Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2535,2,Mod(1,2535)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2535, 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("2535.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2535 = 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2535.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: | \(20.2420769124\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2535.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24698 | −0.881748 | −0.440874 | − | 0.897569i | \(-0.645331\pi\) | ||||
−0.440874 | + | 0.897569i | \(0.645331\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.445042 | −0.222521 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.24698 | 0.509077 | ||||||||
\(7\) | −2.24698 | −0.849278 | −0.424639 | − | 0.905363i | \(-0.639599\pi\) | ||||
−0.424639 | + | 0.905363i | \(0.639599\pi\) | |||||||
\(8\) | 3.04892 | 1.07796 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.24698 | 0.394330 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0.445042 | 0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.80194 | 0.748849 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.91185 | −0.727963 | ||||||||
\(17\) | −6.49396 | −1.57502 | −0.787508 | − | 0.616304i | \(-0.788629\pi\) | ||||
−0.787508 | + | 0.616304i | \(0.788629\pi\) | |||||||
\(18\) | −1.24698 | −0.293916 | ||||||||
\(19\) | 2.33513 | 0.535715 | 0.267857 | − | 0.963459i | \(-0.413684\pi\) | ||||
0.267857 | + | 0.963459i | \(0.413684\pi\) | |||||||
\(20\) | 0.445042 | 0.0995144 | ||||||||
\(21\) | 2.24698 | 0.490331 | ||||||||
\(22\) | −1.24698 | −0.265857 | ||||||||
\(23\) | 0.198062 | 0.0412988 | 0.0206494 | − | 0.999787i | \(-0.493427\pi\) | ||||
0.0206494 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(24\) | −3.04892 | −0.622358 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.82908 | 0.711043 | 0.355522 | − | 0.934668i | \(-0.384303\pi\) | ||||
0.355522 | + | 0.934668i | \(0.384303\pi\) | |||||||
\(30\) | −1.24698 | −0.227666 | ||||||||
\(31\) | 1.71379 | 0.307806 | 0.153903 | − | 0.988086i | \(-0.450816\pi\) | ||||
0.153903 | + | 0.988086i | \(0.450816\pi\) | |||||||
\(32\) | −2.46681 | −0.436075 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 8.09783 | 1.38877 | ||||||||
\(35\) | 2.24698 | 0.379809 | ||||||||
\(36\) | −0.445042 | −0.0741736 | ||||||||
\(37\) | 4.54288 | 0.746844 | 0.373422 | − | 0.927662i | \(-0.378184\pi\) | ||||
0.373422 | + | 0.927662i | \(0.378184\pi\) | |||||||
\(38\) | −2.91185 | −0.472365 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.04892 | −0.482076 | ||||||||
\(41\) | 5.75302 | 0.898471 | 0.449235 | − | 0.893413i | \(-0.351696\pi\) | ||||
0.449235 | + | 0.893413i | \(0.351696\pi\) | |||||||
\(42\) | −2.80194 | −0.432348 | ||||||||
\(43\) | −3.75302 | −0.572330 | −0.286165 | − | 0.958180i | \(-0.592381\pi\) | ||||
−0.286165 | + | 0.958180i | \(0.592381\pi\) | |||||||
\(44\) | −0.445042 | −0.0670926 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −0.246980 | −0.0364152 | ||||||||
\(47\) | −1.97285 | −0.287770 | −0.143885 | − | 0.989594i | \(-0.545960\pi\) | ||||
−0.143885 | + | 0.989594i | \(0.545960\pi\) | |||||||
\(48\) | 2.91185 | 0.420290 | ||||||||
\(49\) | −1.95108 | −0.278726 | ||||||||
\(50\) | −1.24698 | −0.176350 | ||||||||
\(51\) | 6.49396 | 0.909336 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0586 | 1.65638 | 0.828188 | − | 0.560450i | \(-0.189372\pi\) | ||||
0.828188 | + | 0.560450i | \(0.189372\pi\) | |||||||
\(54\) | 1.24698 | 0.169692 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −6.85086 | −0.915484 | ||||||||
\(57\) | −2.33513 | −0.309295 | ||||||||
\(58\) | −4.77479 | −0.626961 | ||||||||
\(59\) | 9.83877 | 1.28090 | 0.640450 | − | 0.768000i | \(-0.278748\pi\) | ||||
0.640450 | + | 0.768000i | \(0.278748\pi\) | |||||||
\(60\) | −0.445042 | −0.0574547 | ||||||||
\(61\) | −13.6136 | −1.74304 | −0.871519 | − | 0.490361i | \(-0.836865\pi\) | ||||
−0.871519 | + | 0.490361i | \(0.836865\pi\) | |||||||
\(62\) | −2.13706 | −0.271407 | ||||||||
\(63\) | −2.24698 | −0.283093 | ||||||||
\(64\) | 8.89977 | 1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.24698 | 0.153493 | ||||||||
\(67\) | 7.91185 | 0.966587 | 0.483293 | − | 0.875458i | \(-0.339440\pi\) | ||||
0.483293 | + | 0.875458i | \(0.339440\pi\) | |||||||
\(68\) | 2.89008 | 0.350474 | ||||||||
\(69\) | −0.198062 | −0.0238439 | ||||||||
\(70\) | −2.80194 | −0.334896 | ||||||||
\(71\) | 7.14675 | 0.848163 | 0.424082 | − | 0.905624i | \(-0.360597\pi\) | ||||
0.424082 | + | 0.905624i | \(0.360597\pi\) | |||||||
\(72\) | 3.04892 | 0.359318 | ||||||||
\(73\) | 14.3545 | 1.68007 | 0.840034 | − | 0.542534i | \(-0.182535\pi\) | ||||
0.840034 | + | 0.542534i | \(0.182535\pi\) | |||||||
\(74\) | −5.66487 | −0.658528 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.03923 | −0.119208 | ||||||||
\(77\) | −2.24698 | −0.256067 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6189 | 1.19472 | 0.597362 | − | 0.801972i | \(-0.296216\pi\) | ||||
0.597362 | + | 0.801972i | \(0.296216\pi\) | |||||||
\(80\) | 2.91185 | 0.325555 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.17390 | −0.792225 | ||||||||
\(83\) | −12.7192 | −1.39611 | −0.698055 | − | 0.716044i | \(-0.745951\pi\) | ||||
−0.698055 | + | 0.716044i | \(0.745951\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 6.49396 | 0.704369 | ||||||||
\(86\) | 4.67994 | 0.504651 | ||||||||
\(87\) | −3.82908 | −0.410521 | ||||||||
\(88\) | 3.04892 | 0.325016 | ||||||||
\(89\) | −6.87263 | −0.728497 | −0.364248 | − | 0.931302i | \(-0.618674\pi\) | ||||
−0.364248 | + | 0.931302i | \(0.618674\pi\) | |||||||
\(90\) | 1.24698 | 0.131443 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0881460 | −0.00918986 | ||||||||
\(93\) | −1.71379 | −0.177712 | ||||||||
\(94\) | 2.46011 | 0.253741 | ||||||||
\(95\) | −2.33513 | −0.239579 | ||||||||
\(96\) | 2.46681 | 0.251768 | ||||||||
\(97\) | −11.1414 | −1.13124 | −0.565618 | − | 0.824668i | \(-0.691362\pi\) | ||||
−0.565618 | + | 0.824668i | \(0.691362\pi\) | |||||||
\(98\) | 2.43296 | 0.245766 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.445042 | −0.0445042 | ||||||||
\(101\) | −8.19136 | −0.815071 | −0.407535 | − | 0.913189i | \(-0.633612\pi\) | ||||
−0.407535 | + | 0.913189i | \(0.633612\pi\) | |||||||
\(102\) | −8.09783 | −0.801805 | ||||||||
\(103\) | −9.52111 | −0.938142 | −0.469071 | − | 0.883160i | \(-0.655411\pi\) | ||||
−0.469071 | + | 0.883160i | \(0.655411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.24698 | −0.219283 | ||||||||
\(106\) | −15.0368 | −1.46051 | ||||||||
\(107\) | −14.1836 | −1.37118 | −0.685590 | − | 0.727988i | \(-0.740456\pi\) | ||||
−0.685590 | + | 0.727988i | \(0.740456\pi\) | |||||||
\(108\) | 0.445042 | 0.0428242 | ||||||||
\(109\) | −10.1957 | −0.976568 | −0.488284 | − | 0.872685i | \(-0.662377\pi\) | ||||
−0.488284 | + | 0.872685i | \(0.662377\pi\) | |||||||
\(110\) | 1.24698 | 0.118895 | ||||||||
\(111\) | −4.54288 | −0.431191 | ||||||||
\(112\) | 6.54288 | 0.618244 | ||||||||
\(113\) | 6.88769 | 0.647939 | 0.323970 | − | 0.946067i | \(-0.394982\pi\) | ||||
0.323970 | + | 0.946067i | \(0.394982\pi\) | |||||||
\(114\) | 2.91185 | 0.272720 | ||||||||
\(115\) | −0.198062 | −0.0184694 | ||||||||
\(116\) | −1.70410 | −0.158222 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.2687 | −1.12943 | ||||||||
\(119\) | 14.5918 | 1.33763 | ||||||||
\(120\) | 3.04892 | 0.278327 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 16.9758 | 1.53692 | ||||||||
\(123\) | −5.75302 | −0.518732 | ||||||||
\(124\) | −0.762709 | −0.0684933 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.80194 | 0.249616 | ||||||||
\(127\) | −18.4547 | −1.63759 | −0.818796 | − | 0.574084i | \(-0.805358\pi\) | ||||
−0.818796 | + | 0.574084i | \(0.805358\pi\) | |||||||
\(128\) | −6.16421 | −0.544844 | ||||||||
\(129\) | 3.75302 | 0.330435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.11960 | 0.709413 | 0.354707 | − | 0.934978i | \(-0.384581\pi\) | ||||
0.354707 | + | 0.934978i | \(0.384581\pi\) | |||||||
\(132\) | 0.445042 | 0.0387359 | ||||||||
\(133\) | −5.24698 | −0.454971 | ||||||||
\(134\) | −9.86592 | −0.852286 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −19.7995 | −1.69780 | ||||||||
\(137\) | 21.7778 | 1.86060 | 0.930300 | − | 0.366798i | \(-0.119546\pi\) | ||||
0.930300 | + | 0.366798i | \(0.119546\pi\) | |||||||
\(138\) | 0.246980 | 0.0210243 | ||||||||
\(139\) | −19.4058 | −1.64598 | −0.822990 | − | 0.568056i | \(-0.807696\pi\) | ||||
−0.822990 | + | 0.568056i | \(0.807696\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 1.97285 | 0.166144 | ||||||||
\(142\) | −8.91185 | −0.747866 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | −3.82908 | −0.317988 | ||||||||
\(146\) | −17.8998 | −1.48140 | ||||||||
\(147\) | 1.95108 | 0.160923 | ||||||||
\(148\) | −2.02177 | −0.166188 | ||||||||
\(149\) | 11.4668 | 0.939398 | 0.469699 | − | 0.882827i | \(-0.344362\pi\) | ||||
0.469699 | + | 0.882827i | \(0.344362\pi\) | |||||||
\(150\) | 1.24698 | 0.101815 | ||||||||
\(151\) | 6.17092 | 0.502182 | 0.251091 | − | 0.967963i | \(-0.419211\pi\) | ||||
0.251091 | + | 0.967963i | \(0.419211\pi\) | |||||||
\(152\) | 7.11960 | 0.577476 | ||||||||
\(153\) | −6.49396 | −0.525005 | ||||||||
\(154\) | 2.80194 | 0.225787 | ||||||||
\(155\) | −1.71379 | −0.137655 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3080 | −1.22171 | −0.610855 | − | 0.791743i | \(-0.709174\pi\) | ||||
−0.610855 | + | 0.791743i | \(0.709174\pi\) | |||||||
\(158\) | −13.2416 | −1.05345 | ||||||||
\(159\) | −12.0586 | −0.956310 | ||||||||
\(160\) | 2.46681 | 0.195019 | ||||||||
\(161\) | −0.445042 | −0.0350742 | ||||||||
\(162\) | −1.24698 | −0.0979720 | ||||||||
\(163\) | −19.5918 | −1.53455 | −0.767274 | − | 0.641320i | \(-0.778387\pi\) | ||||
−0.767274 | + | 0.641320i | \(0.778387\pi\) | |||||||
\(164\) | −2.56033 | −0.199929 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 15.8605 | 1.23102 | ||||||||
\(167\) | 9.05429 | 0.700642 | 0.350321 | − | 0.936630i | \(-0.386072\pi\) | ||||
0.350321 | + | 0.936630i | \(0.386072\pi\) | |||||||
\(168\) | 6.85086 | 0.528555 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.09783 | −0.621076 | ||||||||
\(171\) | 2.33513 | 0.178572 | ||||||||
\(172\) | 1.67025 | 0.127355 | ||||||||
\(173\) | −13.4547 | −1.02294 | −0.511472 | − | 0.859300i | \(-0.670900\pi\) | ||||
−0.511472 | + | 0.859300i | \(0.670900\pi\) | |||||||
\(174\) | 4.77479 | 0.361976 | ||||||||
\(175\) | −2.24698 | −0.169856 | ||||||||
\(176\) | −2.91185 | −0.219489 | ||||||||
\(177\) | −9.83877 | −0.739528 | ||||||||
\(178\) | 8.57002 | 0.642350 | ||||||||
\(179\) | 21.3980 | 1.59936 | 0.799682 | − | 0.600423i | \(-0.205001\pi\) | ||||
0.799682 | + | 0.600423i | \(0.205001\pi\) | |||||||
\(180\) | 0.445042 | 0.0331715 | ||||||||
\(181\) | −14.1032 | −1.04828 | −0.524142 | − | 0.851631i | \(-0.675614\pi\) | ||||
−0.524142 | + | 0.851631i | \(0.675614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6136 | 1.00634 | ||||||||
\(184\) | 0.603875 | 0.0445183 | ||||||||
\(185\) | −4.54288 | −0.333999 | ||||||||
\(186\) | 2.13706 | 0.156697 | ||||||||
\(187\) | −6.49396 | −0.474885 | ||||||||
\(188\) | 0.878002 | 0.0640349 | ||||||||
\(189\) | 2.24698 | 0.163444 | ||||||||
\(190\) | 2.91185 | 0.211248 | ||||||||
\(191\) | 7.19136 | 0.520348 | 0.260174 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260174 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(192\) | −8.89977 | −0.642286 | ||||||||
\(193\) | −11.3013 | −0.813483 | −0.406742 | − | 0.913543i | \(-0.633335\pi\) | ||||
−0.406742 | + | 0.913543i | \(0.633335\pi\) | |||||||
\(194\) | 13.8931 | 0.997464 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.868313 | 0.0620224 | ||||||||
\(197\) | −20.5066 | −1.46104 | −0.730519 | − | 0.682893i | \(-0.760722\pi\) | ||||
−0.730519 | + | 0.682893i | \(0.760722\pi\) | |||||||
\(198\) | −1.24698 | −0.0886190 | ||||||||
\(199\) | 19.9681 | 1.41550 | 0.707749 | − | 0.706464i | \(-0.249711\pi\) | ||||
0.707749 | + | 0.706464i | \(0.249711\pi\) | |||||||
\(200\) | 3.04892 | 0.215591 | ||||||||
\(201\) | −7.91185 | −0.558059 | ||||||||
\(202\) | 10.2145 | 0.718687 | ||||||||
\(203\) | −8.60388 | −0.603874 | ||||||||
\(204\) | −2.89008 | −0.202346 | ||||||||
\(205\) | −5.75302 | −0.401808 | ||||||||
\(206\) | 11.8726 | 0.827205 | ||||||||
\(207\) | 0.198062 | 0.0137663 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.33513 | 0.161524 | ||||||||
\(210\) | 2.80194 | 0.193352 | ||||||||
\(211\) | −9.74632 | −0.670964 | −0.335482 | − | 0.942047i | \(-0.608899\pi\) | ||||
−0.335482 | + | 0.942047i | \(0.608899\pi\) | |||||||
\(212\) | −5.36658 | −0.368579 | ||||||||
\(213\) | −7.14675 | −0.489687 | ||||||||
\(214\) | 17.6866 | 1.20903 | ||||||||
\(215\) | 3.75302 | 0.255954 | ||||||||
\(216\) | −3.04892 | −0.207453 | ||||||||
\(217\) | −3.85086 | −0.261413 | ||||||||
\(218\) | 12.7138 | 0.861087 | ||||||||
\(219\) | −14.3545 | −0.969987 | ||||||||
\(220\) | 0.445042 | 0.0300047 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.66487 | 0.380201 | ||||||||
\(223\) | −24.5351 | −1.64299 | −0.821496 | − | 0.570214i | \(-0.806860\pi\) | ||||
−0.821496 | + | 0.570214i | \(0.806860\pi\) | |||||||
\(224\) | 5.54288 | 0.370349 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −8.58881 | −0.571319 | ||||||||
\(227\) | 0.0217703 | 0.00144494 | 0.000722472 | − | 1.00000i | \(-0.499770\pi\) | ||||
0.000722472 | 1.00000i | \(0.499770\pi\) | ||||||||
\(228\) | 1.03923 | 0.0688246 | ||||||||
\(229\) | 7.36898 | 0.486956 | 0.243478 | − | 0.969906i | \(-0.421712\pi\) | ||||
0.243478 | + | 0.969906i | \(0.421712\pi\) | |||||||
\(230\) | 0.246980 | 0.0162854 | ||||||||
\(231\) | 2.24698 | 0.147840 | ||||||||
\(232\) | 11.6746 | 0.766473 | ||||||||
\(233\) | −8.10992 | −0.531298 | −0.265649 | − | 0.964070i | \(-0.585586\pi\) | ||||
−0.265649 | + | 0.964070i | \(0.585586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.97285 | 0.128695 | ||||||||
\(236\) | −4.37867 | −0.285027 | ||||||||
\(237\) | −10.6189 | −0.689774 | ||||||||
\(238\) | −18.1957 | −1.17945 | ||||||||
\(239\) | −6.38165 | −0.412795 | −0.206397 | − | 0.978468i | \(-0.566174\pi\) | ||||
−0.206397 | + | 0.978468i | \(0.566174\pi\) | |||||||
\(240\) | −2.91185 | −0.187959 | ||||||||
\(241\) | −1.30127 | −0.0838224 | −0.0419112 | − | 0.999121i | \(-0.513345\pi\) | ||||
−0.0419112 | + | 0.999121i | \(0.513345\pi\) | |||||||
\(242\) | 12.4698 | 0.801589 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.05861 | 0.387863 | ||||||||
\(245\) | 1.95108 | 0.124650 | ||||||||
\(246\) | 7.17390 | 0.457391 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.22521 | 0.331801 | ||||||||
\(249\) | 12.7192 | 0.806045 | ||||||||
\(250\) | 1.24698 | 0.0788659 | ||||||||
\(251\) | 9.51142 | 0.600355 | 0.300178 | − | 0.953883i | \(-0.402954\pi\) | ||||
0.300178 | + | 0.953883i | \(0.402954\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 0.198062 | 0.0124521 | ||||||||
\(254\) | 23.0127 | 1.44394 | ||||||||
\(255\) | −6.49396 | −0.406668 | ||||||||
\(256\) | −10.1129 | −0.632056 | ||||||||
\(257\) | 7.38942 | 0.460939 | 0.230470 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230470 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(258\) | −4.67994 | −0.291360 | ||||||||
\(259\) | −10.2078 | −0.634279 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.82908 | 0.237014 | ||||||||
\(262\) | −10.1250 | −0.625523 | ||||||||
\(263\) | −3.06398 | −0.188933 | −0.0944666 | − | 0.995528i | \(-0.530115\pi\) | ||||
−0.0944666 | + | 0.995528i | \(0.530115\pi\) | |||||||
\(264\) | −3.04892 | −0.187648 | ||||||||
\(265\) | −12.0586 | −0.740754 | ||||||||
\(266\) | 6.54288 | 0.401170 | ||||||||
\(267\) | 6.87263 | 0.420598 | ||||||||
\(268\) | −3.52111 | −0.215086 | ||||||||
\(269\) | −18.2687 | −1.11387 | −0.556933 | − | 0.830558i | \(-0.688022\pi\) | ||||
−0.556933 | + | 0.830558i | \(0.688022\pi\) | |||||||
\(270\) | −1.24698 | −0.0758888 | ||||||||
\(271\) | −4.04892 | −0.245954 | −0.122977 | − | 0.992410i | \(-0.539244\pi\) | ||||
−0.122977 | + | 0.992410i | \(0.539244\pi\) | |||||||
\(272\) | 18.9095 | 1.14655 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.1564 | −1.64058 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.0881460 | 0.00530577 | ||||||||
\(277\) | 28.1608 | 1.69202 | 0.846008 | − | 0.533170i | \(-0.179000\pi\) | ||||
0.846008 | + | 0.533170i | \(0.179000\pi\) | |||||||
\(278\) | 24.1987 | 1.45134 | ||||||||
\(279\) | 1.71379 | 0.102602 | ||||||||
\(280\) | 6.85086 | 0.409417 | ||||||||
\(281\) | −24.3937 | −1.45521 | −0.727604 | − | 0.685997i | \(-0.759366\pi\) | ||||
−0.727604 | + | 0.685997i | \(0.759366\pi\) | |||||||
\(282\) | −2.46011 | −0.146497 | ||||||||
\(283\) | −7.16315 | −0.425805 | −0.212902 | − | 0.977073i | \(-0.568292\pi\) | ||||
−0.212902 | + | 0.977073i | \(0.568292\pi\) | |||||||
\(284\) | −3.18060 | −0.188734 | ||||||||
\(285\) | 2.33513 | 0.138321 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.9269 | −0.763052 | ||||||||
\(288\) | −2.46681 | −0.145358 | ||||||||
\(289\) | 25.1715 | 1.48068 | ||||||||
\(290\) | 4.77479 | 0.280385 | ||||||||
\(291\) | 11.1414 | 0.653119 | ||||||||
\(292\) | −6.38835 | −0.373850 | ||||||||
\(293\) | −5.01075 | −0.292731 | −0.146366 | − | 0.989231i | \(-0.546758\pi\) | ||||
−0.146366 | + | 0.989231i | \(0.546758\pi\) | |||||||
\(294\) | −2.43296 | −0.141893 | ||||||||
\(295\) | −9.83877 | −0.572836 | ||||||||
\(296\) | 13.8509 | 0.805065 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −14.2989 | −0.828312 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.445042 | 0.0256945 | ||||||||
\(301\) | 8.43296 | 0.486068 | ||||||||
\(302\) | −7.69501 | −0.442798 | ||||||||
\(303\) | 8.19136 | 0.470581 | ||||||||
\(304\) | −6.79954 | −0.389981 | ||||||||
\(305\) | 13.6136 | 0.779510 | ||||||||
\(306\) | 8.09783 | 0.462922 | ||||||||
\(307\) | −29.8213 | −1.70199 | −0.850996 | − | 0.525172i | \(-0.824001\pi\) | ||||
−0.850996 | + | 0.525172i | \(0.824001\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 9.52111 | 0.541637 | ||||||||
\(310\) | 2.13706 | 0.121377 | ||||||||
\(311\) | −6.22952 | −0.353244 | −0.176622 | − | 0.984279i | \(-0.556517\pi\) | ||||
−0.176622 | + | 0.984279i | \(0.556517\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.22713 | 0.465025 | 0.232512 | − | 0.972593i | \(-0.425305\pi\) | ||||
0.232512 | + | 0.972593i | \(0.425305\pi\) | |||||||
\(314\) | 19.0887 | 1.07724 | ||||||||
\(315\) | 2.24698 | 0.126603 | ||||||||
\(316\) | −4.72587 | −0.265851 | ||||||||
\(317\) | −20.2010 | −1.13460 | −0.567302 | − | 0.823510i | \(-0.692013\pi\) | ||||
−0.567302 | + | 0.823510i | \(0.692013\pi\) | |||||||
\(318\) | 15.0368 | 0.843224 | ||||||||
\(319\) | 3.82908 | 0.214388 | ||||||||
\(320\) | −8.89977 | −0.497512 | ||||||||
\(321\) | 14.1836 | 0.791651 | ||||||||
\(322\) | 0.554958 | 0.0309266 | ||||||||
\(323\) | −15.1642 | −0.843759 | ||||||||
\(324\) | −0.445042 | −0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.4306 | 1.35308 | ||||||||
\(327\) | 10.1957 | 0.563822 | ||||||||
\(328\) | 17.5405 | 0.968511 | ||||||||
\(329\) | 4.43296 | 0.244397 | ||||||||
\(330\) | −1.24698 | −0.0686440 | ||||||||
\(331\) | −11.2771 | −0.619846 | −0.309923 | − | 0.950762i | \(-0.600303\pi\) | ||||
−0.309923 | + | 0.950762i | \(0.600303\pi\) | |||||||
\(332\) | 5.66056 | 0.310664 | ||||||||
\(333\) | 4.54288 | 0.248948 | ||||||||
\(334\) | −11.2905 | −0.617790 | ||||||||
\(335\) | −7.91185 | −0.432271 | ||||||||
\(336\) | −6.54288 | −0.356943 | ||||||||
\(337\) | −21.1075 | −1.14980 | −0.574900 | − | 0.818224i | \(-0.694959\pi\) | ||||
−0.574900 | + | 0.818224i | \(0.694959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.88769 | −0.374088 | ||||||||
\(340\) | −2.89008 | −0.156737 | ||||||||
\(341\) | 1.71379 | 0.0928070 | ||||||||
\(342\) | −2.91185 | −0.157455 | ||||||||
\(343\) | 20.1129 | 1.08599 | ||||||||
\(344\) | −11.4426 | −0.616946 | ||||||||
\(345\) | 0.198062 | 0.0106633 | ||||||||
\(346\) | 16.7778 | 0.901979 | ||||||||
\(347\) | 21.3744 | 1.14744 | 0.573718 | − | 0.819053i | \(-0.305501\pi\) | ||||
0.573718 | + | 0.819053i | \(0.305501\pi\) | |||||||
\(348\) | 1.70410 | 0.0913495 | ||||||||
\(349\) | −4.31527 | −0.230991 | −0.115496 | − | 0.993308i | \(-0.536846\pi\) | ||||
−0.115496 | + | 0.993308i | \(0.536846\pi\) | |||||||
\(350\) | 2.80194 | 0.149770 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.46681 | −0.131482 | ||||||||
\(353\) | −10.2198 | −0.543947 | −0.271973 | − | 0.962305i | \(-0.587676\pi\) | ||||
−0.271973 | + | 0.962305i | \(0.587676\pi\) | |||||||
\(354\) | 12.2687 | 0.652077 | ||||||||
\(355\) | −7.14675 | −0.379310 | ||||||||
\(356\) | 3.05861 | 0.162106 | ||||||||
\(357\) | −14.5918 | −0.772280 | ||||||||
\(358\) | −26.6829 | −1.41024 | ||||||||
\(359\) | −8.71678 | −0.460054 | −0.230027 | − | 0.973184i | \(-0.573881\pi\) | ||||
−0.230027 | + | 0.973184i | \(0.573881\pi\) | |||||||
\(360\) | −3.04892 | −0.160692 | ||||||||
\(361\) | −13.5472 | −0.713010 | ||||||||
\(362\) | 17.5864 | 0.924322 | ||||||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.3545 | −0.751349 | ||||||||
\(366\) | −16.9758 | −0.887341 | ||||||||
\(367\) | −5.37973 | −0.280820 | −0.140410 | − | 0.990093i | \(-0.544842\pi\) | ||||
−0.140410 | + | 0.990093i | \(0.544842\pi\) | |||||||
\(368\) | −0.576728 | −0.0300640 | ||||||||
\(369\) | 5.75302 | 0.299490 | ||||||||
\(370\) | 5.66487 | 0.294503 | ||||||||
\(371\) | −27.0954 | −1.40673 | ||||||||
\(372\) | 0.762709 | 0.0395446 | ||||||||
\(373\) | −12.6843 | −0.656766 | −0.328383 | − | 0.944545i | \(-0.606504\pi\) | ||||
−0.328383 | + | 0.944545i | \(0.606504\pi\) | |||||||
\(374\) | 8.09783 | 0.418729 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −6.01507 | −0.310203 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.80194 | −0.144116 | ||||||||
\(379\) | 7.99223 | 0.410533 | 0.205267 | − | 0.978706i | \(-0.434194\pi\) | ||||
0.205267 | + | 0.978706i | \(0.434194\pi\) | |||||||
\(380\) | 1.03923 | 0.0533113 | ||||||||
\(381\) | 18.4547 | 0.945464 | ||||||||
\(382\) | −8.96748 | −0.458816 | ||||||||
\(383\) | −0.763774 | −0.0390270 | −0.0195135 | − | 0.999810i | \(-0.506212\pi\) | ||||
−0.0195135 | + | 0.999810i | \(0.506212\pi\) | |||||||
\(384\) | 6.16421 | 0.314566 | ||||||||
\(385\) | 2.24698 | 0.114517 | ||||||||
\(386\) | 14.0925 | 0.717287 | ||||||||
\(387\) | −3.75302 | −0.190777 | ||||||||
\(388\) | 4.95838 | 0.251724 | ||||||||
\(389\) | −28.8799 | −1.46427 | −0.732135 | − | 0.681159i | \(-0.761476\pi\) | ||||
−0.732135 | + | 0.681159i | \(0.761476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.28621 | −0.0650463 | ||||||||
\(392\) | −5.94869 | −0.300454 | ||||||||
\(393\) | −8.11960 | −0.409580 | ||||||||
\(394\) | 25.5714 | 1.28827 | ||||||||
\(395\) | −10.6189 | −0.534297 | ||||||||
\(396\) | −0.445042 | −0.0223642 | ||||||||
\(397\) | −33.1347 | −1.66298 | −0.831491 | − | 0.555539i | \(-0.812512\pi\) | ||||
−0.831491 | + | 0.555539i | \(0.812512\pi\) | |||||||
\(398\) | −24.8998 | −1.24811 | ||||||||
\(399\) | 5.24698 | 0.262678 | ||||||||
\(400\) | −2.91185 | −0.145593 | ||||||||
\(401\) | −11.0435 | −0.551488 | −0.275744 | − | 0.961231i | \(-0.588924\pi\) | ||||
−0.275744 | + | 0.961231i | \(0.588924\pi\) | |||||||
\(402\) | 9.86592 | 0.492067 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.64550 | 0.181370 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 10.7289 | 0.532464 | ||||||||
\(407\) | 4.54288 | 0.225182 | ||||||||
\(408\) | 19.7995 | 0.980224 | ||||||||
\(409\) | 33.3424 | 1.64868 | 0.824338 | − | 0.566097i | \(-0.191547\pi\) | ||||
0.824338 | + | 0.566097i | \(0.191547\pi\) | |||||||
\(410\) | 7.17390 | 0.354294 | ||||||||
\(411\) | −21.7778 | −1.07422 | ||||||||
\(412\) | 4.23729 | 0.208756 | ||||||||
\(413\) | −22.1075 | −1.08784 | ||||||||
\(414\) | −0.246980 | −0.0121384 | ||||||||
\(415\) | 12.7192 | 0.624359 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.4058 | 0.950307 | ||||||||
\(418\) | −2.91185 | −0.142423 | ||||||||
\(419\) | 39.9071 | 1.94959 | 0.974794 | − | 0.223107i | \(-0.0716200\pi\) | ||||
0.974794 | + | 0.223107i | \(0.0716200\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | 9.41657 | 0.458935 | 0.229468 | − | 0.973316i | \(-0.426301\pi\) | ||||
0.229468 | + | 0.973316i | \(0.426301\pi\) | |||||||
\(422\) | 12.1535 | 0.591621 | ||||||||
\(423\) | −1.97285 | −0.0959234 | ||||||||
\(424\) | 36.7657 | 1.78550 | ||||||||
\(425\) | −6.49396 | −0.315003 | ||||||||
\(426\) | 8.91185 | 0.431781 | ||||||||
\(427\) | 30.5894 | 1.48032 | ||||||||
\(428\) | 6.31229 | 0.305116 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.67994 | −0.225687 | ||||||||
\(431\) | 25.9976 | 1.25226 | 0.626130 | − | 0.779718i | \(-0.284638\pi\) | ||||
0.626130 | + | 0.779718i | \(0.284638\pi\) | |||||||
\(432\) | 2.91185 | 0.140097 | ||||||||
\(433\) | 6.93661 | 0.333352 | 0.166676 | − | 0.986012i | \(-0.446697\pi\) | ||||
0.166676 | + | 0.986012i | \(0.446697\pi\) | |||||||
\(434\) | 4.80194 | 0.230500 | ||||||||
\(435\) | 3.82908 | 0.183591 | ||||||||
\(436\) | 4.53750 | 0.217307 | ||||||||
\(437\) | 0.462500 | 0.0221244 | ||||||||
\(438\) | 17.8998 | 0.855284 | ||||||||
\(439\) | 18.6775 | 0.891431 | 0.445715 | − | 0.895175i | \(-0.352949\pi\) | ||||
0.445715 | + | 0.895175i | \(0.352949\pi\) | |||||||
\(440\) | −3.04892 | −0.145351 | ||||||||
\(441\) | −1.95108 | −0.0929087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9245 | 1.75434 | 0.877169 | − | 0.480183i | \(-0.159430\pi\) | ||||
0.877169 | + | 0.480183i | \(0.159430\pi\) | |||||||
\(444\) | 2.02177 | 0.0959490 | ||||||||
\(445\) | 6.87263 | 0.325794 | ||||||||
\(446\) | 30.5948 | 1.44870 | ||||||||
\(447\) | −11.4668 | −0.542362 | ||||||||
\(448\) | −19.9976 | −0.944798 | ||||||||
\(449\) | −15.3884 | −0.726221 | −0.363111 | − | 0.931746i | \(-0.618285\pi\) | ||||
−0.363111 | + | 0.931746i | \(0.618285\pi\) | |||||||
\(450\) | −1.24698 | −0.0587832 | ||||||||
\(451\) | 5.75302 | 0.270899 | ||||||||
\(452\) | −3.06531 | −0.144180 | ||||||||
\(453\) | −6.17092 | −0.289935 | ||||||||
\(454\) | −0.0271471 | −0.00127408 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.11960 | −0.333406 | ||||||||
\(457\) | −25.2946 | −1.18323 | −0.591615 | − | 0.806221i | \(-0.701509\pi\) | ||||
−0.591615 | + | 0.806221i | \(0.701509\pi\) | |||||||
\(458\) | −9.18896 | −0.429372 | ||||||||
\(459\) | 6.49396 | 0.303112 | ||||||||
\(460\) | 0.0881460 | 0.00410983 | ||||||||
\(461\) | −8.68664 | −0.404577 | −0.202289 | − | 0.979326i | \(-0.564838\pi\) | ||||
−0.202289 | + | 0.979326i | \(0.564838\pi\) | |||||||
\(462\) | −2.80194 | −0.130358 | ||||||||
\(463\) | 1.73663 | 0.0807079 | 0.0403539 | − | 0.999185i | \(-0.487151\pi\) | ||||
0.0403539 | + | 0.999185i | \(0.487151\pi\) | |||||||
\(464\) | −11.1497 | −0.517613 | ||||||||
\(465\) | 1.71379 | 0.0794752 | ||||||||
\(466\) | 10.1129 | 0.468471 | ||||||||
\(467\) | 22.3177 | 1.03274 | 0.516369 | − | 0.856366i | \(-0.327283\pi\) | ||||
0.516369 | + | 0.856366i | \(0.327283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.7778 | −0.820901 | ||||||||
\(470\) | −2.46011 | −0.113476 | ||||||||
\(471\) | 15.3080 | 0.705354 | ||||||||
\(472\) | 29.9976 | 1.38075 | ||||||||
\(473\) | −3.75302 | −0.172564 | ||||||||
\(474\) | 13.2416 | 0.608207 | ||||||||
\(475\) | 2.33513 | 0.107143 | ||||||||
\(476\) | −6.49396 | −0.297650 | ||||||||
\(477\) | 12.0586 | 0.552126 | ||||||||
\(478\) | 7.95779 | 0.363981 | ||||||||
\(479\) | −26.6765 | −1.21888 | −0.609440 | − | 0.792832i | \(-0.708606\pi\) | ||||
−0.609440 | + | 0.792832i | \(0.708606\pi\) | |||||||
\(480\) | −2.46681 | −0.112594 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.62266 | 0.0739102 | ||||||||
\(483\) | 0.445042 | 0.0202501 | ||||||||
\(484\) | 4.45042 | 0.202292 | ||||||||
\(485\) | 11.1414 | 0.505904 | ||||||||
\(486\) | 1.24698 | 0.0565641 | ||||||||
\(487\) | 8.61655 | 0.390453 | 0.195227 | − | 0.980758i | \(-0.437456\pi\) | ||||
0.195227 | + | 0.980758i | \(0.437456\pi\) | |||||||
\(488\) | −41.5066 | −1.87892 | ||||||||
\(489\) | 19.5918 | 0.885972 | ||||||||
\(490\) | −2.43296 | −0.109910 | ||||||||
\(491\) | −0.992230 | −0.0447787 | −0.0223894 | − | 0.999749i | \(-0.507127\pi\) | ||||
−0.0223894 | + | 0.999749i | \(0.507127\pi\) | |||||||
\(492\) | 2.56033 | 0.115429 | ||||||||
\(493\) | −24.8659 | −1.11990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −4.99031 | −0.224072 | ||||||||
\(497\) | −16.0586 | −0.720327 | ||||||||
\(498\) | −15.8605 | −0.710728 | ||||||||
\(499\) | 16.7138 | 0.748212 | 0.374106 | − | 0.927386i | \(-0.377950\pi\) | ||||
0.374106 | + | 0.927386i | \(0.377950\pi\) | |||||||
\(500\) | 0.445042 | 0.0199029 | ||||||||
\(501\) | −9.05429 | −0.404516 | ||||||||
\(502\) | −11.8605 | −0.529362 | ||||||||
\(503\) | 30.6547 | 1.36683 | 0.683413 | − | 0.730032i | \(-0.260495\pi\) | ||||
0.683413 | + | 0.730032i | \(0.260495\pi\) | |||||||
\(504\) | −6.85086 | −0.305161 | ||||||||
\(505\) | 8.19136 | 0.364511 | ||||||||
\(506\) | −0.246980 | −0.0109796 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.21313 | 0.364399 | ||||||||
\(509\) | 25.9506 | 1.15024 | 0.575120 | − | 0.818069i | \(-0.304955\pi\) | ||||
0.575120 | + | 0.818069i | \(0.304955\pi\) | |||||||
\(510\) | 8.09783 | 0.358578 | ||||||||
\(511\) | −32.2543 | −1.42685 | ||||||||
\(512\) | 24.9390 | 1.10216 | ||||||||
\(513\) | −2.33513 | −0.103098 | ||||||||
\(514\) | −9.21446 | −0.406432 | ||||||||
\(515\) | 9.52111 | 0.419550 | ||||||||
\(516\) | −1.67025 | −0.0735287 | ||||||||
\(517\) | −1.97285 | −0.0867660 | ||||||||
\(518\) | 12.7289 | 0.559274 | ||||||||
\(519\) | 13.4547 | 0.590597 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.3375 | −0.540516 | −0.270258 | − | 0.962788i | \(-0.587109\pi\) | ||||
−0.270258 | + | 0.962788i | \(0.587109\pi\) | |||||||
\(522\) | −4.77479 | −0.208987 | ||||||||
\(523\) | −20.7748 | −0.908418 | −0.454209 | − | 0.890895i | \(-0.650078\pi\) | ||||
−0.454209 | + | 0.890895i | \(0.650078\pi\) | |||||||
\(524\) | −3.61356 | −0.157859 | ||||||||
\(525\) | 2.24698 | 0.0980662 | ||||||||
\(526\) | 3.82072 | 0.166591 | ||||||||
\(527\) | −11.1293 | −0.484800 | ||||||||
\(528\) | 2.91185 | 0.126722 | ||||||||
\(529\) | −22.9608 | −0.998294 | ||||||||
\(530\) | 15.0368 | 0.653158 | ||||||||
\(531\) | 9.83877 | 0.426966 | ||||||||
\(532\) | 2.33513 | 0.101241 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.57002 | −0.370861 | ||||||||
\(535\) | 14.1836 | 0.613210 | ||||||||
\(536\) | 24.1226 | 1.04194 | ||||||||
\(537\) | −21.3980 | −0.923394 | ||||||||
\(538\) | 22.7808 | 0.982148 | ||||||||
\(539\) | −1.95108 | −0.0840391 | ||||||||
\(540\) | −0.445042 | −0.0191516 | ||||||||
\(541\) | 45.5797 | 1.95962 | 0.979812 | − | 0.199919i | \(-0.0640679\pi\) | ||||
0.979812 | + | 0.199919i | \(0.0640679\pi\) | |||||||
\(542\) | 5.04892 | 0.216870 | ||||||||
\(543\) | 14.1032 | 0.605227 | ||||||||
\(544\) | 16.0194 | 0.686825 | ||||||||
\(545\) | 10.1957 | 0.436734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.0194 | −0.599425 | −0.299713 | − | 0.954030i | \(-0.596891\pi\) | ||||
−0.299713 | + | 0.954030i | \(0.596891\pi\) | |||||||
\(548\) | −9.69202 | −0.414023 | ||||||||
\(549\) | −13.6136 | −0.581013 | ||||||||
\(550\) | −1.24698 | −0.0531714 | ||||||||
\(551\) | 8.94139 | 0.380916 | ||||||||
\(552\) | −0.603875 | −0.0257026 | ||||||||
\(553\) | −23.8605 | −1.01465 | ||||||||
\(554\) | −35.1159 | −1.49193 | ||||||||
\(555\) | 4.54288 | 0.192834 | ||||||||
\(556\) | 8.63640 | 0.366265 | ||||||||
\(557\) | −21.2591 | −0.900775 | −0.450388 | − | 0.892833i | \(-0.648714\pi\) | ||||
−0.450388 | + | 0.892833i | \(0.648714\pi\) | |||||||
\(558\) | −2.13706 | −0.0904691 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.54288 | −0.276487 | ||||||||
\(561\) | 6.49396 | 0.274175 | ||||||||
\(562\) | 30.4185 | 1.28313 | ||||||||
\(563\) | 13.5198 | 0.569791 | 0.284895 | − | 0.958559i | \(-0.408041\pi\) | ||||
0.284895 | + | 0.958559i | \(0.408041\pi\) | |||||||
\(564\) | −0.878002 | −0.0369706 | ||||||||
\(565\) | −6.88769 | −0.289767 | ||||||||
\(566\) | 8.93230 | 0.375452 | ||||||||
\(567\) | −2.24698 | −0.0943643 | ||||||||
\(568\) | 21.7899 | 0.914282 | ||||||||
\(569\) | −30.9202 | −1.29624 | −0.648121 | − | 0.761537i | \(-0.724445\pi\) | ||||
−0.648121 | + | 0.761537i | \(0.724445\pi\) | |||||||
\(570\) | −2.91185 | −0.121964 | ||||||||
\(571\) | 5.33645 | 0.223324 | 0.111662 | − | 0.993746i | \(-0.464383\pi\) | ||||
0.111662 | + | 0.993746i | \(0.464383\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.19136 | −0.300423 | ||||||||
\(574\) | 16.1196 | 0.672819 | ||||||||
\(575\) | 0.198062 | 0.00825977 | ||||||||
\(576\) | 8.89977 | 0.370824 | ||||||||
\(577\) | 17.3889 | 0.723911 | 0.361956 | − | 0.932195i | \(-0.382109\pi\) | ||||
0.361956 | + | 0.932195i | \(0.382109\pi\) | |||||||
\(578\) | −31.3884 | −1.30558 | ||||||||
\(579\) | 11.3013 | 0.469665 | ||||||||
\(580\) | 1.70410 | 0.0707590 | ||||||||
\(581\) | 28.5797 | 1.18569 | ||||||||
\(582\) | −13.8931 | −0.575886 | ||||||||
\(583\) | 12.0586 | 0.499416 | ||||||||
\(584\) | 43.7657 | 1.81104 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.24831 | 0.258115 | ||||||||
\(587\) | 21.4668 | 0.886030 | 0.443015 | − | 0.896514i | \(-0.353909\pi\) | ||||
0.443015 | + | 0.896514i | \(0.353909\pi\) | |||||||
\(588\) | −0.868313 | −0.0358086 | ||||||||
\(589\) | 4.00192 | 0.164896 | ||||||||
\(590\) | 12.2687 | 0.505096 | ||||||||
\(591\) | 20.5066 | 0.843530 | ||||||||
\(592\) | −13.2282 | −0.543675 | ||||||||
\(593\) | −4.27605 | −0.175596 | −0.0877981 | − | 0.996138i | \(-0.527983\pi\) | ||||
−0.0877981 | + | 0.996138i | \(0.527983\pi\) | |||||||
\(594\) | 1.24698 | 0.0511642 | ||||||||
\(595\) | −14.5918 | −0.598205 | ||||||||
\(596\) | −5.10321 | −0.209036 | ||||||||
\(597\) | −19.9681 | −0.817239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.2180 | −0.948663 | −0.474332 | − | 0.880346i | \(-0.657310\pi\) | ||||
−0.474332 | + | 0.880346i | \(0.657310\pi\) | |||||||
\(600\) | −3.04892 | −0.124472 | ||||||||
\(601\) | −32.2704 | −1.31634 | −0.658169 | − | 0.752871i | \(-0.728669\pi\) | ||||
−0.658169 | + | 0.752871i | \(0.728669\pi\) | |||||||
\(602\) | −10.5157 | −0.428589 | ||||||||
\(603\) | 7.91185 | 0.322196 | ||||||||
\(604\) | −2.74632 | −0.111746 | ||||||||
\(605\) | 10.0000 | 0.406558 | ||||||||
\(606\) | −10.2145 | −0.414934 | ||||||||
\(607\) | 13.8920 | 0.563859 | 0.281929 | − | 0.959435i | \(-0.409026\pi\) | ||||
0.281929 | + | 0.959435i | \(0.409026\pi\) | |||||||
\(608\) | −5.76032 | −0.233612 | ||||||||
\(609\) | 8.60388 | 0.348647 | ||||||||
\(610\) | −16.9758 | −0.687332 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.89008 | 0.116825 | ||||||||
\(613\) | 27.6668 | 1.11745 | 0.558726 | − | 0.829353i | \(-0.311290\pi\) | ||||
0.558726 | + | 0.829353i | \(0.311290\pi\) | |||||||
\(614\) | 37.1866 | 1.50073 | ||||||||
\(615\) | 5.75302 | 0.231984 | ||||||||
\(616\) | −6.85086 | −0.276029 | ||||||||
\(617\) | 10.3709 | 0.417517 | 0.208758 | − | 0.977967i | \(-0.433058\pi\) | ||||
0.208758 | + | 0.977967i | \(0.433058\pi\) | |||||||
\(618\) | −11.8726 | −0.477587 | ||||||||
\(619\) | −43.1473 | −1.73424 | −0.867119 | − | 0.498101i | \(-0.834031\pi\) | ||||
−0.867119 | + | 0.498101i | \(0.834031\pi\) | |||||||
\(620\) | 0.762709 | 0.0306311 | ||||||||
\(621\) | −0.198062 | −0.00794796 | ||||||||
\(622\) | 7.76809 | 0.311472 | ||||||||
\(623\) | 15.4426 | 0.618697 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.2591 | −0.410035 | ||||||||
\(627\) | −2.33513 | −0.0932559 | ||||||||
\(628\) | 6.81269 | 0.271856 | ||||||||
\(629\) | −29.5013 | −1.17629 | ||||||||
\(630\) | −2.80194 | −0.111632 | ||||||||
\(631\) | −22.6987 | −0.903622 | −0.451811 | − | 0.892114i | \(-0.649222\pi\) | ||||
−0.451811 | + | 0.892114i | \(0.649222\pi\) | |||||||
\(632\) | 32.3763 | 1.28786 | ||||||||
\(633\) | 9.74632 | 0.387381 | ||||||||
\(634\) | 25.1903 | 1.00043 | ||||||||
\(635\) | 18.4547 | 0.732354 | ||||||||
\(636\) | 5.36658 | 0.212799 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.77479 | −0.189036 | ||||||||
\(639\) | 7.14675 | 0.282721 | ||||||||
\(640\) | 6.16421 | 0.243662 | ||||||||
\(641\) | −16.1075 | −0.636209 | −0.318104 | − | 0.948056i | \(-0.603046\pi\) | ||||
−0.318104 | + | 0.948056i | \(0.603046\pi\) | |||||||
\(642\) | −17.6866 | −0.698036 | ||||||||
\(643\) | 32.8732 | 1.29639 | 0.648197 | − | 0.761473i | \(-0.275524\pi\) | ||||
0.648197 | + | 0.761473i | \(0.275524\pi\) | |||||||
\(644\) | 0.198062 | 0.00780475 | ||||||||
\(645\) | −3.75302 | −0.147775 | ||||||||
\(646\) | 18.9095 | 0.743983 | ||||||||
\(647\) | −10.2814 | −0.404204 | −0.202102 | − | 0.979364i | \(-0.564777\pi\) | ||||
−0.202102 | + | 0.979364i | \(0.564777\pi\) | |||||||
\(648\) | 3.04892 | 0.119773 | ||||||||
\(649\) | 9.83877 | 0.386206 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.85086 | 0.150927 | ||||||||
\(652\) | 8.71917 | 0.341469 | ||||||||
\(653\) | 14.3575 | 0.561852 | 0.280926 | − | 0.959729i | \(-0.409358\pi\) | ||||
0.280926 | + | 0.959729i | \(0.409358\pi\) | |||||||
\(654\) | −12.7138 | −0.497149 | ||||||||
\(655\) | −8.11960 | −0.317259 | ||||||||
\(656\) | −16.7520 | −0.654054 | ||||||||
\(657\) | 14.3545 | 0.560022 | ||||||||
\(658\) | −5.52781 | −0.215497 | ||||||||
\(659\) | −16.0258 | −0.624277 | −0.312139 | − | 0.950037i | \(-0.601045\pi\) | ||||
−0.312139 | + | 0.950037i | \(0.601045\pi\) | |||||||
\(660\) | −0.445042 | −0.0173232 | ||||||||
\(661\) | 27.4282 | 1.06683 | 0.533416 | − | 0.845853i | \(-0.320908\pi\) | ||||
0.533416 | + | 0.845853i | \(0.320908\pi\) | |||||||
\(662\) | 14.0623 | 0.546548 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.7797 | −1.50494 | ||||||||
\(665\) | 5.24698 | 0.203469 | ||||||||
\(666\) | −5.66487 | −0.219509 | ||||||||
\(667\) | 0.758397 | 0.0293653 | ||||||||
\(668\) | −4.02954 | −0.155908 | ||||||||
\(669\) | 24.5351 | 0.948582 | ||||||||
\(670\) | 9.86592 | 0.381154 | ||||||||
\(671\) | −13.6136 | −0.525546 | ||||||||
\(672\) | −5.54288 | −0.213821 | ||||||||
\(673\) | 1.10321 | 0.0425257 | 0.0212628 | − | 0.999774i | \(-0.493231\pi\) | ||||
0.0212628 | + | 0.999774i | \(0.493231\pi\) | |||||||
\(674\) | 26.3207 | 1.01383 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.7754 | −1.22123 | −0.610614 | − | 0.791929i | \(-0.709077\pi\) | ||||
−0.610614 | + | 0.791929i | \(0.709077\pi\) | |||||||
\(678\) | 8.58881 | 0.329851 | ||||||||
\(679\) | 25.0344 | 0.960734 | ||||||||
\(680\) | 19.7995 | 0.759278 | ||||||||
\(681\) | −0.0217703 | −0.000834238 0 | ||||||||
\(682\) | −2.13706 | −0.0818324 | ||||||||
\(683\) | 4.45606 | 0.170506 | 0.0852532 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852532 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(684\) | −1.03923 | −0.0397359 | ||||||||
\(685\) | −21.7778 | −0.832086 | ||||||||
\(686\) | −25.0804 | −0.957573 | ||||||||
\(687\) | −7.36898 | −0.281144 | ||||||||
\(688\) | 10.9282 | 0.416636 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.246980 | −0.00940235 | ||||||||
\(691\) | −14.1438 | −0.538054 | −0.269027 | − | 0.963133i | \(-0.586702\pi\) | ||||
−0.269027 | + | 0.963133i | \(0.586702\pi\) | |||||||
\(692\) | 5.98792 | 0.227627 | ||||||||
\(693\) | −2.24698 | −0.0853557 | ||||||||
\(694\) | −26.6534 | −1.01175 | ||||||||
\(695\) | 19.4058 | 0.736104 | ||||||||
\(696\) | −11.6746 | −0.442523 | ||||||||
\(697\) | −37.3599 | −1.41511 | ||||||||
\(698\) | 5.38106 | 0.203676 | ||||||||
\(699\) | 8.10992 | 0.306745 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −4.74632 | −0.179266 | −0.0896329 | − | 0.995975i | \(-0.528569\pi\) | ||||
−0.0896329 | + | 0.995975i | \(0.528569\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6082 | 0.400095 | ||||||||
\(704\) | 8.89977 | 0.335423 | ||||||||
\(705\) | −1.97285 | −0.0743019 | ||||||||
\(706\) | 12.7439 | 0.479624 | ||||||||
\(707\) | 18.4058 | 0.692222 | ||||||||
\(708\) | 4.37867 | 0.164560 | ||||||||
\(709\) | 15.4112 | 0.578779 | 0.289390 | − | 0.957211i | \(-0.406548\pi\) | ||||
0.289390 | + | 0.957211i | \(0.406548\pi\) | |||||||
\(710\) | 8.91185 | 0.334456 | ||||||||
\(711\) | 10.6189 | 0.398241 | ||||||||
\(712\) | −20.9541 | −0.785287 | ||||||||
\(713\) | 0.339437 | 0.0127120 | ||||||||
\(714\) | 18.1957 | 0.680956 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.52303 | −0.355892 | ||||||||
\(717\) | 6.38165 | 0.238327 | ||||||||
\(718\) | 10.8696 | 0.405651 | ||||||||
\(719\) | 11.8194 | 0.440789 | 0.220395 | − | 0.975411i | \(-0.429266\pi\) | ||||
0.220395 | + | 0.975411i | \(0.429266\pi\) | |||||||
\(720\) | 2.91185 | 0.108518 | ||||||||
\(721\) | 21.3937 | 0.796744 | ||||||||
\(722\) | 16.8931 | 0.628695 | ||||||||
\(723\) | 1.30127 | 0.0483949 | ||||||||
\(724\) | 6.27652 | 0.233265 | ||||||||
\(725\) | 3.82908 | 0.142209 | ||||||||
\(726\) | −12.4698 | −0.462798 | ||||||||
\(727\) | −21.9675 | −0.814729 | −0.407364 | − | 0.913266i | \(-0.633552\pi\) | ||||
−0.407364 | + | 0.913266i | \(0.633552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.8998 | 0.662500 | ||||||||
\(731\) | 24.3720 | 0.901430 | ||||||||
\(732\) | −6.05861 | −0.223933 | ||||||||
\(733\) | −36.0586 | −1.33186 | −0.665928 | − | 0.746016i | \(-0.731964\pi\) | ||||
−0.665928 | + | 0.746016i | \(0.731964\pi\) | |||||||
\(734\) | 6.70841 | 0.247612 | ||||||||
\(735\) | −1.95108 | −0.0719668 | ||||||||
\(736\) | −0.488582 | −0.0180094 | ||||||||
\(737\) | 7.91185 | 0.291437 | ||||||||
\(738\) | −7.17390 | −0.264075 | ||||||||
\(739\) | 36.9842 | 1.36049 | 0.680243 | − | 0.732987i | \(-0.261874\pi\) | ||||
0.680243 | + | 0.732987i | \(0.261874\pi\) | |||||||
\(740\) | 2.02177 | 0.0743218 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33.7875 | 1.24038 | ||||||||
\(743\) | 1.42865 | 0.0524120 | 0.0262060 | − | 0.999657i | \(-0.491657\pi\) | ||||
0.0262060 | + | 0.999657i | \(0.491657\pi\) | |||||||
\(744\) | −5.22521 | −0.191565 | ||||||||
\(745\) | −11.4668 | −0.420111 | ||||||||
\(746\) | 15.8170 | 0.579102 | ||||||||
\(747\) | −12.7192 | −0.465370 | ||||||||
\(748\) | 2.89008 | 0.105672 | ||||||||
\(749\) | 31.8702 | 1.16451 | ||||||||
\(750\) | −1.24698 | −0.0455333 | ||||||||
\(751\) | −37.9874 | −1.38618 | −0.693091 | − | 0.720850i | \(-0.743752\pi\) | ||||
−0.693091 | + | 0.720850i | \(0.743752\pi\) | |||||||
\(752\) | 5.74466 | 0.209486 | ||||||||
\(753\) | −9.51142 | −0.346615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.17092 | −0.224583 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 30.6805 | 1.11510 | 0.557551 | − | 0.830142i | \(-0.311741\pi\) | ||||
0.557551 | + | 0.830142i | \(0.311741\pi\) | |||||||
\(758\) | −9.96615 | −0.361987 | ||||||||
\(759\) | −0.198062 | −0.00718920 | ||||||||
\(760\) | −7.11960 | −0.258255 | ||||||||
\(761\) | −52.1213 | −1.88939 | −0.944697 | − | 0.327944i | \(-0.893644\pi\) | ||||
−0.944697 | + | 0.327944i | \(0.893644\pi\) | |||||||
\(762\) | −23.0127 | −0.833661 | ||||||||
\(763\) | 22.9095 | 0.829378 | ||||||||
\(764\) | −3.20046 | −0.115788 | ||||||||
\(765\) | 6.49396 | 0.234790 | ||||||||
\(766\) | 0.952411 | 0.0344120 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.1129 | 0.364918 | ||||||||
\(769\) | 30.4222 | 1.09705 | 0.548526 | − | 0.836133i | \(-0.315189\pi\) | ||||
0.548526 | + | 0.836133i | \(0.315189\pi\) | |||||||
\(770\) | −2.80194 | −0.100975 | ||||||||
\(771\) | −7.38942 | −0.266123 | ||||||||
\(772\) | 5.02954 | 0.181017 | ||||||||
\(773\) | −23.1118 | −0.831275 | −0.415637 | − | 0.909530i | \(-0.636441\pi\) | ||||
−0.415637 | + | 0.909530i | \(0.636441\pi\) | |||||||
\(774\) | 4.67994 | 0.168217 | ||||||||
\(775\) | 1.71379 | 0.0615612 | ||||||||
\(776\) | −33.9691 | −1.21942 | ||||||||
\(777\) | 10.2078 | 0.366201 | ||||||||
\(778\) | 36.0127 | 1.29112 | ||||||||
\(779\) | 13.4340 | 0.481324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.14675 | 0.255731 | ||||||||
\(782\) | 1.60388 | 0.0573545 | ||||||||
\(783\) | −3.82908 | −0.136840 | ||||||||
\(784\) | 5.68127 | 0.202902 | ||||||||
\(785\) | 15.3080 | 0.546365 | ||||||||
\(786\) | 10.1250 | 0.361146 | ||||||||
\(787\) | −16.2929 | −0.580780 | −0.290390 | − | 0.956908i | \(-0.593785\pi\) | ||||
−0.290390 | + | 0.956908i | \(0.593785\pi\) | |||||||
\(788\) | 9.12631 | 0.325111 | ||||||||
\(789\) | 3.06398 | 0.109081 | ||||||||
\(790\) | 13.2416 | 0.471115 | ||||||||
\(791\) | −15.4765 | −0.550281 | ||||||||
\(792\) | 3.04892 | 0.108339 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 41.3183 | 1.46633 | ||||||||
\(795\) | 12.0586 | 0.427675 | ||||||||
\(796\) | −8.88663 | −0.314978 | ||||||||
\(797\) | 18.2573 | 0.646705 | 0.323353 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323353 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(798\) | −6.54288 | −0.231615 | ||||||||
\(799\) | 12.8116 | 0.453243 | ||||||||
\(800\) | −2.46681 | −0.0872150 | ||||||||
\(801\) | −6.87263 | −0.242832 | ||||||||
\(802\) | 13.7711 | 0.486273 | ||||||||
\(803\) | 14.3545 | 0.506559 | ||||||||
\(804\) | 3.52111 | 0.124180 | ||||||||
\(805\) | 0.445042 | 0.0156857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.2687 | 0.643090 | ||||||||
\(808\) | −24.9748 | −0.878609 | ||||||||
\(809\) | −24.7259 | −0.869315 | −0.434658 | − | 0.900596i | \(-0.643131\pi\) | ||||
−0.434658 | + | 0.900596i | \(0.643131\pi\) | |||||||
\(810\) | 1.24698 | 0.0438144 | ||||||||
\(811\) | 3.05429 | 0.107251 | 0.0536254 | − | 0.998561i | \(-0.482922\pi\) | ||||
0.0536254 | + | 0.998561i | \(0.482922\pi\) | |||||||
\(812\) | 3.82908 | 0.134375 | ||||||||
\(813\) | 4.04892 | 0.142002 | ||||||||
\(814\) | −5.66487 | −0.198554 | ||||||||
\(815\) | 19.5918 | 0.686271 | ||||||||
\(816\) | −18.9095 | −0.661964 | ||||||||
\(817\) | −8.76377 | −0.306606 | ||||||||
\(818\) | −41.5773 | −1.45372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.56033 | 0.0894108 | ||||||||
\(821\) | −17.7646 | −0.619990 | −0.309995 | − | 0.950738i | \(-0.600327\pi\) | ||||
−0.309995 | + | 0.950738i | \(0.600327\pi\) | |||||||
\(822\) | 27.1564 | 0.947190 | ||||||||
\(823\) | 32.1333 | 1.12010 | 0.560049 | − | 0.828460i | \(-0.310782\pi\) | ||||
0.560049 | + | 0.828460i | \(0.310782\pi\) | |||||||
\(824\) | −29.0291 | −1.01128 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 27.5676 | 0.959201 | ||||||||
\(827\) | 24.5724 | 0.854467 | 0.427233 | − | 0.904141i | \(-0.359488\pi\) | ||||
0.427233 | + | 0.904141i | \(0.359488\pi\) | |||||||
\(828\) | −0.0881460 | −0.00306329 | ||||||||
\(829\) | −9.57135 | −0.332427 | −0.166213 | − | 0.986090i | \(-0.553154\pi\) | ||||
−0.166213 | + | 0.986090i | \(0.553154\pi\) | |||||||
\(830\) | −15.8605 | −0.550528 | ||||||||
\(831\) | −28.1608 | −0.976886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.6703 | 0.438998 | ||||||||
\(834\) | −24.1987 | −0.837931 | ||||||||
\(835\) | −9.05429 | −0.313337 | ||||||||
\(836\) | −1.03923 | −0.0359425 | ||||||||
\(837\) | −1.71379 | −0.0592373 | ||||||||
\(838\) | −49.7633 | −1.71904 | ||||||||
\(839\) | 48.3510 | 1.66926 | 0.834632 | − | 0.550808i | \(-0.185680\pi\) | ||||
0.834632 | + | 0.550808i | \(0.185680\pi\) | |||||||
\(840\) | −6.85086 | −0.236377 | ||||||||
\(841\) | −14.3381 | −0.494418 | ||||||||
\(842\) | −11.7423 | −0.404665 | ||||||||
\(843\) | 24.3937 | 0.840165 | ||||||||
\(844\) | 4.33752 | 0.149304 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.46011 | 0.0845802 | ||||||||
\(847\) | 22.4698 | 0.772071 | ||||||||
\(848\) | −35.1129 | −1.20578 | ||||||||
\(849\) | 7.16315 | 0.245839 | ||||||||
\(850\) | 8.09783 | 0.277753 | ||||||||
\(851\) | 0.899772 | 0.0308438 | ||||||||
\(852\) | 3.18060 | 0.108966 | ||||||||
\(853\) | 0.524090 | 0.0179445 | 0.00897225 | − | 0.999960i | \(-0.497144\pi\) | ||||
0.00897225 | + | 0.999960i | \(0.497144\pi\) | |||||||
\(854\) | −38.1444 | −1.30527 | ||||||||
\(855\) | −2.33513 | −0.0798596 | ||||||||
\(856\) | −43.2446 | −1.47807 | ||||||||
\(857\) | −19.9377 | −0.681058 | −0.340529 | − | 0.940234i | \(-0.610606\pi\) | ||||
−0.340529 | + | 0.940234i | \(0.610606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8437 | −1.18885 | −0.594425 | − | 0.804151i | \(-0.702620\pi\) | ||||
−0.594425 | + | 0.804151i | \(0.702620\pi\) | |||||||
\(860\) | −1.67025 | −0.0569551 | ||||||||
\(861\) | 12.9269 | 0.440548 | ||||||||
\(862\) | −32.4185 | −1.10418 | ||||||||
\(863\) | 15.4416 | 0.525638 | 0.262819 | − | 0.964845i | \(-0.415348\pi\) | ||||
0.262819 | + | 0.964845i | \(0.415348\pi\) | |||||||
\(864\) | 2.46681 | 0.0839227 | ||||||||
\(865\) | 13.4547 | 0.457475 | ||||||||
\(866\) | −8.64981 | −0.293932 | ||||||||
\(867\) | −25.1715 | −0.854869 | ||||||||
\(868\) | 1.71379 | 0.0581699 | ||||||||
\(869\) | 10.6189 | 0.360223 | ||||||||
\(870\) | −4.77479 | −0.161881 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −31.0858 | −1.05270 | ||||||||
\(873\) | −11.1414 | −0.377078 | ||||||||
\(874\) | −0.576728 | −0.0195081 | ||||||||
\(875\) | 2.24698 | 0.0759618 | ||||||||
\(876\) | 6.38835 | 0.215843 | ||||||||
\(877\) | 7.15751 | 0.241692 | 0.120846 | − | 0.992671i | \(-0.461439\pi\) | ||||
0.120846 | + | 0.992671i | \(0.461439\pi\) | |||||||
\(878\) | −23.2905 | −0.786017 | ||||||||
\(879\) | 5.01075 | 0.169009 | ||||||||
\(880\) | 2.91185 | 0.0981586 | ||||||||
\(881\) | −29.9420 | −1.00877 | −0.504386 | − | 0.863479i | \(-0.668281\pi\) | ||||
−0.504386 | + | 0.863479i | \(0.668281\pi\) | |||||||
\(882\) | 2.43296 | 0.0819220 | ||||||||
\(883\) | 18.5139 | 0.623043 | 0.311522 | − | 0.950239i | \(-0.399161\pi\) | ||||
0.311522 | + | 0.950239i | \(0.399161\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.83877 | 0.330727 | ||||||||
\(886\) | −46.0441 | −1.54688 | ||||||||
\(887\) | −46.5991 | −1.56464 | −0.782322 | − | 0.622874i | \(-0.785965\pi\) | ||||
−0.782322 | + | 0.622874i | \(0.785965\pi\) | |||||||
\(888\) | −13.8509 | −0.464804 | ||||||||
\(889\) | 41.4674 | 1.39077 | ||||||||
\(890\) | −8.57002 | −0.287268 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 10.9191 | 0.365600 | ||||||||
\(893\) | −4.60686 | −0.154163 | ||||||||
\(894\) | 14.2989 | 0.478226 | ||||||||
\(895\) | −21.3980 | −0.715258 | ||||||||
\(896\) | 13.8509 | 0.462725 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.1890 | 0.640344 | ||||||||
\(899\) | 6.56225 | 0.218863 | ||||||||
\(900\) | −0.445042 | −0.0148347 | ||||||||
\(901\) | −78.3081 | −2.60882 | ||||||||
\(902\) | −7.17390 | −0.238865 | ||||||||
\(903\) | −8.43296 | −0.280631 | ||||||||
\(904\) | 21.0000 | 0.698450 | ||||||||
\(905\) | 14.1032 | 0.468807 | ||||||||
\(906\) | 7.69501 | 0.255649 | ||||||||
\(907\) | 25.6004 | 0.850048 | 0.425024 | − | 0.905182i | \(-0.360266\pi\) | ||||
0.425024 | + | 0.905182i | \(0.360266\pi\) | |||||||
\(908\) | −0.00968868 | −0.000321530 0 | ||||||||
\(909\) | −8.19136 | −0.271690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9782 | −0.827566 | −0.413783 | − | 0.910376i | \(-0.635793\pi\) | ||||
−0.413783 | + | 0.910376i | \(0.635793\pi\) | |||||||
\(912\) | 6.79954 | 0.225155 | ||||||||
\(913\) | −12.7192 | −0.420943 | ||||||||
\(914\) | 31.5418 | 1.04331 | ||||||||
\(915\) | −13.6136 | −0.450051 | ||||||||
\(916\) | −3.27950 | −0.108358 | ||||||||
\(917\) | −18.2446 | −0.602489 | ||||||||
\(918\) | −8.09783 | −0.267268 | ||||||||
\(919\) | 38.5338 | 1.27111 | 0.635556 | − | 0.772055i | \(-0.280771\pi\) | ||||
0.635556 | + | 0.772055i | \(0.280771\pi\) | |||||||
\(920\) | −0.603875 | −0.0199092 | ||||||||
\(921\) | 29.8213 | 0.982646 | ||||||||
\(922\) | 10.8321 | 0.356735 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | 4.54288 | 0.149369 | ||||||||
\(926\) | −2.16554 | −0.0711640 | ||||||||
\(927\) | −9.52111 | −0.312714 | ||||||||
\(928\) | −9.44563 | −0.310068 | ||||||||
\(929\) | −36.7840 | −1.20684 | −0.603422 | − | 0.797422i | \(-0.706197\pi\) | ||||
−0.603422 | + | 0.797422i | \(0.706197\pi\) | |||||||
\(930\) | −2.13706 | −0.0700771 | ||||||||
\(931\) | −4.55602 | −0.149318 | ||||||||
\(932\) | 3.60925 | 0.118225 | ||||||||
\(933\) | 6.22952 | 0.203945 | ||||||||
\(934\) | −27.8297 | −0.910615 | ||||||||
\(935\) | 6.49396 | 0.212375 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.3244 | −0.337283 | −0.168641 | − | 0.985677i | \(-0.553938\pi\) | ||||
−0.168641 | + | 0.985677i | \(0.553938\pi\) | |||||||
\(938\) | 22.1685 | 0.723828 | ||||||||
\(939\) | −8.22713 | −0.268482 | ||||||||
\(940\) | −0.878002 | −0.0286373 | ||||||||
\(941\) | 21.8170 | 0.711214 | 0.355607 | − | 0.934636i | \(-0.384274\pi\) | ||||
0.355607 | + | 0.934636i | \(0.384274\pi\) | |||||||
\(942\) | −19.0887 | −0.621945 | ||||||||
\(943\) | 1.13946 | 0.0371058 | ||||||||
\(944\) | −28.6491 | −0.932448 | ||||||||
\(945\) | −2.24698 | −0.0730943 | ||||||||
\(946\) | 4.67994 | 0.152158 | ||||||||
\(947\) | −59.4476 | −1.93179 | −0.965893 | − | 0.258942i | \(-0.916626\pi\) | ||||
−0.965893 | + | 0.258942i | \(0.916626\pi\) | |||||||
\(948\) | 4.72587 | 0.153489 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.91185 | −0.0944730 | ||||||||
\(951\) | 20.2010 | 0.655064 | ||||||||
\(952\) | 44.4892 | 1.44190 | ||||||||
\(953\) | 21.4601 | 0.695161 | 0.347581 | − | 0.937650i | \(-0.387003\pi\) | ||||
0.347581 | + | 0.937650i | \(0.387003\pi\) | |||||||
\(954\) | −15.0368 | −0.486836 | ||||||||
\(955\) | −7.19136 | −0.232707 | ||||||||
\(956\) | 2.84010 | 0.0918554 | ||||||||
\(957\) | −3.82908 | −0.123777 | ||||||||
\(958\) | 33.2650 | 1.07474 | ||||||||
\(959\) | −48.9342 | −1.58017 | ||||||||
\(960\) | 8.89977 | 0.287239 | ||||||||
\(961\) | −28.0629 | −0.905255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.1836 | −0.457060 | ||||||||
\(964\) | 0.579121 | 0.0186522 | ||||||||
\(965\) | 11.3013 | 0.363801 | ||||||||
\(966\) | −0.554958 | −0.0178555 | ||||||||
\(967\) | 8.09379 | 0.260279 | 0.130139 | − | 0.991496i | \(-0.458458\pi\) | ||||
0.130139 | + | 0.991496i | \(0.458458\pi\) | |||||||
\(968\) | −30.4892 | −0.979959 | ||||||||
\(969\) | 15.1642 | 0.487145 | ||||||||
\(970\) | −13.8931 | −0.446080 | ||||||||
\(971\) | 55.6238 | 1.78505 | 0.892527 | − | 0.450994i | \(-0.148930\pi\) | ||||
0.892527 | + | 0.450994i | \(0.148930\pi\) | |||||||
\(972\) | 0.445042 | 0.0142747 | ||||||||
\(973\) | 43.6045 | 1.39790 | ||||||||
\(974\) | −10.7447 | −0.344281 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.6407 | 1.26887 | ||||||||
\(977\) | −38.0847 | −1.21844 | −0.609219 | − | 0.793002i | \(-0.708517\pi\) | ||||
−0.609219 | + | 0.793002i | \(0.708517\pi\) | |||||||
\(978\) | −24.4306 | −0.781203 | ||||||||
\(979\) | −6.87263 | −0.219650 | ||||||||
\(980\) | −0.868313 | −0.0277373 | ||||||||
\(981\) | −10.1957 | −0.325523 | ||||||||
\(982\) | 1.23729 | 0.0394835 | ||||||||
\(983\) | 7.66786 | 0.244567 | 0.122283 | − | 0.992495i | \(-0.460978\pi\) | ||||
0.122283 | + | 0.992495i | \(0.460978\pi\) | |||||||
\(984\) | −17.5405 | −0.559170 | ||||||||
\(985\) | 20.5066 | 0.653396 | ||||||||
\(986\) | 31.0073 | 0.987473 | ||||||||
\(987\) | −4.43296 | −0.141103 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.743332 | −0.0236366 | ||||||||
\(990\) | 1.24698 | 0.0396316 | ||||||||
\(991\) | −34.7784 | −1.10477 | −0.552386 | − | 0.833589i | \(-0.686282\pi\) | ||||
−0.552386 | + | 0.833589i | \(0.686282\pi\) | |||||||
\(992\) | −4.22760 | −0.134227 | ||||||||
\(993\) | 11.2771 | 0.357868 | ||||||||
\(994\) | 20.0248 | 0.635147 | ||||||||
\(995\) | −19.9681 | −0.633030 | ||||||||
\(996\) | −5.66056 | −0.179362 | ||||||||
\(997\) | −59.5220 | −1.88508 | −0.942540 | − | 0.334094i | \(-0.891570\pi\) | ||||
−0.942540 | + | 0.334094i | \(0.891570\pi\) | |||||||
\(998\) | −20.8418 | −0.659734 | ||||||||
\(999\) | −4.54288 | −0.143730 |
(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 | 2535.2.a.bd.1.1 | yes | 3 | |
3.2 | odd | 2 | 7605.2.a.bq.1.3 | 3 | |||
13.12 | even | 2 | 2535.2.a.v.1.3 | ✓ | 3 | ||
39.38 | odd | 2 | 7605.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2535.2.a.v.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
2535.2.a.bd.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
7605.2.a.bq.1.3 | 3 | 3.2 | odd | 2 | |||
7605.2.a.bz.1.1 | 3 | 39.38 | odd | 2 |