Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4160,2,Mod(1,4160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4160 = 2^{6} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4160.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: | \(33.2177672409\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 520) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.73205 | −0.705412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26795 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.46410 | 2.06524 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.19615 | 1.70902 | 0.854508 | − | 0.519438i | \(-0.173859\pi\) | ||||
0.854508 | + | 0.519438i | \(0.173859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.46410 | 1.01466 | 0.507329 | − | 0.861752i | \(-0.330633\pi\) | ||||
0.507329 | + | 0.861752i | \(0.330633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.73205 | 0.849901 | 0.424951 | − | 0.905216i | \(-0.360291\pi\) | ||||
0.424951 | + | 0.905216i | \(0.360291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.9282 | 2.25051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.92820 | 0.481394 | 0.240697 | − | 0.970600i | \(-0.422624\pi\) | ||||
0.240697 | + | 0.970600i | \(0.422624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.73205 | 0.437478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4641 | −1.79039 | −0.895196 | − | 0.445673i | \(-0.852964\pi\) | ||||
−0.895196 | + | 0.445673i | \(0.852964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.73205 | −0.416634 | −0.208317 | − | 0.978061i | \(-0.566799\pi\) | ||||
−0.208317 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46410 | 0.665469 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4641 | 1.67221 | 0.836106 | − | 0.548569i | \(-0.184827\pi\) | ||||
0.836106 | + | 0.548569i | \(0.184827\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.46410 | −1.32524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4641 | −1.57472 | −0.787358 | − | 0.616496i | \(-0.788551\pi\) | ||||
−0.787358 | + | 0.616496i | \(0.788551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.73205 | −0.638070 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.92820 | 1.18257 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.80385 | −0.234841 | −0.117420 | − | 0.993082i | \(-0.537463\pi\) | ||||
−0.117420 | + | 0.993082i | \(0.537463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.46410 | 0.699607 | 0.349803 | − | 0.936823i | \(-0.386248\pi\) | ||||
0.349803 | + | 0.936823i | \(0.386248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.4641 | −1.94829 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8564 | 1.93717 | 0.968584 | − | 0.248686i | \(-0.0799987\pi\) | ||||
0.968584 | + | 0.248686i | \(0.0799987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.3923 | −2.69572 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6603 | −1.38382 | −0.691909 | − | 0.721985i | \(-0.743230\pi\) | ||||
−0.691909 | + | 0.721985i | \(0.743230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.73205 | −0.315470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3923 | 1.86808 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.53590 | −0.285311 | −0.142655 | − | 0.989772i | \(-0.545564\pi\) | ||||
−0.142655 | + | 0.989772i | \(0.545564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4641 | 1.25835 | 0.629174 | − | 0.777264i | \(-0.283393\pi\) | ||||
0.629174 | + | 0.777264i | \(0.283393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.9282 | −1.60047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.92820 | −0.522388 | −0.261194 | − | 0.965286i | \(-0.584116\pi\) | ||||
−0.261194 | + | 0.965286i | \(0.584116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.46410 | 0.363137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.9282 | −1.34059 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.26795 | −0.335285 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8564 | −1.20384 | −0.601918 | − | 0.798558i | \(-0.705597\pi\) | ||||
−0.601918 | + | 0.798558i | \(0.705597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21.1244 | −2.12308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.07180 | 0.305655 | 0.152828 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152828 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.73205 | 0.663329 | 0.331664 | − | 0.943397i | \(-0.392390\pi\) | ||||
0.331664 | + | 0.943397i | \(0.392390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.46410 | 0.923602 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.80385 | −0.367732 | −0.183866 | − | 0.982951i | \(-0.558861\pi\) | ||||
−0.183866 | + | 0.982951i | \(0.558861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.39230 | −0.601337 | −0.300669 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19615 | 0.764295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.46410 | −0.412706 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31.3205 | 2.82408 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.12436 | 0.632184 | 0.316092 | − | 0.948728i | \(-0.397629\pi\) | ||||
0.316092 | + | 0.948728i | \(0.397629\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46410 | 0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.92820 | −0.255838 | −0.127919 | − | 0.991785i | \(-0.540830\pi\) | ||||
−0.127919 | + | 0.991785i | \(0.540830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3205 | 0.981613 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.928203 | 0.0793018 | 0.0396509 | − | 0.999214i | \(-0.487375\pi\) | ||||
0.0396509 | + | 0.999214i | \(0.487375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3923 | −1.05110 | −0.525551 | − | 0.850762i | \(-0.676141\pi\) | ||||
−0.525551 | + | 0.850762i | \(0.676141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.3205 | −2.63766 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.73205 | 0.395714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.46410 | 0.453769 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6603 | −1.12668 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.85641 | −0.315929 | −0.157965 | − | 0.987445i | \(-0.550493\pi\) | ||||
−0.157965 | + | 0.987445i | \(0.550493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.73205 | 0.710604 | 0.355302 | − | 0.934752i | \(-0.384378\pi\) | ||||
0.355302 | + | 0.934752i | \(0.384378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.4641 | 1.25020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.73205 | 0.380087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.3205 | 2.48388 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.3923 | −2.23763 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.8564 | −1.24197 | −0.620985 | − | 0.783823i | \(-0.713267\pi\) | ||||
−0.620985 | + | 0.783823i | \(0.713267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.9282 | 1.00646 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.3923 | −1.11371 | −0.556855 | − | 0.830610i | \(-0.687992\pi\) | ||||
−0.556855 | + | 0.830610i | \(0.687992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.5885 | −1.11561 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.3923 | 1.70246 | 0.851228 | − | 0.524797i | \(-0.175859\pi\) | ||||
0.851228 | + | 0.524797i | \(0.175859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | −0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.92820 | 0.370426 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8564 | 1.03568 | 0.517838 | − | 0.855479i | \(-0.326737\pi\) | ||||
0.517838 | + | 0.855479i | \(0.326737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3205 | −0.841447 | −0.420723 | − | 0.907189i | \(-0.638224\pi\) | ||||
−0.420723 | + | 0.907189i | \(0.638224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.9282 | −1.10352 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.92820 | 0.215286 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.3923 | −1.19872 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8564 | 1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07180 | −0.366982 | −0.183491 | − | 0.983021i | \(-0.558740\pi\) | ||||
−0.183491 | + | 0.983021i | \(0.558740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.73205 | 0.195646 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.928203 | −0.0661317 | −0.0330659 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330659 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9282 | −1.05823 | −0.529116 | − | 0.848549i | \(-0.677476\pi\) | ||||
−0.529116 | + | 0.848549i | \(0.677476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43.3205 | −3.05559 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.9282 | −1.32850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4641 | −0.800688 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.5885 | 2.54307 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.4641 | 1.06967 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7846 | 1.70624 | 0.853121 | − | 0.521712i | \(-0.174707\pi\) | ||||
0.853121 | + | 0.521712i | \(0.174707\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.8564 | 2.18277 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.73205 | −0.186324 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.3923 | −1.11278 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.46410 | −0.233021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.39230 | 0.160201 | 0.0801003 | − | 0.996787i | \(-0.474476\pi\) | ||||
0.0801003 | + | 0.996787i | \(0.474476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.9282 | −1.92003 | −0.960016 | − | 0.279945i | \(-0.909684\pi\) | ||||
−0.960016 | + | 0.279945i | \(0.909684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.535898 | 0.0354132 | 0.0177066 | − | 0.999843i | \(-0.494364\pi\) | ||||
0.0177066 | + | 0.999843i | \(0.494364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −44.7846 | −2.94661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4641 | 0.747836 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.92820 | 0.450035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.5167 | −1.65054 | −0.825268 | − | 0.564742i | \(-0.808976\pi\) | ||||
−0.825268 | + | 0.564742i | \(0.808976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.39230 | 0.154102 | 0.0770510 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770510 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.26795 | 0.207935 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −31.3205 | −1.98486 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4641 | −0.849847 | −0.424923 | − | 0.905229i | \(-0.639699\pi\) | ||||
−0.424923 | + | 0.905229i | \(0.639699\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.7846 | −2.43837 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.46410 | −0.592665 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.8564 | −0.989095 | −0.494548 | − | 0.869150i | \(-0.664666\pi\) | ||||
−0.494548 | + | 0.869150i | \(0.664666\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1436 | −0.630292 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.3923 | 1.50985 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.5885 | −1.51619 | −0.758095 | − | 0.652145i | \(-0.773869\pi\) | ||||
−0.758095 | + | 0.652145i | \(0.773869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.4641 | −0.704234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4641 | 0.823990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.8564 | −0.966782 | −0.483391 | − | 0.875405i | \(-0.660595\pi\) | ||||
−0.483391 | + | 0.875405i | \(0.660595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1962 | −1.10534 | −0.552669 | − | 0.833401i | \(-0.686391\pi\) | ||||
−0.552669 | + | 0.833401i | \(0.686391\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.46410 | −0.572793 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.73205 | −0.285353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.3923 | −1.58576 | −0.792880 | − | 0.609378i | \(-0.791419\pi\) | ||||
−0.792880 | + | 0.609378i | \(0.791419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.1244 | 1.26468 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.3923 | −1.81305 | −0.906526 | − | 0.422149i | \(-0.861276\pi\) | ||||
−0.906526 | + | 0.422149i | \(0.861276\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8038 | −0.939441 | −0.469721 | − | 0.882815i | \(-0.655645\pi\) | ||||
−0.469721 | + | 0.882815i | \(0.655645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.92820 | 0.528861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.7128 | 2.34417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.3923 | 1.89887 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.8564 | 1.51055 | 0.755274 | − | 0.655410i | \(-0.227504\pi\) | ||||
0.755274 | + | 0.655410i | \(0.227504\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.80385 | −0.105024 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9282 | 1.09833 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.19615 | −0.473996 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.46410 | 0.545502 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.39230 | −0.482125 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.46410 | 0.312874 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.53590 | −0.487169 | −0.243585 | − | 0.969880i | \(-0.578323\pi\) | ||||
−0.243585 | + | 0.969880i | \(0.578323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3923 | −1.04630 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.4641 | 0.763479 | 0.381740 | − | 0.924270i | \(-0.375325\pi\) | ||||
0.381740 | + | 0.924270i | \(0.375325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2487 | 1.14452 | 0.572262 | − | 0.820071i | \(-0.306066\pi\) | ||||
0.572262 | + | 0.820071i | \(0.306066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.4641 | −0.871303 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7846 | −0.718055 | −0.359028 | − | 0.933327i | \(-0.616892\pi\) | ||||
−0.359028 | + | 0.933327i | \(0.616892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.8564 | −1.44768 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3923 | 0.580042 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3205 | −0.629890 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.3923 | −0.906497 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.7128 | −2.18944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.9808 | −1.26314 | −0.631568 | − | 0.775320i | \(-0.717589\pi\) | ||||
−0.631568 | + | 0.775320i | \(0.717589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.0718 | 0.716330 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.8564 | 0.866328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3923 | 1.43768 | 0.718840 | − | 0.695175i | \(-0.244673\pi\) | ||||
0.718840 | + | 0.695175i | \(0.244673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.4641 | 0.948520 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.3923 | −1.21261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.3923 | −1.20556 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.6603 | 1.59225 | 0.796123 | − | 0.605135i | \(-0.206881\pi\) | ||||
0.796123 | + | 0.605135i | \(0.206881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.32051 | 0.284800 | 0.142400 | − | 0.989809i | \(-0.454518\pi\) | ||||
0.142400 | + | 0.989809i | \(0.454518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.85641 | 0.0988065 | 0.0494033 | − | 0.998779i | \(-0.484268\pi\) | ||||
0.0494033 | + | 0.998779i | \(0.484268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6603 | −0.618862 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.7846 | 1.73515 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.8038 | −1.36187 | −0.680937 | − | 0.732342i | \(-0.738427\pi\) | ||||
−0.680937 | + | 0.732342i | \(0.738427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.1244 | −1.63361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0526 | −1.56873 | −0.784365 | − | 0.620299i | \(-0.787011\pi\) | ||||
−0.784365 | + | 0.620299i | \(0.787011\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −51.1769 | −2.66416 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.7128 | 2.06179 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0000 | 0.932005 | 0.466002 | − | 0.884783i | \(-0.345694\pi\) | ||||
0.466002 | + | 0.884783i | \(0.345694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.73205 | −0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.46410 | −0.281416 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6603 | −1.42081 | −0.710406 | − | 0.703792i | \(-0.751489\pi\) | ||||
−0.710406 | + | 0.703792i | \(0.751489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4641 | −0.997176 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.60770 | 0.490930 | 0.245465 | − | 0.969405i | \(-0.421059\pi\) | ||||
0.245465 | + | 0.969405i | \(0.421059\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3923 | 0.835429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.1962 | −0.619965 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.7128 | 1.50650 | 0.753250 | − | 0.657735i | \(-0.228485\pi\) | ||||
0.753250 | + | 0.657735i | \(0.228485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3923 | 1.43586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.53590 | −0.127595 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | −0.803017 | −0.401508 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401508 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.9282 | −1.54835 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.78461 | −0.139057 | −0.0695284 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695284 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.73205 | −0.235720 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.46410 | −0.122442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8564 | −0.686837 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.67949 | −0.132492 | −0.0662462 | − | 0.997803i | \(-0.521102\pi\) | ||||
−0.0662462 | + | 0.997803i | \(0.521102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.53590 | −0.125087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.24871 | 0.307479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.4641 | 0.562751 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.8564 | 1.65796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3205 | 0.553043 | 0.276522 | − | 0.961008i | \(-0.410818\pi\) | ||||
0.276522 | + | 0.961008i | \(0.410818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.7846 | 1.11045 | 0.555227 | − | 0.831699i | \(-0.312631\pi\) | ||||
0.555227 | + | 0.831699i | \(0.312631\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 51.1769 | 2.48831 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.9282 | −0.916000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.9282 | −0.624180 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.4449 | 1.56281 | 0.781407 | − | 0.624022i | \(-0.214502\pi\) | ||||
0.781407 | + | 0.624022i | \(0.214502\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7846 | −0.710503 | −0.355251 | − | 0.934771i | \(-0.615605\pi\) | ||||
−0.355251 | + | 0.934771i | \(0.615605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.9282 | −0.715753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.7846 | −1.28128 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.3205 | 1.06288 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1244 | 0.908626 | 0.454313 | − | 0.890842i | \(-0.349885\pi\) | ||||
0.454313 | + | 0.890842i | \(0.349885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.92820 | −0.233619 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5359 | 0.498331 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.3205 | 1.19495 | 0.597474 | − | 0.801888i | \(-0.296171\pi\) | ||||
0.597474 | + | 0.801888i | \(0.296171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.2487 | 2.55447 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.8564 | −1.12087 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.46410 | 0.162400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.7846 | −1.06582 | −0.532910 | − | 0.846172i | \(-0.678901\pi\) | ||||
−0.532910 | + | 0.846172i | \(0.678901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4641 | −0.533936 | −0.266968 | − | 0.963705i | \(-0.586022\pi\) | ||||
−0.266968 | + | 0.963705i | \(0.586022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7846 | −0.501203 | −0.250602 | − | 0.968090i | \(-0.580628\pi\) | ||||
−0.250602 | + | 0.968090i | \(0.580628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.9282 | −0.599531 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.1244 | 1.07007 | 0.535034 | − | 0.844831i | \(-0.320299\pi\) | ||||
0.535034 | + | 0.844831i | \(0.320299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.9282 | −2.53635 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.2487 | 1.76241 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.9282 | 0.594439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.26795 | −0.149944 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −51.1769 | −2.34323 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1962 | 1.01417 | 0.507084 | − | 0.861897i | \(-0.330723\pi\) | ||||
0.507084 | + | 0.861897i | \(0.330723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.92820 | −0.133515 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 77.5692 | 3.52952 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8564 | −0.538372 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.0718 | −1.04548 | −0.522741 | − | 0.852491i | \(-0.675091\pi\) | ||||
−0.522741 | + | 0.852491i | \(0.675091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 43.3205 | 1.95902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4641 | 0.607626 | 0.303813 | − | 0.952732i | \(-0.401740\pi\) | ||||
0.303813 | + | 0.952732i | \(0.401740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9282 | 0.852483 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.1244 | −0.949469 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.3923 | 1.81184 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3397 | −0.731467 | −0.365734 | − | 0.930720i | \(-0.619182\pi\) | ||||
−0.365734 | + | 0.930720i | \(0.619182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.3205 | 1.75671 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.6603 | 1.14413 | 0.572067 | − | 0.820207i | \(-0.306142\pi\) | ||||
0.572067 | + | 0.820207i | \(0.306142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.07180 | 0.136693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.73205 | −0.121335 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.39230 | −0.283334 | −0.141667 | − | 0.989914i | \(-0.545246\pi\) | ||||
−0.141667 | + | 0.989914i | \(0.545246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.0718 | 0.577134 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.73205 | 0.296650 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −54.2487 | −2.38586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −61.1769 | −2.68537 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2487 | −0.799491 | −0.399745 | − | 0.916626i | \(-0.630901\pi\) | ||||
−0.399745 | + | 0.916626i | \(0.630901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3397 | 0.452126 | 0.226063 | − | 0.974113i | \(-0.427415\pi\) | ||||
0.226063 | + | 0.974113i | \(0.427415\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.46410 | 0.413047 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.3923 | 0.714060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.05256 | −0.349451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4641 | 0.496565 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.80385 | −0.164455 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.8564 | −1.63362 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.6603 | −1.01912 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.53590 | −0.195014 | −0.0975068 | − | 0.995235i | \(-0.531087\pi\) | ||||
−0.0975068 | + | 0.995235i | \(0.531087\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.9282 | 1.32726 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.33975 | 0.271068 | 0.135534 | − | 0.990773i | \(-0.456725\pi\) | ||||
0.135534 | + | 0.990773i | \(0.456725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.3923 | 1.04104 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.8564 | −0.760708 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.78461 | 0.373560 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | −0.339581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.9282 | −1.47996 | −0.739978 | − | 0.672631i | \(-0.765164\pi\) | ||||
−0.739978 | + | 0.672631i | \(0.765164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.73205 | 0.115553 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.7846 | 1.89081 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.7321 | −0.789462 | −0.394731 | − | 0.918797i | \(-0.629162\pi\) | ||||
−0.394731 | + | 0.918797i | \(0.629162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.39230 | −0.268926 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.53590 | 0.358474 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.3923 | −0.687201 | −0.343601 | − | 0.939116i | \(-0.611647\pi\) | ||||
−0.343601 | + | 0.939116i | \(0.611647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.2487 | −1.09847 | −0.549237 | − | 0.835667i | \(-0.685082\pi\) | ||||
−0.549237 | + | 0.835667i | \(0.685082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.8564 | 0.578860 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.19615 | 0.341803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.0000 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.2487 | −1.58956 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.7128 | −1.64757 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 54.2487 | 2.24675 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.46410 | −0.184568 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.7128 | −1.55657 | −0.778287 | − | 0.627908i | \(-0.783911\pi\) | ||||
−0.778287 | + | 0.627908i | \(0.783911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4641 | −0.637187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.53590 | 0.104313 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.92820 | 0.202377 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.7846 | 1.66920 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.392305 | 0.0160291 | 0.00801457 | − | 0.999968i | \(-0.497449\pi\) | ||||
0.00801457 | + | 0.999968i | \(0.497449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1436 | 0.495348 | 0.247674 | − | 0.968843i | \(-0.420334\pi\) | ||||
0.247674 | + | 0.968843i | \(0.420334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 70.7846 | 2.88257 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3923 | 0.463163 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.73205 | −0.273246 | −0.136623 | − | 0.990623i | \(-0.543625\pi\) | ||||
−0.136623 | + | 0.990623i | \(0.543625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.7128 | 2.09551 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.4641 | −0.463788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.8564 | 1.77134 | 0.885672 | − | 0.464312i | \(-0.153698\pi\) | ||||
0.885672 | + | 0.464312i | \(0.153698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.3205 | 1.26296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.8038 | −1.03714 | −0.518572 | − | 0.855034i | \(-0.673536\pi\) | ||||
−0.518572 | + | 0.855034i | \(0.673536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.7846 | −1.31560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.0718 | 0.683967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −42.2487 | −1.68725 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1436 | 0.404452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.87564 | −0.273715 | −0.136858 | − | 0.990591i | \(-0.543700\pi\) | ||||
−0.136858 | + | 0.990591i | \(0.543700\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −67.7128 | −2.69134 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.12436 | 0.282721 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.00000 | −0.198107 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −52.0526 | −2.05917 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.9282 | −0.984605 | −0.492302 | − | 0.870424i | \(-0.663845\pi\) | ||||
−0.492302 | + | 0.870424i | \(0.663845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4641 | −0.925334 | −0.462667 | − | 0.886532i | \(-0.653107\pi\) | ||||
−0.462667 | + | 0.886532i | \(0.653107\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.46410 | 0.293899 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.5885 | −0.494903 | −0.247452 | − | 0.968900i | \(-0.579593\pi\) | ||||
−0.247452 | + | 0.968900i | \(0.579593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.53590 | 0.335063 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44.7846 | 1.75525 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.8564 | −1.24664 | −0.623319 | − | 0.781968i | \(-0.714216\pi\) | ||||
−0.623319 | + | 0.781968i | \(0.714216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.92820 | −0.114414 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.5359 | 1.34533 | 0.672664 | − | 0.739948i | \(-0.265150\pi\) | ||||
0.672664 | + | 0.739948i | \(0.265150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7846 | 1.19738 | 0.598691 | − | 0.800980i | \(-0.295688\pi\) | ||||
0.598691 | + | 0.800980i | \(0.295688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.46410 | 0.367555 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3205 | 0.438990 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.7846 | 1.73407 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.53590 | −0.252692 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.8564 | −0.998176 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4641 | −0.596097 | −0.298049 | − | 0.954551i | \(-0.596336\pi\) | ||||
−0.298049 | + | 0.954551i | \(0.596336\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.3923 | 1.62927 | 0.814634 | − | 0.579975i | \(-0.196938\pi\) | ||||
0.814634 | + | 0.579975i | \(0.196938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.0718 | 1.57619 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 79.0333 | 3.02856 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.7128 | −1.28998 | −0.644992 | − | 0.764189i | \(-0.723140\pi\) | ||||
−0.644992 | + | 0.764189i | \(0.723140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.928203 | 0.0354648 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.46410 | −0.0558590 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.4641 | 0.436747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3397 | −0.621593 | −0.310797 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310797 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 73.1769 | 2.77976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.3923 | −0.470067 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.7128 | −1.50423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.4641 | −0.811847 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.56922 | −0.360910 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.3205 | −1.17960 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6410 | −0.400197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3923 | 1.74230 | 0.871150 | − | 0.491017i | \(-0.163375\pi\) | ||||
0.871150 | + | 0.491017i | \(0.163375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3205 | −0.424552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.7846 | 1.45250 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.73205 | 0.176969 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 69.7128 | 2.60347 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.0718 | −0.935020 | −0.467510 | − | 0.883988i | \(-0.654849\pi\) | ||||
−0.467510 | + | 0.883988i | \(0.654849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.3205 | −0.868501 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.53590 | −0.243073 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.46410 | 0.202932 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.9090 | −1.03509 | −0.517543 | − | 0.855657i | \(-0.673153\pi\) | ||||
−0.517543 | + | 0.855657i | \(0.673153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.46410 | −0.350042 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.8564 | −1.02890 | −0.514450 | − | 0.857520i | \(-0.672004\pi\) | ||||
−0.514450 | + | 0.857520i | \(0.672004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.6603 | −0.503866 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −75.0333 | −2.76389 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.58846 | 0.242360 | 0.121180 | − | 0.992631i | \(-0.461332\pi\) | ||||
0.121180 | + | 0.992631i | \(0.461332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.92820 | −0.327986 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.46410 | −0.127086 | −0.0635428 | − | 0.997979i | \(-0.520240\pi\) | ||||
−0.0635428 | + | 0.997979i | \(0.520240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.85641 | −0.141288 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.1769 | 1.87247 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.1769 | 0.481474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4641 | 0.637274 | 0.318637 | − | 0.947877i | \(-0.396775\pi\) | ||||
0.318637 | + | 0.947877i | \(0.396775\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.7846 | 1.34051 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.73205 | 0.317792 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5359 | −0.455625 | −0.227812 | − | 0.973705i | \(-0.573157\pi\) | ||||
−0.227812 | + | 0.973705i | \(0.573157\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 105.962 | 3.84616 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.7128 | 1.65709 | 0.828544 | − | 0.559924i | \(-0.189170\pi\) | ||||
0.828544 | + | 0.559924i | \(0.189170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7846 | −0.752453 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.4641 | 0.559106 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.80385 | 0.0651332 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.7846 | −0.533147 | −0.266573 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266573 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.3205 | 1.56015 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.1436 | −0.364840 | −0.182420 | − | 0.983221i | \(-0.558393\pi\) | ||||
−0.182420 | + | 0.983221i | \(0.558393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.73205 | 0.169980 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.7128 | 0.994192 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.4641 | 1.34229 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55.1769 | 1.97439 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.8564 | −0.781084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4641 | −0.693820 | −0.346910 | − | 0.937898i | \(-0.612769\pi\) | ||||
−0.346910 | + | 0.937898i | \(0.612769\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 67.1769 | 2.39156 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.1436 | 0.787336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.46410 | −0.194036 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.3205 | 1.11082 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.92820 | 0.174566 | 0.0872830 | − | 0.996184i | \(-0.472182\pi\) | ||||
0.0872830 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.7128 | 1.40494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0000 | −0.777332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.3923 | −1.00070 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.3205 | 1.52495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.0333 | 1.37234 | 0.686169 | − | 0.727442i | \(-0.259291\pi\) | ||||
0.686169 | + | 0.727442i | \(0.259291\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.8038 | 0.625178 | 0.312589 | − | 0.949889i | \(-0.398804\pi\) | ||||
0.312589 | + | 0.949889i | \(0.398804\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 49.7128 | 1.74350 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.8564 | −0.555426 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.92820 | 0.312358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.4641 | 0.540359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.928203 | −0.0323945 | −0.0161973 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161973 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.6603 | 1.45219 | 0.726093 | − | 0.687597i | \(-0.241334\pi\) | ||||
0.726093 | + | 0.687597i | \(0.241334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.9282 | 0.450102 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6077 | 1.02956 | 0.514780 | − | 0.857322i | \(-0.327874\pi\) | ||||
0.514780 | + | 0.857322i | \(0.327874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.3923 | 1.12503 | 0.562516 | − | 0.826787i | \(-0.309834\pi\) | ||||
0.562516 | + | 0.826787i | \(0.309834\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 72.1051 | 2.50130 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.3205 | 0.600120 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.3923 | −0.498066 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.9282 | −0.654254 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.3397 | −0.426015 | −0.213008 | − | 0.977051i | \(-0.568326\pi\) | ||||
−0.213008 | + | 0.977051i | \(0.568326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.856406 | 0.0295313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 83.0333 | 2.85982 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.4641 | −1.35600 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.1769 | 1.48183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.6410 | −0.638256 | −0.319128 | − | 0.947712i | \(-0.603390\pi\) | ||||
−0.319128 | + | 0.947712i | \(0.603390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.5885 | −0.498915 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0000 | −0.888143 | −0.444072 | − | 0.895991i | \(-0.646466\pi\) | ||||
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.3205 | −0.932164 | −0.466082 | − | 0.884742i | \(-0.654335\pi\) | ||||
−0.466082 | + | 0.884742i | \(0.654335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −108.497 | −3.69758 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.1769 | 1.46976 | 0.734880 | − | 0.678198i | \(-0.237239\pi\) | ||||
0.734880 | + | 0.678198i | \(0.237239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.3923 | 0.761361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6603 | 0.463927 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | 0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.8564 | −0.537274 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −52.9282 | −1.79135 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.46410 | −0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.7128 | −0.463049 | −0.231524 | − | 0.972829i | \(-0.574371\pi\) | ||||
−0.231524 | + | 0.972829i | \(0.574371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −70.6410 | −2.38266 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3923 | 0.687034 | 0.343517 | − | 0.939146i | \(-0.388382\pi\) | ||||
0.343517 | + | 0.939146i | \(0.388382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.5885 | −1.09669 | −0.548344 | − | 0.836253i | \(-0.684742\pi\) | ||||
−0.548344 | + | 0.836253i | \(0.684742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.92820 | 0.165660 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.0526 | −0.740452 | −0.370226 | − | 0.928942i | \(-0.620720\pi\) | ||||
−0.370226 | + | 0.928942i | \(0.620720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.6795 | −0.827724 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6603 | 0.390633 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.4641 | −1.25369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.8564 | 0.463169 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.3923 | 0.747657 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.8564 | 0.862359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.7128 | −1.32303 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.8564 | −0.860447 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3205 | −0.376306 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.12436 | 0.236560 | 0.118280 | − | 0.992980i | \(-0.462262\pi\) | ||||
0.118280 | + | 0.992980i | \(0.462262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7128 | 0.454825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.7846 | −0.423573 | −0.211787 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211787 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.2487 | −1.79537 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.9282 | −0.493511 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.1436 | 0.334971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.1769 | 1.09441 | 0.547203 | − | 0.837000i | \(-0.315693\pi\) | ||||
0.547203 | + | 0.837000i | \(0.315693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3205 | 0.768437 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6603 | 0.383802 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.92820 | 0.0962787 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.0526 | 0.987056 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.2487 | −1.58299 | −0.791494 | − | 0.611176i | \(-0.790697\pi\) | ||||
−0.791494 | + | 0.611176i | \(0.790697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3397 | −0.535514 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.7846 | −1.20427 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.3923 | −0.536086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.7846 | 0.613666 | 0.306833 | − | 0.951763i | \(-0.400731\pi\) | ||||
0.306833 | + | 0.951763i | \(0.400731\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.3205 | −1.80532 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3205 | 0.564632 | 0.282316 | − | 0.959321i | \(-0.408897\pi\) | ||||
0.282316 | + | 0.959321i | \(0.408897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −93.9615 | −3.05981 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.8564 | 0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.3205 | −0.952788 | −0.476394 | − | 0.879232i | \(-0.658056\pi\) | ||||
−0.476394 | + | 0.879232i | \(0.658056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.9282 | 1.13262 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6410 | 1.44606 | 0.723032 | − | 0.690814i | \(-0.242748\pi\) | ||||
0.723032 | + | 0.690814i | \(0.242748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.07180 | −0.164119 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 70.6410 | 2.28350 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.21539 | −0.103830 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.60770 | −0.277668 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9808 | −0.547197 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.6410 | 0.663770 | 0.331885 | − | 0.943320i | \(-0.392315\pi\) | ||||
0.331885 | + | 0.943320i | \(0.392315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.9282 | 0.993557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0000 | 1.28366 | 0.641831 | − | 0.766846i | \(-0.278175\pi\) | ||||
0.641831 | + | 0.766846i | \(0.278175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9282 | 1.37622 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.73205 | 0.0874957 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.4256 | −1.77322 | −0.886611 | − | 0.462515i | \(-0.846947\pi\) | ||||
−0.886611 | + | 0.462515i | \(0.846947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.3205 | 0.745327 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.7846 | 0.855167 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.6410 | 0.403186 | 0.201593 | − | 0.979469i | \(-0.435388\pi\) | ||||
0.201593 | + | 0.979469i | \(0.435388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.928203 | −0.0295750 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 108.497 | 3.45351 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.3923 | −0.712034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.7128 | 1.38858 | 0.694292 | − | 0.719694i | \(-0.255718\pi\) | ||||
0.694292 | + | 0.719694i | \(0.255718\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 62.7846 | 1.99241 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9282 | −0.473256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.60770 | 0.304279 | 0.152139 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152139 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.7128 | −0.370577 |
(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 | 4160.2.a.v.1.1 | 2 | ||
4.3 | odd | 2 | 4160.2.a.bl.1.2 | 2 | |||
8.3 | odd | 2 | 520.2.a.d.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 1040.2.a.m.1.2 | 2 | |||
24.5 | odd | 2 | 9360.2.a.cq.1.1 | 2 | |||
24.11 | even | 2 | 4680.2.a.be.1.2 | 2 | |||
40.3 | even | 4 | 2600.2.d.l.1249.1 | 4 | |||
40.19 | odd | 2 | 2600.2.a.u.1.2 | 2 | |||
40.27 | even | 4 | 2600.2.d.l.1249.4 | 4 | |||
40.29 | even | 2 | 5200.2.a.bo.1.1 | 2 | |||
104.51 | odd | 2 | 6760.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.a.d.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
1040.2.a.m.1.2 | 2 | 8.5 | even | 2 | |||
2600.2.a.u.1.2 | 2 | 40.19 | odd | 2 | |||
2600.2.d.l.1249.1 | 4 | 40.3 | even | 4 | |||
2600.2.d.l.1249.4 | 4 | 40.27 | even | 4 | |||
4160.2.a.v.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4160.2.a.bl.1.2 | 2 | 4.3 | odd | 2 | |||
4680.2.a.be.1.2 | 2 | 24.11 | even | 2 | |||
5200.2.a.bo.1.1 | 2 | 40.29 | even | 2 | |||
6760.2.a.p.1.1 | 2 | 104.51 | odd | 2 | |||
9360.2.a.cq.1.1 | 2 | 24.5 | odd | 2 |