Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.53756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53756 | −1.08722 | −0.543610 | − | 0.839338i | \(-0.682943\pi\) | ||||
−0.543610 | + | 0.839338i | \(0.682943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.364091 | 0.182046 | ||||||||
\(5\) | 2.97145 | 1.32887 | 0.664435 | − | 0.747346i | \(-0.268672\pi\) | ||||
0.664435 | + | 0.747346i | \(0.268672\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52213 | 0.575313 | 0.287656 | − | 0.957734i | \(-0.407124\pi\) | ||||
0.287656 | + | 0.957734i | \(0.407124\pi\) | |||||||
\(8\) | 2.51531 | 0.889296 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.56878 | −1.44477 | ||||||||
\(11\) | −0.657982 | −0.198389 | −0.0991945 | − | 0.995068i | \(-0.531627\pi\) | ||||
−0.0991945 | + | 0.995068i | \(0.531627\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.12537 | 0.866822 | 0.433411 | − | 0.901196i | \(-0.357310\pi\) | ||||
0.433411 | + | 0.901196i | \(0.357310\pi\) | |||||||
\(14\) | −2.34037 | −0.625491 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.59562 | −1.14890 | ||||||||
\(17\) | −1.99186 | −0.483097 | −0.241549 | − | 0.970389i | \(-0.577655\pi\) | ||||
−0.241549 | + | 0.970389i | \(0.577655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.50919 | 1.49331 | 0.746656 | − | 0.665211i | \(-0.231658\pi\) | ||||
0.746656 | + | 0.665211i | \(0.231658\pi\) | |||||||
\(20\) | 1.08188 | 0.241915 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.01169 | 0.215692 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82949 | 0.765898 | ||||||||
\(26\) | −4.80545 | −0.942426 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.554195 | 0.104733 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.58309 | 1.18236 | 0.591179 | − | 0.806540i | \(-0.298663\pi\) | ||||
0.591179 | + | 0.806540i | \(0.298663\pi\) | |||||||
\(32\) | 2.03543 | 0.359816 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.06261 | 0.525233 | ||||||||
\(35\) | 4.52294 | 0.764516 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52960 | 1.23786 | 0.618929 | − | 0.785447i | \(-0.287567\pi\) | ||||
0.618929 | + | 0.785447i | \(0.287567\pi\) | |||||||
\(38\) | −10.0083 | −1.62356 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.47410 | 1.18176 | ||||||||
\(41\) | −8.68681 | −1.35665 | −0.678326 | − | 0.734761i | \(-0.737294\pi\) | ||||
−0.678326 | + | 0.734761i | \(0.737294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.14842 | −0.480129 | −0.240064 | − | 0.970757i | \(-0.577169\pi\) | ||||
−0.240064 | + | 0.970757i | \(0.577169\pi\) | |||||||
\(44\) | −0.239565 | −0.0361158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.53756 | −0.226701 | ||||||||
\(47\) | −1.88957 | −0.275622 | −0.137811 | − | 0.990459i | \(-0.544007\pi\) | ||||
−0.137811 | + | 0.990459i | \(0.544007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.68311 | −0.669016 | ||||||||
\(50\) | −5.88807 | −0.832699 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.13792 | 0.157801 | ||||||||
\(53\) | 2.78935 | 0.383146 | 0.191573 | − | 0.981478i | \(-0.438641\pi\) | ||||
0.191573 | + | 0.981478i | \(0.438641\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.95516 | −0.263633 | ||||||||
\(56\) | 3.82864 | 0.511623 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.53756 | −0.201892 | ||||||||
\(59\) | −6.26938 | −0.816204 | −0.408102 | − | 0.912936i | \(-0.633809\pi\) | ||||
−0.408102 | + | 0.912936i | \(0.633809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61173 | 0.206361 | 0.103180 | − | 0.994663i | \(-0.467098\pi\) | ||||
0.103180 | + | 0.994663i | \(0.467098\pi\) | |||||||
\(62\) | −10.1219 | −1.28548 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.06165 | 0.757706 | ||||||||
\(65\) | 9.28687 | 1.15189 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.54031 | 0.676857 | 0.338428 | − | 0.940992i | \(-0.390105\pi\) | ||||
0.338428 | + | 0.940992i | \(0.390105\pi\) | |||||||
\(68\) | −0.725219 | −0.0879457 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.95429 | −0.831196 | ||||||||
\(71\) | 9.71587 | 1.15306 | 0.576531 | − | 0.817076i | \(-0.304406\pi\) | ||||
0.576531 | + | 0.817076i | \(0.304406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.17202 | 0.488298 | 0.244149 | − | 0.969738i | \(-0.421491\pi\) | ||||
0.244149 | + | 0.969738i | \(0.421491\pi\) | |||||||
\(74\) | −11.5772 | −1.34582 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.36994 | 0.271851 | ||||||||
\(77\) | −1.00154 | −0.114136 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.99227 | 1.12422 | 0.562109 | − | 0.827063i | \(-0.309990\pi\) | ||||
0.562109 | + | 0.827063i | \(0.309990\pi\) | |||||||
\(80\) | −13.6556 | −1.52675 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.3565 | 1.47498 | ||||||||
\(83\) | −3.81394 | −0.418635 | −0.209317 | − | 0.977848i | \(-0.567124\pi\) | ||||
−0.209317 | + | 0.977848i | \(0.567124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.91871 | −0.641974 | ||||||||
\(86\) | 4.84088 | 0.522005 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.65503 | −0.176427 | ||||||||
\(89\) | 0.899101 | 0.0953045 | 0.0476523 | − | 0.998864i | \(-0.484826\pi\) | ||||
0.0476523 | + | 0.998864i | \(0.484826\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.75723 | 0.498694 | ||||||||
\(92\) | 0.364091 | 0.0379591 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.90533 | 0.299661 | ||||||||
\(95\) | 19.3417 | 1.98442 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.81354 | −0.387206 | −0.193603 | − | 0.981080i | \(-0.562017\pi\) | ||||
−0.193603 | + | 0.981080i | \(0.562017\pi\) | |||||||
\(98\) | 7.20056 | 0.727366 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.39428 | 0.139428 | ||||||||
\(101\) | 9.37952 | 0.933297 | 0.466649 | − | 0.884443i | \(-0.345461\pi\) | ||||
0.466649 | + | 0.884443i | \(0.345461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.04005 | 0.102479 | 0.0512395 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512395 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(104\) | 7.86127 | 0.770861 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.28879 | −0.416564 | ||||||||
\(107\) | 9.51332 | 0.919687 | 0.459843 | − | 0.888000i | \(-0.347906\pi\) | ||||
0.459843 | + | 0.888000i | \(0.347906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0318 | 1.05666 | 0.528329 | − | 0.849040i | \(-0.322819\pi\) | ||||
0.528329 | + | 0.849040i | \(0.322819\pi\) | |||||||
\(110\) | 3.00617 | 0.286627 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.99515 | −0.660979 | ||||||||
\(113\) | 16.5846 | 1.56015 | 0.780076 | − | 0.625685i | \(-0.215181\pi\) | ||||
0.780076 | + | 0.625685i | \(0.215181\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.97145 | 0.277089 | ||||||||
\(116\) | 0.364091 | 0.0338050 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.63955 | 0.887392 | ||||||||
\(119\) | −3.03188 | −0.277932 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5671 | −0.960642 | ||||||||
\(122\) | −2.47813 | −0.224360 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.39685 | 0.215243 | ||||||||
\(125\) | −3.47811 | −0.311092 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.11884 | −0.631695 | −0.315847 | − | 0.948810i | \(-0.602289\pi\) | ||||
−0.315847 | + | 0.948810i | \(0.602289\pi\) | |||||||
\(128\) | −13.3910 | −1.18361 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.2791 | −1.25236 | ||||||||
\(131\) | 2.82852 | 0.247129 | 0.123564 | − | 0.992337i | \(-0.460567\pi\) | ||||
0.123564 | + | 0.992337i | \(0.460567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.90786 | 0.859121 | ||||||||
\(134\) | −8.51856 | −0.735892 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.01014 | −0.429616 | ||||||||
\(137\) | 2.57599 | 0.220082 | 0.110041 | − | 0.993927i | \(-0.464902\pi\) | ||||
0.110041 | + | 0.993927i | \(0.464902\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0031 | −1.27255 | −0.636273 | − | 0.771464i | \(-0.719525\pi\) | ||||
−0.636273 | + | 0.771464i | \(0.719525\pi\) | |||||||
\(140\) | 1.64676 | 0.139177 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.9387 | −1.25363 | ||||||||
\(143\) | −2.05644 | −0.171968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.97145 | 0.246765 | ||||||||
\(146\) | −6.41474 | −0.530887 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.74146 | 0.225347 | ||||||||
\(149\) | −19.2475 | −1.57682 | −0.788409 | − | 0.615151i | \(-0.789095\pi\) | ||||
−0.788409 | + | 0.615151i | \(0.789095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3611 | 1.41283 | 0.706415 | − | 0.707798i | \(-0.250311\pi\) | ||||
0.706415 | + | 0.707798i | \(0.250311\pi\) | |||||||
\(152\) | 16.3726 | 1.32800 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.53992 | 0.124091 | ||||||||
\(155\) | 19.5613 | 1.57120 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.87752 | −0.628694 | −0.314347 | − | 0.949308i | \(-0.601786\pi\) | ||||
−0.314347 | + | 0.949308i | \(0.601786\pi\) | |||||||
\(158\) | −15.3637 | −1.22227 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.04815 | 0.478149 | ||||||||
\(161\) | 1.52213 | 0.119961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.2023 | −1.19074 | −0.595370 | − | 0.803452i | \(-0.702994\pi\) | ||||
−0.595370 | + | 0.803452i | \(0.702994\pi\) | |||||||
\(164\) | −3.16279 | −0.246973 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.86417 | 0.455148 | ||||||||
\(167\) | −10.9193 | −0.844961 | −0.422480 | − | 0.906372i | \(-0.638840\pi\) | ||||
−0.422480 | + | 0.906372i | \(0.638840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.23205 | −0.248620 | ||||||||
\(170\) | 9.10037 | 0.697966 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.14631 | −0.0874053 | ||||||||
\(173\) | −1.77155 | −0.134688 | −0.0673441 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673441 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.82899 | 0.440631 | ||||||||
\(176\) | 3.02384 | 0.227930 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.38242 | −0.103617 | ||||||||
\(179\) | 14.9962 | 1.12087 | 0.560433 | − | 0.828200i | \(-0.310635\pi\) | ||||
0.560433 | + | 0.828200i | \(0.310635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.1518 | 1.86952 | 0.934759 | − | 0.355281i | \(-0.115615\pi\) | ||||
0.934759 | + | 0.355281i | \(0.115615\pi\) | |||||||
\(182\) | −7.31453 | −0.542189 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.51531 | 0.185431 | ||||||||
\(185\) | 22.3738 | 1.64495 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.31061 | 0.0958412 | ||||||||
\(188\) | −0.687975 | −0.0501757 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −29.7390 | −2.15750 | ||||||||
\(191\) | −8.60952 | −0.622963 | −0.311482 | − | 0.950252i | \(-0.600825\pi\) | ||||
−0.311482 | + | 0.950252i | \(0.600825\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.52670 | −0.109894 | −0.0549472 | − | 0.998489i | \(-0.517499\pi\) | ||||
−0.0549472 | + | 0.998489i | \(0.517499\pi\) | |||||||
\(194\) | 5.86354 | 0.420978 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.70508 | −0.121791 | ||||||||
\(197\) | −11.9516 | −0.851513 | −0.425757 | − | 0.904838i | \(-0.639992\pi\) | ||||
−0.425757 | + | 0.904838i | \(0.639992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2312 | −1.43415 | −0.717076 | − | 0.696995i | \(-0.754520\pi\) | ||||
−0.717076 | + | 0.696995i | \(0.754520\pi\) | |||||||
\(200\) | 9.63234 | 0.681110 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.4216 | −1.01470 | ||||||||
\(203\) | 1.52213 | 0.106833 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.8124 | −1.80282 | ||||||||
\(206\) | −1.59914 | −0.111417 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.3630 | −0.995896 | ||||||||
\(209\) | −4.28293 | −0.296257 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2493 | −1.80708 | −0.903539 | − | 0.428505i | \(-0.859040\pi\) | ||||
−0.903539 | + | 0.428505i | \(0.859040\pi\) | |||||||
\(212\) | 1.01558 | 0.0697501 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.6273 | −0.999901 | ||||||||
\(215\) | −9.35534 | −0.638029 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0204 | 0.680226 | ||||||||
\(218\) | −16.9621 | −1.14882 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.711855 | −0.0479933 | ||||||||
\(221\) | −6.22530 | −0.418759 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3354 | −0.893005 | −0.446502 | − | 0.894782i | \(-0.647331\pi\) | ||||
−0.446502 | + | 0.894782i | \(0.647331\pi\) | |||||||
\(224\) | 3.09819 | 0.207006 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.4999 | −1.69623 | ||||||||
\(227\) | 13.9162 | 0.923648 | 0.461824 | − | 0.886972i | \(-0.347195\pi\) | ||||
0.461824 | + | 0.886972i | \(0.347195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.24048 | 0.148055 | 0.0740274 | − | 0.997256i | \(-0.476415\pi\) | ||||
0.0740274 | + | 0.997256i | \(0.476415\pi\) | |||||||
\(230\) | −4.56878 | −0.301256 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.51531 | 0.165138 | ||||||||
\(233\) | 16.1306 | 1.05675 | 0.528376 | − | 0.849011i | \(-0.322801\pi\) | ||||
0.528376 | + | 0.849011i | \(0.322801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.61475 | −0.366266 | ||||||||
\(236\) | −2.28263 | −0.148586 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.66170 | 0.302173 | ||||||||
\(239\) | −25.9374 | −1.67775 | −0.838874 | − | 0.544325i | \(-0.816786\pi\) | ||||
−0.838874 | + | 0.544325i | \(0.816786\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9123 | 1.15384 | 0.576918 | − | 0.816802i | \(-0.304255\pi\) | ||||
0.576918 | + | 0.816802i | \(0.304255\pi\) | |||||||
\(242\) | 16.2475 | 1.04443 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.586817 | 0.0375671 | ||||||||
\(245\) | −13.9156 | −0.889035 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.3436 | 1.29443 | ||||||||
\(248\) | 16.5585 | 1.05147 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.34780 | 0.338225 | ||||||||
\(251\) | 23.8459 | 1.50514 | 0.752569 | − | 0.658513i | \(-0.228814\pi\) | ||||
0.752569 | + | 0.658513i | \(0.228814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.657982 | −0.0413670 | ||||||||
\(254\) | 10.9456 | 0.686791 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.46617 | 0.529136 | ||||||||
\(257\) | −12.0783 | −0.753425 | −0.376713 | − | 0.926330i | \(-0.622946\pi\) | ||||
−0.376713 | + | 0.926330i | \(0.622946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4611 | 0.712156 | ||||||||
\(260\) | 3.38127 | 0.209697 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.34902 | −0.268683 | ||||||||
\(263\) | −10.2132 | −0.629772 | −0.314886 | − | 0.949130i | \(-0.601966\pi\) | ||||
−0.314886 | + | 0.949130i | \(0.601966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.28839 | 0.509152 | ||||||||
\(266\) | −15.2339 | −0.934052 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.01718 | 0.123219 | ||||||||
\(269\) | 16.3462 | 0.996648 | 0.498324 | − | 0.866991i | \(-0.333949\pi\) | ||||
0.498324 | + | 0.866991i | \(0.333949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.90467 | −0.237192 | −0.118596 | − | 0.992943i | \(-0.537839\pi\) | ||||
−0.118596 | + | 0.992943i | \(0.537839\pi\) | |||||||
\(272\) | 9.15383 | 0.555033 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.96074 | −0.239277 | ||||||||
\(275\) | −2.51973 | −0.151946 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0571 | −1.32529 | −0.662643 | − | 0.748936i | \(-0.730565\pi\) | ||||
−0.662643 | + | 0.748936i | \(0.730565\pi\) | |||||||
\(278\) | 23.0682 | 1.38354 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.3766 | 0.679881 | ||||||||
\(281\) | −0.0586985 | −0.00350166 | −0.00175083 | − | 0.999998i | \(-0.500557\pi\) | ||||
−0.00175083 | + | 0.999998i | \(0.500557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6006 | 0.689582 | 0.344791 | − | 0.938679i | \(-0.387950\pi\) | ||||
0.344791 | + | 0.938679i | \(0.387950\pi\) | |||||||
\(284\) | 3.53746 | 0.209910 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.16190 | 0.186967 | ||||||||
\(287\) | −13.2225 | −0.780499 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0325 | −0.766617 | ||||||||
\(290\) | −4.56878 | −0.268288 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.51900 | 0.0888925 | ||||||||
\(293\) | 16.3619 | 0.955873 | 0.477936 | − | 0.878394i | \(-0.341385\pi\) | ||||
0.477936 | + | 0.878394i | \(0.341385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.6291 | −1.08463 | ||||||||
\(296\) | 18.9393 | 1.10082 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 29.5942 | 1.71435 | ||||||||
\(299\) | 3.12537 | 0.180745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.79231 | −0.276224 | ||||||||
\(302\) | −26.6938 | −1.53606 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.9138 | −1.71567 | ||||||||
\(305\) | 4.78917 | 0.274227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.09940 | −0.348111 | −0.174056 | − | 0.984736i | \(-0.555687\pi\) | ||||
−0.174056 | + | 0.984736i | \(0.555687\pi\) | |||||||
\(308\) | −0.364651 | −0.0207779 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −30.0767 | −1.70824 | ||||||||
\(311\) | 11.4644 | 0.650084 | 0.325042 | − | 0.945700i | \(-0.394622\pi\) | ||||
0.325042 | + | 0.945700i | \(0.394622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.2263 | 1.08674 | 0.543368 | − | 0.839495i | \(-0.317149\pi\) | ||||
0.543368 | + | 0.839495i | \(0.317149\pi\) | |||||||
\(314\) | 12.1122 | 0.683528 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63810 | 0.204659 | ||||||||
\(317\) | −9.21199 | −0.517397 | −0.258699 | − | 0.965958i | \(-0.583294\pi\) | ||||
−0.258699 | + | 0.965958i | \(0.583294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.657982 | −0.0368399 | ||||||||
\(320\) | 18.0119 | 1.00689 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.34037 | −0.130424 | ||||||||
\(323\) | −12.9654 | −0.721414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.9686 | 0.663897 | ||||||||
\(326\) | 23.3745 | 1.29459 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −21.8500 | −1.20647 | ||||||||
\(329\) | −2.87618 | −0.158569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.85715 | −0.376903 | −0.188451 | − | 0.982083i | \(-0.560347\pi\) | ||||
−0.188451 | + | 0.982083i | \(0.560347\pi\) | |||||||
\(332\) | −1.38862 | −0.0762105 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.7891 | 0.918657 | ||||||||
\(335\) | 16.4627 | 0.899455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0008 | 0.653725 | 0.326863 | − | 0.945072i | \(-0.394009\pi\) | ||||
0.326863 | + | 0.945072i | \(0.394009\pi\) | |||||||
\(338\) | 4.96948 | 0.270304 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.15495 | −0.116868 | ||||||||
\(341\) | −4.33156 | −0.234567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7833 | −0.960206 | ||||||||
\(344\) | −7.91924 | −0.426977 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.72386 | 0.146436 | ||||||||
\(347\) | −1.31039 | −0.0703454 | −0.0351727 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351727 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3350 | 1.30262 | 0.651310 | − | 0.758811i | \(-0.274220\pi\) | ||||
0.651310 | + | 0.758811i | \(0.274220\pi\) | |||||||
\(350\) | −8.96243 | −0.479062 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.33927 | −0.0713835 | ||||||||
\(353\) | −12.1064 | −0.644361 | −0.322181 | − | 0.946678i | \(-0.604416\pi\) | ||||
−0.322181 | + | 0.946678i | \(0.604416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.8702 | 1.53227 | ||||||||
\(356\) | 0.327355 | 0.0173498 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.0575 | −1.21863 | ||||||||
\(359\) | 0.568054 | 0.0299808 | 0.0149904 | − | 0.999888i | \(-0.495228\pi\) | ||||
0.0149904 | + | 0.999888i | \(0.495228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.3696 | 1.22998 | ||||||||
\(362\) | −38.6724 | −2.03258 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.73207 | 0.0907849 | ||||||||
\(365\) | 12.3969 | 0.648885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8719 | 0.671908 | 0.335954 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335954 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(368\) | −4.59562 | −0.239563 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −34.4011 | −1.78843 | ||||||||
\(371\) | 4.24576 | 0.220429 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.8087 | −1.38810 | −0.694050 | − | 0.719927i | \(-0.744175\pi\) | ||||
−0.694050 | + | 0.719927i | \(0.744175\pi\) | |||||||
\(374\) | −2.01514 | −0.104200 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.75285 | −0.245109 | ||||||||
\(377\) | 3.12537 | 0.160965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5826 | 1.21136 | 0.605678 | − | 0.795710i | \(-0.292902\pi\) | ||||
0.605678 | + | 0.795710i | \(0.292902\pi\) | |||||||
\(380\) | 7.04214 | 0.361254 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.2377 | 0.677298 | ||||||||
\(383\) | −4.55238 | −0.232616 | −0.116308 | − | 0.993213i | \(-0.537106\pi\) | ||||
−0.116308 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.97601 | −0.151672 | ||||||||
\(386\) | 2.34740 | 0.119479 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.38848 | −0.0704892 | ||||||||
\(389\) | −28.4426 | −1.44210 | −0.721048 | − | 0.692885i | \(-0.756339\pi\) | ||||
−0.721048 | + | 0.692885i | \(0.756339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.99186 | −0.100733 | ||||||||
\(392\) | −11.7795 | −0.594953 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.3762 | 0.925782 | ||||||||
\(395\) | 29.6915 | 1.49394 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0063 | −1.00409 | −0.502043 | − | 0.864843i | \(-0.667418\pi\) | ||||
−0.502043 | + | 0.864843i | \(0.667418\pi\) | |||||||
\(398\) | 31.1067 | 1.55924 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.5989 | −0.879944 | ||||||||
\(401\) | −1.05576 | −0.0527220 | −0.0263610 | − | 0.999652i | \(-0.508392\pi\) | ||||
−0.0263610 | + | 0.999652i | \(0.508392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.5746 | 1.02489 | ||||||||
\(404\) | 3.41500 | 0.169903 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.34037 | −0.116151 | ||||||||
\(407\) | −4.95434 | −0.245578 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.8403 | 0.585463 | 0.292732 | − | 0.956195i | \(-0.405436\pi\) | ||||
0.292732 | + | 0.956195i | \(0.405436\pi\) | |||||||
\(410\) | 39.6881 | 1.96006 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.378672 | 0.0186558 | ||||||||
\(413\) | −9.54284 | −0.469572 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3329 | −0.556311 | ||||||||
\(416\) | 6.36146 | 0.311896 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.58526 | 0.322096 | ||||||||
\(419\) | −36.2135 | −1.76915 | −0.884573 | − | 0.466401i | \(-0.845550\pi\) | ||||
−0.884573 | + | 0.466401i | \(0.845550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.5979 | 1.49125 | 0.745625 | − | 0.666366i | \(-0.232151\pi\) | ||||
0.745625 | + | 0.666366i | \(0.232151\pi\) | |||||||
\(422\) | 40.3599 | 1.96469 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.01607 | 0.340730 | ||||||||
\(425\) | −7.62781 | −0.370003 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.45327 | 0.118722 | ||||||||
\(428\) | 3.46371 | 0.167425 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.3844 | 0.693678 | ||||||||
\(431\) | 1.70015 | 0.0818935 | 0.0409467 | − | 0.999161i | \(-0.486963\pi\) | ||||
0.0409467 | + | 0.999161i | \(0.486963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1484 | 1.16050 | 0.580248 | − | 0.814440i | \(-0.302956\pi\) | ||||
0.580248 | + | 0.814440i | \(0.302956\pi\) | |||||||
\(434\) | −15.4069 | −0.739554 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.01659 | 0.192360 | ||||||||
\(437\) | 6.50919 | 0.311377 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.50808 | 0.310614 | 0.155307 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155307 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(440\) | −4.91782 | −0.234448 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.57178 | 0.455283 | ||||||||
\(443\) | −25.4823 | −1.21070 | −0.605349 | − | 0.795960i | \(-0.706967\pi\) | ||||
−0.605349 | + | 0.795960i | \(0.706967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.67163 | 0.126647 | ||||||||
\(446\) | 20.5040 | 0.970892 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.22664 | 0.435918 | ||||||||
\(449\) | 21.8497 | 1.03115 | 0.515575 | − | 0.856845i | \(-0.327578\pi\) | ||||
0.515575 | + | 0.856845i | \(0.327578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.71577 | 0.269145 | ||||||||
\(452\) | 6.03832 | 0.284019 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.3969 | −1.00421 | ||||||||
\(455\) | 14.1359 | 0.662699 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1438 | 1.12940 | 0.564700 | − | 0.825296i | \(-0.308992\pi\) | ||||
0.564700 | + | 0.825296i | \(0.308992\pi\) | |||||||
\(458\) | −3.44487 | −0.160968 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.08188 | 0.0504428 | ||||||||
\(461\) | 23.3197 | 1.08611 | 0.543054 | − | 0.839698i | \(-0.317268\pi\) | ||||
0.543054 | + | 0.839698i | \(0.317268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5951 | 1.14303 | 0.571516 | − | 0.820591i | \(-0.306356\pi\) | ||||
0.571516 | + | 0.820591i | \(0.306356\pi\) | |||||||
\(464\) | −4.59562 | −0.213346 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.8018 | −1.14892 | ||||||||
\(467\) | 6.13480 | 0.283885 | 0.141942 | − | 0.989875i | \(-0.454665\pi\) | ||||
0.141942 | + | 0.989875i | \(0.454665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.43310 | 0.389404 | ||||||||
\(470\) | 8.63302 | 0.398211 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.7694 | −0.725847 | ||||||||
\(473\) | 2.07160 | 0.0952523 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.9269 | 1.14372 | ||||||||
\(476\) | −1.10388 | −0.0505963 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 39.8803 | 1.82408 | ||||||||
\(479\) | 13.6698 | 0.624588 | 0.312294 | − | 0.949986i | \(-0.398903\pi\) | ||||
0.312294 | + | 0.949986i | \(0.398903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.5328 | 1.07300 | ||||||||
\(482\) | −27.5413 | −1.25447 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.84737 | −0.174881 | ||||||||
\(485\) | −11.3317 | −0.514547 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.77831 | −0.171212 | −0.0856058 | − | 0.996329i | \(-0.527283\pi\) | ||||
−0.0856058 | + | 0.996329i | \(0.527283\pi\) | |||||||
\(488\) | 4.05400 | 0.183516 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 21.3961 | 0.966576 | ||||||||
\(491\) | 5.21934 | 0.235545 | 0.117773 | − | 0.993041i | \(-0.462425\pi\) | ||||
0.117773 | + | 0.993041i | \(0.462425\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.99186 | −0.0897089 | ||||||||
\(494\) | −31.2796 | −1.40733 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.2534 | −1.35842 | ||||||||
\(497\) | 14.7888 | 0.663370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8243 | −0.753157 | −0.376579 | − | 0.926385i | \(-0.622900\pi\) | ||||
−0.376579 | + | 0.926385i | \(0.622900\pi\) | |||||||
\(500\) | −1.26635 | −0.0566329 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.6645 | −1.63642 | ||||||||
\(503\) | 17.5168 | 0.781036 | 0.390518 | − | 0.920595i | \(-0.372296\pi\) | ||||
0.390518 | + | 0.920595i | \(0.372296\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.8707 | 1.24023 | ||||||||
\(506\) | 1.01169 | 0.0449750 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.59191 | −0.114997 | ||||||||
\(509\) | 39.8215 | 1.76506 | 0.882530 | − | 0.470257i | \(-0.155839\pi\) | ||||
0.882530 | + | 0.470257i | \(0.155839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.35038 | 0.280924 | ||||||||
\(512\) | 13.7648 | 0.608322 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.5712 | 0.819138 | ||||||||
\(515\) | 3.09045 | 0.136181 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.24330 | 0.0546804 | ||||||||
\(518\) | −17.6221 | −0.774269 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.3593 | 1.02437 | ||||||||
\(521\) | −20.5118 | −0.898637 | −0.449319 | − | 0.893372i | \(-0.648333\pi\) | ||||
−0.449319 | + | 0.893372i | \(0.648333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.217705 | −0.00951957 | −0.00475978 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00475978 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(524\) | 1.02984 | 0.0449887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.7034 | 0.684700 | ||||||||
\(527\) | −13.1126 | −0.571194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −12.7439 | −0.553560 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.60736 | 0.156399 | ||||||||
\(533\) | −27.1495 | −1.17598 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.2683 | 1.22215 | ||||||||
\(536\) | 13.9356 | 0.601926 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.1333 | −1.08357 | ||||||||
\(539\) | 3.08140 | 0.132725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2734 | −0.828630 | −0.414315 | − | 0.910134i | \(-0.635979\pi\) | ||||
−0.414315 | + | 0.910134i | \(0.635979\pi\) | |||||||
\(542\) | 6.00366 | 0.257879 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.05428 | −0.173826 | ||||||||
\(545\) | 32.7805 | 1.40416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3839 | 1.12809 | 0.564047 | − | 0.825743i | \(-0.309244\pi\) | ||||
0.564047 | + | 0.825743i | \(0.309244\pi\) | |||||||
\(548\) | 0.937895 | 0.0400649 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.87424 | 0.165198 | ||||||||
\(551\) | 6.50919 | 0.277301 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2096 | 0.646777 | ||||||||
\(554\) | 33.9142 | 1.44088 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.46250 | −0.231661 | ||||||||
\(557\) | −6.89107 | −0.291984 | −0.145992 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145992 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.83997 | −0.416186 | ||||||||
\(560\) | −20.7857 | −0.878356 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.0902525 | 0.00380707 | ||||||||
\(563\) | 32.6691 | 1.37684 | 0.688418 | − | 0.725314i | \(-0.258305\pi\) | ||||
0.688418 | + | 0.725314i | \(0.258305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.2803 | 2.07324 | ||||||||
\(566\) | −17.8366 | −0.749727 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.4384 | 1.02541 | ||||||||
\(569\) | −13.8851 | −0.582095 | −0.291048 | − | 0.956709i | \(-0.594004\pi\) | ||||
−0.291048 | + | 0.956709i | \(0.594004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.56148 | −0.0653459 | −0.0326729 | − | 0.999466i | \(-0.510402\pi\) | ||||
−0.0326729 | + | 0.999466i | \(0.510402\pi\) | |||||||
\(572\) | −0.748731 | −0.0313060 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.3304 | 0.848574 | ||||||||
\(575\) | 3.82949 | 0.159701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.2938 | −1.34441 | −0.672205 | − | 0.740365i | \(-0.734653\pi\) | ||||
−0.672205 | + | 0.740365i | \(0.734653\pi\) | |||||||
\(578\) | 20.0382 | 0.833481 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.08188 | 0.0449225 | ||||||||
\(581\) | −5.80533 | −0.240846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.83534 | −0.0760120 | ||||||||
\(584\) | 10.4939 | 0.434242 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.1574 | −1.03924 | ||||||||
\(587\) | 0.644254 | 0.0265912 | 0.0132956 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132956 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.8506 | 1.76563 | ||||||||
\(590\) | 28.6434 | 1.17923 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.6032 | −1.42218 | ||||||||
\(593\) | 42.7893 | 1.75715 | 0.878573 | − | 0.477609i | \(-0.158496\pi\) | ||||
0.878573 | + | 0.477609i | \(0.158496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00906 | −0.369336 | ||||||||
\(596\) | −7.00785 | −0.287053 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.80545 | −0.196509 | ||||||||
\(599\) | 27.8106 | 1.13631 | 0.568155 | − | 0.822922i | \(-0.307657\pi\) | ||||
0.568155 | + | 0.822922i | \(0.307657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0213529 | −0.000871004 0 | −0.000435502 | − | 1.00000i | \(-0.500139\pi\) | ||||
−0.000435502 | 1.00000i | \(0.500139\pi\) | ||||||||
\(602\) | 7.36846 | 0.300316 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.32104 | 0.257199 | ||||||||
\(605\) | −31.3994 | −1.27657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.95786 | −0.160645 | −0.0803223 | − | 0.996769i | \(-0.525595\pi\) | ||||
−0.0803223 | + | 0.996769i | \(0.525595\pi\) | |||||||
\(608\) | 13.2490 | 0.537317 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.36364 | −0.298145 | ||||||||
\(611\) | −5.90560 | −0.238915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.77872 | −0.152621 | −0.0763105 | − | 0.997084i | \(-0.524314\pi\) | ||||
−0.0763105 | + | 0.997084i | \(0.524314\pi\) | |||||||
\(614\) | 9.37819 | 0.378473 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.51917 | −0.101500 | ||||||||
\(617\) | 29.3301 | 1.18079 | 0.590393 | − | 0.807116i | \(-0.298973\pi\) | ||||
0.590393 | + | 0.807116i | \(0.298973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.53617 | −0.222517 | −0.111259 | − | 0.993791i | \(-0.535488\pi\) | ||||
−0.111259 | + | 0.993791i | \(0.535488\pi\) | |||||||
\(620\) | 7.12210 | 0.286030 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.6271 | −0.706783 | ||||||||
\(623\) | 1.36855 | 0.0548299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4825 | −1.17930 | ||||||||
\(626\) | −29.5616 | −1.18152 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.86813 | −0.114451 | ||||||||
\(629\) | −14.9979 | −0.598006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4015 | −1.25007 | −0.625037 | − | 0.780595i | \(-0.714916\pi\) | ||||
−0.625037 | + | 0.780595i | \(0.714916\pi\) | |||||||
\(632\) | 25.1336 | 0.999762 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.1640 | 0.562524 | ||||||||
\(635\) | −21.1532 | −0.839441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.6365 | −0.579917 | ||||||||
\(638\) | 1.01169 | 0.0400531 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −39.7906 | −1.57286 | ||||||||
\(641\) | 9.00627 | 0.355726 | 0.177863 | − | 0.984055i | \(-0.443082\pi\) | ||||
0.177863 | + | 0.984055i | \(0.443082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.6816 | −1.95925 | −0.979626 | − | 0.200829i | \(-0.935636\pi\) | ||||
−0.979626 | + | 0.200829i | \(0.935636\pi\) | |||||||
\(644\) | 0.554195 | 0.0218384 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.9351 | 0.784336 | ||||||||
\(647\) | 24.7647 | 0.973601 | 0.486801 | − | 0.873513i | \(-0.338164\pi\) | ||||
0.486801 | + | 0.873513i | \(0.338164\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.12514 | 0.161926 | ||||||||
\(650\) | −18.4024 | −0.721802 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.53504 | −0.216769 | ||||||||
\(653\) | 41.6418 | 1.62957 | 0.814785 | − | 0.579764i | \(-0.196855\pi\) | ||||
0.814785 | + | 0.579764i | \(0.196855\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.40478 | 0.328402 | ||||||||
\(656\) | 39.9213 | 1.55866 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.42229 | 0.172399 | ||||||||
\(659\) | −31.4482 | −1.22505 | −0.612524 | − | 0.790452i | \(-0.709846\pi\) | ||||
−0.612524 | + | 0.790452i | \(0.709846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.1590 | −1.05636 | −0.528181 | − | 0.849132i | \(-0.677126\pi\) | ||||
−0.528181 | + | 0.849132i | \(0.677126\pi\) | |||||||
\(662\) | 10.5433 | 0.409776 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.59324 | −0.372290 | ||||||||
\(665\) | 29.4407 | 1.14166 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −3.97562 | −0.153821 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.3124 | −0.977905 | ||||||||
\(671\) | −1.06049 | −0.0409398 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.7953 | 1.14852 | 0.574262 | − | 0.818672i | \(-0.305289\pi\) | ||||
0.574262 | + | 0.818672i | \(0.305289\pi\) | |||||||
\(674\) | −18.4520 | −0.710743 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.17676 | −0.0452601 | ||||||||
\(677\) | −35.8770 | −1.37887 | −0.689433 | − | 0.724349i | \(-0.742140\pi\) | ||||
−0.689433 | + | 0.724349i | \(0.742140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.80472 | −0.222765 | ||||||||
\(680\) | −14.8874 | −0.570905 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.66003 | 0.255026 | ||||||||
\(683\) | −0.183601 | −0.00702530 | −0.00351265 | − | 0.999994i | \(-0.501118\pi\) | ||||
−0.00351265 | + | 0.999994i | \(0.501118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.65441 | 0.292460 | ||||||||
\(686\) | 27.3428 | 1.04395 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.4689 | 0.551622 | ||||||||
\(689\) | 8.71775 | 0.332120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.73544 | −0.332312 | −0.166156 | − | 0.986099i | \(-0.553136\pi\) | ||||
−0.166156 | + | 0.986099i | \(0.553136\pi\) | |||||||
\(692\) | −0.645005 | −0.0245194 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.01480 | 0.0764808 | ||||||||
\(695\) | −44.5809 | −1.69105 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3029 | 0.655395 | ||||||||
\(698\) | −37.4165 | −1.41623 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.12228 | 0.0802148 | ||||||||
\(701\) | 39.2626 | 1.48293 | 0.741464 | − | 0.670992i | \(-0.234132\pi\) | ||||
0.741464 | + | 0.670992i | \(0.234132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.0116 | 1.84851 | ||||||||
\(704\) | −3.98846 | −0.150321 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.6144 | 0.700562 | ||||||||
\(707\) | 14.2769 | 0.536937 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7413 | 1.07940 | 0.539701 | − | 0.841857i | \(-0.318537\pi\) | ||||
0.539701 | + | 0.841857i | \(0.318537\pi\) | |||||||
\(710\) | −44.3896 | −1.66591 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.26152 | 0.0847539 | ||||||||
\(713\) | 6.58309 | 0.246539 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.11059 | −0.228523 | ||||||||
\(716\) | 5.45997 | 0.204049 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.873417 | −0.0325956 | ||||||||
\(719\) | −9.64982 | −0.359877 | −0.179939 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179939 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.58309 | 0.0589574 | ||||||||
\(722\) | −35.9321 | −1.33726 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.15755 | 0.340338 | ||||||||
\(725\) | 3.82949 | 0.142224 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.623800 | 0.0231355 | 0.0115677 | − | 0.999933i | \(-0.496318\pi\) | ||||
0.0115677 | + | 0.999933i | \(0.496318\pi\) | |||||||
\(728\) | 11.9659 | 0.443486 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.0610 | −0.705481 | ||||||||
\(731\) | 6.27121 | 0.231949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3861 | 0.531362 | 0.265681 | − | 0.964061i | \(-0.414403\pi\) | ||||
0.265681 | + | 0.964061i | \(0.414403\pi\) | |||||||
\(734\) | −19.7913 | −0.730512 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.03543 | 0.0750268 | ||||||||
\(737\) | −3.64543 | −0.134281 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.95277 | −0.145405 | −0.0727025 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0727025 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(740\) | 8.14610 | 0.299457 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.52811 | −0.239654 | ||||||||
\(743\) | −17.5497 | −0.643837 | −0.321919 | − | 0.946767i | \(-0.604328\pi\) | ||||
−0.321919 | + | 0.946767i | \(0.604328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.1930 | −2.09539 | ||||||||
\(746\) | 41.2199 | 1.50917 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.477181 | 0.0174475 | ||||||||
\(749\) | 14.4805 | 0.529107 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.8189 | −1.34354 | −0.671770 | − | 0.740760i | \(-0.734465\pi\) | ||||
−0.671770 | + | 0.740760i | \(0.734465\pi\) | |||||||
\(752\) | 8.68374 | 0.316663 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.80545 | −0.175004 | ||||||||
\(755\) | 51.5877 | 1.87747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.2754 | −1.20942 | −0.604708 | − | 0.796447i | \(-0.706710\pi\) | ||||
−0.604708 | + | 0.796447i | \(0.706710\pi\) | |||||||
\(758\) | −36.2596 | −1.31701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.6504 | 1.76473 | ||||||||
\(761\) | −37.2086 | −1.34881 | −0.674405 | − | 0.738361i | \(-0.735600\pi\) | ||||
−0.674405 | + | 0.738361i | \(0.735600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.7919 | 0.607908 | ||||||||
\(764\) | −3.13465 | −0.113408 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.99956 | 0.252904 | ||||||||
\(767\) | −19.5941 | −0.707503 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.5305 | 1.96642 | 0.983209 | − | 0.182481i | \(-0.0584129\pi\) | ||||
0.983209 | + | 0.182481i | \(0.0584129\pi\) | |||||||
\(770\) | 4.57580 | 0.164900 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.555859 | −0.0200058 | ||||||||
\(773\) | 25.4337 | 0.914787 | 0.457393 | − | 0.889264i | \(-0.348783\pi\) | ||||
0.457393 | + | 0.889264i | \(0.348783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2099 | 0.905566 | ||||||||
\(776\) | −9.59223 | −0.344341 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 43.7322 | 1.56788 | ||||||||
\(779\) | −56.5441 | −2.02590 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.39286 | −0.228755 | ||||||||
\(782\) | 3.06261 | 0.109519 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.5218 | 0.768635 | ||||||||
\(785\) | −23.4076 | −0.835453 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.1336 | −1.68013 | −0.840066 | − | 0.542484i | \(-0.817484\pi\) | ||||
−0.840066 | + | 0.542484i | \(0.817484\pi\) | |||||||
\(788\) | −4.35146 | −0.155014 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −45.6524 | −1.62424 | ||||||||
\(791\) | 25.2440 | 0.897574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.03726 | 0.178878 | ||||||||
\(794\) | 30.7608 | 1.09166 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.36600 | −0.261081 | ||||||||
\(797\) | −33.2908 | −1.17922 | −0.589611 | − | 0.807687i | \(-0.700719\pi\) | ||||
−0.589611 | + | 0.807687i | \(0.700719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.76376 | 0.133152 | ||||||||
\(800\) | 7.79464 | 0.275582 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.62329 | 0.0573204 | ||||||||
\(803\) | −2.74512 | −0.0968730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.52294 | 0.159413 | ||||||||
\(806\) | −31.6347 | −1.11429 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23.5924 | 0.829977 | ||||||||
\(809\) | 8.67983 | 0.305166 | 0.152583 | − | 0.988291i | \(-0.451241\pi\) | ||||
0.152583 | + | 0.988291i | \(0.451241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.8833 | −0.908887 | −0.454444 | − | 0.890776i | \(-0.650162\pi\) | ||||
−0.454444 | + | 0.890776i | \(0.650162\pi\) | |||||||
\(812\) | 0.554195 | 0.0194484 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.61760 | 0.266997 | ||||||||
\(815\) | −45.1729 | −1.58234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.4936 | −0.716982 | ||||||||
\(818\) | −18.2051 | −0.636527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.39806 | −0.328195 | ||||||||
\(821\) | −15.6591 | −0.546507 | −0.273253 | − | 0.961942i | \(-0.588100\pi\) | ||||
−0.273253 | + | 0.961942i | \(0.588100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.7430 | 1.62936 | 0.814679 | − | 0.579912i | \(-0.196913\pi\) | ||||
0.814679 | + | 0.579912i | \(0.196913\pi\) | |||||||
\(824\) | 2.61604 | 0.0911341 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.6727 | 0.510528 | ||||||||
\(827\) | 32.5350 | 1.13135 | 0.565676 | − | 0.824627i | \(-0.308615\pi\) | ||||
0.565676 | + | 0.824627i | \(0.308615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9491 | 0.415008 | 0.207504 | − | 0.978234i | \(-0.433466\pi\) | ||||
0.207504 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(830\) | 17.4250 | 0.604832 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.9449 | 0.656797 | ||||||||
\(833\) | 9.32810 | 0.323200 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.4461 | −1.12284 | ||||||||
\(836\) | −1.55938 | −0.0539322 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 55.6805 | 1.92345 | ||||||||
\(839\) | 17.8539 | 0.616384 | 0.308192 | − | 0.951324i | \(-0.400276\pi\) | ||||
0.308192 | + | 0.951324i | \(0.400276\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −47.0461 | −1.62132 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.55715 | −0.328971 | ||||||||
\(845\) | −9.60387 | −0.330383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0845 | −0.552669 | ||||||||
\(848\) | −12.8188 | −0.440199 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.7282 | 0.402274 | ||||||||
\(851\) | 7.52960 | 0.258111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5605 | 0.772457 | 0.386228 | − | 0.922403i | \(-0.373778\pi\) | ||||
0.386228 | + | 0.922403i | \(0.373778\pi\) | |||||||
\(854\) | −3.77205 | −0.129077 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.9289 | 0.817874 | ||||||||
\(857\) | −22.9279 | −0.783204 | −0.391602 | − | 0.920135i | \(-0.628079\pi\) | ||||
−0.391602 | + | 0.920135i | \(0.628079\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.33959 | −0.0798257 | −0.0399129 | − | 0.999203i | \(-0.512708\pi\) | ||||
−0.0399129 | + | 0.999203i | \(0.512708\pi\) | |||||||
\(860\) | −3.40620 | −0.116150 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.61409 | −0.0890362 | ||||||||
\(863\) | −33.2368 | −1.13140 | −0.565698 | − | 0.824613i | \(-0.691393\pi\) | ||||
−0.565698 | + | 0.824613i | \(0.691393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.26406 | −0.178983 | ||||||||
\(866\) | −37.1296 | −1.26171 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.64832 | 0.123832 | ||||||||
\(869\) | −6.57473 | −0.223033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.3155 | 0.586715 | ||||||||
\(872\) | 27.7484 | 0.939681 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.0083 | −0.338535 | ||||||||
\(875\) | −5.29415 | −0.178975 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6244 | 0.662669 | 0.331335 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(878\) | −10.0066 | −0.337705 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.98516 | 0.302890 | ||||||||
\(881\) | 47.7909 | 1.61012 | 0.805058 | − | 0.593196i | \(-0.202134\pi\) | ||||
0.805058 | + | 0.593196i | \(0.202134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.68739 | 0.326007 | 0.163003 | − | 0.986626i | \(-0.447882\pi\) | ||||
0.163003 | + | 0.986626i | \(0.447882\pi\) | |||||||
\(884\) | −2.26658 | −0.0762333 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.1805 | 1.31629 | ||||||||
\(887\) | 10.9256 | 0.366845 | 0.183422 | − | 0.983034i | \(-0.441282\pi\) | ||||
0.183422 | + | 0.983034i | \(0.441282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8358 | −0.363422 | ||||||||
\(890\) | −4.10779 | −0.137693 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.85530 | −0.162568 | ||||||||
\(893\) | −12.2996 | −0.411589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.5603 | 1.48949 | ||||||||
\(896\) | −20.3829 | −0.680945 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.5952 | −1.12109 | ||||||||
\(899\) | 6.58309 | 0.219559 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.55599 | −0.185097 | ||||||||
\(902\) | −8.78834 | −0.292620 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.7155 | 1.38744 | ||||||||
\(905\) | 74.7372 | 2.48435 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.7832 | −1.05534 | −0.527672 | − | 0.849448i | \(-0.676935\pi\) | ||||
−0.527672 | + | 0.849448i | \(0.676935\pi\) | |||||||
\(908\) | 5.06675 | 0.168146 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21.7347 | −0.720499 | ||||||||
\(911\) | −6.69493 | −0.221813 | −0.110907 | − | 0.993831i | \(-0.535375\pi\) | ||||
−0.110907 | + | 0.993831i | \(0.535375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.50951 | 0.0830525 | ||||||||
\(914\) | −37.1226 | −1.22791 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.815737 | 0.0269527 | ||||||||
\(917\) | 4.30538 | 0.142176 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.2250 | 1.52482 | 0.762411 | − | 0.647093i | \(-0.224015\pi\) | ||||
0.762411 | + | 0.647093i | \(0.224015\pi\) | |||||||
\(920\) | 7.47410 | 0.246414 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.8555 | −1.18084 | ||||||||
\(923\) | 30.3657 | 0.999499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8345 | 0.948073 | ||||||||
\(926\) | −37.8164 | −1.24273 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.03543 | 0.0668161 | ||||||||
\(929\) | 14.9133 | 0.489290 | 0.244645 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244645 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.4833 | −0.999048 | ||||||||
\(932\) | 5.87301 | 0.192377 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.43263 | −0.308645 | ||||||||
\(935\) | 3.89440 | 0.127361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.70593 | −0.219073 | −0.109537 | − | 0.993983i | \(-0.534937\pi\) | ||||
−0.109537 | + | 0.993983i | \(0.534937\pi\) | |||||||
\(938\) | −12.9664 | −0.423368 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.04428 | −0.0666771 | ||||||||
\(941\) | 33.3052 | 1.08572 | 0.542858 | − | 0.839824i | \(-0.317342\pi\) | ||||
0.542858 | + | 0.839824i | \(0.317342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.68681 | −0.282882 | ||||||||
\(944\) | 28.8117 | 0.937741 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.18521 | −0.103560 | ||||||||
\(947\) | −27.4034 | −0.890492 | −0.445246 | − | 0.895408i | \(-0.646884\pi\) | ||||
−0.445246 | + | 0.895408i | \(0.646884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.0391 | 0.423268 | ||||||||
\(950\) | −38.3266 | −1.24348 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.62611 | −0.247164 | ||||||||
\(953\) | 1.09506 | 0.0354723 | 0.0177362 | − | 0.999843i | \(-0.494354\pi\) | ||||
0.0177362 | + | 0.999843i | \(0.494354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.5827 | −0.827838 | ||||||||
\(956\) | −9.44356 | −0.305427 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0181 | −0.679064 | ||||||||
\(959\) | 3.92100 | 0.126616 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3371 | 0.397972 | ||||||||
\(962\) | −36.1831 | −1.16659 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.52173 | 0.210051 | ||||||||
\(965\) | −4.53651 | −0.146035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.9241 | 0.705030 | 0.352515 | − | 0.935806i | \(-0.385327\pi\) | ||||
0.352515 | + | 0.935806i | \(0.385327\pi\) | |||||||
\(968\) | −26.5794 | −0.854295 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.4232 | 0.559425 | ||||||||
\(971\) | 0.0746247 | 0.00239482 | 0.00119741 | − | 0.999999i | \(-0.499619\pi\) | ||||
0.00119741 | + | 0.999999i | \(0.499619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8367 | −0.732112 | ||||||||
\(974\) | 5.80938 | 0.186145 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.40690 | −0.237089 | ||||||||
\(977\) | 58.4019 | 1.86844 | 0.934221 | − | 0.356694i | \(-0.116096\pi\) | ||||
0.934221 | + | 0.356694i | \(0.116096\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.591592 | −0.0189074 | ||||||||
\(980\) | −5.06655 | −0.161845 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.02504 | −0.256089 | ||||||||
\(983\) | −25.8365 | −0.824056 | −0.412028 | − | 0.911171i | \(-0.635179\pi\) | ||||
−0.412028 | + | 0.911171i | \(0.635179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.5134 | −1.13155 | ||||||||
\(986\) | 3.06261 | 0.0975332 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.40694 | 0.235646 | ||||||||
\(989\) | −3.14842 | −0.100114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3585 | −0.614944 | −0.307472 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307472 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(992\) | 13.3994 | 0.425431 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.7387 | −0.721229 | ||||||||
\(995\) | −60.1160 | −1.90580 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.5596 | −0.967833 | −0.483917 | − | 0.875114i | \(-0.660786\pi\) | ||||
−0.483917 | + | 0.875114i | \(0.660786\pi\) | |||||||
\(998\) | 25.8683 | 0.818847 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.r.1.5 | 16 | ||
3.2 | odd | 2 | 2001.2.a.n.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.12 | ✓ | 16 | 3.2 | odd | 2 | ||
6003.2.a.r.1.5 | 16 | 1.1 | even | 1 | trivial |