Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1536) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.16228 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.57649 | −1.72975 | −0.864876 | − | 0.501986i | \(-0.832603\pi\) | ||||
−0.864876 | + | 0.501986i | \(0.832603\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.47214 | −0.745377 | −0.372689 | − | 0.927957i | \(-0.621564\pi\) | ||||
−0.372689 | + | 0.927957i | \(0.621564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.16228 | −0.816497 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.47214 | −1.56972 | −0.784862 | − | 0.619671i | \(-0.787266\pi\) | ||||
−0.784862 | + | 0.619671i | \(0.787266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47214 | 0.567147 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.57649 | −0.998672 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.333851 | −0.0619945 | −0.0309972 | − | 0.999519i | \(-0.509868\pi\) | ||||
−0.0309972 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2333 | −1.83796 | −0.918982 | − | 0.394301i | \(-0.870987\pi\) | ||||
−0.918982 | + | 0.394301i | \(0.870987\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47214 | −0.430344 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.4721 | 2.44624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08191 | 0.342265 | 0.171132 | − | 0.985248i | \(-0.445257\pi\) | ||||
0.171132 | + | 0.985248i | \(0.445257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.47214 | 1.01078 | 0.505389 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505389 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4721 | 1.59699 | 0.798493 | − | 0.602004i | \(-0.205631\pi\) | ||||
0.798493 | + | 0.602004i | \(0.205631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.16228 | −0.471405 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.9443 | 1.99204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.32300 | −0.731171 | −0.365585 | − | 0.930778i | \(-0.619131\pi\) | ||||
−0.365585 | + | 0.930778i | \(0.619131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.81758 | 1.05412 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.47214 | 0.327442 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5672 | 1.35299 | 0.676495 | − | 0.736447i | \(-0.263498\pi\) | ||||
0.676495 | + | 0.736447i | \(0.263498\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.57649 | −0.576584 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | 0.681005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.49613 | 0.414914 | 0.207457 | − | 0.978244i | \(-0.433481\pi\) | ||||
0.207457 | + | 0.978244i | \(0.433481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9443 | −1.74909 | −0.874547 | − | 0.484940i | \(-0.838841\pi\) | ||||
−0.874547 | + | 0.484940i | \(0.838841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.3137 | 1.28932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.08036 | −0.121550 | −0.0607752 | − | 0.998151i | \(-0.519357\pi\) | ||||
−0.0607752 | + | 0.998151i | \(0.519357\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.47214 | 0.271352 | 0.135676 | − | 0.990753i | \(-0.456679\pi\) | ||||
0.135676 | + | 0.990753i | \(0.456679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.4667 | 2.21992 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.333851 | −0.0357925 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.47214 | 0.678464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2333 | −1.06115 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.81758 | −0.802067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.94427 | 0.502015 | 0.251007 | − | 0.967985i | \(-0.419238\pi\) | ||||
0.251007 | + | 0.967985i | \(0.419238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.47214 | −0.248459 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.99070 | −0.596097 | −0.298049 | − | 0.954551i | \(-0.596336\pi\) | ||||
−0.298049 | + | 0.954551i | \(0.596336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.57649 | 0.450935 | 0.225468 | − | 0.974251i | \(-0.427609\pi\) | ||||
0.225468 | + | 0.974251i | \(0.427609\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.4721 | 1.41234 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9443 | 1.63806 | 0.819032 | − | 0.573747i | \(-0.194511\pi\) | ||||
0.819032 | + | 0.573747i | \(0.194511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.40647 | 0.805194 | 0.402597 | − | 0.915377i | \(-0.368108\pi\) | ||||
0.402597 | + | 0.915377i | \(0.368108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.08191 | 0.197607 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.8885 | −1.66812 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | −0.130744 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.6197 | 2.71523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.88854 | −0.444413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.47214 | 0.583573 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.07262 | 0.716329 | 0.358165 | − | 0.933658i | \(-0.383403\pi\) | ||||
0.358165 | + | 0.933658i | \(0.383403\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4721 | 0.922020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.944272 | −0.0825014 | −0.0412507 | − | 0.999149i | \(-0.513134\pi\) | ||||
−0.0412507 | + | 0.999149i | \(0.513134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3137 | −0.981023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.16228 | −0.272166 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.47214 | −0.552952 | −0.276476 | − | 0.961021i | \(-0.589167\pi\) | ||||
−0.276476 | + | 0.961021i | \(0.589167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.944272 | −0.0800921 | −0.0400460 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400460 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.49613 | 0.292361 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05573 | 0.0876734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.9443 | 1.15010 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1437 | −1.24062 | −0.620310 | − | 0.784357i | \(-0.712993\pi\) | ||||
−0.620310 | + | 0.784357i | \(0.712993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5687 | 0.941451 | 0.470726 | − | 0.882280i | \(-0.343992\pi\) | ||||
0.470726 | + | 0.882280i | \(0.343992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.47214 | −0.523241 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.3607 | 2.59927 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.746512 | −0.0595782 | −0.0297891 | − | 0.999556i | \(-0.509484\pi\) | ||||
−0.0297891 | + | 0.999556i | \(0.509484\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.32300 | −0.422142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.8885 | −2.04030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.52786 | 0.432976 | 0.216488 | − | 0.976285i | \(-0.430540\pi\) | ||||
0.216488 | + | 0.976285i | \(0.430540\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.81758 | 0.608598 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.81758 | 0.604943 | 0.302471 | − | 0.953159i | \(-0.402188\pi\) | ||||
0.302471 | + | 0.953159i | \(0.402188\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.47214 | 0.189049 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.48683 | −0.721271 | −0.360635 | − | 0.932707i | \(-0.617440\pi\) | ||||
−0.360635 | + | 0.932707i | \(0.617440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.8825 | −1.72975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.94427 | −0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5563 | 1.15629 | 0.578147 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578147 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5672 | 0.781150 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.58359 | −0.484035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.57649 | −0.332891 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.16073 | 0.156345 | 0.0781723 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781723 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9443 | −0.931749 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.47214 | 0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2967 | 1.73107 | 0.865533 | − | 0.500852i | \(-0.166980\pi\) | ||||
0.865533 | + | 0.500852i | \(0.166980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7295 | 0.973257 | 0.486628 | − | 0.873609i | \(-0.338227\pi\) | ||||
0.486628 | + | 0.873609i | \(0.338227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52786 | 0.107235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.4667 | −1.42946 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | 0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.11146 | −0.422738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9443 | 1.71723 | 0.858617 | − | 0.512617i | \(-0.171324\pi\) | ||||
0.858617 | + | 0.512617i | \(0.171324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.49613 | 0.239551 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.1158 | −2.25848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 46.8328 | 3.17922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.9443 | −1.00984 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.15298 | 0.615696 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2333 | −0.685275 | −0.342638 | − | 0.939468i | \(-0.611320\pi\) | ||||
−0.342638 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.52786 | −0.366897 | −0.183449 | − | 0.983029i | \(-0.558726\pi\) | ||||
−0.183449 | + | 0.983029i | \(0.558726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2349 | −0.742423 | −0.371211 | − | 0.928548i | \(-0.621057\pi\) | ||||
−0.371211 | + | 0.928548i | \(0.621057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.08036 | −0.0701771 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4744 | −0.871589 | −0.435794 | − | 0.900046i | \(-0.643533\pi\) | ||||
−0.435794 | + | 0.900046i | \(0.643533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −44.0957 | −2.81717 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.49613 | −0.222453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.47214 | 0.156665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.4164 | −0.973075 | −0.486538 | − | 0.873660i | \(-0.661740\pi\) | ||||
−0.486538 | + | 0.873660i | \(0.661740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.9845 | −0.879199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.4667 | 1.28167 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.52786 | −0.592033 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.333851 | −0.0206648 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.6491 | −0.779978 | −0.389989 | − | 0.920820i | \(-0.627521\pi\) | ||||
−0.389989 | + | 0.920820i | \(0.627521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.8328 | 1.03403 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6476 | 0.710164 | 0.355082 | − | 0.934835i | \(-0.384453\pi\) | ||||
0.355082 | + | 0.934835i | \(0.384453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.07262 | 0.490377 | 0.245188 | − | 0.969475i | \(-0.421150\pi\) | ||||
0.245188 | + | 0.969475i | \(0.421150\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.47214 | 0.391711 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.3607 | −0.745377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.3848 | 1.10463 | 0.552317 | − | 0.833634i | \(-0.313744\pi\) | ||||
0.552317 | + | 0.833634i | \(0.313744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2333 | −0.612654 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.8885 | −1.90231 | −0.951156 | − | 0.308712i | \(-0.900102\pi\) | ||||
−0.951156 | + | 0.308712i | \(0.900102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8328 | −1.59505 | −0.797523 | − | 0.603289i | \(-0.793857\pi\) | ||||
−0.797523 | + | 0.603289i | \(0.793857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.81758 | −0.463073 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.6197 | −1.74839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.94427 | 0.289838 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6367 | −0.971927 | −0.485964 | − | 0.873979i | \(-0.661531\pi\) | ||||
−0.485964 | + | 0.873979i | \(0.661531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2843 | 1.64677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.47214 | −0.143448 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.00000 | −0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −47.9256 | −2.76239 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.99070 | −0.344157 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.4164 | −1.91342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.8885 | 1.70583 | 0.852915 | − | 0.522050i | \(-0.174833\pi\) | ||||
0.852915 | + | 0.522050i | \(0.174833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.57649 | 0.260347 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.9551 | −1.75530 | −0.877651 | − | 0.479301i | \(-0.840890\pi\) | ||||
−0.877651 | + | 0.479301i | \(0.840890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.05573 | 0.172720 | 0.0863600 | − | 0.996264i | \(-0.472476\pi\) | ||||
0.0863600 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.4721 | 0.815412 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9799 | 0.616690 | 0.308345 | − | 0.951275i | \(-0.400225\pi\) | ||||
0.308345 | + | 0.951275i | \(0.400225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.825324 | 0.0462093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9443 | 0.945737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07107 | −0.392232 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.40647 | 0.464879 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.08191 | 0.114088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.9473 | −2.07328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.94427 | −0.160385 | −0.0801924 | − | 0.996779i | \(-0.525553\pi\) | ||||
−0.0801924 | + | 0.996779i | \(0.525553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2982 | 1.36998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.7804 | −1.71598 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.8885 | −0.963087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5279 | 0.726214 | 0.363107 | − | 0.931747i | \(-0.381716\pi\) | ||||
0.363107 | + | 0.931747i | \(0.381716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8809 | −1.17126 | −0.585629 | − | 0.810579i | \(-0.699152\pi\) | ||||
−0.585629 | + | 0.810579i | \(0.699152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41421 | −0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8885 | 1.27146 | 0.635729 | − | 0.771912i | \(-0.280699\pi\) | ||||
0.635729 | + | 0.771912i | \(0.280699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.0557 | −0.586777 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.6197 | 1.56764 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1235 | 1.37875 | 0.689374 | − | 0.724406i | \(-0.257886\pi\) | ||||
0.689374 | + | 0.724406i | \(0.257886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.88854 | −0.256582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.2579 | 2.47359 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3786 | 1.37695 | 0.688475 | − | 0.725260i | \(-0.258280\pi\) | ||||
0.688475 | + | 0.725260i | \(0.258280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.47214 | 0.336926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.3607 | 1.26474 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.23179 | 0.478004 | 0.239002 | − | 0.971019i | \(-0.423180\pi\) | ||||
0.239002 | + | 0.971019i | \(0.423180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.472136 | 0.0243162 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.583592 | −0.0299771 | −0.0149886 | − | 0.999888i | \(-0.504771\pi\) | ||||
−0.0149886 | + | 0.999888i | \(0.504771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.07262 | 0.413573 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.7804 | 1.62390 | 0.811951 | − | 0.583725i | \(-0.198405\pi\) | ||||
0.811951 | + | 0.583725i | \(0.198405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −35.7771 | −1.82337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4721 | 0.532329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8222 | −0.548709 | −0.274355 | − | 0.961629i | \(-0.588464\pi\) | ||||
−0.274355 | + | 0.961629i | \(0.588464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.6119 | −1.85154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.944272 | −0.0476322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.41641 | 0.171898 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.8732 | 1.44910 | 0.724551 | − | 0.689221i | \(-0.242047\pi\) | ||||
0.724551 | + | 0.689221i | \(0.242047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.3137 | −0.566394 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.4721 | 1.12220 | 0.561102 | − | 0.827746i | \(-0.310377\pi\) | ||||
0.561102 | + | 0.827746i | \(0.310377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4721 | 0.720908 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.16228 | −0.157135 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.14678 | −0.255116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.94427 | 0.244479 | 0.122239 | − | 0.992501i | \(-0.460992\pi\) | ||||
0.122239 | + | 0.992501i | \(0.460992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.47214 | −0.319247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.9334 | 2.01420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.81758 | −0.383750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.944272 | −0.0462412 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.4721 | −0.511597 | −0.255799 | − | 0.966730i | \(-0.582338\pi\) | ||||
−0.255799 | + | 0.966730i | \(0.582338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.07107 | 0.344623 | 0.172311 | − | 0.985043i | \(-0.444876\pi\) | ||||
0.172311 | + | 0.985043i | \(0.444876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.3607 | −1.56972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.3607 | −2.34034 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.49613 | 0.168795 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.99226 | −0.336805 | −0.168403 | − | 0.985718i | \(-0.553861\pi\) | ||||
−0.168403 | + | 0.985718i | \(0.553861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05573 | 0.0506183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9845 | 0.668970 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0432 | 1.19525 | 0.597623 | − | 0.801777i | \(-0.296112\pi\) | ||||
0.597623 | + | 0.801777i | \(0.296112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9443 | 0.664013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.4164 | 0.732456 | 0.366228 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366228 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.6228 | 1.49906 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.1437 | −0.716272 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.41641 | 0.161230 | 0.0806151 | − | 0.996745i | \(-0.474312\pi\) | ||||
0.0806151 | + | 0.996745i | \(0.474312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5687 | 0.543547 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.4667 | −0.959493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9443 | 0.979732 | 0.489866 | − | 0.871798i | \(-0.337046\pi\) | ||||
0.489866 | + | 0.871798i | \(0.337046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.47214 | −0.302093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.49458 | 0.116184 | 0.0580920 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580920 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.08036 | 0.0502087 | 0.0251044 | − | 0.999685i | \(-0.492008\pi\) | ||||
0.0251044 | + | 0.999685i | \(0.492008\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.3607 | 1.50069 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.4164 | −1.45378 | −0.726889 | − | 0.686755i | \(-0.759035\pi\) | ||||
−0.726889 | + | 0.686755i | \(0.759035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.9179 | −2.53587 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.746512 | −0.0343975 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.8885 | −1.19036 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.3607 | 0.567147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.32300 | −0.243724 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.15298 | 0.418210 | 0.209105 | − | 0.977893i | \(-0.432945\pi\) | ||||
0.209105 | + | 0.977893i | \(0.432945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.94427 | −0.134247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.8885 | −1.17797 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.6352 | −0.709956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.41577 | −0.109469 | −0.0547344 | − | 0.998501i | \(-0.517431\pi\) | ||||
−0.0547344 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.52786 | 0.249979 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8885 | −0.626781 | −0.313391 | − | 0.949624i | \(-0.601465\pi\) | ||||
−0.313391 | + | 0.949624i | \(0.601465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.16073 | 0.0973142 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.81758 | 0.351374 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.05573 | −0.315858 | −0.157929 | − | 0.987450i | \(-0.550482\pi\) | ||||
−0.157929 | + | 0.987450i | \(0.550482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.81758 | 0.349264 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.1158 | 1.47656 | 0.738280 | − | 0.674494i | \(-0.235638\pi\) | ||||
0.738280 | + | 0.674494i | \(0.235638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9443 | 0.843009 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.6073 | −1.48962 | −0.744808 | − | 0.667279i | \(-0.767459\pi\) | ||||
−0.744808 | + | 0.667279i | \(0.767459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 68.3923 | 3.02550 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47214 | 0.109147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.4721 | −0.637719 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.48683 | −0.416426 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3607 | 0.716774 | 0.358387 | − | 0.933573i | \(-0.383327\pi\) | ||||
0.358387 | + | 0.933573i | \(0.383327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3607 | 1.24013 | 0.620063 | − | 0.784552i | \(-0.287107\pi\) | ||||
0.620063 | + | 0.784552i | \(0.287107\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.8825 | −0.998672 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 66.2316 | 2.88509 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.15298 | −0.396460 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.5825 | −2.31657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.4721 | −1.48482 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.8840 | −1.02685 | −0.513427 | − | 0.858133i | \(-0.671624\pi\) | ||||
−0.513427 | + | 0.858133i | \(0.671624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.5563 | 0.667587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5836 | −1.13872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3607 | −0.528505 | −0.264252 | − | 0.964454i | \(-0.585125\pi\) | ||||
−0.264252 | + | 0.964454i | \(0.585125\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5672 | 0.450997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.825324 | −0.0351600 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427 | 0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.58359 | −0.279458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.8114 | 0.669950 | 0.334975 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334975 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.8098 | −0.626389 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.4721 | 0.441348 | 0.220674 | − | 0.975348i | \(-0.429174\pi\) | ||||
0.220674 | + | 0.975348i | \(0.429174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32456 | 0.266076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.57649 | −0.192195 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4164 | −0.813978 | −0.406989 | − | 0.913433i | \(-0.633421\pi\) | ||||
−0.406989 | + | 0.913433i | \(0.633421\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.94427 | 0.374306 | 0.187153 | − | 0.982331i | \(-0.440074\pi\) | ||||
0.187153 | + | 0.982331i | \(0.440074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.16073 | 0.0902656 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.2843 | 1.17954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.05573 | 0.376995 | 0.188497 | − | 0.982074i | \(-0.439638\pi\) | ||||
0.188497 | + | 0.982074i | \(0.439638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9443 | −0.537946 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3137 | −0.469372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1592 | 0.544998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.47214 | 0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.0557 | −0.621416 | −0.310708 | − | 0.950505i | \(-0.600566\pi\) | ||||
−0.310708 | + | 0.950505i | \(0.600566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.2982 | −1.04240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.2967 | 0.999431 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.8885 | −1.14525 | −0.572623 | − | 0.819819i | \(-0.694074\pi\) | ||||
−0.572623 | + | 0.819819i | \(0.694074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −93.6656 | −3.83992 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.7295 | 0.561910 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9443 | 0.446426 | 0.223213 | − | 0.974770i | \(-0.428345\pi\) | ||||
0.223213 | + | 0.974770i | \(0.428345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.4589 | 0.628495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8685 | −1.04997 | −0.524985 | − | 0.851111i | \(-0.675929\pi\) | ||||
−0.524985 | + | 0.851111i | \(0.675929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.52786 | 0.0619122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.08191 | −0.0840877 | −0.0420439 | − | 0.999116i | \(-0.513387\pi\) | ||||
−0.0420439 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.4667 | −0.825297 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.8885 | 0.800683 | 0.400341 | − | 0.916366i | \(-0.368892\pi\) | ||||
0.400341 | + | 0.916366i | \(0.368892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.8885 | 1.20132 | 0.600661 | − | 0.799504i | \(-0.294904\pi\) | ||||
0.600661 | + | 0.799504i | \(0.294904\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65685 | 0.227002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.7649 | 1.83353 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.11146 | −0.244068 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.4744 | −0.537261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8747 | 1.18929 | 0.594647 | − | 0.803987i | \(-0.297292\pi\) | ||||
0.594647 | + | 0.803987i | \(0.297292\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.9443 | 0.991446 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.5279 | −1.01304 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.7202 | −0.781342 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.49613 | 0.138305 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.4164 | 1.39886 | 0.699432 | − | 0.714699i | \(-0.253436\pi\) | ||||
0.699432 | + | 0.714699i | \(0.253436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3607 | 1.43393 | 0.716963 | − | 0.697112i | \(-0.245532\pi\) | ||||
0.716963 | + | 0.697112i | \(0.245532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.1158 | −1.30393 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.32766 | 0.327394 | 0.163697 | − | 0.986511i | \(-0.447658\pi\) | ||||
0.163697 | + | 0.986511i | \(0.447658\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1115 | 0.867951 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.8328 | 1.83552 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.81603 | 0.266732 | 0.133366 | − | 0.991067i | \(-0.457421\pi\) | ||||
0.133366 | + | 0.991067i | \(0.457421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.98605 | 0.116675 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.9443 | −0.583032 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.23954 | −0.0871079 | −0.0435540 | − | 0.999051i | \(-0.513868\pi\) | ||||
−0.0435540 | + | 0.999051i | \(0.513868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.15298 | 0.355472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.7771 | 1.38738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.88854 | −0.0731247 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.2333 | −0.395644 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.1235 | −1.00849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8885 | 0.689553 | 0.344776 | − | 0.938685i | \(-0.387955\pi\) | ||||
0.344776 | + | 0.938685i | \(0.387955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.7634 | −1.72040 | −0.860198 | − | 0.509960i | \(-0.829660\pi\) | ||||
−0.860198 | + | 0.509960i | \(0.829660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6274 | −0.868361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.52786 | −0.211828 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.4164 | −0.896004 | −0.448002 | − | 0.894033i | \(-0.647864\pi\) | ||||
−0.448002 | + | 0.894033i | \(0.647864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4667 | 0.781992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.2349 | −0.428638 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.52786 | 0.286789 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.4721 | −1.31138 | −0.655691 | − | 0.755029i | \(-0.727623\pi\) | ||||
−0.655691 | + | 0.755029i | \(0.727623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.3137 | 0.429772 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.98605 | 0.113267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.8885 | −1.58664 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.98760 | −0.150610 | −0.0753048 | − | 0.997161i | \(-0.523993\pi\) | ||||
−0.0753048 | + | 0.997161i | \(0.523993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.14678 | 0.194114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.4164 | 1.03110 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.56409 | 0.321631 | 0.160816 | − | 0.986984i | \(-0.448588\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.08036 | −0.0405168 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −57.8885 | −2.16794 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0557 | −0.413461 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4744 | −0.503212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1452 | 0.602116 | 0.301058 | − | 0.953606i | \(-0.402660\pi\) | ||||
0.301058 | + | 0.953606i | \(0.402660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9443 | −0.780005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.66925 | −0.0619945 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5687 | −0.429061 | −0.214531 | − | 0.976717i | \(-0.568822\pi\) | ||||
−0.214531 | + | 0.976717i | \(0.568822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −67.7771 | −2.50683 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.73567 | −0.211852 | −0.105926 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105926 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −44.0957 | −1.62649 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.6656 | −1.09275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0557 | −0.553834 | −0.276917 | − | 0.960894i | \(-0.589313\pi\) | ||||
−0.276917 | + | 0.960894i | \(0.589313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.49613 | −0.128433 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.8098 | −0.543320 | −0.271660 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271660 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.8885 | 1.75450 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.47214 | 0.0904507 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −77.5453 | −2.83344 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.08036 | 0.0394230 | 0.0197115 | − | 0.999806i | \(-0.493725\pi\) | ||||
0.0197115 | + | 0.999806i | \(0.493725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4164 | −0.561805 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.5836 | −1.33141 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2349 | 0.408339 | 0.204170 | − | 0.978936i | \(-0.434551\pi\) | ||||
0.204170 | + | 0.978936i | \(0.434551\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.9845 | −0.507606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.4164 | 0.703844 | 0.351922 | − | 0.936029i | \(-0.385528\pi\) | ||||
0.351922 | + | 0.936029i | \(0.385528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.4721 | −1.39278 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.4667 | 0.739975 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.6491 | 0.456733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.8328 | 0.823372 | 0.411686 | − | 0.911326i | \(-0.364940\pi\) | ||||
0.411686 | + | 0.911326i | \(0.364940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.3153 | 0.442949 | 0.221475 | − | 0.975166i | \(-0.428913\pi\) | ||||
0.221475 | + | 0.975166i | \(0.428913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −51.1667 | −1.83796 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.52786 | −0.341810 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | 0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.64290 | −0.309267 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.333851 | −0.0119308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.36068 | 0.0842563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.52786 | −0.197047 | −0.0985235 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985235 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.6491 | −0.450320 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.15298 | 0.325443 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.9443 | −0.530687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.8328 | 0.596998 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.1065 | 1.38522 | 0.692612 | − | 0.721311i | \(-0.256460\pi\) | ||||
0.692612 | + | 0.721311i | \(0.256460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9443 | 1.30374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.8668 | 2.88542 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6476 | 0.410013 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.41641 | 0.120115 | 0.0600573 | − | 0.998195i | \(-0.480872\pi\) | ||||
0.0600573 | + | 0.998195i | \(0.480872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.3050 | −1.16950 | −0.584748 | − | 0.811215i | \(-0.698806\pi\) | ||||
−0.584748 | + | 0.811215i | \(0.698806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.07262 | 0.283119 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.4806 | −0.612320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8885 | 0.905725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.47214 | 0.226155 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.6057 | −1.55675 | −0.778375 | − | 0.627799i | \(-0.783956\pi\) | ||||
−0.778375 | + | 0.627799i | \(0.783956\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.57649 | 0.159526 | 0.0797632 | − | 0.996814i | \(-0.474584\pi\) | ||||
0.0797632 | + | 0.996814i | \(0.474584\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.3607 | −0.430344 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.8885 | 1.87389 | 0.936944 | − | 0.349479i | \(-0.113641\pi\) | ||||
0.936944 | + | 0.349479i | \(0.113641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.7202 | 0.684910 | 0.342455 | − | 0.939534i | \(-0.388742\pi\) | ||||
0.342455 | + | 0.939534i | \(0.388742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3848 | 0.637761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −90.2492 | −3.12695 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.7214 | −0.855518 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.2333 | −0.353716 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4295 | −1.53388 | −0.766939 | − | 0.641721i | \(-0.778221\pi\) | ||||
−0.766939 | + | 0.641721i | \(0.778221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8885 | −0.996157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.8885 | −1.09830 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.7851 | 1.19664 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3724 | 0.768724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.8328 | −0.920900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7771 | 0.403713 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.7171 | −0.606621 | −0.303311 | − | 0.952892i | \(-0.598092\pi\) | ||||
−0.303311 | + | 0.952892i | \(0.598092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.81758 | −0.267356 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5836 | 0.976397 | 0.488198 | − | 0.872733i | \(-0.337654\pi\) | ||||
0.488198 | + | 0.872733i | \(0.337654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.5279 | −1.55339 | −0.776695 | − | 0.629876i | \(-0.783106\pi\) | ||||
−0.776695 | + | 0.629876i | \(0.783106\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.6197 | −1.00944 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.4512 | 1.17273 | 0.586366 | − | 0.810046i | \(-0.300558\pi\) | ||||
0.586366 | + | 0.810046i | \(0.300558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.8885 | 0.845259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.67080 | 0.0906008 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9706 | −0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.94427 | 0.167338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8654 | 1.21109 | 0.605545 | − | 0.795811i | \(-0.292955\pi\) | ||||
0.605545 | + | 0.795811i | \(0.292955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.6367 | −0.561142 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.8885 | 0.939589 | 0.469794 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469794 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.4721 | 0.621637 | 0.310818 | − | 0.950469i | \(-0.399397\pi\) | ||||
0.310818 | + | 0.950469i | \(0.399397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.2843 | 0.950765 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.2688 | 1.41925 | 0.709623 | − | 0.704581i | \(-0.248865\pi\) | ||||
0.709623 | + | 0.704581i | \(0.248865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.9443 | −1.23907 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.47214 | −0.0828197 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.9473 | −1.26844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.41641 | 0.113944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4512 | 1.14774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.9256 | −1.59487 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.1935 | −1.63525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.1935 | −1.69985 | −0.849926 | − | 0.526902i | \(-0.823353\pi\) | ||||
−0.849926 | + | 0.526902i | \(0.823353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.99070 | −0.198699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16073 | 0.0715880 | 0.0357940 | − | 0.999359i | \(-0.488604\pi\) | ||||
0.0357940 | + | 0.999359i | \(0.488604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.11146 | −0.202260 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.4164 | −1.10471 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.32145 | 0.142707 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1962 | 1.12803 | 0.564014 | − | 0.825765i | \(-0.309257\pi\) | ||||
0.564014 | + | 0.825765i | \(0.309257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.8885 | 0.984861 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.94427 | −0.162743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4096 | 0.342265 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.57649 | 0.150312 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.47214 | 0.212344 | 0.106172 | − | 0.994348i | \(-0.466141\pi\) | ||||
0.106172 | + | 0.994348i | \(0.466141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.4721 | 1.12978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.9551 | −1.01342 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −50.5964 | −1.65468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.05573 | 0.0997199 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.1220 | 0.818954 | 0.409477 | − | 0.912321i | \(-0.365711\pi\) | ||||
0.409477 | + | 0.912321i | \(0.365711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6119 | 1.19225 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.4721 | 0.470779 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.7771 | −1.55255 | −0.776273 | − | 0.630396i | \(-0.782892\pi\) | ||||
−0.776273 | + | 0.630396i | \(0.782892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.1344 | 0.686051 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9799 | 0.356046 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.52786 | −0.308638 | −0.154319 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154319 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.83282 | −0.221105 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.825324 | 0.0266789 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.6197 | 0.956469 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.7214 | 2.37811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9443 | 0.546022 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.9334 | 1.31769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.5610 | −0.596882 | −0.298441 | − | 0.954428i | \(-0.596467\pi\) | ||||
−0.298441 | + | 0.954428i | \(0.596467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0000 | −0.513994 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3607 | −0.653405 | −0.326703 | − | 0.945127i | \(-0.605938\pi\) | ||||
−0.326703 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.32145 | 0.138539 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.07107 | −0.226455 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5836 | 0.402585 | 0.201292 | − | 0.979531i | \(-0.435486\pi\) | ||||
0.201292 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.7214 | 0.790098 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.40647 | 0.268398 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.5825 | −1.70902 | −0.854508 | − | 0.519438i | \(-0.826141\pi\) | ||||
−0.854508 | + | 0.519438i | \(0.826141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.8328 | −2.44810 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 59.2393 | 1.88370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2256 | −0.547189 | −0.273595 | − | 0.961845i | \(-0.588213\pi\) | ||||
−0.273595 | + | 0.961845i | \(0.588213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.944272 | 0.0299656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −43.4164 | −1.37639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0308 | 0.919414 | 0.459707 | − | 0.888071i | \(-0.347954\pi\) | ||||
0.459707 | + | 0.888071i | \(0.347954\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.08191 | 0.0658689 |
(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 | 3072.2.a.q.1.1 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bd.1.3 | 4 | |||
4.3 | odd | 2 | 3072.2.a.k.1.2 | 4 | |||
8.3 | odd | 2 | inner | 3072.2.a.q.1.4 | 4 | ||
8.5 | even | 2 | 3072.2.a.k.1.3 | 4 | |||
12.11 | even | 2 | 9216.2.a.bj.1.4 | 4 | |||
16.3 | odd | 4 | 3072.2.d.g.1537.3 | 8 | |||
16.5 | even | 4 | 3072.2.d.g.1537.2 | 8 | |||
16.11 | odd | 4 | 3072.2.d.g.1537.5 | 8 | |||
16.13 | even | 4 | 3072.2.d.g.1537.8 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bj.1.1 | 4 | |||
24.11 | even | 2 | 9216.2.a.bd.1.2 | 4 | |||
32.3 | odd | 8 | 1536.2.j.h.1153.2 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.g.385.1 | ✓ | 8 | ||
32.11 | odd | 8 | 1536.2.j.h.385.2 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.g.1153.1 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.g.1153.3 | yes | 8 | ||
32.21 | even | 8 | 1536.2.j.h.385.4 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.g.385.3 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.h.1153.4 | yes | 8 | ||
96.5 | odd | 8 | 4608.2.k.bf.3457.3 | 8 | |||
96.11 | even | 8 | 4608.2.k.bg.3457.2 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bg.1153.2 | 8 | |||
96.35 | even | 8 | 4608.2.k.bg.1153.1 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bg.3457.1 | 8 | |||
96.59 | even | 8 | 4608.2.k.bf.3457.4 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bf.1153.4 | 8 | |||
96.83 | even | 8 | 4608.2.k.bf.1153.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.g.385.1 | ✓ | 8 | 32.5 | even | 8 | ||
1536.2.j.g.385.3 | yes | 8 | 32.27 | odd | 8 | ||
1536.2.j.g.1153.1 | yes | 8 | 32.13 | even | 8 | ||
1536.2.j.g.1153.3 | yes | 8 | 32.19 | odd | 8 | ||
1536.2.j.h.385.2 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.h.385.4 | yes | 8 | 32.21 | even | 8 | ||
1536.2.j.h.1153.2 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.h.1153.4 | yes | 8 | 32.29 | even | 8 | ||
3072.2.a.k.1.2 | 4 | 4.3 | odd | 2 | |||
3072.2.a.k.1.3 | 4 | 8.5 | even | 2 | |||
3072.2.a.q.1.1 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.q.1.4 | 4 | 8.3 | odd | 2 | inner | ||
3072.2.d.g.1537.2 | 8 | 16.5 | even | 4 | |||
3072.2.d.g.1537.3 | 8 | 16.3 | odd | 4 | |||
3072.2.d.g.1537.5 | 8 | 16.11 | odd | 4 | |||
3072.2.d.g.1537.8 | 8 | 16.13 | even | 4 | |||
4608.2.k.bf.1153.3 | 8 | 96.83 | even | 8 | |||
4608.2.k.bf.1153.4 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bf.3457.3 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bf.3457.4 | 8 | 96.59 | even | 8 | |||
4608.2.k.bg.1153.1 | 8 | 96.35 | even | 8 | |||
4608.2.k.bg.1153.2 | 8 | 96.29 | odd | 8 | |||
4608.2.k.bg.3457.1 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bg.3457.2 | 8 | 96.11 | even | 8 | |||
9216.2.a.bd.1.2 | 4 | 24.11 | even | 2 | |||
9216.2.a.bd.1.3 | 4 | 3.2 | odd | 2 | |||
9216.2.a.bj.1.1 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bj.1.4 | 4 | 12.11 | even | 2 |