Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + 6652 x^{11} - 67665 x^{10} - 17345 x^{9} + 174105 x^{8} + 41499 x^{7} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.11583\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | 2.11583 | 1.22158 | 0.610788 | − | 0.791794i | \(-0.290853\pi\) | ||||
0.610788 | + | 0.791794i | \(0.290853\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.51128 | −1.70510 | −0.852552 | − | 0.522642i | \(-0.824947\pi\) | ||||
−0.852552 | + | 0.522642i | \(0.824947\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.47674 | 0.492246 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.71984 | 1.12157 | 0.560786 | − | 0.827960i | \(-0.310499\pi\) | ||||
0.560786 | + | 0.827960i | \(0.310499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.26860 | 0.629195 | 0.314598 | − | 0.949225i | \(-0.398130\pi\) | ||||
0.314598 | + | 0.949225i | \(0.398130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.11583 | 0.546305 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.69906 | −1.86730 | −0.933648 | − | 0.358192i | \(-0.883393\pi\) | ||||
−0.933648 | + | 0.358192i | \(0.883393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.28730 | −0.754159 | −0.377080 | − | 0.926181i | \(-0.623072\pi\) | ||||
−0.377080 | + | 0.926181i | \(0.623072\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.54511 | −2.08291 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.96341 | 0.826427 | 0.413214 | − | 0.910634i | \(-0.364406\pi\) | ||||
0.413214 | + | 0.910634i | \(0.364406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.22296 | −0.620260 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2241 | −1.89856 | −0.949280 | − | 0.314431i | \(-0.898186\pi\) | ||||
−0.949280 | + | 0.314431i | \(0.898186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.05701 | 1.26748 | 0.633738 | − | 0.773548i | \(-0.281520\pi\) | ||||
0.633738 | + | 0.773548i | \(0.281520\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.87054 | 1.37009 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.51128 | −0.762546 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.55251 | −0.419630 | −0.209815 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209815 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.79996 | 0.768609 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.38725 | −0.216652 | −0.108326 | − | 0.994115i | \(-0.534549\pi\) | ||||
−0.108326 | + | 0.994115i | \(0.534549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.98163 | 0.454694 | 0.227347 | − | 0.973814i | \(-0.426995\pi\) | ||||
0.227347 | + | 0.973814i | \(0.426995\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.47674 | 0.220139 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.63223 | 0.238085 | 0.119043 | − | 0.992889i | \(-0.462017\pi\) | ||||
0.119043 | + | 0.992889i | \(0.462017\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.3517 | 1.90738 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.2899 | −2.28104 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1634 | −1.53341 | −0.766706 | − | 0.641999i | \(-0.778105\pi\) | ||||
−0.766706 | + | 0.641999i | \(0.778105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.71984 | 0.501583 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.95538 | −0.921262 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.02460 | −1.04471 | −0.522357 | − | 0.852727i | \(-0.674947\pi\) | ||||
−0.522357 | + | 0.852727i | \(0.674947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.37952 | −1.07289 | −0.536444 | − | 0.843936i | \(-0.680233\pi\) | ||||
−0.536444 | + | 0.843936i | \(0.680233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.66198 | −0.839331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26860 | 0.281385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.46579 | 0.301244 | 0.150622 | − | 0.988591i | \(-0.451872\pi\) | ||||
0.150622 | + | 0.988591i | \(0.451872\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.38590 | 1.00954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4850 | −1.60037 | −0.800186 | − | 0.599752i | \(-0.795266\pi\) | ||||
−0.800186 | + | 0.599752i | \(0.795266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.06681 | 0.827107 | 0.413554 | − | 0.910480i | \(-0.364287\pi\) | ||||
0.413554 | + | 0.910480i | \(0.364287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.11583 | 0.244315 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.7812 | −1.91240 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.66667 | −0.862568 | −0.431284 | − | 0.902216i | \(-0.641939\pi\) | ||||
−0.431284 | + | 0.902216i | \(0.641939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2495 | −1.24994 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.35179 | −0.697200 | −0.348600 | − | 0.937272i | \(-0.613343\pi\) | ||||
−0.348600 | + | 0.937272i | \(0.613343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.69906 | −0.835080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.6324 | −2.31923 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7665 | 1.67125 | 0.835624 | − | 0.549302i | \(-0.185106\pi\) | ||||
0.835624 | + | 0.549302i | \(0.185106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2343 | −1.07284 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.9314 | 1.54832 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.28730 | −0.337270 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.64835 | 0.573503 | 0.286752 | − | 0.958005i | \(-0.407425\pi\) | ||||
0.286752 | + | 0.958005i | \(0.407425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.49322 | 0.552090 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.05229 | 0.303714 | 0.151857 | − | 0.988402i | \(-0.451475\pi\) | ||||
0.151857 | + | 0.988402i | \(0.451475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9624 | −1.17869 | −0.589343 | − | 0.807883i | \(-0.700613\pi\) | ||||
−0.589343 | + | 0.807883i | \(0.700613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.54511 | −0.931507 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.500824 | 0.0484165 | 0.0242083 | − | 0.999707i | \(-0.492294\pi\) | ||||
0.0242083 | + | 0.999707i | \(0.492294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.51650 | −0.145255 | −0.0726274 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726274 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.40068 | −0.512609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.30075 | 0.874941 | 0.437470 | − | 0.899233i | \(-0.355874\pi\) | ||||
0.437470 | + | 0.899233i | \(0.355874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.96341 | 0.369590 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.35012 | 0.309719 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.7326 | 3.18394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.83718 | 0.257926 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.93518 | −0.264656 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.747438 | −0.0663244 | −0.0331622 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331622 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.30863 | 0.555443 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1581 | −1.58648 | −0.793241 | − | 0.608907i | \(-0.791608\pi\) | ||||
−0.793241 | + | 0.608907i | \(0.791608\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.8300 | 1.28592 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.22296 | −0.277389 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.31717 | −0.368841 | −0.184420 | − | 0.982847i | \(-0.559041\pi\) | ||||
−0.184420 | + | 0.982847i | \(0.559041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7431 | −1.58977 | −0.794885 | − | 0.606761i | \(-0.792469\pi\) | ||||
−0.794885 | + | 0.606761i | \(0.792469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.45353 | 0.290839 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.43880 | 0.705688 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2241 | −0.849062 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 28.2499 | 2.33001 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.08849 | −0.744558 | −0.372279 | − | 0.928121i | \(-0.621424\pi\) | ||||
−0.372279 | + | 0.928121i | \(0.621424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.3695 | −0.919169 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.05701 | 0.566833 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.99321 | 0.238884 | 0.119442 | − | 0.992841i | \(-0.461889\pi\) | ||||
0.119442 | + | 0.992841i | \(0.461889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.6199 | −1.87318 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.8800 | −1.40915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.1281 | 1.41990 | 0.709950 | − | 0.704252i | \(-0.248717\pi\) | ||||
0.709950 | + | 0.704252i | \(0.248717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.87054 | 0.612721 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.32933 | −0.489779 | −0.244889 | − | 0.969551i | \(-0.578752\pi\) | ||||
−0.244889 | + | 0.969551i | \(0.578752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.85347 | −0.604113 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85449 | −0.371232 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6860 | 1.42067 | 0.710335 | − | 0.703863i | \(-0.248543\pi\) | ||||
0.710335 | + | 0.703863i | \(0.248543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.51128 | −0.341021 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.9787 | −1.27620 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.0915 | −1.57645 | −0.788227 | − | 0.615384i | \(-0.789001\pi\) | ||||
−0.788227 | + | 0.615384i | \(0.789001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1118 | 1.64355 | 0.821777 | − | 0.569809i | \(-0.192983\pi\) | ||||
0.821777 | + | 0.569809i | \(0.192983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.7296 | −1.31061 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.55251 | −0.187664 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.6392 | −2.09431 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.5397 | 1.05761 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.215454 | 0.0155897 | 0.00779485 | − | 0.999970i | \(-0.497519\pi\) | ||||
0.00779485 | + | 0.999970i | \(0.497519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.0769 | 1.94904 | 0.974519 | − | 0.224304i | \(-0.0720108\pi\) | ||||
0.974519 | + | 0.224304i | \(0.0720108\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.79996 | 0.343733 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1435 | 1.15018 | 0.575090 | − | 0.818090i | \(-0.304967\pi\) | ||||
0.575090 | + | 0.818090i | \(0.304967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.66452 | −0.188883 | −0.0944413 | − | 0.995530i | \(-0.530106\pi\) | ||||
−0.0944413 | + | 0.995530i | \(0.530106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.21720 | 0.367993 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 46.1236 | 3.23724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.38725 | −0.0968896 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.85291 | 0.406806 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2282 | −0.845845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8509 | −1.09122 | −0.545612 | − | 0.838038i | \(-0.683703\pi\) | ||||
−0.545612 | + | 0.838038i | \(0.683703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.5319 | −1.95497 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.98163 | 0.203346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.8362 | −2.16118 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9522 | 1.01037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.4660 | −1.17489 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.8927 | −1.66694 | −0.833470 | − | 0.552564i | \(-0.813649\pi\) | ||||
−0.833470 | + | 0.552564i | \(0.813649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47674 | 0.0984492 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.14663 | 0.540711 | 0.270355 | − | 0.962761i | \(-0.412859\pi\) | ||||
0.270355 | + | 0.962761i | \(0.412859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.1896 | −1.59850 | −0.799248 | − | 0.601002i | \(-0.794768\pi\) | ||||
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.5062 | −2.33614 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1813 | −0.929046 | −0.464523 | − | 0.885561i | \(-0.653774\pi\) | ||||
−0.464523 | + | 0.885561i | \(0.653774\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63223 | 0.106475 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.2214 | −1.05369 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.9426 | −0.707815 | −0.353907 | − | 0.935280i | \(-0.615147\pi\) | ||||
−0.353907 | + | 0.935280i | \(0.615147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5175 | −0.677489 | −0.338745 | − | 0.940878i | \(-0.610002\pi\) | ||||
−0.338745 | + | 0.940878i | \(0.610002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1331 | −0.906636 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.3517 | 0.853007 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.45757 | −0.474514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.4393 | −0.851682 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.2694 | 1.09003 | 0.545016 | − | 0.838425i | \(-0.316523\pi\) | ||||
0.545016 | + | 0.838425i | \(0.316523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7432 | 0.926899 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.2899 | −1.02011 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6380 | 0.913090 | 0.456545 | − | 0.889700i | \(-0.349087\pi\) | ||||
0.456545 | + | 0.889700i | \(0.349087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5151 | 0.715513 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.0983 | −0.934559 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6848 | 0.658851 | 0.329426 | − | 0.944182i | \(-0.393145\pi\) | ||||
0.329426 | + | 0.944182i | \(0.393145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1634 | −0.685762 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.3593 | 2.04155 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8756 | −0.906979 | −0.453490 | − | 0.891262i | \(-0.649821\pi\) | ||||
−0.453490 | + | 0.891262i | \(0.649821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5627 | −1.18835 | −0.594176 | − | 0.804335i | \(-0.702522\pi\) | ||||
−0.594176 | + | 0.804335i | \(0.702522\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.6540 | −1.31056 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.71984 | 0.224315 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.1190 | −1.86976 | −0.934881 | − | 0.354962i | \(-0.884494\pi\) | ||||
−0.934881 | + | 0.354962i | \(0.884494\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.4214 | 0.623910 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0160 | 0.955434 | 0.477717 | − | 0.878514i | \(-0.341464\pi\) | ||||
0.477717 | + | 0.878514i | \(0.341464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7988 | −0.879697 | −0.439848 | − | 0.898072i | \(-0.644968\pi\) | ||||
−0.439848 | + | 0.898072i | \(0.644968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.95538 | −0.412001 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.25827 | 0.369414 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.2755 | 2.48679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9510 | 0.700577 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.05226 | 0.119894 | 0.0599471 | − | 0.998202i | \(-0.480907\pi\) | ||||
0.0599471 | + | 0.998202i | \(0.480907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.02460 | −0.467210 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.9889 | −0.695666 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.99137 | 0.519984 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4510 | −0.775302 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.45813 | 0.371010 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.37952 | −0.479810 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.00621 | −0.0574276 | −0.0287138 | − | 0.999588i | \(-0.509141\pi\) | ||||
−0.0287138 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.3103 | −1.43985 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.83367 | −0.330797 | −0.165399 | − | 0.986227i | \(-0.552891\pi\) | ||||
−0.165399 | + | 0.986227i | \(0.552891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6990 | −0.943883 | −0.471941 | − | 0.881630i | \(-0.656447\pi\) | ||||
−0.471941 | + | 0.881630i | \(0.656447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.66198 | −0.375360 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.4986 | −0.870491 | −0.435245 | − | 0.900312i | \(-0.643338\pi\) | ||||
−0.435245 | + | 0.900312i | \(0.643338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.0318 | −2.12937 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05966 | 0.0591444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.3092 | 1.40824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.26860 | 0.125839 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.20867 | −0.177440 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.36346 | −0.405961 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4348 | 1.28810 | 0.644048 | − | 0.764985i | \(-0.277254\pi\) | ||||
0.644048 | + | 0.764985i | \(0.277254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.76939 | −0.206561 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.46579 | 0.134721 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.6211 | 1.66804 | 0.834018 | − | 0.551737i | \(-0.186035\pi\) | ||||
0.834018 | + | 0.551737i | \(0.186035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.6788 | 1.06881 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2509 | 1.42157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −28.6542 | −1.54718 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.38590 | 0.451481 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.6948 | 1.00359 | 0.501795 | − | 0.864987i | \(-0.332673\pi\) | ||||
0.501795 | + | 0.864987i | \(0.332673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3654 | 0.768960 | 0.384480 | − | 0.923133i | \(-0.374381\pi\) | ||||
0.384480 | + | 0.923133i | \(0.374381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.31160 | −0.390264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.65807 | 0.141475 | 0.0707373 | − | 0.997495i | \(-0.477465\pi\) | ||||
0.0707373 | + | 0.997495i | \(0.477465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4850 | −0.715708 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 73.4884 | 3.88942 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.5446 | −1.03152 | −0.515762 | − | 0.856732i | \(-0.672491\pi\) | ||||
−0.515762 | + | 0.856732i | \(0.672491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19363 | −0.431244 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.00300 | 0.315076 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.06681 | 0.369894 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.69577 | −0.453916 | −0.226958 | − | 0.973905i | \(-0.572878\pi\) | ||||
−0.226958 | + | 0.973905i | \(0.572878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.04860 | −0.106646 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 50.3613 | 2.61463 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.8358 | 0.819946 | 0.409973 | − | 0.912098i | \(-0.365538\pi\) | ||||
0.409973 | + | 0.912098i | \(0.365538\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.11583 | 0.109261 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.1943 | −1.19457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4450 | 0.793359 | 0.396679 | − | 0.917957i | \(-0.370162\pi\) | ||||
0.396679 | + | 0.917957i | \(0.370162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58145 | −0.0810203 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.9134 | 1.01753 | 0.508764 | − | 0.860906i | \(-0.330102\pi\) | ||||
0.508764 | + | 0.860906i | \(0.330102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.7812 | −0.855251 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.40309 | 0.223822 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5704 | −1.29647 | −0.648236 | − | 0.761439i | \(-0.724493\pi\) | ||||
−0.648236 | + | 0.761439i | \(0.724493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.5145 | −1.54318 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −38.4195 | −1.93801 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.66667 | −0.385752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8759 | 0.596032 | 0.298016 | − | 0.954561i | \(-0.403675\pi\) | ||||
0.298016 | + | 0.954561i | \(0.403675\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.3777 | 1.57085 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.94490 | 0.346812 | 0.173406 | − | 0.984850i | \(-0.444523\pi\) | ||||
0.173406 | + | 0.984850i | \(0.444523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0095 | 0.797490 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.2495 | −0.558990 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.49492 | −0.470645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.90345 | −0.291907 | −0.145953 | − | 0.989291i | \(-0.546625\pi\) | ||||
−0.145953 | + | 0.989291i | \(0.546625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.13441 | −0.450567 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.2012 | 1.78135 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.35179 | −0.311797 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39.6572 | −1.94202 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.26629 | 0.159569 | 0.0797844 | − | 0.996812i | \(-0.474577\pi\) | ||||
0.0797844 | + | 0.996812i | \(0.474577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.48828 | −0.316219 | −0.158110 | − | 0.987422i | \(-0.550540\pi\) | ||||
−0.158110 | + | 0.987422i | \(0.550540\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.41038 | 0.117197 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.69906 | −0.373459 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.8024 | 1.82939 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8551 | 0.862051 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.668692 | −0.0322098 | −0.0161049 | − | 0.999870i | \(-0.505127\pi\) | ||||
−0.0161049 | + | 0.999870i | \(0.505127\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.8543 | 1.62693 | 0.813466 | − | 0.581612i | \(-0.197578\pi\) | ||||
0.813466 | + | 0.581612i | \(0.197578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.6324 | −1.03719 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.0289 | −0.623258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3622 | 1.30592 | 0.652962 | − | 0.757390i | \(-0.273526\pi\) | ||||
0.652962 | + | 0.757390i | \(0.273526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.7169 | 0.938901 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.14659 | −0.292033 | −0.146017 | − | 0.989282i | \(-0.546645\pi\) | ||||
−0.146017 | + | 0.989282i | \(0.546645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7665 | 0.747405 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.2297 | −0.909534 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5378 | 0.497310 | 0.248655 | − | 0.968592i | \(-0.420011\pi\) | ||||
0.248655 | + | 0.968592i | \(0.420011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.16034 | −0.242991 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.11583 | 0.0994104 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.2343 | −0.479790 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.1421 | 1.83099 | 0.915495 | − | 0.402329i | \(-0.131799\pi\) | ||||
0.915495 | + | 0.402329i | \(0.131799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.8138 | 1.15821 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.6505 | −1.47411 | −0.737055 | − | 0.675833i | \(-0.763784\pi\) | ||||
−0.737055 | + | 0.675833i | \(0.763784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9119 | −1.01833 | −0.509167 | − | 0.860668i | \(-0.670046\pi\) | ||||
−0.509167 | + | 0.860668i | \(0.670046\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.9314 | 0.692429 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.317363 | −0.0146858 | −0.00734290 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734290 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.1239 | −0.513653 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.33312 | 0.291815 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0912 | 0.509973 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.28730 | −0.150832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.4854 | −0.754815 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.8213 | 1.08842 | 0.544211 | − | 0.838948i | \(-0.316829\pi\) | ||||
0.544211 | + | 0.838948i | \(0.316829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.79061 | −0.264029 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.8311 | −1.72138 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.64835 | 0.256478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.4937 | 1.56306 | 0.781529 | − | 0.623869i | \(-0.214440\pi\) | ||||
0.781529 | + | 0.623869i | \(0.214440\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 38.3559 | 1.73451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9461 | 0.629379 | 0.314690 | − | 0.949195i | \(-0.398100\pi\) | ||||
0.314690 | + | 0.949195i | \(0.398100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 78.7156 | 3.54517 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.49322 | 0.246902 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 60.8345 | 2.72880 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.5897 | 1.32462 | 0.662309 | − | 0.749231i | \(-0.269577\pi\) | ||||
0.662309 | + | 0.749231i | \(0.269577\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.3918 | −0.598301 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.51914 | 0.112323 | 0.0561615 | − | 0.998422i | \(-0.482114\pi\) | ||||
0.0561615 | + | 0.998422i | \(0.482114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.05229 | 0.135825 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6166 | −0.737970 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0469 | −0.489645 | −0.244823 | − | 0.969568i | \(-0.578730\pi\) | ||||
−0.244823 | + | 0.969568i | \(0.578730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.8804 | −1.41030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.5949 | 0.467775 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9624 | −0.527125 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.07164 | 0.267030 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.5364 | 1.73546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7746 | 1.17302 | 0.586508 | − | 0.809944i | \(-0.300502\pi\) | ||||
0.586508 | + | 0.809944i | \(0.300502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.20878 | −0.315218 | −0.157609 | − | 0.987502i | \(-0.550379\pi\) | ||||
−0.157609 | + | 0.987502i | \(0.550379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.54511 | −0.416583 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −54.3323 | −2.36675 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.29141 | −0.317018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.8502 | −0.514256 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.14711 | −0.136316 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.500824 | 0.0216525 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.6261 | −1.92576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 49.6660 | 2.13927 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7310 | 0.504356 | 0.252178 | − | 0.967681i | \(-0.418853\pi\) | ||||
0.252178 | + | 0.967681i | \(0.418853\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.7847 | 2.00773 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.51650 | −0.0649599 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.27482 | −0.268292 | −0.134146 | − | 0.990962i | \(-0.542829\pi\) | ||||
−0.134146 | + | 0.990962i | \(0.542829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3744 | −0.528125 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.6096 | 1.43182 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.5865 | 1.47077 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.40068 | −0.229246 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.9052 | −1.64847 | −0.824234 | − | 0.566249i | \(-0.808394\pi\) | ||||
−0.824234 | + | 0.566249i | \(0.808394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.76411 | 0.286092 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −60.5958 | −2.55836 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3855 | −0.859147 | −0.429574 | − | 0.903032i | \(-0.641336\pi\) | ||||
−0.429574 | + | 0.903032i | \(0.641336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.30075 | 0.391285 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 50.7495 | 2.13128 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.93510 | 0.248812 | 0.124406 | − | 0.992231i | \(-0.460297\pi\) | ||||
0.124406 | + | 0.992231i | \(0.460297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.5842 | −1.57285 | −0.786424 | − | 0.617687i | \(-0.788070\pi\) | ||||
−0.786424 | + | 0.617687i | \(0.788070\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.455864 | 0.0190440 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.96341 | 0.165285 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2644 | 1.63460 | 0.817299 | − | 0.576214i | \(-0.195471\pi\) | ||||
0.817299 | + | 0.576214i | \(0.195471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 57.2901 | 2.38090 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.6547 | 1.18880 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.5260 | −1.71983 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.35012 | 0.138510 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.4387 | −1.09124 | −0.545620 | − | 0.838033i | \(-0.683706\pi\) | ||||
−0.545620 | + | 0.838033i | \(0.683706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.1985 | −0.955879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.1570 | 1.40503 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.3619 | −1.37001 | −0.685004 | − | 0.728539i | \(-0.740200\pi\) | ||||
−0.685004 | + | 0.728539i | \(0.740200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.7326 | 1.42390 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.63767 | −0.230734 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.06454 | 0.206932 | 0.103466 | − | 0.994633i | \(-0.467007\pi\) | ||||
0.103466 | + | 0.994633i | \(0.467007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8712 | 1.21847 | 0.609236 | − | 0.792989i | \(-0.291476\pi\) | ||||
0.609236 | + | 0.792989i | \(0.291476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.64133 | 0.148286 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.83718 | 0.115348 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.3573 | −0.907454 | −0.453727 | − | 0.891141i | \(-0.649906\pi\) | ||||
−0.453727 | + | 0.891141i | \(0.649906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 97.5898 | 3.95454 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.70287 | 0.149802 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00997 | −0.0407925 | −0.0203963 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203963 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.93518 | −0.118358 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.62854 | −0.266855 | −0.133427 | − | 0.991059i | \(-0.542598\pi\) | ||||
−0.133427 | + | 0.991059i | \(0.542598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.77867 | 0.312651 | 0.156326 | − | 0.987706i | \(-0.450035\pi\) | ||||
0.156326 | + | 0.987706i | \(0.450035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7739 | −0.512600 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −71.1272 | −2.84965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.8729 | −1.03326 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.6519 | 0.783573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.7921 | 1.58410 | 0.792050 | − | 0.610457i | \(-0.209014\pi\) | ||||
0.792050 | + | 0.610457i | \(0.209014\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.5379 | −1.33301 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.747438 | −0.0296612 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.2896 | 1.20012 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.9138 | −0.787777 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.02688 | −0.317043 | −0.158521 | − | 0.987356i | \(-0.550673\pi\) | ||||
−0.158521 | + | 0.987356i | \(0.550673\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.8178 | −1.88575 | −0.942876 | − | 0.333144i | \(-0.891890\pi\) | ||||
−0.942876 | + | 0.333144i | \(0.891890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.30863 | 0.248402 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.2488 | −1.07126 | −0.535631 | − | 0.844452i | \(-0.679926\pi\) | ||||
−0.535631 | + | 0.844452i | \(0.679926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.8502 | −1.17172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −67.3599 | −2.64004 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3195 | −0.599498 | −0.299749 | − | 0.954018i | \(-0.596903\pi\) | ||||
−0.299749 | + | 0.954018i | \(0.596903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1581 | −0.709497 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4358 | 0.407140 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0052 | −0.662428 | −0.331214 | − | 0.943556i | \(-0.607458\pi\) | ||||
−0.331214 | + | 0.943556i | \(0.607458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.99978 | −0.272260 | −0.136130 | − | 0.990691i | \(-0.543466\pi\) | ||||
−0.136130 | + | 0.990691i | \(0.543466\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −36.9552 | −1.43522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.8300 | 0.575081 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.5221 | −1.56902 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.6688 | −2.03629 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.1704 | −1.20332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0099 | −0.809872 | −0.404936 | − | 0.914345i | \(-0.632706\pi\) | ||||
−0.404936 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.22296 | −0.124052 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.8381 | 1.72327 | 0.861635 | − | 0.507529i | \(-0.169441\pi\) | ||||
0.861635 | + | 0.507529i | \(0.169441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.4813 | −0.977883 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.2369 | 0.660519 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9167 | 1.33605 | 0.668025 | − | 0.744139i | \(-0.267140\pi\) | ||||
0.668025 | + | 0.744139i | \(0.267140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.31717 | −0.164951 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −51.1811 | −1.95268 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.3252 | −0.964815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4494 | −0.549680 | −0.274840 | − | 0.961490i | \(-0.588625\pi\) | ||||
−0.274840 | + | 0.961490i | \(0.588625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.7815 | −0.941371 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7431 | −0.710966 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6805 | 0.404553 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.0052 | −1.13490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.8408 | 1.76915 | 0.884577 | − | 0.466395i | \(-0.154447\pi\) | ||||
0.884577 | + | 0.466395i | \(0.154447\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.39087 | 0.316468 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.45353 | 0.130067 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.7698 | −0.517865 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0134 | −0.864285 | −0.432143 | − | 0.901805i | \(-0.642242\pi\) | ||||
−0.432143 | + | 0.901805i | \(0.642242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3217 | −0.424595 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.9698 | 1.04748 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.43880 | 0.315593 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.1526 | −0.864649 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.9939 | 0.894821 | 0.447410 | − | 0.894329i | \(-0.352346\pi\) | ||||
0.447410 | + | 0.894329i | \(0.352346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.9656 | 2.00978 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.2532 | −0.827604 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.2241 | −0.379712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6362 | −0.913705 | −0.456853 | − | 0.889542i | \(-0.651023\pi\) | ||||
−0.456853 | + | 0.889542i | \(0.651023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.84523 | 0.142416 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.9558 | −0.849049 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.4171 | −1.45590 | −0.727951 | − | 0.685629i | \(-0.759527\pi\) | ||||
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.2499 | 1.04201 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.17234 | 0.337868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.81176 | 0.213789 | 0.106895 | − | 0.994270i | \(-0.465909\pi\) | ||||
0.106895 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.7789 | −0.579654 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.5844 | 1.19541 | 0.597703 | − | 0.801717i | \(-0.296080\pi\) | ||||
0.597703 | + | 0.801717i | \(0.296080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.08849 | −0.332976 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.37993 | −0.343194 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.25936 | −0.0825552 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8692 | −0.615567 | −0.307784 | − | 0.951456i | \(-0.599587\pi\) | ||||
−0.307784 | + | 0.951456i | \(0.599587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.5390 | 1.33156 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3523 | 0.557989 | 0.278995 | − | 0.960293i | \(-0.409999\pi\) | ||||
0.278995 | + | 0.960293i | \(0.409999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.1942 | 1.13228 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.9605 | 0.832316 | 0.416158 | − | 0.909292i | \(-0.363376\pi\) | ||||
0.416158 | + | 0.909292i | \(0.363376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.84138 | 0.247675 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.3695 | −0.411065 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.2046 | −0.657329 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.65769 | −0.131900 | −0.0659498 | − | 0.997823i | \(-0.521008\pi\) | ||||
−0.0659498 | + | 0.997823i | \(0.521008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.9714 | 1.11541 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.8739 | 1.54207 | 0.771033 | − | 0.636795i | \(-0.219740\pi\) | ||||
0.771033 | + | 0.636795i | \(0.219740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.05701 | 0.253495 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.3640 | 0.874053 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.56031 | 0.163390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.1619 | −1.79493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.9518 | 1.17760 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.99321 | 0.106832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.3175 | 1.54410 | 0.772050 | − | 0.635562i | \(-0.219231\pi\) | ||||
0.772050 | + | 0.635562i | \(0.219231\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6072 | 0.804836 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.9583 | −1.49187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.0097 | −0.675056 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.6199 | −0.837710 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.70540 | −0.202096 | −0.101048 | − | 0.994882i | \(-0.532220\pi\) | ||||
−0.101048 | + | 0.994882i | \(0.532220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5666 | −0.444576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.2830 | 0.822665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.2874 | 0.927661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.8800 | −0.630189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.4742 | −1.10794 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.6999 | −0.446505 | −0.223253 | − | 0.974761i | \(-0.571668\pi\) | ||||
−0.223253 | + | 0.974761i | \(0.571668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.4283 | 0.506645 | 0.253322 | − | 0.967382i | \(-0.418477\pi\) | ||||
0.253322 | + | 0.967382i | \(0.418477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.3914 | −1.45166 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.1281 | 0.634999 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.80153 | −0.342912 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.1133 | −0.528103 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.2371 | 0.496877 | 0.248438 | − | 0.968648i | \(-0.420083\pi\) | ||||
0.248438 | + | 0.968648i | \(0.420083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7627 | 0.444881 | 0.222441 | − | 0.974946i | \(-0.428598\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428598\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.87054 | 0.274017 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.46999 | −0.0511165 | −0.0255583 | − | 0.999673i | \(-0.508136\pi\) | ||||
−0.0255583 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2360 | −1.57111 | −0.785556 | − | 0.618791i | \(-0.787623\pi\) | ||||
−0.785556 | + | 0.618791i | \(0.787623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.8426 | −2.28405 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −102.795 | −3.56165 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.32933 | −0.219036 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.7445 | −0.786164 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.1876 | 1.87076 | 0.935382 | − | 0.353638i | \(-0.115056\pi\) | ||||
0.935382 | + | 0.353638i | \(0.115056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.5314 | 2.60453 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.8871 | 1.16713 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.85347 | −0.270168 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7993 | −0.439790 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.3117 | −1.07462 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1166 | −0.346794 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2809 | 0.694404 | 0.347202 | − | 0.937790i | \(-0.387132\pi\) | ||||
0.347202 | + | 0.937790i | \(0.387132\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.85449 | −0.166020 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.85067 | 0.0632177 | 0.0316088 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316088 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.6235 | −0.976621 | −0.488310 | − | 0.872670i | \(-0.662387\pi\) | ||||
−0.488310 | + | 0.872670i | \(0.662387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.2414 | 0.451267 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.61741 | 0.0550571 | 0.0275286 | − | 0.999621i | \(-0.491236\pi\) | ||||
0.0275286 | + | 0.999621i | \(0.491236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.6860 | 0.635343 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 89.4478 | 3.03781 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.5188 | −0.967433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.59388 | 0.189542 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.34113 | 0.282305 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.51128 | −0.152509 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.4195 | 0.588216 | 0.294108 | − | 0.955772i | \(-0.404977\pi\) | ||||
0.294108 | + | 0.955772i | \(0.404977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.34223 | 0.146460 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.6771 | 1.26937 | 0.634687 | − | 0.772770i | \(-0.281129\pi\) | ||||
0.634687 | + | 0.772770i | \(0.281129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.6986 | −1.94171 | −0.970855 | − | 0.239666i | \(-0.922962\pi\) | ||||
−0.970855 | + | 0.239666i | \(0.922962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.9787 | −0.570732 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.7674 | −1.23453 | −0.617264 | − | 0.786756i | \(-0.711759\pi\) | ||||
−0.617264 | + | 0.786756i | \(0.711759\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.37191 | 0.113090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.8461 | −1.40190 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.36564 | −0.179554 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0915 | −0.705012 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.0242 | 0.635200 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.1513 | −2.40638 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 85.9477 | 2.86333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.4600 | −0.947089 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.1118 | 0.735020 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9585 | −0.430281 | −0.215140 | − | 0.976583i | \(-0.569021\pi\) | ||||
−0.215140 | + | 0.976583i | \(0.569021\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.50744 | 0.149502 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −59.6576 | −1.97654 | −0.988272 | − | 0.152705i | \(-0.951202\pi\) | ||||
−0.988272 | + | 0.152705i | \(0.951202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.6276 | −0.781960 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.7296 | −0.586124 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 81.9164 | 2.70512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.534704 | 0.0176382 | 0.00881912 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881912 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.12897 | −0.0701521 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.5919 | −1.00695 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.55251 | −0.0839260 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.6653 | −0.580204 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.84060 | 0.290051 | 0.145025 | − | 0.989428i | \(-0.453674\pi\) | ||||
0.145025 | + | 0.989428i | \(0.453674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.8910 | −1.43847 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3431 | −0.404094 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.6392 | −0.936603 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.1659 | 0.789466 | 0.394733 | − | 0.918796i | \(-0.370837\pi\) | ||||
0.394733 | + | 0.918796i | \(0.370837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.3322 | −1.15302 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.4887 | −1.15690 | −0.578449 | − | 0.815718i | \(-0.696342\pi\) | ||||
−0.578449 | + | 0.815718i | \(0.696342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.49823 | −0.179047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.5397 | 0.472977 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5918 | 0.441676 | 0.220838 | − | 0.975311i | \(-0.429121\pi\) | ||||
0.220838 | + | 0.975311i | \(0.429121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.0317 | 0.520412 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.7925 | −1.06337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.5249 | −1.92820 | −0.964100 | − | 0.265540i | \(-0.914450\pi\) | ||||
−0.964100 | + | 0.265540i | \(0.914450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.215454 | 0.00697192 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −80.4689 | −2.60119 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.4760 | 0.628913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8014 | 0.606496 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.739586 | 0.0238328 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.0769 | 0.871637 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.6334 | 0.470579 | 0.235290 | − | 0.971925i | \(-0.424396\pi\) | ||||
0.235290 | + | 0.971925i | \(0.424396\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.5499 | 1.72027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.4747 | 1.58772 | 0.793859 | − | 0.608101i | \(-0.208069\pi\) | ||||
0.793859 | + | 0.608101i | \(0.208069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 84.5555 | 2.71072 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.79996 | 0.153722 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.5230 | −1.10449 | −0.552244 | − | 0.833683i | \(-0.686228\pi\) | ||||
−0.552244 | + | 0.833683i | \(0.686228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.6489 | 1.87443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.23948 | −0.0715011 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.0839 | −1.82069 | −0.910347 | − | 0.413847i | \(-0.864185\pi\) | ||||
−0.910347 | + | 0.413847i | \(0.864185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.1435 | 0.514376 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.5798 | −0.495911 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.8174 | 0.375772 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.4457 | 0.776543 | 0.388272 | − | 0.921545i | \(-0.373072\pi\) | ||||
0.388272 | + | 0.921545i | \(0.373072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.5842 | 1.57351 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.66452 | −0.0844709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9859 | −0.379596 | −0.189798 | − | 0.981823i | \(-0.560783\pi\) | ||||
−0.189798 | + | 0.981823i | \(0.560783\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.22664 | 0.260280 |
(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 | 6040.2.a.p.1.18 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.18 | ✓ | 19 | 1.1 | even | 1 | trivial |