) | ||||
0.351125 | + | 0.936329i | \(0.385799\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.90321 | −0.104295 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.87802 | −0.485058 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7239 | 0.584169 | 0.292085 | − | 0.956392i | \(-0.405651\pi\) | ||||
0.292085 | + | 0.956392i | \(0.405651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.0923 | −1.58008 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.15257 | −0.495639 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8889 | 0.911916 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37778 | 0.0741774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.7239 | −1.43462 | −0.717308 | − | 0.696756i | \(-0.754626\pi\) | ||||
−0.717308 | + | 0.696756i | \(0.754626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.56691 | 0.0838750 | 0.0419375 | − | 0.999120i | \(-0.486647\pi\) | ||||
0.0419375 | + | 0.999120i | \(0.486647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3970 | 0.554951 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8573 | 0.577875 | 0.288937 | − | 0.957348i | \(-0.406698\pi\) | ||||
0.288937 | + | 0.957348i | \(0.406698\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0509 | −0.798816 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.9273 | −1.10759 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.37778 | 0.0727167 | 0.0363583 | − | 0.999339i | \(-0.488424\pi\) | ||||
0.0363583 | + | 0.999339i | \(0.488424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.4750 | 2.55132 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.1541 | 1.05782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.622216 | −0.0325683 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.5002 | −0.809106 | −0.404553 | − | 0.914515i | \(-0.632573\pi\) | ||||
−0.404553 | + | 0.914515i | \(0.632573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.62222 | 0.240623 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.26718 | 0.377293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6222 | 1.06778 | 0.533889 | − | 0.845555i | \(-0.320730\pi\) | ||||
0.533889 | + | 0.845555i | \(0.320730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.21432 | 0.114347 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.1936 | −1.14303 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.08250 | −0.261070 | −0.130535 | − | 0.991444i | \(-0.541670\pi\) | ||||
−0.130535 | + | 0.991444i | \(0.541670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8622 | −0.812645 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.16193 | 0.110470 | 0.0552348 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552348 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.90813 | 0.199177 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.25380 | 0.114567 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.3783 | 1.94586 | 0.972928 | − | 0.231110i | \(-0.0742359\pi\) | ||||
0.972928 | + | 0.231110i | \(0.0742359\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.07313 | −0.104843 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.7511 | −1.75296 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.26517 | −0.466182 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.6227 | −1.38634 | −0.693172 | − | 0.720773i | \(-0.743787\pi\) | ||||
−0.693172 | + | 0.720773i | \(0.743787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −51.5941 | −2.58294 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.38715 | 0.318959 | 0.159480 | − | 0.987201i | \(-0.449018\pi\) | ||||
0.159480 | + | 0.987201i | \(0.449018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.4385 | −1.41662 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0874 | 0.550938 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.37778 | −0.0682942 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.8988 | 1.33006 | 0.665029 | − | 0.746817i | \(-0.268419\pi\) | ||||
0.665029 | + | 0.746817i | \(0.268419\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.3368 | 1.20044 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.2212 | 1.92995 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.16346 | −0.155288 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.5718 | 1.49711 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.4572 | 0.803988 | 0.401994 | − | 0.915642i | \(-0.368317\pi\) | ||||
0.401994 | + | 0.915642i | \(0.368317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6860 | 1.15438 | 0.577192 | − | 0.816608i | \(-0.304148\pi\) | ||||
0.577192 | + | 0.816608i | \(0.304148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.83654 | −0.235160 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.33185 | −0.161619 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.0450 | 1.98631 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.0607 | −0.630577 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3575 | −0.787914 | −0.393957 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393957 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.46965 | 0.358968 | 0.179484 | − | 0.983761i | \(-0.442557\pi\) | ||||
0.179484 | + | 0.983761i | \(0.442557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.4795 | −0.550400 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.11108 | −0.244496 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7862 | −1.46934 | −0.734672 | − | 0.678423i | \(-0.762664\pi\) | ||||
−0.734672 | + | 0.678423i | \(0.762664\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.99063 | 0.0947920 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.2973 | −1.53449 | −0.767245 | − | 0.641354i | \(-0.778373\pi\) | ||||
−0.767245 | + | 0.641354i | \(0.778373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4193 | −0.541325 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.77478 | −0.273138 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.3876 | −1.38689 | −0.693444 | − | 0.720511i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720511i | \(0.743908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.34614 | 0.157564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.0321 | −1.73992 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.1432 | 0.569282 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.3689 | −1.46737 | −0.733687 | − | 0.679487i | \(-0.762202\pi\) | ||||
−0.733687 | + | 0.679487i | \(0.762202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.09187 | −0.377696 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.90766 | −0.135423 | −0.0677116 | − | 0.997705i | \(-0.521570\pi\) | ||||
−0.0677116 | + | 0.997705i | \(0.521570\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.7971 | 1.52421 | 0.762104 | − | 0.647454i | \(-0.224166\pi\) | ||||
0.762104 | + | 0.647454i | \(0.224166\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.7096 | −0.682143 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.9911 | 1.57292 | 0.786460 | − | 0.617641i | \(-0.211911\pi\) | ||||
0.786460 | + | 0.617641i | \(0.211911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.1828 | −1.16283 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.520505 | 0.0239836 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.63158 | 0.0750203 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.21432 | −0.376899 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.87601 | −0.223257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.2652 | 1.42854 | 0.714271 | − | 0.699869i | \(-0.246758\pi\) | ||||
0.714271 | + | 0.699869i | \(0.246758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.28100 | −0.195197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.90813 | 0.177826 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4286 | −0.473540 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.8064 | −1.80380 | −0.901901 | − | 0.431944i | \(-0.857828\pi\) | ||||
−0.901901 | + | 0.431944i | \(0.857828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.5526 | −1.69819 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.6450 | −1.83428 | −0.917141 | − | 0.398563i | \(-0.869509\pi\) | ||||
−0.917141 | + | 0.398563i | \(0.869509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2730 | 0.777937 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.62222 | −0.117860 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.6923 | −1.91501 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.3254 | −1.22325 | −0.611626 | − | 0.791147i | \(-0.709484\pi\) | ||||
−0.611626 | + | 0.791147i | \(0.709484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.5303 | −0.470461 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.6953 | −1.01194 | −0.505968 | − | 0.862552i | \(-0.668865\pi\) | ||||
−0.505968 | + | 0.862552i | \(0.668865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.39207 | 0.239944 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.7955 | −0.523858 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.59057 | −0.114825 | −0.0574126 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574126 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.76494 | −0.0780762 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.9496 | −0.880797 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5620 | −0.465417 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.50129 | −0.153987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.5625 | −2.26334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.4242 | −0.982422 | −0.491211 | − | 0.871041i | \(-0.663446\pi\) | ||||
−0.491211 | + | 0.871041i | \(0.663446\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.1432 | −0.530985 | −0.265492 | − | 0.964113i | \(-0.585535\pi\) | ||||
−0.265492 | + | 0.964113i | \(0.585535\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.28100 | 0.274125 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.1334 | 0.964144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6128 | −0.983167 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.3160 | −1.14202 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3970 | 0.450344 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.53188 | 0.325632 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.1383 | 0.825878 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.44107 | 0.0620713 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.5081 | 1.09668 | 0.548339 | − | 0.836256i | \(-0.315260\pi\) | ||||
0.548339 | + | 0.836256i | \(0.315260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2859 | 0.484325 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.80642 | −0.163049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.6829 | 1.44018 | 0.720089 | − | 0.693882i | \(-0.244101\pi\) | ||||
0.720089 | + | 0.693882i | \(0.244101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.5397 | −1.17537 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.5847 | 1.81417 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.2810 | −1.11758 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.21432 | −0.0939926 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.52543 | 0.234120 | 0.117060 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117060 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.06959 | 0.214421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1650 | 0.429166 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.6133 | −1.71165 | −0.855824 | − | 0.517268i | \(-0.826949\pi\) | ||||
−0.855824 | + | 0.517268i | \(0.826949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1383 | −0.552731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.4499 | 1.32077 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.1941 | −0.972345 | −0.486173 | − | 0.873863i | \(-0.661607\pi\) | ||||
−0.486173 | + | 0.873863i | \(0.661607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21585 | −0.0508818 | −0.0254409 | − | 0.999676i | \(-0.508099\pi\) | ||||
−0.0254409 | + | 0.999676i | \(0.508099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.6588 | 0.487053 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.622216 | 0.0259482 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4050 | 0.558057 | 0.279028 | − | 0.960283i | \(-0.409988\pi\) | ||||
0.279028 | + | 0.960283i | \(0.409988\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.08250 | 0.0449871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.97328 | −0.372274 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.52987 | −0.146192 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.14764 | −0.336864 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.0923 | −1.20077 | −0.600385 | − | 0.799711i | \(-0.704986\pi\) | ||||
−0.600385 | + | 0.799711i | \(0.704986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.5674 | 2.24841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.9496 | 1.31423 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.2543 | 1.20133 | 0.600665 | − | 0.799501i | \(-0.294903\pi\) | ||||
0.600665 | + | 0.799501i | \(0.294903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.45091 | −0.387450 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.1383 | −1.27440 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1941 | 1.19284 | 0.596418 | − | 0.802674i | \(-0.296590\pi\) | ||||
0.596418 | + | 0.802674i | \(0.296590\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.02366 | −0.123338 | −0.0616688 | − | 0.998097i | \(-0.519642\pi\) | ||||
−0.0616688 | + | 0.998097i | \(0.519642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.8968 | 0.688089 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.10171 | 0.370037 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6731 | 0.960860 | 0.480430 | − | 0.877033i | \(-0.340481\pi\) | ||||
0.480430 | + | 0.877033i | \(0.340481\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.5620 | −1.31948 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8791 | −0.440120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0830 | 1.21504 | 0.607520 | − | 0.794304i | \(-0.292164\pi\) | ||||
0.607520 | + | 0.794304i | \(0.292164\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.37778 | 0.216853 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.8163 | −1.36139 | −0.680696 | − | 0.732566i | \(-0.738322\pi\) | ||||
−0.680696 | + | 0.732566i | \(0.738322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.9590 | −0.762026 | −0.381013 | − | 0.924570i | \(-0.624425\pi\) | ||||
−0.381013 | + | 0.924570i | \(0.624425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.51114 | 0.0606399 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.3912 | −1.29772 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.0607 | 1.00083 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.33185 | 0.132850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.25533 | 0.0499739 | 0.0249870 | − | 0.999688i | \(-0.492046\pi\) | ||||
0.0249870 | + | 0.999688i | \(0.492046\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.2257 | −1.55908 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.16346 | −0.284273 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47764 | 0.177410 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.6450 | 1.13318 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7891 | 0.781621 | 0.390811 | − | 0.920471i | \(-0.372195\pi\) | ||||
0.390811 | + | 0.920471i | \(0.372195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.20342 | −0.0868944 | −0.0434472 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434472 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.62222 | 0.103250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.64449 | 0.300536 | 0.150268 | − | 0.988645i | \(-0.451986\pi\) | ||||
0.150268 | + | 0.988645i | \(0.451986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0509 | −0.747811 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.7244 | −1.63531 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.7753 | −1.75219 | −0.876096 | − | 0.482137i | \(-0.839861\pi\) | ||||
−0.876096 | + | 0.482137i | \(0.839861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.6938 | −0.613208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.18421 | 0.0462004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.0098 | 0.857382 | 0.428691 | − | 0.903451i | \(-0.358975\pi\) | ||||
0.428691 | + | 0.903451i | \(0.358975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4701 | 0.562823 | 0.281411 | − | 0.959587i | \(-0.409197\pi\) | ||||
0.281411 | + | 0.959587i | \(0.409197\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 31.5843 | 1.22663 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.3002 | −0.903543 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.22570 | −0.124899 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.3511 | 0.709493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.9367 | −0.769648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3872 | −0.400395 | −0.200198 | − | 0.979756i | \(-0.564158\pi\) | ||||
−0.200198 | + | 0.979756i | \(0.564158\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.42864 | 0.0934784 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.8479 | −0.762817 | −0.381409 | − | 0.924407i | \(-0.624561\pi\) | ||||
−0.381409 | + | 0.924407i | \(0.624561\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.5812 | −1.13522 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.91750 | 0.111799 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.09234 | −0.194853 | −0.0974265 | − | 0.995243i | \(-0.531061\pi\) | ||||
−0.0974265 | + | 0.995243i | \(0.531061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.9906 | 0.419930 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.96836 | −0.227707 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.9679 | −0.417843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.5812 | −1.58182 | −0.790912 | − | 0.611930i | \(-0.790393\pi\) | ||||
−0.790912 | + | 0.611930i | \(0.790393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.43801 | −0.282547 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8064 | 0.523708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.09187 | −0.306501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.1941 | 1.25551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6637 | −0.780457 | −0.390229 | − | 0.920718i | \(-0.627604\pi\) | ||||
−0.390229 | + | 0.920718i | \(0.627604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.21432 | 0.309809 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.62714 | −0.211930 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.2948 | 0.575221 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.4572 | 0.542952 | 0.271476 | − | 0.962445i | \(-0.412488\pi\) | ||||
0.271476 | + | 0.962445i | \(0.412488\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.6336 | 0.661311 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.13335 | −0.154795 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.89829 | −0.220584 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −67.5165 | −2.52145 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.8988 | −0.928567 | −0.464284 | − | 0.885687i | \(-0.653688\pi\) | ||||
−0.464284 | + | 0.885687i | \(0.653688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.9595 | −1.11575 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.86665 | 0.143802 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.18421 | −0.192537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.7239 | 1.43619 | 0.718095 | − | 0.695945i | \(-0.245014\pi\) | ||||
0.718095 | + | 0.695945i | \(0.245014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.96836 | −0.184013 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.94561 | −0.145934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.6958 | 1.09684 | 0.548420 | − | 0.836203i | \(-0.315229\pi\) | ||||
0.548420 | + | 0.836203i | \(0.315229\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.31603 | 0.0854281 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.2320 | 0.450572 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.49240 | 0.275612 | 0.137806 | − | 0.990459i | \(-0.455995\pi\) | ||||
0.137806 | + | 0.990459i | \(0.455995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 77.8676 | 2.86054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0306 | 0.441359 | 0.220680 | − | 0.975346i | \(-0.429172\pi\) | ||||
0.220680 | + | 0.975346i | \(0.429172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.60793 | −0.0955470 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.02074 | 0.220287 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.3644 | 0.780640 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.0415 | 1.31517 | 0.657586 | − | 0.753379i | \(-0.271578\pi\) | ||||
0.657586 | + | 0.753379i | \(0.271578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.4148 | 1.65501 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.7239 | −0.608646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.4291 | −1.50577 | −0.752883 | − | 0.658154i | \(-0.771338\pi\) | ||||
−0.752883 | + | 0.658154i | \(0.771338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.89829 | −0.0689036 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4889 | −0.597721 | −0.298860 | − | 0.954297i | \(-0.596606\pi\) | ||||
−0.298860 | + | 0.954297i | \(0.596606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7971 | −0.390880 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.34122 | 0.229267 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −59.1941 | −2.13737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.1941 | −0.979370 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.9398 | −1.00492 | −0.502462 | − | 0.864599i | \(-0.667572\pi\) | ||||
−0.502462 | + | 0.864599i | \(0.667572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.64296 | −0.238622 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.28100 | −0.225329 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.9496 | −0.714769 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7368 | 0.742022 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.5906 | −0.449950 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.235063 | 0.00838977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.27454 | 0.223663 | 0.111832 | − | 0.993727i | \(-0.464328\pi\) | ||||
0.111832 | + | 0.993727i | \(0.464328\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.6686 | 1.05623 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.2672 | −1.32507 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.9466 | −2.19979 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.67307 | −0.201203 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.9545 | 1.45068 | 0.725342 | − | 0.688388i | \(-0.241682\pi\) | ||||
0.725342 | + | 0.688388i | \(0.241682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.46706 | 0.299543 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.7333 | 0.767908 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.857279 | 0.0302527 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.76494 | 0.0622058 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.1022 | 1.37646 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.4889 | −0.720350 | −0.360175 | − | 0.932885i | \(-0.617283\pi\) | ||||
−0.360175 | + | 0.932885i | \(0.617283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8573 | 0.451480 | 0.225740 | − | 0.974188i | \(-0.427520\pi\) | ||||
0.225740 | + | 0.974188i | \(0.427520\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.6735 | −1.00563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9590 | −0.594047 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.72746 | −0.340321 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −23.1111 | −0.807566 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.89829 | −0.275652 | −0.137826 | − | 0.990456i | \(-0.544012\pi\) | ||||
−0.137826 | + | 0.990456i | \(0.544012\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.3763 | 0.570840 | 0.285420 | − | 0.958402i | \(-0.407867\pi\) | ||||
0.285420 | + | 0.958402i | \(0.407867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.05086 | −0.106217 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.05086 | −0.0365418 | −0.0182709 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182709 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.7975 | 1.24330 | 0.621650 | − | 0.783295i | \(-0.286463\pi\) | ||||
0.621650 | + | 0.783295i | \(0.286463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.7659 | −1.86512 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.48489 | −0.120744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.75557 | −0.164573 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.1334 | −0.557650 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.9813 | −0.620782 | −0.310391 | − | 0.950609i | \(-0.600460\pi\) | ||||
−0.310391 | + | 0.950609i | \(0.600460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.12399 | −0.0732409 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.2573 | −1.00768 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.32693 | −0.183252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.8173 | 0.887094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.8765 | 0.613520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.622216 | −0.0213293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.9210 | −1.57231 | −0.786153 | − | 0.618032i | \(-0.787930\pi\) | ||||
−0.786153 | + | 0.618032i | \(0.787930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.6336 | 0.534658 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.5303 | 1.65777 | 0.828883 | − | 0.559423i | \(-0.188977\pi\) | ||||
0.828883 | + | 0.559423i | \(0.188977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.3861 | 1.10500 | 0.552500 | − | 0.833513i | \(-0.313674\pi\) | ||||
0.552500 | + | 0.833513i | \(0.313674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.2543 | 0.519864 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2968 | 0.384548 | 0.192274 | − | 0.981341i | \(-0.438414\pi\) | ||||
0.192274 | + | 0.981341i | \(0.438414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.2859 | −0.791745 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0618 | 0.443600 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.7654 | 0.433037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.0068 | 1.28781 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.8479 | 0.671750 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.83654 | 0.0958924 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9086 | 1.38139 | 0.690693 | − | 0.723148i | \(-0.257306\pi\) | ||||
0.690693 | + | 0.723148i | \(0.257306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.5116 | −1.77117 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3225 | −0.684682 | −0.342341 | − | 0.939576i | \(-0.611220\pi\) | ||||
−0.342341 | + | 0.939576i | \(0.611220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.1561 | 1.21675 | 0.608375 | − | 0.793650i | \(-0.291822\pi\) | ||||
0.608375 | + | 0.793650i | \(0.291822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.6178 | −1.02921 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.16346 | −0.307679 | −0.153840 | − | 0.988096i | \(-0.549164\pi\) | ||||
−0.153840 | + | 0.988096i | \(0.549164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.3194 | −0.681492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.2761 | −0.511768 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.8746 | 0.698543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.64296 | 0.288902 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.89829 | −0.196938 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.4385 | 1.14859 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.53618 | 0.284381 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.43801 | 0.247521 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.09679 | 0.169423 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.07313 | −0.268064 | −0.134032 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134032 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.2623 | −0.340378 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9891 | 0.596005 | 0.298003 | − | 0.954565i | \(-0.403680\pi\) | ||||
0.298003 | + | 0.954565i | \(0.403680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.35857 | 0.144248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.0415 | −1.05926 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.5161 | −1.47005 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.9926 | 1.68209 | 0.841046 | − | 0.540964i | \(-0.181940\pi\) | ||||
0.841046 | + | 0.540964i | \(0.181940\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7511 | 1.01328 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 64.4327 | 2.12083 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1017 | 0.660227 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.7150 | −1.40143 | −0.700717 | − | 0.713439i | \(-0.747137\pi\) | ||||
−0.700717 | + | 0.713439i | \(0.747137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.59163 | −0.281579 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.75065 | 0.122791 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.59057 | 0.150128 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.1467 | 1.60555 | 0.802777 | − | 0.596279i | \(-0.203355\pi\) | ||||
0.802777 | + | 0.596279i | \(0.203355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.9086 | −1.79187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.11906 | −0.264674 | −0.132337 | − | 0.991205i | \(-0.542248\pi\) | ||||
−0.132337 | + | 0.991205i | \(0.542248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.51114 | 0.0492094 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.88892 | 0.224097 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6227 | 1.28756 | 0.643782 | − | 0.765209i | \(-0.277364\pi\) | ||||
0.643782 | + | 0.765209i | \(0.277364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.66370 | 0.0864675 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.5428 | −0.374300 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.4068 | 1.76241 | 0.881205 | − | 0.472734i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472734i | \(0.156733\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.26517 | 0.170377 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.8163 | 0.511267 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.1753 | 1.00670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1289 | 0.423513 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3348 | −0.461931 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.488863 | 0.0157370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.2543 | 1.71254 | 0.856271 | − | 0.516527i | \(-0.172775\pi\) | ||||
0.856271 | + | 0.516527i | \(0.172775\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.6035 | −1.94686 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.0232 | 1.70160 | 0.850798 | − | 0.525493i | \(-0.176119\pi\) | ||||
0.850798 | + | 0.525493i | \(0.176119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.1624 | 1.25549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.47949 | −0.303587 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.1432 | 0.644438 | 0.322219 | − | 0.946665i | \(-0.395571\pi\) | ||||
0.322219 | + | 0.946665i | \(0.395571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7333 | 0.502838 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.24443 | 0.231297 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.1541 | −0.770396 | −0.385198 | − | 0.922834i | \(-0.625867\pi\) | ||||
−0.385198 | + | 0.922834i | \(0.625867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4286 | 0.459735 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.9616 | −0.508063 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.736833 | 0.0234299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6149 | 0.877215 | 0.438607 | − | 0.898679i | \(-0.355472\pi\) | ||||
0.438607 | + | 0.898679i | \(0.355472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.2908 | −0.897783 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0622 | −0.445803 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2034 | 0.449827 | 0.224913 | − | 0.974379i | \(-0.427790\pi\) | ||||
0.224913 | + | 0.974379i | \(0.427790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.42864 | −0.0768388 |
(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 | 2960.2.a.t.1.1 | 3 | ||
4.3 | odd | 2 | 740.2.a.e.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 6660.2.a.q.1.2 | 3 | |||
20.3 | even | 4 | 3700.2.d.h.149.6 | 6 | |||
20.7 | even | 4 | 3700.2.d.h.149.1 | 6 | |||
20.19 | odd | 2 | 3700.2.a.i.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
740.2.a.e.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
2960.2.a.t.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3700.2.a.i.1.1 | 3 | 20.19 | odd | 2 | |||
3700.2.d.h.149.1 | 6 | 20.7 | even | 4 | |||
3700.2.d.h.149.6 | 6 | 20.3 | even | 4 | |||
6660.2.a.q.1.2 | 3 | 12.11 | even | 2 |