Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
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: | \( x^{9} - x^{8} - 11x^{7} + 9x^{6} + 32x^{5} - 17x^{4} - 27x^{3} + 10x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.41589\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0722232 | 0.0416981 | 0.0208490 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208490 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.709626 | −0.268213 | −0.134107 | − | 0.990967i | \(-0.542816\pi\) | ||||
−0.134107 | + | 0.990967i | \(0.542816\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99478 | −0.998261 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.425521 | −0.128299 | −0.0641497 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641497 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.40956 | 1.77769 | 0.888846 | − | 0.458205i | \(-0.151508\pi\) | ||||
0.888846 | + | 0.458205i | \(0.151508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0722232 | 0.0186479 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.34731 | −1.05438 | −0.527189 | − | 0.849748i | \(-0.676754\pi\) | ||||
−0.527189 | + | 0.849748i | \(0.676754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76398 | 0.634099 | 0.317050 | − | 0.948409i | \(-0.397308\pi\) | ||||
0.317050 | + | 0.948409i | \(0.397308\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0512515 | −0.0111840 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.37546 | −0.495317 | −0.247658 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247658 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.432962 | −0.0833237 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.12262 | −0.208466 | −0.104233 | − | 0.994553i | \(-0.533239\pi\) | ||||
−0.104233 | + | 0.994553i | \(0.533239\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.10634 | −0.198705 | −0.0993526 | − | 0.995052i | \(-0.531677\pi\) | ||||
−0.0993526 | + | 0.995052i | \(0.531677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0307325 | −0.00534984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.709626 | −0.119949 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.75024 | −1.27413 | −0.637065 | − | 0.770810i | \(-0.719852\pi\) | ||||
−0.637065 | + | 0.770810i | \(0.719852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.462919 | 0.0741264 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.05857 | −0.633842 | −0.316921 | − | 0.948452i | \(-0.602649\pi\) | ||||
−0.316921 | + | 0.948452i | \(0.602649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.49867 | −1.44853 | −0.724267 | − | 0.689520i | \(-0.757822\pi\) | ||||
−0.724267 | + | 0.689520i | \(0.757822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.99478 | −0.446436 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.25704 | 0.620952 | 0.310476 | − | 0.950581i | \(-0.399511\pi\) | ||||
0.310476 | + | 0.950581i | \(0.399511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.49643 | −0.928062 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.313977 | −0.0439655 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.36390 | −0.736789 | −0.368395 | − | 0.929670i | \(-0.620092\pi\) | ||||
−0.368395 | + | 0.929670i | \(0.620092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.425521 | −0.0573773 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.199623 | 0.0264407 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.25935 | 0.945087 | 0.472544 | − | 0.881307i | \(-0.343336\pi\) | ||||
0.472544 | + | 0.881307i | \(0.343336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.77690 | −0.483582 | −0.241791 | − | 0.970328i | \(-0.577735\pi\) | ||||
−0.241791 | + | 0.970328i | \(0.577735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.12518 | 0.267747 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.40956 | 0.795008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7000 | 1.55155 | 0.775773 | − | 0.631012i | \(-0.217360\pi\) | ||||
0.775773 | + | 0.631012i | \(0.217360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.171563 | −0.0206538 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.91929 | −0.821169 | −0.410584 | − | 0.911823i | \(-0.634675\pi\) | ||||
−0.410584 | + | 0.911823i | \(0.634675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6280 | 1.36096 | 0.680478 | − | 0.732768i | \(-0.261772\pi\) | ||||
0.680478 | + | 0.732768i | \(0.261772\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0722232 | 0.00833962 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.301961 | 0.0344116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0703 | 1.13299 | 0.566497 | − | 0.824064i | \(-0.308298\pi\) | ||||
0.566497 | + | 0.824064i | \(0.308298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.95308 | 0.994787 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.42260 | −0.375680 | −0.187840 | − | 0.982200i | \(-0.560149\pi\) | ||||
−0.187840 | + | 0.982200i | \(0.560149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.34731 | −0.471532 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0810794 | −0.00869263 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.05887 | 0.112240 | 0.0561199 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561199 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.54839 | −0.476801 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0799037 | −0.00828562 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.76398 | 0.283578 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.57137 | −0.464152 | −0.232076 | − | 0.972698i | \(-0.574552\pi\) | ||||
−0.232076 | + | 0.972698i | \(0.574552\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.27434 | 0.128076 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6098 | −1.45373 | −0.726866 | − | 0.686779i | \(-0.759024\pi\) | ||||
−0.726866 | + | 0.686779i | \(0.759024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.19587 | 0.610497 | 0.305249 | − | 0.952273i | \(-0.401260\pi\) | ||||
0.305249 | + | 0.952273i | \(0.401260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0512515 | −0.00500163 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.3924 | −1.39137 | −0.695684 | − | 0.718348i | \(-0.744899\pi\) | ||||
−0.695684 | + | 0.718348i | \(0.744899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.52240 | −0.528950 | −0.264475 | − | 0.964393i | \(-0.585199\pi\) | ||||
−0.264475 | + | 0.964393i | \(0.585199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.559747 | −0.0531288 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9331 | 1.40479 | 0.702396 | − | 0.711787i | \(-0.252114\pi\) | ||||
0.702396 | + | 0.711787i | \(0.252114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.37546 | −0.221512 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.1953 | −1.77460 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.08496 | 0.282798 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8189 | −0.983539 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.293123 | −0.0264300 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.72098 | −0.773862 | −0.386931 | − | 0.922109i | \(-0.626465\pi\) | ||||
−0.386931 | + | 0.922109i | \(0.626465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.686024 | −0.0604011 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1693 | −1.32535 | −0.662676 | − | 0.748906i | \(-0.730579\pi\) | ||||
−0.662676 | + | 0.748906i | \(0.730579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.96139 | −0.170074 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.432962 | −0.0372635 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.4998 | −1.32424 | −0.662118 | − | 0.749400i | \(-0.730342\pi\) | ||||
−0.662118 | + | 0.749400i | \(0.730342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.44923 | 0.547017 | 0.273508 | − | 0.961870i | \(-0.411816\pi\) | ||||
0.273508 | + | 0.961870i | \(0.411816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.307457 | 0.0258925 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.72740 | −0.228077 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.12262 | −0.0932287 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.469193 | −0.0386984 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.80041 | −0.802881 | −0.401441 | − | 0.915885i | \(-0.631490\pi\) | ||||
−0.401441 | + | 0.915885i | \(0.631490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.0193 | 1.05254 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.10634 | −0.0888636 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.30208 | 0.103917 | 0.0519585 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519585 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.387398 | −0.0307227 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.68569 | 0.132851 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.15240 | −0.0902627 | −0.0451314 | − | 0.998981i | \(-0.514371\pi\) | ||||
−0.0451314 | + | 0.998981i | \(0.514371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0307325 | −0.00239252 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.7287 | −1.60403 | −0.802016 | − | 0.597302i | \(-0.796239\pi\) | ||||
−0.802016 | + | 0.597302i | \(0.796239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.0825 | 2.16019 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.27751 | −0.632997 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.9420 | −1.51616 | −0.758080 | − | 0.652161i | \(-0.773863\pi\) | ||||
−0.758080 | + | 0.652161i | \(0.773863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.709626 | −0.0536427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.524294 | 0.0394083 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.27486 | 0.0952877 | 0.0476439 | − | 0.998864i | \(-0.484829\pi\) | ||||
0.0476439 | + | 0.998864i | \(0.484829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.32402 | −0.172743 | −0.0863716 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863716 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.272779 | −0.0201644 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.75024 | −0.569809 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.84987 | 0.135276 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.307241 | 0.0223485 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5672 | 1.56055 | 0.780275 | − | 0.625437i | \(-0.215079\pi\) | ||||
0.780275 | + | 0.625437i | \(0.215079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.0265 | −1.65749 | −0.828743 | − | 0.559629i | \(-0.810944\pi\) | ||||
−0.828743 | + | 0.559629i | \(0.810944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.462919 | 0.0331503 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1640 | 0.795400 | 0.397700 | − | 0.917516i | \(-0.369808\pi\) | ||||
0.397700 | + | 0.917516i | \(0.369808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2879 | 0.941955 | 0.470977 | − | 0.882145i | \(-0.343901\pi\) | ||||
0.470977 | + | 0.882145i | \(0.343901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.917232 | 0.0646965 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.796642 | 0.0559133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.05857 | −0.283463 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.11398 | 0.494456 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.17613 | −0.0813546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3780 | 0.714449 | 0.357225 | − | 0.934018i | \(-0.383723\pi\) | ||||
0.357225 | + | 0.934018i | \(0.383723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.499733 | −0.0342412 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.49867 | −0.647804 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.785090 | 0.0532954 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.839813 | 0.0567493 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.8644 | −1.87436 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2413 | −1.08760 | −0.543799 | − | 0.839215i | \(-0.683015\pi\) | ||||
−0.543799 | + | 0.839215i | \(0.683015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.99478 | −0.199652 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.8156 | 1.04972 | 0.524860 | − | 0.851189i | \(-0.324118\pi\) | ||||
0.524860 | + | 0.851189i | \(0.324118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.4248 | −1.74620 | −0.873101 | − | 0.487540i | \(-0.837894\pi\) | ||||
−0.873101 | + | 0.487540i | \(0.837894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0218086 | 0.00143490 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.08510 | 0.136599 | 0.0682996 | − | 0.997665i | \(-0.478243\pi\) | ||||
0.0682996 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.25704 | 0.277698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.727307 | 0.0472437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1081 | −0.912580 | −0.456290 | − | 0.889831i | \(-0.650822\pi\) | ||||
−0.456290 | + | 0.889831i | \(0.650822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.38114 | 0.475461 | 0.237730 | − | 0.971331i | \(-0.423597\pi\) | ||||
0.237730 | + | 0.971331i | \(0.423597\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.94551 | 0.124804 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.49643 | −0.415042 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.7159 | 1.12723 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.247191 | −0.0156651 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2947 | −1.09163 | −0.545817 | − | 0.837904i | \(-0.683781\pi\) | ||||
−0.545817 | + | 0.837904i | \(0.683781\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.01081 | 0.0635489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.313977 | −0.0196620 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.978328 | 0.0610264 | 0.0305132 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305132 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.49977 | 0.341739 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.36201 | 0.208103 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.8209 | −1.59218 | −0.796092 | − | 0.605175i | \(-0.793103\pi\) | ||||
−0.796092 | + | 0.605175i | \(0.793103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.36390 | −0.329502 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0764748 | 0.00468018 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.91986 | 0.421911 | 0.210956 | − | 0.977496i | \(-0.432342\pi\) | ||||
0.210956 | + | 0.977496i | \(0.432342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0232 | 0.973338 | 0.486669 | − | 0.873586i | \(-0.338212\pi\) | ||||
0.486669 | + | 0.873586i | \(0.338212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.328499 | −0.0198817 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.425521 | −0.0256599 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9286 | −1.19739 | −0.598696 | − | 0.800977i | \(-0.704314\pi\) | ||||
−0.598696 | + | 0.800977i | \(0.704314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.31326 | 0.198360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0361 | −1.07594 | −0.537971 | − | 0.842963i | \(-0.680809\pi\) | ||||
−0.537971 | + | 0.842963i | \(0.680809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.38500 | −0.557880 | −0.278940 | − | 0.960308i | \(-0.589983\pi\) | ||||
−0.278940 | + | 0.960308i | \(0.589983\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.199623 | 0.0118247 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.88007 | 0.170005 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.89911 | 0.111712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.330159 | −0.0193542 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.207112 | −0.0120996 | −0.00604982 | − | 0.999982i | \(-0.501926\pi\) | ||||
−0.00604982 | + | 0.999982i | \(0.501926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.25935 | 0.422656 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.184235 | 0.0106904 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.2256 | −0.880521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.74050 | 0.388516 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.05517 | −0.0606178 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.77690 | −0.216264 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.53418 | 0.258779 | 0.129390 | − | 0.991594i | \(-0.458698\pi\) | ||||
0.129390 | + | 0.991594i | \(0.458698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.447485 | 0.0254566 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3605 | −1.15454 | −0.577269 | − | 0.816554i | \(-0.695882\pi\) | ||||
−0.577269 | + | 0.816554i | \(0.695882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.35555 | −0.415760 | −0.207880 | − | 0.978154i | \(-0.566656\pi\) | ||||
−0.207880 | + | 0.978154i | \(0.566656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.12518 | 0.119740 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4717 | 0.756645 | 0.378322 | − | 0.925674i | \(-0.376501\pi\) | ||||
0.378322 | + | 0.925674i | \(0.376501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.477700 | 0.0267461 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.03947 | −0.0580174 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0159 | −0.668580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.40956 | 0.355539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.398846 | −0.0220562 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.02090 | −0.166548 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.06564 | −0.278433 | −0.139216 | − | 0.990262i | \(-0.544458\pi\) | ||||
−0.139216 | + | 0.990262i | \(0.544458\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.2103 | 1.27192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7000 | 0.693873 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.66912 | 0.308817 | 0.154408 | − | 0.988007i | \(-0.450653\pi\) | ||||
0.154408 | + | 0.988007i | \(0.450653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.07852 | 0.0585771 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.470773 | 0.0254938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.57742 | 0.517132 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.171563 | −0.00923664 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1912 | −0.547091 | −0.273546 | − | 0.961859i | \(-0.588196\pi\) | ||||
−0.273546 | + | 0.961859i | \(0.588196\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8306 | −1.00798 | −0.503990 | − | 0.863710i | \(-0.668135\pi\) | ||||
−0.503990 | + | 0.863710i | \(0.668135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.77510 | −0.148124 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.92794 | 0.475187 | 0.237593 | − | 0.971365i | \(-0.423641\pi\) | ||||
0.237593 | + | 0.971365i | \(0.423641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.91929 | −0.367238 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.222806 | 0.0117921 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4790 | 1.08084 | 0.540419 | − | 0.841396i | \(-0.318266\pi\) | ||||
0.540419 | + | 0.841396i | \(0.318266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3604 | −0.597918 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.781378 | −0.0410117 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6280 | 0.608638 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4178 | 0.648203 | 0.324101 | − | 0.946022i | \(-0.394938\pi\) | ||||
0.324101 | + | 0.946022i | \(0.394938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.1545 | 0.632740 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.80637 | 0.197617 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.4196 | −1.26440 | −0.632198 | − | 0.774807i | \(-0.717847\pi\) | ||||
−0.632198 | + | 0.774807i | \(0.717847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.0722232 | 0.00372959 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.19552 | −0.370588 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9830 | 1.02646 | 0.513228 | − | 0.858252i | \(-0.328449\pi\) | ||||
0.513228 | + | 0.858252i | \(0.328449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.629857 | −0.0322686 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.98342 | −0.152446 | −0.0762228 | − | 0.997091i | \(-0.524286\pi\) | ||||
−0.0762228 | + | 0.997091i | \(0.524286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.301961 | 0.0153893 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.4465 | 1.44602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.79740 | 0.496748 | 0.248374 | − | 0.968664i | \(-0.420104\pi\) | ||||
0.248374 | + | 0.968664i | \(0.420104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3268 | 0.522251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.09558 | −0.0552646 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0703 | 0.506691 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.268968 | 0.0134991 | 0.00674957 | − | 0.999977i | \(-0.497852\pi\) | ||||
0.00674957 | + | 0.999977i | \(0.497852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.141658 | −0.00709176 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.5671 | −1.37663 | −0.688316 | − | 0.725411i | \(-0.741650\pi\) | ||||
−0.688316 | + | 0.725411i | \(0.741650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.09118 | −0.353237 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.95308 | 0.444882 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.29789 | 0.163470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.35099 | −0.314036 | −0.157018 | − | 0.987596i | \(-0.550188\pi\) | ||||
−0.157018 | + | 0.987596i | \(0.550188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.11944 | −0.0552181 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.15143 | −0.253485 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.42260 | −0.168009 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.465784 | 0.0228096 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.8847 | −1.85079 | −0.925393 | − | 0.379008i | \(-0.876265\pi\) | ||||
−0.925393 | + | 0.379008i | \(0.876265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.950439 | −0.0463216 | −0.0231608 | − | 0.999732i | \(-0.507373\pi\) | ||||
−0.0231608 | + | 0.999732i | \(0.507373\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.7489 | −0.619873 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.34731 | −0.210876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.68018 | 0.129703 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.196982 | −0.00951038 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.49509 | −0.120184 | −0.0600921 | − | 0.998193i | \(-0.519139\pi\) | ||||
−0.0600921 | + | 0.998193i | \(0.519139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.35197 | 0.449427 | 0.224713 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224713 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0810794 | −0.00388746 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.56570 | −0.314080 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.1962 | −0.773002 | −0.386501 | − | 0.922289i | \(-0.626316\pi\) | ||||
−0.386501 | + | 0.922289i | \(0.626316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.4554 | 0.926448 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2330 | 1.05632 | 0.528161 | − | 0.849144i | \(-0.322882\pi\) | ||||
0.528161 | + | 0.849144i | \(0.322882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.05887 | 0.0501951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.707817 | −0.0334786 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4972 | 1.15609 | 0.578047 | − | 0.816004i | \(-0.303815\pi\) | ||||
0.578047 | + | 0.816004i | \(0.303815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.72701 | 0.0813216 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.0722232 | −0.00339334 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.54839 | −0.213232 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1628 | 0.849621 | 0.424810 | − | 0.905282i | \(-0.360341\pi\) | ||||
0.424810 | + | 0.905282i | \(0.360341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.88222 | 0.0878546 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.11272 | −0.331272 | −0.165636 | − | 0.986187i | \(-0.552968\pi\) | ||||
−0.165636 | + | 0.986187i | \(0.552968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.63466 | 0.447761 | 0.223880 | − | 0.974617i | \(-0.428128\pi\) | ||||
0.223880 | + | 0.974617i | \(0.428128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.0799037 | −0.00370544 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.59139 | 0.397562 | 0.198781 | − | 0.980044i | \(-0.436302\pi\) | ||||
0.198781 | + | 0.980044i | \(0.436302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.01222 | −0.416146 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0940401 | 0.00433314 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.04189 | 0.185846 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.76398 | 0.126820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0637 | 0.735508 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6154 | 1.12471 | 0.562354 | − | 0.826896i | \(-0.309896\pi\) | ||||
0.562354 | + | 0.826896i | \(0.309896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.6756 | −2.26501 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.121746 | 0.00553962 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.57137 | −0.207575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6149 | 1.43261 | 0.716305 | − | 0.697788i | \(-0.245832\pi\) | ||||
0.716305 | + | 0.697788i | \(0.245832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0832298 | −0.00376378 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4660 | 1.32978 | 0.664890 | − | 0.746941i | \(-0.268478\pi\) | ||||
0.664890 | + | 0.746941i | \(0.268478\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.88039 | 0.219802 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.27434 | 0.0572775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.91011 | 0.220248 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.2934 | −0.774159 | −0.387079 | − | 0.922046i | \(-0.626516\pi\) | ||||
−0.387079 | + | 0.922046i | \(0.626516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.49709 | −0.0668851 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.9170 | 0.977229 | 0.488615 | − | 0.872500i | \(-0.337502\pi\) | ||||
0.488615 | + | 0.872500i | \(0.337502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6098 | −0.650129 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.02821 | 0.0900759 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3000 | −0.899783 | −0.449891 | − | 0.893083i | \(-0.648537\pi\) | ||||
−0.449891 | + | 0.893083i | \(0.648537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.25154 | −0.365027 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.19670 | −0.0528355 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.19587 | 0.273023 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.81146 | −0.0796679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.44027 | −0.0632210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.0111 | −1.79673 | −0.898364 | − | 0.439253i | \(-0.855243\pi\) | ||||
−0.898364 | + | 0.439253i | \(0.855243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.08941 | 0.0913636 | 0.0456818 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456818 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0512515 | −0.00223680 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.80962 | 0.209510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3572 | −0.754661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.7402 | −0.943444 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0136 | −1.12678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3924 | −0.622239 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0920747 | 0.00397332 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.76437 | 0.119070 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1115 | 1.33759 | 0.668795 | − | 0.743447i | \(-0.266810\pi\) | ||||
0.668795 | + | 0.743447i | \(0.266810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.167848 | −0.00720306 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.52240 | −0.236554 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.0295 | 1.15570 | 0.577849 | − | 0.816144i | \(-0.303892\pi\) | ||||
0.577849 | + | 0.816144i | \(0.303892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.3110 | 0.482741 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.10290 | −0.132188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.14613 | −0.303884 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.559747 | −0.0237599 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.37891 | −0.312655 | −0.156327 | − | 0.987705i | \(-0.549965\pi\) | ||||
−0.156327 | + | 0.987705i | \(0.549965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −60.8823 | −2.57505 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.133604 | 0.00564075 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.0319 | 0.633517 | 0.316759 | − | 0.948506i | \(-0.397405\pi\) | ||||
0.316759 | + | 0.948506i | \(0.397405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9331 | 0.628242 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.35334 | −0.266815 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.11822 | 0.130722 | 0.0653612 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653612 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.83446 | −0.160467 | −0.0802335 | − | 0.996776i | \(-0.525567\pi\) | ||||
−0.0802335 | + | 0.996776i | \(0.525567\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.55765 | 0.0650719 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.37546 | −0.0990634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.66270 | −0.152480 | −0.0762401 | − | 0.997089i | \(-0.524292\pi\) | ||||
−0.0762401 | + | 0.997089i | \(0.524292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.66305 | −0.0691140 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.42877 | 0.100762 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.28246 | 0.0945296 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.1953 | −0.793626 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.97122 | 0.246459 | 0.123229 | − | 0.992378i | \(-0.460675\pi\) | ||||
0.123229 | + | 0.992378i | \(0.460675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.05791 | −0.125999 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.806298 | 0.0331667 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.17424 | 0.171416 | 0.0857078 | − | 0.996320i | \(-0.472685\pi\) | ||||
0.0857078 | + | 0.996320i | \(0.472685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.08496 | 0.126471 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.959695 | 0.0392777 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.48902 | −0.183416 | −0.0917082 | − | 0.995786i | \(-0.529233\pi\) | ||||
−0.0917082 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.0849 | −1.71668 | −0.858339 | − | 0.513082i | \(-0.828504\pi\) | ||||
−0.858339 | + | 0.513082i | \(0.828504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.0336 | −1.54885 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8189 | −0.439852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7422 | 1.36955 | 0.684777 | − | 0.728752i | \(-0.259899\pi\) | ||||
0.684777 | + | 0.728752i | \(0.259899\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0575360 | 0.00233148 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.2857 | 1.10386 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.3190 | 0.618729 | 0.309365 | − | 0.950944i | \(-0.399884\pi\) | ||||
0.309365 | + | 0.950944i | \(0.399884\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.293123 | −0.0118199 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3517 | 0.940106 | 0.470053 | − | 0.882638i | \(-0.344235\pi\) | ||||
0.470053 | + | 0.882638i | \(0.344235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.96970 | −0.360523 | −0.180261 | − | 0.983619i | \(-0.557694\pi\) | ||||
−0.180261 | + | 0.983619i | \(0.557694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.02848 | 0.0412716 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.751400 | −0.0301042 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0849439 | −0.00339233 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.6927 | 1.34342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0985 | −0.839919 | −0.419959 | − | 0.907543i | \(-0.637956\pi\) | ||||
−0.419959 | + | 0.907543i | \(0.637956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.749531 | 0.0297912 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.72098 | −0.346082 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.6393 | −1.64981 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.7218 | 0.819741 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9207 | 0.668328 | 0.334164 | − | 0.942515i | \(-0.391546\pi\) | ||||
0.334164 | + | 0.942515i | \(0.391546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.47485 | 0.137035 | 0.0685173 | − | 0.997650i | \(-0.478173\pi\) | ||||
0.0685173 | + | 0.997650i | \(0.478173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.686024 | −0.0270122 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.7346 | −1.28693 | −0.643465 | − | 0.765476i | \(-0.722504\pi\) | ||||
−0.643465 | + | 0.765476i | \(0.722504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.08901 | −0.121254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0567017 | 0.00222232 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.51048 | 0.293908 | 0.146954 | − | 0.989143i | \(-0.453053\pi\) | ||||
0.146954 | + | 0.989143i | \(0.453053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.1693 | −0.592715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.8234 | −1.35859 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.5988 | −0.451824 | −0.225912 | − | 0.974148i | \(-0.572536\pi\) | ||||
−0.225912 | + | 0.974148i | \(0.572536\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9039 | 0.540797 | 0.270399 | − | 0.962748i | \(-0.412845\pi\) | ||||
0.270399 | + | 0.962748i | \(0.412845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.01245 | −0.0781572 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.96139 | −0.0760594 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66674 | 0.103257 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.17300 | −0.0453508 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.60715 | 0.0620433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.5867 | −1.52595 | −0.762977 | − | 0.646425i | \(-0.776263\pi\) | ||||
−0.762977 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.432962 | −0.0166647 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.2265 | 1.12327 | 0.561633 | − | 0.827387i | \(-0.310173\pi\) | ||||
0.561633 | + | 0.827387i | \(0.310173\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.24396 | 0.124492 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.14225 | 0.0437713 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.6734 | 0.408405 | 0.204203 | − | 0.978929i | \(-0.434540\pi\) | ||||
0.204203 | + | 0.978929i | \(0.434540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4998 | −0.592216 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.90849 | −0.0728133 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.3803 | −1.30978 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.74934 | −0.218715 | −0.109358 | − | 0.994002i | \(-0.534879\pi\) | ||||
−0.109358 | + | 0.994002i | \(0.534879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.904307 | −0.0343518 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.44923 | 0.244633 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.6439 | 0.668309 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.150592 | 0.00569593 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.14573 | −0.269890 | −0.134945 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134945 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.4215 | −0.807926 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.307457 | 0.0115795 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3675 | 0.389910 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.10751 | 0.116705 | 0.0583526 | − | 0.998296i | \(-0.481415\pi\) | ||||
0.0583526 | + | 0.998296i | \(0.481415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.1583 | −1.13102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.62807 | 0.0984220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.72740 | −0.101999 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.01894 | −0.0380528 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.755404 | −0.0281718 | −0.0140859 | − | 0.999901i | \(-0.504484\pi\) | ||||
−0.0140859 | + | 0.999901i | \(0.504484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.39675 | −0.163743 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.533089 | 0.0198258 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.12262 | −0.0416932 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.3433 | −1.31081 | −0.655405 | − | 0.755278i | \(-0.727502\pi\) | ||||
−0.655405 | + | 0.755278i | \(0.727502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.7187 | −0.989583 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.2937 | 1.52730 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.3054 | −0.676127 | −0.338064 | − | 0.941123i | \(-0.609772\pi\) | ||||
−0.338064 | + | 0.941123i | \(0.609772\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.469193 | −0.0173064 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.40410 | −0.199063 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.9731 | 1.47044 | 0.735218 | − | 0.677831i | \(-0.237080\pi\) | ||||
0.735218 | + | 0.677831i | \(0.237080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.27950 | 0.0470035 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.6574 | 1.82175 | 0.910876 | − | 0.412679i | \(-0.135407\pi\) | ||||
0.910876 | + | 0.412679i | \(0.135407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.80041 | −0.359059 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.2500 | 0.375026 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2132 | 0.373183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.4001 | −1.91211 | −0.956053 | − | 0.293193i | \(-0.905282\pi\) | ||||
−0.956053 | + | 0.293193i | \(0.905282\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.24908 | −0.0455190 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.176781 | −0.00642521 | −0.00321261 | − | 0.999995i | \(-0.501023\pi\) | ||||
−0.00321261 | + | 0.999995i | \(0.501023\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0730037 | 0.00264987 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.65090 | −0.168595 | −0.0842975 | − | 0.996441i | \(-0.526865\pi\) | ||||
−0.0842975 | + | 0.996441i | \(0.526865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.91884 | 0.141872 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.0193 | 0.470712 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.5293 | 1.68007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.07879 | −0.327390 | −0.163695 | − | 0.986511i | \(-0.552341\pi\) | ||||
−0.163695 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0706580 | 0.00254468 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.3926 | 1.02121 | 0.510605 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510605 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.10634 | −0.0397410 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.397211 | 0.0142499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2178 | −0.401919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.94431 | 0.105356 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.486054 | 0.0173701 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.30208 | 0.0464731 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.8995 | 1.27968 | 0.639839 | − | 0.768509i | \(-0.279001\pi\) | ||||
0.639839 | + | 0.768509i | \(0.279001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.86487 | −0.0663910 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5969 | −0.376784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.2083 | −0.859660 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.387398 | −0.0137396 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.72995 | 0.202965 | 0.101483 | − | 0.994837i | \(-0.467641\pi\) | ||||
0.101483 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.5067 | −0.654718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.17108 | −0.112045 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.94797 | −0.174610 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.68569 | 0.0594126 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.499775 | 0.0175929 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.2161 | −0.675603 | −0.337802 | − | 0.941217i | \(-0.609683\pi\) | ||||
−0.337802 | + | 0.941217i | \(0.609683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.8110 | −0.379627 | −0.189814 | − | 0.981820i | \(-0.560788\pi\) | ||||
−0.189814 | + | 0.981820i | \(0.560788\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.15724 | 0.0405863 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.15240 | −0.0403667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.2541 | −0.918515 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.6214 | 0.475972 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.62772 | −0.266209 | −0.133105 | − | 0.991102i | \(-0.542495\pi\) | ||||
−0.133105 | + | 0.991102i | \(0.542495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5370 | 0.541587 | 0.270794 | − | 0.962637i | \(-0.412714\pi\) | ||||
0.270794 | + | 0.962637i | \(0.412714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0307325 | −0.00106997 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.22755 | −0.147006 | −0.0735031 | − | 0.997295i | \(-0.523418\pi\) | ||||
−0.0735031 | + | 0.997295i | \(0.523418\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9122 | 0.656849 | 0.328424 | − | 0.944530i | \(-0.393482\pi\) | ||||
0.328424 | + | 0.944530i | \(0.393482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.43930 | −0.0499289 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.2420 | 0.978527 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.7287 | −0.717345 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.479005 | 0.0165568 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4110 | −0.877284 | −0.438642 | − | 0.898662i | \(-0.644540\pi\) | ||||
−0.438642 | + | 0.898662i | \(0.644540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7397 | −0.956542 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.30262 | −0.0448648 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.0825 | 0.966067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.67739 | 0.263798 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.677815 | −0.0232625 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4103 | 0.631099 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2801 | 0.728615 | 0.364308 | − | 0.931279i | \(-0.381306\pi\) | ||||
0.364308 | + | 0.931279i | \(0.381306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.27751 | −0.283085 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.9808 | 1.39988 | 0.699939 | − | 0.714202i | \(-0.253210\pi\) | ||||
0.699939 | + | 0.714202i | \(0.253210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.7945 | −1.66485 | −0.832424 | − | 0.554140i | \(-0.813047\pi\) | ||||
−0.832424 | + | 0.554140i | \(0.813047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.208008 | 0.00708888 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.5779 | 0.360075 | 0.180037 | − | 0.983660i | \(-0.442378\pi\) | ||||
0.180037 | + | 0.983660i | \(0.442378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9420 | −0.678048 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.137160 | 0.00465819 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.28512 | −0.145363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.4012 | 2.75817 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.6903 | 0.463345 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.709626 | −0.0239897 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.0020 | 1.45207 | 0.726037 | − | 0.687656i | \(-0.241360\pi\) | ||||
0.726037 | + | 0.687656i | \(0.241360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0149583 | −0.000504532 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.9536 | −1.17762 | −0.588809 | − | 0.808273i | \(-0.700403\pi\) | ||||
−0.588809 | + | 0.808273i | \(0.700403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.2117 | 1.82437 | 0.912185 | − | 0.409778i | \(-0.134394\pi\) | ||||
0.912185 | + | 0.409778i | \(0.134394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.524294 | 0.0176239 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.5465 | 0.522002 | 0.261001 | − | 0.965339i | \(-0.415947\pi\) | ||||
0.261001 | + | 0.965339i | \(0.415947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.18864 | 0.207560 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.80973 | −0.127631 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7663 | 0.393746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.27486 | 0.0426140 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.09964 | −0.0367160 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.24201 | 0.0414232 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3186 | 0.776854 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.486821 | 0.0162004 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.32402 | −0.0772531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.3249 | −1.57140 | −0.785698 | − | 0.618610i | \(-0.787696\pi\) | ||||
−0.785698 | + | 0.618610i | \(0.787696\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.7533 | 1.45120 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.7348 | −0.753236 | −0.376618 | − | 0.926369i | \(-0.622913\pi\) | ||||
−0.376618 | + | 0.926369i | \(0.622913\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.45639 | 0.0481995 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.272779 | −0.00901781 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7646 | 0.355477 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5632 | 0.414422 | 0.207211 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207211 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.327473 | 0.0107906 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.3496 | −1.45979 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.75024 | −0.254826 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.5553 | −0.609436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.9530 | 0.917108 | 0.458554 | − | 0.888666i | \(-0.348367\pi\) | ||||
0.458554 | + | 0.888666i | \(0.348367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.9560 | −0.588483 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.47050 | −0.0481420 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.84987 | 0.0604973 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.67569 | 0.152748 | 0.0763740 | − | 0.997079i | \(-0.475666\pi\) | ||||
0.0763740 | + | 0.997079i | \(0.475666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.531241 | −0.0173364 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.59574 | 0.117218 | 0.0586088 | − | 0.998281i | \(-0.481334\pi\) | ||||
0.0586088 | + | 0.998281i | \(0.481334\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.64095 | 0.313953 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.307241 | 0.00999456 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.9876 | −1.39691 | −0.698454 | − | 0.715655i | \(-0.746128\pi\) | ||||
−0.698454 | + | 0.715655i | \(0.746128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74.5305 | 2.41936 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.972968 | 0.0315506 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.4247 | −1.08273 | −0.541365 | − | 0.840787i | \(-0.682092\pi\) | ||||
−0.541365 | + | 0.840787i | \(0.682092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5672 | 0.697899 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0345010 | 0.00111526 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.9990 | 0.355178 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7760 | −0.960516 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.1022 | 1.38895 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.0265 | −0.741250 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.6070 | 1.85252 | 0.926259 | − | 0.376888i | \(-0.123006\pi\) | ||||
0.926259 | + | 0.376888i | \(0.123006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.867824 | −0.0278785 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7096 | −0.953426 | −0.476713 | − | 0.879059i | \(-0.658172\pi\) | ||||
−0.476713 | + | 0.879059i | \(0.658172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.57654 | −0.146717 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.462919 | 0.0148253 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.2087 | 1.28639 | 0.643195 | − | 0.765702i | \(-0.277608\pi\) | ||||
0.643195 | + | 0.765702i | \(0.277608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.450571 | −0.0144003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.5384 | 0.528031 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.5098 | 0.941216 | 0.470608 | − | 0.882342i | \(-0.344035\pi\) | ||||
0.470608 | + | 0.882342i | \(0.344035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1640 | 0.355714 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.218179 | −0.00694472 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.5637 | 0.717483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7388 | 0.881151 | 0.440576 | − | 0.897716i | \(-0.354774\pi\) | ||||
0.440576 | + | 0.897716i | \(0.354774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.365857 | −0.0116101 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.2879 | 0.421255 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.6362 | 1.25529 | 0.627646 | − | 0.778499i | \(-0.284019\pi\) | ||||
0.627646 | + | 0.778499i | \(0.284019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35556 | 0.106165 |
(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 | 6040.2.a.l.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.l.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |