Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.477260 | −0.337474 | −0.168737 | − | 0.985661i | \(-0.553969\pi\) | ||||
−0.168737 | + | 0.985661i | \(0.553969\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77222 | −0.886111 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.68522 | 1.01492 | 0.507459 | − | 0.861676i | \(-0.330585\pi\) | ||||
0.507459 | + | 0.861676i | \(0.330585\pi\) | |||||||
\(8\) | 1.80033 | 0.636513 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.477260 | −0.150923 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.66785 | −1.29463 | −0.647314 | − | 0.762223i | \(-0.724108\pi\) | ||||
−0.647314 | + | 0.762223i | \(0.724108\pi\) | |||||||
\(14\) | −1.28155 | −0.342508 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.68522 | 0.671305 | ||||||||
\(17\) | 4.62632 | 1.12205 | 0.561024 | − | 0.827799i | \(-0.310407\pi\) | ||||
0.561024 | + | 0.827799i | \(0.310407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34044 | −0.995766 | −0.497883 | − | 0.867244i | \(-0.665889\pi\) | ||||
−0.497883 | + | 0.867244i | \(0.665889\pi\) | |||||||
\(20\) | −1.77222 | −0.396281 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.77222 | −0.578048 | −0.289024 | − | 0.957322i | \(-0.593331\pi\) | ||||
−0.289024 | + | 0.957322i | \(0.593331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.22778 | 0.436903 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.75881 | −0.899330 | ||||||||
\(29\) | 3.01341 | 0.559577 | 0.279789 | − | 0.960062i | \(-0.409736\pi\) | ||||
0.279789 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.38630 | 0.428592 | 0.214296 | − | 0.976769i | \(-0.431254\pi\) | ||||
0.214296 | + | 0.976769i | \(0.431254\pi\) | |||||||
\(32\) | −4.88221 | −0.863061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.20796 | −0.378662 | ||||||||
\(35\) | 2.68522 | 0.453885 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.6429 | −1.74968 | −0.874842 | − | 0.484409i | \(-0.839035\pi\) | ||||
−0.874842 | + | 0.484409i | \(0.839035\pi\) | |||||||
\(38\) | 2.07152 | 0.336045 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.80033 | 0.284657 | ||||||||
\(41\) | 2.21041 | 0.345207 | 0.172604 | − | 0.984991i | \(-0.444782\pi\) | ||||
0.172604 | + | 0.984991i | \(0.444782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.06719 | −1.07774 | −0.538868 | − | 0.842390i | \(-0.681148\pi\) | ||||
−0.538868 | + | 0.842390i | \(0.681148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.32307 | 0.195076 | ||||||||
\(47\) | −4.36215 | −0.636285 | −0.318142 | − | 0.948043i | \(-0.603059\pi\) | ||||
−0.318142 | + | 0.948043i | \(0.603059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.210405 | 0.0300579 | ||||||||
\(50\) | −0.477260 | −0.0674948 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.27247 | 1.14718 | ||||||||
\(53\) | 6.33404 | 0.870047 | 0.435024 | − | 0.900419i | \(-0.356740\pi\) | ||||
0.435024 | + | 0.900419i | \(0.356740\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.83428 | 0.646008 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.43818 | −0.188843 | ||||||||
\(59\) | −11.7473 | −1.52937 | −0.764683 | − | 0.644407i | \(-0.777104\pi\) | ||||
−0.764683 | + | 0.644407i | \(0.777104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.98263 | −0.509923 | −0.254962 | − | 0.966951i | \(-0.582063\pi\) | ||||
−0.254962 | + | 0.966951i | \(0.582063\pi\) | |||||||
\(62\) | −1.13889 | −0.144639 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.04036 | −0.380044 | ||||||||
\(65\) | −4.66785 | −0.578975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.31984 | 0.894260 | 0.447130 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447130 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(68\) | −8.19888 | −0.994260 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.28155 | −0.153174 | ||||||||
\(71\) | −1.19571 | −0.141905 | −0.0709525 | − | 0.997480i | \(-0.522604\pi\) | ||||
−0.0709525 | + | 0.997480i | \(0.522604\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.02171 | 0.119582 | 0.0597908 | − | 0.998211i | \(-0.480957\pi\) | ||||
0.0597908 | + | 0.998211i | \(0.480957\pi\) | |||||||
\(74\) | 5.07943 | 0.590472 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.69223 | 0.882360 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50213 | 0.394021 | 0.197010 | − | 0.980401i | \(-0.436877\pi\) | ||||
0.197010 | + | 0.980401i | \(0.436877\pi\) | |||||||
\(80\) | 2.68522 | 0.300217 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.05494 | −0.116498 | ||||||||
\(83\) | −11.1158 | −1.22012 | −0.610061 | − | 0.792355i | \(-0.708855\pi\) | ||||
−0.610061 | + | 0.792355i | \(0.708855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.62632 | 0.501795 | ||||||||
\(86\) | 3.37289 | 0.363708 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.76978 | −0.293596 | −0.146798 | − | 0.989167i | \(-0.546897\pi\) | ||||
−0.146798 | + | 0.989167i | \(0.546897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5342 | −1.31394 | ||||||||
\(92\) | 4.91300 | 0.512215 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.08188 | 0.214729 | ||||||||
\(95\) | −4.34044 | −0.445320 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.5342 | 1.88186 | 0.940931 | − | 0.338597i | \(-0.109952\pi\) | ||||
0.940931 | + | 0.338597i | \(0.109952\pi\) | |||||||
\(98\) | −0.100418 | −0.0101438 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.77222 | −0.177222 | ||||||||
\(101\) | 7.11455 | 0.707925 | 0.353962 | − | 0.935260i | \(-0.384834\pi\) | ||||
0.353962 | + | 0.935260i | \(0.384834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.52835 | 0.741791 | 0.370895 | − | 0.928675i | \(-0.379051\pi\) | ||||
0.370895 | + | 0.928675i | \(0.379051\pi\) | |||||||
\(104\) | −8.40367 | −0.824048 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.02298 | −0.293618 | ||||||||
\(107\) | −18.0292 | −1.74295 | −0.871475 | − | 0.490441i | \(-0.836836\pi\) | ||||
−0.871475 | + | 0.490441i | \(0.836836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.3653 | −1.56751 | −0.783756 | − | 0.621068i | \(-0.786699\pi\) | ||||
−0.783756 | + | 0.621068i | \(0.786699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.21041 | 0.681319 | ||||||||
\(113\) | 2.05377 | 0.193203 | 0.0966013 | − | 0.995323i | \(-0.469203\pi\) | ||||
0.0966013 | + | 0.995323i | \(0.469203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.77222 | −0.258511 | ||||||||
\(116\) | −5.34044 | −0.495848 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.60651 | 0.516121 | ||||||||
\(119\) | 12.4227 | 1.13879 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.90075 | 0.172086 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.22906 | −0.379780 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0762667 | −0.00676758 | −0.00338379 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338379 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(128\) | 11.2155 | 0.991316 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.22778 | 0.195389 | ||||||||
\(131\) | 11.4831 | 1.00328 | 0.501642 | − | 0.865075i | \(-0.332730\pi\) | ||||
0.501642 | + | 0.865075i | \(0.332730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6550 | −1.01062 | ||||||||
\(134\) | −3.49346 | −0.301789 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.32892 | 0.714199 | ||||||||
\(137\) | 18.3293 | 1.56598 | 0.782989 | − | 0.622036i | \(-0.213694\pi\) | ||||
0.782989 | + | 0.622036i | \(0.213694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.1874 | −1.96673 | −0.983363 | − | 0.181653i | \(-0.941855\pi\) | ||||
−0.983363 | + | 0.181653i | \(0.941855\pi\) | |||||||
\(140\) | −4.75881 | −0.402193 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.570666 | 0.0478892 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.01341 | 0.250250 | ||||||||
\(146\) | −0.487619 | −0.0403557 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.8616 | 1.55041 | ||||||||
\(149\) | −14.6646 | −1.20137 | −0.600686 | − | 0.799485i | \(-0.705106\pi\) | ||||
−0.600686 | + | 0.799485i | \(0.705106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.51902 | −0.611889 | −0.305944 | − | 0.952049i | \(-0.598972\pi\) | ||||
−0.305944 | + | 0.952049i | \(0.598972\pi\) | |||||||
\(152\) | −7.81423 | −0.633818 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.38630 | 0.191672 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3819 | −1.06799 | −0.533996 | − | 0.845487i | \(-0.679310\pi\) | ||||
−0.533996 | + | 0.845487i | \(0.679310\pi\) | |||||||
\(158\) | −1.67143 | −0.132972 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.88221 | −0.385973 | ||||||||
\(161\) | −7.44403 | −0.586672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.771990 | −0.0604669 | −0.0302335 | − | 0.999543i | \(-0.509625\pi\) | ||||
−0.0302335 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(164\) | −3.91733 | −0.305892 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.30514 | 0.411759 | ||||||||
\(167\) | 8.48232 | 0.656381 | 0.328191 | − | 0.944612i | \(-0.393561\pi\) | ||||
0.328191 | + | 0.944612i | \(0.393561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.78880 | 0.676062 | ||||||||
\(170\) | −2.20796 | −0.169343 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5246 | 0.954994 | ||||||||
\(173\) | −5.07871 | −0.386127 | −0.193064 | − | 0.981186i | \(-0.561842\pi\) | ||||
−0.193064 | + | 0.981186i | \(0.561842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.68522 | 0.202984 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.32190 | 0.0990809 | ||||||||
\(179\) | 11.3170 | 0.845876 | 0.422938 | − | 0.906159i | \(-0.360999\pi\) | ||||
0.422938 | + | 0.906159i | \(0.360999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.40006 | 0.550042 | 0.275021 | − | 0.961438i | \(-0.411315\pi\) | ||||
0.275021 | + | 0.961438i | \(0.411315\pi\) | |||||||
\(182\) | 5.98207 | 0.443421 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.99092 | −0.367935 | ||||||||
\(185\) | −10.6429 | −0.782482 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.73070 | 0.563819 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.07152 | 0.150284 | ||||||||
\(191\) | 5.15608 | 0.373081 | 0.186540 | − | 0.982447i | \(-0.440272\pi\) | ||||
0.186540 | + | 0.982447i | \(0.440272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.03230 | −0.290251 | −0.145126 | − | 0.989413i | \(-0.546359\pi\) | ||||
−0.145126 | + | 0.989413i | \(0.546359\pi\) | |||||||
\(194\) | −8.84563 | −0.635079 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.372885 | −0.0266346 | ||||||||
\(197\) | −11.4176 | −0.813469 | −0.406734 | − | 0.913547i | \(-0.633333\pi\) | ||||
−0.406734 | + | 0.913547i | \(0.633333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.16644 | −0.508015 | −0.254008 | − | 0.967202i | \(-0.581749\pi\) | ||||
−0.254008 | + | 0.967202i | \(0.581749\pi\) | |||||||
\(200\) | 1.80033 | 0.127303 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.39549 | −0.238906 | ||||||||
\(203\) | 8.09168 | 0.567925 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.21041 | 0.154381 | ||||||||
\(206\) | −3.59298 | −0.250335 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.5342 | −0.869090 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.48359 | 0.239820 | 0.119910 | − | 0.992785i | \(-0.461739\pi\) | ||||
0.119910 | + | 0.992785i | \(0.461739\pi\) | |||||||
\(212\) | −11.2253 | −0.770959 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.60462 | 0.588200 | ||||||||
\(215\) | −7.06719 | −0.481978 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.40774 | 0.434986 | ||||||||
\(218\) | 7.81051 | 0.528995 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.5950 | −1.45264 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5449 | 0.706141 | 0.353071 | − | 0.935597i | \(-0.385138\pi\) | ||||
0.353071 | + | 0.935597i | \(0.385138\pi\) | |||||||
\(224\) | −13.1098 | −0.875936 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.980183 | −0.0652008 | ||||||||
\(227\) | −0.216018 | −0.0143376 | −0.00716880 | − | 0.999974i | \(-0.502282\pi\) | ||||
−0.00716880 | + | 0.999974i | \(0.502282\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0757097 | −0.00500304 | −0.00250152 | − | 0.999997i | \(-0.500796\pi\) | ||||
−0.00250152 | + | 0.999997i | \(0.500796\pi\) | |||||||
\(230\) | 1.32307 | 0.0872407 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.42514 | 0.356178 | ||||||||
\(233\) | −15.1201 | −0.990548 | −0.495274 | − | 0.868737i | \(-0.664932\pi\) | ||||
−0.495274 | + | 0.868737i | \(0.664932\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.36215 | −0.284555 | ||||||||
\(236\) | 20.8188 | 1.35519 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.92886 | −0.384311 | ||||||||
\(239\) | 23.1646 | 1.49839 | 0.749197 | − | 0.662347i | \(-0.230439\pi\) | ||||
0.749197 | + | 0.662347i | \(0.230439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3349 | −1.37430 | −0.687151 | − | 0.726515i | \(-0.741139\pi\) | ||||
−0.687151 | + | 0.726515i | \(0.741139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.05810 | 0.451849 | ||||||||
\(245\) | 0.210405 | 0.0134423 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.2605 | 1.28915 | ||||||||
\(248\) | 4.29613 | 0.272805 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.477260 | −0.0301846 | ||||||||
\(251\) | 6.22186 | 0.392721 | 0.196360 | − | 0.980532i | \(-0.437088\pi\) | ||||
0.196360 | + | 0.980532i | \(0.437088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.0363991 | 0.00228388 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.728021 | 0.0455013 | ||||||||
\(257\) | 14.2903 | 0.891406 | 0.445703 | − | 0.895181i | \(-0.352954\pi\) | ||||
0.445703 | + | 0.895181i | \(0.352954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.5785 | −1.77578 | ||||||||
\(260\) | 8.27247 | 0.513037 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.48043 | −0.338582 | ||||||||
\(263\) | −4.13132 | −0.254748 | −0.127374 | − | 0.991855i | \(-0.540655\pi\) | ||||
−0.127374 | + | 0.991855i | \(0.540655\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.33404 | 0.389097 | ||||||||
\(266\) | 5.56249 | 0.341058 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.9724 | −0.792414 | ||||||||
\(269\) | 1.68394 | 0.102672 | 0.0513359 | − | 0.998681i | \(-0.483652\pi\) | ||||
0.0513359 | + | 0.998681i | \(0.483652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4310 | −1.11960 | −0.559801 | − | 0.828627i | \(-0.689123\pi\) | ||||
−0.559801 | + | 0.828627i | \(0.689123\pi\) | |||||||
\(272\) | 12.4227 | 0.753237 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.74784 | −0.528476 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.42745 | −0.205935 | −0.102968 | − | 0.994685i | \(-0.532834\pi\) | ||||
−0.102968 | + | 0.994685i | \(0.532834\pi\) | |||||||
\(278\) | 11.0664 | 0.663718 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.83428 | 0.288904 | ||||||||
\(281\) | 22.8217 | 1.36143 | 0.680715 | − | 0.732548i | \(-0.261669\pi\) | ||||
0.680715 | + | 0.732548i | \(0.261669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.0991 | −1.72976 | −0.864880 | − | 0.501978i | \(-0.832606\pi\) | ||||
−0.864880 | + | 0.501978i | \(0.832606\pi\) | |||||||
\(284\) | 2.11907 | 0.125744 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.93542 | 0.350357 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.40288 | 0.258993 | ||||||||
\(290\) | −1.43818 | −0.0844530 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.81069 | −0.105963 | ||||||||
\(293\) | −21.2136 | −1.23931 | −0.619655 | − | 0.784874i | \(-0.712727\pi\) | ||||
−0.619655 | + | 0.784874i | \(0.712727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7473 | −0.683953 | ||||||||
\(296\) | −19.1608 | −1.11370 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.99883 | 0.405432 | ||||||||
\(299\) | 12.9403 | 0.748358 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.9769 | −1.09381 | ||||||||
\(302\) | 3.58853 | 0.206496 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.6550 | −0.668463 | ||||||||
\(305\) | −3.98263 | −0.228045 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.87520 | −0.392388 | −0.196194 | − | 0.980565i | \(-0.562858\pi\) | ||||
−0.196194 | + | 0.980565i | \(0.562858\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.13889 | −0.0646844 | ||||||||
\(311\) | −25.1577 | −1.42656 | −0.713280 | − | 0.700879i | \(-0.752791\pi\) | ||||
−0.713280 | + | 0.700879i | \(0.752791\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5793 | −0.654503 | −0.327251 | − | 0.944937i | \(-0.606122\pi\) | ||||
−0.327251 | + | 0.944937i | \(0.606122\pi\) | |||||||
\(314\) | 6.38664 | 0.360419 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.20656 | −0.349146 | ||||||||
\(317\) | −20.7413 | −1.16495 | −0.582473 | − | 0.812850i | \(-0.697915\pi\) | ||||
−0.582473 | + | 0.812850i | \(0.697915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.04036 | −0.169961 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.55274 | 0.197986 | ||||||||
\(323\) | −20.0803 | −1.11730 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.66785 | −0.258926 | ||||||||
\(326\) | 0.368440 | 0.0204060 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.97946 | 0.219729 | ||||||||
\(329\) | −11.7133 | −0.645777 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.1415 | −1.76665 | −0.883327 | − | 0.468757i | \(-0.844702\pi\) | ||||
−0.883327 | + | 0.468757i | \(0.844702\pi\) | |||||||
\(332\) | 19.6997 | 1.08116 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.04827 | −0.221511 | ||||||||
\(335\) | 7.31984 | 0.399925 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.9964 | −0.980326 | −0.490163 | − | 0.871631i | \(-0.663063\pi\) | ||||
−0.490163 | + | 0.871631i | \(0.663063\pi\) | |||||||
\(338\) | −4.19454 | −0.228153 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.19888 | −0.444647 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2316 | −0.984411 | ||||||||
\(344\) | −12.7233 | −0.685993 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.42387 | 0.130308 | ||||||||
\(347\) | 8.04981 | 0.432137 | 0.216068 | − | 0.976378i | \(-0.430677\pi\) | ||||
0.216068 | + | 0.976378i | \(0.430677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2294 | 1.02932 | 0.514662 | − | 0.857393i | \(-0.327917\pi\) | ||||
0.514662 | + | 0.857393i | \(0.327917\pi\) | |||||||
\(350\) | −1.28155 | −0.0685016 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8497 | −0.790371 | −0.395186 | − | 0.918601i | \(-0.629320\pi\) | ||||
−0.395186 | + | 0.918601i | \(0.629320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.19571 | −0.0634618 | ||||||||
\(356\) | 4.90866 | 0.260159 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.40117 | −0.285461 | ||||||||
\(359\) | −10.2233 | −0.539563 | −0.269782 | − | 0.962922i | \(-0.586952\pi\) | ||||
−0.269782 | + | 0.962922i | \(0.586952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.160555 | −0.00845028 | ||||||||
\(362\) | −3.53175 | −0.185625 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 22.2134 | 1.16430 | ||||||||
\(365\) | 1.02171 | 0.0534785 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1434 | 0.738279 | 0.369139 | − | 0.929374i | \(-0.379653\pi\) | ||||
0.369139 | + | 0.929374i | \(0.379653\pi\) | |||||||
\(368\) | −7.44403 | −0.388047 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.07943 | 0.264067 | ||||||||
\(371\) | 17.0083 | 0.883026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.4600 | 0.645154 | 0.322577 | − | 0.946543i | \(-0.395451\pi\) | ||||
0.322577 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.85331 | −0.405004 | ||||||||
\(377\) | −14.0662 | −0.724444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.3370 | 0.839174 | 0.419587 | − | 0.907715i | \(-0.362175\pi\) | ||||
0.419587 | + | 0.907715i | \(0.362175\pi\) | |||||||
\(380\) | 7.69223 | 0.394603 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.46079 | −0.125905 | ||||||||
\(383\) | 0.812648 | 0.0415244 | 0.0207622 | − | 0.999784i | \(-0.493391\pi\) | ||||
0.0207622 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.92445 | 0.0979522 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −32.8467 | −1.66754 | ||||||||
\(389\) | 30.3941 | 1.54104 | 0.770521 | − | 0.637414i | \(-0.219996\pi\) | ||||
0.770521 | + | 0.637414i | \(0.219996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8252 | −0.648598 | ||||||||
\(392\) | 0.378799 | 0.0191322 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.44915 | 0.274524 | ||||||||
\(395\) | 3.50213 | 0.176211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8996 | −0.747789 | −0.373894 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373894 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(398\) | 3.42025 | 0.171442 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.68522 | 0.134261 | ||||||||
\(401\) | −12.1692 | −0.607700 | −0.303850 | − | 0.952720i | \(-0.598272\pi\) | ||||
−0.303850 | + | 0.952720i | \(0.598272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.1389 | −0.554867 | ||||||||
\(404\) | −12.6086 | −0.627300 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.86184 | −0.191660 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.262108 | −0.0129604 | −0.00648020 | − | 0.999979i | \(-0.502063\pi\) | ||||
−0.00648020 | + | 0.999979i | \(0.502063\pi\) | |||||||
\(410\) | −1.05494 | −0.0520997 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.3419 | −0.657309 | ||||||||
\(413\) | −31.5440 | −1.55218 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.1158 | −0.545655 | ||||||||
\(416\) | 22.7894 | 1.11734 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.26916 | 0.0620023 | 0.0310012 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310012 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6655 | −1.44581 | −0.722903 | − | 0.690949i | \(-0.757193\pi\) | ||||
−0.722903 | + | 0.690949i | \(0.757193\pi\) | |||||||
\(422\) | −1.66258 | −0.0809331 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.4034 | 0.553797 | ||||||||
\(425\) | 4.62632 | 0.224410 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6942 | −0.517530 | ||||||||
\(428\) | 31.9518 | 1.54445 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.37289 | 0.162655 | ||||||||
\(431\) | −31.3549 | −1.51031 | −0.755156 | − | 0.655545i | \(-0.772439\pi\) | ||||
−0.755156 | + | 0.655545i | \(0.772439\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0325 | −1.25104 | −0.625521 | − | 0.780207i | \(-0.715114\pi\) | ||||
−0.625521 | + | 0.780207i | \(0.715114\pi\) | |||||||
\(434\) | −3.05816 | −0.146796 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.0030 | 1.38899 | ||||||||
\(437\) | 12.0327 | 0.575601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4191 | 0.688185 | 0.344093 | − | 0.938936i | \(-0.388187\pi\) | ||||
0.344093 | + | 0.938936i | \(0.388187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.3064 | 0.490226 | ||||||||
\(443\) | 0.330608 | 0.0157077 | 0.00785383 | − | 0.999969i | \(-0.497500\pi\) | ||||
0.00785383 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.76978 | −0.131300 | ||||||||
\(446\) | −5.03268 | −0.238304 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.16402 | −0.385714 | ||||||||
\(449\) | −8.50828 | −0.401531 | −0.200765 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200765 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.63974 | −0.171199 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.103097 | 0.00483856 | ||||||||
\(455\) | −12.5342 | −0.587612 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.13847 | 0.0532555 | 0.0266277 | − | 0.999645i | \(-0.491523\pi\) | ||||
0.0266277 | + | 0.999645i | \(0.491523\pi\) | |||||||
\(458\) | 0.0361332 | 0.00168839 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.91300 | 0.229070 | ||||||||
\(461\) | −14.5073 | −0.675670 | −0.337835 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337835 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89739 | −0.227601 | −0.113801 | − | 0.993504i | \(-0.536302\pi\) | ||||
−0.113801 | + | 0.993504i | \(0.536302\pi\) | |||||||
\(464\) | 8.09168 | 0.375647 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.21620 | 0.334284 | ||||||||
\(467\) | −32.4230 | −1.50036 | −0.750180 | − | 0.661234i | \(-0.770033\pi\) | ||||
−0.750180 | + | 0.661234i | \(0.770033\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.6554 | 0.907601 | ||||||||
\(470\) | 2.08188 | 0.0960299 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.1490 | −0.973461 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.34044 | −0.199153 | ||||||||
\(476\) | −22.0158 | −1.00909 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.0555 | −0.505669 | ||||||||
\(479\) | −17.7354 | −0.810352 | −0.405176 | − | 0.914239i | \(-0.632790\pi\) | ||||
−0.405176 | + | 0.914239i | \(0.632790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.6795 | 2.26519 | ||||||||
\(482\) | 10.1823 | 0.463791 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.5342 | 0.841595 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.4603 | −0.836514 | −0.418257 | − | 0.908329i | \(-0.637359\pi\) | ||||
−0.418257 | + | 0.908329i | \(0.637359\pi\) | |||||||
\(488\) | −7.17005 | −0.324573 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.100418 | −0.00453642 | ||||||||
\(491\) | 11.4338 | 0.516002 | 0.258001 | − | 0.966145i | \(-0.416936\pi\) | ||||
0.258001 | + | 0.966145i | \(0.416936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9410 | 0.627873 | ||||||||
\(494\) | −9.66954 | −0.435053 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.40774 | 0.287716 | ||||||||
\(497\) | −3.21075 | −0.144022 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8815 | 0.487125 | 0.243562 | − | 0.969885i | \(-0.421684\pi\) | ||||
0.243562 | + | 0.969885i | \(0.421684\pi\) | |||||||
\(500\) | −1.77222 | −0.0792562 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.96945 | −0.132533 | ||||||||
\(503\) | −44.7247 | −1.99417 | −0.997087 | − | 0.0762683i | \(-0.975699\pi\) | ||||
−0.997087 | + | 0.0762683i | \(0.975699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11455 | 0.316594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.135162 | 0.00599683 | ||||||||
\(509\) | 13.8093 | 0.612088 | 0.306044 | − | 0.952017i | \(-0.400994\pi\) | ||||
0.306044 | + | 0.952017i | \(0.400994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.74350 | 0.121365 | ||||||||
\(512\) | −22.7784 | −1.00667 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.82020 | −0.300826 | ||||||||
\(515\) | 7.52835 | 0.331739 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.6394 | 0.599281 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.40367 | −0.368525 | ||||||||
\(521\) | 3.64972 | 0.159897 | 0.0799486 | − | 0.996799i | \(-0.474524\pi\) | ||||
0.0799486 | + | 0.996799i | \(0.474524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.98707 | −0.218069 | −0.109035 | − | 0.994038i | \(-0.534776\pi\) | ||||
−0.109035 | + | 0.994038i | \(0.534776\pi\) | |||||||
\(524\) | −20.3506 | −0.889021 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.97171 | 0.0859707 | ||||||||
\(527\) | 11.0398 | 0.480901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3148 | −0.665860 | ||||||||
\(530\) | −3.02298 | −0.131310 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.6553 | 0.895522 | ||||||||
\(533\) | −10.3178 | −0.446915 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0292 | −0.779471 | ||||||||
\(536\) | 13.1781 | 0.569208 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.803678 | −0.0346490 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.247594 | 0.0106449 | 0.00532246 | − | 0.999986i | \(-0.498306\pi\) | ||||
0.00532246 | + | 0.999986i | \(0.498306\pi\) | |||||||
\(542\) | 8.79637 | 0.377837 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22.5867 | −0.968396 | ||||||||
\(545\) | −16.3653 | −0.701013 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3120 | −1.08226 | −0.541132 | − | 0.840938i | \(-0.682004\pi\) | ||||
−0.541132 | + | 0.840938i | \(0.682004\pi\) | |||||||
\(548\) | −32.4836 | −1.38763 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.0796 | −0.557208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.40400 | 0.399899 | ||||||||
\(554\) | 1.63578 | 0.0694978 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 41.0932 | 1.74274 | ||||||||
\(557\) | 38.6671 | 1.63838 | 0.819190 | − | 0.573523i | \(-0.194424\pi\) | ||||
0.819190 | + | 0.573523i | \(0.194424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9885 | 1.39527 | ||||||||
\(560\) | 7.21041 | 0.304695 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8919 | −0.459447 | ||||||||
\(563\) | −13.9362 | −0.587341 | −0.293671 | − | 0.955907i | \(-0.594877\pi\) | ||||
−0.293671 | + | 0.955907i | \(0.594877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.05377 | 0.0864028 | ||||||||
\(566\) | 13.8878 | 0.583749 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.15268 | −0.0903243 | ||||||||
\(569\) | −27.9125 | −1.17015 | −0.585076 | − | 0.810979i | \(-0.698935\pi\) | ||||
−0.585076 | + | 0.810979i | \(0.698935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.4113 | −1.31452 | −0.657261 | − | 0.753663i | \(-0.728285\pi\) | ||||
−0.657261 | + | 0.753663i | \(0.728285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.83274 | −0.118236 | ||||||||
\(575\) | −2.77222 | −0.115610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7349 | 0.863206 | 0.431603 | − | 0.902064i | \(-0.357948\pi\) | ||||
0.431603 | + | 0.902064i | \(0.357948\pi\) | |||||||
\(578\) | −2.10132 | −0.0874034 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.34044 | −0.221750 | ||||||||
\(581\) | −29.8485 | −1.23832 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.83941 | 0.0761153 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.1244 | 0.418235 | ||||||||
\(587\) | −15.2367 | −0.628886 | −0.314443 | − | 0.949276i | \(-0.601818\pi\) | ||||
−0.314443 | + | 0.949276i | \(0.601818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.3576 | −0.426777 | ||||||||
\(590\) | 5.60651 | 0.230816 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.5785 | −1.17457 | ||||||||
\(593\) | −27.5413 | −1.13098 | −0.565492 | − | 0.824754i | \(-0.691314\pi\) | ||||
−0.565492 | + | 0.824754i | \(0.691314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4227 | 0.509281 | ||||||||
\(596\) | 25.9890 | 1.06455 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.17589 | −0.252551 | ||||||||
\(599\) | 26.7331 | 1.09228 | 0.546142 | − | 0.837693i | \(-0.316096\pi\) | ||||
0.546142 | + | 0.837693i | \(0.316096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.40680 | 0.0981753 | 0.0490876 | − | 0.998794i | \(-0.484369\pi\) | ||||
0.0490876 | + | 0.998794i | \(0.484369\pi\) | |||||||
\(602\) | 9.05694 | 0.369133 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.3254 | 0.542202 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2929 | 0.417774 | 0.208887 | − | 0.977940i | \(-0.433016\pi\) | ||||
0.208887 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(608\) | 21.1910 | 0.859407 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.90075 | 0.0769591 | ||||||||
\(611\) | 20.3618 | 0.823752 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.8756 | 1.12589 | 0.562943 | − | 0.826496i | \(-0.309669\pi\) | ||||
0.562943 | + | 0.826496i | \(0.309669\pi\) | |||||||
\(614\) | 3.28126 | 0.132421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.7216 | 1.15629 | 0.578143 | − | 0.815935i | \(-0.303778\pi\) | ||||
0.578143 | + | 0.815935i | \(0.303778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6968 | 0.912261 | 0.456131 | − | 0.889913i | \(-0.349235\pi\) | ||||
0.456131 | + | 0.889913i | \(0.349235\pi\) | |||||||
\(620\) | −4.22906 | −0.169843 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0067 | 0.481427 | ||||||||
\(623\) | −7.43746 | −0.297976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.52635 | 0.220877 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.7157 | 0.946360 | ||||||||
\(629\) | −49.2375 | −1.96323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.5364 | 1.13602 | 0.568008 | − | 0.823023i | \(-0.307714\pi\) | ||||
0.568008 | + | 0.823023i | \(0.307714\pi\) | |||||||
\(632\) | 6.30500 | 0.250799 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.89897 | 0.393138 | ||||||||
\(635\) | −0.0762667 | −0.00302655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.982140 | −0.0389138 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.2155 | 0.443330 | ||||||||
\(641\) | −2.37375 | −0.0937575 | −0.0468788 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468788 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3603 | 0.448007 | 0.224004 | − | 0.974588i | \(-0.428087\pi\) | ||||
0.224004 | + | 0.974588i | \(0.428087\pi\) | |||||||
\(644\) | 13.1925 | 0.519856 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.58352 | 0.377059 | ||||||||
\(647\) | 48.4220 | 1.90366 | 0.951832 | − | 0.306621i | \(-0.0991984\pi\) | ||||
0.951832 | + | 0.306621i | \(0.0991984\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.22778 | 0.0873806 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.36814 | 0.0535804 | ||||||||
\(653\) | −29.7548 | −1.16440 | −0.582198 | − | 0.813047i | \(-0.697807\pi\) | ||||
−0.582198 | + | 0.813047i | \(0.697807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.4831 | 0.448682 | ||||||||
\(656\) | 5.93542 | 0.231739 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.59030 | 0.217933 | ||||||||
\(659\) | 28.4931 | 1.10993 | 0.554966 | − | 0.831873i | \(-0.312731\pi\) | ||||
0.554966 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.02875 | −0.0400139 | −0.0200070 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200070 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(662\) | 15.3398 | 0.596200 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.0122 | −0.776623 | ||||||||
\(665\) | −11.6550 | −0.451963 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.35386 | −0.323463 | ||||||||
\(668\) | −15.0326 | −0.581627 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.49346 | −0.134964 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0369 | 0.502536 | 0.251268 | − | 0.967918i | \(-0.419152\pi\) | ||||
0.251268 | + | 0.967918i | \(0.419152\pi\) | |||||||
\(674\) | 8.58896 | 0.330834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.5757 | −0.599066 | ||||||||
\(677\) | 37.1064 | 1.42612 | 0.713058 | − | 0.701105i | \(-0.247310\pi\) | ||||
0.713058 | + | 0.701105i | \(0.247310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49.7684 | 1.90994 | ||||||||
\(680\) | 8.32892 | 0.319399 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8992 | 1.25885 | 0.629426 | − | 0.777061i | \(-0.283290\pi\) | ||||
0.629426 | + | 0.777061i | \(0.283290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.3293 | 0.700326 | ||||||||
\(686\) | 8.70119 | 0.332213 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.9769 | −0.723489 | ||||||||
\(689\) | −29.5663 | −1.12639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.6998 | 1.39613 | 0.698064 | − | 0.716035i | \(-0.254045\pi\) | ||||
0.698064 | + | 0.716035i | \(0.254045\pi\) | |||||||
\(692\) | 9.00061 | 0.342152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.84185 | −0.145835 | ||||||||
\(695\) | −23.1874 | −0.879546 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.2261 | 0.387339 | ||||||||
\(698\) | −9.17741 | −0.347370 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.75881 | −0.179866 | ||||||||
\(701\) | 36.2497 | 1.36913 | 0.684566 | − | 0.728951i | \(-0.259992\pi\) | ||||
0.684566 | + | 0.728951i | \(0.259992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.1949 | 1.74227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.08718 | 0.266730 | ||||||||
\(707\) | 19.1041 | 0.718485 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6013 | −0.698585 | −0.349293 | − | 0.937014i | \(-0.613578\pi\) | ||||
−0.349293 | + | 0.937014i | \(0.613578\pi\) | |||||||
\(710\) | 0.570666 | 0.0214167 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.98652 | −0.186878 | ||||||||
\(713\) | −6.61536 | −0.247747 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.0563 | −0.749540 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.87915 | 0.182088 | ||||||||
\(719\) | 37.4280 | 1.39583 | 0.697914 | − | 0.716181i | \(-0.254112\pi\) | ||||
0.697914 | + | 0.716181i | \(0.254112\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.2153 | 0.752856 | ||||||||
\(722\) | 0.0766267 | 0.00285175 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.1146 | −0.487399 | ||||||||
\(725\) | 3.01341 | 0.111915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6011 | 0.541526 | 0.270763 | − | 0.962646i | \(-0.412724\pi\) | ||||
0.270763 | + | 0.962646i | \(0.412724\pi\) | |||||||
\(728\) | −22.5657 | −0.836341 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.487619 | −0.0180476 | ||||||||
\(731\) | −32.6951 | −1.20927 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.8369 | 1.54528 | 0.772640 | − | 0.634844i | \(-0.218936\pi\) | ||||
0.772640 | + | 0.634844i | \(0.218936\pi\) | |||||||
\(734\) | −6.75007 | −0.249150 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.5346 | 0.498891 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.9299 | −0.438849 | −0.219424 | − | 0.975630i | \(-0.570418\pi\) | ||||
−0.219424 | + | 0.975630i | \(0.570418\pi\) | |||||||
\(740\) | 18.8616 | 0.693366 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.11738 | −0.297998 | ||||||||
\(743\) | −46.6803 | −1.71253 | −0.856267 | − | 0.516534i | \(-0.827222\pi\) | ||||
−0.856267 | + | 0.516534i | \(0.827222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.6646 | −0.537270 | ||||||||
\(746\) | −5.94666 | −0.217723 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.4124 | −1.76895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4039 | 0.525607 | 0.262803 | − | 0.964849i | \(-0.415353\pi\) | ||||
0.262803 | + | 0.964849i | \(0.415353\pi\) | |||||||
\(752\) | −11.7133 | −0.427141 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.71322 | 0.244481 | ||||||||
\(755\) | −7.51902 | −0.273645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0616 | −0.583768 | −0.291884 | − | 0.956454i | \(-0.594282\pi\) | ||||
−0.291884 | + | 0.956454i | \(0.594282\pi\) | |||||||
\(758\) | −7.79698 | −0.283199 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.81423 | −0.283452 | ||||||||
\(761\) | 38.8840 | 1.40954 | 0.704772 | − | 0.709433i | \(-0.251049\pi\) | ||||
0.704772 | + | 0.709433i | \(0.251049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.9445 | −1.59090 | ||||||||
\(764\) | −9.13772 | −0.330591 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.387844 | −0.0140134 | ||||||||
\(767\) | 54.8345 | 1.97996 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.0017 | 1.55068 | 0.775341 | − | 0.631543i | \(-0.217578\pi\) | ||||
0.775341 | + | 0.631543i | \(0.217578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.14613 | 0.257195 | ||||||||
\(773\) | 7.85462 | 0.282511 | 0.141256 | − | 0.989973i | \(-0.454886\pi\) | ||||
0.141256 | + | 0.989973i | \(0.454886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.38630 | 0.0857184 | ||||||||
\(776\) | 33.3677 | 1.19783 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.5059 | −0.520061 | ||||||||
\(779\) | −9.59414 | −0.343746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.12096 | 0.218885 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.564984 | 0.0201780 | ||||||||
\(785\) | −13.3819 | −0.477620 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4249 | −0.407253 | −0.203627 | − | 0.979049i | \(-0.565273\pi\) | ||||
−0.203627 | + | 0.979049i | \(0.565273\pi\) | |||||||
\(788\) | 20.2345 | 0.720824 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.67143 | −0.0594667 | ||||||||
\(791\) | 5.51483 | 0.196085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5903 | 0.660161 | ||||||||
\(794\) | 7.11097 | 0.252359 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.7005 | 0.450158 | ||||||||
\(797\) | 4.28502 | 0.151783 | 0.0758915 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758915 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1807 | −0.713942 | ||||||||
\(800\) | −4.88221 | −0.172612 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.80787 | 0.205083 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.44403 | −0.262368 | ||||||||
\(806\) | 5.31614 | 0.187253 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.8086 | 0.450603 | ||||||||
\(809\) | 19.8484 | 0.697833 | 0.348917 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348917 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.13836 | −0.110203 | −0.0551014 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0551014 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(812\) | −14.3403 | −0.503245 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.771990 | −0.0270416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.6747 | 1.07317 | ||||||||
\(818\) | 0.125094 | 0.00437379 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.91733 | −0.136799 | ||||||||
\(821\) | −23.4999 | −0.820151 | −0.410076 | − | 0.912052i | \(-0.634498\pi\) | ||||
−0.410076 | + | 0.912052i | \(0.634498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.6564 | −0.441173 | −0.220586 | − | 0.975367i | \(-0.570797\pi\) | ||||
−0.220586 | + | 0.975367i | \(0.570797\pi\) | |||||||
\(824\) | 13.5535 | 0.472159 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0547 | 0.523820 | ||||||||
\(827\) | −30.2236 | −1.05098 | −0.525488 | − | 0.850801i | \(-0.676117\pi\) | ||||
−0.525488 | + | 0.850801i | \(0.676117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00166 | 0.0695204 | 0.0347602 | − | 0.999396i | \(-0.488933\pi\) | ||||
0.0347602 | + | 0.999396i | \(0.488933\pi\) | |||||||
\(830\) | 5.30514 | 0.184144 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.1919 | 0.492016 | ||||||||
\(833\) | 0.973403 | 0.0337264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.48232 | 0.293543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.605717 | −0.0209242 | ||||||||
\(839\) | −35.3744 | −1.22126 | −0.610629 | − | 0.791917i | \(-0.709083\pi\) | ||||
−0.610629 | + | 0.791917i | \(0.709083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.9193 | −0.686873 | ||||||||
\(842\) | 14.1581 | 0.487922 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.17370 | −0.212508 | ||||||||
\(845\) | 8.78880 | 0.302344 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.0083 | 0.584067 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.20796 | −0.0757324 | ||||||||
\(851\) | 29.5045 | 1.01140 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.2034 | −0.623272 | −0.311636 | − | 0.950202i | \(-0.600877\pi\) | ||||
−0.311636 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(854\) | 5.10393 | 0.174653 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.4585 | −1.10941 | ||||||||
\(857\) | 29.2837 | 1.00031 | 0.500156 | − | 0.865935i | \(-0.333276\pi\) | ||||
0.500156 | + | 0.865935i | \(0.333276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.44030 | 0.287979 | 0.143990 | − | 0.989579i | \(-0.454007\pi\) | ||||
0.143990 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(860\) | 12.5246 | 0.427086 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.9644 | 0.509691 | ||||||||
\(863\) | 19.3487 | 0.658636 | 0.329318 | − | 0.944219i | \(-0.393181\pi\) | ||||
0.329318 | + | 0.944219i | \(0.393181\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07871 | −0.172681 | ||||||||
\(866\) | 12.4243 | 0.422194 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.3559 | −0.385446 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.1679 | −1.15773 | ||||||||
\(872\) | −29.4630 | −0.997743 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.74271 | −0.194250 | ||||||||
\(875\) | 2.68522 | 0.0907770 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.5140 | 0.591405 | 0.295702 | − | 0.955280i | \(-0.404446\pi\) | ||||
0.295702 | + | 0.955280i | \(0.404446\pi\) | |||||||
\(878\) | −6.88165 | −0.232245 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0575 | 0.675754 | 0.337877 | − | 0.941190i | \(-0.390291\pi\) | ||||
0.337877 | + | 0.941190i | \(0.390291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.8980 | 0.905189 | 0.452594 | − | 0.891717i | \(-0.350499\pi\) | ||||
0.452594 | + | 0.891717i | \(0.350499\pi\) | |||||||
\(884\) | 38.2711 | 1.28720 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.157786 | −0.00530092 | ||||||||
\(887\) | −6.80568 | −0.228512 | −0.114256 | − | 0.993451i | \(-0.536448\pi\) | ||||
−0.114256 | + | 0.993451i | \(0.536448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.204793 | −0.00686854 | ||||||||
\(890\) | 1.32190 | 0.0443103 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.6880 | −0.625720 | ||||||||
\(893\) | 18.9337 | 0.633591 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.3170 | 0.378287 | ||||||||
\(896\) | 30.1160 | 1.00610 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.06066 | 0.135506 | ||||||||
\(899\) | 7.19091 | 0.239830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.3033 | 0.976235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.69747 | 0.122976 | ||||||||
\(905\) | 7.40006 | 0.245986 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.3313 | −0.708295 | −0.354148 | − | 0.935190i | \(-0.615229\pi\) | ||||
−0.354148 | + | 0.935190i | \(0.615229\pi\) | |||||||
\(908\) | 0.382831 | 0.0127047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.98207 | 0.198304 | ||||||||
\(911\) | 27.5888 | 0.914059 | 0.457029 | − | 0.889452i | \(-0.348913\pi\) | ||||
0.457029 | + | 0.889452i | \(0.348913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.543347 | −0.0179723 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.134174 | 0.00443325 | ||||||||
\(917\) | 30.8347 | 1.01825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.00889 | −0.198215 | −0.0991075 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991075 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(920\) | −4.99092 | −0.164546 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.92373 | 0.228021 | ||||||||
\(923\) | 5.58140 | 0.183714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6429 | −0.349937 | ||||||||
\(926\) | 2.33733 | 0.0768094 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.7121 | −0.482949 | ||||||||
\(929\) | −9.59739 | −0.314880 | −0.157440 | − | 0.987529i | \(-0.550324\pi\) | ||||
−0.157440 | + | 0.987529i | \(0.550324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.913252 | −0.0299306 | ||||||||
\(932\) | 26.7961 | 0.877736 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.4742 | 0.506332 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5917 | −1.26074 | −0.630369 | − | 0.776296i | \(-0.717096\pi\) | ||||
−0.630369 | + | 0.776296i | \(0.717096\pi\) | |||||||
\(938\) | −9.38072 | −0.306291 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.73070 | 0.252148 | ||||||||
\(941\) | 29.1846 | 0.951391 | 0.475695 | − | 0.879610i | \(-0.342196\pi\) | ||||
0.475695 | + | 0.879610i | \(0.342196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.12774 | −0.199547 | ||||||||
\(944\) | −31.5440 | −1.02667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.7623 | −1.51957 | −0.759785 | − | 0.650174i | \(-0.774696\pi\) | ||||
−0.759785 | + | 0.650174i | \(0.774696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.76917 | −0.154814 | ||||||||
\(950\) | 2.07152 | 0.0672090 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.3650 | 0.724853 | ||||||||
\(953\) | 6.15238 | 0.199295 | 0.0996475 | − | 0.995023i | \(-0.468228\pi\) | ||||
0.0996475 | + | 0.995023i | \(0.468228\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.15608 | 0.166847 | ||||||||
\(956\) | −41.0529 | −1.32774 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.46440 | 0.273472 | ||||||||
\(959\) | 49.2182 | 1.58934 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3056 | −0.816309 | ||||||||
\(962\) | −23.7100 | −0.764442 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.8102 | 1.21778 | ||||||||
\(965\) | −4.03230 | −0.129804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.39625 | 0.109216 | 0.0546080 | − | 0.998508i | \(-0.482609\pi\) | ||||
0.0546080 | + | 0.998508i | \(0.482609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.84563 | −0.284016 | ||||||||
\(971\) | 9.39500 | 0.301500 | 0.150750 | − | 0.988572i | \(-0.451831\pi\) | ||||
0.150750 | + | 0.988572i | \(0.451831\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.2631 | −1.99606 | ||||||||
\(974\) | 8.81035 | 0.282302 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.6942 | −0.342314 | ||||||||
\(977\) | 16.5552 | 0.529649 | 0.264824 | − | 0.964297i | \(-0.414686\pi\) | ||||
0.264824 | + | 0.964297i | \(0.414686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.372885 | −0.0119114 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.45692 | −0.174137 | ||||||||
\(983\) | −50.8180 | −1.62084 | −0.810421 | − | 0.585848i | \(-0.800762\pi\) | ||||
−0.810421 | + | 0.585848i | \(0.800762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4176 | −0.363794 | ||||||||
\(986\) | −6.65350 | −0.211891 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −35.9062 | −1.14233 | ||||||||
\(989\) | 19.5918 | 0.622983 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3642 | 0.360996 | 0.180498 | − | 0.983575i | \(-0.442229\pi\) | ||||
0.180498 | + | 0.983575i | \(0.442229\pi\) | |||||||
\(992\) | −11.6504 | −0.369901 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.53236 | 0.0486036 | ||||||||
\(995\) | −7.16644 | −0.227191 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1644 | −0.923647 | −0.461824 | − | 0.886972i | \(-0.652805\pi\) | ||||
−0.461824 | + | 0.886972i | \(0.652805\pi\) | |||||||
\(998\) | −5.19332 | −0.164392 | ||||||||
\(999\) | 0 | 0 |
(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 | 5445.2.a.bp.1.2 | 4 | ||
3.2 | odd | 2 | 605.2.a.j.1.3 | 4 | |||
11.3 | even | 5 | 495.2.n.e.361.1 | 8 | |||
11.4 | even | 5 | 495.2.n.e.181.1 | 8 | |||
11.10 | odd | 2 | 5445.2.a.bi.1.3 | 4 | |||
12.11 | even | 2 | 9680.2.a.cn.1.3 | 4 | |||
15.14 | odd | 2 | 3025.2.a.bd.1.2 | 4 | |||
33.2 | even | 10 | 605.2.g.e.81.2 | 8 | |||
33.5 | odd | 10 | 605.2.g.m.366.1 | 8 | |||
33.8 | even | 10 | 605.2.g.k.251.1 | 8 | |||
33.14 | odd | 10 | 55.2.g.b.31.2 | yes | 8 | ||
33.17 | even | 10 | 605.2.g.e.366.2 | 8 | |||
33.20 | odd | 10 | 605.2.g.m.81.1 | 8 | |||
33.26 | odd | 10 | 55.2.g.b.16.2 | ✓ | 8 | ||
33.29 | even | 10 | 605.2.g.k.511.1 | 8 | |||
33.32 | even | 2 | 605.2.a.k.1.2 | 4 | |||
132.47 | even | 10 | 880.2.bo.h.801.1 | 8 | |||
132.59 | even | 10 | 880.2.bo.h.401.1 | 8 | |||
132.131 | odd | 2 | 9680.2.a.cm.1.3 | 4 | |||
165.14 | odd | 10 | 275.2.h.a.251.1 | 8 | |||
165.47 | even | 20 | 275.2.z.a.174.3 | 16 | |||
165.59 | odd | 10 | 275.2.h.a.126.1 | 8 | |||
165.92 | even | 20 | 275.2.z.a.49.2 | 16 | |||
165.113 | even | 20 | 275.2.z.a.174.2 | 16 | |||
165.158 | even | 20 | 275.2.z.a.49.3 | 16 | |||
165.164 | even | 2 | 3025.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.16.2 | ✓ | 8 | 33.26 | odd | 10 | ||
55.2.g.b.31.2 | yes | 8 | 33.14 | odd | 10 | ||
275.2.h.a.126.1 | 8 | 165.59 | odd | 10 | |||
275.2.h.a.251.1 | 8 | 165.14 | odd | 10 | |||
275.2.z.a.49.2 | 16 | 165.92 | even | 20 | |||
275.2.z.a.49.3 | 16 | 165.158 | even | 20 | |||
275.2.z.a.174.2 | 16 | 165.113 | even | 20 | |||
275.2.z.a.174.3 | 16 | 165.47 | even | 20 | |||
495.2.n.e.181.1 | 8 | 11.4 | even | 5 | |||
495.2.n.e.361.1 | 8 | 11.3 | even | 5 | |||
605.2.a.j.1.3 | 4 | 3.2 | odd | 2 | |||
605.2.a.k.1.2 | 4 | 33.32 | even | 2 | |||
605.2.g.e.81.2 | 8 | 33.2 | even | 10 | |||
605.2.g.e.366.2 | 8 | 33.17 | even | 10 | |||
605.2.g.k.251.1 | 8 | 33.8 | even | 10 | |||
605.2.g.k.511.1 | 8 | 33.29 | even | 10 | |||
605.2.g.m.81.1 | 8 | 33.20 | odd | 10 | |||
605.2.g.m.366.1 | 8 | 33.5 | odd | 10 | |||
880.2.bo.h.401.1 | 8 | 132.59 | even | 10 | |||
880.2.bo.h.801.1 | 8 | 132.47 | even | 10 | |||
3025.2.a.w.1.3 | 4 | 165.164 | even | 2 | |||
3025.2.a.bd.1.2 | 4 | 15.14 | odd | 2 | |||
5445.2.a.bi.1.3 | 4 | 11.10 | odd | 2 | |||
5445.2.a.bp.1.2 | 4 | 1.1 | even | 1 | trivial | ||
9680.2.a.cm.1.3 | 4 | 132.131 | odd | 2 | |||
9680.2.a.cn.1.3 | 4 | 12.11 | even | 2 |