Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2000,2,Mod(1,2000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2000, 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("2000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2000 = 2^{4} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2000.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: | \(15.9700804043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1000) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.54336\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2000.1 |
$q$-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 | ||||||||
\(3\) | −0.543362 | −0.313710 | −0.156855 | − | 0.987622i | \(-0.550136\pi\) | ||||
−0.156855 | + | 0.987622i | \(0.550136\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.11525 | −0.799488 | −0.399744 | − | 0.916627i | \(-0.630901\pi\) | ||||
−0.399744 | + | 0.916627i | \(0.630901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70476 | −0.901586 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.99442 | 1.50588 | 0.752938 | − | 0.658092i | \(-0.228636\pi\) | ||||
0.752938 | + | 0.658092i | \(0.228636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.32279 | −1.75363 | −0.876813 | − | 0.480831i | \(-0.840335\pi\) | ||||
−0.876813 | + | 0.480831i | \(0.840335\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.75836 | −0.911535 | −0.455768 | − | 0.890099i | \(-0.650635\pi\) | ||||
−0.455768 | + | 0.890099i | \(0.650635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.90770 | −0.437656 | −0.218828 | − | 0.975763i | \(-0.570223\pi\) | ||||
−0.218828 | + | 0.975763i | \(0.570223\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14934 | 0.250807 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.35131 | 1.94988 | 0.974942 | − | 0.222460i | \(-0.0714086\pi\) | ||||
0.974942 | + | 0.222460i | \(0.0714086\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.09975 | 0.596547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.22705 | 1.34203 | 0.671014 | − | 0.741444i | \(-0.265859\pi\) | ||||
0.671014 | + | 0.741444i | \(0.265859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.994424 | −0.178604 | −0.0893019 | − | 0.996005i | \(-0.528464\pi\) | ||||
−0.0893019 | + | 0.996005i | \(0.528464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.71378 | −0.472408 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.37984 | 1.04884 | 0.524419 | − | 0.851460i | \(-0.324282\pi\) | ||||
0.524419 | + | 0.851460i | \(0.324282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.43556 | 0.550131 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.18247 | 0.653192 | 0.326596 | − | 0.945164i | \(-0.394098\pi\) | ||||
0.326596 | + | 0.945164i | \(0.394098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.45664 | 0.222135 | 0.111068 | − | 0.993813i | \(-0.464573\pi\) | ||||
0.111068 | + | 0.993813i | \(0.464573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.78501 | 0.406235 | 0.203117 | − | 0.979154i | \(-0.434893\pi\) | ||||
0.203117 | + | 0.979154i | \(0.434893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.52573 | −0.360819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.04215 | 0.285958 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.52786 | −0.209868 | −0.104934 | − | 0.994479i | \(-0.533463\pi\) | ||||
−0.104934 | + | 0.994479i | \(0.533463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.03657 | 0.137297 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.47771 | −0.192382 | −0.0961908 | − | 0.995363i | \(-0.530666\pi\) | ||||
−0.0961908 | + | 0.995363i | \(0.530666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.79148 | 1.12563 | 0.562817 | − | 0.826582i | \(-0.309718\pi\) | ||||
0.562817 | + | 0.826582i | \(0.309718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.72123 | 0.720807 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0811 | −1.47595 | −0.737974 | − | 0.674830i | \(-0.764217\pi\) | ||||
−0.737974 | + | 0.674830i | \(0.764217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.08115 | −0.611698 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3798 | 1.46922 | 0.734608 | − | 0.678492i | \(-0.237366\pi\) | ||||
0.734608 | + | 0.678492i | \(0.237366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.09362 | −1.06433 | −0.532164 | − | 0.846642i | \(-0.678621\pi\) | ||||
−0.532164 | + | 0.846642i | \(0.678621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.5644 | −1.20393 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.91328 | 1.00282 | 0.501411 | − | 0.865209i | \(-0.332814\pi\) | ||||
0.501411 | + | 0.865209i | \(0.332814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.42999 | 0.714443 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1964 | 1.33873 | 0.669364 | − | 0.742935i | \(-0.266567\pi\) | ||||
0.669364 | + | 0.742935i | \(0.266567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.92690 | −0.421008 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.08328 | 0.326827 | 0.163413 | − | 0.986558i | \(-0.447750\pi\) | ||||
0.163413 | + | 0.986558i | \(0.447750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3743 | 1.40200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.540332 | 0.0560298 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1382 | −1.02938 | −0.514689 | − | 0.857377i | \(-0.672093\pi\) | ||||
−0.514689 | + | 0.857377i | \(0.672093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.5087 | −1.35768 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5202 | 1.14630 | 0.573149 | − | 0.819451i | \(-0.305722\pi\) | ||||
0.573149 | + | 0.819451i | \(0.305722\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.20639 | −0.611534 | −0.305767 | − | 0.952106i | \(-0.598913\pi\) | ||||
−0.305767 | + | 0.952106i | \(0.598913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7168 | 1.22938 | 0.614690 | − | 0.788769i | \(-0.289281\pi\) | ||||
0.614690 | + | 0.788769i | \(0.289281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.381966 | 0.0365857 | 0.0182929 | − | 0.999833i | \(-0.494177\pi\) | ||||
0.0182929 | + | 0.999833i | \(0.494177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46656 | −0.329031 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.31164 | 0.781893 | 0.390947 | − | 0.920413i | \(-0.372148\pi\) | ||||
0.390947 | + | 0.920413i | \(0.372148\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.1016 | 1.58105 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.94985 | 0.728761 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.9443 | 1.26766 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.27259 | −0.204913 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3017 | 0.914130 | 0.457065 | − | 0.889433i | \(-0.348901\pi\) | ||||
0.457065 | + | 0.889433i | \(0.348901\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.791482 | −0.0696861 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.08672 | −0.269688 | −0.134844 | − | 0.990867i | \(-0.543053\pi\) | ||||
−0.134844 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.03526 | 0.349901 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1053 | 1.37596 | 0.687982 | − | 0.725728i | \(-0.258497\pi\) | ||||
0.687982 | + | 0.725728i | \(0.258497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5477 | −1.31874 | −0.659370 | − | 0.751819i | \(-0.729177\pi\) | ||||
−0.659370 | + | 0.751819i | \(0.729177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.51327 | −0.127440 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.5787 | −2.64074 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.37239 | 0.113193 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.2636 | −1.25044 | −0.625222 | − | 0.780447i | \(-0.714992\pi\) | ||||
−0.625222 | + | 0.780447i | \(0.714992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1313 | 1.31275 | 0.656373 | − | 0.754436i | \(-0.272090\pi\) | ||||
0.656373 | + | 0.754436i | \(0.272090\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1654 | 0.821827 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.241644 | 0.0192853 | 0.00964264 | − | 0.999954i | \(-0.496931\pi\) | ||||
0.00964264 | + | 0.999954i | \(0.496931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.830183 | 0.0658378 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7803 | −1.55891 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.314742 | 0.0246525 | 0.0123263 | − | 0.999924i | \(-0.496076\pi\) | ||||
0.0123263 | + | 0.999924i | \(0.496076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.71813 | 0.597247 | 0.298623 | − | 0.954371i | \(-0.403473\pi\) | ||||
0.298623 | + | 0.954371i | \(0.403473\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9777 | 2.07521 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.15987 | 0.394585 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.7472 | −1.04518 | −0.522590 | − | 0.852584i | \(-0.675034\pi\) | ||||
−0.522590 | + | 0.852584i | \(0.675034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.802932 | 0.0603521 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.29311 | −0.0966518 | −0.0483259 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483259 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4589 | −1.37204 | −0.686018 | − | 0.727585i | \(-0.740643\pi\) | ||||
−0.686018 | + | 0.727585i | \(0.740643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.77696 | −0.353123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.7708 | −1.37266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.55673 | −0.476932 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.90770 | −0.427466 | −0.213733 | − | 0.976892i | \(-0.568562\pi\) | ||||
−0.213733 | + | 0.976892i | \(0.568562\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8520 | 1.50096 | 0.750479 | − | 0.660894i | \(-0.229823\pi\) | ||||
0.750479 | + | 0.660894i | \(0.229823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.4735 | −1.38743 | −0.693713 | − | 0.720252i | \(-0.744026\pi\) | ||||
−0.693713 | + | 0.720252i | \(0.744026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1989 | 1.64452 | 0.822262 | − | 0.569109i | \(-0.192712\pi\) | ||||
0.822262 | + | 0.569109i | \(0.192712\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.56444 | 0.463020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2870 | −1.07294 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.2930 | −1.75799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.52786 | −0.659056 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.7323 | −1.63380 | −0.816900 | − | 0.576780i | \(-0.804309\pi\) | ||||
−0.816900 | + | 0.576780i | \(0.804309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.72673 | −0.460908 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.10345 | 0.142792 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.94112 | 0.333890 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.7633 | 1.59849 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6314 | 0.711931 | 0.355966 | − | 0.934499i | \(-0.384152\pi\) | ||||
0.355966 | + | 0.934499i | \(0.384152\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.0243 | 1.66092 | 0.830459 | − | 0.557079i | \(-0.188078\pi\) | ||||
0.830459 | + | 0.557079i | \(0.188078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8962 | 0.786126 | 0.393063 | − | 0.919511i | \(-0.371415\pi\) | ||||
0.393063 | + | 0.919511i | \(0.371415\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.74031 | 0.377685 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0347 | 1.05047 | 0.525235 | − | 0.850957i | \(-0.323977\pi\) | ||||
0.525235 | + | 0.850957i | \(0.323977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.84313 | −0.314595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0867 | 0.717141 | 0.358570 | − | 0.933503i | \(-0.383264\pi\) | ||||
0.358570 | + | 0.933503i | \(0.383264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.56473 | 0.422872 | 0.211436 | − | 0.977392i | \(-0.432186\pi\) | ||||
0.211436 | + | 0.977392i | \(0.432186\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.7931 | −0.820675 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0620 | 0.767486 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.62706 | −0.419973 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.22918 | −0.0775849 | −0.0387924 | − | 0.999247i | \(-0.512351\pi\) | ||||
−0.0387924 | + | 0.999247i | \(0.512351\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 46.7044 | 2.93628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.52786 | −0.344819 | −0.172409 | − | 0.985025i | \(-0.555155\pi\) | ||||
−0.172409 | + | 0.985025i | \(0.555155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4949 | −0.838534 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.5474 | −1.20995 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.91631 | 0.426478 | 0.213239 | − | 0.977000i | \(-0.431599\pi\) | ||||
0.213239 | + | 0.977000i | \(0.431599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.67534 | −0.102529 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.94427 | 0.179515 | 0.0897577 | − | 0.995964i | \(-0.471391\pi\) | ||||
0.0897577 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.26706 | −0.439823 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.81408 | −0.169082 | −0.0845410 | − | 0.996420i | \(-0.526942\pi\) | ||||
−0.0845410 | + | 0.996420i | \(0.526942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.68968 | 0.161027 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.59393 | −0.154741 | −0.0773705 | − | 0.997002i | \(-0.524652\pi\) | ||||
−0.0773705 | + | 0.997002i | \(0.524652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6090 | −1.04675 | −0.523374 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523374 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.84695 | −0.522219 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.87476 | −0.169103 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.50871 | 0.322926 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.7392 | 1.03634 | 0.518168 | − | 0.855279i | \(-0.326614\pi\) | ||||
0.518168 | + | 0.855279i | \(0.326614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.4815 | 0.898325 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −59.1264 | −3.41937 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.08115 | −0.177594 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.25962 | −0.359606 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4770 | −0.712102 | −0.356051 | − | 0.934466i | \(-0.615877\pi\) | ||||
−0.356051 | + | 0.934466i | \(0.615877\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.37232 | 0.191844 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.2262 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6456 | −0.714771 | −0.357385 | − | 0.933957i | \(-0.616332\pi\) | ||||
−0.357385 | + | 0.933957i | \(0.616332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.67852 | −0.375103 | −0.187552 | − | 0.982255i | \(-0.560055\pi\) | ||||
−0.187552 | + | 0.982255i | \(0.560055\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0949 | 2.02093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.90983 | −0.385669 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.16982 | 0.398939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.207546 | −0.0114773 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.89097 | −0.324780 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.2628 | −1.49850 | −0.749250 | − | 0.662288i | \(-0.769586\pi\) | ||||
−0.749250 | + | 0.662288i | \(0.769586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.2559 | −0.945618 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.3835 | 1.60062 | 0.800310 | − | 0.599587i | \(-0.204668\pi\) | ||||
0.800310 | + | 0.599587i | \(0.204668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.51623 | −0.245288 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.96658 | −0.268955 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1493 | 1.08796 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5007 | 0.832119 | 0.416059 | − | 0.909337i | \(-0.363411\pi\) | ||||
0.416059 | + | 0.909337i | \(0.363411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.98540 | 0.320391 | 0.160196 | − | 0.987085i | \(-0.448787\pi\) | ||||
0.160196 | + | 0.987085i | \(0.448787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.5991 | −1.04612 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8841 | −1.21800 | −0.608998 | − | 0.793171i | \(-0.708428\pi\) | ||||
−0.608998 | + | 0.793171i | \(0.708428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.31964 | −0.228620 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3525 | −0.599161 | −0.299580 | − | 0.954071i | \(-0.596847\pi\) | ||||
−0.299580 | + | 0.954071i | \(0.596847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3607 | −0.808457 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.57679 | −0.397678 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8123 | −0.929794 | −0.464897 | − | 0.885365i | \(-0.653909\pi\) | ||||
−0.464897 | + | 0.885365i | \(0.653909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.3126 | −0.588909 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.23181 | 0.167787 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0366 | −0.675008 | −0.337504 | − | 0.941324i | \(-0.609583\pi\) | ||||
−0.337504 | + | 0.941324i | \(0.609583\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −45.6951 | −2.35342 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.2800 | 1.60675 | 0.803373 | − | 0.595476i | \(-0.203036\pi\) | ||||
0.803373 | + | 0.595476i | \(0.203036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.59756 | −0.286772 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.3291 | 0.681084 | 0.340542 | − | 0.940229i | \(-0.389389\pi\) | ||||
0.340542 | + | 0.940229i | \(0.389389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.93985 | −0.200274 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.66950 | 0.135349 | 0.0676746 | − | 0.997707i | \(-0.478442\pi\) | ||||
0.0676746 | + | 0.997707i | \(0.478442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.1456 | −1.77739 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.67721 | 0.0846040 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9572 | 1.25257 | 0.626284 | − | 0.779595i | \(-0.284575\pi\) | ||||
0.626284 | + | 0.779595i | \(0.284575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.19260 | −0.109768 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.3039 | −1.41343 | −0.706716 | − | 0.707498i | \(-0.749824\pi\) | ||||
−0.706716 | + | 0.707498i | \(0.749824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.28754 | 0.313204 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.8636 | 1.57942 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5647 | −0.720180 | −0.360090 | − | 0.932918i | \(-0.617254\pi\) | ||||
−0.360090 | + | 0.932918i | \(0.617254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.75098 | −0.431654 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.12572 | 0.153807 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.44803 | 0.413702 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.4610 | −1.39041 | −0.695205 | − | 0.718811i | \(-0.744686\pi\) | ||||
−0.695205 | + | 0.718811i | \(0.744686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.5443 | −1.00127 | −0.500633 | − | 0.865660i | \(-0.666899\pi\) | ||||
−0.500633 | + | 0.865660i | \(0.666899\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.53277 | −0.366256 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.5961 | −0.899931 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.1587 | 0.828428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.9753 | −1.39569 | −0.697845 | − | 0.716249i | \(-0.745857\pi\) | ||||
−0.697845 | + | 0.716249i | \(0.745857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.9002 | −1.00440 | −0.502199 | − | 0.864752i | \(-0.667476\pi\) | ||||
−0.502199 | + | 0.864752i | \(0.667476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.8395 | −0.853379 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.2546 | 1.44397 | 0.721987 | − | 0.691907i | \(-0.243229\pi\) | ||||
0.721987 | + | 0.691907i | \(0.243229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.83150 | 0.325309 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.09346 | 0.289509 | 0.144754 | − | 0.989468i | \(-0.453761\pi\) | ||||
0.144754 | + | 0.989468i | \(0.453761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.29367 | 0.392277 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.3135 | −0.911459 | −0.455730 | − | 0.890118i | \(-0.650622\pi\) | ||||
−0.455730 | + | 0.890118i | \(0.650622\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.8890 | 0.983626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.76513 | −0.411822 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1289 | −0.614143 | −0.307071 | − | 0.951686i | \(-0.599349\pi\) | ||||
−0.307071 | + | 0.951686i | \(0.599349\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.6500 | −0.543773 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.28409 | −0.292679 | −0.146340 | − | 0.989234i | \(-0.546749\pi\) | ||||
−0.146340 | + | 0.989234i | \(0.546749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.705730 | 0.0327981 | 0.0163990 | − | 0.999866i | \(-0.494780\pi\) | ||||
0.0163990 | + | 0.999866i | \(0.494780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1190 | −0.468251 | −0.234126 | − | 0.972206i | \(-0.575223\pi\) | ||||
−0.234126 | + | 0.972206i | \(0.575223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.5546 | 1.18000 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.131300 | −0.00604999 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.27507 | 0.334508 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.13250 | 0.189214 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0533 | 1.32748 | 0.663739 | − | 0.747964i | \(-0.268969\pi\) | ||||
0.663739 | + | 0.747964i | \(0.268969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.3384 | −1.83927 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7479 | 0.489045 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.59798 | −0.344297 | −0.172149 | − | 0.985071i | \(-0.555071\pi\) | ||||
−0.172149 | + | 0.985071i | \(0.555071\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.171019 | −0.00773375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6822 | 0.527208 | 0.263604 | − | 0.964631i | \(-0.415089\pi\) | ||||
0.263604 | + | 0.964631i | \(0.415089\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.1618 | −1.22331 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.1864 | −1.17462 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.21754 | −0.188803 | −0.0944015 | − | 0.995534i | \(-0.530094\pi\) | ||||
−0.0944015 | + | 0.995534i | \(0.530094\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.19374 | −0.187362 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.12640 | 0.362338 | 0.181169 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181169 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.6587 | −0.651014 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.8190 | −0.922787 | −0.461394 | − | 0.887196i | \(-0.652650\pi\) | ||||
−0.461394 | + | 0.887196i | \(0.652650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.2352 | 0.850917 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.91339 | −0.261083 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9095 | 0.611739 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.46971 | 0.327884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.7390 | 0.689539 | 0.344769 | − | 0.938687i | \(-0.387957\pi\) | ||||
0.344769 | + | 0.938687i | \(0.387957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.6698 | 1.73464 | 0.867319 | − | 0.497753i | \(-0.165841\pi\) | ||||
0.867319 | + | 0.497753i | \(0.165841\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.73740 | 0.162804 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 64.4471 | 2.80205 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.99685 | 0.173449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.4449 | −1.14546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.702628 | 0.0303206 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.6146 | −0.543349 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1162 | 0.434930 | 0.217465 | − | 0.976068i | \(-0.430221\pi\) | ||||
0.217465 | + | 0.976068i | \(0.430221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0298 | 0.430422 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.91575 | −0.167425 | −0.0837127 | − | 0.996490i | \(-0.526678\pi\) | ||||
−0.0837127 | + | 0.996490i | \(0.526678\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.7788 | −1.01486 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.7870 | −0.587348 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.8538 | −0.801744 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9095 | 1.09782 | 0.548910 | − | 0.835881i | \(-0.315043\pi\) | ||||
0.548910 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.21002 | −0.389542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1994 | 0.430617 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.7156 | 1.29451 | 0.647254 | − | 0.762275i | \(-0.275917\pi\) | ||||
0.647254 | + | 0.762275i | \(0.275917\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.6010 | −0.571189 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.3448 | −0.517519 | −0.258760 | − | 0.965942i | \(-0.583314\pi\) | ||||
−0.258760 | + | 0.965942i | \(0.583314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9368 | −1.42021 | −0.710104 | − | 0.704096i | \(-0.751352\pi\) | ||||
−0.710104 | + | 0.704096i | \(0.751352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.21002 | 0.134100 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.2207 | 1.88256 | 0.941280 | − | 0.337626i | \(-0.109624\pi\) | ||||
0.941280 | + | 0.337626i | \(0.109624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.3302 | −0.470866 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.7984 | −1.07030 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.63080 | −0.316035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.6710 | 1.55485 | 0.777424 | − | 0.628976i | \(-0.216526\pi\) | ||||
0.777424 | + | 0.628976i | \(0.216526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.89706 | 0.0781671 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.5811 | 0.435250 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.19524 | −0.254408 | −0.127204 | − | 0.991877i | \(-0.540600\pi\) | ||||
−0.127204 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.6054 | −0.515904 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.03100 | 0.164702 | 0.0823510 | − | 0.996603i | \(-0.473757\pi\) | ||||
0.0823510 | + | 0.996603i | \(0.473757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.2631 | 1.72395 | 0.861974 | − | 0.506953i | \(-0.169228\pi\) | ||||
0.861974 | + | 0.506953i | \(0.169228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.6766 | 1.33069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9920 | 1.25793 | 0.628963 | − | 0.777436i | \(-0.283480\pi\) | ||||
0.628963 | + | 0.777436i | \(0.283480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.30636 | 0.336591 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.6090 | −0.712384 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.63443 | 0.267962 | 0.133981 | − | 0.990984i | \(-0.457224\pi\) | ||||
0.133981 | + | 0.990984i | \(0.457224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2862 | −0.856951 | −0.428475 | − | 0.903553i | \(-0.640949\pi\) | ||||
−0.428475 | + | 0.903553i | \(0.640949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.4244 | −0.700346 | −0.350173 | − | 0.936685i | \(-0.613877\pi\) | ||||
−0.350173 | + | 0.936685i | \(0.613877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9867 | 1.16320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.52189 | −0.261294 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.17708 | 0.206753 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.9777 | −0.956053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5148 | −0.458396 | −0.229198 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229198 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.8952 | 0.512539 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9697 | 0.632742 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.4845 | −1.32462 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.2710 | −1.78810 | −0.894048 | − | 0.447970i | \(-0.852147\pi\) | ||||
−0.894048 | + | 0.447970i | \(0.852147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6449 | −0.932464 | −0.466232 | − | 0.884662i | \(-0.654389\pi\) | ||||
−0.466232 | + | 0.884662i | \(0.654389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.6264 | −0.968165 | −0.484082 | − | 0.875022i | \(-0.660846\pi\) | ||||
−0.484082 | + | 0.875022i | \(0.660846\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.38032 | −0.289703 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.14294 | −0.0447952 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.93000 | −0.310325 | −0.155163 | − | 0.987889i | \(-0.549590\pi\) | ||||
−0.155163 | + | 0.987889i | \(0.549590\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.5960 | 0.959582 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3575 | 0.793017 | 0.396508 | − | 0.918031i | \(-0.370222\pi\) | ||||
0.396508 | + | 0.918031i | \(0.370222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.5617 | −1.53877 | −0.769385 | − | 0.638785i | \(-0.779437\pi\) | ||||
−0.769385 | + | 0.638785i | \(0.779437\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.9121 | −0.501463 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 67.5824 | 2.61680 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.77670 | −0.223340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.9084 | 1.69506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.46282 | −0.0563874 | −0.0281937 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281937 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.0148 | 0.500199 | 0.250099 | − | 0.968220i | \(-0.419537\pi\) | ||||
0.250099 | + | 0.968220i | \(0.419537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.4448 | 0.822975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.5972 | −0.521047 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.11337 | 0.0808660 | 0.0404330 | − | 0.999182i | \(-0.487126\pi\) | ||||
0.0404330 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.46397 | −0.246616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.66037 | 0.368031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.92443 | 0.263418 | 0.131709 | − | 0.991288i | \(-0.457954\pi\) | ||||
0.131709 | + | 0.991288i | \(0.457954\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.5742 | 1.08545 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7192 | −0.595408 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.71267 | −0.329543 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.65310 | 0.0624369 | 0.0312185 | − | 0.999513i | \(-0.490061\pi\) | ||||
0.0312185 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1708 | −0.459031 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.3680 | −0.916452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.67982 | −0.0630870 | −0.0315435 | − | 0.999502i | \(-0.510042\pi\) | ||||
−0.0315435 | + | 0.999502i | \(0.510042\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.1083 | −0.904130 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.29917 | −0.348257 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.02410 | −0.224974 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.2441 | 1.87379 | 0.936895 | − | 0.349611i | \(-0.113686\pi\) | ||||
0.936895 | + | 0.349611i | \(0.113686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1280 | 0.488914 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.56703 | −0.132659 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2324 | −0.676203 | −0.338101 | − | 0.941110i | \(-0.609785\pi\) | ||||
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.3387 | −0.456989 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.47456 | −0.202484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.5137 | 1.90270 | 0.951350 | − | 0.308112i | \(-0.0996971\pi\) | ||||
0.951350 | + | 0.308112i | \(0.0996971\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −60.3384 | −2.22259 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.3261 | 0.490207 | 0.245103 | − | 0.969497i | \(-0.421178\pi\) | ||||
0.245103 | + | 0.969497i | \(0.421178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.55403 | −0.240768 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.9448 | 0.878448 | 0.439224 | − | 0.898378i | \(-0.355253\pi\) | ||||
0.439224 | + | 0.898378i | \(0.355253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.9883 | −1.20698 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.8992 | −0.982875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0607894 | −0.00221823 | −0.00110912 | − | 0.999999i | \(-0.500353\pi\) | ||||
−0.00110912 | + | 0.999999i | \(0.500353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.667887 | 0.0243392 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3402 | −1.06639 | −0.533194 | − | 0.845993i | \(-0.679008\pi\) | ||||
−0.533194 | + | 0.845993i | \(0.679008\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.3774 | −0.921142 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.1931 | 1.20325 | 0.601625 | − | 0.798779i | \(-0.294520\pi\) | ||||
0.601625 | + | 0.798779i | \(0.294520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.807952 | −0.0292498 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.34326 | 0.337366 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.90557 | 0.285082 | 0.142541 | − | 0.989789i | \(-0.454473\pi\) | ||||
0.142541 | + | 0.989789i | \(0.454473\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00363 | 0.108173 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7151 | 0.996843 | 0.498421 | − | 0.866935i | \(-0.333913\pi\) | ||||
0.498421 | + | 0.866935i | \(0.333913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.33263 | 0.263057 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.97890 | −0.285874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.8302 | 2.21246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.4020 | 0.800583 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.1468 | −0.611217 | −0.305609 | − | 0.952157i | \(-0.598860\pi\) | ||||
−0.305609 | + | 0.952157i | \(0.598860\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.75806 | −0.133790 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.5812 | −0.625114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.5867 | −1.97394 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0575 | 0.745896 | 0.372948 | − | 0.927852i | \(-0.378347\pi\) | ||||
0.372948 | + | 0.927852i | \(0.378347\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.4670 | −0.370297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.33952 | −0.294662 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.4174 | −1.60274 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.59981 | −0.0563158 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.8466 | 1.36577 | 0.682887 | − | 0.730524i | \(-0.260724\pi\) | ||||
0.682887 | + | 0.730524i | \(0.260724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.2820 | −1.09846 | −0.549229 | − | 0.835672i | \(-0.685079\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.69379 | −0.304905 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.77883 | −0.0972189 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.1741 | −1.26403 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.50658 | 0.296882 | 0.148441 | − | 0.988921i | \(-0.452575\pi\) | ||||
0.148441 | + | 0.988921i | \(0.452575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.6746 | −1.55726 | −0.778630 | − | 0.627483i | \(-0.784085\pi\) | ||||
−0.778630 | + | 0.627483i | \(0.784085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.6536 | −0.926836 | −0.463418 | − | 0.886140i | \(-0.653377\pi\) | ||||
−0.463418 | + | 0.886140i | \(0.653377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.21967 | 0.146555 | 0.0732776 | − | 0.997312i | \(-0.476654\pi\) | ||||
0.0732776 | + | 0.997312i | \(0.476654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.52907 | 0.0530427 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.49261 | 0.328899 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.08246 | −0.106546 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.1897 | −0.593453 | −0.296726 | − | 0.954963i | \(-0.595895\pi\) | ||||
−0.296726 | + | 0.954963i | \(0.595895\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2302 | 0.801041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.40944 | 0.0485438 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4956 | −1.01348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.56807 | 0.328375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.6599 | 2.04511 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2243 | −0.966381 | −0.483191 | − | 0.875515i | \(-0.660522\pi\) | ||||
−0.483191 | + | 0.875515i | \(0.660522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.2310 | 1.75002 | 0.875008 | − | 0.484108i | \(-0.160856\pi\) | ||||
0.875008 | + | 0.484108i | \(0.160856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.1686 | 1.81409 | 0.907044 | − | 0.421036i | \(-0.138333\pi\) | ||||
0.907044 | + | 0.421036i | \(0.138333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.80710 | 0.163825 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.8953 | −0.915526 | −0.457763 | − | 0.889074i | \(-0.651349\pi\) | ||||
−0.457763 | + | 0.889074i | \(0.651349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.56203 | 0.0530495 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.5167 | 1.51012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.3866 | 2.58826 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.4214 | 0.928072 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7008 | −0.530178 | −0.265089 | − | 0.964224i | \(-0.585401\pi\) | ||||
−0.265089 | + | 0.964224i | \(0.585401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.63881 | −0.325109 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.32804 | 0.0784336 | 0.0392168 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392168 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0863 | −1.51727 | −0.758637 | − | 0.651514i | \(-0.774134\pi\) | ||||
−0.758637 | + | 0.651514i | \(0.774134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.9907 | 1.54422 | 0.772108 | − | 0.635491i | \(-0.219202\pi\) | ||||
0.772108 | + | 0.635491i | \(0.219202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.7907 | −0.730836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.1141 | 1.07586 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.31296 | −0.177791 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.1270 | 1.07269 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.18675 | −0.239691 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.74226 | 0.191302 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.67418 | 0.0557132 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.9462 | 1.39280 | 0.696401 | − | 0.717653i | \(-0.254784\pi\) | ||||
0.696401 | + | 0.717653i | \(0.254784\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.1592 | −1.03349 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6141 | 1.27934 | 0.639671 | − | 0.768649i | \(-0.279071\pi\) | ||||
0.639671 | + | 0.768649i | \(0.279071\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.9140 | 2.01596 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.52918 | 0.215613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.7156 | 1.54100 | 0.770502 | − | 0.637437i | \(-0.220005\pi\) | ||||
0.770502 | + | 0.637437i | \(0.220005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.77955 | 0.223394 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −78.2751 | −2.57646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.7868 | 0.551350 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.49036 | −0.180133 | −0.0900665 | − | 0.995936i | \(-0.528708\pi\) | ||||
−0.0900665 | + | 0.995936i | \(0.528708\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.81834 | 0.157915 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.9902 | 0.359802 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6902 | −0.577912 | −0.288956 | − | 0.957342i | \(-0.593308\pi\) | ||||
−0.288956 | + | 0.957342i | \(0.593308\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.87113 | 0.224231 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.0472 | 1.33810 | 0.669050 | − | 0.743217i | \(-0.266701\pi\) | ||||
0.669050 | + | 0.743217i | \(0.266701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.1116 | 1.27365 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.6027 | 0.864472 | 0.432236 | − | 0.901760i | \(-0.357725\pi\) | ||||
0.432236 | + | 0.901760i | \(0.357725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.4970 | 1.86643 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.62886 | 0.117674 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.1029 | 0.715984 | 0.357992 | − | 0.933725i | \(-0.383461\pi\) | ||||
0.357992 | + | 0.933725i | \(0.383461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.6126 | −0.633986 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.0666 | −1.10007 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0111 | −0.968101 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.3959 | −1.10839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.05390 | 0.0338912 | 0.0169456 | − | 0.999856i | \(-0.494606\pi\) | ||||
0.0169456 | + | 0.999856i | \(0.494606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.89581 | −0.125151 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.47456 | 0.0473210 | 0.0236605 | − | 0.999720i | \(-0.492468\pi\) | ||||
0.0236605 | + | 0.999720i | \(0.492468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.8872 | 1.05432 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.53670 | 0.177135 | 0.0885674 | − | 0.996070i | \(-0.471771\pi\) | ||||
0.0885674 | + | 0.996070i | \(0.471771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3992 | 0.492160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.03313 | −0.0329852 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.18145 | −0.133368 | −0.0666838 | − | 0.997774i | \(-0.521242\pi\) | ||||
−0.0666838 | + | 0.997774i | \(0.521242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.20093 | 0.101887 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.6215 | 0.433138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5056 | 0.683147 | 0.341573 | − | 0.939855i | \(-0.389040\pi\) | ||||
0.341573 | + | 0.939855i | \(0.389040\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8136 | 0.470094 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3446 | 0.834341 | 0.417171 | − | 0.908828i | \(-0.363022\pi\) | ||||
0.417171 | + | 0.908828i | \(0.363022\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.7759 | 0.625681 |
(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 | 2000.2.a.r.1.2 | 4 | ||
4.3 | odd | 2 | 1000.2.a.e.1.3 | ✓ | 4 | ||
5.2 | odd | 4 | 2000.2.c.j.1249.5 | 8 | |||
5.3 | odd | 4 | 2000.2.c.j.1249.4 | 8 | |||
5.4 | even | 2 | 2000.2.a.m.1.3 | 4 | |||
8.3 | odd | 2 | 8000.2.a.br.1.2 | 4 | |||
8.5 | even | 2 | 8000.2.a.bb.1.3 | 4 | |||
12.11 | even | 2 | 9000.2.a.r.1.4 | 4 | |||
20.3 | even | 4 | 1000.2.c.d.249.5 | 8 | |||
20.7 | even | 4 | 1000.2.c.d.249.4 | 8 | |||
20.19 | odd | 2 | 1000.2.a.h.1.2 | yes | 4 | ||
40.19 | odd | 2 | 8000.2.a.ba.1.3 | 4 | |||
40.29 | even | 2 | 8000.2.a.bq.1.2 | 4 | |||
60.59 | even | 2 | 9000.2.a.ba.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1000.2.a.e.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
1000.2.a.h.1.2 | yes | 4 | 20.19 | odd | 2 | ||
1000.2.c.d.249.4 | 8 | 20.7 | even | 4 | |||
1000.2.c.d.249.5 | 8 | 20.3 | even | 4 | |||
2000.2.a.m.1.3 | 4 | 5.4 | even | 2 | |||
2000.2.a.r.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2000.2.c.j.1249.4 | 8 | 5.3 | odd | 4 | |||
2000.2.c.j.1249.5 | 8 | 5.2 | odd | 4 | |||
8000.2.a.ba.1.3 | 4 | 40.19 | odd | 2 | |||
8000.2.a.bb.1.3 | 4 | 8.5 | even | 2 | |||
8000.2.a.bq.1.2 | 4 | 40.29 | even | 2 | |||
8000.2.a.br.1.2 | 4 | 8.3 | odd | 2 | |||
9000.2.a.r.1.4 | 4 | 12.11 | even | 2 | |||
9000.2.a.ba.1.1 | 4 | 60.59 | even | 2 |