Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | 2.41421 | 0.912487 | 0.456243 | − | 0.889855i | \(-0.349195\pi\) | ||||
0.456243 | + | 0.889855i | \(0.349195\pi\) | |||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.82843 | −0.527821 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0.414214 | 0.100462 | 0.0502308 | − | 0.998738i | \(-0.484004\pi\) | ||||
0.0502308 | + | 0.998738i | \(0.484004\pi\) | |||||||
\(18\) | 0.414214 | 0.0976311 | ||||||||
\(19\) | −3.58579 | −0.822636 | −0.411318 | − | 0.911492i | \(-0.634931\pi\) | ||||
−0.411318 | + | 0.911492i | \(0.634931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.41421 | 0.526825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | −1.58579 | −0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.17157 | −0.229764 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.41421 | −0.834208 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528 | 1.52400 | 0.762001 | − | 0.647576i | \(-0.224217\pi\) | ||||
0.762001 | + | 0.647576i | \(0.224217\pi\) | |||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.171573 | 0.0294245 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | −5.82843 | −0.958188 | −0.479094 | − | 0.877764i | \(-0.659035\pi\) | ||||
−0.479094 | + | 0.877764i | \(0.659035\pi\) | |||||||
\(38\) | −1.48528 | −0.240944 | ||||||||
\(39\) | −2.82843 | −0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.89949 | −1.38987 | −0.694934 | − | 0.719074i | \(-0.744566\pi\) | ||||
−0.694934 | + | 0.719074i | \(0.744566\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 0.343146 | 0.0523292 | 0.0261646 | − | 0.999658i | \(-0.491671\pi\) | ||||
0.0261646 | + | 0.999658i | \(0.491671\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.414214 | 0.0610725 | ||||||||
\(47\) | 9.48528 | 1.38357 | 0.691785 | − | 0.722103i | \(-0.256824\pi\) | ||||
0.691785 | + | 0.722103i | \(0.256824\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | −1.17157 | −0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.414214 | 0.0580015 | ||||||||
\(52\) | 5.17157 | 0.717168 | ||||||||
\(53\) | −3.65685 | −0.502308 | −0.251154 | − | 0.967947i | \(-0.580810\pi\) | ||||
−0.251154 | + | 0.967947i | \(0.580810\pi\) | |||||||
\(54\) | 0.414214 | 0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.82843 | −0.511595 | ||||||||
\(57\) | −3.58579 | −0.474949 | ||||||||
\(58\) | −2.82843 | −0.371391 | ||||||||
\(59\) | 11.0000 | 1.43208 | 0.716039 | − | 0.698060i | \(-0.245953\pi\) | ||||
0.716039 | + | 0.698060i | \(0.245953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.17157 | −0.406078 | −0.203039 | − | 0.979171i | \(-0.565082\pi\) | ||||
−0.203039 | + | 0.979171i | \(0.565082\pi\) | |||||||
\(62\) | 3.51472 | 0.446370 | ||||||||
\(63\) | 2.41421 | 0.304162 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6569 | −1.42411 | −0.712056 | − | 0.702123i | \(-0.752236\pi\) | ||||
−0.712056 | + | 0.702123i | \(0.752236\pi\) | |||||||
\(68\) | −0.757359 | −0.0918433 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.17157 | 0.257718 | 0.128859 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128859 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(72\) | −1.58579 | −0.186887 | ||||||||
\(73\) | 3.17157 | 0.371205 | 0.185602 | − | 0.982625i | \(-0.440576\pi\) | ||||
0.185602 | + | 0.982625i | \(0.440576\pi\) | |||||||
\(74\) | −2.41421 | −0.280647 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.55635 | 0.752065 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.17157 | −0.132655 | ||||||||
\(79\) | −4.75736 | −0.535245 | −0.267622 | − | 0.963524i | \(-0.586238\pi\) | ||||
−0.267622 | + | 0.963524i | \(0.586238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.68629 | −0.407083 | ||||||||
\(83\) | −12.4853 | −1.37044 | −0.685219 | − | 0.728337i | \(-0.740293\pi\) | ||||
−0.685219 | + | 0.728337i | \(0.740293\pi\) | |||||||
\(84\) | −4.41421 | −0.481630 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.142136 | 0.0153269 | ||||||||
\(87\) | −6.82843 | −0.732084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.65685 | −0.811625 | −0.405812 | − | 0.913956i | \(-0.633011\pi\) | ||||
−0.405812 | + | 0.913956i | \(0.633011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.82843 | −0.715814 | ||||||||
\(92\) | −1.82843 | −0.190627 | ||||||||
\(93\) | 8.48528 | 0.879883 | ||||||||
\(94\) | 3.92893 | 0.405238 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.41421 | 0.450524 | ||||||||
\(97\) | 0.171573 | 0.0174206 | 0.00871029 | − | 0.999962i | \(-0.497227\pi\) | ||||
0.00871029 | + | 0.999962i | \(0.497227\pi\) | |||||||
\(98\) | −0.485281 | −0.0490208 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.89949 | 0.487518 | 0.243759 | − | 0.969836i | \(-0.421619\pi\) | ||||
0.243759 | + | 0.969836i | \(0.421619\pi\) | |||||||
\(102\) | 0.171573 | 0.0169882 | ||||||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 4.48528 | 0.439818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.51472 | −0.147122 | ||||||||
\(107\) | −17.3137 | −1.67378 | −0.836890 | − | 0.547372i | \(-0.815628\pi\) | ||||
−0.836890 | + | 0.547372i | \(0.815628\pi\) | |||||||
\(108\) | −1.82843 | −0.175940 | ||||||||
\(109\) | 17.3137 | 1.65835 | 0.829176 | − | 0.558987i | \(-0.188810\pi\) | ||||
0.829176 | + | 0.558987i | \(0.188810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.82843 | −0.553210 | ||||||||
\(112\) | 7.24264 | 0.684365 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | −1.48528 | −0.139109 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.4853 | 1.15923 | ||||||||
\(117\) | −2.82843 | −0.261488 | ||||||||
\(118\) | 4.55635 | 0.419446 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.31371 | −0.118938 | ||||||||
\(123\) | −8.89949 | −0.802440 | ||||||||
\(124\) | −15.5147 | −1.39326 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 1.24264 | 0.110267 | 0.0551333 | − | 0.998479i | \(-0.482442\pi\) | ||||
0.0551333 | + | 0.998479i | \(0.482442\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | 0.343146 | 0.0302123 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.17157 | −0.102361 | −0.0511804 | − | 0.998689i | \(-0.516298\pi\) | ||||
−0.0511804 | + | 0.998689i | \(0.516298\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.65685 | −0.750644 | ||||||||
\(134\) | −4.82843 | −0.417113 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.656854 | −0.0563248 | ||||||||
\(137\) | 16.1421 | 1.37912 | 0.689558 | − | 0.724231i | \(-0.257805\pi\) | ||||
0.689558 | + | 0.724231i | \(0.257805\pi\) | |||||||
\(138\) | 0.414214 | 0.0352602 | ||||||||
\(139\) | −14.9706 | −1.26979 | −0.634893 | − | 0.772600i | \(-0.718956\pi\) | ||||
−0.634893 | + | 0.772600i | \(0.718956\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.48528 | 0.798805 | ||||||||
\(142\) | 0.899495 | 0.0754839 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.31371 | 0.108723 | ||||||||
\(147\) | −1.17157 | −0.0966297 | ||||||||
\(148\) | 10.6569 | 0.875988 | ||||||||
\(149\) | 17.7279 | 1.45233 | 0.726164 | − | 0.687522i | \(-0.241301\pi\) | ||||
0.726164 | + | 0.687522i | \(0.241301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0000 | −1.13930 | −0.569652 | − | 0.821886i | \(-0.692922\pi\) | ||||
−0.569652 | + | 0.821886i | \(0.692922\pi\) | |||||||
\(152\) | 5.68629 | 0.461219 | ||||||||
\(153\) | 0.414214 | 0.0334872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.17157 | 0.414057 | ||||||||
\(157\) | 6.00000 | 0.478852 | 0.239426 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239426 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(158\) | −1.97056 | −0.156770 | ||||||||
\(159\) | −3.65685 | −0.290007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.41421 | 0.190267 | ||||||||
\(162\) | 0.414214 | 0.0325437 | ||||||||
\(163\) | −23.7990 | −1.86408 | −0.932040 | − | 0.362354i | \(-0.881973\pi\) | ||||
−0.932040 | + | 0.362354i | \(0.881973\pi\) | |||||||
\(164\) | 16.2721 | 1.27064 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.17157 | −0.401392 | ||||||||
\(167\) | 17.7990 | 1.37733 | 0.688664 | − | 0.725081i | \(-0.258198\pi\) | ||||
0.688664 | + | 0.725081i | \(0.258198\pi\) | |||||||
\(168\) | −3.82843 | −0.295370 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.58579 | −0.274212 | ||||||||
\(172\) | −0.627417 | −0.0478401 | ||||||||
\(173\) | −18.5563 | −1.41081 | −0.705407 | − | 0.708803i | \(-0.749236\pi\) | ||||
−0.705407 | + | 0.708803i | \(0.749236\pi\) | |||||||
\(174\) | −2.82843 | −0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0000 | 0.826811 | ||||||||
\(178\) | −3.17157 | −0.237719 | ||||||||
\(179\) | −22.7990 | −1.70408 | −0.852038 | − | 0.523480i | \(-0.824634\pi\) | ||||
−0.852038 | + | 0.523480i | \(0.824634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9706 | 0.889765 | 0.444882 | − | 0.895589i | \(-0.353245\pi\) | ||||
0.444882 | + | 0.895589i | \(0.353245\pi\) | |||||||
\(182\) | −2.82843 | −0.209657 | ||||||||
\(183\) | −3.17157 | −0.234449 | ||||||||
\(184\) | −1.58579 | −0.116906 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.51472 | 0.257712 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.3431 | −1.26488 | ||||||||
\(189\) | 2.41421 | 0.175608 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8284 | 0.855875 | 0.427937 | − | 0.903808i | \(-0.359240\pi\) | ||||
0.427937 | + | 0.903808i | \(0.359240\pi\) | |||||||
\(192\) | −4.17157 | −0.301057 | ||||||||
\(193\) | 19.3137 | 1.39023 | 0.695116 | − | 0.718898i | \(-0.255353\pi\) | ||||
0.695116 | + | 0.718898i | \(0.255353\pi\) | |||||||
\(194\) | 0.0710678 | 0.00510237 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14214 | 0.153010 | ||||||||
\(197\) | −13.2426 | −0.943499 | −0.471750 | − | 0.881733i | \(-0.656377\pi\) | ||||
−0.471750 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.17157 | 0.366603 | 0.183302 | − | 0.983057i | \(-0.441322\pi\) | ||||
0.183302 | + | 0.983057i | \(0.441322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6569 | −0.822211 | ||||||||
\(202\) | 2.02944 | 0.142791 | ||||||||
\(203\) | −16.4853 | −1.15704 | ||||||||
\(204\) | −0.757359 | −0.0530258 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.970563 | −0.0676223 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −8.48528 | −0.588348 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.31371 | −0.641182 | −0.320591 | − | 0.947218i | \(-0.603882\pi\) | ||||
−0.320591 | + | 0.947218i | \(0.603882\pi\) | |||||||
\(212\) | 6.68629 | 0.459216 | ||||||||
\(213\) | 2.17157 | 0.148794 | ||||||||
\(214\) | −7.17157 | −0.490239 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.58579 | −0.107899 | ||||||||
\(217\) | 20.4853 | 1.39063 | ||||||||
\(218\) | 7.17157 | 0.485720 | ||||||||
\(219\) | 3.17157 | 0.214315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.17157 | −0.0788085 | ||||||||
\(222\) | −2.41421 | −0.162031 | ||||||||
\(223\) | −26.8284 | −1.79656 | −0.898282 | − | 0.439419i | \(-0.855184\pi\) | ||||
−0.898282 | + | 0.439419i | \(0.855184\pi\) | |||||||
\(224\) | 10.6569 | 0.712041 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.14214 | −0.275531 | ||||||||
\(227\) | 1.51472 | 0.100535 | 0.0502677 | − | 0.998736i | \(-0.483993\pi\) | ||||
0.0502677 | + | 0.998736i | \(0.483993\pi\) | |||||||
\(228\) | 6.55635 | 0.434205 | ||||||||
\(229\) | −19.4853 | −1.28762 | −0.643812 | − | 0.765184i | \(-0.722648\pi\) | ||||
−0.643812 | + | 0.765184i | \(0.722648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8284 | 0.710921 | ||||||||
\(233\) | 14.5563 | 0.953618 | 0.476809 | − | 0.879007i | \(-0.341793\pi\) | ||||
0.476809 | + | 0.879007i | \(0.341793\pi\) | |||||||
\(234\) | −1.17157 | −0.0765881 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20.1127 | −1.30923 | ||||||||
\(237\) | −4.75736 | −0.309024 | ||||||||
\(238\) | 0.414214 | 0.0268495 | ||||||||
\(239\) | −12.3431 | −0.798412 | −0.399206 | − | 0.916861i | \(-0.630714\pi\) | ||||
−0.399206 | + | 0.916861i | \(0.630714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1421 | 0.910975 | 0.455488 | − | 0.890242i | \(-0.349465\pi\) | ||||
0.455488 | + | 0.890242i | \(0.349465\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.79899 | 0.371242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.68629 | −0.235029 | ||||||||
\(247\) | 10.1421 | 0.645329 | ||||||||
\(248\) | −13.4558 | −0.854447 | ||||||||
\(249\) | −12.4853 | −0.791223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9706 | −1.57613 | −0.788064 | − | 0.615593i | \(-0.788916\pi\) | ||||
−0.788064 | + | 0.615593i | \(0.788916\pi\) | |||||||
\(252\) | −4.41421 | −0.278069 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.514719 | 0.0322963 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −13.3137 | −0.830486 | −0.415243 | − | 0.909710i | \(-0.636304\pi\) | ||||
−0.415243 | + | 0.909710i | \(0.636304\pi\) | |||||||
\(258\) | 0.142136 | 0.00884898 | ||||||||
\(259\) | −14.0711 | −0.874334 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.82843 | −0.422669 | ||||||||
\(262\) | −0.485281 | −0.0299808 | ||||||||
\(263\) | 10.9706 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390169\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.58579 | −0.219859 | ||||||||
\(267\) | −7.65685 | −0.468592 | ||||||||
\(268\) | 21.3137 | 1.30194 | ||||||||
\(269\) | 23.7990 | 1.45105 | 0.725525 | − | 0.688196i | \(-0.241597\pi\) | ||||
0.725525 | + | 0.688196i | \(0.241597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8995 | 0.662097 | 0.331049 | − | 0.943614i | \(-0.392598\pi\) | ||||
0.331049 | + | 0.943614i | \(0.392598\pi\) | |||||||
\(272\) | 1.24264 | 0.0753462 | ||||||||
\(273\) | −6.82843 | −0.413275 | ||||||||
\(274\) | 6.68629 | 0.403934 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.82843 | −0.110058 | ||||||||
\(277\) | 0.828427 | 0.0497754 | 0.0248877 | − | 0.999690i | \(-0.492077\pi\) | ||||
0.0248877 | + | 0.999690i | \(0.492077\pi\) | |||||||
\(278\) | −6.20101 | −0.371912 | ||||||||
\(279\) | 8.48528 | 0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9289 | −1.06955 | −0.534775 | − | 0.844994i | \(-0.679604\pi\) | ||||
−0.534775 | + | 0.844994i | \(0.679604\pi\) | |||||||
\(282\) | 3.92893 | 0.233965 | ||||||||
\(283\) | −18.8995 | −1.12346 | −0.561729 | − | 0.827321i | \(-0.689864\pi\) | ||||
−0.561729 | + | 0.827321i | \(0.689864\pi\) | |||||||
\(284\) | −3.97056 | −0.235610 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.4853 | −1.26824 | ||||||||
\(288\) | 4.41421 | 0.260110 | ||||||||
\(289\) | −16.8284 | −0.989907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.171573 | 0.0100578 | ||||||||
\(292\) | −5.79899 | −0.339360 | ||||||||
\(293\) | −20.4142 | −1.19261 | −0.596306 | − | 0.802758i | \(-0.703365\pi\) | ||||
−0.596306 | + | 0.802758i | \(0.703365\pi\) | |||||||
\(294\) | −0.485281 | −0.0283022 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.24264 | 0.537218 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.34315 | 0.425377 | ||||||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.828427 | 0.0477497 | ||||||||
\(302\) | −5.79899 | −0.333694 | ||||||||
\(303\) | 4.89949 | 0.281469 | ||||||||
\(304\) | −10.7574 | −0.616977 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.171573 | 0.00980817 | ||||||||
\(307\) | −29.3137 | −1.67302 | −0.836511 | − | 0.547950i | \(-0.815408\pi\) | ||||
−0.836511 | + | 0.547950i | \(0.815408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.34315 | −0.133297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.34315 | 0.132868 | 0.0664338 | − | 0.997791i | \(-0.478838\pi\) | ||||
0.0664338 | + | 0.997791i | \(0.478838\pi\) | |||||||
\(312\) | 4.48528 | 0.253929 | ||||||||
\(313\) | 1.14214 | 0.0645573 | 0.0322787 | − | 0.999479i | \(-0.489724\pi\) | ||||
0.0322787 | + | 0.999479i | \(0.489724\pi\) | |||||||
\(314\) | 2.48528 | 0.140253 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.69848 | 0.489328 | ||||||||
\(317\) | 25.1716 | 1.41378 | 0.706888 | − | 0.707325i | \(-0.250098\pi\) | ||||
0.706888 | + | 0.707325i | \(0.250098\pi\) | |||||||
\(318\) | −1.51472 | −0.0849412 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3137 | −0.966357 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −1.48528 | −0.0826433 | ||||||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.85786 | −0.545977 | ||||||||
\(327\) | 17.3137 | 0.957450 | ||||||||
\(328\) | 14.1127 | 0.779243 | ||||||||
\(329\) | 22.8995 | 1.26249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.85786 | −0.212047 | −0.106024 | − | 0.994364i | \(-0.533812\pi\) | ||||
−0.106024 | + | 0.994364i | \(0.533812\pi\) | |||||||
\(332\) | 22.8284 | 1.25287 | ||||||||
\(333\) | −5.82843 | −0.319396 | ||||||||
\(334\) | 7.37258 | 0.403410 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.24264 | 0.395118 | ||||||||
\(337\) | 24.1421 | 1.31511 | 0.657553 | − | 0.753408i | \(-0.271592\pi\) | ||||
0.657553 | + | 0.753408i | \(0.271592\pi\) | |||||||
\(338\) | −2.07107 | −0.112651 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.48528 | −0.0803148 | ||||||||
\(343\) | −19.7279 | −1.06521 | ||||||||
\(344\) | −0.544156 | −0.0293389 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.68629 | −0.413218 | ||||||||
\(347\) | 26.8284 | 1.44023 | 0.720113 | − | 0.693857i | \(-0.244090\pi\) | ||||
0.720113 | + | 0.693857i | \(0.244090\pi\) | |||||||
\(348\) | 12.4853 | 0.669281 | ||||||||
\(349\) | −14.4853 | −0.775379 | −0.387690 | − | 0.921790i | \(-0.626727\pi\) | ||||
−0.387690 | + | 0.921790i | \(0.626727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82843 | −0.150970 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.4853 | 0.664524 | 0.332262 | − | 0.943187i | \(-0.392188\pi\) | ||||
0.332262 | + | 0.943187i | \(0.392188\pi\) | |||||||
\(354\) | 4.55635 | 0.242167 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | −9.44365 | −0.499112 | ||||||||
\(359\) | −32.4853 | −1.71451 | −0.857254 | − | 0.514894i | \(-0.827831\pi\) | ||||
−0.857254 | + | 0.514894i | \(0.827831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.14214 | −0.323270 | ||||||||
\(362\) | 4.95837 | 0.260606 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.4853 | 0.654407 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.31371 | −0.0686686 | ||||||||
\(367\) | −21.3137 | −1.11257 | −0.556283 | − | 0.830993i | \(-0.687773\pi\) | ||||
−0.556283 | + | 0.830993i | \(0.687773\pi\) | |||||||
\(368\) | 3.00000 | 0.156386 | ||||||||
\(369\) | −8.89949 | −0.463289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.82843 | −0.458349 | ||||||||
\(372\) | −15.5147 | −0.804401 | ||||||||
\(373\) | 12.3431 | 0.639104 | 0.319552 | − | 0.947569i | \(-0.396468\pi\) | ||||
0.319552 | + | 0.947569i | \(0.396468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.0416 | −0.775713 | ||||||||
\(377\) | 19.3137 | 0.994707 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 14.8284 | 0.761685 | 0.380843 | − | 0.924640i | \(-0.375634\pi\) | ||||
0.380843 | + | 0.924640i | \(0.375634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24264 | 0.0636624 | ||||||||
\(382\) | 4.89949 | 0.250680 | ||||||||
\(383\) | 20.0000 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(384\) | −10.5563 | −0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 0.343146 | 0.0174431 | ||||||||
\(388\) | −0.313708 | −0.0159261 | ||||||||
\(389\) | −6.34315 | −0.321610 | −0.160805 | − | 0.986986i | \(-0.551409\pi\) | ||||
−0.160805 | + | 0.986986i | \(0.551409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.414214 | 0.0209477 | ||||||||
\(392\) | 1.85786 | 0.0938363 | ||||||||
\(393\) | −1.17157 | −0.0590980 | ||||||||
\(394\) | −5.48528 | −0.276344 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.9411 | 1.60308 | 0.801540 | − | 0.597942i | \(-0.204015\pi\) | ||||
0.801540 | + | 0.597942i | \(0.204015\pi\) | |||||||
\(398\) | 2.14214 | 0.107376 | ||||||||
\(399\) | −8.65685 | −0.433385 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.79899 | −0.389463 | −0.194731 | − | 0.980857i | \(-0.562384\pi\) | ||||
−0.194731 | + | 0.980857i | \(0.562384\pi\) | |||||||
\(402\) | −4.82843 | −0.240820 | ||||||||
\(403\) | −24.0000 | −1.19553 | ||||||||
\(404\) | −8.95837 | −0.445696 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.82843 | −0.338889 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.656854 | −0.0325191 | ||||||||
\(409\) | −24.1421 | −1.19375 | −0.596876 | − | 0.802334i | \(-0.703592\pi\) | ||||
−0.596876 | + | 0.802334i | \(0.703592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.1421 | 0.796233 | ||||||||
\(412\) | 4.28427 | 0.211071 | ||||||||
\(413\) | 26.5563 | 1.30675 | ||||||||
\(414\) | 0.414214 | 0.0203575 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.4853 | −0.612141 | ||||||||
\(417\) | −14.9706 | −0.733112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.51472 | −0.415971 | −0.207986 | − | 0.978132i | \(-0.566691\pi\) | ||||
−0.207986 | + | 0.978132i | \(0.566691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | −3.85786 | −0.187798 | ||||||||
\(423\) | 9.48528 | 0.461190 | ||||||||
\(424\) | 5.79899 | 0.281624 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.899495 | 0.0435807 | ||||||||
\(427\) | −7.65685 | −0.370541 | ||||||||
\(428\) | 31.6569 | 1.53019 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.82843 | −0.328914 | −0.164457 | − | 0.986384i | \(-0.552587\pi\) | ||||
−0.164457 | + | 0.986384i | \(0.552587\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 9.31371 | 0.447588 | 0.223794 | − | 0.974636i | \(-0.428156\pi\) | ||||
0.223794 | + | 0.974636i | \(0.428156\pi\) | |||||||
\(434\) | 8.48528 | 0.407307 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.6569 | −1.51609 | ||||||||
\(437\) | −3.58579 | −0.171531 | ||||||||
\(438\) | 1.31371 | 0.0627714 | ||||||||
\(439\) | −27.7279 | −1.32338 | −0.661691 | − | 0.749777i | \(-0.730161\pi\) | ||||
−0.661691 | + | 0.749777i | \(0.730161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.17157 | −0.0557892 | ||||||||
\(442\) | −0.485281 | −0.0230825 | ||||||||
\(443\) | 25.9706 | 1.23390 | 0.616949 | − | 0.787003i | \(-0.288368\pi\) | ||||
0.616949 | + | 0.787003i | \(0.288368\pi\) | |||||||
\(444\) | 10.6569 | 0.505752 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.1127 | −0.526202 | ||||||||
\(447\) | 17.7279 | 0.838502 | ||||||||
\(448\) | −10.0711 | −0.475813 | ||||||||
\(449\) | 10.4853 | 0.494831 | 0.247416 | − | 0.968909i | \(-0.420419\pi\) | ||||
0.247416 | + | 0.968909i | \(0.420419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.2843 | 0.860020 | ||||||||
\(453\) | −14.0000 | −0.657777 | ||||||||
\(454\) | 0.627417 | 0.0294461 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.68629 | 0.266285 | ||||||||
\(457\) | −32.1421 | −1.50355 | −0.751773 | − | 0.659422i | \(-0.770801\pi\) | ||||
−0.751773 | + | 0.659422i | \(0.770801\pi\) | |||||||
\(458\) | −8.07107 | −0.377136 | ||||||||
\(459\) | 0.414214 | 0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.7696 | −1.89883 | −0.949414 | − | 0.314028i | \(-0.898321\pi\) | ||||
−0.949414 | + | 0.314028i | \(0.898321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.02944 | 0.0478420 | 0.0239210 | − | 0.999714i | \(-0.492385\pi\) | ||||
0.0239210 | + | 0.999714i | \(0.492385\pi\) | |||||||
\(464\) | −20.4853 | −0.951005 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.02944 | 0.279308 | ||||||||
\(467\) | −34.6274 | −1.60237 | −0.801183 | − | 0.598420i | \(-0.795796\pi\) | ||||
−0.801183 | + | 0.598420i | \(0.795796\pi\) | |||||||
\(468\) | 5.17157 | 0.239056 | ||||||||
\(469\) | −28.1421 | −1.29948 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | −17.4437 | −0.802909 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.97056 | −0.0905109 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.82843 | −0.0838058 | ||||||||
\(477\) | −3.65685 | −0.167436 | ||||||||
\(478\) | −5.11270 | −0.233849 | ||||||||
\(479\) | 7.51472 | 0.343356 | 0.171678 | − | 0.985153i | \(-0.445081\pi\) | ||||
0.171678 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4853 | 0.751664 | ||||||||
\(482\) | 5.85786 | 0.266818 | ||||||||
\(483\) | 2.41421 | 0.109851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.414214 | 0.0187891 | ||||||||
\(487\) | 10.4853 | 0.475133 | 0.237567 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237567 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(488\) | 5.02944 | 0.227672 | ||||||||
\(489\) | −23.7990 | −1.07623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.14214 | −0.186932 | −0.0934660 | − | 0.995622i | \(-0.529795\pi\) | ||||
−0.0934660 | + | 0.995622i | \(0.529795\pi\) | |||||||
\(492\) | 16.2721 | 0.733602 | ||||||||
\(493\) | −2.82843 | −0.127386 | ||||||||
\(494\) | 4.20101 | 0.189012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.4558 | 1.14300 | ||||||||
\(497\) | 5.24264 | 0.235165 | ||||||||
\(498\) | −5.17157 | −0.231744 | ||||||||
\(499\) | 40.8284 | 1.82773 | 0.913866 | − | 0.406017i | \(-0.133082\pi\) | ||||
0.913866 | + | 0.406017i | \(0.133082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7990 | 0.795200 | ||||||||
\(502\) | −10.3431 | −0.461637 | ||||||||
\(503\) | −22.2843 | −0.993607 | −0.496803 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496803 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(504\) | −3.82843 | −0.170532 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | −0.222058 | ||||||||
\(508\) | −2.27208 | −0.100807 | ||||||||
\(509\) | −40.6274 | −1.80078 | −0.900389 | − | 0.435085i | \(-0.856718\pi\) | ||||
−0.900389 | + | 0.435085i | \(0.856718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.65685 | 0.338719 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | −3.58579 | −0.158316 | ||||||||
\(514\) | −5.51472 | −0.243244 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.627417 | −0.0276205 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −5.82843 | −0.256086 | ||||||||
\(519\) | −18.5563 | −0.814533 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.85786 | −0.344259 | −0.172130 | − | 0.985074i | \(-0.555065\pi\) | ||||
−0.172130 | + | 0.985074i | \(0.555065\pi\) | |||||||
\(522\) | −2.82843 | −0.123797 | ||||||||
\(523\) | 0.213203 | 0.00932274 | 0.00466137 | − | 0.999989i | \(-0.498516\pi\) | ||||
0.00466137 | + | 0.999989i | \(0.498516\pi\) | |||||||
\(524\) | 2.14214 | 0.0935796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.54416 | 0.198135 | ||||||||
\(527\) | 3.51472 | 0.153104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | 15.8284 | 0.686249 | ||||||||
\(533\) | 25.1716 | 1.09030 | ||||||||
\(534\) | −3.17157 | −0.137247 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.4853 | 0.798443 | ||||||||
\(537\) | −22.7990 | −0.983849 | ||||||||
\(538\) | 9.85786 | 0.425003 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3137 | 0.486414 | 0.243207 | − | 0.969974i | \(-0.421801\pi\) | ||||
0.243207 | + | 0.969974i | \(0.421801\pi\) | |||||||
\(542\) | 4.51472 | 0.193924 | ||||||||
\(543\) | 11.9706 | 0.513706 | ||||||||
\(544\) | 1.82843 | 0.0783932 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.82843 | −0.121046 | ||||||||
\(547\) | 17.8701 | 0.764068 | 0.382034 | − | 0.924148i | \(-0.375224\pi\) | ||||
0.382034 | + | 0.924148i | \(0.375224\pi\) | |||||||
\(548\) | −29.5147 | −1.26081 | ||||||||
\(549\) | −3.17157 | −0.135359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.4853 | 1.04311 | ||||||||
\(552\) | −1.58579 | −0.0674956 | ||||||||
\(553\) | −11.4853 | −0.488404 | ||||||||
\(554\) | 0.343146 | 0.0145789 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.3726 | 1.16086 | ||||||||
\(557\) | 10.8284 | 0.458815 | 0.229408 | − | 0.973330i | \(-0.426321\pi\) | ||||
0.229408 | + | 0.973330i | \(0.426321\pi\) | |||||||
\(558\) | 3.51472 | 0.148790 | ||||||||
\(559\) | −0.970563 | −0.0410504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.42641 | −0.313264 | ||||||||
\(563\) | 7.31371 | 0.308236 | 0.154118 | − | 0.988052i | \(-0.450746\pi\) | ||||
0.154118 | + | 0.988052i | \(0.450746\pi\) | |||||||
\(564\) | −17.3431 | −0.730278 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.82843 | −0.329053 | ||||||||
\(567\) | 2.41421 | 0.101387 | ||||||||
\(568\) | −3.44365 | −0.144492 | ||||||||
\(569\) | −6.75736 | −0.283283 | −0.141642 | − | 0.989918i | \(-0.545238\pi\) | ||||
−0.141642 | + | 0.989918i | \(0.545238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.9706 | 1.79826 | 0.899131 | − | 0.437680i | \(-0.144200\pi\) | ||||
0.899131 | + | 0.437680i | \(0.144200\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.8284 | 0.494140 | ||||||||
\(574\) | −8.89949 | −0.371458 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | −9.97056 | −0.415080 | −0.207540 | − | 0.978227i | \(-0.566546\pi\) | ||||
−0.207540 | + | 0.978227i | \(0.566546\pi\) | |||||||
\(578\) | −6.97056 | −0.289937 | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.1421 | −1.25051 | ||||||||
\(582\) | 0.0710678 | 0.00294586 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.02944 | −0.208120 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.45584 | −0.349308 | ||||||||
\(587\) | −25.3431 | −1.04602 | −0.523012 | − | 0.852325i | \(-0.675192\pi\) | ||||
−0.523012 | + | 0.852325i | \(0.675192\pi\) | |||||||
\(588\) | 2.14214 | 0.0883402 | ||||||||
\(589\) | −30.4264 | −1.25370 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2426 | −0.544729 | ||||||||
\(592\) | −17.4853 | −0.718641 | ||||||||
\(593\) | 35.7990 | 1.47009 | 0.735044 | − | 0.678019i | \(-0.237161\pi\) | ||||
0.735044 | + | 0.678019i | \(0.237161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.4142 | −1.32774 | ||||||||
\(597\) | 5.17157 | 0.211658 | ||||||||
\(598\) | −1.17157 | −0.0479092 | ||||||||
\(599\) | 13.6863 | 0.559207 | 0.279603 | − | 0.960116i | \(-0.409797\pi\) | ||||
0.279603 | + | 0.960116i | \(0.409797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.17157 | 0.374116 | 0.187058 | − | 0.982349i | \(-0.440105\pi\) | ||||
0.187058 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(602\) | 0.343146 | 0.0139856 | ||||||||
\(603\) | −11.6569 | −0.474704 | ||||||||
\(604\) | 25.5980 | 1.04157 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.02944 | 0.0824403 | ||||||||
\(607\) | −30.9706 | −1.25706 | −0.628528 | − | 0.777787i | \(-0.716342\pi\) | ||||
−0.628528 | + | 0.777787i | \(0.716342\pi\) | |||||||
\(608\) | −15.8284 | −0.641927 | ||||||||
\(609\) | −16.4853 | −0.668017 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.8284 | −1.08536 | ||||||||
\(612\) | −0.757359 | −0.0306144 | ||||||||
\(613\) | 42.0000 | 1.69636 | 0.848182 | − | 0.529705i | \(-0.177697\pi\) | ||||
0.848182 | + | 0.529705i | \(0.177697\pi\) | |||||||
\(614\) | −12.1421 | −0.490017 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.1421 | −1.53554 | −0.767772 | − | 0.640723i | \(-0.778635\pi\) | ||||
−0.767772 | + | 0.640723i | \(0.778635\pi\) | |||||||
\(618\) | −0.970563 | −0.0390418 | ||||||||
\(619\) | −6.62742 | −0.266378 | −0.133189 | − | 0.991091i | \(-0.542522\pi\) | ||||
−0.133189 | + | 0.991091i | \(0.542522\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0.970563 | 0.0389160 | ||||||||
\(623\) | −18.4853 | −0.740597 | ||||||||
\(624\) | −8.48528 | −0.339683 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.473088 | 0.0189084 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.9706 | −0.437773 | ||||||||
\(629\) | −2.41421 | −0.0962610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6274 | −0.741546 | −0.370773 | − | 0.928724i | \(-0.620907\pi\) | ||||
−0.370773 | + | 0.928724i | \(0.620907\pi\) | |||||||
\(632\) | 7.54416 | 0.300090 | ||||||||
\(633\) | −9.31371 | −0.370187 | ||||||||
\(634\) | 10.4264 | 0.414086 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.68629 | 0.265129 | ||||||||
\(637\) | 3.31371 | 0.131294 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.17157 | 0.0859061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.5147 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668097\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668097\pi\) | |||||||
\(642\) | −7.17157 | −0.283039 | ||||||||
\(643\) | 0.970563 | 0.0382753 | 0.0191376 | − | 0.999817i | \(-0.493908\pi\) | ||||
0.0191376 | + | 0.999817i | \(0.493908\pi\) | |||||||
\(644\) | −4.41421 | −0.173944 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.615224 | −0.0242057 | ||||||||
\(647\) | 28.6569 | 1.12662 | 0.563309 | − | 0.826247i | \(-0.309528\pi\) | ||||
0.563309 | + | 0.826247i | \(0.309528\pi\) | |||||||
\(648\) | −1.58579 | −0.0622956 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.4853 | 0.802881 | ||||||||
\(652\) | 43.5147 | 1.70417 | ||||||||
\(653\) | −23.5147 | −0.920202 | −0.460101 | − | 0.887867i | \(-0.652187\pi\) | ||||
−0.460101 | + | 0.887867i | \(0.652187\pi\) | |||||||
\(654\) | 7.17157 | 0.280431 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −26.6985 | −1.04240 | ||||||||
\(657\) | 3.17157 | 0.123735 | ||||||||
\(658\) | 9.48528 | 0.369775 | ||||||||
\(659\) | 47.1127 | 1.83525 | 0.917625 | − | 0.397447i | \(-0.130104\pi\) | ||||
0.917625 | + | 0.397447i | \(0.130104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3431 | −0.907943 | −0.453972 | − | 0.891016i | \(-0.649993\pi\) | ||||
−0.453972 | + | 0.891016i | \(0.649993\pi\) | |||||||
\(662\) | −1.59798 | −0.0621072 | ||||||||
\(663\) | −1.17157 | −0.0455001 | ||||||||
\(664\) | 19.7990 | 0.768350 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.41421 | −0.0935489 | ||||||||
\(667\) | −6.82843 | −0.264398 | ||||||||
\(668\) | −32.5442 | −1.25917 | ||||||||
\(669\) | −26.8284 | −1.03725 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.6569 | 0.411097 | ||||||||
\(673\) | −0.343146 | −0.0132273 | −0.00661365 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661365 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(674\) | 10.0000 | 0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.14214 | 0.351621 | ||||||||
\(677\) | −23.5147 | −0.903744 | −0.451872 | − | 0.892083i | \(-0.649244\pi\) | ||||
−0.451872 | + | 0.892083i | \(0.649244\pi\) | |||||||
\(678\) | −4.14214 | −0.159078 | ||||||||
\(679\) | 0.414214 | 0.0158961 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.51472 | 0.0580441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.5147 | 0.478862 | 0.239431 | − | 0.970913i | \(-0.423039\pi\) | ||||
0.239431 | + | 0.970913i | \(0.423039\pi\) | |||||||
\(684\) | 6.55635 | 0.250688 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.17157 | −0.311992 | ||||||||
\(687\) | −19.4853 | −0.743410 | ||||||||
\(688\) | 1.02944 | 0.0392469 | ||||||||
\(689\) | 10.3431 | 0.394042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.4558 | −1.34880 | −0.674402 | − | 0.738364i | \(-0.735598\pi\) | ||||
−0.674402 | + | 0.738364i | \(0.735598\pi\) | |||||||
\(692\) | 33.9289 | 1.28978 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.1127 | 0.421832 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.8284 | 0.410450 | ||||||||
\(697\) | −3.68629 | −0.139628 | ||||||||
\(698\) | −6.00000 | −0.227103 | ||||||||
\(699\) | 14.5563 | 0.550572 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.3848 | 1.56308 | 0.781541 | − | 0.623854i | \(-0.214434\pi\) | ||||
0.781541 | + | 0.623854i | \(0.214434\pi\) | |||||||
\(702\) | −1.17157 | −0.0442182 | ||||||||
\(703\) | 20.8995 | 0.788239 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.17157 | 0.194635 | ||||||||
\(707\) | 11.8284 | 0.444854 | ||||||||
\(708\) | −20.1127 | −0.755881 | ||||||||
\(709\) | −29.1421 | −1.09446 | −0.547228 | − | 0.836984i | \(-0.684317\pi\) | ||||
−0.547228 | + | 0.836984i | \(0.684317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.75736 | −0.178415 | ||||||||
\(712\) | 12.1421 | 0.455046 | ||||||||
\(713\) | 8.48528 | 0.317776 | ||||||||
\(714\) | 0.414214 | 0.0155016 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 41.6863 | 1.55789 | ||||||||
\(717\) | −12.3431 | −0.460963 | ||||||||
\(718\) | −13.4558 | −0.502168 | ||||||||
\(719\) | 9.65685 | 0.360140 | 0.180070 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180070 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.65685 | −0.210672 | ||||||||
\(722\) | −2.54416 | −0.0946837 | ||||||||
\(723\) | 14.1421 | 0.525952 | ||||||||
\(724\) | −21.8873 | −0.813435 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9706 | 0.629403 | 0.314702 | − | 0.949191i | \(-0.398096\pi\) | ||||
0.314702 | + | 0.949191i | \(0.398096\pi\) | |||||||
\(728\) | 10.8284 | 0.401328 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.142136 | 0.00525708 | ||||||||
\(732\) | 5.79899 | 0.214337 | ||||||||
\(733\) | −32.1421 | −1.18720 | −0.593598 | − | 0.804761i | \(-0.702293\pi\) | ||||
−0.593598 | + | 0.804761i | \(0.702293\pi\) | |||||||
\(734\) | −8.82843 | −0.325863 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.41421 | 0.162710 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.68629 | −0.135694 | ||||||||
\(739\) | −20.4142 | −0.750949 | −0.375474 | − | 0.926833i | \(-0.622520\pi\) | ||||
−0.375474 | + | 0.926833i | \(0.622520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1421 | 0.372581 | ||||||||
\(742\) | −3.65685 | −0.134247 | ||||||||
\(743\) | 31.1127 | 1.14141 | 0.570707 | − | 0.821154i | \(-0.306669\pi\) | ||||
0.570707 | + | 0.821154i | \(0.306669\pi\) | |||||||
\(744\) | −13.4558 | −0.493315 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.11270 | 0.187189 | ||||||||
\(747\) | −12.4853 | −0.456813 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.7990 | −1.52730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5980 | 1.15303 | 0.576513 | − | 0.817088i | \(-0.304413\pi\) | ||||
0.576513 | + | 0.817088i | \(0.304413\pi\) | |||||||
\(752\) | 28.4558 | 1.03768 | ||||||||
\(753\) | −24.9706 | −0.909978 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.41421 | −0.160543 | ||||||||
\(757\) | −10.6863 | −0.388400 | −0.194200 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194200 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(758\) | 6.14214 | 0.223092 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.17157 | 0.187469 | 0.0937347 | − | 0.995597i | \(-0.470119\pi\) | ||||
0.0937347 | + | 0.995597i | \(0.470119\pi\) | |||||||
\(762\) | 0.514719 | 0.0186463 | ||||||||
\(763\) | 41.7990 | 1.51323 | ||||||||
\(764\) | −21.6274 | −0.782452 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.28427 | 0.299323 | ||||||||
\(767\) | −31.1127 | −1.12341 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | 7.65685 | 0.276113 | 0.138057 | − | 0.990424i | \(-0.455914\pi\) | ||||
0.138057 | + | 0.990424i | \(0.455914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3137 | −0.479481 | ||||||||
\(772\) | −35.3137 | −1.27097 | ||||||||
\(773\) | −0.828427 | −0.0297965 | −0.0148982 | − | 0.999889i | \(-0.504742\pi\) | ||||
−0.0148982 | + | 0.999889i | \(0.504742\pi\) | |||||||
\(774\) | 0.142136 | 0.00510896 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.272078 | −0.00976703 | ||||||||
\(777\) | −14.0711 | −0.504797 | ||||||||
\(778\) | −2.62742 | −0.0941975 | ||||||||
\(779\) | 31.9117 | 1.14335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.171573 | 0.00613543 | ||||||||
\(783\) | −6.82843 | −0.244028 | ||||||||
\(784\) | −3.51472 | −0.125526 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.485281 | −0.0173094 | ||||||||
\(787\) | 7.92893 | 0.282636 | 0.141318 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141318 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(788\) | 24.2132 | 0.862560 | ||||||||
\(789\) | 10.9706 | 0.390562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.1421 | −0.858396 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.97056 | 0.318554 | ||||||||
\(794\) | 13.2304 | 0.469531 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.45584 | −0.335154 | ||||||||
\(797\) | 40.9706 | 1.45125 | 0.725626 | − | 0.688089i | \(-0.241550\pi\) | ||||
0.725626 | + | 0.688089i | \(0.241550\pi\) | |||||||
\(798\) | −3.58579 | −0.126935 | ||||||||
\(799\) | 3.92893 | 0.138996 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | −3.23045 | −0.114071 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.3137 | 0.751677 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.94113 | −0.350161 | ||||||||
\(807\) | 23.7990 | 0.837764 | ||||||||
\(808\) | −7.76955 | −0.273332 | ||||||||
\(809\) | −7.72792 | −0.271699 | −0.135850 | − | 0.990729i | \(-0.543376\pi\) | ||||
−0.135850 | + | 0.990729i | \(0.543376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.2132 | −0.358634 | −0.179317 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179317 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(812\) | 30.1421 | 1.05778 | ||||||||
\(813\) | 10.8995 | 0.382262 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.24264 | 0.0435011 | ||||||||
\(817\) | −1.23045 | −0.0430479 | ||||||||
\(818\) | −10.0000 | −0.349642 | ||||||||
\(819\) | −6.82843 | −0.238605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7990 | −0.551389 | −0.275694 | − | 0.961245i | \(-0.588908\pi\) | ||||
−0.275694 | + | 0.961245i | \(0.588908\pi\) | |||||||
\(822\) | 6.68629 | 0.233211 | ||||||||
\(823\) | −14.9706 | −0.521841 | −0.260921 | − | 0.965360i | \(-0.584026\pi\) | ||||
−0.260921 | + | 0.965360i | \(0.584026\pi\) | |||||||
\(824\) | 3.71573 | 0.129444 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.0000 | 0.382739 | ||||||||
\(827\) | 12.6863 | 0.441146 | 0.220573 | − | 0.975371i | \(-0.429207\pi\) | ||||
0.220573 | + | 0.975371i | \(0.429207\pi\) | |||||||
\(828\) | −1.82843 | −0.0635422 | ||||||||
\(829\) | −47.9411 | −1.66506 | −0.832532 | − | 0.553977i | \(-0.813110\pi\) | ||||
−0.832532 | + | 0.553977i | \(0.813110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.828427 | 0.0287378 | ||||||||
\(832\) | 11.7990 | 0.409056 | ||||||||
\(833\) | −0.485281 | −0.0168140 | ||||||||
\(834\) | −6.20101 | −0.214723 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.48528 | 0.293294 | ||||||||
\(838\) | −3.52691 | −0.121835 | ||||||||
\(839\) | −47.3137 | −1.63345 | −0.816725 | − | 0.577027i | \(-0.804213\pi\) | ||||
−0.816725 | + | 0.577027i | \(0.804213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −11.1838 | −0.385418 | ||||||||
\(843\) | −17.9289 | −0.617505 | ||||||||
\(844\) | 17.0294 | 0.586177 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.92893 | 0.135079 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.9706 | −0.376731 | ||||||||
\(849\) | −18.8995 | −0.648629 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.82843 | −0.199796 | ||||||||
\(852\) | −3.97056 | −0.136029 | ||||||||
\(853\) | 19.1716 | 0.656422 | 0.328211 | − | 0.944604i | \(-0.393554\pi\) | ||||
0.328211 | + | 0.944604i | \(0.393554\pi\) | |||||||
\(854\) | −3.17157 | −0.108529 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.4558 | 0.938421 | ||||||||
\(857\) | 36.6985 | 1.25360 | 0.626798 | − | 0.779182i | \(-0.284365\pi\) | ||||
0.626798 | + | 0.779182i | \(0.284365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4853 | −0.698949 | −0.349474 | − | 0.936946i | \(-0.613640\pi\) | ||||
−0.349474 | + | 0.936946i | \(0.613640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.4853 | −0.732216 | ||||||||
\(862\) | −2.82843 | −0.0963366 | ||||||||
\(863\) | −28.6863 | −0.976493 | −0.488246 | − | 0.872706i | \(-0.662363\pi\) | ||||
−0.488246 | + | 0.872706i | \(0.662363\pi\) | |||||||
\(864\) | 4.41421 | 0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.85786 | 0.131096 | ||||||||
\(867\) | −16.8284 | −0.571523 | ||||||||
\(868\) | −37.4558 | −1.27133 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.9706 | 1.11716 | ||||||||
\(872\) | −27.4558 | −0.929772 | ||||||||
\(873\) | 0.171573 | 0.00580686 | ||||||||
\(874\) | −1.48528 | −0.0502404 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.79899 | −0.195930 | ||||||||
\(877\) | −15.1127 | −0.510320 | −0.255160 | − | 0.966899i | \(-0.582128\pi\) | ||||
−0.255160 | + | 0.966899i | \(0.582128\pi\) | |||||||
\(878\) | −11.4853 | −0.387609 | ||||||||
\(879\) | −20.4142 | −0.688554 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | −0.485281 | −0.0163403 | ||||||||
\(883\) | 38.6274 | 1.29992 | 0.649958 | − | 0.759970i | \(-0.274786\pi\) | ||||
0.649958 | + | 0.759970i | \(0.274786\pi\) | |||||||
\(884\) | 2.14214 | 0.0720478 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.7574 | 0.361401 | ||||||||
\(887\) | 22.1421 | 0.743460 | 0.371730 | − | 0.928341i | \(-0.378765\pi\) | ||||
0.371730 | + | 0.928341i | \(0.378765\pi\) | |||||||
\(888\) | 9.24264 | 0.310163 | ||||||||
\(889\) | 3.00000 | 0.100617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 49.0538 | 1.64244 | ||||||||
\(893\) | −34.0122 | −1.13817 | ||||||||
\(894\) | 7.34315 | 0.245592 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.4853 | −0.851403 | ||||||||
\(897\) | −2.82843 | −0.0944384 | ||||||||
\(898\) | 4.34315 | 0.144933 | ||||||||
\(899\) | −57.9411 | −1.93244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51472 | −0.0504626 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.828427 | 0.0275683 | ||||||||
\(904\) | 15.8579 | 0.527425 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.79899 | −0.192659 | ||||||||
\(907\) | −2.48528 | −0.0825224 | −0.0412612 | − | 0.999148i | \(-0.513138\pi\) | ||||
−0.0412612 | + | 0.999148i | \(0.513138\pi\) | |||||||
\(908\) | −2.76955 | −0.0919108 | ||||||||
\(909\) | 4.89949 | 0.162506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5147 | 0.944735 | 0.472367 | − | 0.881402i | \(-0.343400\pi\) | ||||
0.472367 | + | 0.881402i | \(0.343400\pi\) | |||||||
\(912\) | −10.7574 | −0.356212 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −13.3137 | −0.440378 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 35.6274 | 1.17716 | ||||||||
\(917\) | −2.82843 | −0.0934029 | ||||||||
\(918\) | 0.171573 | 0.00566275 | ||||||||
\(919\) | −1.78680 | −0.0589410 | −0.0294705 | − | 0.999566i | \(-0.509382\pi\) | ||||
−0.0294705 | + | 0.999566i | \(0.509382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.3137 | −0.965920 | ||||||||
\(922\) | −16.8873 | −0.556154 | ||||||||
\(923\) | −6.14214 | −0.202171 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.426407 | 0.0140126 | ||||||||
\(927\) | −2.34315 | −0.0769590 | ||||||||
\(928\) | −30.1421 | −0.989464 | ||||||||
\(929\) | −13.7990 | −0.452730 | −0.226365 | − | 0.974043i | \(-0.572684\pi\) | ||||
−0.226365 | + | 0.974043i | \(0.572684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.20101 | 0.137683 | ||||||||
\(932\) | −26.6152 | −0.871811 | ||||||||
\(933\) | 2.34315 | 0.0767111 | ||||||||
\(934\) | −14.3431 | −0.469322 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.48528 | 0.146606 | ||||||||
\(937\) | 16.0000 | 0.522697 | 0.261349 | − | 0.965244i | \(-0.415833\pi\) | ||||
0.261349 | + | 0.965244i | \(0.415833\pi\) | |||||||
\(938\) | −11.6569 | −0.380610 | ||||||||
\(939\) | 1.14214 | 0.0372722 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.8995 | 0.746502 | 0.373251 | − | 0.927730i | \(-0.378243\pi\) | ||||
0.373251 | + | 0.927730i | \(0.378243\pi\) | |||||||
\(942\) | 2.48528 | 0.0809748 | ||||||||
\(943\) | −8.89949 | −0.289807 | ||||||||
\(944\) | 33.0000 | 1.07406 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7990 | −1.19581 | −0.597903 | − | 0.801568i | \(-0.703999\pi\) | ||||
−0.597903 | + | 0.801568i | \(0.703999\pi\) | |||||||
\(948\) | 8.69848 | 0.282514 | ||||||||
\(949\) | −8.97056 | −0.291197 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.1716 | 0.816244 | ||||||||
\(952\) | −1.58579 | −0.0513956 | ||||||||
\(953\) | 29.0416 | 0.940751 | 0.470375 | − | 0.882466i | \(-0.344119\pi\) | ||||
0.470375 | + | 0.882466i | \(0.344119\pi\) | |||||||
\(954\) | −1.51472 | −0.0490408 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.5685 | 0.729919 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.11270 | 0.100567 | ||||||||
\(959\) | 38.9706 | 1.25843 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 6.82843 | 0.220157 | ||||||||
\(963\) | −17.3137 | −0.557926 | ||||||||
\(964\) | −25.8579 | −0.832826 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | −38.0000 | −1.22200 | −0.610999 | − | 0.791632i | \(-0.709232\pi\) | ||||
−0.610999 | + | 0.791632i | \(0.709232\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.48528 | −0.0477141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.3137 | −1.61464 | −0.807322 | − | 0.590111i | \(-0.799084\pi\) | ||||
−0.807322 | + | 0.590111i | \(0.799084\pi\) | |||||||
\(972\) | −1.82843 | −0.0586468 | ||||||||
\(973\) | −36.1421 | −1.15866 | ||||||||
\(974\) | 4.34315 | 0.139163 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.51472 | −0.304559 | ||||||||
\(977\) | 60.5685 | 1.93776 | 0.968880 | − | 0.247532i | \(-0.0796196\pi\) | ||||
0.968880 | + | 0.247532i | \(0.0796196\pi\) | |||||||
\(978\) | −9.85786 | −0.315220 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3137 | 0.552784 | ||||||||
\(982\) | −1.71573 | −0.0547511 | ||||||||
\(983\) | 51.2843 | 1.63571 | 0.817857 | − | 0.575421i | \(-0.195162\pi\) | ||||
0.817857 | + | 0.575421i | \(0.195162\pi\) | |||||||
\(984\) | 14.1127 | 0.449896 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.17157 | −0.0373105 | ||||||||
\(987\) | 22.8995 | 0.728899 | ||||||||
\(988\) | −18.5442 | −0.589968 | ||||||||
\(989\) | 0.343146 | 0.0109114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.2843 | −1.34320 | −0.671602 | − | 0.740912i | \(-0.734394\pi\) | ||||
−0.671602 | + | 0.740912i | \(0.734394\pi\) | |||||||
\(992\) | 37.4558 | 1.18922 | ||||||||
\(993\) | −3.85786 | −0.122426 | ||||||||
\(994\) | 2.17157 | 0.0688781 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.8284 | 0.723346 | ||||||||
\(997\) | 47.2548 | 1.49658 | 0.748288 | − | 0.663374i | \(-0.230876\pi\) | ||||
0.748288 | + | 0.663374i | \(0.230876\pi\) | |||||||
\(998\) | 16.9117 | 0.535330 | ||||||||
\(999\) | −5.82843 | −0.184403 |
(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 | 9075.2.a.w.1.2 | 2 | ||
5.4 | even | 2 | 9075.2.a.ca.1.1 | 2 | |||
11.10 | odd | 2 | 825.2.a.f.1.1 | yes | 2 | ||
33.32 | even | 2 | 2475.2.a.l.1.2 | 2 | |||
55.32 | even | 4 | 825.2.c.d.199.2 | 4 | |||
55.43 | even | 4 | 825.2.c.d.199.3 | 4 | |||
55.54 | odd | 2 | 825.2.a.d.1.2 | ✓ | 2 | ||
165.32 | odd | 4 | 2475.2.c.o.199.3 | 4 | |||
165.98 | odd | 4 | 2475.2.c.o.199.2 | 4 | |||
165.164 | even | 2 | 2475.2.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.d.1.2 | ✓ | 2 | 55.54 | odd | 2 | ||
825.2.a.f.1.1 | yes | 2 | 11.10 | odd | 2 | ||
825.2.c.d.199.2 | 4 | 55.32 | even | 4 | |||
825.2.c.d.199.3 | 4 | 55.43 | even | 4 | |||
2475.2.a.l.1.2 | 2 | 33.32 | even | 2 | |||
2475.2.a.w.1.1 | 2 | 165.164 | even | 2 | |||
2475.2.c.o.199.2 | 4 | 165.98 | odd | 4 | |||
2475.2.c.o.199.3 | 4 | 165.32 | odd | 4 | |||
9075.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9075.2.a.ca.1.1 | 2 | 5.4 | even | 2 |