Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.46410 | −1.23812 | −0.619060 | − | 0.785344i | \(-0.712486\pi\) | ||||
−0.619060 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 2.00000 | 0.471405 | ||||||||
\(19\) | −5.92820 | −1.36002 | −0.680012 | − | 0.733201i | \(-0.738025\pi\) | ||||
−0.680012 | + | 0.733201i | \(0.738025\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.46410 | −0.930830 | −0.465415 | − | 0.885093i | \(-0.654095\pi\) | ||||
−0.465415 | + | 0.885093i | \(0.654095\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.46410 | 0.875482 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −0.535898 | −0.0962502 | −0.0481251 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481251 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.46410 | −1.28008 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −8.92820 | −1.46779 | −0.733894 | − | 0.679264i | \(-0.762299\pi\) | ||||
−0.733894 | + | 0.679264i | \(0.762299\pi\) | |||||||
\(38\) | 5.92820 | 0.961682 | ||||||||
\(39\) | 4.46410 | 0.714828 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.39230 | 1.31066 | 0.655329 | − | 0.755344i | \(-0.272530\pi\) | ||||
0.655329 | + | 0.755344i | \(0.272530\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 12.3923 | 1.88981 | 0.944904 | − | 0.327346i | \(-0.106154\pi\) | ||||
0.944904 | + | 0.327346i | \(0.106154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 4.46410 | 0.658196 | ||||||||
\(47\) | −0.535898 | −0.0781688 | −0.0390844 | − | 0.999236i | \(-0.512444\pi\) | ||||
−0.0390844 | + | 0.999236i | \(0.512444\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −7.46410 | −1.04518 | ||||||||
\(52\) | −4.46410 | −0.619060 | ||||||||
\(53\) | −7.46410 | −1.02527 | −0.512637 | − | 0.858606i | \(-0.671331\pi\) | ||||
−0.512637 | + | 0.858606i | \(0.671331\pi\) | |||||||
\(54\) | −5.00000 | −0.680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.92820 | 0.785210 | ||||||||
\(58\) | −6.92820 | −0.909718 | ||||||||
\(59\) | 9.92820 | 1.29254 | 0.646271 | − | 0.763108i | \(-0.276328\pi\) | ||||
0.646271 | + | 0.763108i | \(0.276328\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0.535898 | 0.0680592 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.46410 | −0.553704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.39230 | 0.780944 | 0.390472 | − | 0.920615i | \(-0.372312\pi\) | ||||
0.390472 | + | 0.920615i | \(0.372312\pi\) | |||||||
\(68\) | 7.46410 | 0.905155 | ||||||||
\(69\) | 4.46410 | 0.537415 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 2.00000 | 0.235702 | ||||||||
\(73\) | 0.535898 | 0.0627222 | 0.0313611 | − | 0.999508i | \(-0.490016\pi\) | ||||
0.0313611 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(74\) | 8.92820 | 1.03788 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −5.92820 | −0.680012 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.46410 | −0.505460 | ||||||||
\(79\) | 7.53590 | 0.847855 | 0.423927 | − | 0.905696i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905696i | \(0.360651\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.39230 | −0.926775 | ||||||||
\(83\) | 1.00000 | 0.109764 | 0.0548821 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548821 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 7.46410 | 0.809595 | ||||||||
\(86\) | −12.3923 | −1.33630 | ||||||||
\(87\) | −6.92820 | −0.742781 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.4641 | −1.85119 | −0.925596 | − | 0.378514i | \(-0.876435\pi\) | ||||
−0.925596 | + | 0.378514i | \(0.876435\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 4.46410 | 0.467965 | ||||||||
\(92\) | −4.46410 | −0.465415 | ||||||||
\(93\) | 0.535898 | 0.0555701 | ||||||||
\(94\) | 0.535898 | 0.0552737 | ||||||||
\(95\) | −5.92820 | −0.608221 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.07180 | −0.108824 | −0.0544122 | − | 0.998519i | \(-0.517329\pi\) | ||||
−0.0544122 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.5359 | 1.14786 | 0.573932 | − | 0.818903i | \(-0.305417\pi\) | ||||
0.573932 | + | 0.818903i | \(0.305417\pi\) | |||||||
\(102\) | 7.46410 | 0.739056 | ||||||||
\(103\) | −1.46410 | −0.144262 | −0.0721311 | − | 0.997395i | \(-0.522980\pi\) | ||||
−0.0721311 | + | 0.997395i | \(0.522980\pi\) | |||||||
\(104\) | 4.46410 | 0.437741 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 7.46410 | 0.724978 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | −18.3923 | −1.76166 | −0.880832 | − | 0.473430i | \(-0.843016\pi\) | ||||
−0.880832 | + | 0.473430i | \(0.843016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.92820 | 0.847428 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 1.00000 | 0.0940721 | 0.0470360 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470360 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(114\) | −5.92820 | −0.555227 | ||||||||
\(115\) | −4.46410 | −0.416280 | ||||||||
\(116\) | 6.92820 | 0.643268 | ||||||||
\(117\) | 8.92820 | 0.825413 | ||||||||
\(118\) | −9.92820 | −0.913965 | ||||||||
\(119\) | −7.46410 | −0.684233 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.92820 | 0.446179 | ||||||||
\(123\) | −8.39230 | −0.756709 | ||||||||
\(124\) | −0.535898 | −0.0481251 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −13.3923 | −1.18837 | −0.594187 | − | 0.804327i | \(-0.702526\pi\) | ||||
−0.594187 | + | 0.804327i | \(0.702526\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.3923 | −1.09108 | ||||||||
\(130\) | 4.46410 | 0.391528 | ||||||||
\(131\) | 10.8564 | 0.948529 | 0.474264 | − | 0.880383i | \(-0.342714\pi\) | ||||
0.474264 | + | 0.880383i | \(0.342714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.92820 | 0.514040 | ||||||||
\(134\) | −6.39230 | −0.552211 | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | −7.46410 | −0.640041 | ||||||||
\(137\) | 7.92820 | 0.677352 | 0.338676 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(138\) | −4.46410 | −0.380010 | ||||||||
\(139\) | −16.8564 | −1.42974 | −0.714871 | − | 0.699256i | \(-0.753515\pi\) | ||||
−0.714871 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0.535898 | 0.0451308 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 6.92820 | 0.575356 | ||||||||
\(146\) | −0.535898 | −0.0443513 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −8.92820 | −0.733894 | ||||||||
\(149\) | 3.07180 | 0.251651 | 0.125826 | − | 0.992052i | \(-0.459842\pi\) | ||||
0.125826 | + | 0.992052i | \(0.459842\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 5.53590 | 0.450505 | 0.225253 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225253 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(152\) | 5.92820 | 0.480841 | ||||||||
\(153\) | −14.9282 | −1.20687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.535898 | −0.0430444 | ||||||||
\(156\) | 4.46410 | 0.357414 | ||||||||
\(157\) | −20.3205 | −1.62175 | −0.810877 | − | 0.585217i | \(-0.801009\pi\) | ||||
−0.810877 | + | 0.585217i | \(0.801009\pi\) | |||||||
\(158\) | −7.53590 | −0.599524 | ||||||||
\(159\) | 7.46410 | 0.591942 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.46410 | 0.351820 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −22.0000 | −1.72317 | −0.861586 | − | 0.507611i | \(-0.830529\pi\) | ||||
−0.861586 | + | 0.507611i | \(0.830529\pi\) | |||||||
\(164\) | 8.39230 | 0.655329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | −0.0776151 | ||||||||
\(167\) | 4.39230 | 0.339887 | 0.169943 | − | 0.985454i | \(-0.445642\pi\) | ||||
0.169943 | + | 0.985454i | \(0.445642\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | −7.46410 | −0.572470 | ||||||||
\(171\) | 11.8564 | 0.906682 | ||||||||
\(172\) | 12.3923 | 0.944904 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 6.92820 | 0.525226 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.92820 | −0.746249 | ||||||||
\(178\) | 17.4641 | 1.30899 | ||||||||
\(179\) | −8.39230 | −0.627270 | −0.313635 | − | 0.949544i | \(-0.601547\pi\) | ||||
−0.313635 | + | 0.949544i | \(0.601547\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 10.4641 | 0.777791 | 0.388895 | − | 0.921282i | \(-0.372857\pi\) | ||||
0.388895 | + | 0.921282i | \(0.372857\pi\) | |||||||
\(182\) | −4.46410 | −0.330901 | ||||||||
\(183\) | 4.92820 | 0.364303 | ||||||||
\(184\) | 4.46410 | 0.329098 | ||||||||
\(185\) | −8.92820 | −0.656415 | ||||||||
\(186\) | −0.535898 | −0.0392940 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.535898 | −0.0390844 | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 5.92820 | 0.430077 | ||||||||
\(191\) | 3.39230 | 0.245459 | 0.122729 | − | 0.992440i | \(-0.460835\pi\) | ||||
0.122729 | + | 0.992440i | \(0.460835\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −19.0000 | −1.36765 | −0.683825 | − | 0.729646i | \(-0.739685\pi\) | ||||
−0.683825 | + | 0.729646i | \(0.739685\pi\) | |||||||
\(194\) | 1.07180 | 0.0769505 | ||||||||
\(195\) | 4.46410 | 0.319681 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.8564 | −1.83291 | −0.916456 | − | 0.400135i | \(-0.868963\pi\) | ||||
−0.916456 | + | 0.400135i | \(0.868963\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.39230 | −0.450878 | ||||||||
\(202\) | −11.5359 | −0.811663 | ||||||||
\(203\) | −6.92820 | −0.486265 | ||||||||
\(204\) | −7.46410 | −0.522592 | ||||||||
\(205\) | 8.39230 | 0.586144 | ||||||||
\(206\) | 1.46410 | 0.102009 | ||||||||
\(207\) | 8.92820 | 0.620553 | ||||||||
\(208\) | −4.46410 | −0.309530 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.00000 | −0.0690066 | ||||||||
\(211\) | 24.0000 | 1.65223 | 0.826114 | − | 0.563503i | \(-0.190547\pi\) | ||||
0.826114 | + | 0.563503i | \(0.190547\pi\) | |||||||
\(212\) | −7.46410 | −0.512637 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | 12.3923 | 0.845148 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0.535898 | 0.0363792 | ||||||||
\(218\) | 18.3923 | 1.24568 | ||||||||
\(219\) | −0.535898 | −0.0362127 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.3205 | −2.24138 | ||||||||
\(222\) | −8.92820 | −0.599222 | ||||||||
\(223\) | −3.46410 | −0.231973 | −0.115987 | − | 0.993251i | \(-0.537003\pi\) | ||||
−0.115987 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | −1.00000 | −0.0665190 | ||||||||
\(227\) | 16.0000 | 1.06196 | 0.530979 | − | 0.847385i | \(-0.321824\pi\) | ||||
0.530979 | + | 0.847385i | \(0.321824\pi\) | |||||||
\(228\) | 5.92820 | 0.392605 | ||||||||
\(229\) | −18.0000 | −1.18947 | −0.594737 | − | 0.803921i | \(-0.702744\pi\) | ||||
−0.594737 | + | 0.803921i | \(0.702744\pi\) | |||||||
\(230\) | 4.46410 | 0.294354 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.92820 | −0.454859 | ||||||||
\(233\) | 18.8564 | 1.23532 | 0.617662 | − | 0.786444i | \(-0.288080\pi\) | ||||
0.617662 | + | 0.786444i | \(0.288080\pi\) | |||||||
\(234\) | −8.92820 | −0.583655 | ||||||||
\(235\) | −0.535898 | −0.0349582 | ||||||||
\(236\) | 9.92820 | 0.646271 | ||||||||
\(237\) | −7.53590 | −0.489509 | ||||||||
\(238\) | 7.46410 | 0.483826 | ||||||||
\(239\) | 12.4641 | 0.806236 | 0.403118 | − | 0.915148i | \(-0.367926\pi\) | ||||
0.403118 | + | 0.915148i | \(0.367926\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | −4.92820 | −0.315496 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 8.39230 | 0.535074 | ||||||||
\(247\) | 26.4641 | 1.68387 | ||||||||
\(248\) | 0.535898 | 0.0340296 | ||||||||
\(249\) | −1.00000 | −0.0633724 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 13.3923 | 0.840308 | ||||||||
\(255\) | −7.46410 | −0.467420 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.39230 | 0.149228 | 0.0746139 | − | 0.997212i | \(-0.476228\pi\) | ||||
0.0746139 | + | 0.997212i | \(0.476228\pi\) | |||||||
\(258\) | 12.3923 | 0.771511 | ||||||||
\(259\) | 8.92820 | 0.554772 | ||||||||
\(260\) | −4.46410 | −0.276852 | ||||||||
\(261\) | −13.8564 | −0.857690 | ||||||||
\(262\) | −10.8564 | −0.670711 | ||||||||
\(263\) | −16.4641 | −1.01522 | −0.507610 | − | 0.861587i | \(-0.669471\pi\) | ||||
−0.507610 | + | 0.861587i | \(0.669471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.46410 | −0.458516 | ||||||||
\(266\) | −5.92820 | −0.363481 | ||||||||
\(267\) | 17.4641 | 1.06879 | ||||||||
\(268\) | 6.39230 | 0.390472 | ||||||||
\(269\) | −10.3205 | −0.629252 | −0.314626 | − | 0.949216i | \(-0.601879\pi\) | ||||
−0.314626 | + | 0.949216i | \(0.601879\pi\) | |||||||
\(270\) | −5.00000 | −0.304290 | ||||||||
\(271\) | −29.8564 | −1.81365 | −0.906824 | − | 0.421510i | \(-0.861500\pi\) | ||||
−0.906824 | + | 0.421510i | \(0.861500\pi\) | |||||||
\(272\) | 7.46410 | 0.452578 | ||||||||
\(273\) | −4.46410 | −0.270180 | ||||||||
\(274\) | −7.92820 | −0.478960 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.46410 | 0.268707 | ||||||||
\(277\) | −27.3205 | −1.64153 | −0.820765 | − | 0.571266i | \(-0.806453\pi\) | ||||
−0.820765 | + | 0.571266i | \(0.806453\pi\) | |||||||
\(278\) | 16.8564 | 1.01098 | ||||||||
\(279\) | 1.07180 | 0.0641668 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −17.0000 | −1.01413 | −0.507067 | − | 0.861906i | \(-0.669271\pi\) | ||||
−0.507067 | + | 0.861906i | \(0.669271\pi\) | |||||||
\(282\) | −0.535898 | −0.0319123 | ||||||||
\(283\) | 13.7846 | 0.819410 | 0.409705 | − | 0.912218i | \(-0.365632\pi\) | ||||
0.409705 | + | 0.912218i | \(0.365632\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 5.92820 | 0.351156 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.39230 | −0.495382 | ||||||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | −6.92820 | −0.406838 | ||||||||
\(291\) | 1.07180 | 0.0628298 | ||||||||
\(292\) | 0.535898 | 0.0313611 | ||||||||
\(293\) | 20.4641 | 1.19553 | 0.597763 | − | 0.801673i | \(-0.296056\pi\) | ||||
0.597763 | + | 0.801673i | \(0.296056\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 9.92820 | 0.578042 | ||||||||
\(296\) | 8.92820 | 0.518941 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.07180 | −0.177944 | ||||||||
\(299\) | 19.9282 | 1.15248 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −12.3923 | −0.714281 | ||||||||
\(302\) | −5.53590 | −0.318555 | ||||||||
\(303\) | −11.5359 | −0.662720 | ||||||||
\(304\) | −5.92820 | −0.340006 | ||||||||
\(305\) | −4.92820 | −0.282188 | ||||||||
\(306\) | 14.9282 | 0.853389 | ||||||||
\(307\) | 14.9282 | 0.851998 | 0.425999 | − | 0.904724i | \(-0.359923\pi\) | ||||
0.425999 | + | 0.904724i | \(0.359923\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.46410 | 0.0832898 | ||||||||
\(310\) | 0.535898 | 0.0304370 | ||||||||
\(311\) | 23.3205 | 1.32238 | 0.661192 | − | 0.750216i | \(-0.270051\pi\) | ||||
0.661192 | + | 0.750216i | \(0.270051\pi\) | |||||||
\(312\) | −4.46410 | −0.252730 | ||||||||
\(313\) | 14.7846 | 0.835676 | 0.417838 | − | 0.908522i | \(-0.362788\pi\) | ||||
0.417838 | + | 0.908522i | \(0.362788\pi\) | |||||||
\(314\) | 20.3205 | 1.14675 | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 7.53590 | 0.423927 | ||||||||
\(317\) | −22.3923 | −1.25768 | −0.628839 | − | 0.777536i | \(-0.716469\pi\) | ||||
−0.628839 | + | 0.777536i | \(0.716469\pi\) | |||||||
\(318\) | −7.46410 | −0.418566 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | −4.46410 | −0.248775 | ||||||||
\(323\) | −44.2487 | −2.46206 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.46410 | −0.247624 | ||||||||
\(326\) | 22.0000 | 1.21847 | ||||||||
\(327\) | 18.3923 | 1.01710 | ||||||||
\(328\) | −8.39230 | −0.463388 | ||||||||
\(329\) | 0.535898 | 0.0295450 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.46410 | 0.0804743 | 0.0402372 | − | 0.999190i | \(-0.487189\pi\) | ||||
0.0402372 | + | 0.999190i | \(0.487189\pi\) | |||||||
\(332\) | 1.00000 | 0.0548821 | ||||||||
\(333\) | 17.8564 | 0.978525 | ||||||||
\(334\) | −4.39230 | −0.240336 | ||||||||
\(335\) | 6.39230 | 0.349249 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −31.7846 | −1.73142 | −0.865709 | − | 0.500548i | \(-0.833132\pi\) | ||||
−0.865709 | + | 0.500548i | \(0.833132\pi\) | |||||||
\(338\) | −6.92820 | −0.376845 | ||||||||
\(339\) | −1.00000 | −0.0543125 | ||||||||
\(340\) | 7.46410 | 0.404798 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −11.8564 | −0.641121 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −12.3923 | −0.668148 | ||||||||
\(345\) | 4.46410 | 0.240339 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | −0.928203 | −0.0498286 | −0.0249143 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249143 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(348\) | −6.92820 | −0.371391 | ||||||||
\(349\) | 1.53590 | 0.0822148 | 0.0411074 | − | 0.999155i | \(-0.486911\pi\) | ||||
0.0411074 | + | 0.999155i | \(0.486911\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −22.3205 | −1.19138 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5359 | −1.09302 | −0.546508 | − | 0.837454i | \(-0.684043\pi\) | ||||
−0.546508 | + | 0.837454i | \(0.684043\pi\) | |||||||
\(354\) | 9.92820 | 0.527678 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | −17.4641 | −0.925596 | ||||||||
\(357\) | 7.46410 | 0.395042 | ||||||||
\(358\) | 8.39230 | 0.443547 | ||||||||
\(359\) | 19.7128 | 1.04040 | 0.520201 | − | 0.854044i | \(-0.325857\pi\) | ||||
0.520201 | + | 0.854044i | \(0.325857\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | 16.1436 | 0.849663 | ||||||||
\(362\) | −10.4641 | −0.549981 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.46410 | 0.233983 | ||||||||
\(365\) | 0.535898 | 0.0280502 | ||||||||
\(366\) | −4.92820 | −0.257601 | ||||||||
\(367\) | −21.4641 | −1.12042 | −0.560208 | − | 0.828352i | \(-0.689279\pi\) | ||||
−0.560208 | + | 0.828352i | \(0.689279\pi\) | |||||||
\(368\) | −4.46410 | −0.232707 | ||||||||
\(369\) | −16.7846 | −0.873772 | ||||||||
\(370\) | 8.92820 | 0.464155 | ||||||||
\(371\) | 7.46410 | 0.387517 | ||||||||
\(372\) | 0.535898 | 0.0277850 | ||||||||
\(373\) | −24.9282 | −1.29073 | −0.645367 | − | 0.763873i | \(-0.723295\pi\) | ||||
−0.645367 | + | 0.763873i | \(0.723295\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0.535898 | 0.0276368 | ||||||||
\(377\) | −30.9282 | −1.59288 | ||||||||
\(378\) | 5.00000 | 0.257172 | ||||||||
\(379\) | 23.8564 | 1.22542 | 0.612711 | − | 0.790307i | \(-0.290079\pi\) | ||||
0.612711 | + | 0.790307i | \(0.290079\pi\) | |||||||
\(380\) | −5.92820 | −0.304110 | ||||||||
\(381\) | 13.3923 | 0.686109 | ||||||||
\(382\) | −3.39230 | −0.173565 | ||||||||
\(383\) | −21.4641 | −1.09676 | −0.548382 | − | 0.836228i | \(-0.684756\pi\) | ||||
−0.548382 | + | 0.836228i | \(0.684756\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | −24.7846 | −1.25987 | ||||||||
\(388\) | −1.07180 | −0.0544122 | ||||||||
\(389\) | −13.3205 | −0.675377 | −0.337688 | − | 0.941258i | \(-0.609645\pi\) | ||||
−0.337688 | + | 0.941258i | \(0.609645\pi\) | |||||||
\(390\) | −4.46410 | −0.226049 | ||||||||
\(391\) | −33.3205 | −1.68509 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −10.8564 | −0.547633 | ||||||||
\(394\) | 4.00000 | 0.201517 | ||||||||
\(395\) | 7.53590 | 0.379172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0718 | −0.555678 | −0.277839 | − | 0.960628i | \(-0.589618\pi\) | ||||
−0.277839 | + | 0.960628i | \(0.589618\pi\) | |||||||
\(398\) | 25.8564 | 1.29606 | ||||||||
\(399\) | −5.92820 | −0.296781 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 4.14359 | 0.206921 | 0.103461 | − | 0.994634i | \(-0.467008\pi\) | ||||
0.103461 | + | 0.994634i | \(0.467008\pi\) | |||||||
\(402\) | 6.39230 | 0.318819 | ||||||||
\(403\) | 2.39230 | 0.119169 | ||||||||
\(404\) | 11.5359 | 0.573932 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 6.92820 | 0.343841 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.46410 | 0.369528 | ||||||||
\(409\) | 31.7128 | 1.56810 | 0.784049 | − | 0.620699i | \(-0.213151\pi\) | ||||
0.784049 | + | 0.620699i | \(0.213151\pi\) | |||||||
\(410\) | −8.39230 | −0.414466 | ||||||||
\(411\) | −7.92820 | −0.391069 | ||||||||
\(412\) | −1.46410 | −0.0721311 | ||||||||
\(413\) | −9.92820 | −0.488535 | ||||||||
\(414\) | −8.92820 | −0.438797 | ||||||||
\(415\) | 1.00000 | 0.0490881 | ||||||||
\(416\) | 4.46410 | 0.218871 | ||||||||
\(417\) | 16.8564 | 0.825462 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.7128 | 1.89124 | 0.945622 | − | 0.325267i | \(-0.105454\pi\) | ||||
0.945622 | + | 0.325267i | \(0.105454\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | 5.85641 | 0.285424 | 0.142712 | − | 0.989764i | \(-0.454418\pi\) | ||||
0.142712 | + | 0.989764i | \(0.454418\pi\) | |||||||
\(422\) | −24.0000 | −1.16830 | ||||||||
\(423\) | 1.07180 | 0.0521125 | ||||||||
\(424\) | 7.46410 | 0.362489 | ||||||||
\(425\) | 7.46410 | 0.362062 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 4.92820 | 0.238492 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.3923 | −0.597610 | ||||||||
\(431\) | 10.3205 | 0.497121 | 0.248561 | − | 0.968616i | \(-0.420042\pi\) | ||||
0.248561 | + | 0.968616i | \(0.420042\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | 22.2487 | 1.06920 | 0.534602 | − | 0.845104i | \(-0.320461\pi\) | ||||
0.534602 | + | 0.845104i | \(0.320461\pi\) | |||||||
\(434\) | −0.535898 | −0.0257239 | ||||||||
\(435\) | −6.92820 | −0.332182 | ||||||||
\(436\) | −18.3923 | −0.880832 | ||||||||
\(437\) | 26.4641 | 1.26595 | ||||||||
\(438\) | 0.535898 | 0.0256062 | ||||||||
\(439\) | 22.5359 | 1.07558 | 0.537790 | − | 0.843079i | \(-0.319259\pi\) | ||||
0.537790 | + | 0.843079i | \(0.319259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 33.3205 | 1.58489 | ||||||||
\(443\) | −15.7128 | −0.746538 | −0.373269 | − | 0.927723i | \(-0.621763\pi\) | ||||
−0.373269 | + | 0.927723i | \(0.621763\pi\) | |||||||
\(444\) | 8.92820 | 0.423714 | ||||||||
\(445\) | −17.4641 | −0.827878 | ||||||||
\(446\) | 3.46410 | 0.164030 | ||||||||
\(447\) | −3.07180 | −0.145291 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −8.07180 | −0.380932 | −0.190466 | − | 0.981694i | \(-0.561000\pi\) | ||||
−0.190466 | + | 0.981694i | \(0.561000\pi\) | |||||||
\(450\) | 2.00000 | 0.0942809 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.00000 | 0.0470360 | ||||||||
\(453\) | −5.53590 | −0.260099 | ||||||||
\(454\) | −16.0000 | −0.750917 | ||||||||
\(455\) | 4.46410 | 0.209280 | ||||||||
\(456\) | −5.92820 | −0.277614 | ||||||||
\(457\) | 39.6410 | 1.85433 | 0.927164 | − | 0.374655i | \(-0.122239\pi\) | ||||
0.927164 | + | 0.374655i | \(0.122239\pi\) | |||||||
\(458\) | 18.0000 | 0.841085 | ||||||||
\(459\) | 37.3205 | 1.74197 | ||||||||
\(460\) | −4.46410 | −0.208140 | ||||||||
\(461\) | −12.1436 | −0.565584 | −0.282792 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282792 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.46410 | −0.393360 | −0.196680 | − | 0.980468i | \(-0.563016\pi\) | ||||
−0.196680 | + | 0.980468i | \(0.563016\pi\) | |||||||
\(464\) | 6.92820 | 0.321634 | ||||||||
\(465\) | 0.535898 | 0.0248517 | ||||||||
\(466\) | −18.8564 | −0.873506 | ||||||||
\(467\) | −15.9282 | −0.737069 | −0.368535 | − | 0.929614i | \(-0.620140\pi\) | ||||
−0.368535 | + | 0.929614i | \(0.620140\pi\) | |||||||
\(468\) | 8.92820 | 0.412706 | ||||||||
\(469\) | −6.39230 | −0.295169 | ||||||||
\(470\) | 0.535898 | 0.0247191 | ||||||||
\(471\) | 20.3205 | 0.936320 | ||||||||
\(472\) | −9.92820 | −0.456983 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.53590 | 0.346135 | ||||||||
\(475\) | −5.92820 | −0.272005 | ||||||||
\(476\) | −7.46410 | −0.342117 | ||||||||
\(477\) | 14.9282 | 0.683515 | ||||||||
\(478\) | −12.4641 | −0.570095 | ||||||||
\(479\) | 2.53590 | 0.115868 | 0.0579341 | − | 0.998320i | \(-0.481549\pi\) | ||||
0.0579341 | + | 0.998320i | \(0.481549\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 39.8564 | 1.81730 | ||||||||
\(482\) | −4.00000 | −0.182195 | ||||||||
\(483\) | −4.46410 | −0.203124 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.07180 | −0.0486678 | ||||||||
\(486\) | 16.0000 | 0.725775 | ||||||||
\(487\) | 2.32051 | 0.105152 | 0.0525761 | − | 0.998617i | \(-0.483257\pi\) | ||||
0.0525761 | + | 0.998617i | \(0.483257\pi\) | |||||||
\(488\) | 4.92820 | 0.223089 | ||||||||
\(489\) | 22.0000 | 0.994874 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −23.4641 | −1.05892 | −0.529460 | − | 0.848335i | \(-0.677605\pi\) | ||||
−0.529460 | + | 0.848335i | \(0.677605\pi\) | |||||||
\(492\) | −8.39230 | −0.378354 | ||||||||
\(493\) | 51.7128 | 2.32903 | ||||||||
\(494\) | −26.4641 | −1.19068 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.535898 | −0.0240625 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 1.00000 | 0.0448111 | ||||||||
\(499\) | −8.92820 | −0.399681 | −0.199841 | − | 0.979828i | \(-0.564042\pi\) | ||||
−0.199841 | + | 0.979828i | \(0.564042\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −4.39230 | −0.196234 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2487 | −1.34872 | −0.674362 | − | 0.738401i | \(-0.735581\pi\) | ||||
−0.674362 | + | 0.738401i | \(0.735581\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 11.5359 | 0.513341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.92820 | −0.307692 | ||||||||
\(508\) | −13.3923 | −0.594187 | ||||||||
\(509\) | −26.3205 | −1.16664 | −0.583318 | − | 0.812244i | \(-0.698246\pi\) | ||||
−0.583318 | + | 0.812244i | \(0.698246\pi\) | |||||||
\(510\) | 7.46410 | 0.330516 | ||||||||
\(511\) | −0.535898 | −0.0237067 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −29.6410 | −1.30868 | ||||||||
\(514\) | −2.39230 | −0.105520 | ||||||||
\(515\) | −1.46410 | −0.0645160 | ||||||||
\(516\) | −12.3923 | −0.545541 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.92820 | −0.392283 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 4.46410 | 0.195764 | ||||||||
\(521\) | 16.0000 | 0.700973 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(522\) | 13.8564 | 0.606478 | ||||||||
\(523\) | 3.92820 | 0.171768 | 0.0858842 | − | 0.996305i | \(-0.472629\pi\) | ||||
0.0858842 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(524\) | 10.8564 | 0.474264 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 16.4641 | 0.717869 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.07180 | −0.133556 | ||||||||
\(530\) | 7.46410 | 0.324220 | ||||||||
\(531\) | −19.8564 | −0.861695 | ||||||||
\(532\) | 5.92820 | 0.257020 | ||||||||
\(533\) | −37.4641 | −1.62275 | ||||||||
\(534\) | −17.4641 | −0.755746 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | −6.39230 | −0.276106 | ||||||||
\(537\) | 8.39230 | 0.362155 | ||||||||
\(538\) | 10.3205 | 0.444949 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.00000 | 0.215166 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 29.8564 | 1.28244 | ||||||||
\(543\) | −10.4641 | −0.449058 | ||||||||
\(544\) | −7.46410 | −0.320021 | ||||||||
\(545\) | −18.3923 | −0.787840 | ||||||||
\(546\) | 4.46410 | 0.191046 | ||||||||
\(547\) | 34.5359 | 1.47665 | 0.738324 | − | 0.674446i | \(-0.235617\pi\) | ||||
0.738324 | + | 0.674446i | \(0.235617\pi\) | |||||||
\(548\) | 7.92820 | 0.338676 | ||||||||
\(549\) | 9.85641 | 0.420661 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.0718 | −1.74972 | ||||||||
\(552\) | −4.46410 | −0.190005 | ||||||||
\(553\) | −7.53590 | −0.320459 | ||||||||
\(554\) | 27.3205 | 1.16074 | ||||||||
\(555\) | 8.92820 | 0.378981 | ||||||||
\(556\) | −16.8564 | −0.714871 | ||||||||
\(557\) | −21.3205 | −0.903379 | −0.451689 | − | 0.892175i | \(-0.649178\pi\) | ||||
−0.451689 | + | 0.892175i | \(0.649178\pi\) | |||||||
\(558\) | −1.07180 | −0.0453728 | ||||||||
\(559\) | −55.3205 | −2.33981 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.0000 | 0.717102 | ||||||||
\(563\) | −42.7128 | −1.80013 | −0.900065 | − | 0.435755i | \(-0.856481\pi\) | ||||
−0.900065 | + | 0.435755i | \(0.856481\pi\) | |||||||
\(564\) | 0.535898 | 0.0225654 | ||||||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | −13.7846 | −0.579410 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | 32.7128 | 1.37139 | 0.685696 | − | 0.727888i | \(-0.259498\pi\) | ||||
0.685696 | + | 0.727888i | \(0.259498\pi\) | |||||||
\(570\) | −5.92820 | −0.248305 | ||||||||
\(571\) | −1.85641 | −0.0776882 | −0.0388441 | − | 0.999245i | \(-0.512368\pi\) | ||||
−0.0388441 | + | 0.999245i | \(0.512368\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.39230 | −0.141716 | ||||||||
\(574\) | 8.39230 | 0.350288 | ||||||||
\(575\) | −4.46410 | −0.186166 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | 35.3205 | 1.47041 | 0.735206 | − | 0.677844i | \(-0.237085\pi\) | ||||
0.735206 | + | 0.677844i | \(0.237085\pi\) | |||||||
\(578\) | −38.7128 | −1.61024 | ||||||||
\(579\) | 19.0000 | 0.789613 | ||||||||
\(580\) | 6.92820 | 0.287678 | ||||||||
\(581\) | −1.00000 | −0.0414870 | ||||||||
\(582\) | −1.07180 | −0.0444274 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.535898 | −0.0221756 | ||||||||
\(585\) | 8.92820 | 0.369136 | ||||||||
\(586\) | −20.4641 | −0.845364 | ||||||||
\(587\) | −28.8564 | −1.19103 | −0.595516 | − | 0.803344i | \(-0.703052\pi\) | ||||
−0.595516 | + | 0.803344i | \(0.703052\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 3.17691 | 0.130902 | ||||||||
\(590\) | −9.92820 | −0.408738 | ||||||||
\(591\) | 4.00000 | 0.164538 | ||||||||
\(592\) | −8.92820 | −0.366947 | ||||||||
\(593\) | −28.0000 | −1.14982 | −0.574911 | − | 0.818216i | \(-0.694963\pi\) | ||||
−0.574911 | + | 0.818216i | \(0.694963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.46410 | −0.305998 | ||||||||
\(596\) | 3.07180 | 0.125826 | ||||||||
\(597\) | 25.8564 | 1.05823 | ||||||||
\(598\) | −19.9282 | −0.814925 | ||||||||
\(599\) | −25.3923 | −1.03750 | −0.518751 | − | 0.854926i | \(-0.673603\pi\) | ||||
−0.518751 | + | 0.854926i | \(0.673603\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −2.67949 | −0.109299 | −0.0546494 | − | 0.998506i | \(-0.517404\pi\) | ||||
−0.0546494 | + | 0.998506i | \(0.517404\pi\) | |||||||
\(602\) | 12.3923 | 0.505073 | ||||||||
\(603\) | −12.7846 | −0.520630 | ||||||||
\(604\) | 5.53590 | 0.225253 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.5359 | 0.468614 | ||||||||
\(607\) | −14.0000 | −0.568242 | −0.284121 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284121 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(608\) | 5.92820 | 0.240420 | ||||||||
\(609\) | 6.92820 | 0.280745 | ||||||||
\(610\) | 4.92820 | 0.199537 | ||||||||
\(611\) | 2.39230 | 0.0967823 | ||||||||
\(612\) | −14.9282 | −0.603437 | ||||||||
\(613\) | −26.5359 | −1.07177 | −0.535887 | − | 0.844289i | \(-0.680023\pi\) | ||||
−0.535887 | + | 0.844289i | \(0.680023\pi\) | |||||||
\(614\) | −14.9282 | −0.602453 | ||||||||
\(615\) | −8.39230 | −0.338410 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.21539 | −0.0489298 | −0.0244649 | − | 0.999701i | \(-0.507788\pi\) | ||||
−0.0244649 | + | 0.999701i | \(0.507788\pi\) | |||||||
\(618\) | −1.46410 | −0.0588948 | ||||||||
\(619\) | 6.07180 | 0.244046 | 0.122023 | − | 0.992527i | \(-0.461062\pi\) | ||||
0.122023 | + | 0.992527i | \(0.461062\pi\) | |||||||
\(620\) | −0.535898 | −0.0215222 | ||||||||
\(621\) | −22.3205 | −0.895691 | ||||||||
\(622\) | −23.3205 | −0.935067 | ||||||||
\(623\) | 17.4641 | 0.699684 | ||||||||
\(624\) | 4.46410 | 0.178707 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −14.7846 | −0.590912 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.3205 | −0.810877 | ||||||||
\(629\) | −66.6410 | −2.65715 | ||||||||
\(630\) | −2.00000 | −0.0796819 | ||||||||
\(631\) | 38.9282 | 1.54971 | 0.774854 | − | 0.632141i | \(-0.217824\pi\) | ||||
0.774854 | + | 0.632141i | \(0.217824\pi\) | |||||||
\(632\) | −7.53590 | −0.299762 | ||||||||
\(633\) | −24.0000 | −0.953914 | ||||||||
\(634\) | 22.3923 | 0.889312 | ||||||||
\(635\) | −13.3923 | −0.531457 | ||||||||
\(636\) | 7.46410 | 0.295971 | ||||||||
\(637\) | −4.46410 | −0.176874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.0000 | −0.632950 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −34.8564 | −1.37675 | −0.688373 | − | 0.725357i | \(-0.741675\pi\) | ||||
−0.688373 | + | 0.725357i | \(0.741675\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | −41.5692 | −1.63933 | −0.819665 | − | 0.572843i | \(-0.805840\pi\) | ||||
−0.819665 | + | 0.572843i | \(0.805840\pi\) | |||||||
\(644\) | 4.46410 | 0.175910 | ||||||||
\(645\) | −12.3923 | −0.487947 | ||||||||
\(646\) | 44.2487 | 1.74094 | ||||||||
\(647\) | −11.3205 | −0.445055 | −0.222528 | − | 0.974926i | \(-0.571431\pi\) | ||||
−0.222528 | + | 0.974926i | \(0.571431\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.46410 | 0.175096 | ||||||||
\(651\) | −0.535898 | −0.0210035 | ||||||||
\(652\) | −22.0000 | −0.861586 | ||||||||
\(653\) | −25.4641 | −0.996487 | −0.498244 | − | 0.867037i | \(-0.666021\pi\) | ||||
−0.498244 | + | 0.867037i | \(0.666021\pi\) | |||||||
\(654\) | −18.3923 | −0.719196 | ||||||||
\(655\) | 10.8564 | 0.424195 | ||||||||
\(656\) | 8.39230 | 0.327664 | ||||||||
\(657\) | −1.07180 | −0.0418148 | ||||||||
\(658\) | −0.535898 | −0.0208915 | ||||||||
\(659\) | 29.3205 | 1.14216 | 0.571082 | − | 0.820893i | \(-0.306524\pi\) | ||||
0.571082 | + | 0.820893i | \(0.306524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.607695 | −0.0236366 | −0.0118183 | − | 0.999930i | \(-0.503762\pi\) | ||||
−0.0118183 | + | 0.999930i | \(0.503762\pi\) | |||||||
\(662\) | −1.46410 | −0.0569039 | ||||||||
\(663\) | 33.3205 | 1.29406 | ||||||||
\(664\) | −1.00000 | −0.0388075 | ||||||||
\(665\) | 5.92820 | 0.229886 | ||||||||
\(666\) | −17.8564 | −0.691922 | ||||||||
\(667\) | −30.9282 | −1.19754 | ||||||||
\(668\) | 4.39230 | 0.169943 | ||||||||
\(669\) | 3.46410 | 0.133930 | ||||||||
\(670\) | −6.39230 | −0.246956 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −38.8564 | −1.49780 | −0.748902 | − | 0.662681i | \(-0.769419\pi\) | ||||
−0.748902 | + | 0.662681i | \(0.769419\pi\) | |||||||
\(674\) | 31.7846 | 1.22430 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 6.92820 | 0.266469 | ||||||||
\(677\) | 33.3923 | 1.28337 | 0.641685 | − | 0.766968i | \(-0.278236\pi\) | ||||
0.641685 | + | 0.766968i | \(0.278236\pi\) | |||||||
\(678\) | 1.00000 | 0.0384048 | ||||||||
\(679\) | 1.07180 | 0.0411318 | ||||||||
\(680\) | −7.46410 | −0.286235 | ||||||||
\(681\) | −16.0000 | −0.613121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7846 | −1.25447 | −0.627234 | − | 0.778831i | \(-0.715813\pi\) | ||||
−0.627234 | + | 0.778831i | \(0.715813\pi\) | |||||||
\(684\) | 11.8564 | 0.453341 | ||||||||
\(685\) | 7.92820 | 0.302921 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 18.0000 | 0.686743 | ||||||||
\(688\) | 12.3923 | 0.472452 | ||||||||
\(689\) | 33.3205 | 1.26941 | ||||||||
\(690\) | −4.46410 | −0.169945 | ||||||||
\(691\) | 4.00000 | 0.152167 | 0.0760836 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760836 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.928203 | 0.0352341 | ||||||||
\(695\) | −16.8564 | −0.639400 | ||||||||
\(696\) | 6.92820 | 0.262613 | ||||||||
\(697\) | 62.6410 | 2.37270 | ||||||||
\(698\) | −1.53590 | −0.0581346 | ||||||||
\(699\) | −18.8564 | −0.713215 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −30.3923 | −1.14790 | −0.573951 | − | 0.818890i | \(-0.694590\pi\) | ||||
−0.573951 | + | 0.818890i | \(0.694590\pi\) | |||||||
\(702\) | 22.3205 | 0.842433 | ||||||||
\(703\) | 52.9282 | 1.99622 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.535898 | 0.0201831 | ||||||||
\(706\) | 20.5359 | 0.772879 | ||||||||
\(707\) | −11.5359 | −0.433852 | ||||||||
\(708\) | −9.92820 | −0.373125 | ||||||||
\(709\) | 19.8564 | 0.745723 | 0.372861 | − | 0.927887i | \(-0.378377\pi\) | ||||
0.372861 | + | 0.927887i | \(0.378377\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | −15.0718 | −0.565237 | ||||||||
\(712\) | 17.4641 | 0.654495 | ||||||||
\(713\) | 2.39230 | 0.0895925 | ||||||||
\(714\) | −7.46410 | −0.279337 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.39230 | −0.313635 | ||||||||
\(717\) | −12.4641 | −0.465480 | ||||||||
\(718\) | −19.7128 | −0.735676 | ||||||||
\(719\) | 39.7128 | 1.48104 | 0.740519 | − | 0.672035i | \(-0.234580\pi\) | ||||
0.740519 | + | 0.672035i | \(0.234580\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 1.46410 | 0.0545260 | ||||||||
\(722\) | −16.1436 | −0.600802 | ||||||||
\(723\) | −4.00000 | −0.148762 | ||||||||
\(724\) | 10.4641 | 0.388895 | ||||||||
\(725\) | 6.92820 | 0.257307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7846 | −0.770859 | −0.385429 | − | 0.922737i | \(-0.625947\pi\) | ||||
−0.385429 | + | 0.922737i | \(0.625947\pi\) | |||||||
\(728\) | −4.46410 | −0.165451 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −0.535898 | −0.0198345 | ||||||||
\(731\) | 92.4974 | 3.42114 | ||||||||
\(732\) | 4.92820 | 0.182152 | ||||||||
\(733\) | 48.1769 | 1.77945 | 0.889727 | − | 0.456492i | \(-0.150894\pi\) | ||||
0.889727 | + | 0.456492i | \(0.150894\pi\) | |||||||
\(734\) | 21.4641 | 0.792254 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 4.46410 | 0.164549 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.7846 | 0.617850 | ||||||||
\(739\) | 20.2487 | 0.744861 | 0.372430 | − | 0.928060i | \(-0.378525\pi\) | ||||
0.372430 | + | 0.928060i | \(0.378525\pi\) | |||||||
\(740\) | −8.92820 | −0.328207 | ||||||||
\(741\) | −26.4641 | −0.972183 | ||||||||
\(742\) | −7.46410 | −0.274016 | ||||||||
\(743\) | −33.0718 | −1.21329 | −0.606643 | − | 0.794974i | \(-0.707484\pi\) | ||||
−0.606643 | + | 0.794974i | \(0.707484\pi\) | |||||||
\(744\) | −0.535898 | −0.0196470 | ||||||||
\(745\) | 3.07180 | 0.112542 | ||||||||
\(746\) | 24.9282 | 0.912686 | ||||||||
\(747\) | −2.00000 | −0.0731762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −26.1769 | −0.955209 | −0.477605 | − | 0.878575i | \(-0.658495\pi\) | ||||
−0.477605 | + | 0.878575i | \(0.658495\pi\) | |||||||
\(752\) | −0.535898 | −0.0195422 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.9282 | 1.12634 | ||||||||
\(755\) | 5.53590 | 0.201472 | ||||||||
\(756\) | −5.00000 | −0.181848 | ||||||||
\(757\) | −27.3205 | −0.992981 | −0.496490 | − | 0.868042i | \(-0.665378\pi\) | ||||
−0.496490 | + | 0.868042i | \(0.665378\pi\) | |||||||
\(758\) | −23.8564 | −0.866504 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.92820 | 0.215039 | ||||||||
\(761\) | −48.2487 | −1.74901 | −0.874507 | − | 0.485013i | \(-0.838815\pi\) | ||||
−0.874507 | + | 0.485013i | \(0.838815\pi\) | |||||||
\(762\) | −13.3923 | −0.485152 | ||||||||
\(763\) | 18.3923 | 0.665846 | ||||||||
\(764\) | 3.39230 | 0.122729 | ||||||||
\(765\) | −14.9282 | −0.539730 | ||||||||
\(766\) | 21.4641 | 0.775530 | ||||||||
\(767\) | −44.3205 | −1.60032 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 22.7846 | 0.821634 | 0.410817 | − | 0.911718i | \(-0.365244\pi\) | ||||
0.410817 | + | 0.911718i | \(0.365244\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.39230 | −0.0861568 | ||||||||
\(772\) | −19.0000 | −0.683825 | ||||||||
\(773\) | 2.46410 | 0.0886276 | 0.0443138 | − | 0.999018i | \(-0.485890\pi\) | ||||
0.0443138 | + | 0.999018i | \(0.485890\pi\) | |||||||
\(774\) | 24.7846 | 0.890864 | ||||||||
\(775\) | −0.535898 | −0.0192500 | ||||||||
\(776\) | 1.07180 | 0.0384753 | ||||||||
\(777\) | −8.92820 | −0.320298 | ||||||||
\(778\) | 13.3205 | 0.477563 | ||||||||
\(779\) | −49.7513 | −1.78252 | ||||||||
\(780\) | 4.46410 | 0.159840 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 33.3205 | 1.19154 | ||||||||
\(783\) | 34.6410 | 1.23797 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −20.3205 | −0.725270 | ||||||||
\(786\) | 10.8564 | 0.387235 | ||||||||
\(787\) | −48.4974 | −1.72875 | −0.864373 | − | 0.502851i | \(-0.832285\pi\) | ||||
−0.864373 | + | 0.502851i | \(0.832285\pi\) | |||||||
\(788\) | −4.00000 | −0.142494 | ||||||||
\(789\) | 16.4641 | 0.586138 | ||||||||
\(790\) | −7.53590 | −0.268115 | ||||||||
\(791\) | −1.00000 | −0.0355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0000 | 0.781243 | ||||||||
\(794\) | 11.0718 | 0.392923 | ||||||||
\(795\) | 7.46410 | 0.264724 | ||||||||
\(796\) | −25.8564 | −0.916456 | ||||||||
\(797\) | −21.3923 | −0.757754 | −0.378877 | − | 0.925447i | \(-0.623690\pi\) | ||||
−0.378877 | + | 0.925447i | \(0.623690\pi\) | |||||||
\(798\) | 5.92820 | 0.209856 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 34.9282 | 1.23413 | ||||||||
\(802\) | −4.14359 | −0.146315 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.39230 | −0.225439 | ||||||||
\(805\) | 4.46410 | 0.157339 | ||||||||
\(806\) | −2.39230 | −0.0842653 | ||||||||
\(807\) | 10.3205 | 0.363299 | ||||||||
\(808\) | −11.5359 | −0.405831 | ||||||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −35.7128 | −1.25405 | −0.627023 | − | 0.779001i | \(-0.715727\pi\) | ||||
−0.627023 | + | 0.779001i | \(0.715727\pi\) | |||||||
\(812\) | −6.92820 | −0.243132 | ||||||||
\(813\) | 29.8564 | 1.04711 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0000 | −0.770626 | ||||||||
\(816\) | −7.46410 | −0.261296 | ||||||||
\(817\) | −73.4641 | −2.57018 | ||||||||
\(818\) | −31.7128 | −1.10881 | ||||||||
\(819\) | −8.92820 | −0.311977 | ||||||||
\(820\) | 8.39230 | 0.293072 | ||||||||
\(821\) | −36.9282 | −1.28880 | −0.644402 | − | 0.764687i | \(-0.722893\pi\) | ||||
−0.644402 | + | 0.764687i | \(0.722893\pi\) | |||||||
\(822\) | 7.92820 | 0.276528 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | 1.46410 | 0.0510044 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.92820 | 0.345446 | ||||||||
\(827\) | 18.3923 | 0.639563 | 0.319782 | − | 0.947491i | \(-0.396390\pi\) | ||||
0.319782 | + | 0.947491i | \(0.396390\pi\) | |||||||
\(828\) | 8.92820 | 0.310277 | ||||||||
\(829\) | −21.3923 | −0.742985 | −0.371493 | − | 0.928436i | \(-0.621154\pi\) | ||||
−0.371493 | + | 0.928436i | \(0.621154\pi\) | |||||||
\(830\) | −1.00000 | −0.0347105 | ||||||||
\(831\) | 27.3205 | 0.947738 | ||||||||
\(832\) | −4.46410 | −0.154765 | ||||||||
\(833\) | 7.46410 | 0.258616 | ||||||||
\(834\) | −16.8564 | −0.583690 | ||||||||
\(835\) | 4.39230 | 0.152002 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.67949 | −0.0926168 | ||||||||
\(838\) | −38.7128 | −1.33731 | ||||||||
\(839\) | 6.24871 | 0.215729 | 0.107865 | − | 0.994166i | \(-0.465599\pi\) | ||||
0.107865 | + | 0.994166i | \(0.465599\pi\) | |||||||
\(840\) | −1.00000 | −0.0345033 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | −5.85641 | −0.201825 | ||||||||
\(843\) | 17.0000 | 0.585511 | ||||||||
\(844\) | 24.0000 | 0.826114 | ||||||||
\(845\) | 6.92820 | 0.238337 | ||||||||
\(846\) | −1.07180 | −0.0368491 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.46410 | −0.256318 | ||||||||
\(849\) | −13.7846 | −0.473087 | ||||||||
\(850\) | −7.46410 | −0.256017 | ||||||||
\(851\) | 39.8564 | 1.36626 | ||||||||
\(852\) | −8.00000 | −0.274075 | ||||||||
\(853\) | −9.53590 | −0.326503 | −0.163251 | − | 0.986584i | \(-0.552198\pi\) | ||||
−0.163251 | + | 0.986584i | \(0.552198\pi\) | |||||||
\(854\) | −4.92820 | −0.168640 | ||||||||
\(855\) | 11.8564 | 0.405481 | ||||||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | −6.92820 | −0.236663 | −0.118331 | − | 0.992974i | \(-0.537755\pi\) | ||||
−0.118331 | + | 0.992974i | \(0.537755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.6410 | −0.908980 | −0.454490 | − | 0.890752i | \(-0.650178\pi\) | ||||
−0.454490 | + | 0.890752i | \(0.650178\pi\) | |||||||
\(860\) | 12.3923 | 0.422574 | ||||||||
\(861\) | 8.39230 | 0.286009 | ||||||||
\(862\) | −10.3205 | −0.351518 | ||||||||
\(863\) | 0.784610 | 0.0267084 | 0.0133542 | − | 0.999911i | \(-0.495749\pi\) | ||||
0.0133542 | + | 0.999911i | \(0.495749\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | −22.2487 | −0.756042 | ||||||||
\(867\) | −38.7128 | −1.31476 | ||||||||
\(868\) | 0.535898 | 0.0181896 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.92820 | 0.234888 | ||||||||
\(871\) | −28.5359 | −0.966902 | ||||||||
\(872\) | 18.3923 | 0.622842 | ||||||||
\(873\) | 2.14359 | 0.0725496 | ||||||||
\(874\) | −26.4641 | −0.895162 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −0.535898 | −0.0181063 | ||||||||
\(877\) | 8.39230 | 0.283388 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(878\) | −22.5359 | −0.760550 | ||||||||
\(879\) | −20.4641 | −0.690237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.71281 | −0.192470 | −0.0962348 | − | 0.995359i | \(-0.530680\pi\) | ||||
−0.0962348 | + | 0.995359i | \(0.530680\pi\) | |||||||
\(882\) | 2.00000 | 0.0673435 | ||||||||
\(883\) | −34.7846 | −1.17060 | −0.585298 | − | 0.810819i | \(-0.699022\pi\) | ||||
−0.585298 | + | 0.810819i | \(0.699022\pi\) | |||||||
\(884\) | −33.3205 | −1.12069 | ||||||||
\(885\) | −9.92820 | −0.333733 | ||||||||
\(886\) | 15.7128 | 0.527882 | ||||||||
\(887\) | 26.5359 | 0.890988 | 0.445494 | − | 0.895285i | \(-0.353028\pi\) | ||||
0.445494 | + | 0.895285i | \(0.353028\pi\) | |||||||
\(888\) | −8.92820 | −0.299611 | ||||||||
\(889\) | 13.3923 | 0.449163 | ||||||||
\(890\) | 17.4641 | 0.585398 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.46410 | −0.115987 | ||||||||
\(893\) | 3.17691 | 0.106311 | ||||||||
\(894\) | 3.07180 | 0.102736 | ||||||||
\(895\) | −8.39230 | −0.280524 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −19.9282 | −0.665383 | ||||||||
\(898\) | 8.07180 | 0.269359 | ||||||||
\(899\) | −3.71281 | −0.123829 | ||||||||
\(900\) | −2.00000 | −0.0666667 | ||||||||
\(901\) | −55.7128 | −1.85606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.3923 | 0.412390 | ||||||||
\(904\) | −1.00000 | −0.0332595 | ||||||||
\(905\) | 10.4641 | 0.347839 | ||||||||
\(906\) | 5.53590 | 0.183918 | ||||||||
\(907\) | −42.6410 | −1.41587 | −0.707936 | − | 0.706277i | \(-0.750373\pi\) | ||||
−0.707936 | + | 0.706277i | \(0.750373\pi\) | |||||||
\(908\) | 16.0000 | 0.530979 | ||||||||
\(909\) | −23.0718 | −0.765243 | ||||||||
\(910\) | −4.46410 | −0.147984 | ||||||||
\(911\) | 9.39230 | 0.311181 | 0.155590 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155590 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(912\) | 5.92820 | 0.196302 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −39.6410 | −1.31121 | ||||||||
\(915\) | 4.92820 | 0.162921 | ||||||||
\(916\) | −18.0000 | −0.594737 | ||||||||
\(917\) | −10.8564 | −0.358510 | ||||||||
\(918\) | −37.3205 | −1.23176 | ||||||||
\(919\) | −3.71281 | −0.122474 | −0.0612372 | − | 0.998123i | \(-0.519505\pi\) | ||||
−0.0612372 | + | 0.998123i | \(0.519505\pi\) | |||||||
\(920\) | 4.46410 | 0.147177 | ||||||||
\(921\) | −14.9282 | −0.491901 | ||||||||
\(922\) | 12.1436 | 0.399928 | ||||||||
\(923\) | −35.7128 | −1.17550 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.92820 | −0.293558 | ||||||||
\(926\) | 8.46410 | 0.278148 | ||||||||
\(927\) | 2.92820 | 0.0961748 | ||||||||
\(928\) | −6.92820 | −0.227429 | ||||||||
\(929\) | −25.8564 | −0.848321 | −0.424161 | − | 0.905587i | \(-0.639431\pi\) | ||||
−0.424161 | + | 0.905587i | \(0.639431\pi\) | |||||||
\(930\) | −0.535898 | −0.0175728 | ||||||||
\(931\) | −5.92820 | −0.194289 | ||||||||
\(932\) | 18.8564 | 0.617662 | ||||||||
\(933\) | −23.3205 | −0.763479 | ||||||||
\(934\) | 15.9282 | 0.521187 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.92820 | −0.291827 | ||||||||
\(937\) | −6.14359 | −0.200702 | −0.100351 | − | 0.994952i | \(-0.531997\pi\) | ||||
−0.100351 | + | 0.994952i | \(0.531997\pi\) | |||||||
\(938\) | 6.39230 | 0.208716 | ||||||||
\(939\) | −14.7846 | −0.482478 | ||||||||
\(940\) | −0.535898 | −0.0174791 | ||||||||
\(941\) | 38.0000 | 1.23876 | 0.619382 | − | 0.785090i | \(-0.287383\pi\) | ||||
0.619382 | + | 0.785090i | \(0.287383\pi\) | |||||||
\(942\) | −20.3205 | −0.662078 | ||||||||
\(943\) | −37.4641 | −1.22000 | ||||||||
\(944\) | 9.92820 | 0.323135 | ||||||||
\(945\) | −5.00000 | −0.162650 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.6077 | 0.962121 | 0.481060 | − | 0.876687i | \(-0.340252\pi\) | ||||
0.481060 | + | 0.876687i | \(0.340252\pi\) | |||||||
\(948\) | −7.53590 | −0.244755 | ||||||||
\(949\) | −2.39230 | −0.0776575 | ||||||||
\(950\) | 5.92820 | 0.192336 | ||||||||
\(951\) | 22.3923 | 0.726120 | ||||||||
\(952\) | 7.46410 | 0.241913 | ||||||||
\(953\) | −32.5692 | −1.05502 | −0.527510 | − | 0.849549i | \(-0.676874\pi\) | ||||
−0.527510 | + | 0.849549i | \(0.676874\pi\) | |||||||
\(954\) | −14.9282 | −0.483318 | ||||||||
\(955\) | 3.39230 | 0.109772 | ||||||||
\(956\) | 12.4641 | 0.403118 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.53590 | −0.0819312 | ||||||||
\(959\) | −7.92820 | −0.256015 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | −39.8564 | −1.28502 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 4.00000 | 0.128831 | ||||||||
\(965\) | −19.0000 | −0.611632 | ||||||||
\(966\) | 4.46410 | 0.143630 | ||||||||
\(967\) | −11.7128 | −0.376659 | −0.188329 | − | 0.982106i | \(-0.560307\pi\) | ||||
−0.188329 | + | 0.982106i | \(0.560307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.2487 | 1.42147 | ||||||||
\(970\) | 1.07180 | 0.0344133 | ||||||||
\(971\) | 12.7128 | 0.407974 | 0.203987 | − | 0.978974i | \(-0.434610\pi\) | ||||
0.203987 | + | 0.978974i | \(0.434610\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | 16.8564 | 0.540392 | ||||||||
\(974\) | −2.32051 | −0.0743539 | ||||||||
\(975\) | 4.46410 | 0.142966 | ||||||||
\(976\) | −4.92820 | −0.157748 | ||||||||
\(977\) | 18.8564 | 0.603270 | 0.301635 | − | 0.953423i | \(-0.402468\pi\) | ||||
0.301635 | + | 0.953423i | \(0.402468\pi\) | |||||||
\(978\) | −22.0000 | −0.703482 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 36.7846 | 1.17444 | ||||||||
\(982\) | 23.4641 | 0.748770 | ||||||||
\(983\) | 14.7846 | 0.471556 | 0.235778 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235778 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(984\) | 8.39230 | 0.267537 | ||||||||
\(985\) | −4.00000 | −0.127451 | ||||||||
\(986\) | −51.7128 | −1.64687 | ||||||||
\(987\) | −0.535898 | −0.0170578 | ||||||||
\(988\) | 26.4641 | 0.841935 | ||||||||
\(989\) | −55.3205 | −1.75909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.1051 | 1.36928 | 0.684640 | − | 0.728882i | \(-0.259960\pi\) | ||||
0.684640 | + | 0.728882i | \(0.259960\pi\) | |||||||
\(992\) | 0.535898 | 0.0170148 | ||||||||
\(993\) | −1.46410 | −0.0464619 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −25.8564 | −0.819703 | ||||||||
\(996\) | −1.00000 | −0.0316862 | ||||||||
\(997\) | 30.3205 | 0.960260 | 0.480130 | − | 0.877197i | \(-0.340589\pi\) | ||||
0.480130 | + | 0.877197i | \(0.340589\pi\) | |||||||
\(998\) | 8.92820 | 0.282617 | ||||||||
\(999\) | −44.6410 | −1.41238 |
(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 | 8470.2.a.bi.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.bw.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bi.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.bw.1.2 | yes | 2 | 11.10 | odd | 2 |