Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.131472.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 19x^{2} + 20x + 52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.64466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.64466 | 1.37755 | 0.688776 | − | 0.724974i | \(-0.258148\pi\) | ||||
0.688776 | + | 0.724974i | \(0.258148\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.66808 | −0.502944 | −0.251472 | − | 0.967865i | \(-0.580915\pi\) | ||||
−0.251472 | + | 0.967865i | \(0.580915\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.64466 | −0.974076 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.31274 | 1.44824 | 0.724120 | − | 0.689674i | \(-0.242246\pi\) | ||||
0.724120 | + | 0.689674i | \(0.242246\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.64466 | 0.795330 | ||||||||
\(22\) | 1.66808 | 0.355635 | ||||||||
\(23\) | 1.24453 | 0.259503 | 0.129752 | − | 0.991547i | \(-0.458582\pi\) | ||||
0.129752 | + | 0.991547i | \(0.458582\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.64466 | 0.688776 | ||||||||
\(29\) | 10.0448 | 1.86527 | 0.932635 | − | 0.360821i | \(-0.117504\pi\) | ||||
0.932635 | + | 0.360821i | \(0.117504\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −4.21957 | −0.757857 | −0.378928 | − | 0.925426i | \(-0.623707\pi\) | ||||
−0.378928 | + | 0.925426i | \(0.623707\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.66808 | −0.290375 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 3.64466 | 0.616060 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.86423 | 1.62167 | 0.810835 | − | 0.585275i | \(-0.199014\pi\) | ||||
0.810835 | + | 0.585275i | \(0.199014\pi\) | |||||||
\(38\) | −6.31274 | −1.02406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.28932 | −1.45075 | −0.725374 | − | 0.688355i | \(-0.758333\pi\) | ||||
−0.725374 | + | 0.688355i | \(0.758333\pi\) | |||||||
\(42\) | −3.64466 | −0.562383 | ||||||||
\(43\) | −7.57286 | −1.15485 | −0.577425 | − | 0.816443i | \(-0.695943\pi\) | ||||
−0.577425 | + | 0.816443i | \(0.695943\pi\) | |||||||
\(44\) | −1.66808 | −0.251472 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −1.24453 | −0.183496 | ||||||||
\(47\) | −6.82522 | −0.995560 | −0.497780 | − | 0.867303i | \(-0.665851\pi\) | ||||
−0.497780 | + | 0.867303i | \(0.665851\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 6.28354 | 0.897649 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.848634 | −0.116569 | −0.0582844 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582844 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.66808 | −0.224923 | ||||||||
\(56\) | −3.64466 | −0.487038 | ||||||||
\(57\) | 6.31274 | 0.836142 | ||||||||
\(58\) | −10.0448 | −1.31895 | ||||||||
\(59\) | −6.10876 | −0.795293 | −0.397646 | − | 0.917539i | \(-0.630173\pi\) | ||||
−0.397646 | + | 0.917539i | \(0.630173\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 7.46410 | 0.955680 | 0.477840 | − | 0.878447i | \(-0.341420\pi\) | ||||
0.477840 | + | 0.878447i | \(0.341420\pi\) | |||||||
\(62\) | 4.21957 | 0.535886 | ||||||||
\(63\) | 3.64466 | 0.459184 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.66808 | 0.205326 | ||||||||
\(67\) | −14.7534 | −1.80242 | −0.901209 | − | 0.433386i | \(-0.857319\pi\) | ||||
−0.901209 | + | 0.433386i | \(0.857319\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 1.24453 | 0.149824 | ||||||||
\(70\) | −3.64466 | −0.435620 | ||||||||
\(71\) | −3.51093 | −0.416671 | −0.208336 | − | 0.978057i | \(-0.566805\pi\) | ||||
−0.208336 | + | 0.978057i | \(0.566805\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.2175 | 1.42995 | 0.714976 | − | 0.699149i | \(-0.246437\pi\) | ||||
0.714976 | + | 0.699149i | \(0.246437\pi\) | |||||||
\(74\) | −9.86423 | −1.14669 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.31274 | 0.724120 | ||||||||
\(77\) | −6.07957 | −0.692831 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.93398 | 1.11766 | 0.558830 | − | 0.829282i | \(-0.311250\pi\) | ||||
0.558830 | + | 0.829282i | \(0.311250\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.28932 | 1.02583 | ||||||||
\(83\) | −7.95317 | −0.872974 | −0.436487 | − | 0.899711i | \(-0.643777\pi\) | ||||
−0.436487 | + | 0.899711i | \(0.643777\pi\) | |||||||
\(84\) | 3.64466 | 0.397665 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 7.57286 | 0.816603 | ||||||||
\(87\) | 10.0448 | 1.07691 | ||||||||
\(88\) | 1.66808 | 0.177817 | ||||||||
\(89\) | 5.95162 | 0.630870 | 0.315435 | − | 0.948947i | \(-0.397850\pi\) | ||||
0.315435 | + | 0.948947i | \(0.397850\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.24453 | 0.129752 | ||||||||
\(93\) | −4.21957 | −0.437549 | ||||||||
\(94\) | 6.82522 | 0.703967 | ||||||||
\(95\) | 6.31274 | 0.647673 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.75342 | −0.279568 | −0.139784 | − | 0.990182i | \(-0.544641\pi\) | ||||
−0.139784 | + | 0.990182i | \(0.544641\pi\) | |||||||
\(98\) | −6.28354 | −0.634734 | ||||||||
\(99\) | −1.66808 | −0.167648 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.33615 | 0.530967 | 0.265483 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265483 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | 7.51248 | 0.740227 | 0.370113 | − | 0.928987i | \(-0.379319\pi\) | ||||
0.370113 | + | 0.928987i | \(0.379319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.64466 | 0.355682 | ||||||||
\(106\) | 0.848634 | 0.0824266 | ||||||||
\(107\) | 16.9282 | 1.63651 | 0.818256 | − | 0.574855i | \(-0.194941\pi\) | ||||
0.818256 | + | 0.574855i | \(0.194941\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −0.663848 | −0.0635851 | −0.0317926 | − | 0.999494i | \(-0.510122\pi\) | ||||
−0.0317926 | + | 0.999494i | \(0.510122\pi\) | |||||||
\(110\) | 1.66808 | 0.159045 | ||||||||
\(111\) | 9.86423 | 0.936271 | ||||||||
\(112\) | 3.64466 | 0.344388 | ||||||||
\(113\) | −17.8700 | −1.68107 | −0.840534 | − | 0.541758i | \(-0.817759\pi\) | ||||
−0.840534 | + | 0.541758i | \(0.817759\pi\) | |||||||
\(114\) | −6.31274 | −0.591242 | ||||||||
\(115\) | 1.24453 | 0.116053 | ||||||||
\(116\) | 10.0448 | 0.932635 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.10876 | 0.562357 | ||||||||
\(119\) | 14.5786 | 1.33642 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −8.21752 | −0.747047 | ||||||||
\(122\) | −7.46410 | −0.675768 | ||||||||
\(123\) | −9.28932 | −0.837590 | ||||||||
\(124\) | −4.21957 | −0.378928 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.64466 | −0.324692 | ||||||||
\(127\) | 14.4407 | 1.28140 | 0.640702 | − | 0.767790i | \(-0.278643\pi\) | ||||
0.640702 | + | 0.767790i | \(0.278643\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.57286 | −0.666753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8892 | −0.951393 | −0.475697 | − | 0.879609i | \(-0.657804\pi\) | ||||
−0.475697 | + | 0.879609i | \(0.657804\pi\) | |||||||
\(132\) | −1.66808 | −0.145187 | ||||||||
\(133\) | 23.0078 | 1.99503 | ||||||||
\(134\) | 14.7534 | 1.27450 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −7.03696 | −0.601208 | −0.300604 | − | 0.953749i | \(-0.597188\pi\) | ||||
−0.300604 | + | 0.953749i | \(0.597188\pi\) | |||||||
\(138\) | −1.24453 | −0.105942 | ||||||||
\(139\) | 11.6447 | 0.987687 | 0.493844 | − | 0.869551i | \(-0.335592\pi\) | ||||
0.493844 | + | 0.869551i | \(0.335592\pi\) | |||||||
\(140\) | 3.64466 | 0.308030 | ||||||||
\(141\) | −6.82522 | −0.574787 | ||||||||
\(142\) | 3.51093 | 0.294631 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.0448 | 0.834174 | ||||||||
\(146\) | −12.2175 | −1.01113 | ||||||||
\(147\) | 6.28354 | 0.518258 | ||||||||
\(148\) | 9.86423 | 0.810835 | ||||||||
\(149\) | −0.772609 | −0.0632946 | −0.0316473 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316473 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −9.77838 | −0.795754 | −0.397877 | − | 0.917439i | \(-0.630253\pi\) | ||||
−0.397877 | + | 0.917439i | \(0.630253\pi\) | |||||||
\(152\) | −6.31274 | −0.512030 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 6.07957 | 0.489906 | ||||||||
\(155\) | −4.21957 | −0.338924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0135 | −0.958786 | −0.479393 | − | 0.877600i | \(-0.659143\pi\) | ||||
−0.479393 | + | 0.877600i | \(0.659143\pi\) | |||||||
\(158\) | −9.93398 | −0.790305 | ||||||||
\(159\) | −0.848634 | −0.0673011 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.53590 | 0.357479 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.0916 | 0.790437 | 0.395218 | − | 0.918587i | \(-0.370669\pi\) | ||||
0.395218 | + | 0.918587i | \(0.370669\pi\) | |||||||
\(164\) | −9.28932 | −0.725374 | ||||||||
\(165\) | −1.66808 | −0.129860 | ||||||||
\(166\) | 7.95317 | 0.617285 | ||||||||
\(167\) | −7.89701 | −0.611089 | −0.305545 | − | 0.952178i | \(-0.598839\pi\) | ||||
−0.305545 | + | 0.952178i | \(0.598839\pi\) | |||||||
\(168\) | −3.64466 | −0.281192 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 6.31274 | 0.482747 | ||||||||
\(172\) | −7.57286 | −0.577425 | ||||||||
\(173\) | −0.440685 | −0.0335047 | −0.0167523 | − | 0.999860i | \(-0.505333\pi\) | ||||
−0.0167523 | + | 0.999860i | \(0.505333\pi\) | |||||||
\(174\) | −10.0448 | −0.761493 | ||||||||
\(175\) | 3.64466 | 0.275510 | ||||||||
\(176\) | −1.66808 | −0.125736 | ||||||||
\(177\) | −6.10876 | −0.459163 | ||||||||
\(178\) | −5.95162 | −0.446093 | ||||||||
\(179\) | −19.6368 | −1.46773 | −0.733863 | − | 0.679297i | \(-0.762285\pi\) | ||||
−0.733863 | + | 0.679297i | \(0.762285\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −6.21752 | −0.462145 | −0.231072 | − | 0.972937i | \(-0.574223\pi\) | ||||
−0.231072 | + | 0.972937i | \(0.574223\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.46410 | 0.551762 | ||||||||
\(184\) | −1.24453 | −0.0917482 | ||||||||
\(185\) | 9.86423 | 0.725232 | ||||||||
\(186\) | 4.21957 | 0.309394 | ||||||||
\(187\) | −6.67230 | −0.487927 | ||||||||
\(188\) | −6.82522 | −0.497780 | ||||||||
\(189\) | 3.64466 | 0.265110 | ||||||||
\(190\) | −6.31274 | −0.457974 | ||||||||
\(191\) | 15.6816 | 1.13468 | 0.567341 | − | 0.823483i | \(-0.307972\pi\) | ||||
0.567341 | + | 0.823483i | \(0.307972\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 8.12795 | 0.585063 | 0.292531 | − | 0.956256i | \(-0.405502\pi\) | ||||
0.292531 | + | 0.956256i | \(0.405502\pi\) | |||||||
\(194\) | 2.75342 | 0.197684 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.28354 | 0.448825 | ||||||||
\(197\) | −0.891239 | −0.0634981 | −0.0317491 | − | 0.999496i | \(-0.510108\pi\) | ||||
−0.0317491 | + | 0.999496i | \(0.510108\pi\) | |||||||
\(198\) | 1.66808 | 0.118545 | ||||||||
\(199\) | 0.361116 | 0.0255988 | 0.0127994 | − | 0.999918i | \(-0.495926\pi\) | ||||
0.0127994 | + | 0.999918i | \(0.495926\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −14.7534 | −1.04063 | ||||||||
\(202\) | −5.33615 | −0.375450 | ||||||||
\(203\) | 36.6098 | 2.56951 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −9.28932 | −0.648794 | ||||||||
\(206\) | −7.51248 | −0.523419 | ||||||||
\(207\) | 1.24453 | 0.0865010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5301 | −0.728384 | ||||||||
\(210\) | −3.64466 | −0.251505 | ||||||||
\(211\) | 2.22739 | 0.153340 | 0.0766700 | − | 0.997057i | \(-0.475571\pi\) | ||||
0.0766700 | + | 0.997057i | \(0.475571\pi\) | |||||||
\(212\) | −0.848634 | −0.0582844 | ||||||||
\(213\) | −3.51093 | −0.240565 | ||||||||
\(214\) | −16.9282 | −1.15719 | ||||||||
\(215\) | −7.57286 | −0.516465 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −15.3789 | −1.04399 | ||||||||
\(218\) | 0.663848 | 0.0449615 | ||||||||
\(219\) | 12.2175 | 0.825584 | ||||||||
\(220\) | −1.66808 | −0.112462 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.86423 | −0.662044 | ||||||||
\(223\) | −6.08380 | −0.407401 | −0.203701 | − | 0.979033i | \(-0.565297\pi\) | ||||
−0.203701 | + | 0.979033i | \(0.565297\pi\) | |||||||
\(224\) | −3.64466 | −0.243519 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 17.8700 | 1.18869 | ||||||||
\(227\) | −15.3205 | −1.01686 | −0.508429 | − | 0.861104i | \(-0.669774\pi\) | ||||
−0.508429 | + | 0.861104i | \(0.669774\pi\) | |||||||
\(228\) | 6.31274 | 0.418071 | ||||||||
\(229\) | −22.2644 | −1.47127 | −0.735635 | − | 0.677378i | \(-0.763116\pi\) | ||||
−0.735635 | + | 0.677378i | \(0.763116\pi\) | |||||||
\(230\) | −1.24453 | −0.0820621 | ||||||||
\(231\) | −6.07957 | −0.400006 | ||||||||
\(232\) | −10.0448 | −0.659473 | ||||||||
\(233\) | −10.8366 | −0.709928 | −0.354964 | − | 0.934880i | \(-0.615507\pi\) | ||||
−0.354964 | + | 0.934880i | \(0.615507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.82522 | −0.445228 | ||||||||
\(236\) | −6.10876 | −0.397646 | ||||||||
\(237\) | 9.93398 | 0.645281 | ||||||||
\(238\) | −14.5786 | −0.944993 | ||||||||
\(239\) | −16.4975 | −1.06714 | −0.533568 | − | 0.845757i | \(-0.679149\pi\) | ||||
−0.533568 | + | 0.845757i | \(0.679149\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −4.40435 | −0.283709 | −0.141855 | − | 0.989887i | \(-0.545307\pi\) | ||||
−0.141855 | + | 0.989887i | \(0.545307\pi\) | |||||||
\(242\) | 8.21752 | 0.528242 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.46410 | 0.477840 | ||||||||
\(245\) | 6.28354 | 0.401441 | ||||||||
\(246\) | 9.28932 | 0.592265 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.21957 | 0.267943 | ||||||||
\(249\) | −7.95317 | −0.504011 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.9453 | 0.753984 | 0.376992 | − | 0.926217i | \(-0.376959\pi\) | ||||
0.376992 | + | 0.926217i | \(0.376959\pi\) | |||||||
\(252\) | 3.64466 | 0.229592 | ||||||||
\(253\) | −2.07598 | −0.130515 | ||||||||
\(254\) | −14.4407 | −0.906089 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.4621 | 1.21401 | 0.607005 | − | 0.794698i | \(-0.292371\pi\) | ||||
0.607005 | + | 0.794698i | \(0.292371\pi\) | |||||||
\(258\) | 7.57286 | 0.471466 | ||||||||
\(259\) | 35.9518 | 2.23393 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0448 | 0.621757 | ||||||||
\(262\) | 10.8892 | 0.672737 | ||||||||
\(263\) | 2.03478 | 0.125470 | 0.0627350 | − | 0.998030i | \(-0.480018\pi\) | ||||
0.0627350 | + | 0.998030i | \(0.480018\pi\) | |||||||
\(264\) | 1.66808 | 0.102663 | ||||||||
\(265\) | −0.848634 | −0.0521312 | ||||||||
\(266\) | −23.0078 | −1.41070 | ||||||||
\(267\) | 5.95162 | 0.364233 | ||||||||
\(268\) | −14.7534 | −0.901209 | ||||||||
\(269\) | 20.5287 | 1.25166 | 0.625829 | − | 0.779960i | \(-0.284761\pi\) | ||||
0.625829 | + | 0.779960i | \(0.284761\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 25.5401 | 1.55145 | 0.775725 | − | 0.631072i | \(-0.217385\pi\) | ||||
0.775725 | + | 0.631072i | \(0.217385\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.03696 | 0.425119 | ||||||||
\(275\) | −1.66808 | −0.100589 | ||||||||
\(276\) | 1.24453 | 0.0749121 | ||||||||
\(277\) | 18.0604 | 1.08514 | 0.542572 | − | 0.840010i | \(-0.317451\pi\) | ||||
0.542572 | + | 0.840010i | \(0.317451\pi\) | |||||||
\(278\) | −11.6447 | −0.698400 | ||||||||
\(279\) | −4.21957 | −0.252619 | ||||||||
\(280\) | −3.64466 | −0.217810 | ||||||||
\(281\) | 20.2175 | 1.20608 | 0.603038 | − | 0.797712i | \(-0.293957\pi\) | ||||
0.603038 | + | 0.797712i | \(0.293957\pi\) | |||||||
\(282\) | 6.82522 | 0.406436 | ||||||||
\(283\) | 8.69149 | 0.516656 | 0.258328 | − | 0.966057i | \(-0.416829\pi\) | ||||
0.258328 | + | 0.966057i | \(0.416829\pi\) | |||||||
\(284\) | −3.51093 | −0.208336 | ||||||||
\(285\) | 6.31274 | 0.373934 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.8564 | −1.99848 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −10.0448 | −0.589850 | ||||||||
\(291\) | −2.75342 | −0.161408 | ||||||||
\(292\) | 12.2175 | 0.714976 | ||||||||
\(293\) | −7.54790 | −0.440953 | −0.220476 | − | 0.975392i | \(-0.570761\pi\) | ||||
−0.220476 | + | 0.975392i | \(0.570761\pi\) | |||||||
\(294\) | −6.28354 | −0.366464 | ||||||||
\(295\) | −6.10876 | −0.355666 | ||||||||
\(296\) | −9.86423 | −0.573347 | ||||||||
\(297\) | −1.66808 | −0.0967916 | ||||||||
\(298\) | 0.772609 | 0.0447560 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −27.6005 | −1.59087 | ||||||||
\(302\) | 9.77838 | 0.562683 | ||||||||
\(303\) | 5.33615 | 0.306554 | ||||||||
\(304\) | 6.31274 | 0.362060 | ||||||||
\(305\) | 7.46410 | 0.427393 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | 26.0427 | 1.48634 | 0.743169 | − | 0.669104i | \(-0.233322\pi\) | ||||
0.743169 | + | 0.669104i | \(0.233322\pi\) | |||||||
\(308\) | −6.07957 | −0.346416 | ||||||||
\(309\) | 7.51248 | 0.427370 | ||||||||
\(310\) | 4.21957 | 0.239655 | ||||||||
\(311\) | −25.3789 | −1.43910 | −0.719552 | − | 0.694438i | \(-0.755653\pi\) | ||||
−0.719552 | + | 0.694438i | \(0.755653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.4600 | −1.77822 | −0.889112 | − | 0.457689i | \(-0.848677\pi\) | ||||
−0.889112 | + | 0.457689i | \(0.848677\pi\) | |||||||
\(314\) | 12.0135 | 0.677964 | ||||||||
\(315\) | 3.64466 | 0.205353 | ||||||||
\(316\) | 9.93398 | 0.558830 | ||||||||
\(317\) | 24.7093 | 1.38781 | 0.693905 | − | 0.720066i | \(-0.255889\pi\) | ||||
0.693905 | + | 0.720066i | \(0.255889\pi\) | |||||||
\(318\) | 0.848634 | 0.0475890 | ||||||||
\(319\) | −16.7555 | −0.938126 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 16.9282 | 0.944840 | ||||||||
\(322\) | −4.53590 | −0.252776 | ||||||||
\(323\) | 25.2509 | 1.40500 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.0916 | −0.558923 | ||||||||
\(327\) | −0.663848 | −0.0367109 | ||||||||
\(328\) | 9.28932 | 0.512917 | ||||||||
\(329\) | −24.8756 | −1.37144 | ||||||||
\(330\) | 1.66808 | 0.0918246 | ||||||||
\(331\) | −5.60360 | −0.308002 | −0.154001 | − | 0.988071i | \(-0.549216\pi\) | ||||
−0.154001 | + | 0.988071i | \(0.549216\pi\) | |||||||
\(332\) | −7.95317 | −0.436487 | ||||||||
\(333\) | 9.86423 | 0.540556 | ||||||||
\(334\) | 7.89701 | 0.432105 | ||||||||
\(335\) | −14.7534 | −0.806065 | ||||||||
\(336\) | 3.64466 | 0.198832 | ||||||||
\(337\) | −21.7868 | −1.18680 | −0.593402 | − | 0.804906i | \(-0.702216\pi\) | ||||
−0.593402 | + | 0.804906i | \(0.702216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.8700 | −0.970565 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 7.03856 | 0.381159 | ||||||||
\(342\) | −6.31274 | −0.341354 | ||||||||
\(343\) | −2.61124 | −0.140994 | ||||||||
\(344\) | 7.57286 | 0.408301 | ||||||||
\(345\) | 1.24453 | 0.0670034 | ||||||||
\(346\) | 0.440685 | 0.0236914 | ||||||||
\(347\) | 9.68162 | 0.519737 | 0.259868 | − | 0.965644i | \(-0.416321\pi\) | ||||
0.259868 | + | 0.965644i | \(0.416321\pi\) | |||||||
\(348\) | 10.0448 | 0.538457 | ||||||||
\(349\) | 19.3205 | 1.03420 | 0.517102 | − | 0.855924i | \(-0.327011\pi\) | ||||
0.517102 | + | 0.855924i | \(0.327011\pi\) | |||||||
\(350\) | −3.64466 | −0.194815 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.66808 | 0.0889087 | ||||||||
\(353\) | 22.9750 | 1.22284 | 0.611419 | − | 0.791307i | \(-0.290599\pi\) | ||||
0.611419 | + | 0.791307i | \(0.290599\pi\) | |||||||
\(354\) | 6.10876 | 0.324677 | ||||||||
\(355\) | −3.51093 | −0.186341 | ||||||||
\(356\) | 5.95162 | 0.315435 | ||||||||
\(357\) | 14.5786 | 0.771583 | ||||||||
\(358\) | 19.6368 | 1.03784 | ||||||||
\(359\) | −2.21752 | −0.117036 | −0.0585182 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585182 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 20.8506 | 1.09740 | ||||||||
\(362\) | 6.21752 | 0.326786 | ||||||||
\(363\) | −8.21752 | −0.431308 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.2175 | 0.639494 | ||||||||
\(366\) | −7.46410 | −0.390155 | ||||||||
\(367\) | −6.08112 | −0.317432 | −0.158716 | − | 0.987324i | \(-0.550735\pi\) | ||||
−0.158716 | + | 0.987324i | \(0.550735\pi\) | |||||||
\(368\) | 1.24453 | 0.0648758 | ||||||||
\(369\) | −9.28932 | −0.483583 | ||||||||
\(370\) | −9.86423 | −0.512817 | ||||||||
\(371\) | −3.09298 | −0.160580 | ||||||||
\(372\) | −4.21957 | −0.218774 | ||||||||
\(373\) | 15.6781 | 0.811780 | 0.405890 | − | 0.913922i | \(-0.366962\pi\) | ||||
0.405890 | + | 0.913922i | \(0.366962\pi\) | |||||||
\(374\) | 6.67230 | 0.345017 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 6.82522 | 0.351984 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.64466 | −0.187461 | ||||||||
\(379\) | −30.7166 | −1.57781 | −0.788903 | − | 0.614518i | \(-0.789350\pi\) | ||||
−0.788903 | + | 0.614518i | \(0.789350\pi\) | |||||||
\(380\) | 6.31274 | 0.323837 | ||||||||
\(381\) | 14.4407 | 0.739819 | ||||||||
\(382\) | −15.6816 | −0.802342 | ||||||||
\(383\) | 20.0619 | 1.02512 | 0.512558 | − | 0.858652i | \(-0.328698\pi\) | ||||
0.512558 | + | 0.858652i | \(0.328698\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −6.07957 | −0.309844 | ||||||||
\(386\) | −8.12795 | −0.413702 | ||||||||
\(387\) | −7.57286 | −0.384950 | ||||||||
\(388\) | −2.75342 | −0.139784 | ||||||||
\(389\) | −27.0314 | −1.37055 | −0.685273 | − | 0.728287i | \(-0.740317\pi\) | ||||
−0.685273 | + | 0.728287i | \(0.740317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.97813 | 0.251755 | ||||||||
\(392\) | −6.28354 | −0.317367 | ||||||||
\(393\) | −10.8892 | −0.549287 | ||||||||
\(394\) | 0.891239 | 0.0449000 | ||||||||
\(395\) | 9.93398 | 0.499833 | ||||||||
\(396\) | −1.66808 | −0.0838240 | ||||||||
\(397\) | 3.73628 | 0.187518 | 0.0937592 | − | 0.995595i | \(-0.470112\pi\) | ||||
0.0937592 | + | 0.995595i | \(0.470112\pi\) | |||||||
\(398\) | −0.361116 | −0.0181011 | ||||||||
\(399\) | 23.0078 | 1.15183 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 28.0911 | 1.40280 | 0.701402 | − | 0.712766i | \(-0.252558\pi\) | ||||
0.701402 | + | 0.712766i | \(0.252558\pi\) | |||||||
\(402\) | 14.7534 | 0.735834 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.33615 | 0.265483 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −36.6098 | −1.81692 | ||||||||
\(407\) | −16.4543 | −0.815609 | ||||||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 27.3804 | 1.35388 | 0.676938 | − | 0.736040i | \(-0.263307\pi\) | ||||
0.676938 | + | 0.736040i | \(0.263307\pi\) | |||||||
\(410\) | 9.28932 | 0.458767 | ||||||||
\(411\) | −7.03696 | −0.347108 | ||||||||
\(412\) | 7.51248 | 0.370113 | ||||||||
\(413\) | −22.2644 | −1.09556 | ||||||||
\(414\) | −1.24453 | −0.0611654 | ||||||||
\(415\) | −7.95317 | −0.390406 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6447 | 0.570241 | ||||||||
\(418\) | 10.5301 | 0.515045 | ||||||||
\(419\) | −13.1614 | −0.642975 | −0.321487 | − | 0.946914i | \(-0.604183\pi\) | ||||
−0.321487 | + | 0.946914i | \(0.604183\pi\) | |||||||
\(420\) | 3.64466 | 0.177841 | ||||||||
\(421\) | 1.29341 | 0.0630370 | 0.0315185 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315185 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(422\) | −2.22739 | −0.108428 | ||||||||
\(423\) | −6.82522 | −0.331853 | ||||||||
\(424\) | 0.848634 | 0.0412133 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 3.51093 | 0.170105 | ||||||||
\(427\) | 27.2041 | 1.31650 | ||||||||
\(428\) | 16.9282 | 0.818256 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.57286 | 0.365196 | ||||||||
\(431\) | −12.1279 | −0.584183 | −0.292091 | − | 0.956390i | \(-0.594351\pi\) | ||||
−0.292091 | + | 0.956390i | \(0.594351\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −2.07802 | −0.0998633 | −0.0499317 | − | 0.998753i | \(-0.515900\pi\) | ||||
−0.0499317 | + | 0.998753i | \(0.515900\pi\) | |||||||
\(434\) | 15.3789 | 0.738210 | ||||||||
\(435\) | 10.0448 | 0.481611 | ||||||||
\(436\) | −0.663848 | −0.0317926 | ||||||||
\(437\) | 7.85641 | 0.375823 | ||||||||
\(438\) | −12.2175 | −0.583776 | ||||||||
\(439\) | −2.39640 | −0.114374 | −0.0571869 | − | 0.998363i | \(-0.518213\pi\) | ||||
−0.0571869 | + | 0.998363i | \(0.518213\pi\) | |||||||
\(440\) | 1.66808 | 0.0795224 | ||||||||
\(441\) | 6.28354 | 0.299216 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9959 | 1.04506 | 0.522529 | − | 0.852622i | \(-0.324989\pi\) | ||||
0.522529 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(444\) | 9.86423 | 0.468136 | ||||||||
\(445\) | 5.95162 | 0.282134 | ||||||||
\(446\) | 6.08380 | 0.288076 | ||||||||
\(447\) | −0.772609 | −0.0365432 | ||||||||
\(448\) | 3.64466 | 0.172194 | ||||||||
\(449\) | −29.2253 | −1.37923 | −0.689613 | − | 0.724178i | \(-0.742220\pi\) | ||||
−0.689613 | + | 0.724178i | \(0.742220\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 15.4953 | 0.729645 | ||||||||
\(452\) | −17.8700 | −0.840534 | ||||||||
\(453\) | −9.77838 | −0.459429 | ||||||||
\(454\) | 15.3205 | 0.719027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.31274 | −0.295621 | ||||||||
\(457\) | 39.6432 | 1.85443 | 0.927216 | − | 0.374526i | \(-0.122195\pi\) | ||||
0.927216 | + | 0.374526i | \(0.122195\pi\) | |||||||
\(458\) | 22.2644 | 1.04034 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 1.24453 | 0.0580266 | ||||||||
\(461\) | 16.6758 | 0.776672 | 0.388336 | − | 0.921518i | \(-0.373050\pi\) | ||||
0.388336 | + | 0.921518i | \(0.373050\pi\) | |||||||
\(462\) | 6.07957 | 0.282847 | ||||||||
\(463\) | 32.2175 | 1.49728 | 0.748638 | − | 0.662979i | \(-0.230708\pi\) | ||||
0.748638 | + | 0.662979i | \(0.230708\pi\) | |||||||
\(464\) | 10.0448 | 0.466318 | ||||||||
\(465\) | −4.21957 | −0.195678 | ||||||||
\(466\) | 10.8366 | 0.501995 | ||||||||
\(467\) | 6.88137 | 0.318432 | 0.159216 | − | 0.987244i | \(-0.449103\pi\) | ||||
0.159216 | + | 0.987244i | \(0.449103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −53.7712 | −2.48292 | ||||||||
\(470\) | 6.82522 | 0.314824 | ||||||||
\(471\) | −12.0135 | −0.553555 | ||||||||
\(472\) | 6.10876 | 0.281179 | ||||||||
\(473\) | 12.6321 | 0.580825 | ||||||||
\(474\) | −9.93398 | −0.456283 | ||||||||
\(475\) | 6.31274 | 0.289648 | ||||||||
\(476\) | 14.5786 | 0.668211 | ||||||||
\(477\) | −0.848634 | −0.0388563 | ||||||||
\(478\) | 16.4975 | 0.754579 | ||||||||
\(479\) | −18.9709 | −0.866805 | −0.433402 | − | 0.901201i | \(-0.642687\pi\) | ||||
−0.433402 | + | 0.901201i | \(0.642687\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.40435 | 0.200613 | ||||||||
\(483\) | 4.53590 | 0.206391 | ||||||||
\(484\) | −8.21752 | −0.373524 | ||||||||
\(485\) | −2.75342 | −0.125026 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.91620 | 0.0868314 | 0.0434157 | − | 0.999057i | \(-0.486176\pi\) | ||||
0.0434157 | + | 0.999057i | \(0.486176\pi\) | |||||||
\(488\) | −7.46410 | −0.337884 | ||||||||
\(489\) | 10.0916 | 0.456359 | ||||||||
\(490\) | −6.28354 | −0.283862 | ||||||||
\(491\) | −33.6375 | −1.51804 | −0.759019 | − | 0.651069i | \(-0.774321\pi\) | ||||
−0.759019 | + | 0.651069i | \(0.774321\pi\) | |||||||
\(492\) | −9.28932 | −0.418795 | ||||||||
\(493\) | 40.1791 | 1.80958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.66808 | −0.0749744 | ||||||||
\(496\) | −4.21957 | −0.189464 | ||||||||
\(497\) | −12.7962 | −0.573986 | ||||||||
\(498\) | 7.95317 | 0.356390 | ||||||||
\(499\) | 1.82522 | 0.0817080 | 0.0408540 | − | 0.999165i | \(-0.486992\pi\) | ||||
0.0408540 | + | 0.999165i | \(0.486992\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −7.89701 | −0.352813 | ||||||||
\(502\) | −11.9453 | −0.533147 | ||||||||
\(503\) | −19.9985 | −0.891687 | −0.445843 | − | 0.895111i | \(-0.647096\pi\) | ||||
−0.445843 | + | 0.895111i | \(0.647096\pi\) | |||||||
\(504\) | −3.64466 | −0.162346 | ||||||||
\(505\) | 5.33615 | 0.237456 | ||||||||
\(506\) | 2.07598 | 0.0922884 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.4407 | 0.640702 | ||||||||
\(509\) | −5.89124 | −0.261125 | −0.130562 | − | 0.991440i | \(-0.541678\pi\) | ||||
−0.130562 | + | 0.991440i | \(0.541678\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 44.5287 | 1.96983 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.31274 | 0.278714 | ||||||||
\(514\) | −19.4621 | −0.858434 | ||||||||
\(515\) | 7.51248 | 0.331040 | ||||||||
\(516\) | −7.57286 | −0.333377 | ||||||||
\(517\) | 11.3850 | 0.500711 | ||||||||
\(518\) | −35.9518 | −1.57963 | ||||||||
\(519\) | −0.440685 | −0.0193439 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0370 | 1.40356 | 0.701782 | − | 0.712391i | \(-0.252388\pi\) | ||||
0.701782 | + | 0.712391i | \(0.252388\pi\) | |||||||
\(522\) | −10.0448 | −0.439648 | ||||||||
\(523\) | 38.7186 | 1.69305 | 0.846523 | − | 0.532352i | \(-0.178692\pi\) | ||||
0.846523 | + | 0.532352i | \(0.178692\pi\) | |||||||
\(524\) | −10.8892 | −0.475697 | ||||||||
\(525\) | 3.64466 | 0.159066 | ||||||||
\(526\) | −2.03478 | −0.0887207 | ||||||||
\(527\) | −16.8783 | −0.735229 | ||||||||
\(528\) | −1.66808 | −0.0725937 | ||||||||
\(529\) | −21.4511 | −0.932658 | ||||||||
\(530\) | 0.848634 | 0.0368623 | ||||||||
\(531\) | −6.10876 | −0.265098 | ||||||||
\(532\) | 23.0078 | 0.997513 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.95162 | −0.257552 | ||||||||
\(535\) | 16.9282 | 0.731870 | ||||||||
\(536\) | 14.7534 | 0.637251 | ||||||||
\(537\) | −19.6368 | −0.847392 | ||||||||
\(538\) | −20.5287 | −0.885056 | ||||||||
\(539\) | −10.4814 | −0.451467 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −25.9616 | −1.11618 | −0.558089 | − | 0.829781i | \(-0.688465\pi\) | ||||
−0.558089 | + | 0.829781i | \(0.688465\pi\) | |||||||
\(542\) | −25.5401 | −1.09704 | ||||||||
\(543\) | −6.21752 | −0.266819 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | −0.663848 | −0.0284361 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7596 | −0.759348 | −0.379674 | − | 0.925120i | \(-0.623964\pi\) | ||||
−0.379674 | + | 0.925120i | \(0.623964\pi\) | |||||||
\(548\) | −7.03696 | −0.300604 | ||||||||
\(549\) | 7.46410 | 0.318560 | ||||||||
\(550\) | 1.66808 | 0.0711270 | ||||||||
\(551\) | 63.4101 | 2.70136 | ||||||||
\(552\) | −1.24453 | −0.0529708 | ||||||||
\(553\) | 36.2060 | 1.53963 | ||||||||
\(554\) | −18.0604 | −0.767312 | ||||||||
\(555\) | 9.86423 | 0.418713 | ||||||||
\(556\) | 11.6447 | 0.493844 | ||||||||
\(557\) | −26.2202 | −1.11099 | −0.555493 | − | 0.831521i | \(-0.687470\pi\) | ||||
−0.555493 | + | 0.831521i | \(0.687470\pi\) | |||||||
\(558\) | 4.21957 | 0.178629 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.64466 | 0.154015 | ||||||||
\(561\) | −6.67230 | −0.281705 | ||||||||
\(562\) | −20.2175 | −0.852825 | ||||||||
\(563\) | −25.9928 | −1.09547 | −0.547733 | − | 0.836653i | \(-0.684509\pi\) | ||||
−0.547733 | + | 0.836653i | \(0.684509\pi\) | |||||||
\(564\) | −6.82522 | −0.287394 | ||||||||
\(565\) | −17.8700 | −0.751797 | ||||||||
\(566\) | −8.69149 | −0.365331 | ||||||||
\(567\) | 3.64466 | 0.153061 | ||||||||
\(568\) | 3.51093 | 0.147316 | ||||||||
\(569\) | −25.4699 | −1.06775 | −0.533876 | − | 0.845563i | \(-0.679265\pi\) | ||||
−0.533876 | + | 0.845563i | \(0.679265\pi\) | |||||||
\(570\) | −6.31274 | −0.264411 | ||||||||
\(571\) | 8.44491 | 0.353409 | 0.176704 | − | 0.984264i | \(-0.443456\pi\) | ||||
0.176704 | + | 0.984264i | \(0.443456\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6816 | 0.655109 | ||||||||
\(574\) | 33.8564 | 1.41314 | ||||||||
\(575\) | 1.24453 | 0.0519006 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −35.4216 | −1.47462 | −0.737311 | − | 0.675554i | \(-0.763905\pi\) | ||||
−0.737311 | + | 0.675554i | \(0.763905\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 8.12795 | 0.337786 | ||||||||
\(580\) | 10.0448 | 0.417087 | ||||||||
\(581\) | −28.9866 | −1.20257 | ||||||||
\(582\) | 2.75342 | 0.114133 | ||||||||
\(583\) | 1.41559 | 0.0586276 | ||||||||
\(584\) | −12.2175 | −0.505565 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.54790 | 0.311801 | ||||||||
\(587\) | −27.3789 | −1.13005 | −0.565024 | − | 0.825075i | \(-0.691133\pi\) | ||||
−0.565024 | + | 0.825075i | \(0.691133\pi\) | |||||||
\(588\) | 6.28354 | 0.259129 | ||||||||
\(589\) | −26.6370 | −1.09756 | ||||||||
\(590\) | 6.10876 | 0.251494 | ||||||||
\(591\) | −0.891239 | −0.0366607 | ||||||||
\(592\) | 9.86423 | 0.405417 | ||||||||
\(593\) | −12.0619 | −0.495324 | −0.247662 | − | 0.968846i | \(-0.579662\pi\) | ||||
−0.247662 | + | 0.968846i | \(0.579662\pi\) | |||||||
\(594\) | 1.66808 | 0.0684420 | ||||||||
\(595\) | 14.5786 | 0.597666 | ||||||||
\(596\) | −0.772609 | −0.0316473 | ||||||||
\(597\) | 0.361116 | 0.0147795 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.6129 | −1.16909 | −0.584546 | − | 0.811360i | \(-0.698727\pi\) | ||||
−0.584546 | + | 0.811360i | \(0.698727\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −19.1676 | −0.781862 | −0.390931 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390931 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(602\) | 27.6005 | 1.12491 | ||||||||
\(603\) | −14.7534 | −0.600806 | ||||||||
\(604\) | −9.77838 | −0.397877 | ||||||||
\(605\) | −8.21752 | −0.334090 | ||||||||
\(606\) | −5.33615 | −0.216766 | ||||||||
\(607\) | 18.9382 | 0.768678 | 0.384339 | − | 0.923192i | \(-0.374429\pi\) | ||||
0.384339 | + | 0.923192i | \(0.374429\pi\) | |||||||
\(608\) | −6.31274 | −0.256015 | ||||||||
\(609\) | 36.6098 | 1.48351 | ||||||||
\(610\) | −7.46410 | −0.302213 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 17.9694 | 0.725779 | 0.362890 | − | 0.931832i | \(-0.381790\pi\) | ||||
0.362890 | + | 0.931832i | \(0.381790\pi\) | |||||||
\(614\) | −26.0427 | −1.05100 | ||||||||
\(615\) | −9.28932 | −0.374582 | ||||||||
\(616\) | 6.07957 | 0.244953 | ||||||||
\(617\) | −18.0151 | −0.725260 | −0.362630 | − | 0.931933i | \(-0.618121\pi\) | ||||
−0.362630 | + | 0.931933i | \(0.618121\pi\) | |||||||
\(618\) | −7.51248 | −0.302196 | ||||||||
\(619\) | −25.0505 | −1.00687 | −0.503433 | − | 0.864035i | \(-0.667930\pi\) | ||||
−0.503433 | + | 0.864035i | \(0.667930\pi\) | |||||||
\(620\) | −4.21957 | −0.169462 | ||||||||
\(621\) | 1.24453 | 0.0499414 | ||||||||
\(622\) | 25.3789 | 1.01760 | ||||||||
\(623\) | 21.6916 | 0.869057 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.4600 | 1.25739 | ||||||||
\(627\) | −10.5301 | −0.420533 | ||||||||
\(628\) | −12.0135 | −0.479393 | ||||||||
\(629\) | 39.4569 | 1.57325 | ||||||||
\(630\) | −3.64466 | −0.145207 | ||||||||
\(631\) | 1.41727 | 0.0564206 | 0.0282103 | − | 0.999602i | \(-0.491019\pi\) | ||||
0.0282103 | + | 0.999602i | \(0.491019\pi\) | |||||||
\(632\) | −9.93398 | −0.395152 | ||||||||
\(633\) | 2.22739 | 0.0885308 | ||||||||
\(634\) | −24.7093 | −0.981330 | ||||||||
\(635\) | 14.4407 | 0.573061 | ||||||||
\(636\) | −0.848634 | −0.0336505 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.7555 | 0.663355 | ||||||||
\(639\) | −3.51093 | −0.138890 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.61970 | 0.182467 | 0.0912335 | − | 0.995830i | \(-0.470919\pi\) | ||||
0.0912335 | + | 0.995830i | \(0.470919\pi\) | |||||||
\(642\) | −16.9282 | −0.668103 | ||||||||
\(643\) | 48.0896 | 1.89647 | 0.948234 | − | 0.317573i | \(-0.102868\pi\) | ||||
0.948234 | + | 0.317573i | \(0.102868\pi\) | |||||||
\(644\) | 4.53590 | 0.178739 | ||||||||
\(645\) | −7.57286 | −0.298181 | ||||||||
\(646\) | −25.2509 | −0.993485 | ||||||||
\(647\) | 3.74565 | 0.147257 | 0.0736283 | − | 0.997286i | \(-0.476542\pi\) | ||||
0.0736283 | + | 0.997286i | \(0.476542\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 10.1899 | 0.399988 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.3789 | −0.602746 | ||||||||
\(652\) | 10.0916 | 0.395218 | ||||||||
\(653\) | 42.2899 | 1.65493 | 0.827466 | − | 0.561516i | \(-0.189782\pi\) | ||||
0.827466 | + | 0.561516i | \(0.189782\pi\) | |||||||
\(654\) | 0.663848 | 0.0259585 | ||||||||
\(655\) | −10.8892 | −0.425476 | ||||||||
\(656\) | −9.28932 | −0.362687 | ||||||||
\(657\) | 12.2175 | 0.476651 | ||||||||
\(658\) | 24.8756 | 0.969752 | ||||||||
\(659\) | −29.1750 | −1.13650 | −0.568248 | − | 0.822858i | \(-0.692378\pi\) | ||||
−0.568248 | + | 0.822858i | \(0.692378\pi\) | |||||||
\(660\) | −1.66808 | −0.0649298 | ||||||||
\(661\) | −44.4662 | −1.72954 | −0.864768 | − | 0.502172i | \(-0.832535\pi\) | ||||
−0.864768 | + | 0.502172i | \(0.832535\pi\) | |||||||
\(662\) | 5.60360 | 0.217790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.95317 | 0.308643 | ||||||||
\(665\) | 23.0078 | 0.892203 | ||||||||
\(666\) | −9.86423 | −0.382231 | ||||||||
\(667\) | 12.5011 | 0.484043 | ||||||||
\(668\) | −7.89701 | −0.305545 | ||||||||
\(669\) | −6.08380 | −0.235213 | ||||||||
\(670\) | 14.7534 | 0.569974 | ||||||||
\(671\) | −12.4507 | −0.480654 | ||||||||
\(672\) | −3.64466 | −0.140596 | ||||||||
\(673\) | 7.90633 | 0.304767 | 0.152383 | − | 0.988321i | \(-0.451305\pi\) | ||||
0.152383 | + | 0.988321i | \(0.451305\pi\) | |||||||
\(674\) | 21.7868 | 0.839198 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.05615 | −0.271190 | −0.135595 | − | 0.990764i | \(-0.543295\pi\) | ||||
−0.135595 | + | 0.990764i | \(0.543295\pi\) | |||||||
\(678\) | 17.8700 | 0.686293 | ||||||||
\(679\) | −10.0353 | −0.385119 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | −15.3205 | −0.587083 | ||||||||
\(682\) | −7.03856 | −0.269520 | ||||||||
\(683\) | 5.95317 | 0.227792 | 0.113896 | − | 0.993493i | \(-0.463667\pi\) | ||||
0.113896 | + | 0.993493i | \(0.463667\pi\) | |||||||
\(684\) | 6.31274 | 0.241373 | ||||||||
\(685\) | −7.03696 | −0.268869 | ||||||||
\(686\) | 2.61124 | 0.0996976 | ||||||||
\(687\) | −22.2644 | −0.849438 | ||||||||
\(688\) | −7.57286 | −0.288713 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.24453 | −0.0473786 | ||||||||
\(691\) | −18.7591 | −0.713628 | −0.356814 | − | 0.934175i | \(-0.616137\pi\) | ||||
−0.356814 | + | 0.934175i | \(0.616137\pi\) | |||||||
\(692\) | −0.440685 | −0.0167523 | ||||||||
\(693\) | −6.07957 | −0.230944 | ||||||||
\(694\) | −9.68162 | −0.367509 | ||||||||
\(695\) | 11.6447 | 0.441707 | ||||||||
\(696\) | −10.0448 | −0.380747 | ||||||||
\(697\) | −37.1573 | −1.40743 | ||||||||
\(698\) | −19.3205 | −0.731292 | ||||||||
\(699\) | −10.8366 | −0.409877 | ||||||||
\(700\) | 3.64466 | 0.137755 | ||||||||
\(701\) | 28.5298 | 1.07755 | 0.538777 | − | 0.842448i | \(-0.318887\pi\) | ||||
0.538777 | + | 0.842448i | \(0.318887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.2703 | 2.34857 | ||||||||
\(704\) | −1.66808 | −0.0628680 | ||||||||
\(705\) | −6.82522 | −0.257053 | ||||||||
\(706\) | −22.9750 | −0.864677 | ||||||||
\(707\) | 19.4485 | 0.731435 | ||||||||
\(708\) | −6.10876 | −0.229581 | ||||||||
\(709\) | 23.1926 | 0.871015 | 0.435507 | − | 0.900185i | \(-0.356569\pi\) | ||||
0.435507 | + | 0.900185i | \(0.356569\pi\) | |||||||
\(710\) | 3.51093 | 0.131763 | ||||||||
\(711\) | 9.93398 | 0.372553 | ||||||||
\(712\) | −5.95162 | −0.223046 | ||||||||
\(713\) | −5.25139 | −0.196666 | ||||||||
\(714\) | −14.5786 | −0.545592 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.6368 | −0.733863 | ||||||||
\(717\) | −16.4975 | −0.616111 | ||||||||
\(718\) | 2.21752 | 0.0827572 | ||||||||
\(719\) | 11.7128 | 0.436814 | 0.218407 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218407 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 27.3804 | 1.01970 | ||||||||
\(722\) | −20.8506 | −0.775980 | ||||||||
\(723\) | −4.40435 | −0.163800 | ||||||||
\(724\) | −6.21752 | −0.231072 | ||||||||
\(725\) | 10.0448 | 0.373054 | ||||||||
\(726\) | 8.21752 | 0.304981 | ||||||||
\(727\) | −3.82677 | −0.141927 | −0.0709634 | − | 0.997479i | \(-0.522607\pi\) | ||||
−0.0709634 | + | 0.997479i | \(0.522607\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.2175 | −0.452191 | ||||||||
\(731\) | −30.2915 | −1.12037 | ||||||||
\(732\) | 7.46410 | 0.275881 | ||||||||
\(733\) | 12.9340 | 0.477727 | 0.238864 | − | 0.971053i | \(-0.423225\pi\) | ||||
0.238864 | + | 0.971053i | \(0.423225\pi\) | |||||||
\(734\) | 6.08112 | 0.224458 | ||||||||
\(735\) | 6.28354 | 0.231772 | ||||||||
\(736\) | −1.24453 | −0.0458741 | ||||||||
\(737\) | 24.6098 | 0.906515 | ||||||||
\(738\) | 9.28932 | 0.341945 | ||||||||
\(739\) | −35.3462 | −1.30023 | −0.650115 | − | 0.759836i | \(-0.725279\pi\) | ||||
−0.650115 | + | 0.759836i | \(0.725279\pi\) | |||||||
\(740\) | 9.86423 | 0.362616 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.09298 | 0.113547 | ||||||||
\(743\) | 37.0953 | 1.36090 | 0.680448 | − | 0.732796i | \(-0.261785\pi\) | ||||
0.680448 | + | 0.732796i | \(0.261785\pi\) | |||||||
\(744\) | 4.21957 | 0.154697 | ||||||||
\(745\) | −0.772609 | −0.0283062 | ||||||||
\(746\) | −15.6781 | −0.574015 | ||||||||
\(747\) | −7.95317 | −0.290991 | ||||||||
\(748\) | −6.67230 | −0.243964 | ||||||||
\(749\) | 61.6975 | 2.25438 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −9.65807 | −0.352428 | −0.176214 | − | 0.984352i | \(-0.556385\pi\) | ||||
−0.176214 | + | 0.984352i | \(0.556385\pi\) | |||||||
\(752\) | −6.82522 | −0.248890 | ||||||||
\(753\) | 11.9453 | 0.435313 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.77838 | −0.355872 | ||||||||
\(756\) | 3.64466 | 0.132555 | ||||||||
\(757\) | −43.6885 | −1.58789 | −0.793943 | − | 0.607992i | \(-0.791975\pi\) | ||||
−0.793943 | + | 0.607992i | \(0.791975\pi\) | |||||||
\(758\) | 30.7166 | 1.11568 | ||||||||
\(759\) | −2.07598 | −0.0753531 | ||||||||
\(760\) | −6.31274 | −0.228987 | ||||||||
\(761\) | −39.9007 | −1.44640 | −0.723200 | − | 0.690639i | \(-0.757329\pi\) | ||||
−0.723200 | + | 0.690639i | \(0.757329\pi\) | |||||||
\(762\) | −14.4407 | −0.523131 | ||||||||
\(763\) | −2.41950 | −0.0875918 | ||||||||
\(764\) | 15.6816 | 0.567341 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | −20.0619 | −0.724867 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 17.5588 | 0.633187 | 0.316594 | − | 0.948561i | \(-0.397461\pi\) | ||||
0.316594 | + | 0.948561i | \(0.397461\pi\) | |||||||
\(770\) | 6.07957 | 0.219092 | ||||||||
\(771\) | 19.4621 | 0.700909 | ||||||||
\(772\) | 8.12795 | 0.292531 | ||||||||
\(773\) | 12.8372 | 0.461723 | 0.230861 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230861 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(774\) | 7.57286 | 0.272201 | ||||||||
\(775\) | −4.21957 | −0.151571 | ||||||||
\(776\) | 2.75342 | 0.0988420 | ||||||||
\(777\) | 35.9518 | 1.28976 | ||||||||
\(778\) | 27.0314 | 0.969122 | ||||||||
\(779\) | −58.6410 | −2.10103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.85651 | 0.209562 | ||||||||
\(782\) | −4.97813 | −0.178018 | ||||||||
\(783\) | 10.0448 | 0.358971 | ||||||||
\(784\) | 6.28354 | 0.224412 | ||||||||
\(785\) | −12.0135 | −0.428782 | ||||||||
\(786\) | 10.8892 | 0.388405 | ||||||||
\(787\) | 6.95735 | 0.248003 | 0.124001 | − | 0.992282i | \(-0.460427\pi\) | ||||
0.124001 | + | 0.992282i | \(0.460427\pi\) | |||||||
\(788\) | −0.891239 | −0.0317491 | ||||||||
\(789\) | 2.03478 | 0.0724402 | ||||||||
\(790\) | −9.93398 | −0.353435 | ||||||||
\(791\) | −65.1301 | −2.31576 | ||||||||
\(792\) | 1.66808 | 0.0592725 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.73628 | −0.132596 | ||||||||
\(795\) | −0.848634 | −0.0300979 | ||||||||
\(796\) | 0.361116 | 0.0127994 | ||||||||
\(797\) | 34.1354 | 1.20914 | 0.604569 | − | 0.796553i | \(-0.293345\pi\) | ||||
0.604569 | + | 0.796553i | \(0.293345\pi\) | |||||||
\(798\) | −23.0078 | −0.814466 | ||||||||
\(799\) | −27.3009 | −0.965835 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 5.95162 | 0.210290 | ||||||||
\(802\) | −28.0911 | −0.991932 | ||||||||
\(803\) | −20.3798 | −0.719186 | ||||||||
\(804\) | −14.7534 | −0.520313 | ||||||||
\(805\) | 4.53590 | 0.159869 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.5287 | 0.722645 | ||||||||
\(808\) | −5.33615 | −0.187725 | ||||||||
\(809\) | −3.32770 | −0.116996 | −0.0584978 | − | 0.998288i | \(-0.518631\pi\) | ||||
−0.0584978 | + | 0.998288i | \(0.518631\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −20.6083 | −0.723655 | −0.361827 | − | 0.932245i | \(-0.617847\pi\) | ||||
−0.361827 | + | 0.932245i | \(0.617847\pi\) | |||||||
\(812\) | 36.6098 | 1.28475 | ||||||||
\(813\) | 25.5401 | 0.895730 | ||||||||
\(814\) | 16.4543 | 0.576722 | ||||||||
\(815\) | 10.0916 | 0.353494 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | −47.8055 | −1.67250 | ||||||||
\(818\) | −27.3804 | −0.957335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.28932 | −0.324397 | ||||||||
\(821\) | −1.58005 | −0.0551442 | −0.0275721 | − | 0.999620i | \(-0.508778\pi\) | ||||
−0.0275721 | + | 0.999620i | \(0.508778\pi\) | |||||||
\(822\) | 7.03696 | 0.245442 | ||||||||
\(823\) | 37.5168 | 1.30776 | 0.653878 | − | 0.756600i | \(-0.273141\pi\) | ||||
0.653878 | + | 0.756600i | \(0.273141\pi\) | |||||||
\(824\) | −7.51248 | −0.261710 | ||||||||
\(825\) | −1.66808 | −0.0580750 | ||||||||
\(826\) | 22.2644 | 0.774676 | ||||||||
\(827\) | 49.4912 | 1.72098 | 0.860489 | − | 0.509469i | \(-0.170158\pi\) | ||||
0.860489 | + | 0.509469i | \(0.170158\pi\) | |||||||
\(828\) | 1.24453 | 0.0432505 | ||||||||
\(829\) | 49.1385 | 1.70665 | 0.853326 | − | 0.521378i | \(-0.174582\pi\) | ||||
0.853326 | + | 0.521378i | \(0.174582\pi\) | |||||||
\(830\) | 7.95317 | 0.276058 | ||||||||
\(831\) | 18.0604 | 0.626508 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.1342 | 0.870848 | ||||||||
\(834\) | −11.6447 | −0.403222 | ||||||||
\(835\) | −7.89701 | −0.273287 | ||||||||
\(836\) | −10.5301 | −0.364192 | ||||||||
\(837\) | −4.21957 | −0.145850 | ||||||||
\(838\) | 13.1614 | 0.454652 | ||||||||
\(839\) | 21.5421 | 0.743717 | 0.371858 | − | 0.928289i | \(-0.378721\pi\) | ||||
0.371858 | + | 0.928289i | \(0.378721\pi\) | |||||||
\(840\) | −3.64466 | −0.125753 | ||||||||
\(841\) | 71.8977 | 2.47923 | ||||||||
\(842\) | −1.29341 | −0.0445739 | ||||||||
\(843\) | 20.2175 | 0.696328 | ||||||||
\(844\) | 2.22739 | 0.0766700 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.82522 | 0.234656 | ||||||||
\(847\) | −29.9501 | −1.02910 | ||||||||
\(848\) | −0.848634 | −0.0291422 | ||||||||
\(849\) | 8.69149 | 0.298291 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | 12.2764 | 0.420828 | ||||||||
\(852\) | −3.51093 | −0.120283 | ||||||||
\(853\) | −2.79821 | −0.0958088 | −0.0479044 | − | 0.998852i | \(-0.515254\pi\) | ||||
−0.0479044 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(854\) | −27.2041 | −0.930905 | ||||||||
\(855\) | 6.31274 | 0.215891 | ||||||||
\(856\) | −16.9282 | −0.578594 | ||||||||
\(857\) | 48.9658 | 1.67264 | 0.836320 | − | 0.548242i | \(-0.184703\pi\) | ||||
0.836320 | + | 0.548242i | \(0.184703\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.22739 | 0.144237 | 0.0721184 | − | 0.997396i | \(-0.477024\pi\) | ||||
0.0721184 | + | 0.997396i | \(0.477024\pi\) | |||||||
\(860\) | −7.57286 | −0.258232 | ||||||||
\(861\) | −33.8564 | −1.15382 | ||||||||
\(862\) | 12.1279 | 0.413080 | ||||||||
\(863\) | −19.0285 | −0.647738 | −0.323869 | − | 0.946102i | \(-0.604984\pi\) | ||||
−0.323869 | + | 0.946102i | \(0.604984\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −0.440685 | −0.0149837 | ||||||||
\(866\) | 2.07802 | 0.0706141 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −15.3789 | −0.521994 | ||||||||
\(869\) | −16.5706 | −0.562120 | ||||||||
\(870\) | −10.0448 | −0.340550 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.663848 | 0.0224807 | ||||||||
\(873\) | −2.75342 | −0.0931892 | ||||||||
\(874\) | −7.85641 | −0.265747 | ||||||||
\(875\) | 3.64466 | 0.123212 | ||||||||
\(876\) | 12.2175 | 0.412792 | ||||||||
\(877\) | 13.5473 | 0.457459 | 0.228729 | − | 0.973490i | \(-0.426543\pi\) | ||||
0.228729 | + | 0.973490i | \(0.426543\pi\) | |||||||
\(878\) | 2.39640 | 0.0808745 | ||||||||
\(879\) | −7.54790 | −0.254584 | ||||||||
\(880\) | −1.66808 | −0.0562308 | ||||||||
\(881\) | 4.98081 | 0.167808 | 0.0839039 | − | 0.996474i | \(-0.473261\pi\) | ||||
0.0839039 | + | 0.996474i | \(0.473261\pi\) | |||||||
\(882\) | −6.28354 | −0.211578 | ||||||||
\(883\) | −30.9829 | −1.04266 | −0.521330 | − | 0.853355i | \(-0.674564\pi\) | ||||
−0.521330 | + | 0.853355i | \(0.674564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.10876 | −0.205344 | ||||||||
\(886\) | −21.9959 | −0.738967 | ||||||||
\(887\) | 17.1765 | 0.576731 | 0.288365 | − | 0.957520i | \(-0.406888\pi\) | ||||
0.288365 | + | 0.957520i | \(0.406888\pi\) | |||||||
\(888\) | −9.86423 | −0.331022 | ||||||||
\(889\) | 52.6314 | 1.76520 | ||||||||
\(890\) | −5.95162 | −0.199499 | ||||||||
\(891\) | −1.66808 | −0.0558826 | ||||||||
\(892\) | −6.08380 | −0.203701 | ||||||||
\(893\) | −43.0858 | −1.44181 | ||||||||
\(894\) | 0.772609 | 0.0258399 | ||||||||
\(895\) | −19.6368 | −0.656387 | ||||||||
\(896\) | −3.64466 | −0.121760 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.2253 | 0.975261 | ||||||||
\(899\) | −42.3847 | −1.41361 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −3.39454 | −0.113088 | ||||||||
\(902\) | −15.4953 | −0.515937 | ||||||||
\(903\) | −27.6005 | −0.918487 | ||||||||
\(904\) | 17.8700 | 0.594347 | ||||||||
\(905\) | −6.21752 | −0.206677 | ||||||||
\(906\) | 9.77838 | 0.324865 | ||||||||
\(907\) | −25.0797 | −0.832758 | −0.416379 | − | 0.909191i | \(-0.636701\pi\) | ||||
−0.416379 | + | 0.909191i | \(0.636701\pi\) | |||||||
\(908\) | −15.3205 | −0.508429 | ||||||||
\(909\) | 5.33615 | 0.176989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.2332 | 0.604092 | 0.302046 | − | 0.953293i | \(-0.402330\pi\) | ||||
0.302046 | + | 0.953293i | \(0.402330\pi\) | |||||||
\(912\) | 6.31274 | 0.209036 | ||||||||
\(913\) | 13.2665 | 0.439057 | ||||||||
\(914\) | −39.6432 | −1.31128 | ||||||||
\(915\) | 7.46410 | 0.246756 | ||||||||
\(916\) | −22.2644 | −0.735635 | ||||||||
\(917\) | −39.6874 | −1.31059 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | −34.3882 | −1.13436 | −0.567181 | − | 0.823593i | \(-0.691966\pi\) | ||||
−0.567181 | + | 0.823593i | \(0.691966\pi\) | |||||||
\(920\) | −1.24453 | −0.0410310 | ||||||||
\(921\) | 26.0427 | 0.858137 | ||||||||
\(922\) | −16.6758 | −0.549190 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −6.07957 | −0.200003 | ||||||||
\(925\) | 9.86423 | 0.324334 | ||||||||
\(926\) | −32.2175 | −1.05873 | ||||||||
\(927\) | 7.51248 | 0.246742 | ||||||||
\(928\) | −10.0448 | −0.329736 | ||||||||
\(929\) | 31.0904 | 1.02004 | 0.510022 | − | 0.860161i | \(-0.329637\pi\) | ||||
0.510022 | + | 0.860161i | \(0.329637\pi\) | |||||||
\(930\) | 4.21957 | 0.138365 | ||||||||
\(931\) | 39.6663 | 1.30001 | ||||||||
\(932\) | −10.8366 | −0.354964 | ||||||||
\(933\) | −25.3789 | −0.830868 | ||||||||
\(934\) | −6.88137 | −0.225165 | ||||||||
\(935\) | −6.67230 | −0.218208 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.8783 | −0.616726 | −0.308363 | − | 0.951269i | \(-0.599781\pi\) | ||||
−0.308363 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(938\) | 53.7712 | 1.75569 | ||||||||
\(939\) | −31.4600 | −1.02666 | ||||||||
\(940\) | −6.82522 | −0.222614 | ||||||||
\(941\) | −28.9398 | −0.943409 | −0.471705 | − | 0.881757i | \(-0.656361\pi\) | ||||
−0.471705 | + | 0.881757i | \(0.656361\pi\) | |||||||
\(942\) | 12.0135 | 0.391423 | ||||||||
\(943\) | −11.5609 | −0.376473 | ||||||||
\(944\) | −6.10876 | −0.198823 | ||||||||
\(945\) | 3.64466 | 0.118561 | ||||||||
\(946\) | −12.6321 | −0.410705 | ||||||||
\(947\) | 7.86896 | 0.255707 | 0.127853 | − | 0.991793i | \(-0.459191\pi\) | ||||
0.127853 | + | 0.991793i | \(0.459191\pi\) | |||||||
\(948\) | 9.93398 | 0.322641 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.31274 | −0.204812 | ||||||||
\(951\) | 24.7093 | 0.801253 | ||||||||
\(952\) | −14.5786 | −0.472496 | ||||||||
\(953\) | −55.0968 | −1.78476 | −0.892381 | − | 0.451283i | \(-0.850967\pi\) | ||||
−0.892381 | + | 0.451283i | \(0.850967\pi\) | |||||||
\(954\) | 0.848634 | 0.0274755 | ||||||||
\(955\) | 15.6816 | 0.507445 | ||||||||
\(956\) | −16.4975 | −0.533568 | ||||||||
\(957\) | −16.7555 | −0.541627 | ||||||||
\(958\) | 18.9709 | 0.612923 | ||||||||
\(959\) | −25.6473 | −0.828196 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −13.1952 | −0.425653 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9282 | 0.545504 | ||||||||
\(964\) | −4.40435 | −0.141855 | ||||||||
\(965\) | 8.12795 | 0.261648 | ||||||||
\(966\) | −4.53590 | −0.145940 | ||||||||
\(967\) | 31.5523 | 1.01465 | 0.507326 | − | 0.861754i | \(-0.330634\pi\) | ||||
0.507326 | + | 0.861754i | \(0.330634\pi\) | |||||||
\(968\) | 8.21752 | 0.264121 | ||||||||
\(969\) | 25.2509 | 0.811177 | ||||||||
\(970\) | 2.75342 | 0.0884070 | ||||||||
\(971\) | 3.67585 | 0.117964 | 0.0589818 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589818 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 42.4408 | 1.36059 | ||||||||
\(974\) | −1.91620 | −0.0613991 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.46410 | 0.238920 | ||||||||
\(977\) | −42.0205 | −1.34435 | −0.672177 | − | 0.740391i | \(-0.734641\pi\) | ||||
−0.672177 | + | 0.740391i | \(0.734641\pi\) | |||||||
\(978\) | −10.0916 | −0.322694 | ||||||||
\(979\) | −9.92775 | −0.317292 | ||||||||
\(980\) | 6.28354 | 0.200720 | ||||||||
\(981\) | −0.663848 | −0.0211950 | ||||||||
\(982\) | 33.6375 | 1.07341 | ||||||||
\(983\) | 13.4307 | 0.428372 | 0.214186 | − | 0.976793i | \(-0.431290\pi\) | ||||
0.214186 | + | 0.976793i | \(0.431290\pi\) | |||||||
\(984\) | 9.28932 | 0.296133 | ||||||||
\(985\) | −0.891239 | −0.0283972 | ||||||||
\(986\) | −40.1791 | −1.27956 | ||||||||
\(987\) | −24.8756 | −0.791799 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.42468 | −0.299687 | ||||||||
\(990\) | 1.66808 | 0.0530149 | ||||||||
\(991\) | 43.7988 | 1.39132 | 0.695658 | − | 0.718373i | \(-0.255113\pi\) | ||||
0.695658 | + | 0.718373i | \(0.255113\pi\) | |||||||
\(992\) | 4.21957 | 0.133971 | ||||||||
\(993\) | −5.60360 | −0.177825 | ||||||||
\(994\) | 12.7962 | 0.405870 | ||||||||
\(995\) | 0.361116 | 0.0114481 | ||||||||
\(996\) | −7.95317 | −0.252006 | ||||||||
\(997\) | −23.5125 | −0.744648 | −0.372324 | − | 0.928103i | \(-0.621439\pi\) | ||||
−0.372324 | + | 0.928103i | \(0.621439\pi\) | |||||||
\(998\) | −1.82522 | −0.0577763 | ||||||||
\(999\) | 9.86423 | 0.312090 |
(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 | 5070.2.a.bz.1.4 | 4 | ||
13.5 | odd | 4 | 5070.2.b.ba.1351.8 | 8 | |||
13.6 | odd | 12 | 390.2.bb.c.361.3 | yes | 8 | ||
13.8 | odd | 4 | 5070.2.b.ba.1351.1 | 8 | |||
13.11 | odd | 12 | 390.2.bb.c.121.3 | ✓ | 8 | ||
13.12 | even | 2 | 5070.2.a.ca.1.1 | 4 | |||
39.11 | even | 12 | 1170.2.bs.f.901.1 | 8 | |||
39.32 | even | 12 | 1170.2.bs.f.361.1 | 8 | |||
65.19 | odd | 12 | 1950.2.bc.g.751.2 | 8 | |||
65.24 | odd | 12 | 1950.2.bc.g.901.2 | 8 | |||
65.32 | even | 12 | 1950.2.y.k.49.2 | 8 | |||
65.37 | even | 12 | 1950.2.y.j.199.3 | 8 | |||
65.58 | even | 12 | 1950.2.y.j.49.3 | 8 | |||
65.63 | even | 12 | 1950.2.y.k.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.3 | ✓ | 8 | 13.11 | odd | 12 | ||
390.2.bb.c.361.3 | yes | 8 | 13.6 | odd | 12 | ||
1170.2.bs.f.361.1 | 8 | 39.32 | even | 12 | |||
1170.2.bs.f.901.1 | 8 | 39.11 | even | 12 | |||
1950.2.y.j.49.3 | 8 | 65.58 | even | 12 | |||
1950.2.y.j.199.3 | 8 | 65.37 | even | 12 | |||
1950.2.y.k.49.2 | 8 | 65.32 | even | 12 | |||
1950.2.y.k.199.2 | 8 | 65.63 | even | 12 | |||
1950.2.bc.g.751.2 | 8 | 65.19 | odd | 12 | |||
1950.2.bc.g.901.2 | 8 | 65.24 | odd | 12 | |||
5070.2.a.bz.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.a.ca.1.1 | 4 | 13.12 | even | 2 | |||
5070.2.b.ba.1351.1 | 8 | 13.8 | odd | 4 | |||
5070.2.b.ba.1351.8 | 8 | 13.5 | odd | 4 |