Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} - 43 x^{14} + 234 x^{13} + 634 x^{12} - 4048 x^{11} - 3483 x^{10} + 32512 x^{9} + \cdots - 208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.66915\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.66915 | −1.19368 | −0.596840 | − | 0.802360i | \(-0.703577\pi\) | ||||
−0.596840 | + | 0.802360i | \(0.703577\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40707 | −0.909787 | −0.454893 | − | 0.890546i | \(-0.650323\pi\) | ||||
−0.454893 | + | 0.890546i | \(0.650323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.449906 | −0.135652 | −0.0678259 | − | 0.997697i | \(-0.521606\pi\) | ||||
−0.0678259 | + | 0.997697i | \(0.521606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.00023 | −1.94152 | −0.970758 | − | 0.240061i | \(-0.922833\pi\) | ||||
−0.970758 | + | 0.240061i | \(0.922833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.66915 | 0.689171 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.21903 | −1.02327 | −0.511633 | − | 0.859204i | \(-0.670959\pi\) | ||||
−0.511633 | + | 0.859204i | \(0.670959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.92988 | 1.36041 | 0.680204 | − | 0.733023i | \(-0.261891\pi\) | ||||
0.680204 | + | 0.733023i | \(0.261891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.40707 | 0.525266 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12436 | 0.424872 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.72098 | 0.309098 | 0.154549 | − | 0.987985i | \(-0.450608\pi\) | ||||
0.154549 | + | 0.987985i | \(0.450608\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.449906 | 0.0783186 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.42483 | 1.08599 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3678 | −1.70445 | −0.852226 | − | 0.523174i | \(-0.824748\pi\) | ||||
−0.852226 | + | 0.523174i | \(0.824748\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.00023 | 1.12093 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.78180 | −0.434445 | −0.217222 | − | 0.976122i | \(-0.569700\pi\) | ||||
−0.217222 | + | 0.976122i | \(0.569700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.55621 | −0.542317 | −0.271159 | − | 0.962535i | \(-0.587407\pi\) | ||||
−0.271159 | + | 0.962535i | \(0.587407\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66915 | −0.397893 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5877 | −1.54438 | −0.772190 | − | 0.635392i | \(-0.780838\pi\) | ||||
−0.772190 | + | 0.635392i | \(0.780838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.20602 | −0.172288 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.21903 | 0.590783 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.2130 | −1.95230 | −0.976150 | − | 0.217098i | \(-0.930341\pi\) | ||||
−0.976150 | + | 0.217098i | \(0.930341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.20087 | 0.161925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.92988 | −0.785432 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.05076 | −0.266986 | −0.133493 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133493 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.9792 | −1.91789 | −0.958943 | − | 0.283600i | \(-0.908471\pi\) | ||||
−0.958943 | + | 0.283600i | \(0.908471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.40707 | −0.303262 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.6847 | 2.31755 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.71769 | −0.942866 | −0.471433 | − | 0.881902i | \(-0.656263\pi\) | ||||
−0.471433 | + | 0.881902i | \(0.656263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9512 | −1.29967 | −0.649833 | − | 0.760077i | \(-0.725161\pi\) | ||||
−0.649833 | + | 0.760077i | \(0.725161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.88086 | 0.688302 | 0.344151 | − | 0.938914i | \(-0.388167\pi\) | ||||
0.344151 | + | 0.938914i | \(0.388167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.12436 | −0.245300 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.08296 | 0.123414 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0372 | −1.69182 | −0.845909 | − | 0.533328i | \(-0.820941\pi\) | ||||
−0.845909 | + | 0.533328i | \(0.820941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2646 | 1.23645 | 0.618224 | − | 0.786002i | \(-0.287852\pi\) | ||||
0.618224 | + | 0.786002i | \(0.287852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2612 | 1.22145 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.99588 | −0.741561 | −0.370781 | − | 0.928720i | \(-0.620910\pi\) | ||||
−0.370781 | + | 0.928720i | \(0.620910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.8501 | 1.76637 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.72098 | −0.178458 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.8277 | −1.62389 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7094 | −1.39197 | −0.695987 | − | 0.718054i | \(-0.745033\pi\) | ||||
−0.695987 | + | 0.718054i | \(0.745033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.449906 | −0.0452173 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.74398 | −0.969562 | −0.484781 | − | 0.874635i | \(-0.661101\pi\) | ||||
−0.484781 | + | 0.874635i | \(0.661101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.67993 | −0.165529 | −0.0827643 | − | 0.996569i | \(-0.526375\pi\) | ||||
−0.0827643 | + | 0.996569i | \(0.526375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.42483 | −0.626999 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.89307 | 0.763052 | 0.381526 | − | 0.924358i | \(-0.375399\pi\) | ||||
0.381526 | + | 0.924358i | \(0.375399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1653 | 1.35679 | 0.678397 | − | 0.734696i | \(-0.262675\pi\) | ||||
0.678397 | + | 0.734696i | \(0.262675\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3678 | 0.984066 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.79851 | −0.357334 | −0.178667 | − | 0.983910i | \(-0.557178\pi\) | ||||
−0.178667 | + | 0.983910i | \(0.557178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.66915 | −0.248899 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.00023 | −0.647172 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.1555 | 0.930954 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7976 | −0.981599 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.78180 | 0.250827 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.67552 | 0.686519 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8892 | 1.40994 | 0.704970 | − | 0.709238i | \(-0.250961\pi\) | ||||
0.704970 | + | 0.709238i | \(0.250961\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.55621 | 0.313107 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5379 | 1.35755 | 0.678775 | − | 0.734346i | \(-0.262511\pi\) | ||||
0.678775 | + | 0.734346i | \(0.262511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.2736 | −1.23768 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66915 | 0.229724 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8302 | 1.18159 | 0.590797 | − | 0.806820i | \(-0.298813\pi\) | ||||
0.590797 | + | 0.806820i | \(0.298813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.638550 | 0.0541611 | 0.0270806 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270806 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.5877 | 0.891648 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.14945 | 0.263370 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.66915 | −0.221661 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.20602 | 0.0994705 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.8241 | 1.62405 | 0.812027 | − | 0.583620i | \(-0.198364\pi\) | ||||
0.812027 | + | 0.583620i | \(0.198364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9692 | −1.13680 | −0.568400 | − | 0.822753i | \(-0.692437\pi\) | ||||
−0.568400 | + | 0.822753i | \(0.692437\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.21903 | −0.341089 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.59357 | −0.368964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.437155 | −0.0348887 | −0.0174444 | − | 0.999848i | \(-0.505553\pi\) | ||||
−0.0174444 | + | 0.999848i | \(0.505553\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.2130 | 1.12716 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.40707 | −0.189704 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0126 | 1.56751 | 0.783753 | − | 0.621073i | \(-0.213303\pi\) | ||||
0.783753 | + | 0.621073i | \(0.213303\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.20087 | −0.0934874 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.73360 | −0.211532 | −0.105766 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105766 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.0033 | 2.76948 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.92988 | 0.453470 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.25088 | −0.703332 | −0.351666 | − | 0.936126i | \(-0.614385\pi\) | ||||
−0.351666 | + | 0.936126i | \(0.614385\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.11348 | −0.386543 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.05076 | 0.154144 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7996 | 1.03143 | 0.515716 | − | 0.856760i | \(-0.327526\pi\) | ||||
0.515716 | + | 0.856760i | \(0.327526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.740084 | 0.0550100 | 0.0275050 | − | 0.999622i | \(-0.491244\pi\) | ||||
0.0275050 | + | 0.999622i | \(0.491244\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.9792 | 1.10729 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.6731 | 2.03457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.89817 | 0.138808 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.40707 | 0.175089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.6565 | −1.85644 | −0.928219 | − | 0.372034i | \(-0.878660\pi\) | ||||
−0.928219 | + | 0.372034i | \(0.878660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.108371 | −0.00780073 | −0.00390037 | − | 0.999992i | \(-0.501242\pi\) | ||||
−0.00390037 | + | 0.999992i | \(0.501242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.6847 | −1.33804 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.44256 | −0.459014 | −0.229507 | − | 0.973307i | \(-0.573711\pi\) | ||||
−0.229507 | + | 0.973307i | \(0.573711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.6398 | −1.67578 | −0.837892 | − | 0.545836i | \(-0.816212\pi\) | ||||
−0.837892 | + | 0.545836i | \(0.816212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.71769 | 0.544364 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.40707 | −0.168943 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.42505 | 0.518588 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.66789 | −0.184542 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.615086 | −0.0423443 | −0.0211721 | − | 0.999776i | \(-0.506740\pi\) | ||||
−0.0211721 | + | 0.999776i | \(0.506740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.9512 | 0.750363 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.49206 | 0.647353 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.14253 | −0.281213 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.88086 | −0.397392 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.5342 | 1.98669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.9551 | −1.47022 | −0.735110 | − | 0.677948i | \(-0.762870\pi\) | ||||
−0.735110 | + | 0.677948i | \(0.762870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.12436 | 0.141624 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.38076 | 0.158017 | 0.0790084 | − | 0.996874i | \(-0.474825\pi\) | ||||
0.0790084 | + | 0.996874i | \(0.474825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.7836 | 1.17517 | 0.587586 | − | 0.809161i | \(-0.300078\pi\) | ||||
0.587586 | + | 0.809161i | \(0.300078\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.08296 | −0.0712532 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.3471 | −1.66054 | −0.830271 | − | 0.557359i | \(-0.811815\pi\) | ||||
−0.830271 | + | 0.557359i | \(0.811815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.2602 | 1.84349 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0372 | 0.976771 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.87771 | 0.444882 | 0.222441 | − | 0.974946i | \(-0.428597\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428597\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.68799 | 0.108733 | 0.0543663 | − | 0.998521i | \(-0.482686\pi\) | ||||
0.0543663 | + | 0.998521i | \(0.482686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.21903 | 0.205657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.5106 | −2.64125 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.2646 | −0.713864 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9014 | −1.19305 | −0.596524 | − | 0.802595i | \(-0.703452\pi\) | ||||
−0.596524 | + | 0.802595i | \(0.703452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.449906 | −0.0282854 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.2612 | −0.705206 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.03066 | 0.126669 | 0.0633345 | − | 0.997992i | \(-0.479826\pi\) | ||||
0.0633345 | + | 0.997992i | \(0.479826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.9560 | 1.55069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.51086 | −0.154826 | −0.0774130 | − | 0.996999i | \(-0.524666\pi\) | ||||
−0.0774130 | + | 0.996999i | \(0.524666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.9365 | 2.33042 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.99588 | 0.428141 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1102 | −0.921287 | −0.460643 | − | 0.887585i | \(-0.652381\pi\) | ||||
−0.460643 | + | 0.887585i | \(0.652381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.81007 | −0.170700 | −0.0853499 | − | 0.996351i | \(-0.527201\pi\) | ||||
−0.0853499 | + | 0.996351i | \(0.527201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.8501 | −1.01981 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.955762 | −0.0576346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3519 | 0.621983 | 0.310992 | − | 0.950413i | \(-0.399339\pi\) | ||||
0.310992 | + | 0.950413i | \(0.399339\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.72098 | 0.103033 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0253 | 0.657716 | 0.328858 | − | 0.944379i | \(-0.393336\pi\) | ||||
0.328858 | + | 0.944379i | \(0.393336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1196 | −1.31487 | −0.657437 | − | 0.753510i | \(-0.728359\pi\) | ||||
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8277 | 0.937555 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.69599 | 0.395252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.800250 | 0.0470735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7094 | 0.803657 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.71146 | 0.158405 | 0.0792026 | − | 0.996859i | \(-0.474763\pi\) | ||||
0.0792026 | + | 0.996859i | \(0.474763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.47378 | 0.318696 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.449906 | 0.0261062 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.00023 | −0.404834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.56005 | 0.493393 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.74398 | 0.559777 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.9816 | 2.28934 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.99953 | −0.570703 | −0.285352 | − | 0.958423i | \(-0.592110\pi\) | ||||
−0.285352 | + | 0.958423i | \(0.592110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.67993 | 0.0955680 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.8982 | 1.63867 | 0.819334 | − | 0.573317i | \(-0.194344\pi\) | ||||
0.819334 | + | 0.573317i | \(0.194344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.7841 | −1.34436 | −0.672178 | − | 0.740389i | \(-0.734641\pi\) | ||||
−0.672178 | + | 0.740389i | \(0.734641\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.42483 | 0.361998 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7561 | 0.604124 | 0.302062 | − | 0.953288i | \(-0.402325\pi\) | ||||
0.302062 | + | 0.953288i | \(0.402325\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.449906 | −0.0251899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.89307 | −0.440548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.0184 | −1.39206 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.8710 | −0.824895 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1653 | −0.783345 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.4854 | 1.40506 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.47707 | −0.246082 | −0.123041 | − | 0.992402i | \(-0.539265\pi\) | ||||
−0.123041 | + | 0.992402i | \(0.539265\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.3678 | −0.568151 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.5997 | 1.12548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.61471 | −0.360326 | −0.180163 | − | 0.983637i | \(-0.557663\pi\) | ||||
−0.180163 | + | 0.983637i | \(0.557663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.79851 | 0.206307 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.774282 | −0.0419297 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7525 | 1.06653 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.66915 | 0.143702 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.2158 | −1.19261 | −0.596303 | − | 0.802760i | \(-0.703364\pi\) | ||||
−0.596303 | + | 0.802760i | \(0.703364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2496 | 1.45864 | 0.729318 | − | 0.684175i | \(-0.239838\pi\) | ||||
0.729318 | + | 0.684175i | \(0.239838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.00023 | 0.373645 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.64067 | 0.140549 | 0.0702744 | − | 0.997528i | \(-0.477613\pi\) | ||||
0.0702744 | + | 0.997528i | \(0.477613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.2303 | 1.55139 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.1555 | −0.537487 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.65624 | 0.140191 | 0.0700954 | − | 0.997540i | \(-0.477670\pi\) | ||||
0.0700954 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1635 | 0.850712 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7976 | 0.566726 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6969 | −0.821613 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.6512 | −1.02578 | −0.512892 | − | 0.858453i | \(-0.671426\pi\) | ||||
−0.512892 | + | 0.858453i | \(0.671426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.78180 | −0.144815 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.2116 | 1.77618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.7065 | 1.17570 | 0.587850 | − | 0.808970i | \(-0.299974\pi\) | ||||
0.587850 | + | 0.808970i | \(0.299974\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.67552 | −0.396362 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.00023 | −0.360530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4758 | −0.949040 | −0.474520 | − | 0.880245i | \(-0.657378\pi\) | ||||
−0.474520 | + | 0.880245i | \(0.657378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8892 | −0.814029 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.3973 | 0.735668 | 0.367834 | − | 0.929891i | \(-0.380099\pi\) | ||||
0.367834 | + | 0.929891i | \(0.380099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.89057 | −0.147317 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.55621 | −0.180772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5518 | 0.940614 | 0.470307 | − | 0.882503i | \(-0.344143\pi\) | ||||
0.470307 | + | 0.882503i | \(0.344143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.21903 | −0.213366 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5379 | −0.783782 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.1365 | 2.01949 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.6792 | −0.837104 | −0.418552 | − | 0.908193i | \(-0.637462\pi\) | ||||
−0.418552 | + | 0.908193i | \(0.637462\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.2736 | 0.714576 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2765 | 1.16237 | 0.581186 | − | 0.813771i | \(-0.302589\pi\) | ||||
0.581186 | + | 0.813771i | \(0.302589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0473 | −0.600119 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.66915 | −0.132631 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.66453 | 0.231212 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3692 | −1.45221 | −0.726107 | − | 0.687582i | \(-0.758672\pi\) | ||||
−0.726107 | + | 0.687582i | \(0.758672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.8302 | −0.682194 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.93632 | 0.242900 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.0668 | −1.47592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.638550 | −0.0312699 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.70884 | −0.327748 | −0.163874 | − | 0.986481i | \(-0.552399\pi\) | ||||
−0.163874 | + | 0.986481i | \(0.552399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5441 | −0.562623 | −0.281311 | − | 0.959617i | \(-0.590769\pi\) | ||||
−0.281311 | + | 0.959617i | \(0.590769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.5877 | −0.514793 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.96274 | −0.434757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.0559 | 1.74487 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.14945 | −0.152057 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.32052 | 0.159944 | 0.0799720 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799720 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.0947 | −1.97489 | −0.987443 | − | 0.157979i | \(-0.949502\pi\) | ||||
−0.987443 | + | 0.157979i | \(0.949502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66915 | 0.127976 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.92988 | 0.283665 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.7312 | 1.84854 | 0.924270 | − | 0.381740i | \(-0.124675\pi\) | ||||
0.924270 | + | 0.381740i | \(0.124675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.20602 | −0.0574293 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.2691 | 1.39062 | 0.695308 | − | 0.718712i | \(-0.255268\pi\) | ||||
0.695308 | + | 0.718712i | \(0.255268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.6730 | 0.885187 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.8241 | −0.937648 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8790 | 0.985339 | 0.492669 | − | 0.870217i | \(-0.336021\pi\) | ||||
0.492669 | + | 0.870217i | \(0.336021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.25155 | 0.0589332 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.9692 | 0.656331 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −44.9753 | −2.10847 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.93241 | 0.371063 | 0.185531 | − | 0.982638i | \(-0.440599\pi\) | ||||
0.185531 | + | 0.982638i | \(0.440599\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.21903 | 0.196928 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.72475 | −0.266628 | −0.133314 | − | 0.991074i | \(-0.542562\pi\) | ||||
−0.133314 | + | 0.991074i | \(0.542562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.2304 | −0.475447 | −0.237724 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237724 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.59357 | 0.213021 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3498 | 0.664031 | 0.332015 | − | 0.943274i | \(-0.392271\pi\) | ||||
0.332015 | + | 0.943274i | \(0.392271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.5770 | 0.857807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.437155 | 0.0201430 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.59996 | 0.0735663 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.5972 | 0.577999 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.2130 | −0.650767 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.2456 | 0.879354 | 0.439677 | − | 0.898156i | \(-0.355093\pi\) | ||||
0.439677 | + | 0.898156i | \(0.355093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 72.5769 | 3.30922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.40707 | 0.109525 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.5923 | 1.66157 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.45404 | −0.156517 | −0.0782587 | − | 0.996933i | \(-0.524936\pi\) | ||||
−0.0782587 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0126 | −0.905000 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.13006 | −0.276646 | −0.138323 | − | 0.990387i | \(-0.544171\pi\) | ||||
−0.138323 | + | 0.990387i | \(0.544171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.21903 | −0.190016 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.20087 | 0.0539750 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.3603 | 1.18242 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.886059 | −0.0396654 | −0.0198327 | − | 0.999803i | \(-0.506313\pi\) | ||||
−0.0198327 | + | 0.999803i | \(0.506313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.73360 | 0.122128 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.9578 | 1.51410 | 0.757051 | − | 0.653356i | \(-0.226639\pi\) | ||||
0.757051 | + | 0.653356i | \(0.226639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.0081 | 1.15735 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.0033 | −1.59896 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.31256 | 0.324123 | 0.162062 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162062 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1556 | −0.626209 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.92988 | −0.261811 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.48399 | 0.197588 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.76349 | 0.209498 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.25088 | 0.406069 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9412 | 1.48699 | 0.743495 | − | 0.668742i | \(-0.233167\pi\) | ||||
0.743495 | + | 0.668742i | \(0.233167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.0212 | −0.962919 | −0.481459 | − | 0.876468i | \(-0.659893\pi\) | ||||
−0.481459 | + | 0.876468i | \(0.659893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.11348 | 0.223171 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.26089 | −0.316289 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.05076 | −0.0889954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4733 | 0.843481 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.0678 | −0.910840 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7996 | −0.595497 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.542594 | 0.0233712 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.3084 | 1.21707 | 0.608537 | − | 0.793525i | \(-0.291757\pi\) | ||||
0.608537 | + | 0.793525i | \(0.291757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.740084 | −0.0317600 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.8094 | −1.61958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6366 | −0.967870 | −0.483935 | − | 0.875104i | \(-0.660793\pi\) | ||||
−0.483935 | + | 0.875104i | \(0.660793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.9792 | −0.639295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.92988 | 0.252622 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.1956 | 1.53919 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.6731 | −1.17466 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.6407 | −1.80674 | −0.903372 | − | 0.428857i | \(-0.858916\pi\) | ||||
−0.903372 | + | 0.428857i | \(0.858916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.8943 | 1.05292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.89817 | −0.0801408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.7479 | 1.04300 | 0.521500 | − | 0.853251i | \(-0.325372\pi\) | ||||
0.521500 | + | 0.853251i | \(0.325372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1388 | 0.426542 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.40707 | −0.101087 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.6922 | −1.62206 | −0.811030 | − | 0.585004i | \(-0.801093\pi\) | ||||
−0.811030 | + | 0.585004i | \(0.801093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6552 | −0.613299 | −0.306650 | − | 0.951822i | \(-0.599208\pi\) | ||||
−0.306650 | + | 0.951822i | \(0.599208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.6565 | 1.07181 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.12436 | 0.0885919 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8436 | −0.493054 | −0.246527 | − | 0.969136i | \(-0.579289\pi\) | ||||
−0.246527 | + | 0.969136i | \(0.579289\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.108371 | 0.00450376 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.1146 | −1.12490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.39450 | 0.264833 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.6847 | 0.772516 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.9403 | −1.40086 | −0.700432 | − | 0.713719i | \(-0.747009\pi\) | ||||
−0.700432 | + | 0.713719i | \(0.747009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.2052 | 0.420500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.44256 | 0.265012 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8322 | −0.814411 | −0.407205 | − | 0.913337i | \(-0.633497\pi\) | ||||
−0.407205 | + | 0.913337i | \(0.633497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.1066 | −1.11126 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.6398 | 0.967515 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02753 | 0.0419839 | 0.0209919 | − | 0.999780i | \(-0.493318\pi\) | ||||
0.0209919 | + | 0.999780i | \(0.493318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5376 | 0.633791 | 0.316896 | − | 0.948460i | \(-0.397359\pi\) | ||||
0.316896 | + | 0.948460i | \(0.397359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.71769 | −0.314289 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.8204 | 1.17171 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.2532 | 1.02500 | 0.512498 | − | 0.858688i | \(-0.328720\pi\) | ||||
0.512498 | + | 0.858688i | \(0.328720\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.40707 | 0.0975394 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 74.1166 | 2.99844 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5036 | 0.464628 | 0.232314 | − | 0.972641i | \(-0.425370\pi\) | ||||
0.232314 | + | 0.972641i | \(0.425370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.42505 | −0.299407 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.6255 | 1.95759 | 0.978795 | − | 0.204841i | \(-0.0656676\pi\) | ||||
0.978795 | + | 0.204841i | \(0.0656676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.75055 | 0.150748 | 0.0753738 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753738 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.8396 | 0.674663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1089 | −1.24436 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.66789 | 0.106545 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.7420 | 1.74411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5526 | −0.539521 | −0.269760 | − | 0.962927i | \(-0.586944\pi\) | ||||
−0.269760 | + | 0.962927i | \(0.586944\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.615086 | 0.0244475 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.4107 | −1.68302 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.44239 | 0.334500 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.9512 | −0.433222 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.80626 | −0.229334 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8634 | −0.980516 | −0.490258 | − | 0.871577i | \(-0.663097\pi\) | ||||
−0.490258 | + | 0.871577i | \(0.663097\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.49206 | −0.373749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.929782 | −0.0365535 | −0.0182768 | − | 0.999833i | \(-0.505818\pi\) | ||||
−0.0182768 | + | 0.999833i | \(0.505818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.922649 | 0.0362172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.14253 | 0.162359 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.2741 | 1.45865 | 0.729324 | − | 0.684169i | \(-0.239835\pi\) | ||||
0.729324 | + | 0.684169i | \(0.239835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.4729 | −1.62048 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.88086 | 0.229434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.651527 | −0.0253799 | −0.0126899 | − | 0.999919i | \(-0.504039\pi\) | ||||
−0.0126899 | + | 0.999919i | \(0.504039\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7004 | 1.15521 | 0.577605 | − | 0.816316i | \(-0.303987\pi\) | ||||
0.577605 | + | 0.816316i | \(0.303987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.5342 | −1.14701 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38.0985 | 1.47740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.9551 | 0.848832 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.73922 | 0.260165 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.1497 | −0.892357 | −0.446179 | − | 0.894944i | \(-0.647215\pi\) | ||||
−0.446179 | + | 0.894944i | \(0.647215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.12436 | −0.0817666 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.30960 | −0.165631 | −0.0828157 | − | 0.996565i | \(-0.526391\pi\) | ||||
−0.0828157 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.9994 | 1.26640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.38076 | −0.0912310 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.5128 | 0.708373 | 0.354186 | − | 0.935175i | \(-0.384758\pi\) | ||||
0.354186 | + | 0.935175i | \(0.384758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.9149 | −1.41045 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.7836 | −0.678486 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 99.4940 | 3.79042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.3777 | −1.38387 | −0.691936 | − | 0.721959i | \(-0.743242\pi\) | ||||
−0.691936 | + | 0.721959i | \(0.743242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.08296 | 0.0411381 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.70439 | −0.0646511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7365 | 0.444552 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.3471 | 0.958715 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.5888 | −0.399935 | −0.199968 | − | 0.979803i | \(-0.564084\pi\) | ||||
−0.199968 | + | 0.979803i | \(0.564084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −61.4797 | −2.31875 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.2602 | −1.06434 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.4544 | 0.882095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.6458 | −1.11337 | −0.556686 | − | 0.830723i | \(-0.687927\pi\) | ||||
−0.556686 | + | 0.830723i | \(0.687927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0372 | −0.563939 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.72098 | 0.0644514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.40635 | −0.314380 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.87771 | −0.256853 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.8976 | −0.630175 | −0.315087 | − | 0.949063i | \(-0.602034\pi\) | ||||
−0.315087 | + | 0.949063i | \(0.602034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.04371 | 0.150596 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.68799 | −0.0627768 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.12436 | 0.0788967 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.6130 | −1.35790 | −0.678950 | − | 0.734184i | \(-0.737565\pi\) | ||||
−0.678950 | + | 0.734184i | \(0.737565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0038 | 0.554935 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.31448 | −0.159359 | −0.0796795 | − | 0.996821i | \(-0.525390\pi\) | ||||
−0.0796795 | + | 0.996821i | \(0.525390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.21903 | −0.118736 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.47224 | 0.127902 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.0753 | −1.51098 | −0.755490 | − | 0.655160i | \(-0.772601\pi\) | ||||
−0.755490 | + | 0.655160i | \(0.772601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 41.5106 | 1.52493 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6566 | 1.38149 | 0.690743 | − | 0.723100i | \(-0.257284\pi\) | ||||
0.690743 | + | 0.723100i | \(0.257284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.9135 | −1.93860 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2646 | 0.412149 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.9992 | −0.694215 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9634 | 0.436551 | 0.218275 | − | 0.975887i | \(-0.429957\pi\) | ||||
0.218275 | + | 0.975887i | \(0.429957\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.9014 | 0.688806 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.2860 | 1.35697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.3223 | −1.17477 | −0.587387 | − | 0.809306i | \(-0.699843\pi\) | ||||
−0.587387 | + | 0.809306i | \(0.699843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.449906 | 0.0163306 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.1869 | −0.985524 | −0.492762 | − | 0.870164i | \(-0.664013\pi\) | ||||
−0.492762 | + | 0.870164i | \(0.664013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.0970 | −1.23439 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.2612 | 0.407151 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.3558 | 0.518358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.1911 | −1.37721 | −0.688603 | − | 0.725138i | \(-0.741776\pi\) | ||||
−0.688603 | + | 0.725138i | \(0.741776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.03066 | −0.0731324 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1603 | −0.401409 | −0.200704 | − | 0.979652i | \(-0.564323\pi\) | ||||
−0.200704 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.65599 | 0.131327 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.9560 | −0.895290 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.4958 | −0.591022 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.92701 | 0.176302 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.16683 | 0.0416460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0856 | −0.609035 | −0.304518 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304518 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.51086 | 0.0893889 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.14327 | 0.325097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 104.858 | 3.72360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37.9365 | −1.34547 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.7388 | −0.876294 | −0.438147 | − | 0.898903i | \(-0.644365\pi\) | ||||
−0.438147 | + | 0.898903i | \(0.644365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.6700 | 1.58031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.99588 | −0.247187 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.64583 | −0.0933695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.42483 | 0.226445 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1102 | 0.531905 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3789 | 0.505533 | 0.252767 | − | 0.967527i | \(-0.418659\pi\) | ||||
0.252767 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6400 | 0.443852 | 0.221926 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221926 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.81007 | 0.0985535 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −53.4165 | −1.87110 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0879 | −0.737773 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.8501 | 0.588788 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.4996 | −1.44835 | −0.724173 | − | 0.689618i | \(-0.757778\pi\) | ||||
−0.724173 | + | 0.689618i | \(0.757778\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.67046 | −0.197660 | −0.0988299 | − | 0.995104i | \(-0.531510\pi\) | ||||
−0.0988299 | + | 0.995104i | \(0.531510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.955762 | 0.0332754 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9498 | 0.450307 | 0.225154 | − | 0.974323i | \(-0.427712\pi\) | ||||
0.225154 | + | 0.974323i | \(0.427712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.4241 | −1.47345 | −0.736725 | − | 0.676192i | \(-0.763629\pi\) | ||||
−0.736725 | + | 0.676192i | \(0.763629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.3519 | −0.359102 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.08822 | 0.176296 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.29638 | 0.252502 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.72098 | −0.0594859 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.2397 | −1.83804 | −0.919019 | − | 0.394213i | \(-0.871017\pi\) | ||||
−0.919019 | + | 0.394213i | \(0.871017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0253 | −0.379733 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −96.0981 | −3.30588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.9905 | 0.893045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.1196 | 0.759142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3678 | −0.355403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.8955 | 0.407296 | 0.203648 | − | 0.979044i | \(-0.434720\pi\) | ||||
0.203648 | + | 0.979044i | \(0.434720\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.8277 | −0.541298 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4990 | −0.563595 | −0.281797 | − | 0.959474i | \(-0.590931\pi\) | ||||
−0.281797 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.9828 | 0.715923 | 0.357962 | − | 0.933736i | \(-0.383472\pi\) | ||||
0.357962 | + | 0.933736i | \(0.383472\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.69599 | −0.228199 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3952 | −0.660220 | −0.330110 | − | 0.943943i | \(-0.607086\pi\) | ||||
−0.330110 | + | 0.943943i | \(0.607086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.6920 | 0.839553 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.800250 | −0.0271779 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.76533 | 0.229498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.0256 | 1.83059 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.7094 | −0.463991 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.4755 | −0.624586 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.29776 | 0.111357 | 0.0556787 | − | 0.998449i | \(-0.482268\pi\) | ||||
0.0556787 | + | 0.998449i | \(0.482268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.71146 | −0.0914552 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.5936 | 1.73823 | 0.869116 | − | 0.494609i | \(-0.164689\pi\) | ||||
0.869116 | + | 0.494609i | \(0.164689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.1958 | −0.410422 | −0.205211 | − | 0.978718i | \(-0.565788\pi\) | ||||
−0.205211 | + | 0.978718i | \(0.565788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.47378 | −0.183999 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.3971 | −0.617714 | −0.308857 | − | 0.951108i | \(-0.599946\pi\) | ||||
−0.308857 | + | 0.951108i | \(0.599946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.2464 | −1.28274 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.449906 | −0.0150724 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62.7840 | −2.10099 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.8332 | −1.23120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.00023 | 0.233731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.72098 | 0.0573981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.9649 | 1.99772 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.56005 | −0.284861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.97539 | −0.0656643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.2532 | −1.63543 | −0.817713 | − | 0.575626i | \(-0.804759\pi\) | ||||
−0.817713 | + | 0.575626i | \(0.804759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.74398 | −0.323187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.5858 | 0.880828 | 0.440414 | − | 0.897795i | \(-0.354832\pi\) | ||||
0.440414 | + | 0.897795i | \(0.354832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.06800 | −0.167726 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.9816 | −1.32175 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.4008 | −1.23508 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8848 | −0.721913 | −0.360956 | − | 0.932583i | \(-0.617550\pi\) | ||||
−0.360956 | + | 0.932583i | \(0.617550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.99953 | 0.329496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 76.6609 | 2.52332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.0249 | −0.724174 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.67993 | −0.0551762 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3640 | −0.405648 | −0.202824 | − | 0.979215i | \(-0.565012\pi\) | ||||
−0.202824 | + | 0.979215i | \(0.565012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.15153 | −0.234382 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.8982 | −0.946085 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.06650 | −0.165692 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.8561 | −1.17137 | −0.585684 | − | 0.810539i | \(-0.699174\pi\) | ||||
−0.585684 | + | 0.810539i | \(0.699174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.7841 | 0.776165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.6024 | −1.19320 | −0.596602 | − | 0.802537i | \(-0.703483\pi\) | ||||
−0.596602 | + | 0.802537i | \(0.703483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.78180 | −0.0905880 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.42483 | −0.209000 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7935 | 1.52058 | 0.760292 | − | 0.649582i | \(-0.225056\pi\) | ||||
0.760292 | + | 0.649582i | \(0.225056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.1674 | −1.33635 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.7561 | −0.348791 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.94600 | 0.289789 | 0.144895 | − | 0.989447i | \(-0.453716\pi\) | ||||
0.144895 | + | 0.989447i | \(0.453716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 68.4810 | 2.21599 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.449906 | 0.0145434 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.2903 | −1.07500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0382 | −0.904458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.89307 | 0.254351 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.289259 | 0.00931158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6114 | 0.791450 | 0.395725 | − | 0.918369i | \(-0.370493\pi\) | ||||
0.395725 | + | 0.918369i | \(0.370493\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.0184 | 0.803706 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2735 | 0.393876 | 0.196938 | − | 0.980416i | \(-0.436900\pi\) | ||||
0.196938 | + | 0.980416i | \(0.436900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.53704 | −0.0492751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.8710 | 0.476253 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.3612 | 1.09931 | 0.549655 | − | 0.835391i | \(-0.314759\pi\) | ||||
0.549655 | + | 0.835391i | \(0.314759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.14749 | 0.100594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.1653 | 0.452265 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.1793 | −0.866885 | −0.433442 | − | 0.901181i | \(-0.642701\pi\) | ||||
−0.433442 | + | 0.901181i | \(0.642701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.1962 | 0.547915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.4854 | −0.811209 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.55621 | −0.113081 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.74004 | 0.118806 | 0.0594032 | − | 0.998234i | \(-0.481080\pi\) | ||||
0.0594032 | + | 0.998234i | \(0.481080\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.47707 | 0.142076 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 63.0983 | 2.00035 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7393 | 0.371786 | 0.185893 | − | 0.982570i | \(-0.440482\pi\) | ||||
0.185893 | + | 0.982570i | \(0.440482\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3678 | 0.328022 |
(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 | 8004.2.a.i.1.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.i.1.3 | ✓ | 16 | 1.1 | even | 1 | trivial |