Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 35 x^{13} + 32 x^{12} + 477 x^{11} - 392 x^{10} - 3236 x^{9} + 2330 x^{8} + \cdots + 2560 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.42593\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 2.42593 | 1.40061 | 0.700305 | − | 0.713843i | \(-0.253047\pi\) | ||||
0.700305 | + | 0.713843i | \(0.253047\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.43967 | 1.53827 | 0.769134 | − | 0.639088i | \(-0.220688\pi\) | ||||
0.769134 | + | 0.639088i | \(0.220688\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.88513 | 0.961710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.34439 | 2.15451 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.39446 | −1.06581 | −0.532907 | − | 0.846174i | \(-0.678900\pi\) | ||||
−0.532907 | + | 0.846174i | \(0.678900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.63761 | 0.834525 | 0.417263 | − | 0.908786i | \(-0.362990\pi\) | ||||
0.417263 | + | 0.908786i | \(0.362990\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.42593 | −0.529381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.12036 | −0.233611 | −0.116806 | − | 0.993155i | \(-0.537265\pi\) | ||||
−0.116806 | + | 0.993155i | \(0.537265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.83133 | 1.36627 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.278666 | −0.0536292 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.89071 | −0.722487 | −0.361244 | − | 0.932472i | \(-0.617648\pi\) | ||||
−0.361244 | + | 0.932472i | \(0.617648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.45333 | 1.69787 | 0.848935 | − | 0.528498i | \(-0.177245\pi\) | ||||
0.848935 | + | 0.528498i | \(0.177245\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.42593 | −0.422300 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.43967 | −0.581410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.37053 | 0.389713 | 0.194856 | − | 0.980832i | \(-0.437576\pi\) | ||||
0.194856 | + | 0.980832i | \(0.437576\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.42593 | 0.388459 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58480 | 0.716026 | 0.358013 | − | 0.933717i | \(-0.383454\pi\) | ||||
0.358013 | + | 0.933717i | \(0.383454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.49006 | 1.14222 | 0.571112 | − | 0.820872i | \(-0.306512\pi\) | ||||
0.571112 | + | 0.820872i | \(0.306512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.92390 | 1.47937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.83430 | 0.705155 | 0.352578 | − | 0.935783i | \(-0.385305\pi\) | ||||
0.352578 | + | 0.935783i | \(0.385305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.6606 | −1.49279 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.84952 | −0.254051 | −0.127025 | − | 0.991899i | \(-0.540543\pi\) | ||||
−0.127025 | + | 0.991899i | \(0.540543\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.43967 | −0.463805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.82459 | 1.16885 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.91141 | 1.29036 | 0.645178 | − | 0.764032i | \(-0.276783\pi\) | ||||
0.645178 | + | 0.764032i | \(0.276783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.650840 | −0.0833316 | −0.0416658 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416658 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.88513 | −0.363492 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.43967 | 0.426639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.75105 | −0.946941 | −0.473471 | − | 0.880810i | \(-0.656999\pi\) | ||||
−0.473471 | + | 0.880810i | \(0.656999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.71791 | −0.327198 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.76069 | 1.15838 | 0.579190 | − | 0.815192i | \(-0.303369\pi\) | ||||
0.579190 | + | 0.815192i | \(0.303369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.15596 | 0.252336 | 0.126168 | − | 0.992009i | \(-0.459732\pi\) | ||||
0.126168 | + | 0.992009i | \(0.459732\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.5723 | 1.91361 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.46419 | 0.164734 | 0.0823670 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823670 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.33141 | −1.03682 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.343435 | −0.0376969 | −0.0188485 | − | 0.999822i | \(-0.506000\pi\) | ||||
−0.0188485 | + | 0.999822i | \(0.506000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1155 | −1.63951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.43859 | −1.01192 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6650 | 1.23649 | 0.618243 | − | 0.785987i | \(-0.287845\pi\) | ||||
0.618243 | + | 0.785987i | \(0.287845\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.9331 | 2.37805 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.5122 | 1.28372 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.2176 | 1.95125 | 0.975624 | − | 0.219449i | \(-0.0704260\pi\) | ||||
0.975624 | + | 0.219449i | \(0.0704260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.88513 | −0.289967 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0837 | 1.20238 | 0.601189 | − | 0.799107i | \(-0.294694\pi\) | ||||
0.601189 | + | 0.799107i | \(0.294694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3618 | −1.21804 | −0.609020 | − | 0.793155i | \(-0.708437\pi\) | ||||
−0.609020 | + | 0.793155i | \(0.708437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.34439 | −0.814330 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.62696 | 0.447305 | 0.223653 | − | 0.974669i | \(-0.428202\pi\) | ||||
0.223653 | + | 0.974669i | \(0.428202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.56094 | −0.724206 | −0.362103 | − | 0.932138i | \(-0.617941\pi\) | ||||
−0.362103 | + | 0.932138i | \(0.617941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.75074 | 0.545836 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1550 | 1.23752 | 0.618758 | − | 0.785581i | \(-0.287636\pi\) | ||||
0.618758 | + | 0.785581i | \(0.287636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.85367 | −0.359356 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.88513 | 0.266730 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.39446 | 0.402840 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.1224 | 1.00287 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.29917 | 0.563415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.71926 | −0.152560 | −0.0762798 | − | 0.997086i | \(-0.524304\pi\) | ||||
−0.0762798 | + | 0.997086i | \(0.524304\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.1704 | 1.59981 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.54999 | −0.659646 | −0.329823 | − | 0.944043i | \(-0.606989\pi\) | ||||
−0.329823 | + | 0.944043i | \(0.606989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.63761 | −0.315421 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.958517 | −0.0824960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.8810 | 1.10050 | 0.550250 | − | 0.835000i | \(-0.314532\pi\) | ||||
0.550250 | + | 0.835000i | \(0.314532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.2450 | −1.54752 | −0.773758 | − | 0.633481i | \(-0.781625\pi\) | ||||
−0.773758 | + | 0.633481i | \(0.781625\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.7277 | 0.987648 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.3828 | −1.11138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.42593 | 0.200087 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.65303 | −0.545037 | −0.272519 | − | 0.962151i | \(-0.587857\pi\) | ||||
−0.272519 | + | 0.962151i | \(0.587857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.54966 | 0.695762 | 0.347881 | − | 0.937539i | \(-0.386901\pi\) | ||||
0.347881 | + | 0.937539i | \(0.386901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.6786 | −1.02500 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.5164 | 2.61178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.9131 | −1.27001 | −0.635003 | − | 0.772510i | \(-0.719001\pi\) | ||||
−0.635003 | + | 0.772510i | \(0.719001\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.48680 | −0.355826 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.12036 | 0.0882967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0212 | −1.48985 | −0.744927 | − | 0.667146i | \(-0.767516\pi\) | ||||
−0.744927 | + | 0.667146i | \(0.767516\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.34439 | −0.649610 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.7915 | −1.76366 | −0.881830 | − | 0.471567i | \(-0.843689\pi\) | ||||
−0.881830 | + | 0.471567i | \(0.843689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.4950 | 0.802571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0035 | 1.44481 | 0.722406 | − | 0.691469i | \(-0.243036\pi\) | ||||
0.722406 | + | 0.691469i | \(0.243036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.83133 | −0.516400 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.0444 | 1.80729 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.3235 | −0.921102 | −0.460551 | − | 0.887633i | \(-0.652348\pi\) | ||||
−0.460551 | + | 0.887633i | \(0.652348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9713 | 1.11281 | 0.556404 | − | 0.830912i | \(-0.312181\pi\) | ||||
0.556404 | + | 0.830912i | \(0.312181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57889 | −0.116715 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.15384 | 0.599482 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.39446 | 0.321355 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.278666 | 0.0202699 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8565 | −0.785550 | −0.392775 | − | 0.919635i | \(-0.628485\pi\) | ||||
−0.392775 | + | 0.919635i | \(0.628485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.42633 | 0.174651 | 0.0873257 | − | 0.996180i | \(-0.472168\pi\) | ||||
0.0873257 | + | 0.996180i | \(0.472168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.34439 | 0.597555 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.00290513 | 0.000206982 0 | 0.000103491 | − | 1.00000i | \(-0.499967\pi\) | ||||
0.000103491 | 1.00000i | \(0.499967\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.31984 | 0.164449 | 0.0822246 | − | 0.996614i | \(-0.473798\pi\) | ||||
0.0822246 | + | 0.996614i | \(0.473798\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8035 | −1.32630 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.89071 | 0.273074 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7702 | 1.10144 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.23238 | −0.224666 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.63761 | −0.251619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.9952 | −1.85842 | −0.929212 | − | 0.369546i | \(-0.879513\pi\) | ||||
−0.929212 | + | 0.369546i | \(0.879513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.6787 | 1.62244 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.7633 | 1.75705 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.45333 | −0.641734 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.23020 | 0.353424 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.39446 | −0.295603 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.87673 | −0.326570 | −0.163285 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163285 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.7093 | 1.31395 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.57904 | −0.237549 | −0.118775 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118775 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.43624 | 0.227073 | 0.113537 | − | 0.993534i | \(-0.463782\pi\) | ||||
0.113537 | + | 0.993534i | \(0.463782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.42593 | 0.159614 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.1985 | 1.32325 | 0.661623 | − | 0.749837i | \(-0.269868\pi\) | ||||
0.661623 | + | 0.749837i | \(0.269868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.6284 | 1.08472 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.55201 | 0.230728 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.3332 | −1.31524 | −0.657622 | − | 0.753348i | \(-0.728438\pi\) | ||||
−0.657622 | + | 0.753348i | \(0.728438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0403 | 0.839999 | 0.420000 | − | 0.907524i | \(-0.362030\pi\) | ||||
0.420000 | + | 0.907524i | \(0.362030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.8013 | −1.39856 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.43967 | 0.219752 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.63761 | 0.231456 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.833150 | −0.0527987 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.35716 | −0.401261 | −0.200630 | − | 0.979667i | \(-0.564299\pi\) | ||||
−0.200630 | + | 0.979667i | \(0.564299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.12036 | 0.0704364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.6691 | −2.29631 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.9787 | −0.809589 | −0.404794 | − | 0.914408i | \(-0.632657\pi\) | ||||
−0.404794 | + | 0.914408i | \(0.632657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.37053 | −0.147298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.2252 | −0.694823 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6095 | 1.51749 | 0.758744 | − | 0.651389i | \(-0.225814\pi\) | ||||
0.758744 | + | 0.651389i | \(0.225814\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.36173 | −0.390798 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.2984 | 1.73184 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.34666 | 0.569876 | 0.284938 | − | 0.958546i | \(-0.408027\pi\) | ||||
0.284938 | + | 0.958546i | \(0.408027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.21743 | −0.316936 | −0.158468 | − | 0.987364i | \(-0.550656\pi\) | ||||
−0.158468 | + | 0.987364i | \(0.550656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.42593 | −0.146824 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.83133 | −0.411945 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.04369 | −0.242962 | −0.121481 | − | 0.992594i | \(-0.538764\pi\) | ||||
−0.121481 | + | 0.992594i | \(0.538764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.2741 | 1.63286 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.7220 | −1.65376 | −0.826879 | − | 0.562380i | \(-0.809886\pi\) | ||||
−0.826879 | + | 0.562380i | \(0.809886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.542146 | −0.0322272 | −0.0161136 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161136 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 30.3537 | 1.79800 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.58480 | −0.270632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.31129 | 0.135958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.6204 | 2.73294 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0888 | −1.05676 | −0.528380 | − | 0.849008i | \(-0.677200\pi\) | ||||
−0.528380 | + | 0.849008i | \(0.677200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.0920 | 1.98491 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.278666 | 0.0161698 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.12036 | −0.0647921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.49006 | −0.431720 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.3143 | 1.68406 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.23868 | −0.128186 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.22000 | −0.526213 | −0.263107 | − | 0.964767i | \(-0.584747\pi\) | ||||
−0.263107 | + | 0.964767i | \(0.584747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.9887 | −1.70600 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4886 | 0.821572 | 0.410786 | − | 0.911732i | \(-0.365254\pi\) | ||||
0.410786 | + | 0.911732i | \(0.365254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.851282 | 0.0481173 | 0.0240586 | − | 0.999711i | \(-0.492341\pi\) | ||||
0.0240586 | + | 0.999711i | \(0.492341\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.92390 | −0.559148 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.07945 | 0.116794 | 0.0583969 | − | 0.998293i | \(-0.481401\pi\) | ||||
0.0583969 | + | 0.998293i | \(0.481401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.89071 | 0.217838 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.2247 | 0.626500 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.9853 | −0.889448 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.83133 | 0.378934 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.3423 | −1.01433 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.83430 | −0.266524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1667 | −0.723708 | −0.361854 | − | 0.932235i | \(-0.617856\pi\) | ||||
−0.361854 | + | 0.932235i | \(0.617856\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.83929 | 0.374791 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.6610 | −1.45665 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.1014 | −0.986048 | −0.493024 | − | 0.870016i | \(-0.664108\pi\) | ||||
−0.493024 | + | 0.870016i | \(0.664108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.9131 | 1.73328 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.45333 | −0.511927 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.34872 | −0.503318 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.6464 | −0.893625 | −0.446812 | − | 0.894628i | \(-0.647441\pi\) | ||||
−0.446812 | + | 0.894628i | \(0.647441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.136903 | −0.00732825 | −0.00366413 | − | 0.999993i | \(-0.501166\pi\) | ||||
−0.00366413 | + | 0.999993i | \(0.501166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.278666 | −0.0148741 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6570 | 0.567216 | 0.283608 | − | 0.958940i | \(-0.408469\pi\) | ||||
0.283608 | + | 0.958940i | \(0.408469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.5736 | 1.78190 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.6606 | 0.564221 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.9224 | −1.31535 | −0.657677 | − | 0.753300i | \(-0.728461\pi\) | ||||
−0.657677 | + | 0.753300i | \(0.728461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.76778 | −0.303567 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.42593 | 0.127328 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.41578 | 0.388159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.71677 | 0.246214 | 0.123107 | − | 0.992393i | \(-0.460714\pi\) | ||||
0.123107 | + | 0.992393i | \(0.460714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.2278 | 0.688610 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.84952 | 0.0960222 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.53298 | −0.338265 | −0.169132 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169132 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.2813 | 0.789125 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.89071 | −0.200382 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.2490 | −1.50242 | −0.751210 | − | 0.660063i | \(-0.770529\pi\) | ||||
−0.751210 | + | 0.660063i | \(0.770529\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.17080 | −0.213676 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.0743 | 0.565869 | 0.282934 | − | 0.959139i | \(-0.408692\pi\) | ||||
0.282934 | + | 0.959139i | \(0.408692\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.43967 | 0.175302 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.6098 | 1.09849 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7247 | −0.645168 | −0.322584 | − | 0.946541i | \(-0.604551\pi\) | ||||
−0.322584 | + | 0.946541i | \(0.604551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.92338 | 0.248986 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.3157 | −0.923907 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.03632 | 0.253405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0119 | 1.70701 | 0.853505 | − | 0.521084i | \(-0.174472\pi\) | ||||
0.853505 | + | 0.521084i | \(0.174472\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.82459 | −0.441782 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.96380 | −0.297818 | −0.148909 | − | 0.988851i | \(-0.547576\pi\) | ||||
−0.148909 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.45333 | 0.470904 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.0970 | −1.59491 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.37053 | −0.117503 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.32269 | 0.263190 | 0.131595 | − | 0.991304i | \(-0.457990\pi\) | ||||
0.131595 | + | 0.991304i | \(0.457990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2484 | 1.54137 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.91141 | −0.487709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18130 | −0.0579879 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44.2610 | −2.16747 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.7043 | −0.669499 | −0.334750 | − | 0.942307i | \(-0.608652\pi\) | ||||
−0.334750 | + | 0.942307i | \(0.608652\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.63192 | 0.128272 | 0.0641359 | − | 0.997941i | \(-0.479571\pi\) | ||||
0.0641359 | + | 0.997941i | \(0.479571\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.9476 | 0.678155 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.0200 | −1.45618 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.650840 | 0.0314964 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.42593 | −0.117125 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.69378 | −0.370596 | −0.185298 | − | 0.982682i | \(-0.559325\pi\) | ||||
−0.185298 | + | 0.982682i | \(0.559325\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.6632 | −1.56970 | −0.784848 | − | 0.619689i | \(-0.787259\pi\) | ||||
−0.784848 | + | 0.619689i | \(0.787259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.4656 | −1.55661 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.07543 | −0.194954 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.99271 | −0.429199 | −0.214599 | − | 0.976702i | \(-0.568845\pi\) | ||||
−0.214599 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.88513 | 0.137387 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.5622 | −1.64210 | −0.821050 | − | 0.570856i | \(-0.806612\pi\) | ||||
−0.821050 | + | 0.570856i | \(0.806612\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.1237 | 1.90205 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.1398 | −0.763385 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.75887 | 0.366164 | 0.183082 | − | 0.983098i | \(-0.441393\pi\) | ||||
0.183082 | + | 0.983098i | \(0.441393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58480 | −0.215890 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.7409 | 0.974491 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.43967 | −0.161254 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9485 | −0.839596 | −0.419798 | − | 0.907617i | \(-0.637899\pi\) | ||||
−0.419798 | + | 0.907617i | \(0.637899\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.22458 | 0.0571587 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.07951 | −0.376300 | −0.188150 | − | 0.982140i | \(-0.560249\pi\) | ||||
−0.188150 | + | 0.982140i | \(0.560249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.5133 | 1.27865 | 0.639326 | − | 0.768936i | \(-0.279213\pi\) | ||||
0.639326 | + | 0.768936i | \(0.279213\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 78.8824 | 3.65808 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.3596 | 1.58997 | 0.794986 | − | 0.606628i | \(-0.207478\pi\) | ||||
0.794986 | + | 0.606628i | \(0.207478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.75105 | 0.357910 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −38.6041 | −1.77878 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.49006 | −0.344393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.8497 | 1.14018 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.33610 | −0.244323 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.7006 | −1.26567 | −0.632836 | − | 0.774286i | \(-0.718109\pi\) | ||||
−0.632836 | + | 0.774286i | \(0.718109\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.37053 | 0.108087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.71791 | 0.123669 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 66.1021 | 3.00154 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.9726 | −1.13162 | −0.565809 | − | 0.824536i | \(-0.691436\pi\) | ||||
−0.565809 | + | 0.824536i | \(0.691436\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.1441 | −2.08671 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.47595 | 0.201997 | 0.100998 | − | 0.994887i | \(-0.467796\pi\) | ||||
0.100998 | + | 0.994887i | \(0.467796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0976 | 0.770036 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.92390 | −0.446046 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.76069 | −0.437827 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.5884 | −1.05596 | −0.527982 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527982 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.2906 | −2.47020 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8609 | 0.885553 | 0.442776 | − | 0.896632i | \(-0.353994\pi\) | ||||
0.442776 | + | 0.896632i | \(0.353994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.5641 | 1.84958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.42593 | 0.107739 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6950 | 0.695668 | 0.347834 | − | 0.937556i | \(-0.386917\pi\) | ||||
0.347834 | + | 0.937556i | \(0.386917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.15596 | −0.0953739 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01368 | −0.0447549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.5204 | −1.87367 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.83430 | −0.212612 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.1012 | 2.02362 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.1916 | −1.36653 | −0.683265 | − | 0.730171i | \(-0.739441\pi\) | ||||
−0.683265 | + | 0.730171i | \(0.739441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.13776 | −0.312113 | −0.156056 | − | 0.987748i | \(-0.549878\pi\) | ||||
−0.156056 | + | 0.987748i | \(0.549878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.5723 | −0.723275 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.5423 | −1.80961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7448 | −0.945426 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.5957 | 1.24095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.58480 | 0.198590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9152 | 0.688075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.8959 | −1.29011 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5896 | −1.44413 | −0.722064 | − | 0.691826i | \(-0.756807\pi\) | ||||
−0.722064 | + | 0.691826i | \(0.756807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.3193 | 1.55861 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.0071 | −1.11402 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4328 | 1.04467 | 0.522335 | − | 0.852741i | \(-0.325061\pi\) | ||||
0.522335 | + | 0.852741i | \(0.325061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.87776 | −0.0801408 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1529 | −0.602934 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.46419 | −0.0622636 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.7806 | 0.839641 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.5692 | −1.25289 | −0.626444 | − | 0.779466i | \(-0.715490\pi\) | ||||
−0.626444 | + | 0.779466i | \(0.715490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.49006 | 0.316796 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6606 | 0.450093 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0903 | 1.26815 | 0.634077 | − | 0.773270i | \(-0.281380\pi\) | ||||
0.634077 | + | 0.773270i | \(0.281380\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.2488 | 1.90363 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.33141 | 0.391883 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.9871 | −1.00559 | −0.502796 | − | 0.864405i | \(-0.667695\pi\) | ||||
−0.502796 | + | 0.864405i | \(0.667695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.07260 | −0.379676 | −0.189838 | − | 0.981815i | \(-0.560796\pi\) | ||||
−0.189838 | + | 0.981815i | \(0.560796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.3371 | −1.10025 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.65355 | −0.319175 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2386 | −0.676023 | −0.338011 | − | 0.941142i | \(-0.609754\pi\) | ||||
−0.338011 | + | 0.941142i | \(0.609754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.88611 | 0.244618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.343435 | 0.0142481 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.84952 | 0.0765992 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.92390 | 0.410303 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.1644 | −0.667178 | −0.333589 | − | 0.942719i | \(-0.608260\pi\) | ||||
−0.333589 | + | 0.942719i | \(0.608260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.3876 | 1.41691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.00704763 | 0.000289901 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.65555 | −0.273311 | −0.136655 | − | 0.990619i | \(-0.543635\pi\) | ||||
−0.136655 | + | 0.990619i | \(0.543635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.1155 | 0.619675 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.62777 | 0.230329 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.6931 | −0.477768 | −0.238884 | − | 0.971048i | \(-0.576782\pi\) | ||||
−0.238884 | + | 0.971048i | \(0.576782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0615 | 0.532791 | 0.266396 | − | 0.963864i | \(-0.414167\pi\) | ||||
0.266396 | + | 0.963864i | \(0.414167\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.3628 | −0.910683 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43967 | 0.139842 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.4942 | 0.466535 | 0.233268 | − | 0.972413i | \(-0.425058\pi\) | ||||
0.233268 | + | 0.972413i | \(0.425058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.43859 | 0.382471 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.83430 | 0.195575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.173262 | 0.00699801 | 0.00349900 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00349900 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.2574 | 1.54269 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0799 | 1.37200 | 0.686002 | − | 0.727600i | \(-0.259364\pi\) | ||||
0.686002 | + | 0.727600i | \(0.259364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.6506 | 0.588859 | 0.294429 | − | 0.955673i | \(-0.404870\pi\) | ||||
0.294429 | + | 0.955673i | \(0.404870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.312206 | 0.0125284 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6650 | −0.467348 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4896 | −0.499583 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.82459 | −0.352420 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.4172 | −0.415361 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9339 | 1.35089 | 0.675443 | − | 0.737412i | \(-0.263953\pi\) | ||||
0.675443 | + | 0.737412i | \(0.263953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −65.4884 | −2.60293 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.91368 | −0.234677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.1609 | 1.11403 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.5354 | 1.48256 | 0.741280 | − | 0.671196i | \(-0.234219\pi\) | ||||
0.741280 | + | 0.671196i | \(0.234219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.50207 | −0.335289 | −0.167644 | − | 0.985848i | \(-0.553616\pi\) | ||||
−0.167644 | + | 0.985848i | \(0.553616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 62.5000 | 2.46094 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.99110 | 0.392791 | 0.196395 | − | 0.980525i | \(-0.437076\pi\) | ||||
0.196395 | + | 0.980525i | \(0.437076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.91141 | −0.389057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.9331 | −0.898820 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.8978 | 1.36565 | 0.682827 | − | 0.730580i | \(-0.260750\pi\) | ||||
0.682827 | + | 0.730580i | \(0.260750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.9695 | −1.01471 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.22021 | 0.242674 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.98982 | 0.350194 | 0.175097 | − | 0.984551i | \(-0.443976\pi\) | ||||
0.175097 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.0385 | −1.47953 | −0.739763 | − | 0.672867i | \(-0.765063\pi\) | ||||
−0.739763 | + | 0.672867i | \(0.765063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.6606 | −0.414025 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.5122 | −0.485202 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.35900 | 0.168781 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.8306 | −0.457397 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.650840 | 0.0251254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0582 | −0.734641 | −0.367321 | − | 0.930094i | \(-0.619725\pi\) | ||||
−0.367321 | + | 0.930094i | \(0.619725\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.90366 | −0.0732718 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.32867 | −0.281664 | −0.140832 | − | 0.990034i | \(-0.544978\pi\) | ||||
−0.140832 | + | 0.990034i | \(0.544978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.2176 | −0.737502 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.68249 | −0.332714 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.0488 | −0.652356 | −0.326178 | − | 0.945308i | \(-0.605761\pi\) | ||||
−0.326178 | + | 0.945308i | \(0.605761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.3065 | 1.69286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.33608 | 0.318041 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.84952 | −0.0704610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.6681 | −0.938419 | −0.469209 | − | 0.883087i | \(-0.655461\pi\) | ||||
−0.469209 | + | 0.883087i | \(0.655461\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.88513 | 0.109597 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −62.7566 | −2.38049 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1477 | −0.763150 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 49.0000 | 1.85335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.0516 | −1.47496 | −0.737480 | − | 0.675369i | \(-0.763984\pi\) | ||||
−0.737480 | + | 0.675369i | \(0.763984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.62307 | 0.325225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.3393 | 1.51927 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.0837 | −0.454456 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.3790 | −0.878017 | −0.439008 | − | 0.898483i | \(-0.644670\pi\) | ||||
−0.439008 | + | 0.898483i | \(0.644670\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.22437 | 0.158426 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5911 | −0.396641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.43967 | −0.128636 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.3269 | −1.84215 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0261 | −0.634966 | −0.317483 | − | 0.948264i | \(-0.602838\pi\) | ||||
−0.317483 | + | 0.948264i | \(0.602838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3618 | 0.460376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.6348 | 1.17651 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.5787 | −0.987110 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.2062 | −1.60243 | −0.801214 | − | 0.598378i | \(-0.795812\pi\) | ||||
−0.801214 | + | 0.598378i | \(0.795812\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.8943 | −0.922010 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.9148 | −1.21740 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.9053 | 1.65861 | 0.829307 | − | 0.558793i | \(-0.188735\pi\) | ||||
0.829307 | + | 0.558793i | \(0.188735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.34439 | 0.307788 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.75105 | 0.285513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6940 | −0.503743 | −0.251871 | − | 0.967761i | \(-0.581046\pi\) | ||||
−0.251871 | + | 0.967761i | \(0.581046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.82459 | 0.324179 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.0544 | −0.478918 | −0.239459 | − | 0.970906i | \(-0.576970\pi\) | ||||
−0.239459 | + | 0.970906i | \(0.576970\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.8842 | −0.838413 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.990856 | −0.0362535 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.62696 | −0.169065 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5301 | −0.384248 | −0.192124 | − | 0.981371i | \(-0.561538\pi\) | ||||
−0.192124 | + | 0.981371i | \(0.561538\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4220 | −0.562010 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.4080 | 1.07027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4193 | 1.17830 | 0.589150 | − | 0.808023i | \(-0.299463\pi\) | ||||
0.589150 | + | 0.808023i | \(0.299463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.71791 | 0.0986540 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.5052 | 1.35956 | 0.679781 | − | 0.733415i | \(-0.262075\pi\) | ||||
0.679781 | + | 0.733415i | \(0.262075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.56094 | 0.273724 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −43.6102 | −1.57673 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.91141 | 0.357880 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.3325 | 1.31018 | 0.655091 | − | 0.755550i | \(-0.272630\pi\) | ||||
0.655091 | + | 0.755550i | \(0.272630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.4854 | −1.13392 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.0878 | 1.33396 | 0.666978 | − | 0.745078i | \(-0.267588\pi\) | ||||
0.666978 | + | 0.745078i | \(0.267588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 64.5788 | 2.31974 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.75074 | −0.206307 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.6777 | 0.597542 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.76069 | −0.349265 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.08421 | 0.0387464 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.7359 | −1.95361 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.3705 | 0.797421 | 0.398710 | − | 0.917077i | \(-0.369458\pi\) | ||||
0.398710 | + | 0.917077i | \(0.369458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59.7009 | 2.12541 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.1550 | −0.467737 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.650840 | −0.0231120 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.4331 | −0.547356 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.42396 | 0.333814 | 0.166907 | − | 0.985973i | \(-0.446622\pi\) | ||||
0.166907 | + | 0.985973i | \(0.446622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.2441 | −0.751564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.6550 | 1.18914 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.15596 | −0.0760820 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.85367 | 0.135824 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.6743 | 0.798174 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.0837 | 1.69053 | 0.845267 | − | 0.534345i | \(-0.179442\pi\) | ||||
0.845267 | + | 0.534345i | \(0.179442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.7446 | 1.25516 | 0.627581 | − | 0.778552i | \(-0.284045\pi\) | ||||
0.627581 | + | 0.778552i | \(0.284045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.6571 | −0.443904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −65.4266 | −2.29179 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.2459 | 0.953215 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.88513 | −0.100815 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.9272 | −1.00957 | −0.504783 | − | 0.863246i | \(-0.668427\pi\) | ||||
−0.504783 | + | 0.863246i | \(0.668427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1149 | 0.596587 | 0.298293 | − | 0.954474i | \(-0.403583\pi\) | ||||
0.298293 | + | 0.954474i | \(0.403583\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.5723 | −0.576974 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9579 | 0.867870 | 0.433935 | − | 0.900944i | \(-0.357125\pi\) | ||||
0.433935 | + | 0.900944i | \(0.357125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.6164 | 1.23701 | 0.618505 | − | 0.785781i | \(-0.287739\pi\) | ||||
0.618505 | + | 0.785781i | \(0.287739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.80972 | −0.340295 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.39446 | −0.152259 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −78.3953 | −2.71298 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.63432 | −0.0910554 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.9135 | 0.894634 | 0.447317 | − | 0.894376i | \(-0.352380\pi\) | ||||
0.447317 | + | 0.894376i | \(0.352380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.8624 | −0.478012 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −67.2517 | −2.31627 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.43967 | 0.118328 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.31521 | −0.0451378 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.65585 | −0.0910412 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.6882 | 1.63281 | 0.816406 | − | 0.577479i | \(-0.195963\pi\) | ||||
0.816406 | + | 0.577479i | \(0.195963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.0993 | 1.23457 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.18455 | 0.211260 | 0.105630 | − | 0.994405i | \(-0.466314\pi\) | ||||
0.105630 | + | 0.994405i | \(0.466314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.04710 | −0.308683 | −0.154342 | − | 0.988018i | \(-0.549326\pi\) | ||||
−0.154342 | + | 0.988018i | \(0.549326\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1224 | −0.379051 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4843 | 1.58234 | 0.791171 | − | 0.611595i | \(-0.209472\pi\) | ||||
0.791171 | + | 0.611595i | \(0.209472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.3659 | 2.22251 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.60702 | 0.190424 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.46419 | −0.0496691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.75105 | −0.262634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 55.4452 | 1.87653 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.29917 | −0.212951 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.1617 | 0.714581 | 0.357290 | − | 0.933993i | \(-0.383701\pi\) | ||||
0.357290 | + | 0.933993i | \(0.383701\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.8822 | −1.48011 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.8315 | 1.20719 | 0.603597 | − | 0.797289i | \(-0.293734\pi\) | ||||
0.603597 | + | 0.797289i | \(0.293734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5652 | 0.692074 | 0.346037 | − | 0.938221i | \(-0.387527\pi\) | ||||
0.346037 | + | 0.938221i | \(0.387527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 82.7047 | 2.78009 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.4208 | 0.719241 | 0.359621 | − | 0.933099i | \(-0.382906\pi\) | ||||
0.359621 | + | 0.933099i | \(0.382906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71926 | 0.0576621 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.33141 | 0.312614 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.5853 | 0.588470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.3888 | −1.41690 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.71791 | −0.0907485 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.7802 | −1.22669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.12763 | 0.270771 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.1704 | −0.604672 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.4964 | 1.71180 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3939 | 0.444739 | 0.222369 | − | 0.974963i | \(-0.428621\pi\) | ||||
0.222369 | + | 0.974963i | \(0.428621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.8632 | 1.15634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.6453 | −1.61169 | −0.805845 | − | 0.592127i | \(-0.798288\pi\) | ||||
−0.805845 | + | 0.592127i | \(0.798288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.343435 | 0.0113661 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.43087 | −0.179539 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.54999 | 0.249323 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.5391 | −1.30428 | −0.652138 | − | 0.758100i | \(-0.726128\pi\) | ||||
−0.652138 | + | 0.758100i | \(0.726128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3671 | −0.737020 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.76069 | 0.321277 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.1939 | 0.532451 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −35.6653 | −1.17140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.60362 | 0.118231 | 0.0591154 | − | 0.998251i | \(-0.481172\pi\) | ||||
0.0591154 | + | 0.998251i | \(0.481172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.63761 | 0.119218 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.1483 | 1.15070 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.1155 | 0.494330 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.43742 | −0.210301 | −0.105151 | − | 0.994456i | \(-0.533532\pi\) | ||||
−0.105151 | + | 0.994456i | \(0.533532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.06515 | 0.0673936 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.6353 | 1.48767 | 0.743833 | − | 0.668365i | \(-0.233006\pi\) | ||||
0.743833 | + | 0.668365i | \(0.233006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.13663 | −0.167272 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.958517 | 0.0311806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.98768 | 0.227069 | 0.113535 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113535 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.15596 | 0.0699853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.04461 | 0.163583 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.5062 | 0.534687 | 0.267343 | − | 0.963601i | \(-0.413854\pi\) | ||||
0.267343 | + | 0.963601i | \(0.413854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.3428 | −1.20839 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.43859 | 0.305106 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.8810 | −0.415950 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.3655 | 1.88276 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.3494 | 0.430178 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.34579 | 0.268660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3163 | 0.363908 | 0.181954 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181954 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.7793 | −1.24577 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4783 | 0.785545 | 0.392772 | − | 0.919636i | \(-0.371516\pi\) | ||||
0.392772 | + | 0.919636i | \(0.371516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.2450 | 0.584906 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.5723 | 0.530739 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.4595 | −1.03847 | −0.519236 | − | 0.854631i | \(-0.673783\pi\) | ||||
−0.519236 | + | 0.854631i | \(0.673783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.6650 | −0.372815 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.8143 | −0.696477 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.0393 | 1.53221 | 0.766107 | − | 0.642713i | \(-0.222191\pi\) | ||||
0.766107 | + | 0.642713i | \(0.222191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.00999267 | 0.000318393 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.7277 | −0.373296 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.39156 | −0.266836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.9924 | −1.14334 | −0.571668 | − | 0.820485i | \(-0.693704\pi\) | ||||
−0.571668 | + | 0.820485i | \(0.693704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.9415 | −1.01363 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.97949 | 0.252967 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3025 | 0.769667 | 0.384834 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384834 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.660585 | −0.0209000 |
(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 | 8008.2.a.z.1.13 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.z.1.13 | ✓ | 15 | 1.1 | even | 1 | trivial |