Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.312617.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.447481\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.10891 | −1.49122 | −0.745611 | − | 0.666382i | \(-0.767842\pi\) | ||||
−0.745611 | + | 0.666382i | \(0.767842\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.44748 | 1.22374 | ||||||||
\(5\) | −1.70032 | −0.760407 | −0.380204 | − | 0.924903i | \(-0.624146\pi\) | ||||
−0.380204 | + | 0.924903i | \(0.624146\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.14780 | −1.56772 | −0.783861 | − | 0.620936i | \(-0.786753\pi\) | ||||
−0.783861 | + | 0.620936i | \(0.786753\pi\) | |||||||
\(8\) | −0.943696 | −0.333647 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.58582 | 1.13394 | ||||||||
\(11\) | 1.69086 | 0.509812 | 0.254906 | − | 0.966966i | \(-0.417955\pi\) | ||||
0.254906 | + | 0.966966i | \(0.417955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.39118 | −0.385843 | −0.192922 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192922 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(14\) | 8.74732 | 2.33782 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.90480 | −0.726199 | ||||||||
\(17\) | 0.447481 | 0.108530 | 0.0542651 | − | 0.998527i | \(-0.482718\pi\) | ||||
0.0542651 | + | 0.998527i | \(0.482718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61829 | −0.371261 | −0.185631 | − | 0.982620i | \(-0.559433\pi\) | ||||
−0.185631 | + | 0.982620i | \(0.559433\pi\) | |||||||
\(20\) | −4.16151 | −0.930541 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.56585 | −0.760242 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.10891 | −0.421781 | ||||||||
\(26\) | 2.93386 | 0.575377 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.1517 | −1.91849 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.36561 | −1.68211 | −0.841057 | − | 0.540947i | \(-0.818066\pi\) | ||||
−0.841057 | + | 0.540947i | \(0.818066\pi\) | |||||||
\(32\) | 8.01333 | 1.41657 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.943696 | −0.161842 | ||||||||
\(35\) | 7.05260 | 1.19211 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24301 | 0.697546 | 0.348773 | − | 0.937207i | \(-0.386598\pi\) | ||||
0.348773 | + | 0.937207i | \(0.386598\pi\) | |||||||
\(38\) | 3.41282 | 0.553632 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.60459 | 0.253707 | ||||||||
\(41\) | −6.78622 | −1.05983 | −0.529915 | − | 0.848051i | \(-0.677776\pi\) | ||||
−0.529915 | + | 0.848051i | \(0.677776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.81869 | −1.34484 | −0.672419 | − | 0.740171i | \(-0.734745\pi\) | ||||
−0.672419 | + | 0.740171i | \(0.734745\pi\) | |||||||
\(44\) | 4.13834 | 0.623878 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.10891 | 0.310941 | ||||||||
\(47\) | 5.76510 | 0.840926 | 0.420463 | − | 0.907310i | \(-0.361868\pi\) | ||||
0.420463 | + | 0.907310i | \(0.361868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.2043 | 1.45775 | ||||||||
\(50\) | 4.44748 | 0.628969 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.40488 | −0.472172 | ||||||||
\(53\) | 3.27411 | 0.449734 | 0.224867 | − | 0.974389i | \(-0.427805\pi\) | ||||
0.224867 | + | 0.974389i | \(0.427805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87500 | −0.387665 | ||||||||
\(56\) | 3.91426 | 0.523066 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.10891 | 0.276913 | ||||||||
\(59\) | −3.19131 | −0.415473 | −0.207736 | − | 0.978185i | \(-0.566610\pi\) | ||||
−0.207736 | + | 0.978185i | \(0.566610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.01720 | −0.770424 | −0.385212 | − | 0.922828i | \(-0.625872\pi\) | ||||
−0.385212 | + | 0.922828i | \(0.625872\pi\) | |||||||
\(62\) | 19.7512 | 2.50840 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.0898 | −1.38622 | ||||||||
\(65\) | 2.36545 | 0.293398 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.789098 | −0.0964037 | −0.0482018 | − | 0.998838i | \(-0.515349\pi\) | ||||
−0.0482018 | + | 0.998838i | \(0.515349\pi\) | |||||||
\(68\) | 1.09520 | 0.132813 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −14.8733 | −1.77770 | ||||||||
\(71\) | 4.82663 | 0.572816 | 0.286408 | − | 0.958108i | \(-0.407539\pi\) | ||||
0.286408 | + | 0.958108i | \(0.407539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.62623 | 0.190336 | 0.0951679 | − | 0.995461i | \(-0.469661\pi\) | ||||
0.0951679 | + | 0.995461i | \(0.469661\pi\) | |||||||
\(74\) | −8.94810 | −1.04020 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.96073 | −0.454327 | ||||||||
\(77\) | −7.01333 | −0.799244 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.87113 | 0.323027 | 0.161514 | − | 0.986870i | \(-0.448362\pi\) | ||||
0.161514 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(80\) | 4.93909 | 0.552207 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.3115 | 1.58044 | ||||||||
\(83\) | −12.3502 | −1.35561 | −0.677804 | − | 0.735242i | \(-0.737068\pi\) | ||||
−0.677804 | + | 0.735242i | \(0.737068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.760862 | −0.0825271 | ||||||||
\(86\) | 18.5978 | 2.00545 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.59565 | −0.170097 | ||||||||
\(89\) | 1.11874 | 0.118586 | 0.0592931 | − | 0.998241i | \(-0.481115\pi\) | ||||
0.0592931 | + | 0.998241i | \(0.481115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.77033 | 0.604895 | ||||||||
\(92\) | −2.44748 | −0.255168 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.1580 | −1.25401 | ||||||||
\(95\) | 2.75161 | 0.282310 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3358 | 1.35405 | 0.677023 | − | 0.735961i | \(-0.263270\pi\) | ||||
0.677023 | + | 0.735961i | \(0.263270\pi\) | |||||||
\(98\) | −21.5198 | −2.17383 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.16151 | −0.516151 | ||||||||
\(101\) | −4.12480 | −0.410433 | −0.205216 | − | 0.978717i | \(-0.565790\pi\) | ||||
−0.205216 | + | 0.978717i | \(0.565790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1520 | −1.49297 | −0.746487 | − | 0.665400i | \(-0.768261\pi\) | ||||
−0.746487 | + | 0.665400i | \(0.768261\pi\) | |||||||
\(104\) | 1.31285 | 0.128735 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.90480 | −0.670653 | ||||||||
\(107\) | −19.3559 | −1.87121 | −0.935605 | − | 0.353049i | \(-0.885145\pi\) | ||||
−0.935605 | + | 0.353049i | \(0.885145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5279 | −1.39153 | −0.695763 | − | 0.718272i | \(-0.744933\pi\) | ||||
−0.695763 | + | 0.718272i | \(0.744933\pi\) | |||||||
\(110\) | 6.06310 | 0.578094 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.0485 | 1.13848 | ||||||||
\(113\) | −11.9621 | −1.12530 | −0.562650 | − | 0.826695i | \(-0.690218\pi\) | ||||
−0.562650 | + | 0.826695i | \(0.690218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70032 | 0.158556 | ||||||||
\(116\) | −2.44748 | −0.227243 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.73016 | 0.619562 | ||||||||
\(119\) | −1.85606 | −0.170145 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.14101 | −0.740092 | ||||||||
\(122\) | 12.6897 | 1.14887 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −22.9222 | −2.05847 | ||||||||
\(125\) | 12.0874 | 1.08113 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.739002 | −0.0655758 | −0.0327879 | − | 0.999462i | \(-0.510439\pi\) | ||||
−0.0327879 | + | 0.999462i | \(0.510439\pi\) | |||||||
\(128\) | 7.36060 | 0.650591 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.98851 | −0.437521 | ||||||||
\(131\) | 8.68511 | 0.758821 | 0.379411 | − | 0.925228i | \(-0.376127\pi\) | ||||
0.379411 | + | 0.925228i | \(0.376127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.71235 | 0.582034 | ||||||||
\(134\) | 1.66413 | 0.143759 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.422286 | −0.0362107 | ||||||||
\(137\) | −3.99995 | −0.341739 | −0.170869 | − | 0.985294i | \(-0.554658\pi\) | ||||
−0.170869 | + | 0.985294i | \(0.554658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0685 | −1.44773 | −0.723865 | − | 0.689941i | \(-0.757636\pi\) | ||||
−0.723865 | + | 0.689941i | \(0.757636\pi\) | |||||||
\(140\) | 17.2611 | 1.45883 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.1789 | −0.854195 | ||||||||
\(143\) | −2.35228 | −0.196707 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.70032 | 0.141204 | ||||||||
\(146\) | −3.42956 | −0.283833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.3847 | 0.853615 | ||||||||
\(149\) | −5.30507 | −0.434609 | −0.217304 | − | 0.976104i | \(-0.569726\pi\) | ||||
−0.217304 | + | 0.976104i | \(0.569726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.37769 | −0.356252 | −0.178126 | − | 0.984008i | \(-0.557003\pi\) | ||||
−0.178126 | + | 0.984008i | \(0.557003\pi\) | |||||||
\(152\) | 1.52717 | 0.123870 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.7905 | 1.19185 | ||||||||
\(155\) | 15.9246 | 1.27909 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.43735 | 0.593565 | 0.296783 | − | 0.954945i | \(-0.404086\pi\) | ||||
0.296783 | + | 0.954945i | \(0.404086\pi\) | |||||||
\(158\) | −6.05494 | −0.481705 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.6252 | −1.07717 | ||||||||
\(161\) | 4.14780 | 0.326893 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.68883 | 0.602236 | 0.301118 | − | 0.953587i | \(-0.402640\pi\) | ||||
0.301118 | + | 0.953587i | \(0.402640\pi\) | |||||||
\(164\) | −16.6092 | −1.29696 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 26.0454 | 2.02151 | ||||||||
\(167\) | −19.9394 | −1.54296 | −0.771479 | − | 0.636254i | \(-0.780483\pi\) | ||||
−0.771479 | + | 0.636254i | \(0.780483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0646 | −0.851125 | ||||||||
\(170\) | 1.60459 | 0.123066 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21.5836 | −1.64573 | ||||||||
\(173\) | 12.0607 | 0.916958 | 0.458479 | − | 0.888705i | \(-0.348394\pi\) | ||||
0.458479 | + | 0.888705i | \(0.348394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74732 | 0.661236 | ||||||||
\(176\) | −4.91159 | −0.370225 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.35932 | −0.176838 | ||||||||
\(179\) | −1.21963 | −0.0911596 | −0.0455798 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455798 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.67942 | −0.347818 | −0.173909 | − | 0.984762i | \(-0.555640\pi\) | ||||
−0.173909 | + | 0.984762i | \(0.555640\pi\) | |||||||
\(182\) | −12.1691 | −0.902032 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.943696 | 0.0695702 | ||||||||
\(185\) | −7.21448 | −0.530419 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.756626 | 0.0553300 | ||||||||
\(188\) | 14.1100 | 1.02908 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.80289 | −0.420986 | ||||||||
\(191\) | 2.03591 | 0.147313 | 0.0736567 | − | 0.997284i | \(-0.476533\pi\) | ||||
0.0736567 | + | 0.997284i | \(0.476533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.35495 | −0.241495 | −0.120747 | − | 0.992683i | \(-0.538529\pi\) | ||||
−0.120747 | + | 0.992683i | \(0.538529\pi\) | |||||||
\(194\) | −28.1240 | −2.01918 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 24.9748 | 1.78391 | ||||||||
\(197\) | 17.6069 | 1.25444 | 0.627219 | − | 0.778843i | \(-0.284193\pi\) | ||||
0.627219 | + | 0.778843i | \(0.284193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0483 | 1.27941 | 0.639705 | − | 0.768620i | \(-0.279056\pi\) | ||||
0.639705 | + | 0.768620i | \(0.279056\pi\) | |||||||
\(200\) | 1.99016 | 0.140726 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.69881 | 0.612046 | ||||||||
\(203\) | 4.14780 | 0.291119 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5388 | 0.805902 | ||||||||
\(206\) | 31.9542 | 2.22636 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.04109 | 0.280199 | ||||||||
\(209\) | −2.73629 | −0.189273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7200 | 1.49527 | 0.747634 | − | 0.664111i | \(-0.231190\pi\) | ||||
0.747634 | + | 0.664111i | \(0.231190\pi\) | |||||||
\(212\) | 8.01333 | 0.550358 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 40.8199 | 2.79039 | ||||||||
\(215\) | 14.9946 | 1.02262 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 38.8467 | 2.63709 | ||||||||
\(218\) | 30.6381 | 2.07507 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.03650 | −0.474401 | ||||||||
\(221\) | −0.622526 | −0.0418756 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.71850 | −0.115080 | −0.0575398 | − | 0.998343i | \(-0.518326\pi\) | ||||
−0.0575398 | + | 0.998343i | \(0.518326\pi\) | |||||||
\(224\) | −33.2377 | −2.22079 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.2269 | 1.67807 | ||||||||
\(227\) | 6.95007 | 0.461292 | 0.230646 | − | 0.973038i | \(-0.425916\pi\) | ||||
0.230646 | + | 0.973038i | \(0.425916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.10462 | 0.535568 | 0.267784 | − | 0.963479i | \(-0.413709\pi\) | ||||
0.267784 | + | 0.963479i | \(0.413709\pi\) | |||||||
\(230\) | −3.58582 | −0.236442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.943696 | 0.0619567 | ||||||||
\(233\) | 2.41871 | 0.158455 | 0.0792276 | − | 0.996857i | \(-0.474755\pi\) | ||||
0.0792276 | + | 0.996857i | \(0.474755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.80252 | −0.639446 | ||||||||
\(236\) | −7.81066 | −0.508431 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.91426 | 0.253724 | ||||||||
\(239\) | −22.4055 | −1.44929 | −0.724646 | − | 0.689122i | \(-0.757997\pi\) | ||||
−0.724646 | + | 0.689122i | \(0.757997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2500 | −1.24000 | −0.620000 | − | 0.784602i | \(-0.712867\pi\) | ||||
−0.620000 | + | 0.784602i | \(0.712867\pi\) | |||||||
\(242\) | 17.1686 | 1.10364 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.7270 | −0.942799 | ||||||||
\(245\) | −17.3505 | −1.10849 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.25133 | 0.143249 | ||||||||
\(248\) | 8.83829 | 0.561232 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.4912 | −1.61221 | ||||||||
\(251\) | −6.38401 | −0.402955 | −0.201478 | − | 0.979493i | \(-0.564574\pi\) | ||||
−0.201478 | + | 0.979493i | \(0.564574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.69086 | −0.106303 | ||||||||
\(254\) | 1.55849 | 0.0977881 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.65673 | 0.416045 | ||||||||
\(257\) | −16.9585 | −1.05784 | −0.528922 | − | 0.848670i | \(-0.677404\pi\) | ||||
−0.528922 | + | 0.848670i | \(0.677404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5992 | −1.09356 | ||||||||
\(260\) | 5.78939 | 0.359043 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.3161 | −1.13157 | ||||||||
\(263\) | 20.9475 | 1.29168 | 0.645840 | − | 0.763473i | \(-0.276507\pi\) | ||||
0.645840 | + | 0.763473i | \(0.276507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.56705 | −0.341981 | ||||||||
\(266\) | −14.1557 | −0.867942 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.93130 | −0.117973 | ||||||||
\(269\) | 21.3774 | 1.30341 | 0.651703 | − | 0.758475i | \(-0.274055\pi\) | ||||
0.651703 | + | 0.758475i | \(0.274055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9086 | 0.662651 | 0.331326 | − | 0.943517i | \(-0.392504\pi\) | ||||
0.331326 | + | 0.943517i | \(0.392504\pi\) | |||||||
\(272\) | −1.29984 | −0.0788145 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.43551 | 0.509608 | ||||||||
\(275\) | −3.56585 | −0.215029 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2829 | −1.09851 | −0.549256 | − | 0.835654i | \(-0.685089\pi\) | ||||
−0.549256 | + | 0.835654i | \(0.685089\pi\) | |||||||
\(278\) | 35.9958 | 2.15889 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.65551 | −0.397743 | ||||||||
\(281\) | 12.5221 | 0.747005 | 0.373503 | − | 0.927629i | \(-0.378157\pi\) | ||||
0.373503 | + | 0.927629i | \(0.378157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4946 | 0.980502 | 0.490251 | − | 0.871581i | \(-0.336905\pi\) | ||||
0.490251 | + | 0.871581i | \(0.336905\pi\) | |||||||
\(284\) | 11.8131 | 0.700978 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.96073 | 0.293334 | ||||||||
\(287\) | 28.1479 | 1.66152 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7998 | −0.988221 | ||||||||
\(290\) | −3.58582 | −0.210566 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.98017 | 0.232922 | ||||||||
\(293\) | −16.6292 | −0.971486 | −0.485743 | − | 0.874102i | \(-0.661451\pi\) | ||||
−0.485743 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.42625 | 0.315928 | ||||||||
\(296\) | −4.00411 | −0.232734 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.1879 | 0.648097 | ||||||||
\(299\) | 1.39118 | 0.0804539 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.5782 | 2.10833 | ||||||||
\(302\) | 9.23214 | 0.531250 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.70080 | 0.269610 | ||||||||
\(305\) | 10.2312 | 0.585836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.19558 | −0.467747 | −0.233873 | − | 0.972267i | \(-0.575140\pi\) | ||||
−0.233873 | + | 0.972267i | \(0.575140\pi\) | |||||||
\(308\) | −17.1650 | −0.978067 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −33.5834 | −1.90741 | ||||||||
\(311\) | 1.00832 | 0.0571767 | 0.0285883 | − | 0.999591i | \(-0.490899\pi\) | ||||
0.0285883 | + | 0.999591i | \(0.490899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.3396 | 1.14966 | 0.574832 | − | 0.818271i | \(-0.305067\pi\) | ||||
0.574832 | + | 0.818271i | \(0.305067\pi\) | |||||||
\(314\) | −15.6847 | −0.885137 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.02704 | 0.395302 | ||||||||
\(317\) | 16.9983 | 0.954719 | 0.477359 | − | 0.878708i | \(-0.341594\pi\) | ||||
0.477359 | + | 0.878708i | \(0.341594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.69086 | −0.0946697 | ||||||||
\(320\) | 18.8562 | 1.05409 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.74732 | −0.487469 | ||||||||
\(323\) | −0.724154 | −0.0402930 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.93386 | 0.162741 | ||||||||
\(326\) | −16.2150 | −0.898067 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.40413 | 0.353609 | ||||||||
\(329\) | −23.9125 | −1.31834 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8638 | −1.64146 | −0.820732 | − | 0.571314i | \(-0.806434\pi\) | ||||
−0.820732 | + | 0.571314i | \(0.806434\pi\) | |||||||
\(332\) | −30.2268 | −1.65891 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 42.0503 | 2.30089 | ||||||||
\(335\) | 1.34172 | 0.0733060 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.68783 | 0.0919420 | 0.0459710 | − | 0.998943i | \(-0.485362\pi\) | ||||
0.0459710 | + | 0.998943i | \(0.485362\pi\) | |||||||
\(338\) | 23.3342 | 1.26922 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.86220 | −0.100992 | ||||||||
\(341\) | −15.8359 | −0.857562 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2907 | −0.717630 | ||||||||
\(344\) | 8.32216 | 0.448701 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.4349 | −1.36739 | ||||||||
\(347\) | 12.4406 | 0.667848 | 0.333924 | − | 0.942600i | \(-0.391627\pi\) | ||||
0.333924 | + | 0.942600i | \(0.391627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6676 | 0.731612 | 0.365806 | − | 0.930691i | \(-0.380793\pi\) | ||||
0.365806 | + | 0.930691i | \(0.380793\pi\) | |||||||
\(350\) | −18.4473 | −0.986048 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.5494 | 0.722185 | ||||||||
\(353\) | −19.9111 | −1.05976 | −0.529881 | − | 0.848072i | \(-0.677764\pi\) | ||||
−0.529881 | + | 0.848072i | \(0.677764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.20683 | −0.435573 | ||||||||
\(356\) | 2.73810 | 0.145119 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.57209 | 0.135939 | ||||||||
\(359\) | 2.91592 | 0.153896 | 0.0769482 | − | 0.997035i | \(-0.475482\pi\) | ||||
0.0769482 | + | 0.997035i | \(0.475482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3811 | −0.862165 | ||||||||
\(362\) | 9.86845 | 0.518674 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.1228 | 0.740234 | ||||||||
\(365\) | −2.76511 | −0.144733 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.02666 | −0.314589 | −0.157294 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157294 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(368\) | 2.90480 | 0.151423 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.2146 | 0.790972 | ||||||||
\(371\) | −13.5804 | −0.705058 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.7097 | 1.53831 | 0.769155 | − | 0.639063i | \(-0.220678\pi\) | ||||
0.769155 | + | 0.639063i | \(0.220678\pi\) | |||||||
\(374\) | −1.59565 | −0.0825092 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.44050 | −0.280572 | ||||||||
\(377\) | 1.39118 | 0.0716493 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1750 | −1.39589 | −0.697943 | − | 0.716153i | \(-0.745901\pi\) | ||||
−0.697943 | + | 0.716153i | \(0.745901\pi\) | |||||||
\(380\) | 6.73452 | 0.345474 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.29354 | −0.219677 | ||||||||
\(383\) | 21.6492 | 1.10622 | 0.553111 | − | 0.833108i | \(-0.313440\pi\) | ||||
0.553111 | + | 0.833108i | \(0.313440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9249 | 0.607751 | ||||||||
\(386\) | 7.07527 | 0.360122 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 32.6392 | 1.65700 | ||||||||
\(389\) | −19.9748 | −1.01276 | −0.506382 | − | 0.862309i | \(-0.669017\pi\) | ||||
−0.506382 | + | 0.862309i | \(0.669017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.447481 | −0.0226301 | ||||||||
\(392\) | −9.62973 | −0.486375 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −37.1313 | −1.87065 | ||||||||
\(395\) | −4.88185 | −0.245632 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0159 | 0.502683 | 0.251342 | − | 0.967898i | \(-0.419128\pi\) | ||||
0.251342 | + | 0.967898i | \(0.419128\pi\) | |||||||
\(398\) | −38.0622 | −1.90788 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.12594 | 0.306297 | ||||||||
\(401\) | 32.7020 | 1.63306 | 0.816529 | − | 0.577304i | \(-0.195895\pi\) | ||||
0.816529 | + | 0.577304i | \(0.195895\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0292 | 0.649032 | ||||||||
\(404\) | −10.0954 | −0.502263 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.74732 | −0.434122 | ||||||||
\(407\) | 7.17431 | 0.355617 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.79151 | 0.0885843 | 0.0442921 | − | 0.999019i | \(-0.485897\pi\) | ||||
0.0442921 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(410\) | −24.3342 | −1.20178 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −37.0843 | −1.82701 | ||||||||
\(413\) | 13.2369 | 0.651346 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.9993 | 1.03081 | ||||||||
\(416\) | −11.1480 | −0.546574 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.77058 | 0.282248 | ||||||||
\(419\) | 13.5809 | 0.663469 | 0.331734 | − | 0.943373i | \(-0.392366\pi\) | ||||
0.331734 | + | 0.943373i | \(0.392366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.9168 | 1.06816 | 0.534079 | − | 0.845435i | \(-0.320658\pi\) | ||||
0.534079 | + | 0.845435i | \(0.320658\pi\) | |||||||
\(422\) | −45.8055 | −2.22978 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.08977 | −0.150052 | ||||||||
\(425\) | −0.943696 | −0.0457760 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.9582 | 1.20781 | ||||||||
\(428\) | −47.3733 | −2.28988 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −31.6222 | −1.52496 | ||||||||
\(431\) | −39.4774 | −1.90156 | −0.950780 | − | 0.309866i | \(-0.899716\pi\) | ||||
−0.950780 | + | 0.309866i | \(0.899716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.4149 | 1.84610 | 0.923051 | − | 0.384677i | \(-0.125687\pi\) | ||||
0.923051 | + | 0.384677i | \(0.125687\pi\) | |||||||
\(434\) | −81.9241 | −3.93248 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.5569 | −1.70287 | ||||||||
\(437\) | 1.61829 | 0.0774133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6601 | −1.17696 | −0.588480 | − | 0.808512i | \(-0.700274\pi\) | ||||
−0.588480 | + | 0.808512i | \(0.700274\pi\) | |||||||
\(440\) | 2.71312 | 0.129343 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.31285 | 0.0624458 | ||||||||
\(443\) | 18.1723 | 0.863394 | 0.431697 | − | 0.902019i | \(-0.357915\pi\) | ||||
0.431697 | + | 0.902019i | \(0.357915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.90222 | −0.0901738 | ||||||||
\(446\) | 3.62416 | 0.171609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 45.9982 | 2.17321 | ||||||||
\(449\) | 12.8184 | 0.604939 | 0.302469 | − | 0.953159i | \(-0.402189\pi\) | ||||
0.302469 | + | 0.953159i | \(0.402189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4745 | −0.540314 | ||||||||
\(452\) | −29.2770 | −1.37707 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.6570 | −0.687889 | ||||||||
\(455\) | −9.81142 | −0.459966 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00643 | −0.327747 | −0.163873 | − | 0.986481i | \(-0.552399\pi\) | ||||
−0.163873 | + | 0.986481i | \(0.552399\pi\) | |||||||
\(458\) | −17.0919 | −0.798651 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.16151 | 0.194031 | ||||||||
\(461\) | −9.09038 | −0.423381 | −0.211691 | − | 0.977337i | \(-0.567897\pi\) | ||||
−0.211691 | + | 0.977337i | \(0.567897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3440 | −0.806045 | −0.403023 | − | 0.915190i | \(-0.632040\pi\) | ||||
−0.403023 | + | 0.915190i | \(0.632040\pi\) | |||||||
\(464\) | 2.90480 | 0.134852 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.10084 | −0.236292 | ||||||||
\(467\) | 3.25749 | 0.150738 | 0.0753692 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753692 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.27302 | 0.151134 | ||||||||
\(470\) | 20.6726 | 0.953556 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.01162 | 0.138621 | ||||||||
\(473\) | −14.9111 | −0.685615 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.41282 | 0.156591 | ||||||||
\(476\) | −4.54268 | −0.208214 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 47.2511 | 2.16121 | ||||||||
\(479\) | 29.1623 | 1.33246 | 0.666230 | − | 0.745747i | \(-0.267907\pi\) | ||||
0.666230 | + | 0.745747i | \(0.267907\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.90277 | −0.269143 | ||||||||
\(482\) | 40.5964 | 1.84911 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.9250 | −0.905680 | ||||||||
\(485\) | −22.6752 | −1.02963 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.20908 | −0.190732 | −0.0953658 | − | 0.995442i | \(-0.530402\pi\) | ||||
−0.0953658 | + | 0.995442i | \(0.530402\pi\) | |||||||
\(488\) | 5.67841 | 0.257049 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 36.5907 | 1.65300 | ||||||||
\(491\) | −3.86511 | −0.174430 | −0.0872150 | − | 0.996190i | \(-0.527797\pi\) | ||||
−0.0872150 | + | 0.996190i | \(0.527797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.447481 | −0.0201535 | ||||||||
\(494\) | −4.74784 | −0.213615 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.2052 | 1.22155 | ||||||||
\(497\) | −20.0199 | −0.898016 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.52762 | −0.113152 | −0.0565759 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565759 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(500\) | 29.5838 | 1.32303 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.4633 | 0.600896 | ||||||||
\(503\) | 31.9416 | 1.42420 | 0.712102 | − | 0.702076i | \(-0.247743\pi\) | ||||
0.712102 | + | 0.702076i | \(0.247743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.01349 | 0.312096 | ||||||||
\(506\) | 3.56585 | 0.158522 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.80869 | −0.0802478 | ||||||||
\(509\) | −17.0955 | −0.757745 | −0.378873 | − | 0.925449i | \(-0.623688\pi\) | ||||
−0.378873 | + | 0.925449i | \(0.623688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.74528 | −0.298394 | ||||||||
\(512\) | −28.7596 | −1.27101 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 35.7640 | 1.57748 | ||||||||
\(515\) | 25.7633 | 1.13527 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.74795 | 0.428714 | ||||||||
\(518\) | 37.1149 | 1.63074 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.23226 | −0.0978913 | ||||||||
\(521\) | −5.35710 | −0.234699 | −0.117349 | − | 0.993091i | \(-0.537440\pi\) | ||||
−0.117349 | + | 0.993091i | \(0.537440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.9503 | 1.79063 | 0.895316 | − | 0.445432i | \(-0.146950\pi\) | ||||
0.895316 | + | 0.445432i | \(0.146950\pi\) | |||||||
\(524\) | 21.2566 | 0.928600 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −44.1763 | −1.92618 | ||||||||
\(527\) | −4.19094 | −0.182560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 11.7404 | 0.509969 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.4283 | 0.712259 | ||||||||
\(533\) | 9.44084 | 0.408928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.9113 | 1.42288 | ||||||||
\(536\) | 0.744668 | 0.0321648 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −45.0830 | −1.94367 | ||||||||
\(539\) | 17.2539 | 0.743180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8469 | −0.552333 | −0.276166 | − | 0.961110i | \(-0.589064\pi\) | ||||
−0.276166 | + | 0.961110i | \(0.589064\pi\) | |||||||
\(542\) | −23.0052 | −0.988159 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.58582 | 0.153741 | ||||||||
\(545\) | 24.7022 | 1.05813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.13191 | 0.347695 | 0.173848 | − | 0.984773i | \(-0.444380\pi\) | ||||
0.173848 | + | 0.984773i | \(0.444380\pi\) | |||||||
\(548\) | −9.78980 | −0.418199 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.52005 | 0.320656 | ||||||||
\(551\) | 1.61829 | 0.0689415 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.9089 | −0.506417 | ||||||||
\(554\) | 38.5569 | 1.63812 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.7748 | −1.77165 | ||||||||
\(557\) | 23.6634 | 1.00265 | 0.501326 | − | 0.865259i | \(-0.332846\pi\) | ||||
0.501326 | + | 0.865259i | \(0.332846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.2684 | 0.518897 | ||||||||
\(560\) | −20.4864 | −0.865708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.4079 | −1.11395 | ||||||||
\(563\) | 3.36335 | 0.141748 | 0.0708742 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708742 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3394 | 0.855685 | ||||||||
\(566\) | −34.7855 | −1.46215 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.55487 | −0.191118 | ||||||||
\(569\) | 20.7465 | 0.869737 | 0.434868 | − | 0.900494i | \(-0.356795\pi\) | ||||
0.434868 | + | 0.900494i | \(0.356795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.6361 | −1.78427 | −0.892133 | − | 0.451773i | \(-0.850792\pi\) | ||||
−0.892133 | + | 0.451773i | \(0.850792\pi\) | |||||||
\(572\) | −5.75716 | −0.240719 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −59.3613 | −2.47769 | ||||||||
\(575\) | 2.10891 | 0.0879474 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.2162 | −1.50770 | −0.753851 | − | 0.657045i | \(-0.771806\pi\) | ||||
−0.753851 | + | 0.657045i | \(0.771806\pi\) | |||||||
\(578\) | 35.4291 | 1.47366 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.16151 | 0.172797 | ||||||||
\(581\) | 51.2261 | 2.12522 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.53605 | 0.229280 | ||||||||
\(584\) | −1.53467 | −0.0635049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.0693 | 1.44870 | ||||||||
\(587\) | 5.87794 | 0.242609 | 0.121304 | − | 0.992615i | \(-0.461292\pi\) | ||||
0.121304 | + | 0.992615i | \(0.461292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.1563 | 0.624503 | ||||||||
\(590\) | −11.4434 | −0.471119 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.3251 | −0.506557 | ||||||||
\(593\) | 6.08323 | 0.249808 | 0.124904 | − | 0.992169i | \(-0.460138\pi\) | ||||
0.124904 | + | 0.992169i | \(0.460138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.15591 | 0.129380 | ||||||||
\(596\) | −12.9841 | −0.531848 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.93386 | −0.119974 | ||||||||
\(599\) | 31.2292 | 1.27599 | 0.637995 | − | 0.770040i | \(-0.279764\pi\) | ||||
0.637995 | + | 0.770040i | \(0.279764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2896 | 1.48028 | 0.740142 | − | 0.672451i | \(-0.234758\pi\) | ||||
0.740142 | + | 0.672451i | \(0.234758\pi\) | |||||||
\(602\) | −77.1400 | −3.14399 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.7143 | −0.435959 | ||||||||
\(605\) | 13.8423 | 0.562771 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8055 | 1.29095 | 0.645473 | − | 0.763783i | \(-0.276660\pi\) | ||||
0.645473 | + | 0.763783i | \(0.276660\pi\) | |||||||
\(608\) | −12.9679 | −0.525918 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.5766 | −0.873611 | ||||||||
\(611\) | −8.02027 | −0.324466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.64787 | 0.228115 | 0.114058 | − | 0.993474i | \(-0.463615\pi\) | ||||
0.114058 | + | 0.993474i | \(0.463615\pi\) | |||||||
\(614\) | 17.2837 | 0.697514 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.61845 | 0.266665 | ||||||||
\(617\) | 9.45805 | 0.380767 | 0.190383 | − | 0.981710i | \(-0.439027\pi\) | ||||
0.190383 | + | 0.981710i | \(0.439027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.5412 | −1.22756 | −0.613778 | − | 0.789479i | \(-0.710351\pi\) | ||||
−0.613778 | + | 0.789479i | \(0.710351\pi\) | |||||||
\(620\) | 38.9751 | 1.56528 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.12646 | −0.0852631 | ||||||||
\(623\) | −4.64031 | −0.185910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0080 | −0.400320 | ||||||||
\(626\) | −42.8944 | −1.71440 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.2028 | 0.726370 | ||||||||
\(629\) | 1.89867 | 0.0757048 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0399 | 1.27549 | 0.637743 | − | 0.770249i | \(-0.279868\pi\) | ||||
0.637743 | + | 0.770249i | \(0.279868\pi\) | |||||||
\(632\) | −2.70947 | −0.107777 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35.8478 | −1.42370 | ||||||||
\(635\) | 1.25654 | 0.0498643 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1960 | −0.562464 | ||||||||
\(638\) | 3.56585 | 0.141173 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.5154 | −0.494714 | ||||||||
\(641\) | −11.6295 | −0.459337 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.2518 | 0.877527 | 0.438763 | − | 0.898603i | \(-0.355417\pi\) | ||||
0.438763 | + | 0.898603i | \(0.355417\pi\) | |||||||
\(644\) | 10.1517 | 0.400032 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.52717 | 0.0600858 | ||||||||
\(647\) | 49.8578 | 1.96011 | 0.980056 | − | 0.198721i | \(-0.0636788\pi\) | ||||
0.980056 | + | 0.198721i | \(0.0636788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.39604 | −0.211813 | ||||||||
\(650\) | −6.18723 | −0.242683 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.8183 | 0.736980 | ||||||||
\(653\) | 11.6765 | 0.456938 | 0.228469 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228469 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7675 | −0.577013 | ||||||||
\(656\) | 19.7126 | 0.769648 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 50.4292 | 1.96593 | ||||||||
\(659\) | 4.04973 | 0.157755 | 0.0788775 | − | 0.996884i | \(-0.474866\pi\) | ||||
0.0788775 | + | 0.996884i | \(0.474866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.81096 | −0.303811 | −0.151905 | − | 0.988395i | \(-0.548541\pi\) | ||||
−0.151905 | + | 0.988395i | \(0.548541\pi\) | |||||||
\(662\) | 62.9800 | 2.44779 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.6548 | 0.452294 | ||||||||
\(665\) | −11.4132 | −0.442583 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −48.8014 | −1.88818 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.82956 | −0.109315 | ||||||||
\(671\) | −10.1742 | −0.392771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0017 | 0.616819 | 0.308410 | − | 0.951254i | \(-0.400203\pi\) | ||||
0.308410 | + | 0.951254i | \(0.400203\pi\) | |||||||
\(674\) | −3.55948 | −0.137106 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −27.0805 | −1.04156 | ||||||||
\(677\) | 34.7639 | 1.33609 | 0.668043 | − | 0.744123i | \(-0.267132\pi\) | ||||
0.668043 | + | 0.744123i | \(0.267132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −55.3143 | −2.12277 | ||||||||
\(680\) | 0.718023 | 0.0275349 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.3964 | 1.27881 | ||||||||
\(683\) | 18.2709 | 0.699118 | 0.349559 | − | 0.936914i | \(-0.386331\pi\) | ||||
0.349559 | + | 0.936914i | \(0.386331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.80120 | 0.259860 | ||||||||
\(686\) | 28.0288 | 1.07014 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.6165 | 0.976621 | ||||||||
\(689\) | −4.55487 | −0.173527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3284 | −0.849411 | −0.424705 | − | 0.905332i | \(-0.639622\pi\) | ||||
−0.424705 | + | 0.905332i | \(0.639622\pi\) | |||||||
\(692\) | 29.5184 | 1.12212 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.2361 | −0.995909 | ||||||||
\(695\) | 29.0219 | 1.10086 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.03671 | −0.115024 | ||||||||
\(698\) | −28.8237 | −1.09099 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.4089 | 0.809181 | ||||||||
\(701\) | 8.51917 | 0.321765 | 0.160882 | − | 0.986974i | \(-0.448566\pi\) | ||||
0.160882 | + | 0.986974i | \(0.448566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.86641 | −0.258972 | ||||||||
\(704\) | −18.7512 | −0.706712 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41.9907 | 1.58034 | ||||||||
\(707\) | 17.1089 | 0.643445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.3762 | −1.32858 | −0.664291 | − | 0.747474i | \(-0.731266\pi\) | ||||
−0.664291 | + | 0.747474i | \(0.731266\pi\) | |||||||
\(710\) | 17.3074 | 0.649536 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.05575 | −0.0395659 | ||||||||
\(713\) | 9.36561 | 0.350745 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.99963 | 0.149578 | ||||||||
\(716\) | −2.98503 | −0.111556 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.14940 | −0.229493 | ||||||||
\(719\) | 6.90935 | 0.257675 | 0.128838 | − | 0.991666i | \(-0.458875\pi\) | ||||
0.128838 | + | 0.991666i | \(0.458875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.8477 | 2.34057 | ||||||||
\(722\) | 34.5463 | 1.28568 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.4528 | −0.425639 | ||||||||
\(725\) | 2.10891 | 0.0783228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7011 | 1.13864 | 0.569321 | − | 0.822115i | \(-0.307206\pi\) | ||||
0.569321 | + | 0.822115i | \(0.307206\pi\) | |||||||
\(728\) | −5.44544 | −0.201821 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.83136 | 0.215828 | ||||||||
\(731\) | −3.94620 | −0.145956 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.6874 | 0.764108 | 0.382054 | − | 0.924140i | \(-0.375217\pi\) | ||||
0.382054 | + | 0.924140i | \(0.375217\pi\) | |||||||
\(734\) | 12.7096 | 0.469122 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.01333 | −0.295375 | ||||||||
\(737\) | −1.33425 | −0.0491477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.99509 | −0.330890 | −0.165445 | − | 0.986219i | \(-0.552906\pi\) | ||||
−0.165445 | + | 0.986219i | \(0.552906\pi\) | |||||||
\(740\) | −17.6573 | −0.649095 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.6397 | 1.05140 | ||||||||
\(743\) | −48.0981 | −1.76455 | −0.882274 | − | 0.470737i | \(-0.843988\pi\) | ||||
−0.882274 | + | 0.470737i | \(0.843988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.02033 | 0.330479 | ||||||||
\(746\) | −62.6549 | −2.29396 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.85183 | 0.0677096 | ||||||||
\(749\) | 80.2846 | 2.93354 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.7371 | −0.902670 | −0.451335 | − | 0.892355i | \(-0.649052\pi\) | ||||
−0.451335 | + | 0.892355i | \(0.649052\pi\) | |||||||
\(752\) | −16.7464 | −0.610680 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.93386 | −0.106845 | ||||||||
\(755\) | 7.44349 | 0.270896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0418 | −1.38265 | −0.691327 | − | 0.722542i | \(-0.742973\pi\) | ||||
−0.691327 | + | 0.722542i | \(0.742973\pi\) | |||||||
\(758\) | 57.3095 | 2.08158 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.59669 | −0.0941917 | ||||||||
\(761\) | 33.9991 | 1.23247 | 0.616233 | − | 0.787564i | \(-0.288658\pi\) | ||||
0.616233 | + | 0.787564i | \(0.288658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60.2591 | 2.18152 | ||||||||
\(764\) | 4.98285 | 0.180273 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −45.6561 | −1.64962 | ||||||||
\(767\) | 4.43967 | 0.160307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6812 | 1.07033 | 0.535167 | − | 0.844747i | \(-0.320249\pi\) | ||||
0.535167 | + | 0.844747i | \(0.320249\pi\) | |||||||
\(770\) | −25.1485 | −0.906291 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.21118 | −0.295527 | ||||||||
\(773\) | 18.1304 | 0.652104 | 0.326052 | − | 0.945352i | \(-0.394282\pi\) | ||||
0.326052 | + | 0.945352i | \(0.394282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.7512 | 0.709484 | ||||||||
\(776\) | −12.5850 | −0.451773 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42.1250 | 1.51025 | ||||||||
\(779\) | 10.9821 | 0.393474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.16114 | 0.292028 | ||||||||
\(782\) | 0.943696 | 0.0337465 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29.6413 | −1.05862 | ||||||||
\(785\) | −12.6459 | −0.451351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.4897 | −0.979904 | −0.489952 | − | 0.871750i | \(-0.662986\pi\) | ||||
−0.489952 | + | 0.871750i | \(0.662986\pi\) | |||||||
\(788\) | 43.0925 | 1.53511 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.2954 | 0.366292 | ||||||||
\(791\) | 49.6164 | 1.76416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.37099 | 0.297263 | ||||||||
\(794\) | −21.1226 | −0.749612 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 44.1729 | 1.56567 | ||||||||
\(797\) | 18.9492 | 0.671217 | 0.335608 | − | 0.942002i | \(-0.391058\pi\) | ||||
0.335608 | + | 0.942002i | \(0.391058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.57977 | 0.0912658 | ||||||||
\(800\) | −16.8994 | −0.597483 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −68.9653 | −2.43525 | ||||||||
\(803\) | 2.74972 | 0.0970354 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.05260 | −0.248572 | ||||||||
\(806\) | −27.4774 | −0.967850 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.89255 | 0.136940 | ||||||||
\(809\) | 31.3371 | 1.10176 | 0.550878 | − | 0.834586i | \(-0.314293\pi\) | ||||
0.550878 | + | 0.834586i | \(0.314293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.22969 | −0.0782948 | −0.0391474 | − | 0.999233i | \(-0.512464\pi\) | ||||
−0.0391474 | + | 0.999233i | \(0.512464\pi\) | |||||||
\(812\) | 10.1517 | 0.356254 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.1299 | −0.530304 | ||||||||
\(815\) | −13.0735 | −0.457944 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.2712 | 0.499286 | ||||||||
\(818\) | −3.77812 | −0.132099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.2409 | 0.986215 | ||||||||
\(821\) | 8.93914 | 0.311978 | 0.155989 | − | 0.987759i | \(-0.450144\pi\) | ||||
0.155989 | + | 0.987759i | \(0.450144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.05732 | −0.0368559 | −0.0184279 | − | 0.999830i | \(-0.505866\pi\) | ||||
−0.0184279 | + | 0.999830i | \(0.505866\pi\) | |||||||
\(824\) | 14.2989 | 0.498126 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.9154 | −0.971301 | ||||||||
\(827\) | 1.63075 | 0.0567066 | 0.0283533 | − | 0.999598i | \(-0.490974\pi\) | ||||
0.0283533 | + | 0.999598i | \(0.490974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.4947 | −1.68429 | −0.842145 | − | 0.539252i | \(-0.818707\pi\) | ||||
−0.842145 | + | 0.539252i | \(0.818707\pi\) | |||||||
\(830\) | −44.2855 | −1.53717 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.4278 | 0.534864 | ||||||||
\(833\) | 4.56622 | 0.158210 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9034 | 1.17328 | ||||||||
\(836\) | −6.69703 | −0.231622 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.6408 | −0.989379 | ||||||||
\(839\) | 11.4182 | 0.394201 | 0.197100 | − | 0.980383i | \(-0.436848\pi\) | ||||
0.197100 | + | 0.980383i | \(0.436848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −46.2204 | −1.59286 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 53.1594 | 1.82982 | ||||||||
\(845\) | 18.8134 | 0.647202 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.7673 | 1.16026 | ||||||||
\(848\) | −9.51064 | −0.326597 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.99016 | 0.0682621 | ||||||||
\(851\) | −4.24301 | −0.145448 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.33060 | −0.285234 | −0.142617 | − | 0.989778i | \(-0.545552\pi\) | ||||
−0.142617 | + | 0.989778i | \(0.545552\pi\) | |||||||
\(854\) | −52.6344 | −1.80111 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.2661 | 0.624323 | ||||||||
\(857\) | 16.7918 | 0.573597 | 0.286799 | − | 0.957991i | \(-0.407409\pi\) | ||||
0.286799 | + | 0.957991i | \(0.407409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9260 | 0.679867 | 0.339934 | − | 0.940449i | \(-0.389595\pi\) | ||||
0.339934 | + | 0.940449i | \(0.389595\pi\) | |||||||
\(860\) | 36.6991 | 1.25143 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 83.2541 | 2.83565 | ||||||||
\(863\) | 6.97593 | 0.237463 | 0.118732 | − | 0.992926i | \(-0.462117\pi\) | ||||
0.118732 | + | 0.992926i | \(0.462117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.5071 | −0.697262 | ||||||||
\(866\) | −81.0134 | −2.75295 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 95.0766 | 3.22711 | ||||||||
\(869\) | 4.85467 | 0.164683 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.09777 | 0.0371967 | ||||||||
\(872\) | 13.7100 | 0.464278 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.41282 | −0.115440 | ||||||||
\(875\) | −50.1363 | −1.69492 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.4415 | −1.26431 | −0.632154 | − | 0.774843i | \(-0.717829\pi\) | ||||
−0.632154 | + | 0.774843i | \(0.717829\pi\) | |||||||
\(878\) | 52.0057 | 1.75511 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.35129 | 0.281522 | ||||||||
\(881\) | 25.2931 | 0.852147 | 0.426073 | − | 0.904689i | \(-0.359897\pi\) | ||||
0.426073 | + | 0.904689i | \(0.359897\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2727 | 0.749536 | 0.374768 | − | 0.927119i | \(-0.377722\pi\) | ||||
0.374768 | + | 0.927119i | \(0.377722\pi\) | |||||||
\(884\) | −1.52362 | −0.0512449 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.3237 | −1.28751 | ||||||||
\(887\) | 31.6882 | 1.06399 | 0.531993 | − | 0.846749i | \(-0.321443\pi\) | ||||
0.531993 | + | 0.846749i | \(0.321443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.06524 | 0.102805 | ||||||||
\(890\) | 4.01160 | 0.134469 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.20601 | −0.140828 | ||||||||
\(893\) | −9.32960 | −0.312203 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.07377 | 0.0693184 | ||||||||
\(896\) | −30.5303 | −1.01995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.0328 | −0.902098 | ||||||||
\(899\) | 9.36561 | 0.312361 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.46511 | 0.0488097 | ||||||||
\(902\) | 24.1987 | 0.805728 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2886 | 0.375453 | ||||||||
\(905\) | 7.95651 | 0.264483 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1899 | −1.03564 | −0.517822 | − | 0.855489i | \(-0.673257\pi\) | ||||
−0.517822 | + | 0.855489i | \(0.673257\pi\) | |||||||
\(908\) | 17.0102 | 0.564502 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.6913 | 0.685912 | ||||||||
\(911\) | −22.9836 | −0.761481 | −0.380740 | − | 0.924682i | \(-0.624331\pi\) | ||||
−0.380740 | + | 0.924682i | \(0.624331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.8824 | −0.691105 | ||||||||
\(914\) | 14.7759 | 0.488743 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.8359 | 0.655396 | ||||||||
\(917\) | −36.0241 | −1.18962 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.47938 | 0.312696 | 0.156348 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156348 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(920\) | −1.60459 | −0.0529017 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.1708 | 0.631355 | ||||||||
\(923\) | −6.71470 | −0.221017 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.94810 | −0.294212 | ||||||||
\(926\) | 36.5769 | 1.20199 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.01333 | −0.263051 | ||||||||
\(929\) | −32.5207 | −1.06697 | −0.533485 | − | 0.845810i | \(-0.679118\pi\) | ||||
−0.533485 | + | 0.845810i | \(0.679118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5135 | −0.541207 | ||||||||
\(932\) | 5.91975 | 0.193908 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.86973 | −0.224784 | ||||||||
\(935\) | −1.28651 | −0.0420733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.9482 | 0.749684 | 0.374842 | − | 0.927089i | \(-0.377697\pi\) | ||||
0.374842 | + | 0.927089i | \(0.377697\pi\) | |||||||
\(938\) | −6.90250 | −0.225374 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.9915 | −0.782516 | ||||||||
\(941\) | 40.6049 | 1.32368 | 0.661840 | − | 0.749645i | \(-0.269776\pi\) | ||||
0.661840 | + | 0.749645i | \(0.269776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.78622 | 0.220990 | ||||||||
\(944\) | 9.27010 | 0.301716 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.4462 | 1.02240 | ||||||||
\(947\) | 5.50625 | 0.178929 | 0.0894646 | − | 0.995990i | \(-0.471484\pi\) | ||||
0.0894646 | + | 0.995990i | \(0.471484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.26237 | −0.0734397 | ||||||||
\(950\) | −7.19731 | −0.233512 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.75156 | 0.0567684 | ||||||||
\(953\) | −0.342739 | −0.0111024 | −0.00555120 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555120 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.46170 | −0.112018 | ||||||||
\(956\) | −54.8371 | −1.77356 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −61.5005 | −1.98699 | ||||||||
\(959\) | 16.5910 | 0.535751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.7147 | 1.82951 | ||||||||
\(962\) | 12.4484 | 0.401352 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −47.1139 | −1.51744 | ||||||||
\(965\) | 5.70450 | 0.183634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.4218 | 0.656722 | 0.328361 | − | 0.944552i | \(-0.393504\pi\) | ||||
0.328361 | + | 0.944552i | \(0.393504\pi\) | |||||||
\(968\) | 7.68264 | 0.246929 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 47.8198 | 1.53540 | ||||||||
\(971\) | −61.1290 | −1.96172 | −0.980861 | − | 0.194710i | \(-0.937623\pi\) | ||||
−0.980861 | + | 0.194710i | \(0.937623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.7968 | 2.26964 | ||||||||
\(974\) | 8.87655 | 0.284423 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.4788 | 0.559481 | ||||||||
\(977\) | −3.33305 | −0.106634 | −0.0533169 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533169 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.89163 | 0.0604567 | ||||||||
\(980\) | −42.4651 | −1.35650 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.15115 | 0.260114 | ||||||||
\(983\) | 15.6569 | 0.499377 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.9374 | −0.953884 | ||||||||
\(986\) | 0.943696 | 0.0300534 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.51008 | 0.175299 | ||||||||
\(989\) | 8.81869 | 0.280418 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7559 | −0.564036 | −0.282018 | − | 0.959409i | \(-0.591004\pi\) | ||||
−0.282018 | + | 0.959409i | \(0.591004\pi\) | |||||||
\(992\) | −75.0498 | −2.38283 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.2201 | 1.33914 | ||||||||
\(995\) | −30.6879 | −0.972873 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.3955 | −1.18433 | −0.592164 | − | 0.805818i | \(-0.701726\pi\) | ||||
−0.592164 | + | 0.805818i | \(0.701726\pi\) | |||||||
\(998\) | 5.33051 | 0.168734 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.h.1.1 | 5 | ||
3.2 | odd | 2 | 2001.2.a.h.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.h.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
6003.2.a.h.1.1 | 5 | 1.1 | even | 1 | trivial |