Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.67705\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.09554 | 1.20986 | 0.604930 | − | 0.796278i | \(-0.293201\pi\) | ||||
0.604930 | + | 0.796278i | \(0.293201\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.36827 | 1.50634 | 0.753168 | − | 0.657828i | \(-0.228525\pi\) | ||||
0.753168 | + | 0.657828i | \(0.228525\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.47116 | −1.68994 | −0.844970 | − | 0.534813i | \(-0.820382\pi\) | ||||
−0.844970 | + | 0.534813i | \(0.820382\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.39129 | 0.463764 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.608709 | 0.183533 | 0.0917664 | − | 0.995781i | \(-0.470749\pi\) | ||||
0.0917664 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.03922 | 0.288228 | 0.144114 | − | 0.989561i | \(-0.453967\pi\) | ||||
0.144114 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.05835 | 1.82246 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06367 | −0.743050 | −0.371525 | − | 0.928423i | \(-0.621165\pi\) | ||||
−0.371525 | + | 0.928423i | \(0.621165\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.36950 | −2.04459 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.50224 | 1.77284 | 0.886419 | − | 0.462883i | \(-0.153185\pi\) | ||||
0.886419 | + | 0.462883i | \(0.153185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.34525 | 1.26905 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.37112 | −0.648772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.27343 | 1.35064 | 0.675321 | − | 0.737524i | \(-0.264005\pi\) | ||||
0.675321 | + | 0.737524i | \(0.264005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02054 | 0.722111 | 0.361055 | − | 0.932544i | \(-0.382417\pi\) | ||||
0.361055 | + | 0.932544i | \(0.382417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.27558 | 0.222049 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.0601 | −2.54562 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.31265 | 0.708995 | 0.354498 | − | 0.935057i | \(-0.384652\pi\) | ||||
0.354498 | + | 0.935057i | \(0.384652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.17773 | 0.348715 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.15770 | 0.649323 | 0.324661 | − | 0.945830i | \(-0.394750\pi\) | ||||
0.324661 | + | 0.945830i | \(0.394750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.27910 | −0.957554 | −0.478777 | − | 0.877937i | \(-0.658920\pi\) | ||||
−0.478777 | + | 0.877937i | \(0.658920\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.68624 | 0.698584 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.73522 | 0.690702 | 0.345351 | − | 0.938474i | \(-0.387760\pi\) | ||||
0.345351 | + | 0.938474i | \(0.387760\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9913 | 1.85590 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.42005 | −0.898987 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.98132 | 0.958958 | 0.479479 | − | 0.877553i | \(-0.340826\pi\) | ||||
0.479479 | + | 0.877553i | \(0.340826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.05030 | 0.276462 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.09554 | 0.277561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.64652 | −0.344547 | −0.172274 | − | 0.985049i | \(-0.555111\pi\) | ||||
−0.172274 | + | 0.985049i | \(0.555111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11145 | −0.654454 | −0.327227 | − | 0.944946i | \(-0.606114\pi\) | ||||
−0.327227 | + | 0.944946i | \(0.606114\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.22069 | −0.783733 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.50037 | 0.434168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62178 | 0.320301 | 0.160150 | − | 0.987093i | \(-0.448802\pi\) | ||||
0.160150 | + | 0.987093i | \(0.448802\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.8168 | 2.14489 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0085 | −1.42514 | −0.712572 | − | 0.701599i | \(-0.752470\pi\) | ||||
−0.712572 | + | 0.701599i | \(0.752470\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5175 | 1.46507 | 0.732533 | − | 0.680731i | \(-0.238338\pi\) | ||||
0.732533 | + | 0.680731i | \(0.238338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.2967 | 1.53537 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.72164 | −0.310159 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.913307 | −0.102755 | −0.0513775 | − | 0.998679i | \(-0.516361\pi\) | ||||
−0.0513775 | + | 0.998679i | \(0.516361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2382 | −1.24869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.887809 | −0.0974497 | −0.0487249 | − | 0.998812i | \(-0.515516\pi\) | ||||
−0.0487249 | + | 0.998812i | \(0.515516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3193 | −1.11928 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.2418 | 1.63409 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.61792 | 0.807498 | 0.403749 | − | 0.914870i | \(-0.367707\pi\) | ||||
0.403749 | + | 0.914870i | \(0.367707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.64652 | −0.487087 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.42521 | 0.873653 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.36827 | 0.345577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.93426 | −0.602533 | −0.301267 | − | 0.953540i | \(-0.597409\pi\) | ||||
−0.301267 | + | 0.953540i | \(0.597409\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.846892 | 0.0851158 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5793 | 1.64970 | 0.824849 | − | 0.565353i | \(-0.191260\pi\) | ||||
0.824849 | + | 0.565353i | \(0.191260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6631 | 1.14920 | 0.574600 | − | 0.818434i | \(-0.305158\pi\) | ||||
0.574600 | + | 0.818434i | \(0.305158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −31.5590 | −3.07985 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3213 | −0.997801 | −0.498900 | − | 0.866659i | \(-0.666263\pi\) | ||||
−0.498900 | + | 0.866659i | \(0.666263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.85592 | 0.177765 | 0.0888824 | − | 0.996042i | \(-0.471670\pi\) | ||||
0.0888824 | + | 0.996042i | \(0.471670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.03734 | 0.857786 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4343 | 1.73415 | 0.867077 | − | 0.498174i | \(-0.165996\pi\) | ||||
0.867077 | + | 0.498174i | \(0.165996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.6378 | 2.67049 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.44586 | 0.133669 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.6982 | 1.25571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6295 | −0.966316 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.71262 | 0.785591 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.53117 | 0.405281 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.29686 | −0.824963 | −0.412481 | − | 0.910966i | \(-0.635338\pi\) | ||||
−0.412481 | + | 0.910966i | \(0.635338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1581 | −1.15851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.15016 | −0.712083 | −0.356042 | − | 0.934470i | \(-0.615874\pi\) | ||||
−0.356042 | + | 0.934470i | \(0.615874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.47116 | −0.387699 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.3548 | −0.977268 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0756 | −0.946254 | −0.473127 | − | 0.880994i | \(-0.656875\pi\) | ||||
−0.473127 | + | 0.880994i | \(0.656875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2091 | 1.03557 | 0.517783 | − | 0.855512i | \(-0.326758\pi\) | ||||
0.517783 | + | 0.855512i | \(0.326758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.92284 | 0.835654 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.632582 | 0.0528992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.4989 | 2.03452 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 27.2238 | 2.24538 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.31060 | −0.353138 | −0.176569 | − | 0.984288i | \(-0.556500\pi\) | ||||
−0.176569 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.89022 | 0.804855 | 0.402428 | − | 0.915452i | \(-0.368167\pi\) | ||||
0.402428 | + | 0.915452i | \(0.368167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.26246 | −0.344599 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.5423 | 1.08774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39359 | −0.590073 | −0.295036 | − | 0.955486i | \(-0.595332\pi\) | ||||
−0.295036 | + | 0.955486i | \(0.595332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.6296 | 1.16021 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −38.0149 | −2.99599 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5566 | 0.983509 | 0.491755 | − | 0.870734i | \(-0.336356\pi\) | ||||
0.491755 | + | 0.870734i | \(0.336356\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.29648 | 0.334481 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.00624861 | 0.000483532 0 | 0.000241766 | − | 1.00000i | \(-0.499923\pi\) | ||||
0.000241766 | 1.00000i | \(0.499923\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9200 | −0.916925 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.39129 | 0.106395 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.45345 | 0.338589 | 0.169295 | − | 0.985565i | \(-0.445851\pi\) | ||||
0.169295 | + | 0.985565i | \(0.445851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28.3707 | −2.14462 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.54589 | −0.416854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.80470 | −0.732838 | −0.366419 | − | 0.930450i | \(-0.619416\pi\) | ||||
−0.366419 | + | 0.930450i | \(0.619416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9475 | 1.33403 | 0.667013 | − | 0.745046i | \(-0.267573\pi\) | ||||
0.667013 | + | 0.745046i | \(0.267573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7113 | −0.791799 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.5262 | 1.06799 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.86489 | −0.136374 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.0728 | 1.09639 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.85328 | 0.278814 | 0.139407 | − | 0.990235i | \(-0.455480\pi\) | ||||
0.139407 | + | 0.990235i | \(0.455480\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5610 | 1.40803 | 0.704017 | − | 0.710183i | \(-0.251388\pi\) | ||||
0.704017 | + | 0.710183i | \(0.251388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.33517 | 0.525283 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.44831 | −0.245682 | −0.122841 | − | 0.992426i | \(-0.539201\pi\) | ||||
−0.122841 | + | 0.992426i | \(0.539201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.64829 | 0.542173 | 0.271087 | − | 0.962555i | \(-0.412617\pi\) | ||||
0.271087 | + | 0.962555i | \(0.412617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.49404 | 0.387520 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −32.5207 | −2.28251 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0042 | 0.978099 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8291 | 0.822178 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.608709 | 0.0421053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.4648 | −0.995801 | −0.497900 | − | 0.867234i | \(-0.665895\pi\) | ||||
−0.497900 | + | 0.867234i | \(0.665895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.1643 | −1.72423 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.1497 | −1.44240 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.9765 | −1.22032 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.2310 | 1.77253 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.18383 | −0.214167 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.74734 | 0.317906 | 0.158953 | − | 0.987286i | \(-0.449188\pi\) | ||||
0.158953 | + | 0.987286i | \(0.449188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.82809 | 0.588539 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.67149 | −0.177313 | −0.0886566 | − | 0.996062i | \(-0.528257\pi\) | ||||
−0.0886566 | + | 0.996062i | \(0.528257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.87392 | 0.520323 | 0.260162 | − | 0.965565i | \(-0.416224\pi\) | ||||
0.260162 | + | 0.965565i | \(0.416224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.70330 | −0.375250 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.2320 | 0.670321 | 0.335160 | − | 0.942161i | \(-0.391209\pi\) | ||||
0.335160 | + | 0.942161i | \(0.391209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9495 | 1.04043 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.91387 | −0.124319 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1051 | −0.977067 | −0.488533 | − | 0.872545i | \(-0.662468\pi\) | ||||
−0.488533 | + | 0.872545i | \(0.662468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17274 | 0.397621 | 0.198811 | − | 0.980038i | \(-0.436292\pi\) | ||||
0.198811 | + | 0.980038i | \(0.436292\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.4367 | −0.861966 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.7582 | 2.79561 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03922 | 0.0661239 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.86044 | −0.117901 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.78315 | −0.428149 | −0.214074 | − | 0.976817i | \(-0.568673\pi\) | ||||
−0.214074 | + | 0.976817i | \(0.568673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.17539 | 0.325374 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.6245 | −1.35418 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.6333 | −1.66134 | −0.830669 | − | 0.556766i | \(-0.812042\pi\) | ||||
−0.830669 | + | 0.556766i | \(0.812042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.2826 | −1.19816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1195 | 0.626379 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6785 | −0.905117 | −0.452559 | − | 0.891735i | \(-0.649489\pi\) | ||||
−0.452559 | + | 0.891735i | \(0.649489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.5150 | 1.44451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9637 | 0.976961 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6590 | 0.710862 | 0.355431 | − | 0.934702i | \(-0.384334\pi\) | ||||
0.355431 | + | 0.934702i | \(0.384334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.125029 | 0.00759496 | 0.00379748 | − | 0.999993i | \(-0.498791\pi\) | ||||
0.00379748 | + | 0.999993i | \(0.498791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.73697 | −0.589308 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.86241 | 0.232912 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8203 | 1.19088 | 0.595442 | − | 0.803398i | \(-0.296977\pi\) | ||||
0.595442 | + | 0.803398i | \(0.296977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.59374 | 0.334889 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.24019 | −0.551223 | −0.275612 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275612 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.3491 | −1.80407 | −0.902035 | − | 0.431664i | \(-0.857927\pi\) | ||||
−0.902035 | + | 0.431664i | \(0.857927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.05835 | 0.418101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.5897 | −1.09732 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.61391 | −0.447877 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4355 | −0.728981 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5780 | −1.14376 | −0.571880 | − | 0.820337i | \(-0.693786\pi\) | ||||
−0.571880 | + | 0.820337i | \(0.693786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.91419 | −0.519004 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.05203 | −0.119071 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.83569 | 0.510981 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.0749 | 1.61821 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.7425 | 1.99591 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.2168 | −0.985829 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.54809 | −0.0883541 | −0.0441770 | − | 0.999024i | \(-0.514067\pi\) | ||||
−0.0441770 | + | 0.999024i | \(0.514067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.4405 | 1.39037 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.34671 | 0.189774 | 0.0948872 | − | 0.995488i | \(-0.469751\pi\) | ||||
0.0948872 | + | 0.995488i | \(0.469751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.40232 | −0.361881 | −0.180940 | − | 0.983494i | \(-0.557914\pi\) | ||||
−0.180940 | + | 0.983494i | \(0.557914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.9530 | −1.18057 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.23830 | −0.518875 | −0.259437 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259437 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.42741 | 0.247887 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.6288 | −1.20720 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.06367 | −0.170467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.59411 | 0.365775 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.88915 | 0.215071 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.1719 | −1.16725 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.65778 | 0.256015 | 0.128007 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128007 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00015 | 0.328806 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.83085 | 0.482481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.34371 | −0.508984 | −0.254492 | − | 0.967075i | \(-0.581908\pi\) | ||||
−0.254492 | + | 0.967075i | \(0.581908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 38.6298 | 2.09808 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.44734 | 0.132531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.7881 | −1.44642 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 60.0117 | 3.23092 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.9185 | −1.65979 | −0.829897 | − | 0.557917i | \(-0.811601\pi\) | ||||
−0.829897 | + | 0.557917i | \(0.811601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.2445 | −1.35131 | −0.675653 | − | 0.737220i | \(-0.736138\pi\) | ||||
−0.675653 | + | 0.737220i | \(0.736138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.50333 | −0.186994 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.15727 | −0.114820 | −0.0574099 | − | 0.998351i | \(-0.518284\pi\) | ||||
−0.0574099 | + | 0.998351i | \(0.518284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.4478 | −2.14675 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.7051 | 1.51923 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.0925 | −1.69378 | −0.846889 | − | 0.531770i | \(-0.821527\pi\) | ||||
−0.846889 | + | 0.531770i | \(0.821527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.2745 | −1.16911 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.1624 | 2.20688 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3206 | 0.538729 | 0.269365 | − | 0.963038i | \(-0.413186\pi\) | ||||
0.269365 | + | 0.963038i | \(0.413186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.78456 | 0.301132 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.2146 | −1.62058 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3031 | −1.05125 | −0.525627 | − | 0.850715i | \(-0.676169\pi\) | ||||
−0.525627 | + | 0.850715i | \(0.676169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.49526 | 0.490333 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.55869 | 0.389292 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4355 | 0.792867 | 0.396433 | − | 0.918063i | \(-0.370248\pi\) | ||||
0.396433 | + | 0.918063i | \(0.370248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4819 | −0.998090 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.7837 | −1.93066 | −0.965328 | − | 0.261041i | \(-0.915934\pi\) | ||||
−0.965328 | + | 0.261041i | \(0.915934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.16722 | −0.467205 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.73605 | −0.444079 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.7943 | −0.699399 | −0.349700 | − | 0.936862i | \(-0.613716\pi\) | ||||
−0.349700 | + | 0.936862i | \(0.613716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.0481 | −1.31731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.0790 | −0.861522 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.07627 | −0.154784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.1665 | −1.66458 | −0.832288 | − | 0.554343i | \(-0.812970\pi\) | ||||
−0.832288 | + | 0.554343i | \(0.812970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.36950 | −0.469062 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.24620 | −0.411796 | −0.205898 | − | 0.978573i | \(-0.566011\pi\) | ||||
−0.205898 | + | 0.978573i | \(0.566011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.17822 | 0.208132 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −37.8532 | −1.88094 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.62515 | 0.130124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.4291 | −1.50462 | −0.752312 | − | 0.658807i | \(-0.771061\pi\) | ||||
−0.752312 | + | 0.658807i | \(0.771061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.2094 | −1.14484 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.8330 | 0.582264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.99038 | −0.146792 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.5847 | 1.25289 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.11734 | 0.249999 | 0.124999 | − | 0.992157i | \(-0.460107\pi\) | ||||
0.124999 | + | 0.992157i | \(0.460107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.8854 | −1.40779 | −0.703894 | − | 0.710305i | \(-0.748557\pi\) | ||||
−0.703894 | + | 0.710305i | \(0.748557\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.58806 | 0.320323 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.4398 | −0.942967 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8541 | 1.10599 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.32560 | 0.0640007 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3963 | −0.934288 | −0.467144 | − | 0.884181i | \(-0.654717\pi\) | ||||
−0.467144 | + | 0.884181i | \(0.654717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5791 | 1.46954 | 0.734770 | − | 0.678317i | \(-0.237290\pi\) | ||||
0.734770 | + | 0.678317i | \(0.237290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 51.3384 | 2.46149 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.50224 | 0.406717 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.4056 | 1.02163 | 0.510817 | − | 0.859690i | \(-0.329343\pi\) | ||||
0.510817 | + | 0.859690i | \(0.329343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0747 | 0.860699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.83665 | 0.419842 | 0.209921 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209921 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.6592 | 1.21636 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.03303 | −0.427248 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.9257 | 0.845968 | 0.422984 | − | 0.906137i | \(-0.360983\pi\) | ||||
0.422984 | + | 0.906137i | \(0.360983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.53083 | 0.119172 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.7254 | 0.973763 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.6507 | −0.733718 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8630 | 0.554930 | 0.277465 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277465 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.3280 | 0.482069 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.03036 | 0.327436 | 0.163718 | − | 0.986507i | \(-0.447651\pi\) | ||||
0.163718 | + | 0.986507i | \(0.447651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.523381 | −0.0243236 | −0.0121618 | − | 0.999926i | \(-0.503871\pi\) | ||||
−0.0121618 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.3784 | 1.31602 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1010 | −0.698789 | −0.349395 | − | 0.936976i | \(-0.613613\pi\) | ||||
−0.349395 | + | 0.936976i | \(0.613613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7224 | −0.541290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4936 | −0.713906 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.82215 | −0.175742 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.34525 | 0.291140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.71305 | 0.444730 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.8653 | 1.95857 | 0.979284 | − | 0.202493i | \(-0.0649043\pi\) | ||||
0.979284 | + | 0.202493i | \(0.0649043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.48179 | 0.204352 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −79.6617 | −3.62473 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.9882 | −0.907618 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1098 | 1.18315 | 0.591573 | − | 0.806251i | \(-0.298507\pi\) | ||||
0.591573 | + | 0.806251i | \(0.298507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.3129 | 1.18991 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.5875 | 1.42552 | 0.712761 | − | 0.701407i | \(-0.247444\pi\) | ||||
0.712761 | + | 0.701407i | \(0.247444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2834 | −1.00359 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.85256 | 0.128213 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 53.6919 | 2.40841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1119 | 0.721268 | 0.360634 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360634 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0130942 | 0.000585007 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.81093 | −0.303684 | −0.151842 | − | 0.988405i | \(-0.548521\pi\) | ||||
−0.151842 | + | 0.988405i | \(0.548521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.8435 | 2.48500 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.9789 | −1.10935 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5299 | 0.688350 | 0.344175 | − | 0.938905i | \(-0.388159\pi\) | ||||
0.344175 | + | 0.938905i | \(0.388159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.9679 | −2.47588 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.37112 | −0.148838 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.2845 | 1.73108 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.88237 | 0.126766 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.33238 | 0.409646 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.33054 | 0.189724 | 0.0948622 | − | 0.995490i | \(-0.469759\pi\) | ||||
0.0948622 | + | 0.995490i | \(0.469759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.17275 | −0.226189 | −0.113094 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113094 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −59.4519 | −2.59469 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.3176 | −0.536564 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.2880 | 2.14296 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.68208 | −0.159788 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.32076 | 0.187153 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.7650 | −1.50302 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.5462 | −0.886632 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.90792 | 0.340618 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2195 | 0.783316 | 0.391658 | − | 0.920111i | \(-0.371902\pi\) | ||||
0.391658 | + | 0.920111i | \(0.371902\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.6097 | 1.61399 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.25124 | 0.267774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.0195 | 1.66835 | 0.834176 | − | 0.551499i | \(-0.185944\pi\) | ||||
0.834176 | + | 0.551499i | \(0.185944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.11152 | −0.303512 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.27343 | 0.309859 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.08354 | 0.173650 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.4402 | 1.29211 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3116 | 0.733516 | 0.366758 | − | 0.930316i | \(-0.380468\pi\) | ||||
0.366758 | + | 0.930316i | \(0.380468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.52536 | −0.275993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.90794 | −0.164994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.53556 | 0.0647162 | 0.0323581 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323581 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 62.0917 | 2.61222 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 50.2477 | 2.11021 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.4671 | −1.06764 | −0.533818 | − | 0.845600i | \(-0.679243\pi\) | ||||
−0.533818 | + | 0.845600i | \(0.679243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.1021 | −1.30158 | −0.650792 | − | 0.759256i | \(-0.725563\pi\) | ||||
−0.650792 | + | 0.759256i | \(0.725563\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.07471 | 0.337326 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.9488 | 2.24982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.93064 | 0.288526 | 0.144263 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144263 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 40.9909 | 1.70353 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.96954 | 0.164684 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.24960 | 0.176000 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.87004 | 0.201351 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.2948 | 0.590009 | 0.295005 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295005 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.02054 | 0.165664 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.22608 | −0.297241 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.2046 | −0.870770 | −0.435385 | − | 0.900244i | \(-0.643388\pi\) | ||||
−0.435385 | + | 0.900244i | \(0.643388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46.1392 | 1.89152 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.0273 | 0.655954 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.52684 | −0.266679 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.6306 | 1.53498 | 0.767492 | − | 0.641059i | \(-0.221505\pi\) | ||||
0.767492 | + | 0.641059i | \(0.221505\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.64765 | 0.148544 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.8029 | −1.45560 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.8911 | −1.01030 | −0.505150 | − | 0.863032i | \(-0.668563\pi\) | ||||
−0.505150 | + | 0.863032i | \(0.668563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −68.1484 | −2.76151 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.92093 | 0.199079 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.491774 | 0.0198626 | 0.00993128 | − | 0.999951i | \(-0.496839\pi\) | ||||
0.00993128 | + | 0.999951i | \(0.496839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.3465 | 1.18336 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2755 | −0.574711 | −0.287356 | − | 0.957824i | \(-0.592776\pi\) | ||||
−0.287356 | + | 0.957824i | \(0.592776\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6251 | −0.708411 | −0.354206 | − | 0.935168i | \(-0.615249\pi\) | ||||
−0.354206 | + | 0.935168i | \(0.615249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.6620 | −1.15017 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −34.0610 | −1.36462 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.4640 | −0.658561 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.27558 | 0.0509416 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.2125 | −0.526819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.532668 | 0.0212052 | 0.0106026 | − | 0.999944i | \(-0.496625\pi\) | ||||
0.0106026 | + | 0.999944i | \(0.496625\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.3117 | −1.20478 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.3143 | −1.24267 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5008 | 0.534921 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.7073 | −0.660930 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5745 | 0.654654 | 0.327327 | − | 0.944911i | \(-0.393852\pi\) | ||||
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.17617 | −0.361873 | −0.180936 | − | 0.983495i | \(-0.557913\pi\) | ||||
−0.180936 | + | 0.983495i | \(0.557913\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −44.3201 | −1.74510 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.1025 | 0.790311 | 0.395155 | − | 0.918614i | \(-0.370691\pi\) | ||||
0.395155 | + | 0.918614i | \(0.370691\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.61096 | −0.0632357 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.6705 | −1.47642 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.6830 | −1.67031 | −0.835157 | − | 0.550012i | \(-0.814623\pi\) | ||||
−0.835157 | + | 0.550012i | \(0.814623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.4520 | −1.07264 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.4155 | 0.679444 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.7270 | 1.35277 | 0.676385 | − | 0.736548i | \(-0.263546\pi\) | ||||
0.676385 | + | 0.736548i | \(0.263546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0670508 | −0.00260797 | −0.00130399 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130399 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.67184 | −0.259113 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.0601 | −0.584005 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 61.8404 | 2.39447 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.94825 | 0.384622 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.11139 | −0.120114 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.4049 | −1.01783 | −0.508917 | − | 0.860816i | \(-0.669954\pi\) | ||||
−0.508917 | + | 0.860816i | \(0.669954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.3906 | −0.823324 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9627 | −0.690361 | −0.345181 | − | 0.938536i | \(-0.612182\pi\) | ||||
−0.345181 | + | 0.938536i | \(0.612182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.5331 | 1.01825 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.59822 | −0.214524 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3268 | 1.23695 | 0.618475 | − | 0.785805i | \(-0.287751\pi\) | ||||
0.618475 | + | 0.785805i | \(0.287751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.3057 | −1.42538 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.5001 | 0.629519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.25512 | 0.276398 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.75007 | −0.0665757 | −0.0332878 | − | 0.999446i | \(-0.510598\pi\) | ||||
−0.0332878 | + | 0.999446i | \(0.510598\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.78659 | −0.143841 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.1237 | 1.55991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.7378 | −0.482479 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.4416 | 0.810995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7248 | 1.04715 | 0.523576 | − | 0.851979i | \(-0.324597\pi\) | ||||
0.523576 | + | 0.851979i | \(0.324597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.31265 | 0.162655 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.4228 | 1.25878 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −74.1286 | −2.78789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.2818 | 1.88837 | 0.944186 | − | 0.329412i | \(-0.106850\pi\) | ||||
0.944186 | + | 0.329412i | \(0.106850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27068 | −0.0476541 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.1836 | 1.28019 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.13071 | 0.0796840 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.6533 | −1.18211 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.1202 | −0.489300 | −0.244650 | − | 0.969611i | \(-0.578673\pi\) | ||||
−0.244650 | + | 0.969611i | \(0.578673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.1477 | −1.94208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.9352 | 0.481066 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46.1518 | 1.71403 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.5922 | −1.20878 | −0.604389 | − | 0.796690i | \(-0.706583\pi\) | ||||
−0.604389 | + | 0.796690i | \(0.706583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.55735 | 0.205828 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2371 | 0.711510 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.28509 | 0.306017 | 0.153008 | − | 0.988225i | \(-0.451104\pi\) | ||||
0.153008 | + | 0.988225i | \(0.451104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 91.6971 | 3.38230 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.59590 | 0.0587857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.5291 | −1.78517 | −0.892587 | − | 0.450876i | \(-0.851112\pi\) | ||||
−0.892587 | + | 0.450876i | \(0.851112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.17773 | 0.0800008 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.81374 | −0.139913 | −0.0699563 | − | 0.997550i | \(-0.522286\pi\) | ||||
−0.0699563 | + | 0.997550i | \(0.522286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.5193 | −0.531945 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.23520 | −0.0451936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.1483 | 1.68622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.7083 | 1.70441 | 0.852205 | − | 0.523208i | \(-0.175265\pi\) | ||||
0.852205 | + | 0.523208i | \(0.175265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.2144 | −0.518000 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3130 | 1.21238 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.8886 | −1.41343 | −0.706716 | − | 0.707498i | \(-0.749824\pi\) | ||||
−0.706716 | + | 0.707498i | \(0.749824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.8452 | 0.393657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.7676 | −1.33283 | −0.666413 | − | 0.745583i | \(-0.732171\pi\) | ||||
−0.666413 | + | 0.745583i | \(0.732171\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.29812 | −0.300412 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.3571 | −0.519083 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.75031 | −0.0993080 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.3408 | 1.88746 | 0.943730 | − | 0.330718i | \(-0.107291\pi\) | ||||
0.943730 | + | 0.330718i | \(0.107291\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.8111 | −2.00999 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.8632 | −0.498626 | −0.249313 | − | 0.968423i | \(-0.580205\pi\) | ||||
−0.249313 | + | 0.968423i | \(0.580205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.5113 | 0.916395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −40.4074 | −1.44961 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.15770 | 0.148965 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.30967 | −0.261561 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.5196 | −0.876258 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.9036 | −0.888848 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.53623 | −0.268638 | −0.134319 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134319 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.7595 | −1.09507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −82.4228 | −2.93062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.31192 | −0.188632 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 49.2766 | 1.74766 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.5030 | 1.57638 | 0.788189 | − | 0.615433i | \(-0.211019\pi\) | ||||
0.788189 | + | 0.615433i | \(0.211019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.5071 | −0.513226 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5987 | 0.374488 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.61954 | 0.268888 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −128.044 | −4.51297 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.4319 | 0.860044 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.45607 | 0.121509 | 0.0607544 | − | 0.998153i | \(-0.480649\pi\) | ||||
0.0607544 | + | 0.998153i | \(0.480649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.9470 | 0.524860 | 0.262430 | − | 0.964951i | \(-0.415476\pi\) | ||||
0.262430 | + | 0.964951i | \(0.415476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.262003 | 0.00918885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42.2941 | 1.48150 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.27910 | −0.219678 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.46466 | −0.225893 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.72440 | −0.129982 | −0.0649912 | − | 0.997886i | \(-0.520702\pi\) | ||||
−0.0649912 | + | 0.997886i | \(0.520702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0687 | −0.525262 | −0.262631 | − | 0.964896i | \(-0.584590\pi\) | ||||
−0.262631 | + | 0.964896i | \(0.584590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.09385 | 0.281792 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.8202 | −1.31514 | −0.657568 | − | 0.753395i | \(-0.728415\pi\) | ||||
−0.657568 | + | 0.753395i | \(0.728415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.8523 | −1.34940 | −0.674698 | − | 0.738094i | \(-0.735726\pi\) | ||||
−0.674698 | + | 0.738094i | \(0.735726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.5342 | 1.44080 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.8011 | −1.37903 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0210470 | 0.000728362 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5537 | −0.468485 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8272 | 0.546417 | 0.273209 | − | 0.961955i | \(-0.411915\pi\) | ||||
0.273209 | + | 0.961955i | \(0.411915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.9028 | 0.824235 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.3632 | −0.666904 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.1499 | −1.38120 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.5261 | 1.63302 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.5979 | −2.18267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.6672 | 1.25693 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.18601 | 0.211805 | 0.105902 | − | 0.994377i | \(-0.466227\pi\) | ||||
0.105902 | + | 0.994377i | \(0.466227\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.68624 | 0.160266 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.2246 | −0.417583 | −0.208792 | − | 0.977960i | \(-0.566953\pi\) | ||||
−0.208792 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9215 | −1.53270 | −0.766350 | − | 0.642423i | \(-0.777929\pi\) | ||||
−0.766350 | + | 0.642423i | \(0.777929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.9555 | −1.32760 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.2268 | 0.722568 | 0.361284 | − | 0.932456i | \(-0.382339\pi\) | ||||
0.361284 | + | 0.932456i | \(0.382339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0004 | 0.510029 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.9553 | −0.541869 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.555938 | −0.0188589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.72460 | 0.0923196 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.25628 | −0.279433 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.2596 | −0.684900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.4462 | −0.521582 | −0.260791 | − | 0.965395i | \(-0.583983\pi\) | ||||
−0.260791 | + | 0.965395i | \(0.583983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.0266 | −1.38379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.4049 | −0.855912 | −0.427956 | − | 0.903800i | \(-0.640766\pi\) | ||||
−0.427956 | + | 0.903800i | \(0.640766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9928 | 1.00934 | 0.504669 | − | 0.863313i | \(-0.331615\pi\) | ||||
0.504669 | + | 0.863313i | \(0.331615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.6800 | −0.627923 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.5162 | 0.923903 | 0.461952 | − | 0.886905i | \(-0.347149\pi\) | ||||
0.461952 | + | 0.886905i | \(0.347149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.5678 | 1.39414 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.84079 | −0.229175 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.73522 | 0.158458 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.0249 | −1.10390 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5155 | 0.618216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.2431 | 0.975313 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3885 | −0.712554 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 58.8321 | 1.95781 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 60.4520 | 2.00949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8589 | −0.891837 | −0.445918 | − | 0.895074i | \(-0.647123\pi\) | ||||
−0.445918 | + | 0.895074i | \(0.647123\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.0666 | 0.765070 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.5330 | −1.14413 | −0.572065 | − | 0.820208i | \(-0.693858\pi\) | ||||
−0.572065 | + | 0.820208i | \(0.693858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.540418 | −0.0178852 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.0784 | −1.19272 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.4407 | 1.20338 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0300 | 0.660729 | 0.330365 | − | 0.943853i | \(-0.392828\pi\) | ||||
0.330365 | + | 0.943853i | \(0.392828\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.24408 | −0.106896 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4794 | −0.410766 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.3649 | 0.899751 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.2268 | 0.532957 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.91198 | 0.0955389 | 0.0477695 | − | 0.998858i | \(-0.484789\pi\) | ||||
0.0477695 | + | 0.998858i | \(0.484789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.9913 | 0.425773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.01316 | 0.229601 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.28144 | −0.205425 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.03574 | −0.131842 | −0.0659210 | − | 0.997825i | \(-0.520999\pi\) | ||||
−0.0659210 | + | 0.997825i | \(0.520999\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.4163 | −0.437825 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.2751 | 1.67152 | 0.835760 | − | 0.549096i | \(-0.185028\pi\) | ||||
0.835760 | + | 0.549096i | \(0.185028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.3497 | 1.15114 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 50.7693 | 1.65153 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.7009 | 1.22511 | 0.612557 | − | 0.790426i | \(-0.290141\pi\) | ||||
0.612557 | + | 0.790426i | \(0.290141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.0085 | 0.422272 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.3592 | −0.627766 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.4066 | −1.34129 | −0.670645 | − | 0.741779i | \(-0.733983\pi\) | ||||
−0.670645 | + | 0.741779i | \(0.733983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.9789 | 0.419987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.27781 | 0.299909 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.5209 | 1.59911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.8352 | −0.478556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.3600 | −0.462744 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 65.8869 | 2.12097 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.9529 | −0.963220 | −0.481610 | − | 0.876386i | \(-0.659948\pi\) | ||||
−0.481610 | + | 0.876386i | \(0.659948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.42005 | −0.206242 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.5633 | 1.71893 | 0.859465 | − | 0.511195i | \(-0.170797\pi\) | ||||
0.859465 | + | 0.511195i | \(0.170797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.5890 | −1.75004 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.8182 | 0.442537 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.2092 | −0.838506 | −0.419253 | − | 0.907869i | \(-0.637708\pi\) | ||||
−0.419253 | + | 0.907869i | \(0.637708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.63710 | 0.148202 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.58212 | 0.0824408 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.77344 | −0.216039 | −0.108020 | − | 0.994149i | \(-0.534451\pi\) | ||||
−0.108020 | + | 0.994149i | \(0.534451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6149 | −0.370080 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.3666 | −1.41221 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.3864 | −1.69759 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.71348 | −0.276793 | −0.138396 | − | 0.990377i | \(-0.544195\pi\) | ||||
−0.138396 | + | 0.990377i | \(0.544195\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.76058 | 0.309743 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.7615 | 0.816695 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.7540 | −1.86076 | −0.930379 | − | 0.366599i | \(-0.880522\pi\) | ||||
−0.930379 | + | 0.366599i | \(0.880522\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.5384 | −0.459976 |
(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 | 4864.2.a.bq.1.7 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bp.1.2 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bn.1.7 | 8 | |||
8.5 | even | 2 | 4864.2.a.bo.1.2 | 8 | |||
16.3 | odd | 4 | 608.2.c.b.305.4 | 16 | |||
16.5 | even | 4 | 152.2.c.b.77.10 | yes | 16 | ||
16.11 | odd | 4 | 608.2.c.b.305.13 | 16 | |||
16.13 | even | 4 | 152.2.c.b.77.9 | ✓ | 16 | ||
48.5 | odd | 4 | 1368.2.g.b.685.7 | 16 | |||
48.11 | even | 4 | 5472.2.g.b.2737.2 | 16 | |||
48.29 | odd | 4 | 1368.2.g.b.685.8 | 16 | |||
48.35 | even | 4 | 5472.2.g.b.2737.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.9 | ✓ | 16 | 16.13 | even | 4 | ||
152.2.c.b.77.10 | yes | 16 | 16.5 | even | 4 | ||
608.2.c.b.305.4 | 16 | 16.3 | odd | 4 | |||
608.2.c.b.305.13 | 16 | 16.11 | odd | 4 | |||
1368.2.g.b.685.7 | 16 | 48.5 | odd | 4 | |||
1368.2.g.b.685.8 | 16 | 48.29 | odd | 4 | |||
4864.2.a.bn.1.7 | 8 | 8.3 | odd | 2 | |||
4864.2.a.bo.1.2 | 8 | 8.5 | even | 2 | |||
4864.2.a.bp.1.2 | 8 | 4.3 | odd | 2 | |||
4864.2.a.bq.1.7 | 8 | 1.1 | even | 1 | trivial | ||
5472.2.g.b.2737.2 | 16 | 48.11 | even | 4 | |||
5472.2.g.b.2737.15 | 16 | 48.35 | even | 4 |