Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, 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("2025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 405) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.52434\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52434 | 1.78498 | 0.892488 | − | 0.451071i | \(-0.148958\pi\) | ||||
0.892488 | + | 0.451071i | \(0.148958\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.37228 | 2.18614 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 5.98844 | 2.11723 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.37228 | 0.413758 | 0.206879 | − | 0.978366i | \(-0.433669\pi\) | ||||
0.206879 | + | 0.978366i | \(0.433669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10891 | 1.13961 | 0.569804 | − | 0.821781i | \(-0.307019\pi\) | ||||
0.569804 | + | 0.821781i | \(0.307019\pi\) | |||||||
\(14\) | −8.74456 | −2.33708 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | 2.52434 | 0.612242 | 0.306121 | − | 0.951993i | \(-0.400969\pi\) | ||||
0.306121 | + | 0.951993i | \(0.400969\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.37228 | 1.23249 | 0.616243 | − | 0.787556i | \(-0.288654\pi\) | ||||
0.616243 | + | 0.787556i | \(0.288654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.46410 | 0.738549 | ||||||||
\(23\) | 5.04868 | 1.05272 | 0.526361 | − | 0.850261i | \(-0.323556\pi\) | ||||
0.526361 | + | 0.850261i | \(0.323556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.3723 | 2.03417 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −15.1460 | −2.86233 | ||||||||
\(29\) | 5.74456 | 1.06674 | 0.533369 | − | 0.845883i | \(-0.320926\pi\) | ||||
0.533369 | + | 0.845883i | \(0.320926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.627719 | 0.112742 | 0.0563708 | − | 0.998410i | \(-0.482047\pi\) | ||||
0.0563708 | + | 0.998410i | \(0.482047\pi\) | |||||||
\(32\) | 4.10891 | 0.726360 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.37228 | 1.09284 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.57301 | −1.24500 | −0.622498 | − | 0.782621i | \(-0.713882\pi\) | ||||
−0.622498 | + | 0.782621i | \(0.713882\pi\) | |||||||
\(38\) | 13.5615 | 2.19996 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.37228 | −0.214314 | −0.107157 | − | 0.994242i | \(-0.534175\pi\) | ||||
−0.107157 | + | 0.994242i | \(0.534175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.7446 | 1.87908 | ||||||||
\(47\) | −8.51278 | −1.24172 | −0.620858 | − | 0.783923i | \(-0.713216\pi\) | ||||
−0.620858 | + | 0.783923i | \(0.713216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17.9653 | 2.49134 | ||||||||
\(53\) | −5.34363 | −0.734004 | −0.367002 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367002 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −20.7446 | −2.77211 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.5012 | 1.90410 | ||||||||
\(59\) | 7.37228 | 0.959789 | 0.479895 | − | 0.877326i | \(-0.340675\pi\) | ||||
0.479895 | + | 0.877326i | \(0.340675\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62772 | 0.464482 | 0.232241 | − | 0.972658i | \(-0.425394\pi\) | ||||
0.232241 | + | 0.972658i | \(0.425394\pi\) | |||||||
\(62\) | 1.58457 | 0.201241 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.37228 | −0.296535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.21782 | 1.00397 | 0.501983 | − | 0.864877i | \(-0.332604\pi\) | ||||
0.501983 | + | 0.864877i | \(0.332604\pi\) | |||||||
\(68\) | 11.0371 | 1.33845 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.11684 | −0.488579 | −0.244290 | − | 0.969702i | \(-0.578555\pi\) | ||||
−0.244290 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.57301 | −0.886354 | −0.443177 | − | 0.896434i | \(-0.646149\pi\) | ||||
−0.443177 | + | 0.896434i | \(0.646149\pi\) | |||||||
\(74\) | −19.1168 | −2.22229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.4891 | 2.69439 | ||||||||
\(77\) | −4.75372 | −0.541737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.74456 | −0.533805 | −0.266903 | − | 0.963724i | \(-0.586000\pi\) | ||||
−0.266903 | + | 0.963724i | \(0.586000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.46410 | −0.382546 | ||||||||
\(83\) | −5.34363 | −0.586540 | −0.293270 | − | 0.956030i | \(-0.594743\pi\) | ||||
−0.293270 | + | 0.956030i | \(0.594743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.74456 | 0.942950 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.21782 | 0.876023 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2337 | −1.49210 | ||||||||
\(92\) | 22.0742 | 2.30140 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.4891 | −2.21643 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.6101 | −1.88957 | −0.944786 | − | 0.327688i | \(-0.893731\pi\) | ||||
−0.944786 | + | 0.327688i | \(0.893731\pi\) | |||||||
\(98\) | 12.6217 | 1.27498 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6277 | −1.05750 | −0.528749 | − | 0.848778i | \(-0.677339\pi\) | ||||
−0.528749 | + | 0.848778i | \(0.677339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820 | 0.682656 | 0.341328 | − | 0.939944i | \(-0.389123\pi\) | ||||
0.341328 | + | 0.939944i | \(0.389123\pi\) | |||||||
\(104\) | 24.6060 | 2.41281 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.4891 | −1.31018 | ||||||||
\(107\) | −13.2665 | −1.28252 | −0.641260 | − | 0.767323i | \(-0.721588\pi\) | ||||
−0.641260 | + | 0.767323i | \(0.721588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.74456 | −0.167099 | −0.0835494 | − | 0.996504i | \(-0.526626\pi\) | ||||
−0.0835494 | + | 0.996504i | \(0.526626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −22.0742 | −2.08582 | ||||||||
\(113\) | −9.45254 | −0.889220 | −0.444610 | − | 0.895724i | \(-0.646658\pi\) | ||||
−0.444610 | + | 0.895724i | \(0.646658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 25.1168 | 2.33204 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.6101 | 1.71320 | ||||||||
\(119\) | −8.74456 | −0.801613 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.11684 | −0.828804 | ||||||||
\(122\) | 9.15759 | 0.829089 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.74456 | 0.246469 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923 | 0.922168 | 0.461084 | − | 0.887357i | \(-0.347461\pi\) | ||||
0.461084 | + | 0.887357i | \(0.347461\pi\) | |||||||
\(128\) | −14.2063 | −1.25567 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.37228 | −0.119897 | −0.0599484 | − | 0.998201i | \(-0.519094\pi\) | ||||
−0.0599484 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.6101 | −1.61370 | ||||||||
\(134\) | 20.7446 | 1.79206 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.1168 | 1.29626 | ||||||||
\(137\) | −2.22938 | −0.190469 | −0.0952346 | − | 0.995455i | \(-0.530360\pi\) | ||||
−0.0952346 | + | 0.995455i | \(0.530360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.11684 | −0.518824 | −0.259412 | − | 0.965767i | \(-0.583529\pi\) | ||||
−0.259412 | + | 0.965767i | \(0.583529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3923 | −0.872103 | ||||||||
\(143\) | 5.63858 | 0.471522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.1168 | −1.58212 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.1113 | −2.72174 | ||||||||
\(149\) | 16.3723 | 1.34127 | 0.670635 | − | 0.741788i | \(-0.266022\pi\) | ||||
0.670635 | + | 0.741788i | \(0.266022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1168 | 1.47433 | 0.737164 | − | 0.675714i | \(-0.236165\pi\) | ||||
0.737164 | + | 0.675714i | \(0.236165\pi\) | |||||||
\(152\) | 32.1716 | 2.60946 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.4294 | 1.71025 | 0.855127 | − | 0.518419i | \(-0.173479\pi\) | ||||
0.855127 | + | 0.518419i | \(0.173479\pi\) | |||||||
\(158\) | −11.9769 | −0.952829 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.4891 | −1.37834 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.75372 | 0.372340 | 0.186170 | − | 0.982518i | \(-0.440392\pi\) | ||||
0.186170 | + | 0.982518i | \(0.440392\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.4891 | −1.04696 | ||||||||
\(167\) | −0.294954 | −0.0228242 | −0.0114121 | − | 0.999935i | \(-0.503633\pi\) | ||||
−0.0114121 | + | 0.999935i | \(0.503633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.88316 | 0.298704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.1460 | 1.15487 | ||||||||
\(173\) | 7.86797 | 0.598190 | 0.299095 | − | 0.954223i | \(-0.403315\pi\) | ||||
0.299095 | + | 0.954223i | \(0.403315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.74456 | 0.659146 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.57301 | −0.567621 | ||||||||
\(179\) | −22.1168 | −1.65309 | −0.826545 | − | 0.562870i | \(-0.809697\pi\) | ||||
−0.826545 | + | 0.562870i | \(0.809697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8614 | 1.10464 | 0.552320 | − | 0.833632i | \(-0.313743\pi\) | ||||
0.552320 | + | 0.833632i | \(0.313743\pi\) | |||||||
\(182\) | −35.9306 | −2.66336 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 30.2337 | 2.22886 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410 | 0.253320 | ||||||||
\(188\) | −37.2203 | −2.71457 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3723 | 0.967584 | 0.483792 | − | 0.875183i | \(-0.339259\pi\) | ||||
0.483792 | + | 0.875183i | \(0.339259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4294 | −1.54252 | −0.771262 | − | 0.636518i | \(-0.780374\pi\) | ||||
−0.771262 | + | 0.636518i | \(0.780374\pi\) | |||||||
\(194\) | −46.9783 | −3.37284 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.8614 | 1.56153 | ||||||||
\(197\) | −23.0140 | −1.63968 | −0.819840 | − | 0.572593i | \(-0.805937\pi\) | ||||
−0.819840 | + | 0.572593i | \(0.805937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26.8280 | −1.88761 | ||||||||
\(203\) | −19.8997 | −1.39669 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.4891 | 1.21853 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.1831 | 1.81547 | ||||||||
\(209\) | 7.37228 | 0.509951 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.8614 | 1.84922 | 0.924608 | − | 0.380921i | \(-0.124393\pi\) | ||||
0.924608 | + | 0.380921i | \(0.124393\pi\) | |||||||
\(212\) | −23.3639 | −1.60464 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −33.4891 | −2.28927 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.17448 | −0.147613 | ||||||||
\(218\) | −4.40387 | −0.298267 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3723 | 0.697715 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.28962 | −0.0863594 | −0.0431797 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431797 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(224\) | −14.2337 | −0.951028 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.8614 | −1.58724 | ||||||||
\(227\) | −0.294954 | −0.0195768 | −0.00978838 | − | 0.999952i | \(-0.503116\pi\) | ||||
−0.00978838 | + | 0.999952i | \(0.503116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.6060 | 1.49384 | 0.746922 | − | 0.664911i | \(-0.231531\pi\) | ||||
0.746922 | + | 0.664911i | \(0.231531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 34.4010 | 2.25853 | ||||||||
\(233\) | −9.45254 | −0.619257 | −0.309628 | − | 0.950858i | \(-0.600205\pi\) | ||||
−0.309628 | + | 0.950858i | \(0.600205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32.2337 | 2.09823 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.0742 | −1.43086 | ||||||||
\(239\) | −22.9783 | −1.48634 | −0.743170 | − | 0.669103i | \(-0.766679\pi\) | ||||
−0.743170 | + | 0.669103i | \(0.766679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.4891 | −1.57748 | −0.788742 | − | 0.614725i | \(-0.789267\pi\) | ||||
−0.788742 | + | 0.614725i | \(0.789267\pi\) | |||||||
\(242\) | −23.0140 | −1.47940 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.8614 | 1.01542 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.0742 | 1.40455 | ||||||||
\(248\) | 3.75906 | 0.238700 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2337 | 0.898422 | 0.449211 | − | 0.893426i | \(-0.351705\pi\) | ||||
0.449211 | + | 0.893426i | \(0.351705\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92820 | 0.435572 | ||||||||
\(254\) | 26.2337 | 1.64605 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | −23.0140 | −1.43557 | −0.717787 | − | 0.696263i | \(-0.754845\pi\) | ||||
−0.717787 | + | 0.696263i | \(0.754845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.2337 | 1.63008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.46410 | −0.214013 | ||||||||
\(263\) | −26.5330 | −1.63609 | −0.818047 | − | 0.575151i | \(-0.804943\pi\) | ||||
−0.818047 | + | 0.575151i | \(0.804943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −46.9783 | −2.88042 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.9306 | 2.19481 | ||||||||
\(269\) | 5.23369 | 0.319104 | 0.159552 | − | 0.987190i | \(-0.448995\pi\) | ||||
0.159552 | + | 0.987190i | \(0.448995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.7446 | 1.01716 | 0.508580 | − | 0.861015i | \(-0.330171\pi\) | ||||
0.508580 | + | 0.861015i | \(0.330171\pi\) | |||||||
\(272\) | 16.0858 | 0.975344 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.62772 | −0.339983 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17448 | 0.130652 | 0.0653260 | − | 0.997864i | \(-0.479191\pi\) | ||||
0.0653260 | + | 0.997864i | \(0.479191\pi\) | |||||||
\(278\) | −15.4410 | −0.926088 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.37228 | 0.260828 | 0.130414 | − | 0.991460i | \(-0.458369\pi\) | ||||
0.130414 | + | 0.991460i | \(0.458369\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7128 | 1.64736 | 0.823678 | − | 0.567058i | \(-0.191918\pi\) | ||||
0.823678 | + | 0.567058i | \(0.191918\pi\) | |||||||
\(284\) | −18.0000 | −1.06810 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.2337 | 0.841656 | ||||||||
\(287\) | 4.75372 | 0.280603 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6277 | −0.625160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −33.1113 | −1.93769 | ||||||||
\(293\) | −2.52434 | −0.147473 | −0.0737367 | − | 0.997278i | \(-0.523492\pi\) | ||||
−0.0737367 | + | 0.997278i | \(0.523492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −45.3505 | −2.63595 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 41.3292 | 2.39413 | ||||||||
\(299\) | 20.7446 | 1.19969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 45.7330 | 2.63164 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34.2337 | 1.96344 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.75372 | −0.271309 | −0.135655 | − | 0.990756i | \(-0.543314\pi\) | ||||
−0.135655 | + | 0.990756i | \(0.543314\pi\) | |||||||
\(308\) | −20.7846 | −1.18431 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8614 | 0.729303 | 0.364652 | − | 0.931144i | \(-0.381188\pi\) | ||||
0.364652 | + | 0.931144i | \(0.381188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.39853 | 0.305143 | 0.152572 | − | 0.988292i | \(-0.451245\pi\) | ||||
0.152572 | + | 0.988292i | \(0.451245\pi\) | |||||||
\(314\) | 54.0951 | 3.05276 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.7446 | −1.16697 | ||||||||
\(317\) | −6.98311 | −0.392210 | −0.196105 | − | 0.980583i | \(-0.562829\pi\) | ||||
−0.196105 | + | 0.980583i | \(0.562829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.88316 | 0.441372 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −44.1485 | −2.46030 | ||||||||
\(323\) | 13.5615 | 0.754579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.21782 | −0.453753 | ||||||||
\(329\) | 29.4891 | 1.62579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.11684 | −0.446142 | −0.223071 | − | 0.974802i | \(-0.571608\pi\) | ||||
−0.223071 | + | 0.974802i | \(0.571608\pi\) | |||||||
\(332\) | −23.3639 | −1.28226 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.744563 | −0.0407407 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.92820 | −0.377403 | −0.188702 | − | 0.982034i | \(-0.560428\pi\) | ||||
−0.188702 | + | 0.982034i | \(0.560428\pi\) | |||||||
\(338\) | 9.80240 | 0.533180 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.861407 | 0.0466478 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 20.7446 | 1.11847 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8614 | 1.06776 | ||||||||
\(347\) | −23.6588 | −1.27007 | −0.635036 | − | 0.772483i | \(-0.719015\pi\) | ||||
−0.635036 | + | 0.772483i | \(0.719015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6060 | 0.728311 | 0.364155 | − | 0.931338i | \(-0.381358\pi\) | ||||
0.364155 | + | 0.931338i | \(0.381358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.63858 | 0.300537 | ||||||||
\(353\) | 8.51278 | 0.453089 | 0.226545 | − | 0.974001i | \(-0.427257\pi\) | ||||
0.226545 | + | 0.974001i | \(0.427257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.1168 | −0.695191 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −55.8304 | −2.95073 | ||||||||
\(359\) | −28.1168 | −1.48395 | −0.741975 | − | 0.670427i | \(-0.766111\pi\) | ||||
−0.741975 | + | 0.670427i | \(0.766111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.86141 | 0.519021 | ||||||||
\(362\) | 37.5152 | 1.97176 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −62.2337 | −3.26193 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3639 | −1.21958 | −0.609792 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609792 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(368\) | 32.1716 | 1.67706 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.5109 | 0.961037 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6819 | 0.604867 | 0.302434 | − | 0.953170i | \(-0.402201\pi\) | ||||
0.302434 | + | 0.953170i | \(0.402201\pi\) | |||||||
\(374\) | 8.74456 | 0.452171 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −50.9783 | −2.62900 | ||||||||
\(377\) | 23.6039 | 1.21566 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4891 | 1.10382 | 0.551911 | − | 0.833903i | \(-0.313899\pi\) | ||||
0.551911 | + | 0.833903i | \(0.313899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.7562 | 1.72712 | ||||||||
\(383\) | 35.3407 | 1.80583 | 0.902913 | − | 0.429822i | \(-0.141424\pi\) | ||||
0.902913 | + | 0.429822i | \(0.141424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −54.0951 | −2.75337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −81.3687 | −4.13087 | ||||||||
\(389\) | −23.4891 | −1.19095 | −0.595473 | − | 0.803375i | \(-0.703035\pi\) | ||||
−0.595473 | + | 0.803375i | \(0.703035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7446 | 0.644520 | ||||||||
\(392\) | 29.9422 | 1.51231 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −58.0951 | −2.92679 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.3267 | 0.618661 | 0.309331 | − | 0.950955i | \(-0.399895\pi\) | ||||
0.309331 | + | 0.950955i | \(0.399895\pi\) | |||||||
\(398\) | 40.3894 | 2.02454 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.6277 | 0.980161 | 0.490081 | − | 0.871677i | \(-0.336967\pi\) | ||||
0.490081 | + | 0.871677i | \(0.336967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.57924 | 0.128481 | ||||||||
\(404\) | −46.4674 | −2.31184 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.2337 | −2.49306 | ||||||||
\(407\) | −10.3923 | −0.515127 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.86141 | −0.289828 | −0.144914 | − | 0.989444i | \(-0.546291\pi\) | ||||
−0.144914 | + | 0.989444i | \(0.546291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.2921 | 1.49238 | ||||||||
\(413\) | −25.5383 | −1.25666 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.8832 | 0.827765 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.6101 | 0.910251 | ||||||||
\(419\) | 5.48913 | 0.268161 | 0.134081 | − | 0.990970i | \(-0.457192\pi\) | ||||
0.134081 | + | 0.990970i | \(0.457192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2554 | −0.499819 | −0.249910 | − | 0.968269i | \(-0.580401\pi\) | ||||
−0.249910 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(422\) | 67.8073 | 3.30081 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.0000 | −1.55406 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5668 | −0.608149 | ||||||||
\(428\) | −58.0049 | −2.80377 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3505 | 0.883914 | 0.441957 | − | 0.897036i | \(-0.354284\pi\) | ||||
0.441957 | + | 0.897036i | \(0.354284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.81929 | 0.135487 | 0.0677433 | − | 0.997703i | \(-0.478420\pi\) | ||||
0.0677433 | + | 0.997703i | \(0.478420\pi\) | |||||||
\(434\) | −5.48913 | −0.263486 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.62772 | −0.365301 | ||||||||
\(437\) | 27.1229 | 1.29746 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.13859 | 0.149797 | 0.0748984 | − | 0.997191i | \(-0.476137\pi\) | ||||
0.0748984 | + | 0.997191i | \(0.476137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.1831 | 1.24541 | ||||||||
\(443\) | 24.9484 | 1.18534 | 0.592668 | − | 0.805447i | \(-0.298075\pi\) | ||||
0.592668 | + | 0.805447i | \(0.298075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.25544 | −0.154149 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.21782 | 0.388256 | ||||||||
\(449\) | −28.1168 | −1.32692 | −0.663458 | − | 0.748214i | \(-0.730912\pi\) | ||||
−0.663458 | + | 0.748214i | \(0.730912\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.88316 | −0.0886744 | ||||||||
\(452\) | −41.3292 | −1.94396 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.744563 | −0.0349441 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.86263 | 0.414577 | 0.207288 | − | 0.978280i | \(-0.433536\pi\) | ||||
0.207288 | + | 0.978280i | \(0.433536\pi\) | |||||||
\(458\) | 57.0651 | 2.66648 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.0951 | −1.82084 | −0.910420 | − | 0.413685i | \(-0.864241\pi\) | ||||
−0.910420 | + | 0.413685i | \(0.864241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8564 | −0.643962 | −0.321981 | − | 0.946746i | \(-0.604349\pi\) | ||||
−0.321981 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(464\) | 36.6060 | 1.69939 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.8614 | −1.10536 | ||||||||
\(467\) | 14.8511 | 0.687226 | 0.343613 | − | 0.939111i | \(-0.388349\pi\) | ||||
0.343613 | + | 0.939111i | \(0.388349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.4674 | −1.31450 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 44.1485 | 2.03210 | ||||||||
\(473\) | 4.75372 | 0.218576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −38.2337 | −1.75244 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −58.0049 | −2.65308 | ||||||||
\(479\) | −21.6060 | −0.987202 | −0.493601 | − | 0.869688i | \(-0.664320\pi\) | ||||
−0.493601 | + | 0.869688i | \(0.664320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.1168 | −1.41881 | ||||||||
\(482\) | −61.8188 | −2.81577 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.8614 | −1.81188 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2921 | −1.37266 | −0.686332 | − | 0.727288i | \(-0.740780\pi\) | ||||
−0.686332 | + | 0.727288i | \(0.740780\pi\) | |||||||
\(488\) | 21.7244 | 0.983416 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.3723 | −1.68659 | −0.843294 | − | 0.537453i | \(-0.819387\pi\) | ||||
−0.843294 | + | 0.537453i | \(0.819387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5012 | 0.653102 | ||||||||
\(494\) | 55.7228 | 2.50709 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 14.2612 | 0.639701 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6277 | −0.833891 | −0.416946 | − | 0.908931i | \(-0.636899\pi\) | ||||
−0.416946 | + | 0.908931i | \(0.636899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 35.9306 | 1.60366 | ||||||||
\(503\) | −10.0974 | −0.450219 | −0.225109 | − | 0.974334i | \(-0.572274\pi\) | ||||
−0.225109 | + | 0.974334i | \(0.572274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.4891 | 0.777486 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 45.4381 | 2.01599 | ||||||||
\(509\) | 23.4891 | 1.04114 | 0.520569 | − | 0.853820i | \(-0.325720\pi\) | ||||
0.520569 | + | 0.853820i | \(0.325720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.2337 | 1.16051 | ||||||||
\(512\) | −50.1369 | −2.21576 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −58.0951 | −2.56246 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6819 | −0.513770 | ||||||||
\(518\) | 66.2227 | 2.90966 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1460 | −0.662290 | −0.331145 | − | 0.943580i | \(-0.607435\pi\) | ||||
−0.331145 | + | 0.943580i | \(0.607435\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −66.9783 | −2.92039 | ||||||||
\(527\) | 1.58457 | 0.0690251 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.48913 | 0.108223 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −81.3687 | −3.52778 | ||||||||
\(533\) | −5.63858 | −0.244234 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 49.2119 | 2.12563 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.2116 | 0.569592 | ||||||||
\(539\) | 6.86141 | 0.295542 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2337 | −0.654947 | −0.327474 | − | 0.944860i | \(-0.606197\pi\) | ||||
−0.327474 | + | 0.944860i | \(0.606197\pi\) | |||||||
\(542\) | 42.2689 | 1.81561 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.3723 | 0.444708 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.92820 | 0.296229 | 0.148114 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148114 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(548\) | −9.74749 | −0.416392 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.8614 | 1.31474 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.4356 | 0.698915 | ||||||||
\(554\) | 5.48913 | 0.233211 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.7446 | −1.13422 | ||||||||
\(557\) | −21.7244 | −0.920491 | −0.460246 | − | 0.887792i | \(-0.652239\pi\) | ||||
−0.460246 | + | 0.887792i | \(0.652239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2337 | 0.602021 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.0371 | 0.465573 | ||||||||
\(563\) | −0.994667 | −0.0419202 | −0.0209601 | − | 0.999780i | \(-0.506672\pi\) | ||||
−0.0209601 | + | 0.999780i | \(0.506672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 69.9565 | 2.94049 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.6535 | −1.03444 | ||||||||
\(569\) | −2.48913 | −0.104350 | −0.0521748 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521748 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.8614 | 1.37521 | 0.687604 | − | 0.726086i | \(-0.258663\pi\) | ||||
0.687604 | + | 0.726086i | \(0.258663\pi\) | |||||||
\(572\) | 24.6535 | 1.03081 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.3576 | −1.18054 | −0.590272 | − | 0.807205i | \(-0.700979\pi\) | ||||
−0.590272 | + | 0.807205i | \(0.700979\pi\) | |||||||
\(578\) | −26.8280 | −1.11590 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.5109 | 0.767960 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.33296 | −0.303700 | ||||||||
\(584\) | −45.3505 | −1.87662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.37228 | −0.263237 | ||||||||
\(587\) | −9.80240 | −0.404588 | −0.202294 | − | 0.979325i | \(-0.564840\pi\) | ||||
−0.202294 | + | 0.979325i | \(0.564840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.37228 | 0.138952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −48.2574 | −1.98337 | ||||||||
\(593\) | 38.1600 | 1.56704 | 0.783522 | − | 0.621364i | \(-0.213421\pi\) | ||||
0.783522 | + | 0.621364i | \(0.213421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 71.5842 | 2.93220 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 52.3663 | 2.14142 | ||||||||
\(599\) | 7.37228 | 0.301223 | 0.150612 | − | 0.988593i | \(-0.451876\pi\) | ||||
0.150612 | + | 0.988593i | \(0.451876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.9783 | 1.14126 | 0.570628 | − | 0.821208i | \(-0.306700\pi\) | ||||
0.570628 | + | 0.821208i | \(0.306700\pi\) | |||||||
\(602\) | −30.2921 | −1.23461 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 79.2119 | 3.22309 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.3354 | −1.47481 | −0.737404 | − | 0.675452i | \(-0.763949\pi\) | ||||
−0.737404 | + | 0.675452i | \(0.763949\pi\) | |||||||
\(608\) | 22.0742 | 0.895228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.9783 | −1.41507 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.50744 | −0.384002 | −0.192001 | − | 0.981395i | \(-0.561498\pi\) | ||||
−0.192001 | + | 0.981395i | \(0.561498\pi\) | |||||||
\(614\) | −12.0000 | −0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.4674 | −1.14698 | ||||||||
\(617\) | 22.4241 | 0.902760 | 0.451380 | − | 0.892332i | \(-0.350932\pi\) | ||||
0.451380 | + | 0.892332i | \(0.350932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.4665 | 1.30179 | ||||||||
\(623\) | 10.3923 | 0.416359 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.6277 | 0.544673 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 93.6955 | 3.73886 | ||||||||
\(629\) | −19.1168 | −0.762238 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.627719 | 0.0249891 | 0.0124945 | − | 0.999922i | \(-0.496023\pi\) | ||||
0.0124945 | + | 0.999922i | \(0.496023\pi\) | |||||||
\(632\) | −28.4125 | −1.13019 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.6277 | −0.700086 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.5446 | 0.814005 | ||||||||
\(638\) | 19.8997 | 0.787839 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.9783 | −1.50005 | −0.750025 | − | 0.661409i | \(-0.769959\pi\) | ||||
−0.750025 | + | 0.661409i | \(0.769959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6101 | −0.733912 | −0.366956 | − | 0.930238i | \(-0.619600\pi\) | ||||
−0.366956 | + | 0.930238i | \(0.619600\pi\) | |||||||
\(644\) | −76.4674 | −3.01324 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.2337 | 1.34691 | ||||||||
\(647\) | 4.45877 | 0.175292 | 0.0876461 | − | 0.996152i | \(-0.472066\pi\) | ||||
0.0876461 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1168 | 0.397121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.7846 | 0.813988 | ||||||||
\(653\) | 20.1947 | 0.790280 | 0.395140 | − | 0.918621i | \(-0.370696\pi\) | ||||
0.395140 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.74456 | −0.341418 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 74.4405 | 2.90199 | ||||||||
\(659\) | 32.7446 | 1.27555 | 0.637774 | − | 0.770224i | \(-0.279856\pi\) | ||||
0.637774 | + | 0.770224i | \(0.279856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2337 | 0.748104 | 0.374052 | − | 0.927408i | \(-0.377968\pi\) | ||||
0.374052 | + | 0.927408i | \(0.377968\pi\) | |||||||
\(662\) | −20.4897 | −0.796353 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.0000 | −1.24184 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.0024 | 1.12298 | ||||||||
\(668\) | −1.28962 | −0.0498969 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.97825 | 0.192183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.2549 | −0.742223 | −0.371112 | − | 0.928588i | \(-0.621023\pi\) | ||||
−0.371112 | + | 0.928588i | \(0.621023\pi\) | |||||||
\(674\) | −17.4891 | −0.673656 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.9783 | 0.653010 | ||||||||
\(677\) | 26.5330 | 1.01975 | 0.509873 | − | 0.860250i | \(-0.329692\pi\) | ||||
0.509873 | + | 0.860250i | \(0.329692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.4674 | 2.47403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.17448 | 0.0832652 | ||||||||
\(683\) | −0.589907 | −0.0225722 | −0.0112861 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112861 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.4891 | 0.667738 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 22.0742 | 0.841572 | ||||||||
\(689\) | −21.9565 | −0.836476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7228 | −0.445957 | −0.222978 | − | 0.974823i | \(-0.571578\pi\) | ||||
−0.222978 | + | 0.974823i | \(0.571578\pi\) | |||||||
\(692\) | 34.4010 | 1.30773 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −59.7228 | −2.26705 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.46410 | −0.131212 | ||||||||
\(698\) | 34.3461 | 1.30002 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2337 | −0.650907 | −0.325454 | − | 0.945558i | \(-0.605517\pi\) | ||||
−0.325454 | + | 0.945558i | \(0.605517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.6844 | −1.53444 | ||||||||
\(704\) | −3.25544 | −0.122694 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.4891 | 0.808754 | ||||||||
\(707\) | 36.8155 | 1.38459 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.649468 | 0.0243913 | 0.0121956 | − | 0.999926i | \(-0.496118\pi\) | ||||
0.0121956 | + | 0.999926i | \(0.496118\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.9653 | −0.673279 | ||||||||
\(713\) | 3.16915 | 0.118686 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −96.7011 | −3.61389 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −70.9764 | −2.64882 | ||||||||
\(719\) | 28.1168 | 1.04858 | 0.524291 | − | 0.851539i | \(-0.324331\pi\) | ||||
0.524291 | + | 0.851539i | \(0.324331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 24.8935 | 0.926441 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 64.9783 | 2.41490 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7971 | 0.400441 | 0.200220 | − | 0.979751i | \(-0.435834\pi\) | ||||
0.200220 | + | 0.979751i | \(0.435834\pi\) | |||||||
\(728\) | −85.2376 | −3.15911 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.74456 | 0.323429 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.3639 | −0.862964 | −0.431482 | − | 0.902122i | \(-0.642009\pi\) | ||||
−0.431482 | + | 0.902122i | \(0.642009\pi\) | |||||||
\(734\) | −58.9783 | −2.17693 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.7446 | 0.764655 | ||||||||
\(737\) | 11.2772 | 0.415400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3723 | 0.418336 | 0.209168 | − | 0.977880i | \(-0.432924\pi\) | ||||
0.209168 | + | 0.977880i | \(0.432924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46.7277 | 1.71543 | ||||||||
\(743\) | −42.5639 | −1.56152 | −0.780759 | − | 0.624833i | \(-0.785167\pi\) | ||||
−0.780759 | + | 0.624833i | \(0.785167\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.4891 | 1.07967 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.1460 | 0.553794 | ||||||||
\(749\) | 45.9565 | 1.67921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.7228 | −1.30354 | −0.651772 | − | 0.758415i | \(-0.725974\pi\) | ||||
−0.651772 | + | 0.758415i | \(0.725974\pi\) | |||||||
\(752\) | −54.2458 | −1.97814 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 59.5842 | 2.16993 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.5692 | 1.51086 | 0.755429 | − | 0.655230i | \(-0.227428\pi\) | ||||
0.755429 | + | 0.655230i | \(0.227428\pi\) | |||||||
\(758\) | 54.2458 | 1.97030 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.51087 | 0.344769 | 0.172384 | − | 0.985030i | \(-0.444853\pi\) | ||||
0.172384 | + | 0.985030i | \(0.444853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.04334 | 0.218784 | ||||||||
\(764\) | 58.4674 | 2.11528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 89.2119 | 3.22336 | ||||||||
\(767\) | 30.2921 | 1.09378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.48913 | 0.234004 | 0.117002 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.117002 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −93.6955 | −3.37217 | ||||||||
\(773\) | 18.2603 | 0.656776 | 0.328388 | − | 0.944543i | \(-0.393495\pi\) | ||||
0.328388 | + | 0.944543i | \(0.393495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −111.446 | −4.00066 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −59.2945 | −2.12581 | ||||||||
\(779\) | −7.37228 | −0.264139 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.64947 | −0.202154 | ||||||||
\(782\) | 32.1716 | 1.15045 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.8614 | 1.13791 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3205 | −0.617409 | −0.308705 | − | 0.951158i | \(-0.599895\pi\) | ||||
−0.308705 | + | 0.951158i | \(0.599895\pi\) | |||||||
\(788\) | −100.624 | −3.58457 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.7446 | 1.16426 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9060 | 0.529327 | ||||||||
\(794\) | 31.1168 | 1.10430 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 69.9565 | 2.47954 | ||||||||
\(797\) | 48.8473 | 1.73026 | 0.865130 | − | 0.501548i | \(-0.167236\pi\) | ||||
0.865130 | + | 0.501548i | \(0.167236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.4891 | −0.760231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49.5470 | 1.74957 | ||||||||
\(803\) | −10.3923 | −0.366736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.51087 | 0.229336 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −63.6434 | −2.23897 | ||||||||
\(809\) | 21.0000 | 0.738321 | 0.369160 | − | 0.929366i | \(-0.379645\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.1168 | 1.47892 | 0.739461 | − | 0.673199i | \(-0.235080\pi\) | ||||
0.739461 | + | 0.673199i | \(0.235080\pi\) | |||||||
\(812\) | −87.0073 | −3.05336 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.2337 | −0.919490 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.6101 | 0.651086 | ||||||||
\(818\) | −14.7962 | −0.517336 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.7228 | 0.583630 | 0.291815 | − | 0.956475i | \(-0.405741\pi\) | ||||
0.291815 | + | 0.956475i | \(0.405741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1485 | −1.53892 | −0.769459 | − | 0.638696i | \(-0.779474\pi\) | ||||
−0.769459 | + | 0.638696i | \(0.779474\pi\) | |||||||
\(824\) | 41.4891 | 1.44534 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −64.4674 | −2.24311 | ||||||||
\(827\) | 15.7359 | 0.547192 | 0.273596 | − | 0.961845i | \(-0.411787\pi\) | ||||
0.273596 | + | 0.961845i | \(0.411787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3505 | 0.984655 | 0.492327 | − | 0.870410i | \(-0.336146\pi\) | ||||
0.492327 | + | 0.870410i | \(0.336146\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.74749 | −0.337934 | ||||||||
\(833\) | 12.6217 | 0.437316 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.2337 | 1.11483 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8564 | 0.478662 | ||||||||
\(839\) | −17.1386 | −0.591690 | −0.295845 | − | 0.955236i | \(-0.595601\pi\) | ||||
−0.295845 | + | 0.955236i | \(0.595601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00000 | 0.137931 | ||||||||
\(842\) | −25.8882 | −0.892166 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 117.446 | 4.04265 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.5817 | 1.08516 | ||||||||
\(848\) | −34.0511 | −1.16932 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.2337 | −1.31063 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.9022 | 1.67438 | 0.837189 | − | 0.546913i | \(-0.184197\pi\) | ||||
0.837189 | + | 0.546913i | \(0.184197\pi\) | |||||||
\(854\) | −31.7228 | −1.08553 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −79.4456 | −2.71540 | ||||||||
\(857\) | −26.8829 | −0.918301 | −0.459150 | − | 0.888359i | \(-0.651846\pi\) | ||||
−0.459150 | + | 0.888359i | \(0.651846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.3288 | −1.68308 | −0.841538 | − | 0.540198i | \(-0.818349\pi\) | ||||
−0.841538 | + | 0.540198i | \(0.818349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.3229 | 1.57777 | ||||||||
\(863\) | 9.80240 | 0.333677 | 0.166839 | − | 0.985984i | \(-0.446644\pi\) | ||||
0.166839 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.11684 | 0.241840 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.50744 | −0.322704 | ||||||||
\(869\) | −6.51087 | −0.220866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.7663 | 1.14413 | ||||||||
\(872\) | −10.4472 | −0.353787 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 68.4674 | 2.31594 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0371 | 0.372697 | 0.186348 | − | 0.982484i | \(-0.440335\pi\) | ||||
0.186348 | + | 0.982484i | \(0.440335\pi\) | |||||||
\(878\) | 7.92287 | 0.267384 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.1168 | 0.947281 | 0.473640 | − | 0.880718i | \(-0.342940\pi\) | ||||
0.473640 | + | 0.880718i | \(0.342940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5532 | 1.49934 | 0.749668 | − | 0.661815i | \(-0.230213\pi\) | ||||
0.749668 | + | 0.661815i | \(0.230213\pi\) | |||||||
\(884\) | 45.3505 | 1.52530 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 62.9783 | 2.11580 | ||||||||
\(887\) | 9.21249 | 0.309325 | 0.154663 | − | 0.987967i | \(-0.450571\pi\) | ||||
0.154663 | + | 0.987967i | \(0.450571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.0000 | −1.20740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.63858 | −0.188794 | ||||||||
\(893\) | −45.7330 | −1.53040 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 49.2119 | 1.64406 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −70.9764 | −2.36851 | ||||||||
\(899\) | 3.60597 | 0.120266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4891 | −0.449388 | ||||||||
\(902\) | −4.75372 | −0.158282 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −56.6060 | −1.88269 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.0049 | 1.92602 | 0.963010 | − | 0.269466i | \(-0.0868471\pi\) | ||||
0.963010 | + | 0.269466i | \(0.0868471\pi\) | |||||||
\(908\) | −1.28962 | −0.0427976 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.6060 | 0.715838 | 0.357919 | − | 0.933753i | \(-0.383486\pi\) | ||||
0.357919 | + | 0.933753i | \(0.383486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.33296 | −0.242686 | ||||||||
\(914\) | 22.3723 | 0.740009 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.8397 | 3.26575 | ||||||||
\(917\) | 4.75372 | 0.156982 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.64947 | 0.120385 | 0.0601924 | − | 0.998187i | \(-0.480829\pi\) | ||||
0.0601924 | + | 0.998187i | \(0.480829\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −98.6892 | −3.25016 | ||||||||
\(923\) | −16.9157 | −0.556789 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.9783 | −1.14946 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.6039 | 0.774836 | ||||||||
\(929\) | −26.4891 | −0.869080 | −0.434540 | − | 0.900653i | \(-0.643089\pi\) | ||||
−0.434540 | + | 0.900653i | \(0.643089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8614 | 0.880347 | ||||||||
\(932\) | −41.3292 | −1.35378 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.4891 | 1.22668 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4728 | −0.897496 | −0.448748 | − | 0.893658i | \(-0.648130\pi\) | ||||
−0.448748 | + | 0.893658i | \(0.648130\pi\) | |||||||
\(938\) | −71.8613 | −2.34635 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.8614 | 0.712661 | 0.356331 | − | 0.934360i | \(-0.384028\pi\) | ||||
0.356331 | + | 0.934360i | \(0.384028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.92820 | −0.225613 | ||||||||
\(944\) | 46.9783 | 1.52901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 36.5205 | 1.18676 | 0.593379 | − | 0.804923i | \(-0.297794\pi\) | ||||
0.593379 | + | 0.804923i | \(0.297794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.1168 | −1.01010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −52.3663 | −1.69720 | ||||||||
\(953\) | 21.7244 | 0.703721 | 0.351861 | − | 0.936052i | \(-0.385549\pi\) | ||||
0.351861 | + | 0.936052i | \(0.385549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −100.467 | −3.24935 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −54.5408 | −1.76213 | ||||||||
\(959\) | 7.72281 | 0.249383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6060 | −0.987289 | ||||||||
\(962\) | −78.5494 | −2.53254 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −107.073 | −3.44860 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.3354 | −1.16847 | −0.584234 | − | 0.811585i | \(-0.698605\pi\) | ||||
−0.584234 | + | 0.811585i | \(0.698605\pi\) | |||||||
\(968\) | −54.5957 | −1.75477 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.5842 | −1.43078 | −0.715388 | − | 0.698728i | \(-0.753750\pi\) | ||||
−0.715388 | + | 0.698728i | \(0.753750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.1894 | 0.679300 | ||||||||
\(974\) | −76.4674 | −2.45017 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.1168 | 0.739952 | ||||||||
\(977\) | −54.8357 | −1.75435 | −0.877175 | − | 0.480171i | \(-0.840575\pi\) | ||||
−0.877175 | + | 0.480171i | \(0.840575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.11684 | −0.131575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −94.3403 | −3.01052 | ||||||||
\(983\) | 57.0102 | 1.81834 | 0.909171 | − | 0.416422i | \(-0.136716\pi\) | ||||
0.909171 | + | 0.416422i | \(0.136716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.6060 | 1.16577 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 96.5147 | 3.07054 | ||||||||
\(989\) | 17.4891 | 0.556122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.60597 | −0.0510153 | −0.0255076 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255076 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(992\) | 2.57924 | 0.0818910 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.0000 | 1.14185 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.6324 | 0.336730 | 0.168365 | − | 0.985725i | \(-0.446151\pi\) | ||||
0.168365 | + | 0.985725i | \(0.446151\pi\) | |||||||
\(998\) | −47.0227 | −1.48848 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2025.2.a.w.1.4 | 4 | ||
3.2 | odd | 2 | 2025.2.a.x.1.1 | 4 | |||
5.2 | odd | 4 | 405.2.b.a.244.4 | yes | 4 | ||
5.3 | odd | 4 | 405.2.b.a.244.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 2025.2.a.w.1.1 | 4 | ||
15.2 | even | 4 | 405.2.b.b.244.1 | yes | 4 | ||
15.8 | even | 4 | 405.2.b.b.244.4 | yes | 4 | ||
15.14 | odd | 2 | 2025.2.a.x.1.4 | 4 | |||
45.2 | even | 12 | 405.2.j.a.109.1 | 4 | |||
45.7 | odd | 12 | 405.2.j.e.109.2 | 4 | |||
45.13 | odd | 12 | 405.2.j.e.379.2 | 4 | |||
45.22 | odd | 12 | 405.2.j.b.379.1 | 4 | |||
45.23 | even | 12 | 405.2.j.a.379.1 | 4 | |||
45.32 | even | 12 | 405.2.j.d.379.2 | 4 | |||
45.38 | even | 12 | 405.2.j.d.109.2 | 4 | |||
45.43 | odd | 12 | 405.2.j.b.109.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.b.a.244.1 | ✓ | 4 | 5.3 | odd | 4 | ||
405.2.b.a.244.4 | yes | 4 | 5.2 | odd | 4 | ||
405.2.b.b.244.1 | yes | 4 | 15.2 | even | 4 | ||
405.2.b.b.244.4 | yes | 4 | 15.8 | even | 4 | ||
405.2.j.a.109.1 | 4 | 45.2 | even | 12 | |||
405.2.j.a.379.1 | 4 | 45.23 | even | 12 | |||
405.2.j.b.109.1 | 4 | 45.43 | odd | 12 | |||
405.2.j.b.379.1 | 4 | 45.22 | odd | 12 | |||
405.2.j.d.109.2 | 4 | 45.38 | even | 12 | |||
405.2.j.d.379.2 | 4 | 45.32 | even | 12 | |||
405.2.j.e.109.2 | 4 | 45.7 | odd | 12 | |||
405.2.j.e.379.2 | 4 | 45.13 | odd | 12 | |||
2025.2.a.w.1.1 | 4 | 5.4 | even | 2 | inner | ||
2025.2.a.w.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2025.2.a.x.1.1 | 4 | 3.2 | odd | 2 | |||
2025.2.a.x.1.4 | 4 | 15.14 | odd | 2 |