Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.737640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.262360 | 0.185516 | 0.0927582 | − | 0.995689i | \(-0.470432\pi\) | ||||
0.0927582 | + | 0.995689i | \(0.470432\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.93117 | −0.965584 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.262360 | 0.107108 | ||||||||
\(7\) | 3.19353 | 1.20704 | 0.603520 | − | 0.797348i | \(-0.293764\pi\) | ||||
0.603520 | + | 0.797348i | \(0.293764\pi\) | |||||||
\(8\) | −1.03138 | −0.364648 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.262360 | 0.0829654 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.93117 | −0.557480 | ||||||||
\(13\) | 1.11961 | 0.310523 | 0.155261 | − | 0.987873i | \(-0.450378\pi\) | ||||
0.155261 | + | 0.987873i | \(0.450378\pi\) | |||||||
\(14\) | 0.837853 | 0.223926 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.59174 | 0.897936 | ||||||||
\(17\) | 0.0882264 | 0.0213981 | 0.0106990 | − | 0.999943i | \(-0.496594\pi\) | ||||
0.0106990 | + | 0.999943i | \(0.496594\pi\) | |||||||
\(18\) | 0.262360 | 0.0618388 | ||||||||
\(19\) | 0.0688326 | 0.0157913 | 0.00789564 | − | 0.999969i | \(-0.497487\pi\) | ||||
0.00789564 | + | 0.999969i | \(0.497487\pi\) | |||||||
\(20\) | −1.93117 | −0.431822 | ||||||||
\(21\) | 3.19353 | 0.696885 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.65450 | 1.38756 | 0.693780 | − | 0.720187i | \(-0.255944\pi\) | ||||
0.693780 | + | 0.720187i | \(0.255944\pi\) | |||||||
\(24\) | −1.03138 | −0.210530 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.293740 | 0.0576071 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.16724 | −1.16550 | ||||||||
\(29\) | −3.73583 | −0.693726 | −0.346863 | − | 0.937916i | \(-0.612753\pi\) | ||||
−0.346863 | + | 0.937916i | \(0.612753\pi\) | |||||||
\(30\) | 0.262360 | 0.0479001 | ||||||||
\(31\) | −9.58484 | −1.72149 | −0.860744 | − | 0.509037i | \(-0.830002\pi\) | ||||
−0.860744 | + | 0.509037i | \(0.830002\pi\) | |||||||
\(32\) | 3.00509 | 0.531230 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0231471 | 0.00396969 | ||||||||
\(35\) | 3.19353 | 0.539805 | ||||||||
\(36\) | −1.93117 | −0.321861 | ||||||||
\(37\) | −8.33021 | −1.36948 | −0.684739 | − | 0.728789i | \(-0.740084\pi\) | ||||
−0.684739 | + | 0.728789i | \(0.740084\pi\) | |||||||
\(38\) | 0.0180589 | 0.00292954 | ||||||||
\(39\) | 1.11961 | 0.179280 | ||||||||
\(40\) | −1.03138 | −0.163075 | ||||||||
\(41\) | 11.6657 | 1.82187 | 0.910935 | − | 0.412549i | \(-0.135362\pi\) | ||||
0.910935 | + | 0.412549i | \(0.135362\pi\) | |||||||
\(42\) | 0.837853 | 0.129283 | ||||||||
\(43\) | 11.8217 | 1.80280 | 0.901399 | − | 0.432989i | \(-0.142541\pi\) | ||||
0.901399 | + | 0.432989i | \(0.142541\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.74587 | 0.257415 | ||||||||
\(47\) | 0.908020 | 0.132448 | 0.0662242 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662242 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(48\) | 3.59174 | 0.518423 | ||||||||
\(49\) | 3.19862 | 0.456945 | ||||||||
\(50\) | 0.262360 | 0.0371033 | ||||||||
\(51\) | 0.0882264 | 0.0123542 | ||||||||
\(52\) | −2.16215 | −0.299836 | ||||||||
\(53\) | 0.872377 | 0.119830 | 0.0599151 | − | 0.998203i | \(-0.480917\pi\) | ||||
0.0599151 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(54\) | 0.262360 | 0.0357026 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.29374 | −0.440144 | ||||||||
\(57\) | 0.0688326 | 0.00911710 | ||||||||
\(58\) | −0.980131 | −0.128698 | ||||||||
\(59\) | 1.83604 | 0.239032 | 0.119516 | − | 0.992832i | \(-0.461866\pi\) | ||||
0.119516 | + | 0.992832i | \(0.461866\pi\) | |||||||
\(60\) | −1.93117 | −0.249313 | ||||||||
\(61\) | 10.0601 | 1.28807 | 0.644034 | − | 0.764997i | \(-0.277260\pi\) | ||||
0.644034 | + | 0.764997i | \(0.277260\pi\) | |||||||
\(62\) | −2.51468 | −0.319364 | ||||||||
\(63\) | 3.19353 | 0.402347 | ||||||||
\(64\) | −6.39507 | −0.799384 | ||||||||
\(65\) | 1.11961 | 0.138870 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.53916 | 1.16539 | 0.582697 | − | 0.812690i | \(-0.301997\pi\) | ||||
0.582697 | + | 0.812690i | \(0.301997\pi\) | |||||||
\(68\) | −0.170380 | −0.0206616 | ||||||||
\(69\) | 6.65450 | 0.801108 | ||||||||
\(70\) | 0.837853 | 0.100143 | ||||||||
\(71\) | −4.66454 | −0.553580 | −0.276790 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276790 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(72\) | −1.03138 | −0.121549 | ||||||||
\(73\) | 7.16034 | 0.838054 | 0.419027 | − | 0.907974i | \(-0.362371\pi\) | ||||
0.419027 | + | 0.907974i | \(0.362371\pi\) | |||||||
\(74\) | −2.18551 | −0.254060 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −0.132927 | −0.0152478 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.293740 | 0.0332595 | ||||||||
\(79\) | −0.791342 | −0.0890330 | −0.0445165 | − | 0.999009i | \(-0.514175\pi\) | ||||
−0.0445165 | + | 0.999009i | \(0.514175\pi\) | |||||||
\(80\) | 3.59174 | 0.401569 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.06060 | 0.337987 | ||||||||
\(83\) | −0.247229 | −0.0271369 | −0.0135685 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135685 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(84\) | −6.16724 | −0.672901 | ||||||||
\(85\) | 0.0882264 | 0.00956950 | ||||||||
\(86\) | 3.10155 | 0.334448 | ||||||||
\(87\) | −3.73583 | −0.400523 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5788 | −1.54535 | −0.772673 | − | 0.634804i | \(-0.781081\pi\) | ||||
−0.772673 | + | 0.634804i | \(0.781081\pi\) | |||||||
\(90\) | 0.262360 | 0.0276551 | ||||||||
\(91\) | 3.57549 | 0.374814 | ||||||||
\(92\) | −12.8510 | −1.33980 | ||||||||
\(93\) | −9.58484 | −0.993902 | ||||||||
\(94\) | 0.238228 | 0.0245713 | ||||||||
\(95\) | 0.0688326 | 0.00706208 | ||||||||
\(96\) | 3.00509 | 0.306706 | ||||||||
\(97\) | −4.09198 | −0.415478 | −0.207739 | − | 0.978184i | \(-0.566610\pi\) | ||||
−0.207739 | + | 0.978184i | \(0.566610\pi\) | |||||||
\(98\) | 0.839188 | 0.0847708 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.93117 | −0.193117 | ||||||||
\(101\) | −4.29171 | −0.427041 | −0.213521 | − | 0.976939i | \(-0.568493\pi\) | ||||
−0.213521 | + | 0.976939i | \(0.568493\pi\) | |||||||
\(102\) | 0.0231471 | 0.00229190 | ||||||||
\(103\) | 2.09280 | 0.206210 | 0.103105 | − | 0.994670i | \(-0.467122\pi\) | ||||
0.103105 | + | 0.994670i | \(0.467122\pi\) | |||||||
\(104\) | −1.15474 | −0.113232 | ||||||||
\(105\) | 3.19353 | 0.311656 | ||||||||
\(106\) | 0.228877 | 0.0222305 | ||||||||
\(107\) | 15.7409 | 1.52173 | 0.760866 | − | 0.648909i | \(-0.224774\pi\) | ||||
0.760866 | + | 0.648909i | \(0.224774\pi\) | |||||||
\(108\) | −1.93117 | −0.185827 | ||||||||
\(109\) | 4.13271 | 0.395842 | 0.197921 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197921 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.33021 | −0.790668 | ||||||||
\(112\) | 11.4703 | 1.08384 | ||||||||
\(113\) | 13.7550 | 1.29396 | 0.646981 | − | 0.762506i | \(-0.276031\pi\) | ||||
0.646981 | + | 0.762506i | \(0.276031\pi\) | |||||||
\(114\) | 0.0180589 | 0.00169137 | ||||||||
\(115\) | 6.65450 | 0.620536 | ||||||||
\(116\) | 7.21451 | 0.669851 | ||||||||
\(117\) | 1.11961 | 0.103508 | ||||||||
\(118\) | 0.481704 | 0.0443444 | ||||||||
\(119\) | 0.281754 | 0.0258283 | ||||||||
\(120\) | −1.03138 | −0.0941517 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.63937 | 0.238957 | ||||||||
\(123\) | 11.6657 | 1.05186 | ||||||||
\(124\) | 18.5099 | 1.66224 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.837853 | 0.0746419 | ||||||||
\(127\) | −7.89979 | −0.700993 | −0.350496 | − | 0.936564i | \(-0.613987\pi\) | ||||
−0.350496 | + | 0.936564i | \(0.613987\pi\) | |||||||
\(128\) | −7.68799 | −0.679528 | ||||||||
\(129\) | 11.8217 | 1.04085 | ||||||||
\(130\) | 0.293740 | 0.0257627 | ||||||||
\(131\) | 16.3539 | 1.42884 | 0.714422 | − | 0.699715i | \(-0.246690\pi\) | ||||
0.714422 | + | 0.699715i | \(0.246690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.219819 | 0.0190607 | ||||||||
\(134\) | 2.50269 | 0.216200 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −0.0909950 | −0.00780275 | ||||||||
\(137\) | 7.73208 | 0.660596 | 0.330298 | − | 0.943877i | \(-0.392851\pi\) | ||||
0.330298 | + | 0.943877i | \(0.392851\pi\) | |||||||
\(138\) | 1.74587 | 0.148619 | ||||||||
\(139\) | −20.1865 | −1.71219 | −0.856097 | − | 0.516815i | \(-0.827117\pi\) | ||||
−0.856097 | + | 0.516815i | \(0.827117\pi\) | |||||||
\(140\) | −6.16724 | −0.521227 | ||||||||
\(141\) | 0.908020 | 0.0764691 | ||||||||
\(142\) | −1.22379 | −0.102698 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.59174 | 0.299312 | ||||||||
\(145\) | −3.73583 | −0.310244 | ||||||||
\(146\) | 1.87858 | 0.155473 | ||||||||
\(147\) | 3.19862 | 0.263817 | ||||||||
\(148\) | 16.0870 | 1.32235 | ||||||||
\(149\) | −9.69523 | −0.794264 | −0.397132 | − | 0.917761i | \(-0.629995\pi\) | ||||
−0.397132 | + | 0.917761i | \(0.629995\pi\) | |||||||
\(150\) | 0.262360 | 0.0214216 | ||||||||
\(151\) | −15.1615 | −1.23382 | −0.616911 | − | 0.787033i | \(-0.711616\pi\) | ||||
−0.616911 | + | 0.787033i | \(0.711616\pi\) | |||||||
\(152\) | −0.0709926 | −0.00575826 | ||||||||
\(153\) | 0.0882264 | 0.00713268 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.58484 | −0.769873 | ||||||||
\(156\) | −2.16215 | −0.173110 | ||||||||
\(157\) | −14.8805 | −1.18760 | −0.593798 | − | 0.804614i | \(-0.702372\pi\) | ||||
−0.593798 | + | 0.804614i | \(0.702372\pi\) | |||||||
\(158\) | −0.207616 | −0.0165171 | ||||||||
\(159\) | 0.872377 | 0.0691840 | ||||||||
\(160\) | 3.00509 | 0.237573 | ||||||||
\(161\) | 21.2513 | 1.67484 | ||||||||
\(162\) | 0.262360 | 0.0206129 | ||||||||
\(163\) | 3.40114 | 0.266398 | 0.133199 | − | 0.991089i | \(-0.457475\pi\) | ||||
0.133199 | + | 0.991089i | \(0.457475\pi\) | |||||||
\(164\) | −22.5283 | −1.75917 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0648629 | −0.00503434 | ||||||||
\(167\) | 22.6164 | 1.75011 | 0.875053 | − | 0.484027i | \(-0.160826\pi\) | ||||
0.875053 | + | 0.484027i | \(0.160826\pi\) | |||||||
\(168\) | −3.29374 | −0.254118 | ||||||||
\(169\) | −11.7465 | −0.903576 | ||||||||
\(170\) | 0.0231471 | 0.00177530 | ||||||||
\(171\) | 0.0688326 | 0.00526376 | ||||||||
\(172\) | −22.8298 | −1.74075 | ||||||||
\(173\) | 13.0913 | 0.995312 | 0.497656 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497656 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(174\) | −0.980131 | −0.0743036 | ||||||||
\(175\) | 3.19353 | 0.241408 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.83604 | 0.138005 | ||||||||
\(178\) | −3.82488 | −0.286687 | ||||||||
\(179\) | −15.1774 | −1.13441 | −0.567207 | − | 0.823576i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823576i | \(0.691976\pi\) | |||||||
\(180\) | −1.93117 | −0.143941 | ||||||||
\(181\) | 1.41348 | 0.105063 | 0.0525316 | − | 0.998619i | \(-0.483271\pi\) | ||||
0.0525316 | + | 0.998619i | \(0.483271\pi\) | |||||||
\(182\) | 0.938065 | 0.0695340 | ||||||||
\(183\) | 10.0601 | 0.743666 | ||||||||
\(184\) | −6.86332 | −0.505971 | ||||||||
\(185\) | −8.33021 | −0.612449 | ||||||||
\(186\) | −2.51468 | −0.184385 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.75354 | −0.127890 | ||||||||
\(189\) | 3.19353 | 0.232295 | ||||||||
\(190\) | 0.0180589 | 0.00131013 | ||||||||
\(191\) | 4.90914 | 0.355213 | 0.177606 | − | 0.984102i | \(-0.443165\pi\) | ||||
0.177606 | + | 0.984102i | \(0.443165\pi\) | |||||||
\(192\) | −6.39507 | −0.461524 | ||||||||
\(193\) | −9.71987 | −0.699652 | −0.349826 | − | 0.936815i | \(-0.613759\pi\) | ||||
−0.349826 | + | 0.936815i | \(0.613759\pi\) | |||||||
\(194\) | −1.07357 | −0.0770779 | ||||||||
\(195\) | 1.11961 | 0.0801767 | ||||||||
\(196\) | −6.17706 | −0.441219 | ||||||||
\(197\) | 8.88764 | 0.633218 | 0.316609 | − | 0.948556i | \(-0.397456\pi\) | ||||
0.316609 | + | 0.948556i | \(0.397456\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0381 | 1.27869 | 0.639343 | − | 0.768921i | \(-0.279206\pi\) | ||||
0.639343 | + | 0.768921i | \(0.279206\pi\) | |||||||
\(200\) | −1.03138 | −0.0729296 | ||||||||
\(201\) | 9.53916 | 0.672840 | ||||||||
\(202\) | −1.12597 | −0.0792232 | ||||||||
\(203\) | −11.9305 | −0.837355 | ||||||||
\(204\) | −0.170380 | −0.0119290 | ||||||||
\(205\) | 11.6657 | 0.814765 | ||||||||
\(206\) | 0.549068 | 0.0382554 | ||||||||
\(207\) | 6.65450 | 0.462520 | ||||||||
\(208\) | 4.02134 | 0.278830 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.837853 | 0.0578173 | ||||||||
\(211\) | −17.9778 | −1.23764 | −0.618822 | − | 0.785531i | \(-0.712390\pi\) | ||||
−0.618822 | + | 0.785531i | \(0.712390\pi\) | |||||||
\(212\) | −1.68471 | −0.115706 | ||||||||
\(213\) | −4.66454 | −0.319609 | ||||||||
\(214\) | 4.12978 | 0.282306 | ||||||||
\(215\) | 11.8217 | 0.806236 | ||||||||
\(216\) | −1.03138 | −0.0701765 | ||||||||
\(217\) | −30.6095 | −2.07791 | ||||||||
\(218\) | 1.08426 | 0.0734351 | ||||||||
\(219\) | 7.16034 | 0.483851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0987789 | 0.00664459 | ||||||||
\(222\) | −2.18551 | −0.146682 | ||||||||
\(223\) | −13.7489 | −0.920697 | −0.460348 | − | 0.887738i | \(-0.652276\pi\) | ||||
−0.460348 | + | 0.887738i | \(0.652276\pi\) | |||||||
\(224\) | 9.59683 | 0.641215 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.60876 | 0.240051 | ||||||||
\(227\) | −0.662735 | −0.0439873 | −0.0219936 | − | 0.999758i | \(-0.507001\pi\) | ||||
−0.0219936 | + | 0.999758i | \(0.507001\pi\) | |||||||
\(228\) | −0.132927 | −0.00880332 | ||||||||
\(229\) | −7.49041 | −0.494980 | −0.247490 | − | 0.968890i | \(-0.579606\pi\) | ||||
−0.247490 | + | 0.968890i | \(0.579606\pi\) | |||||||
\(230\) | 1.74587 | 0.115119 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.85306 | 0.252966 | ||||||||
\(233\) | −10.5254 | −0.689539 | −0.344770 | − | 0.938687i | \(-0.612043\pi\) | ||||
−0.344770 | + | 0.938687i | \(0.612043\pi\) | |||||||
\(234\) | 0.293740 | 0.0192024 | ||||||||
\(235\) | 0.908020 | 0.0592327 | ||||||||
\(236\) | −3.54571 | −0.230806 | ||||||||
\(237\) | −0.791342 | −0.0514032 | ||||||||
\(238\) | 0.0739208 | 0.00479157 | ||||||||
\(239\) | −17.0762 | −1.10457 | −0.552284 | − | 0.833656i | \(-0.686244\pi\) | ||||
−0.552284 | + | 0.833656i | \(0.686244\pi\) | |||||||
\(240\) | 3.59174 | 0.231846 | ||||||||
\(241\) | 16.7082 | 1.07627 | 0.538135 | − | 0.842859i | \(-0.319129\pi\) | ||||
0.538135 | + | 0.842859i | \(0.319129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −19.4278 | −1.24374 | ||||||||
\(245\) | 3.19862 | 0.204352 | ||||||||
\(246\) | 3.06060 | 0.195137 | ||||||||
\(247\) | 0.0770654 | 0.00490356 | ||||||||
\(248\) | 9.88562 | 0.627737 | ||||||||
\(249\) | −0.247229 | −0.0156675 | ||||||||
\(250\) | 0.262360 | 0.0165931 | ||||||||
\(251\) | −5.13767 | −0.324287 | −0.162143 | − | 0.986767i | \(-0.551841\pi\) | ||||
−0.162143 | + | 0.986767i | \(0.551841\pi\) | |||||||
\(252\) | −6.16724 | −0.388499 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.07259 | −0.130046 | ||||||||
\(255\) | 0.0882264 | 0.00552495 | ||||||||
\(256\) | 10.7731 | 0.673320 | ||||||||
\(257\) | −3.69824 | −0.230690 | −0.115345 | − | 0.993325i | \(-0.536797\pi\) | ||||
−0.115345 | + | 0.993325i | \(0.536797\pi\) | |||||||
\(258\) | 3.10155 | 0.193094 | ||||||||
\(259\) | −26.6027 | −1.65301 | ||||||||
\(260\) | −2.16215 | −0.134091 | ||||||||
\(261\) | −3.73583 | −0.231242 | ||||||||
\(262\) | 4.29059 | 0.265074 | ||||||||
\(263\) | −31.6315 | −1.95048 | −0.975241 | − | 0.221147i | \(-0.929020\pi\) | ||||
−0.975241 | + | 0.221147i | \(0.929020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.872377 | 0.0535897 | ||||||||
\(266\) | 0.0576716 | 0.00353607 | ||||||||
\(267\) | −14.5788 | −0.892206 | ||||||||
\(268\) | −18.4217 | −1.12529 | ||||||||
\(269\) | −14.7754 | −0.900875 | −0.450437 | − | 0.892808i | \(-0.648732\pi\) | ||||
−0.450437 | + | 0.892808i | \(0.648732\pi\) | |||||||
\(270\) | 0.262360 | 0.0159667 | ||||||||
\(271\) | 19.5869 | 1.18982 | 0.594910 | − | 0.803792i | \(-0.297188\pi\) | ||||
0.594910 | + | 0.803792i | \(0.297188\pi\) | |||||||
\(272\) | 0.316887 | 0.0192141 | ||||||||
\(273\) | 3.57549 | 0.216399 | ||||||||
\(274\) | 2.02859 | 0.122551 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.8510 | −0.773537 | ||||||||
\(277\) | −25.7104 | −1.54479 | −0.772393 | − | 0.635145i | \(-0.780940\pi\) | ||||
−0.772393 | + | 0.635145i | \(0.780940\pi\) | |||||||
\(278\) | −5.29612 | −0.317640 | ||||||||
\(279\) | −9.58484 | −0.573830 | ||||||||
\(280\) | −3.29374 | −0.196839 | ||||||||
\(281\) | 26.7109 | 1.59344 | 0.796719 | − | 0.604350i | \(-0.206567\pi\) | ||||
0.796719 | + | 0.604350i | \(0.206567\pi\) | |||||||
\(282\) | 0.238228 | 0.0141863 | ||||||||
\(283\) | −7.23375 | −0.430002 | −0.215001 | − | 0.976614i | \(-0.568975\pi\) | ||||
−0.215001 | + | 0.976614i | \(0.568975\pi\) | |||||||
\(284\) | 9.00802 | 0.534527 | ||||||||
\(285\) | 0.0688326 | 0.00407729 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.2546 | 2.19907 | ||||||||
\(288\) | 3.00509 | 0.177077 | ||||||||
\(289\) | −16.9922 | −0.999542 | ||||||||
\(290\) | −0.980131 | −0.0575553 | ||||||||
\(291\) | −4.09198 | −0.239876 | ||||||||
\(292\) | −13.8278 | −0.809211 | ||||||||
\(293\) | −14.5947 | −0.852633 | −0.426317 | − | 0.904574i | \(-0.640189\pi\) | ||||
−0.426317 | + | 0.904574i | \(0.640189\pi\) | |||||||
\(294\) | 0.839188 | 0.0489424 | ||||||||
\(295\) | 1.83604 | 0.106899 | ||||||||
\(296\) | 8.59161 | 0.499377 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.54364 | −0.147349 | ||||||||
\(299\) | 7.45042 | 0.430869 | ||||||||
\(300\) | −1.93117 | −0.111496 | ||||||||
\(301\) | 37.7530 | 2.17605 | ||||||||
\(302\) | −3.97775 | −0.228894 | ||||||||
\(303\) | −4.29171 | −0.246552 | ||||||||
\(304\) | 0.247229 | 0.0141796 | ||||||||
\(305\) | 10.0601 | 0.576041 | ||||||||
\(306\) | 0.0231471 | 0.00132323 | ||||||||
\(307\) | −28.5445 | −1.62912 | −0.814559 | − | 0.580080i | \(-0.803021\pi\) | ||||
−0.814559 | + | 0.580080i | \(0.803021\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.09280 | 0.119055 | ||||||||
\(310\) | −2.51468 | −0.142824 | ||||||||
\(311\) | −9.94803 | −0.564101 | −0.282050 | − | 0.959400i | \(-0.591015\pi\) | ||||
−0.282050 | + | 0.959400i | \(0.591015\pi\) | |||||||
\(312\) | −1.15474 | −0.0653742 | ||||||||
\(313\) | −16.4309 | −0.928731 | −0.464366 | − | 0.885644i | \(-0.653718\pi\) | ||||
−0.464366 | + | 0.885644i | \(0.653718\pi\) | |||||||
\(314\) | −3.90405 | −0.220318 | ||||||||
\(315\) | 3.19353 | 0.179935 | ||||||||
\(316\) | 1.52821 | 0.0859688 | ||||||||
\(317\) | 14.2106 | 0.798147 | 0.399073 | − | 0.916919i | \(-0.369332\pi\) | ||||
0.399073 | + | 0.916919i | \(0.369332\pi\) | |||||||
\(318\) | 0.228877 | 0.0128348 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −6.39507 | −0.357495 | ||||||||
\(321\) | 15.7409 | 0.878572 | ||||||||
\(322\) | 5.57549 | 0.310710 | ||||||||
\(323\) | 0.00607286 | 0.000337903 0 | ||||||||
\(324\) | −1.93117 | −0.107287 | ||||||||
\(325\) | 1.11961 | 0.0621046 | ||||||||
\(326\) | 0.892323 | 0.0494212 | ||||||||
\(327\) | 4.13271 | 0.228539 | ||||||||
\(328\) | −12.0317 | −0.664341 | ||||||||
\(329\) | 2.89979 | 0.159870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9119 | −0.599773 | −0.299886 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299886 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(332\) | 0.477441 | 0.0262030 | ||||||||
\(333\) | −8.33021 | −0.456493 | ||||||||
\(334\) | 5.93362 | 0.324673 | ||||||||
\(335\) | 9.53916 | 0.521180 | ||||||||
\(336\) | 11.4703 | 0.625758 | ||||||||
\(337\) | 5.88609 | 0.320636 | 0.160318 | − | 0.987065i | \(-0.448748\pi\) | ||||
0.160318 | + | 0.987065i | \(0.448748\pi\) | |||||||
\(338\) | −3.08180 | −0.167628 | ||||||||
\(339\) | 13.7550 | 0.747069 | ||||||||
\(340\) | −0.170380 | −0.00924015 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0180589 | 0.000976514 0 | ||||||||
\(343\) | −12.1398 | −0.655489 | ||||||||
\(344\) | −12.1927 | −0.657386 | ||||||||
\(345\) | 6.65450 | 0.358266 | ||||||||
\(346\) | 3.43463 | 0.184647 | ||||||||
\(347\) | −34.5043 | −1.85229 | −0.926143 | − | 0.377173i | \(-0.876896\pi\) | ||||
−0.926143 | + | 0.377173i | \(0.876896\pi\) | |||||||
\(348\) | 7.21451 | 0.386739 | ||||||||
\(349\) | 5.51356 | 0.295134 | 0.147567 | − | 0.989052i | \(-0.452856\pi\) | ||||
0.147567 | + | 0.989052i | \(0.452856\pi\) | |||||||
\(350\) | 0.837853 | 0.0447851 | ||||||||
\(351\) | 1.11961 | 0.0597602 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.8740 | −1.59003 | −0.795016 | − | 0.606589i | \(-0.792537\pi\) | ||||
−0.795016 | + | 0.606589i | \(0.792537\pi\) | |||||||
\(354\) | 0.481704 | 0.0256023 | ||||||||
\(355\) | −4.66454 | −0.247568 | ||||||||
\(356\) | 28.1540 | 1.49216 | ||||||||
\(357\) | 0.281754 | 0.0149120 | ||||||||
\(358\) | −3.98194 | −0.210452 | ||||||||
\(359\) | 35.9131 | 1.89542 | 0.947710 | − | 0.319133i | \(-0.103392\pi\) | ||||
0.947710 | + | 0.319133i | \(0.103392\pi\) | |||||||
\(360\) | −1.03138 | −0.0543585 | ||||||||
\(361\) | −18.9953 | −0.999751 | ||||||||
\(362\) | 0.370840 | 0.0194909 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.90488 | −0.361914 | ||||||||
\(365\) | 7.16034 | 0.374789 | ||||||||
\(366\) | 2.63937 | 0.137962 | ||||||||
\(367\) | −9.03087 | −0.471408 | −0.235704 | − | 0.971825i | \(-0.575740\pi\) | ||||
−0.235704 | + | 0.971825i | \(0.575740\pi\) | |||||||
\(368\) | 23.9013 | 1.24594 | ||||||||
\(369\) | 11.6657 | 0.607290 | ||||||||
\(370\) | −2.18551 | −0.113619 | ||||||||
\(371\) | 2.78596 | 0.144640 | ||||||||
\(372\) | 18.5099 | 0.959696 | ||||||||
\(373\) | −17.1994 | −0.890553 | −0.445277 | − | 0.895393i | \(-0.646895\pi\) | ||||
−0.445277 | + | 0.895393i | \(0.646895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −0.936514 | −0.0482970 | ||||||||
\(377\) | −4.18266 | −0.215418 | ||||||||
\(378\) | 0.837853 | 0.0430945 | ||||||||
\(379\) | −8.00208 | −0.411039 | −0.205520 | − | 0.978653i | \(-0.565888\pi\) | ||||
−0.205520 | + | 0.978653i | \(0.565888\pi\) | |||||||
\(380\) | −0.132927 | −0.00681903 | ||||||||
\(381\) | −7.89979 | −0.404718 | ||||||||
\(382\) | 1.28796 | 0.0658978 | ||||||||
\(383\) | 29.7131 | 1.51827 | 0.759135 | − | 0.650933i | \(-0.225622\pi\) | ||||
0.759135 | + | 0.650933i | \(0.225622\pi\) | |||||||
\(384\) | −7.68799 | −0.392326 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.55010 | −0.129797 | ||||||||
\(387\) | 11.8217 | 0.600933 | ||||||||
\(388\) | 7.90230 | 0.401178 | ||||||||
\(389\) | −0.595397 | −0.0301878 | −0.0150939 | − | 0.999886i | \(-0.504805\pi\) | ||||
−0.0150939 | + | 0.999886i | \(0.504805\pi\) | |||||||
\(390\) | 0.293740 | 0.0148741 | ||||||||
\(391\) | 0.587103 | 0.0296911 | ||||||||
\(392\) | −3.29899 | −0.166624 | ||||||||
\(393\) | 16.3539 | 0.824943 | ||||||||
\(394\) | 2.33176 | 0.117472 | ||||||||
\(395\) | −0.791342 | −0.0398167 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66950 | 0.0837898 | 0.0418949 | − | 0.999122i | \(-0.486661\pi\) | ||||
0.0418949 | + | 0.999122i | \(0.486661\pi\) | |||||||
\(398\) | 4.73247 | 0.237217 | ||||||||
\(399\) | 0.219819 | 0.0110047 | ||||||||
\(400\) | 3.59174 | 0.179587 | ||||||||
\(401\) | −11.3690 | −0.567741 | −0.283870 | − | 0.958863i | \(-0.591619\pi\) | ||||
−0.283870 | + | 0.958863i | \(0.591619\pi\) | |||||||
\(402\) | 2.50269 | 0.124823 | ||||||||
\(403\) | −10.7313 | −0.534562 | ||||||||
\(404\) | 8.28802 | 0.412344 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −3.13008 | −0.155343 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.0909950 | −0.00450492 | ||||||||
\(409\) | 8.59766 | 0.425127 | 0.212563 | − | 0.977147i | \(-0.431819\pi\) | ||||
0.212563 | + | 0.977147i | \(0.431819\pi\) | |||||||
\(410\) | 3.06060 | 0.151152 | ||||||||
\(411\) | 7.73208 | 0.381395 | ||||||||
\(412\) | −4.04156 | −0.199113 | ||||||||
\(413\) | 5.86345 | 0.288522 | ||||||||
\(414\) | 1.74587 | 0.0858050 | ||||||||
\(415\) | −0.247229 | −0.0121360 | ||||||||
\(416\) | 3.36452 | 0.164959 | ||||||||
\(417\) | −20.1865 | −0.988536 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.3915 | 1.53358 | 0.766789 | − | 0.641899i | \(-0.221853\pi\) | ||||
0.766789 | + | 0.641899i | \(0.221853\pi\) | |||||||
\(420\) | −6.16724 | −0.300930 | ||||||||
\(421\) | −4.57893 | −0.223163 | −0.111582 | − | 0.993755i | \(-0.535592\pi\) | ||||
−0.111582 | + | 0.993755i | \(0.535592\pi\) | |||||||
\(422\) | −4.71665 | −0.229603 | ||||||||
\(423\) | 0.908020 | 0.0441495 | ||||||||
\(424\) | −0.899752 | −0.0436958 | ||||||||
\(425\) | 0.0882264 | 0.00427961 | ||||||||
\(426\) | −1.22379 | −0.0592927 | ||||||||
\(427\) | 32.1273 | 1.55475 | ||||||||
\(428\) | −30.3983 | −1.46936 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.10155 | 0.149570 | ||||||||
\(431\) | −15.9074 | −0.766234 | −0.383117 | − | 0.923700i | \(-0.625149\pi\) | ||||
−0.383117 | + | 0.923700i | \(0.625149\pi\) | |||||||
\(432\) | 3.59174 | 0.172808 | ||||||||
\(433\) | 15.8030 | 0.759441 | 0.379721 | − | 0.925101i | \(-0.376020\pi\) | ||||
0.379721 | + | 0.925101i | \(0.376020\pi\) | |||||||
\(434\) | −8.03069 | −0.385485 | ||||||||
\(435\) | −3.73583 | −0.179119 | ||||||||
\(436\) | −7.98096 | −0.382218 | ||||||||
\(437\) | 0.458047 | 0.0219113 | ||||||||
\(438\) | 1.87858 | 0.0897622 | ||||||||
\(439\) | −21.5227 | −1.02722 | −0.513611 | − | 0.858023i | \(-0.671693\pi\) | ||||
−0.513611 | + | 0.858023i | \(0.671693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.19862 | 0.152315 | ||||||||
\(442\) | 0.0259156 | 0.00123268 | ||||||||
\(443\) | 10.1769 | 0.483519 | 0.241760 | − | 0.970336i | \(-0.422275\pi\) | ||||
0.241760 | + | 0.970336i | \(0.422275\pi\) | |||||||
\(444\) | 16.0870 | 0.763456 | ||||||||
\(445\) | −14.5788 | −0.691100 | ||||||||
\(446\) | −3.60717 | −0.170804 | ||||||||
\(447\) | −9.69523 | −0.458569 | ||||||||
\(448\) | −20.4228 | −0.964888 | ||||||||
\(449\) | 38.6088 | 1.82206 | 0.911031 | − | 0.412338i | \(-0.135288\pi\) | ||||
0.911031 | + | 0.412338i | \(0.135288\pi\) | |||||||
\(450\) | 0.262360 | 0.0123678 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −26.5632 | −1.24943 | ||||||||
\(453\) | −15.1615 | −0.712347 | ||||||||
\(454\) | −0.173875 | −0.00816035 | ||||||||
\(455\) | 3.57549 | 0.167622 | ||||||||
\(456\) | −0.0709926 | −0.00332453 | ||||||||
\(457\) | −23.3637 | −1.09291 | −0.546455 | − | 0.837488i | \(-0.684023\pi\) | ||||
−0.546455 | + | 0.837488i | \(0.684023\pi\) | |||||||
\(458\) | −1.96518 | −0.0918269 | ||||||||
\(459\) | 0.0882264 | 0.00411806 | ||||||||
\(460\) | −12.8510 | −0.599179 | ||||||||
\(461\) | −4.93120 | −0.229669 | −0.114834 | − | 0.993385i | \(-0.536634\pi\) | ||||
−0.114834 | + | 0.993385i | \(0.536634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9648 | 1.25316 | 0.626580 | − | 0.779357i | \(-0.284454\pi\) | ||||
0.626580 | + | 0.779357i | \(0.284454\pi\) | |||||||
\(464\) | −13.4181 | −0.622922 | ||||||||
\(465\) | −9.58484 | −0.444487 | ||||||||
\(466\) | −2.76143 | −0.127921 | ||||||||
\(467\) | −23.6778 | −1.09568 | −0.547839 | − | 0.836584i | \(-0.684550\pi\) | ||||
−0.547839 | + | 0.836584i | \(0.684550\pi\) | |||||||
\(468\) | −2.16215 | −0.0999453 | ||||||||
\(469\) | 30.4636 | 1.40668 | ||||||||
\(470\) | 0.238228 | 0.0109886 | ||||||||
\(471\) | −14.8805 | −0.685659 | ||||||||
\(472\) | −1.89366 | −0.0871627 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.207616 | −0.00953613 | ||||||||
\(475\) | 0.0688326 | 0.00315826 | ||||||||
\(476\) | −0.544113 | −0.0249394 | ||||||||
\(477\) | 0.872377 | 0.0399434 | ||||||||
\(478\) | −4.48011 | −0.204915 | ||||||||
\(479\) | 13.5240 | 0.617929 | 0.308964 | − | 0.951074i | \(-0.400018\pi\) | ||||
0.308964 | + | 0.951074i | \(0.400018\pi\) | |||||||
\(480\) | 3.00509 | 0.137163 | ||||||||
\(481\) | −9.32655 | −0.425254 | ||||||||
\(482\) | 4.38356 | 0.199666 | ||||||||
\(483\) | 21.2513 | 0.966969 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.09198 | −0.185807 | ||||||||
\(486\) | 0.262360 | 0.0119009 | ||||||||
\(487\) | −8.62704 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(488\) | −10.3758 | −0.469691 | ||||||||
\(489\) | 3.40114 | 0.153805 | ||||||||
\(490\) | 0.839188 | 0.0379106 | ||||||||
\(491\) | 25.9068 | 1.16916 | 0.584579 | − | 0.811337i | \(-0.301260\pi\) | ||||
0.584579 | + | 0.811337i | \(0.301260\pi\) | |||||||
\(492\) | −22.5283 | −1.01566 | ||||||||
\(493\) | −0.329599 | −0.0148444 | ||||||||
\(494\) | 0.0202189 | 0.000909690 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.4263 | −1.54579 | ||||||||
\(497\) | −14.8963 | −0.668193 | ||||||||
\(498\) | −0.0648629 | −0.00290658 | ||||||||
\(499\) | −28.0475 | −1.25558 | −0.627790 | − | 0.778383i | \(-0.716040\pi\) | ||||
−0.627790 | + | 0.778383i | \(0.716040\pi\) | |||||||
\(500\) | −1.93117 | −0.0863644 | ||||||||
\(501\) | 22.6164 | 1.01042 | ||||||||
\(502\) | −1.34792 | −0.0601604 | ||||||||
\(503\) | −29.3999 | −1.31088 | −0.655438 | − | 0.755249i | \(-0.727516\pi\) | ||||
−0.655438 | + | 0.755249i | \(0.727516\pi\) | |||||||
\(504\) | −3.29374 | −0.146715 | ||||||||
\(505\) | −4.29171 | −0.190979 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.7465 | −0.521680 | ||||||||
\(508\) | 15.2558 | 0.676867 | ||||||||
\(509\) | −19.3904 | −0.859463 | −0.429731 | − | 0.902957i | \(-0.641392\pi\) | ||||
−0.429731 | + | 0.902957i | \(0.641392\pi\) | |||||||
\(510\) | 0.0231471 | 0.00102497 | ||||||||
\(511\) | 22.8667 | 1.01156 | ||||||||
\(512\) | 18.2024 | 0.804440 | ||||||||
\(513\) | 0.0688326 | 0.00303903 | ||||||||
\(514\) | −0.970270 | −0.0427968 | ||||||||
\(515\) | 2.09280 | 0.0922200 | ||||||||
\(516\) | −22.8298 | −1.00502 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6.97949 | −0.306661 | ||||||||
\(519\) | 13.0913 | 0.574644 | ||||||||
\(520\) | −1.15474 | −0.0506387 | ||||||||
\(521\) | 25.0062 | 1.09554 | 0.547771 | − | 0.836628i | \(-0.315477\pi\) | ||||
0.547771 | + | 0.836628i | \(0.315477\pi\) | |||||||
\(522\) | −0.980131 | −0.0428992 | ||||||||
\(523\) | 2.18761 | 0.0956577 | 0.0478288 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478288 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(524\) | −31.5820 | −1.37967 | ||||||||
\(525\) | 3.19353 | 0.139377 | ||||||||
\(526\) | −8.29883 | −0.361846 | ||||||||
\(527\) | −0.845637 | −0.0368365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2824 | 0.925322 | ||||||||
\(530\) | 0.228877 | 0.00994177 | ||||||||
\(531\) | 1.83604 | 0.0796775 | ||||||||
\(532\) | −0.424507 | −0.0184047 | ||||||||
\(533\) | 13.0610 | 0.565733 | ||||||||
\(534\) | −3.82488 | −0.165519 | ||||||||
\(535\) | 15.7409 | 0.680539 | ||||||||
\(536\) | −9.83850 | −0.424958 | ||||||||
\(537\) | −15.1774 | −0.654954 | ||||||||
\(538\) | −3.87648 | −0.167127 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.93117 | −0.0831042 | ||||||||
\(541\) | −13.5583 | −0.582918 | −0.291459 | − | 0.956583i | \(-0.594141\pi\) | ||||
−0.291459 | + | 0.956583i | \(0.594141\pi\) | |||||||
\(542\) | 5.13882 | 0.220731 | ||||||||
\(543\) | 1.41348 | 0.0606582 | ||||||||
\(544\) | 0.265128 | 0.0113673 | ||||||||
\(545\) | 4.13271 | 0.177026 | ||||||||
\(546\) | 0.938065 | 0.0401455 | ||||||||
\(547\) | 3.71282 | 0.158749 | 0.0793743 | − | 0.996845i | \(-0.474708\pi\) | ||||
0.0793743 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(548\) | −14.9319 | −0.637861 | ||||||||
\(549\) | 10.0601 | 0.429356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.257147 | −0.0109548 | ||||||||
\(552\) | −6.86332 | −0.292122 | ||||||||
\(553\) | −2.52717 | −0.107466 | ||||||||
\(554\) | −6.74536 | −0.286583 | ||||||||
\(555\) | −8.33021 | −0.353598 | ||||||||
\(556\) | 38.9835 | 1.65327 | ||||||||
\(557\) | −6.57520 | −0.278600 | −0.139300 | − | 0.990250i | \(-0.544485\pi\) | ||||
−0.139300 | + | 0.990250i | \(0.544485\pi\) | |||||||
\(558\) | −2.51468 | −0.106455 | ||||||||
\(559\) | 13.2357 | 0.559810 | ||||||||
\(560\) | 11.4703 | 0.484710 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.00786 | 0.295609 | ||||||||
\(563\) | 6.90876 | 0.291170 | 0.145585 | − | 0.989346i | \(-0.453494\pi\) | ||||
0.145585 | + | 0.989346i | \(0.453494\pi\) | |||||||
\(564\) | −1.75354 | −0.0738373 | ||||||||
\(565\) | 13.7550 | 0.578678 | ||||||||
\(566\) | −1.89784 | −0.0797723 | ||||||||
\(567\) | 3.19353 | 0.134116 | ||||||||
\(568\) | 4.81092 | 0.201862 | ||||||||
\(569\) | 6.74768 | 0.282878 | 0.141439 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141439 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(570\) | 0.0180589 | 0.000756404 0 | ||||||||
\(571\) | −9.68928 | −0.405484 | −0.202742 | − | 0.979232i | \(-0.564985\pi\) | ||||
−0.202742 | + | 0.979232i | \(0.564985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.90914 | 0.205082 | ||||||||
\(574\) | 9.77411 | 0.407963 | ||||||||
\(575\) | 6.65450 | 0.277512 | ||||||||
\(576\) | −6.39507 | −0.266461 | ||||||||
\(577\) | 15.1498 | 0.630695 | 0.315348 | − | 0.948976i | \(-0.397879\pi\) | ||||
0.315348 | + | 0.948976i | \(0.397879\pi\) | |||||||
\(578\) | −4.45807 | −0.185431 | ||||||||
\(579\) | −9.71987 | −0.403944 | ||||||||
\(580\) | 7.21451 | 0.299566 | ||||||||
\(581\) | −0.789532 | −0.0327553 | ||||||||
\(582\) | −1.07357 | −0.0445009 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.38503 | −0.305595 | ||||||||
\(585\) | 1.11961 | 0.0462900 | ||||||||
\(586\) | −3.82907 | −0.158177 | ||||||||
\(587\) | −27.0112 | −1.11487 | −0.557436 | − | 0.830220i | \(-0.688215\pi\) | ||||
−0.557436 | + | 0.830220i | \(0.688215\pi\) | |||||||
\(588\) | −6.17706 | −0.254738 | ||||||||
\(589\) | −0.659750 | −0.0271845 | ||||||||
\(590\) | 0.481704 | 0.0198314 | ||||||||
\(591\) | 8.88764 | 0.365589 | ||||||||
\(592\) | −29.9200 | −1.22970 | ||||||||
\(593\) | 22.1863 | 0.911084 | 0.455542 | − | 0.890214i | \(-0.349446\pi\) | ||||
0.455542 | + | 0.890214i | \(0.349446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.281754 | 0.0115508 | ||||||||
\(596\) | 18.7231 | 0.766929 | ||||||||
\(597\) | 18.0381 | 0.738250 | ||||||||
\(598\) | 1.95469 | 0.0799332 | ||||||||
\(599\) | 11.7487 | 0.480038 | 0.240019 | − | 0.970768i | \(-0.422846\pi\) | ||||
0.240019 | + | 0.970768i | \(0.422846\pi\) | |||||||
\(600\) | −1.03138 | −0.0421059 | ||||||||
\(601\) | −34.3806 | −1.40242 | −0.701208 | − | 0.712957i | \(-0.747355\pi\) | ||||
−0.701208 | + | 0.712957i | \(0.747355\pi\) | |||||||
\(602\) | 9.90488 | 0.403693 | ||||||||
\(603\) | 9.53916 | 0.388465 | ||||||||
\(604\) | 29.2793 | 1.19136 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.12597 | −0.0457395 | ||||||||
\(607\) | −13.6298 | −0.553215 | −0.276607 | − | 0.960983i | \(-0.589210\pi\) | ||||
−0.276607 | + | 0.960983i | \(0.589210\pi\) | |||||||
\(608\) | 0.206848 | 0.00838880 | ||||||||
\(609\) | −11.9305 | −0.483447 | ||||||||
\(610\) | 2.63937 | 0.106865 | ||||||||
\(611\) | 1.01663 | 0.0411283 | ||||||||
\(612\) | −0.170380 | −0.00688720 | ||||||||
\(613\) | 6.82994 | 0.275858 | 0.137929 | − | 0.990442i | \(-0.455955\pi\) | ||||
0.137929 | + | 0.990442i | \(0.455955\pi\) | |||||||
\(614\) | −7.48892 | −0.302228 | ||||||||
\(615\) | 11.6657 | 0.470405 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.3730 | 1.22277 | 0.611386 | − | 0.791333i | \(-0.290612\pi\) | ||||
0.611386 | + | 0.791333i | \(0.290612\pi\) | |||||||
\(618\) | 0.549068 | 0.0220867 | ||||||||
\(619\) | −25.7879 | −1.03650 | −0.518252 | − | 0.855228i | \(-0.673417\pi\) | ||||
−0.518252 | + | 0.855228i | \(0.673417\pi\) | |||||||
\(620\) | 18.5099 | 0.743377 | ||||||||
\(621\) | 6.65450 | 0.267036 | ||||||||
\(622\) | −2.60996 | −0.104650 | ||||||||
\(623\) | −46.5577 | −1.86529 | ||||||||
\(624\) | 4.02134 | 0.160982 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.31081 | −0.172295 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.7368 | 1.14672 | ||||||||
\(629\) | −0.734945 | −0.0293042 | ||||||||
\(630\) | 0.837853 | 0.0333809 | ||||||||
\(631\) | −25.5656 | −1.01775 | −0.508876 | − | 0.860840i | \(-0.669939\pi\) | ||||
−0.508876 | + | 0.860840i | \(0.669939\pi\) | |||||||
\(632\) | 0.816174 | 0.0324657 | ||||||||
\(633\) | −17.9778 | −0.714554 | ||||||||
\(634\) | 3.72829 | 0.148069 | ||||||||
\(635\) | −7.89979 | −0.313494 | ||||||||
\(636\) | −1.68471 | −0.0668030 | ||||||||
\(637\) | 3.58119 | 0.141892 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.66454 | −0.184527 | ||||||||
\(640\) | −7.68799 | −0.303894 | ||||||||
\(641\) | −4.07262 | −0.160859 | −0.0804294 | − | 0.996760i | \(-0.525629\pi\) | ||||
−0.0804294 | + | 0.996760i | \(0.525629\pi\) | |||||||
\(642\) | 4.12978 | 0.162990 | ||||||||
\(643\) | 11.3298 | 0.446804 | 0.223402 | − | 0.974726i | \(-0.428284\pi\) | ||||
0.223402 | + | 0.974726i | \(0.428284\pi\) | |||||||
\(644\) | −41.0399 | −1.61720 | ||||||||
\(645\) | 11.8217 | 0.465480 | ||||||||
\(646\) | 0.00159327 | 6.26865e−5 0 | ||||||||
\(647\) | −36.8480 | −1.44864 | −0.724322 | − | 0.689462i | \(-0.757847\pi\) | ||||
−0.724322 | + | 0.689462i | \(0.757847\pi\) | |||||||
\(648\) | −1.03138 | −0.0405164 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.293740 | 0.0115214 | ||||||||
\(651\) | −30.6095 | −1.19968 | ||||||||
\(652\) | −6.56818 | −0.257230 | ||||||||
\(653\) | 15.2768 | 0.597827 | 0.298914 | − | 0.954280i | \(-0.403376\pi\) | ||||
0.298914 | + | 0.954280i | \(0.403376\pi\) | |||||||
\(654\) | 1.08426 | 0.0423978 | ||||||||
\(655\) | 16.3539 | 0.638998 | ||||||||
\(656\) | 41.9001 | 1.63592 | ||||||||
\(657\) | 7.16034 | 0.279351 | ||||||||
\(658\) | 0.760787 | 0.0296586 | ||||||||
\(659\) | −11.8996 | −0.463544 | −0.231772 | − | 0.972770i | \(-0.574452\pi\) | ||||
−0.231772 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.8648 | −1.74504 | −0.872520 | − | 0.488578i | \(-0.837516\pi\) | ||||
−0.872520 | + | 0.488578i | \(0.837516\pi\) | |||||||
\(662\) | −2.86284 | −0.111268 | ||||||||
\(663\) | 0.0987789 | 0.00383625 | ||||||||
\(664\) | 0.254987 | 0.00989542 | ||||||||
\(665\) | 0.219819 | 0.00852421 | ||||||||
\(666\) | −2.18551 | −0.0846868 | ||||||||
\(667\) | −24.8601 | −0.962587 | ||||||||
\(668\) | −43.6760 | −1.68987 | ||||||||
\(669\) | −13.7489 | −0.531565 | ||||||||
\(670\) | 2.50269 | 0.0966874 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 9.59683 | 0.370206 | ||||||||
\(673\) | 19.1067 | 0.736508 | 0.368254 | − | 0.929725i | \(-0.379956\pi\) | ||||
0.368254 | + | 0.929725i | \(0.379956\pi\) | |||||||
\(674\) | 1.54427 | 0.0594832 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 22.6844 | 0.872478 | ||||||||
\(677\) | −46.4614 | −1.78566 | −0.892829 | − | 0.450396i | \(-0.851283\pi\) | ||||
−0.892829 | + | 0.450396i | \(0.851283\pi\) | |||||||
\(678\) | 3.60876 | 0.138594 | ||||||||
\(679\) | −13.0678 | −0.501498 | ||||||||
\(680\) | −0.0909950 | −0.00348950 | ||||||||
\(681\) | −0.662735 | −0.0253961 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.5651 | −1.62871 | −0.814355 | − | 0.580367i | \(-0.802909\pi\) | ||||
−0.814355 | + | 0.580367i | \(0.802909\pi\) | |||||||
\(684\) | −0.132927 | −0.00508260 | ||||||||
\(685\) | 7.73208 | 0.295427 | ||||||||
\(686\) | −3.18500 | −0.121604 | ||||||||
\(687\) | −7.49041 | −0.285777 | ||||||||
\(688\) | 42.4606 | 1.61880 | ||||||||
\(689\) | 0.976719 | 0.0372100 | ||||||||
\(690\) | 1.74587 | 0.0664643 | ||||||||
\(691\) | 35.1352 | 1.33660 | 0.668302 | − | 0.743890i | \(-0.267021\pi\) | ||||
0.668302 | + | 0.743890i | \(0.267021\pi\) | |||||||
\(692\) | −25.2815 | −0.961057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.05253 | −0.343629 | ||||||||
\(695\) | −20.1865 | −0.765716 | ||||||||
\(696\) | 3.85306 | 0.146050 | ||||||||
\(697\) | 1.02922 | 0.0389845 | ||||||||
\(698\) | 1.44654 | 0.0547522 | ||||||||
\(699\) | −10.5254 | −0.398106 | ||||||||
\(700\) | −6.16724 | −0.233100 | ||||||||
\(701\) | 30.6713 | 1.15844 | 0.579219 | − | 0.815172i | \(-0.303358\pi\) | ||||
0.579219 | + | 0.815172i | \(0.303358\pi\) | |||||||
\(702\) | 0.293740 | 0.0110865 | ||||||||
\(703\) | −0.573390 | −0.0216258 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.908020 | 0.0341980 | ||||||||
\(706\) | −7.83773 | −0.294977 | ||||||||
\(707\) | −13.7057 | −0.515456 | ||||||||
\(708\) | −3.54571 | −0.133256 | ||||||||
\(709\) | 15.0924 | 0.566806 | 0.283403 | − | 0.959001i | \(-0.408537\pi\) | ||||
0.283403 | + | 0.959001i | \(0.408537\pi\) | |||||||
\(710\) | −1.22379 | −0.0459280 | ||||||||
\(711\) | −0.791342 | −0.0296777 | ||||||||
\(712\) | 15.0363 | 0.563507 | ||||||||
\(713\) | −63.7824 | −2.38867 | ||||||||
\(714\) | 0.0739208 | 0.00276642 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.3101 | 1.09537 | ||||||||
\(717\) | −17.0762 | −0.637723 | ||||||||
\(718\) | 9.42215 | 0.351631 | ||||||||
\(719\) | −6.19020 | −0.230856 | −0.115428 | − | 0.993316i | \(-0.536824\pi\) | ||||
−0.115428 | + | 0.993316i | \(0.536824\pi\) | |||||||
\(720\) | 3.59174 | 0.133856 | ||||||||
\(721\) | 6.68343 | 0.248904 | ||||||||
\(722\) | −4.98359 | −0.185470 | ||||||||
\(723\) | 16.7082 | 0.621385 | ||||||||
\(724\) | −2.72967 | −0.101447 | ||||||||
\(725\) | −3.73583 | −0.138745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.1515 | −0.673200 | −0.336600 | − | 0.941648i | \(-0.609277\pi\) | ||||
−0.336600 | + | 0.941648i | \(0.609277\pi\) | |||||||
\(728\) | −3.68769 | −0.136675 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.87858 | 0.0695295 | ||||||||
\(731\) | 1.04299 | 0.0385764 | ||||||||
\(732\) | −19.4278 | −0.718072 | ||||||||
\(733\) | 28.7409 | 1.06157 | 0.530785 | − | 0.847507i | \(-0.321897\pi\) | ||||
0.530785 | + | 0.847507i | \(0.321897\pi\) | |||||||
\(734\) | −2.36934 | −0.0874538 | ||||||||
\(735\) | 3.19862 | 0.117983 | ||||||||
\(736\) | 19.9974 | 0.737113 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.06060 | 0.112662 | ||||||||
\(739\) | 46.8341 | 1.72282 | 0.861411 | − | 0.507909i | \(-0.169581\pi\) | ||||
0.861411 | + | 0.507909i | \(0.169581\pi\) | |||||||
\(740\) | 16.0870 | 0.591371 | ||||||||
\(741\) | 0.0770654 | 0.00283107 | ||||||||
\(742\) | 0.730924 | 0.0268331 | ||||||||
\(743\) | −26.6108 | −0.976254 | −0.488127 | − | 0.872773i | \(-0.662320\pi\) | ||||
−0.488127 | + | 0.872773i | \(0.662320\pi\) | |||||||
\(744\) | 9.88562 | 0.362424 | ||||||||
\(745\) | −9.69523 | −0.355206 | ||||||||
\(746\) | −4.51244 | −0.165212 | ||||||||
\(747\) | −0.247229 | −0.00904564 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.2691 | 1.83679 | ||||||||
\(750\) | 0.262360 | 0.00958002 | ||||||||
\(751\) | 40.5821 | 1.48086 | 0.740431 | − | 0.672132i | \(-0.234621\pi\) | ||||
0.740431 | + | 0.672132i | \(0.234621\pi\) | |||||||
\(752\) | 3.26137 | 0.118930 | ||||||||
\(753\) | −5.13767 | −0.187227 | ||||||||
\(754\) | −1.09736 | −0.0399635 | ||||||||
\(755\) | −15.1615 | −0.551782 | ||||||||
\(756\) | −6.16724 | −0.224300 | ||||||||
\(757\) | 32.7179 | 1.18915 | 0.594576 | − | 0.804039i | \(-0.297320\pi\) | ||||
0.594576 | + | 0.804039i | \(0.297320\pi\) | |||||||
\(758\) | −2.09942 | −0.0762545 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0709926 | −0.00257517 | ||||||||
\(761\) | 2.62938 | 0.0953148 | 0.0476574 | − | 0.998864i | \(-0.484824\pi\) | ||||
0.0476574 | + | 0.998864i | \(0.484824\pi\) | |||||||
\(762\) | −2.07259 | −0.0750819 | ||||||||
\(763\) | 13.1979 | 0.477797 | ||||||||
\(764\) | −9.48037 | −0.342988 | ||||||||
\(765\) | 0.0882264 | 0.00318983 | ||||||||
\(766\) | 7.79553 | 0.281664 | ||||||||
\(767\) | 2.05565 | 0.0742251 | ||||||||
\(768\) | 10.7731 | 0.388742 | ||||||||
\(769\) | −3.23559 | −0.116678 | −0.0583392 | − | 0.998297i | \(-0.518581\pi\) | ||||
−0.0583392 | + | 0.998297i | \(0.518581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.69824 | −0.133189 | ||||||||
\(772\) | 18.7707 | 0.675572 | ||||||||
\(773\) | 43.6365 | 1.56950 | 0.784748 | − | 0.619815i | \(-0.212792\pi\) | ||||
0.784748 | + | 0.619815i | \(0.212792\pi\) | |||||||
\(774\) | 3.10155 | 0.111483 | ||||||||
\(775\) | −9.58484 | −0.344298 | ||||||||
\(776\) | 4.22039 | 0.151503 | ||||||||
\(777\) | −26.6027 | −0.954368 | ||||||||
\(778\) | −0.156208 | −0.00560033 | ||||||||
\(779\) | 0.802978 | 0.0287697 | ||||||||
\(780\) | −2.16215 | −0.0774173 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.154032 | 0.00550818 | ||||||||
\(783\) | −3.73583 | −0.133508 | ||||||||
\(784\) | 11.4886 | 0.410307 | ||||||||
\(785\) | −14.8805 | −0.531109 | ||||||||
\(786\) | 4.29059 | 0.153040 | ||||||||
\(787\) | 4.56420 | 0.162696 | 0.0813480 | − | 0.996686i | \(-0.474077\pi\) | ||||
0.0813480 | + | 0.996686i | \(0.474077\pi\) | |||||||
\(788\) | −17.1635 | −0.611425 | ||||||||
\(789\) | −31.6315 | −1.12611 | ||||||||
\(790\) | −0.207616 | −0.00738666 | ||||||||
\(791\) | 43.9270 | 1.56186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2634 | 0.399974 | ||||||||
\(794\) | 0.438009 | 0.0155444 | ||||||||
\(795\) | 0.872377 | 0.0309400 | ||||||||
\(796\) | −34.8346 | −1.23468 | ||||||||
\(797\) | −11.1806 | −0.396036 | −0.198018 | − | 0.980198i | \(-0.563450\pi\) | ||||
−0.198018 | + | 0.980198i | \(0.563450\pi\) | |||||||
\(798\) | 0.0576716 | 0.00204155 | ||||||||
\(799\) | 0.0801114 | 0.00283414 | ||||||||
\(800\) | 3.00509 | 0.106246 | ||||||||
\(801\) | −14.5788 | −0.515116 | ||||||||
\(802\) | −2.98277 | −0.105325 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18.4217 | −0.649684 | ||||||||
\(805\) | 21.2513 | 0.749011 | ||||||||
\(806\) | −2.81545 | −0.0991699 | ||||||||
\(807\) | −14.7754 | −0.520120 | ||||||||
\(808\) | 4.42639 | 0.155720 | ||||||||
\(809\) | 45.5417 | 1.60116 | 0.800581 | − | 0.599225i | \(-0.204525\pi\) | ||||
0.800581 | + | 0.599225i | \(0.204525\pi\) | |||||||
\(810\) | 0.262360 | 0.00921838 | ||||||||
\(811\) | −2.82363 | −0.0991511 | −0.0495755 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495755 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(812\) | 23.0397 | 0.808537 | ||||||||
\(813\) | 19.5869 | 0.686943 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.40114 | 0.119137 | ||||||||
\(816\) | 0.316887 | 0.0110933 | ||||||||
\(817\) | 0.813721 | 0.0284685 | ||||||||
\(818\) | 2.25568 | 0.0788679 | ||||||||
\(819\) | 3.57549 | 0.124938 | ||||||||
\(820\) | −22.5283 | −0.786724 | ||||||||
\(821\) | 23.4117 | 0.817073 | 0.408536 | − | 0.912742i | \(-0.366039\pi\) | ||||
0.408536 | + | 0.912742i | \(0.366039\pi\) | |||||||
\(822\) | 2.02859 | 0.0707550 | ||||||||
\(823\) | 46.1046 | 1.60711 | 0.803553 | − | 0.595233i | \(-0.202940\pi\) | ||||
0.803553 | + | 0.595233i | \(0.202940\pi\) | |||||||
\(824\) | −2.15848 | −0.0751941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.53833 | 0.0535255 | ||||||||
\(827\) | 43.4496 | 1.51089 | 0.755445 | − | 0.655212i | \(-0.227421\pi\) | ||||
0.755445 | + | 0.655212i | \(0.227421\pi\) | |||||||
\(828\) | −12.8510 | −0.446602 | ||||||||
\(829\) | 15.4712 | 0.537335 | 0.268668 | − | 0.963233i | \(-0.413417\pi\) | ||||
0.268668 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(830\) | −0.0648629 | −0.00225142 | ||||||||
\(831\) | −25.7104 | −0.891883 | ||||||||
\(832\) | −7.15996 | −0.248227 | ||||||||
\(833\) | 0.282202 | 0.00977773 | ||||||||
\(834\) | −5.29612 | −0.183389 | ||||||||
\(835\) | 22.6164 | 0.782671 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.58484 | −0.331301 | ||||||||
\(838\) | 8.23588 | 0.284504 | ||||||||
\(839\) | 30.2181 | 1.04324 | 0.521622 | − | 0.853177i | \(-0.325327\pi\) | ||||
0.521622 | + | 0.853177i | \(0.325327\pi\) | |||||||
\(840\) | −3.29374 | −0.113645 | ||||||||
\(841\) | −15.0436 | −0.518744 | ||||||||
\(842\) | −1.20133 | −0.0414005 | ||||||||
\(843\) | 26.7109 | 0.919971 | ||||||||
\(844\) | 34.7182 | 1.19505 | ||||||||
\(845\) | −11.7465 | −0.404091 | ||||||||
\(846\) | 0.238228 | 0.00819045 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.13335 | 0.107600 | ||||||||
\(849\) | −7.23375 | −0.248262 | ||||||||
\(850\) | 0.0231471 | 0.000793938 0 | ||||||||
\(851\) | −55.4334 | −1.90023 | ||||||||
\(852\) | 9.00802 | 0.308610 | ||||||||
\(853\) | 2.00908 | 0.0687897 | 0.0343949 | − | 0.999408i | \(-0.489050\pi\) | ||||
0.0343949 | + | 0.999408i | \(0.489050\pi\) | |||||||
\(854\) | 8.42890 | 0.288431 | ||||||||
\(855\) | 0.0688326 | 0.00235403 | ||||||||
\(856\) | −16.2349 | −0.554896 | ||||||||
\(857\) | 33.6095 | 1.14808 | 0.574039 | − | 0.818828i | \(-0.305376\pi\) | ||||
0.574039 | + | 0.818828i | \(0.305376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7301 | −0.468466 | −0.234233 | − | 0.972180i | \(-0.575258\pi\) | ||||
−0.234233 | + | 0.972180i | \(0.575258\pi\) | |||||||
\(860\) | −22.8298 | −0.778488 | ||||||||
\(861\) | 37.2546 | 1.26963 | ||||||||
\(862\) | −4.17347 | −0.142149 | ||||||||
\(863\) | 8.75829 | 0.298136 | 0.149068 | − | 0.988827i | \(-0.452373\pi\) | ||||
0.149068 | + | 0.988827i | \(0.452373\pi\) | |||||||
\(864\) | 3.00509 | 0.102235 | ||||||||
\(865\) | 13.0913 | 0.445117 | ||||||||
\(866\) | 4.14606 | 0.140889 | ||||||||
\(867\) | −16.9922 | −0.577086 | ||||||||
\(868\) | 59.1120 | 2.00639 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.980131 | −0.0332296 | ||||||||
\(871\) | 10.6801 | 0.361881 | ||||||||
\(872\) | −4.26239 | −0.144343 | ||||||||
\(873\) | −4.09198 | −0.138493 | ||||||||
\(874\) | 0.120173 | 0.00406491 | ||||||||
\(875\) | 3.19353 | 0.107961 | ||||||||
\(876\) | −13.8278 | −0.467198 | ||||||||
\(877\) | 15.2463 | 0.514830 | 0.257415 | − | 0.966301i | \(-0.417129\pi\) | ||||
0.257415 | + | 0.966301i | \(0.417129\pi\) | |||||||
\(878\) | −5.64669 | −0.190566 | ||||||||
\(879\) | −14.5947 | −0.492268 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8486 | −0.533953 | −0.266977 | − | 0.963703i | \(-0.586025\pi\) | ||||
−0.266977 | + | 0.963703i | \(0.586025\pi\) | |||||||
\(882\) | 0.839188 | 0.0282569 | ||||||||
\(883\) | −32.9606 | −1.10921 | −0.554606 | − | 0.832113i | \(-0.687131\pi\) | ||||
−0.554606 | + | 0.832113i | \(0.687131\pi\) | |||||||
\(884\) | −0.190759 | −0.00641590 | ||||||||
\(885\) | 1.83604 | 0.0617179 | ||||||||
\(886\) | 2.67001 | 0.0897007 | ||||||||
\(887\) | −11.2525 | −0.377820 | −0.188910 | − | 0.981994i | \(-0.560495\pi\) | ||||
−0.188910 | + | 0.981994i | \(0.560495\pi\) | |||||||
\(888\) | 8.59161 | 0.288316 | ||||||||
\(889\) | −25.2282 | −0.846126 | ||||||||
\(890\) | −3.82488 | −0.128210 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.5515 | 0.889010 | ||||||||
\(893\) | 0.0625014 | 0.00209153 | ||||||||
\(894\) | −2.54364 | −0.0850720 | ||||||||
\(895\) | −15.1774 | −0.507325 | ||||||||
\(896\) | −24.5518 | −0.820218 | ||||||||
\(897\) | 7.45042 | 0.248762 | ||||||||
\(898\) | 10.1294 | 0.338022 | ||||||||
\(899\) | 35.8074 | 1.19424 | ||||||||
\(900\) | −1.93117 | −0.0643722 | ||||||||
\(901\) | 0.0769667 | 0.00256413 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.7530 | 1.25634 | ||||||||
\(904\) | −14.1866 | −0.471841 | ||||||||
\(905\) | 1.41348 | 0.0469857 | ||||||||
\(906\) | −3.97775 | −0.132152 | ||||||||
\(907\) | −25.3745 | −0.842546 | −0.421273 | − | 0.906934i | \(-0.638417\pi\) | ||||
−0.421273 | + | 0.906934i | \(0.638417\pi\) | |||||||
\(908\) | 1.27985 | 0.0424734 | ||||||||
\(909\) | −4.29171 | −0.142347 | ||||||||
\(910\) | 0.938065 | 0.0310966 | ||||||||
\(911\) | −17.4070 | −0.576718 | −0.288359 | − | 0.957522i | \(-0.593110\pi\) | ||||
−0.288359 | + | 0.957522i | \(0.593110\pi\) | |||||||
\(912\) | 0.247229 | 0.00818657 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.12971 | −0.202753 | ||||||||
\(915\) | 10.0601 | 0.332577 | ||||||||
\(916\) | 14.4652 | 0.477945 | ||||||||
\(917\) | 52.2265 | 1.72467 | ||||||||
\(918\) | 0.0231471 | 0.000763967 0 | ||||||||
\(919\) | 32.8958 | 1.08513 | 0.542566 | − | 0.840013i | \(-0.317453\pi\) | ||||
0.542566 | + | 0.840013i | \(0.317453\pi\) | |||||||
\(920\) | −6.86332 | −0.226277 | ||||||||
\(921\) | −28.5445 | −0.940572 | ||||||||
\(922\) | −1.29375 | −0.0426073 | ||||||||
\(923\) | −5.22245 | −0.171899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.33021 | −0.273896 | ||||||||
\(926\) | 7.07448 | 0.232482 | ||||||||
\(927\) | 2.09280 | 0.0687367 | ||||||||
\(928\) | −11.2265 | −0.368528 | ||||||||
\(929\) | 33.3131 | 1.09297 | 0.546484 | − | 0.837469i | \(-0.315966\pi\) | ||||
0.546484 | + | 0.837469i | \(0.315966\pi\) | |||||||
\(930\) | −2.51468 | −0.0824595 | ||||||||
\(931\) | 0.220169 | 0.00721575 | ||||||||
\(932\) | 20.3262 | 0.665808 | ||||||||
\(933\) | −9.94803 | −0.325684 | ||||||||
\(934\) | −6.21211 | −0.203266 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.15474 | −0.0377438 | ||||||||
\(937\) | 23.8637 | 0.779593 | 0.389797 | − | 0.920901i | \(-0.372545\pi\) | ||||
0.389797 | + | 0.920901i | \(0.372545\pi\) | |||||||
\(938\) | 7.99241 | 0.260961 | ||||||||
\(939\) | −16.4309 | −0.536203 | ||||||||
\(940\) | −1.75354 | −0.0571941 | ||||||||
\(941\) | 7.92557 | 0.258366 | 0.129183 | − | 0.991621i | \(-0.458765\pi\) | ||||
0.129183 | + | 0.991621i | \(0.458765\pi\) | |||||||
\(942\) | −3.90405 | −0.127201 | ||||||||
\(943\) | 77.6292 | 2.52795 | ||||||||
\(944\) | 6.59459 | 0.214636 | ||||||||
\(945\) | 3.19353 | 0.103885 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.15429 | −0.0700050 | −0.0350025 | − | 0.999387i | \(-0.511144\pi\) | ||||
−0.0350025 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(948\) | 1.52821 | 0.0496341 | ||||||||
\(949\) | 8.01676 | 0.260235 | ||||||||
\(950\) | 0.0180589 | 0.000585908 0 | ||||||||
\(951\) | 14.2106 | 0.460810 | ||||||||
\(952\) | −0.290595 | −0.00941824 | ||||||||
\(953\) | 5.99303 | 0.194133 | 0.0970666 | − | 0.995278i | \(-0.469054\pi\) | ||||
0.0970666 | + | 0.995278i | \(0.469054\pi\) | |||||||
\(954\) | 0.228877 | 0.00741016 | ||||||||
\(955\) | 4.90914 | 0.158856 | ||||||||
\(956\) | 32.9770 | 1.06655 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.54816 | 0.114636 | ||||||||
\(959\) | 24.6926 | 0.797366 | ||||||||
\(960\) | −6.39507 | −0.206400 | ||||||||
\(961\) | 60.8692 | 1.96352 | ||||||||
\(962\) | −2.44691 | −0.0788916 | ||||||||
\(963\) | 15.7409 | 0.507244 | ||||||||
\(964\) | −32.2663 | −1.03923 | ||||||||
\(965\) | −9.71987 | −0.312894 | ||||||||
\(966\) | 5.57549 | 0.179389 | ||||||||
\(967\) | −22.2784 | −0.716424 | −0.358212 | − | 0.933640i | \(-0.616613\pi\) | ||||
−0.358212 | + | 0.933640i | \(0.616613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.00607286 | 0.000195088 0 | ||||||||
\(970\) | −1.07357 | −0.0344703 | ||||||||
\(971\) | −36.6909 | −1.17747 | −0.588734 | − | 0.808327i | \(-0.700374\pi\) | ||||
−0.588734 | + | 0.808327i | \(0.700374\pi\) | |||||||
\(972\) | −1.93117 | −0.0619422 | ||||||||
\(973\) | −64.4660 | −2.06669 | ||||||||
\(974\) | −2.26339 | −0.0725236 | ||||||||
\(975\) | 1.11961 | 0.0358561 | ||||||||
\(976\) | 36.1334 | 1.15660 | ||||||||
\(977\) | 27.9044 | 0.892740 | 0.446370 | − | 0.894848i | \(-0.352717\pi\) | ||||
0.446370 | + | 0.894848i | \(0.352717\pi\) | |||||||
\(978\) | 0.892323 | 0.0285333 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.17706 | −0.197319 | ||||||||
\(981\) | 4.13271 | 0.131947 | ||||||||
\(982\) | 6.79691 | 0.216898 | ||||||||
\(983\) | 9.79220 | 0.312323 | 0.156161 | − | 0.987732i | \(-0.450088\pi\) | ||||
0.156161 | + | 0.987732i | \(0.450088\pi\) | |||||||
\(984\) | −12.0317 | −0.383558 | ||||||||
\(985\) | 8.88764 | 0.283184 | ||||||||
\(986\) | −0.0864735 | −0.00275388 | ||||||||
\(987\) | 2.89979 | 0.0923013 | ||||||||
\(988\) | −0.148826 | −0.00473479 | ||||||||
\(989\) | 78.6678 | 2.50149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.9794 | 1.11116 | 0.555578 | − | 0.831464i | \(-0.312497\pi\) | ||||
0.555578 | + | 0.831464i | \(0.312497\pi\) | |||||||
\(992\) | −28.8033 | −0.914506 | ||||||||
\(993\) | −10.9119 | −0.346279 | ||||||||
\(994\) | −3.90820 | −0.123961 | ||||||||
\(995\) | 18.0381 | 0.571846 | ||||||||
\(996\) | 0.477441 | 0.0151283 | ||||||||
\(997\) | 12.7753 | 0.404599 | 0.202299 | − | 0.979324i | \(-0.435159\pi\) | ||||
0.202299 | + | 0.979324i | \(0.435159\pi\) | |||||||
\(998\) | −7.35855 | −0.232931 | ||||||||
\(999\) | −8.33021 | −0.263556 |
(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 | 1815.2.a.w.1.2 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bf.1.3 | 4 | |||
5.4 | even | 2 | 9075.2.a.cm.1.3 | 4 | |||
11.2 | odd | 10 | 165.2.m.d.136.1 | yes | 8 | ||
11.6 | odd | 10 | 165.2.m.d.91.1 | ✓ | 8 | ||
11.10 | odd | 2 | 1815.2.a.p.1.3 | 4 | |||
33.2 | even | 10 | 495.2.n.a.136.2 | 8 | |||
33.17 | even | 10 | 495.2.n.a.91.2 | 8 | |||
33.32 | even | 2 | 5445.2.a.bt.1.2 | 4 | |||
55.2 | even | 20 | 825.2.bx.f.499.2 | 16 | |||
55.13 | even | 20 | 825.2.bx.f.499.3 | 16 | |||
55.17 | even | 20 | 825.2.bx.f.124.3 | 16 | |||
55.24 | odd | 10 | 825.2.n.g.301.2 | 8 | |||
55.28 | even | 20 | 825.2.bx.f.124.2 | 16 | |||
55.39 | odd | 10 | 825.2.n.g.751.2 | 8 | |||
55.54 | odd | 2 | 9075.2.a.di.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.91.1 | ✓ | 8 | 11.6 | odd | 10 | ||
165.2.m.d.136.1 | yes | 8 | 11.2 | odd | 10 | ||
495.2.n.a.91.2 | 8 | 33.17 | even | 10 | |||
495.2.n.a.136.2 | 8 | 33.2 | even | 10 | |||
825.2.n.g.301.2 | 8 | 55.24 | odd | 10 | |||
825.2.n.g.751.2 | 8 | 55.39 | odd | 10 | |||
825.2.bx.f.124.2 | 16 | 55.28 | even | 20 | |||
825.2.bx.f.124.3 | 16 | 55.17 | even | 20 | |||
825.2.bx.f.499.2 | 16 | 55.2 | even | 20 | |||
825.2.bx.f.499.3 | 16 | 55.13 | even | 20 | |||
1815.2.a.p.1.3 | 4 | 11.10 | odd | 2 | |||
1815.2.a.w.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bf.1.3 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bt.1.2 | 4 | 33.32 | even | 2 | |||
9075.2.a.cm.1.3 | 4 | 5.4 | even | 2 | |||
9075.2.a.di.1.2 | 4 | 55.54 | odd | 2 |