Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, 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("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.144344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 5x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.51533\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.51533 | −1.07150 | −0.535749 | − | 0.844377i | \(-0.679971\pi\) | ||||
−0.535749 | + | 0.844377i | \(0.679971\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.296215 | 0.148108 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.58179 | 0.912801 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.51533 | 0.479188 | ||||||||
\(11\) | −2.21911 | −0.669087 | −0.334544 | − | 0.942380i | \(-0.608582\pi\) | ||||
−0.334544 | + | 0.942380i | \(0.608582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.18846 | 0.329619 | 0.164809 | − | 0.986325i | \(-0.447299\pi\) | ||||
0.164809 | + | 0.986325i | \(0.447299\pi\) | |||||||
\(14\) | −1.51533 | −0.404988 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.50469 | −1.12617 | ||||||||
\(17\) | −3.39333 | −0.823004 | −0.411502 | − | 0.911409i | \(-0.634996\pi\) | ||||
−0.411502 | + | 0.911409i | \(0.634996\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.61244 | 1.74641 | 0.873207 | − | 0.487349i | \(-0.162036\pi\) | ||||
0.873207 | + | 0.487349i | \(0.162036\pi\) | |||||||
\(20\) | −0.296215 | −0.0662357 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.36268 | 0.716926 | ||||||||
\(23\) | −3.39333 | −0.707559 | −0.353779 | − | 0.935329i | \(-0.615104\pi\) | ||||
−0.353779 | + | 0.935329i | \(0.615104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.80090 | −0.353186 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.296215 | 0.0559794 | ||||||||
\(29\) | −1.40757 | −0.261379 | −0.130690 | − | 0.991423i | \(-0.541719\pi\) | ||||
−0.130690 | + | 0.991423i | \(0.541719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.42399 | −0.794571 | −0.397286 | − | 0.917695i | \(-0.630048\pi\) | ||||
−0.397286 | + | 0.917695i | \(0.630048\pi\) | |||||||
\(32\) | 1.66249 | 0.293890 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.14201 | 0.881847 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.03065 | 0.827034 | 0.413517 | − | 0.910496i | \(-0.364300\pi\) | ||||
0.413517 | + | 0.910496i | \(0.364300\pi\) | |||||||
\(38\) | −11.5353 | −1.87128 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.58179 | −0.408217 | ||||||||
\(41\) | 7.80090 | 1.21830 | 0.609148 | − | 0.793056i | \(-0.291511\pi\) | ||||
0.609148 | + | 0.793056i | \(0.291511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.42399 | −0.217156 | −0.108578 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108578 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(44\) | −0.657335 | −0.0990969 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.14201 | 0.758148 | ||||||||
\(47\) | 7.86221 | 1.14682 | 0.573411 | − | 0.819268i | \(-0.305620\pi\) | ||||
0.573411 | + | 0.819268i | \(0.305620\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.51533 | −0.214300 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.352039 | 0.0488191 | ||||||||
\(53\) | 1.17422 | 0.161292 | 0.0806458 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806458 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.21911 | 0.299225 | ||||||||
\(56\) | 2.58179 | 0.345006 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.13293 | 0.280067 | ||||||||
\(59\) | 3.03065 | 0.394557 | 0.197279 | − | 0.980347i | \(-0.436790\pi\) | ||||
0.197279 | + | 0.980347i | \(0.436790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.39333 | 0.690545 | 0.345273 | − | 0.938502i | \(-0.387786\pi\) | ||||
0.345273 | + | 0.938502i | \(0.387786\pi\) | |||||||
\(62\) | 6.70378 | 0.851382 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.49016 | 0.811270 | ||||||||
\(65\) | −1.18846 | −0.147410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.01424 | 0.368248 | 0.184124 | − | 0.982903i | \(-0.441055\pi\) | ||||
0.184124 | + | 0.982903i | \(0.441055\pi\) | |||||||
\(68\) | −1.00516 | −0.121893 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.51533 | 0.181116 | ||||||||
\(71\) | 14.8764 | 1.76551 | 0.882755 | − | 0.469834i | \(-0.155686\pi\) | ||||
0.882755 | + | 0.469834i | \(0.155686\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.18846 | −0.373181 | −0.186590 | − | 0.982438i | \(-0.559744\pi\) | ||||
−0.186590 | + | 0.982438i | \(0.559744\pi\) | |||||||
\(74\) | −7.62308 | −0.886166 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.25492 | 0.258657 | ||||||||
\(77\) | −2.21911 | −0.252891 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4546 | 1.28875 | 0.644374 | − | 0.764711i | \(-0.277118\pi\) | ||||
0.644374 | + | 0.764711i | \(0.277118\pi\) | |||||||
\(80\) | 4.50469 | 0.503639 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.8209 | −1.30540 | ||||||||
\(83\) | −7.37692 | −0.809722 | −0.404861 | − | 0.914378i | \(-0.632680\pi\) | ||||
−0.404861 | + | 0.914378i | \(0.632680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.39333 | 0.368059 | ||||||||
\(86\) | 2.15780 | 0.232682 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.72928 | −0.610743 | ||||||||
\(89\) | 16.8929 | 1.79064 | 0.895320 | − | 0.445424i | \(-0.146947\pi\) | ||||
0.895320 | + | 0.445424i | \(0.146947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.18846 | 0.124584 | ||||||||
\(92\) | −1.00516 | −0.104795 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.9138 | −1.22882 | ||||||||
\(95\) | −7.61244 | −0.781020 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.75601 | −0.178296 | −0.0891480 | − | 0.996018i | \(-0.528414\pi\) | ||||
−0.0891480 | + | 0.996018i | \(0.528414\pi\) | |||||||
\(98\) | −1.51533 | −0.153071 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.296215 | 0.0296215 | ||||||||
\(101\) | −0.393333 | −0.0391381 | −0.0195690 | − | 0.999809i | \(-0.506229\pi\) | ||||
−0.0195690 | + | 0.999809i | \(0.506229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6938 | −1.64489 | −0.822443 | − | 0.568848i | \(-0.807389\pi\) | ||||
−0.822443 | + | 0.568848i | \(0.807389\pi\) | |||||||
\(104\) | 3.06835 | 0.300876 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.77933 | −0.172824 | ||||||||
\(107\) | 4.43822 | 0.429059 | 0.214530 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214530 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4995 | 1.48459 | 0.742293 | − | 0.670076i | \(-0.233738\pi\) | ||||
0.742293 | + | 0.670076i | \(0.233738\pi\) | |||||||
\(110\) | −3.36268 | −0.320619 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.50469 | −0.425653 | ||||||||
\(113\) | 6.87285 | 0.646543 | 0.323272 | − | 0.946306i | \(-0.395217\pi\) | ||||
0.323272 | + | 0.946306i | \(0.395217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.39333 | 0.316430 | ||||||||
\(116\) | −0.416944 | −0.0387122 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.59243 | −0.422767 | ||||||||
\(119\) | −3.39333 | −0.311066 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.07554 | −0.552322 | ||||||||
\(122\) | −8.17266 | −0.739918 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.31045 | −0.117682 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.6182 | 1.74084 | 0.870418 | − | 0.492314i | \(-0.163849\pi\) | ||||
0.870418 | + | 0.492314i | \(0.163849\pi\) | |||||||
\(128\) | −13.1597 | −1.16316 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.80090 | 0.157950 | ||||||||
\(131\) | 15.8786 | 1.38732 | 0.693661 | − | 0.720302i | \(-0.255997\pi\) | ||||
0.693661 | + | 0.720302i | \(0.255997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.61244 | 0.660083 | ||||||||
\(134\) | −4.56755 | −0.394577 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.76087 | −0.751239 | ||||||||
\(137\) | −1.17422 | −0.100320 | −0.0501602 | − | 0.998741i | \(-0.515973\pi\) | ||||
−0.0501602 | + | 0.998741i | \(0.515973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.78667 | 0.745275 | 0.372638 | − | 0.927977i | \(-0.378453\pi\) | ||||
0.372638 | + | 0.927977i | \(0.378453\pi\) | |||||||
\(140\) | −0.296215 | −0.0250348 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.5427 | −1.89174 | ||||||||
\(143\) | −2.63732 | −0.220544 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.40757 | 0.116892 | ||||||||
\(146\) | 4.83156 | 0.399862 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.49016 | 0.122490 | ||||||||
\(149\) | 23.2249 | 1.90266 | 0.951328 | − | 0.308179i | \(-0.0997195\pi\) | ||||
0.951328 | + | 0.308179i | \(0.0997195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 19.6537 | 1.59413 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.36268 | 0.270972 | ||||||||
\(155\) | 4.42399 | 0.355343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8458 | −1.26463 | −0.632316 | − | 0.774711i | \(-0.717896\pi\) | ||||
−0.632316 | + | 0.774711i | \(0.717896\pi\) | |||||||
\(158\) | −17.3575 | −1.38089 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.66249 | −0.131431 | ||||||||
\(161\) | −3.39333 | −0.267432 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.0707 | −1.65038 | −0.825192 | − | 0.564853i | \(-0.808933\pi\) | ||||
−0.825192 | + | 0.564853i | \(0.808933\pi\) | |||||||
\(164\) | 2.31075 | 0.180439 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1784 | 0.867615 | ||||||||
\(167\) | −0.485293 | −0.0375531 | −0.0187766 | − | 0.999824i | \(-0.505977\pi\) | ||||
−0.0187766 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5876 | −0.891351 | ||||||||
\(170\) | −5.14201 | −0.394374 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.421806 | −0.0321624 | ||||||||
\(173\) | 5.01642 | 0.381391 | 0.190696 | − | 0.981649i | \(-0.438926\pi\) | ||||
0.190696 | + | 0.981649i | \(0.438926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 9.99640 | 0.753507 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.5982 | −1.91867 | ||||||||
\(179\) | −5.31107 | −0.396968 | −0.198484 | − | 0.980104i | \(-0.563602\pi\) | ||||
−0.198484 | + | 0.980104i | \(0.563602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9542 | −1.78050 | −0.890250 | − | 0.455473i | \(-0.849470\pi\) | ||||
−0.890250 | + | 0.455473i | \(0.849470\pi\) | |||||||
\(182\) | −1.80090 | −0.133492 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.76087 | −0.645860 | ||||||||
\(185\) | −5.03065 | −0.369861 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.53018 | 0.550662 | ||||||||
\(188\) | 2.32891 | 0.169853 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.5353 | 0.836862 | ||||||||
\(191\) | −19.4440 | −1.40692 | −0.703459 | − | 0.710736i | \(-0.748362\pi\) | ||||
−0.703459 | + | 0.710736i | \(0.748362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.315609 | 0.0227180 | 0.0113590 | − | 0.999935i | \(-0.496384\pi\) | ||||
0.0113590 | + | 0.999935i | \(0.496384\pi\) | |||||||
\(194\) | 2.66093 | 0.191044 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.296215 | 0.0211582 | ||||||||
\(197\) | −3.20269 | −0.228183 | −0.114091 | − | 0.993470i | \(-0.536396\pi\) | ||||
−0.114091 | + | 0.993470i | \(0.536396\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.43463 | 0.314362 | 0.157181 | − | 0.987570i | \(-0.449759\pi\) | ||||
0.157181 | + | 0.987570i | \(0.449759\pi\) | |||||||
\(200\) | 2.58179 | 0.182560 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.596028 | 0.0419364 | ||||||||
\(203\) | −1.40757 | −0.0987920 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.80090 | −0.544839 | ||||||||
\(206\) | 25.2965 | 1.76249 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.35363 | −0.371208 | ||||||||
\(209\) | −16.8929 | −1.16850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.36050 | 0.0936606 | 0.0468303 | − | 0.998903i | \(-0.485088\pi\) | ||||
0.0468303 | + | 0.998903i | \(0.485088\pi\) | |||||||
\(212\) | 0.347822 | 0.0238885 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.72536 | −0.459736 | ||||||||
\(215\) | 1.42399 | 0.0971151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.42399 | −0.300320 | ||||||||
\(218\) | −23.4869 | −1.59073 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.657335 | 0.0443175 | ||||||||
\(221\) | −4.03283 | −0.271278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.3168 | 1.89624 | 0.948118 | − | 0.317918i | \(-0.102984\pi\) | ||||
0.948118 | + | 0.317918i | \(0.102984\pi\) | |||||||
\(224\) | 1.66249 | 0.111080 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4146 | −0.692770 | ||||||||
\(227\) | 14.9502 | 0.992283 | 0.496141 | − | 0.868242i | \(-0.334750\pi\) | ||||
0.496141 | + | 0.868242i | \(0.334750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.16844 | −0.539786 | −0.269893 | − | 0.962890i | \(-0.586988\pi\) | ||||
−0.269893 | + | 0.962890i | \(0.586988\pi\) | |||||||
\(230\) | −5.14201 | −0.339054 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.63405 | −0.238587 | ||||||||
\(233\) | −18.0364 | −1.18161 | −0.590803 | − | 0.806816i | \(-0.701189\pi\) | ||||
−0.590803 | + | 0.806816i | \(0.701189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.86221 | −0.512874 | ||||||||
\(236\) | 0.897726 | 0.0584370 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.14201 | 0.333307 | ||||||||
\(239\) | 12.0613 | 0.780181 | 0.390091 | − | 0.920777i | \(-0.372444\pi\) | ||||
0.390091 | + | 0.920777i | \(0.372444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.2698 | −1.43452 | −0.717261 | − | 0.696804i | \(-0.754605\pi\) | ||||
−0.717261 | + | 0.696804i | \(0.754605\pi\) | |||||||
\(242\) | 9.20643 | 0.591812 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.59759 | 0.102275 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.04707 | 0.575651 | ||||||||
\(248\) | −11.4218 | −0.725285 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.51533 | 0.0958377 | ||||||||
\(251\) | −15.8173 | −0.998380 | −0.499190 | − | 0.866492i | \(-0.666369\pi\) | ||||
−0.499190 | + | 0.866492i | \(0.666369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.53018 | 0.473419 | ||||||||
\(254\) | −29.7280 | −1.86530 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.96092 | 0.435057 | ||||||||
\(257\) | −14.6182 | −0.911860 | −0.455930 | − | 0.890016i | \(-0.650693\pi\) | ||||
−0.455930 | + | 0.890016i | \(0.650693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.03065 | 0.312590 | ||||||||
\(260\) | −0.352039 | −0.0218326 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.0613 | −1.48651 | ||||||||
\(263\) | −21.6631 | −1.33580 | −0.667902 | − | 0.744249i | \(-0.732808\pi\) | ||||
−0.667902 | + | 0.744249i | \(0.732808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17422 | −0.0721318 | ||||||||
\(266\) | −11.5353 | −0.707277 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.892863 | 0.0545403 | ||||||||
\(269\) | −24.2271 | −1.47715 | −0.738575 | − | 0.674171i | \(-0.764501\pi\) | ||||
−0.738575 | + | 0.674171i | \(0.764501\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.2142 | −1.53166 | −0.765828 | − | 0.643045i | \(-0.777671\pi\) | ||||
−0.765828 | + | 0.643045i | \(0.777671\pi\) | |||||||
\(272\) | 15.2859 | 0.926844 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.77933 | 0.107493 | ||||||||
\(275\) | −2.21911 | −0.133817 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6346 | 1.29990 | 0.649950 | − | 0.759977i | \(-0.274790\pi\) | ||||
0.649950 | + | 0.759977i | \(0.274790\pi\) | |||||||
\(278\) | −13.3147 | −0.798561 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.58179 | −0.154292 | ||||||||
\(281\) | 22.9481 | 1.36897 | 0.684483 | − | 0.729028i | \(-0.260028\pi\) | ||||
0.684483 | + | 0.729028i | \(0.260028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.0729 | 1.54987 | 0.774935 | − | 0.632041i | \(-0.217782\pi\) | ||||
0.774935 | + | 0.632041i | \(0.217782\pi\) | |||||||
\(284\) | 4.40663 | 0.261485 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.99640 | 0.236312 | ||||||||
\(287\) | 7.80090 | 0.460473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.48529 | −0.322664 | ||||||||
\(290\) | −2.13293 | −0.125250 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.944470 | −0.0552709 | ||||||||
\(293\) | −2.66797 | −0.155865 | −0.0779324 | − | 0.996959i | \(-0.524832\pi\) | ||||
−0.0779324 | + | 0.996959i | \(0.524832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.03065 | −0.176451 | ||||||||
\(296\) | 12.9881 | 0.754918 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −35.1933 | −2.03869 | ||||||||
\(299\) | −4.03283 | −0.233225 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.42399 | −0.0820772 | ||||||||
\(302\) | −12.1226 | −0.697578 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −34.2917 | −1.96676 | ||||||||
\(305\) | −5.39333 | −0.308821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.63246 | −0.264388 | −0.132194 | − | 0.991224i | \(-0.542202\pi\) | ||||
−0.132194 | + | 0.991224i | \(0.542202\pi\) | |||||||
\(308\) | −0.657335 | −0.0374551 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.70378 | −0.380749 | ||||||||
\(311\) | 3.12355 | 0.177120 | 0.0885602 | − | 0.996071i | \(-0.471773\pi\) | ||||
0.0885602 | + | 0.996071i | \(0.471773\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.56537 | −0.427620 | −0.213810 | − | 0.976875i | \(-0.568587\pi\) | ||||
−0.213810 | + | 0.976875i | \(0.568587\pi\) | |||||||
\(314\) | 24.0116 | 1.35505 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.39304 | 0.190873 | ||||||||
\(317\) | 1.29684 | 0.0728375 | 0.0364188 | − | 0.999337i | \(-0.488405\pi\) | ||||
0.0364188 | + | 0.999337i | \(0.488405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.12355 | 0.174885 | ||||||||
\(320\) | −6.49016 | −0.362811 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.14201 | 0.286553 | ||||||||
\(323\) | −25.8316 | −1.43731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.18846 | 0.0659238 | ||||||||
\(326\) | 31.9290 | 1.76838 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.1403 | 1.11206 | ||||||||
\(329\) | 7.86221 | 0.433458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6631 | 0.970852 | 0.485426 | − | 0.874278i | \(-0.338664\pi\) | ||||
0.485426 | + | 0.874278i | \(0.338664\pi\) | |||||||
\(332\) | −2.18515 | −0.119926 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.735378 | 0.0402381 | ||||||||
\(335\) | −3.01424 | −0.164685 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8480 | 0.808821 | 0.404410 | − | 0.914578i | \(-0.367477\pi\) | ||||
0.404410 | + | 0.914578i | \(0.367477\pi\) | |||||||
\(338\) | 17.5590 | 0.955081 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00516 | 0.0545123 | ||||||||
\(341\) | 9.81732 | 0.531638 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.67643 | −0.198220 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.60151 | −0.408660 | ||||||||
\(347\) | −22.4995 | −1.20784 | −0.603919 | − | 0.797046i | \(-0.706395\pi\) | ||||
−0.603919 | + | 0.797046i | \(0.706395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0564 | 0.805953 | 0.402976 | − | 0.915210i | \(-0.367976\pi\) | ||||
0.402976 | + | 0.915210i | \(0.367976\pi\) | |||||||
\(350\) | −1.51533 | −0.0809976 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.68925 | −0.196638 | ||||||||
\(353\) | 22.4382 | 1.19427 | 0.597133 | − | 0.802142i | \(-0.296306\pi\) | ||||
0.597133 | + | 0.802142i | \(0.296306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8764 | −0.789560 | ||||||||
\(356\) | 5.00392 | 0.265207 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.04801 | 0.425351 | ||||||||
\(359\) | −6.44182 | −0.339986 | −0.169993 | − | 0.985445i | \(-0.554375\pi\) | ||||
−0.169993 | + | 0.985445i | \(0.554375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.9493 | 2.04996 | ||||||||
\(362\) | 36.2984 | 1.90780 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.352039 | 0.0184519 | ||||||||
\(365\) | 3.18846 | 0.166892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.66311 | −0.0868137 | −0.0434069 | − | 0.999057i | \(-0.513821\pi\) | ||||
−0.0434069 | + | 0.999057i | \(0.513821\pi\) | |||||||
\(368\) | 15.2859 | 0.796833 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.62308 | 0.396305 | ||||||||
\(371\) | 1.17422 | 0.0609625 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.843613 | 0.0436806 | 0.0218403 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218403 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(374\) | −11.4107 | −0.590033 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.2986 | 1.04682 | ||||||||
\(377\) | −1.67284 | −0.0861555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5854 | 0.954667 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(380\) | −2.25492 | −0.115675 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.4640 | 1.50751 | ||||||||
\(383\) | 22.0871 | 1.12860 | 0.564299 | − | 0.825571i | \(-0.309147\pi\) | ||||
0.564299 | + | 0.825571i | \(0.309147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.21911 | 0.113096 | ||||||||
\(386\) | −0.478251 | −0.0243423 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.520157 | −0.0264070 | ||||||||
\(389\) | 13.3463 | 0.676682 | 0.338341 | − | 0.941024i | \(-0.390134\pi\) | ||||
0.338341 | + | 0.941024i | \(0.390134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5147 | 0.582324 | ||||||||
\(392\) | 2.58179 | 0.130400 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.85313 | 0.244497 | ||||||||
\(395\) | −11.4546 | −0.576345 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6938 | −1.44010 | −0.720049 | − | 0.693923i | \(-0.755881\pi\) | ||||
−0.720049 | + | 0.693923i | \(0.755881\pi\) | |||||||
\(398\) | −6.71991 | −0.336839 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.50469 | −0.225234 | ||||||||
\(401\) | 3.71286 | 0.185412 | 0.0927058 | − | 0.995694i | \(-0.470448\pi\) | ||||
0.0927058 | + | 0.995694i | \(0.470448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.25772 | −0.261906 | ||||||||
\(404\) | −0.116511 | −0.00579665 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.13293 | 0.105855 | ||||||||
\(407\) | −11.1636 | −0.553358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5854 | −1.01788 | −0.508941 | − | 0.860801i | \(-0.669963\pi\) | ||||
−0.508941 | + | 0.860801i | \(0.669963\pi\) | |||||||
\(410\) | 11.8209 | 0.583793 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.94495 | −0.243620 | ||||||||
\(413\) | 3.03065 | 0.149129 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.37692 | 0.362119 | ||||||||
\(416\) | 1.97580 | 0.0968716 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.5982 | 1.25205 | ||||||||
\(419\) | 33.3863 | 1.63103 | 0.815513 | − | 0.578738i | \(-0.196455\pi\) | ||||
0.815513 | + | 0.578738i | \(0.196455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.9706 | −1.55815 | −0.779076 | − | 0.626930i | \(-0.784311\pi\) | ||||
−0.779076 | + | 0.626930i | \(0.784311\pi\) | |||||||
\(422\) | −2.06160 | −0.100357 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.03159 | 0.147227 | ||||||||
\(425\) | −3.39333 | −0.164601 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.39333 | 0.261002 | ||||||||
\(428\) | 1.31467 | 0.0635469 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.15780 | −0.104059 | ||||||||
\(431\) | 10.4133 | 0.501593 | 0.250797 | − | 0.968040i | \(-0.419307\pi\) | ||||
0.250797 | + | 0.968040i | \(0.419307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.35422 | 0.0650796 | 0.0325398 | − | 0.999470i | \(-0.489640\pi\) | ||||
0.0325398 | + | 0.999470i | \(0.489640\pi\) | |||||||
\(434\) | 6.70378 | 0.321792 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.59120 | 0.219878 | ||||||||
\(437\) | −25.8316 | −1.23569 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.32531 | 0.254163 | 0.127082 | − | 0.991892i | \(-0.459439\pi\) | ||||
0.127082 | + | 0.991892i | \(0.459439\pi\) | |||||||
\(440\) | 5.72928 | 0.273133 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.11106 | 0.290673 | ||||||||
\(443\) | 1.89286 | 0.0899326 | 0.0449663 | − | 0.998989i | \(-0.485682\pi\) | ||||
0.0449663 | + | 0.998989i | \(0.485682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8929 | −0.800798 | ||||||||
\(446\) | −42.9093 | −2.03181 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.49016 | 0.306631 | ||||||||
\(449\) | 12.0729 | 0.569754 | 0.284877 | − | 0.958564i | \(-0.408047\pi\) | ||||
0.284877 | + | 0.958564i | \(0.408047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.3111 | −0.815147 | ||||||||
\(452\) | 2.03584 | 0.0957580 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.6545 | −1.06323 | ||||||||
\(455\) | −1.18846 | −0.0557158 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7551 | 1.25155 | 0.625775 | − | 0.780004i | \(-0.284783\pi\) | ||||
0.625775 | + | 0.780004i | \(0.284783\pi\) | |||||||
\(458\) | 12.3779 | 0.578380 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.00516 | 0.0468657 | ||||||||
\(461\) | −23.5751 | −1.09800 | −0.549000 | − | 0.835822i | \(-0.684991\pi\) | ||||
−0.549000 | + | 0.835822i | \(0.684991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.1769 | 1.63481 | 0.817404 | − | 0.576065i | \(-0.195412\pi\) | ||||
0.817404 | + | 0.576065i | \(0.195412\pi\) | |||||||
\(464\) | 6.34066 | 0.294358 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.3311 | 1.26609 | ||||||||
\(467\) | −19.1493 | −0.886126 | −0.443063 | − | 0.896490i | \(-0.646108\pi\) | ||||
−0.443063 | + | 0.896490i | \(0.646108\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.01424 | 0.139185 | ||||||||
\(470\) | 11.9138 | 0.549543 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.82451 | 0.360152 | ||||||||
\(473\) | 3.15998 | 0.145296 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.61244 | 0.349283 | ||||||||
\(476\) | −1.00516 | −0.0460713 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.2768 | −0.835962 | ||||||||
\(479\) | 2.96935 | 0.135673 | 0.0678365 | − | 0.997696i | \(-0.478390\pi\) | ||||
0.0678365 | + | 0.997696i | \(0.478390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.97872 | 0.272606 | ||||||||
\(482\) | 33.7460 | 1.53709 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.79967 | −0.0818031 | ||||||||
\(485\) | 1.75601 | 0.0797364 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0440 | 1.76925 | 0.884625 | − | 0.466303i | \(-0.154414\pi\) | ||||
0.884625 | + | 0.466303i | \(0.154414\pi\) | |||||||
\(488\) | 13.9245 | 0.630331 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.51533 | 0.0684555 | ||||||||
\(491\) | 38.8764 | 1.75447 | 0.877235 | − | 0.480062i | \(-0.159386\pi\) | ||||
0.877235 | + | 0.480062i | \(0.159386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.77635 | 0.215116 | ||||||||
\(494\) | −13.7093 | −0.616809 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.9287 | 0.894824 | ||||||||
\(497\) | 14.8764 | 0.667300 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.0893 | −1.74988 | −0.874938 | − | 0.484235i | \(-0.839098\pi\) | ||||
−0.874938 | + | 0.484235i | \(0.839098\pi\) | |||||||
\(500\) | −0.296215 | −0.0132471 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.9684 | 1.06976 | ||||||||
\(503\) | −21.9706 | −0.979620 | −0.489810 | − | 0.871829i | \(-0.662934\pi\) | ||||
−0.489810 | + | 0.871829i | \(0.662934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.393333 | 0.0175031 | ||||||||
\(506\) | −11.4107 | −0.507267 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.81122 | 0.257831 | ||||||||
\(509\) | −30.5396 | −1.35364 | −0.676821 | − | 0.736148i | \(-0.736643\pi\) | ||||
−0.676821 | + | 0.736148i | \(0.736643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.18846 | −0.141049 | ||||||||
\(512\) | 15.7713 | 0.697000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.1514 | 0.977056 | ||||||||
\(515\) | 16.6938 | 0.735615 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4471 | −0.767323 | ||||||||
\(518\) | −7.62308 | −0.334939 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.06835 | −0.134556 | ||||||||
\(521\) | 14.0280 | 0.614577 | 0.307288 | − | 0.951616i | \(-0.400578\pi\) | ||||
0.307288 | + | 0.951616i | \(0.400578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.182681 | −0.00798809 | −0.00399404 | − | 0.999992i | \(-0.501271\pi\) | ||||
−0.00399404 | + | 0.999992i | \(0.501271\pi\) | |||||||
\(524\) | 4.70349 | 0.205473 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.8267 | 1.43131 | ||||||||
\(527\) | 15.0121 | 0.653935 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4853 | −0.499361 | ||||||||
\(530\) | 1.77933 | 0.0772891 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.25492 | 0.0977633 | ||||||||
\(533\) | 9.27104 | 0.401574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.43822 | −0.191881 | ||||||||
\(536\) | 7.78213 | 0.336137 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 36.7119 | 1.58276 | ||||||||
\(539\) | −2.21911 | −0.0955839 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.45246 | −0.148433 | −0.0742164 | − | 0.997242i | \(-0.523646\pi\) | ||||
−0.0742164 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(542\) | 38.2078 | 1.64117 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.64139 | −0.241872 | ||||||||
\(545\) | −15.4995 | −0.663927 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.8289 | −1.36090 | −0.680452 | − | 0.732793i | \(-0.738217\pi\) | ||||
−0.680452 | + | 0.732793i | \(0.738217\pi\) | |||||||
\(548\) | −0.347822 | −0.0148582 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.36268 | 0.143385 | ||||||||
\(551\) | −10.7150 | −0.456476 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4546 | 0.487101 | ||||||||
\(554\) | −32.7835 | −1.39284 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.60274 | 0.110381 | ||||||||
\(557\) | −16.3769 | −0.693912 | −0.346956 | − | 0.937881i | \(-0.612785\pi\) | ||||
−0.346956 | + | 0.937881i | \(0.612785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.69235 | −0.0715787 | ||||||||
\(560\) | 4.50469 | 0.190358 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −34.7738 | −1.46685 | ||||||||
\(563\) | −21.1769 | −0.892499 | −0.446250 | − | 0.894909i | \(-0.647241\pi\) | ||||
−0.446250 | + | 0.894909i | \(0.647241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.87285 | −0.289143 | ||||||||
\(566\) | −39.5089 | −1.66068 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.4079 | 1.61156 | ||||||||
\(569\) | 31.6346 | 1.32619 | 0.663097 | − | 0.748534i | \(-0.269242\pi\) | ||||
0.663097 | + | 0.748534i | \(0.269242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.5685 | 1.69774 | 0.848869 | − | 0.528604i | \(-0.177284\pi\) | ||||
0.848869 | + | 0.528604i | \(0.177284\pi\) | |||||||
\(572\) | −0.781215 | −0.0326642 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.8209 | −0.493396 | ||||||||
\(575\) | −3.39333 | −0.141512 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.50531 | 0.395711 | 0.197856 | − | 0.980231i | \(-0.436602\pi\) | ||||
0.197856 | + | 0.980231i | \(0.436602\pi\) | |||||||
\(578\) | 8.31201 | 0.345734 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.416944 | 0.0173126 | ||||||||
\(581\) | −7.37692 | −0.306046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.60573 | −0.107918 | ||||||||
\(584\) | −8.23193 | −0.340640 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.04285 | 0.167009 | ||||||||
\(587\) | −21.6702 | −0.894423 | −0.447211 | − | 0.894428i | \(-0.647583\pi\) | ||||
−0.447211 | + | 0.894428i | \(0.647583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6773 | −1.38765 | ||||||||
\(590\) | 4.59243 | 0.189067 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.6615 | −0.931383 | ||||||||
\(593\) | −40.8422 | −1.67719 | −0.838593 | − | 0.544758i | \(-0.816622\pi\) | ||||
−0.838593 | + | 0.544758i | \(0.816622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39333 | 0.139113 | ||||||||
\(596\) | 6.87957 | 0.281798 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.11106 | 0.249900 | ||||||||
\(599\) | 30.0977 | 1.22976 | 0.614880 | − | 0.788621i | \(-0.289204\pi\) | ||||
0.614880 | + | 0.788621i | \(0.289204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2298 | −0.825189 | −0.412594 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412594 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(602\) | 2.15780 | 0.0879455 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.36972 | 0.0964226 | ||||||||
\(605\) | 6.07554 | 0.247006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.88894 | 0.320202 | 0.160101 | − | 0.987101i | \(-0.448818\pi\) | ||||
0.160101 | + | 0.987101i | \(0.448818\pi\) | |||||||
\(608\) | 12.6556 | 0.513253 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.17266 | 0.330901 | ||||||||
\(611\) | 9.34391 | 0.378014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.6725 | −1.72353 | −0.861763 | − | 0.507312i | \(-0.830639\pi\) | ||||
−0.861763 | + | 0.507312i | \(0.830639\pi\) | |||||||
\(614\) | 7.01969 | 0.283292 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.72928 | −0.230839 | ||||||||
\(617\) | −34.0755 | −1.37183 | −0.685915 | − | 0.727682i | \(-0.740598\pi\) | ||||
−0.685915 | + | 0.727682i | \(0.740598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.85157 | −0.275388 | −0.137694 | − | 0.990475i | \(-0.543969\pi\) | ||||
−0.137694 | + | 0.990475i | \(0.543969\pi\) | |||||||
\(620\) | 1.31045 | 0.0526290 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.73320 | −0.189784 | ||||||||
\(623\) | 16.8929 | 0.676798 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.4640 | 0.458194 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.69377 | −0.187302 | ||||||||
\(629\) | −17.0707 | −0.680653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.6795 | 0.664002 | 0.332001 | − | 0.943279i | \(-0.392276\pi\) | ||||
0.332001 | + | 0.943279i | \(0.392276\pi\) | |||||||
\(632\) | 29.5735 | 1.17637 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.96513 | −0.0780453 | ||||||||
\(635\) | −19.6182 | −0.778525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.18846 | 0.0470884 | ||||||||
\(638\) | −4.73320 | −0.187389 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13.1597 | 0.520182 | ||||||||
\(641\) | 18.5098 | 0.731095 | 0.365547 | − | 0.930793i | \(-0.380882\pi\) | ||||
0.365547 | + | 0.930793i | \(0.380882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9399 | 0.944099 | 0.472049 | − | 0.881572i | \(-0.343514\pi\) | ||||
0.472049 | + | 0.881572i | \(0.343514\pi\) | |||||||
\(644\) | −1.00516 | −0.0396087 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.1432 | 1.54007 | ||||||||
\(647\) | −26.5690 | −1.04453 | −0.522267 | − | 0.852782i | \(-0.674914\pi\) | ||||
−0.522267 | + | 0.852782i | \(0.674914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.72536 | −0.263993 | ||||||||
\(650\) | −1.80090 | −0.0706372 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.24146 | −0.244434 | ||||||||
\(653\) | 40.4312 | 1.58219 | 0.791097 | − | 0.611690i | \(-0.209510\pi\) | ||||
0.791097 | + | 0.611690i | \(0.209510\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.8786 | −0.620429 | ||||||||
\(656\) | −35.1406 | −1.37201 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.9138 | −0.464449 | ||||||||
\(659\) | −23.2364 | −0.905163 | −0.452582 | − | 0.891723i | \(-0.649497\pi\) | ||||
−0.452582 | + | 0.891723i | \(0.649497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.43822 | −0.0948359 | −0.0474179 | − | 0.998875i | \(-0.515099\pi\) | ||||
−0.0474179 | + | 0.998875i | \(0.515099\pi\) | |||||||
\(662\) | −26.7654 | −1.04027 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.0457 | −0.739115 | ||||||||
\(665\) | −7.61244 | −0.295198 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.77635 | 0.184941 | ||||||||
\(668\) | −0.143751 | −0.00556190 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.56755 | 0.176460 | ||||||||
\(671\) | −11.9684 | −0.462035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.2956 | 0.936525 | 0.468263 | − | 0.883589i | \(-0.344880\pi\) | ||||
0.468263 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(674\) | −22.4995 | −0.866650 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.43241 | −0.132016 | ||||||||
\(677\) | 7.06944 | 0.271701 | 0.135850 | − | 0.990729i | \(-0.456623\pi\) | ||||
0.135850 | + | 0.990729i | \(0.456623\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75601 | −0.0673895 | ||||||||
\(680\) | 8.76087 | 0.335964 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.8764 | −0.569649 | ||||||||
\(683\) | 1.05644 | 0.0404237 | 0.0202119 | − | 0.999796i | \(-0.493566\pi\) | ||||
0.0202119 | + | 0.999796i | \(0.493566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.17422 | 0.0448647 | ||||||||
\(686\) | −1.51533 | −0.0578554 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.41461 | 0.244555 | ||||||||
\(689\) | 1.39551 | 0.0531648 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.18577 | 0.121193 | 0.0605963 | − | 0.998162i | \(-0.480700\pi\) | ||||
0.0605963 | + | 0.998162i | \(0.480700\pi\) | |||||||
\(692\) | 1.48594 | 0.0564869 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.0941 | 1.29420 | ||||||||
\(695\) | −8.78667 | −0.333297 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.4711 | −1.00266 | ||||||||
\(698\) | −22.8154 | −0.863577 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.296215 | 0.0111959 | ||||||||
\(701\) | −33.1467 | −1.25193 | −0.625966 | − | 0.779850i | \(-0.715295\pi\) | ||||
−0.625966 | + | 0.779850i | \(0.715295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.2956 | 1.44434 | ||||||||
\(704\) | −14.4024 | −0.542810 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.0012 | −1.27965 | ||||||||
\(707\) | −0.393333 | −0.0147928 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.26760 | −0.235385 | −0.117692 | − | 0.993050i | \(-0.537550\pi\) | ||||
−0.117692 | + | 0.993050i | \(0.537550\pi\) | |||||||
\(710\) | 22.5427 | 0.846012 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 43.6138 | 1.63450 | ||||||||
\(713\) | 15.0121 | 0.562206 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.63732 | 0.0986302 | ||||||||
\(716\) | −1.57322 | −0.0587940 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.76146 | 0.364295 | ||||||||
\(719\) | 28.4995 | 1.06285 | 0.531427 | − | 0.847104i | \(-0.321656\pi\) | ||||
0.531427 | + | 0.847104i | \(0.321656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6938 | −0.621708 | ||||||||
\(722\) | −59.0209 | −2.19653 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.09559 | −0.263706 | ||||||||
\(725\) | −1.40757 | −0.0522758 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.0444 | 1.55934 | 0.779670 | − | 0.626191i | \(-0.215387\pi\) | ||||
0.779670 | + | 0.626191i | \(0.215387\pi\) | |||||||
\(728\) | 3.06835 | 0.113721 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.83156 | −0.178824 | ||||||||
\(731\) | 4.83206 | 0.178720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.1284 | −1.37137 | −0.685684 | − | 0.727899i | \(-0.740497\pi\) | ||||
−0.685684 | + | 0.727899i | \(0.740497\pi\) | |||||||
\(734\) | 2.52016 | 0.0930207 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.64139 | −0.207944 | ||||||||
\(737\) | −6.68893 | −0.246390 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.2404 | 1.66419 | 0.832097 | − | 0.554630i | \(-0.187140\pi\) | ||||
0.832097 | + | 0.554630i | \(0.187140\pi\) | |||||||
\(740\) | −1.49016 | −0.0547792 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.77933 | −0.0653212 | ||||||||
\(743\) | 27.6018 | 1.01261 | 0.506306 | − | 0.862354i | \(-0.331011\pi\) | ||||
0.506306 | + | 0.862354i | \(0.331011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2249 | −0.850894 | ||||||||
\(746\) | −1.27835 | −0.0468037 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.23056 | 0.0815572 | ||||||||
\(749\) | 4.43822 | 0.162169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5454 | 0.384806 | 0.192403 | − | 0.981316i | \(-0.438372\pi\) | ||||
0.192403 | + | 0.981316i | \(0.438372\pi\) | |||||||
\(752\) | −35.4168 | −1.29152 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.53490 | 0.0923154 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.1636 | −0.769203 | −0.384602 | − | 0.923083i | \(-0.625661\pi\) | ||||
−0.384602 | + | 0.923083i | \(0.625661\pi\) | |||||||
\(758\) | −28.1629 | −1.02292 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.6537 | −0.712916 | ||||||||
\(761\) | −39.1708 | −1.41994 | −0.709970 | − | 0.704232i | \(-0.751291\pi\) | ||||
−0.709970 | + | 0.704232i | \(0.751291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4995 | 0.561121 | ||||||||
\(764\) | −5.75961 | −0.208375 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.4692 | −1.20929 | ||||||||
\(767\) | 3.60180 | 0.130054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0236 | −1.33511 | −0.667553 | − | 0.744562i | \(-0.732658\pi\) | ||||
−0.667553 | + | 0.744562i | \(0.732658\pi\) | |||||||
\(770\) | −3.36268 | −0.121183 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.0934882 | 0.00336471 | ||||||||
\(773\) | 33.7490 | 1.21387 | 0.606933 | − | 0.794753i | \(-0.292400\pi\) | ||||
0.606933 | + | 0.794753i | \(0.292400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.42399 | −0.158914 | ||||||||
\(776\) | −4.53365 | −0.162749 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.2239 | −0.725064 | ||||||||
\(779\) | 59.3839 | 2.12765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.0125 | −1.18128 | ||||||||
\(782\) | −17.4485 | −0.623959 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.50469 | −0.160882 | ||||||||
\(785\) | 15.8458 | 0.565561 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7275 | −0.631918 | −0.315959 | − | 0.948773i | \(-0.602326\pi\) | ||||
−0.315959 | + | 0.948773i | \(0.602326\pi\) | |||||||
\(788\) | −0.948687 | −0.0337956 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.3575 | 0.617553 | ||||||||
\(791\) | 6.87285 | 0.244370 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.40975 | 0.227617 | ||||||||
\(794\) | 43.4804 | 1.54306 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.31360 | 0.0465595 | ||||||||
\(797\) | −5.74177 | −0.203384 | −0.101692 | − | 0.994816i | \(-0.532426\pi\) | ||||
−0.101692 | + | 0.994816i | \(0.532426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.6791 | −0.943838 | ||||||||
\(800\) | 1.66249 | 0.0587779 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.62620 | −0.198668 | ||||||||
\(803\) | 7.07554 | 0.249691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.39333 | 0.119599 | ||||||||
\(806\) | 7.96717 | 0.280631 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.01550 | −0.0357253 | ||||||||
\(809\) | −21.1964 | −0.745226 | −0.372613 | − | 0.927987i | \(-0.621538\pi\) | ||||
−0.372613 | + | 0.927987i | \(0.621538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.3226 | −1.38080 | −0.690402 | − | 0.723426i | \(-0.742566\pi\) | ||||
−0.690402 | + | 0.723426i | \(0.742566\pi\) | |||||||
\(812\) | −0.416944 | −0.0146318 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.9165 | 0.592922 | ||||||||
\(815\) | 21.0707 | 0.738074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.8400 | −0.379244 | ||||||||
\(818\) | 31.1936 | 1.09066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.31075 | −0.0806948 | ||||||||
\(821\) | −29.5690 | −1.03196 | −0.515982 | − | 0.856599i | \(-0.672573\pi\) | ||||
−0.515982 | + | 0.856599i | \(0.672573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.0249 | −0.907169 | −0.453585 | − | 0.891213i | \(-0.649855\pi\) | ||||
−0.453585 | + | 0.891213i | \(0.649855\pi\) | |||||||
\(824\) | −43.0998 | −1.50145 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.59243 | −0.159791 | ||||||||
\(827\) | −39.7490 | −1.38221 | −0.691104 | − | 0.722756i | \(-0.742875\pi\) | ||||
−0.691104 | + | 0.722756i | \(0.742875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.19206 | 0.110865 | 0.0554323 | − | 0.998462i | \(-0.482346\pi\) | ||||
0.0554323 | + | 0.998462i | \(0.482346\pi\) | |||||||
\(830\) | −11.1784 | −0.388009 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.71328 | 0.267410 | ||||||||
\(833\) | −3.39333 | −0.117572 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.485293 | 0.0167943 | ||||||||
\(836\) | −5.00392 | −0.173064 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −50.5911 | −1.74764 | ||||||||
\(839\) | 1.66623 | 0.0575247 | 0.0287623 | − | 0.999586i | \(-0.490843\pi\) | ||||
0.0287623 | + | 0.999586i | \(0.490843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0187 | −0.931681 | ||||||||
\(842\) | 48.4459 | 1.66956 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.403001 | 0.0138719 | ||||||||
\(845\) | 11.5876 | 0.398624 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.07554 | −0.208758 | ||||||||
\(848\) | −5.28950 | −0.181642 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.14201 | 0.176369 | ||||||||
\(851\) | −17.0707 | −0.585175 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.4097 | −1.04121 | −0.520605 | − | 0.853798i | \(-0.674294\pi\) | ||||
−0.520605 | + | 0.853798i | \(0.674294\pi\) | |||||||
\(854\) | −8.17266 | −0.279663 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.4586 | 0.391646 | ||||||||
\(857\) | −18.7365 | −0.640026 | −0.320013 | − | 0.947413i | \(-0.603687\pi\) | ||||
−0.320013 | + | 0.947413i | \(0.603687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.5299 | −1.21226 | −0.606132 | − | 0.795364i | \(-0.707280\pi\) | ||||
−0.606132 | + | 0.795364i | \(0.707280\pi\) | |||||||
\(860\) | 0.421806 | 0.0143835 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.7796 | −0.537456 | ||||||||
\(863\) | 36.4039 | 1.23920 | 0.619602 | − | 0.784916i | \(-0.287294\pi\) | ||||
0.619602 | + | 0.784916i | \(0.287294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.01642 | −0.170563 | ||||||||
\(866\) | −2.05208 | −0.0697327 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.31045 | −0.0444796 | ||||||||
\(869\) | −25.4191 | −0.862285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.58229 | 0.121381 | ||||||||
\(872\) | 40.0165 | 1.35513 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 39.1432 | 1.32404 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8502 | 0.737827 | 0.368914 | − | 0.929464i | \(-0.379730\pi\) | ||||
0.368914 | + | 0.929464i | \(0.379730\pi\) | |||||||
\(878\) | −8.06958 | −0.272335 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.99640 | −0.336979 | ||||||||
\(881\) | −10.9481 | −0.368850 | −0.184425 | − | 0.982847i | \(-0.559042\pi\) | ||||
−0.184425 | + | 0.982847i | \(0.559042\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −59.1605 | −1.99091 | −0.995454 | − | 0.0952432i | \(-0.969637\pi\) | ||||
−0.995454 | + | 0.0952432i | \(0.969637\pi\) | |||||||
\(884\) | −1.19459 | −0.0401783 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.86831 | −0.0963626 | ||||||||
\(887\) | 15.4426 | 0.518511 | 0.259256 | − | 0.965809i | \(-0.416523\pi\) | ||||
0.259256 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.6182 | 0.657974 | ||||||||
\(890\) | 25.5982 | 0.858054 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.38788 | 0.280847 | ||||||||
\(893\) | 59.8506 | 2.00282 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.31107 | 0.177530 | ||||||||
\(896\) | −13.1597 | −0.439634 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.2943 | −0.610490 | ||||||||
\(899\) | 6.22707 | 0.207684 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.98452 | −0.132744 | ||||||||
\(902\) | 26.2319 | 0.873428 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.7443 | 0.590165 | ||||||||
\(905\) | 23.9542 | 0.796264 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.483113 | −0.0160415 | −0.00802076 | − | 0.999968i | \(-0.502553\pi\) | ||||
−0.00802076 | + | 0.999968i | \(0.502553\pi\) | |||||||
\(908\) | 4.42849 | 0.146965 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.80090 | 0.0596993 | ||||||||
\(911\) | 39.0173 | 1.29270 | 0.646351 | − | 0.763040i | \(-0.276294\pi\) | ||||
0.646351 | + | 0.763040i | \(0.276294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3702 | 0.541775 | ||||||||
\(914\) | −40.5427 | −1.34103 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.41962 | −0.0799464 | ||||||||
\(917\) | 15.8786 | 0.524358 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7939 | 0.817874 | 0.408937 | − | 0.912563i | \(-0.365900\pi\) | ||||
0.408937 | + | 0.912563i | \(0.365900\pi\) | |||||||
\(920\) | 8.76087 | 0.288837 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35.7239 | 1.17651 | ||||||||
\(923\) | 17.6800 | 0.581945 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.03065 | 0.165407 | ||||||||
\(926\) | −53.3045 | −1.75169 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.34007 | −0.0768166 | ||||||||
\(929\) | 19.2298 | 0.630908 | 0.315454 | − | 0.948941i | \(-0.397843\pi\) | ||||
0.315454 | + | 0.948941i | \(0.397843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.61244 | 0.249488 | ||||||||
\(932\) | −5.34267 | −0.175005 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.0175 | 0.949482 | ||||||||
\(935\) | −7.53018 | −0.246263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.5867 | −0.574531 | −0.287265 | − | 0.957851i | \(-0.592746\pi\) | ||||
−0.287265 | + | 0.957851i | \(0.592746\pi\) | |||||||
\(938\) | −4.56755 | −0.149136 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.32891 | −0.0759605 | ||||||||
\(941\) | −3.50533 | −0.114271 | −0.0571353 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571353 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.4711 | −0.862016 | ||||||||
\(944\) | −13.6521 | −0.444339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.78841 | −0.155685 | ||||||||
\(947\) | −28.3880 | −0.922487 | −0.461244 | − | 0.887274i | \(-0.652597\pi\) | ||||
−0.461244 | + | 0.887274i | \(0.652597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.78935 | −0.123007 | ||||||||
\(950\) | −11.5353 | −0.374256 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.76087 | −0.283942 | ||||||||
\(953\) | −4.49953 | −0.145754 | −0.0728770 | − | 0.997341i | \(-0.523218\pi\) | ||||
−0.0728770 | + | 0.997341i | \(0.523218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.4440 | 0.629193 | ||||||||
\(956\) | 3.57274 | 0.115551 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.49953 | −0.145373 | ||||||||
\(959\) | −1.17422 | −0.0379176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.4283 | −0.368656 | ||||||||
\(962\) | −9.05972 | −0.292097 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.59665 | −0.212464 | ||||||||
\(965\) | −0.315609 | −0.0101598 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0574 | −0.355581 | −0.177791 | − | 0.984068i | \(-0.556895\pi\) | ||||
−0.177791 | + | 0.984068i | \(0.556895\pi\) | |||||||
\(968\) | −15.6858 | −0.504160 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.66093 | −0.0854374 | ||||||||
\(971\) | −44.4570 | −1.42669 | −0.713346 | − | 0.700812i | \(-0.752821\pi\) | ||||
−0.713346 | + | 0.700812i | \(0.752821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.78667 | 0.281688 | ||||||||
\(974\) | −59.1643 | −1.89575 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.2953 | −0.777673 | ||||||||
\(977\) | 27.2942 | 0.873217 | 0.436609 | − | 0.899652i | \(-0.356179\pi\) | ||||
0.436609 | + | 0.899652i | \(0.356179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.4871 | −1.19809 | ||||||||
\(980\) | −0.296215 | −0.00946225 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −58.9105 | −1.87991 | ||||||||
\(983\) | 26.1440 | 0.833866 | 0.416933 | − | 0.908937i | \(-0.363105\pi\) | ||||
0.416933 | + | 0.908937i | \(0.363105\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20269 | 0.102046 | ||||||||
\(986\) | −7.23773 | −0.230496 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.67988 | 0.0852583 | ||||||||
\(989\) | 4.83206 | 0.153651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2413 | 1.15124 | 0.575621 | − | 0.817716i | \(-0.304760\pi\) | ||||
0.575621 | + | 0.817716i | \(0.304760\pi\) | |||||||
\(992\) | −7.35484 | −0.233516 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.5427 | −0.715010 | ||||||||
\(995\) | −4.43463 | −0.140587 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.94683 | 0.0933269 | 0.0466635 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466635 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(998\) | 59.2330 | 1.87499 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.a.m.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 945.2.a.n.1.3 | yes | 4 | ||
5.4 | even | 2 | 4725.2.a.bx.1.3 | 4 | |||
7.6 | odd | 2 | 6615.2.a.be.1.2 | 4 | |||
15.14 | odd | 2 | 4725.2.a.bo.1.2 | 4 | |||
21.20 | even | 2 | 6615.2.a.bh.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.m.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
945.2.a.n.1.3 | yes | 4 | 3.2 | odd | 2 | ||
4725.2.a.bo.1.2 | 4 | 15.14 | odd | 2 | |||
4725.2.a.bx.1.3 | 4 | 5.4 | even | 2 | |||
6615.2.a.be.1.2 | 4 | 7.6 | odd | 2 | |||
6615.2.a.bh.1.3 | 4 | 21.20 | even | 2 |