Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.6148961.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.33906\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.404061 | −0.180701 | −0.0903507 | − | 0.995910i | \(-0.528799\pi\) | ||||
−0.0903507 | + | 0.995910i | \(0.528799\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.404061 | 0.127775 | ||||||||
\(11\) | 4.72704 | 1.42526 | 0.712629 | − | 0.701541i | \(-0.247504\pi\) | ||||
0.712629 | + | 0.701541i | \(0.247504\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.404061 | −0.104328 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.50459 | 1.09252 | 0.546261 | − | 0.837615i | \(-0.316051\pi\) | ||||
0.546261 | + | 0.837615i | \(0.316051\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.94294 | −1.13399 | −0.566994 | − | 0.823722i | \(-0.691894\pi\) | ||||
−0.566994 | + | 0.823722i | \(0.691894\pi\) | |||||||
\(20\) | −0.404061 | −0.0903507 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −4.72704 | −1.00781 | ||||||||
\(23\) | −5.73373 | −1.19557 | −0.597783 | − | 0.801658i | \(-0.703952\pi\) | ||||
−0.597783 | + | 0.801658i | \(0.703952\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.83673 | −0.967347 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −0.647042 | −0.120153 | −0.0600763 | − | 0.998194i | \(-0.519134\pi\) | ||||
−0.0600763 | + | 0.998194i | \(0.519134\pi\) | |||||||
\(30\) | 0.404061 | 0.0737711 | ||||||||
\(31\) | −6.14471 | −1.10362 | −0.551812 | − | 0.833969i | \(-0.686063\pi\) | ||||
−0.551812 | + | 0.833969i | \(0.686063\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.72704 | 0.822873 | ||||||||
\(34\) | −4.50459 | −0.772530 | ||||||||
\(35\) | −0.404061 | −0.0682987 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.41291 | −0.725478 | −0.362739 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362739 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(38\) | 4.94294 | 0.801851 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.404061 | 0.0638876 | ||||||||
\(41\) | −9.13551 | −1.42673 | −0.713363 | − | 0.700794i | \(-0.752829\pi\) | ||||
−0.713363 | + | 0.700794i | \(0.752829\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −0.666578 | −0.101652 | −0.0508261 | − | 0.998708i | \(-0.516185\pi\) | ||||
−0.0508261 | + | 0.998708i | \(0.516185\pi\) | |||||||
\(44\) | 4.72704 | 0.712629 | ||||||||
\(45\) | −0.404061 | −0.0602338 | ||||||||
\(46\) | 5.73373 | 0.845393 | ||||||||
\(47\) | −6.47213 | −0.944057 | −0.472028 | − | 0.881583i | \(-0.656478\pi\) | ||||
−0.472028 | + | 0.881583i | \(0.656478\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.83673 | 0.684018 | ||||||||
\(51\) | 4.50459 | 0.630768 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.811429 | −0.111458 | −0.0557291 | − | 0.998446i | \(-0.517748\pi\) | ||||
−0.0557291 | + | 0.998446i | \(0.517748\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.91001 | −0.257546 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −4.94294 | −0.654708 | ||||||||
\(58\) | 0.647042 | 0.0849607 | ||||||||
\(59\) | −15.0444 | −1.95861 | −0.979305 | − | 0.202388i | \(-0.935130\pi\) | ||||
−0.979305 | + | 0.202388i | \(0.935130\pi\) | |||||||
\(60\) | −0.404061 | −0.0521640 | ||||||||
\(61\) | 2.83178 | 0.362572 | 0.181286 | − | 0.983430i | \(-0.441974\pi\) | ||||
0.181286 | + | 0.983430i | \(0.441974\pi\) | |||||||
\(62\) | 6.14471 | 0.780379 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.72704 | −0.581859 | ||||||||
\(67\) | −5.97874 | −0.730419 | −0.365209 | − | 0.930925i | \(-0.619003\pi\) | ||||
−0.365209 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(68\) | 4.50459 | 0.546261 | ||||||||
\(69\) | −5.73373 | −0.690260 | ||||||||
\(70\) | 0.404061 | 0.0482945 | ||||||||
\(71\) | −14.3974 | −1.70866 | −0.854331 | − | 0.519729i | \(-0.826033\pi\) | ||||
−0.854331 | + | 0.519729i | \(0.826033\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.92648 | 0.459560 | 0.229780 | − | 0.973243i | \(-0.426199\pi\) | ||||
0.229780 | + | 0.973243i | \(0.426199\pi\) | |||||||
\(74\) | 4.41291 | 0.512990 | ||||||||
\(75\) | −4.83673 | −0.558498 | ||||||||
\(76\) | −4.94294 | −0.566994 | ||||||||
\(77\) | 4.72704 | 0.538697 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.69273 | −0.978008 | −0.489004 | − | 0.872282i | \(-0.662640\pi\) | ||||
−0.489004 | + | 0.872282i | \(0.662640\pi\) | |||||||
\(80\) | −0.404061 | −0.0451754 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.13551 | 1.00885 | ||||||||
\(83\) | 4.51350 | 0.495420 | 0.247710 | − | 0.968834i | \(-0.420322\pi\) | ||||
0.247710 | + | 0.968834i | \(0.420322\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −1.82013 | −0.197420 | ||||||||
\(86\) | 0.666578 | 0.0718789 | ||||||||
\(87\) | −0.647042 | −0.0693702 | ||||||||
\(88\) | −4.72704 | −0.503905 | ||||||||
\(89\) | −9.32298 | −0.988234 | −0.494117 | − | 0.869395i | \(-0.664509\pi\) | ||||
−0.494117 | + | 0.869395i | \(0.664509\pi\) | |||||||
\(90\) | 0.404061 | 0.0425918 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.73373 | −0.597783 | ||||||||
\(93\) | −6.14471 | −0.637177 | ||||||||
\(94\) | 6.47213 | 0.667549 | ||||||||
\(95\) | 1.99725 | 0.204913 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.19694 | −0.629204 | −0.314602 | − | 0.949224i | \(-0.601871\pi\) | ||||
−0.314602 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.72704 | 0.475086 | ||||||||
\(100\) | −4.83673 | −0.483673 | ||||||||
\(101\) | 10.7135 | 1.06603 | 0.533015 | − | 0.846106i | \(-0.321059\pi\) | ||||
0.533015 | + | 0.846106i | \(0.321059\pi\) | |||||||
\(102\) | −4.50459 | −0.446021 | ||||||||
\(103\) | −1.21750 | −0.119964 | −0.0599818 | − | 0.998199i | \(-0.519104\pi\) | ||||
−0.0599818 | + | 0.998199i | \(0.519104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.404061 | −0.0394323 | ||||||||
\(106\) | 0.811429 | 0.0788129 | ||||||||
\(107\) | 13.5610 | 1.31100 | 0.655498 | − | 0.755197i | \(-0.272459\pi\) | ||||
0.655498 | + | 0.755197i | \(0.272459\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.5344 | 1.20058 | 0.600289 | − | 0.799783i | \(-0.295052\pi\) | ||||
0.600289 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(110\) | 1.91001 | 0.182113 | ||||||||
\(111\) | −4.41291 | −0.418855 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −18.1761 | −1.70987 | −0.854933 | − | 0.518739i | \(-0.826402\pi\) | ||||
−0.854933 | + | 0.518739i | \(0.826402\pi\) | |||||||
\(114\) | 4.94294 | 0.462949 | ||||||||
\(115\) | 2.31678 | 0.216041 | ||||||||
\(116\) | −0.647042 | −0.0600763 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0444 | 1.38495 | ||||||||
\(119\) | 4.50459 | 0.412935 | ||||||||
\(120\) | 0.404061 | 0.0368855 | ||||||||
\(121\) | 11.3449 | 1.03136 | ||||||||
\(122\) | −2.83178 | −0.256377 | ||||||||
\(123\) | −9.13551 | −0.823721 | ||||||||
\(124\) | −6.14471 | −0.551812 | ||||||||
\(125\) | 3.97464 | 0.355503 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 11.2447 | 0.997803 | 0.498902 | − | 0.866659i | \(-0.333737\pi\) | ||||
0.498902 | + | 0.866659i | \(0.333737\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.666578 | −0.0586889 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.57875 | −0.312677 | −0.156338 | − | 0.987704i | \(-0.549969\pi\) | ||||
−0.156338 | + | 0.987704i | \(0.549969\pi\) | |||||||
\(132\) | 4.72704 | 0.411436 | ||||||||
\(133\) | −4.94294 | −0.428607 | ||||||||
\(134\) | 5.97874 | 0.516484 | ||||||||
\(135\) | −0.404061 | −0.0347760 | ||||||||
\(136\) | −4.50459 | −0.386265 | ||||||||
\(137\) | 3.27155 | 0.279507 | 0.139754 | − | 0.990186i | \(-0.455369\pi\) | ||||
0.139754 | + | 0.990186i | \(0.455369\pi\) | |||||||
\(138\) | 5.73373 | 0.488088 | ||||||||
\(139\) | −10.7168 | −0.908984 | −0.454492 | − | 0.890751i | \(-0.650179\pi\) | ||||
−0.454492 | + | 0.890751i | \(0.650179\pi\) | |||||||
\(140\) | −0.404061 | −0.0341494 | ||||||||
\(141\) | −6.47213 | −0.545051 | ||||||||
\(142\) | 14.3974 | 1.20821 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.261444 | 0.0217118 | ||||||||
\(146\) | −3.92648 | −0.324958 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −4.41291 | −0.362739 | ||||||||
\(149\) | −1.18034 | −0.0966972 | −0.0483486 | − | 0.998831i | \(-0.515396\pi\) | ||||
−0.0483486 | + | 0.998831i | \(0.515396\pi\) | |||||||
\(150\) | 4.83673 | 0.394918 | ||||||||
\(151\) | 20.7040 | 1.68487 | 0.842434 | − | 0.538799i | \(-0.181122\pi\) | ||||
0.842434 | + | 0.538799i | \(0.181122\pi\) | |||||||
\(152\) | 4.94294 | 0.400925 | ||||||||
\(153\) | 4.50459 | 0.364174 | ||||||||
\(154\) | −4.72704 | −0.380916 | ||||||||
\(155\) | 2.48284 | 0.199426 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8774 | 1.02772 | 0.513862 | − | 0.857873i | \(-0.328214\pi\) | ||||
0.513862 | + | 0.857873i | \(0.328214\pi\) | |||||||
\(158\) | 8.69273 | 0.691556 | ||||||||
\(159\) | −0.811429 | −0.0643505 | ||||||||
\(160\) | 0.404061 | 0.0319438 | ||||||||
\(161\) | −5.73373 | −0.451881 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 21.0202 | 1.64643 | 0.823215 | − | 0.567729i | \(-0.192178\pi\) | ||||
0.823215 | + | 0.567729i | \(0.192178\pi\) | |||||||
\(164\) | −9.13551 | −0.713363 | ||||||||
\(165\) | −1.91001 | −0.148694 | ||||||||
\(166\) | −4.51350 | −0.350315 | ||||||||
\(167\) | −13.8944 | −1.07518 | −0.537592 | − | 0.843205i | \(-0.680666\pi\) | ||||
−0.537592 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.82013 | 0.139597 | ||||||||
\(171\) | −4.94294 | −0.377996 | ||||||||
\(172\) | −0.666578 | −0.0508261 | ||||||||
\(173\) | 8.88152 | 0.675250 | 0.337625 | − | 0.941281i | \(-0.390376\pi\) | ||||
0.337625 | + | 0.941281i | \(0.390376\pi\) | |||||||
\(174\) | 0.647042 | 0.0490521 | ||||||||
\(175\) | −4.83673 | −0.365623 | ||||||||
\(176\) | 4.72704 | 0.356314 | ||||||||
\(177\) | −15.0444 | −1.13080 | ||||||||
\(178\) | 9.32298 | 0.698787 | ||||||||
\(179\) | −17.7757 | −1.32862 | −0.664308 | − | 0.747459i | \(-0.731274\pi\) | ||||
−0.664308 | + | 0.747459i | \(0.731274\pi\) | |||||||
\(180\) | −0.404061 | −0.0301169 | ||||||||
\(181\) | 20.2125 | 1.50239 | 0.751193 | − | 0.660082i | \(-0.229479\pi\) | ||||
0.751193 | + | 0.660082i | \(0.229479\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.83178 | 0.209331 | ||||||||
\(184\) | 5.73373 | 0.422696 | ||||||||
\(185\) | 1.78308 | 0.131095 | ||||||||
\(186\) | 6.14471 | 0.450552 | ||||||||
\(187\) | 21.2934 | 1.55713 | ||||||||
\(188\) | −6.47213 | −0.472028 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −1.99725 | −0.144896 | ||||||||
\(191\) | −17.5158 | −1.26740 | −0.633698 | − | 0.773580i | \(-0.718464\pi\) | ||||
−0.633698 | + | 0.773580i | \(0.718464\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −19.7673 | −1.42288 | −0.711441 | − | 0.702746i | \(-0.751957\pi\) | ||||
−0.711441 | + | 0.702746i | \(0.751957\pi\) | |||||||
\(194\) | 6.19694 | 0.444915 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −9.54410 | −0.679989 | −0.339994 | − | 0.940427i | \(-0.610425\pi\) | ||||
−0.339994 | + | 0.940427i | \(0.610425\pi\) | |||||||
\(198\) | −4.72704 | −0.335936 | ||||||||
\(199\) | 5.57473 | 0.395182 | 0.197591 | − | 0.980285i | \(-0.436688\pi\) | ||||
0.197591 | + | 0.980285i | \(0.436688\pi\) | |||||||
\(200\) | 4.83673 | 0.342009 | ||||||||
\(201\) | −5.97874 | −0.421707 | ||||||||
\(202\) | −10.7135 | −0.753797 | ||||||||
\(203\) | −0.647042 | −0.0454134 | ||||||||
\(204\) | 4.50459 | 0.315384 | ||||||||
\(205\) | 3.69130 | 0.257812 | ||||||||
\(206\) | 1.21750 | 0.0848271 | ||||||||
\(207\) | −5.73373 | −0.398522 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.3655 | −1.61622 | ||||||||
\(210\) | 0.404061 | 0.0278828 | ||||||||
\(211\) | 15.1334 | 1.04183 | 0.520914 | − | 0.853609i | \(-0.325591\pi\) | ||||
0.520914 | + | 0.853609i | \(0.325591\pi\) | |||||||
\(212\) | −0.811429 | −0.0557291 | ||||||||
\(213\) | −14.3974 | −0.986497 | ||||||||
\(214\) | −13.5610 | −0.927014 | ||||||||
\(215\) | 0.269338 | 0.0183687 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −6.14471 | −0.417130 | ||||||||
\(218\) | −12.5344 | −0.848936 | ||||||||
\(219\) | 3.92648 | 0.265327 | ||||||||
\(220\) | −1.91001 | −0.128773 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.41291 | 0.296175 | ||||||||
\(223\) | −7.60285 | −0.509124 | −0.254562 | − | 0.967056i | \(-0.581931\pi\) | ||||
−0.254562 | + | 0.967056i | \(0.581931\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.83673 | −0.322449 | ||||||||
\(226\) | 18.1761 | 1.20906 | ||||||||
\(227\) | −0.478747 | −0.0317756 | −0.0158878 | − | 0.999874i | \(-0.505057\pi\) | ||||
−0.0158878 | + | 0.999874i | \(0.505057\pi\) | |||||||
\(228\) | −4.94294 | −0.327354 | ||||||||
\(229\) | 20.0110 | 1.32237 | 0.661183 | − | 0.750224i | \(-0.270055\pi\) | ||||
0.661183 | + | 0.750224i | \(0.270055\pi\) | |||||||
\(230\) | −2.31678 | −0.152764 | ||||||||
\(231\) | 4.72704 | 0.311017 | ||||||||
\(232\) | 0.647042 | 0.0424804 | ||||||||
\(233\) | 5.45868 | 0.357610 | 0.178805 | − | 0.983885i | \(-0.442777\pi\) | ||||
0.178805 | + | 0.983885i | \(0.442777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.61513 | 0.170592 | ||||||||
\(236\) | −15.0444 | −0.979305 | ||||||||
\(237\) | −8.69273 | −0.564653 | ||||||||
\(238\) | −4.50459 | −0.291989 | ||||||||
\(239\) | −6.30483 | −0.407826 | −0.203913 | − | 0.978989i | \(-0.565366\pi\) | ||||
−0.203913 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(240\) | −0.404061 | −0.0260820 | ||||||||
\(241\) | 2.62771 | 0.169265 | 0.0846327 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846327 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(242\) | −11.3449 | −0.729280 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.83178 | 0.181286 | ||||||||
\(245\) | −0.404061 | −0.0258145 | ||||||||
\(246\) | 9.13551 | 0.582459 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.14471 | 0.390190 | ||||||||
\(249\) | 4.51350 | 0.286031 | ||||||||
\(250\) | −3.97464 | −0.251378 | ||||||||
\(251\) | −25.4341 | −1.60538 | −0.802692 | − | 0.596394i | \(-0.796599\pi\) | ||||
−0.802692 | + | 0.596394i | \(0.796599\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −27.1036 | −1.70399 | ||||||||
\(254\) | −11.2447 | −0.705553 | ||||||||
\(255\) | −1.82013 | −0.113981 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.822060 | 0.0512787 | 0.0256393 | − | 0.999671i | \(-0.491838\pi\) | ||||
0.0256393 | + | 0.999671i | \(0.491838\pi\) | |||||||
\(258\) | 0.666578 | 0.0414993 | ||||||||
\(259\) | −4.41291 | −0.274205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.647042 | −0.0400509 | ||||||||
\(262\) | 3.57875 | 0.221096 | ||||||||
\(263\) | 23.7426 | 1.46403 | 0.732015 | − | 0.681288i | \(-0.238580\pi\) | ||||
0.732015 | + | 0.681288i | \(0.238580\pi\) | |||||||
\(264\) | −4.72704 | −0.290929 | ||||||||
\(265\) | 0.327867 | 0.0201407 | ||||||||
\(266\) | 4.94294 | 0.303071 | ||||||||
\(267\) | −9.32298 | −0.570557 | ||||||||
\(268\) | −5.97874 | −0.365209 | ||||||||
\(269\) | −6.81198 | −0.415334 | −0.207667 | − | 0.978200i | \(-0.566587\pi\) | ||||
−0.207667 | + | 0.978200i | \(0.566587\pi\) | |||||||
\(270\) | 0.404061 | 0.0245904 | ||||||||
\(271\) | 13.3555 | 0.811288 | 0.405644 | − | 0.914031i | \(-0.367047\pi\) | ||||
0.405644 | + | 0.914031i | \(0.367047\pi\) | |||||||
\(272\) | 4.50459 | 0.273131 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.27155 | −0.197642 | ||||||||
\(275\) | −22.8635 | −1.37872 | ||||||||
\(276\) | −5.73373 | −0.345130 | ||||||||
\(277\) | 23.3676 | 1.40402 | 0.702012 | − | 0.712166i | \(-0.252285\pi\) | ||||
0.702012 | + | 0.712166i | \(0.252285\pi\) | |||||||
\(278\) | 10.7168 | 0.642749 | ||||||||
\(279\) | −6.14471 | −0.367874 | ||||||||
\(280\) | 0.404061 | 0.0241473 | ||||||||
\(281\) | −1.31057 | −0.0781820 | −0.0390910 | − | 0.999236i | \(-0.512446\pi\) | ||||
−0.0390910 | + | 0.999236i | \(0.512446\pi\) | |||||||
\(282\) | 6.47213 | 0.385410 | ||||||||
\(283\) | −27.0743 | −1.60940 | −0.804699 | − | 0.593683i | \(-0.797673\pi\) | ||||
−0.804699 | + | 0.593683i | \(0.797673\pi\) | |||||||
\(284\) | −14.3974 | −0.854331 | ||||||||
\(285\) | 1.99725 | 0.118307 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.13551 | −0.539252 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 3.29130 | 0.193606 | ||||||||
\(290\) | −0.261444 | −0.0153525 | ||||||||
\(291\) | −6.19694 | −0.363271 | ||||||||
\(292\) | 3.92648 | 0.229780 | ||||||||
\(293\) | −17.1700 | −1.00308 | −0.501541 | − | 0.865134i | \(-0.667233\pi\) | ||||
−0.501541 | + | 0.865134i | \(0.667233\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 6.07884 | 0.353924 | ||||||||
\(296\) | 4.41291 | 0.256495 | ||||||||
\(297\) | 4.72704 | 0.274291 | ||||||||
\(298\) | 1.18034 | 0.0683753 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.83673 | −0.279249 | ||||||||
\(301\) | −0.666578 | −0.0384209 | ||||||||
\(302\) | −20.7040 | −1.19138 | ||||||||
\(303\) | 10.7135 | 0.615473 | ||||||||
\(304\) | −4.94294 | −0.283497 | ||||||||
\(305\) | −1.14421 | −0.0655173 | ||||||||
\(306\) | −4.50459 | −0.257510 | ||||||||
\(307\) | 20.6481 | 1.17845 | 0.589225 | − | 0.807969i | \(-0.299433\pi\) | ||||
0.589225 | + | 0.807969i | \(0.299433\pi\) | |||||||
\(308\) | 4.72704 | 0.269348 | ||||||||
\(309\) | −1.21750 | −0.0692610 | ||||||||
\(310\) | −2.48284 | −0.141016 | ||||||||
\(311\) | 31.1584 | 1.76683 | 0.883415 | − | 0.468591i | \(-0.155238\pi\) | ||||
0.883415 | + | 0.468591i | \(0.155238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2384 | −1.20046 | −0.600232 | − | 0.799826i | \(-0.704925\pi\) | ||||
−0.600232 | + | 0.799826i | \(0.704925\pi\) | |||||||
\(314\) | −12.8774 | −0.726711 | ||||||||
\(315\) | −0.404061 | −0.0227662 | ||||||||
\(316\) | −8.69273 | −0.489004 | ||||||||
\(317\) | −3.67433 | −0.206371 | −0.103185 | − | 0.994662i | \(-0.532903\pi\) | ||||
−0.103185 | + | 0.994662i | \(0.532903\pi\) | |||||||
\(318\) | 0.811429 | 0.0455027 | ||||||||
\(319\) | −3.05859 | −0.171248 | ||||||||
\(320\) | −0.404061 | −0.0225877 | ||||||||
\(321\) | 13.5610 | 0.756903 | ||||||||
\(322\) | 5.73373 | 0.319528 | ||||||||
\(323\) | −22.2659 | −1.23891 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.0202 | −1.16420 | ||||||||
\(327\) | 12.5344 | 0.693154 | ||||||||
\(328\) | 9.13551 | 0.504424 | ||||||||
\(329\) | −6.47213 | −0.356820 | ||||||||
\(330\) | 1.91001 | 0.105143 | ||||||||
\(331\) | −25.6685 | −1.41087 | −0.705434 | − | 0.708776i | \(-0.749248\pi\) | ||||
−0.705434 | + | 0.708776i | \(0.749248\pi\) | |||||||
\(332\) | 4.51350 | 0.247710 | ||||||||
\(333\) | −4.41291 | −0.241826 | ||||||||
\(334\) | 13.8944 | 0.760270 | ||||||||
\(335\) | 2.41577 | 0.131988 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −19.8182 | −1.07956 | −0.539782 | − | 0.841805i | \(-0.681493\pi\) | ||||
−0.539782 | + | 0.841805i | \(0.681493\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.1761 | −0.987192 | ||||||||
\(340\) | −1.82013 | −0.0987102 | ||||||||
\(341\) | −29.0463 | −1.57295 | ||||||||
\(342\) | 4.94294 | 0.267284 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.666578 | 0.0359395 | ||||||||
\(345\) | 2.31678 | 0.124731 | ||||||||
\(346\) | −8.88152 | −0.477474 | ||||||||
\(347\) | −7.05961 | −0.378980 | −0.189490 | − | 0.981883i | \(-0.560683\pi\) | ||||
−0.189490 | + | 0.981883i | \(0.560683\pi\) | |||||||
\(348\) | −0.647042 | −0.0346851 | ||||||||
\(349\) | 8.96825 | 0.480059 | 0.240030 | − | 0.970766i | \(-0.422843\pi\) | ||||
0.240030 | + | 0.970766i | \(0.422843\pi\) | |||||||
\(350\) | 4.83673 | 0.258534 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.72704 | −0.251952 | ||||||||
\(353\) | 19.6812 | 1.04753 | 0.523763 | − | 0.851864i | \(-0.324528\pi\) | ||||
0.523763 | + | 0.851864i | \(0.324528\pi\) | |||||||
\(354\) | 15.0444 | 0.799600 | ||||||||
\(355\) | 5.81744 | 0.308758 | ||||||||
\(356\) | −9.32298 | −0.494117 | ||||||||
\(357\) | 4.50459 | 0.238408 | ||||||||
\(358\) | 17.7757 | 0.939473 | ||||||||
\(359\) | 32.8782 | 1.73524 | 0.867622 | − | 0.497224i | \(-0.165647\pi\) | ||||
0.867622 | + | 0.497224i | \(0.165647\pi\) | |||||||
\(360\) | 0.404061 | 0.0212959 | ||||||||
\(361\) | 5.43264 | 0.285929 | ||||||||
\(362\) | −20.2125 | −1.06235 | ||||||||
\(363\) | 11.3449 | 0.595455 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.58654 | −0.0830431 | ||||||||
\(366\) | −2.83178 | −0.148019 | ||||||||
\(367\) | −25.2819 | −1.31970 | −0.659852 | − | 0.751395i | \(-0.729381\pi\) | ||||
−0.659852 | + | 0.751395i | \(0.729381\pi\) | |||||||
\(368\) | −5.73373 | −0.298892 | ||||||||
\(369\) | −9.13551 | −0.475576 | ||||||||
\(370\) | −1.78308 | −0.0926981 | ||||||||
\(371\) | −0.811429 | −0.0421273 | ||||||||
\(372\) | −6.14471 | −0.318589 | ||||||||
\(373\) | 11.3971 | 0.590118 | 0.295059 | − | 0.955479i | \(-0.404661\pi\) | ||||
0.295059 | + | 0.955479i | \(0.404661\pi\) | |||||||
\(374\) | −21.2934 | −1.10105 | ||||||||
\(375\) | 3.97464 | 0.205249 | ||||||||
\(376\) | 6.47213 | 0.333775 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 19.2765 | 0.990168 | 0.495084 | − | 0.868845i | \(-0.335137\pi\) | ||||
0.495084 | + | 0.868845i | \(0.335137\pi\) | |||||||
\(380\) | 1.99725 | 0.102457 | ||||||||
\(381\) | 11.2447 | 0.576082 | ||||||||
\(382\) | 17.5158 | 0.896184 | ||||||||
\(383\) | 14.4663 | 0.739192 | 0.369596 | − | 0.929193i | \(-0.379496\pi\) | ||||
0.369596 | + | 0.929193i | \(0.379496\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −1.91001 | −0.0973433 | ||||||||
\(386\) | 19.7673 | 1.00613 | ||||||||
\(387\) | −0.666578 | −0.0338840 | ||||||||
\(388\) | −6.19694 | −0.314602 | ||||||||
\(389\) | −0.913387 | −0.0463106 | −0.0231553 | − | 0.999732i | \(-0.507371\pi\) | ||||
−0.0231553 | + | 0.999732i | \(0.507371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8281 | −1.30618 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −3.57875 | −0.180524 | ||||||||
\(394\) | 9.54410 | 0.480825 | ||||||||
\(395\) | 3.51239 | 0.176728 | ||||||||
\(396\) | 4.72704 | 0.237543 | ||||||||
\(397\) | −33.5036 | −1.68150 | −0.840748 | − | 0.541427i | \(-0.817884\pi\) | ||||
−0.840748 | + | 0.541427i | \(0.817884\pi\) | |||||||
\(398\) | −5.57473 | −0.279436 | ||||||||
\(399\) | −4.94294 | −0.247456 | ||||||||
\(400\) | −4.83673 | −0.241837 | ||||||||
\(401\) | 20.0314 | 1.00032 | 0.500160 | − | 0.865933i | \(-0.333275\pi\) | ||||
0.500160 | + | 0.865933i | \(0.333275\pi\) | |||||||
\(402\) | 5.97874 | 0.298192 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.7135 | 0.533015 | ||||||||
\(405\) | −0.404061 | −0.0200779 | ||||||||
\(406\) | 0.647042 | 0.0321121 | ||||||||
\(407\) | −20.8600 | −1.03399 | ||||||||
\(408\) | −4.50459 | −0.223010 | ||||||||
\(409\) | −12.2787 | −0.607142 | −0.303571 | − | 0.952809i | \(-0.598179\pi\) | ||||
−0.303571 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(410\) | −3.69130 | −0.182300 | ||||||||
\(411\) | 3.27155 | 0.161374 | ||||||||
\(412\) | −1.21750 | −0.0599818 | ||||||||
\(413\) | −15.0444 | −0.740285 | ||||||||
\(414\) | 5.73373 | 0.281798 | ||||||||
\(415\) | −1.82373 | −0.0895232 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.7168 | −0.524802 | ||||||||
\(418\) | 23.3655 | 1.14284 | ||||||||
\(419\) | −9.98508 | −0.487803 | −0.243902 | − | 0.969800i | \(-0.578427\pi\) | ||||
−0.243902 | + | 0.969800i | \(0.578427\pi\) | |||||||
\(420\) | −0.404061 | −0.0197161 | ||||||||
\(421\) | 12.1776 | 0.593498 | 0.296749 | − | 0.954956i | \(-0.404098\pi\) | ||||
0.296749 | + | 0.954956i | \(0.404098\pi\) | |||||||
\(422\) | −15.1334 | −0.736684 | ||||||||
\(423\) | −6.47213 | −0.314686 | ||||||||
\(424\) | 0.811429 | 0.0394065 | ||||||||
\(425\) | −21.7875 | −1.05685 | ||||||||
\(426\) | 14.3974 | 0.697558 | ||||||||
\(427\) | 2.83178 | 0.137039 | ||||||||
\(428\) | 13.5610 | 0.655498 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.269338 | −0.0129886 | ||||||||
\(431\) | 30.1287 | 1.45125 | 0.725623 | − | 0.688092i | \(-0.241552\pi\) | ||||
0.725623 | + | 0.688092i | \(0.241552\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 26.4737 | 1.27225 | 0.636123 | − | 0.771588i | \(-0.280537\pi\) | ||||
0.636123 | + | 0.771588i | \(0.280537\pi\) | |||||||
\(434\) | 6.14471 | 0.294956 | ||||||||
\(435\) | 0.261444 | 0.0125353 | ||||||||
\(436\) | 12.5344 | 0.600289 | ||||||||
\(437\) | 28.3415 | 1.35576 | ||||||||
\(438\) | −3.92648 | −0.187614 | ||||||||
\(439\) | −34.7765 | −1.65979 | −0.829896 | − | 0.557918i | \(-0.811600\pi\) | ||||
−0.829896 | + | 0.557918i | \(0.811600\pi\) | |||||||
\(440\) | 1.91001 | 0.0910563 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.91795 | −0.423704 | −0.211852 | − | 0.977302i | \(-0.567950\pi\) | ||||
−0.211852 | + | 0.977302i | \(0.567950\pi\) | |||||||
\(444\) | −4.41291 | −0.209427 | ||||||||
\(445\) | 3.76705 | 0.178575 | ||||||||
\(446\) | 7.60285 | 0.360005 | ||||||||
\(447\) | −1.18034 | −0.0558282 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −18.0313 | −0.850949 | −0.425475 | − | 0.904970i | \(-0.639893\pi\) | ||||
−0.425475 | + | 0.904970i | \(0.639893\pi\) | |||||||
\(450\) | 4.83673 | 0.228006 | ||||||||
\(451\) | −43.1839 | −2.03345 | ||||||||
\(452\) | −18.1761 | −0.854933 | ||||||||
\(453\) | 20.7040 | 0.972760 | ||||||||
\(454\) | 0.478747 | 0.0224687 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.94294 | 0.231474 | ||||||||
\(457\) | −18.9373 | −0.885849 | −0.442925 | − | 0.896559i | \(-0.646059\pi\) | ||||
−0.442925 | + | 0.896559i | \(0.646059\pi\) | |||||||
\(458\) | −20.0110 | −0.935054 | ||||||||
\(459\) | 4.50459 | 0.210256 | ||||||||
\(460\) | 2.31678 | 0.108020 | ||||||||
\(461\) | −6.51876 | −0.303609 | −0.151804 | − | 0.988411i | \(-0.548508\pi\) | ||||
−0.151804 | + | 0.988411i | \(0.548508\pi\) | |||||||
\(462\) | −4.72704 | −0.219922 | ||||||||
\(463\) | −13.1560 | −0.611409 | −0.305705 | − | 0.952126i | \(-0.598892\pi\) | ||||
−0.305705 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(464\) | −0.647042 | −0.0300382 | ||||||||
\(465\) | 2.48284 | 0.115139 | ||||||||
\(466\) | −5.45868 | −0.252869 | ||||||||
\(467\) | 2.00592 | 0.0928230 | 0.0464115 | − | 0.998922i | \(-0.485221\pi\) | ||||
0.0464115 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.97874 | −0.276072 | ||||||||
\(470\) | −2.61513 | −0.120627 | ||||||||
\(471\) | 12.8774 | 0.593357 | ||||||||
\(472\) | 15.0444 | 0.692474 | ||||||||
\(473\) | −3.15094 | −0.144880 | ||||||||
\(474\) | 8.69273 | 0.399270 | ||||||||
\(475\) | 23.9077 | 1.09696 | ||||||||
\(476\) | 4.50459 | 0.206467 | ||||||||
\(477\) | −0.811429 | −0.0371528 | ||||||||
\(478\) | 6.30483 | 0.288376 | ||||||||
\(479\) | −12.1195 | −0.553756 | −0.276878 | − | 0.960905i | \(-0.589300\pi\) | ||||
−0.276878 | + | 0.960905i | \(0.589300\pi\) | |||||||
\(480\) | 0.404061 | 0.0184428 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.62771 | −0.119689 | ||||||||
\(483\) | −5.73373 | −0.260894 | ||||||||
\(484\) | 11.3449 | 0.515679 | ||||||||
\(485\) | 2.50394 | 0.113698 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 43.1568 | 1.95562 | 0.977810 | − | 0.209492i | \(-0.0671809\pi\) | ||||
0.977810 | + | 0.209492i | \(0.0671809\pi\) | |||||||
\(488\) | −2.83178 | −0.128188 | ||||||||
\(489\) | 21.0202 | 0.950567 | ||||||||
\(490\) | 0.404061 | 0.0182536 | ||||||||
\(491\) | 16.5276 | 0.745880 | 0.372940 | − | 0.927856i | \(-0.378350\pi\) | ||||
0.372940 | + | 0.927856i | \(0.378350\pi\) | |||||||
\(492\) | −9.13551 | −0.411861 | ||||||||
\(493\) | −2.91466 | −0.131269 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.91001 | −0.0858487 | ||||||||
\(496\) | −6.14471 | −0.275906 | ||||||||
\(497\) | −14.3974 | −0.645814 | ||||||||
\(498\) | −4.51350 | −0.202255 | ||||||||
\(499\) | 15.6585 | 0.700972 | 0.350486 | − | 0.936568i | \(-0.386016\pi\) | ||||
0.350486 | + | 0.936568i | \(0.386016\pi\) | |||||||
\(500\) | 3.97464 | 0.177751 | ||||||||
\(501\) | −13.8944 | −0.620758 | ||||||||
\(502\) | 25.4341 | 1.13518 | ||||||||
\(503\) | −5.85397 | −0.261016 | −0.130508 | − | 0.991447i | \(-0.541661\pi\) | ||||
−0.130508 | + | 0.991447i | \(0.541661\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −4.32890 | −0.192633 | ||||||||
\(506\) | 27.1036 | 1.20490 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.2447 | 0.498902 | ||||||||
\(509\) | −23.1149 | −1.02455 | −0.512274 | − | 0.858822i | \(-0.671197\pi\) | ||||
−0.512274 | + | 0.858822i | \(0.671197\pi\) | |||||||
\(510\) | 1.82013 | 0.0805966 | ||||||||
\(511\) | 3.92648 | 0.173697 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.94294 | −0.218236 | ||||||||
\(514\) | −0.822060 | −0.0362595 | ||||||||
\(515\) | 0.491943 | 0.0216776 | ||||||||
\(516\) | −0.666578 | −0.0293444 | ||||||||
\(517\) | −30.5940 | −1.34552 | ||||||||
\(518\) | 4.41291 | 0.193892 | ||||||||
\(519\) | 8.88152 | 0.389856 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4240 | 1.46433 | 0.732167 | − | 0.681125i | \(-0.238509\pi\) | ||||
0.732167 | + | 0.681125i | \(0.238509\pi\) | |||||||
\(522\) | 0.647042 | 0.0283202 | ||||||||
\(523\) | 6.05442 | 0.264741 | 0.132371 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132371 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(524\) | −3.57875 | −0.156338 | ||||||||
\(525\) | −4.83673 | −0.211092 | ||||||||
\(526\) | −23.7426 | −1.03523 | ||||||||
\(527\) | −27.6794 | −1.20573 | ||||||||
\(528\) | 4.72704 | 0.205718 | ||||||||
\(529\) | 9.87570 | 0.429378 | ||||||||
\(530\) | −0.327867 | −0.0142416 | ||||||||
\(531\) | −15.0444 | −0.652870 | ||||||||
\(532\) | −4.94294 | −0.214304 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.32298 | 0.403445 | ||||||||
\(535\) | −5.47948 | −0.236899 | ||||||||
\(536\) | 5.97874 | 0.258242 | ||||||||
\(537\) | −17.7757 | −0.767077 | ||||||||
\(538\) | 6.81198 | 0.293685 | ||||||||
\(539\) | 4.72704 | 0.203608 | ||||||||
\(540\) | −0.404061 | −0.0173880 | ||||||||
\(541\) | 31.8120 | 1.36770 | 0.683851 | − | 0.729621i | \(-0.260304\pi\) | ||||
0.683851 | + | 0.729621i | \(0.260304\pi\) | |||||||
\(542\) | −13.3555 | −0.573667 | ||||||||
\(543\) | 20.2125 | 0.867403 | ||||||||
\(544\) | −4.50459 | −0.193133 | ||||||||
\(545\) | −5.06466 | −0.216946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.5362 | 1.09185 | 0.545926 | − | 0.837834i | \(-0.316178\pi\) | ||||
0.545926 | + | 0.837834i | \(0.316178\pi\) | |||||||
\(548\) | 3.27155 | 0.139754 | ||||||||
\(549\) | 2.83178 | 0.120857 | ||||||||
\(550\) | 22.8635 | 0.974901 | ||||||||
\(551\) | 3.19829 | 0.136252 | ||||||||
\(552\) | 5.73373 | 0.244044 | ||||||||
\(553\) | −8.69273 | −0.369652 | ||||||||
\(554\) | −23.3676 | −0.992794 | ||||||||
\(555\) | 1.78308 | 0.0756877 | ||||||||
\(556\) | −10.7168 | −0.454492 | ||||||||
\(557\) | 8.41516 | 0.356562 | 0.178281 | − | 0.983980i | \(-0.442946\pi\) | ||||
0.178281 | + | 0.983980i | \(0.442946\pi\) | |||||||
\(558\) | 6.14471 | 0.260126 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.404061 | −0.0170747 | ||||||||
\(561\) | 21.2934 | 0.899007 | ||||||||
\(562\) | 1.31057 | 0.0552830 | ||||||||
\(563\) | −4.82618 | −0.203399 | −0.101700 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101700 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(564\) | −6.47213 | −0.272526 | ||||||||
\(565\) | 7.34426 | 0.308975 | ||||||||
\(566\) | 27.0743 | 1.13802 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 14.3974 | 0.604103 | ||||||||
\(569\) | 17.8366 | 0.747751 | 0.373876 | − | 0.927479i | \(-0.378029\pi\) | ||||
0.373876 | + | 0.927479i | \(0.378029\pi\) | |||||||
\(570\) | −1.99725 | −0.0836555 | ||||||||
\(571\) | −3.04959 | −0.127621 | −0.0638107 | − | 0.997962i | \(-0.520325\pi\) | ||||
−0.0638107 | + | 0.997962i | \(0.520325\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.5158 | −0.731732 | ||||||||
\(574\) | 9.13551 | 0.381309 | ||||||||
\(575\) | 27.7325 | 1.15653 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −39.2941 | −1.63583 | −0.817917 | − | 0.575336i | \(-0.804871\pi\) | ||||
−0.817917 | + | 0.575336i | \(0.804871\pi\) | |||||||
\(578\) | −3.29130 | −0.136900 | ||||||||
\(579\) | −19.7673 | −0.821501 | ||||||||
\(580\) | 0.261444 | 0.0108559 | ||||||||
\(581\) | 4.51350 | 0.187251 | ||||||||
\(582\) | 6.19694 | 0.256872 | ||||||||
\(583\) | −3.83566 | −0.158857 | ||||||||
\(584\) | −3.92648 | −0.162479 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.1700 | 0.709286 | ||||||||
\(587\) | −1.76826 | −0.0729840 | −0.0364920 | − | 0.999334i | \(-0.511618\pi\) | ||||
−0.0364920 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 30.3729 | 1.25150 | ||||||||
\(590\) | −6.07884 | −0.250262 | ||||||||
\(591\) | −9.54410 | −0.392592 | ||||||||
\(592\) | −4.41291 | −0.181369 | ||||||||
\(593\) | −23.0287 | −0.945673 | −0.472837 | − | 0.881150i | \(-0.656770\pi\) | ||||
−0.472837 | + | 0.881150i | \(0.656770\pi\) | |||||||
\(594\) | −4.72704 | −0.193953 | ||||||||
\(595\) | −1.82013 | −0.0746179 | ||||||||
\(596\) | −1.18034 | −0.0483486 | ||||||||
\(597\) | 5.57473 | 0.228158 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.68489 | 0.395714 | 0.197857 | − | 0.980231i | \(-0.436602\pi\) | ||||
0.197857 | + | 0.980231i | \(0.436602\pi\) | |||||||
\(600\) | 4.83673 | 0.197459 | ||||||||
\(601\) | 25.4886 | 1.03970 | 0.519850 | − | 0.854257i | \(-0.325988\pi\) | ||||
0.519850 | + | 0.854257i | \(0.325988\pi\) | |||||||
\(602\) | 0.666578 | 0.0271677 | ||||||||
\(603\) | −5.97874 | −0.243473 | ||||||||
\(604\) | 20.7040 | 0.842434 | ||||||||
\(605\) | −4.58405 | −0.186368 | ||||||||
\(606\) | −10.7135 | −0.435205 | ||||||||
\(607\) | 15.3612 | 0.623493 | 0.311747 | − | 0.950165i | \(-0.399086\pi\) | ||||
0.311747 | + | 0.950165i | \(0.399086\pi\) | |||||||
\(608\) | 4.94294 | 0.200463 | ||||||||
\(609\) | −0.647042 | −0.0262195 | ||||||||
\(610\) | 1.14421 | 0.0463277 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.50459 | 0.182087 | ||||||||
\(613\) | 28.4105 | 1.14749 | 0.573744 | − | 0.819035i | \(-0.305491\pi\) | ||||
0.573744 | + | 0.819035i | \(0.305491\pi\) | |||||||
\(614\) | −20.6481 | −0.833290 | ||||||||
\(615\) | 3.69130 | 0.148848 | ||||||||
\(616\) | −4.72704 | −0.190458 | ||||||||
\(617\) | −21.9379 | −0.883186 | −0.441593 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441593 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(618\) | 1.21750 | 0.0489750 | ||||||||
\(619\) | 15.4136 | 0.619526 | 0.309763 | − | 0.950814i | \(-0.399750\pi\) | ||||
0.309763 | + | 0.950814i | \(0.399750\pi\) | |||||||
\(620\) | 2.48284 | 0.0997132 | ||||||||
\(621\) | −5.73373 | −0.230087 | ||||||||
\(622\) | −31.1584 | −1.24934 | ||||||||
\(623\) | −9.32298 | −0.373517 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.5777 | 0.903107 | ||||||||
\(626\) | 21.2384 | 0.848856 | ||||||||
\(627\) | −23.3655 | −0.933128 | ||||||||
\(628\) | 12.8774 | 0.513862 | ||||||||
\(629\) | −19.8783 | −0.792601 | ||||||||
\(630\) | 0.404061 | 0.0160982 | ||||||||
\(631\) | −24.4822 | −0.974623 | −0.487311 | − | 0.873228i | \(-0.662022\pi\) | ||||
−0.487311 | + | 0.873228i | \(0.662022\pi\) | |||||||
\(632\) | 8.69273 | 0.345778 | ||||||||
\(633\) | 15.1334 | 0.601500 | ||||||||
\(634\) | 3.67433 | 0.145926 | ||||||||
\(635\) | −4.54353 | −0.180305 | ||||||||
\(636\) | −0.811429 | −0.0321752 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.05859 | 0.121091 | ||||||||
\(639\) | −14.3974 | −0.569554 | ||||||||
\(640\) | 0.404061 | 0.0159719 | ||||||||
\(641\) | −17.5668 | −0.693848 | −0.346924 | − | 0.937893i | \(-0.612774\pi\) | ||||
−0.346924 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(642\) | −13.5610 | −0.535211 | ||||||||
\(643\) | −7.41189 | −0.292297 | −0.146148 | − | 0.989263i | \(-0.546688\pi\) | ||||
−0.146148 | + | 0.989263i | \(0.546688\pi\) | |||||||
\(644\) | −5.73373 | −0.225941 | ||||||||
\(645\) | 0.269338 | 0.0106052 | ||||||||
\(646\) | 22.2659 | 0.876040 | ||||||||
\(647\) | −15.3162 | −0.602143 | −0.301071 | − | 0.953602i | \(-0.597344\pi\) | ||||
−0.301071 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −71.1154 | −2.79152 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.14471 | −0.240830 | ||||||||
\(652\) | 21.0202 | 0.823215 | ||||||||
\(653\) | 1.48147 | 0.0579746 | 0.0289873 | − | 0.999580i | \(-0.490772\pi\) | ||||
0.0289873 | + | 0.999580i | \(0.490772\pi\) | |||||||
\(654\) | −12.5344 | −0.490134 | ||||||||
\(655\) | 1.44603 | 0.0565012 | ||||||||
\(656\) | −9.13551 | −0.356682 | ||||||||
\(657\) | 3.92648 | 0.153187 | ||||||||
\(658\) | 6.47213 | 0.252310 | ||||||||
\(659\) | −31.9552 | −1.24480 | −0.622399 | − | 0.782700i | \(-0.713842\pi\) | ||||
−0.622399 | + | 0.782700i | \(0.713842\pi\) | |||||||
\(660\) | −1.91001 | −0.0743472 | ||||||||
\(661\) | −33.7430 | −1.31245 | −0.656226 | − | 0.754564i | \(-0.727848\pi\) | ||||
−0.656226 | + | 0.754564i | \(0.727848\pi\) | |||||||
\(662\) | 25.6685 | 0.997634 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.51350 | −0.175158 | ||||||||
\(665\) | 1.99725 | 0.0774500 | ||||||||
\(666\) | 4.41291 | 0.170997 | ||||||||
\(667\) | 3.70996 | 0.143650 | ||||||||
\(668\) | −13.8944 | −0.537592 | ||||||||
\(669\) | −7.60285 | −0.293943 | ||||||||
\(670\) | −2.41577 | −0.0933294 | ||||||||
\(671\) | 13.3859 | 0.516758 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −37.5539 | −1.44760 | −0.723798 | − | 0.690011i | \(-0.757605\pi\) | ||||
−0.723798 | + | 0.690011i | \(0.757605\pi\) | |||||||
\(674\) | 19.8182 | 0.763367 | ||||||||
\(675\) | −4.83673 | −0.186166 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.53554 | 0.174315 | 0.0871574 | − | 0.996195i | \(-0.472222\pi\) | ||||
0.0871574 | + | 0.996195i | \(0.472222\pi\) | |||||||
\(678\) | 18.1761 | 0.698050 | ||||||||
\(679\) | −6.19694 | −0.237817 | ||||||||
\(680\) | 1.82013 | 0.0697987 | ||||||||
\(681\) | −0.478747 | −0.0183456 | ||||||||
\(682\) | 29.0463 | 1.11224 | ||||||||
\(683\) | −43.7634 | −1.67456 | −0.837281 | − | 0.546773i | \(-0.815856\pi\) | ||||
−0.837281 | + | 0.546773i | \(0.815856\pi\) | |||||||
\(684\) | −4.94294 | −0.188998 | ||||||||
\(685\) | −1.32191 | −0.0505074 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 20.0110 | 0.763469 | ||||||||
\(688\) | −0.666578 | −0.0254130 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.31678 | −0.0881982 | ||||||||
\(691\) | −25.7358 | −0.979037 | −0.489518 | − | 0.871993i | \(-0.662827\pi\) | ||||
−0.489518 | + | 0.871993i | \(0.662827\pi\) | |||||||
\(692\) | 8.88152 | 0.337625 | ||||||||
\(693\) | 4.72704 | 0.179566 | ||||||||
\(694\) | 7.05961 | 0.267979 | ||||||||
\(695\) | 4.33023 | 0.164255 | ||||||||
\(696\) | 0.647042 | 0.0245261 | ||||||||
\(697\) | −41.1517 | −1.55873 | ||||||||
\(698\) | −8.96825 | −0.339453 | ||||||||
\(699\) | 5.45868 | 0.206466 | ||||||||
\(700\) | −4.83673 | −0.182811 | ||||||||
\(701\) | −10.6876 | −0.403664 | −0.201832 | − | 0.979420i | \(-0.564689\pi\) | ||||
−0.201832 | + | 0.979420i | \(0.564689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.8127 | 0.822683 | ||||||||
\(704\) | 4.72704 | 0.178157 | ||||||||
\(705\) | 2.61513 | 0.0984916 | ||||||||
\(706\) | −19.6812 | −0.740712 | ||||||||
\(707\) | 10.7135 | 0.402922 | ||||||||
\(708\) | −15.0444 | −0.565402 | ||||||||
\(709\) | 33.5571 | 1.26026 | 0.630132 | − | 0.776488i | \(-0.283001\pi\) | ||||
0.630132 | + | 0.776488i | \(0.283001\pi\) | |||||||
\(710\) | −5.81744 | −0.218325 | ||||||||
\(711\) | −8.69273 | −0.326003 | ||||||||
\(712\) | 9.32298 | 0.349394 | ||||||||
\(713\) | 35.2321 | 1.31945 | ||||||||
\(714\) | −4.50459 | −0.168580 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.7757 | −0.664308 | ||||||||
\(717\) | −6.30483 | −0.235458 | ||||||||
\(718\) | −32.8782 | −1.22700 | ||||||||
\(719\) | 34.1548 | 1.27376 | 0.636879 | − | 0.770964i | \(-0.280225\pi\) | ||||
0.636879 | + | 0.770964i | \(0.280225\pi\) | |||||||
\(720\) | −0.404061 | −0.0150585 | ||||||||
\(721\) | −1.21750 | −0.0453420 | ||||||||
\(722\) | −5.43264 | −0.202182 | ||||||||
\(723\) | 2.62771 | 0.0977254 | ||||||||
\(724\) | 20.2125 | 0.751193 | ||||||||
\(725\) | 3.12957 | 0.116229 | ||||||||
\(726\) | −11.3449 | −0.421050 | ||||||||
\(727\) | −21.3381 | −0.791388 | −0.395694 | − | 0.918383i | \(-0.629496\pi\) | ||||
−0.395694 | + | 0.918383i | \(0.629496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.58654 | 0.0587204 | ||||||||
\(731\) | −3.00266 | −0.111057 | ||||||||
\(732\) | 2.83178 | 0.104665 | ||||||||
\(733\) | −27.5592 | −1.01792 | −0.508961 | − | 0.860790i | \(-0.669970\pi\) | ||||
−0.508961 | + | 0.860790i | \(0.669970\pi\) | |||||||
\(734\) | 25.2819 | 0.933172 | ||||||||
\(735\) | −0.404061 | −0.0149040 | ||||||||
\(736\) | 5.73373 | 0.211348 | ||||||||
\(737\) | −28.2617 | −1.04103 | ||||||||
\(738\) | 9.13551 | 0.336283 | ||||||||
\(739\) | 31.3875 | 1.15461 | 0.577304 | − | 0.816529i | \(-0.304105\pi\) | ||||
0.577304 | + | 0.816529i | \(0.304105\pi\) | |||||||
\(740\) | 1.78308 | 0.0655475 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.811429 | 0.0297885 | ||||||||
\(743\) | −22.8912 | −0.839797 | −0.419899 | − | 0.907571i | \(-0.637934\pi\) | ||||
−0.419899 | + | 0.907571i | \(0.637934\pi\) | |||||||
\(744\) | 6.14471 | 0.225276 | ||||||||
\(745\) | 0.476929 | 0.0174733 | ||||||||
\(746\) | −11.3971 | −0.417276 | ||||||||
\(747\) | 4.51350 | 0.165140 | ||||||||
\(748\) | 21.2934 | 0.778563 | ||||||||
\(749\) | 13.5610 | 0.495510 | ||||||||
\(750\) | −3.97464 | −0.145133 | ||||||||
\(751\) | 18.3810 | 0.670733 | 0.335366 | − | 0.942088i | \(-0.391140\pi\) | ||||
0.335366 | + | 0.942088i | \(0.391140\pi\) | |||||||
\(752\) | −6.47213 | −0.236014 | ||||||||
\(753\) | −25.4341 | −0.926868 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.36568 | −0.304458 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 2.10502 | 0.0765083 | 0.0382541 | − | 0.999268i | \(-0.487820\pi\) | ||||
0.0382541 | + | 0.999268i | \(0.487820\pi\) | |||||||
\(758\) | −19.2765 | −0.700155 | ||||||||
\(759\) | −27.1036 | −0.983799 | ||||||||
\(760\) | −1.99725 | −0.0724478 | ||||||||
\(761\) | −29.8044 | −1.08041 | −0.540204 | − | 0.841534i | \(-0.681653\pi\) | ||||
−0.540204 | + | 0.841534i | \(0.681653\pi\) | |||||||
\(762\) | −11.2447 | −0.407351 | ||||||||
\(763\) | 12.5344 | 0.453776 | ||||||||
\(764\) | −17.5158 | −0.633698 | ||||||||
\(765\) | −1.82013 | −0.0658068 | ||||||||
\(766\) | −14.4663 | −0.522688 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 8.71023 | 0.314099 | 0.157049 | − | 0.987591i | \(-0.449802\pi\) | ||||
0.157049 | + | 0.987591i | \(0.449802\pi\) | |||||||
\(770\) | 1.91001 | 0.0688321 | ||||||||
\(771\) | 0.822060 | 0.0296058 | ||||||||
\(772\) | −19.7673 | −0.711441 | ||||||||
\(773\) | 42.0212 | 1.51140 | 0.755699 | − | 0.654920i | \(-0.227298\pi\) | ||||
0.755699 | + | 0.654920i | \(0.227298\pi\) | |||||||
\(774\) | 0.666578 | 0.0239596 | ||||||||
\(775\) | 29.7203 | 1.06759 | ||||||||
\(776\) | 6.19694 | 0.222457 | ||||||||
\(777\) | −4.41291 | −0.158312 | ||||||||
\(778\) | 0.913387 | 0.0327465 | ||||||||
\(779\) | 45.1563 | 1.61789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −68.0573 | −2.43528 | ||||||||
\(782\) | 25.8281 | 0.923611 | ||||||||
\(783\) | −0.647042 | −0.0231234 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −5.20323 | −0.185711 | ||||||||
\(786\) | 3.57875 | 0.127650 | ||||||||
\(787\) | 33.7001 | 1.20128 | 0.600639 | − | 0.799520i | \(-0.294913\pi\) | ||||
0.600639 | + | 0.799520i | \(0.294913\pi\) | |||||||
\(788\) | −9.54410 | −0.339994 | ||||||||
\(789\) | 23.7426 | 0.845258 | ||||||||
\(790\) | −3.51239 | −0.124965 | ||||||||
\(791\) | −18.1761 | −0.646269 | ||||||||
\(792\) | −4.72704 | −0.167968 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 33.5036 | 1.18900 | ||||||||
\(795\) | 0.327867 | 0.0116282 | ||||||||
\(796\) | 5.57473 | 0.197591 | ||||||||
\(797\) | 19.1578 | 0.678603 | 0.339301 | − | 0.940678i | \(-0.389809\pi\) | ||||
0.339301 | + | 0.940678i | \(0.389809\pi\) | |||||||
\(798\) | 4.94294 | 0.174978 | ||||||||
\(799\) | −29.1543 | −1.03140 | ||||||||
\(800\) | 4.83673 | 0.171004 | ||||||||
\(801\) | −9.32298 | −0.329411 | ||||||||
\(802\) | −20.0314 | −0.707333 | ||||||||
\(803\) | 18.5606 | 0.654991 | ||||||||
\(804\) | −5.97874 | −0.210854 | ||||||||
\(805\) | 2.31678 | 0.0816557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.81198 | −0.239793 | ||||||||
\(808\) | −10.7135 | −0.376899 | ||||||||
\(809\) | −3.88293 | −0.136516 | −0.0682582 | − | 0.997668i | \(-0.521744\pi\) | ||||
−0.0682582 | + | 0.997668i | \(0.521744\pi\) | |||||||
\(810\) | 0.404061 | 0.0141973 | ||||||||
\(811\) | 55.8930 | 1.96267 | 0.981334 | − | 0.192311i | \(-0.0615981\pi\) | ||||
0.981334 | + | 0.192311i | \(0.0615981\pi\) | |||||||
\(812\) | −0.647042 | −0.0227067 | ||||||||
\(813\) | 13.3555 | 0.468397 | ||||||||
\(814\) | 20.8600 | 0.731143 | ||||||||
\(815\) | −8.49345 | −0.297513 | ||||||||
\(816\) | 4.50459 | 0.157692 | ||||||||
\(817\) | 3.29485 | 0.115272 | ||||||||
\(818\) | 12.2787 | 0.429314 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.69130 | 0.128906 | ||||||||
\(821\) | 12.0332 | 0.419963 | 0.209982 | − | 0.977705i | \(-0.432660\pi\) | ||||
0.209982 | + | 0.977705i | \(0.432660\pi\) | |||||||
\(822\) | −3.27155 | −0.114108 | ||||||||
\(823\) | −18.6745 | −0.650954 | −0.325477 | − | 0.945550i | \(-0.605525\pi\) | ||||
−0.325477 | + | 0.945550i | \(0.605525\pi\) | |||||||
\(824\) | 1.21750 | 0.0424136 | ||||||||
\(825\) | −22.8635 | −0.796003 | ||||||||
\(826\) | 15.0444 | 0.523461 | ||||||||
\(827\) | −55.3970 | −1.92634 | −0.963172 | − | 0.268888i | \(-0.913344\pi\) | ||||
−0.963172 | + | 0.268888i | \(0.913344\pi\) | |||||||
\(828\) | −5.73373 | −0.199261 | ||||||||
\(829\) | −35.7473 | −1.24155 | −0.620777 | − | 0.783987i | \(-0.713183\pi\) | ||||
−0.620777 | + | 0.783987i | \(0.713183\pi\) | |||||||
\(830\) | 1.82373 | 0.0633025 | ||||||||
\(831\) | 23.3676 | 0.810613 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.50459 | 0.156075 | ||||||||
\(834\) | 10.7168 | 0.371091 | ||||||||
\(835\) | 5.61420 | 0.194287 | ||||||||
\(836\) | −23.3655 | −0.808112 | ||||||||
\(837\) | −6.14471 | −0.212392 | ||||||||
\(838\) | 9.98508 | 0.344929 | ||||||||
\(839\) | 0.500765 | 0.0172883 | 0.00864417 | − | 0.999963i | \(-0.497248\pi\) | ||||
0.00864417 | + | 0.999963i | \(0.497248\pi\) | |||||||
\(840\) | 0.404061 | 0.0139414 | ||||||||
\(841\) | −28.5813 | −0.985563 | ||||||||
\(842\) | −12.1776 | −0.419666 | ||||||||
\(843\) | −1.31057 | −0.0451384 | ||||||||
\(844\) | 15.1334 | 0.520914 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.47213 | 0.222516 | ||||||||
\(847\) | 11.3449 | 0.389817 | ||||||||
\(848\) | −0.811429 | −0.0278646 | ||||||||
\(849\) | −27.0743 | −0.929187 | ||||||||
\(850\) | 21.7875 | 0.747305 | ||||||||
\(851\) | 25.3024 | 0.867356 | ||||||||
\(852\) | −14.3974 | −0.493248 | ||||||||
\(853\) | 24.2025 | 0.828677 | 0.414338 | − | 0.910123i | \(-0.364013\pi\) | ||||
0.414338 | + | 0.910123i | \(0.364013\pi\) | |||||||
\(854\) | −2.83178 | −0.0969014 | ||||||||
\(855\) | 1.99725 | 0.0683044 | ||||||||
\(856\) | −13.5610 | −0.463507 | ||||||||
\(857\) | −41.5477 | −1.41924 | −0.709621 | − | 0.704583i | \(-0.751134\pi\) | ||||
−0.709621 | + | 0.704583i | \(0.751134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.09866 | 0.139845 | 0.0699223 | − | 0.997552i | \(-0.477725\pi\) | ||||
0.0699223 | + | 0.997552i | \(0.477725\pi\) | |||||||
\(860\) | 0.269338 | 0.00918435 | ||||||||
\(861\) | −9.13551 | −0.311337 | ||||||||
\(862\) | −30.1287 | −1.02619 | ||||||||
\(863\) | 40.4001 | 1.37523 | 0.687617 | − | 0.726074i | \(-0.258657\pi\) | ||||
0.687617 | + | 0.726074i | \(0.258657\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −3.58868 | −0.122019 | ||||||||
\(866\) | −26.4737 | −0.899614 | ||||||||
\(867\) | 3.29130 | 0.111778 | ||||||||
\(868\) | −6.14471 | −0.208565 | ||||||||
\(869\) | −41.0909 | −1.39391 | ||||||||
\(870\) | −0.261444 | −0.00886379 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −12.5344 | −0.424468 | ||||||||
\(873\) | −6.19694 | −0.209735 | ||||||||
\(874\) | −28.3415 | −0.958665 | ||||||||
\(875\) | 3.97464 | 0.134367 | ||||||||
\(876\) | 3.92648 | 0.132663 | ||||||||
\(877\) | −38.1960 | −1.28979 | −0.644893 | − | 0.764273i | \(-0.723098\pi\) | ||||
−0.644893 | + | 0.764273i | \(0.723098\pi\) | |||||||
\(878\) | 34.7765 | 1.17365 | ||||||||
\(879\) | −17.1700 | −0.579130 | ||||||||
\(880\) | −1.91001 | −0.0643865 | ||||||||
\(881\) | 27.4214 | 0.923850 | 0.461925 | − | 0.886919i | \(-0.347159\pi\) | ||||
0.461925 | + | 0.886919i | \(0.347159\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −32.2272 | −1.08453 | −0.542266 | − | 0.840207i | \(-0.682433\pi\) | ||||
−0.542266 | + | 0.840207i | \(0.682433\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.07884 | 0.204338 | ||||||||
\(886\) | 8.91795 | 0.299604 | ||||||||
\(887\) | −53.7465 | −1.80463 | −0.902316 | − | 0.431075i | \(-0.858134\pi\) | ||||
−0.902316 | + | 0.431075i | \(0.858134\pi\) | |||||||
\(888\) | 4.41291 | 0.148088 | ||||||||
\(889\) | 11.2447 | 0.377134 | ||||||||
\(890\) | −3.76705 | −0.126272 | ||||||||
\(891\) | 4.72704 | 0.158362 | ||||||||
\(892\) | −7.60285 | −0.254562 | ||||||||
\(893\) | 31.9913 | 1.07055 | ||||||||
\(894\) | 1.18034 | 0.0394765 | ||||||||
\(895\) | 7.18245 | 0.240083 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0313 | 0.601712 | ||||||||
\(899\) | 3.97589 | 0.132603 | ||||||||
\(900\) | −4.83673 | −0.161224 | ||||||||
\(901\) | −3.65515 | −0.121771 | ||||||||
\(902\) | 43.1839 | 1.43787 | ||||||||
\(903\) | −0.666578 | −0.0221823 | ||||||||
\(904\) | 18.1761 | 0.604529 | ||||||||
\(905\) | −8.16710 | −0.271483 | ||||||||
\(906\) | −20.7040 | −0.687845 | ||||||||
\(907\) | −41.6640 | −1.38343 | −0.691715 | − | 0.722171i | \(-0.743145\pi\) | ||||
−0.691715 | + | 0.722171i | \(0.743145\pi\) | |||||||
\(908\) | −0.478747 | −0.0158878 | ||||||||
\(909\) | 10.7135 | 0.355343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.42098 | −0.146474 | −0.0732368 | − | 0.997315i | \(-0.523333\pi\) | ||||
−0.0732368 | + | 0.997315i | \(0.523333\pi\) | |||||||
\(912\) | −4.94294 | −0.163677 | ||||||||
\(913\) | 21.3355 | 0.706102 | ||||||||
\(914\) | 18.9373 | 0.626390 | ||||||||
\(915\) | −1.14421 | −0.0378264 | ||||||||
\(916\) | 20.0110 | 0.661183 | ||||||||
\(917\) | −3.57875 | −0.118181 | ||||||||
\(918\) | −4.50459 | −0.148674 | ||||||||
\(919\) | 48.0655 | 1.58553 | 0.792767 | − | 0.609525i | \(-0.208640\pi\) | ||||
0.792767 | + | 0.609525i | \(0.208640\pi\) | |||||||
\(920\) | −2.31678 | −0.0763819 | ||||||||
\(921\) | 20.6481 | 0.680379 | ||||||||
\(922\) | 6.51876 | 0.214684 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.72704 | 0.155508 | ||||||||
\(925\) | 21.3441 | 0.701789 | ||||||||
\(926\) | 13.1560 | 0.432332 | ||||||||
\(927\) | −1.21750 | −0.0399879 | ||||||||
\(928\) | 0.647042 | 0.0212402 | ||||||||
\(929\) | 43.3028 | 1.42072 | 0.710359 | − | 0.703840i | \(-0.248533\pi\) | ||||
0.710359 | + | 0.703840i | \(0.248533\pi\) | |||||||
\(930\) | −2.48284 | −0.0814155 | ||||||||
\(931\) | −4.94294 | −0.161998 | ||||||||
\(932\) | 5.45868 | 0.178805 | ||||||||
\(933\) | 31.1584 | 1.02008 | ||||||||
\(934\) | −2.00592 | −0.0656358 | ||||||||
\(935\) | −8.60382 | −0.281375 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.1899 | 0.790249 | 0.395124 | − | 0.918628i | \(-0.370701\pi\) | ||||
0.395124 | + | 0.918628i | \(0.370701\pi\) | |||||||
\(938\) | 5.97874 | 0.195213 | ||||||||
\(939\) | −21.2384 | −0.693088 | ||||||||
\(940\) | 2.61513 | 0.0852962 | ||||||||
\(941\) | −41.3649 | −1.34846 | −0.674228 | − | 0.738523i | \(-0.735524\pi\) | ||||
−0.674228 | + | 0.738523i | \(0.735524\pi\) | |||||||
\(942\) | −12.8774 | −0.419567 | ||||||||
\(943\) | 52.3806 | 1.70575 | ||||||||
\(944\) | −15.0444 | −0.489653 | ||||||||
\(945\) | −0.404061 | −0.0131441 | ||||||||
\(946\) | 3.15094 | 0.102446 | ||||||||
\(947\) | 36.8712 | 1.19815 | 0.599076 | − | 0.800692i | \(-0.295535\pi\) | ||||
0.599076 | + | 0.800692i | \(0.295535\pi\) | |||||||
\(948\) | −8.69273 | −0.282327 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −23.9077 | −0.775668 | ||||||||
\(951\) | −3.67433 | −0.119148 | ||||||||
\(952\) | −4.50459 | −0.145994 | ||||||||
\(953\) | −4.43358 | −0.143618 | −0.0718089 | − | 0.997418i | \(-0.522877\pi\) | ||||
−0.0718089 | + | 0.997418i | \(0.522877\pi\) | |||||||
\(954\) | 0.811429 | 0.0262710 | ||||||||
\(955\) | 7.07743 | 0.229020 | ||||||||
\(956\) | −6.30483 | −0.203913 | ||||||||
\(957\) | −3.05859 | −0.0988703 | ||||||||
\(958\) | 12.1195 | 0.391564 | ||||||||
\(959\) | 3.27155 | 0.105644 | ||||||||
\(960\) | −0.404061 | −0.0130410 | ||||||||
\(961\) | 6.75750 | 0.217984 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.5610 | 0.436998 | ||||||||
\(964\) | 2.62771 | 0.0846327 | ||||||||
\(965\) | 7.98719 | 0.257117 | ||||||||
\(966\) | 5.73373 | 0.184480 | ||||||||
\(967\) | 20.5363 | 0.660403 | 0.330201 | − | 0.943911i | \(-0.392883\pi\) | ||||
0.330201 | + | 0.943911i | \(0.392883\pi\) | |||||||
\(968\) | −11.3449 | −0.364640 | ||||||||
\(969\) | −22.2659 | −0.715284 | ||||||||
\(970\) | −2.50394 | −0.0803967 | ||||||||
\(971\) | −18.4314 | −0.591492 | −0.295746 | − | 0.955267i | \(-0.595568\pi\) | ||||
−0.295746 | + | 0.955267i | \(0.595568\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −10.7168 | −0.343564 | ||||||||
\(974\) | −43.1568 | −1.38283 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.83178 | 0.0906429 | ||||||||
\(977\) | 33.6168 | 1.07550 | 0.537749 | − | 0.843105i | \(-0.319275\pi\) | ||||
0.537749 | + | 0.843105i | \(0.319275\pi\) | |||||||
\(978\) | −21.0202 | −0.672153 | ||||||||
\(979\) | −44.0701 | −1.40849 | ||||||||
\(980\) | −0.404061 | −0.0129072 | ||||||||
\(981\) | 12.5344 | 0.400193 | ||||||||
\(982\) | −16.5276 | −0.527417 | ||||||||
\(983\) | −7.35152 | −0.234477 | −0.117239 | − | 0.993104i | \(-0.537404\pi\) | ||||
−0.117239 | + | 0.993104i | \(0.537404\pi\) | |||||||
\(984\) | 9.13551 | 0.291229 | ||||||||
\(985\) | 3.85640 | 0.122875 | ||||||||
\(986\) | 2.91466 | 0.0928215 | ||||||||
\(987\) | −6.47213 | −0.206010 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.82198 | 0.121532 | ||||||||
\(990\) | 1.91001 | 0.0607042 | ||||||||
\(991\) | 34.1050 | 1.08338 | 0.541691 | − | 0.840578i | \(-0.317784\pi\) | ||||
0.541691 | + | 0.840578i | \(0.317784\pi\) | |||||||
\(992\) | 6.14471 | 0.195095 | ||||||||
\(993\) | −25.6685 | −0.814565 | ||||||||
\(994\) | 14.3974 | 0.456659 | ||||||||
\(995\) | −2.25253 | −0.0714100 | ||||||||
\(996\) | 4.51350 | 0.143016 | ||||||||
\(997\) | 3.62122 | 0.114685 | 0.0573425 | − | 0.998355i | \(-0.481737\pi\) | ||||
0.0573425 | + | 0.998355i | \(0.481737\pi\) | |||||||
\(998\) | −15.6585 | −0.495662 | ||||||||
\(999\) | −4.41291 | −0.139618 |
(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 | 7098.2.a.cq.1.4 | ✓ | 6 | |
13.12 | even | 2 | 7098.2.a.cu.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cq.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7098.2.a.cu.1.3 | yes | 6 | 13.12 | even | 2 |