Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,2,Mod(1,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, 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("2008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.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: | \(16.0339607259\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 2008.1 |
$q$-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 | ||||||||
\(3\) | −0.347951 | −0.200890 | −0.100445 | − | 0.994943i | \(-0.532027\pi\) | ||||
−0.100445 | + | 0.994943i | \(0.532027\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.66668 | −0.745362 | −0.372681 | − | 0.927959i | \(-0.621561\pi\) | ||||
−0.372681 | + | 0.927959i | \(0.621561\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.92094 | 1.48198 | 0.740988 | − | 0.671518i | \(-0.234358\pi\) | ||||
0.740988 | + | 0.671518i | \(0.234358\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87893 | −0.959643 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.50416 | 1.96108 | 0.980540 | − | 0.196321i | \(-0.0628995\pi\) | ||||
0.980540 | + | 0.196321i | \(0.0628995\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.17112 | −0.879511 | −0.439756 | − | 0.898117i | \(-0.644935\pi\) | ||||
−0.439756 | + | 0.898117i | \(0.644935\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.579924 | 0.149736 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56558 | 0.864781 | 0.432390 | − | 0.901687i | \(-0.357670\pi\) | ||||
0.432390 | + | 0.901687i | \(0.357670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.45462 | 1.93962 | 0.969812 | − | 0.243855i | \(-0.0784121\pi\) | ||||
0.969812 | + | 0.243855i | \(0.0784121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.36430 | −0.297714 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47235 | −0.932550 | −0.466275 | − | 0.884640i | \(-0.654404\pi\) | ||||
−0.466275 | + | 0.884640i | \(0.654404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.22218 | −0.444435 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.04558 | 0.393672 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.13094 | −1.69557 | −0.847787 | − | 0.530337i | \(-0.822065\pi\) | ||||
−0.847787 | + | 0.530337i | \(0.822065\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.27043 | −0.766993 | −0.383496 | − | 0.923542i | \(-0.625280\pi\) | ||||
−0.383496 | + | 0.923542i | \(0.625280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.26313 | −0.393961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.53495 | −1.10461 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.328479 | 0.0540016 | 0.0270008 | − | 0.999635i | \(-0.491404\pi\) | ||||
0.0270008 | + | 0.999635i | \(0.491404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10340 | 0.176685 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.75568 | 1.36741 | 0.683704 | − | 0.729760i | \(-0.260368\pi\) | ||||
0.683704 | + | 0.729760i | \(0.260368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.27318 | −0.651653 | −0.325827 | − | 0.945430i | \(-0.605643\pi\) | ||||
−0.325827 | + | 0.945430i | \(0.605643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.79826 | 0.715282 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.78246 | 0.843458 | 0.421729 | − | 0.906722i | \(-0.361423\pi\) | ||||
0.421729 | + | 0.906722i | \(0.361423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.37376 | 1.19625 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.24065 | −0.173726 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1862 | 1.81127 | 0.905635 | − | 0.424058i | \(-0.139395\pi\) | ||||
0.905635 | + | 0.424058i | \(0.139395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.8404 | −1.46171 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.94180 | −0.389650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.76862 | 0.881199 | 0.440599 | − | 0.897704i | \(-0.354766\pi\) | ||||
0.440599 | + | 0.897704i | \(0.354766\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.71677 | −1.24410 | −0.622052 | − | 0.782976i | \(-0.713701\pi\) | ||||
−0.622052 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.2881 | −1.42217 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.28525 | 0.655554 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0508 | 1.35007 | 0.675035 | − | 0.737786i | \(-0.264129\pi\) | ||||
0.675035 | + | 0.737786i | \(0.264129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.55616 | 0.187340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3491 | 1.58425 | 0.792126 | − | 0.610357i | \(-0.208974\pi\) | ||||
0.792126 | + | 0.610357i | \(0.208974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0593 | 1.52847 | 0.764235 | − | 0.644938i | \(-0.223117\pi\) | ||||
0.764235 | + | 0.644938i | \(0.223117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.773209 | 0.0892825 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.5024 | 2.90627 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.45561 | 0.501295 | 0.250648 | − | 0.968078i | \(-0.419356\pi\) | ||||
0.250648 | + | 0.968078i | \(0.419356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.92503 | 0.880559 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.31224 | −0.802623 | −0.401312 | − | 0.915942i | \(-0.631446\pi\) | ||||
−0.401312 | + | 0.915942i | \(0.631446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.94269 | −0.644575 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.17712 | 0.340623 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.686662 | 0.0727860 | 0.0363930 | − | 0.999338i | \(-0.488413\pi\) | ||||
0.0363930 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4338 | −1.30341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.48590 | 0.154081 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.0912 | −1.44572 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.21983 | −0.733062 | −0.366531 | − | 0.930406i | \(-0.619455\pi\) | ||||
−0.366531 | + | 0.930406i | \(0.619455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.7250 | −1.88194 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.30192 | −0.627064 | −0.313532 | − | 0.949578i | \(-0.601512\pi\) | ||||
−0.313532 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.81097 | 0.572572 | 0.286286 | − | 0.958144i | \(-0.407579\pi\) | ||||
0.286286 | + | 0.958144i | \(0.407579\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.27385 | 0.221905 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.64340 | −0.255547 | −0.127773 | − | 0.991803i | \(-0.540783\pi\) | ||||
−0.127773 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7569 | −1.12611 | −0.563054 | − | 0.826420i | \(-0.690374\pi\) | ||||
−0.563054 | + | 0.826420i | \(0.690374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.114295 | −0.0108484 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.65054 | −0.625630 | −0.312815 | − | 0.949814i | \(-0.601272\pi\) | ||||
−0.312815 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.45398 | 0.695087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.12944 | 0.844017 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.9804 | 1.28158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.3042 | 2.84583 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.04655 | −0.274698 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0371 | 1.07663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.19210 | 0.105782 | 0.0528909 | − | 0.998600i | \(-0.483156\pi\) | ||||
0.0528909 | + | 0.998600i | \(0.483156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.48686 | 0.130910 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2112 | 0.892155 | 0.446078 | − | 0.894994i | \(-0.352821\pi\) | ||||
0.446078 | + | 0.894994i | \(0.352821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 33.1501 | 2.87447 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.40933 | −0.293428 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1759 | 1.55287 | 0.776436 | − | 0.630196i | \(-0.217025\pi\) | ||||
0.776436 | + | 0.630196i | \(0.217025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5710 | −1.23590 | −0.617948 | − | 0.786219i | \(-0.712036\pi\) | ||||
−0.617948 | + | 0.786219i | \(0.712036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.01201 | −0.169442 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.6255 | −1.72479 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2184 | 1.26382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.91366 | −0.240315 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.11426 | −0.582823 | −0.291411 | − | 0.956598i | \(-0.594125\pi\) | ||||
−0.291411 | + | 0.956598i | \(0.594125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.04215 | 0.735840 | 0.367920 | − | 0.929857i | \(-0.380070\pi\) | ||||
0.367920 | + | 0.929857i | \(0.380070\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.2651 | −0.829881 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.11745 | 0.571687 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3571 | 0.826584 | 0.413292 | − | 0.910599i | \(-0.364379\pi\) | ||||
0.413292 | + | 0.910599i | \(0.364379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.58817 | −0.363866 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.5358 | −1.38202 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.36738 | 0.185427 | 0.0927137 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927137 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.77192 | 0.293643 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5789 | 1.51506 | 0.757529 | − | 0.652801i | \(-0.226406\pi\) | ||||
0.757529 | + | 0.652801i | \(0.226406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.94398 | −0.226460 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.3403 | −1.86135 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.03914 | −0.155033 | −0.0775166 | − | 0.996991i | \(-0.524699\pi\) | ||||
−0.0775166 | + | 0.996991i | \(0.524699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.71302 | −0.658642 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.35515 | −0.177024 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.6524 | 1.16992 | 0.584958 | − | 0.811063i | \(-0.301111\pi\) | ||||
0.584958 | + | 0.811063i | \(0.301111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9573 | −1.26043 | −0.630214 | − | 0.776421i | \(-0.717033\pi\) | ||||
−0.630214 | + | 0.776421i | \(0.717033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.38096 | 0.249928 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.547470 | −0.0402508 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.1911 | 1.69590 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.02060 | 0.583413 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6370 | 1.05910 | 0.529550 | − | 0.848279i | \(-0.322361\pi\) | ||||
0.529550 | + | 0.848279i | \(0.322361\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2700 | −1.17114 | −0.585571 | − | 0.810621i | \(-0.699130\pi\) | ||||
−0.585571 | + | 0.810621i | \(0.699130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.83901 | −0.131694 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.90922 | −0.563509 | −0.281754 | − | 0.959487i | \(-0.590916\pi\) | ||||
−0.281754 | + | 0.959487i | \(0.590916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5711 | 1.03292 | 0.516458 | − | 0.856313i | \(-0.327250\pi\) | ||||
0.516458 | + | 0.856313i | \(0.327250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.84514 | −0.271215 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −35.8019 | −2.51280 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.5929 | −1.01921 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8756 | 0.894915 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 54.9903 | 3.80376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8646 | −1.64291 | −0.821455 | − | 0.570274i | \(-0.806837\pi\) | ||||
−0.821455 | + | 0.570274i | \(0.806837\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.64485 | −0.318260 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.12202 | 0.485718 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.7441 | −1.13666 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.54398 | −0.307054 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.3069 | −0.760584 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.7426 | 0.786342 | 0.393171 | − | 0.919465i | \(-0.371378\pi\) | ||||
0.393171 | + | 0.919465i | \(0.371378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.39749 | 0.426499 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6612 | −0.773980 | −0.386990 | − | 0.922084i | \(-0.626485\pi\) | ||||
−0.386990 | + | 0.922084i | \(0.626485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.59660 | −0.435916 | −0.217958 | − | 0.975958i | \(-0.569940\pi\) | ||||
−0.217958 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.87360 | −0.583840 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.263500 | 0.0172624 | 0.00863122 | − | 0.999963i | \(-0.497253\pi\) | ||||
0.00863122 | + | 0.999963i | \(0.497253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.63751 | −0.628682 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.55033 | −0.100705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.24923 | 0.404229 | 0.202115 | − | 0.979362i | \(-0.435219\pi\) | ||||
0.202115 | + | 0.979362i | \(0.435219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.05529 | −0.518887 | −0.259443 | − | 0.965758i | \(-0.583539\pi\) | ||||
−0.259443 | + | 0.965758i | \(0.583539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.89427 | −0.570567 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9564 | −0.891641 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.8106 | −1.70592 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.54430 | 0.161239 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.0889 | −1.82880 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.06777 | 0.129488 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.1938 | 0.698247 | 0.349124 | − | 0.937077i | \(-0.386479\pi\) | ||||
0.349124 | + | 0.937077i | \(0.386479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.28795 | 0.0800291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.2873 | 1.62715 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.38663 | −0.455479 | −0.227740 | − | 0.973722i | \(-0.573134\pi\) | ||||
−0.227740 | + | 0.973722i | \(0.573134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.9773 | −1.35005 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.238925 | −0.0146220 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.1530 | −1.16778 | −0.583890 | − | 0.811833i | \(-0.698470\pi\) | ||||
−0.583890 | + | 0.811833i | \(0.698470\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7960 | 1.26327 | 0.631633 | − | 0.775268i | \(-0.282385\pi\) | ||||
0.631633 | + | 0.775268i | \(0.282385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.32635 | 0.261843 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4534 | −0.871573 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.4617 | 1.04917 | 0.524585 | − | 0.851358i | \(-0.324220\pi\) | ||||
0.524585 | + | 0.851358i | \(0.324220\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.2943 | 0.736039 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1823 | −1.26363 | −0.631816 | − | 0.775118i | \(-0.717690\pi\) | ||||
−0.631816 | + | 0.775118i | \(0.717690\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9193 | −1.00575 | −0.502873 | − | 0.864360i | \(-0.667724\pi\) | ||||
−0.502873 | + | 0.864360i | \(0.667724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.90304 | 0.290431 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.3305 | 2.02646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.28663 | −0.252154 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.51215 | 0.147265 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.4063 | 1.48425 | 0.742126 | − | 0.670260i | \(-0.233817\pi\) | ||||
0.742126 | + | 0.670260i | \(0.233817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2811 | −0.656812 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.3048 | 0.772023 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.1824 | 0.820188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.7549 | −0.965735 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.19276 | 0.125971 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1947 | 0.927308 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7326 | −0.612542 | −0.306271 | − | 0.951944i | \(-0.599081\pi\) | ||||
−0.306271 | + | 0.951944i | \(0.599081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.02193 | −0.115024 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.4659 | −1.16052 | −0.580258 | − | 0.814433i | \(-0.697048\pi\) | ||||
−0.580258 | + | 0.814433i | \(0.697048\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4162 | −1.04095 | −0.520474 | − | 0.853878i | \(-0.674245\pi\) | ||||
−0.520474 | + | 0.853878i | \(0.674245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.8137 | 1.06003 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.7775 | −1.05465 | −0.527324 | − | 0.849665i | \(-0.676804\pi\) | ||||
−0.527324 | + | 0.849665i | \(0.676804\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −59.3892 | −3.32515 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.919774 | 0.0513368 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.1457 | 1.67735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.04679 | 0.390886 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.09084 | 0.226224 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.6727 | 1.24998 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4697 | −0.795325 | −0.397663 | − | 0.917532i | \(-0.630179\pi\) | ||||
−0.397663 | + | 0.917532i | \(0.630179\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.945668 | −0.0518223 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.4181 | −1.00629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4434 | 0.732308 | 0.366154 | − | 0.930554i | \(-0.380674\pi\) | ||||
0.366154 | + | 0.930554i | \(0.380674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.31406 | 0.125683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.7756 | −1.50413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.38644 | 0.290841 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.59362 | −0.139636 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.0973 | 1.23993 | 0.619965 | − | 0.784629i | \(-0.287147\pi\) | ||||
0.619965 | + | 0.784629i | \(0.287147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.67019 | −0.142932 | −0.0714661 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714661 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.48679 | −0.346239 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.94957 | −0.103765 | −0.0518826 | − | 0.998653i | \(-0.516522\pi\) | ||||
−0.0518826 | + | 0.998653i | \(0.516522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.2488 | −1.18084 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.86451 | −0.257457 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.9417 | 1.42193 | 0.710964 | − | 0.703228i | \(-0.248259\pi\) | ||||
0.710964 | + | 0.703228i | \(0.248259\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.4806 | 2.76214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8923 | −0.571699 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.7656 | −1.13926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.6009 | −1.64956 | −0.824778 | − | 0.565457i | \(-0.808700\pi\) | ||||
−0.824778 | + | 0.565457i | \(0.808700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.2070 | −1.31222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 51.7025 | 2.68426 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.09475 | 0.470908 | 0.235454 | − | 0.971885i | \(-0.424342\pi\) | ||||
0.235454 | + | 0.971885i | \(0.424342\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.18831 | −0.216283 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.9553 | 1.49128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.83464 | −0.453805 | −0.226903 | − | 0.973917i | \(-0.572860\pi\) | ||||
−0.226903 | + | 0.973917i | \(0.572860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.414793 | −0.0212505 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.2103 | −1.03270 | −0.516350 | − | 0.856378i | \(-0.672710\pi\) | ||||
−0.516350 | + | 0.856378i | \(0.672710\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −42.5044 | −2.16623 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.3022 | 0.625355 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.0488 | −0.965811 | −0.482906 | − | 0.875672i | \(-0.660419\pi\) | ||||
−0.482906 | + | 0.875672i | \(0.660419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.9465 | −0.806451 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.55299 | −0.179225 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.42608 | −0.373646 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.45788 | −0.173546 | −0.0867729 | − | 0.996228i | \(-0.527655\pi\) | ||||
−0.0867729 | + | 0.996228i | \(0.527655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.5346 | −0.577453 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9333 | 0.695793 | 0.347897 | − | 0.937533i | \(-0.386896\pi\) | ||||
0.347897 | + | 0.937533i | \(0.386896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5421 | 0.674579 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2085 | −0.656335 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.13648 | 0.105901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4690 | 0.814340 | 0.407170 | − | 0.913352i | \(-0.366516\pi\) | ||||
0.407170 | + | 0.913352i | \(0.366516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.32433 | −0.311956 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.5393 | 1.30592 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.1872 | 0.598245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.06999 | 0.248279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8528 | 0.774460 | 0.387230 | − | 0.921983i | \(-0.373432\pi\) | ||||
0.387230 | + | 0.921983i | \(0.373432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.60533 | 0.224450 | 0.112225 | − | 0.993683i | \(-0.464202\pi\) | ||||
0.112225 | + | 0.993683i | \(0.464202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.6473 | −0.809419 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.92335 | −0.384339 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.0988 | −1.84373 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.17667 | 0.346493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8906 | −0.717255 | −0.358627 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358627 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.48236 | 0.263466 | 0.131733 | − | 0.991285i | \(-0.457946\pi\) | ||||
0.131733 | + | 0.991285i | \(0.457946\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.29525 | −0.253888 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.8121 | −1.80880 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.5571 | −1.79250 | −0.896251 | − | 0.443548i | \(-0.853720\pi\) | ||||
−0.896251 | + | 0.443548i | \(0.853720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.1075 | −1.14798 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7730 | −1.12949 | −0.564744 | − | 0.825266i | \(-0.691025\pi\) | ||||
−0.564744 | + | 0.825266i | \(0.691025\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.14445 | −0.0542520 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.47541 | 0.117083 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.102297 | 0.00482769 | 0.00241384 | − | 0.999997i | \(-0.499232\pi\) | ||||
0.00241384 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.9484 | 2.68159 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.14623 | −0.147823 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.7231 | 0.971516 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0706 | −0.658196 | −0.329098 | − | 0.944296i | \(-0.606745\pi\) | ||||
−0.329098 | + | 0.944296i | \(0.606745\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.29369 | 0.340440 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.3917 | −1.69493 | −0.847466 | − | 0.530850i | \(-0.821873\pi\) | ||||
−0.847466 | + | 0.530850i | \(0.821873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.66002 | 0.170095 | 0.0850477 | − | 0.996377i | \(-0.472896\pi\) | ||||
0.0850477 | + | 0.996377i | \(0.472896\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.47653 | −0.114846 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.6336 | 1.55638 | 0.778190 | − | 0.628029i | \(-0.216138\pi\) | ||||
0.778190 | + | 0.628029i | \(0.216138\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.3295 | 2.00077 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.60375 | −0.166052 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.7934 | −1.27794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7877 | −0.862037 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −37.9623 | −1.73817 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5330 | −0.664030 | −0.332015 | − | 0.943274i | \(-0.607728\pi\) | ||||
−0.332015 | + | 0.943274i | \(0.607728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04165 | −0.0474950 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.10161 | 0.277633 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0331 | 0.546397 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.46156 | −0.338115 | −0.169058 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169058 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.823732 | −0.0372504 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8325 | 0.759641 | 0.379821 | − | 0.925060i | \(-0.375986\pi\) | ||||
0.379821 | + | 0.925060i | \(0.375986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.5571 | −1.46630 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.2086 | 1.40272 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.3412 | 2.34782 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.87038 | −0.218028 | −0.109014 | − | 0.994040i | \(-0.534769\pi\) | ||||
−0.109014 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.81249 | −0.304360 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5924 | −0.962756 | −0.481378 | − | 0.876513i | \(-0.659864\pi\) | ||||
−0.481378 | + | 0.876513i | \(0.659864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5033 | 0.467390 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.02436 | 0.0454935 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.12405 | 0.315768 | 0.157884 | − | 0.987458i | \(-0.449533\pi\) | ||||
0.157884 | + | 0.987458i | \(0.449533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.2045 | 2.26516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.2946 | 0.763576 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.68503 | −0.426773 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.6101 | 1.65409 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.709523 | 0.0311446 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.73427 | 0.119790 | 0.0598952 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598952 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8346 | −1.21712 | −0.608562 | − | 0.793506i | \(-0.708253\pi\) | ||||
−0.608562 | + | 0.793506i | \(0.708253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.03171 | 0.132314 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.2266 | −0.663280 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.99807 | −0.130351 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.4864 | −0.845636 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.7653 | −1.20265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.40570 | 0.190475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.44628 | −0.235024 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 54.4643 | 2.34595 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.64489 | −0.414666 | −0.207333 | − | 0.978270i | \(-0.566478\pi\) | ||||
−0.207333 | + | 0.978270i | \(0.566478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.90032 | 0.253207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5950 | 0.839359 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.28761 | 0.140568 | 0.0702841 | − | 0.997527i | \(-0.477609\pi\) | ||||
0.0702841 | + | 0.997527i | \(0.477609\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.9739 | 1.19390 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −77.1987 | −3.28877 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.4702 | 0.742907 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.190493 | 0.00808597 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.8810 | 1.52033 | 0.760163 | − | 0.649732i | \(-0.225119\pi\) | ||||
0.760163 | + | 0.649732i | \(0.225119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.5508 | 0.573137 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.06938 | −0.340690 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.9369 | 0.882386 | 0.441193 | − | 0.897412i | \(-0.354555\pi\) | ||||
0.441193 | + | 0.897412i | \(0.354555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0843 | 0.466321 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.0735 | 1.30497 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.39753 | −0.352043 | −0.176021 | − | 0.984386i | \(-0.556323\pi\) | ||||
−0.176021 | + | 0.984386i | \(0.556323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4903 | −1.69446 | −0.847232 | − | 0.531223i | \(-0.821733\pi\) | ||||
−0.847232 | + | 0.531223i | \(0.821733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.09298 | −0.212762 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.93835 | 0.414458 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.9105 | −0.454211 | −0.227106 | − | 0.973870i | \(-0.572926\pi\) | ||||
−0.227106 | + | 0.973870i | \(0.572926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.66118 | 0.235271 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.6709 | −1.18947 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 85.7655 | 3.55204 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.2159 | −0.629098 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.1630 | −1.12114 | −0.560568 | − | 0.828108i | \(-0.689417\pi\) | ||||
−0.560568 | + | 0.828108i | \(0.689417\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.1049 | −1.48768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.75202 | 0.113203 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1133 | 0.497433 | 0.248717 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248717 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.3009 | −0.955244 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.07002 | −0.207502 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8923 | 0.731060 | 0.365530 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365530 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6781 | 0.476361 | 0.238181 | − | 0.971221i | \(-0.423449\pi\) | ||||
0.238181 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.8145 | −1.29558 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −52.1740 | −2.12118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7156 | −1.20612 | −0.603060 | − | 0.797696i | \(-0.706052\pi\) | ||||
−0.603060 | + | 0.797696i | \(0.706052\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.4573 | 0.504796 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.3369 | −0.741831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.87567 | 0.196926 | 0.0984632 | − | 0.995141i | \(-0.468607\pi\) | ||||
0.0984632 | + | 0.995141i | \(0.468607\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.07763 | 0.204750 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.4345 | −0.943437 | −0.471718 | − | 0.881749i | \(-0.656366\pi\) | ||||
−0.471718 | + | 0.881749i | \(0.656366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1139 | 0.808446 | 0.404223 | − | 0.914660i | \(-0.367542\pi\) | ||||
0.404223 | + | 0.914660i | \(0.367542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.14856 | −0.367119 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.69236 | 0.107867 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.95105 | −0.358042 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.1339 | −0.764136 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.17122 | 0.0466995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.46796 | 0.217676 | 0.108838 | − | 0.994059i | \(-0.465287\pi\) | ||||
0.108838 | + | 0.994059i | \(0.465287\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.30373 | 0.330044 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.98685 | −0.0788458 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.5542 | −1.05212 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.4313 | −1.52032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.9490 | −1.49889 | −0.749447 | − | 0.662065i | \(-0.769680\pi\) | ||||
−0.749447 | + | 0.662065i | \(0.769680\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.32952 | 0.367921 | 0.183960 | − | 0.982934i | \(-0.441108\pi\) | ||||
0.183960 | + | 0.982934i | \(0.441108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.47812 | −0.0975757 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0456503 | 0.00179470 | 0.000897349 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000897349 | 1.00000i | \(0.499714\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.0242 | 1.72810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.82613 | 0.228344 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.7896 | 1.12662 | 0.563311 | − | 0.826245i | \(-0.309527\pi\) | ||||
0.563311 | + | 0.826245i | \(0.309527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.0188 | −0.664979 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.5967 | −1.46679 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9516 | 1.47838 | 0.739192 | − | 0.673495i | \(-0.235208\pi\) | ||||
0.739192 | + | 0.673495i | \(0.235208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0516 | −0.818811 | −0.409406 | − | 0.912353i | \(-0.634264\pi\) | ||||
−0.409406 | + | 0.912353i | \(0.634264\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.93425 | 0.152794 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −55.2506 | −2.14252 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.8368 | 1.58121 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.08585 | −0.157968 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.1994 | −2.43979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9974 | −0.423919 | −0.211960 | − | 0.977278i | \(-0.567985\pi\) | ||||
−0.211960 | + | 0.977278i | \(0.567985\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.54564 | −0.174962 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.64047 | −0.293647 | −0.146823 | − | 0.989163i | \(-0.546905\pi\) | ||||
−0.146823 | + | 0.989163i | \(0.546905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.3085 | −1.08638 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.05752 | 0.155485 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.4797 | 0.400994 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.2934 | −1.15745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.29530 | 0.0875710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.8152 | −1.59303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.01626 | −0.114744 | −0.0573719 | − | 0.998353i | \(-0.518272\pi\) | ||||
−0.0573719 | + | 0.998353i | \(0.518272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −73.4197 | −2.78898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.2852 | 0.921189 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.2191 | 1.18251 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0916850 | −0.00346785 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9027 | 1.46933 | 0.734667 | − | 0.678428i | \(-0.237338\pi\) | ||||
0.734667 | + | 0.678428i | \(0.237338\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.77717 | 0.104743 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.35338 | 0.126296 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.7094 | −0.929294 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5906 | −0.923521 | −0.461760 | − | 0.887005i | \(-0.652782\pi\) | ||||
−0.461760 | + | 0.887005i | \(0.652782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8274 | −0.481065 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.0989 | 0.715259 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.3761 | 1.28559 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.17443 | −0.0812055 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.156573 | −0.00583918 | −0.00291959 | − | 0.999996i | \(-0.500929\pi\) | ||||
−0.00291959 | + | 0.999996i | \(0.500929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.7845 | 0.848538 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.80285 | 0.104239 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.2906 | 0.753573 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.1047 | −0.411852 | −0.205926 | − | 0.978568i | \(-0.566021\pi\) | ||||
−0.205926 | + | 0.978568i | \(0.566021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.6803 | −0.765937 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.2364 | −0.563537 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.81269 | −0.288568 | −0.144284 | − | 0.989536i | \(-0.546088\pi\) | ||||
−0.144284 | + | 0.989536i | \(0.546088\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.85614 | 0.179122 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 71.8762 | 2.64759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.3982 | −1.08143 | −0.540714 | − | 0.841206i | \(-0.681846\pi\) | ||||
−0.540714 | + | 0.841206i | \(0.681846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.32880 | 0.342702 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.40008 | −0.271483 | −0.135741 | − | 0.990744i | \(-0.543342\pi\) | ||||
−0.135741 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8572 | 0.434414 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.0514 | 0.770232 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3646 | −0.378714 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4408 | 0.928348 | 0.464174 | − | 0.885744i | \(-0.346351\pi\) | ||||
0.464174 | + | 0.885744i | \(0.346351\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.347951 | 0.0126800 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.0704 | −0.548467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1043 | 1.05781 | 0.528906 | − | 0.848680i | \(-0.322602\pi\) | ||||
0.528906 | + | 0.848680i | \(0.322602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.1215 | 0.367388 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.7236 | −0.424980 | −0.212490 | − | 0.977163i | \(-0.568157\pi\) | ||||
−0.212490 | + | 0.977163i | \(0.568157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.0982 | −1.66887 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.1086 | 0.618562 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4641 | −0.775024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.6306 | 0.671837 | 0.335918 | − | 0.941891i | \(-0.390953\pi\) | ||||
0.335918 | + | 0.941891i | \(0.390953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.89488 | −0.140271 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.06926 | −0.0744261 | −0.0372130 | − | 0.999307i | \(-0.511848\pi\) | ||||
−0.0372130 | + | 0.999307i | \(0.511848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.48965 | 0.340878 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.448142 | −0.0160770 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 74.0260 | 2.65226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86.8250 | 3.10684 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.6781 | −0.667500 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.2619 | −0.616104 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1887 | −0.862232 | −0.431116 | − | 0.902296i | \(-0.641880\pi\) | ||||
−0.431116 | + | 0.902296i | \(0.641880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.57019 | 0.0915011 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.0764 | −0.927169 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.8131 | 1.09420 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.64702 | 0.271212 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −48.7623 | −1.72725 | −0.863625 | − | 0.504135i | \(-0.831811\pi\) | ||||
−0.863625 | + | 0.504135i | \(0.831811\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.6178 | 0.729406 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.97685 | −0.0698486 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 84.9395 | 2.99745 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.2266 | 1.03010 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.66431 | 0.234595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4974 | −0.580018 | −0.290009 | − | 0.957024i | \(-0.593658\pi\) | ||||
−0.290009 | + | 0.957024i | \(0.593658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8204 | 0.906678 | 0.453339 | − | 0.891338i | \(-0.350233\pi\) | ||||
0.453339 | + | 0.891338i | \(0.350233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.23599 | −0.253777 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.94566 | −0.138211 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.1281 | −1.26396 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.7960 | 1.25081 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.0442 | 1.25795 | 0.628975 | − | 0.777425i | \(-0.283475\pi\) | ||||
0.628975 | + | 0.777425i | \(0.283475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4497 | 0.747691 | 0.373846 | − | 0.927491i | \(-0.378039\pi\) | ||||
0.373846 | + | 0.927491i | \(0.378039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.02908 | 0.175090 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.7729 | −1.07008 | −0.535039 | − | 0.844827i | \(-0.679703\pi\) | ||||
−0.535039 | + | 0.844827i | \(0.679703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.71459 | 0.198476 | 0.0992380 | − | 0.995064i | \(-0.468359\pi\) | ||||
0.0992380 | + | 0.995064i | \(0.468359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.07581 | −0.210768 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.8573 | 1.03450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.6317 | −1.12927 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.73552 | −0.301944 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.0740 | −0.865651 | −0.432825 | − | 0.901478i | \(-0.642483\pi\) | ||||
−0.432825 | + | 0.901478i | \(0.642483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.3741 | 1.87497 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.37042 | 0.253851 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.90667 | 0.168795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 122.742 | 4.21745 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.88708 | 0.202044 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.46907 | −0.0503592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.4866 | −1.69439 | −0.847194 | − | 0.531283i | \(-0.821710\pi\) | ||||
−0.847194 | + | 0.531283i | \(0.821710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.5674 | 1.38738 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0799 | −0.344323 | −0.172162 | − | 0.985069i | \(-0.555075\pi\) | ||||
−0.172162 | + | 0.985069i | \(0.555075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.05552 | 0.308971 | 0.154485 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154485 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.9453 | −0.407096 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.5844 | 0.870905 | 0.435452 | − | 0.900212i | \(-0.356588\pi\) | ||||
0.435452 | + | 0.900212i | \(0.356588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39860 | 0.115556 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.49154 | 0.0506552 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.9800 | 0.983079 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.0434 | −1.18740 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7854 | 0.703478 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 47.1966 | 1.59554 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.382964 | 0.0129318 | 0.00646589 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646589 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.84016 | −0.298171 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0150 | 1.04492 | 0.522461 | − | 0.852663i | \(-0.325014\pi\) | ||||
0.522461 | + | 0.852663i | \(0.325014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.08867 | −0.204900 | −0.102450 | − | 0.994738i | \(-0.532668\pi\) | ||||
−0.102450 | + | 0.994738i | \(0.532668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.92528 | 0.131947 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8796 | −0.566761 | −0.283381 | − | 0.959008i | \(-0.591456\pi\) | ||||
−0.283381 | + | 0.959008i | \(0.591456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.67415 | 0.156766 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.5457 | 1.72685 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.8885 | 1.63599 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0876 | −0.872012 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.93478 | −0.164767 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.9931 | 1.30049 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.0166 | 1.56635 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.82988 | 0.194006 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.2625 | 0.939476 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.9172 | 1.35863 | 0.679316 | − | 0.733846i | \(-0.262277\pi\) | ||||
0.679316 | + | 0.733846i | \(0.262277\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.1428 | 0.601758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.6427 | −0.584528 | −0.292264 | − | 0.956338i | \(-0.594409\pi\) | ||||
−0.292264 | + | 0.956338i | \(0.594409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.5600 | −1.57401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.63498 | −0.186287 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.0374 | 1.32215 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.10409 | 0.267329 | 0.133665 | − | 0.991027i | \(-0.457325\pi\) | ||||
0.133665 | + | 0.991027i | \(0.457325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.73443 | 0.123054 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.3318 | −1.39337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.729938 | −0.0240002 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.7294 | −0.549465 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.87593 | 0.0615473 | 0.0307736 | − | 0.999526i | \(-0.490203\pi\) | ||||
0.0307736 | + | 0.999526i | \(0.490203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70.7970 | 2.32028 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.12114 | 0.233136 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −38.6522 | −1.26406 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.0032 | −1.40485 | −0.702427 | − | 0.711756i | \(-0.747900\pi\) | ||||
−0.702427 | + | 0.711756i | \(0.747900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.40796 | 0.209116 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.6146 | −1.58479 | −0.792396 | − | 0.610007i | \(-0.791167\pi\) | ||||
−0.792396 | + | 0.610007i | \(0.791167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.1585 | −1.27518 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.3678 | −0.434854 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.0841 | 1.04259 | 0.521296 | − | 0.853376i | \(-0.325449\pi\) | ||||
0.521296 | + | 0.853376i | \(0.325449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.4125 | −1.34431 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.53364 | 0.211868 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.6969 | −1.12394 | −0.561971 | − | 0.827157i | \(-0.689957\pi\) | ||||
−0.561971 | + | 0.827157i | \(0.689957\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.3953 | −0.789413 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.6645 | 0.667990 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 71.2666 | 2.30132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7634 | −0.411722 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.61016 | 0.245234 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.1169 | 0.872925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.10488 | 0.132004 | 0.0660020 | − | 0.997819i | \(-0.478976\pi\) | ||||
0.0660020 | + | 0.997819i | \(0.478976\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.4892 | −0.336962 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.5760 | −0.981230 | −0.490615 | − | 0.871377i | \(-0.663228\pi\) | ||||
−0.490615 | + | 0.871377i | \(0.663228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.1320 | −1.83157 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.45194 | −0.0785249 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3109 | −0.553824 | −0.276912 | − | 0.960895i | \(-0.589311\pi\) | ||||
−0.276912 | + | 0.960895i | \(0.589311\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.46616 | 0.142739 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.8474 | 1.08066 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.9316 | 0.827090 | 0.413545 | − | 0.910484i | \(-0.364290\pi\) | ||||
0.413545 | + | 0.910484i | \(0.364290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1821 | 0.420018 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.88898 | −0.251109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.1112 | 0.607699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.3995 | 1.50569 | 0.752847 | − | 0.658195i | \(-0.228680\pi\) | ||||
0.752847 | + | 0.658195i | \(0.228680\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.03474 | 0.159773 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.2853 | −0.769896 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.4331 | 1.56556 | 0.782781 | − | 0.622297i | \(-0.213800\pi\) | ||||
0.782781 | + | 0.622297i | \(0.213800\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.671930 | 0.0212589 |
(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 | 2008.2.a.d.1.10 | ✓ | 23 | |
4.3 | odd | 2 | 4016.2.a.m.1.14 | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.10 | ✓ | 23 | 1.1 | even | 1 | trivial | |
4016.2.a.m.1.14 | 23 | 4.3 | odd | 2 |