Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80194 | 1.27416 | 0.637081 | − | 0.770797i | \(-0.280142\pi\) | ||||
0.637081 | + | 0.770797i | \(0.280142\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | 1.44504 | 0.646242 | 0.323121 | − | 0.946358i | \(-0.395268\pi\) | ||||
0.323121 | + | 0.946358i | \(0.395268\pi\) | |||||||
\(6\) | 1.80194 | 0.735638 | ||||||||
\(7\) | 3.44504 | 1.30210 | 0.651052 | − | 0.759033i | \(-0.274328\pi\) | ||||
0.651052 | + | 0.759033i | \(0.274328\pi\) | |||||||
\(8\) | −1.35690 | −0.479735 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.60388 | 0.823418 | ||||||||
\(11\) | −5.18598 | −1.56363 | −0.781816 | − | 0.623509i | \(-0.785706\pi\) | ||||
−0.781816 | + | 0.623509i | \(0.785706\pi\) | |||||||
\(12\) | 1.24698 | 0.359972 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.20775 | 1.65909 | ||||||||
\(15\) | 1.44504 | 0.373108 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | −0.753020 | −0.182634 | −0.0913171 | − | 0.995822i | \(-0.529108\pi\) | ||||
−0.0913171 | + | 0.995822i | \(0.529108\pi\) | |||||||
\(18\) | 1.80194 | 0.424721 | ||||||||
\(19\) | 7.96077 | 1.82633 | 0.913163 | − | 0.407594i | \(-0.133632\pi\) | ||||
0.913163 | + | 0.407594i | \(0.133632\pi\) | |||||||
\(20\) | 1.80194 | 0.402926 | ||||||||
\(21\) | 3.44504 | 0.751770 | ||||||||
\(22\) | −9.34481 | −1.99232 | ||||||||
\(23\) | −2.82908 | −0.589905 | −0.294952 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294952 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(24\) | −1.35690 | −0.276975 | ||||||||
\(25\) | −2.91185 | −0.582371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.29590 | 0.811848 | ||||||||
\(29\) | −3.91185 | −0.726413 | −0.363207 | − | 0.931709i | \(-0.618318\pi\) | ||||
−0.363207 | + | 0.931709i | \(0.618318\pi\) | |||||||
\(30\) | 2.60388 | 0.475400 | ||||||||
\(31\) | −4.89977 | −0.880025 | −0.440013 | − | 0.897992i | \(-0.645026\pi\) | ||||
−0.440013 | + | 0.897992i | \(0.645026\pi\) | |||||||
\(32\) | −6.18598 | −1.09354 | ||||||||
\(33\) | −5.18598 | −0.902763 | ||||||||
\(34\) | −1.35690 | −0.232706 | ||||||||
\(35\) | 4.97823 | 0.841474 | ||||||||
\(36\) | 1.24698 | 0.207830 | ||||||||
\(37\) | 6.24698 | 1.02700 | 0.513499 | − | 0.858090i | \(-0.328349\pi\) | ||||
0.513499 | + | 0.858090i | \(0.328349\pi\) | |||||||
\(38\) | 14.3448 | 2.32704 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.96077 | −0.310025 | ||||||||
\(41\) | 1.80194 | 0.281415 | 0.140708 | − | 0.990051i | \(-0.455062\pi\) | ||||
0.140708 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(42\) | 6.20775 | 0.957877 | ||||||||
\(43\) | −7.09783 | −1.08241 | −0.541205 | − | 0.840891i | \(-0.682032\pi\) | ||||
−0.541205 | + | 0.840891i | \(0.682032\pi\) | |||||||
\(44\) | −6.46681 | −0.974909 | ||||||||
\(45\) | 1.44504 | 0.215414 | ||||||||
\(46\) | −5.09783 | −0.751635 | ||||||||
\(47\) | 10.5526 | 1.53925 | 0.769625 | − | 0.638496i | \(-0.220443\pi\) | ||||
0.769625 | + | 0.638496i | \(0.220443\pi\) | |||||||
\(48\) | −4.93900 | −0.712883 | ||||||||
\(49\) | 4.86831 | 0.695473 | ||||||||
\(50\) | −5.24698 | −0.742035 | ||||||||
\(51\) | −0.753020 | −0.105444 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.08815 | −0.424189 | −0.212095 | − | 0.977249i | \(-0.568029\pi\) | ||||
−0.212095 | + | 0.977249i | \(0.568029\pi\) | |||||||
\(54\) | 1.80194 | 0.245213 | ||||||||
\(55\) | −7.49396 | −1.01049 | ||||||||
\(56\) | −4.67456 | −0.624665 | ||||||||
\(57\) | 7.96077 | 1.05443 | ||||||||
\(58\) | −7.04892 | −0.925568 | ||||||||
\(59\) | 1.87800 | 0.244495 | 0.122248 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122248 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(60\) | 1.80194 | 0.232629 | ||||||||
\(61\) | 3.34481 | 0.428260 | 0.214130 | − | 0.976805i | \(-0.431308\pi\) | ||||
0.214130 | + | 0.976805i | \(0.431308\pi\) | |||||||
\(62\) | −8.82908 | −1.12129 | ||||||||
\(63\) | 3.44504 | 0.434034 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.34481 | −1.15027 | ||||||||
\(67\) | −4.54288 | −0.555001 | −0.277500 | − | 0.960726i | \(-0.589506\pi\) | ||||
−0.277500 | + | 0.960726i | \(0.589506\pi\) | |||||||
\(68\) | −0.939001 | −0.113871 | ||||||||
\(69\) | −2.82908 | −0.340582 | ||||||||
\(70\) | 8.97046 | 1.07218 | ||||||||
\(71\) | −9.11960 | −1.08230 | −0.541149 | − | 0.840927i | \(-0.682011\pi\) | ||||
−0.541149 | + | 0.840927i | \(0.682011\pi\) | |||||||
\(72\) | −1.35690 | −0.159912 | ||||||||
\(73\) | 2.95108 | 0.345398 | 0.172699 | − | 0.984975i | \(-0.444751\pi\) | ||||
0.172699 | + | 0.984975i | \(0.444751\pi\) | |||||||
\(74\) | 11.2567 | 1.30856 | ||||||||
\(75\) | −2.91185 | −0.336232 | ||||||||
\(76\) | 9.92692 | 1.13870 | ||||||||
\(77\) | −17.8659 | −2.03601 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.43296 | −1.06129 | −0.530645 | − | 0.847594i | \(-0.678050\pi\) | ||||
−0.530645 | + | 0.847594i | \(0.678050\pi\) | |||||||
\(80\) | −7.13706 | −0.797948 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.24698 | 0.358569 | ||||||||
\(83\) | −6.46681 | −0.709825 | −0.354912 | − | 0.934900i | \(-0.615489\pi\) | ||||
−0.354912 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(84\) | 4.29590 | 0.468721 | ||||||||
\(85\) | −1.08815 | −0.118026 | ||||||||
\(86\) | −12.7899 | −1.37917 | ||||||||
\(87\) | −3.91185 | −0.419395 | ||||||||
\(88\) | 7.03684 | 0.750129 | ||||||||
\(89\) | 1.15883 | 0.122836 | 0.0614181 | − | 0.998112i | \(-0.480438\pi\) | ||||
0.0614181 | + | 0.998112i | \(0.480438\pi\) | |||||||
\(90\) | 2.60388 | 0.274473 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.52781 | −0.367800 | ||||||||
\(93\) | −4.89977 | −0.508083 | ||||||||
\(94\) | 19.0151 | 1.96125 | ||||||||
\(95\) | 11.5036 | 1.18025 | ||||||||
\(96\) | −6.18598 | −0.631354 | ||||||||
\(97\) | 8.65817 | 0.879104 | 0.439552 | − | 0.898217i | \(-0.355137\pi\) | ||||
0.439552 | + | 0.898217i | \(0.355137\pi\) | |||||||
\(98\) | 8.77240 | 0.886146 | ||||||||
\(99\) | −5.18598 | −0.521211 | ||||||||
\(100\) | −3.63102 | −0.363102 | ||||||||
\(101\) | −8.47650 | −0.843443 | −0.421722 | − | 0.906725i | \(-0.638574\pi\) | ||||
−0.421722 | + | 0.906725i | \(0.638574\pi\) | |||||||
\(102\) | −1.35690 | −0.134353 | ||||||||
\(103\) | 5.64742 | 0.556456 | 0.278228 | − | 0.960515i | \(-0.410253\pi\) | ||||
0.278228 | + | 0.960515i | \(0.410253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.97823 | 0.485825 | ||||||||
\(106\) | −5.56465 | −0.540486 | ||||||||
\(107\) | −6.73556 | −0.651151 | −0.325576 | − | 0.945516i | \(-0.605558\pi\) | ||||
−0.325576 | + | 0.945516i | \(0.605558\pi\) | |||||||
\(108\) | 1.24698 | 0.119991 | ||||||||
\(109\) | −2.07606 | −0.198851 | −0.0994255 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994255 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(110\) | −13.5036 | −1.28752 | ||||||||
\(111\) | 6.24698 | 0.592937 | ||||||||
\(112\) | −17.0151 | −1.60777 | ||||||||
\(113\) | 6.16852 | 0.580286 | 0.290143 | − | 0.956983i | \(-0.406297\pi\) | ||||
0.290143 | + | 0.956983i | \(0.406297\pi\) | |||||||
\(114\) | 14.3448 | 1.34351 | ||||||||
\(115\) | −4.08815 | −0.381222 | ||||||||
\(116\) | −4.87800 | −0.452911 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.38404 | 0.311526 | ||||||||
\(119\) | −2.59419 | −0.237809 | ||||||||
\(120\) | −1.96077 | −0.178993 | ||||||||
\(121\) | 15.8944 | 1.44495 | ||||||||
\(122\) | 6.02715 | 0.545672 | ||||||||
\(123\) | 1.80194 | 0.162475 | ||||||||
\(124\) | −6.10992 | −0.548687 | ||||||||
\(125\) | −11.4330 | −1.02260 | ||||||||
\(126\) | 6.20775 | 0.553030 | ||||||||
\(127\) | −14.2620 | −1.26555 | −0.632776 | − | 0.774335i | \(-0.718085\pi\) | ||||
−0.632776 | + | 0.774335i | \(0.718085\pi\) | |||||||
\(128\) | 10.0858 | 0.891463 | ||||||||
\(129\) | −7.09783 | −0.624929 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6015 | 1.97470 | 0.987350 | − | 0.158554i | \(-0.0506831\pi\) | ||||
0.987350 | + | 0.158554i | \(0.0506831\pi\) | |||||||
\(132\) | −6.46681 | −0.562864 | ||||||||
\(133\) | 27.4252 | 2.37807 | ||||||||
\(134\) | −8.18598 | −0.707161 | ||||||||
\(135\) | 1.44504 | 0.124369 | ||||||||
\(136\) | 1.02177 | 0.0876161 | ||||||||
\(137\) | −13.6353 | −1.16495 | −0.582473 | − | 0.812850i | \(-0.697915\pi\) | ||||
−0.582473 | + | 0.812850i | \(0.697915\pi\) | |||||||
\(138\) | −5.09783 | −0.433957 | ||||||||
\(139\) | 17.6015 | 1.49294 | 0.746469 | − | 0.665420i | \(-0.231748\pi\) | ||||
0.746469 | + | 0.665420i | \(0.231748\pi\) | |||||||
\(140\) | 6.20775 | 0.524651 | ||||||||
\(141\) | 10.5526 | 0.888686 | ||||||||
\(142\) | −16.4330 | −1.37902 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.93900 | −0.411583 | ||||||||
\(145\) | −5.65279 | −0.469439 | ||||||||
\(146\) | 5.31767 | 0.440093 | ||||||||
\(147\) | 4.86831 | 0.401532 | ||||||||
\(148\) | 7.78986 | 0.640322 | ||||||||
\(149\) | 12.7385 | 1.04358 | 0.521791 | − | 0.853073i | \(-0.325264\pi\) | ||||
0.521791 | + | 0.853073i | \(0.325264\pi\) | |||||||
\(150\) | −5.24698 | −0.428414 | ||||||||
\(151\) | 15.6407 | 1.27282 | 0.636412 | − | 0.771350i | \(-0.280418\pi\) | ||||
0.636412 | + | 0.771350i | \(0.280418\pi\) | |||||||
\(152\) | −10.8019 | −0.876153 | ||||||||
\(153\) | −0.753020 | −0.0608781 | ||||||||
\(154\) | −32.1933 | −2.59421 | ||||||||
\(155\) | −7.08038 | −0.568710 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.823708 | −0.0657391 | −0.0328695 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328695 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(158\) | −16.9976 | −1.35226 | ||||||||
\(159\) | −3.08815 | −0.244906 | ||||||||
\(160\) | −8.93900 | −0.706690 | ||||||||
\(161\) | −9.74632 | −0.768117 | ||||||||
\(162\) | 1.80194 | 0.141574 | ||||||||
\(163\) | 6.26875 | 0.491006 | 0.245503 | − | 0.969396i | \(-0.421047\pi\) | ||||
0.245503 | + | 0.969396i | \(0.421047\pi\) | |||||||
\(164\) | 2.24698 | 0.175460 | ||||||||
\(165\) | −7.49396 | −0.583404 | ||||||||
\(166\) | −11.6528 | −0.904432 | ||||||||
\(167\) | −7.45042 | −0.576531 | −0.288265 | − | 0.957551i | \(-0.593079\pi\) | ||||
−0.288265 | + | 0.957551i | \(0.593079\pi\) | |||||||
\(168\) | −4.67456 | −0.360650 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.96077 | −0.150384 | ||||||||
\(171\) | 7.96077 | 0.608775 | ||||||||
\(172\) | −8.85086 | −0.674871 | ||||||||
\(173\) | −2.00969 | −0.152794 | −0.0763969 | − | 0.997077i | \(-0.524342\pi\) | ||||
−0.0763969 | + | 0.997077i | \(0.524342\pi\) | |||||||
\(174\) | −7.04892 | −0.534377 | ||||||||
\(175\) | −10.0315 | −0.758307 | ||||||||
\(176\) | 25.6136 | 1.93070 | ||||||||
\(177\) | 1.87800 | 0.141159 | ||||||||
\(178\) | 2.08815 | 0.156513 | ||||||||
\(179\) | 20.0368 | 1.49762 | 0.748812 | − | 0.662783i | \(-0.230625\pi\) | ||||
0.748812 | + | 0.662783i | \(0.230625\pi\) | |||||||
\(180\) | 1.80194 | 0.134309 | ||||||||
\(181\) | 24.1226 | 1.79302 | 0.896509 | − | 0.443026i | \(-0.146095\pi\) | ||||
0.896509 | + | 0.443026i | \(0.146095\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.34481 | 0.247256 | ||||||||
\(184\) | 3.83877 | 0.282998 | ||||||||
\(185\) | 9.02715 | 0.663689 | ||||||||
\(186\) | −8.82908 | −0.647380 | ||||||||
\(187\) | 3.90515 | 0.285573 | ||||||||
\(188\) | 13.1588 | 0.959707 | ||||||||
\(189\) | 3.44504 | 0.250590 | ||||||||
\(190\) | 20.7289 | 1.50383 | ||||||||
\(191\) | −7.08038 | −0.512318 | −0.256159 | − | 0.966635i | \(-0.582457\pi\) | ||||
−0.256159 | + | 0.966635i | \(0.582457\pi\) | |||||||
\(192\) | −1.26875 | −0.0915641 | ||||||||
\(193\) | 9.76809 | 0.703122 | 0.351561 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351561 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(194\) | 15.6015 | 1.12012 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.07069 | 0.433621 | ||||||||
\(197\) | 23.4112 | 1.66798 | 0.833989 | − | 0.551781i | \(-0.186052\pi\) | ||||
0.833989 | + | 0.551781i | \(0.186052\pi\) | |||||||
\(198\) | −9.34481 | −0.664107 | ||||||||
\(199\) | 4.02475 | 0.285307 | 0.142654 | − | 0.989773i | \(-0.454437\pi\) | ||||
0.142654 | + | 0.989773i | \(0.454437\pi\) | |||||||
\(200\) | 3.95108 | 0.279384 | ||||||||
\(201\) | −4.54288 | −0.320430 | ||||||||
\(202\) | −15.2741 | −1.07468 | ||||||||
\(203\) | −13.4765 | −0.945865 | ||||||||
\(204\) | −0.939001 | −0.0657432 | ||||||||
\(205\) | 2.60388 | 0.181863 | ||||||||
\(206\) | 10.1763 | 0.709016 | ||||||||
\(207\) | −2.82908 | −0.196635 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.2844 | −2.85570 | ||||||||
\(210\) | 8.97046 | 0.619021 | ||||||||
\(211\) | −3.91185 | −0.269303 | −0.134652 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134652 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(212\) | −3.85086 | −0.264478 | ||||||||
\(213\) | −9.11960 | −0.624865 | ||||||||
\(214\) | −12.1371 | −0.829673 | ||||||||
\(215\) | −10.2567 | −0.699499 | ||||||||
\(216\) | −1.35690 | −0.0923251 | ||||||||
\(217\) | −16.8799 | −1.14588 | ||||||||
\(218\) | −3.74094 | −0.253368 | ||||||||
\(219\) | 2.95108 | 0.199416 | ||||||||
\(220\) | −9.34481 | −0.630027 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.2567 | 0.755498 | ||||||||
\(223\) | 7.44935 | 0.498846 | 0.249423 | − | 0.968395i | \(-0.419759\pi\) | ||||
0.249423 | + | 0.968395i | \(0.419759\pi\) | |||||||
\(224\) | −21.3110 | −1.42390 | ||||||||
\(225\) | −2.91185 | −0.194124 | ||||||||
\(226\) | 11.1153 | 0.739378 | ||||||||
\(227\) | −21.2500 | −1.41041 | −0.705205 | − | 0.709004i | \(-0.749145\pi\) | ||||
−0.705205 | + | 0.709004i | \(0.749145\pi\) | |||||||
\(228\) | 9.92692 | 0.657426 | ||||||||
\(229\) | 9.29590 | 0.614290 | 0.307145 | − | 0.951663i | \(-0.400626\pi\) | ||||
0.307145 | + | 0.951663i | \(0.400626\pi\) | |||||||
\(230\) | −7.36658 | −0.485738 | ||||||||
\(231\) | −17.8659 | −1.17549 | ||||||||
\(232\) | 5.30798 | 0.348486 | ||||||||
\(233\) | 16.2107 | 1.06200 | 0.531000 | − | 0.847372i | \(-0.321816\pi\) | ||||
0.531000 | + | 0.847372i | \(0.321816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.2489 | 0.994728 | ||||||||
\(236\) | 2.34183 | 0.152440 | ||||||||
\(237\) | −9.43296 | −0.612737 | ||||||||
\(238\) | −4.67456 | −0.303007 | ||||||||
\(239\) | −13.5090 | −0.873826 | −0.436913 | − | 0.899504i | \(-0.643928\pi\) | ||||
−0.436913 | + | 0.899504i | \(0.643928\pi\) | |||||||
\(240\) | −7.13706 | −0.460695 | ||||||||
\(241\) | 6.26875 | 0.403806 | 0.201903 | − | 0.979406i | \(-0.435287\pi\) | ||||
0.201903 | + | 0.979406i | \(0.435287\pi\) | |||||||
\(242\) | 28.6407 | 1.84109 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.17092 | 0.267015 | ||||||||
\(245\) | 7.03492 | 0.449444 | ||||||||
\(246\) | 3.24698 | 0.207020 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.64848 | 0.422179 | ||||||||
\(249\) | −6.46681 | −0.409818 | ||||||||
\(250\) | −20.6015 | −1.30295 | ||||||||
\(251\) | −0.753020 | −0.0475302 | −0.0237651 | − | 0.999718i | \(-0.507565\pi\) | ||||
−0.0237651 | + | 0.999718i | \(0.507565\pi\) | |||||||
\(252\) | 4.29590 | 0.270616 | ||||||||
\(253\) | 14.6716 | 0.922394 | ||||||||
\(254\) | −25.6993 | −1.61252 | ||||||||
\(255\) | −1.08815 | −0.0681423 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 19.7265 | 1.23050 | 0.615252 | − | 0.788331i | \(-0.289054\pi\) | ||||
0.615252 | + | 0.788331i | \(0.289054\pi\) | |||||||
\(258\) | −12.7899 | −0.796262 | ||||||||
\(259\) | 21.5211 | 1.33726 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.91185 | −0.242138 | ||||||||
\(262\) | 40.7265 | 2.51609 | ||||||||
\(263\) | −17.6093 | −1.08583 | −0.542917 | − | 0.839787i | \(-0.682680\pi\) | ||||
−0.542917 | + | 0.839787i | \(0.682680\pi\) | |||||||
\(264\) | 7.03684 | 0.433087 | ||||||||
\(265\) | −4.46250 | −0.274129 | ||||||||
\(266\) | 49.4185 | 3.03004 | ||||||||
\(267\) | 1.15883 | 0.0709195 | ||||||||
\(268\) | −5.66487 | −0.346037 | ||||||||
\(269\) | −16.3870 | −0.999135 | −0.499567 | − | 0.866275i | \(-0.666508\pi\) | ||||
−0.499567 | + | 0.866275i | \(0.666508\pi\) | |||||||
\(270\) | 2.60388 | 0.158467 | ||||||||
\(271\) | −0.795233 | −0.0483070 | −0.0241535 | − | 0.999708i | \(-0.507689\pi\) | ||||
−0.0241535 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(272\) | 3.71917 | 0.225508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.5700 | −1.48433 | ||||||||
\(275\) | 15.1008 | 0.910614 | ||||||||
\(276\) | −3.52781 | −0.212349 | ||||||||
\(277\) | −4.83340 | −0.290411 | −0.145205 | − | 0.989402i | \(-0.546384\pi\) | ||||
−0.145205 | + | 0.989402i | \(0.546384\pi\) | |||||||
\(278\) | 31.7168 | 1.90225 | ||||||||
\(279\) | −4.89977 | −0.293342 | ||||||||
\(280\) | −6.75494 | −0.403685 | ||||||||
\(281\) | 18.7748 | 1.12001 | 0.560005 | − | 0.828489i | \(-0.310799\pi\) | ||||
0.560005 | + | 0.828489i | \(0.310799\pi\) | |||||||
\(282\) | 19.0151 | 1.13233 | ||||||||
\(283\) | −7.91723 | −0.470631 | −0.235315 | − | 0.971919i | \(-0.575612\pi\) | ||||
−0.235315 | + | 0.971919i | \(0.575612\pi\) | |||||||
\(284\) | −11.3720 | −0.674802 | ||||||||
\(285\) | 11.5036 | 0.681417 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.20775 | 0.366432 | ||||||||
\(288\) | −6.18598 | −0.364512 | ||||||||
\(289\) | −16.4330 | −0.966645 | ||||||||
\(290\) | −10.1860 | −0.598141 | ||||||||
\(291\) | 8.65817 | 0.507551 | ||||||||
\(292\) | 3.67994 | 0.215352 | ||||||||
\(293\) | 6.57912 | 0.384356 | 0.192178 | − | 0.981360i | \(-0.438445\pi\) | ||||
0.192178 | + | 0.981360i | \(0.438445\pi\) | |||||||
\(294\) | 8.77240 | 0.511617 | ||||||||
\(295\) | 2.71379 | 0.158003 | ||||||||
\(296\) | −8.47650 | −0.492687 | ||||||||
\(297\) | −5.18598 | −0.300921 | ||||||||
\(298\) | 22.9541 | 1.32969 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.63102 | −0.209637 | ||||||||
\(301\) | −24.4523 | −1.40941 | ||||||||
\(302\) | 28.1836 | 1.62178 | ||||||||
\(303\) | −8.47650 | −0.486962 | ||||||||
\(304\) | −39.3183 | −2.25506 | ||||||||
\(305\) | 4.83340 | 0.276759 | ||||||||
\(306\) | −1.35690 | −0.0775686 | ||||||||
\(307\) | −24.8649 | −1.41911 | −0.709556 | − | 0.704649i | \(-0.751105\pi\) | ||||
−0.709556 | + | 0.704649i | \(0.751105\pi\) | |||||||
\(308\) | −22.2784 | −1.26943 | ||||||||
\(309\) | 5.64742 | 0.321270 | ||||||||
\(310\) | −12.7584 | −0.724628 | ||||||||
\(311\) | −17.0804 | −0.968539 | −0.484270 | − | 0.874919i | \(-0.660915\pi\) | ||||
−0.484270 | + | 0.874919i | \(0.660915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6974 | 0.887269 | 0.443635 | − | 0.896208i | \(-0.353689\pi\) | ||||
0.443635 | + | 0.896208i | \(0.353689\pi\) | |||||||
\(314\) | −1.48427 | −0.0837622 | ||||||||
\(315\) | 4.97823 | 0.280491 | ||||||||
\(316\) | −11.7627 | −0.661704 | ||||||||
\(317\) | 32.7821 | 1.84123 | 0.920613 | − | 0.390477i | \(-0.127690\pi\) | ||||
0.920613 | + | 0.390477i | \(0.127690\pi\) | |||||||
\(318\) | −5.56465 | −0.312050 | ||||||||
\(319\) | 20.2868 | 1.13584 | ||||||||
\(320\) | −1.83340 | −0.102490 | ||||||||
\(321\) | −6.73556 | −0.375942 | ||||||||
\(322\) | −17.5623 | −0.978706 | ||||||||
\(323\) | −5.99462 | −0.333550 | ||||||||
\(324\) | 1.24698 | 0.0692766 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.2959 | 0.625622 | ||||||||
\(327\) | −2.07606 | −0.114807 | ||||||||
\(328\) | −2.44504 | −0.135005 | ||||||||
\(329\) | 36.3540 | 2.00426 | ||||||||
\(330\) | −13.5036 | −0.743351 | ||||||||
\(331\) | −29.1618 | −1.60288 | −0.801439 | − | 0.598076i | \(-0.795932\pi\) | ||||
−0.801439 | + | 0.598076i | \(0.795932\pi\) | |||||||
\(332\) | −8.06398 | −0.442569 | ||||||||
\(333\) | 6.24698 | 0.342332 | ||||||||
\(334\) | −13.4252 | −0.734594 | ||||||||
\(335\) | −6.56465 | −0.358665 | ||||||||
\(336\) | −17.0151 | −0.928248 | ||||||||
\(337\) | −33.2911 | −1.81348 | −0.906741 | − | 0.421688i | \(-0.861438\pi\) | ||||
−0.906741 | + | 0.421688i | \(0.861438\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.16852 | 0.335028 | ||||||||
\(340\) | −1.35690 | −0.0735880 | ||||||||
\(341\) | 25.4101 | 1.37604 | ||||||||
\(342\) | 14.3448 | 0.775679 | ||||||||
\(343\) | −7.34375 | −0.396525 | ||||||||
\(344\) | 9.63102 | 0.519270 | ||||||||
\(345\) | −4.08815 | −0.220098 | ||||||||
\(346\) | −3.62133 | −0.194684 | ||||||||
\(347\) | −0.873690 | −0.0469022 | −0.0234511 | − | 0.999725i | \(-0.507465\pi\) | ||||
−0.0234511 | + | 0.999725i | \(0.507465\pi\) | |||||||
\(348\) | −4.87800 | −0.261488 | ||||||||
\(349\) | −3.23191 | −0.173000 | −0.0865002 | − | 0.996252i | \(-0.527568\pi\) | ||||
−0.0865002 | + | 0.996252i | \(0.527568\pi\) | |||||||
\(350\) | −18.0761 | −0.966206 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32.0804 | 1.70989 | ||||||||
\(353\) | 8.14675 | 0.433608 | 0.216804 | − | 0.976215i | \(-0.430437\pi\) | ||||
0.216804 | + | 0.976215i | \(0.430437\pi\) | |||||||
\(354\) | 3.38404 | 0.179860 | ||||||||
\(355\) | −13.1782 | −0.699427 | ||||||||
\(356\) | 1.44504 | 0.0765871 | ||||||||
\(357\) | −2.59419 | −0.137299 | ||||||||
\(358\) | 36.1051 | 1.90822 | ||||||||
\(359\) | 2.64071 | 0.139371 | 0.0696857 | − | 0.997569i | \(-0.477800\pi\) | ||||
0.0696857 | + | 0.997569i | \(0.477800\pi\) | |||||||
\(360\) | −1.96077 | −0.103342 | ||||||||
\(361\) | 44.3739 | 2.33547 | ||||||||
\(362\) | 43.4674 | 2.28460 | ||||||||
\(363\) | 15.8944 | 0.834239 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.26444 | 0.223211 | ||||||||
\(366\) | 6.02715 | 0.315044 | ||||||||
\(367\) | −2.90408 | −0.151592 | −0.0757960 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757960 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(368\) | 13.9729 | 0.728385 | ||||||||
\(369\) | 1.80194 | 0.0938051 | ||||||||
\(370\) | 16.2664 | 0.845648 | ||||||||
\(371\) | −10.6388 | −0.552339 | ||||||||
\(372\) | −6.10992 | −0.316784 | ||||||||
\(373\) | −8.39852 | −0.434859 | −0.217429 | − | 0.976076i | \(-0.569767\pi\) | ||||
−0.217429 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(374\) | 7.03684 | 0.363866 | ||||||||
\(375\) | −11.4330 | −0.590396 | ||||||||
\(376\) | −14.3187 | −0.738432 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.20775 | 0.319292 | ||||||||
\(379\) | 15.7482 | 0.808932 | 0.404466 | − | 0.914553i | \(-0.367457\pi\) | ||||
0.404466 | + | 0.914553i | \(0.367457\pi\) | |||||||
\(380\) | 14.3448 | 0.735873 | ||||||||
\(381\) | −14.2620 | −0.730667 | ||||||||
\(382\) | −12.7584 | −0.652776 | ||||||||
\(383\) | 12.7385 | 0.650909 | 0.325455 | − | 0.945558i | \(-0.394483\pi\) | ||||
0.325455 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(384\) | 10.0858 | 0.514686 | ||||||||
\(385\) | −25.8170 | −1.31576 | ||||||||
\(386\) | 17.6015 | 0.895892 | ||||||||
\(387\) | −7.09783 | −0.360803 | ||||||||
\(388\) | 10.7966 | 0.548112 | ||||||||
\(389\) | −0.310371 | −0.0157365 | −0.00786823 | − | 0.999969i | \(-0.502505\pi\) | ||||
−0.00786823 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.13036 | 0.107737 | ||||||||
\(392\) | −6.60579 | −0.333643 | ||||||||
\(393\) | 22.6015 | 1.14009 | ||||||||
\(394\) | 42.1855 | 2.12528 | ||||||||
\(395\) | −13.6310 | −0.685851 | ||||||||
\(396\) | −6.46681 | −0.324970 | ||||||||
\(397\) | 1.49098 | 0.0748299 | 0.0374150 | − | 0.999300i | \(-0.488088\pi\) | ||||
0.0374150 | + | 0.999300i | \(0.488088\pi\) | |||||||
\(398\) | 7.25236 | 0.363528 | ||||||||
\(399\) | 27.4252 | 1.37298 | ||||||||
\(400\) | 14.3817 | 0.719083 | ||||||||
\(401\) | −23.8334 | −1.19018 | −0.595092 | − | 0.803658i | \(-0.702884\pi\) | ||||
−0.595092 | + | 0.803658i | \(0.702884\pi\) | |||||||
\(402\) | −8.18598 | −0.408280 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.5700 | −0.525878 | ||||||||
\(405\) | 1.44504 | 0.0718047 | ||||||||
\(406\) | −24.2838 | −1.20519 | ||||||||
\(407\) | −32.3967 | −1.60585 | ||||||||
\(408\) | 1.02177 | 0.0505852 | ||||||||
\(409\) | 4.26742 | 0.211010 | 0.105505 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105505 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(410\) | 4.69202 | 0.231722 | ||||||||
\(411\) | −13.6353 | −0.672581 | ||||||||
\(412\) | 7.04221 | 0.346945 | ||||||||
\(413\) | 6.46980 | 0.318358 | ||||||||
\(414\) | −5.09783 | −0.250545 | ||||||||
\(415\) | −9.34481 | −0.458719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6015 | 0.861948 | ||||||||
\(418\) | −74.3919 | −3.63863 | ||||||||
\(419\) | 29.6896 | 1.45043 | 0.725217 | − | 0.688521i | \(-0.241740\pi\) | ||||
0.725217 | + | 0.688521i | \(0.241740\pi\) | |||||||
\(420\) | 6.20775 | 0.302907 | ||||||||
\(421\) | 29.3991 | 1.43282 | 0.716412 | − | 0.697677i | \(-0.245783\pi\) | ||||
0.716412 | + | 0.697677i | \(0.245783\pi\) | |||||||
\(422\) | −7.04892 | −0.343136 | ||||||||
\(423\) | 10.5526 | 0.513083 | ||||||||
\(424\) | 4.19029 | 0.203499 | ||||||||
\(425\) | 2.19269 | 0.106361 | ||||||||
\(426\) | −16.4330 | −0.796180 | ||||||||
\(427\) | 11.5230 | 0.557638 | ||||||||
\(428\) | −8.39911 | −0.405986 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.4819 | −0.891275 | ||||||||
\(431\) | −33.0562 | −1.59226 | −0.796131 | − | 0.605124i | \(-0.793123\pi\) | ||||
−0.796131 | + | 0.605124i | \(0.793123\pi\) | |||||||
\(432\) | −4.93900 | −0.237628 | ||||||||
\(433\) | −29.2664 | −1.40645 | −0.703226 | − | 0.710967i | \(-0.748258\pi\) | ||||
−0.703226 | + | 0.710967i | \(0.748258\pi\) | |||||||
\(434\) | −30.4166 | −1.46004 | ||||||||
\(435\) | −5.65279 | −0.271031 | ||||||||
\(436\) | −2.58881 | −0.123982 | ||||||||
\(437\) | −22.5217 | −1.07736 | ||||||||
\(438\) | 5.31767 | 0.254088 | ||||||||
\(439\) | −2.13169 | −0.101740 | −0.0508699 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508699 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(440\) | 10.1685 | 0.484765 | ||||||||
\(441\) | 4.86831 | 0.231824 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.9922 | −1.09239 | −0.546197 | − | 0.837657i | \(-0.683925\pi\) | ||||
−0.546197 | + | 0.837657i | \(0.683925\pi\) | |||||||
\(444\) | 7.78986 | 0.369690 | ||||||||
\(445\) | 1.67456 | 0.0793819 | ||||||||
\(446\) | 13.4233 | 0.635610 | ||||||||
\(447\) | 12.7385 | 0.602513 | ||||||||
\(448\) | −4.37090 | −0.206505 | ||||||||
\(449\) | −12.9379 | −0.610579 | −0.305289 | − | 0.952260i | \(-0.598753\pi\) | ||||
−0.305289 | + | 0.952260i | \(0.598753\pi\) | |||||||
\(450\) | −5.24698 | −0.247345 | ||||||||
\(451\) | −9.34481 | −0.440030 | ||||||||
\(452\) | 7.69202 | 0.361802 | ||||||||
\(453\) | 15.6407 | 0.734865 | ||||||||
\(454\) | −38.2911 | −1.79709 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.8019 | −0.505847 | ||||||||
\(457\) | −4.85325 | −0.227025 | −0.113513 | − | 0.993537i | \(-0.536210\pi\) | ||||
−0.113513 | + | 0.993537i | \(0.536210\pi\) | |||||||
\(458\) | 16.7506 | 0.782705 | ||||||||
\(459\) | −0.753020 | −0.0351480 | ||||||||
\(460\) | −5.09783 | −0.237688 | ||||||||
\(461\) | 18.8345 | 0.877208 | 0.438604 | − | 0.898680i | \(-0.355473\pi\) | ||||
0.438604 | + | 0.898680i | \(0.355473\pi\) | |||||||
\(462\) | −32.1933 | −1.49777 | ||||||||
\(463\) | −22.8767 | −1.06317 | −0.531585 | − | 0.847005i | \(-0.678403\pi\) | ||||
−0.531585 | + | 0.847005i | \(0.678403\pi\) | |||||||
\(464\) | 19.3207 | 0.896939 | ||||||||
\(465\) | −7.08038 | −0.328345 | ||||||||
\(466\) | 29.2107 | 1.35316 | ||||||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6504 | −0.722668 | ||||||||
\(470\) | 27.4776 | 1.26745 | ||||||||
\(471\) | −0.823708 | −0.0379545 | ||||||||
\(472\) | −2.54825 | −0.117293 | ||||||||
\(473\) | 36.8092 | 1.69249 | ||||||||
\(474\) | −16.9976 | −0.780726 | ||||||||
\(475\) | −23.1806 | −1.06360 | ||||||||
\(476\) | −3.23490 | −0.148271 | ||||||||
\(477\) | −3.08815 | −0.141396 | ||||||||
\(478\) | −24.3424 | −1.11340 | ||||||||
\(479\) | −38.0901 | −1.74038 | −0.870190 | − | 0.492717i | \(-0.836004\pi\) | ||||
−0.870190 | + | 0.492717i | \(0.836004\pi\) | |||||||
\(480\) | −8.93900 | −0.408008 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.2959 | 0.514514 | ||||||||
\(483\) | −9.74632 | −0.443473 | ||||||||
\(484\) | 19.8200 | 0.900909 | ||||||||
\(485\) | 12.5114 | 0.568114 | ||||||||
\(486\) | 1.80194 | 0.0817376 | ||||||||
\(487\) | −21.2500 | −0.962928 | −0.481464 | − | 0.876466i | \(-0.659895\pi\) | ||||
−0.481464 | + | 0.876466i | \(0.659895\pi\) | |||||||
\(488\) | −4.53856 | −0.205451 | ||||||||
\(489\) | 6.26875 | 0.283483 | ||||||||
\(490\) | 12.6765 | 0.572665 | ||||||||
\(491\) | −6.35019 | −0.286580 | −0.143290 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143290 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(492\) | 2.24698 | 0.101302 | ||||||||
\(493\) | 2.94571 | 0.132668 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.49396 | −0.336828 | ||||||||
\(496\) | 24.2000 | 1.08661 | ||||||||
\(497\) | −31.4174 | −1.40926 | ||||||||
\(498\) | −11.6528 | −0.522174 | ||||||||
\(499\) | −4.65087 | −0.208202 | −0.104101 | − | 0.994567i | \(-0.533196\pi\) | ||||
−0.104101 | + | 0.994567i | \(0.533196\pi\) | |||||||
\(500\) | −14.2567 | −0.637578 | ||||||||
\(501\) | −7.45042 | −0.332860 | ||||||||
\(502\) | −1.35690 | −0.0605612 | ||||||||
\(503\) | 15.4752 | 0.690004 | 0.345002 | − | 0.938602i | \(-0.387878\pi\) | ||||
0.345002 | + | 0.938602i | \(0.387878\pi\) | |||||||
\(504\) | −4.67456 | −0.208222 | ||||||||
\(505\) | −12.2489 | −0.545069 | ||||||||
\(506\) | 26.4373 | 1.17528 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7845 | −0.789059 | ||||||||
\(509\) | −20.5047 | −0.908855 | −0.454428 | − | 0.890784i | \(-0.650156\pi\) | ||||
−0.454428 | + | 0.890784i | \(0.650156\pi\) | |||||||
\(510\) | −1.96077 | −0.0868244 | ||||||||
\(511\) | 10.1666 | 0.449744 | ||||||||
\(512\) | 17.1491 | 0.757892 | ||||||||
\(513\) | 7.96077 | 0.351477 | ||||||||
\(514\) | 35.5459 | 1.56786 | ||||||||
\(515\) | 8.16075 | 0.359606 | ||||||||
\(516\) | −8.85086 | −0.389637 | ||||||||
\(517\) | −54.7254 | −2.40682 | ||||||||
\(518\) | 38.7797 | 1.70388 | ||||||||
\(519\) | −2.00969 | −0.0882155 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.0267 | −1.84122 | −0.920611 | − | 0.390481i | \(-0.872309\pi\) | ||||
−0.920611 | + | 0.390481i | \(0.872309\pi\) | |||||||
\(522\) | −7.04892 | −0.308523 | ||||||||
\(523\) | −29.9885 | −1.31131 | −0.655653 | − | 0.755062i | \(-0.727607\pi\) | ||||
−0.655653 | + | 0.755062i | \(0.727607\pi\) | |||||||
\(524\) | 28.1836 | 1.23121 | ||||||||
\(525\) | −10.0315 | −0.437809 | ||||||||
\(526\) | −31.7308 | −1.38353 | ||||||||
\(527\) | 3.68963 | 0.160723 | ||||||||
\(528\) | 25.6136 | 1.11469 | ||||||||
\(529\) | −14.9963 | −0.652012 | ||||||||
\(530\) | −8.04115 | −0.349285 | ||||||||
\(531\) | 1.87800 | 0.0814984 | ||||||||
\(532\) | 34.1987 | 1.48270 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.08815 | 0.0903629 | ||||||||
\(535\) | −9.73317 | −0.420802 | ||||||||
\(536\) | 6.16421 | 0.266253 | ||||||||
\(537\) | 20.0368 | 0.864653 | ||||||||
\(538\) | −29.5284 | −1.27306 | ||||||||
\(539\) | −25.2470 | −1.08746 | ||||||||
\(540\) | 1.80194 | 0.0775431 | ||||||||
\(541\) | 36.3803 | 1.56411 | 0.782056 | − | 0.623208i | \(-0.214171\pi\) | ||||
0.782056 | + | 0.623208i | \(0.214171\pi\) | |||||||
\(542\) | −1.43296 | −0.0615509 | ||||||||
\(543\) | 24.1226 | 1.03520 | ||||||||
\(544\) | 4.65817 | 0.199717 | ||||||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.8159 | −1.10381 | −0.551905 | − | 0.833907i | \(-0.686099\pi\) | ||||
−0.551905 | + | 0.833907i | \(0.686099\pi\) | |||||||
\(548\) | −17.0030 | −0.726331 | ||||||||
\(549\) | 3.34481 | 0.142753 | ||||||||
\(550\) | 27.2107 | 1.16027 | ||||||||
\(551\) | −31.1414 | −1.32667 | ||||||||
\(552\) | 3.83877 | 0.163389 | ||||||||
\(553\) | −32.4969 | −1.38191 | ||||||||
\(554\) | −8.70948 | −0.370030 | ||||||||
\(555\) | 9.02715 | 0.383181 | ||||||||
\(556\) | 21.9487 | 0.930832 | ||||||||
\(557\) | 17.9903 | 0.762274 | 0.381137 | − | 0.924519i | \(-0.375533\pi\) | ||||
0.381137 | + | 0.924519i | \(0.375533\pi\) | |||||||
\(558\) | −8.82908 | −0.373765 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.5875 | −1.03901 | ||||||||
\(561\) | 3.90515 | 0.164876 | ||||||||
\(562\) | 33.8310 | 1.42707 | ||||||||
\(563\) | −39.1323 | −1.64923 | −0.824614 | − | 0.565695i | \(-0.808608\pi\) | ||||
−0.824614 | + | 0.565695i | \(0.808608\pi\) | |||||||
\(564\) | 13.1588 | 0.554087 | ||||||||
\(565\) | 8.91377 | 0.375005 | ||||||||
\(566\) | −14.2664 | −0.599660 | ||||||||
\(567\) | 3.44504 | 0.144678 | ||||||||
\(568\) | 12.3744 | 0.519216 | ||||||||
\(569\) | 30.6002 | 1.28283 | 0.641413 | − | 0.767196i | \(-0.278349\pi\) | ||||
0.641413 | + | 0.767196i | \(0.278349\pi\) | |||||||
\(570\) | 20.7289 | 0.868236 | ||||||||
\(571\) | −2.96184 | −0.123949 | −0.0619745 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619745 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.08038 | −0.295787 | ||||||||
\(574\) | 11.1860 | 0.466894 | ||||||||
\(575\) | 8.23788 | 0.343543 | ||||||||
\(576\) | −1.26875 | −0.0528646 | ||||||||
\(577\) | −0.819396 | −0.0341119 | −0.0170560 | − | 0.999855i | \(-0.505429\pi\) | ||||
−0.0170560 | + | 0.999855i | \(0.505429\pi\) | |||||||
\(578\) | −29.6112 | −1.23166 | ||||||||
\(579\) | 9.76809 | 0.405948 | ||||||||
\(580\) | −7.04892 | −0.292690 | ||||||||
\(581\) | −22.2784 | −0.924265 | ||||||||
\(582\) | 15.6015 | 0.646702 | ||||||||
\(583\) | 16.0151 | 0.663276 | ||||||||
\(584\) | −4.00431 | −0.165700 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8552 | 0.489732 | ||||||||
\(587\) | −31.7995 | −1.31251 | −0.656254 | − | 0.754540i | \(-0.727860\pi\) | ||||
−0.656254 | + | 0.754540i | \(0.727860\pi\) | |||||||
\(588\) | 6.07069 | 0.250351 | ||||||||
\(589\) | −39.0060 | −1.60721 | ||||||||
\(590\) | 4.89008 | 0.201322 | ||||||||
\(591\) | 23.4112 | 0.963008 | ||||||||
\(592\) | −30.8538 | −1.26808 | ||||||||
\(593\) | −4.26337 | −0.175076 | −0.0875379 | − | 0.996161i | \(-0.527900\pi\) | ||||
−0.0875379 | + | 0.996161i | \(0.527900\pi\) | |||||||
\(594\) | −9.34481 | −0.383422 | ||||||||
\(595\) | −3.74871 | −0.153682 | ||||||||
\(596\) | 15.8847 | 0.650663 | ||||||||
\(597\) | 4.02475 | 0.164722 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.7278 | 1.01035 | 0.505175 | − | 0.863017i | \(-0.331428\pi\) | ||||
0.505175 | + | 0.863017i | \(0.331428\pi\) | |||||||
\(600\) | 3.95108 | 0.161302 | ||||||||
\(601\) | 6.82371 | 0.278345 | 0.139172 | − | 0.990268i | \(-0.455556\pi\) | ||||
0.139172 | + | 0.990268i | \(0.455556\pi\) | |||||||
\(602\) | −44.0616 | −1.79582 | ||||||||
\(603\) | −4.54288 | −0.185000 | ||||||||
\(604\) | 19.5036 | 0.793592 | ||||||||
\(605\) | 22.9681 | 0.933785 | ||||||||
\(606\) | −15.2741 | −0.620469 | ||||||||
\(607\) | 31.9963 | 1.29869 | 0.649344 | − | 0.760494i | \(-0.275043\pi\) | ||||
0.649344 | + | 0.760494i | \(0.275043\pi\) | |||||||
\(608\) | −49.2452 | −1.99716 | ||||||||
\(609\) | −13.4765 | −0.546095 | ||||||||
\(610\) | 8.70948 | 0.352637 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.939001 | −0.0379569 | ||||||||
\(613\) | 33.5875 | 1.35659 | 0.678293 | − | 0.734792i | \(-0.262720\pi\) | ||||
0.678293 | + | 0.734792i | \(0.262720\pi\) | |||||||
\(614\) | −44.8049 | −1.80818 | ||||||||
\(615\) | 2.60388 | 0.104998 | ||||||||
\(616\) | 24.2422 | 0.976746 | ||||||||
\(617\) | −26.5870 | −1.07035 | −0.535176 | − | 0.844740i | \(-0.679755\pi\) | ||||
−0.535176 | + | 0.844740i | \(0.679755\pi\) | |||||||
\(618\) | 10.1763 | 0.409350 | ||||||||
\(619\) | −9.17928 | −0.368946 | −0.184473 | − | 0.982838i | \(-0.559058\pi\) | ||||
−0.184473 | + | 0.982838i | \(0.559058\pi\) | |||||||
\(620\) | −8.82908 | −0.354585 | ||||||||
\(621\) | −2.82908 | −0.113527 | ||||||||
\(622\) | −30.7778 | −1.23408 | ||||||||
\(623\) | 3.99223 | 0.159945 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96184 | −0.0784735 | ||||||||
\(626\) | 28.2857 | 1.13053 | ||||||||
\(627\) | −41.2844 | −1.64874 | ||||||||
\(628\) | −1.02715 | −0.0409876 | ||||||||
\(629\) | −4.70410 | −0.187565 | ||||||||
\(630\) | 8.97046 | 0.357392 | ||||||||
\(631\) | 17.0043 | 0.676931 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(632\) | 12.7995 | 0.509139 | ||||||||
\(633\) | −3.91185 | −0.155482 | ||||||||
\(634\) | 59.0713 | 2.34602 | ||||||||
\(635\) | −20.6093 | −0.817853 | ||||||||
\(636\) | −3.85086 | −0.152696 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.5555 | 1.44725 | ||||||||
\(639\) | −9.11960 | −0.360766 | ||||||||
\(640\) | 14.5743 | 0.576101 | ||||||||
\(641\) | −21.6649 | −0.855711 | −0.427856 | − | 0.903847i | \(-0.640731\pi\) | ||||
−0.427856 | + | 0.903847i | \(0.640731\pi\) | |||||||
\(642\) | −12.1371 | −0.479012 | ||||||||
\(643\) | 9.35557 | 0.368948 | 0.184474 | − | 0.982837i | \(-0.440942\pi\) | ||||
0.184474 | + | 0.982837i | \(0.440942\pi\) | |||||||
\(644\) | −12.1535 | −0.478913 | ||||||||
\(645\) | −10.2567 | −0.403856 | ||||||||
\(646\) | −10.8019 | −0.424997 | ||||||||
\(647\) | −0.702775 | −0.0276289 | −0.0138145 | − | 0.999905i | \(-0.504397\pi\) | ||||
−0.0138145 | + | 0.999905i | \(0.504397\pi\) | |||||||
\(648\) | −1.35690 | −0.0533039 | ||||||||
\(649\) | −9.73928 | −0.382300 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8799 | −0.661576 | ||||||||
\(652\) | 7.81700 | 0.306137 | ||||||||
\(653\) | −37.3411 | −1.46127 | −0.730635 | − | 0.682768i | \(-0.760776\pi\) | ||||
−0.730635 | + | 0.682768i | \(0.760776\pi\) | |||||||
\(654\) | −3.74094 | −0.146282 | ||||||||
\(655\) | 32.6601 | 1.27614 | ||||||||
\(656\) | −8.89977 | −0.347478 | ||||||||
\(657\) | 2.95108 | 0.115133 | ||||||||
\(658\) | 65.5077 | 2.55376 | ||||||||
\(659\) | −0.735562 | −0.0286534 | −0.0143267 | − | 0.999897i | \(-0.504560\pi\) | ||||
−0.0143267 | + | 0.999897i | \(0.504560\pi\) | |||||||
\(660\) | −9.34481 | −0.363746 | ||||||||
\(661\) | 13.8485 | 0.538643 | 0.269321 | − | 0.963050i | \(-0.413201\pi\) | ||||
0.269321 | + | 0.963050i | \(0.413201\pi\) | |||||||
\(662\) | −52.5478 | −2.04233 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.77479 | 0.340528 | ||||||||
\(665\) | 39.6305 | 1.53681 | ||||||||
\(666\) | 11.2567 | 0.436187 | ||||||||
\(667\) | 11.0670 | 0.428515 | ||||||||
\(668\) | −9.29052 | −0.359461 | ||||||||
\(669\) | 7.44935 | 0.288009 | ||||||||
\(670\) | −11.8291 | −0.456997 | ||||||||
\(671\) | −17.3461 | −0.669640 | ||||||||
\(672\) | −21.3110 | −0.822088 | ||||||||
\(673\) | −6.35019 | −0.244782 | −0.122391 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122391 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(674\) | −59.9885 | −2.31067 | ||||||||
\(675\) | −2.91185 | −0.112077 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7241 | 1.29612 | 0.648061 | − | 0.761589i | \(-0.275580\pi\) | ||||
0.648061 | + | 0.761589i | \(0.275580\pi\) | |||||||
\(678\) | 11.1153 | 0.426880 | ||||||||
\(679\) | 29.8278 | 1.14468 | ||||||||
\(680\) | 1.47650 | 0.0566212 | ||||||||
\(681\) | −21.2500 | −0.814300 | ||||||||
\(682\) | 45.7875 | 1.75329 | ||||||||
\(683\) | 19.2687 | 0.737298 | 0.368649 | − | 0.929569i | \(-0.379820\pi\) | ||||
0.368649 | + | 0.929569i | \(0.379820\pi\) | |||||||
\(684\) | 9.92692 | 0.379565 | ||||||||
\(685\) | −19.7036 | −0.752837 | ||||||||
\(686\) | −13.2330 | −0.505237 | ||||||||
\(687\) | 9.29590 | 0.354661 | ||||||||
\(688\) | 35.0562 | 1.33651 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.36658 | −0.280441 | ||||||||
\(691\) | −39.4010 | −1.49889 | −0.749443 | − | 0.662069i | \(-0.769679\pi\) | ||||
−0.749443 | + | 0.662069i | \(0.769679\pi\) | |||||||
\(692\) | −2.50604 | −0.0952654 | ||||||||
\(693\) | −17.8659 | −0.678670 | ||||||||
\(694\) | −1.57434 | −0.0597610 | ||||||||
\(695\) | 25.4349 | 0.964800 | ||||||||
\(696\) | 5.30798 | 0.201198 | ||||||||
\(697\) | −1.35690 | −0.0513961 | ||||||||
\(698\) | −5.82371 | −0.220431 | ||||||||
\(699\) | 16.2107 | 0.613146 | ||||||||
\(700\) | −12.5090 | −0.472797 | ||||||||
\(701\) | 18.3985 | 0.694902 | 0.347451 | − | 0.937698i | \(-0.387047\pi\) | ||||
0.347451 | + | 0.937698i | \(0.387047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.7308 | 1.87563 | ||||||||
\(704\) | 6.57971 | 0.247982 | ||||||||
\(705\) | 15.2489 | 0.574307 | ||||||||
\(706\) | 14.6799 | 0.552487 | ||||||||
\(707\) | −29.2019 | −1.09825 | ||||||||
\(708\) | 2.34183 | 0.0880114 | ||||||||
\(709\) | −38.4553 | −1.44422 | −0.722110 | − | 0.691778i | \(-0.756828\pi\) | ||||
−0.722110 | + | 0.691778i | \(0.756828\pi\) | |||||||
\(710\) | −23.7463 | −0.891183 | ||||||||
\(711\) | −9.43296 | −0.353764 | ||||||||
\(712\) | −1.57242 | −0.0589288 | ||||||||
\(713\) | 13.8619 | 0.519131 | ||||||||
\(714\) | −4.67456 | −0.174941 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.9855 | 0.933753 | ||||||||
\(717\) | −13.5090 | −0.504504 | ||||||||
\(718\) | 4.75840 | 0.177582 | ||||||||
\(719\) | 48.4999 | 1.80874 | 0.904371 | − | 0.426747i | \(-0.140341\pi\) | ||||
0.904371 | + | 0.426747i | \(0.140341\pi\) | |||||||
\(720\) | −7.13706 | −0.265983 | ||||||||
\(721\) | 19.4556 | 0.724564 | ||||||||
\(722\) | 79.9590 | 2.97576 | ||||||||
\(723\) | 6.26875 | 0.233137 | ||||||||
\(724\) | 30.0804 | 1.11793 | ||||||||
\(725\) | 11.3907 | 0.423042 | ||||||||
\(726\) | 28.6407 | 1.06296 | ||||||||
\(727\) | 19.0344 | 0.705948 | 0.352974 | − | 0.935633i | \(-0.385170\pi\) | ||||
0.352974 | + | 0.935633i | \(0.385170\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.68425 | 0.284407 | ||||||||
\(731\) | 5.34481 | 0.197685 | ||||||||
\(732\) | 4.17092 | 0.154161 | ||||||||
\(733\) | 24.6213 | 0.909410 | 0.454705 | − | 0.890642i | \(-0.349745\pi\) | ||||
0.454705 | + | 0.890642i | \(0.349745\pi\) | |||||||
\(734\) | −5.23298 | −0.193153 | ||||||||
\(735\) | 7.03492 | 0.259487 | ||||||||
\(736\) | 17.5007 | 0.645083 | ||||||||
\(737\) | 23.5593 | 0.867817 | ||||||||
\(738\) | 3.24698 | 0.119523 | ||||||||
\(739\) | −44.5115 | −1.63738 | −0.818692 | − | 0.574233i | \(-0.805300\pi\) | ||||
−0.818692 | + | 0.574233i | \(0.805300\pi\) | |||||||
\(740\) | 11.2567 | 0.413803 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.1704 | −0.703769 | ||||||||
\(743\) | 10.4112 | 0.381950 | 0.190975 | − | 0.981595i | \(-0.438835\pi\) | ||||
0.190975 | + | 0.981595i | \(0.438835\pi\) | |||||||
\(744\) | 6.64848 | 0.243745 | ||||||||
\(745\) | 18.4077 | 0.674407 | ||||||||
\(746\) | −15.1336 | −0.554081 | ||||||||
\(747\) | −6.46681 | −0.236608 | ||||||||
\(748\) | 4.86964 | 0.178052 | ||||||||
\(749\) | −23.2043 | −0.847866 | ||||||||
\(750\) | −20.6015 | −0.752260 | ||||||||
\(751\) | 1.69979 | 0.0620263 | 0.0310131 | − | 0.999519i | \(-0.490127\pi\) | ||||
0.0310131 | + | 0.999519i | \(0.490127\pi\) | |||||||
\(752\) | −52.1191 | −1.90059 | ||||||||
\(753\) | −0.753020 | −0.0274416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6015 | 0.822552 | ||||||||
\(756\) | 4.29590 | 0.156240 | ||||||||
\(757\) | 27.4252 | 0.996786 | 0.498393 | − | 0.866951i | \(-0.333924\pi\) | ||||
0.498393 | + | 0.866951i | \(0.333924\pi\) | |||||||
\(758\) | 28.3773 | 1.03071 | ||||||||
\(759\) | 14.6716 | 0.532545 | ||||||||
\(760\) | −15.6093 | −0.566207 | ||||||||
\(761\) | −5.02608 | −0.182195 | −0.0910977 | − | 0.995842i | \(-0.529038\pi\) | ||||
−0.0910977 | + | 0.995842i | \(0.529038\pi\) | |||||||
\(762\) | −25.6993 | −0.930988 | ||||||||
\(763\) | −7.15213 | −0.258924 | ||||||||
\(764\) | −8.82908 | −0.319425 | ||||||||
\(765\) | −1.08815 | −0.0393420 | ||||||||
\(766\) | 22.9541 | 0.829364 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20.7114 | 0.747358 | ||||||||
\(769\) | 42.4456 | 1.53063 | 0.765314 | − | 0.643657i | \(-0.222584\pi\) | ||||
0.765314 | + | 0.643657i | \(0.222584\pi\) | |||||||
\(770\) | −46.5206 | −1.67649 | ||||||||
\(771\) | 19.7265 | 0.710431 | ||||||||
\(772\) | 12.1806 | 0.438390 | ||||||||
\(773\) | 26.3593 | 0.948078 | 0.474039 | − | 0.880504i | \(-0.342796\pi\) | ||||
0.474039 | + | 0.880504i | \(0.342796\pi\) | |||||||
\(774\) | −12.7899 | −0.459722 | ||||||||
\(775\) | 14.2674 | 0.512501 | ||||||||
\(776\) | −11.7482 | −0.421737 | ||||||||
\(777\) | 21.5211 | 0.772065 | ||||||||
\(778\) | −0.559270 | −0.0200508 | ||||||||
\(779\) | 14.3448 | 0.513956 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.2941 | 1.69232 | ||||||||
\(782\) | 3.83877 | 0.137274 | ||||||||
\(783\) | −3.91185 | −0.139798 | ||||||||
\(784\) | −24.0446 | −0.858736 | ||||||||
\(785\) | −1.19029 | −0.0424834 | ||||||||
\(786\) | 40.7265 | 1.45266 | ||||||||
\(787\) | 17.1424 | 0.611062 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(788\) | 29.1933 | 1.03997 | ||||||||
\(789\) | −17.6093 | −0.626906 | ||||||||
\(790\) | −24.5623 | −0.873886 | ||||||||
\(791\) | 21.2508 | 0.755592 | ||||||||
\(792\) | 7.03684 | 0.250043 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2.68664 | 0.0953455 | ||||||||
\(795\) | −4.46250 | −0.158269 | ||||||||
\(796\) | 5.01879 | 0.177886 | ||||||||
\(797\) | 30.1629 | 1.06842 | 0.534212 | − | 0.845351i | \(-0.320608\pi\) | ||||
0.534212 | + | 0.845351i | \(0.320608\pi\) | |||||||
\(798\) | 49.4185 | 1.74940 | ||||||||
\(799\) | −7.94630 | −0.281120 | ||||||||
\(800\) | 18.0127 | 0.636844 | ||||||||
\(801\) | 1.15883 | 0.0409454 | ||||||||
\(802\) | −42.9463 | −1.51649 | ||||||||
\(803\) | −15.3043 | −0.540076 | ||||||||
\(804\) | −5.66487 | −0.199785 | ||||||||
\(805\) | −14.0838 | −0.496390 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.3870 | −0.576851 | ||||||||
\(808\) | 11.5017 | 0.404629 | ||||||||
\(809\) | −29.8504 | −1.04948 | −0.524742 | − | 0.851261i | \(-0.675838\pi\) | ||||
−0.524742 | + | 0.851261i | \(0.675838\pi\) | |||||||
\(810\) | 2.60388 | 0.0914909 | ||||||||
\(811\) | 47.7362 | 1.67624 | 0.838122 | − | 0.545484i | \(-0.183654\pi\) | ||||
0.838122 | + | 0.545484i | \(0.183654\pi\) | |||||||
\(812\) | −16.8049 | −0.589737 | ||||||||
\(813\) | −0.795233 | −0.0278900 | ||||||||
\(814\) | −58.3769 | −2.04611 | ||||||||
\(815\) | 9.05861 | 0.317309 | ||||||||
\(816\) | 3.71917 | 0.130197 | ||||||||
\(817\) | −56.5042 | −1.97683 | ||||||||
\(818\) | 7.68963 | 0.268862 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.24698 | 0.113389 | ||||||||
\(821\) | −17.9299 | −0.625758 | −0.312879 | − | 0.949793i | \(-0.601293\pi\) | ||||
−0.312879 | + | 0.949793i | \(0.601293\pi\) | |||||||
\(822\) | −24.5700 | −0.856978 | ||||||||
\(823\) | 54.3196 | 1.89346 | 0.946731 | − | 0.322026i | \(-0.104364\pi\) | ||||
0.946731 | + | 0.322026i | \(0.104364\pi\) | |||||||
\(824\) | −7.66296 | −0.266952 | ||||||||
\(825\) | 15.1008 | 0.525743 | ||||||||
\(826\) | 11.6582 | 0.405640 | ||||||||
\(827\) | 49.1041 | 1.70752 | 0.853758 | − | 0.520670i | \(-0.174318\pi\) | ||||
0.853758 | + | 0.520670i | \(0.174318\pi\) | |||||||
\(828\) | −3.52781 | −0.122600 | ||||||||
\(829\) | −7.35796 | −0.255553 | −0.127776 | − | 0.991803i | \(-0.540784\pi\) | ||||
−0.127776 | + | 0.991803i | \(0.540784\pi\) | |||||||
\(830\) | −16.8388 | −0.584482 | ||||||||
\(831\) | −4.83340 | −0.167669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.66594 | −0.127017 | ||||||||
\(834\) | 31.7168 | 1.09826 | ||||||||
\(835\) | −10.7662 | −0.372579 | ||||||||
\(836\) | −51.4808 | −1.78050 | ||||||||
\(837\) | −4.89977 | −0.169361 | ||||||||
\(838\) | 53.4989 | 1.84809 | ||||||||
\(839\) | −36.5013 | −1.26016 | −0.630082 | − | 0.776529i | \(-0.716979\pi\) | ||||
−0.630082 | + | 0.776529i | \(0.716979\pi\) | |||||||
\(840\) | −6.75494 | −0.233068 | ||||||||
\(841\) | −13.6974 | −0.472324 | ||||||||
\(842\) | 52.9754 | 1.82565 | ||||||||
\(843\) | 18.7748 | 0.646638 | ||||||||
\(844\) | −4.87800 | −0.167908 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 19.0151 | 0.653751 | ||||||||
\(847\) | 54.7569 | 1.88147 | ||||||||
\(848\) | 15.2524 | 0.523768 | ||||||||
\(849\) | −7.91723 | −0.271719 | ||||||||
\(850\) | 3.95108 | 0.135521 | ||||||||
\(851\) | −17.6732 | −0.605831 | ||||||||
\(852\) | −11.3720 | −0.389597 | ||||||||
\(853\) | −9.73855 | −0.333441 | −0.166721 | − | 0.986004i | \(-0.553318\pi\) | ||||
−0.166721 | + | 0.986004i | \(0.553318\pi\) | |||||||
\(854\) | 20.7638 | 0.710522 | ||||||||
\(855\) | 11.5036 | 0.393416 | ||||||||
\(856\) | 9.13946 | 0.312380 | ||||||||
\(857\) | −15.2030 | −0.519323 | −0.259662 | − | 0.965700i | \(-0.583611\pi\) | ||||
−0.259662 | + | 0.965700i | \(0.583611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.9885 | −1.09143 | −0.545717 | − | 0.837970i | \(-0.683743\pi\) | ||||
−0.545717 | + | 0.837970i | \(0.683743\pi\) | |||||||
\(860\) | −12.7899 | −0.436130 | ||||||||
\(861\) | 6.20775 | 0.211560 | ||||||||
\(862\) | −59.5652 | −2.02880 | ||||||||
\(863\) | −35.2905 | −1.20130 | −0.600652 | − | 0.799511i | \(-0.705092\pi\) | ||||
−0.600652 | + | 0.799511i | \(0.705092\pi\) | |||||||
\(864\) | −6.18598 | −0.210451 | ||||||||
\(865\) | −2.90408 | −0.0987418 | ||||||||
\(866\) | −52.7362 | −1.79205 | ||||||||
\(867\) | −16.4330 | −0.558093 | ||||||||
\(868\) | −21.0489 | −0.714447 | ||||||||
\(869\) | 48.9191 | 1.65947 | ||||||||
\(870\) | −10.1860 | −0.345337 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.81700 | 0.0953958 | ||||||||
\(873\) | 8.65817 | 0.293035 | ||||||||
\(874\) | −40.5827 | −1.37273 | ||||||||
\(875\) | −39.3870 | −1.33152 | ||||||||
\(876\) | 3.67994 | 0.124334 | ||||||||
\(877\) | −15.3263 | −0.517532 | −0.258766 | − | 0.965940i | \(-0.583316\pi\) | ||||
−0.258766 | + | 0.965940i | \(0.583316\pi\) | |||||||
\(878\) | −3.84117 | −0.129633 | ||||||||
\(879\) | 6.57912 | 0.221908 | ||||||||
\(880\) | 37.0127 | 1.24770 | ||||||||
\(881\) | −36.4306 | −1.22738 | −0.613689 | − | 0.789548i | \(-0.710315\pi\) | ||||
−0.613689 | + | 0.789548i | \(0.710315\pi\) | |||||||
\(882\) | 8.77240 | 0.295382 | ||||||||
\(883\) | −37.6819 | −1.26810 | −0.634048 | − | 0.773294i | \(-0.718608\pi\) | ||||
−0.634048 | + | 0.773294i | \(0.718608\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.71379 | 0.0912231 | ||||||||
\(886\) | −41.4306 | −1.39189 | ||||||||
\(887\) | 4.24890 | 0.142664 | 0.0713320 | − | 0.997453i | \(-0.477275\pi\) | ||||
0.0713320 | + | 0.997453i | \(0.477275\pi\) | |||||||
\(888\) | −8.47650 | −0.284453 | ||||||||
\(889\) | −49.1333 | −1.64788 | ||||||||
\(890\) | 3.01746 | 0.101145 | ||||||||
\(891\) | −5.18598 | −0.173737 | ||||||||
\(892\) | 9.28919 | 0.311025 | ||||||||
\(893\) | 84.0066 | 2.81117 | ||||||||
\(894\) | 22.9541 | 0.767699 | ||||||||
\(895\) | 28.9541 | 0.967828 | ||||||||
\(896\) | 34.7458 | 1.16078 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.3134 | −0.777977 | ||||||||
\(899\) | 19.1672 | 0.639262 | ||||||||
\(900\) | −3.63102 | −0.121034 | ||||||||
\(901\) | 2.32544 | 0.0774715 | ||||||||
\(902\) | −16.8388 | −0.560670 | ||||||||
\(903\) | −24.4523 | −0.813723 | ||||||||
\(904\) | −8.37004 | −0.278383 | ||||||||
\(905\) | 34.8582 | 1.15872 | ||||||||
\(906\) | 28.1836 | 0.936337 | ||||||||
\(907\) | −12.6183 | −0.418985 | −0.209493 | − | 0.977810i | \(-0.567181\pi\) | ||||
−0.209493 | + | 0.977810i | \(0.567181\pi\) | |||||||
\(908\) | −26.4983 | −0.879376 | ||||||||
\(909\) | −8.47650 | −0.281148 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.77777 | 0.224558 | 0.112279 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112279 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(912\) | −39.3183 | −1.30196 | ||||||||
\(913\) | 33.5368 | 1.10990 | ||||||||
\(914\) | −8.74525 | −0.289267 | ||||||||
\(915\) | 4.83340 | 0.159787 | ||||||||
\(916\) | 11.5918 | 0.383004 | ||||||||
\(917\) | 77.8631 | 2.57126 | ||||||||
\(918\) | −1.35690 | −0.0447842 | ||||||||
\(919\) | −20.4674 | −0.675157 | −0.337579 | − | 0.941297i | \(-0.609608\pi\) | ||||
−0.337579 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(920\) | 5.54719 | 0.182885 | ||||||||
\(921\) | −24.8649 | −0.819325 | ||||||||
\(922\) | 33.9385 | 1.11771 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −22.2784 | −0.732907 | ||||||||
\(925\) | −18.1903 | −0.598093 | ||||||||
\(926\) | −41.2223 | −1.35465 | ||||||||
\(927\) | 5.64742 | 0.185485 | ||||||||
\(928\) | 24.1987 | 0.794360 | ||||||||
\(929\) | −4.65220 | −0.152634 | −0.0763169 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763169 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(930\) | −12.7584 | −0.418364 | ||||||||
\(931\) | 38.7555 | 1.27016 | ||||||||
\(932\) | 20.2145 | 0.662147 | ||||||||
\(933\) | −17.0804 | −0.559186 | ||||||||
\(934\) | 23.4252 | 0.766496 | ||||||||
\(935\) | 5.64310 | 0.184549 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8544 | −1.36732 | −0.683662 | − | 0.729798i | \(-0.739614\pi\) | ||||
−0.683662 | + | 0.729798i | \(0.739614\pi\) | |||||||
\(938\) | −28.2010 | −0.920797 | ||||||||
\(939\) | 15.6974 | 0.512265 | ||||||||
\(940\) | 19.0151 | 0.620203 | ||||||||
\(941\) | 30.3454 | 0.989232 | 0.494616 | − | 0.869112i | \(-0.335309\pi\) | ||||
0.494616 | + | 0.869112i | \(0.335309\pi\) | |||||||
\(942\) | −1.48427 | −0.0483601 | ||||||||
\(943\) | −5.09783 | −0.166008 | ||||||||
\(944\) | −9.27545 | −0.301890 | ||||||||
\(945\) | 4.97823 | 0.161942 | ||||||||
\(946\) | 66.3279 | 2.15651 | ||||||||
\(947\) | 12.0325 | 0.391004 | 0.195502 | − | 0.980703i | \(-0.437366\pi\) | ||||
0.195502 | + | 0.980703i | \(0.437366\pi\) | |||||||
\(948\) | −11.7627 | −0.382035 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −41.7700 | −1.35520 | ||||||||
\(951\) | 32.7821 | 1.06303 | ||||||||
\(952\) | 3.52004 | 0.114085 | ||||||||
\(953\) | 22.9825 | 0.744478 | 0.372239 | − | 0.928137i | \(-0.378590\pi\) | ||||
0.372239 | + | 0.928137i | \(0.378590\pi\) | |||||||
\(954\) | −5.56465 | −0.180162 | ||||||||
\(955\) | −10.2314 | −0.331082 | ||||||||
\(956\) | −16.8455 | −0.544822 | ||||||||
\(957\) | 20.2868 | 0.655779 | ||||||||
\(958\) | −68.6359 | −2.21753 | ||||||||
\(959\) | −46.9743 | −1.51688 | ||||||||
\(960\) | −1.83340 | −0.0591726 | ||||||||
\(961\) | −6.99223 | −0.225556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.73556 | −0.217050 | ||||||||
\(964\) | 7.81700 | 0.251769 | ||||||||
\(965\) | 14.1153 | 0.454387 | ||||||||
\(966\) | −17.5623 | −0.565056 | ||||||||
\(967\) | −38.8883 | −1.25056 | −0.625281 | − | 0.780399i | \(-0.715016\pi\) | ||||
−0.625281 | + | 0.780399i | \(0.715016\pi\) | |||||||
\(968\) | −21.5670 | −0.693191 | ||||||||
\(969\) | −5.99462 | −0.192575 | ||||||||
\(970\) | 22.5448 | 0.723870 | ||||||||
\(971\) | −57.5133 | −1.84569 | −0.922845 | − | 0.385171i | \(-0.874143\pi\) | ||||
−0.922845 | + | 0.385171i | \(0.874143\pi\) | |||||||
\(972\) | 1.24698 | 0.0399969 | ||||||||
\(973\) | 60.6378 | 1.94396 | ||||||||
\(974\) | −38.2911 | −1.22693 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.5200 | −0.528794 | ||||||||
\(977\) | 16.3690 | 0.523690 | 0.261845 | − | 0.965110i | \(-0.415669\pi\) | ||||
0.261845 | + | 0.965110i | \(0.415669\pi\) | |||||||
\(978\) | 11.2959 | 0.361203 | ||||||||
\(979\) | −6.00969 | −0.192070 | ||||||||
\(980\) | 8.77240 | 0.280224 | ||||||||
\(981\) | −2.07606 | −0.0662836 | ||||||||
\(982\) | −11.4426 | −0.365150 | ||||||||
\(983\) | −15.6963 | −0.500635 | −0.250318 | − | 0.968164i | \(-0.580535\pi\) | ||||
−0.250318 | + | 0.968164i | \(0.580535\pi\) | |||||||
\(984\) | −2.44504 | −0.0779451 | ||||||||
\(985\) | 33.8301 | 1.07792 | ||||||||
\(986\) | 5.30798 | 0.169040 | ||||||||
\(987\) | 36.3540 | 1.15716 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0804 | 0.638519 | ||||||||
\(990\) | −13.5036 | −0.429174 | ||||||||
\(991\) | −11.2644 | −0.357827 | −0.178913 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178913 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(992\) | 30.3099 | 0.962340 | ||||||||
\(993\) | −29.1618 | −0.925422 | ||||||||
\(994\) | −56.6122 | −1.79563 | ||||||||
\(995\) | 5.81594 | 0.184378 | ||||||||
\(996\) | −8.06398 | −0.255517 | ||||||||
\(997\) | −7.70112 | −0.243897 | −0.121948 | − | 0.992536i | \(-0.538914\pi\) | ||||
−0.121948 | + | 0.992536i | \(0.538914\pi\) | |||||||
\(998\) | −8.38059 | −0.265283 | ||||||||
\(999\) | 6.24698 | 0.197646 |
(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 | 507.2.a.k.1.3 | yes | 3 | |
3.2 | odd | 2 | 1521.2.a.p.1.1 | 3 | |||
4.3 | odd | 2 | 8112.2.a.cf.1.2 | 3 | |||
13.2 | odd | 12 | 507.2.j.h.316.6 | 12 | |||
13.3 | even | 3 | 507.2.e.j.22.1 | 6 | |||
13.4 | even | 6 | 507.2.e.k.484.3 | 6 | |||
13.5 | odd | 4 | 507.2.b.g.337.1 | 6 | |||
13.6 | odd | 12 | 507.2.j.h.361.1 | 12 | |||
13.7 | odd | 12 | 507.2.j.h.361.6 | 12 | |||
13.8 | odd | 4 | 507.2.b.g.337.6 | 6 | |||
13.9 | even | 3 | 507.2.e.j.484.1 | 6 | |||
13.10 | even | 6 | 507.2.e.k.22.3 | 6 | |||
13.11 | odd | 12 | 507.2.j.h.316.1 | 12 | |||
13.12 | even | 2 | 507.2.a.j.1.1 | ✓ | 3 | ||
39.5 | even | 4 | 1521.2.b.m.1351.6 | 6 | |||
39.8 | even | 4 | 1521.2.b.m.1351.1 | 6 | |||
39.38 | odd | 2 | 1521.2.a.q.1.3 | 3 | |||
52.51 | odd | 2 | 8112.2.a.by.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
507.2.a.k.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
507.2.b.g.337.1 | 6 | 13.5 | odd | 4 | |||
507.2.b.g.337.6 | 6 | 13.8 | odd | 4 | |||
507.2.e.j.22.1 | 6 | 13.3 | even | 3 | |||
507.2.e.j.484.1 | 6 | 13.9 | even | 3 | |||
507.2.e.k.22.3 | 6 | 13.10 | even | 6 | |||
507.2.e.k.484.3 | 6 | 13.4 | even | 6 | |||
507.2.j.h.316.1 | 12 | 13.11 | odd | 12 | |||
507.2.j.h.316.6 | 12 | 13.2 | odd | 12 | |||
507.2.j.h.361.1 | 12 | 13.6 | odd | 12 | |||
507.2.j.h.361.6 | 12 | 13.7 | odd | 12 | |||
1521.2.a.p.1.1 | 3 | 3.2 | odd | 2 | |||
1521.2.a.q.1.3 | 3 | 39.38 | odd | 2 | |||
1521.2.b.m.1351.1 | 6 | 39.8 | even | 4 | |||
1521.2.b.m.1351.6 | 6 | 39.5 | even | 4 | |||
8112.2.a.by.1.2 | 3 | 52.51 | odd | 2 | |||
8112.2.a.cf.1.2 | 3 | 4.3 | odd | 2 |