Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.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: | \(24.1547466114\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 605) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.517638 | −0.366025 | −0.183013 | − | 0.983111i | \(-0.558585\pi\) | ||||
−0.183013 | + | 0.983111i | \(0.558585\pi\) | |||||||
\(3\) | 1.93185 | 1.11536 | 0.557678 | − | 0.830058i | \(-0.311693\pi\) | ||||
0.557678 | + | 0.830058i | \(0.311693\pi\) | |||||||
\(4\) | −1.73205 | −0.866025 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.34607 | 1.26469 | 0.632347 | − | 0.774685i | \(-0.282092\pi\) | ||||
0.632347 | + | 0.774685i | \(0.282092\pi\) | |||||||
\(8\) | 1.93185 | 0.683013 | ||||||||
\(9\) | 0.732051 | 0.244017 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.34607 | −0.965926 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | −1.73205 | −0.462910 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | −3.86370 | −0.937086 | −0.468543 | − | 0.883441i | \(-0.655221\pi\) | ||||
−0.468543 | + | 0.883441i | \(0.655221\pi\) | |||||||
\(18\) | −0.378937 | −0.0893164 | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.46410 | 1.41058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.48477 | −0.726624 | −0.363312 | − | 0.931668i | \(-0.618354\pi\) | ||||
−0.363312 | + | 0.931668i | \(0.618354\pi\) | |||||||
\(24\) | 3.73205 | 0.761802 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.19615 | 0.430701 | ||||||||
\(27\) | −4.38134 | −0.843190 | ||||||||
\(28\) | −5.79555 | −1.09526 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.73205 | −1.56832 | −0.784161 | − | 0.620557i | \(-0.786907\pi\) | ||||
−0.784161 | + | 0.620557i | \(0.786907\pi\) | |||||||
\(32\) | −5.13922 | −0.908494 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.26795 | −0.211325 | ||||||||
\(37\) | −1.79315 | −0.294792 | −0.147396 | − | 0.989078i | \(-0.547089\pi\) | ||||
−0.147396 | + | 0.989078i | \(0.547089\pi\) | |||||||
\(38\) | 2.17209 | 0.352359 | ||||||||
\(39\) | −8.19615 | −1.31243 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.73205 | 0.270501 | 0.135250 | − | 0.990811i | \(-0.456816\pi\) | ||||
0.135250 | + | 0.990811i | \(0.456816\pi\) | |||||||
\(42\) | −3.34607 | −0.516309 | ||||||||
\(43\) | 6.45189 | 0.983905 | 0.491952 | − | 0.870622i | \(-0.336283\pi\) | ||||
0.491952 | + | 0.870622i | \(0.336283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.80385 | 0.265963 | ||||||||
\(47\) | −11.4524 | −1.67051 | −0.835253 | − | 0.549866i | \(-0.814679\pi\) | ||||
−0.835253 | + | 0.549866i | \(0.814679\pi\) | |||||||
\(48\) | 4.76028 | 0.687087 | ||||||||
\(49\) | 4.19615 | 0.599450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.46410 | −1.04518 | ||||||||
\(52\) | 7.34847 | 1.01905 | ||||||||
\(53\) | −2.17209 | −0.298359 | −0.149180 | − | 0.988810i | \(-0.547663\pi\) | ||||
−0.149180 | + | 0.988810i | \(0.547663\pi\) | |||||||
\(54\) | 2.26795 | 0.308629 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.46410 | 0.863802 | ||||||||
\(57\) | −8.10634 | −1.07371 | ||||||||
\(58\) | −3.58630 | −0.470905 | ||||||||
\(59\) | −1.26795 | −0.165073 | −0.0825365 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825365 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7321 | −1.50214 | −0.751068 | − | 0.660225i | \(-0.770461\pi\) | ||||
−0.751068 | + | 0.660225i | \(0.770461\pi\) | |||||||
\(62\) | 4.52004 | 0.574046 | ||||||||
\(63\) | 2.44949 | 0.308607 | ||||||||
\(64\) | −2.26795 | −0.283494 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.20925 | −0.269903 | −0.134952 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134952 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(68\) | 6.69213 | 0.811540 | ||||||||
\(69\) | −6.73205 | −0.810444 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.19615 | −0.972704 | −0.486352 | − | 0.873763i | \(-0.661673\pi\) | ||||
−0.486352 | + | 0.873763i | \(0.661673\pi\) | |||||||
\(72\) | 1.41421 | 0.166667 | ||||||||
\(73\) | 4.89898 | 0.573382 | 0.286691 | − | 0.958023i | \(-0.407445\pi\) | ||||
0.286691 | + | 0.958023i | \(0.407445\pi\) | |||||||
\(74\) | 0.928203 | 0.107901 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.26795 | 0.833691 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.24264 | 0.480384 | ||||||||
\(79\) | 1.46410 | 0.164724 | 0.0823622 | − | 0.996602i | \(-0.473754\pi\) | ||||
0.0823622 | + | 0.996602i | \(0.473754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6603 | −1.18447 | ||||||||
\(82\) | −0.896575 | −0.0990102 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | −11.1962 | −1.22160 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.33975 | −0.360134 | ||||||||
\(87\) | 13.3843 | 1.43494 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.464102 | 0.0491947 | 0.0245973 | − | 0.999697i | \(-0.492170\pi\) | ||||
0.0245973 | + | 0.999697i | \(0.492170\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.1962 | −1.48816 | ||||||||
\(92\) | 6.03579 | 0.629275 | ||||||||
\(93\) | −16.8690 | −1.74924 | ||||||||
\(94\) | 5.92820 | 0.611447 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.92820 | −1.01329 | ||||||||
\(97\) | 9.14162 | 0.928191 | 0.464095 | − | 0.885785i | \(-0.346379\pi\) | ||||
0.464095 | + | 0.885785i | \(0.346379\pi\) | |||||||
\(98\) | −2.17209 | −0.219414 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.3923 | 1.92961 | 0.964803 | − | 0.262973i | \(-0.0847030\pi\) | ||||
0.964803 | + | 0.262973i | \(0.0847030\pi\) | |||||||
\(102\) | 3.86370 | 0.382564 | ||||||||
\(103\) | −4.24264 | −0.418040 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(104\) | −8.19615 | −0.803699 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.12436 | 0.109207 | ||||||||
\(107\) | −2.96713 | −0.286843 | −0.143422 | − | 0.989662i | \(-0.545810\pi\) | ||||
−0.143422 | + | 0.989662i | \(0.545810\pi\) | |||||||
\(108\) | 7.58871 | 0.730224 | ||||||||
\(109\) | 9.19615 | 0.880832 | 0.440416 | − | 0.897794i | \(-0.354831\pi\) | ||||
0.440416 | + | 0.897794i | \(0.354831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.46410 | −0.328798 | ||||||||
\(112\) | 8.24504 | 0.779083 | ||||||||
\(113\) | −2.82843 | −0.266076 | −0.133038 | − | 0.991111i | \(-0.542473\pi\) | ||||
−0.133038 | + | 0.991111i | \(0.542473\pi\) | |||||||
\(114\) | 4.19615 | 0.393006 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.0000 | −1.11417 | ||||||||
\(117\) | −3.10583 | −0.287134 | ||||||||
\(118\) | 0.656339 | 0.0604209 | ||||||||
\(119\) | −12.9282 | −1.18513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.07296 | 0.549820 | ||||||||
\(123\) | 3.34607 | 0.301705 | ||||||||
\(124\) | 15.1244 | 1.35821 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.26795 | −0.112958 | ||||||||
\(127\) | 0.896575 | 0.0795582 | 0.0397791 | − | 0.999208i | \(-0.487335\pi\) | ||||
0.0397791 | + | 0.999208i | \(0.487335\pi\) | |||||||
\(128\) | 11.4524 | 1.01226 | ||||||||
\(129\) | 12.4641 | 1.09740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.12436 | −0.272976 | −0.136488 | − | 0.990642i | \(-0.543582\pi\) | ||||
−0.136488 | + | 0.990642i | \(0.543582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.0406 | −1.21747 | ||||||||
\(134\) | 1.14359 | 0.0987914 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.46410 | −0.640041 | ||||||||
\(137\) | 8.86422 | 0.757321 | 0.378661 | − | 0.925536i | \(-0.376385\pi\) | ||||
0.378661 | + | 0.925536i | \(0.376385\pi\) | |||||||
\(138\) | 3.48477 | 0.296643 | ||||||||
\(139\) | −14.5885 | −1.23738 | −0.618688 | − | 0.785636i | \(-0.712336\pi\) | ||||
−0.618688 | + | 0.785636i | \(0.712336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.1244 | −1.86321 | ||||||||
\(142\) | 4.24264 | 0.356034 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.80385 | 0.150321 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.53590 | −0.209872 | ||||||||
\(147\) | 8.10634 | 0.668600 | ||||||||
\(148\) | 3.10583 | 0.255298 | ||||||||
\(149\) | −10.2679 | −0.841183 | −0.420592 | − | 0.907250i | \(-0.638177\pi\) | ||||
−0.420592 | + | 0.907250i | \(0.638177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.19615 | 0.341478 | 0.170739 | − | 0.985316i | \(-0.445384\pi\) | ||||
0.170739 | + | 0.985316i | \(0.445384\pi\) | |||||||
\(152\) | −8.10634 | −0.657511 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.1962 | 1.13660 | ||||||||
\(157\) | 21.8695 | 1.74538 | 0.872690 | − | 0.488275i | \(-0.162374\pi\) | ||||
0.872690 | + | 0.488275i | \(0.162374\pi\) | |||||||
\(158\) | −0.757875 | −0.0602933 | ||||||||
\(159\) | −4.19615 | −0.332777 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.6603 | −0.918957 | ||||||||
\(162\) | 5.51815 | 0.433547 | ||||||||
\(163\) | 5.13922 | 0.402534 | 0.201267 | − | 0.979536i | \(-0.435494\pi\) | ||||
0.201267 | + | 0.979536i | \(0.435494\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.12436 | −0.397727 | ||||||||
\(167\) | −0.517638 | −0.0400560 | −0.0200280 | − | 0.999799i | \(-0.506376\pi\) | ||||
−0.0200280 | + | 0.999799i | \(0.506376\pi\) | |||||||
\(168\) | 12.4877 | 0.963446 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.07180 | −0.234906 | ||||||||
\(172\) | −11.1750 | −0.852086 | ||||||||
\(173\) | −21.7680 | −1.65499 | −0.827495 | − | 0.561472i | \(-0.810235\pi\) | ||||
−0.827495 | + | 0.561472i | \(0.810235\pi\) | |||||||
\(174\) | −6.92820 | −0.525226 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.44949 | −0.184115 | ||||||||
\(178\) | −0.240237 | −0.0180065 | ||||||||
\(179\) | −15.4641 | −1.15584 | −0.577921 | − | 0.816093i | \(-0.696136\pi\) | ||||
−0.577921 | + | 0.816093i | \(0.696136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3923 | −1.29276 | −0.646380 | − | 0.763016i | \(-0.723718\pi\) | ||||
−0.646380 | + | 0.763016i | \(0.723718\pi\) | |||||||
\(182\) | 7.34847 | 0.544705 | ||||||||
\(183\) | −22.6646 | −1.67541 | ||||||||
\(184\) | −6.73205 | −0.496293 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.73205 | 0.640265 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 19.8362 | 1.44670 | ||||||||
\(189\) | −14.6603 | −1.06638 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.26795 | −0.525890 | −0.262945 | − | 0.964811i | \(-0.584694\pi\) | ||||
−0.262945 | + | 0.964811i | \(0.584694\pi\) | |||||||
\(192\) | −4.38134 | −0.316196 | ||||||||
\(193\) | −15.1774 | −1.09249 | −0.546247 | − | 0.837624i | \(-0.683944\pi\) | ||||
−0.546247 | + | 0.837624i | \(0.683944\pi\) | |||||||
\(194\) | −4.73205 | −0.339741 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.26795 | −0.519139 | ||||||||
\(197\) | −17.2480 | −1.22887 | −0.614433 | − | 0.788969i | \(-0.710615\pi\) | ||||
−0.614433 | + | 0.788969i | \(0.710615\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.26795 | −0.301038 | ||||||||
\(202\) | −10.0382 | −0.706285 | ||||||||
\(203\) | 23.1822 | 1.62707 | ||||||||
\(204\) | 12.9282 | 0.905155 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.19615 | 0.153013 | ||||||||
\(207\) | −2.55103 | −0.177309 | ||||||||
\(208\) | −10.4543 | −0.724875 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1244 | −0.903518 | −0.451759 | − | 0.892140i | \(-0.649203\pi\) | ||||
−0.451759 | + | 0.892140i | \(0.649203\pi\) | |||||||
\(212\) | 3.76217 | 0.258387 | ||||||||
\(213\) | −15.8338 | −1.08491 | ||||||||
\(214\) | 1.53590 | 0.104992 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.46410 | −0.575909 | ||||||||
\(217\) | −29.2180 | −1.98345 | ||||||||
\(218\) | −4.76028 | −0.322407 | ||||||||
\(219\) | 9.46410 | 0.639525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3923 | 1.10267 | ||||||||
\(222\) | 1.79315 | 0.120348 | ||||||||
\(223\) | −1.55291 | −0.103991 | −0.0519954 | − | 0.998647i | \(-0.516558\pi\) | ||||
−0.0519954 | + | 0.998647i | \(0.516558\pi\) | |||||||
\(224\) | −17.1962 | −1.14897 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.46410 | 0.0973906 | ||||||||
\(227\) | −20.1136 | −1.33498 | −0.667492 | − | 0.744617i | \(-0.732632\pi\) | ||||
−0.667492 | + | 0.744617i | \(0.732632\pi\) | |||||||
\(228\) | 14.0406 | 0.929861 | ||||||||
\(229\) | −4.07180 | −0.269072 | −0.134536 | − | 0.990909i | \(-0.542954\pi\) | ||||
−0.134536 | + | 0.990909i | \(0.542954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.3843 | 0.878720 | ||||||||
\(233\) | −1.69161 | −0.110821 | −0.0554107 | − | 0.998464i | \(-0.517647\pi\) | ||||
−0.0554107 | + | 0.998464i | \(0.517647\pi\) | |||||||
\(234\) | 1.60770 | 0.105098 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.19615 | 0.142957 | ||||||||
\(237\) | 2.82843 | 0.183726 | ||||||||
\(238\) | 6.69213 | 0.433786 | ||||||||
\(239\) | 5.66025 | 0.366131 | 0.183066 | − | 0.983101i | \(-0.441398\pi\) | ||||
0.183066 | + | 0.983101i | \(0.441398\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1244 | 0.909830 | 0.454915 | − | 0.890535i | \(-0.349670\pi\) | ||||
0.454915 | + | 0.890535i | \(0.349670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.45001 | −0.477918 | ||||||||
\(244\) | 20.3205 | 1.30089 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.73205 | −0.110432 | ||||||||
\(247\) | 17.8028 | 1.13276 | ||||||||
\(248\) | −16.8690 | −1.07118 | ||||||||
\(249\) | 19.1244 | 1.21196 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.80385 | −0.240097 | −0.120048 | − | 0.992768i | \(-0.538305\pi\) | ||||
−0.120048 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(252\) | −4.24264 | −0.267261 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.464102 | −0.0291203 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | −14.7985 | −0.923103 | −0.461552 | − | 0.887113i | \(-0.652707\pi\) | ||||
−0.461552 | + | 0.887113i | \(0.652707\pi\) | |||||||
\(258\) | −6.45189 | −0.401677 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.07180 | 0.313936 | ||||||||
\(262\) | 1.61729 | 0.0999162 | ||||||||
\(263\) | 6.79367 | 0.418915 | 0.209458 | − | 0.977818i | \(-0.432830\pi\) | ||||
0.209458 | + | 0.977818i | \(0.432830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.26795 | 0.445627 | ||||||||
\(267\) | 0.896575 | 0.0548695 | ||||||||
\(268\) | 3.82654 | 0.233743 | ||||||||
\(269\) | −16.2679 | −0.991874 | −0.495937 | − | 0.868358i | \(-0.665175\pi\) | ||||
−0.495937 | + | 0.868358i | \(0.665175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4641 | 0.696395 | 0.348197 | − | 0.937421i | \(-0.386794\pi\) | ||||
0.348197 | + | 0.937421i | \(0.386794\pi\) | |||||||
\(272\) | −9.52056 | −0.577269 | ||||||||
\(273\) | −27.4249 | −1.65983 | ||||||||
\(274\) | −4.58846 | −0.277199 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.6603 | 0.701865 | ||||||||
\(277\) | 31.1870 | 1.87385 | 0.936923 | − | 0.349535i | \(-0.113660\pi\) | ||||
0.936923 | + | 0.349535i | \(0.113660\pi\) | |||||||
\(278\) | 7.55154 | 0.452911 | ||||||||
\(279\) | −6.39230 | −0.382697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3205 | −1.03325 | −0.516627 | − | 0.856210i | \(-0.672813\pi\) | ||||
−0.516627 | + | 0.856210i | \(0.672813\pi\) | |||||||
\(282\) | 11.4524 | 0.681981 | ||||||||
\(283\) | 8.06918 | 0.479663 | 0.239831 | − | 0.970815i | \(-0.422908\pi\) | ||||
0.239831 | + | 0.970815i | \(0.422908\pi\) | |||||||
\(284\) | 14.1962 | 0.842387 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.79555 | 0.342101 | ||||||||
\(288\) | −3.76217 | −0.221688 | ||||||||
\(289\) | −2.07180 | −0.121870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.6603 | 1.03526 | ||||||||
\(292\) | −8.48528 | −0.496564 | ||||||||
\(293\) | −15.0759 | −0.880742 | −0.440371 | − | 0.897816i | \(-0.645153\pi\) | ||||
−0.440371 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(294\) | −4.19615 | −0.244725 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.46410 | −0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.31508 | 0.307894 | ||||||||
\(299\) | 14.7846 | 0.855016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.5885 | 1.24434 | ||||||||
\(302\) | −2.17209 | −0.124990 | ||||||||
\(303\) | 37.4631 | 2.15220 | ||||||||
\(304\) | −10.3397 | −0.593025 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.46410 | 0.0836971 | ||||||||
\(307\) | 7.82894 | 0.446821 | 0.223411 | − | 0.974724i | \(-0.428281\pi\) | ||||
0.223411 | + | 0.974724i | \(0.428281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.19615 | −0.466263 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0526 | 0.570028 | 0.285014 | − | 0.958523i | \(-0.408002\pi\) | ||||
0.285014 | + | 0.958523i | \(0.408002\pi\) | |||||||
\(312\) | −15.8338 | −0.896410 | ||||||||
\(313\) | 17.1464 | 0.969173 | 0.484587 | − | 0.874743i | \(-0.338970\pi\) | ||||
0.484587 | + | 0.874743i | \(0.338970\pi\) | |||||||
\(314\) | −11.3205 | −0.638853 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.53590 | −0.142655 | ||||||||
\(317\) | 12.6264 | 0.709168 | 0.354584 | − | 0.935024i | \(-0.384622\pi\) | ||||
0.354584 | + | 0.935024i | \(0.384622\pi\) | |||||||
\(318\) | 2.17209 | 0.121805 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.73205 | −0.319932 | ||||||||
\(322\) | 6.03579 | 0.336362 | ||||||||
\(323\) | 16.2127 | 0.902098 | ||||||||
\(324\) | 18.4641 | 1.02578 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.66025 | −0.147338 | ||||||||
\(327\) | 17.7656 | 0.982440 | ||||||||
\(328\) | 3.34607 | 0.184756 | ||||||||
\(329\) | −38.3205 | −2.11268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1962 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(332\) | −17.1464 | −0.941033 | ||||||||
\(333\) | −1.31268 | −0.0719343 | ||||||||
\(334\) | 0.267949 | 0.0146615 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.9282 | 0.868955 | ||||||||
\(337\) | 17.6269 | 0.960199 | 0.480099 | − | 0.877214i | \(-0.340601\pi\) | ||||
0.480099 | + | 0.877214i | \(0.340601\pi\) | |||||||
\(338\) | −2.58819 | −0.140779 | ||||||||
\(339\) | −5.46410 | −0.296769 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.59008 | 0.0859816 | ||||||||
\(343\) | −9.38186 | −0.506573 | ||||||||
\(344\) | 12.4641 | 0.672019 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.2679 | 0.605769 | ||||||||
\(347\) | 4.38134 | 0.235203 | 0.117601 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117601 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(348\) | −23.1822 | −1.24270 | ||||||||
\(349\) | −7.32051 | −0.391858 | −0.195929 | − | 0.980618i | \(-0.562772\pi\) | ||||
−0.195929 | + | 0.980618i | \(0.562772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5885 | 0.992178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0053 | 0.692204 | 0.346102 | − | 0.938197i | \(-0.387505\pi\) | ||||
0.346102 | + | 0.938197i | \(0.387505\pi\) | |||||||
\(354\) | 1.26795 | 0.0673907 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.803848 | −0.0426038 | ||||||||
\(357\) | −24.9754 | −1.32184 | ||||||||
\(358\) | 8.00481 | 0.423067 | ||||||||
\(359\) | 35.6603 | 1.88208 | 0.941038 | − | 0.338301i | \(-0.109852\pi\) | ||||
0.941038 | + | 0.338301i | \(0.109852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | 9.00292 | 0.473183 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 24.5885 | 1.28879 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.7321 | 0.613244 | ||||||||
\(367\) | 16.9062 | 0.882496 | 0.441248 | − | 0.897385i | \(-0.354536\pi\) | ||||
0.441248 | + | 0.897385i | \(0.354536\pi\) | |||||||
\(368\) | −8.58682 | −0.447619 | ||||||||
\(369\) | 1.26795 | 0.0660068 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.26795 | −0.377333 | ||||||||
\(372\) | 29.2180 | 1.51488 | ||||||||
\(373\) | −0.175865 | −0.00910597 | −0.00455298 | − | 0.999990i | \(-0.501449\pi\) | ||||
−0.00455298 | + | 0.999990i | \(0.501449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.1244 | −1.14098 | ||||||||
\(377\) | −29.3939 | −1.51386 | ||||||||
\(378\) | 7.58871 | 0.390321 | ||||||||
\(379\) | 1.46410 | 0.0752058 | 0.0376029 | − | 0.999293i | \(-0.488028\pi\) | ||||
0.0376029 | + | 0.999293i | \(0.488028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.73205 | 0.0887357 | ||||||||
\(382\) | 3.76217 | 0.192489 | ||||||||
\(383\) | 38.4612 | 1.96527 | 0.982637 | − | 0.185539i | \(-0.0594031\pi\) | ||||
0.982637 | + | 0.185539i | \(0.0594031\pi\) | |||||||
\(384\) | 22.1244 | 1.12903 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.85641 | 0.399881 | ||||||||
\(387\) | 4.72311 | 0.240089 | ||||||||
\(388\) | −15.8338 | −0.803837 | ||||||||
\(389\) | 6.12436 | 0.310517 | 0.155259 | − | 0.987874i | \(-0.450379\pi\) | ||||
0.155259 | + | 0.987874i | \(0.450379\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.4641 | 0.680909 | ||||||||
\(392\) | 8.10634 | 0.409432 | ||||||||
\(393\) | −6.03579 | −0.304465 | ||||||||
\(394\) | 8.92820 | 0.449796 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.9802 | −1.65523 | −0.827614 | − | 0.561298i | \(-0.810302\pi\) | ||||
−0.827614 | + | 0.561298i | \(0.810302\pi\) | |||||||
\(398\) | 1.03528 | 0.0518937 | ||||||||
\(399\) | −27.1244 | −1.35792 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.32051 | 0.115881 | 0.0579403 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579403 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(402\) | 2.20925 | 0.110188 | ||||||||
\(403\) | 37.0470 | 1.84544 | ||||||||
\(404\) | −33.5885 | −1.67109 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.4195 | −0.713873 | ||||||||
\(409\) | −26.1244 | −1.29177 | −0.645883 | − | 0.763436i | \(-0.723511\pi\) | ||||
−0.645883 | + | 0.763436i | \(0.723511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.1244 | 0.844682 | ||||||||
\(412\) | 7.34847 | 0.362033 | ||||||||
\(413\) | −4.24264 | −0.208767 | ||||||||
\(414\) | 1.32051 | 0.0648994 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.8038 | 1.06902 | ||||||||
\(417\) | −28.1827 | −1.38011 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.3397 | −0.602836 | −0.301418 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301418 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0526 | −0.831091 | −0.415545 | − | 0.909572i | \(-0.636409\pi\) | ||||
−0.415545 | + | 0.909572i | \(0.636409\pi\) | |||||||
\(422\) | 6.79367 | 0.330711 | ||||||||
\(423\) | −8.38375 | −0.407632 | ||||||||
\(424\) | −4.19615 | −0.203783 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.19615 | 0.397105 | ||||||||
\(427\) | −39.2562 | −1.89974 | ||||||||
\(428\) | 5.13922 | 0.248413 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.07180 | −0.244300 | −0.122150 | − | 0.992512i | \(-0.538979\pi\) | ||||
−0.122150 | + | 0.992512i | \(0.538979\pi\) | |||||||
\(432\) | −10.7961 | −0.519426 | ||||||||
\(433\) | 28.7375 | 1.38104 | 0.690519 | − | 0.723314i | \(-0.257382\pi\) | ||||
0.690519 | + | 0.723314i | \(0.257382\pi\) | |||||||
\(434\) | 15.1244 | 0.725992 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.9282 | −0.762823 | ||||||||
\(437\) | 14.6226 | 0.699494 | ||||||||
\(438\) | −4.89898 | −0.234082 | ||||||||
\(439\) | 28.2487 | 1.34824 | 0.674119 | − | 0.738623i | \(-0.264524\pi\) | ||||
0.674119 | + | 0.738623i | \(0.264524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.07180 | 0.146276 | ||||||||
\(442\) | −8.48528 | −0.403604 | ||||||||
\(443\) | −27.5636 | −1.30958 | −0.654792 | − | 0.755809i | \(-0.727244\pi\) | ||||
−0.654792 | + | 0.755809i | \(0.727244\pi\) | |||||||
\(444\) | 6.00000 | 0.284747 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.803848 | 0.0380633 | ||||||||
\(447\) | −19.8362 | −0.938218 | ||||||||
\(448\) | −7.58871 | −0.358533 | ||||||||
\(449\) | 34.5167 | 1.62894 | 0.814471 | − | 0.580204i | \(-0.197027\pi\) | ||||
0.814471 | + | 0.580204i | \(0.197027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.89898 | 0.230429 | ||||||||
\(453\) | 8.10634 | 0.380869 | ||||||||
\(454\) | 10.4115 | 0.488638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.6603 | −0.733359 | ||||||||
\(457\) | 21.2132 | 0.992312 | 0.496156 | − | 0.868233i | \(-0.334744\pi\) | ||||
0.496156 | + | 0.868233i | \(0.334744\pi\) | |||||||
\(458\) | 2.10772 | 0.0984872 | ||||||||
\(459\) | 16.9282 | 0.790141 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3166 | 0.944194 | 0.472097 | − | 0.881547i | \(-0.343497\pi\) | ||||
0.472097 | + | 0.881547i | \(0.343497\pi\) | |||||||
\(464\) | 17.0718 | 0.792538 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.875644 | 0.0405634 | ||||||||
\(467\) | 0.619174 | 0.0286520 | 0.0143260 | − | 0.999897i | \(-0.495440\pi\) | ||||
0.0143260 | + | 0.999897i | \(0.495440\pi\) | |||||||
\(468\) | 5.37945 | 0.248665 | ||||||||
\(469\) | −7.39230 | −0.341345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 42.2487 | 1.94672 | ||||||||
\(472\) | −2.44949 | −0.112747 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.46410 | −0.0672484 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.3923 | 1.02635 | ||||||||
\(477\) | −1.59008 | −0.0728047 | ||||||||
\(478\) | −2.92996 | −0.134013 | ||||||||
\(479\) | 2.53590 | 0.115868 | 0.0579341 | − | 0.998320i | \(-0.481549\pi\) | ||||
0.0579341 | + | 0.998320i | \(0.481549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.60770 | 0.346881 | ||||||||
\(482\) | −7.31130 | −0.333021 | ||||||||
\(483\) | −22.5259 | −1.02496 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.85641 | 0.174930 | ||||||||
\(487\) | −12.7279 | −0.576757 | −0.288379 | − | 0.957516i | \(-0.593116\pi\) | ||||
−0.288379 | + | 0.957516i | \(0.593116\pi\) | |||||||
\(488\) | −22.6646 | −1.02598 | ||||||||
\(489\) | 9.92820 | 0.448969 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.7128 | 1.79221 | 0.896107 | − | 0.443838i | \(-0.146383\pi\) | ||||
0.896107 | + | 0.443838i | \(0.146383\pi\) | |||||||
\(492\) | −5.79555 | −0.261284 | ||||||||
\(493\) | −26.7685 | −1.20559 | ||||||||
\(494\) | −9.21539 | −0.414620 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5167 | −0.966127 | ||||||||
\(497\) | −27.4249 | −1.23017 | ||||||||
\(498\) | −9.89949 | −0.443607 | ||||||||
\(499\) | 17.6077 | 0.788229 | 0.394114 | − | 0.919061i | \(-0.371051\pi\) | ||||
0.394114 | + | 0.919061i | \(0.371051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 1.96902 | 0.0878815 | ||||||||
\(503\) | 7.38563 | 0.329309 | 0.164655 | − | 0.986351i | \(-0.447349\pi\) | ||||
0.164655 | + | 0.986351i | \(0.447349\pi\) | |||||||
\(504\) | 4.73205 | 0.210782 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.65926 | 0.428983 | ||||||||
\(508\) | −1.55291 | −0.0688994 | ||||||||
\(509\) | −8.07180 | −0.357776 | −0.178888 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178888 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3923 | 0.725153 | ||||||||
\(512\) | −22.1841 | −0.980408 | ||||||||
\(513\) | 18.3848 | 0.811708 | ||||||||
\(514\) | 7.66025 | 0.337879 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.5885 | −0.950379 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.10583 | 0.136462 | ||||||||
\(519\) | −42.0526 | −1.84590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.24871 | −0.405193 | −0.202597 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202597 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(522\) | −2.62536 | −0.114909 | ||||||||
\(523\) | −25.6317 | −1.12080 | −0.560398 | − | 0.828223i | \(-0.689352\pi\) | ||||
−0.560398 | + | 0.828223i | \(0.689352\pi\) | |||||||
\(524\) | 5.41154 | 0.236404 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.51666 | −0.153334 | ||||||||
\(527\) | 33.7381 | 1.46965 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8564 | −0.472018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.928203 | −0.0402806 | ||||||||
\(532\) | 24.3190 | 1.05436 | ||||||||
\(533\) | −7.34847 | −0.318298 | ||||||||
\(534\) | −0.464102 | −0.0200836 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.26795 | −0.184347 | ||||||||
\(537\) | −29.8744 | −1.28917 | ||||||||
\(538\) | 8.42091 | 0.363051 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.60770 | −0.112114 | −0.0560568 | − | 0.998428i | \(-0.517853\pi\) | ||||
−0.0560568 | + | 0.998428i | \(0.517853\pi\) | |||||||
\(542\) | −5.93426 | −0.254898 | ||||||||
\(543\) | −33.5994 | −1.44189 | ||||||||
\(544\) | 19.8564 | 0.851336 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.1962 | 0.607539 | ||||||||
\(547\) | 28.7375 | 1.22873 | 0.614364 | − | 0.789023i | \(-0.289413\pi\) | ||||
0.614364 | + | 0.789023i | \(0.289413\pi\) | |||||||
\(548\) | −15.3533 | −0.655859 | ||||||||
\(549\) | −8.58846 | −0.366546 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.0718 | −1.23850 | ||||||||
\(552\) | −13.0053 | −0.553543 | ||||||||
\(553\) | 4.89898 | 0.208326 | ||||||||
\(554\) | −16.1436 | −0.685876 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.2679 | 1.07160 | ||||||||
\(557\) | 37.6018 | 1.59324 | 0.796619 | − | 0.604482i | \(-0.206620\pi\) | ||||
0.796619 | + | 0.604482i | \(0.206620\pi\) | |||||||
\(558\) | 3.30890 | 0.140077 | ||||||||
\(559\) | −27.3731 | −1.15776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.96575 | 0.378198 | ||||||||
\(563\) | −15.9725 | −0.673159 | −0.336579 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336579 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(564\) | 38.3205 | 1.61358 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.17691 | −0.175569 | ||||||||
\(567\) | −35.6699 | −1.49800 | ||||||||
\(568\) | −15.8338 | −0.664369 | ||||||||
\(569\) | 30.1244 | 1.26288 | 0.631439 | − | 0.775425i | \(-0.282464\pi\) | ||||
0.631439 | + | 0.775425i | \(0.282464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7128 | −0.824956 | −0.412478 | − | 0.910968i | \(-0.635337\pi\) | ||||
−0.412478 | + | 0.910968i | \(0.635337\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.0406 | −0.586554 | ||||||||
\(574\) | −3.00000 | −0.125218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.66025 | −0.0691773 | ||||||||
\(577\) | 3.76217 | 0.156621 | 0.0783105 | − | 0.996929i | \(-0.475047\pi\) | ||||
0.0783105 | + | 0.996929i | \(0.475047\pi\) | |||||||
\(578\) | 1.07244 | 0.0446077 | ||||||||
\(579\) | −29.3205 | −1.21852 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.1244 | 1.37423 | ||||||||
\(582\) | −9.14162 | −0.378932 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.46410 | 0.391627 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.80385 | 0.322374 | ||||||||
\(587\) | 20.3910 | 0.841625 | 0.420812 | − | 0.907148i | \(-0.361745\pi\) | ||||
0.420812 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(588\) | −14.0406 | −0.579025 | ||||||||
\(589\) | 36.6410 | 1.50977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.3205 | −1.37062 | ||||||||
\(592\) | −4.41851 | −0.181599 | ||||||||
\(593\) | −0.859411 | −0.0352918 | −0.0176459 | − | 0.999844i | \(-0.505617\pi\) | ||||
−0.0176459 | + | 0.999844i | \(0.505617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.7846 | 0.728486 | ||||||||
\(597\) | −3.86370 | −0.158131 | ||||||||
\(598\) | −7.65308 | −0.312958 | ||||||||
\(599\) | −38.4449 | −1.57081 | −0.785407 | − | 0.618979i | \(-0.787546\pi\) | ||||
−0.785407 | + | 0.618979i | \(0.787546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | 0.815817 | 0.407909 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407909 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(602\) | −11.1750 | −0.455459 | ||||||||
\(603\) | −1.61729 | −0.0658610 | ||||||||
\(604\) | −7.26795 | −0.295729 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.3923 | −0.787759 | ||||||||
\(607\) | −36.3906 | −1.47705 | −0.738525 | − | 0.674226i | \(-0.764477\pi\) | ||||
−0.738525 | + | 0.674226i | \(0.764477\pi\) | |||||||
\(608\) | 21.5649 | 0.874574 | ||||||||
\(609\) | 44.7846 | 1.81476 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.5885 | 1.96568 | ||||||||
\(612\) | 4.89898 | 0.198030 | ||||||||
\(613\) | −1.79315 | −0.0724247 | −0.0362123 | − | 0.999344i | \(-0.511529\pi\) | ||||
−0.0362123 | + | 0.999344i | \(0.511529\pi\) | |||||||
\(614\) | −4.05256 | −0.163548 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0053 | −0.523575 | −0.261787 | − | 0.965126i | \(-0.584312\pi\) | ||||
−0.261787 | + | 0.965126i | \(0.584312\pi\) | |||||||
\(618\) | 4.24264 | 0.170664 | ||||||||
\(619\) | 12.7846 | 0.513857 | 0.256928 | − | 0.966430i | \(-0.417290\pi\) | ||||
0.256928 | + | 0.966430i | \(0.417290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2679 | 0.612682 | ||||||||
\(622\) | −5.20359 | −0.208645 | ||||||||
\(623\) | 1.55291 | 0.0622162 | ||||||||
\(624\) | −20.1962 | −0.808493 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.87564 | −0.354742 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37.8792 | −1.51154 | ||||||||
\(629\) | 6.92820 | 0.276246 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.3205 | −0.609900 | −0.304950 | − | 0.952368i | \(-0.598640\pi\) | ||||
−0.304950 | + | 0.952368i | \(0.598640\pi\) | |||||||
\(632\) | 2.82843 | 0.112509 | ||||||||
\(633\) | −25.3543 | −1.00774 | ||||||||
\(634\) | −6.53590 | −0.259574 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.26795 | 0.288193 | ||||||||
\(637\) | −17.8028 | −0.705371 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.85641 | −0.310309 | −0.155155 | − | 0.987890i | \(-0.549588\pi\) | ||||
−0.155155 | + | 0.987890i | \(0.549588\pi\) | |||||||
\(642\) | 2.96713 | 0.117103 | ||||||||
\(643\) | 10.5187 | 0.414816 | 0.207408 | − | 0.978255i | \(-0.433497\pi\) | ||||
0.207408 | + | 0.978255i | \(0.433497\pi\) | |||||||
\(644\) | 20.1962 | 0.795840 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.39230 | −0.330191 | ||||||||
\(647\) | 37.3615 | 1.46883 | 0.734416 | − | 0.678699i | \(-0.237456\pi\) | ||||
0.734416 | + | 0.678699i | \(0.237456\pi\) | |||||||
\(648\) | −20.5940 | −0.809010 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.4449 | −2.21225 | ||||||||
\(652\) | −8.90138 | −0.348605 | ||||||||
\(653\) | −12.1459 | −0.475306 | −0.237653 | − | 0.971350i | \(-0.576378\pi\) | ||||
−0.237653 | + | 0.971350i | \(0.576378\pi\) | |||||||
\(654\) | −9.19615 | −0.359598 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.26795 | 0.166635 | ||||||||
\(657\) | 3.58630 | 0.139915 | ||||||||
\(658\) | 19.8362 | 0.773294 | ||||||||
\(659\) | −23.3205 | −0.908438 | −0.454219 | − | 0.890890i | \(-0.650082\pi\) | ||||
−0.454219 | + | 0.890890i | \(0.650082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5885 | 1.15086 | 0.575429 | − | 0.817852i | \(-0.304835\pi\) | ||||
0.575429 | + | 0.817852i | \(0.304835\pi\) | |||||||
\(662\) | 9.41902 | 0.366081 | ||||||||
\(663\) | 31.6675 | 1.22986 | ||||||||
\(664\) | 19.1244 | 0.742169 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.679492 | 0.0263298 | ||||||||
\(667\) | −24.1432 | −0.934827 | ||||||||
\(668\) | 0.896575 | 0.0346895 | ||||||||
\(669\) | −3.00000 | −0.115987 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −33.2204 | −1.28151 | ||||||||
\(673\) | 40.8091 | 1.57308 | 0.786538 | − | 0.617542i | \(-0.211871\pi\) | ||||
0.786538 | + | 0.617542i | \(0.211871\pi\) | |||||||
\(674\) | −9.12436 | −0.351457 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.66025 | −0.333087 | ||||||||
\(677\) | −20.3538 | −0.782260 | −0.391130 | − | 0.920335i | \(-0.627916\pi\) | ||||
−0.391130 | + | 0.920335i | \(0.627916\pi\) | |||||||
\(678\) | 2.82843 | 0.108625 | ||||||||
\(679\) | 30.5885 | 1.17388 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.8564 | −1.48898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.8372 | −1.14169 | −0.570844 | − | 0.821058i | \(-0.693384\pi\) | ||||
−0.570844 | + | 0.821058i | \(0.693384\pi\) | |||||||
\(684\) | 5.32051 | 0.203435 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.85641 | 0.185418 | ||||||||
\(687\) | −7.86611 | −0.300111 | ||||||||
\(688\) | 15.8981 | 0.606110 | ||||||||
\(689\) | 9.21539 | 0.351078 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.9090 | 1.44213 | 0.721063 | − | 0.692870i | \(-0.243654\pi\) | ||||
0.721063 | + | 0.692870i | \(0.243654\pi\) | |||||||
\(692\) | 37.7033 | 1.43326 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.26795 | −0.0860902 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 25.8564 | 0.980085 | ||||||||
\(697\) | −6.69213 | −0.253483 | ||||||||
\(698\) | 3.78937 | 0.143430 | ||||||||
\(699\) | −3.26795 | −0.123605 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.8564 | 1.42982 | 0.714908 | − | 0.699218i | \(-0.246468\pi\) | ||||
0.714908 | + | 0.699218i | \(0.246468\pi\) | |||||||
\(702\) | −9.62209 | −0.363163 | ||||||||
\(703\) | 7.52433 | 0.283786 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.73205 | −0.253364 | ||||||||
\(707\) | 64.8879 | 2.44036 | ||||||||
\(708\) | 4.24264 | 0.159448 | ||||||||
\(709\) | 2.60770 | 0.0979340 | 0.0489670 | − | 0.998800i | \(-0.484407\pi\) | ||||
0.0489670 | + | 0.998800i | \(0.484407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.07180 | 0.0401955 | ||||||||
\(712\) | 0.896575 | 0.0336006 | ||||||||
\(713\) | 30.4292 | 1.13958 | ||||||||
\(714\) | 12.9282 | 0.483826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.7846 | 1.00099 | ||||||||
\(717\) | 10.9348 | 0.408367 | ||||||||
\(718\) | −18.4591 | −0.688888 | ||||||||
\(719\) | −50.1962 | −1.87200 | −0.936000 | − | 0.351999i | \(-0.885502\pi\) | ||||
−0.936000 | + | 0.351999i | \(0.885502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1962 | −0.528692 | ||||||||
\(722\) | 0.720710 | 0.0268220 | ||||||||
\(723\) | 27.2862 | 1.01478 | ||||||||
\(724\) | 30.1244 | 1.11956 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.24504 | 0.305792 | 0.152896 | − | 0.988242i | \(-0.451140\pi\) | ||||
0.152896 | + | 0.988242i | \(0.451140\pi\) | |||||||
\(728\) | −27.4249 | −1.01643 | ||||||||
\(729\) | 17.5885 | 0.651424 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9282 | −0.922003 | ||||||||
\(732\) | 39.2562 | 1.45095 | ||||||||
\(733\) | 9.31749 | 0.344149 | 0.172075 | − | 0.985084i | \(-0.444953\pi\) | ||||
0.172075 | + | 0.985084i | \(0.444953\pi\) | |||||||
\(734\) | −8.75129 | −0.323016 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.9090 | 0.660133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.656339 | −0.0241602 | ||||||||
\(739\) | −38.9282 | −1.43200 | −0.715999 | − | 0.698102i | \(-0.754028\pi\) | ||||
−0.715999 | + | 0.698102i | \(0.754028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.3923 | 1.26343 | ||||||||
\(742\) | 3.76217 | 0.138114 | ||||||||
\(743\) | −43.3973 | −1.59209 | −0.796046 | − | 0.605235i | \(-0.793079\pi\) | ||||
−0.796046 | + | 0.605235i | \(0.793079\pi\) | |||||||
\(744\) | −32.5885 | −1.19475 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.0910347 | 0.00333302 | ||||||||
\(747\) | 7.24693 | 0.265151 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.92820 | −0.362769 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.6410 | 1.77494 | 0.887468 | − | 0.460869i | \(-0.152462\pi\) | ||||
0.887468 | + | 0.460869i | \(0.152462\pi\) | |||||||
\(752\) | −28.2199 | −1.02907 | ||||||||
\(753\) | −7.34847 | −0.267793 | ||||||||
\(754\) | 15.2154 | 0.554112 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 25.3923 | 0.923509 | ||||||||
\(757\) | 49.7749 | 1.80910 | 0.904549 | − | 0.426369i | \(-0.140207\pi\) | ||||
0.904549 | + | 0.426369i | \(0.140207\pi\) | |||||||
\(758\) | −0.757875 | −0.0275273 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8564 | −0.719794 | −0.359897 | − | 0.932992i | \(-0.617188\pi\) | ||||
−0.359897 | + | 0.932992i | \(0.617188\pi\) | |||||||
\(762\) | −0.896575 | −0.0324795 | ||||||||
\(763\) | 30.7709 | 1.11398 | ||||||||
\(764\) | 12.5885 | 0.455434 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.9090 | −0.719340 | ||||||||
\(767\) | 5.37945 | 0.194241 | ||||||||
\(768\) | −2.68973 | −0.0970571 | ||||||||
\(769\) | −9.85641 | −0.355431 | −0.177716 | − | 0.984082i | \(-0.556871\pi\) | ||||
−0.177716 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.5885 | −1.02959 | ||||||||
\(772\) | 26.2880 | 0.946128 | ||||||||
\(773\) | 12.0444 | 0.433206 | 0.216603 | − | 0.976260i | \(-0.430502\pi\) | ||||
0.216603 | + | 0.976260i | \(0.430502\pi\) | |||||||
\(774\) | −2.44486 | −0.0878788 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.6603 | 0.633966 | ||||||||
\(777\) | −11.5911 | −0.415829 | ||||||||
\(778\) | −3.17020 | −0.113657 | ||||||||
\(779\) | −7.26795 | −0.260401 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.96953 | −0.249230 | ||||||||
\(783\) | −30.3548 | −1.08479 | ||||||||
\(784\) | 10.3397 | 0.369277 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.12436 | 0.111442 | ||||||||
\(787\) | 17.3867 | 0.619768 | 0.309884 | − | 0.950774i | \(-0.399710\pi\) | ||||
0.309884 | + | 0.950774i | \(0.399710\pi\) | |||||||
\(788\) | 29.8744 | 1.06423 | ||||||||
\(789\) | 13.1244 | 0.467239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.46410 | −0.336505 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7749 | 1.76756 | ||||||||
\(794\) | 17.0718 | 0.605855 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.46410 | 0.122782 | ||||||||
\(797\) | −36.1875 | −1.28183 | −0.640914 | − | 0.767612i | \(-0.721445\pi\) | ||||
−0.640914 | + | 0.767612i | \(0.721445\pi\) | |||||||
\(798\) | 14.0406 | 0.497032 | ||||||||
\(799\) | 44.2487 | 1.56541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.339746 | 0.0120043 | ||||||||
\(802\) | −1.20118 | −0.0424153 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.39230 | 0.260706 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.1769 | −0.675478 | ||||||||
\(807\) | −31.4273 | −1.10629 | ||||||||
\(808\) | 37.4631 | 1.31795 | ||||||||
\(809\) | −14.5359 | −0.511055 | −0.255527 | − | 0.966802i | \(-0.582249\pi\) | ||||
−0.255527 | + | 0.966802i | \(0.582249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.9808 | 0.666505 | 0.333252 | − | 0.942838i | \(-0.391854\pi\) | ||||
0.333252 | + | 0.942838i | \(0.391854\pi\) | |||||||
\(812\) | −40.1528 | −1.40909 | ||||||||
\(813\) | 22.1469 | 0.776727 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −18.3923 | −0.643859 | ||||||||
\(817\) | −27.0731 | −0.947169 | ||||||||
\(818\) | 13.5230 | 0.472819 | ||||||||
\(819\) | −10.3923 | −0.363137 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.1962 | 1.01895 | 0.509476 | − | 0.860485i | \(-0.329839\pi\) | ||||
0.509476 | + | 0.860485i | \(0.329839\pi\) | |||||||
\(822\) | −8.86422 | −0.309175 | ||||||||
\(823\) | 6.75650 | 0.235517 | 0.117758 | − | 0.993042i | \(-0.462429\pi\) | ||||
0.117758 | + | 0.993042i | \(0.462429\pi\) | |||||||
\(824\) | −8.19615 | −0.285526 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19615 | 0.0764139 | ||||||||
\(827\) | 34.0798 | 1.18507 | 0.592536 | − | 0.805544i | \(-0.298127\pi\) | ||||
0.592536 | + | 0.805544i | \(0.298127\pi\) | |||||||
\(828\) | 4.41851 | 0.153554 | ||||||||
\(829\) | −9.98076 | −0.346646 | −0.173323 | − | 0.984865i | \(-0.555450\pi\) | ||||
−0.173323 | + | 0.984865i | \(0.555450\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 60.2487 | 2.09000 | ||||||||
\(832\) | 9.62209 | 0.333586 | ||||||||
\(833\) | −16.2127 | −0.561736 | ||||||||
\(834\) | 14.5885 | 0.505157 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.2581 | 1.32239 | ||||||||
\(838\) | 6.38752 | 0.220653 | ||||||||
\(839\) | −38.7846 | −1.33899 | −0.669497 | − | 0.742815i | \(-0.733490\pi\) | ||||
−0.669497 | + | 0.742815i | \(0.733490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 8.82705 | 0.304200 | ||||||||
\(843\) | −33.4607 | −1.15245 | ||||||||
\(844\) | 22.7321 | 0.782469 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.33975 | 0.149204 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.35225 | −0.183797 | ||||||||
\(849\) | 15.5885 | 0.534994 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.24871 | 0.214203 | ||||||||
\(852\) | 27.4249 | 0.939560 | ||||||||
\(853\) | 46.3644 | 1.58749 | 0.793744 | − | 0.608252i | \(-0.208129\pi\) | ||||
0.793744 | + | 0.608252i | \(0.208129\pi\) | |||||||
\(854\) | 20.3205 | 0.695353 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.73205 | −0.195917 | ||||||||
\(857\) | −29.3195 | −1.00154 | −0.500768 | − | 0.865581i | \(-0.666949\pi\) | ||||
−0.500768 | + | 0.865581i | \(0.666949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1962 | −0.757323 | −0.378661 | − | 0.925535i | \(-0.623616\pi\) | ||||
−0.378661 | + | 0.925535i | \(0.623616\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.1962 | 0.381564 | ||||||||
\(862\) | 2.62536 | 0.0894200 | ||||||||
\(863\) | −17.1093 | −0.582406 | −0.291203 | − | 0.956661i | \(-0.594056\pi\) | ||||
−0.291203 | + | 0.956661i | \(0.594056\pi\) | |||||||
\(864\) | 22.5167 | 0.766032 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.8756 | −0.505495 | ||||||||
\(867\) | −4.00240 | −0.135929 | ||||||||
\(868\) | 50.6071 | 1.71772 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.37307 | 0.317594 | ||||||||
\(872\) | 17.7656 | 0.601619 | ||||||||
\(873\) | 6.69213 | 0.226494 | ||||||||
\(874\) | −7.56922 | −0.256033 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.3923 | −0.553845 | ||||||||
\(877\) | −11.8957 | −0.401690 | −0.200845 | − | 0.979623i | \(-0.564369\pi\) | ||||
−0.200845 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(878\) | −14.6226 | −0.493489 | ||||||||
\(879\) | −29.1244 | −0.982340 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9090 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(882\) | −1.59008 | −0.0535407 | ||||||||
\(883\) | 21.5649 | 0.725718 | 0.362859 | − | 0.931844i | \(-0.381801\pi\) | ||||
0.362859 | + | 0.931844i | \(0.381801\pi\) | |||||||
\(884\) | −28.3923 | −0.954937 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.2679 | 0.479341 | ||||||||
\(887\) | −15.6950 | −0.526988 | −0.263494 | − | 0.964661i | \(-0.584875\pi\) | ||||
−0.263494 | + | 0.964661i | \(0.584875\pi\) | |||||||
\(888\) | −6.69213 | −0.224573 | ||||||||
\(889\) | 3.00000 | 0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.68973 | 0.0900587 | ||||||||
\(893\) | 48.0561 | 1.60813 | ||||||||
\(894\) | 10.2679 | 0.343412 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 38.3205 | 1.28020 | ||||||||
\(897\) | 28.5617 | 0.953646 | ||||||||
\(898\) | −17.8671 | −0.596234 | ||||||||
\(899\) | −60.4974 | −2.01770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.39230 | 0.279588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.7057 | 1.38788 | ||||||||
\(904\) | −5.46410 | −0.181733 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.19615 | −0.139408 | ||||||||
\(907\) | 30.1146 | 0.999938 | 0.499969 | − | 0.866043i | \(-0.333345\pi\) | ||||
0.499969 | + | 0.866043i | \(0.333345\pi\) | |||||||
\(908\) | 34.8377 | 1.15613 | ||||||||
\(909\) | 14.1962 | 0.470857 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.2487 | −1.00218 | −0.501092 | − | 0.865394i | \(-0.667068\pi\) | ||||
−0.501092 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(912\) | −19.9749 | −0.661434 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10.9808 | −0.363211 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.05256 | 0.233023 | ||||||||
\(917\) | −10.4543 | −0.345231 | ||||||||
\(918\) | −8.76268 | −0.289212 | ||||||||
\(919\) | −18.9808 | −0.626118 | −0.313059 | − | 0.949734i | \(-0.601354\pi\) | ||||
−0.313059 | + | 0.949734i | \(0.601354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.1244 | 0.498364 | ||||||||
\(922\) | 17.0821 | 0.562568 | ||||||||
\(923\) | 34.7733 | 1.14458 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.5167 | −0.345599 | ||||||||
\(927\) | −3.10583 | −0.102009 | ||||||||
\(928\) | −35.6055 | −1.16881 | ||||||||
\(929\) | −43.8564 | −1.43888 | −0.719441 | − | 0.694554i | \(-0.755602\pi\) | ||||
−0.719441 | + | 0.694554i | \(0.755602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.6077 | −0.577069 | ||||||||
\(932\) | 2.92996 | 0.0959741 | ||||||||
\(933\) | 19.4201 | 0.635784 | ||||||||
\(934\) | −0.320508 | −0.0104873 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.00000 | −0.196116 | ||||||||
\(937\) | 31.1870 | 1.01884 | 0.509418 | − | 0.860519i | \(-0.329861\pi\) | ||||
0.509418 | + | 0.860519i | \(0.329861\pi\) | |||||||
\(938\) | 3.82654 | 0.124941 | ||||||||
\(939\) | 33.1244 | 1.08097 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | −0.880175 | −0.440087 | − | 0.897955i | \(-0.645053\pi\) | ||||
−0.440087 | + | 0.897955i | \(0.645053\pi\) | |||||||
\(942\) | −21.8695 | −0.712548 | ||||||||
\(943\) | −6.03579 | −0.196552 | ||||||||
\(944\) | −3.12436 | −0.101689 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9749 | 0.649096 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(948\) | −4.89898 | −0.159111 | ||||||||
\(949\) | −20.7846 | −0.674697 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.3923 | 0.790975 | ||||||||
\(952\) | −24.9754 | −0.809456 | ||||||||
\(953\) | −16.6932 | −0.540745 | −0.270372 | − | 0.962756i | \(-0.587147\pi\) | ||||
−0.270372 | + | 0.962756i | \(0.587147\pi\) | |||||||
\(954\) | 0.823085 | 0.0266484 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.80385 | −0.317079 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.31268 | −0.0424107 | ||||||||
\(959\) | 29.6603 | 0.957780 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.2487 | 1.45964 | ||||||||
\(962\) | −3.93803 | −0.126967 | ||||||||
\(963\) | −2.17209 | −0.0699946 | ||||||||
\(964\) | −24.4641 | −0.787936 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11.6603 | 0.375163 | ||||||||
\(967\) | −4.24264 | −0.136434 | −0.0682171 | − | 0.997671i | \(-0.521731\pi\) | ||||
−0.0682171 | + | 0.997671i | \(0.521731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.3205 | 1.00616 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.9282 | −0.799984 | −0.399992 | − | 0.916519i | \(-0.630987\pi\) | ||||
−0.399992 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(972\) | 12.9038 | 0.413889 | ||||||||
\(973\) | −48.8139 | −1.56490 | ||||||||
\(974\) | 6.58846 | 0.211108 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.9090 | −0.925353 | ||||||||
\(977\) | 29.1165 | 0.931519 | 0.465759 | − | 0.884911i | \(-0.345781\pi\) | ||||
0.465759 | + | 0.884911i | \(0.345781\pi\) | |||||||
\(978\) | −5.13922 | −0.164334 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.73205 | 0.214938 | ||||||||
\(982\) | −20.5569 | −0.655996 | ||||||||
\(983\) | 56.0237 | 1.78688 | 0.893439 | − | 0.449184i | \(-0.148285\pi\) | ||||
0.893439 | + | 0.449184i | \(0.148285\pi\) | |||||||
\(984\) | 6.46410 | 0.206068 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.8564 | 0.441278 | ||||||||
\(987\) | −74.0295 | −2.35639 | ||||||||
\(988\) | −30.8353 | −0.981001 | ||||||||
\(989\) | −22.4833 | −0.714929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9090 | 0.632429 | 0.316215 | − | 0.948688i | \(-0.397588\pi\) | ||||
0.316215 | + | 0.948688i | \(0.397588\pi\) | |||||||
\(992\) | 44.8759 | 1.42481 | ||||||||
\(993\) | −35.1523 | −1.11552 | ||||||||
\(994\) | 14.1962 | 0.450275 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −33.1244 | −1.04959 | ||||||||
\(997\) | 34.1170 | 1.08050 | 0.540248 | − | 0.841506i | \(-0.318330\pi\) | ||||
0.540248 | + | 0.841506i | \(0.318330\pi\) | |||||||
\(998\) | −9.11441 | −0.288512 | ||||||||
\(999\) | 7.85641 | 0.248566 |
(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 | 3025.2.a.y.1.2 | 4 | ||
5.2 | odd | 4 | 605.2.b.d.364.2 | ✓ | 4 | ||
5.3 | odd | 4 | 605.2.b.d.364.3 | yes | 4 | ||
5.4 | even | 2 | inner | 3025.2.a.y.1.3 | 4 | ||
11.10 | odd | 2 | 3025.2.a.z.1.3 | 4 | |||
55.2 | even | 20 | 605.2.j.e.444.3 | 16 | |||
55.3 | odd | 20 | 605.2.j.f.9.3 | 16 | |||
55.7 | even | 20 | 605.2.j.e.269.2 | 16 | |||
55.8 | even | 20 | 605.2.j.e.9.2 | 16 | |||
55.13 | even | 20 | 605.2.j.e.444.2 | 16 | |||
55.17 | even | 20 | 605.2.j.e.124.2 | 16 | |||
55.18 | even | 20 | 605.2.j.e.269.3 | 16 | |||
55.27 | odd | 20 | 605.2.j.f.124.3 | 16 | |||
55.28 | even | 20 | 605.2.j.e.124.3 | 16 | |||
55.32 | even | 4 | 605.2.b.e.364.3 | yes | 4 | ||
55.37 | odd | 20 | 605.2.j.f.269.3 | 16 | |||
55.38 | odd | 20 | 605.2.j.f.124.2 | 16 | |||
55.42 | odd | 20 | 605.2.j.f.444.2 | 16 | |||
55.43 | even | 4 | 605.2.b.e.364.2 | yes | 4 | ||
55.47 | odd | 20 | 605.2.j.f.9.2 | 16 | |||
55.48 | odd | 20 | 605.2.j.f.269.2 | 16 | |||
55.52 | even | 20 | 605.2.j.e.9.3 | 16 | |||
55.53 | odd | 20 | 605.2.j.f.444.3 | 16 | |||
55.54 | odd | 2 | 3025.2.a.z.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.d.364.2 | ✓ | 4 | 5.2 | odd | 4 | ||
605.2.b.d.364.3 | yes | 4 | 5.3 | odd | 4 | ||
605.2.b.e.364.2 | yes | 4 | 55.43 | even | 4 | ||
605.2.b.e.364.3 | yes | 4 | 55.32 | even | 4 | ||
605.2.j.e.9.2 | 16 | 55.8 | even | 20 | |||
605.2.j.e.9.3 | 16 | 55.52 | even | 20 | |||
605.2.j.e.124.2 | 16 | 55.17 | even | 20 | |||
605.2.j.e.124.3 | 16 | 55.28 | even | 20 | |||
605.2.j.e.269.2 | 16 | 55.7 | even | 20 | |||
605.2.j.e.269.3 | 16 | 55.18 | even | 20 | |||
605.2.j.e.444.2 | 16 | 55.13 | even | 20 | |||
605.2.j.e.444.3 | 16 | 55.2 | even | 20 | |||
605.2.j.f.9.2 | 16 | 55.47 | odd | 20 | |||
605.2.j.f.9.3 | 16 | 55.3 | odd | 20 | |||
605.2.j.f.124.2 | 16 | 55.38 | odd | 20 | |||
605.2.j.f.124.3 | 16 | 55.27 | odd | 20 | |||
605.2.j.f.269.2 | 16 | 55.48 | odd | 20 | |||
605.2.j.f.269.3 | 16 | 55.37 | odd | 20 | |||
605.2.j.f.444.2 | 16 | 55.42 | odd | 20 | |||
605.2.j.f.444.3 | 16 | 55.53 | odd | 20 | |||
3025.2.a.y.1.2 | 4 | 1.1 | even | 1 | trivial | ||
3025.2.a.y.1.3 | 4 | 5.4 | even | 2 | inner | ||
3025.2.a.z.1.2 | 4 | 55.54 | odd | 2 | |||
3025.2.a.z.1.3 | 4 | 11.10 | odd | 2 |