Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2368,2,Mod(1,2368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2368.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.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: | \(18.9085751986\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2368.1 |
$q$-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 | ||||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.85410 | −1.72361 | −0.861803 | − | 0.507242i | \(-0.830665\pi\) | ||||
−0.861803 | + | 0.507242i | \(0.830665\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.38197 | −0.416678 | −0.208339 | − | 0.978057i | \(-0.566806\pi\) | ||||
−0.208339 | + | 0.978057i | \(0.566806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.85410 | 0.791585 | 0.395793 | − | 0.918340i | \(-0.370470\pi\) | ||||
0.395793 | + | 0.918340i | \(0.370470\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.23607 | 1.61015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.23607 | −1.14260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.85410 | −0.595121 | −0.297561 | − | 0.954703i | \(-0.596173\pi\) | ||||
−0.297561 | + | 0.954703i | \(0.596173\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.85410 | 1.97082 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.32624 | 1.73184 | 0.865919 | − | 0.500183i | \(-0.166734\pi\) | ||||
0.865919 | + | 0.500183i | \(0.166734\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.38197 | −1.32584 | −0.662920 | − | 0.748690i | \(-0.730683\pi\) | ||||
−0.662920 | + | 0.748690i | \(0.730683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.4721 | −2.10818 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.61803 | −0.739477 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.61803 | 1.50208 | 0.751042 | − | 0.660254i | \(-0.229551\pi\) | ||||
0.751042 | + | 0.660254i | \(0.229551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.23607 | −0.798493 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.47214 | 0.219453 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.23607 | 0.180299 | 0.0901495 | − | 0.995928i | \(-0.471266\pi\) | ||||
0.0901495 | + | 0.995928i | \(0.471266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.23607 | 1.01325 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.32624 | 0.718190 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.23607 | −0.958441 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.76393 | −0.620211 | −0.310106 | − | 0.950702i | \(-0.600364\pi\) | ||||
−0.310106 | + | 0.950702i | \(0.600364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6180 | −1.35950 | −0.679750 | − | 0.733444i | \(-0.737912\pi\) | ||||
−0.679750 | + | 0.733444i | \(0.737912\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.0000 | −1.36438 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.09017 | 0.133185 | 0.0665927 | − | 0.997780i | \(-0.478787\pi\) | ||||
0.0665927 | + | 0.997780i | \(0.478787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.61803 | 0.555946 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.94427 | −0.349421 | −0.174710 | − | 0.984620i | \(-0.555899\pi\) | ||||
−0.174710 | + | 0.984620i | \(0.555899\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.09017 | 0.829842 | 0.414921 | − | 0.909858i | \(-0.363809\pi\) | ||||
0.414921 | + | 0.909858i | \(0.363809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −15.9443 | −1.84109 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.47214 | −0.509647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.56231 | 0.963335 | 0.481667 | − | 0.876354i | \(-0.340031\pi\) | ||||
0.481667 | + | 0.876354i | \(0.340031\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.4721 | −1.58852 | −0.794262 | − | 0.607576i | \(-0.792142\pi\) | ||||
−0.794262 | + | 0.607576i | \(0.792142\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.2361 | 1.86951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.0902 | −1.61784 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.52786 | −0.161953 | −0.0809766 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809766 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.23607 | 0.968203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.9443 | 1.23856 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.2361 | −1.76838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.472136 | −0.0479381 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.527864 | 0.0530523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52786 | −0.351036 | −0.175518 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175518 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.2705 | −1.70171 | −0.850857 | − | 0.525397i | \(-0.823917\pi\) | ||||
−0.850857 | + | 0.525397i | \(0.823917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.1803 | 1.96940 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.32624 | −0.708254 | −0.354127 | − | 0.935197i | \(-0.615222\pi\) | ||||
−0.354127 | + | 0.935197i | \(0.615222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94427 | −0.282010 | −0.141005 | − | 0.990009i | \(-0.545033\pi\) | ||||
−0.141005 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.61803 | −0.153577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.94427 | −0.653262 | −0.326631 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326631 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0000 | 1.02576 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.09017 | −0.100786 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.4721 | −1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.5623 | −1.40321 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.7082 | −1.67331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.47214 | 0.751780 | 0.375890 | − | 0.926664i | \(-0.377337\pi\) | ||||
0.375890 | + | 0.926664i | \(0.377337\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.47214 | 0.745930 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.6525 | −1.97916 | −0.989578 | − | 0.143998i | \(-0.954004\pi\) | ||||
−0.989578 | + | 0.143998i | \(0.954004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4721 | 1.25489 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.0902 | −1.81515 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.67376 | 0.313871 | 0.156935 | − | 0.987609i | \(-0.449839\pi\) | ||||
0.156935 | + | 0.987609i | \(0.449839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.85410 | 0.411720 | 0.205860 | − | 0.978581i | \(-0.434001\pi\) | ||||
0.205860 | + | 0.978581i | \(0.434001\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.94427 | −0.329837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.9443 | −2.98501 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.61803 | −0.463368 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.1803 | −1.32555 | −0.662773 | − | 0.748821i | \(-0.730620\pi\) | ||||
−0.662773 | + | 0.748821i | \(0.730620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.29180 | −0.349261 | −0.174631 | − | 0.984634i | \(-0.555873\pi\) | ||||
−0.174631 | + | 0.984634i | \(0.555873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.70820 | 0.138100 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.4508 | 2.28523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4721 | 1.31462 | 0.657310 | − | 0.753620i | \(-0.271694\pi\) | ||||
0.657310 | + | 0.753620i | \(0.271694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.763932 | 0.0605838 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.23607 | −0.727904 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.52786 | −0.276324 | −0.138162 | − | 0.990410i | \(-0.544119\pi\) | ||||
−0.138162 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.61803 | −0.670913 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.8541 | −1.07206 | −0.536031 | − | 0.844198i | \(-0.680077\pi\) | ||||
−0.536031 | + | 0.844198i | \(0.680077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.85410 | −0.373392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.70820 | −0.130630 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.472136 | 0.0358958 | 0.0179479 | − | 0.999839i | \(-0.494287\pi\) | ||||
0.0179479 | + | 0.999839i | \(0.494287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.8885 | 2.41055 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.70820 | 0.579384 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6525 | −0.945690 | −0.472845 | − | 0.881146i | \(-0.656773\pi\) | ||||
−0.472845 | + | 0.881146i | \(0.656773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4721 | −1.07571 | −0.537853 | − | 0.843039i | \(-0.680764\pi\) | ||||
−0.537853 | + | 0.843039i | \(0.680764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.1803 | 1.27001 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.85410 | −0.283359 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.18034 | 0.451951 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.7082 | 1.28808 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.09017 | 0.513027 | 0.256513 | − | 0.966541i | \(-0.417426\pi\) | ||||
0.256513 | + | 0.966541i | \(0.417426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.7984 | 1.27457 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.52786 | 0.536338 | 0.268169 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268169 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.05573 | −0.216615 | −0.108307 | − | 0.994117i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994117i | \(0.534543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.76393 | −0.124418 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.1803 | 2.11824 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.0689 | −2.58900 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.09017 | 0.0757720 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.18034 | −0.427503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2705 | 0.775894 | 0.387947 | − | 0.921682i | \(-0.373184\pi\) | ||||
0.387947 | + | 0.921682i | \(0.373184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.76393 | 0.326419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.1803 | 1.37629 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.8885 | −1.62166 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.4721 | −0.775215 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.7639 | −0.858595 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1803 | −0.949586 | −0.474793 | − | 0.880098i | \(-0.657477\pi\) | ||||
−0.474793 | + | 0.880098i | \(0.657477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.76393 | −0.250929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.29180 | −0.284857 | −0.142428 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142428 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.1246 | 1.52812 | 0.764059 | − | 0.645147i | \(-0.223204\pi\) | ||||
0.764059 | + | 0.645147i | \(0.223204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.23607 | 0.476098 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.56231 | −0.429911 | −0.214955 | − | 0.976624i | \(-0.568961\pi\) | ||||
−0.214955 | + | 0.976624i | \(0.568961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.76393 | −0.310765 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8541 | −0.899921 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.85410 | −0.637409 | −0.318704 | − | 0.947854i | \(-0.603248\pi\) | ||||
−0.318704 | + | 0.947854i | \(0.603248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.52786 | −0.0984184 | −0.0492092 | − | 0.998788i | \(-0.515670\pi\) | ||||
−0.0492092 | + | 0.998788i | \(0.515670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3820 | −0.854942 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.7639 | 0.812150 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.4164 | 1.48395 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.9443 | −1.32199 | −0.660995 | − | 0.750390i | \(-0.729866\pi\) | ||||
−0.660995 | + | 0.750390i | \(0.729866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.94427 | 0.247974 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −27.8885 | −1.74645 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.05573 | −0.0658545 | −0.0329273 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329273 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.23607 | 0.201079 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.56231 | −0.220501 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2361 | 0.816171 | 0.408085 | − | 0.912944i | \(-0.366197\pi\) | ||||
0.408085 | + | 0.912944i | \(0.366197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.81966 | 0.111781 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.47214 | 0.151292 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9443 | −0.786309 | −0.393154 | − | 0.919473i | \(-0.628616\pi\) | ||||
−0.393154 | + | 0.919473i | \(0.628616\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.9443 | −0.904468 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.6180 | −0.821198 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7984 | −1.00932 | −0.504658 | − | 0.863319i | \(-0.668381\pi\) | ||||
−0.504658 | + | 0.863319i | \(0.668381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.81966 | 0.168809 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.8885 | 1.78300 | 0.891501 | − | 0.453020i | \(-0.149653\pi\) | ||||
0.891501 | + | 0.453020i | \(0.149653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.76393 | 0.402074 | 0.201037 | − | 0.979584i | \(-0.435569\pi\) | ||||
0.201037 | + | 0.979584i | \(0.435569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27.8885 | 1.65197 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.1246 | 1.83723 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.763932 | 0.0447825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6525 | 0.739166 | 0.369583 | − | 0.929198i | \(-0.379501\pi\) | ||||
0.369583 | + | 0.929198i | \(0.379501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3607 | 1.06900 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.56231 | −0.438809 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.14590 | −0.471089 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9443 | −0.976652 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.70820 | 0.327928 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 40.9230 | 2.34324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.8541 | −0.733622 | −0.366811 | − | 0.930295i | \(-0.619550\pi\) | ||||
−0.366811 | + | 0.930295i | \(0.619550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.9443 | 1.58969 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.0344 | 1.53298 | 0.766491 | − | 0.642255i | \(-0.222001\pi\) | ||||
0.766491 | + | 0.642255i | \(0.222001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.1803 | 1.59285 | 0.796423 | − | 0.604739i | \(-0.206723\pi\) | ||||
0.796423 | + | 0.604739i | \(0.206723\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.76393 | 0.268417 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.9443 | −1.17635 | −0.588174 | − | 0.808735i | \(-0.700153\pi\) | ||||
−0.588174 | + | 0.808735i | \(0.700153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8885 | −0.721620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8541 | 0.661631 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.1246 | 1.56007 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.76393 | 0.263446 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.381966 | −0.0209316 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.20163 | −0.229559 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0344 | 0.655558 | 0.327779 | − | 0.944754i | \(-0.393700\pi\) | ||||
0.327779 | + | 0.944754i | \(0.393700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2361 | 0.610259 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2016 | 0.552449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.7984 | −0.958232 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2361 | 0.925281 | 0.462640 | − | 0.886546i | \(-0.346902\pi\) | ||||
0.462640 | + | 0.886546i | \(0.346902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1803 | 0.544941 | 0.272471 | − | 0.962164i | \(-0.412159\pi\) | ||||
0.272471 | + | 0.962164i | \(0.412159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.6180 | 0.833629 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.2918 | 0.867125 | 0.433562 | − | 0.901124i | \(-0.357256\pi\) | ||||
0.433562 | + | 0.901124i | \(0.357256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3475 | 0.602264 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.4164 | 1.23933 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.47214 | 0.236030 | 0.118015 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118015 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.7082 | 0.771980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.3262 | −1.43032 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1246 | −0.685099 | −0.342550 | − | 0.939500i | \(-0.611290\pi\) | ||||
−0.342550 | + | 0.939500i | \(0.611290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.67376 | −0.191248 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7082 | −1.43468 | −0.717338 | − | 0.696725i | \(-0.754640\pi\) | ||||
−0.717338 | + | 0.696725i | \(0.754640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.2705 | 1.56316 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.6180 | 1.37090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0902 | 1.44290 | 0.721448 | − | 0.692469i | \(-0.243477\pi\) | ||||
0.721448 | + | 0.692469i | \(0.243477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.7082 | −0.702293 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8885 | −0.914062 | −0.457031 | − | 0.889451i | \(-0.651087\pi\) | ||||
−0.457031 | + | 0.889451i | \(0.651087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.2361 | 0.878431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.85410 | 0.347517 | 0.173758 | − | 0.984788i | \(-0.444409\pi\) | ||||
0.173758 | + | 0.984788i | \(0.444409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7639 | 0.645500 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.6525 | 1.84887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.0000 | −1.66041 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6525 | −1.03652 | −0.518259 | − | 0.855224i | \(-0.673420\pi\) | ||||
−0.518259 | + | 0.855224i | \(0.673420\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.4164 | −1.17229 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.76393 | −0.237899 | −0.118950 | − | 0.992900i | \(-0.537953\pi\) | ||||
−0.118950 | + | 0.992900i | \(0.537953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0689 | −1.04952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.7082 | 1.47621 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.38197 | −0.0685015 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.1803 | −1.29453 | −0.647267 | − | 0.762263i | \(-0.724088\pi\) | ||||
−0.647267 | + | 0.762263i | \(0.724088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.94427 | −0.293209 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.4164 | −0.758592 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55.7771 | 2.73799 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.85410 | −0.384617 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5623 | −0.516002 | −0.258001 | − | 0.966145i | \(-0.583064\pi\) | ||||
−0.258001 | + | 0.966145i | \(0.583064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.0344 | 1.51253 | 0.756263 | − | 0.654268i | \(-0.227023\pi\) | ||||
0.756263 | + | 0.654268i | \(0.227023\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.472136 | −0.0229560 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.0689 | −2.13765 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.3607 | −1.66283 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.38197 | 0.308124 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3607 | −0.595393 | −0.297696 | − | 0.954661i | \(-0.596218\pi\) | ||||
−0.297696 | + | 0.954661i | \(0.596218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6738 | −0.993518 | −0.496759 | − | 0.867889i | \(-0.665477\pi\) | ||||
−0.496759 | + | 0.867889i | \(0.665477\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 58.1591 | 2.78851 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.7639 | −0.610582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.79837 | −0.372196 | −0.186098 | − | 0.982531i | \(-0.559584\pi\) | ||||
−0.186098 | + | 0.982531i | \(0.559584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.32624 | −0.0631542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.2705 | 0.725524 | 0.362762 | − | 0.931882i | \(-0.381834\pi\) | ||||
0.362762 | + | 0.931882i | \(0.381834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.88854 | 0.279144 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.1803 | 1.23829 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.4721 | −1.34368 | −0.671842 | − | 0.740695i | \(-0.734496\pi\) | ||||
−0.671842 | + | 0.740695i | \(0.734496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.2918 | −0.625886 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.94427 | 0.326270 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.5967 | −1.66880 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.7639 | −1.15841 | −0.579204 | − | 0.815183i | \(-0.696637\pi\) | ||||
−0.579204 | + | 0.815183i | \(0.696637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.4721 | −1.14226 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.9443 | 1.81382 | 0.906908 | − | 0.421329i | \(-0.138436\pi\) | ||||
0.906908 | + | 0.421329i | \(0.138436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.56231 | 0.212028 | 0.106014 | − | 0.994365i | \(-0.466191\pi\) | ||||
0.106014 | + | 0.994365i | \(0.466191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −46.0344 | −2.13480 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.3607 | −1.12728 | −0.563639 | − | 0.826021i | \(-0.690599\pi\) | ||||
−0.563639 | + | 0.826021i | \(0.690599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.52786 | 0.162902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.6525 | −1.22808 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.23607 | 0.332715 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 44.0689 | 2.02202 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.180340 | 0.00825720 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.5623 | −1.67057 | −0.835287 | − | 0.549814i | \(-0.814699\pi\) | ||||
−0.835287 | + | 0.549814i | \(0.814699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.85410 | 0.130136 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.9443 | 0.679988 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.81966 | 0.0826265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.3050 | −1.69045 | −0.845224 | − | 0.534412i | \(-0.820533\pi\) | ||||
−0.845224 | + | 0.534412i | \(0.820533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.70820 | 0.258134 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.4508 | −1.28397 | −0.641984 | − | 0.766718i | \(-0.721889\pi\) | ||||
−0.641984 | + | 0.766718i | \(0.721889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.7082 | −1.87844 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.03444 | −0.0914414 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.52786 | −0.427383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2918 | 0.460724 | 0.230362 | − | 0.973105i | \(-0.426009\pi\) | ||||
0.230362 | + | 0.973105i | \(0.426009\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4164 | 1.00149 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.0902 | −0.851189 | −0.425594 | − | 0.904914i | \(-0.639935\pi\) | ||||
−0.425594 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5967 | 0.605047 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.85410 | 0.348813 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7082 | 0.784902 | 0.392451 | − | 0.919773i | \(-0.371627\pi\) | ||||
0.392451 | + | 0.919773i | \(0.371627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.9443 | 1.01499 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.4721 | 1.08047 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 66.5623 | 2.93309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70820 | −0.0751267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.763932 | −0.0335329 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.41641 | −0.0620540 | −0.0310270 | − | 0.999519i | \(-0.509878\pi\) | ||||
−0.0310270 | + | 0.999519i | \(0.509878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8197 | 0.516838 | 0.258419 | − | 0.966033i | \(-0.416799\pi\) | ||||
0.258419 | + | 0.966033i | \(0.416799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −51.5967 | −2.25187 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.0132 | 1.43808 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.81966 | 0.0789665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.4508 | 1.18903 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.2361 | 1.22075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.4721 | 0.883438 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.79837 | −0.206681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.3262 | 0.443960 | 0.221980 | − | 0.975051i | \(-0.428748\pi\) | ||||
0.221980 | + | 0.975051i | \(0.428748\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.4164 | 1.00489 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3475 | 0.486075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.0689 | −0.687056 | −0.343528 | − | 0.939142i | \(-0.611622\pi\) | ||||
−0.343528 | + | 0.939142i | \(0.611622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.05573 | 0.173094 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.7082 | 1.77683 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.7082 | 1.17827 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.23607 | 0.264706 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.5623 | −0.828882 | −0.414441 | − | 0.910076i | \(-0.636023\pi\) | ||||
−0.414441 | + | 0.910076i | \(0.636023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.9443 | −0.632075 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.0000 | −0.422200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.88854 | 0.332462 | 0.166231 | − | 0.986087i | \(-0.446840\pi\) | ||||
0.166231 | + | 0.986087i | \(0.446840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.7639 | 1.12597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.9443 | −1.04756 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.8885 | 0.582238 | 0.291119 | − | 0.956687i | \(-0.405972\pi\) | ||||
0.291119 | + | 0.956687i | \(0.405972\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5623 | −0.442019 | −0.221009 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221009 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.4721 | −0.479255 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.1246 | −1.17288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.6525 | 0.443468 | 0.221734 | − | 0.975107i | \(-0.428828\pi\) | ||||
0.221734 | + | 0.975107i | \(0.428828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.47214 | −0.268973 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.8328 | −1.94295 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.652476 | 0.0270228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.20163 | 0.173716 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.0557 | −0.538868 | −0.269434 | − | 0.963019i | \(-0.586837\pi\) | ||||
−0.269434 | + | 0.963019i | \(0.586837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.0132 | −1.36028 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1803 | −0.501032 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5623 | 0.721197 | 0.360599 | − | 0.932721i | \(-0.382572\pi\) | ||||
0.360599 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 55.7771 | 2.28664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.94427 | 0.202356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.36068 | 0.259890 | 0.129945 | − | 0.991521i | \(-0.458520\pi\) | ||||
0.129945 | + | 0.991521i | \(0.458520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6869 | −1.00700 | −0.503500 | − | 0.863995i | \(-0.667955\pi\) | ||||
−0.503500 | + | 0.863995i | \(0.667955\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.416408 | −0.0169574 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.0344 | 1.42435 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.0344 | −1.42200 | −0.711002 | − | 0.703190i | \(-0.751758\pi\) | ||||
−0.711002 | + | 0.703190i | \(0.751758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.8328 | −1.97881 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.52786 | 0.142722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8197 | 0.558171 | 0.279085 | − | 0.960266i | \(-0.409969\pi\) | ||||
0.279085 | + | 0.960266i | \(0.409969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 59.9787 | 2.41858 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0901699 | 0.00363011 | 0.00181505 | − | 0.999998i | \(-0.499422\pi\) | ||||
0.00181505 | + | 0.999998i | \(0.499422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2705 | −0.613774 | −0.306887 | − | 0.951746i | \(-0.599287\pi\) | ||||
−0.306887 | + | 0.951746i | \(0.599287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.6180 | −0.626730 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.94427 | −0.198088 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0000 | 0.399362 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.47214 | −0.178316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.3951 | 1.88677 | 0.943385 | − | 0.331700i | \(-0.107622\pi\) | ||||
0.943385 | + | 0.331700i | \(0.107622\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.2361 | −0.724819 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.6525 | −1.29577 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.90983 | 0.392642 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.12461 | 0.0444890 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5066 | 0.612473 | 0.306236 | − | 0.951955i | \(-0.400930\pi\) | ||||
0.306236 | + | 0.951955i | \(0.400930\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.7639 | −1.13434 | −0.567169 | − | 0.823601i | \(-0.691962\pi\) | ||||
−0.567169 | + | 0.823601i | \(0.691962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.6525 | −1.28569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0902 | −1.18297 | −0.591483 | − | 0.806317i | \(-0.701457\pi\) | ||||
−0.591483 | + | 0.806317i | \(0.701457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.58359 | 0.258429 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.6525 | 1.51491 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.2705 | 1.49764 | 0.748820 | − | 0.662773i | \(-0.230621\pi\) | ||||
0.748820 | + | 0.662773i | \(0.230621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 87.3050 | 3.41129 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.70820 | −0.105657 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4508 | 1.57574 | 0.787871 | − | 0.615841i | \(-0.211184\pi\) | ||||
0.787871 | + | 0.615841i | \(0.211184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3262 | −0.673913 | −0.336956 | − | 0.941520i | \(-0.609397\pi\) | ||||
−0.336956 | + | 0.941520i | \(0.609397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.6525 | 0.802076 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −55.7771 | −2.16294 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.6180 | −1.03065 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.9443 | 0.887077 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6738 | 0.566474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1459 | 0.429643 | 0.214821 | − | 0.976653i | \(-0.431083\pi\) | ||||
0.214821 | + | 0.976653i | \(0.431083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 53.9230 | 2.07550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.6525 | −1.33180 | −0.665901 | − | 0.746040i | \(-0.731953\pi\) | ||||
−0.665901 | + | 0.746040i | \(0.731953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.52786 | −0.0586340 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.94427 | 0.266105 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.58359 | −0.328442 | −0.164221 | − | 0.986424i | \(-0.552511\pi\) | ||||
−0.164221 | + | 0.986424i | \(0.552511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.1591 | −0.540990 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.4164 | −1.42752 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.34752 | −0.0513366 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7771 | 1.36102 | 0.680512 | − | 0.732737i | \(-0.261757\pi\) | ||||
0.680512 | + | 0.732737i | \(0.261757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.70820 | 0.0648893 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7082 | −0.709643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −43.0132 | −1.62924 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.6180 | 0.401611 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9787 | 1.62328 | 0.811642 | − | 0.584155i | \(-0.198574\pi\) | ||||
0.811642 | + | 0.584155i | \(0.198574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.47214 | 0.168670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.70820 | 0.290308 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4164 | −0.429358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.21478 | 0.308513 | 0.154256 | − | 0.988031i | \(-0.450702\pi\) | ||||
0.154256 | + | 0.988031i | \(0.450702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.27051 | −0.122654 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0689 | 0.789036 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.2016 | 0.568509 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.9443 | 0.595450 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.4164 | −1.02246 | −0.511230 | − | 0.859444i | \(-0.670810\pi\) | ||||
−0.511230 | + | 0.859444i | \(0.670810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.8885 | −2.08140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.47214 | 0.0919397 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 91.9017 | 3.41314 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.8541 | 1.10723 | 0.553614 | − | 0.832774i | \(-0.313248\pi\) | ||||
0.553614 | + | 0.832774i | \(0.313248\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.4164 | 0.866087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.5279 | −1.01676 | −0.508382 | − | 0.861131i | \(-0.669756\pi\) | ||||
−0.508382 | + | 0.861131i | \(0.669756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.6525 | 0.798664 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.50658 | −0.0554955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9098 | −0.401325 | −0.200662 | − | 0.979660i | \(-0.564309\pi\) | ||||
−0.200662 | + | 0.979660i | \(0.564309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.6525 | −0.758688 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0689 | 1.76348 | 0.881738 | − | 0.471739i | \(-0.156374\pi\) | ||||
0.881738 | + | 0.471739i | \(0.156374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.3607 | 2.28472 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.52786 | 0.202254 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.7082 | −0.866279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.05573 | 0.0385241 | 0.0192620 | − | 0.999814i | \(-0.493868\pi\) | ||||
0.0192620 | + | 0.999814i | \(0.493868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.8885 | 1.23497 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.5410 | 0.601989 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.14590 | 0.150685 | 0.0753426 | − | 0.997158i | \(-0.475995\pi\) | ||||
0.0753426 | + | 0.997158i | \(0.475995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.38197 | −0.231651 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1459 | −0.694038 | −0.347019 | − | 0.937858i | \(-0.612806\pi\) | ||||
−0.347019 | + | 0.937858i | \(0.612806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.52786 | −0.344932 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.58359 | −0.238030 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.5967 | −0.490950 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8885 | 0.861443 | 0.430721 | − | 0.902485i | \(-0.358259\pi\) | ||||
0.430721 | + | 0.902485i | \(0.358259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.70820 | 0.0615195 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0000 | 0.863220 | 0.431610 | − | 0.902060i | \(-0.357946\pi\) | ||||
0.431610 | + | 0.902060i | \(0.357946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.7426 | −2.61299 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.23607 | −0.187843 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.0132 | 1.54111 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.06888 | 0.145596 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 51.0344 | 1.82382 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.4853 | −2.26589 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5279 | −0.909970 | −0.454985 | − | 0.890499i | \(-0.650355\pi\) | ||||
−0.454985 | + | 0.890499i | \(0.650355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.4164 | −0.762444 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.4721 | −0.799017 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.3050 | −1.07616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.94427 | −0.104423 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.2705 | −1.63899 | −0.819493 | − | 0.573090i | \(-0.805745\pi\) | ||||
−0.819493 | + | 0.573090i | \(0.805745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.52786 | −0.195562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.583592 | 0.0206202 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.79837 | −0.345777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.5967 | 1.25462 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.47214 | 0.227830 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.1246 | −0.461437 | −0.230718 | − | 0.973021i | \(-0.574108\pi\) | ||||
−0.230718 | + | 0.973021i | \(0.574108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.1033 | −1.19753 | −0.598765 | − | 0.800925i | \(-0.704342\pi\) | ||||
−0.598765 | + | 0.800925i | \(0.704342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.9443 | 0.734548 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5967 | 0.476273 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.4164 | −0.819236 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.52786 | −0.123274 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41641 | 0.189034 | 0.0945170 | − | 0.995523i | \(-0.469869\pi\) | ||||
0.0945170 | + | 0.995523i | \(0.469869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.88854 | −0.0658305 | −0.0329152 | − | 0.999458i | \(-0.510479\pi\) | ||||
−0.0329152 | + | 0.999458i | \(0.510479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.0344 | 0.767141 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.06888 | −0.0719421 | −0.0359711 | − | 0.999353i | \(-0.511452\pi\) | ||||
−0.0359711 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.7984 | −1.93796 | −0.968979 | − | 0.247144i | \(-0.920508\pi\) | ||||
−0.968979 | + | 0.247144i | \(0.920508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.1803 | 0.942876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5279 | −0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53.3951 | 1.84781 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.3951 | −1.39626 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.6525 | 1.26538 | 0.632692 | − | 0.774404i | \(-0.281950\pi\) | ||||
0.632692 | + | 0.774404i | \(0.281950\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.9787 | 1.99927 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −48.3607 | −1.66563 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.7082 | 0.643582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4164 | −1.01076 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.9443 | −0.375606 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.85410 | −0.0978374 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7426 | −1.01837 | −0.509184 | − | 0.860657i | \(-0.670053\pi\) | ||||
−0.509184 | + | 0.860657i | \(0.670053\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.58359 | 0.225154 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.05573 | −0.309338 | −0.154669 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154669 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.4164 | 1.82254 | 0.911272 | − | 0.411805i | \(-0.135101\pi\) | ||||
0.911272 | + | 0.411805i | \(0.135101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −50.3607 | −1.71629 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.4164 | −0.660942 | −0.330471 | − | 0.943816i | \(-0.607208\pi\) | ||||
−0.330471 | + | 0.943816i | \(0.607208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.81966 | −0.0618703 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.85410 | −0.164854 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.8328 | −0.401401 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.11146 | 0.105428 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.180340 | 0.00610358 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −60.5410 | −2.04666 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8328 | 0.568404 | 0.284202 | − | 0.958764i | \(-0.408271\pi\) | ||||
0.284202 | + | 0.958764i | \(0.408271\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.4721 | −0.690508 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7426 | 0.665147 | 0.332573 | − | 0.943077i | \(-0.392083\pi\) | ||||
0.332573 | + | 0.943077i | \(0.392083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3050 | −1.12080 | −0.560400 | − | 0.828222i | \(-0.689353\pi\) | ||||
−0.560400 | + | 0.828222i | \(0.689353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.7082 | −0.998630 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.8885 | −0.936406 | −0.468203 | − | 0.883621i | \(-0.655098\pi\) | ||||
−0.468203 | + | 0.883621i | \(0.655098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.4164 | 0.919517 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6525 | 0.356871 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.52786 | 0.184983 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.7639 | 1.63000 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.1803 | 0.440079 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −68.8460 | −2.29614 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11146 | 0.0703428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.4164 | 0.912361 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.7771 | 1.85409 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.8885 | −1.85575 | −0.927874 | − | 0.372893i | \(-0.878366\pi\) | ||||
−0.927874 | + | 0.372893i | \(0.878366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.34752 | 0.0446946 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.8885 | −0.460148 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.0000 | 0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −66.2148 | −2.18899 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −73.3050 | −2.42074 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.88854 | 0.194245 | 0.0971226 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971226 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7984 | 0.685330 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.40325 | −0.276596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.85410 | 0.324001 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.59675 | 0.216666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.4508 | −0.900633 | −0.450317 | − | 0.892869i | \(-0.648689\pi\) | ||||
−0.450317 | + | 0.892869i | \(0.648689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5279 | 0.508905 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −43.7426 | −1.43207 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.8197 | −0.778986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.0476 | −1.56965 | −0.784823 | − | 0.619720i | \(-0.787246\pi\) | ||||
−0.784823 | + | 0.619720i | \(0.787246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −45.5967 | −1.48799 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1803 | 0.853455 | 0.426727 | − | 0.904380i | \(-0.359666\pi\) | ||||
0.426727 | + | 0.904380i | \(0.359666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.4508 | −0.893923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −68.2492 | −2.22015 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.8328 | 0.611984 | 0.305992 | − | 0.952034i | \(-0.401012\pi\) | ||||
0.305992 | + | 0.952034i | \(0.401012\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.2361 | 0.656891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.8885 | 1.09891 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4508 | 0.370929 | 0.185465 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185465 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.3262 | −0.884256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.8541 | 0.674117 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.8885 | 0.383901 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4934 | 0.757852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.79837 | 0.0901763 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4164 | −0.496272 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.2705 | −1.45580 | −0.727901 | − | 0.685683i | \(-0.759504\pi\) | ||||
−0.727901 | + | 0.685683i | \(0.759504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.3607 | 1.03957 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.3262 | 1.35831 | 0.679157 | − | 0.733993i | \(-0.262346\pi\) | ||||
0.679157 | + | 0.733993i | \(0.262346\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.7082 | 0.503582 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45.5066 | −1.45738 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.5279 | 1.39258 | 0.696290 | − | 0.717761i | \(-0.254833\pi\) | ||||
0.696290 | + | 0.717761i | \(0.254833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.11146 | 0.0674824 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12461 | 0.0359061 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.7771 | 1.01353 | 0.506766 | − | 0.862084i | \(-0.330841\pi\) | ||||
0.506766 | + | 0.862084i | \(0.330841\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.0132 | −0.924436 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.47214 | −0.206010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9443 | 0.475200 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.1033 | −1.05156 | −0.525781 | − | 0.850620i | \(-0.676227\pi\) | ||||
−0.525781 | + | 0.850620i | \(0.676227\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −45.3050 | −1.43771 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7771 | 0.373359 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7771 | 0.563006 | 0.281503 | − | 0.959560i | \(-0.409167\pi\) | ||||
0.281503 | + | 0.959560i | \(0.409167\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.47214 | 0.173131 |
(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 | 2368.2.a.u.1.1 | 2 | ||
4.3 | odd | 2 | 2368.2.a.y.1.2 | 2 | |||
8.3 | odd | 2 | 74.2.a.b.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 592.2.a.g.1.2 | 2 | |||
24.5 | odd | 2 | 5328.2.a.bc.1.1 | 2 | |||
24.11 | even | 2 | 666.2.a.i.1.1 | 2 | |||
40.3 | even | 4 | 1850.2.b.j.149.1 | 4 | |||
40.19 | odd | 2 | 1850.2.a.t.1.2 | 2 | |||
40.27 | even | 4 | 1850.2.b.j.149.4 | 4 | |||
56.27 | even | 2 | 3626.2.a.s.1.2 | 2 | |||
88.43 | even | 2 | 8954.2.a.j.1.1 | 2 | |||
296.147 | odd | 2 | 2738.2.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.b.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
592.2.a.g.1.2 | 2 | 8.5 | even | 2 | |||
666.2.a.i.1.1 | 2 | 24.11 | even | 2 | |||
1850.2.a.t.1.2 | 2 | 40.19 | odd | 2 | |||
1850.2.b.j.149.1 | 4 | 40.3 | even | 4 | |||
1850.2.b.j.149.4 | 4 | 40.27 | even | 4 | |||
2368.2.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2368.2.a.y.1.2 | 2 | 4.3 | odd | 2 | |||
2738.2.a.g.1.1 | 2 | 296.147 | odd | 2 | |||
3626.2.a.s.1.2 | 2 | 56.27 | even | 2 | |||
5328.2.a.bc.1.1 | 2 | 24.5 | odd | 2 | |||
8954.2.a.j.1.1 | 2 | 88.43 | even | 2 |