Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
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, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.5 | ||
Root | \(0.437016 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.g.1537.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.16228i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 2.47214i | 0.745377i | 0.927957 | + | 0.372689i | \(0.121564\pi\) | ||||
−0.927957 | + | 0.372689i | \(0.878436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421i | 0.392232i | 0.980581 | + | 0.196116i | \(0.0628330\pi\) | ||||
−0.980581 | + | 0.196116i | \(0.937167\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 2.47214i | 0.567147i | 0.958951 | + | 0.283573i | \(0.0915200\pi\) | ||||
−0.958951 | + | 0.283573i | \(0.908480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 4.57649i | − 0.998672i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.333851i | 0.0619945i | 0.999519 | + | 0.0309972i | \(0.00986831\pi\) | ||||
−0.999519 | + | 0.0309972i | \(0.990132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2333 | 1.83796 | 0.918982 | − | 0.394301i | \(-0.129013\pi\) | ||||
0.918982 | + | 0.394301i | \(0.129013\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47214 | −0.430344 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.4721i | 2.44624i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08191i | 0.342265i | 0.985248 | + | 0.171132i | \(0.0547426\pi\) | ||||
−0.985248 | + | 0.171132i | \(0.945257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.47214 | −1.01078 | −0.505389 | − | 0.862892i | \(-0.668651\pi\) | ||||
−0.505389 | + | 0.862892i | \(0.668651\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.4721i | − 1.59699i | −0.602004 | − | 0.798493i | \(-0.705631\pi\) | ||||
0.602004 | − | 0.798493i | \(-0.294369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16228i | 0.471405i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | − 6.47214i | − 0.906280i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.32300i | − 0.731171i | −0.930778 | − | 0.365585i | \(-0.880869\pi\) | ||||
0.930778 | − | 0.365585i | \(-0.119131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.81758 | 1.05412 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.47214 | −0.327442 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427i | 1.16445i | 0.813029 | + | 0.582223i | \(0.197817\pi\) | ||||
−0.813029 | + | 0.582223i | \(0.802183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 10.5672i | − 1.35299i | −0.736447 | − | 0.676495i | \(-0.763498\pi\) | ||||
0.736447 | − | 0.676495i | \(-0.236502\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.57649 | 0.576584 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685i | 0.681005i | ||||||||
\(70\) | 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 | \(-0.161159\pi\) | ||||
0.874547 | + | 0.484940i | \(0.161159\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 5.00000i | − 0.577350i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 11.3137i | − 1.28932i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.08036 | 0.121550 | 0.0607752 | − | 0.998151i | \(-0.480643\pi\) | ||||
0.0607752 | + | 0.998151i | \(0.480643\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.47214i | 0.271352i | 0.990753 | + | 0.135676i | \(0.0433206\pi\) | ||||
−0.990753 | + | 0.135676i | \(0.956679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.4667i | 2.21992i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.333851 | −0.0357925 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 6.47214i | − 0.678464i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2333i | 1.06115i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 2.47214i | − 0.248459i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.99070i | − 0.596097i | −0.954551 | − | 0.298049i | \(-0.903664\pi\) | ||||
0.954551 | − | 0.298049i | \(-0.0963358\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − 16.9443i | − 1.63806i | −0.573747 | − | 0.819032i | \(-0.694511\pi\) | ||||
0.573747 | − | 0.819032i | \(-0.305489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.40647i | − 0.805194i | −0.915377 | − | 0.402597i | \(-0.868108\pi\) | ||||
0.915377 | − | 0.402597i | \(-0.131892\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 17.8885i | − 1.66812i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.41421i | − 0.130744i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.6197 | 2.71523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.88854 | 0.444413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 6.47214i | − 0.583573i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.07262 | −0.716329 | −0.358165 | − | 0.933658i | \(-0.616597\pi\) | ||||
−0.358165 | + | 0.933658i | \(0.616597\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4721 | 0.922020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 0.944272i | − 0.0825014i | −0.999149 | − | 0.0412507i | \(-0.986866\pi\) | ||||
0.999149 | − | 0.0412507i | \(-0.0131342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 11.3137i | − 0.981023i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.16228 | −0.272166 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.47214 | 0.552952 | 0.276476 | − | 0.961021i | \(-0.410833\pi\) | ||||
0.276476 | + | 0.961021i | \(0.410833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.944272i | 0.0800921i | 0.999198 | + | 0.0400460i | \(0.0127505\pi\) | ||||
−0.999198 | + | 0.0400460i | \(0.987250\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.49613 | −0.292361 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05573 | 0.0876734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.9443i | 1.15010i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 15.1437i | − 1.24062i | −0.784357 | − | 0.620310i | \(-0.787007\pi\) | ||||
0.784357 | − | 0.620310i | \(-0.212993\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | − 32.3607i | − 2.59927i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.746512i | 0.0595782i | 0.999556 | + | 0.0297891i | \(0.00948357\pi\) | ||||
−0.999556 | + | 0.0297891i | \(0.990516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.32300 | 0.422142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.8885 | −2.04030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.52786i | 0.432976i | 0.976285 | + | 0.216488i | \(0.0694602\pi\) | ||||
−0.976285 | + | 0.216488i | \(0.930540\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.81758i | 0.608598i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | − 2.47214i | − 0.189049i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.48683i | 0.721271i | 0.932707 | + | 0.360635i | \(0.117440\pi\) | ||||
−0.932707 | + | 0.360635i | \(0.882560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.8825 | 1.72975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.94427 | −0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5563i | 1.15629i | 0.815933 | + | 0.578147i | \(0.196224\pi\) | ||||
−0.815933 | + | 0.578147i | \(0.803776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5672 | 0.781150 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.58359 | 0.484035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.0000i | − 1.17004i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.57649i | 0.332891i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.16073 | −0.156345 | −0.0781723 | − | 0.996940i | \(-0.524908\pi\) | ||||
−0.0781723 | + | 0.996940i | \(0.524908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9443 | −0.931749 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.47214i | 0.320256i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2967i | 1.73107i | 0.500852 | + | 0.865533i | \(0.333020\pi\) | ||||
−0.500852 | + | 0.865533i | \(0.666980\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 1.52786i | − 0.107235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.4667i | 1.42946i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.65685 | −0.393179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.11146 | −0.422738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9443i | 1.71723i | 0.512617 | + | 0.858617i | \(0.328676\pi\) | ||||
−0.512617 | + | 0.858617i | \(0.671324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.49613i | 0.239551i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.1158 | −2.25848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −46.8328 | −3.17922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9443i | 1.00984i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.15298i | − 0.615696i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2333 | 0.685275 | 0.342638 | − | 0.939468i | \(-0.388680\pi\) | ||||
0.342638 | + | 0.939468i | \(0.388680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.52786i | − 0.366897i | −0.983029 | − | 0.183449i | \(-0.941274\pi\) | ||||
0.983029 | − | 0.183449i | \(-0.0587261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.2349i | − 0.742423i | −0.928548 | − | 0.371211i | \(-0.878943\pi\) | ||||
0.928548 | − | 0.371211i | \(-0.121057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3137 | 0.744387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.08036i | 0.0701771i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4744 | 0.871589 | 0.435794 | − | 0.900046i | \(-0.356467\pi\) | ||||
0.435794 | + | 0.900046i | \(0.356467\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 44.0957i | − 2.81717i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.49613 | −0.222453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.47214 | −0.156665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4164i | 0.973075i | 0.873660 | + | 0.486538i | \(0.161740\pi\) | ||||
−0.873660 | + | 0.486538i | \(0.838260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.9845i | 0.879199i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 9.52786i | − 0.592033i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 0.333851i | − 0.0206648i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 11.6476i | − 0.710164i | −0.934835 | − | 0.355082i | \(-0.884453\pi\) | ||||
0.934835 | − | 0.355082i | \(-0.115547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.07262 | −0.490377 | −0.245188 | − | 0.969475i | \(-0.578850\pi\) | ||||
−0.245188 | + | 0.969475i | \(0.578850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.47214 | 0.391711 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 12.3607i | − 0.745377i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.3848i | 1.10463i | 0.833634 | + | 0.552317i | \(0.186256\pi\) | ||||
−0.833634 | + | 0.552317i | \(0.813744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.2333 | −0.612654 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.8885 | 1.90231 | 0.951156 | − | 0.308712i | \(-0.0998980\pi\) | ||||
0.951156 | + | 0.308712i | \(0.0998980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8328i | 1.59505i | 0.603289 | + | 0.797523i | \(0.293857\pi\) | ||||
−0.603289 | + | 0.797523i | \(0.706143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.81758i | 0.463073i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.6197 | 1.74839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.94427i | 0.289838i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 16.6367i | − 0.971927i | −0.873979 | − | 0.485964i | \(-0.838469\pi\) | ||||
0.873979 | − | 0.485964i | \(-0.161531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2843 | 1.64677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.47214 | 0.143448 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000i | 0.462652i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.9256i | 2.76239i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.99070 | 0.344157 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.4164 | −1.91342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.8885i | 1.70583i | 0.522050 | + | 0.852915i | \(0.325167\pi\) | ||||
−0.522050 | + | 0.852915i | \(0.674833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.57649i | 0.260347i | ||||||||
\(310\) | 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 | \(-0.527524\pi\) | ||||
−0.0863600 | + | 0.996264i | \(0.527524\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 14.4721i | − 0.815412i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 10.9799i | − 0.616690i | −0.951275 | − | 0.308345i | \(-0.900225\pi\) | ||||
0.951275 | − | 0.308345i | \(-0.0997752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.825324 | −0.0462093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9443 | 0.945737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 16.0000i | − 0.890264i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.07107i | − 0.392232i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.40647 | 0.464879 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 0.944272i | − 0.0519019i | −0.999663 | − | 0.0259509i | \(-0.991739\pi\) | ||||
0.999663 | − | 0.0259509i | \(-0.00826137\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.08191i | − 0.114088i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 2.00000i | − 0.108625i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2982i | 1.36998i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.7804 | −1.71598 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.8885 | 0.963087 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 13.5279i | − 0.726214i | −0.931747 | − | 0.363107i | \(-0.881716\pi\) | ||||
0.931747 | − | 0.363107i | \(-0.118284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8809i | 1.17126i | 0.810579 | + | 0.585629i | \(0.199152\pi\) | ||||
−0.810579 | + | 0.585629i | \(0.800848\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | − 11.0557i | − 0.586777i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.6197i | 1.56764i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 4.88854i | 0.256582i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 47.2579i | − 2.47359i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.3786 | −1.37695 | −0.688475 | − | 0.725260i | \(-0.741720\pi\) | ||||
−0.688475 | + | 0.725260i | \(0.741720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.47214 | 0.336926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.3607i | 1.26474i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.23179i | 0.478004i | 0.971019 | + | 0.239002i | \(0.0768203\pi\) | ||||
−0.971019 | + | 0.239002i | \(0.923180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.472136 | −0.0243162 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.583592i | 0.0299771i | 0.999888 | + | 0.0149886i | \(0.00477118\pi\) | ||||
−0.999888 | + | 0.0149886i | \(0.995229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 8.07262i | − 0.413573i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.7804 | −1.62390 | −0.811951 | − | 0.583725i | \(-0.801595\pi\) | ||||
−0.811951 | + | 0.583725i | \(0.801595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −35.7771 | −1.82337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4721i | 0.532329i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 10.8222i | − 0.548709i | −0.961629 | − | 0.274355i | \(-0.911536\pi\) | ||||
0.961629 | − | 0.274355i | \(-0.0884642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.6119 | −1.85154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.944272 | 0.0476322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3.41641i | − 0.171898i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 28.8732i | − 1.44910i | −0.689221 | − | 0.724551i | \(-0.742047\pi\) | ||||
0.689221 | − | 0.724551i | \(-0.257953\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 14.4721i | 0.720908i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.16228i | − 0.157135i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.14678 | −0.255116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.94427 | −0.244479 | −0.122239 | − | 0.992501i | \(-0.539008\pi\) | ||||
−0.122239 | + | 0.992501i | \(0.539008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.47214i | 0.319247i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 40.9334i | − 2.01420i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.81758 | 0.383750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.944272 | −0.0462412 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10.4721i | − 0.511597i | −0.966730 | − | 0.255799i | \(-0.917662\pi\) | ||||
0.966730 | − | 0.255799i | \(-0.0823384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.07107i | 0.344623i | 0.985043 | + | 0.172311i | \(0.0551235\pi\) | ||||
−0.985043 | + | 0.172311i | \(0.944876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.3607 | 1.56972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.3607i | 2.34034i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.49613i | − 0.168795i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.99226 | 0.336805 | 0.168403 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168403 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05573i | 0.0506183i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9845i | 0.668970i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 15.4164i | − 0.732456i | −0.930525 | − | 0.366228i | \(-0.880649\pi\) | ||||
0.930525 | − | 0.366228i | \(-0.119351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 31.6228i | − 1.49906i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 16.0000i | − 0.753411i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5687i | 0.543547i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.4667 | −0.959493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.9443 | −0.979732 | −0.489866 | − | 0.871798i | \(-0.662954\pi\) | ||||
−0.489866 | + | 0.871798i | \(0.662954\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.47214i | 0.302093i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.49458i | − 0.116184i | −0.998311 | − | 0.0580920i | \(-0.981498\pi\) | ||||
0.998311 | − | 0.0580920i | \(-0.0185017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.08036 | −0.0502087 | −0.0251044 | − | 0.999685i | \(-0.507992\pi\) | ||||
−0.0251044 | + | 0.999685i | \(0.507992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.3607 | 1.50069 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 31.4164i | − 1.45378i | −0.686755 | − | 0.726889i | \(-0.740965\pi\) | ||||
0.686755 | − | 0.726889i | \(-0.259035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 54.9179i | − 2.53587i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.746512 | −0.0343975 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.8885 | 1.19036 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 12.3607i | − 0.567147i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.32300i | 0.243724i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.15298 | −0.418210 | −0.209105 | − | 0.977893i | \(-0.567055\pi\) | ||||
−0.209105 | + | 0.977893i | \(0.567055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.94427 | −0.134247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 25.8885i | − 1.17797i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 15.6352i | − 0.709956i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 13.8885i | 0.626781i | 0.949624 | + | 0.313391i | \(0.101465\pi\) | ||||
−0.949624 | + | 0.313391i | \(0.898535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.16073i | − 0.0973142i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.81758 | −0.351374 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 7.05573i | − 0.315858i | −0.987450 | − | 0.157929i | \(-0.949518\pi\) | ||||
0.987450 | − | 0.157929i | \(-0.0504817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.81758i | 0.349264i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 11.0000i | 0.488527i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.6073i | 1.48962i | 0.667279 | + | 0.744808i | \(0.267459\pi\) | ||||
−0.667279 | + | 0.744808i | \(0.732541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −68.3923 | −3.02550 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47214 | 0.109147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 14.4721i | − 0.637719i | ||||||||
\(516\) | 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 | \(-0.616673\pi\) | ||||
−0.358387 | + | 0.933573i | \(0.616673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.3607i | − 1.24013i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) | ||||
0.784552 | − | 0.620063i | \(-0.212893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.8825i | 0.998672i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −66.2316 | −2.88509 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8.94427i | − 0.388148i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.15298i | − 0.396460i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.5825 | −2.31657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.4721i | 1.48482i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8840i | 1.02685i | 0.858133 | + | 0.513427i | \(0.171624\pi\) | ||||
−0.858133 | + | 0.513427i | \(0.828376\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.5563 | −0.667587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5836 | −1.13872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12.3607i | − 0.528505i | −0.964454 | − | 0.264252i | \(-0.914875\pi\) | ||||
0.964454 | − | 0.264252i | \(-0.0851251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5672i | 0.450997i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.825324 | −0.0351600 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.94427 | −0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.58359i | 0.279458i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15.8114i | − 0.669950i | −0.942227 | − | 0.334975i | \(-0.891272\pi\) | ||||
0.942227 | − | 0.334975i | \(-0.108728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.8098 | 0.626389 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.4721i | 0.441348i | 0.975348 | + | 0.220674i | \(0.0708257\pi\) | ||||
−0.975348 | + | 0.220674i | \(0.929174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32456i | 0.266076i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.57649 | −0.192195 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.4164 | 0.813978 | 0.406989 | − | 0.913433i | \(-0.366579\pi\) | ||||
0.406989 | + | 0.913433i | \(0.366579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 8.94427i | − 0.374306i | −0.982331 | − | 0.187153i | \(-0.940074\pi\) | ||||
0.982331 | − | 0.187153i | \(-0.0599260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.16073i | − 0.0902656i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 12.9443i | − 0.537946i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 11.3137i | − 0.469372i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1592 | 0.544998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0557i | 0.621416i | 0.950505 | + | 0.310708i | \(0.100566\pi\) | ||||
−0.950505 | + | 0.310708i | \(0.899434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.2982i | 1.04240i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 93.6656i | − 3.83992i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.7295i | 0.561910i | ||||||||
\(598\) | 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 | \(-0.571655\pi\) | ||||
−0.223213 | + | 0.974770i | \(0.571655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 12.0000i | − 0.488678i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 15.4589i | − 0.628495i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8685 | 1.04997 | 0.524985 | − | 0.851111i | \(-0.324071\pi\) | ||||
0.524985 | + | 0.851111i | \(0.324071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.52786 | 0.0619122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.08191i | − 0.0840877i | −0.999116 | − | 0.0420439i | \(-0.986613\pi\) | ||||
0.999116 | − | 0.0420439i | \(-0.0133869\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.4667 | −0.825297 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.8885 | −0.800683 | −0.400341 | − | 0.916366i | \(-0.631108\pi\) | ||||
−0.400341 | + | 0.916366i | \(0.631108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 29.8885i | − 1.20132i | −0.799504 | − | 0.600661i | \(-0.794904\pi\) | ||||
0.799504 | − | 0.600661i | \(-0.205096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.65685i | − 0.227002i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.7649 | −1.83353 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6.11146i | − 0.244068i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 13.4744i | − 0.537261i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 25.5279i | 1.01304i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7202i | 0.781342i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 36.3607i | 1.43393i | 0.697112 | + | 0.716963i | \(0.254468\pi\) | ||||
−0.697112 | + | 0.716963i | \(0.745532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 33.1158i | − 1.30393i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | − 46.8328i | − 1.83552i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 6.81603i | − 0.266732i | −0.991067 | − | 0.133366i | \(-0.957421\pi\) | ||||
0.991067 | − | 0.133366i | \(-0.0425785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.98605 | −0.116675 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.9443 | −0.583032 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 4.00000i | − 0.155818i | −0.996960 | − | 0.0779089i | \(-0.975176\pi\) | ||||
0.996960 | − | 0.0779089i | \(-0.0248243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2.23954i | − 0.0871079i | −0.999051 | − | 0.0435540i | \(-0.986132\pi\) | ||||
0.999051 | − | 0.0435540i | \(-0.0138680\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.15298 | 0.355472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −35.7771 | −1.38738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88854i | 0.0731247i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.2333i | 0.395644i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 5.00000i | 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 44.7634i | − 1.72040i | −0.509960 | − | 0.860198i | \(-0.670340\pi\) | ||||
0.509960 | − | 0.860198i | \(-0.329660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6274 | −0.868361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.52786 | 0.211828 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.4164i | 0.896004i | 0.894033 | + | 0.448002i | \(0.147864\pi\) | ||||
−0.894033 | + | 0.448002i | \(0.852136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20.4667i | − 0.781992i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.2349 | 0.428638 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.52786 | 0.286789 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 34.4721i | − 1.31138i | −0.755029 | − | 0.655691i | \(-0.772377\pi\) | ||||
0.755029 | − | 0.655691i | \(-0.227623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.3137i | 0.429772i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.98605 | 0.113267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.8885 | 1.58664 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0000i | 0.378235i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.98760i | 0.150610i | 0.997161 | + | 0.0753048i | \(0.0239930\pi\) | ||||
−0.997161 | + | 0.0753048i | \(0.976007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.14678 | −0.194114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.4164i | 1.03110i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.56409i | 0.321631i | 0.986984 | + | 0.160816i | \(0.0514125\pi\) | ||||
−0.986984 | + | 0.160816i | \(0.948588\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.08036 | −0.0405168 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.8885 | 2.16794 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0557i | 0.413461i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4744i | 0.503212i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.1452 | −0.602116 | −0.301058 | − | 0.953606i | \(-0.597340\pi\) | ||||
−0.301058 | + | 0.953606i | \(0.597340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.9443 | −0.780005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.66925i | − 0.0619945i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 67.7771i | 2.50683i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.73567i | 0.211852i | 0.994374 | + | 0.105926i | \(0.0337806\pi\) | ||||
−0.994374 | + | 0.105926i | \(0.966219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 44.0957 | 1.62649 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.6656 | −1.09275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 15.0557i | − 0.553834i | −0.960894 | − | 0.276917i | \(-0.910687\pi\) | ||||
0.960894 | − | 0.276917i | \(-0.0893127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 3.49613i | − 0.128433i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 2.47214i | − 0.0904507i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 77.5453i | 2.83344i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.08036 | −0.0394230 | −0.0197115 | − | 0.999806i | \(-0.506275\pi\) | ||||
−0.0197115 | + | 0.999806i | \(0.506275\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4164 | −0.561805 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 36.5836i | − 1.33141i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2349i | 0.408339i | 0.978936 | + | 0.204170i | \(0.0654494\pi\) | ||||
−0.978936 | + | 0.204170i | \(0.934551\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.9845 | −0.507606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.4164 | −0.703844 | −0.351922 | − | 0.936029i | \(-0.614472\pi\) | ||||
−0.351922 | + | 0.936029i | \(0.614472\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.4721i | 1.39278i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 20.4667i | − 0.739975i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 14.0000i | − 0.504198i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.3153i | 0.442949i | 0.975166 | + | 0.221475i | \(0.0710870\pi\) | ||||
−0.975166 | + | 0.221475i | \(0.928913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −51.1667 | −1.83796 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.52786 | 0.341810 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 16.0000i | − 0.573259i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.64290i | 0.309267i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.333851 | 0.0119308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.36068 | 0.0842563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.52786i | − 0.197047i | −0.995135 | − | 0.0985235i | \(-0.968588\pi\) | ||||
0.995135 | − | 0.0985235i | \(-0.0314120\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 12.6491i | − 0.450320i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.15298 | 0.325443 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9443 | 0.530687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 16.8328i | − 0.596998i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 39.1065i | − 1.38522i | −0.721311 | − | 0.692612i | \(-0.756460\pi\) | ||||
0.721311 | − | 0.692612i | \(-0.243540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | −0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9443i | 1.30374i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 81.8668i | 2.88542i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6476 | 0.410013 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.41641 | −0.120115 | −0.0600573 | − | 0.998195i | \(-0.519128\pi\) | ||||
−0.0600573 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.3050i | 1.16950i | 0.811215 | + | 0.584748i | \(0.198806\pi\) | ||||
−0.811215 | + | 0.584748i | \(0.801194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 8.07262i | − 0.283119i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.4806 | 0.612320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.8885 | 0.905725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.47214i | 0.226155i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 44.6057i | − 1.55675i | −0.627799 | − | 0.778375i | \(-0.716044\pi\) | ||||
0.627799 | − | 0.778375i | \(-0.283956\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − 53.8885i | − 1.87389i | −0.349479 | − | 0.936944i | \(-0.613641\pi\) | ||||
0.349479 | − | 0.936944i | \(-0.386359\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 19.7202i | − 0.684910i | −0.939534 | − | 0.342455i | \(-0.888742\pi\) | ||||
0.939534 | − | 0.342455i | \(-0.111258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.3848 | −0.637761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −90.2492 | −3.12695 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 24.7214i | − 0.855518i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 10.2333i | − 0.353716i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 31.8885i | 1.09830i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 34.7851i | − 1.19664i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.3724 | −0.768724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.8328 | −0.920900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.7771i | 0.403713i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 17.7171i | − 0.606621i | −0.952892 | − | 0.303311i | \(-0.901908\pi\) | ||||
0.952892 | − | 0.303311i | \(-0.0980920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.81758 | −0.267356 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5836 | −0.976397 | −0.488198 | − | 0.872733i | \(-0.662346\pi\) | ||||
−0.488198 | + | 0.872733i | \(0.662346\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.5279i | 1.55339i | 0.629876 | + | 0.776695i | \(0.283106\pi\) | ||||
−0.629876 | + | 0.776695i | \(0.716894\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.6197i | 1.00944i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.4512 | −1.17273 | −0.586366 | − | 0.810046i | \(-0.699442\pi\) | ||||
−0.586366 | + | 0.810046i | \(0.699442\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.8885i | 0.845259i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.67080i | 0.0906008i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9706 | −0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.94427 | −0.167338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35.8654i | − 1.21109i | −0.795811 | − | 0.605545i | \(-0.792955\pi\) | ||||
0.795811 | − | 0.605545i | \(-0.207045\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 18.4721i | 0.621637i | 0.950469 | + | 0.310818i | \(0.100603\pi\) | ||||
−0.950469 | + | 0.310818i | \(0.899397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.2843i | 0.950765i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 2.47214i | 0.0828197i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9473 | 1.26844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.41641i | 0.113944i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4512i | 1.14774i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.9256 | −1.59487 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.1935 | 1.63525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.1935i | 1.69985i | 0.526902 | + | 0.849926i | \(0.323353\pi\) | ||||
−0.526902 | + | 0.849926i | \(0.676647\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.99070i | 0.198699i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.16073 | −0.0715880 | −0.0357940 | − | 0.999359i | \(-0.511396\pi\) | ||||
−0.0357940 | + | 0.999359i | \(0.511396\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.11146 | −0.202260 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 33.4164i | − 1.10471i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.32145i | 0.142707i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 4.94427i | 0.162743i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 10.4096i | − 0.342265i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 34.4721i | 1.12978i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 30.9551i | − 1.01342i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −50.5964 | −1.65468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 3.05573i | − 0.0997199i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 25.1220i | − 0.818954i | −0.912321 | − | 0.409477i | \(-0.865711\pi\) | ||||
0.912321 | − | 0.409477i | \(-0.134289\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.6119 | −1.19225 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.4721 | 0.470779 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 47.7771i | − 1.55255i | −0.630396 | − | 0.776273i | \(-0.717108\pi\) | ||||
0.630396 | − | 0.776273i | \(-0.282892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.1344i | 0.686051i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9799 | 0.356046 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.52786 | 0.308638 | 0.154319 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154319 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.83282i | 0.221105i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 0.825324i | − 0.0266789i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.6197 | −0.956469 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.7214 | 2.37811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9443i | 0.546022i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 40.9334i | 1.31769i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 20.3607i | 0.653405i | 0.945127 | + | 0.326703i | \(0.105938\pi\) | ||||
−0.945127 | + | 0.326703i | \(0.894062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.32145i | − 0.138539i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 24.7214i | 0.790098i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.40647i | 0.268398i | ||||||||
\(982\) | 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 | ||||||||
\(989\) | − 59.2393i | − 1.88370i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2256 | 0.547189 | 0.273595 | − | 0.961845i | \(-0.411787\pi\) | ||||
0.273595 | + | 0.961845i | \(0.411787\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.944272 | 0.0299656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 43.4164i | − 1.37639i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0308i | 0.919414i | 0.888071 | + | 0.459707i | \(0.152046\pi\) | ||||
−0.888071 | + | 0.459707i | \(0.847954\pi\) | |||||||
\(998\) | 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.d.g.1537.5 | 8 | ||
4.3 | odd | 2 | inner | 3072.2.d.g.1537.2 | 8 | ||
8.3 | odd | 2 | inner | 3072.2.d.g.1537.8 | 8 | ||
8.5 | even | 2 | inner | 3072.2.d.g.1537.3 | 8 | ||
16.3 | odd | 4 | 3072.2.a.q.1.1 | 4 | |||
16.5 | even | 4 | 3072.2.a.q.1.4 | 4 | |||
16.11 | odd | 4 | 3072.2.a.k.1.3 | 4 | |||
16.13 | even | 4 | 3072.2.a.k.1.2 | 4 | |||
32.3 | odd | 8 | 1536.2.j.h.385.4 | yes | 8 | ||
32.5 | even | 8 | 1536.2.j.h.1153.2 | yes | 8 | ||
32.11 | odd | 8 | 1536.2.j.g.1153.1 | yes | 8 | ||
32.13 | even | 8 | 1536.2.j.g.385.3 | yes | 8 | ||
32.19 | odd | 8 | 1536.2.j.g.385.1 | ✓ | 8 | ||
32.21 | even | 8 | 1536.2.j.g.1153.3 | yes | 8 | ||
32.27 | odd | 8 | 1536.2.j.h.1153.4 | yes | 8 | ||
32.29 | even | 8 | 1536.2.j.h.385.2 | yes | 8 | ||
48.5 | odd | 4 | 9216.2.a.bd.1.2 | 4 | |||
48.11 | even | 4 | 9216.2.a.bj.1.1 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bj.1.4 | 4 | |||
48.35 | even | 4 | 9216.2.a.bd.1.3 | 4 | |||
96.5 | odd | 8 | 4608.2.k.bg.1153.1 | 8 | |||
96.11 | even | 8 | 4608.2.k.bf.1153.4 | 8 | |||
96.29 | odd | 8 | 4608.2.k.bg.3457.2 | 8 | |||
96.35 | even | 8 | 4608.2.k.bg.3457.1 | 8 | |||
96.53 | odd | 8 | 4608.2.k.bf.1153.3 | 8 | |||
96.59 | even | 8 | 4608.2.k.bg.1153.2 | 8 | |||
96.77 | odd | 8 | 4608.2.k.bf.3457.4 | 8 | |||
96.83 | even | 8 | 4608.2.k.bf.3457.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.g.385.1 | ✓ | 8 | 32.19 | odd | 8 | ||
1536.2.j.g.385.3 | yes | 8 | 32.13 | even | 8 | ||
1536.2.j.g.1153.1 | yes | 8 | 32.11 | odd | 8 | ||
1536.2.j.g.1153.3 | yes | 8 | 32.21 | even | 8 | ||
1536.2.j.h.385.2 | yes | 8 | 32.29 | even | 8 | ||
1536.2.j.h.385.4 | yes | 8 | 32.3 | odd | 8 | ||
1536.2.j.h.1153.2 | yes | 8 | 32.5 | even | 8 | ||
1536.2.j.h.1153.4 | yes | 8 | 32.27 | odd | 8 | ||
3072.2.a.k.1.2 | 4 | 16.13 | even | 4 | |||
3072.2.a.k.1.3 | 4 | 16.11 | odd | 4 | |||
3072.2.a.q.1.1 | 4 | 16.3 | odd | 4 | |||
3072.2.a.q.1.4 | 4 | 16.5 | even | 4 | |||
3072.2.d.g.1537.2 | 8 | 4.3 | odd | 2 | inner | ||
3072.2.d.g.1537.3 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.g.1537.5 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.g.1537.8 | 8 | 8.3 | odd | 2 | inner | ||
4608.2.k.bf.1153.3 | 8 | 96.53 | odd | 8 | |||
4608.2.k.bf.1153.4 | 8 | 96.11 | even | 8 | |||
4608.2.k.bf.3457.3 | 8 | 96.83 | even | 8 | |||
4608.2.k.bf.3457.4 | 8 | 96.77 | odd | 8 | |||
4608.2.k.bg.1153.1 | 8 | 96.5 | odd | 8 | |||
4608.2.k.bg.1153.2 | 8 | 96.59 | even | 8 | |||
4608.2.k.bg.3457.1 | 8 | 96.35 | even | 8 | |||
4608.2.k.bg.3457.2 | 8 | 96.29 | odd | 8 | |||
9216.2.a.bd.1.2 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bd.1.3 | 4 | 48.35 | even | 4 | |||
9216.2.a.bj.1.1 | 4 | 48.11 | even | 4 | |||
9216.2.a.bj.1.4 | 4 | 48.29 | odd | 4 |