Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4508,2,Mod(1,4508)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4508, 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("4508.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4508 = 2^{2} \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4508.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: | \(35.9965612312\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.6963152.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 644) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.11181\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4508.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.11181 | 1.21926 | 0.609628 | − | 0.792688i | \(-0.291319\pi\) | ||||
0.609628 | + | 0.792688i | \(0.291319\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.77860 | −0.795415 | −0.397708 | − | 0.917512i | \(-0.630194\pi\) | ||||
−0.397708 | + | 0.917512i | \(0.630194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.45975 | 0.486584 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.612946 | 0.184810 | 0.0924051 | − | 0.995721i | \(-0.470545\pi\) | ||||
0.0924051 | + | 0.995721i | \(0.470545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.84681 | −0.512212 | −0.256106 | − | 0.966649i | \(-0.582440\pi\) | ||||
−0.256106 | + | 0.966649i | \(0.582440\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.75608 | −0.969815 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.26501 | −1.03442 | −0.517208 | − | 0.855860i | \(-0.673029\pi\) | ||||
−0.517208 | + | 0.855860i | \(0.673029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.70034 | 1.07833 | 0.539166 | − | 0.842200i | \(-0.318740\pi\) | ||||
0.539166 | + | 0.842200i | \(0.318740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.83657 | −0.367314 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.25271 | −0.625985 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2406 | 1.90163 | 0.950814 | − | 0.309761i | \(-0.100249\pi\) | ||||
0.950814 | + | 0.309761i | \(0.100249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2181 | −1.83522 | −0.917609 | − | 0.397485i | \(-0.869883\pi\) | ||||
−0.917609 | + | 0.397485i | \(0.869883\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.29443 | 0.225331 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47671 | −0.407169 | −0.203584 | − | 0.979057i | \(-0.565259\pi\) | ||||
−0.203584 | + | 0.979057i | \(0.565259\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.90011 | −0.624517 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37682 | −0.995892 | −0.497946 | − | 0.867208i | \(-0.665912\pi\) | ||||
−0.497946 | + | 0.867208i | \(0.665912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9240 | 1.66589 | 0.832944 | − | 0.553357i | \(-0.186653\pi\) | ||||
0.832944 | + | 0.553357i | \(0.186653\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.59632 | −0.387037 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.544914 | −0.0794838 | −0.0397419 | − | 0.999210i | \(-0.512654\pi\) | ||||
−0.0397419 | + | 0.999210i | \(0.512654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00689 | −1.26122 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.61984 | −1.04667 | −0.523333 | − | 0.852128i | \(-0.675312\pi\) | ||||
−0.523333 | + | 0.852128i | \(0.675312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.09019 | −0.147001 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.92623 | 1.31476 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74172 | 0.356941 | 0.178471 | − | 0.983945i | \(-0.442885\pi\) | ||||
0.178471 | + | 0.983945i | \(0.442885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.1454 | −1.93916 | −0.969582 | − | 0.244766i | \(-0.921289\pi\) | ||||
−0.969582 | + | 0.244766i | \(0.921289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.28473 | 0.407421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.27937 | −0.644977 | −0.322489 | − | 0.946573i | \(-0.604519\pi\) | ||||
−0.322489 | + | 0.946573i | \(0.604519\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.11181 | −0.254232 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.21583 | −0.262970 | −0.131485 | − | 0.991318i | \(-0.541975\pi\) | ||||
−0.131485 | + | 0.991318i | \(0.541975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.62764 | −0.658665 | −0.329333 | − | 0.944214i | \(-0.606824\pi\) | ||||
−0.329333 | + | 0.944214i | \(0.606824\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.87849 | −0.447850 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.46755 | −0.277621 | −0.138810 | − | 0.990319i | \(-0.544328\pi\) | ||||
−0.138810 | + | 0.990319i | \(0.544328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2484 | −1.24982 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.84347 | −0.641404 | −0.320702 | − | 0.947180i | \(-0.603919\pi\) | ||||
−0.320702 | + | 0.947180i | \(0.603919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.58575 | 0.822790 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6262 | 2.31857 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.00746465 | −0.000791251 0 | −0.000395626 | − | 1.00000i | \(-0.500126\pi\) | ||||
−0.000395626 | 1.00000i | \(0.500126\pi\) | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.5786 | −2.23760 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.36003 | −0.857721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.58815 | 0.770460 | 0.385230 | − | 0.922821i | \(-0.374122\pi\) | ||||
0.385230 | + | 0.922821i | \(0.374122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.894750 | 0.0899257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5904 | −1.15329 | −0.576643 | − | 0.816996i | \(-0.695638\pi\) | ||||
−0.576643 | + | 0.816996i | \(0.695638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.666419 | 0.0656642 | 0.0328321 | − | 0.999461i | \(-0.489547\pi\) | ||||
0.0328321 | + | 0.999461i | \(0.489547\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92396 | 0.669365 | 0.334682 | − | 0.942331i | \(-0.391371\pi\) | ||||
0.334682 | + | 0.942331i | \(0.391371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.06263 | 0.389130 | 0.194565 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194565 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.23035 | −0.496443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5926 | −1.18462 | −0.592308 | − | 0.805711i | \(-0.701783\pi\) | ||||
−0.592308 | + | 0.805711i | \(0.701783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.77860 | 0.165856 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.69588 | −0.249234 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6243 | −0.965845 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.4666 | −1.21425 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1595 | 1.08758 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8535 | −1.14057 | −0.570283 | − | 0.821448i | \(-0.693167\pi\) | ||||
−0.570283 | + | 0.821448i | \(0.693167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.0694 | 2.03114 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6948 | 1.28389 | 0.641944 | − | 0.766752i | \(-0.278128\pi\) | ||||
0.641944 | + | 0.766752i | \(0.278128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.78529 | 0.497918 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.2303 | −1.64296 | −0.821480 | − | 0.570238i | \(-0.806851\pi\) | ||||
−0.821480 | + | 0.570238i | \(0.806851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.14573 | 0.521274 | 0.260637 | − | 0.965437i | \(-0.416067\pi\) | ||||
0.260637 | + | 0.965437i | \(0.416067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.15076 | −0.0969111 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.13199 | −0.0946620 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.2139 | −1.51258 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.66642 | −0.546134 | −0.273067 | − | 0.961995i | \(-0.588038\pi\) | ||||
−0.273067 | + | 0.961995i | \(0.588038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.07270 | −0.0872950 | −0.0436475 | − | 0.999047i | \(-0.513898\pi\) | ||||
−0.0436475 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.22585 | −0.503330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.1739 | 1.45976 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.76664 | 0.220802 | 0.110401 | − | 0.993887i | \(-0.464786\pi\) | ||||
0.110401 | + | 0.993887i | \(0.464786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0917 | −1.27615 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.94336 | 0.465520 | 0.232760 | − | 0.972534i | \(-0.425224\pi\) | ||||
0.232760 | + | 0.972534i | \(0.425224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.30227 | −0.179232 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.52778 | −0.350371 | −0.175185 | − | 0.984535i | \(-0.556052\pi\) | ||||
−0.175185 | + | 0.984535i | \(0.556052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.58931 | −0.737639 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.86133 | 0.524699 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.7003 | 0.813531 | 0.406766 | − | 0.913533i | \(-0.366657\pi\) | ||||
0.406766 | + | 0.913533i | \(0.366657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.78999 | 0.435203 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3590 | 0.849008 | 0.424504 | − | 0.905426i | \(-0.360448\pi\) | ||||
0.424504 | + | 0.905426i | \(0.360448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2162 | −1.50266 | −0.751328 | − | 0.659929i | \(-0.770586\pi\) | ||||
−0.751328 | + | 0.659929i | \(0.770586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −31.9842 | −2.36434 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.40509 | 0.323868 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.61422 | −0.191171 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.97054 | 0.142583 | 0.0712916 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712916 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7995 | 1.06529 | 0.532645 | − | 0.846339i | \(-0.321198\pi\) | ||||
0.532645 | + | 0.846339i | \(0.321198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.93674 | 0.496751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3496 | 1.09362 | 0.546808 | − | 0.837258i | \(-0.315843\pi\) | ||||
0.546808 | + | 0.837258i | \(0.315843\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7071 | −0.971668 | −0.485834 | − | 0.874051i | \(-0.661484\pi\) | ||||
−0.485834 | + | 0.874051i | \(0.661484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1490 | −0.786392 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3418 | 0.792148 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.45975 | −0.101460 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.88105 | 0.199287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0376 | 1.51713 | 0.758567 | − | 0.651596i | \(-0.225900\pi\) | ||||
0.758567 | + | 0.651596i | \(0.225900\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.67941 | −0.320628 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.4294 | −1.32507 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.8845 | −0.803081 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.87664 | 0.529840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.01419 | 0.201845 | 0.100922 | − | 0.994894i | \(-0.467821\pi\) | ||||
0.100922 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.68094 | −0.178729 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3269 | 1.54826 | 0.774130 | − | 0.633026i | \(-0.218187\pi\) | ||||
0.774130 | + | 0.633026i | \(0.218187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8111 | −1.83781 | −0.918904 | − | 0.394482i | \(-0.870924\pi\) | ||||
−0.918904 | + | 0.394482i | \(0.870924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.2000 | −1.45437 | −0.727185 | − | 0.686442i | \(-0.759172\pi\) | ||||
−0.727185 | + | 0.686442i | \(0.759172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.969185 | 0.0632227 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.21100 | −0.338491 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2136 | 0.854714 | 0.427357 | − | 0.904083i | \(-0.359445\pi\) | ||||
0.427357 | + | 0.904083i | \(0.359445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9586 | −0.770322 | −0.385161 | − | 0.922849i | \(-0.625854\pi\) | ||||
−0.385161 | + | 0.922849i | \(0.625854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.9963 | −0.897865 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.68061 | −0.552334 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.3403 | −0.782035 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0805 | −0.951872 | −0.475936 | − | 0.879480i | \(-0.657891\pi\) | ||||
−0.475936 | + | 0.879480i | \(0.657891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.612946 | −0.0385356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.0197 | 1.00319 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8822 | 0.803573 | 0.401786 | − | 0.915733i | \(-0.368389\pi\) | ||||
0.401786 | + | 0.915733i | \(0.368389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.9487 | 0.925302 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.4881 | −1.57166 | −0.785831 | − | 0.618442i | \(-0.787764\pi\) | ||||
−0.785831 | + | 0.618442i | \(0.787764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5527 | 0.832534 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0157639 | −0.000964737 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.0772 | 0.919270 | 0.459635 | − | 0.888108i | \(-0.347980\pi\) | ||||
0.459635 | + | 0.888108i | \(0.347980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4014 | −0.631841 | −0.315920 | − | 0.948786i | \(-0.602313\pi\) | ||||
−0.315920 | + | 0.948786i | \(0.602313\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.12572 | −0.0678834 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.01848 | −0.541868 | −0.270934 | − | 0.962598i | \(-0.587333\pi\) | ||||
−0.270934 | + | 0.962598i | \(0.587333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9158 | −0.892988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.91724 | 0.114373 | 0.0571864 | − | 0.998364i | \(-0.481787\pi\) | ||||
0.0571864 | + | 0.998364i | \(0.481787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.49457 | −0.564394 | −0.282197 | − | 0.959357i | \(-0.591063\pi\) | ||||
−0.282197 | + | 0.959357i | \(0.591063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.6548 | −1.04578 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.19028 | 0.0700165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.0248 | 0.939388 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.6936 | 0.975249 | 0.487624 | − | 0.873053i | \(-0.337864\pi\) | ||||
0.487624 | + | 0.873053i | \(0.337864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.87643 | −0.283917 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.99374 | −0.115688 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.84681 | 0.106804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.4767 | −1.40615 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.9376 | 1.54244 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9285 | −1.47982 | −0.739908 | − | 0.672709i | \(-0.765131\pi\) | ||||
−0.739908 | + | 0.672709i | \(0.765131\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.40735 | 0.0800615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4581 | 1.44360 | 0.721798 | − | 0.692104i | \(-0.243316\pi\) | ||||
0.721798 | + | 0.692104i | \(0.243316\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.5490 | −0.991928 | −0.495964 | − | 0.868343i | \(-0.665185\pi\) | ||||
−0.495964 | + | 0.868343i | \(0.665185\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.42250 | −0.248392 | −0.124196 | − | 0.992258i | \(-0.539635\pi\) | ||||
−0.124196 | + | 0.992258i | \(0.539635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.27693 | 0.351440 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6221 | 0.816126 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0470 | −1.11544 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.39179 | 0.188143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.57952 | 0.474449 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.9340 | 1.75525 | 0.877626 | − | 0.479345i | \(-0.159126\pi\) | ||||
0.877626 | + | 0.479345i | \(0.159126\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.61538 | −0.198122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.38990 | 0.513025 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.31791 | −0.398632 | −0.199316 | − | 0.979935i | \(-0.563872\pi\) | ||||
−0.199316 | + | 0.979935i | \(0.563872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.5933 | −1.44435 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.26312 | −0.339167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.75608 | 0.202220 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0287 | 0.753101 | 0.376551 | − | 0.926396i | \(-0.377110\pi\) | ||||
0.376551 | + | 0.926396i | \(0.377110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.8241 | 1.43586 | 0.717930 | − | 0.696116i | \(-0.245090\pi\) | ||||
0.717930 | + | 0.696116i | \(0.245090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00713 | 0.320637 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.37529 | 0.392547 | 0.196274 | − | 0.980549i | \(-0.437116\pi\) | ||||
0.196274 | + | 0.980549i | \(0.437116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.94108 | 0.209171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5656 | −1.03263 | −0.516317 | − | 0.856397i | \(-0.672697\pi\) | ||||
−0.516317 | + | 0.856397i | \(0.672697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.09316 | 0.162798 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.4365 | −1.17761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0093 | 0.523912 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.63696 | 0.450846 | 0.225423 | − | 0.974261i | \(-0.427624\pi\) | ||||
0.225423 | + | 0.974261i | \(0.427624\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.30858 | −0.484585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.1338 | −0.680042 | −0.340021 | − | 0.940418i | \(-0.610434\pi\) | ||||
−0.340021 | + | 0.940418i | \(0.610434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.6787 | 1.32604 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.9124 | −0.974037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.07360 | 0.106514 | 0.0532569 | − | 0.998581i | \(-0.483040\pi\) | ||||
0.0532569 | + | 0.998581i | \(0.483040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.1442 | −1.39064 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.61051 | −0.388879 | −0.194439 | − | 0.980915i | \(-0.562289\pi\) | ||||
−0.194439 | + | 0.980915i | \(0.562289\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.9463 | 0.810595 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.6243 | −0.792183 | −0.396092 | − | 0.918211i | \(-0.629634\pi\) | ||||
−0.396092 | + | 0.918211i | \(0.629634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.26501 | 0.215691 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.0326 | 1.56539 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.38879 | 0.220824 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.53335 | −0.227522 | −0.113761 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.8569 | 1.29123 | 0.645616 | − | 0.763662i | \(-0.276601\pi\) | ||||
0.645616 | + | 0.763662i | \(0.276601\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8708 | 0.940020 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.0064 | 0.994126 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.51809 | −0.0752490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3124 | 0.707702 | 0.353851 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353851 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.6109 | −2.00319 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3932 | 0.510182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.9786 | 0.635566 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4145 | 1.14387 | 0.571936 | − | 0.820299i | \(-0.306193\pi\) | ||||
0.571936 | + | 0.820299i | \(0.306193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4946 | 0.755159 | 0.377580 | − | 0.925977i | \(-0.376756\pi\) | ||||
0.377580 | + | 0.925977i | \(0.376756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.795439 | −0.0386756 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.83299 | 0.379956 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.39056 | −0.115417 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.6016 | 1.66670 | 0.833349 | − | 0.552747i | \(-0.186420\pi\) | ||||
0.833349 | + | 0.552747i | \(0.186420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.8051 | 0.903713 | 0.451857 | − | 0.892091i | \(-0.350762\pi\) | ||||
0.451857 | + | 0.892091i | \(0.350762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.4644 | −1.84423 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.70034 | −0.224848 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.7000 | 1.79933 | 0.899663 | − | 0.436586i | \(-0.143813\pi\) | ||||
0.899663 | + | 0.436586i | \(0.143813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6027 | −0.646284 | −0.323142 | − | 0.946350i | \(-0.604739\pi\) | ||||
−0.323142 | + | 0.946350i | \(0.604739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0132766 | 0.000629373 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0782 | −0.665877 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.95586 | 0.186689 | 0.0933443 | − | 0.995634i | \(-0.470244\pi\) | ||||
0.0933443 | + | 0.995634i | \(0.470244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.90865 | −0.184051 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.26534 | −0.106435 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3668 | 0.905939 | 0.452969 | − | 0.891526i | \(-0.350365\pi\) | ||||
0.452969 | + | 0.891526i | \(0.350365\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8728 | 0.647529 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0772 | 1.26111 | 0.630554 | − | 0.776145i | \(-0.282828\pi\) | ||||
0.630554 | + | 0.776145i | \(0.282828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6172 | −0.958164 | −0.479082 | − | 0.877770i | \(-0.659030\pi\) | ||||
−0.479082 | + | 0.877770i | \(0.659030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 38.3798 | 1.77982 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.54603 | −0.302914 | −0.151457 | − | 0.988464i | \(-0.548397\pi\) | ||||
−0.151457 | + | 0.988464i | \(0.548397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.84263 | 0.269214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.69580 | 0.307873 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.63250 | −0.396086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.1231 | −0.509291 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8457 | 1.04385 | 0.521924 | − | 0.852992i | \(-0.325214\pi\) | ||||
0.521924 | + | 0.852992i | \(0.325214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.57400 | 0.208557 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.4963 | −0.612836 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.3458 | −1.32979 | −0.664893 | − | 0.746938i | \(-0.731523\pi\) | ||||
−0.664893 | + | 0.746938i | \(0.731523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5513 | 0.567587 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.7264 | 1.83796 | 0.918978 | − | 0.394309i | \(-0.129016\pi\) | ||||
0.918978 | + | 0.394309i | \(0.129016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.6762 | −1.96708 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.59140 | −0.0715283 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.9806 | −0.491559 | −0.245780 | − | 0.969326i | \(-0.579044\pi\) | ||||
−0.245780 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.56183 | −0.427191 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.67314 | −0.431304 | −0.215652 | − | 0.976470i | \(-0.569188\pi\) | ||||
−0.215652 | + | 0.976470i | \(0.569188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.6147 | 0.917341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.2508 | −0.899370 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.7619 | −0.698634 | −0.349317 | − | 0.937005i | \(-0.613586\pi\) | ||||
−0.349317 | + | 0.937005i | \(0.613586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.2888 | −0.675019 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.18530 | −0.0522303 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.334003 | −0.0146894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.5971 | 0.991903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4428 | 0.588938 | 0.294469 | − | 0.955661i | \(-0.404857\pi\) | ||||
0.294469 | + | 0.955661i | \(0.404857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.5415 | 1.46667 | 0.733334 | − | 0.679868i | \(-0.237963\pi\) | ||||
0.733334 | + | 0.679868i | \(0.237963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.5801 | 1.89838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00223 | 0.173682 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7767 | 0.510108 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3150 | −0.532423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.9880 | 1.03516 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7411 | −0.977718 | −0.488859 | − | 0.872363i | \(-0.662587\pi\) | ||||
−0.488859 | + | 0.872363i | \(0.662587\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −42.6927 | −1.83212 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.22581 | −0.309520 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4551 | 1.51595 | 0.757975 | − | 0.652284i | \(-0.226189\pi\) | ||||
0.757975 | + | 0.652284i | \(0.226189\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.1085 | −0.943567 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.1342 | 2.05059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.30271 | 0.394878 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.3269 | −1.58159 | −0.790796 | − | 0.612080i | \(-0.790333\pi\) | ||||
−0.790796 | + | 0.612080i | \(0.790333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.1744 | −0.853288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.52074 | −0.233086 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.80022 | 0.328740 | 0.164370 | − | 0.986399i | \(-0.447441\pi\) | ||||
0.164370 | + | 0.986399i | \(0.447441\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3973 | 0.942262 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.4450 | −0.563643 | −0.281822 | − | 0.959467i | \(-0.590939\pi\) | ||||
−0.281822 | + | 0.959467i | \(0.590939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.6776 | −0.990877 | −0.495438 | − | 0.868643i | \(-0.664993\pi\) | ||||
−0.495438 | + | 0.868643i | \(0.664993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.16141 | 0.173845 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.83657 | 0.0765903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.6414 | −1.31725 | −0.658625 | − | 0.752471i | \(-0.728862\pi\) | ||||
−0.658625 | + | 0.752471i | \(0.728862\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.2537 | 1.29886 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.67055 | −0.193435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.79490 | 0.198245 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.5237 | −1.83769 | −0.918844 | − | 0.394621i | \(-0.870876\pi\) | ||||
−0.918844 | + | 0.394621i | \(0.870876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0283 | −1.97897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 32.4155 | 1.33340 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.774107 | 0.0317888 | 0.0158944 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158944 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.9467 | −1.18471 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.1838 | 0.906404 | 0.453202 | − | 0.891408i | \(-0.350282\pi\) | ||||
0.453202 | + | 0.891408i | \(0.350282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5006 | 0.795445 | 0.397722 | − | 0.917506i | \(-0.369801\pi\) | ||||
0.397722 | + | 0.917506i | \(0.369801\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.70657 | −0.313836 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.8964 | 0.768248 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.99336 | −0.365029 | −0.182515 | − | 0.983203i | \(-0.558424\pi\) | ||||
−0.182515 | + | 0.983203i | \(0.558424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00635 | 0.0407126 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.21656 | −0.210695 | −0.105347 | − | 0.994435i | \(-0.533595\pi\) | ||||
−0.105347 | + | 0.994435i | \(0.533595\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.9518 | 0.965831 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.1908 | −0.853111 | −0.426555 | − | 0.904461i | \(-0.640273\pi\) | ||||
−0.426555 | + | 0.904461i | \(0.640273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6076 | −0.426355 | −0.213177 | − | 0.977014i | \(-0.568381\pi\) | ||||
−0.213177 | + | 0.977014i | \(0.568381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.25271 | 0.130527 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4441 | −0.497766 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.08424 | 0.242981 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5632 | 0.421182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.393777 | 0.0156760 | 0.00783802 | − | 0.999969i | \(-0.497505\pi\) | ||||
0.00783802 | + | 0.999969i | \(0.497505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 46.5393 | 1.84977 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.8613 | 0.907224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.23456 | −0.127957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.8922 | −1.02268 | −0.511341 | − | 0.859378i | \(-0.670851\pi\) | ||||
−0.511341 | + | 0.859378i | \(0.670851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.5479 | 1.67793 | 0.838963 | − | 0.544188i | \(-0.183162\pi\) | ||||
0.838963 | + | 0.544188i | \(0.183162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41.0312 | −1.61560 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.7238 | −1.91553 | −0.957765 | − | 0.287551i | \(-0.907159\pi\) | ||||
−0.957765 | + | 0.287551i | \(0.907159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.68053 | 0.0659664 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.7238 | 0.771854 | 0.385927 | − | 0.922529i | \(-0.373882\pi\) | ||||
0.385927 | + | 0.922529i | \(0.373882\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.1362 | −1.02122 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.21496 | −0.320496 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.48604 | 0.252660 | 0.126330 | − | 0.991988i | \(-0.459680\pi\) | ||||
0.126330 | + | 0.991988i | \(0.459680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.1204 | −1.44382 | −0.721909 | − | 0.691988i | \(-0.756735\pi\) | ||||
−0.721909 | + | 0.691988i | \(0.756735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.6340 | 0.646011 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.2406 | −0.396517 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.36540 | 0.246101 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.28329 | −0.358377 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9763 | 1.54097 | 0.770486 | − | 0.637457i | \(-0.220013\pi\) | ||||
0.770486 | + | 0.637457i | \(0.220013\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.97384 | 0.229933 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1898 | −0.468492 | −0.234246 | − | 0.972177i | \(-0.575262\pi\) | ||||
−0.234246 | + | 0.972177i | \(0.575262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.2620 | 1.88773 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0880 | 0.845174 | 0.422587 | − | 0.906322i | \(-0.361122\pi\) | ||||
0.422587 | + | 0.906322i | \(0.361122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.2032 | 1.30684 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.7318 | −2.24076 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0724 | 0.536115 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.7055 | −1.13005 | −0.565025 | − | 0.825074i | \(-0.691134\pi\) | ||||
−0.565025 | + | 0.825074i | \(0.691134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.9308 | −0.414629 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.1972 | 1.03017 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.8822 | −1.77325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.4972 | −1.41625 | −0.708125 | − | 0.706087i | \(-0.750459\pi\) | ||||
−0.708125 | + | 0.706087i | \(0.750459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6414 | −0.439063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.04674 | 0.0770846 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.4163 | 0.503861 | 0.251931 | − | 0.967745i | \(-0.418935\pi\) | ||||
0.251931 | + | 0.967745i | \(0.418935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.60201 | −0.135086 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.2181 | 0.382669 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.01337 | 0.0752956 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.9046 | 1.04212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.14090 | 0.191723 | 0.0958616 | − | 0.995395i | \(-0.469439\pi\) | ||||
0.0958616 | + | 0.995395i | \(0.469439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.2544 | −0.939220 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.8076 | −0.698495 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3224 | −1.23586 | −0.617929 | − | 0.786234i | \(-0.712028\pi\) | ||||
−0.617929 | + | 0.786234i | \(0.712028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.18752 | 0.155093 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.5908 | −1.72322 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.2546 | 1.37603 | 0.688015 | − | 0.725696i | \(-0.258482\pi\) | ||||
0.688015 | + | 0.725696i | \(0.258482\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.23597 | −0.119198 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.52222 | −0.239924 | −0.119962 | − | 0.992779i | \(-0.538277\pi\) | ||||
−0.119962 | + | 0.992779i | \(0.538277\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.3318 | −0.673436 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.6151 | −0.572864 | −0.286432 | − | 0.958101i | \(-0.592469\pi\) | ||||
−0.286432 | + | 0.958101i | \(0.592469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8569 | 0.434404 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.53001 | −0.312097 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.7568 | −1.85214 | −0.926071 | − | 0.377350i | \(-0.876835\pi\) | ||||
−0.926071 | + | 0.377350i | \(0.876835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.8472 | −1.16058 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.90790 | 0.0694358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.5904 | −1.29355 | −0.646777 | − | 0.762679i | \(-0.723884\pi\) | ||||
−0.646777 | + | 0.762679i | \(0.723884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.29443 | −0.0469847 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.59153 | −0.0939429 | −0.0469715 | − | 0.998896i | \(-0.514957\pi\) | ||||
−0.0469715 | + | 0.998896i | \(0.514957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.0733 | 0.400357 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.06342 | −0.182830 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.9098 | −0.862208 | −0.431104 | − | 0.902302i | \(-0.641876\pi\) | ||||
−0.431104 | + | 0.902302i | \(0.641876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.2049 | 0.979760 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0909 | 0.434879 | 0.217440 | − | 0.976074i | \(-0.430229\pi\) | ||||
0.217440 | + | 0.976074i | \(0.430229\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.7662 | 0.674101 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.9732 | −1.07390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.35818 | −0.0485996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −33.3097 | −1.19039 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.92076 | −0.175629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.7979 | −0.384905 | −0.192453 | − | 0.981306i | \(-0.561644\pi\) | ||||
−0.192453 | + | 0.981306i | \(0.561644\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −53.8260 | −1.91626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9705 | 0.993263 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.6207 | 1.01507 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.5076 | 0.726417 | 0.363209 | − | 0.931708i | \(-0.381681\pi\) | ||||
0.363209 | + | 0.931708i | \(0.381681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32406 | 0.0822194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0108965 | −0.000385010 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.44944 | −0.121728 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.8401 | 1.12083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.4089 | 1.31523 | 0.657614 | − | 0.753355i | \(-0.271566\pi\) | ||||
0.657614 | + | 0.753355i | \(0.271566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2121 | −0.674627 | −0.337314 | − | 0.941392i | \(-0.609518\pi\) | ||||
−0.337314 | + | 0.941392i | \(0.609518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9658 | −0.770375 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.5709 | −0.370282 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.3463 | 1.79638 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.3982 | 1.06091 | 0.530453 | − | 0.847714i | \(-0.322022\pi\) | ||||
0.530453 | + | 0.847714i | \(0.322022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.8890 | −0.693286 | −0.346643 | − | 0.937997i | \(-0.612678\pi\) | ||||
−0.346643 | + | 0.937997i | \(0.612678\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.37731 | −0.0827673 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.2952 | 0.775279 | 0.387640 | − | 0.921811i | \(-0.373291\pi\) | ||||
0.387640 | + | 0.921811i | \(0.373291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1144 | −0.872260 | −0.436130 | − | 0.899884i | \(-0.643651\pi\) | ||||
−0.436130 | + | 0.899884i | \(0.643651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0453 | −0.660676 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.05313 | 0.278690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 33.2364 | 1.14882 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.8696 | −0.513355 | −0.256677 | − | 0.966497i | \(-0.582628\pi\) | ||||
−0.256677 | + | 0.966497i | \(0.582628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.8696 | 2.61619 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.04885 | 0.139450 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.0556 | 0.586729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0508 | −0.688140 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.47671 | 0.0849005 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.0320 | 1.57611 | 0.788053 | − | 0.615607i | \(-0.211089\pi\) | ||||
0.788053 | + | 0.615607i | \(0.211089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.2036 | −0.417353 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.0239 | 0.786480 | 0.393240 | − | 0.919436i | \(-0.371354\pi\) | ||||
0.393240 | + | 0.919436i | \(0.371354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.46024 | −0.254540 | −0.127270 | − | 0.991868i | \(-0.540622\pi\) | ||||
−0.127270 | + | 0.991868i | \(0.540622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0366 | 1.39690 | 0.698450 | − | 0.715659i | \(-0.253873\pi\) | ||||
0.698450 | + | 0.715659i | \(0.253873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.0316 | −0.647095 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.51365 | 0.0853680 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.51247 | −0.0513072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.74996 | 0.330365 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.0768 | 0.374894 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.4646 | 1.70407 | 0.852034 | − | 0.523487i | \(-0.175369\pi\) | ||||
0.852034 | + | 0.523487i | \(0.175369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.2537 | 1.18908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7525 | −1.33930 | −0.669648 | − | 0.742679i | \(-0.733555\pi\) | ||||
−0.669648 | + | 0.742679i | \(0.733555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.64149 | 0.0888933 | 0.0444467 | − | 0.999012i | \(-0.485848\pi\) | ||||
0.0444467 | + | 0.999012i | \(0.485848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.2981 | −0.346167 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.0485 | 0.908199 | 0.454100 | − | 0.890951i | \(-0.349961\pi\) | ||||
0.454100 | + | 0.890951i | \(0.349961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.89465 | −0.230980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.56128 | −0.0857099 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.2031 | −0.675314 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.90011 | 0.130221 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −104.639 | −3.48990 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.4987 | 1.08269 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.9565 | 1.19524 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.5751 | 0.716390 | 0.358195 | − | 0.933647i | \(-0.383392\pi\) | ||||
0.358195 | + | 0.933647i | \(0.383392\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.9191 | −0.561171 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.6282 | −1.57799 | −0.788996 | − | 0.614398i | \(-0.789399\pi\) | ||||
−0.788996 | + | 0.614398i | \(0.789399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.58173 | −0.118538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 56.8871 | 1.88063 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.5481 | −1.40353 | −0.701766 | − | 0.712408i | \(-0.747605\pi\) | ||||
−0.701766 | + | 0.712408i | \(0.747605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −54.7560 | −1.80427 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.09221 | 0.134697 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.54866 | 0.149559 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.972807 | 0.0319512 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.6564 | 1.59636 | 0.798182 | − | 0.602416i | \(-0.205795\pi\) | ||||
0.798182 | + | 0.602416i | \(0.205795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.7627 | 1.76011 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.64966 | 0.152060 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.35816 | 0.207712 | 0.103856 | − | 0.994592i | \(-0.466882\pi\) | ||||
0.103856 | + | 0.994592i | \(0.466882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.0602 | −1.20941 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.4618 | 0.732234 | 0.366117 | − | 0.930569i | \(-0.380687\pi\) | ||||
0.366117 | + | 0.930569i | \(0.380687\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.37682 | 0.207658 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.2098 | −1.37163 | −0.685817 | − | 0.727774i | \(-0.740555\pi\) | ||||
−0.685817 | + | 0.727774i | \(0.740555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3932 | 0.337376 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.33948 | −0.302853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.6146 | 1.96350 | 0.981750 | − | 0.190177i | \(-0.0609061\pi\) | ||||
0.981750 | + | 0.190177i | \(0.0609061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.50481 | −0.113413 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.2557 | 0.428496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.4087 | 2.36802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1073 | 0.325702 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.3224 | −0.847348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.1364 | −1.67659 | −0.838297 | − | 0.545213i | \(-0.816449\pi\) | ||||
−0.838297 | + | 0.545213i | \(0.816449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.3354 | −1.36001 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.8055 | 1.63042 | 0.815212 | − | 0.579162i | \(-0.196620\pi\) | ||||
0.815212 | + | 0.579162i | \(0.196620\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.16283 | 0.229394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.63804 | 0.276355 | 0.138178 | − | 0.990407i | \(-0.455875\pi\) | ||||
0.138178 | + | 0.990407i | \(0.455875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.00457543 | −0.000146231 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.93044 | 0.189344 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.0179 | −0.797946 | −0.398973 | − | 0.916963i | \(-0.630633\pi\) | ||||
−0.398973 | + | 0.916963i | \(0.630633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.3009 | −0.869879 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.9240 | −0.347362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4716 | 0.364406 | 0.182203 | − | 0.983261i | \(-0.441677\pi\) | ||||
0.182203 | + | 0.983261i | \(0.441677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 67.4387 | 2.14010 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.3794 | 0.772879 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.9322 | 0.472908 | 0.236454 | − | 0.971643i | \(-0.424015\pi\) | ||||
0.236454 | + | 0.971643i | \(0.424015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.05603 | 0.254882 |
(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 | 4508.2.a.f.1.5 | 5 | ||
7.6 | odd | 2 | 644.2.a.d.1.1 | ✓ | 5 | ||
21.20 | even | 2 | 5796.2.a.t.1.3 | 5 | |||
28.27 | even | 2 | 2576.2.a.bb.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.d.1.1 | ✓ | 5 | 7.6 | odd | 2 | ||
2576.2.a.bb.1.5 | 5 | 28.27 | even | 2 | |||
4508.2.a.f.1.5 | 5 | 1.1 | even | 1 | trivial | ||
5796.2.a.t.1.3 | 5 | 21.20 | even | 2 |