Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4000,2,Mod(1,4000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4000, 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("4000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4000 = 2^{5} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4000.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: | \(31.9401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 13x^{2} + 41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.31991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4000.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | 0.233595 | 0.116797 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116797 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63981 | 1.39896 | 0.699478 | − | 0.714654i | \(-0.253416\pi\) | ||||
0.699478 | + | 0.714654i | \(0.253416\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.63981 | 1.28685 | 0.643426 | − | 0.765508i | \(-0.277512\pi\) | ||||
0.643426 | + | 0.765508i | \(0.277512\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.50738 | 1.82081 | 0.910403 | − | 0.413723i | \(-0.135772\pi\) | ||||
0.910403 | + | 0.413723i | \(0.135772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.50738 | 1.72231 | 0.861155 | − | 0.508343i | \(-0.169742\pi\) | ||||
0.861155 | + | 0.508343i | \(0.169742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.61803 | 0.962927 | 0.481463 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481463 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0902 | −1.87370 | −0.936849 | − | 0.349735i | \(-0.886272\pi\) | ||||
−0.936849 | + | 0.349735i | \(0.886272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.63981 | −0.833335 | −0.416668 | − | 0.909059i | \(-0.636802\pi\) | ||||
−0.416668 | + | 0.909059i | \(0.636802\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.50738 | −1.30687 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.86756 | −0.471424 | −0.235712 | − | 0.971823i | \(-0.575742\pi\) | ||||
−0.235712 | + | 0.971823i | \(0.575742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.50738 | −1.20214 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.854102 | −0.133388 | −0.0666942 | − | 0.997773i | \(-0.521245\pi\) | ||||
−0.0666942 | + | 0.997773i | \(0.521245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.32624 | −0.507247 | −0.253623 | − | 0.967303i | \(-0.581622\pi\) | ||||
−0.253623 | + | 0.967303i | \(0.581622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0902 | 1.47180 | 0.735901 | − | 0.677089i | \(-0.236759\pi\) | ||||
0.735901 | + | 0.677089i | \(0.236759\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.1472 | −1.70095 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.27963 | −1.27465 | −0.637327 | − | 0.770593i | \(-0.719960\pi\) | ||||
−0.637327 | + | 0.770593i | \(0.719960\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.1472 | −1.60893 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3749 | −1.35070 | −0.675351 | − | 0.737497i | \(-0.736008\pi\) | ||||
−0.675351 | + | 0.737497i | \(0.736008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.85410 | 1.00561 | 0.502807 | − | 0.864398i | \(-0.332301\pi\) | ||||
0.502807 | + | 0.864398i | \(0.332301\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.236068 | −0.0297418 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.47214 | −0.899539 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50738 | 0.890961 | 0.445481 | − | 0.895292i | \(-0.353033\pi\) | ||||
0.445481 | + | 0.895292i | \(0.353033\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3749 | 1.21429 | 0.607147 | − | 0.794589i | \(-0.292314\pi\) | ||||
0.607147 | + | 0.794589i | \(0.292314\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.86756 | 0.326789 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.86756 | 0.322626 | 0.161313 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161313 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.56231 | −0.830071 | −0.415035 | − | 0.909805i | \(-0.636231\pi\) | ||||
−0.415035 | + | 0.909805i | \(0.636231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.3262 | 1.75036 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.85410 | 1.04453 | 0.522266 | − | 0.852782i | \(-0.325087\pi\) | ||||
0.522266 | + | 0.852782i | \(0.325087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.86756 | 0.300602 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.50738 | 0.778479 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.3749 | −1.05342 | −0.526708 | − | 0.850047i | \(-0.676574\pi\) | ||||
−0.526708 | + | 0.850047i | \(0.676574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.77225 | −0.178118 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.90983 | −0.289539 | −0.144769 | − | 0.989465i | \(-0.546244\pi\) | ||||
−0.144769 | + | 0.989465i | \(0.546244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.8541 | 1.62935 | 0.814674 | − | 0.579920i | \(-0.196916\pi\) | ||||
0.814674 | + | 0.579920i | \(0.196916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.32624 | −0.893292 | −0.446646 | − | 0.894711i | \(-0.647382\pi\) | ||||
−0.446646 | + | 0.894711i | \(0.647382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.63981 | 0.440392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.63981 | 0.436477 | 0.218238 | − | 0.975895i | \(-0.429969\pi\) | ||||
0.218238 | + | 0.975895i | \(0.429969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.77225 | −0.163845 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.63981 | 0.425331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5279 | 0.957079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.38197 | 0.124608 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.09017 | 0.185473 | 0.0927363 | − | 0.995691i | \(-0.470439\pi\) | ||||
0.0927363 | + | 0.995691i | \(0.470439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.38197 | 0.473856 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1472 | 1.06130 | 0.530652 | − | 0.847590i | \(-0.321947\pi\) | ||||
0.530652 | + | 0.847590i | \(0.321947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.63981 | 0.402323 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.50738 | 0.641398 | 0.320699 | − | 0.947181i | \(-0.396082\pi\) | ||||
0.320699 | + | 0.947181i | \(0.396082\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1472 | 1.03031 | 0.515156 | − | 0.857097i | \(-0.327734\pi\) | ||||
0.515156 | + | 0.857097i | \(0.327734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.3262 | −1.37492 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.5279 | 1.80025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7082 | 0.883198 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8541 | −1.29882 | −0.649409 | − | 0.760439i | \(-0.724984\pi\) | ||||
−0.649409 | + | 0.760439i | \(0.724984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.41206 | 0.521806 | 0.260903 | − | 0.965365i | \(-0.415980\pi\) | ||||
0.260903 | + | 0.965365i | \(0.415980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.86756 | −0.231829 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.7870 | 1.33975 | 0.669874 | − | 0.742475i | \(-0.266348\pi\) | ||||
0.669874 | + | 0.742475i | \(0.266348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.0148 | 1.19075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.85410 | 0.224935 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.2705 | −1.19608 | −0.598039 | − | 0.801467i | \(-0.704053\pi\) | ||||
−0.598039 | + | 0.801467i | \(0.704053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.3820 | 0.958145 | 0.479073 | − | 0.877775i | \(-0.340973\pi\) | ||||
0.479073 | + | 0.877775i | \(0.340973\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.52786 | 0.655990 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.86756 | −0.219288 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.5221 | −1.71233 | −0.856163 | − | 0.516706i | \(-0.827158\pi\) | ||||
−0.856163 | + | 0.516706i | \(0.827158\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.7870 | 1.26179 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3749 | −0.775459 | −0.387730 | − | 0.921773i | \(-0.626741\pi\) | ||||
−0.387730 | + | 0.921773i | \(0.626741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.90983 | −0.736592 | −0.368296 | − | 0.929709i | \(-0.620059\pi\) | ||||
−0.368296 | + | 0.929709i | \(0.620059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7082 | −0.939417 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.8328 | 2.54723 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.38197 | 0.246002 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5221 | −1.62964 | −0.814822 | − | 0.579711i | \(-0.803165\pi\) | ||||
−0.814822 | + | 0.579711i | \(0.803165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.86756 | −0.206412 | −0.103206 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103206 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.50738 | −0.534878 | −0.267439 | − | 0.963575i | \(-0.586177\pi\) | ||||
−0.267439 | + | 0.963575i | \(0.586177\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.77225 | 0.125632 | 0.0628158 | − | 0.998025i | \(-0.479992\pi\) | ||||
0.0628158 | + | 0.998025i | \(0.479992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.47214 | −0.174371 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.23607 | −0.437686 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.76393 | −0.122602 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 34.8328 | 2.40944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4268 | −1.47508 | −0.737541 | − | 0.675302i | \(-0.764013\pi\) | ||||
−0.737541 | + | 0.675302i | \(0.764013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.1472 | −0.832312 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.86756 | −0.194663 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.7870 | −1.13436 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.8328 | 2.34311 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.67376 | 0.179048 | 0.0895242 | − | 0.995985i | \(-0.471465\pi\) | ||||
0.0895242 | + | 0.995985i | \(0.471465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.85410 | −0.255806 | −0.127903 | − | 0.991787i | \(-0.540825\pi\) | ||||
−0.127903 | + | 0.991787i | \(0.540825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.67376 | −0.639260 | −0.319630 | − | 0.947542i | \(-0.603559\pi\) | ||||
−0.319630 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.63981 | −0.305277 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.50738 | 0.491824 | 0.245912 | − | 0.969292i | \(-0.420912\pi\) | ||||
0.245912 | + | 0.969292i | \(0.420912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.63981 | −0.301388 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.86756 | 0.185487 | 0.0927436 | − | 0.995690i | \(-0.470436\pi\) | ||||
0.0927436 | + | 0.995690i | \(0.470436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.56231 | −0.358300 | −0.179150 | − | 0.983822i | \(-0.557335\pi\) | ||||
−0.179150 | + | 0.983822i | \(0.557335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.8328 | 2.21636 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.2361 | 0.775429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7499 | 1.30972 | 0.654860 | − | 0.755750i | \(-0.272727\pi\) | ||||
0.654860 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4268 | 1.34709 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.73512 | 0.357747 | 0.178874 | − | 0.983872i | \(-0.442755\pi\) | ||||
0.178874 | + | 0.983872i | \(0.442755\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.77225 | −0.110122 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85410 | 0.238563 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.67376 | 0.164871 | 0.0824356 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824356 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.9443 | −0.975774 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4721 | 0.760440 | 0.380220 | − | 0.924896i | \(-0.375848\pi\) | ||||
0.380220 | + | 0.924896i | \(0.375848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.27963 | −0.563697 | −0.281849 | − | 0.959459i | \(-0.590948\pi\) | ||||
−0.281849 | + | 0.959459i | \(0.590948\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.63981 | −0.280814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.50738 | −0.451074 | −0.225537 | − | 0.974235i | \(-0.572414\pi\) | ||||
−0.225537 | + | 0.974235i | \(0.572414\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.77225 | 0.106102 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.43769 | 0.145421 | 0.0727103 | − | 0.997353i | \(-0.476835\pi\) | ||||
0.0727103 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.527864 | −0.0311588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.3607 | 2.31533 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.7870 | 0.984071 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6546 | 1.14823 | 0.574116 | − | 0.818774i | \(-0.305346\pi\) | ||||
0.574116 | + | 0.818774i | \(0.305346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.3897 | 1.47326 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.4268 | 1.23914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.05573 | −0.118490 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.70820 | 0.270479 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3820 | 0.763749 | 0.381875 | − | 0.924214i | \(-0.375279\pi\) | ||||
0.381875 | + | 0.924214i | \(0.375279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.9443 | −0.736374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.09531 | 0.0621094 | 0.0310547 | − | 0.999518i | \(-0.490113\pi\) | ||||
0.0310547 | + | 0.999518i | \(0.490113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.5593 | −1.04903 | −0.524515 | − | 0.851401i | \(-0.675754\pi\) | ||||
−0.524515 | + | 0.851401i | \(0.675754\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.6174 | −1.32649 | −0.663244 | − | 0.748404i | \(-0.730821\pi\) | ||||
−0.663244 | + | 0.748404i | \(0.730821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46.8165 | −2.62122 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.2705 | −1.52209 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 56.3607 | 3.13599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.0902 | 0.834488 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.23607 | 0.343806 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.60269 | −0.472846 | −0.236423 | − | 0.971650i | \(-0.575975\pi\) | ||||
−0.236423 | + | 0.971650i | \(0.575975\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.09531 | 0.0600227 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4268 | −1.16719 | −0.583596 | − | 0.812044i | \(-0.698355\pi\) | ||||
−0.583596 | + | 0.812044i | \(0.698355\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.50738 | −0.407745 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5279 | −1.16580 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.41641 | −0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.3262 | 1.19854 | 0.599268 | − | 0.800549i | \(-0.295459\pi\) | ||||
0.599268 | + | 0.800549i | \(0.295459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6180 | −0.568370 | −0.284185 | − | 0.958769i | \(-0.591723\pi\) | ||||
−0.284185 | + | 0.958769i | \(0.591723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.3897 | 1.35520 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3749 | 0.552202 | 0.276101 | − | 0.961129i | \(-0.410958\pi\) | ||||
0.276101 | + | 0.961129i | \(0.410958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.50738 | −0.397332 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.18431 | −0.431952 | −0.215976 | − | 0.976399i | \(-0.569293\pi\) | ||||
−0.215976 | + | 0.976399i | \(0.569293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.3607 | 1.96635 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.0344 | −0.894076 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9787 | −1.72147 | −0.860737 | − | 0.509049i | \(-0.829997\pi\) | ||||
−0.860737 | + | 0.509049i | \(0.829997\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.326238 | 0.0169833 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.73512 | −0.297753 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.1619 | 1.40639 | 0.703196 | − | 0.710996i | \(-0.251756\pi\) | ||||
0.703196 | + | 0.710996i | \(0.251756\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.8165 | −2.41117 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.73512 | 0.294594 | 0.147297 | − | 0.989092i | \(-0.452943\pi\) | ||||
0.147297 | + | 0.989092i | \(0.452943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.38197 | −0.173263 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.0902 | −1.74193 | −0.870963 | − | 0.491348i | \(-0.836504\pi\) | ||||
−0.870963 | + | 0.491348i | \(0.836504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.27051 | 0.0645836 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.14590 | 0.260907 | 0.130454 | − | 0.991454i | \(-0.458357\pi\) | ||||
0.130454 | + | 0.991454i | \(0.458357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.6693 | 1.75330 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.6546 | −0.991442 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.1101 | 0.808541 | 0.404270 | − | 0.914640i | \(-0.367525\pi\) | ||||
0.404270 | + | 0.914640i | \(0.367525\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.50738 | −0.375839 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0902 | 0.553817 | 0.276908 | − | 0.960896i | \(-0.410690\pi\) | ||||
0.276908 | + | 0.960896i | \(0.410690\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.5279 | −1.07238 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.3050 | −0.659502 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5066 | 1.50845 | 0.754227 | − | 0.656614i | \(-0.228012\pi\) | ||||
0.754227 | + | 0.656614i | \(0.228012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.1472 | −0.599177 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.41206 | −0.315517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.6546 | −0.962488 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.5740 | 1.64020 | 0.820099 | − | 0.572222i | \(-0.193918\pi\) | ||||
0.820099 | + | 0.572222i | \(0.193918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.61803 | −0.176332 | −0.0881661 | − | 0.996106i | \(-0.528101\pi\) | ||||
−0.0881661 | + | 0.996106i | \(0.528101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.85410 | −0.187393 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.85410 | 0.234906 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −34.8328 | −1.68174 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.41206 | 0.308858 | 0.154429 | − | 0.988004i | \(-0.450646\pi\) | ||||
0.154429 | + | 0.988004i | \(0.450646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.86756 | 0.137806 | 0.0689031 | − | 0.997623i | \(-0.478050\pi\) | ||||
0.0689031 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.6693 | 1.65846 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5221 | 1.07492 | 0.537461 | − | 0.843288i | \(-0.319383\pi\) | ||||
0.537461 | + | 0.843288i | \(0.319383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.52786 | 0.120374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.7984 | 1.55830 | 0.779149 | − | 0.626839i | \(-0.215652\pi\) | ||||
0.779149 | + | 0.626839i | \(0.215652\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.6525 | 1.21332 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.4721 | −0.588596 | −0.294298 | − | 0.955714i | \(-0.595086\pi\) | ||||
−0.294298 | + | 0.955714i | \(0.595086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.96287 | −0.186604 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.3749 | −0.487457 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.8389 | 1.30225 | 0.651124 | − | 0.758971i | \(-0.274298\pi\) | ||||
0.651124 | + | 0.758971i | \(0.274298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 41.0814 | 1.91751 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.5066 | 1.51398 | 0.756991 | − | 0.653425i | \(-0.226669\pi\) | ||||
0.756991 | + | 0.653425i | \(0.226669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7426 | −0.731623 | −0.365811 | − | 0.930689i | \(-0.619208\pi\) | ||||
−0.365811 | + | 0.930689i | \(0.619208\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4508 | −1.36282 | −0.681411 | − | 0.731901i | \(-0.738634\pi\) | ||||
−0.681411 | + | 0.731901i | \(0.738634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.944272 | 0.0436024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.1619 | −1.25156 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.4331 | −0.709616 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.54450 | 0.162292 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1472 | 0.555019 | 0.277510 | − | 0.960723i | \(-0.410491\pi\) | ||||
0.277510 | + | 0.960723i | \(0.410491\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3050 | −0.606654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.61803 | −0.210128 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.27051 | 0.284144 | 0.142072 | − | 0.989856i | \(-0.454624\pi\) | ||||
0.142072 | + | 0.989856i | \(0.454624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.7082 | 1.11734 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.5369 | −1.69402 | −0.847008 | − | 0.531581i | \(-0.821598\pi\) | ||||
−0.847008 | + | 0.531581i | \(0.821598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −75.7507 | −3.41164 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.63981 | 0.208124 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.5369 | −1.68038 | −0.840191 | − | 0.542291i | \(-0.817557\pi\) | ||||
−0.840191 | + | 0.542291i | \(0.817557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0344 | −0.895073 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1591 | 1.38931 | 0.694657 | − | 0.719341i | \(-0.255556\pi\) | ||||
0.694657 | + | 0.719341i | \(0.255556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.7984 | −0.612807 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.3050 | −0.855677 | −0.427838 | − | 0.903855i | \(-0.640725\pi\) | ||||
−0.427838 | + | 0.903855i | \(0.640725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.41206 | 0.283653 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 41.0814 | 1.81379 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.8165 | 2.05899 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.4416 | 1.59961 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.09017 | −0.179194 | −0.0895968 | − | 0.995978i | \(-0.528558\pi\) | ||||
−0.0895968 | + | 0.995978i | \(0.528558\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.9787 | 1.48579 | 0.742893 | − | 0.669411i | \(-0.233453\pi\) | ||||
0.742893 | + | 0.669411i | \(0.233453\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.8328 | −1.51734 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67376 | −0.0727723 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.96287 | 0.171974 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.96287 | −0.171651 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.7870 | 0.724413 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.7064 | −1.32262 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.43769 | −0.319771 | −0.159886 | − | 0.987136i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987136i | \(0.551113\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.0344 | 0.688104 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0902 | −1.24381 | −0.621903 | − | 0.783094i | \(-0.713640\pi\) | ||||
−0.621903 | + | 0.783094i | \(0.713640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.00000 | −0.128037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −75.7507 | −3.22709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.77225 | 0.0753638 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.3463 | −1.49767 | −0.748834 | − | 0.662757i | \(-0.769386\pi\) | ||||
−0.748834 | + | 0.662757i | \(0.769386\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4331 | −0.652751 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −56.3607 | −2.37955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.94427 | −0.376956 | −0.188478 | − | 0.982077i | \(-0.560355\pi\) | ||||
−0.188478 | + | 0.982077i | \(0.560355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.76393 | −0.200066 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.90983 | 0.163909 | 0.0819543 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819543 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.4850 | 1.10836 | 0.554181 | − | 0.832396i | \(-0.313031\pi\) | ||||
0.554181 | + | 0.832396i | \(0.313031\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.4416 | 1.52237 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4702 | 0.477513 | 0.238756 | − | 0.971080i | \(-0.423260\pi\) | ||||
0.238756 | + | 0.971080i | \(0.423260\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.63981 | 0.192824 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.67376 | −0.193900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.0557 | −1.78319 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7771 | 1.47668 | 0.738339 | − | 0.674430i | \(-0.235610\pi\) | ||||
0.738339 | + | 0.674430i | \(0.235610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.8328 | −1.43526 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.1472 | 0.499669 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.6174 | 0.969852 | 0.484926 | − | 0.874555i | \(-0.338847\pi\) | ||||
0.484926 | + | 0.874555i | \(0.338847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.86756 | −0.117362 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.9713 | −1.02030 | −0.510150 | − | 0.860085i | \(-0.670410\pi\) | ||||
−0.510150 | + | 0.860085i | \(0.670410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.5623 | 1.08350 | 0.541750 | − | 0.840540i | \(-0.317762\pi\) | ||||
0.541750 | + | 0.840540i | \(0.317762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.583592 | −0.0237657 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.3607 | −1.63819 | −0.819095 | − | 0.573658i | \(-0.805524\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0902 | 0.408874 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.8165 | 1.89399 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.27963 | 0.374801 | 0.187400 | − | 0.982284i | \(-0.439994\pi\) | ||||
0.187400 | + | 0.982284i | \(0.439994\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7870 | 0.675819 | 0.337910 | − | 0.941179i | \(-0.390280\pi\) | ||||
0.337910 | + | 0.941179i | \(0.390280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.0666 | −1.04771 | −0.523853 | − | 0.851809i | \(-0.675506\pi\) | ||||
−0.523853 | + | 0.851809i | \(0.675506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.2705 | 1.01407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.09017 | 0.243998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −56.3607 | −2.25083 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.5279 | −0.858372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.63981 | 0.184708 | 0.0923540 | − | 0.995726i | \(-0.470561\pi\) | ||||
0.0923540 | + | 0.995726i | \(0.470561\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.6693 | 1.37798 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.7064 | −1.21663 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.86756 | −0.113439 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.72949 | 0.305297 | 0.152648 | − | 0.988281i | \(-0.451220\pi\) | ||||
0.152648 | + | 0.988281i | \(0.451220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.90983 | 0.272497 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9443 | 0.823404 | 0.411702 | − | 0.911318i | \(-0.364934\pi\) | ||||
0.411702 | + | 0.911318i | \(0.364934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.1378 | −1.88957 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.63981 | 0.181849 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.1619 | 1.06293 | 0.531464 | − | 0.847081i | \(-0.321642\pi\) | ||||
0.531464 | + | 0.847081i | \(0.321642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.96287 | −0.154606 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.0519 | −0.430520 | −0.215260 | − | 0.976557i | \(-0.569060\pi\) | ||||
−0.215260 | + | 0.976557i | \(0.569060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.43769 | 0.289293 | 0.144646 | − | 0.989483i | \(-0.453796\pi\) | ||||
0.144646 | + | 0.989483i | \(0.453796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −56.3607 | −2.18887 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.5967 | −1.80423 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.32624 | −0.167262 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.4416 | 1.40681 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1991 | −0.894258 | −0.447129 | − | 0.894469i | \(-0.647554\pi\) | ||||
−0.447129 | + | 0.894469i | \(0.647554\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.73512 | 0.220419 | 0.110209 | − | 0.993908i | \(-0.464848\pi\) | ||||
0.110209 | + | 0.993908i | \(0.464848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.41206 | −0.246072 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.23607 | 0.238967 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.6869 | 0.447187 | 0.223594 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223594 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.6525 | 0.597179 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.0557 | −1.64029 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6174 | 0.898450 | 0.449225 | − | 0.893419i | \(-0.351700\pi\) | ||||
0.449225 | + | 0.893419i | \(0.351700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.09531 | −0.0416074 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.41206 | −0.242874 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1472 | −0.459449 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.05573 | 0.342030 | 0.171015 | − | 0.985268i | \(-0.445295\pi\) | ||||
0.171015 | + | 0.985268i | \(0.445295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.5279 | −0.811939 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.79837 | −0.0676348 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.6180 | −1.45033 | −0.725165 | − | 0.688575i | \(-0.758237\pi\) | ||||
−0.725165 | + | 0.688575i | \(0.758237\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.09531 | −0.0410774 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.4268 | −0.802440 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.63981 | −0.173277 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.9118 | 1.78681 | 0.893405 | − | 0.449253i | \(-0.148310\pi\) | ||||
0.893405 | + | 0.449253i | \(0.148310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | 0.184134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.00000 | 0.334714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.0902 | −1.70939 | −0.854695 | − | 0.519131i | \(-0.826256\pi\) | ||||
−0.854695 | + | 0.519131i | \(0.826256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9713 | −0.923597 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.9342 | −1.06871 | −0.534354 | − | 0.845261i | \(-0.679445\pi\) | ||||
−0.534354 | + | 0.845261i | \(0.679445\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.08900 | 0.261127 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.676940 | 0.0249016 | 0.0124508 | − | 0.999922i | \(-0.496037\pi\) | ||||
0.0124508 | + | 0.999922i | \(0.496037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −56.3607 | −2.07046 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.8885 | 1.68349 | 0.841744 | − | 0.539877i | \(-0.181529\pi\) | ||||
0.841744 | + | 0.539877i | \(0.181529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.88854 | 0.105686 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4164 | 0.380607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.676940 | −0.0247019 | −0.0123509 | − | 0.999924i | \(-0.503932\pi\) | ||||
−0.0123509 | + | 0.999924i | \(0.503932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.5740 | −1.22350 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.9489 | −1.59735 | −0.798676 | − | 0.601762i | \(-0.794466\pi\) | ||||
−0.798676 | + | 0.601762i | \(0.794466\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.6693 | −1.25842 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.85410 | −0.212211 | −0.106106 | − | 0.994355i | \(-0.533838\pi\) | ||||
−0.106106 | + | 0.994355i | \(0.533838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.76393 | −0.208668 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.1378 | −1.73815 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.79837 | −0.353338 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.27963 | −0.334198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.1038 | −0.795017 | −0.397508 | − | 0.917599i | \(-0.630125\pi\) | ||||
−0.397508 | + | 0.917599i | \(0.630125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.86756 | 0.102873 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.41206 | −0.229736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.8328 | 1.24642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.2148 | −1.97322 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4377 | −0.479002 | −0.239501 | − | 0.970896i | \(-0.576984\pi\) | ||||
−0.239501 | + | 0.970896i | \(0.576984\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.32624 | −0.154018 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.86756 | 0.101959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.4416 | 1.29408 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.44919 | 0.0867548 | 0.0433774 | − | 0.999059i | \(-0.486188\pi\) | ||||
0.0433774 | + | 0.999059i | \(0.486188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.7507 | 2.67987 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.76393 | −0.132992 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.1378 | 1.69874 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.1803 | −0.710382 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.61803 | −0.162361 | −0.0811807 | − | 0.996699i | \(-0.525869\pi\) | ||||
−0.0811807 | + | 0.996699i | \(0.525869\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.44919 | 0.0860027 | 0.0430014 | − | 0.999075i | \(-0.486308\pi\) | ||||
0.0430014 | + | 0.999075i | \(0.486308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.0148 | 0.526590 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9713 | −0.873636 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.09531 | −0.0382733 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.43769 | 0.154877 | 0.0774383 | − | 0.996997i | \(-0.475326\pi\) | ||||
0.0774383 | + | 0.996997i | \(0.475326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.2492 | 0.914990 | 0.457495 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457495 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.83282 | −0.237600 | −0.118800 | − | 0.992918i | \(-0.537905\pi\) | ||||
−0.118800 | + | 0.992918i | \(0.537905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.14590 | 0.0397987 | 0.0198993 | − | 0.999802i | \(-0.493665\pi\) | ||||
0.0198993 | + | 0.999802i | \(0.493665\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1472 | 0.421381 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.6841 | −1.72145 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.3897 | −0.877596 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.3526 | −1.01336 | −0.506681 | − | 0.862133i | \(-0.669128\pi\) | ||||
−0.506681 | + | 0.862133i | \(0.669128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 72.8115 | 2.51074 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.94427 | −0.135848 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.50658 | 0.223569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.47214 | 0.222123 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.2425 | −0.453947 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.5740 | −1.14955 | −0.574776 | − | 0.818311i | \(-0.694911\pi\) | ||||
−0.574776 | + | 0.818311i | \(0.694911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.83044 | 0.233323 | 0.116662 | − | 0.993172i | \(-0.462781\pi\) | ||||
0.116662 | + | 0.993172i | \(0.462781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.0148 | −0.512297 | −0.256148 | − | 0.966637i | \(-0.582454\pi\) | ||||
−0.256148 | + | 0.966637i | \(0.582454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.854102 | 0.0291077 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5066 | 0.766133 | 0.383066 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383066 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −63.6869 | −2.16292 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3050 | 0.451340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.08900 | 0.240202 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.96287 | 0.134123 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.41206 | 0.216520 | 0.108260 | − | 0.994123i | \(-0.465472\pi\) | ||||
0.108260 | + | 0.994123i | \(0.465472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.8018 | −1.07265 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.9787 | −0.572027 | −0.286014 | − | 0.958226i | \(-0.592330\pi\) | ||||
−0.286014 | + | 0.958226i | \(0.592330\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.1459 | −1.08180 | −0.540898 | − | 0.841088i | \(-0.681915\pi\) | ||||
−0.540898 | + | 0.841088i | \(0.681915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.5623 | −0.858298 | −0.429149 | − | 0.903234i | \(-0.641187\pi\) | ||||
−0.429149 | + | 0.903234i | \(0.641187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.29180 | 0.0433254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.7646 | −1.19816 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 75.7507 | 2.53490 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.6693 | −1.15757 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.8165 | 1.56142 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.6656 | −2.32090 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.32624 | 0.110690 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.20163 | 0.106308 | 0.0531541 | − | 0.998586i | \(-0.483073\pi\) | ||||
0.0531541 | + | 0.998586i | \(0.483073\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.11146 | 0.0368647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.6693 | −1.14865 | −0.574323 | − | 0.818629i | \(-0.694735\pi\) | ||||
−0.574323 | + | 0.818629i | \(0.694735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.0877 | −1.16123 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50738 | 0.247915 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9776 | 0.626014 | 0.313007 | − | 0.949751i | \(-0.398664\pi\) | ||||
0.313007 | + | 0.949751i | \(0.398664\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.6525 | −0.713473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.8328 | 1.14654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.05573 | −0.100363 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0344 | 0.919780 | 0.459890 | − | 0.887976i | \(-0.347889\pi\) | ||||
0.459890 | + | 0.887976i | \(0.347889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.6841 | −1.62833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.77225 | −0.0580209 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5593 | −0.606304 | −0.303152 | − | 0.952942i | \(-0.598039\pi\) | ||||
−0.303152 | + | 0.952942i | \(0.598039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.0295 | 0.979976 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.8885 | 1.16993 | 0.584967 | − | 0.811057i | \(-0.301108\pi\) | ||||
0.584967 | + | 0.811057i | \(0.301108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.94427 | −0.128443 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.72949 | 0.121192 | 0.0605961 | − | 0.998162i | \(-0.480700\pi\) | ||||
0.0605961 | + | 0.998162i | \(0.480700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.1378 | 1.56262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.2138 | 1.23917 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.2054 | 0.557337 | 0.278668 | − | 0.960387i | \(-0.410107\pi\) | ||||
0.278668 | + | 0.960387i | \(0.410107\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 75.7507 | 2.44867 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.63981 | 0.149827 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.47214 | −0.305553 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.43769 | −0.207452 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.3951 | −1.00960 | −0.504800 | − | 0.863237i | \(-0.668434\pi\) | ||||
−0.504800 | + | 0.863237i | \(0.668434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −91.1935 | −2.92956 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1472 | −0.389822 | −0.194911 | − | 0.980821i | \(-0.562442\pi\) | ||||
−0.194911 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50738 | 0.240675 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.0814 | 1.31431 | 0.657155 | − | 0.753756i | \(-0.271760\pi\) | ||||
0.657155 | + | 0.753756i | \(0.271760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.7212 | 1.46126 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.56231 | 0.113736 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4164 | 0.619287 | 0.309644 | − | 0.950853i | \(-0.399790\pi\) | ||||
0.309644 | + | 0.950853i | \(0.399790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.0902 | −0.321174 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.3607 | −0.488441 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.1333 | −1.65607 | −0.828034 | − | 0.560678i | \(-0.810540\pi\) | ||||
−0.828034 | + | 0.560678i | \(0.810540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9194 | 0.441720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.2572 | −0.894916 | −0.447458 | − | 0.894305i | \(-0.647671\pi\) | ||||
−0.447458 | + | 0.894305i | \(0.647671\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.6917 | −0.496463 |
(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 | 4000.2.a.c.1.2 | yes | 4 | |
4.3 | odd | 2 | 4000.2.a.h.1.3 | yes | 4 | ||
5.2 | odd | 4 | 4000.2.c.e.1249.8 | 8 | |||
5.3 | odd | 4 | 4000.2.c.e.1249.2 | 8 | |||
5.4 | even | 2 | 4000.2.a.h.1.4 | yes | 4 | ||
8.3 | odd | 2 | 8000.2.a.bc.1.2 | 4 | |||
8.5 | even | 2 | 8000.2.a.bp.1.3 | 4 | |||
20.3 | even | 4 | 4000.2.c.e.1249.7 | 8 | |||
20.7 | even | 4 | 4000.2.c.e.1249.1 | 8 | |||
20.19 | odd | 2 | inner | 4000.2.a.c.1.1 | ✓ | 4 | |
40.19 | odd | 2 | 8000.2.a.bp.1.4 | 4 | |||
40.29 | even | 2 | 8000.2.a.bc.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4000.2.a.c.1.1 | ✓ | 4 | 20.19 | odd | 2 | inner | |
4000.2.a.c.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
4000.2.a.h.1.3 | yes | 4 | 4.3 | odd | 2 | ||
4000.2.a.h.1.4 | yes | 4 | 5.4 | even | 2 | ||
4000.2.c.e.1249.1 | 8 | 20.7 | even | 4 | |||
4000.2.c.e.1249.2 | 8 | 5.3 | odd | 4 | |||
4000.2.c.e.1249.7 | 8 | 20.3 | even | 4 | |||
4000.2.c.e.1249.8 | 8 | 5.2 | odd | 4 | |||
8000.2.a.bc.1.1 | 4 | 40.29 | even | 2 | |||
8000.2.a.bc.1.2 | 4 | 8.3 | odd | 2 | |||
8000.2.a.bp.1.3 | 4 | 8.5 | even | 2 | |||
8000.2.a.bp.1.4 | 4 | 40.19 | odd | 2 |