Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 539) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.15293\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.15293 | −1.24300 | −0.621499 | − | 0.783415i | \(-0.713476\pi\) | ||||
−0.621499 | + | 0.783415i | \(0.713476\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.87589 | −1.73335 | −0.866675 | − | 0.498873i | \(-0.833747\pi\) | ||||
−0.866675 | + | 0.498873i | \(0.833747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.63513 | 0.545042 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.09860 | 1.13675 | 0.568373 | − | 0.822771i | \(-0.307573\pi\) | ||||
0.568373 | + | 0.822771i | \(0.307573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.34453 | 2.15455 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.824752 | −0.200032 | −0.100016 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100016 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.50196 | −1.03282 | −0.516410 | − | 0.856342i | \(-0.672732\pi\) | ||||
−0.516410 | + | 0.856342i | \(0.672732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.86320 | −1.01405 | −0.507023 | − | 0.861932i | \(-0.669254\pi\) | ||||
−0.507023 | + | 0.861932i | \(0.669254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0225 | 2.00450 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.93849 | 0.565512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.79629 | 1.44774 | 0.723868 | − | 0.689939i | \(-0.242363\pi\) | ||||
0.723868 | + | 0.689939i | \(0.242363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.82646 | −0.687253 | −0.343627 | − | 0.939106i | \(-0.611655\pi\) | ||||
−0.343627 | + | 0.939106i | \(0.611655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.15293 | 0.374778 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.11646 | 1.33434 | 0.667169 | − | 0.744907i | \(-0.267506\pi\) | ||||
0.667169 | + | 0.744907i | \(0.267506\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.82401 | −1.41297 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2329 | −1.75428 | −0.877142 | − | 0.480232i | \(-0.840553\pi\) | ||||
−0.877142 | + | 0.480232i | \(0.840553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86134 | 0.283852 | 0.141926 | − | 0.989877i | \(-0.454670\pi\) | ||||
0.141926 | + | 0.989877i | \(0.454670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.33756 | −0.944748 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.69973 | −1.12312 | −0.561561 | − | 0.827436i | \(-0.689799\pi\) | ||||
−0.561561 | + | 0.827436i | \(0.689799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.77564 | 0.248639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.93495 | −0.540507 | −0.270253 | − | 0.962789i | \(-0.587107\pi\) | ||||
−0.270253 | + | 0.962789i | \(0.587107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.87589 | 0.522625 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.69242 | 1.28379 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.45193 | 1.23054 | 0.615268 | − | 0.788318i | \(-0.289048\pi\) | ||||
0.615268 | + | 0.788318i | \(0.289048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.40447 | −1.07608 | −0.538041 | − | 0.842919i | \(-0.680835\pi\) | ||||
−0.538041 | + | 0.842919i | \(0.680835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.8857 | −1.97038 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.45914 | −1.15562 | −0.577809 | − | 0.816172i | \(-0.696092\pi\) | ||||
−0.577809 | + | 0.816172i | \(0.696092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.4701 | 1.26046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4591 | −1.59731 | −0.798653 | − | 0.601792i | \(-0.794454\pi\) | ||||
−0.798653 | + | 0.601792i | \(0.794454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.19352 | 0.724897 | 0.362448 | − | 0.932004i | \(-0.381941\pi\) | ||||
0.362448 | + | 0.932004i | \(0.381941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.5778 | −2.49159 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.868405 | −0.0977032 | −0.0488516 | − | 0.998806i | \(-0.515556\pi\) | ||||
−0.0488516 | + | 0.998806i | \(0.515556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2317 | −1.24797 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.19720 | −0.899759 | −0.449880 | − | 0.893089i | \(-0.648533\pi\) | ||||
−0.449880 | + | 0.893089i | \(0.648533\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.19665 | 0.346725 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.7849 | −1.79953 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.87589 | −0.410843 | −0.205422 | − | 0.978674i | \(-0.565857\pi\) | ||||
−0.205422 | + | 0.978674i | \(0.565857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.23813 | 0.854254 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.4491 | 1.79024 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.10351 | −0.213579 | −0.106790 | − | 0.994282i | \(-0.534057\pi\) | ||||
−0.106790 | + | 0.994282i | \(0.534057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63513 | −0.164336 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.8092 | −1.27456 | −0.637281 | − | 0.770632i | \(-0.719941\pi\) | ||||
−0.637281 | + | 0.770632i | \(0.719941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.23897 | −0.220612 | −0.110306 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110306 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.60300 | 0.735010 | 0.367505 | − | 0.930022i | \(-0.380212\pi\) | ||||
0.367505 | + | 0.930022i | \(0.380212\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.56337 | 0.724440 | 0.362220 | − | 0.932093i | \(-0.382019\pi\) | ||||
0.362220 | + | 0.932093i | \(0.382019\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.4742 | −1.65858 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.17816 | −0.298976 | −0.149488 | − | 0.988764i | \(-0.547763\pi\) | ||||
−0.149488 | + | 0.988764i | \(0.547763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.8492 | 1.75770 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.70172 | 0.619574 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.1837 | 2.18057 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.4667 | −1.74115 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.72640 | −0.508136 | −0.254068 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00735 | −0.352828 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0240271 | 0.00209926 | 0.00104963 | − | 0.999999i | \(-0.499666\pi\) | ||||
0.00104963 | + | 0.999999i | \(0.499666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.3892 | −0.980230 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.83915 | 0.328001 | 0.164000 | − | 0.986460i | \(-0.447560\pi\) | ||||
0.164000 | + | 0.986460i | \(0.447560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.59639 | −0.305042 | −0.152521 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152521 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5770 | 1.39604 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.09860 | −0.342742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.2176 | −2.50943 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5456 | −1.02777 | −0.513886 | − | 0.857858i | \(-0.671795\pi\) | ||||
−0.513886 | + | 0.857858i | \(0.671795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.591093 | 0.0481025 | 0.0240512 | − | 0.999711i | \(-0.492344\pi\) | ||||
0.0240512 | + | 0.999711i | \(0.492344\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.34857 | −0.109026 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.8309 | 1.19125 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2795 | −1.21943 | −0.609717 | − | 0.792619i | \(-0.708717\pi\) | ||||
−0.609717 | + | 0.792619i | \(0.708717\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.47169 | 0.671848 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.30282 | 0.180370 | 0.0901852 | − | 0.995925i | \(-0.471254\pi\) | ||||
0.0901852 | + | 0.995925i | \(0.471254\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.34453 | −0.649621 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.60081 | 0.356021 | 0.178011 | − | 0.984029i | \(-0.443034\pi\) | ||||
0.178011 | + | 0.984029i | \(0.443034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.79851 | 0.292193 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.36126 | −0.562930 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.0515 | 1.37243 | 0.686215 | − | 0.727399i | \(-0.259271\pi\) | ||||
0.686215 | + | 0.727399i | \(0.259271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.3494 | −1.52955 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5109 | −1.15934 | −0.579670 | − | 0.814851i | \(-0.696818\pi\) | ||||
−0.579670 | + | 0.814851i | \(0.696818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.64371 | 0.493823 | 0.246912 | − | 0.969038i | \(-0.420584\pi\) | ||||
0.246912 | + | 0.969038i | \(0.420584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0943 | 1.33757 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.4585 | −2.31287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.824752 | 0.0603118 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.94524 | −0.357825 | −0.178912 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.37008 | 0.386547 | 0.193273 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193273 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 34.2009 | 2.44918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0487 | −1.57091 | −0.785454 | − | 0.618921i | \(-0.787570\pi\) | ||||
−0.785454 | + | 0.618921i | \(0.787570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4218 | −0.880558 | −0.440279 | − | 0.897861i | \(-0.645121\pi\) | ||||
−0.440279 | + | 0.897861i | \(0.645121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.3649 | 1.43643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43.5374 | 3.04079 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.95194 | −0.552698 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.50196 | 0.311407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.7445 | 1.84117 | 0.920584 | − | 0.390545i | \(-0.127713\pi\) | ||||
0.920584 | + | 0.390545i | \(0.127713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.9766 | 1.98545 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.21436 | −0.492015 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.3342 | −0.901045 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.38033 | −0.227385 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.79215 | −0.120011 | −0.0600055 | − | 0.998198i | \(-0.519112\pi\) | ||||
−0.0600055 | + | 0.998198i | \(0.519112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.3881 | 1.09254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.6173 | −1.16930 | −0.584649 | − | 0.811286i | \(-0.698768\pi\) | ||||
−0.584649 | + | 0.811286i | \(0.698768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.25609 | 0.347332 | 0.173666 | − | 0.984805i | \(-0.444439\pi\) | ||||
0.173666 | + | 0.984805i | \(0.444439\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.7069 | −0.897967 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.8433 | 1.94676 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.86962 | 0.121445 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.17883 | −0.529045 | −0.264522 | − | 0.964380i | \(-0.585214\pi\) | ||||
−0.264522 | + | 0.964380i | \(0.585214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3061 | −0.728290 | −0.364145 | − | 0.931342i | \(-0.618639\pi\) | ||||
−0.364145 | + | 0.931342i | \(0.618639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3657 | 0.985713 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4517 | −1.17405 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6480 | 1.11840 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9903 | 1.26178 | 0.630889 | − | 0.775873i | \(-0.282691\pi\) | ||||
0.630889 | + | 0.775873i | \(0.282691\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.86320 | 0.305747 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.88217 | −0.430978 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.13629 | −0.382771 | −0.191386 | − | 0.981515i | \(-0.561298\pi\) | ||||
−0.191386 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7479 | 0.789076 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.3223 | 1.37645 | 0.688227 | − | 0.725495i | \(-0.258389\pi\) | ||||
0.688227 | + | 0.725495i | \(0.258389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.2514 | 0.936888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.34453 | 0.510677 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.43592 | 0.209492 | 0.104746 | − | 0.994499i | \(-0.466597\pi\) | ||||
0.104746 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8410 | −1.08376 | −0.541880 | − | 0.840456i | \(-0.682287\pi\) | ||||
−0.541880 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0225 | −0.604380 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9426 | 1.01798 | 0.508990 | − | 0.860772i | \(-0.330019\pi\) | ||||
0.508990 | + | 0.860772i | \(0.330019\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.25675 | −0.374582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2080 | 1.44413 | 0.722066 | − | 0.691825i | \(-0.243193\pi\) | ||||
0.722066 | + | 0.691825i | \(0.243193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.24541 | 0.133475 | 0.0667377 | − | 0.997771i | \(-0.478741\pi\) | ||||
0.0667377 | + | 0.997771i | \(0.478741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −37.5667 | −2.22526 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3198 | −0.959987 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.52872 | 0.265478 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.635515 | −0.0371272 | −0.0185636 | − | 0.999828i | \(-0.505909\pi\) | ||||
−0.0185636 | + | 0.999828i | \(0.505909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.6346 | −2.13295 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.93849 | −0.170508 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.9323 | −1.15271 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.5773 | 1.58428 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.5748 | 1.86523 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7490 | 1.01299 | 0.506493 | − | 0.862244i | \(-0.330941\pi\) | ||||
0.506493 | + | 0.862244i | \(0.330941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.82034 | 0.274220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.2429 | −0.637525 | −0.318763 | − | 0.947835i | \(-0.603267\pi\) | ||||
−0.318763 | + | 0.947835i | \(0.603267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.25546 | −0.240533 | −0.120266 | − | 0.992742i | \(-0.538375\pi\) | ||||
−0.120266 | + | 0.992742i | \(0.538375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2336 | 1.19260 | 0.596299 | − | 0.802763i | \(-0.296637\pi\) | ||||
0.596299 | + | 0.802763i | \(0.296637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.79629 | −0.436509 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.3688 | −0.913615 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.71300 | 0.206597 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.0783 | 2.27861 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.2834 | −0.900477 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4568 | −1.28930 | −0.644652 | − | 0.764476i | \(-0.722998\pi\) | ||||
−0.644652 | + | 0.764476i | \(0.722998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.2714 | 0.727270 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.6626 | 2.00309 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.7640 | −1.89372 | −0.946859 | − | 0.321650i | \(-0.895762\pi\) | ||||
−0.946859 | + | 0.321650i | \(0.895762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.84236 | 0.371626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82646 | 0.207215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −40.5811 | −2.18481 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.689571 | 0.0370181 | 0.0185090 | − | 0.999829i | \(-0.494108\pi\) | ||||
0.0185090 | + | 0.999829i | \(0.494108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9995 | 1.07055 | 0.535275 | − | 0.844678i | \(-0.320208\pi\) | ||||
0.535275 | + | 0.844678i | \(0.320208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.0437 | 0.642844 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.57359 | 0.190203 | 0.0951014 | − | 0.995468i | \(-0.469682\pi\) | ||||
0.0951014 | + | 0.995468i | \(0.469682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 52.1661 | 2.76869 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.6809 | 1.67205 | 0.836026 | − | 0.548690i | \(-0.184873\pi\) | ||||
0.836026 | + | 0.548690i | \(0.184873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.26762 | 0.0667169 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.15293 | −0.113000 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.0054 | −1.25650 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.6491 | 0.921277 | 0.460638 | − | 0.887588i | \(-0.347620\pi\) | ||||
0.460638 | + | 0.887588i | \(0.347620\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.3672 | −0.956158 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.0524 | −1.24539 | −0.622694 | − | 0.782465i | \(-0.713962\pi\) | ||||
−0.622694 | + | 0.782465i | \(0.713962\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 41.9105 | 2.16425 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.9539 | 1.64571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.73645 | −0.294662 | −0.147331 | − | 0.989087i | \(-0.547068\pi\) | ||||
−0.147331 | + | 0.989087i | \(0.547068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3286 | 0.631611 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.45929 | 0.483347 | 0.241674 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241674 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.04353 | 0.154711 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3482 | 0.828887 | 0.414443 | − | 0.910075i | \(-0.363976\pi\) | ||||
0.414443 | + | 0.910075i | \(0.363976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.01093 | 0.202841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0517288 | −0.00260937 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.36584 | 0.169354 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2208 | 1.56693 | 0.783464 | − | 0.621437i | \(-0.213451\pi\) | ||||
0.783464 | + | 0.621437i | \(0.213451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.6480 | 0.681550 | 0.340775 | − | 0.940145i | \(-0.389311\pi\) | ||||
0.340775 | + | 0.940145i | \(0.389311\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6831 | −0.781233 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 43.5330 | 2.16317 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.11646 | −0.402318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6468 | 0.674790 | 0.337395 | − | 0.941363i | \(-0.390454\pi\) | ||||
0.337395 | + | 0.941363i | \(0.390454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.26543 | −0.407704 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.7714 | 1.55960 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.74279 | 0.379166 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1381 | −0.641840 | −0.320920 | − | 0.947106i | \(-0.603992\pi\) | ||||
−0.320920 | + | 0.947106i | \(0.603992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6056 | 0.516883 | 0.258441 | − | 0.966027i | \(-0.416791\pi\) | ||||
0.258441 | + | 0.966027i | \(0.416791\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.5900 | −0.612148 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.26608 | −0.400964 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.82401 | 0.426027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.5575 | 1.42373 | 0.711867 | − | 0.702315i | \(-0.247850\pi\) | ||||
0.711867 | + | 0.702315i | \(0.247850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7665 | 1.57466 | 0.787329 | − | 0.616534i | \(-0.211464\pi\) | ||||
0.787329 | + | 0.616534i | \(0.211464\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 65.0564 | 3.11922 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.8939 | 1.04733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.5068 | 1.83783 | 0.918914 | − | 0.394459i | \(-0.129068\pi\) | ||||
0.918914 | + | 0.394459i | \(0.129068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.2823 | −1.48627 | −0.743134 | − | 0.669142i | \(-0.766662\pi\) | ||||
−0.743134 | + | 0.669142i | \(0.766662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0225 | 0.712135 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.0098 | 1.27752 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.82808 | −0.416623 | −0.208311 | − | 0.978063i | \(-0.566797\pi\) | ||||
−0.208311 | + | 0.978063i | \(0.566797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2329 | 0.528936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.27259 | −0.0597913 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.1378 | −0.895228 | −0.447614 | − | 0.894227i | \(-0.647726\pi\) | ||||
−0.447614 | + | 0.894227i | \(0.647726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.42352 | −0.113120 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.9755 | 0.976926 | 0.488463 | − | 0.872584i | \(-0.337558\pi\) | ||||
0.488463 | + | 0.872584i | \(0.337558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.4558 | 1.50835 | 0.754174 | − | 0.656674i | \(-0.228037\pi\) | ||||
0.754174 | + | 0.656674i | \(0.228037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.9301 | −1.48072 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.99179 | 0.230993 | 0.115496 | − | 0.993308i | \(-0.463154\pi\) | ||||
0.115496 | + | 0.993308i | \(0.463154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.8957 | 1.51575 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.86134 | −0.0855847 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.1209 | −2.07029 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.43414 | −0.294599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8655 | 0.953368 | 0.476684 | − | 0.879075i | \(-0.341839\pi\) | ||||
0.476684 | + | 0.879075i | \(0.341839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.2661 | 1.51680 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.15297 | 0.370207 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.9012 | 1.08307 | 0.541533 | − | 0.840680i | \(-0.317844\pi\) | ||||
0.541533 | + | 0.840680i | \(0.317844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.95781 | −0.224200 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.3897 | −0.875044 | −0.437522 | − | 0.899208i | \(-0.644144\pi\) | ||||
−0.437522 | + | 0.899208i | \(0.644144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.43001 | −0.289593 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.33756 | 0.284852 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.100167 | 0.00448408 | 0.00224204 | − | 0.999997i | \(-0.499286\pi\) | ||||
0.00224204 | + | 0.999997i | \(0.499286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.90523 | −0.442533 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2263 | −0.634317 | −0.317159 | − | 0.948372i | \(-0.602729\pi\) | ||||
−0.317159 | + | 0.948372i | \(0.602729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.6470 | 2.20926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.17794 | −0.363195 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.67585 | 0.384550 | 0.192275 | − | 0.981341i | \(-0.438413\pi\) | ||||
0.192275 | + | 0.981341i | \(0.438413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.2289 | −0.584072 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.67798 | 0.382397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.69973 | 0.338634 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −38.8637 | −1.70593 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0313 | −0.483288 | −0.241644 | − | 0.970365i | \(-0.577687\pi\) | ||||
−0.241644 | + | 0.970365i | \(0.577687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4402 | 0.500243 | 0.250122 | − | 0.968214i | \(-0.419529\pi\) | ||||
0.250122 | + | 0.968214i | \(0.419529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.15588 | 0.137472 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.650700 | 0.0282913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.4551 | 0.670694 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.0391 | −1.99418 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.4684 | −1.27403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.3940 | 1.44106 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20512 | 0.0518122 | 0.0259061 | − | 0.999664i | \(-0.491753\pi\) | ||||
0.0259061 | + | 0.999664i | \(0.491753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.3035 | −0.613821 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.3148 | −1.25571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.64802 | −0.241492 | −0.120746 | − | 0.992683i | \(-0.538529\pi\) | ||||
−0.120746 | + | 0.992683i | \(0.538529\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.7424 | −0.586509 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.0986 | −1.49525 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 67.7281 | 2.87490 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.89754 | −0.292258 | −0.146129 | − | 0.989266i | \(-0.546681\pi\) | ||||
−0.146129 | + | 0.989266i | \(0.546681\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.62890 | 0.322668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.77564 | −0.0749674 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.52144 | −0.0641211 | −0.0320605 | − | 0.999486i | \(-0.510207\pi\) | ||||
−0.0320605 | + | 0.999486i | \(0.510207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.3182 | 0.518230 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5468 | 1.19674 | 0.598372 | − | 0.801219i | \(-0.295815\pi\) | ||||
0.598372 | + | 0.801219i | \(0.295815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.5519 | −1.57150 | −0.785749 | − | 0.618545i | \(-0.787722\pi\) | ||||
−0.785749 | + | 0.618545i | \(0.787722\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6468 | 0.444775 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.7415 | −2.03266 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5401 | 0.522051 | 0.261025 | − | 0.965332i | \(-0.415939\pi\) | ||||
0.261025 | + | 0.965332i | \(0.415939\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5614 | −0.480477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.93495 | 0.162969 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.9751 | −1.07394 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.6526 | 1.38899 | 0.694496 | − | 0.719496i | \(-0.255627\pi\) | ||||
0.694496 | + | 0.719496i | \(0.255627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.2266 | 0.709809 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 47.4695 | 1.95263 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.4214 | −1.00287 | −0.501434 | − | 0.865196i | \(-0.667194\pi\) | ||||
−0.501434 | + | 0.865196i | \(0.667194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.7433 | 1.09453 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.56936 | −0.227558 | −0.113779 | − | 0.993506i | \(-0.536296\pi\) | ||||
−0.113779 | + | 0.993506i | \(0.536296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8079 | −0.440864 | −0.220432 | − | 0.975402i | \(-0.570747\pi\) | ||||
−0.220432 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4669 | −0.629860 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.87589 | −0.157577 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5106 | 0.426611 | 0.213305 | − | 0.976986i | \(-0.431577\pi\) | ||||
0.213305 | + | 0.976986i | \(0.431577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.5581 | −1.27670 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.4044 | −0.945293 | −0.472647 | − | 0.881252i | \(-0.656701\pi\) | ||||
−0.472647 | + | 0.881252i | \(0.656701\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −93.7332 | −3.77969 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.4432 | −1.10482 | −0.552410 | − | 0.833572i | \(-0.686292\pi\) | ||||
−0.552410 | + | 0.833572i | \(0.686292\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.37072 | −0.336448 | −0.168224 | − | 0.985749i | \(-0.553803\pi\) | ||||
−0.168224 | + | 0.985749i | \(0.553803\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.2904 | −0.573455 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.3382 | 1.01353 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.69242 | −0.387078 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.69406 | −0.266910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.8816 | 1.62747 | 0.813736 | − | 0.581235i | \(-0.197430\pi\) | ||||
0.813736 | + | 0.581235i | \(0.197430\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −57.5792 | −2.28857 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.1949 | 0.880777 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.0074 | −0.870598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8987 | −1.14143 | −0.570714 | − | 0.821149i | \(-0.693334\pi\) | ||||
−0.570714 | + | 0.821149i | \(0.693334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.9484 | 1.77259 | 0.886296 | − | 0.463120i | \(-0.153270\pi\) | ||||
0.886296 | + | 0.463120i | \(0.153270\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.5320 | 0.611574 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.45440 | −0.0571784 | −0.0285892 | − | 0.999591i | \(-0.509101\pi\) | ||||
−0.0285892 | + | 0.999591i | \(0.509101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.45193 | −0.371021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.89313 | 0.191483 | 0.0957415 | − | 0.995406i | \(-0.469478\pi\) | ||||
0.0957415 | + | 0.995406i | \(0.469478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0931263 | −0.00363875 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.1272 | 0.395099 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.2035 | −0.553291 | −0.276646 | − | 0.960972i | \(-0.589223\pi\) | ||||
−0.276646 | + | 0.960972i | \(0.589223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.4970 | −1.30288 | −0.651442 | − | 0.758698i | \(-0.725836\pi\) | ||||
−0.651442 | + | 0.758698i | \(0.725836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.27762 | 0.282639 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.9149 | −1.46807 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.85837 | 0.149173 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.40447 | 0.324451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.4763 | −1.94572 | −0.972859 | − | 0.231398i | \(-0.925670\pi\) | ||||
−0.972859 | + | 0.231398i | \(0.925670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 29.4510 | 1.13357 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.4961 | −1.59482 | −0.797412 | − | 0.603436i | \(-0.793798\pi\) | ||||
−0.797412 | + | 0.603436i | \(0.793798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.9288 | 1.45343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.914566 | 0.0349949 | 0.0174975 | − | 0.999847i | \(-0.494430\pi\) | ||||
0.0174975 | + | 0.999847i | \(0.494430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8801 | −0.568540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.3160 | −0.431733 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.1278 | −0.614419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6540 | 1.28026 | 0.640130 | − | 0.768267i | \(-0.278881\pi\) | ||||
0.640130 | + | 0.768267i | \(0.278881\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.9392 | 0.528744 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.26435 | 0.350912 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.5100 | 1.11617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9539 | −0.753649 | −0.376825 | − | 0.926285i | \(-0.622984\pi\) | ||||
−0.376825 | + | 0.926285i | \(0.622984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.5400 | −1.37813 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −64.2507 | −2.41982 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.9062 | 0.672481 | 0.336240 | − | 0.941776i | \(-0.390845\pi\) | ||||
0.336240 | + | 0.941776i | \(0.390845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.41995 | −0.0532523 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.6089 | 0.696907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8857 | 0.594092 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.6085 | 0.657601 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.99817 | 0.111813 | 0.0559064 | − | 0.998436i | \(-0.482195\pi\) | ||||
0.0559064 | + | 0.998436i | \(0.482195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.3413 | 0.905263 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 78.1384 | 2.90199 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.4088 | 1.09071 | 0.545355 | − | 0.838205i | \(-0.316395\pi\) | ||||
0.545355 | + | 0.838205i | \(0.316395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.613791 | 0.0227330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.53515 | −0.0567794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.39138 | −0.0513918 | −0.0256959 | − | 0.999670i | \(-0.508180\pi\) | ||||
−0.0256959 | + | 0.999670i | \(0.508180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.45914 | 0.348432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.54756 | −0.351213 | −0.175606 | − | 0.984460i | \(-0.556189\pi\) | ||||
−0.175606 | + | 0.984460i | \(0.556189\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.7253 | 1.45935 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7641 | 0.578328 | 0.289164 | − | 0.957280i | \(-0.406623\pi\) | ||||
0.289164 | + | 0.957280i | \(0.406623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.6252 | 1.78149 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.4034 | −0.490406 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.1559 | 1.57478 | 0.787391 | − | 0.616455i | \(-0.211432\pi\) | ||||
0.787391 | + | 0.616455i | \(0.211432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −43.0378 | −1.56839 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.29101 | −0.0833785 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7539 | −1.33584 | −0.667922 | − | 0.744231i | \(-0.732816\pi\) | ||||
−0.667922 | + | 0.744231i | \(0.732816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.4701 | −0.380042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6094 | 1.25459 | 0.627296 | − | 0.778781i | \(-0.284162\pi\) | ||||
0.627296 | + | 0.778781i | \(0.284162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.22692 | 0.188980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.7397 | 1.39881 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.4872 | −1.02728 | −0.513638 | − | 0.858007i | \(-0.671703\pi\) | ||||
−0.513638 | + | 0.858007i | \(0.671703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.2110 | 0.475783 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.5635 | 0.415910 | 0.207955 | − | 0.978138i | \(-0.433319\pi\) | ||||
0.207955 | + | 0.978138i | \(0.433319\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.3508 | −1.37760 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.5700 | 1.81186 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4591 | 0.481606 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.9093 | 0.818711 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 59.2215 | 2.11371 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.02977 | 0.143646 | 0.0718229 | − | 0.997417i | \(-0.477118\pi\) | ||||
0.0718229 | + | 0.997417i | \(0.477118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.0585 | −1.71093 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.4465 | −1.22323 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.8353 | −1.16455 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.65757 | 0.200401 | 0.100201 | − | 0.994967i | \(-0.468052\pi\) | ||||
0.100201 | + | 0.994967i | \(0.468052\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.35036 | 0.224660 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.33756 | −0.223927 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.19352 | −0.218565 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.39732 | −0.260398 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.2095 | 0.605052 | 0.302526 | − | 0.953141i | \(-0.402170\pi\) | ||||
0.302526 | + | 0.953141i | \(0.402170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.3821 | 1.17221 | 0.586103 | − | 0.810237i | \(-0.300662\pi\) | ||||
0.586103 | + | 0.810237i | \(0.300662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.4104 | 1.34711 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.92546 | −0.312645 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.37969 | −0.293168 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.263189 | 0.00918537 | 0.00459269 | − | 0.999989i | \(-0.498538\pi\) | ||||
0.00459269 | + | 0.999989i | \(0.498538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.8315 | −0.516995 | −0.258497 | − | 0.966012i | \(-0.583227\pi\) | ||||
−0.258497 | + | 0.966012i | \(0.583227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.5778 | 0.751243 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.1437 | −1.32639 | −0.663194 | − | 0.748448i | \(-0.730799\pi\) | ||||
−0.663194 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4064 | −0.361429 | −0.180715 | − | 0.983536i | \(-0.557841\pi\) | ||||
−0.180715 | + | 0.983536i | \(0.557841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4762 | −1.26535 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.8322 | −0.617109 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.2440 | −0.388650 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.4338 | −1.22331 | −0.611655 | − | 0.791125i | \(-0.709496\pi\) | ||||
−0.611655 | + | 0.791125i | \(0.709496\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.7822 | 1.09594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −52.1183 | −1.79505 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.7226 | −0.506473 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.83421 | −0.165910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.4720 | −1.35308 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5950 | 0.362765 | 0.181382 | − | 0.983413i | \(-0.441943\pi\) | ||||
0.181382 | + | 0.983413i | \(0.441943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.5314 | 0.975755 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.4041 | −1.44850 | −0.724248 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724248 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.47204 | −0.254943 | −0.127471 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127471 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5892 | −1.04127 | −0.520635 | − | 0.853779i | \(-0.674305\pi\) | ||||
−0.520635 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −69.9656 | −2.37890 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.1354 | 1.19326 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.868405 | 0.0294586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.7692 | −1.31364 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.43950 | −0.116410 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.7674 | 1.74806 | 0.874030 | − | 0.485872i | \(-0.161498\pi\) | ||||
0.874030 | + | 0.485872i | \(0.161498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.36822 | 0.0461490 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.8750 | 1.41081 | 0.705403 | − | 0.708807i | \(-0.250766\pi\) | ||||
0.705403 | + | 0.708807i | \(0.250766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.7098 | 1.30269 | 0.651344 | − | 0.758782i | \(-0.274205\pi\) | ||||
0.651344 | + | 0.758782i | \(0.274205\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 78.8719 | 2.65125 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1008 | 1.48076 | 0.740380 | − | 0.672188i | \(-0.234645\pi\) | ||||
0.740380 | + | 0.672188i | \(0.234645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.2317 | 0.376277 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.6639 | 1.15998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60.1185 | 2.00954 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.9129 | 1.43282 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.8322 | −0.994961 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.24536 | 0.108118 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.7503 | −0.855968 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.5463 | 1.24670 | 0.623351 | − | 0.781942i | \(-0.285771\pi\) | ||||
0.623351 | + | 0.781942i | \(0.285771\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.9446 | −0.694689 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.2965 | −0.374269 | −0.187134 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187134 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.19720 | 0.271288 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −70.1313 | −2.31847 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.68871 | 0.253627 | 0.126814 | − | 0.991927i | \(-0.459525\pi\) | ||||
0.126814 | + | 0.991927i | \(0.459525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.2123 | −1.25914 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.1636 | −1.81573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 81.3473 | 2.67468 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.66099 | −0.120243 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.5573 | 1.29783 | 0.648916 | − | 0.760860i | \(-0.275223\pi\) | ||||
0.648916 | + | 0.760860i | \(0.275223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.2052 | 0.792442 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.19665 | −0.104541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.4348 | −1.71297 | −0.856485 | − | 0.516173i | \(-0.827356\pi\) | ||||
−0.856485 | + | 0.516173i | \(0.827356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.16172 | 0.298981 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.1101 | 1.60094 | 0.800472 | − | 0.599370i | \(-0.204582\pi\) | ||||
0.800472 | + | 0.599370i | \(0.204582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.6278 | 1.77893 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.82953 | 0.124443 | 0.0622216 | − | 0.998062i | \(-0.480181\pi\) | ||||
0.0622216 | + | 0.998062i | \(0.480181\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3848 | 0.824024 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.7145 | −1.48240 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7248 | −1.48117 | −0.740585 | − | 0.671963i | \(-0.765452\pi\) | ||||
−0.740585 | + | 0.671963i | \(0.765452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1672 | 0.620236 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.7849 | 0.542579 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.3582 | −0.527683 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4319 | 0.400611 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.8138 | −0.670021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.7847 | −1.31155 | −0.655773 | − | 0.754958i | \(-0.727657\pi\) | ||||
−0.655773 | + | 0.754958i | \(0.727657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.99384 | −0.256799 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.1520 | −1.51318 | −0.756589 | − | 0.653890i | \(-0.773136\pi\) | ||||
−0.756589 | + | 0.653890i | \(0.773136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −88.4388 | −2.83231 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3516 | −0.811068 | −0.405534 | − | 0.914080i | \(-0.632914\pi\) | ||||
−0.405534 | + | 0.914080i | \(0.632914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.87589 | 0.123874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.3671 | 0.394850 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.6984 | −1.96787 | −0.983936 | − | 0.178520i | \(-0.942869\pi\) | ||||
−0.983936 | + | 0.178520i | \(0.942869\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 85.4584 | 2.72293 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.05209 | −0.287840 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.8014 | −1.39140 | −0.695698 | − | 0.718334i | \(-0.744905\pi\) | ||||
−0.695698 | + | 0.718334i | \(0.744905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50.5010 | 1.60260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.1455 | 1.52632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.6657 | −0.939522 | −0.469761 | − | 0.882794i | \(-0.655660\pi\) | ||||
−0.469761 | + | 0.882794i | \(0.655660\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.8501 | 0.754584 |
(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 | 8624.2.a.df.1.3 | 10 | ||
4.3 | odd | 2 | 539.2.a.l.1.4 | yes | 10 | ||
7.6 | odd | 2 | inner | 8624.2.a.df.1.8 | 10 | ||
12.11 | even | 2 | 4851.2.a.cg.1.8 | 10 | |||
28.3 | even | 6 | 539.2.e.o.177.8 | 20 | |||
28.11 | odd | 6 | 539.2.e.o.177.7 | 20 | |||
28.19 | even | 6 | 539.2.e.o.67.8 | 20 | |||
28.23 | odd | 6 | 539.2.e.o.67.7 | 20 | |||
28.27 | even | 2 | 539.2.a.l.1.3 | ✓ | 10 | ||
44.43 | even | 2 | 5929.2.a.bv.1.8 | 10 | |||
84.83 | odd | 2 | 4851.2.a.cg.1.7 | 10 | |||
308.307 | odd | 2 | 5929.2.a.bv.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
539.2.a.l.1.3 | ✓ | 10 | 28.27 | even | 2 | ||
539.2.a.l.1.4 | yes | 10 | 4.3 | odd | 2 | ||
539.2.e.o.67.7 | 20 | 28.23 | odd | 6 | |||
539.2.e.o.67.8 | 20 | 28.19 | even | 6 | |||
539.2.e.o.177.7 | 20 | 28.11 | odd | 6 | |||
539.2.e.o.177.8 | 20 | 28.3 | even | 6 | |||
4851.2.a.cg.1.7 | 10 | 84.83 | odd | 2 | |||
4851.2.a.cg.1.8 | 10 | 12.11 | even | 2 | |||
5929.2.a.bv.1.7 | 10 | 308.307 | odd | 2 | |||
5929.2.a.bv.1.8 | 10 | 44.43 | even | 2 | |||
8624.2.a.df.1.3 | 10 | 1.1 | even | 1 | trivial | ||
8624.2.a.df.1.8 | 10 | 7.6 | odd | 2 | inner |