Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.31567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0830530 | −0.0587274 | −0.0293637 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293637 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99310 | −0.996551 | ||||||||
\(5\) | −2.25024 | −1.00634 | −0.503170 | − | 0.864188i | \(-0.667833\pi\) | ||||
−0.503170 | + | 0.864188i | \(0.667833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.20647 | −1.21193 | −0.605966 | − | 0.795491i | \(-0.707213\pi\) | ||||
−0.605966 | + | 0.795491i | \(0.707213\pi\) | |||||||
\(8\) | 0.331639 | 0.117252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.186890 | 0.0590997 | ||||||||
\(11\) | 0.218022 | 0.0657362 | 0.0328681 | − | 0.999460i | \(-0.489536\pi\) | ||||
0.0328681 | + | 0.999460i | \(0.489536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.17856 | −1.15892 | −0.579462 | − | 0.814999i | \(-0.696737\pi\) | ||||
−0.579462 | + | 0.814999i | \(0.696737\pi\) | |||||||
\(14\) | 0.266307 | 0.0711735 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95866 | 0.989665 | ||||||||
\(17\) | 4.68939 | 1.13734 | 0.568672 | − | 0.822564i | \(-0.307457\pi\) | ||||
0.568672 | + | 0.822564i | \(0.307457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.43926 | 0.789020 | 0.394510 | − | 0.918892i | \(-0.370914\pi\) | ||||
0.394510 | + | 0.918892i | \(0.370914\pi\) | |||||||
\(20\) | 4.48497 | 1.00287 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0181074 | −0.00386052 | ||||||||
\(23\) | 3.99816 | 0.833673 | 0.416837 | − | 0.908981i | \(-0.363139\pi\) | ||||
0.416837 | + | 0.908981i | \(0.363139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0635992 | 0.0127198 | ||||||||
\(26\) | 0.347042 | 0.0680606 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.39082 | 1.20775 | ||||||||
\(29\) | 0.712153 | 0.132243 | 0.0661217 | − | 0.997812i | \(-0.478937\pi\) | ||||
0.0661217 | + | 0.997812i | \(0.478937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.04933 | 0.188466 | 0.0942329 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942329 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(32\) | −0.992057 | −0.175373 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.389468 | −0.0667932 | ||||||||
\(35\) | 7.21534 | 1.21961 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70998 | 0.281119 | 0.140560 | − | 0.990072i | \(-0.455110\pi\) | ||||
0.140560 | + | 0.990072i | \(0.455110\pi\) | |||||||
\(38\) | −0.285641 | −0.0463371 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.746269 | −0.117996 | ||||||||
\(41\) | −3.18460 | −0.497351 | −0.248675 | − | 0.968587i | \(-0.579995\pi\) | ||||
−0.248675 | + | 0.968587i | \(0.579995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.35890 | −0.969723 | −0.484861 | − | 0.874591i | \(-0.661130\pi\) | ||||
−0.484861 | + | 0.874591i | \(0.661130\pi\) | |||||||
\(44\) | −0.434541 | −0.0655095 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.332059 | −0.0489594 | ||||||||
\(47\) | 3.87861 | 0.565754 | 0.282877 | − | 0.959156i | \(-0.408711\pi\) | ||||
0.282877 | + | 0.959156i | \(0.408711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.28144 | 0.468777 | ||||||||
\(50\) | −0.00528210 | −0.000747002 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.32830 | 1.15493 | ||||||||
\(53\) | 10.8877 | 1.49555 | 0.747773 | − | 0.663954i | \(-0.231123\pi\) | ||||
0.747773 | + | 0.663954i | \(0.231123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.490604 | −0.0661530 | ||||||||
\(56\) | −1.06339 | −0.142102 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0591465 | −0.00776631 | ||||||||
\(59\) | 2.63793 | 0.343429 | 0.171715 | − | 0.985147i | \(-0.445069\pi\) | ||||
0.171715 | + | 0.985147i | \(0.445069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1544 | 1.42817 | 0.714084 | − | 0.700060i | \(-0.246843\pi\) | ||||
0.714084 | + | 0.700060i | \(0.246843\pi\) | |||||||
\(62\) | −0.0871503 | −0.0110681 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.83493 | −0.979366 | ||||||||
\(65\) | 9.40279 | 1.16627 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09170 | 0.744219 | 0.372110 | − | 0.928189i | \(-0.378635\pi\) | ||||
0.372110 | + | 0.928189i | \(0.378635\pi\) | |||||||
\(68\) | −9.34643 | −1.13342 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.599256 | −0.0716247 | ||||||||
\(71\) | −9.40515 | −1.11619 | −0.558093 | − | 0.829778i | \(-0.688467\pi\) | ||||
−0.558093 | + | 0.829778i | \(0.688467\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.78532 | −0.325997 | −0.162998 | − | 0.986626i | \(-0.552117\pi\) | ||||
−0.162998 | + | 0.986626i | \(0.552117\pi\) | |||||||
\(74\) | −0.142019 | −0.0165094 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.85479 | −0.786299 | ||||||||
\(77\) | −0.699082 | −0.0796678 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.16993 | 0.581662 | 0.290831 | − | 0.956774i | \(-0.406068\pi\) | ||||
0.290831 | + | 0.956774i | \(0.406068\pi\) | |||||||
\(80\) | −8.90795 | −0.995939 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.264491 | 0.0292081 | ||||||||
\(83\) | −1.83793 | −0.201739 | −0.100870 | − | 0.994900i | \(-0.532162\pi\) | ||||
−0.100870 | + | 0.994900i | \(0.532162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.5523 | −1.14455 | ||||||||
\(86\) | 0.528126 | 0.0569493 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0723048 | 0.00770772 | ||||||||
\(89\) | 8.08786 | 0.857311 | 0.428656 | − | 0.903468i | \(-0.358987\pi\) | ||||
0.428656 | + | 0.903468i | \(0.358987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3984 | 1.40454 | ||||||||
\(92\) | −7.96873 | −0.830798 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.322130 | −0.0332252 | ||||||||
\(95\) | −7.73917 | −0.794022 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9058 | −1.31039 | −0.655193 | − | 0.755462i | \(-0.727413\pi\) | ||||
−0.655193 | + | 0.755462i | \(0.727413\pi\) | |||||||
\(98\) | −0.272533 | −0.0275300 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.126760 | −0.0126760 | ||||||||
\(101\) | −2.17744 | −0.216663 | −0.108331 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108331 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.7612 | 1.45447 | 0.727234 | − | 0.686390i | \(-0.240806\pi\) | ||||
0.727234 | + | 0.686390i | \(0.240806\pi\) | |||||||
\(104\) | −1.38578 | −0.135886 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.904260 | −0.0878295 | ||||||||
\(107\) | −10.4459 | −1.00984 | −0.504920 | − | 0.863166i | \(-0.668478\pi\) | ||||
−0.504920 | + | 0.863166i | \(0.668478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.69014 | −0.545017 | −0.272508 | − | 0.962153i | \(-0.587853\pi\) | ||||
−0.272508 | + | 0.962153i | \(0.587853\pi\) | |||||||
\(110\) | 0.0407461 | 0.00388499 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.6933 | −1.19941 | ||||||||
\(113\) | −20.9980 | −1.97533 | −0.987665 | − | 0.156584i | \(-0.949952\pi\) | ||||
−0.987665 | + | 0.156584i | \(0.949952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.99683 | −0.838958 | ||||||||
\(116\) | −1.41939 | −0.131787 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.219088 | −0.0201687 | ||||||||
\(119\) | −15.0364 | −1.37838 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9525 | −0.995679 | ||||||||
\(122\) | −0.926403 | −0.0838726 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.09143 | −0.187816 | ||||||||
\(125\) | 11.1081 | 0.993539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0956906 | −0.00849117 | −0.00424558 | − | 0.999991i | \(-0.501351\pi\) | ||||
−0.00424558 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(128\) | 2.63483 | 0.232888 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.780930 | −0.0684921 | ||||||||
\(131\) | −14.5638 | −1.27244 | −0.636221 | − | 0.771507i | \(-0.719504\pi\) | ||||
−0.636221 | + | 0.771507i | \(0.719504\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.0279 | −0.956238 | ||||||||
\(134\) | −0.505934 | −0.0437060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.55519 | 0.133356 | ||||||||
\(137\) | 17.1079 | 1.46162 | 0.730811 | − | 0.682579i | \(-0.239142\pi\) | ||||
0.730811 | + | 0.682579i | \(0.239142\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.7270 | −1.50358 | −0.751791 | − | 0.659402i | \(-0.770810\pi\) | ||||
−0.751791 | + | 0.659402i | \(0.770810\pi\) | |||||||
\(140\) | −14.3809 | −1.21541 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.781126 | 0.0655507 | ||||||||
\(143\) | −0.911020 | −0.0761833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.60252 | −0.133082 | ||||||||
\(146\) | 0.231329 | 0.0191449 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.40817 | −0.280150 | ||||||||
\(149\) | 3.37396 | 0.276406 | 0.138203 | − | 0.990404i | \(-0.455867\pi\) | ||||
0.138203 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76168 | 0.224742 | 0.112371 | − | 0.993666i | \(-0.464155\pi\) | ||||
0.112371 | + | 0.993666i | \(0.464155\pi\) | |||||||
\(152\) | 1.14059 | 0.0925143 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0580609 | 0.00467868 | ||||||||
\(155\) | −2.36126 | −0.189661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.93566 | −0.713144 | −0.356572 | − | 0.934268i | \(-0.616054\pi\) | ||||
−0.356572 | + | 0.934268i | \(0.616054\pi\) | |||||||
\(158\) | −0.429378 | −0.0341595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.23237 | 0.176484 | ||||||||
\(161\) | −12.8200 | −1.01035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.75660 | −0.685870 | −0.342935 | − | 0.939359i | \(-0.611421\pi\) | ||||
−0.342935 | + | 0.939359i | \(0.611421\pi\) | |||||||
\(164\) | 6.34723 | 0.495635 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.152646 | 0.0118476 | ||||||||
\(167\) | −14.3605 | −1.11125 | −0.555623 | − | 0.831434i | \(-0.687520\pi\) | ||||
−0.555623 | + | 0.831434i | \(0.687520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.46038 | 0.343106 | ||||||||
\(170\) | 0.876398 | 0.0672167 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.6739 | 0.966378 | ||||||||
\(173\) | 11.0498 | 0.840098 | 0.420049 | − | 0.907501i | \(-0.362013\pi\) | ||||
0.420049 | + | 0.907501i | \(0.362013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.203929 | −0.0154156 | ||||||||
\(176\) | 0.863077 | 0.0650569 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.671721 | −0.0503476 | ||||||||
\(179\) | 6.55060 | 0.489615 | 0.244808 | − | 0.969572i | \(-0.421275\pi\) | ||||
0.244808 | + | 0.969572i | \(0.421275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9694 | −1.03834 | −0.519169 | − | 0.854672i | \(-0.673758\pi\) | ||||
−0.519169 | + | 0.854672i | \(0.673758\pi\) | |||||||
\(182\) | −1.11278 | −0.0824848 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.32595 | 0.0977500 | ||||||||
\(185\) | −3.84787 | −0.282901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.02239 | 0.0747647 | ||||||||
\(188\) | −7.73047 | −0.563802 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.642762 | 0.0466308 | ||||||||
\(191\) | −2.23996 | −0.162078 | −0.0810390 | − | 0.996711i | \(-0.525824\pi\) | ||||
−0.0810390 | + | 0.996711i | \(0.525824\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.1924 | 1.59744 | 0.798722 | − | 0.601700i | \(-0.205510\pi\) | ||||
0.798722 | + | 0.601700i | \(0.205510\pi\) | |||||||
\(194\) | 1.07187 | 0.0769555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.54024 | −0.467160 | ||||||||
\(197\) | 11.0264 | 0.785595 | 0.392797 | − | 0.919625i | \(-0.371507\pi\) | ||||
0.392797 | + | 0.919625i | \(0.371507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6196 | 1.03636 | 0.518179 | − | 0.855272i | \(-0.326610\pi\) | ||||
0.518179 | + | 0.855272i | \(0.326610\pi\) | |||||||
\(200\) | 0.0210920 | 0.00149143 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.180843 | 0.0127240 | ||||||||
\(203\) | −2.28350 | −0.160270 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.16612 | 0.500504 | ||||||||
\(206\) | −1.22597 | −0.0854170 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −16.5415 | −1.14695 | ||||||||
\(209\) | 0.749835 | 0.0518672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.54449 | 0.106327 | 0.0531635 | − | 0.998586i | \(-0.483070\pi\) | ||||
0.0531635 | + | 0.998586i | \(0.483070\pi\) | |||||||
\(212\) | −21.7004 | −1.49039 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.867562 | 0.0593053 | ||||||||
\(215\) | 14.3091 | 0.975871 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.36465 | −0.228408 | ||||||||
\(218\) | 0.472584 | 0.0320074 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.977823 | 0.0659248 | ||||||||
\(221\) | −19.5949 | −1.31810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.6878 | −1.78715 | −0.893573 | − | 0.448918i | \(-0.851810\pi\) | ||||
−0.893573 | + | 0.448918i | \(0.851810\pi\) | |||||||
\(224\) | 3.18100 | 0.212540 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.74395 | 0.116006 | ||||||||
\(227\) | 6.41989 | 0.426103 | 0.213052 | − | 0.977041i | \(-0.431660\pi\) | ||||
0.213052 | + | 0.977041i | \(0.431660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8670 | −1.84150 | −0.920752 | − | 0.390149i | \(-0.872423\pi\) | ||||
−0.920752 | + | 0.390149i | \(0.872423\pi\) | |||||||
\(230\) | 0.747214 | 0.0492698 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.236178 | 0.0155058 | ||||||||
\(233\) | −0.647350 | −0.0424093 | −0.0212047 | − | 0.999775i | \(-0.506750\pi\) | ||||
−0.0212047 | + | 0.999775i | \(0.506750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.72782 | −0.569340 | ||||||||
\(236\) | −5.25766 | −0.342245 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.24882 | 0.0809488 | ||||||||
\(239\) | 12.3635 | 0.799727 | 0.399864 | − | 0.916575i | \(-0.369057\pi\) | ||||
0.399864 | + | 0.916575i | \(0.369057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.7531 | −0.821497 | −0.410748 | − | 0.911749i | \(-0.634732\pi\) | ||||
−0.410748 | + | 0.911749i | \(0.634732\pi\) | |||||||
\(242\) | 0.909636 | 0.0584736 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22.2318 | −1.42324 | ||||||||
\(245\) | −7.38404 | −0.471749 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3712 | −0.914415 | ||||||||
\(248\) | 0.348000 | 0.0220980 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.922562 | −0.0583480 | ||||||||
\(251\) | 13.4917 | 0.851588 | 0.425794 | − | 0.904820i | \(-0.359995\pi\) | ||||
0.425794 | + | 0.904820i | \(0.359995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.871688 | 0.0548025 | ||||||||
\(254\) | 0.00794739 | 0.000498664 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4510 | 0.965689 | ||||||||
\(257\) | 4.56318 | 0.284643 | 0.142322 | − | 0.989820i | \(-0.454543\pi\) | ||||
0.142322 | + | 0.989820i | \(0.454543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.48300 | −0.340697 | ||||||||
\(260\) | −18.7407 | −1.16225 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.20957 | 0.0747272 | ||||||||
\(263\) | −16.0985 | −0.992674 | −0.496337 | − | 0.868130i | \(-0.665322\pi\) | ||||
−0.496337 | + | 0.868130i | \(0.665322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.5001 | −1.50503 | ||||||||
\(266\) | 0.915898 | 0.0561573 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.1414 | −0.741652 | ||||||||
\(269\) | 7.49840 | 0.457186 | 0.228593 | − | 0.973522i | \(-0.426588\pi\) | ||||
0.228593 | + | 0.973522i | \(0.426588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.47424 | 0.393282 | 0.196641 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196641 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(272\) | 18.5637 | 1.12559 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.42086 | −0.0858373 | ||||||||
\(275\) | 0.0138660 | 0.000836154 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.32050 | 0.499930 | 0.249965 | − | 0.968255i | \(-0.419581\pi\) | ||||
0.249965 | + | 0.968255i | \(0.419581\pi\) | |||||||
\(278\) | 1.47228 | 0.0883014 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.39289 | 0.143002 | ||||||||
\(281\) | 26.3798 | 1.57369 | 0.786844 | − | 0.617152i | \(-0.211714\pi\) | ||||
0.786844 | + | 0.617152i | \(0.211714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4048 | −1.39127 | −0.695637 | − | 0.718394i | \(-0.744878\pi\) | ||||
−0.695637 | + | 0.718394i | \(0.744878\pi\) | |||||||
\(284\) | 18.7454 | 1.11234 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0756630 | 0.00447405 | ||||||||
\(287\) | 10.2113 | 0.602755 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.99036 | 0.293551 | ||||||||
\(290\) | 0.133094 | 0.00781555 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.55142 | 0.324872 | ||||||||
\(293\) | 3.57088 | 0.208613 | 0.104307 | − | 0.994545i | \(-0.466738\pi\) | ||||
0.104307 | + | 0.994545i | \(0.466738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.93598 | −0.345606 | ||||||||
\(296\) | 0.567097 | 0.0329618 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.280218 | −0.0162326 | ||||||||
\(299\) | −16.7065 | −0.966164 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3896 | 1.17524 | ||||||||
\(302\) | −0.229366 | −0.0131985 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.6149 | 0.780866 | ||||||||
\(305\) | −25.1000 | −1.43722 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.46828 | −0.140872 | −0.0704362 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704362 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(308\) | 1.39334 | 0.0793930 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.196110 | 0.0111383 | ||||||||
\(311\) | 19.8949 | 1.12814 | 0.564069 | − | 0.825727i | \(-0.309235\pi\) | ||||
0.564069 | + | 0.825727i | \(0.309235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0179 | −0.566246 | −0.283123 | − | 0.959084i | \(-0.591370\pi\) | ||||
−0.283123 | + | 0.959084i | \(0.591370\pi\) | |||||||
\(314\) | 0.742134 | 0.0418810 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.3042 | −0.579656 | ||||||||
\(317\) | 11.2440 | 0.631529 | 0.315764 | − | 0.948838i | \(-0.397739\pi\) | ||||
0.315764 | + | 0.948838i | \(0.397739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.155265 | 0.00869319 | ||||||||
\(320\) | 17.6305 | 0.985575 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.06474 | 0.0593354 | ||||||||
\(323\) | 16.1280 | 0.897387 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.265753 | −0.0147413 | ||||||||
\(326\) | 0.727262 | 0.0402793 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.05614 | −0.0583155 | ||||||||
\(329\) | −12.4366 | −0.685654 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0728 | −1.65295 | −0.826475 | − | 0.562974i | \(-0.809657\pi\) | ||||
−0.826475 | + | 0.562974i | \(0.809657\pi\) | |||||||
\(332\) | 3.66319 | 0.201043 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.19268 | 0.0652606 | ||||||||
\(335\) | −13.7078 | −0.748937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3224 | −0.943613 | −0.471807 | − | 0.881702i | \(-0.656398\pi\) | ||||
−0.471807 | + | 0.881702i | \(0.656398\pi\) | |||||||
\(338\) | −0.370448 | −0.0201497 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21.0317 | 1.14061 | ||||||||
\(341\) | 0.228778 | 0.0123890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.9234 | 0.643806 | ||||||||
\(344\) | −2.10886 | −0.113702 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.917716 | −0.0493367 | ||||||||
\(347\) | −21.2412 | −1.14029 | −0.570143 | − | 0.821545i | \(-0.693112\pi\) | ||||
−0.570143 | + | 0.821545i | \(0.693112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6817 | 0.625308 | 0.312654 | − | 0.949867i | \(-0.398782\pi\) | ||||
0.312654 | + | 0.949867i | \(0.398782\pi\) | |||||||
\(350\) | 0.0169369 | 0.000905315 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.216291 | −0.0115283 | ||||||||
\(353\) | −14.0775 | −0.749271 | −0.374636 | − | 0.927172i | \(-0.622232\pi\) | ||||
−0.374636 | + | 0.927172i | \(0.622232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.1639 | 1.12326 | ||||||||
\(356\) | −16.1199 | −0.854355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.544048 | −0.0287538 | ||||||||
\(359\) | −7.85706 | −0.414680 | −0.207340 | − | 0.978269i | \(-0.566481\pi\) | ||||
−0.207340 | + | 0.978269i | \(0.566481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.17150 | −0.377448 | ||||||||
\(362\) | 1.16020 | 0.0609788 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −26.7044 | −1.39969 | ||||||||
\(365\) | 6.26764 | 0.328063 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7726 | −1.03212 | −0.516062 | − | 0.856551i | \(-0.672602\pi\) | ||||
−0.516062 | + | 0.856551i | \(0.672602\pi\) | |||||||
\(368\) | 15.8273 | 0.825057 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.319578 | 0.0166141 | ||||||||
\(371\) | −34.9112 | −1.81250 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.49088 | 0.387863 | 0.193931 | − | 0.981015i | \(-0.437876\pi\) | ||||
0.193931 | + | 0.981015i | \(0.437876\pi\) | |||||||
\(374\) | −0.0849127 | −0.00439073 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.28630 | 0.0663358 | ||||||||
\(377\) | −2.97577 | −0.153260 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.5064 | 1.41291 | 0.706455 | − | 0.707758i | \(-0.250293\pi\) | ||||
0.706455 | + | 0.707758i | \(0.250293\pi\) | |||||||
\(380\) | 15.4250 | 0.791284 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.186036 | 0.00951842 | ||||||||
\(383\) | −4.92412 | −0.251611 | −0.125805 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125805 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.57311 | 0.0801729 | ||||||||
\(386\) | −1.84315 | −0.0938137 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 25.7226 | 1.30587 | ||||||||
\(389\) | −38.9916 | −1.97696 | −0.988478 | − | 0.151368i | \(-0.951632\pi\) | ||||
−0.988478 | + | 0.151368i | \(0.951632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7489 | 0.948173 | ||||||||
\(392\) | 1.08825 | 0.0549651 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.915772 | −0.0461359 | ||||||||
\(395\) | −11.6336 | −0.585350 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.6661 | −0.635694 | −0.317847 | − | 0.948142i | \(-0.602960\pi\) | ||||
−0.317847 | + | 0.948142i | \(0.602960\pi\) | |||||||
\(398\) | −1.21420 | −0.0608626 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.251767 | 0.0125884 | ||||||||
\(401\) | −26.7959 | −1.33812 | −0.669062 | − | 0.743207i | \(-0.733304\pi\) | ||||
−0.669062 | + | 0.743207i | \(0.733304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.38471 | −0.218418 | ||||||||
\(404\) | 4.33985 | 0.215916 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.189651 | 0.00941223 | ||||||||
\(407\) | 0.372814 | 0.0184797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.3472 | 1.74781 | 0.873903 | − | 0.486101i | \(-0.161581\pi\) | ||||
0.873903 | + | 0.486101i | \(0.161581\pi\) | |||||||
\(410\) | −0.595168 | −0.0293933 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.4206 | −1.44945 | ||||||||
\(413\) | −8.45844 | −0.416212 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.13580 | 0.203018 | ||||||||
\(416\) | 4.14537 | 0.203244 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0622761 | −0.00304602 | ||||||||
\(419\) | 2.49358 | 0.121819 | 0.0609096 | − | 0.998143i | \(-0.480600\pi\) | ||||
0.0609096 | + | 0.998143i | \(0.480600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2671 | 0.841547 | 0.420773 | − | 0.907166i | \(-0.361759\pi\) | ||||
0.420773 | + | 0.907166i | \(0.361759\pi\) | |||||||
\(422\) | −0.128274 | −0.00624430 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.61080 | 0.175356 | ||||||||
\(425\) | 0.298241 | 0.0144668 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.7661 | −1.73084 | ||||||||
\(428\) | 20.8197 | 1.00636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.18841 | −0.0573103 | ||||||||
\(431\) | −31.0699 | −1.49659 | −0.748293 | − | 0.663368i | \(-0.769126\pi\) | ||||
−0.748293 | + | 0.663368i | \(0.769126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4828 | 0.792112 | 0.396056 | − | 0.918226i | \(-0.370379\pi\) | ||||
0.396056 | + | 0.918226i | \(0.370379\pi\) | |||||||
\(434\) | 0.279445 | 0.0134138 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.3410 | 0.543137 | ||||||||
\(437\) | 13.7507 | 0.657785 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.0499 | 1.57739 | 0.788693 | − | 0.614787i | \(-0.210758\pi\) | ||||
0.788693 | + | 0.614787i | \(0.210758\pi\) | |||||||
\(440\) | −0.162703 | −0.00775658 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.62742 | 0.0774083 | ||||||||
\(443\) | 24.8330 | 1.17985 | 0.589925 | − | 0.807458i | \(-0.299157\pi\) | ||||
0.589925 | + | 0.807458i | \(0.299157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.1997 | −0.862747 | ||||||||
\(446\) | 2.21650 | 0.104954 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.1224 | 1.18692 | ||||||||
\(449\) | 18.6217 | 0.878811 | 0.439405 | − | 0.898289i | \(-0.355189\pi\) | ||||
0.439405 | + | 0.898289i | \(0.355189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.694314 | −0.0326940 | ||||||||
\(452\) | 41.8512 | 1.96852 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.533192 | −0.0250239 | ||||||||
\(455\) | −30.1497 | −1.41344 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.2762 | −1.60337 | −0.801686 | − | 0.597745i | \(-0.796063\pi\) | ||||
−0.801686 | + | 0.597745i | \(0.796063\pi\) | |||||||
\(458\) | 2.31444 | 0.108147 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.9316 | 0.836065 | ||||||||
\(461\) | −11.2220 | −0.522659 | −0.261329 | − | 0.965250i | \(-0.584161\pi\) | ||||
−0.261329 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.9770 | −1.25373 | −0.626863 | − | 0.779129i | \(-0.715662\pi\) | ||||
−0.626863 | + | 0.779129i | \(0.715662\pi\) | |||||||
\(464\) | 2.81917 | 0.130877 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0537644 | 0.00249059 | ||||||||
\(467\) | −11.5336 | −0.533711 | −0.266856 | − | 0.963737i | \(-0.585985\pi\) | ||||
−0.266856 | + | 0.963737i | \(0.585985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.5328 | −0.901942 | ||||||||
\(470\) | 0.724872 | 0.0334359 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.874841 | 0.0402678 | ||||||||
\(473\) | −1.38638 | −0.0637459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.218734 | 0.0100362 | ||||||||
\(476\) | 29.9690 | 1.37363 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.02682 | −0.0469659 | ||||||||
\(479\) | 28.8893 | 1.31998 | 0.659992 | − | 0.751272i | \(-0.270559\pi\) | ||||
0.659992 | + | 0.751272i | \(0.270559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.14526 | −0.325796 | ||||||||
\(482\) | 1.05918 | 0.0482443 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.8294 | 0.992245 | ||||||||
\(485\) | 29.0412 | 1.31869 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.63083 | 0.0739001 | 0.0369501 | − | 0.999317i | \(-0.488236\pi\) | ||||
0.0369501 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(488\) | 3.69922 | 0.167456 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.613267 | 0.0277046 | ||||||||
\(491\) | 6.45592 | 0.291352 | 0.145676 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145676 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.33956 | 0.150406 | ||||||||
\(494\) | 1.19357 | 0.0537012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.15396 | 0.186518 | ||||||||
\(497\) | 30.1573 | 1.35274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.7187 | 1.33039 | 0.665196 | − | 0.746669i | \(-0.268348\pi\) | ||||
0.665196 | + | 0.746669i | \(0.268348\pi\) | |||||||
\(500\) | −22.1396 | −0.990113 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.12053 | −0.0500115 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.89976 | 0.218037 | ||||||||
\(506\) | −0.0723963 | −0.00321841 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.190721 | 0.00846188 | ||||||||
\(509\) | −7.29140 | −0.323186 | −0.161593 | − | 0.986858i | \(-0.551663\pi\) | ||||
−0.161593 | + | 0.986858i | \(0.551663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.93103 | 0.395086 | ||||||||
\(512\) | −6.55291 | −0.289601 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.378986 | −0.0167163 | ||||||||
\(515\) | −33.2164 | −1.46369 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.845624 | 0.0371905 | ||||||||
\(518\) | 0.455380 | 0.0200082 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.11833 | 0.136748 | ||||||||
\(521\) | −1.73107 | −0.0758394 | −0.0379197 | − | 0.999281i | \(-0.512073\pi\) | ||||
−0.0379197 | + | 0.999281i | \(0.512073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8653 | 0.693742 | 0.346871 | − | 0.937913i | \(-0.387244\pi\) | ||||
0.346871 | + | 0.937913i | \(0.387244\pi\) | |||||||
\(524\) | 29.0271 | 1.26805 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.33703 | 0.0582971 | ||||||||
\(527\) | 4.92073 | 0.214350 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.01475 | −0.304989 | ||||||||
\(530\) | 2.03481 | 0.0883863 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.9797 | 0.952940 | ||||||||
\(533\) | 13.3070 | 0.576392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.5058 | 1.01624 | ||||||||
\(536\) | 2.02025 | 0.0872613 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.622765 | −0.0268493 | ||||||||
\(539\) | 0.715427 | 0.0308156 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.384069 | 0.0165124 | 0.00825621 | − | 0.999966i | \(-0.497372\pi\) | ||||
0.00825621 | + | 0.999966i | \(0.497372\pi\) | |||||||
\(542\) | −0.537705 | −0.0230964 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.65214 | −0.199459 | ||||||||
\(545\) | 12.8042 | 0.548472 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.3367 | 1.63916 | 0.819579 | − | 0.572967i | \(-0.194208\pi\) | ||||
0.819579 | + | 0.572967i | \(0.194208\pi\) | |||||||
\(548\) | −34.0977 | −1.45658 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.00115162 | −4.91051e−5 0 | ||||||||
\(551\) | 2.44928 | 0.104343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5772 | −0.704935 | ||||||||
\(554\) | −0.691043 | −0.0293596 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 35.3317 | 1.49840 | ||||||||
\(557\) | −25.2935 | −1.07172 | −0.535860 | − | 0.844307i | \(-0.680013\pi\) | ||||
−0.535860 | + | 0.844307i | \(0.680013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.5710 | 1.12384 | ||||||||
\(560\) | 28.5631 | 1.20701 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.19092 | −0.0924185 | ||||||||
\(563\) | −32.5764 | −1.37293 | −0.686465 | − | 0.727163i | \(-0.740839\pi\) | ||||
−0.686465 | + | 0.727163i | \(0.740839\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 47.2507 | 1.98785 | ||||||||
\(566\) | 1.94384 | 0.0817058 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.11912 | −0.130875 | ||||||||
\(569\) | 36.9548 | 1.54923 | 0.774614 | − | 0.632435i | \(-0.217944\pi\) | ||||
0.774614 | + | 0.632435i | \(0.217944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.4941 | −1.35984 | −0.679919 | − | 0.733288i | \(-0.737985\pi\) | ||||
−0.679919 | + | 0.733288i | \(0.737985\pi\) | |||||||
\(572\) | 1.81576 | 0.0759206 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.848081 | −0.0353982 | ||||||||
\(575\) | 0.254279 | 0.0106042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.08889 | −0.128592 | −0.0642960 | − | 0.997931i | \(-0.520480\pi\) | ||||
−0.0642960 | + | 0.997931i | \(0.520480\pi\) | |||||||
\(578\) | −0.414465 | −0.0172395 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.19398 | 0.132623 | ||||||||
\(581\) | 5.89327 | 0.244494 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.37377 | 0.0983116 | ||||||||
\(584\) | −0.923721 | −0.0382238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.296572 | −0.0122513 | ||||||||
\(587\) | 39.5581 | 1.63274 | 0.816369 | − | 0.577530i | \(-0.195983\pi\) | ||||
0.816369 | + | 0.577530i | \(0.195983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.60893 | 0.148703 | ||||||||
\(590\) | 0.493002 | 0.0202966 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.76923 | 0.278214 | ||||||||
\(593\) | −37.0809 | −1.52273 | −0.761366 | − | 0.648323i | \(-0.775471\pi\) | ||||
−0.761366 | + | 0.648323i | \(0.775471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33.8355 | 1.38712 | ||||||||
\(596\) | −6.72465 | −0.275453 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.38753 | 0.0567403 | ||||||||
\(599\) | 7.21058 | 0.294616 | 0.147308 | − | 0.989091i | \(-0.452939\pi\) | ||||
0.147308 | + | 0.989091i | \(0.452939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.6443 | −0.638145 | −0.319072 | − | 0.947730i | \(-0.603371\pi\) | ||||
−0.319072 | + | 0.947730i | \(0.603371\pi\) | |||||||
\(602\) | −1.69342 | −0.0690186 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.50431 | −0.223967 | ||||||||
\(605\) | 24.6457 | 1.00199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.03996 | −0.204566 | −0.102283 | − | 0.994755i | \(-0.532615\pi\) | ||||
−0.102283 | + | 0.994755i | \(0.532615\pi\) | |||||||
\(608\) | −3.41194 | −0.138372 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.08463 | 0.0844043 | ||||||||
\(611\) | −16.2070 | −0.655666 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.4393 | −1.67372 | −0.836858 | − | 0.547420i | \(-0.815610\pi\) | ||||
−0.836858 | + | 0.547420i | \(0.815610\pi\) | |||||||
\(614\) | 0.204998 | 0.00827306 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.231843 | −0.00934122 | ||||||||
\(617\) | −17.1685 | −0.691178 | −0.345589 | − | 0.938386i | \(-0.612321\pi\) | ||||
−0.345589 | + | 0.938386i | \(0.612321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.9228 | −0.680186 | −0.340093 | − | 0.940392i | \(-0.610459\pi\) | ||||
−0.340093 | + | 0.940392i | \(0.610459\pi\) | |||||||
\(620\) | 4.70623 | 0.189007 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.65234 | −0.0662526 | ||||||||
\(623\) | −25.9335 | −1.03900 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.3140 | −1.01256 | ||||||||
\(626\) | 0.832018 | 0.0332541 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.8097 | 0.710684 | ||||||||
\(629\) | 8.01876 | 0.319729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9640 | 0.635518 | 0.317759 | − | 0.948171i | \(-0.397070\pi\) | ||||
0.317759 | + | 0.948171i | \(0.397070\pi\) | |||||||
\(632\) | 1.71455 | 0.0682012 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.933852 | −0.0370880 | ||||||||
\(635\) | 0.215327 | 0.00854500 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7117 | −0.543277 | ||||||||
\(638\) | −0.0128953 | −0.000510528 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.92901 | −0.234365 | ||||||||
\(641\) | −34.1774 | −1.34993 | −0.674964 | − | 0.737851i | \(-0.735841\pi\) | ||||
−0.674964 | + | 0.737851i | \(0.735841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.27460 | −0.0502653 | −0.0251326 | − | 0.999684i | \(-0.508001\pi\) | ||||
−0.0251326 | + | 0.999684i | \(0.508001\pi\) | |||||||
\(644\) | 25.5515 | 1.00687 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.33948 | −0.0527012 | ||||||||
\(647\) | −16.4300 | −0.645930 | −0.322965 | − | 0.946411i | \(-0.604680\pi\) | ||||
−0.322965 | + | 0.946411i | \(0.604680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.575128 | 0.0225757 | ||||||||
\(650\) | 0.0220716 | 0.000865719 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.4528 | 0.683504 | ||||||||
\(653\) | −46.5637 | −1.82218 | −0.911088 | − | 0.412211i | \(-0.864757\pi\) | ||||
−0.911088 | + | 0.412211i | \(0.864757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.7720 | 1.28051 | ||||||||
\(656\) | −12.6067 | −0.492211 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.03290 | 0.0402667 | ||||||||
\(659\) | 21.2263 | 0.826861 | 0.413431 | − | 0.910536i | \(-0.364330\pi\) | ||||
0.413431 | + | 0.910536i | \(0.364330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.5049 | 1.22540 | 0.612700 | − | 0.790316i | \(-0.290084\pi\) | ||||
0.612700 | + | 0.790316i | \(0.290084\pi\) | |||||||
\(662\) | 2.49764 | 0.0970734 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.609530 | −0.0236544 | ||||||||
\(665\) | 24.8154 | 0.962300 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.84730 | 0.110248 | ||||||||
\(668\) | 28.6219 | 1.10741 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.13847 | 0.0439831 | ||||||||
\(671\) | 2.43190 | 0.0938824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0920 | −1.77672 | −0.888359 | − | 0.459150i | \(-0.848154\pi\) | ||||
−0.888359 | + | 0.459150i | \(0.848154\pi\) | |||||||
\(674\) | 1.43868 | 0.0554159 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.89000 | −0.341923 | ||||||||
\(677\) | −5.22605 | −0.200853 | −0.100427 | − | 0.994944i | \(-0.532021\pi\) | ||||
−0.100427 | + | 0.994944i | \(0.532021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.3820 | 1.58810 | ||||||||
\(680\) | −3.49955 | −0.134201 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0190007 | −0.000727575 0 | ||||||||
\(683\) | 26.7163 | 1.02227 | 0.511135 | − | 0.859500i | \(-0.329225\pi\) | ||||
0.511135 | + | 0.859500i | \(0.329225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.4969 | −1.47089 | ||||||||
\(686\) | −0.990279 | −0.0378090 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.1727 | −0.959701 | ||||||||
\(689\) | −45.4951 | −1.73323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.7575 | −0.789653 | −0.394826 | − | 0.918756i | \(-0.629195\pi\) | ||||
−0.394826 | + | 0.918756i | \(0.629195\pi\) | |||||||
\(692\) | −22.0233 | −0.837200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.76414 | 0.0669660 | ||||||||
\(695\) | 39.8900 | 1.51311 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.9338 | −0.565659 | ||||||||
\(698\) | −0.970202 | −0.0367227 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.406451 | 0.0153624 | ||||||||
\(701\) | 48.5428 | 1.83344 | 0.916719 | − | 0.399533i | \(-0.130828\pi\) | ||||
0.916719 | + | 0.399533i | \(0.130828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.88106 | 0.221809 | ||||||||
\(704\) | −1.70819 | −0.0643798 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.16918 | 0.0440027 | ||||||||
\(707\) | 6.98188 | 0.262581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9935 | −0.825981 | −0.412991 | − | 0.910735i | \(-0.635516\pi\) | ||||
−0.412991 | + | 0.910735i | \(0.635516\pi\) | |||||||
\(710\) | −1.75772 | −0.0659662 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.68225 | 0.100522 | ||||||||
\(713\) | 4.19540 | 0.157119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.05002 | 0.0766663 | ||||||||
\(716\) | −13.0560 | −0.487926 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.652552 | 0.0243530 | ||||||||
\(719\) | −9.78228 | −0.364817 | −0.182409 | − | 0.983223i | \(-0.558389\pi\) | ||||
−0.182409 | + | 0.983223i | \(0.558389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.3314 | −1.76271 | ||||||||
\(722\) | 0.595615 | 0.0221665 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27.8425 | 1.03476 | ||||||||
\(725\) | 0.0452923 | 0.00168211 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.0223 | −1.52143 | −0.760716 | − | 0.649085i | \(-0.775152\pi\) | ||||
−0.760716 | + | 0.649085i | \(0.775152\pi\) | |||||||
\(728\) | 4.44344 | 0.164685 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.520547 | −0.0192663 | ||||||||
\(731\) | −29.8193 | −1.10291 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7580 | 0.729780 | 0.364890 | − | 0.931051i | \(-0.381107\pi\) | ||||
0.364890 | + | 0.931051i | \(0.381107\pi\) | |||||||
\(734\) | 1.64218 | 0.0606139 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.96640 | −0.146203 | ||||||||
\(737\) | 1.32813 | 0.0489222 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.08268 | 0.297326 | 0.148663 | − | 0.988888i | \(-0.452503\pi\) | ||||
0.148663 | + | 0.988888i | \(0.452503\pi\) | |||||||
\(740\) | 7.66921 | 0.281926 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.89948 | 0.106443 | ||||||||
\(743\) | −10.5995 | −0.388859 | −0.194429 | − | 0.980917i | \(-0.562286\pi\) | ||||
−0.194429 | + | 0.980917i | \(0.562286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.59224 | −0.278158 | ||||||||
\(746\) | −0.622140 | −0.0227782 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.03773 | −0.0745068 | ||||||||
\(749\) | 33.4944 | 1.22386 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0003 | 0.510877 | 0.255438 | − | 0.966825i | \(-0.417780\pi\) | ||||
0.255438 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(752\) | 15.3541 | 0.559907 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.247147 | 0.00900057 | ||||||||
\(755\) | −6.21445 | −0.226167 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.8413 | −1.04826 | −0.524128 | − | 0.851640i | \(-0.675609\pi\) | ||||
−0.524128 | + | 0.851640i | \(0.675609\pi\) | |||||||
\(758\) | −2.28449 | −0.0829765 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.56661 | −0.0931008 | ||||||||
\(761\) | 14.2005 | 0.514767 | 0.257383 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257383 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.2453 | 0.660523 | ||||||||
\(764\) | 4.46448 | 0.161519 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.408963 | 0.0147764 | ||||||||
\(767\) | −11.0228 | −0.398008 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1077 | 0.689043 | 0.344521 | − | 0.938778i | \(-0.388041\pi\) | ||||
0.344521 | + | 0.938778i | \(0.388041\pi\) | |||||||
\(770\) | −0.130651 | −0.00470834 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −44.2317 | −1.59193 | ||||||||
\(773\) | 29.5204 | 1.06178 | 0.530888 | − | 0.847442i | \(-0.321859\pi\) | ||||
0.530888 | + | 0.847442i | \(0.321859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0667367 | 0.00239725 | ||||||||
\(776\) | −4.28007 | −0.153646 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.23837 | 0.116101 | ||||||||
\(779\) | −10.9527 | −0.392420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05053 | −0.0733739 | ||||||||
\(782\) | −1.55715 | −0.0556837 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.9901 | 0.463932 | ||||||||
\(785\) | 20.1074 | 0.717665 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.3547 | −0.725568 | −0.362784 | − | 0.931873i | \(-0.618174\pi\) | ||||
−0.362784 | + | 0.931873i | \(0.618174\pi\) | |||||||
\(788\) | −21.9766 | −0.782886 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.966206 | 0.0343761 | ||||||||
\(791\) | 67.3295 | 2.39396 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.6092 | −1.65514 | ||||||||
\(794\) | 1.05196 | 0.0373326 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.1384 | −1.03278 | ||||||||
\(797\) | −51.2687 | −1.81603 | −0.908016 | − | 0.418935i | \(-0.862403\pi\) | ||||
−0.908016 | + | 0.418935i | \(0.862403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.1883 | 0.643456 | ||||||||
\(800\) | −0.0630940 | −0.00223071 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.22548 | 0.0785845 | ||||||||
\(803\) | −0.607262 | −0.0214298 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.8480 | 1.01676 | ||||||||
\(806\) | 0.364163 | 0.0128271 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.722123 | −0.0254042 | ||||||||
\(809\) | −53.5568 | −1.88296 | −0.941478 | − | 0.337073i | \(-0.890563\pi\) | ||||
−0.941478 | + | 0.337073i | \(0.890563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.8963 | 1.50629 | 0.753146 | − | 0.657854i | \(-0.228535\pi\) | ||||
0.753146 | + | 0.657854i | \(0.228535\pi\) | |||||||
\(812\) | 4.55124 | 0.159717 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0309633 | −0.00108526 | ||||||||
\(815\) | 19.7045 | 0.690218 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.8699 | −0.765130 | ||||||||
\(818\) | −2.93569 | −0.102644 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.2828 | −0.498778 | ||||||||
\(821\) | −5.52686 | −0.192889 | −0.0964444 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964444 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0939 | −0.665572 | −0.332786 | − | 0.943002i | \(-0.607989\pi\) | ||||
−0.332786 | + | 0.943002i | \(0.607989\pi\) | |||||||
\(824\) | 4.89540 | 0.170539 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.702499 | 0.0244431 | ||||||||
\(827\) | 47.8774 | 1.66486 | 0.832430 | − | 0.554130i | \(-0.186949\pi\) | ||||
0.832430 | + | 0.554130i | \(0.186949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1461 | 0.456583 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(830\) | −0.343490 | −0.0119227 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.7387 | 1.13501 | ||||||||
\(833\) | 15.3879 | 0.533161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.3146 | 1.11829 | ||||||||
\(836\) | −1.49450 | −0.0516883 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.207099 | −0.00715412 | ||||||||
\(839\) | −33.7580 | −1.16545 | −0.582727 | − | 0.812668i | \(-0.698014\pi\) | ||||
−0.582727 | + | 0.812668i | \(0.698014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4928 | −0.982512 | ||||||||
\(842\) | −1.43408 | −0.0494218 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.07832 | −0.105960 | ||||||||
\(845\) | −10.0370 | −0.345282 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.1187 | 1.20669 | ||||||||
\(848\) | 43.1009 | 1.48009 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.0247698 | −0.000849598 0 | ||||||||
\(851\) | 6.83677 | 0.234361 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1494 | 0.552946 | 0.276473 | − | 0.961022i | \(-0.410834\pi\) | ||||
0.276473 | + | 0.961022i | \(0.410834\pi\) | |||||||
\(854\) | 2.97048 | 0.101648 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.46426 | −0.118406 | ||||||||
\(857\) | −21.1749 | −0.723322 | −0.361661 | − | 0.932310i | \(-0.617790\pi\) | ||||
−0.361661 | + | 0.932310i | \(0.617790\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2136 | −0.723798 | −0.361899 | − | 0.932217i | \(-0.617871\pi\) | ||||
−0.361899 | + | 0.932217i | \(0.617871\pi\) | |||||||
\(860\) | −28.5194 | −0.972505 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.58045 | 0.0878906 | ||||||||
\(863\) | 45.3619 | 1.54414 | 0.772068 | − | 0.635539i | \(-0.219222\pi\) | ||||
0.772068 | + | 0.635539i | \(0.219222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.8647 | −0.845424 | ||||||||
\(866\) | −1.36895 | −0.0465186 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.70610 | 0.227620 | ||||||||
\(869\) | 1.12716 | 0.0382363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.4545 | −0.862494 | ||||||||
\(872\) | −1.88707 | −0.0639044 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.14204 | −0.0386300 | ||||||||
\(875\) | −35.6178 | −1.20410 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1962 | 0.411837 | 0.205918 | − | 0.978569i | \(-0.433982\pi\) | ||||
0.205918 | + | 0.978569i | \(0.433982\pi\) | |||||||
\(878\) | −2.74490 | −0.0926358 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.94213 | −0.0654693 | ||||||||
\(881\) | −8.50736 | −0.286620 | −0.143310 | − | 0.989678i | \(-0.545775\pi\) | ||||
−0.143310 | + | 0.989678i | \(0.545775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.5027 | −0.891888 | −0.445944 | − | 0.895061i | \(-0.647132\pi\) | ||||
−0.445944 | + | 0.895061i | \(0.647132\pi\) | |||||||
\(884\) | 39.0546 | 1.31355 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.06245 | −0.0692895 | ||||||||
\(887\) | −33.1863 | −1.11429 | −0.557144 | − | 0.830416i | \(-0.688103\pi\) | ||||
−0.557144 | + | 0.830416i | \(0.688103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.306829 | 0.0102907 | ||||||||
\(890\) | 1.51154 | 0.0506668 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 53.1915 | 1.78098 | ||||||||
\(893\) | 13.3395 | 0.446391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.7405 | −0.492719 | ||||||||
\(896\) | −8.44850 | −0.282244 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.54659 | −0.0516102 | ||||||||
\(899\) | 0.747286 | 0.0249234 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.0568 | 1.70095 | ||||||||
\(902\) | 0.0576649 | 0.00192003 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.96377 | −0.231612 | ||||||||
\(905\) | 31.4346 | 1.04492 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.31486 | 0.209682 | 0.104841 | − | 0.994489i | \(-0.466567\pi\) | ||||
0.104841 | + | 0.994489i | \(0.466567\pi\) | |||||||
\(908\) | −12.7955 | −0.424634 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.50403 | 0.0830077 | ||||||||
\(911\) | −43.0949 | −1.42780 | −0.713898 | − | 0.700249i | \(-0.753072\pi\) | ||||
−0.713898 | + | 0.700249i | \(0.753072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.400710 | −0.0132616 | ||||||||
\(914\) | 2.84674 | 0.0941618 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 55.5418 | 1.83515 | ||||||||
\(917\) | 46.6983 | 1.54211 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.4088 | −0.640236 | −0.320118 | − | 0.947378i | \(-0.603723\pi\) | ||||
−0.320118 | + | 0.947378i | \(0.603723\pi\) | |||||||
\(920\) | −2.98370 | −0.0983697 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.932018 | 0.0306944 | ||||||||
\(923\) | 39.3000 | 1.29358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.108753 | 0.00357579 | ||||||||
\(926\) | 2.24052 | 0.0736281 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.706496 | −0.0231919 | ||||||||
\(929\) | 28.3914 | 0.931493 | 0.465747 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465747 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.2857 | 0.369874 | ||||||||
\(932\) | 1.29024 | 0.0422631 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.957900 | 0.0313434 | ||||||||
\(935\) | −2.30063 | −0.0752387 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.00280 | −0.130766 | −0.0653829 | − | 0.997860i | \(-0.520827\pi\) | ||||
−0.0653829 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(938\) | 1.62226 | 0.0529687 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.3954 | 0.567377 | ||||||||
\(941\) | −13.9675 | −0.455328 | −0.227664 | − | 0.973740i | \(-0.573109\pi\) | ||||
−0.227664 | + | 0.973740i | \(0.573109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7325 | −0.414628 | ||||||||
\(944\) | 10.4427 | 0.339880 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.115143 | 0.00374363 | ||||||||
\(947\) | −57.2963 | −1.86188 | −0.930940 | − | 0.365171i | \(-0.881010\pi\) | ||||
−0.930940 | + | 0.365171i | \(0.881010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.6386 | 0.377806 | ||||||||
\(950\) | −0.0181665 | −0.000589400 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.98665 | −0.161618 | ||||||||
\(953\) | −5.29452 | −0.171506 | −0.0857532 | − | 0.996316i | \(-0.527330\pi\) | ||||
−0.0857532 | + | 0.996316i | \(0.527330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.04047 | 0.163106 | ||||||||
\(956\) | −24.6417 | −0.796969 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.39934 | −0.0775192 | ||||||||
\(959\) | −54.8558 | −1.77139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8989 | −0.964481 | ||||||||
\(962\) | 0.593436 | 0.0191331 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.4181 | 0.818663 | ||||||||
\(965\) | −49.9383 | −1.60757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.3615 | 1.42657 | 0.713284 | − | 0.700875i | \(-0.247207\pi\) | ||||
0.713284 | + | 0.700875i | \(0.247207\pi\) | |||||||
\(968\) | −3.63227 | −0.116746 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.41196 | −0.0774434 | ||||||||
\(971\) | −51.4789 | −1.65204 | −0.826018 | − | 0.563644i | \(-0.809399\pi\) | ||||
−0.826018 | + | 0.563644i | \(0.809399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.8410 | 1.82224 | ||||||||
\(974\) | −0.135446 | −0.00433996 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.1563 | 1.41341 | ||||||||
\(977\) | 0.892938 | 0.0285676 | 0.0142838 | − | 0.999898i | \(-0.495453\pi\) | ||||
0.0142838 | + | 0.999898i | \(0.495453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.76333 | 0.0563564 | ||||||||
\(980\) | 14.7171 | 0.470122 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.536184 | −0.0171103 | ||||||||
\(983\) | −36.2679 | −1.15677 | −0.578384 | − | 0.815765i | \(-0.696316\pi\) | ||||
−0.578384 | + | 0.815765i | \(0.696316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.8120 | −0.790576 | ||||||||
\(986\) | −0.277361 | −0.00883296 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.6432 | 0.911261 | ||||||||
\(989\) | −25.4239 | −0.808432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3407 | 0.932036 | 0.466018 | − | 0.884775i | \(-0.345688\pi\) | ||||
0.466018 | + | 0.884775i | \(0.345688\pi\) | |||||||
\(992\) | −1.04100 | −0.0330518 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.50466 | −0.0794429 | ||||||||
\(995\) | −32.8977 | −1.04293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.6388 | 0.590296 | 0.295148 | − | 0.955452i | \(-0.404631\pi\) | ||||
0.295148 | + | 0.955452i | \(0.404631\pi\) | |||||||
\(998\) | −2.46823 | −0.0781304 | ||||||||
\(999\) | 0 | 0 |
(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 | 4527.2.a.k.1.4 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.7 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.7 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.4 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.3 | 10 | 12.11 | even | 2 |