Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.368464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 6x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 185) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.14884\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-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 | ||||||||
\(3\) | −2.51369 | −1.45128 | −0.725639 | − | 0.688075i | \(-0.758456\pi\) | ||||
−0.725639 | + | 0.688075i | \(0.758456\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.281955 | −0.106569 | −0.0532845 | − | 0.998579i | \(-0.516969\pi\) | ||||
−0.0532845 | + | 0.998579i | \(0.516969\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.31863 | 1.10621 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.160490 | 0.0483894 | 0.0241947 | − | 0.999707i | \(-0.492298\pi\) | ||||
0.0241947 | + | 0.999707i | \(0.492298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.61752 | 0.448620 | 0.224310 | − | 0.974518i | \(-0.427987\pi\) | ||||
0.224310 | + | 0.974518i | \(0.427987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.51369 | −0.649032 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.88783 | −0.700402 | −0.350201 | − | 0.936675i | \(-0.613887\pi\) | ||||
−0.350201 | + | 0.936675i | \(0.613887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.15216 | −0.952570 | −0.476285 | − | 0.879291i | \(-0.658017\pi\) | ||||
−0.476285 | + | 0.879291i | \(0.658017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.708747 | 0.154661 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.52202 | 0.525878 | 0.262939 | − | 0.964813i | \(-0.415308\pi\) | ||||
0.262939 | + | 0.964813i | \(0.415308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.800936 | −0.154140 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.70640 | 0.502565 | 0.251283 | − | 0.967914i | \(-0.419148\pi\) | ||||
0.251283 | + | 0.967914i | \(0.419148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.41915 | −0.793703 | −0.396851 | − | 0.917883i | \(-0.629897\pi\) | ||||
−0.396851 | + | 0.917883i | \(0.629897\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.403421 | −0.0702265 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.281955 | −0.0476591 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.06595 | −0.651073 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1646 | −1.74361 | −0.871807 | − | 0.489850i | \(-0.837051\pi\) | ||||
−0.871807 | + | 0.489850i | \(0.837051\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.88897 | 0.898060 | 0.449030 | − | 0.893517i | \(-0.351770\pi\) | ||||
0.449030 | + | 0.893517i | \(0.351770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.31863 | 0.494712 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.3827 | 1.95206 | 0.976032 | − | 0.217626i | \(-0.0698311\pi\) | ||||
0.976032 | + | 0.217626i | \(0.0698311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92050 | −0.988643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.25911 | 1.01648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.86689 | −0.943240 | −0.471620 | − | 0.881802i | \(-0.656331\pi\) | ||||
−0.471620 | + | 0.881802i | \(0.656331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.160490 | 0.0216404 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4372 | 1.38244 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.42986 | 0.706908 | 0.353454 | − | 0.935452i | \(-0.385007\pi\) | ||||
0.353454 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3251 | 1.70610 | 0.853050 | − | 0.521830i | \(-0.174750\pi\) | ||||
0.853050 | + | 0.521830i | \(0.174750\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.935704 | −0.117888 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.61752 | 0.200629 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.09956 | −0.134332 | −0.0671660 | − | 0.997742i | \(-0.521396\pi\) | ||||
−0.0671660 | + | 0.997742i | \(0.521396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.33957 | −0.763195 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.5022 | −1.83977 | −0.919887 | − | 0.392183i | \(-0.871720\pi\) | ||||
−0.919887 | + | 0.392183i | \(0.871720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.701106 | 0.0820582 | 0.0410291 | − | 0.999158i | \(-0.486936\pi\) | ||||
0.0410291 | + | 0.999158i | \(0.486936\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.51369 | −0.290256 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0452508 | −0.00515681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.24549 | 0.140128 | 0.0700640 | − | 0.997542i | \(-0.477680\pi\) | ||||
0.0700640 | + | 0.997542i | \(0.477680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.94259 | −0.882510 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.157450 | −0.0172823 | −0.00864117 | − | 0.999963i | \(-0.502751\pi\) | ||||
−0.00864117 | + | 0.999963i | \(0.502751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.88783 | −0.313229 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.80304 | −0.729363 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.21783 | −0.765089 | −0.382544 | − | 0.923937i | \(-0.624952\pi\) | ||||
−0.382544 | + | 0.923937i | \(0.624952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.456069 | −0.0478090 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.1084 | 1.15188 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.15216 | −0.426002 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.79246 | 0.689669 | 0.344835 | − | 0.938663i | \(-0.387935\pi\) | ||||
0.344835 | + | 0.938663i | \(0.387935\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.532605 | 0.0535288 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.41515 | 0.538827 | 0.269414 | − | 0.963025i | \(-0.413170\pi\) | ||||
0.269414 | + | 0.963025i | \(0.413170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.64784 | 0.655032 | 0.327516 | − | 0.944846i | \(-0.393789\pi\) | ||||
0.327516 | + | 0.944846i | \(0.393789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.708747 | 0.0691666 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.22219 | −0.504848 | −0.252424 | − | 0.967617i | \(-0.581228\pi\) | ||||
−0.252424 | + | 0.967617i | \(0.581228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.37345 | −0.227336 | −0.113668 | − | 0.993519i | \(-0.536260\pi\) | ||||
−0.113668 | + | 0.993519i | \(0.536260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.51369 | 0.238589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.7642 | 1.67112 | 0.835559 | − | 0.549401i | \(-0.185144\pi\) | ||||
0.835559 | + | 0.549401i | \(0.185144\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.52202 | 0.235180 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.36796 | 0.496268 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.814239 | 0.0746412 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9742 | −0.997658 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.0643 | 2.53047 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2934 | −1.71202 | −0.856008 | − | 0.516963i | \(-0.827062\pi\) | ||||
−0.856008 | + | 0.516963i | \(0.827062\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.8030 | −1.30334 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8127 | −1.29419 | −0.647096 | − | 0.762408i | \(-0.724017\pi\) | ||||
−0.647096 | + | 0.762408i | \(0.724017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.17072 | 0.101514 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.800936 | −0.0689336 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.5368 | −1.92545 | −0.962725 | − | 0.270482i | \(-0.912817\pi\) | ||||
−0.962725 | + | 0.270482i | \(0.912817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3710 | −1.21894 | −0.609468 | − | 0.792811i | \(-0.708617\pi\) | ||||
−0.609468 | + | 0.792811i | \(0.708617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.6399 | −2.83299 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.259596 | 0.0217085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.70640 | 0.224754 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.3960 | 1.43480 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.782096 | 0.0640718 | 0.0320359 | − | 0.999487i | \(-0.489801\pi\) | ||||
0.0320359 | + | 0.999487i | \(0.489801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.52865 | −0.205779 | −0.102889 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102889 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.58365 | −0.774792 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.41915 | −0.354955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.4789 | −1.55459 | −0.777294 | − | 0.629138i | \(-0.783408\pi\) | ||||
−0.777294 | + | 0.629138i | \(0.783408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.2612 | 1.36890 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.711097 | −0.0560423 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1867 | −1.26784 | −0.633918 | − | 0.773400i | \(-0.718555\pi\) | ||||
−0.633918 | + | 0.773400i | \(0.718555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.403421 | −0.0314063 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.3864 | −1.03587 | −0.517937 | − | 0.855419i | \(-0.673300\pi\) | ||||
−0.517937 | + | 0.855419i | \(0.673300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3836 | −0.798740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.7795 | −1.05374 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3160 | 1.62062 | 0.810312 | − | 0.585999i | \(-0.199298\pi\) | ||||
0.810312 | + | 0.585999i | \(0.199298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.281955 | −0.0213138 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.6490 | −1.02592 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.279850 | 0.0209169 | 0.0104585 | − | 0.999945i | \(-0.496671\pi\) | ||||
0.0104585 | + | 0.999945i | \(0.496671\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1663 | 0.755652 | 0.377826 | − | 0.925877i | \(-0.376672\pi\) | ||||
0.377826 | + | 0.925877i | \(0.376672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.4951 | −2.47603 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.463467 | −0.0338920 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.225828 | 0.0164266 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.40464 | 0.680496 | 0.340248 | − | 0.940336i | \(-0.389489\pi\) | ||||
0.340248 | + | 0.940336i | \(0.389489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2852 | −0.884310 | −0.442155 | − | 0.896939i | \(-0.645786\pi\) | ||||
−0.442155 | + | 0.896939i | \(0.645786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.06595 | −0.291169 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.8525 | −1.20069 | −0.600346 | − | 0.799741i | \(-0.704970\pi\) | ||||
−0.600346 | + | 0.799741i | \(0.704970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2801 | −1.50851 | −0.754254 | − | 0.656582i | \(-0.772001\pi\) | ||||
−0.754254 | + | 0.656582i | \(0.772001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.76394 | 0.194953 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.763083 | −0.0535579 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1646 | −0.779768 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.36965 | 0.581731 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.666378 | −0.0460943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.24034 | −0.360760 | −0.180380 | − | 0.983597i | \(-0.557733\pi\) | ||||
−0.180380 | + | 0.983597i | \(0.557733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38.9677 | 2.67003 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.88897 | 0.401625 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.24600 | 0.0845841 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.76236 | −0.119089 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.67114 | −0.314215 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0192 | 0.804863 | 0.402432 | − | 0.915450i | \(-0.368165\pi\) | ||||
0.402432 | + | 0.915450i | \(0.368165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.31863 | 0.221242 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8369 | 0.719272 | 0.359636 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359636 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.1312 | −0.999901 | −0.499950 | − | 0.866054i | \(-0.666648\pi\) | ||||
−0.499950 | + | 0.866054i | \(0.666648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.113746 | 0.00748397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.1614 | −1.32082 | −0.660410 | − | 0.750905i | \(-0.729617\pi\) | ||||
−0.660410 | + | 0.750905i | \(0.729617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.3827 | 0.872990 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.13076 | −0.203365 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65751 | −0.301270 | −0.150635 | − | 0.988589i | \(-0.548132\pi\) | ||||
−0.150635 | + | 0.988589i | \(0.548132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.01197 | 0.129602 | 0.0648011 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648011 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3680 | 1.43491 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.92050 | −0.442135 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.71621 | −0.427342 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.395779 | 0.0250815 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0033 | −1.70443 | −0.852217 | − | 0.523188i | \(-0.824743\pi\) | ||||
−0.852217 | + | 0.523188i | \(0.824743\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.404758 | 0.0254469 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.25911 | 0.454583 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.85270 | −0.614595 | −0.307297 | − | 0.951614i | \(-0.599425\pi\) | ||||
−0.307297 | + | 0.951614i | \(0.599425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.281955 | 0.0175198 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.98153 | 0.555943 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.07097 | −0.312689 | −0.156345 | − | 0.987703i | \(-0.549971\pi\) | ||||
−0.156345 | + | 0.987703i | \(0.549971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.86689 | −0.421830 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.1434 | 1.11036 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.6998 | 1.32306 | 0.661530 | − | 0.749919i | \(-0.269908\pi\) | ||||
0.661530 | + | 0.749919i | \(0.269908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.9216 | −1.39239 | −0.696195 | − | 0.717852i | \(-0.745125\pi\) | ||||
−0.696195 | + | 0.717852i | \(0.745125\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.14642 | 0.0693842 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.160490 | 0.00967788 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.611022 | −0.0367128 | −0.0183564 | − | 0.999832i | \(-0.505843\pi\) | ||||
−0.0183564 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.6655 | −0.878002 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.25171 | 0.551911 | 0.275955 | − | 0.961170i | \(-0.411006\pi\) | ||||
0.275955 | + | 0.961170i | \(0.411006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9836 | 1.36623 | 0.683117 | − | 0.730309i | \(-0.260624\pi\) | ||||
0.683117 | + | 0.730309i | \(0.260624\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4372 | 0.618248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.14791 | 0.185815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.66043 | −0.509437 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.0741 | −1.00090 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.62462 | 0.445435 | 0.222717 | − | 0.974883i | \(-0.428507\pi\) | ||||
0.222717 | + | 0.974883i | \(0.428507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.42986 | 0.316139 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.128542 | −0.00745875 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.07943 | 0.235919 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.66043 | −0.0957053 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.6120 | −0.781988 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3251 | 0.762991 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.09745 | 0.176781 | 0.0883904 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883904 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.7106 | −0.950633 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1070 | 0.629818 | 0.314909 | − | 0.949122i | \(-0.398026\pi\) | ||||
0.314909 | + | 0.949122i | \(0.398026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.80559 | −0.102058 | −0.0510289 | − | 0.998697i | \(-0.516250\pi\) | ||||
−0.0510289 | + | 0.998697i | \(0.516250\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.935704 | −0.0527210 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.53528 | −0.142395 | −0.0711977 | − | 0.997462i | \(-0.522682\pi\) | ||||
−0.0711977 | + | 0.997462i | \(0.522682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.434348 | 0.0243188 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1270 | 0.732676 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.9907 | 0.667182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.61752 | 0.0897241 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.96612 | 0.329927 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.77331 | −0.208030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2147 | 0.561449 | 0.280724 | − | 0.959788i | \(-0.409425\pi\) | ||||
0.280724 | + | 0.959788i | \(0.409425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.31863 | −0.181860 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.09956 | −0.0600751 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.365331 | −0.0199009 | −0.00995043 | − | 0.999950i | \(-0.503167\pi\) | ||||
−0.00995043 | + | 0.999950i | \(0.503167\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −44.6537 | −2.42526 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.709227 | −0.0384068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.92496 | 0.211928 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.33957 | −0.341311 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5941 | −1.05187 | −0.525934 | − | 0.850526i | \(-0.676284\pi\) | ||||
−0.525934 | + | 0.850526i | \(0.676284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7079 | 1.69729 | 0.848644 | − | 0.528965i | \(-0.177420\pi\) | ||||
0.848644 | + | 0.528965i | \(0.177420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.29553 | −0.0691504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0549 | −1.12064 | −0.560319 | − | 0.828277i | \(-0.689322\pi\) | ||||
−0.560319 | + | 0.828277i | \(0.689322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5022 | −0.822772 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.04674 | −0.108325 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.50782 | −0.132358 | −0.0661788 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661788 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.75959 | −0.0926100 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.5858 | 1.44788 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.701106 | 0.0366975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.5047 | −1.85333 | −0.926666 | − | 0.375886i | \(-0.877338\pi\) | ||||
−0.926666 | + | 0.375886i | \(0.877338\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.0511 | −1.92880 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.93615 | 0.100520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2671 | 1.20472 | 0.602362 | − | 0.798223i | \(-0.294226\pi\) | ||||
0.602362 | + | 0.798223i | \(0.294226\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.51369 | −0.129806 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.37766 | 0.225461 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.89632 | −0.251507 | −0.125754 | − | 0.992062i | \(-0.540135\pi\) | ||||
−0.125754 | + | 0.992062i | \(0.540135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.4977 | 2.48461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.6187 | 0.644784 | 0.322392 | − | 0.946606i | \(-0.395513\pi\) | ||||
0.322392 | + | 0.946606i | \(0.395513\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0452508 | −0.00230620 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.5433 | 0.993443 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.1847 | −0.516386 | −0.258193 | − | 0.966093i | \(-0.583127\pi\) | ||||
−0.258193 | + | 0.966093i | \(0.583127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.28317 | −0.368326 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.2345 | 1.87823 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.24549 | 0.0626672 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.1107 | −0.658008 | −0.329004 | − | 0.944329i | \(-0.606713\pi\) | ||||
−0.329004 | + | 0.944329i | \(0.606713\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.94283 | −0.147326 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6608 | 0.881940 | 0.440970 | − | 0.897522i | \(-0.354635\pi\) | ||||
0.440970 | + | 0.897522i | \(0.354635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.14808 | −0.356071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.94259 | −0.394670 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.160490 | −0.00795517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6108 | −1.26637 | −0.633187 | − | 0.773999i | \(-0.718254\pi\) | ||||
−0.633187 | + | 0.773999i | \(0.718254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 56.6505 | 2.79436 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.53098 | −0.0753345 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.157450 | −0.00772889 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.1243 | 1.76901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.3511 | −0.994216 | −0.497108 | − | 0.867689i | \(-0.665605\pi\) | ||||
−0.497108 | + | 0.867689i | \(0.665605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0941 | −0.638167 | −0.319084 | − | 0.947727i | \(-0.603375\pi\) | ||||
−0.319084 | + | 0.947727i | \(0.603375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.4122 | 2.15939 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.88783 | −0.140080 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.75707 | −0.181817 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.652543 | −0.0315051 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3248 | −0.786337 | −0.393169 | − | 0.919466i | \(-0.628621\pi\) | ||||
−0.393169 | + | 0.919466i | \(0.628621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7539 | 1.38183 | 0.690913 | − | 0.722938i | \(-0.257209\pi\) | ||||
0.690913 | + | 0.722938i | \(0.257209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.80304 | −0.326181 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.4718 | −0.500935 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1331 | 0.483625 | 0.241813 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241813 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.9666 | −1.09365 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.66136 | 0.173956 | 0.0869782 | − | 0.996210i | \(-0.472279\pi\) | ||||
0.0869782 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.21783 | −0.342158 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.96595 | −0.0929861 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.81556 | −0.321646 | −0.160823 | − | 0.986983i | \(-0.551415\pi\) | ||||
−0.160823 | + | 0.986983i | \(0.551415\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.79180 | −0.0843724 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.35624 | 0.298642 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.456069 | −0.0213809 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7873 | 1.53372 | 0.766862 | − | 0.641812i | \(-0.221817\pi\) | ||||
0.766862 | + | 0.641812i | \(0.221817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.31297 | 0.107960 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.73107 | −0.406647 | −0.203323 | − | 0.979112i | \(-0.565174\pi\) | ||||
−0.203323 | + | 0.979112i | \(0.565174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.22462 | 0.428704 | 0.214352 | − | 0.976756i | \(-0.431236\pi\) | ||||
0.214352 | + | 0.976756i | \(0.431236\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.1084 | 0.515138 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.83042 | −0.454898 | −0.227449 | − | 0.973790i | \(-0.573038\pi\) | ||||
−0.227449 | + | 0.973790i | \(0.573038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.310025 | 0.0143156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.9639 | 2.25614 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.945118 | 0.0434566 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.15216 | −0.190514 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.7887 | −1.04342 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0355 | 1.37236 | 0.686178 | − | 0.727434i | \(-0.259287\pi\) | ||||
0.686178 | + | 0.727434i | \(0.259287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.61752 | −0.0737527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.78748 | 0.0813329 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.79246 | 0.308430 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.5018 | −1.88063 | −0.940314 | − | 0.340308i | \(-0.889469\pi\) | ||||
−0.940314 | + | 0.340308i | \(0.889469\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.6882 | 1.83998 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.3046 | 1.32250 | 0.661249 | − | 0.750167i | \(-0.270027\pi\) | ||||
0.661249 | + | 0.750167i | \(0.270027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.81562 | −0.351998 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.532605 | 0.0239388 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.37093 | 0.196063 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5959 | 1.10106 | 0.550532 | − | 0.834814i | \(-0.314425\pi\) | ||||
0.550532 | + | 0.834814i | \(0.314425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.6494 | 1.50334 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.0315 | −0.447281 | −0.223640 | − | 0.974672i | \(-0.571794\pi\) | ||||
−0.223640 | + | 0.974672i | \(0.571794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.41515 | 0.240971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.1012 | 1.15919 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3474 | −0.946208 | −0.473104 | − | 0.881007i | \(-0.656867\pi\) | ||||
−0.473104 | + | 0.881007i | \(0.656867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.197680 | −0.00874486 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.32561 | 0.146829 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.64784 | 0.292939 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.14778 | 0.0944593 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −53.5817 | −2.35198 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.4370 | 1.77158 | 0.885790 | − | 0.464087i | \(-0.153618\pi\) | ||||
0.885790 | + | 0.464087i | \(0.153618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5202 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.708747 | 0.0309323 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.7618 | 0.555911 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6394 | −0.723453 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0197 | 0.781989 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0590 | −0.782221 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.22219 | −0.225775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.703455 | −0.0303563 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.11067 | −0.0478399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.8160 | −1.19590 | −0.597952 | − | 0.801532i | \(-0.704019\pi\) | ||||
−0.597952 | + | 0.801532i | \(0.704019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.5548 | −1.09666 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.37345 | −0.101668 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.83360 | −0.292184 | −0.146092 | − | 0.989271i | \(-0.546670\pi\) | ||||
−0.146092 | + | 0.989271i | \(0.546670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 44.2209 | 1.88730 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2374 | −0.478729 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.351171 | −0.0149333 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.51369 | 0.106700 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3389 | 0.946530 | 0.473265 | − | 0.880920i | \(-0.343075\pi\) | ||||
0.473265 | + | 0.880920i | \(0.343075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.52555 | 0.402888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.16501 | 0.0491868 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.2527 | 1.40143 | 0.700717 | − | 0.713440i | \(-0.252864\pi\) | ||||
0.700717 | + | 0.713440i | \(0.252864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.7642 | 0.747346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.23945 | 0.0940482 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.1937 | 1.68501 | 0.842504 | − | 0.538691i | \(-0.181081\pi\) | ||||
0.842504 | + | 0.538691i | \(0.181081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.49128 | 0.146106 | 0.0730528 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730528 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.6403 | −0.987589 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.52202 | 0.105176 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.1865 | 1.33994 | 0.669972 | − | 0.742387i | \(-0.266306\pi\) | ||||
0.669972 | + | 0.742387i | \(0.266306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.8812 | 1.28338 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0443937 | 0.00184176 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.10206 | −0.0456428 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.36796 | 0.221938 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.5196 | 1.50733 | 0.753663 | − | 0.657261i | \(-0.228285\pi\) | ||||
0.753663 | + | 0.657261i | \(0.228285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.3490 | 0.756058 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.3619 | 1.74254 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.93223 | −0.366803 | −0.183401 | − | 0.983038i | \(-0.558711\pi\) | ||||
−0.183401 | + | 0.983038i | \(0.558711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.814239 | 0.0333805 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.4916 | 2.18927 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.2408 | −1.43990 | −0.719949 | − | 0.694027i | \(-0.755835\pi\) | ||||
−0.719949 | + | 0.694027i | \(0.755835\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3066 | −0.461205 | −0.230603 | − | 0.973048i | \(-0.574070\pi\) | ||||
−0.230603 | + | 0.973048i | \(0.574070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.64902 | −0.148599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9742 | −0.446166 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.7839 | −1.00595 | −0.502974 | − | 0.864302i | \(-0.667761\pi\) | ||||
−0.502974 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.91815 | 0.0777274 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.6468 | 0.875736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.23397 | −0.130619 | −0.0653093 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653093 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.0643 | 1.13166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0009 | 0.966242 | 0.483121 | − | 0.875554i | \(-0.339503\pi\) | ||||
0.483121 | + | 0.875554i | \(0.339503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5590 | 0.987111 | 0.493555 | − | 0.869714i | \(-0.335697\pi\) | ||||
0.493555 | + | 0.869714i | \(0.335697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.01998 | −0.0810589 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.03510 | 0.0815348 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.67507 | 0.0668957 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.88783 | 0.115145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2104 | −1.24247 | −0.621234 | − | 0.783625i | \(-0.713368\pi\) | ||||
−0.621234 | + | 0.783625i | \(0.713368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.1726 | 0.523563 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.2934 | −0.765637 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.1941 | −0.443525 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −51.4461 | −2.03518 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.5272 | 0.494795 | 0.247397 | − | 0.968914i | \(-0.420425\pi\) | ||||
0.247397 | + | 0.968914i | \(0.420425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.76315 | 0.227276 | 0.113638 | − | 0.993522i | \(-0.463750\pi\) | ||||
0.113638 | + | 0.993522i | \(0.463750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.8030 | −0.582869 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.59926 | −0.102188 | −0.0510938 | − | 0.998694i | \(-0.516271\pi\) | ||||
−0.0510938 | + | 0.998694i | \(0.516271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.871436 | 0.0342069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.13206 | −0.122755 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.79108 | −0.187489 | −0.0937446 | − | 0.995596i | \(-0.529884\pi\) | ||||
−0.0937446 | + | 0.995596i | \(0.529884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.8127 | −0.578781 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.32671 | 0.0907736 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.8970 | −1.47626 | −0.738128 | − | 0.674661i | \(-0.764290\pi\) | ||||
−0.738128 | + | 0.674661i | \(0.764290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.57407 | 0.216806 | 0.108403 | − | 0.994107i | \(-0.465426\pi\) | ||||
0.108403 | + | 0.994107i | \(0.465426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.7418 | 0.456013 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.17072 | 0.0453986 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.82559 | 0.264288 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.2125 | −1.16808 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.13853 | 0.0825571 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.9396 | −0.614425 | −0.307212 | − | 0.951641i | \(-0.599396\pi\) | ||||
−0.307212 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.800936 | −0.0308280 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.9932 | −1.38333 | −0.691665 | − | 0.722218i | \(-0.743123\pi\) | ||||
−0.691665 | + | 0.722218i | \(0.743123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.91517 | −0.0734974 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.2406 | −1.04386 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.4996 | 1.62620 | 0.813101 | − | 0.582122i | \(-0.197777\pi\) | ||||
0.813101 | + | 0.582122i | \(0.197777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5368 | −0.861087 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.0352 | 1.45113 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1074 | −0.423157 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.62722 | 0.252111 | 0.126056 | − | 0.992023i | \(-0.459768\pi\) | ||||
0.126056 | + | 0.992023i | \(0.459768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.150171 | −0.00570452 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.3710 | −0.545124 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.2414 | 1.22123 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 50.6796 | 1.91688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.6044 | −1.49584 | −0.747919 | − | 0.663790i | \(-0.768947\pi\) | ||||
−0.747919 | + | 0.663790i | \(0.768947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.15216 | 0.156602 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.6399 | −1.26695 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.52683 | −0.0574223 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7832 | 0.592750 | 0.296375 | − | 0.955072i | \(-0.404222\pi\) | ||||
0.296375 | + | 0.955072i | \(0.404222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.13331 | 0.155011 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.1452 | −0.417391 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.259596 | 0.00970833 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.7075 | 0.437226 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.8483 | 0.852098 | 0.426049 | − | 0.904700i | \(-0.359905\pi\) | ||||
0.426049 | + | 0.904700i | \(0.359905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87439 | −0.0698061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.05746 | −0.188089 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.70640 | 0.100513 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.8290 | 1.14339 | 0.571693 | − | 0.820468i | \(-0.306287\pi\) | ||||
0.571693 | + | 0.820468i | \(0.306287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.3984 | −1.19994 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.0064 | −0.629003 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.87159 | −0.106064 | −0.0530322 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530322 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.3960 | 0.641661 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.176467 | −0.00650025 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5586 | 0.719473 | 0.359736 | − | 0.933054i | \(-0.382867\pi\) | ||||
0.359736 | + | 0.933054i | \(0.382867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.8825 | 0.620193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.67284 | 0.281489 | 0.140745 | − | 0.990046i | \(-0.455050\pi\) | ||||
0.140745 | + | 0.990046i | \(0.455050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.782096 | 0.0286538 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.522517 | −0.0191179 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.47242 | 0.0538012 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8710 | 0.396690 | 0.198345 | − | 0.980132i | \(-0.436443\pi\) | ||||
0.198345 | + | 0.980132i | \(0.436443\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 67.8779 | 2.47361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.52865 | −0.0920270 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.45938 | 0.271116 | 0.135558 | − | 0.990769i | \(-0.456717\pi\) | ||||
0.135558 | + | 0.990769i | \(0.456717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.01744 | −0.0369306 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.8693 | 1.66276 | 0.831380 | − | 0.555704i | \(-0.187551\pi\) | ||||
0.831380 | + | 0.555704i | \(0.187551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.669207 | 0.0242269 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.58365 | −0.346497 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.78293 | 0.317133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.9990 | −1.44240 | −0.721201 | − | 0.692726i | \(-0.756410\pi\) | ||||
−0.721201 | + | 0.692726i | \(0.756410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7666 | 0.891948 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.9576 | 0.933629 | 0.466815 | − | 0.884355i | \(-0.345402\pi\) | ||||
0.466815 | + | 0.884355i | \(0.345402\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.41915 | −0.158741 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.708747 | −0.0254262 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.3571 | 1.66091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48794 | −0.0890256 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.16765 | −0.0774655 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.4789 | −0.695233 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4524 | 0.515174 | 0.257587 | − | 0.966255i | \(-0.417073\pi\) | ||||
0.257587 | + | 0.966255i | \(0.417073\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7468 | 0.453799 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.00871 | −0.178089 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.5536 | 0.765391 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.2612 | 0.612192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.88581 | 0.102221 | 0.0511103 | − | 0.998693i | \(-0.483724\pi\) | ||||
0.0511103 | + | 0.998693i | \(0.483724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.6469 | −1.36723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.9533 | −0.846349 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.112520 | 0.00397075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.711097 | −0.0250629 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.5465 | −1.92013 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.66435 | 0.234306 | 0.117153 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117153 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2301 | −0.605031 | −0.302515 | − | 0.953144i | \(-0.597826\pi\) | ||||
−0.302515 | + | 0.953144i | \(0.597826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57.6179 | 2.02075 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1867 | −0.566994 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.4519 | −0.855465 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.51352 | −0.0528868 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.96739 | 0.173363 | 0.0866816 | − | 0.996236i | \(-0.472374\pi\) | ||||
0.0866816 | + | 0.996236i | \(0.472374\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5539 | −0.611892 | −0.305946 | − | 0.952049i | \(-0.598973\pi\) | ||||
−0.305946 | + | 0.952049i | \(0.598973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.403421 | −0.0140453 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.3418 | 1.36805 | 0.684024 | − | 0.729459i | \(-0.260228\pi\) | ||||
0.684024 | + | 0.729459i | \(0.260228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.4784 | −1.37114 | −0.685571 | − | 0.728006i | \(-0.740447\pi\) | ||||
−0.685571 | + | 0.728006i | \(0.740447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.53592 | 0.0532805 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.9852 | 0.692448 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.3864 | −0.463257 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.53946 | 0.122341 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.3840 | 0.738259 | 0.369129 | − | 0.929378i | \(-0.379656\pi\) | ||||
0.369129 | + | 0.929378i | \(0.379656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6754 | −0.747428 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.2559 | −0.800977 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3836 | −0.357207 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.09424 | 0.106319 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −57.7737 | −1.98279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.52202 | −0.0864538 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.4715 | −0.632451 | −0.316226 | − | 0.948684i | \(-0.602416\pi\) | ||||
−0.316226 | + | 0.948684i | \(0.602416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.7795 | −0.471248 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.6073 | 1.11385 | 0.556923 | − | 0.830564i | \(-0.311982\pi\) | ||||
0.556923 | + | 0.830564i | \(0.311982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.3456 | −1.13774 | −0.568869 | − | 0.822428i | \(-0.692619\pi\) | ||||
−0.568869 | + | 0.822428i | \(0.692619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.91286 | −0.269670 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.3578 | −1.37380 | −0.686898 | − | 0.726754i | \(-0.741028\pi\) | ||||
−0.686898 | + | 0.726754i | \(0.741028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3160 | 0.724765 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.7696 | 0.739335 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.199887 | 0.00678072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.77856 | −0.0602641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.5416 | 0.762919 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.281955 | −0.00953182 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.5768 | −0.559758 | −0.279879 | − | 0.960035i | \(-0.590294\pi\) | ||||
−0.279879 | + | 0.960035i | \(0.590294\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.1659 | −0.646450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1872 | 0.477978 | 0.238989 | − | 0.971022i | \(-0.423184\pi\) | ||||
0.238989 | + | 0.971022i | \(0.423184\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.2999 | −1.89464 | −0.947321 | − | 0.320286i | \(-0.896221\pi\) | ||||
−0.947321 | + | 0.320286i | \(0.896221\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.6490 | −0.458806 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.2070 | −1.11498 | −0.557491 | − | 0.830183i | \(-0.688236\pi\) | ||||
−0.557491 | + | 0.830183i | \(0.688236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.43988 | 0.182448 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.27470 | −0.0427041 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.5670 | −1.85948 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.279850 | 0.00935434 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.2544 | −0.342385 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.9600 | −0.398888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8304 | 0.660647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.17379 | 0.138895 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.1663 | 0.337938 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.0317 | −1.82730 | −0.913650 | − | 0.406503i | \(-0.866748\pi\) | ||||
−0.913650 | + | 0.406503i | \(0.866748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.9709 | 0.596056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.8532 | 0.889688 | 0.444844 | − | 0.895608i | \(-0.353259\pi\) | ||||
0.444844 | + | 0.895608i | \(0.353259\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0252690 | −0.000836282 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.4951 | −1.10731 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.17652 | 0.137921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.2839 | 1.06495 | 0.532473 | − | 0.846447i | \(-0.321263\pi\) | ||||
0.532473 | + | 0.846447i | \(0.321263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.78602 | −0.256558 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0752 | −0.825361 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.0617 | 0.724602 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.8991 | 0.652867 | 0.326434 | − | 0.945220i | \(-0.394153\pi\) | ||||
0.326434 | + | 0.945220i | \(0.394153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.7350 | 0.941752 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.9194 | −0.914041 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.463467 | −0.0151570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.121019 | −0.00395351 | −0.00197676 | − | 0.999998i | \(-0.500629\pi\) | ||||
−0.00197676 | + | 0.999998i | \(0.500629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.53869 | 0.148114 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.1748 | −1.63565 | −0.817826 | − | 0.575466i | \(-0.804821\pi\) | ||||
−0.817826 | + | 0.575466i | \(0.804821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.1573 | −0.916927 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.225828 | 0.00734618 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.20738 | 0.266704 | 0.133352 | − | 0.991069i | \(-0.457426\pi\) | ||||
0.133352 | + | 0.991069i | \(0.457426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.13406 | 0.0368130 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.37290 | 0.206656 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.2409 | −0.558489 | −0.279244 | − | 0.960220i | \(-0.590084\pi\) | ||||
−0.279244 | + | 0.960220i | \(0.590084\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.40464 | 0.304327 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.09182 | −0.0352934 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.35437 | 0.205193 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.4711 | −0.370036 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.3305 | −0.558468 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.2852 | −0.395476 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1538 | −0.390840 | −0.195420 | − | 0.980720i | \(-0.562607\pi\) | ||||
−0.195420 | + | 0.980720i | \(0.562607\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.1410 | −0.968267 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.6672 | 0.759517 | 0.379758 | − | 0.925086i | \(-0.376007\pi\) | ||||
0.379758 | + | 0.925086i | \(0.376007\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.05199 | 0.129901 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.06595 | −0.130215 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.6954 | 0.982033 | 0.491017 | − | 0.871150i | \(-0.336625\pi\) | ||||
0.491017 | + | 0.871150i | \(0.336625\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.15839 | −0.0370222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.87661 | −0.251481 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.3677 | 1.70216 | 0.851082 | − | 0.525032i | \(-0.175947\pi\) | ||||
0.851082 | + | 0.525032i | \(0.175947\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8525 | −0.536965 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.48494 | 0.301909 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.8521 | 0.472270 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.4497 | 1.85672 | 0.928358 | − | 0.371687i | \(-0.121221\pi\) | ||||
0.928358 | + | 0.371687i | \(0.121221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.6765 | −0.814819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.2801 | −0.674626 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.1177 | −1.90395 | −0.951973 | − | 0.306182i | \(-0.900948\pi\) | ||||
−0.951973 | + | 0.306182i | \(0.900948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.800936 | 0.0253405 |
(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 | 2960.2.a.ba.1.1 | 5 | ||
4.3 | odd | 2 | 185.2.a.d.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 1665.2.a.q.1.4 | 5 | |||
20.3 | even | 4 | 925.2.b.g.149.7 | 10 | |||
20.7 | even | 4 | 925.2.b.g.149.4 | 10 | |||
20.19 | odd | 2 | 925.2.a.h.1.4 | 5 | |||
28.27 | even | 2 | 9065.2.a.j.1.2 | 5 | |||
60.59 | even | 2 | 8325.2.a.cc.1.2 | 5 | |||
148.147 | odd | 2 | 6845.2.a.g.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
185.2.a.d.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
925.2.a.h.1.4 | 5 | 20.19 | odd | 2 | |||
925.2.b.g.149.4 | 10 | 20.7 | even | 4 | |||
925.2.b.g.149.7 | 10 | 20.3 | even | 4 | |||
1665.2.a.q.1.4 | 5 | 12.11 | even | 2 | |||
2960.2.a.ba.1.1 | 5 | 1.1 | even | 1 | trivial | ||
6845.2.a.g.1.4 | 5 | 148.147 | odd | 2 | |||
8325.2.a.cc.1.2 | 5 | 60.59 | even | 2 | |||
9065.2.a.j.1.2 | 5 | 28.27 | even | 2 |