Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.381966 | 0.144370 | 0.0721848 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721848 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.47214 | 1.51770 | 0.758849 | − | 0.651267i | \(-0.225762\pi\) | ||||
0.758849 | + | 0.651267i | \(0.225762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.09017 | −1.23455 | −0.617274 | − | 0.786748i | \(-0.711763\pi\) | ||||
−0.617274 | + | 0.786748i | \(0.711763\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.76393 | 0.863505 | 0.431753 | − | 0.901992i | \(-0.357895\pi\) | ||||
0.431753 | + | 0.901992i | \(0.357895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.236068 | 0.0515143 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.381966 | −0.0796454 | −0.0398227 | − | 0.999207i | \(-0.512679\pi\) | ||||
−0.0398227 | + | 0.999207i | \(0.512679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.32624 | 1.54614 | 0.773072 | − | 0.634319i | \(-0.218719\pi\) | ||||
0.773072 | + | 0.634319i | \(0.218719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.70820 | 1.56404 | 0.782020 | − | 0.623254i | \(-0.214190\pi\) | ||||
0.782020 | + | 0.623254i | \(0.214190\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.618034 | −0.107586 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.38197 | 0.541548 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7082 | −1.67234 | −0.836170 | − | 0.548470i | \(-0.815210\pi\) | ||||
−0.836170 | + | 0.548470i | \(0.815210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.94427 | −1.05899 | −0.529496 | − | 0.848313i | \(-0.677619\pi\) | ||||
−0.529496 | + | 0.848313i | \(0.677619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.23607 | 0.326164 | 0.163082 | − | 0.986613i | \(-0.447856\pi\) | ||||
0.163082 | + | 0.986613i | \(0.447856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.14590 | −0.440514 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.61803 | 0.496975 | 0.248488 | − | 0.968635i | \(-0.420066\pi\) | ||||
0.248488 | + | 0.968635i | \(0.420066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.32624 | 0.308118 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7082 | 1.39409 | 0.697045 | − | 0.717028i | \(-0.254498\pi\) | ||||
0.697045 | + | 0.717028i | \(0.254498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.90983 | −0.244529 | −0.122264 | − | 0.992498i | \(-0.539016\pi\) | ||||
−0.122264 | + | 0.992498i | \(0.539016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.236068 | −0.0284192 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.18034 | −0.970828 | −0.485414 | − | 0.874284i | \(-0.661331\pi\) | ||||
−0.485414 | + | 0.874284i | \(0.661331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6180 | 1.35979 | 0.679894 | − | 0.733310i | \(-0.262026\pi\) | ||||
0.679894 | + | 0.733310i | \(0.262026\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.381966 | −0.0435291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.38197 | 0.830536 | 0.415268 | − | 0.909699i | \(-0.363688\pi\) | ||||
0.415268 | + | 0.909699i | \(0.363688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.5623 | 1.48866 | 0.744328 | − | 0.667814i | \(-0.232770\pi\) | ||||
0.744328 | + | 0.667814i | \(0.232770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.14590 | 0.551698 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3262 | −1.51858 | −0.759289 | − | 0.650753i | \(-0.774453\pi\) | ||||
−0.759289 | + | 0.650753i | \(0.774453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09017 | 0.219109 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.38197 | 0.558084 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3820 | 1.05413 | 0.527064 | − | 0.849825i | \(-0.323293\pi\) | ||||
0.527064 | + | 0.849825i | \(0.323293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.61803 | 0.263122 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6180 | −1.35505 | −0.677523 | − | 0.735502i | \(-0.736946\pi\) | ||||
−0.677523 | + | 0.735502i | \(0.736946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3262 | 1.21454 | 0.607270 | − | 0.794495i | \(-0.292265\pi\) | ||||
0.607270 | + | 0.794495i | \(0.292265\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1803 | 1.27419 | 0.637096 | − | 0.770785i | \(-0.280136\pi\) | ||||
0.637096 | + | 0.770785i | \(0.280136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.56231 | 0.341207 | 0.170604 | − | 0.985340i | \(-0.445428\pi\) | ||||
0.170604 | + | 0.985340i | \(0.445428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.145898 | 0.0138480 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.23607 | 0.774784 | 0.387392 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387392 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.3262 | −1.32446 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.94427 | −0.178231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.61803 | −0.596728 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.14590 | 0.190418 | 0.0952088 | − | 0.995457i | \(-0.469648\pi\) | ||||
0.0952088 | + | 0.995457i | \(0.469648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.29180 | −0.377872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5623 | 1.09757 | 0.548787 | − | 0.835962i | \(-0.315090\pi\) | ||||
0.548787 | + | 0.835962i | \(0.315090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.43769 | 0.124664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.56231 | −0.816963 | −0.408481 | − | 0.912767i | \(-0.633942\pi\) | ||||
−0.408481 | + | 0.912767i | \(0.633942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1803 | 0.948304 | 0.474152 | − | 0.880443i | \(-0.342755\pi\) | ||||
0.474152 | + | 0.880443i | \(0.342755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.38197 | 0.116383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.47214 | −0.457603 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.23607 | −0.349385 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.41641 | −0.607576 | −0.303788 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303788 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9443 | −1.29753 | −0.648763 | − | 0.760990i | \(-0.724713\pi\) | ||||
−0.648763 | + | 0.760990i | \(0.724713\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.3262 | 1.07736 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.47214 | −0.356915 | −0.178458 | − | 0.983948i | \(-0.557111\pi\) | ||||
−0.178458 | + | 0.983948i | \(0.557111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.23607 | 0.177332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.145898 | −0.0114984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.38197 | 0.499874 | 0.249937 | − | 0.968262i | \(-0.419590\pi\) | ||||
0.249937 | + | 0.968262i | \(0.419590\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.70820 | −0.519096 | −0.259548 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259548 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9443 | 1.30341 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.85410 | −0.753562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2918 | 0.858499 | 0.429250 | − | 0.903186i | \(-0.358778\pi\) | ||||
0.429250 | + | 0.903186i | \(0.358778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.61803 | 0.497442 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.09017 | −0.156227 | −0.0781133 | − | 0.996944i | \(-0.524890\pi\) | ||||
−0.0781133 | + | 0.996944i | \(0.524890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.38197 | 0.325709 | 0.162854 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162854 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18034 | −0.0872532 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.09017 | 0.372230 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32624 | −0.0964696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0344 | 0.870782 | 0.435391 | − | 0.900242i | \(-0.356610\pi\) | ||||
0.435391 | + | 0.900242i | \(0.356610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.52786 | 0.685831 | 0.342915 | − | 0.939366i | \(-0.388586\pi\) | ||||
0.342915 | + | 0.939366i | \(0.388586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0344 | 0.786171 | 0.393086 | − | 0.919502i | \(-0.371408\pi\) | ||||
0.393086 | + | 0.919502i | \(0.371408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6180 | 1.03624 | 0.518122 | − | 0.855306i | \(-0.326631\pi\) | ||||
0.518122 | + | 0.855306i | \(0.326631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.41641 | 0.523113 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.18034 | 0.223216 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.76393 | −0.260357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | 0.0688428 | 0.0344214 | − | 0.999407i | \(-0.489041\pi\) | ||||
0.0344214 | + | 0.999407i | \(0.489041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.05573 | −0.346413 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.32624 | 0.225800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.18034 | 0.485202 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.8541 | −1.87367 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.6525 | 1.71782 | 0.858908 | − | 0.512129i | \(-0.171143\pi\) | ||||
0.858908 | + | 0.512129i | \(0.171143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.8541 | −0.919529 | −0.459765 | − | 0.888041i | \(-0.652066\pi\) | ||||
−0.459765 | + | 0.888041i | \(0.652066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6180 | 0.833823 | 0.416912 | − | 0.908947i | \(-0.363112\pi\) | ||||
0.416912 | + | 0.908947i | \(0.363112\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.236068 | −0.0155321 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.5623 | −1.08503 | −0.542516 | − | 0.840045i | \(-0.682528\pi\) | ||||
−0.542516 | + | 0.840045i | \(0.682528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.56231 | 0.296354 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3820 | 1.44777 | 0.723885 | − | 0.689921i | \(-0.242355\pi\) | ||||
0.723885 | + | 0.689921i | \(0.242355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.145898 | 0.00939812 | 0.00469906 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469906 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.5967 | 1.31054 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.38197 | 0.531186 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5066 | −1.16812 | −0.584062 | − | 0.811709i | \(-0.698538\pi\) | ||||
−0.584062 | + | 0.811709i | \(0.698538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.381966 | 0.0240140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.05573 | 0.315368 | 0.157684 | − | 0.987490i | \(-0.449597\pi\) | ||||
0.157684 | + | 0.987490i | \(0.449597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0901699 | 0.00560289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.7984 | −1.34929 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4721 | 0.954053 | 0.477026 | − | 0.878889i | \(-0.341715\pi\) | ||||
0.477026 | + | 0.878889i | \(0.341715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.85410 | −0.541862 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.61803 | −0.159624 | −0.0798122 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798122 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7082 | −0.771968 | −0.385984 | − | 0.922505i | \(-0.626138\pi\) | ||||
−0.385984 | + | 0.922505i | \(0.626138\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.29180 | 0.0781831 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1246 | −1.56968 | −0.784838 | − | 0.619701i | \(-0.787254\pi\) | ||||
−0.784838 | + | 0.619701i | \(0.787254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.7984 | −1.36490 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.23607 | 0.252703 | 0.126351 | − | 0.991986i | \(-0.459673\pi\) | ||||
0.126351 | + | 0.991986i | \(0.459673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.4508 | −1.63178 | −0.815892 | − | 0.578205i | \(-0.803754\pi\) | ||||
−0.815892 | + | 0.578205i | \(0.803754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.09017 | −0.241435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.90983 | 0.524108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.41641 | 0.376136 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5279 | −0.673465 | −0.336733 | − | 0.941600i | \(-0.609322\pi\) | ||||
−0.336733 | + | 0.941600i | \(0.609322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.47214 | 0.201474 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.09017 | −0.120878 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.65248 | −0.152886 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.41641 | −0.483510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8541 | 1.36143 | 0.680713 | − | 0.732550i | \(-0.261670\pi\) | ||||
0.680713 | + | 0.732550i | \(0.261670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.61803 | 0.433375 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.94427 | −0.337069 | −0.168534 | − | 0.985696i | \(-0.553903\pi\) | ||||
−0.168534 | + | 0.985696i | \(0.553903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6525 | −0.602114 | −0.301057 | − | 0.953606i | \(-0.597339\pi\) | ||||
−0.301057 | + | 0.953606i | \(0.597339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.38197 | 0.189950 | 0.0949751 | − | 0.995480i | \(-0.469723\pi\) | ||||
0.0949751 | + | 0.995480i | \(0.469723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.32624 | −0.466180 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.14590 | 0.454660 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.1591 | −1.06604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.20163 | 0.121750 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.854102 | 0.0470882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3607 | −0.734369 | −0.367185 | − | 0.930148i | \(-0.619678\pi\) | ||||
−0.367185 | + | 0.930148i | \(0.619678\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.618034 | −0.0338681 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.8885 | 1.95497 | 0.977487 | − | 0.210997i | \(-0.0676709\pi\) | ||||
0.977487 | + | 0.210997i | \(0.0676709\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.09017 | 0.276460 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.70820 | −0.471576 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.29180 | −0.285730 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.61803 | −0.194226 | −0.0971131 | − | 0.995273i | \(-0.530961\pi\) | ||||
−0.0971131 | + | 0.995273i | \(0.530961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.12461 | −0.434900 | −0.217450 | − | 0.976071i | \(-0.569774\pi\) | ||||
−0.217450 | + | 0.976071i | \(0.569774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.0000 | −1.01414 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3607 | 1.03047 | 0.515233 | − | 0.857050i | \(-0.327706\pi\) | ||||
0.515233 | + | 0.857050i | \(0.327706\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.20163 | −0.0635968 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.8885 | −1.68301 | −0.841506 | − | 0.540247i | \(-0.818331\pi\) | ||||
−0.841506 | + | 0.540247i | \(0.818331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.83282 | −0.254359 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.618034 | 0.0324384 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.9787 | −1.87807 | −0.939037 | − | 0.343817i | \(-0.888280\pi\) | ||||
−0.939037 | + | 0.343817i | \(0.888280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.0344 | 1.45941 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.38197 | 0.0717481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4164 | 0.746453 | 0.373227 | − | 0.927740i | \(-0.378251\pi\) | ||||
0.373227 | + | 0.927740i | \(0.378251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45.5623 | 2.34658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.4721 | −1.51388 | −0.756941 | − | 0.653483i | \(-0.773307\pi\) | ||||
−0.756941 | + | 0.653483i | \(0.773307\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.32624 | 0.0679452 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9443 | 0.968007 | 0.484004 | − | 0.875066i | \(-0.339182\pi\) | ||||
0.484004 | + | 0.875066i | \(0.339182\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.1803 | 0.924159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.9443 | 1.67034 | 0.835170 | − | 0.549991i | \(-0.185369\pi\) | ||||
0.835170 | + | 0.549991i | \(0.185369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94427 | 0.0983261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.76393 | 0.391639 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7984 | −1.24459 | −0.622297 | − | 0.782781i | \(-0.713801\pi\) | ||||
−0.622297 | + | 0.782781i | \(0.713801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.888544 | 0.0444828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.472136 | 0.0235773 | 0.0117887 | − | 0.999931i | \(-0.496247\pi\) | ||||
0.0117887 | + | 0.999931i | \(0.496247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.6525 | 2.37374 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.236068 | −0.0117015 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5279 | −1.01504 | −0.507519 | − | 0.861641i | \(-0.669437\pi\) | ||||
−0.507519 | + | 0.861641i | \(0.669437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.90983 | −0.291510 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.09017 | 0.201264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.90983 | 0.338376 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.5279 | 0.612026 | 0.306013 | − | 0.952027i | \(-0.401005\pi\) | ||||
0.306013 | + | 0.952027i | \(0.401005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.67376 | 0.227785 | 0.113893 | − | 0.993493i | \(-0.463668\pi\) | ||||
0.113893 | + | 0.993493i | \(0.463668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.85410 | −0.284636 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.729490 | −0.0353025 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.38197 | −0.163283 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.76393 | 0.277639 | 0.138819 | − | 0.990318i | \(-0.455669\pi\) | ||||
0.138819 | + | 0.990318i | \(0.455669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.8885 | 0.523270 | 0.261635 | − | 0.965167i | \(-0.415738\pi\) | ||||
0.261635 | + | 0.965167i | \(0.415738\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.43769 | −0.0687742 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9230 | −1.14178 | −0.570891 | − | 0.821026i | \(-0.693402\pi\) | ||||
−0.570891 | + | 0.821026i | \(0.693402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.9443 | 0.854489 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2918 | 1.15414 | 0.577069 | − | 0.816695i | \(-0.304196\pi\) | ||||
0.577069 | + | 0.816695i | \(0.304196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.58359 | −0.216796 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.72949 | 0.364777 | 0.182389 | − | 0.983227i | \(-0.441617\pi\) | ||||
0.182389 | + | 0.983227i | \(0.441617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7082 | 0.504230 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.85410 | −0.462986 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1459 | 0.895607 | 0.447804 | − | 0.894132i | \(-0.352206\pi\) | ||||
0.447804 | + | 0.894132i | \(0.352206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.6738 | 0.824941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.88854 | 0.320831 | 0.160416 | − | 0.987050i | \(-0.448717\pi\) | ||||
0.160416 | + | 0.987050i | \(0.448717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2361 | −1.68403 | −0.842016 | − | 0.539452i | \(-0.818631\pi\) | ||||
−0.842016 | + | 0.539452i | \(0.818631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.7082 | −1.60610 | −0.803052 | − | 0.595909i | \(-0.796792\pi\) | ||||
−0.803052 | + | 0.595909i | \(0.796792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.58359 | 0.211651 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.76393 | −0.127355 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.94427 | 0.319298 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.47214 | −0.433699 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.41641 | 0.201791 | 0.100895 | − | 0.994897i | \(-0.467829\pi\) | ||||
0.100895 | + | 0.994897i | \(0.467829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.29180 | 0.0589008 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0901699 | −0.00410287 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1803 | 1.14103 | 0.570515 | − | 0.821287i | \(-0.306744\pi\) | ||||
0.570515 | + | 0.821287i | \(0.306744\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.94427 | 0.178366 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.65248 | 0.345351 | 0.172676 | − | 0.984979i | \(-0.444759\pi\) | ||||
0.172676 | + | 0.984979i | \(0.444759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.3820 | −1.90879 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.12461 | −0.140158 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.5623 | −1.81582 | −0.907909 | − | 0.419167i | \(-0.862322\pi\) | ||||
−0.907909 | + | 0.419167i | \(0.862322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.14590 | −0.185225 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.1803 | 1.25650 | 0.628250 | − | 0.778012i | \(-0.283772\pi\) | ||||
0.628250 | + | 0.778012i | \(0.283772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.4721 | 0.465084 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8541 | 1.19029 | 0.595144 | − | 0.803619i | \(-0.297095\pi\) | ||||
0.595144 | + | 0.803619i | \(0.297095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.43769 | 0.196312 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.0689 | −0.577005 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.23607 | −0.0983422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.97871 | 0.306332 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.76393 | 0.121090 | 0.0605450 | − | 0.998165i | \(-0.480716\pi\) | ||||
0.0605450 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4164 | 0.761566 | 0.380783 | − | 0.924664i | \(-0.375654\pi\) | ||||
0.380783 | + | 0.924664i | \(0.375654\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −44.3262 | −1.93088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8541 | −0.993657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.0344 | −1.21659 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58.5967 | −2.53811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.29180 | −0.0557451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.85410 | 0.295227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.4508 | 1.73912 | 0.869559 | − | 0.493829i | \(-0.164403\pi\) | ||||
0.869559 | + | 0.493829i | \(0.164403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.70820 | 0.116220 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.67376 | 0.114322 | 0.0571609 | − | 0.998365i | \(-0.481795\pi\) | ||||
0.0571609 | + | 0.998365i | \(0.481795\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.00000 | 0.213395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.3394 | 1.33510 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.81966 | 0.119904 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.47214 | −0.316605 | −0.158302 | − | 0.987391i | \(-0.550602\pi\) | ||||
−0.158302 | + | 0.987391i | \(0.550602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.0000 | −1.60723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.14590 | 0.132820 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03444 | 0.0435965 | 0.0217983 | − | 0.999762i | \(-0.493061\pi\) | ||||
0.0217983 | + | 0.999762i | \(0.493061\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.18034 | 0.0915657 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.2016 | −0.846896 | −0.423448 | − | 0.905920i | \(-0.639180\pi\) | ||||
−0.423448 | + | 0.905920i | \(0.639180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.1591 | 1.42951 | 0.714756 | − | 0.699374i | \(-0.246538\pi\) | ||||
0.714756 | + | 0.699374i | \(0.246538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.43769 | 0.310714 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.7426 | 1.23820 | 0.619101 | − | 0.785311i | \(-0.287497\pi\) | ||||
0.619101 | + | 0.785311i | \(0.287497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.88854 | 0.244720 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.18034 | 0.214917 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.61803 | −0.149844 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.20163 | −0.297243 | −0.148621 | − | 0.988894i | \(-0.547484\pi\) | ||||
−0.148621 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.7771 | 1.35056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.81966 | 0.280523 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.3475 | −0.671312 | −0.335656 | − | 0.941985i | \(-0.608958\pi\) | ||||
−0.335656 | + | 0.941985i | \(0.608958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.03444 | 0.369755 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.3951 | 1.40535 | 0.702673 | − | 0.711513i | \(-0.251990\pi\) | ||||
0.702673 | + | 0.711513i | \(0.251990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.67376 | 0.190647 | 0.0953234 | − | 0.995446i | \(-0.469611\pi\) | ||||
0.0953234 | + | 0.995446i | \(0.469611\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.4164 | −1.27938 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.83282 | −0.358513 | −0.179256 | − | 0.983802i | \(-0.557369\pi\) | ||||
−0.179256 | + | 0.983802i | \(0.557369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.96556 | 0.0796484 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.2361 | 0.495018 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.3262 | 1.87110 | 0.935550 | − | 0.353195i | \(-0.114905\pi\) | ||||
0.935550 | + | 0.353195i | \(0.114905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2361 | −0.532864 | −0.266432 | − | 0.963854i | \(-0.585845\pi\) | ||||
−0.266432 | + | 0.963854i | \(0.585845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.7082 | −1.63620 | −0.818100 | − | 0.575075i | \(-0.804973\pi\) | ||||
−0.818100 | + | 0.575075i | \(0.804973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.32624 | 0.0532201 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.47214 | −0.219236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.32624 | −0.0929010 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.20163 | −0.0479120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.4508 | −1.53070 | −0.765352 | − | 0.643612i | \(-0.777435\pi\) | ||||
−0.765352 | + | 0.643612i | \(0.777435\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.618034 | 0.0245646 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.5066 | −1.48606 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.4164 | 0.847220 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4164 | −0.411423 | −0.205712 | − | 0.978613i | \(-0.565951\pi\) | ||||
−0.205712 | + | 0.978613i | \(0.565951\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.4164 | −1.00233 | −0.501163 | − | 0.865353i | \(-0.667094\pi\) | ||||
−0.501163 | + | 0.865353i | \(0.667094\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.4164 | −0.645396 | −0.322698 | − | 0.946502i | \(-0.604590\pi\) | ||||
−0.322698 | + | 0.946502i | \(0.604590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.7082 | −0.420334 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.05573 | 0.0805703 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.3820 | −1.85420 | −0.927100 | − | 0.374815i | \(-0.877706\pi\) | ||||
−0.927100 | + | 0.374815i | \(0.877706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.4164 | −1.18666 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7426 | 0.769064 | 0.384532 | − | 0.923112i | \(-0.374363\pi\) | ||||
0.384532 | + | 0.923112i | \(0.374363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5967 | 1.03449 | 0.517247 | − | 0.855836i | \(-0.326957\pi\) | ||||
0.517247 | + | 0.855836i | \(0.326957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.2148 | −0.668567 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.18034 | −0.123143 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.8541 | 0.612955 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.90983 | 0.0737282 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5967 | 0.716852 | 0.358426 | − | 0.933558i | \(-0.383314\pi\) | ||||
0.358426 | + | 0.933558i | \(0.383314\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.59675 | −0.0613680 | −0.0306840 | − | 0.999529i | \(-0.509769\pi\) | ||||
−0.0306840 | + | 0.999529i | \(0.509769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.96556 | 0.152184 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.56231 | −0.328108 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.18034 | 0.0451645 | 0.0225822 | − | 0.999745i | \(-0.492811\pi\) | ||||
0.0225822 | + | 0.999745i | \(0.492811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.79837 | 0.297527 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.7984 | 0.754258 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.6312 | −1.54568 | −0.772842 | − | 0.634599i | \(-0.781165\pi\) | ||||
−0.772842 | + | 0.634599i | \(0.781165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.5066 | 2.06458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2361 | −0.387164 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.5279 | −1.41741 | −0.708704 | − | 0.705506i | \(-0.750720\pi\) | ||||
−0.708704 | + | 0.705506i | \(0.750720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.888544 | 0.0335121 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.20163 | −0.195627 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3607 | −0.914885 | −0.457442 | − | 0.889239i | \(-0.651234\pi\) | ||||
−0.457442 | + | 0.889239i | \(0.651234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.3262 | −0.724791 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.32624 | −0.124569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.8328 | 0.516596 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.8328 | −1.85845 | −0.929225 | − | 0.369514i | \(-0.879524\pi\) | ||||
−0.929225 | + | 0.369514i | \(0.879524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.70820 | 0.175343 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0901699 | 0.00335346 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0902 | 0.485488 | 0.242744 | − | 0.970090i | \(-0.421953\pi\) | ||||
0.242744 | + | 0.970090i | \(0.421953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3475 | 1.30738 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.12461 | 0.152346 | 0.0761730 | − | 0.997095i | \(-0.475730\pi\) | ||||
0.0761730 | + | 0.997095i | \(0.475730\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.85410 | 0.104990 | 0.0524949 | − | 0.998621i | \(-0.483283\pi\) | ||||
0.0524949 | + | 0.998621i | \(0.483283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.7295 | 0.467630 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.2148 | 1.73214 | 0.866071 | − | 0.499921i | \(-0.166638\pi\) | ||||
0.866071 | + | 0.499921i | \(0.166638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.5066 | −1.29912 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.03444 | 0.183955 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0344419 | 0.00125680 | 0.000628401 | − | 1.00000i | \(-0.499800\pi\) | ||||
0.000628401 | 1.00000i | \(0.499800\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4377 | −0.416813 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.88854 | 0.177677 | 0.0888386 | − | 0.996046i | \(-0.471684\pi\) | ||||
0.0888386 | + | 0.996046i | \(0.471684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.236068 | 0.00856872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00000 | 0.290000 | 0.145000 | − | 0.989432i | \(-0.453682\pi\) | ||||
0.145000 | + | 0.989432i | \(0.453682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36068 | 0.0492599 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.5967 | 2.11581 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.6525 | −1.50203 | −0.751013 | − | 0.660287i | \(-0.770435\pi\) | ||||
−0.751013 | + | 0.660287i | \(0.770435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.12461 | 0.112530 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.6312 | −1.74914 | −0.874571 | − | 0.484897i | \(-0.838857\pi\) | ||||
−0.874571 | + | 0.484897i | \(0.838857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0557281 | 0.00199923 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.3050 | −1.44407 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.18034 | 0.292716 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.9098 | −1.03315 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.76393 | 0.0628774 | 0.0314387 | − | 0.999506i | \(-0.489991\pi\) | ||||
0.0314387 | + | 0.999506i | \(0.489991\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.56231 | 0.340427 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.14590 | 0.111855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.4508 | −0.371121 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.5623 | −1.25968 | −0.629841 | − | 0.776724i | \(-0.716880\pi\) | ||||
−0.629841 | + | 0.776724i | \(0.716880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3820 | −0.402665 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.5066 | 1.32523 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.6180 | −0.409992 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.61803 | −0.0569575 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.2492 | −1.76667 | −0.883334 | − | 0.468744i | \(-0.844707\pi\) | ||||
−0.883334 | + | 0.468744i | \(0.844707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9443 | 0.489650 | 0.244825 | − | 0.969567i | \(-0.421270\pi\) | ||||
0.244825 | + | 0.969567i | \(0.421270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.85410 | −0.275455 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.1378 | −0.914445 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.47214 | −0.191212 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.7214 | −1.83999 | −0.919994 | − | 0.391932i | \(-0.871807\pi\) | ||||
−0.919994 | + | 0.391932i | \(0.871807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.8328 | −0.517039 | −0.258520 | − | 0.966006i | \(-0.583235\pi\) | ||||
−0.258520 | + | 0.966006i | \(0.583235\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.23607 | −0.321170 | −0.160585 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160585 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1591 | −0.804347 | −0.402174 | − | 0.915563i | \(-0.631745\pi\) | ||||
−0.402174 | + | 0.915563i | \(0.631745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.1459 | −0.560095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.8885 | 1.20882 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.2361 | −1.04511 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.85410 | 0.305678 | 0.152839 | − | 0.988251i | \(-0.451158\pi\) | ||||
0.152839 | + | 0.988251i | \(0.451158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.3262 | 1.39056 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.61803 | 0.0901699 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.381966 | 0.0131245 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.9656 | −0.582256 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0901699 | −0.00309099 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5623 | −0.395886 | −0.197943 | − | 0.980214i | \(-0.563426\pi\) | ||||
−0.197943 | + | 0.980214i | \(0.563426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8328 | −0.404201 | −0.202101 | − | 0.979365i | \(-0.564777\pi\) | ||||
−0.202101 | + | 0.979365i | \(0.564777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7082 | 0.740674 | 0.370337 | − | 0.928897i | \(-0.379242\pi\) | ||||
0.370337 | + | 0.928897i | \(0.379242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.52786 | −0.0861494 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.4164 | −1.78428 | −0.892138 | − | 0.451764i | \(-0.850795\pi\) | ||||
−0.892138 | + | 0.451764i | \(0.850795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.50658 | 0.187013 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.38197 | −0.250416 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.6656 | 2.22500 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.1803 | −0.919915 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8885 | −1.54955 | −0.774773 | − | 0.632239i | \(-0.782136\pi\) | ||||
−0.774773 | + | 0.632239i | \(0.782136\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.12461 | −0.240307 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.4508 | 0.486861 | 0.243431 | − | 0.969918i | \(-0.421727\pi\) | ||||
0.243431 | + | 0.969918i | \(0.421727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8328 | 0.869343 | 0.434672 | − | 0.900589i | \(-0.356864\pi\) | ||||
0.434672 | + | 0.900589i | \(0.356864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0000 | −0.570804 | −0.285402 | − | 0.958408i | \(-0.592127\pi\) | ||||
−0.285402 | + | 0.958408i | \(0.592127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.819660 | 0.0274905 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.70820 | −0.191232 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.41641 | 0.281644 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29180 | −0.0431318 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72.5066 | 2.41823 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4164 | −0.613540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.63932 | −0.0545532 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.7771 | −0.789505 | −0.394753 | − | 0.918787i | \(-0.629170\pi\) | ||||
−0.394753 | + | 0.918787i | \(0.629170\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.6525 | 1.18252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.0557 | 0.432556 | 0.216278 | − | 0.976332i | \(-0.430608\pi\) | ||||
0.216278 | + | 0.976332i | \(0.430608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5623 | −0.448847 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.79837 | 0.158456 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.3607 | 1.72722 | 0.863610 | − | 0.504161i | \(-0.168198\pi\) | ||||
0.863610 | + | 0.504161i | \(0.168198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7426 | 0.485787 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.7639 | −1.47342 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.2705 | −1.05990 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.8197 | −1.20801 | −0.604007 | − | 0.796979i | \(-0.706430\pi\) | ||||
−0.604007 | + | 0.796979i | \(0.706430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.7984 | −0.845508 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.67376 | −0.120274 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.583592 | −0.0190651 | −0.00953256 | − | 0.999955i | \(-0.503034\pi\) | ||||
−0.00953256 | + | 0.999955i | \(0.503034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.58359 | −0.214847 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.81966 | −0.287513 | −0.143756 | − | 0.989613i | \(-0.545918\pi\) | ||||
−0.143756 | + | 0.989613i | \(0.545918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.09017 | 0.133194 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.12461 | −0.264014 | −0.132007 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132007 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.5755 | 2.06375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.09017 | 0.0677784 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.111456 | −0.00361042 | −0.00180521 | − | 0.999998i | \(-0.500575\pi\) | ||||
−0.00180521 | + | 0.999998i | \(0.500575\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.14590 | −0.166343 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.65248 | −0.117945 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.8328 | 1.44622 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.5066 | −1.11196 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.72949 | 0.0877745 | 0.0438872 | − | 0.999036i | \(-0.486026\pi\) | ||||
0.0438872 | + | 0.999036i | \(0.486026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8409 | −0.380386 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.381966 | 0.0122579 | 0.00612894 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612894 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.27051 | 0.136906 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.5410 | 1.07307 | 0.536536 | − | 0.843877i | \(-0.319733\pi\) | ||||
0.536536 | + | 0.843877i | \(0.319733\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3262 | 0.457869 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.32624 | −0.297764 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.9443 | 1.30592 | 0.652960 | − | 0.757393i | \(-0.273527\pi\) | ||||
0.652960 | + | 0.757393i | \(0.273527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.527864 | 0.0168021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.65248 | 0.0843438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.0902 | 1.55940 | 0.779700 | − | 0.626153i | \(-0.215371\pi\) | ||||
0.779700 | + | 0.626153i | \(0.215371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.25735 | −0.262039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.0344 | 1.77463 | 0.887314 | − | 0.461165i | \(-0.152568\pi\) | ||||
0.887314 | + | 0.461165i | \(0.152568\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.819660 | −0.0259329 |
(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 | 4400.2.a.bm.1.2 | 2 | ||
4.3 | odd | 2 | 2200.2.a.q.1.1 | yes | 2 | ||
5.2 | odd | 4 | 4400.2.b.z.4049.2 | 4 | |||
5.3 | odd | 4 | 4400.2.b.z.4049.3 | 4 | |||
5.4 | even | 2 | 4400.2.a.bo.1.1 | 2 | |||
20.3 | even | 4 | 2200.2.b.k.1849.2 | 4 | |||
20.7 | even | 4 | 2200.2.b.k.1849.3 | 4 | |||
20.19 | odd | 2 | 2200.2.a.p.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.p.1.2 | ✓ | 2 | 20.19 | odd | 2 | ||
2200.2.a.q.1.1 | yes | 2 | 4.3 | odd | 2 | ||
2200.2.b.k.1849.2 | 4 | 20.3 | even | 4 | |||
2200.2.b.k.1849.3 | 4 | 20.7 | even | 4 | |||
4400.2.a.bm.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.a.bo.1.1 | 2 | 5.4 | even | 2 | |||
4400.2.b.z.4049.2 | 4 | 5.2 | odd | 4 | |||
4400.2.b.z.4049.3 | 4 | 5.3 | odd | 4 |