Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9405,2,Mod(1,9405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9405, 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("9405.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9405.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: | \(75.0993031010\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 9x^{7} + 29x^{6} + 23x^{5} - 84x^{4} - 23x^{3} + 89x^{2} + 8x - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1045) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.682920\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.682920 | −0.482898 | −0.241449 | − | 0.970414i | \(-0.577623\pi\) | ||||
−0.241449 | + | 0.970414i | \(0.577623\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.53362 | −0.766810 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.856948 | 0.323896 | 0.161948 | − | 0.986799i | \(-0.448222\pi\) | ||||
0.161948 | + | 0.986799i | \(0.448222\pi\) | |||||||
\(8\) | 2.41318 | 0.853188 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.682920 | 0.215958 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.50630 | 1.52717 | 0.763586 | − | 0.645706i | \(-0.223437\pi\) | ||||
0.763586 | + | 0.645706i | \(0.223437\pi\) | |||||||
\(14\) | −0.585228 | −0.156409 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.41923 | 0.354807 | ||||||||
\(17\) | 3.50630 | 0.850402 | 0.425201 | − | 0.905099i | \(-0.360203\pi\) | ||||
0.425201 | + | 0.905099i | \(0.360203\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.53362 | 0.342928 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.682920 | 0.145599 | ||||||||
\(23\) | −6.75237 | −1.40797 | −0.703984 | − | 0.710216i | \(-0.748597\pi\) | ||||
−0.703984 | + | 0.710216i | \(0.748597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.76036 | −0.737468 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.31423 | −0.248367 | ||||||||
\(29\) | 0.474680 | 0.0881458 | 0.0440729 | − | 0.999028i | \(-0.485967\pi\) | ||||
0.0440729 | + | 0.999028i | \(0.485967\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.19745 | −0.933489 | −0.466745 | − | 0.884392i | \(-0.654573\pi\) | ||||
−0.466745 | + | 0.884392i | \(0.654573\pi\) | |||||||
\(32\) | −5.79558 | −1.02452 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.39452 | −0.410657 | ||||||||
\(35\) | −0.856948 | −0.144851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.420904 | 0.0691961 | 0.0345981 | − | 0.999401i | \(-0.488985\pi\) | ||||
0.0345981 | + | 0.999401i | \(0.488985\pi\) | |||||||
\(38\) | −0.682920 | −0.110784 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.41318 | −0.381557 | ||||||||
\(41\) | −8.25141 | −1.28865 | −0.644327 | − | 0.764750i | \(-0.722862\pi\) | ||||
−0.644327 | + | 0.764750i | \(0.722862\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53320 | −0.233811 | −0.116905 | − | 0.993143i | \(-0.537297\pi\) | ||||
−0.116905 | + | 0.993143i | \(0.537297\pi\) | |||||||
\(44\) | 1.53362 | 0.231202 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.61133 | 0.679904 | ||||||||
\(47\) | −2.48849 | −0.362984 | −0.181492 | − | 0.983392i | \(-0.558093\pi\) | ||||
−0.181492 | + | 0.983392i | \(0.558093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.26564 | −0.895091 | ||||||||
\(50\) | −0.682920 | −0.0965795 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.44457 | −1.17105 | ||||||||
\(53\) | 4.79753 | 0.658991 | 0.329495 | − | 0.944157i | \(-0.393121\pi\) | ||||
0.329495 | + | 0.944157i | \(0.393121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.06797 | 0.276344 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.324169 | −0.0425654 | ||||||||
\(59\) | −1.75917 | −0.229025 | −0.114513 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114513 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.42433 | 0.438440 | 0.219220 | − | 0.975675i | \(-0.429649\pi\) | ||||
0.219220 | + | 0.975675i | \(0.429649\pi\) | |||||||
\(62\) | 3.54944 | 0.450780 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.11946 | 0.139933 | ||||||||
\(65\) | −5.50630 | −0.682972 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.12424 | −0.626026 | −0.313013 | − | 0.949749i | \(-0.601338\pi\) | ||||
−0.313013 | + | 0.949749i | \(0.601338\pi\) | |||||||
\(68\) | −5.37733 | −0.652097 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.585228 | 0.0699481 | ||||||||
\(71\) | 12.1937 | 1.44713 | 0.723563 | − | 0.690258i | \(-0.242503\pi\) | ||||
0.723563 | + | 0.690258i | \(0.242503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7638 | −1.49389 | −0.746945 | − | 0.664886i | \(-0.768480\pi\) | ||||
−0.746945 | + | 0.664886i | \(0.768480\pi\) | |||||||
\(74\) | −0.287444 | −0.0334146 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.53362 | −0.175918 | ||||||||
\(77\) | −0.856948 | −0.0976583 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8691 | 1.22287 | 0.611437 | − | 0.791293i | \(-0.290592\pi\) | ||||
0.611437 | + | 0.791293i | \(0.290592\pi\) | |||||||
\(80\) | −1.41923 | −0.158675 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.63505 | 0.622288 | ||||||||
\(83\) | −2.94669 | −0.323441 | −0.161721 | − | 0.986837i | \(-0.551704\pi\) | ||||
−0.161721 | + | 0.986837i | \(0.551704\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.50630 | −0.380311 | ||||||||
\(86\) | 1.04705 | 0.112907 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.41318 | −0.257246 | ||||||||
\(89\) | −3.08736 | −0.327259 | −0.163629 | − | 0.986522i | \(-0.552320\pi\) | ||||
−0.163629 | + | 0.986522i | \(0.552320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.71861 | 0.494645 | ||||||||
\(92\) | 10.3556 | 1.07964 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.69944 | 0.175284 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.88210 | −0.901840 | −0.450920 | − | 0.892564i | \(-0.648904\pi\) | ||||
−0.450920 | + | 0.892564i | \(0.648904\pi\) | |||||||
\(98\) | 4.27893 | 0.432238 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.53362 | −0.153362 | ||||||||
\(101\) | 2.09965 | 0.208923 | 0.104462 | − | 0.994529i | \(-0.466688\pi\) | ||||
0.104462 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.91556 | −0.385812 | −0.192906 | − | 0.981217i | \(-0.561791\pi\) | ||||
−0.192906 | + | 0.981217i | \(0.561791\pi\) | |||||||
\(104\) | 13.2877 | 1.30297 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.27633 | −0.318225 | ||||||||
\(107\) | 18.0439 | 1.74437 | 0.872184 | − | 0.489178i | \(-0.162703\pi\) | ||||
0.872184 | + | 0.489178i | \(0.162703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.34558 | 0.320448 | 0.160224 | − | 0.987081i | \(-0.448778\pi\) | ||||
0.160224 | + | 0.987081i | \(0.448778\pi\) | |||||||
\(110\) | −0.682920 | −0.0651139 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.21621 | 0.114921 | ||||||||
\(113\) | −7.26819 | −0.683733 | −0.341867 | − | 0.939748i | \(-0.611059\pi\) | ||||
−0.341867 | + | 0.939748i | \(0.611059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.75237 | 0.629662 | ||||||||
\(116\) | −0.727978 | −0.0675911 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.20138 | 0.110596 | ||||||||
\(119\) | 3.00472 | 0.275442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.33854 | −0.211722 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.97091 | 0.715809 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9303 | −1.50232 | −0.751162 | − | 0.660118i | \(-0.770506\pi\) | ||||
−0.751162 | + | 0.660118i | \(0.770506\pi\) | |||||||
\(128\) | 10.8267 | 0.956951 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.76036 | 0.329806 | ||||||||
\(131\) | −5.26619 | −0.460109 | −0.230055 | − | 0.973178i | \(-0.573891\pi\) | ||||
−0.230055 | + | 0.973178i | \(0.573891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.856948 | 0.0743069 | ||||||||
\(134\) | 3.49945 | 0.302307 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.46133 | 0.725553 | ||||||||
\(137\) | 20.6078 | 1.76064 | 0.880321 | − | 0.474378i | \(-0.157327\pi\) | ||||
0.880321 | + | 0.474378i | \(0.157327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.26192 | 0.107034 | 0.0535171 | − | 0.998567i | \(-0.482957\pi\) | ||||
0.0535171 | + | 0.998567i | \(0.482957\pi\) | |||||||
\(140\) | 1.31423 | 0.111073 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.32733 | −0.698814 | ||||||||
\(143\) | −5.50630 | −0.460460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.474680 | −0.0394200 | ||||||||
\(146\) | 8.71666 | 0.721396 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.645506 | −0.0530603 | ||||||||
\(149\) | 11.3117 | 0.926692 | 0.463346 | − | 0.886177i | \(-0.346649\pi\) | ||||
0.463346 | + | 0.886177i | \(0.346649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.70074 | −0.301162 | −0.150581 | − | 0.988598i | \(-0.548114\pi\) | ||||
−0.150581 | + | 0.988598i | \(0.548114\pi\) | |||||||
\(152\) | 2.41318 | 0.195735 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.585228 | 0.0471590 | ||||||||
\(155\) | 5.19745 | 0.417469 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.91493 | 0.232637 | 0.116318 | − | 0.993212i | \(-0.462891\pi\) | ||||
0.116318 | + | 0.993212i | \(0.462891\pi\) | |||||||
\(158\) | −7.42276 | −0.590523 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.79558 | 0.458181 | ||||||||
\(161\) | −5.78644 | −0.456035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4278 | 1.44338 | 0.721690 | − | 0.692216i | \(-0.243366\pi\) | ||||
0.721690 | + | 0.692216i | \(0.243366\pi\) | |||||||
\(164\) | 12.6545 | 0.988152 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.01235 | 0.156189 | ||||||||
\(167\) | −15.1433 | −1.17182 | −0.585912 | − | 0.810374i | \(-0.699264\pi\) | ||||
−0.585912 | + | 0.810374i | \(0.699264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.3193 | 1.33226 | ||||||||
\(170\) | 2.39452 | 0.183652 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.35135 | 0.179288 | ||||||||
\(173\) | 0.110615 | 0.00840989 | 0.00420495 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420495 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.856948 | 0.0647792 | ||||||||
\(176\) | −1.41923 | −0.106978 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.10842 | 0.158033 | ||||||||
\(179\) | 9.42389 | 0.704375 | 0.352187 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352187 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2876 | −0.913334 | −0.456667 | − | 0.889638i | \(-0.650957\pi\) | ||||
−0.456667 | + | 0.889638i | \(0.650957\pi\) | |||||||
\(182\) | −3.22244 | −0.238863 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.2947 | −1.20126 | ||||||||
\(185\) | −0.420904 | −0.0309454 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.50630 | −0.256406 | ||||||||
\(188\) | 3.81640 | 0.278340 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.682920 | 0.0495443 | ||||||||
\(191\) | −16.4558 | −1.19070 | −0.595351 | − | 0.803466i | \(-0.702987\pi\) | ||||
−0.595351 | + | 0.803466i | \(0.702987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.79958 | 0.201518 | 0.100759 | − | 0.994911i | \(-0.467873\pi\) | ||||
0.100759 | + | 0.994911i | \(0.467873\pi\) | |||||||
\(194\) | 6.06577 | 0.435497 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.60911 | 0.686365 | ||||||||
\(197\) | 7.19454 | 0.512589 | 0.256295 | − | 0.966599i | \(-0.417498\pi\) | ||||
0.256295 | + | 0.966599i | \(0.417498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.9287 | −0.845607 | −0.422803 | − | 0.906221i | \(-0.638954\pi\) | ||||
−0.422803 | + | 0.906221i | \(0.638954\pi\) | |||||||
\(200\) | 2.41318 | 0.170638 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.43390 | −0.100889 | ||||||||
\(203\) | 0.406776 | 0.0285501 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.25141 | 0.576303 | ||||||||
\(206\) | 2.67402 | 0.186308 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.81470 | 0.541852 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0430 | 1.24213 | 0.621065 | − | 0.783759i | \(-0.286700\pi\) | ||||
0.621065 | + | 0.783759i | \(0.286700\pi\) | |||||||
\(212\) | −7.35758 | −0.505321 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.3225 | −0.842351 | ||||||||
\(215\) | 1.53320 | 0.104563 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.45395 | −0.302354 | ||||||||
\(218\) | −2.28476 | −0.154744 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.53362 | −0.103397 | ||||||||
\(221\) | 19.3067 | 1.29871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.5001 | −1.64065 | −0.820323 | − | 0.571901i | \(-0.806206\pi\) | ||||
−0.820323 | + | 0.571901i | \(0.806206\pi\) | |||||||
\(224\) | −4.96652 | −0.331839 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.96359 | 0.330173 | ||||||||
\(227\) | −16.6675 | −1.10626 | −0.553131 | − | 0.833094i | \(-0.686567\pi\) | ||||
−0.553131 | + | 0.833094i | \(0.686567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8344 | 0.980282 | 0.490141 | − | 0.871643i | \(-0.336945\pi\) | ||||
0.490141 | + | 0.871643i | \(0.336945\pi\) | |||||||
\(230\) | −4.61133 | −0.304062 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.14549 | 0.0752050 | ||||||||
\(233\) | −28.8509 | −1.89009 | −0.945043 | − | 0.326947i | \(-0.893980\pi\) | ||||
−0.945043 | + | 0.326947i | \(0.893980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.48849 | 0.162331 | ||||||||
\(236\) | 2.69790 | 0.175619 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.05198 | −0.133010 | ||||||||
\(239\) | −8.29173 | −0.536347 | −0.268174 | − | 0.963371i | \(-0.586420\pi\) | ||||
−0.268174 | + | 0.963371i | \(0.586420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.48268 | 0.224339 | 0.112170 | − | 0.993689i | \(-0.464220\pi\) | ||||
0.112170 | + | 0.993689i | \(0.464220\pi\) | |||||||
\(242\) | −0.682920 | −0.0438998 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.25162 | −0.336200 | ||||||||
\(245\) | 6.26564 | 0.400297 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.50630 | 0.350357 | ||||||||
\(248\) | −12.5424 | −0.796442 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.682920 | 0.0431917 | ||||||||
\(251\) | 28.8156 | 1.81883 | 0.909413 | − | 0.415895i | \(-0.136532\pi\) | ||||
0.909413 | + | 0.415895i | \(0.136532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.75237 | 0.424518 | ||||||||
\(254\) | 11.5621 | 0.725469 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.63267 | −0.602042 | ||||||||
\(257\) | 8.44177 | 0.526583 | 0.263292 | − | 0.964716i | \(-0.415192\pi\) | ||||
0.263292 | + | 0.964716i | \(0.415192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.360693 | 0.0224124 | ||||||||
\(260\) | 8.44457 | 0.523710 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.59639 | 0.222186 | ||||||||
\(263\) | −21.4210 | −1.32088 | −0.660438 | − | 0.750881i | \(-0.729629\pi\) | ||||
−0.660438 | + | 0.750881i | \(0.729629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.79753 | −0.294710 | ||||||||
\(266\) | −0.585228 | −0.0358826 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.85864 | 0.480043 | ||||||||
\(269\) | −10.3642 | −0.631916 | −0.315958 | − | 0.948773i | \(-0.602326\pi\) | ||||
−0.315958 | + | 0.948773i | \(0.602326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1079 | −1.58594 | −0.792972 | − | 0.609258i | \(-0.791467\pi\) | ||||
−0.792972 | + | 0.609258i | \(0.791467\pi\) | |||||||
\(272\) | 4.97624 | 0.301729 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.0735 | −0.850210 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7663 | −1.12756 | −0.563779 | − | 0.825925i | \(-0.690653\pi\) | ||||
−0.563779 | + | 0.825925i | \(0.690653\pi\) | |||||||
\(278\) | −0.861788 | −0.0516866 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.06797 | −0.123585 | ||||||||
\(281\) | −24.6322 | −1.46944 | −0.734718 | − | 0.678373i | \(-0.762685\pi\) | ||||
−0.734718 | + | 0.678373i | \(0.762685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7870 | −0.819550 | −0.409775 | − | 0.912187i | \(-0.634393\pi\) | ||||
−0.409775 | + | 0.912187i | \(0.634393\pi\) | |||||||
\(284\) | −18.7005 | −1.10967 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.76036 | 0.222355 | ||||||||
\(287\) | −7.07103 | −0.417390 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.70587 | −0.276816 | ||||||||
\(290\) | 0.324169 | 0.0190358 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.5748 | 1.14553 | ||||||||
\(293\) | 3.53033 | 0.206244 | 0.103122 | − | 0.994669i | \(-0.467117\pi\) | ||||
0.103122 | + | 0.994669i | \(0.467117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.75917 | 0.102423 | ||||||||
\(296\) | 1.01572 | 0.0590373 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.72501 | −0.447498 | ||||||||
\(299\) | −37.1806 | −2.15021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31387 | −0.0757304 | ||||||||
\(302\) | 2.52731 | 0.145430 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.41923 | 0.0813984 | ||||||||
\(305\) | −3.42433 | −0.196076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.59192 | 0.319148 | 0.159574 | − | 0.987186i | \(-0.448988\pi\) | ||||
0.159574 | + | 0.987186i | \(0.448988\pi\) | |||||||
\(308\) | 1.31423 | 0.0748854 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.54944 | −0.201595 | ||||||||
\(311\) | 3.38109 | 0.191724 | 0.0958621 | − | 0.995395i | \(-0.469439\pi\) | ||||
0.0958621 | + | 0.995395i | \(0.469439\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5676 | 0.766886 | 0.383443 | − | 0.923565i | \(-0.374738\pi\) | ||||
0.383443 | + | 0.923565i | \(0.374738\pi\) | |||||||
\(314\) | −1.99066 | −0.112340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.6691 | −0.937712 | ||||||||
\(317\) | 9.02947 | 0.507145 | 0.253573 | − | 0.967316i | \(-0.418394\pi\) | ||||
0.253573 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.474680 | −0.0265770 | ||||||||
\(320\) | −1.11946 | −0.0625799 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.95167 | 0.220218 | ||||||||
\(323\) | 3.50630 | 0.195096 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50630 | 0.305434 | ||||||||
\(326\) | −12.5847 | −0.697005 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.9121 | −1.09946 | ||||||||
\(329\) | −2.13251 | −0.117569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6966 | −1.02766 | −0.513829 | − | 0.857892i | \(-0.671774\pi\) | ||||
−0.513829 | + | 0.857892i | \(0.671774\pi\) | |||||||
\(332\) | 4.51910 | 0.248018 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.3417 | 0.565871 | ||||||||
\(335\) | 5.12424 | 0.279967 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.3264 | 1.59751 | 0.798755 | − | 0.601657i | \(-0.205492\pi\) | ||||
0.798755 | + | 0.601657i | \(0.205492\pi\) | |||||||
\(338\) | −11.8277 | −0.643343 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.37733 | 0.291627 | ||||||||
\(341\) | 5.19745 | 0.281458 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.3680 | −0.613813 | ||||||||
\(344\) | −3.69989 | −0.199485 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0755411 | −0.00406112 | ||||||||
\(347\) | −11.0048 | −0.590768 | −0.295384 | − | 0.955379i | \(-0.595448\pi\) | ||||
−0.295384 | + | 0.955379i | \(0.595448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1430 | −1.29235 | −0.646174 | − | 0.763190i | \(-0.723632\pi\) | ||||
−0.646174 | + | 0.763190i | \(0.723632\pi\) | |||||||
\(350\) | −0.585228 | −0.0312817 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.79558 | 0.308906 | ||||||||
\(353\) | −13.1068 | −0.697602 | −0.348801 | − | 0.937197i | \(-0.613411\pi\) | ||||
−0.348801 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.1937 | −0.647175 | ||||||||
\(356\) | 4.73483 | 0.250945 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.43577 | −0.340141 | ||||||||
\(359\) | 11.2347 | 0.592942 | 0.296471 | − | 0.955042i | \(-0.404190\pi\) | ||||
0.296471 | + | 0.955042i | \(0.404190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 8.39149 | 0.441047 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.23656 | −0.379299 | ||||||||
\(365\) | 12.7638 | 0.668088 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.796321 | 0.0415676 | 0.0207838 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207838 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(368\) | −9.58316 | −0.499557 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.287444 | 0.0149435 | ||||||||
\(371\) | 4.11123 | 0.213445 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.22370 | 0.218695 | 0.109347 | − | 0.994004i | \(-0.465124\pi\) | ||||
0.109347 | + | 0.994004i | \(0.465124\pi\) | |||||||
\(374\) | 2.39452 | 0.123818 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00518 | −0.309694 | ||||||||
\(377\) | 2.61373 | 0.134614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5751 | −1.15961 | −0.579803 | − | 0.814757i | \(-0.696870\pi\) | ||||
−0.579803 | + | 0.814757i | \(0.696870\pi\) | |||||||
\(380\) | 1.53362 | 0.0786730 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.2380 | 0.574987 | ||||||||
\(383\) | −32.5159 | −1.66148 | −0.830742 | − | 0.556658i | \(-0.812083\pi\) | ||||
−0.830742 | + | 0.556658i | \(0.812083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.856948 | 0.0436741 | ||||||||
\(386\) | −1.91189 | −0.0973128 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.6218 | 0.691540 | ||||||||
\(389\) | 35.4867 | 1.79925 | 0.899624 | − | 0.436665i | \(-0.143840\pi\) | ||||
0.899624 | + | 0.436665i | \(0.143840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.6758 | −1.19734 | ||||||||
\(392\) | −15.1201 | −0.763681 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.91329 | −0.247528 | ||||||||
\(395\) | −10.8691 | −0.546886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7223 | 0.588325 | 0.294162 | − | 0.955755i | \(-0.404959\pi\) | ||||
0.294162 | + | 0.955755i | \(0.404959\pi\) | |||||||
\(398\) | 8.14639 | 0.408341 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.41923 | 0.0709614 | ||||||||
\(401\) | 33.5093 | 1.67337 | 0.836687 | − | 0.547681i | \(-0.184489\pi\) | ||||
0.836687 | + | 0.547681i | \(0.184489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.6187 | −1.42560 | ||||||||
\(404\) | −3.22007 | −0.160205 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.277796 | −0.0137868 | ||||||||
\(407\) | −0.420904 | −0.0208634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50358 | −0.321581 | −0.160791 | − | 0.986989i | \(-0.551404\pi\) | ||||
−0.160791 | + | 0.986989i | \(0.551404\pi\) | |||||||
\(410\) | −5.63505 | −0.278295 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.00499 | 0.295844 | ||||||||
\(413\) | −1.50752 | −0.0741803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.94669 | 0.144647 | ||||||||
\(416\) | −31.9122 | −1.56462 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.682920 | 0.0334027 | ||||||||
\(419\) | 7.49790 | 0.366296 | 0.183148 | − | 0.983085i | \(-0.441371\pi\) | ||||
0.183148 | + | 0.983085i | \(0.441371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5280 | 0.561840 | 0.280920 | − | 0.959731i | \(-0.409360\pi\) | ||||
0.280920 | + | 0.959731i | \(0.409360\pi\) | |||||||
\(422\) | −12.3219 | −0.599822 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5773 | 0.562243 | ||||||||
\(425\) | 3.50630 | 0.170080 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.93447 | 0.142009 | ||||||||
\(428\) | −27.6724 | −1.33760 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.04705 | −0.0504934 | ||||||||
\(431\) | −22.4459 | −1.08118 | −0.540590 | − | 0.841286i | \(-0.681799\pi\) | ||||
−0.540590 | + | 0.841286i | \(0.681799\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.4999 | −1.32156 | −0.660781 | − | 0.750579i | \(-0.729775\pi\) | ||||
−0.660781 | + | 0.750579i | \(0.729775\pi\) | |||||||
\(434\) | 3.04169 | 0.146006 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.13084 | −0.245723 | ||||||||
\(437\) | −6.75237 | −0.323010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.18489 | 0.390644 | 0.195322 | − | 0.980739i | \(-0.437425\pi\) | ||||
0.195322 | + | 0.980739i | \(0.437425\pi\) | |||||||
\(440\) | 2.41318 | 0.115044 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.1850 | −0.627144 | ||||||||
\(443\) | 11.1175 | 0.528209 | 0.264104 | − | 0.964494i | \(-0.414924\pi\) | ||||
0.264104 | + | 0.964494i | \(0.414924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.08736 | 0.146355 | ||||||||
\(446\) | 16.7316 | 0.792264 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.959323 | 0.0453237 | ||||||||
\(449\) | −11.1426 | −0.525854 | −0.262927 | − | 0.964816i | \(-0.584688\pi\) | ||||
−0.262927 | + | 0.964816i | \(0.584688\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.25141 | 0.388544 | ||||||||
\(452\) | 11.1466 | 0.524294 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.3826 | 0.534212 | ||||||||
\(455\) | −4.71861 | −0.221212 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3241 | 0.857164 | 0.428582 | − | 0.903503i | \(-0.359013\pi\) | ||||
0.428582 | + | 0.903503i | \(0.359013\pi\) | |||||||
\(458\) | −10.1307 | −0.473376 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.3556 | −0.482831 | ||||||||
\(461\) | −31.6216 | −1.47276 | −0.736382 | − | 0.676566i | \(-0.763467\pi\) | ||||
−0.736382 | + | 0.676566i | \(0.763467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.76077 | −0.360674 | −0.180337 | − | 0.983605i | \(-0.557719\pi\) | ||||
−0.180337 | + | 0.983605i | \(0.557719\pi\) | |||||||
\(464\) | 0.673679 | 0.0312748 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.7029 | 0.912718 | ||||||||
\(467\) | −31.2308 | −1.44519 | −0.722594 | − | 0.691273i | \(-0.757050\pi\) | ||||
−0.722594 | + | 0.691273i | \(0.757050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.39121 | −0.202767 | ||||||||
\(470\) | −1.69944 | −0.0783894 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.24521 | −0.195401 | ||||||||
\(473\) | 1.53320 | 0.0704966 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | −4.60809 | −0.211212 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.66259 | 0.259001 | ||||||||
\(479\) | 18.2169 | 0.832353 | 0.416177 | − | 0.909284i | \(-0.363370\pi\) | ||||
0.416177 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31762 | 0.105674 | ||||||||
\(482\) | −2.37840 | −0.108333 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.53362 | −0.0697100 | ||||||||
\(485\) | 8.88210 | 0.403315 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2194 | 1.77720 | 0.888600 | − | 0.458683i | \(-0.151679\pi\) | ||||
0.888600 | + | 0.458683i | \(0.151679\pi\) | |||||||
\(488\) | 8.26352 | 0.374072 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.27893 | −0.193302 | ||||||||
\(491\) | −36.5478 | −1.64938 | −0.824688 | − | 0.565587i | \(-0.808650\pi\) | ||||
−0.824688 | + | 0.565587i | \(0.808650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.66437 | 0.0749594 | ||||||||
\(494\) | −3.76036 | −0.169187 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.37637 | −0.331209 | ||||||||
\(497\) | 10.4494 | 0.468719 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.4475 | 1.40778 | 0.703892 | − | 0.710307i | \(-0.251444\pi\) | ||||
0.703892 | + | 0.710307i | \(0.251444\pi\) | |||||||
\(500\) | 1.53362 | 0.0685856 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.6788 | −0.878307 | ||||||||
\(503\) | −20.7020 | −0.923057 | −0.461528 | − | 0.887125i | \(-0.652699\pi\) | ||||
−0.461528 | + | 0.887125i | \(0.652699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.09965 | −0.0934334 | ||||||||
\(506\) | −4.61133 | −0.204999 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.9647 | 1.15200 | ||||||||
\(509\) | −23.5196 | −1.04249 | −0.521245 | − | 0.853407i | \(-0.674532\pi\) | ||||
−0.521245 | + | 0.853407i | \(0.674532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.9379 | −0.483865 | ||||||||
\(512\) | −15.0750 | −0.666226 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.76506 | −0.254286 | ||||||||
\(515\) | 3.91556 | 0.172540 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.48849 | 0.109444 | ||||||||
\(518\) | −0.246324 | −0.0108229 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.2877 | −0.582704 | ||||||||
\(521\) | −28.6887 | −1.25687 | −0.628437 | − | 0.777860i | \(-0.716305\pi\) | ||||
−0.628437 | + | 0.777860i | \(0.716305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.70672 | 0.249537 | 0.124769 | − | 0.992186i | \(-0.460181\pi\) | ||||
0.124769 | + | 0.992186i | \(0.460181\pi\) | |||||||
\(524\) | 8.07634 | 0.352816 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.6288 | 0.637848 | ||||||||
\(527\) | −18.2238 | −0.793842 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5945 | 0.982371 | ||||||||
\(530\) | 3.27633 | 0.142315 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.31423 | −0.0569792 | ||||||||
\(533\) | −45.4347 | −1.96800 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0439 | −0.780105 | ||||||||
\(536\) | −12.3657 | −0.534118 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.07792 | 0.305151 | ||||||||
\(539\) | 6.26564 | 0.269880 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.50382 | 0.150641 | 0.0753205 | − | 0.997159i | \(-0.476002\pi\) | ||||
0.0753205 | + | 0.997159i | \(0.476002\pi\) | |||||||
\(542\) | 17.8296 | 0.765849 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.3210 | −0.871257 | ||||||||
\(545\) | −3.34558 | −0.143309 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.3788 | 1.21339 | 0.606696 | − | 0.794934i | \(-0.292495\pi\) | ||||
0.606696 | + | 0.794934i | \(0.292495\pi\) | |||||||
\(548\) | −31.6045 | −1.35008 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.682920 | 0.0291198 | ||||||||
\(551\) | 0.474680 | 0.0202220 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.31430 | 0.396084 | ||||||||
\(554\) | 12.8159 | 0.544495 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.93530 | −0.0820749 | ||||||||
\(557\) | 0.440370 | 0.0186591 | 0.00932953 | − | 0.999956i | \(-0.497030\pi\) | ||||
0.00932953 | + | 0.999956i | \(0.497030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.44226 | −0.357069 | ||||||||
\(560\) | −1.21621 | −0.0513941 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.8219 | 0.709587 | ||||||||
\(563\) | −44.5147 | −1.87607 | −0.938036 | − | 0.346537i | \(-0.887358\pi\) | ||||
−0.938036 | + | 0.346537i | \(0.887358\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.26819 | 0.305775 | ||||||||
\(566\) | 9.41540 | 0.395759 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.4256 | 1.23467 | ||||||||
\(569\) | −5.32611 | −0.223282 | −0.111641 | − | 0.993749i | \(-0.535611\pi\) | ||||
−0.111641 | + | 0.993749i | \(0.535611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2850 | 0.472264 | 0.236132 | − | 0.971721i | \(-0.424120\pi\) | ||||
0.236132 | + | 0.971721i | \(0.424120\pi\) | |||||||
\(572\) | 8.44457 | 0.353085 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.82895 | 0.201557 | ||||||||
\(575\) | −6.75237 | −0.281593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.9805 | 1.87256 | 0.936281 | − | 0.351251i | \(-0.114243\pi\) | ||||
0.936281 | + | 0.351251i | \(0.114243\pi\) | |||||||
\(578\) | 3.21374 | 0.133674 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.727978 | 0.0302277 | ||||||||
\(581\) | −2.52516 | −0.104761 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79753 | −0.198693 | ||||||||
\(584\) | −30.8014 | −1.27457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.41094 | −0.0995948 | ||||||||
\(587\) | 12.8765 | 0.531470 | 0.265735 | − | 0.964046i | \(-0.414385\pi\) | ||||
0.265735 | + | 0.964046i | \(0.414385\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.19745 | −0.214157 | ||||||||
\(590\) | −1.20138 | −0.0494599 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.597359 | 0.0245513 | ||||||||
\(593\) | 25.1716 | 1.03367 | 0.516837 | − | 0.856084i | \(-0.327109\pi\) | ||||
0.516837 | + | 0.856084i | \(0.327109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00472 | −0.123181 | ||||||||
\(596\) | −17.3479 | −0.710597 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.3914 | 1.03833 | ||||||||
\(599\) | −30.2614 | −1.23645 | −0.618224 | − | 0.786002i | \(-0.712147\pi\) | ||||
−0.618224 | + | 0.786002i | \(0.712147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1672 | 1.35292 | 0.676458 | − | 0.736481i | \(-0.263514\pi\) | ||||
0.676458 | + | 0.736481i | \(0.263514\pi\) | |||||||
\(602\) | 0.897271 | 0.0365700 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.67552 | 0.230934 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.4625 | −0.424660 | −0.212330 | − | 0.977198i | \(-0.568105\pi\) | ||||
−0.212330 | + | 0.977198i | \(0.568105\pi\) | |||||||
\(608\) | −5.79558 | −0.235042 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.33854 | 0.0946848 | ||||||||
\(611\) | −13.7024 | −0.554339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.24317 | −0.373328 | −0.186664 | − | 0.982424i | \(-0.559768\pi\) | ||||
−0.186664 | + | 0.982424i | \(0.559768\pi\) | |||||||
\(614\) | −3.81884 | −0.154116 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.06797 | −0.0833210 | ||||||||
\(617\) | 1.95689 | 0.0787814 | 0.0393907 | − | 0.999224i | \(-0.487458\pi\) | ||||
0.0393907 | + | 0.999224i | \(0.487458\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.3987 | −1.94531 | −0.972653 | − | 0.232263i | \(-0.925387\pi\) | ||||
−0.972653 | + | 0.232263i | \(0.925387\pi\) | |||||||
\(620\) | −7.97091 | −0.320119 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.30902 | −0.0925832 | ||||||||
\(623\) | −2.64570 | −0.105998 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.26559 | −0.370327 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.47039 | −0.178388 | ||||||||
\(629\) | 1.47581 | 0.0588445 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.8039 | 1.22628 | 0.613141 | − | 0.789973i | \(-0.289906\pi\) | ||||
0.613141 | + | 0.789973i | \(0.289906\pi\) | |||||||
\(632\) | 26.2292 | 1.04334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.16641 | −0.244899 | ||||||||
\(635\) | 16.9303 | 0.671860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.5005 | −1.36696 | ||||||||
\(638\) | 0.324169 | 0.0128340 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.8267 | −0.427961 | ||||||||
\(641\) | 7.12059 | 0.281246 | 0.140623 | − | 0.990063i | \(-0.455089\pi\) | ||||
0.140623 | + | 0.990063i | \(0.455089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.8135 | −1.72783 | −0.863917 | − | 0.503634i | \(-0.831996\pi\) | ||||
−0.863917 | + | 0.503634i | \(0.831996\pi\) | |||||||
\(644\) | 8.87419 | 0.349692 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.39452 | −0.0942112 | ||||||||
\(647\) | −19.4584 | −0.764988 | −0.382494 | − | 0.923958i | \(-0.624935\pi\) | ||||
−0.382494 | + | 0.923958i | \(0.624935\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75917 | 0.0690536 | ||||||||
\(650\) | −3.76036 | −0.147494 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.2613 | −1.10680 | ||||||||
\(653\) | 35.4429 | 1.38699 | 0.693493 | − | 0.720463i | \(-0.256071\pi\) | ||||
0.693493 | + | 0.720463i | \(0.256071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.26619 | 0.205767 | ||||||||
\(656\) | −11.7106 | −0.457224 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.45633 | 0.0567738 | ||||||||
\(659\) | 7.91185 | 0.308202 | 0.154101 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154101 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.9285 | −1.47525 | −0.737625 | − | 0.675211i | \(-0.764053\pi\) | ||||
−0.737625 | + | 0.675211i | \(0.764053\pi\) | |||||||
\(662\) | 12.7683 | 0.496254 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.11090 | −0.275956 | ||||||||
\(665\) | −0.856948 | −0.0332310 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.20522 | −0.124106 | ||||||||
\(668\) | 23.2241 | 0.898567 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.49945 | −0.135196 | ||||||||
\(671\) | −3.42433 | −0.132195 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.19834 | −0.200381 | −0.100191 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100191 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(674\) | −20.0276 | −0.771434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.5613 | −1.02159 | ||||||||
\(677\) | 12.7010 | 0.488137 | 0.244069 | − | 0.969758i | \(-0.421518\pi\) | ||||
0.244069 | + | 0.969758i | \(0.421518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.61150 | −0.292103 | ||||||||
\(680\) | −8.46133 | −0.324477 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.54944 | −0.135915 | ||||||||
\(683\) | −45.3282 | −1.73444 | −0.867219 | − | 0.497928i | \(-0.834095\pi\) | ||||
−0.867219 | + | 0.497928i | \(0.834095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.6078 | −0.787383 | ||||||||
\(686\) | 7.76342 | 0.296409 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.17596 | −0.0829578 | ||||||||
\(689\) | 26.4166 | 1.00639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.5149 | 1.16084 | 0.580421 | − | 0.814317i | \(-0.302888\pi\) | ||||
0.580421 | + | 0.814317i | \(0.302888\pi\) | |||||||
\(692\) | −0.169641 | −0.00644879 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.51539 | 0.285280 | ||||||||
\(695\) | −1.26192 | −0.0478672 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9319 | −1.09587 | ||||||||
\(698\) | 16.4878 | 0.624072 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.31423 | −0.0496733 | ||||||||
\(701\) | −0.621590 | −0.0234771 | −0.0117386 | − | 0.999931i | \(-0.503737\pi\) | ||||
−0.0117386 | + | 0.999931i | \(0.503737\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.420904 | 0.0158747 | ||||||||
\(704\) | −1.11946 | −0.0421914 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.95087 | 0.336870 | ||||||||
\(707\) | 1.79930 | 0.0676695 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9142 | −0.823004 | −0.411502 | − | 0.911409i | \(-0.634996\pi\) | ||||
−0.411502 | + | 0.911409i | \(0.634996\pi\) | |||||||
\(710\) | 8.32733 | 0.312519 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.45035 | −0.279214 | ||||||||
\(713\) | 35.0951 | 1.31432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.50630 | 0.205924 | ||||||||
\(716\) | −14.4527 | −0.540121 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.67238 | −0.286331 | ||||||||
\(719\) | 43.0880 | 1.60691 | 0.803455 | − | 0.595365i | \(-0.202993\pi\) | ||||
0.803455 | + | 0.595365i | \(0.202993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.35544 | −0.124963 | ||||||||
\(722\) | −0.682920 | −0.0254157 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.8446 | 0.700353 | ||||||||
\(725\) | 0.474680 | 0.0176292 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.8306 | 1.14344 | 0.571721 | − | 0.820448i | \(-0.306276\pi\) | ||||
0.571721 | + | 0.820448i | \(0.306276\pi\) | |||||||
\(728\) | 11.3869 | 0.422025 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.71666 | −0.322618 | ||||||||
\(731\) | −5.37586 | −0.198833 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6688 | −0.652610 | −0.326305 | − | 0.945264i | \(-0.605804\pi\) | ||||
−0.326305 | + | 0.945264i | \(0.605804\pi\) | |||||||
\(734\) | −0.543824 | −0.0200729 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 39.1339 | 1.44250 | ||||||||
\(737\) | 5.12424 | 0.188754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.72966 | −0.247555 | −0.123777 | − | 0.992310i | \(-0.539501\pi\) | ||||
−0.123777 | + | 0.992310i | \(0.539501\pi\) | |||||||
\(740\) | 0.645506 | 0.0237293 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.80764 | −0.103072 | ||||||||
\(743\) | −48.4780 | −1.77848 | −0.889242 | − | 0.457437i | \(-0.848767\pi\) | ||||
−0.889242 | + | 0.457437i | \(0.848767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.3117 | −0.414429 | ||||||||
\(746\) | −2.88445 | −0.105607 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.37733 | 0.196615 | ||||||||
\(749\) | 15.4627 | 0.564994 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2684 | −1.32345 | −0.661726 | − | 0.749746i | \(-0.730176\pi\) | ||||
−0.661726 | + | 0.749746i | \(0.730176\pi\) | |||||||
\(752\) | −3.53174 | −0.128789 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.78497 | −0.0650047 | ||||||||
\(755\) | 3.70074 | 0.134684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.13939 | −0.186794 | −0.0933972 | − | 0.995629i | \(-0.529773\pi\) | ||||
−0.0933972 | + | 0.995629i | \(0.529773\pi\) | |||||||
\(758\) | 15.4170 | 0.559971 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.41318 | −0.0875353 | ||||||||
\(761\) | −10.2119 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.86699 | 0.103792 | ||||||||
\(764\) | 25.2370 | 0.913042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.2057 | 0.802326 | ||||||||
\(767\) | −9.68654 | −0.349761 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.2015 | −1.77425 | −0.887126 | − | 0.461527i | \(-0.847302\pi\) | ||||
−0.887126 | + | 0.461527i | \(0.847302\pi\) | |||||||
\(770\) | −0.585228 | −0.0210901 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.29350 | −0.154526 | ||||||||
\(773\) | 40.7240 | 1.46474 | 0.732371 | − | 0.680906i | \(-0.238414\pi\) | ||||
0.732371 | + | 0.680906i | \(0.238414\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.19745 | −0.186698 | ||||||||
\(776\) | −21.4341 | −0.769440 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.2346 | −0.868853 | ||||||||
\(779\) | −8.25141 | −0.295637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1937 | −0.436325 | ||||||||
\(782\) | 16.1687 | 0.578192 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.89238 | −0.317585 | ||||||||
\(785\) | −2.91493 | −0.104038 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.23417 | 0.257870 | 0.128935 | − | 0.991653i | \(-0.458844\pi\) | ||||
0.128935 | + | 0.991653i | \(0.458844\pi\) | |||||||
\(788\) | −11.0337 | −0.393059 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.42276 | 0.264090 | ||||||||
\(791\) | −6.22846 | −0.221459 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.8554 | 0.669574 | ||||||||
\(794\) | −8.00539 | −0.284101 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.2942 | 0.648420 | ||||||||
\(797\) | −43.9784 | −1.55779 | −0.778897 | − | 0.627152i | \(-0.784220\pi\) | ||||
−0.778897 | + | 0.627152i | \(0.784220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.72540 | −0.308682 | ||||||||
\(800\) | −5.79558 | −0.204905 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.8842 | −0.808068 | ||||||||
\(803\) | 12.7638 | 0.450425 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.78644 | 0.203945 | ||||||||
\(806\) | 19.5443 | 0.688419 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.06685 | 0.178251 | ||||||||
\(809\) | −11.9798 | −0.421187 | −0.210593 | − | 0.977574i | \(-0.567540\pi\) | ||||
−0.210593 | + | 0.977574i | \(0.567540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0059 | 1.05365 | 0.526825 | − | 0.849974i | \(-0.323382\pi\) | ||||
0.526825 | + | 0.849974i | \(0.323382\pi\) | |||||||
\(812\) | −0.623840 | −0.0218925 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.287444 | 0.0100749 | ||||||||
\(815\) | −18.4278 | −0.645499 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.53320 | −0.0536399 | ||||||||
\(818\) | 4.44143 | 0.155291 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.6545 | −0.441915 | ||||||||
\(821\) | −26.5123 | −0.925284 | −0.462642 | − | 0.886545i | \(-0.653099\pi\) | ||||
−0.462642 | + | 0.886545i | \(0.653099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.2244 | 0.460972 | 0.230486 | − | 0.973076i | \(-0.425968\pi\) | ||||
0.230486 | + | 0.973076i | \(0.425968\pi\) | |||||||
\(824\) | −9.44896 | −0.329170 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.02952 | 0.0358215 | ||||||||
\(827\) | −25.4465 | −0.884861 | −0.442431 | − | 0.896803i | \(-0.645884\pi\) | ||||
−0.442431 | + | 0.896803i | \(0.645884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.6999 | −0.996789 | −0.498395 | − | 0.866950i | \(-0.666077\pi\) | ||||
−0.498395 | + | 0.866950i | \(0.666077\pi\) | |||||||
\(830\) | −2.01235 | −0.0698498 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.16410 | 0.213702 | ||||||||
\(833\) | −21.9692 | −0.761188 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1433 | 0.524056 | ||||||||
\(836\) | 1.53362 | 0.0530413 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.12047 | −0.176884 | ||||||||
\(839\) | 4.10582 | 0.141749 | 0.0708743 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708743 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7747 | −0.992230 | ||||||||
\(842\) | −7.87271 | −0.271311 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −27.6711 | −0.952478 | ||||||||
\(845\) | −17.3193 | −0.595803 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.856948 | 0.0294451 | ||||||||
\(848\) | 6.80879 | 0.233815 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.39452 | −0.0821315 | ||||||||
\(851\) | −2.84210 | −0.0974259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.2689 | −1.75541 | −0.877707 | − | 0.479198i | \(-0.840928\pi\) | ||||
−0.877707 | + | 0.479198i | \(0.840928\pi\) | |||||||
\(854\) | −2.00401 | −0.0685758 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.5431 | 1.48827 | ||||||||
\(857\) | 34.2836 | 1.17110 | 0.585552 | − | 0.810635i | \(-0.300878\pi\) | ||||
0.585552 | + | 0.810635i | \(0.300878\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.5431 | 1.34919 | 0.674596 | − | 0.738187i | \(-0.264318\pi\) | ||||
0.674596 | + | 0.738187i | \(0.264318\pi\) | |||||||
\(860\) | −2.35135 | −0.0801802 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3288 | 0.522100 | ||||||||
\(863\) | 13.1157 | 0.446462 | 0.223231 | − | 0.974766i | \(-0.428340\pi\) | ||||
0.223231 | + | 0.974766i | \(0.428340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.110615 | −0.00376102 | ||||||||
\(866\) | 18.7802 | 0.638179 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.83066 | 0.231848 | ||||||||
\(869\) | −10.8691 | −0.368711 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.2156 | −0.956050 | ||||||||
\(872\) | 8.07349 | 0.273403 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.61133 | 0.155981 | ||||||||
\(875\) | −0.856948 | −0.0289701 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.1036 | −1.15160 | −0.575798 | − | 0.817592i | \(-0.695309\pi\) | ||||
−0.575798 | + | 0.817592i | \(0.695309\pi\) | |||||||
\(878\) | −5.58963 | −0.188641 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.41923 | 0.0478422 | ||||||||
\(881\) | −39.1343 | −1.31847 | −0.659234 | − | 0.751938i | \(-0.729119\pi\) | ||||
−0.659234 | + | 0.751938i | \(0.729119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.1281 | 1.48503 | 0.742515 | − | 0.669829i | \(-0.233633\pi\) | ||||
0.742515 | + | 0.669829i | \(0.233633\pi\) | |||||||
\(884\) | −29.6092 | −0.995864 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.59238 | −0.255071 | ||||||||
\(887\) | 48.8255 | 1.63940 | 0.819700 | − | 0.572793i | \(-0.194140\pi\) | ||||
0.819700 | + | 0.572793i | \(0.194140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.5084 | −0.486597 | ||||||||
\(890\) | −2.10842 | −0.0706743 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 37.5738 | 1.25806 | ||||||||
\(893\) | −2.48849 | −0.0832742 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.42389 | −0.315006 | ||||||||
\(896\) | 9.27789 | 0.309953 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.60954 | 0.253934 | ||||||||
\(899\) | −2.46712 | −0.0822832 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8216 | 0.560407 | ||||||||
\(902\) | −5.63505 | −0.187627 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.5394 | −0.583353 | ||||||||
\(905\) | 12.2876 | 0.408455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4676 | −0.845638 | −0.422819 | − | 0.906214i | \(-0.638959\pi\) | ||||
−0.422819 | + | 0.906214i | \(0.638959\pi\) | |||||||
\(908\) | 25.5617 | 0.848293 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.22244 | 0.106823 | ||||||||
\(911\) | 23.4140 | 0.775740 | 0.387870 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387870 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.94669 | 0.0975212 | ||||||||
\(914\) | −12.5139 | −0.413923 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.7503 | −0.751690 | ||||||||
\(917\) | −4.51286 | −0.149028 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.7511 | −0.618542 | −0.309271 | − | 0.950974i | \(-0.600085\pi\) | ||||
−0.309271 | + | 0.950974i | \(0.600085\pi\) | |||||||
\(920\) | 16.2947 | 0.537220 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.5950 | 0.711194 | ||||||||
\(923\) | 67.1422 | 2.21001 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.420904 | 0.0138392 | ||||||||
\(926\) | 5.29999 | 0.174169 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.75105 | −0.0903075 | ||||||||
\(929\) | −40.7701 | −1.33762 | −0.668812 | − | 0.743432i | \(-0.733197\pi\) | ||||
−0.668812 | + | 0.743432i | \(0.733197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.26564 | −0.205348 | ||||||||
\(932\) | 44.2463 | 1.44934 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.3281 | 0.697878 | ||||||||
\(935\) | 3.50630 | 0.114668 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.54322 | −0.213758 | −0.106879 | − | 0.994272i | \(-0.534086\pi\) | ||||
−0.106879 | + | 0.994272i | \(0.534086\pi\) | |||||||
\(938\) | 2.99885 | 0.0979159 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.81640 | −0.124477 | ||||||||
\(941\) | 34.5714 | 1.12700 | 0.563498 | − | 0.826117i | \(-0.309455\pi\) | ||||
0.563498 | + | 0.826117i | \(0.309455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.7166 | 1.81438 | ||||||||
\(944\) | −2.49667 | −0.0812597 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.04705 | −0.0340427 | ||||||||
\(947\) | −17.6584 | −0.573822 | −0.286911 | − | 0.957957i | \(-0.592628\pi\) | ||||
−0.286911 | + | 0.957957i | \(0.592628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −70.2813 | −2.28143 | ||||||||
\(950\) | −0.682920 | −0.0221569 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.25093 | 0.235004 | ||||||||
\(953\) | 42.7340 | 1.38429 | 0.692145 | − | 0.721758i | \(-0.256666\pi\) | ||||
0.692145 | + | 0.721758i | \(0.256666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4558 | 0.532498 | ||||||||
\(956\) | 12.7164 | 0.411276 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.4407 | −0.401941 | ||||||||
\(959\) | 17.6598 | 0.570265 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.98652 | −0.128597 | ||||||||
\(962\) | −1.58275 | −0.0510299 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.34111 | −0.172026 | ||||||||
\(965\) | −2.79958 | −0.0901218 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.62541 | −0.116585 | −0.0582927 | − | 0.998300i | \(-0.518566\pi\) | ||||
−0.0582927 | + | 0.998300i | \(0.518566\pi\) | |||||||
\(968\) | 2.41318 | 0.0775626 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.06577 | −0.194760 | ||||||||
\(971\) | −2.86101 | −0.0918142 | −0.0459071 | − | 0.998946i | \(-0.514618\pi\) | ||||
−0.0459071 | + | 0.998946i | \(0.514618\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.08140 | 0.0346680 | ||||||||
\(974\) | −26.7837 | −0.858206 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.85990 | 0.155562 | ||||||||
\(977\) | −29.4990 | −0.943756 | −0.471878 | − | 0.881664i | \(-0.656424\pi\) | ||||
−0.471878 | + | 0.881664i | \(0.656424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.08736 | 0.0986723 | ||||||||
\(980\) | −9.60911 | −0.306952 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.9592 | 0.796480 | ||||||||
\(983\) | −31.1737 | −0.994287 | −0.497144 | − | 0.867668i | \(-0.665618\pi\) | ||||
−0.497144 | + | 0.867668i | \(0.665618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.19454 | −0.229237 | ||||||||
\(986\) | −1.13663 | −0.0361977 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.44457 | −0.268657 | ||||||||
\(989\) | 10.3527 | 0.329198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.9145 | −1.77618 | −0.888092 | − | 0.459666i | \(-0.847969\pi\) | ||||
−0.888092 | + | 0.459666i | \(0.847969\pi\) | |||||||
\(992\) | 30.1222 | 0.956382 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.13609 | −0.226343 | ||||||||
\(995\) | 11.9287 | 0.378167 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.1768 | 1.33575 | 0.667877 | − | 0.744272i | \(-0.267203\pi\) | ||||
0.667877 | + | 0.744272i | \(0.267203\pi\) | |||||||
\(998\) | −21.4762 | −0.679816 | ||||||||
\(999\) | 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 | 9405.2.a.bh.1.5 | 9 | ||
3.2 | odd | 2 | 1045.2.a.k.1.5 | ✓ | 9 | ||
15.14 | odd | 2 | 5225.2.a.p.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.k.1.5 | ✓ | 9 | 3.2 | odd | 2 | ||
5225.2.a.p.1.5 | 9 | 15.14 | odd | 2 | |||
9405.2.a.bh.1.5 | 9 | 1.1 | even | 1 | trivial |