Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.258228.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 6x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48761\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.48761 | 1.43622 | 0.718110 | − | 0.695929i | \(-0.245007\pi\) | ||||
0.718110 | + | 0.695929i | \(0.245007\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.48761 | 0.665278 | 0.332639 | − | 0.943054i | \(-0.392061\pi\) | ||||
0.332639 | + | 0.943054i | \(0.392061\pi\) | |||||||
\(6\) | −2.48761 | −1.01556 | ||||||||
\(7\) | −4.90325 | −1.85325 | −0.926627 | − | 0.375981i | \(-0.877306\pi\) | ||||
−0.926627 | + | 0.375981i | \(0.877306\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.18819 | 1.06273 | ||||||||
\(10\) | −1.48761 | −0.470422 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.48761 | 0.718110 | ||||||||
\(13\) | 3.09144 | 0.857410 | 0.428705 | − | 0.903444i | \(-0.358970\pi\) | ||||
0.428705 | + | 0.903444i | \(0.358970\pi\) | |||||||
\(14\) | 4.90325 | 1.31045 | ||||||||
\(15\) | 3.70058 | 0.955486 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.90325 | 1.43175 | 0.715874 | − | 0.698229i | \(-0.246028\pi\) | ||||
0.715874 | + | 0.698229i | \(0.246028\pi\) | |||||||
\(18\) | −3.18819 | −0.751463 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.48761 | 0.332639 | ||||||||
\(21\) | −12.1974 | −2.66168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.09144 | 0.436095 | 0.218047 | − | 0.975938i | \(-0.430031\pi\) | ||||
0.218047 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(24\) | −2.48761 | −0.507781 | ||||||||
\(25\) | −2.78703 | −0.557405 | ||||||||
\(26\) | −3.09144 | −0.606281 | ||||||||
\(27\) | 0.468133 | 0.0900922 | ||||||||
\(28\) | −4.90325 | −0.926627 | ||||||||
\(29\) | 0.700580 | 0.130094 | 0.0650472 | − | 0.997882i | \(-0.479280\pi\) | ||||
0.0650472 | + | 0.997882i | \(0.479280\pi\) | |||||||
\(30\) | −3.70058 | −0.675630 | ||||||||
\(31\) | 4.97521 | 0.893575 | 0.446787 | − | 0.894640i | \(-0.352568\pi\) | ||||
0.446787 | + | 0.894640i | \(0.352568\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.90325 | −1.01240 | ||||||||
\(35\) | −7.29411 | −1.23293 | ||||||||
\(36\) | 3.18819 | 0.531364 | ||||||||
\(37\) | 9.31889 | 1.53202 | 0.766008 | − | 0.642831i | \(-0.222240\pi\) | ||||
0.766008 | + | 0.642831i | \(0.222240\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 7.69028 | 1.23143 | ||||||||
\(40\) | −1.48761 | −0.235211 | ||||||||
\(41\) | 6.48229 | 1.01236 | 0.506182 | − | 0.862427i | \(-0.331056\pi\) | ||||
0.506182 | + | 0.862427i | \(0.331056\pi\) | |||||||
\(42\) | 12.1974 | 1.88209 | ||||||||
\(43\) | −0.792340 | −0.120831 | −0.0604154 | − | 0.998173i | \(-0.519243\pi\) | ||||
−0.0604154 | + | 0.998173i | \(0.519243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.74277 | 0.707010 | ||||||||
\(46\) | −2.09144 | −0.308365 | ||||||||
\(47\) | −2.18819 | −0.319180 | −0.159590 | − | 0.987183i | \(-0.551017\pi\) | ||||
−0.159590 | + | 0.987183i | \(0.551017\pi\) | |||||||
\(48\) | 2.48761 | 0.359055 | ||||||||
\(49\) | 17.0419 | 2.43455 | ||||||||
\(50\) | 2.78703 | 0.394145 | ||||||||
\(51\) | 14.6850 | 2.05631 | ||||||||
\(52\) | 3.09144 | 0.428705 | ||||||||
\(53\) | −5.29942 | −0.727931 | −0.363966 | − | 0.931412i | \(-0.618577\pi\) | ||||
−0.363966 | + | 0.931412i | \(0.618577\pi\) | |||||||
\(54\) | −0.468133 | −0.0637048 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.90325 | 0.655224 | ||||||||
\(57\) | −2.48761 | −0.329492 | ||||||||
\(58\) | −0.700580 | −0.0919906 | ||||||||
\(59\) | −0.603830 | −0.0786119 | −0.0393060 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393060 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(60\) | 3.70058 | 0.477743 | ||||||||
\(61\) | −5.11123 | −0.654426 | −0.327213 | − | 0.944951i | \(-0.606110\pi\) | ||||
−0.327213 | + | 0.944951i | \(0.606110\pi\) | |||||||
\(62\) | −4.97521 | −0.631853 | ||||||||
\(63\) | −15.6325 | −1.96951 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.59884 | 0.570416 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8731 | −1.45054 | −0.725268 | − | 0.688467i | \(-0.758284\pi\) | ||||
−0.725268 | + | 0.688467i | \(0.758284\pi\) | |||||||
\(68\) | 5.90325 | 0.715874 | ||||||||
\(69\) | 5.20267 | 0.626328 | ||||||||
\(70\) | 7.29411 | 0.871813 | ||||||||
\(71\) | 9.45751 | 1.12240 | 0.561200 | − | 0.827680i | \(-0.310340\pi\) | ||||
0.561200 | + | 0.827680i | \(0.310340\pi\) | |||||||
\(72\) | −3.18819 | −0.375731 | ||||||||
\(73\) | −1.90325 | −0.222759 | −0.111379 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111379 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(74\) | −9.31889 | −1.08330 | ||||||||
\(75\) | −6.93303 | −0.800557 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.69028 | −0.870752 | ||||||||
\(79\) | −14.4823 | −1.62939 | −0.814693 | − | 0.579893i | \(-0.803094\pi\) | ||||
−0.814693 | + | 0.579893i | \(0.803094\pi\) | |||||||
\(80\) | 1.48761 | 0.166319 | ||||||||
\(81\) | −8.40003 | −0.933336 | ||||||||
\(82\) | −6.48229 | −0.715850 | ||||||||
\(83\) | 7.48761 | 0.821872 | 0.410936 | − | 0.911664i | \(-0.365202\pi\) | ||||
0.410936 | + | 0.911664i | \(0.365202\pi\) | |||||||
\(84\) | −12.1974 | −1.33084 | ||||||||
\(85\) | 8.78171 | 0.952511 | ||||||||
\(86\) | 0.792340 | 0.0854403 | ||||||||
\(87\) | 1.74277 | 0.186844 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50708 | 0.371750 | 0.185875 | − | 0.982573i | \(-0.440488\pi\) | ||||
0.185875 | + | 0.982573i | \(0.440488\pi\) | |||||||
\(90\) | −4.74277 | −0.499931 | ||||||||
\(91\) | −15.1581 | −1.58900 | ||||||||
\(92\) | 2.09144 | 0.218047 | ||||||||
\(93\) | 12.3764 | 1.28337 | ||||||||
\(94\) | 2.18819 | 0.225694 | ||||||||
\(95\) | −1.48761 | −0.152625 | ||||||||
\(96\) | −2.48761 | −0.253890 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −17.0419 | −1.72149 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.78703 | −0.278703 | ||||||||
\(101\) | 6.08645 | 0.605624 | 0.302812 | − | 0.953050i | \(-0.402075\pi\) | ||||
0.302812 | + | 0.953050i | \(0.402075\pi\) | |||||||
\(102\) | −14.6850 | −1.45403 | ||||||||
\(103\) | 17.5071 | 1.72502 | 0.862512 | − | 0.506037i | \(-0.168890\pi\) | ||||
0.862512 | + | 0.506037i | \(0.168890\pi\) | |||||||
\(104\) | −3.09144 | −0.303140 | ||||||||
\(105\) | −18.1449 | −1.77076 | ||||||||
\(106\) | 5.29942 | 0.514725 | ||||||||
\(107\) | 11.7424 | 1.13518 | 0.567592 | − | 0.823310i | \(-0.307875\pi\) | ||||
0.567592 | + | 0.823310i | \(0.307875\pi\) | |||||||
\(108\) | 0.468133 | 0.0450461 | ||||||||
\(109\) | −2.60383 | −0.249402 | −0.124701 | − | 0.992194i | \(-0.539797\pi\) | ||||
−0.124701 | + | 0.992194i | \(0.539797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.1817 | 2.20031 | ||||||||
\(112\) | −4.90325 | −0.463314 | ||||||||
\(113\) | 12.4823 | 1.17424 | 0.587118 | − | 0.809502i | \(-0.300263\pi\) | ||||
0.587118 | + | 0.809502i | \(0.300263\pi\) | |||||||
\(114\) | 2.48761 | 0.232986 | ||||||||
\(115\) | 3.11123 | 0.290124 | ||||||||
\(116\) | 0.700580 | 0.0650472 | ||||||||
\(117\) | 9.85607 | 0.911194 | ||||||||
\(118\) | 0.603830 | 0.0555870 | ||||||||
\(119\) | −28.9451 | −2.65339 | ||||||||
\(120\) | −3.70058 | −0.337815 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.11123 | 0.462749 | ||||||||
\(123\) | 16.1254 | 1.45398 | ||||||||
\(124\) | 4.97521 | 0.446787 | ||||||||
\(125\) | −11.5840 | −1.03611 | ||||||||
\(126\) | 15.6325 | 1.39265 | ||||||||
\(127\) | 18.7817 | 1.66661 | 0.833304 | − | 0.552815i | \(-0.186447\pi\) | ||||
0.833304 | + | 0.552815i | \(0.186447\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.97103 | −0.173540 | ||||||||
\(130\) | −4.59884 | −0.403345 | ||||||||
\(131\) | 9.98937 | 0.872776 | 0.436388 | − | 0.899759i | \(-0.356258\pi\) | ||||
0.436388 | + | 0.899759i | \(0.356258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.90325 | 0.425166 | ||||||||
\(134\) | 11.8731 | 1.02568 | ||||||||
\(135\) | 0.696398 | 0.0599364 | ||||||||
\(136\) | −5.90325 | −0.506200 | ||||||||
\(137\) | 10.6956 | 0.913786 | 0.456893 | − | 0.889522i | \(-0.348962\pi\) | ||||
0.456893 | + | 0.889522i | \(0.348962\pi\) | |||||||
\(138\) | −5.20267 | −0.442881 | ||||||||
\(139\) | 8.32680 | 0.706270 | 0.353135 | − | 0.935572i | \(-0.385116\pi\) | ||||
0.353135 | + | 0.935572i | \(0.385116\pi\) | |||||||
\(140\) | −7.29411 | −0.616465 | ||||||||
\(141\) | −5.44335 | −0.458412 | ||||||||
\(142\) | −9.45751 | −0.793656 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.18819 | 0.265682 | ||||||||
\(145\) | 1.04219 | 0.0865489 | ||||||||
\(146\) | 1.90325 | 0.157514 | ||||||||
\(147\) | 42.3934 | 3.49655 | ||||||||
\(148\) | 9.31889 | 0.766008 | ||||||||
\(149\) | 23.3410 | 1.91217 | 0.956083 | − | 0.293096i | \(-0.0946857\pi\) | ||||
0.956083 | + | 0.293096i | \(0.0946857\pi\) | |||||||
\(150\) | 6.93303 | 0.566079 | ||||||||
\(151\) | 3.32421 | 0.270520 | 0.135260 | − | 0.990810i | \(-0.456813\pi\) | ||||
0.135260 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 18.8207 | 1.52156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.40116 | 0.594475 | ||||||||
\(156\) | 7.69028 | 0.615715 | ||||||||
\(157\) | 22.9177 | 1.82903 | 0.914517 | − | 0.404547i | \(-0.132571\pi\) | ||||
0.914517 | + | 0.404547i | \(0.132571\pi\) | |||||||
\(158\) | 14.4823 | 1.15215 | ||||||||
\(159\) | −13.1829 | −1.04547 | ||||||||
\(160\) | −1.48761 | −0.117606 | ||||||||
\(161\) | −10.2548 | −0.808194 | ||||||||
\(162\) | 8.40003 | 0.659968 | ||||||||
\(163\) | −20.4053 | −1.59827 | −0.799135 | − | 0.601152i | \(-0.794709\pi\) | ||||
−0.799135 | + | 0.601152i | \(0.794709\pi\) | |||||||
\(164\) | 6.48229 | 0.506182 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.48761 | −0.581151 | ||||||||
\(167\) | 14.7817 | 1.14384 | 0.571922 | − | 0.820308i | \(-0.306198\pi\) | ||||
0.571922 | + | 0.820308i | \(0.306198\pi\) | |||||||
\(168\) | 12.1974 | 0.941047 | ||||||||
\(169\) | −3.44302 | −0.264848 | ||||||||
\(170\) | −8.78171 | −0.673527 | ||||||||
\(171\) | −3.18819 | −0.243807 | ||||||||
\(172\) | −0.792340 | −0.0604154 | ||||||||
\(173\) | 18.2640 | 1.38859 | 0.694293 | − | 0.719692i | \(-0.255717\pi\) | ||||
0.694293 | + | 0.719692i | \(0.255717\pi\) | |||||||
\(174\) | −1.74277 | −0.132119 | ||||||||
\(175\) | 13.6655 | 1.03301 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50209 | −0.112904 | ||||||||
\(178\) | −3.50708 | −0.262867 | ||||||||
\(179\) | −15.6262 | −1.16796 | −0.583979 | − | 0.811769i | \(-0.698505\pi\) | ||||
−0.583979 | + | 0.811769i | \(0.698505\pi\) | |||||||
\(180\) | 4.74277 | 0.353505 | ||||||||
\(181\) | 22.6378 | 1.68265 | 0.841327 | − | 0.540527i | \(-0.181775\pi\) | ||||
0.841327 | + | 0.540527i | \(0.181775\pi\) | |||||||
\(182\) | 15.1581 | 1.12359 | ||||||||
\(183\) | −12.7147 | −0.939901 | ||||||||
\(184\) | −2.09144 | −0.154183 | ||||||||
\(185\) | 13.8628 | 1.01922 | ||||||||
\(186\) | −12.3764 | −0.907480 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.18819 | −0.159590 | ||||||||
\(189\) | −2.29537 | −0.166964 | ||||||||
\(190\) | 1.48761 | 0.107922 | ||||||||
\(191\) | 13.5021 | 0.976977 | 0.488489 | − | 0.872570i | \(-0.337548\pi\) | ||||
0.488489 | + | 0.872570i | \(0.337548\pi\) | |||||||
\(192\) | 2.48761 | 0.179528 | ||||||||
\(193\) | −8.00000 | −0.575853 | −0.287926 | − | 0.957653i | \(-0.592966\pi\) | ||||
−0.287926 | + | 0.957653i | \(0.592966\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 11.4401 | 0.819243 | ||||||||
\(196\) | 17.0419 | 1.21728 | ||||||||
\(197\) | −13.3806 | −0.953325 | −0.476663 | − | 0.879086i | \(-0.658154\pi\) | ||||
−0.476663 | + | 0.879086i | \(0.658154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.6354 | −1.74636 | −0.873178 | − | 0.487401i | \(-0.837945\pi\) | ||||
−0.873178 | + | 0.487401i | \(0.837945\pi\) | |||||||
\(200\) | 2.78703 | 0.197073 | ||||||||
\(201\) | −29.5357 | −2.08329 | ||||||||
\(202\) | −6.08645 | −0.428241 | ||||||||
\(203\) | −3.43512 | −0.241098 | ||||||||
\(204\) | 14.6850 | 1.02815 | ||||||||
\(205\) | 9.64310 | 0.673503 | ||||||||
\(206\) | −17.5071 | −1.21978 | ||||||||
\(207\) | 6.66789 | 0.463450 | ||||||||
\(208\) | 3.09144 | 0.214353 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 18.1449 | 1.25211 | ||||||||
\(211\) | 21.4522 | 1.47683 | 0.738415 | − | 0.674347i | \(-0.235575\pi\) | ||||
0.738415 | + | 0.674347i | \(0.235575\pi\) | |||||||
\(212\) | −5.29942 | −0.363966 | ||||||||
\(213\) | 23.5266 | 1.61201 | ||||||||
\(214\) | −11.7424 | −0.802697 | ||||||||
\(215\) | −1.17869 | −0.0803860 | ||||||||
\(216\) | −0.468133 | −0.0318524 | ||||||||
\(217\) | −24.3947 | −1.65602 | ||||||||
\(218\) | 2.60383 | 0.176354 | ||||||||
\(219\) | −4.73454 | −0.319930 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.2495 | 1.22760 | ||||||||
\(222\) | −23.1817 | −1.55586 | ||||||||
\(223\) | −7.26401 | −0.486434 | −0.243217 | − | 0.969972i | \(-0.578203\pi\) | ||||
−0.243217 | + | 0.969972i | \(0.578203\pi\) | |||||||
\(224\) | 4.90325 | 0.327612 | ||||||||
\(225\) | −8.88556 | −0.592371 | ||||||||
\(226\) | −12.4823 | −0.830310 | ||||||||
\(227\) | −6.44302 | −0.427638 | −0.213819 | − | 0.976873i | \(-0.568590\pi\) | ||||
−0.213819 | + | 0.976873i | \(0.568590\pi\) | |||||||
\(228\) | −2.48761 | −0.164746 | ||||||||
\(229\) | −14.1333 | −0.933955 | −0.466977 | − | 0.884269i | \(-0.654657\pi\) | ||||
−0.466977 | + | 0.884269i | \(0.654657\pi\) | |||||||
\(230\) | −3.11123 | −0.205149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.700580 | −0.0459953 | ||||||||
\(233\) | 24.1776 | 1.58392 | 0.791962 | − | 0.610570i | \(-0.209060\pi\) | ||||
0.791962 | + | 0.610570i | \(0.209060\pi\) | |||||||
\(234\) | −9.85607 | −0.644312 | ||||||||
\(235\) | −3.25516 | −0.212343 | ||||||||
\(236\) | −0.603830 | −0.0393060 | ||||||||
\(237\) | −36.0262 | −2.34016 | ||||||||
\(238\) | 28.9451 | 1.87623 | ||||||||
\(239\) | −28.1581 | −1.82140 | −0.910698 | − | 0.413074i | \(-0.864455\pi\) | ||||
−0.910698 | + | 0.413074i | \(0.864455\pi\) | |||||||
\(240\) | 3.70058 | 0.238871 | ||||||||
\(241\) | 17.7843 | 1.14559 | 0.572794 | − | 0.819699i | \(-0.305860\pi\) | ||||
0.572794 | + | 0.819699i | \(0.305860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3004 | −1.43057 | ||||||||
\(244\) | −5.11123 | −0.327213 | ||||||||
\(245\) | 25.3516 | 1.61965 | ||||||||
\(246\) | −16.1254 | −1.02812 | ||||||||
\(247\) | −3.09144 | −0.196703 | ||||||||
\(248\) | −4.97521 | −0.315926 | ||||||||
\(249\) | 18.6262 | 1.18039 | ||||||||
\(250\) | 11.5840 | 0.732639 | ||||||||
\(251\) | 1.20766 | 0.0762268 | 0.0381134 | − | 0.999273i | \(-0.487865\pi\) | ||||
0.0381134 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(252\) | −15.6325 | −0.984753 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.7817 | −1.17847 | ||||||||
\(255\) | 21.8454 | 1.36801 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.4053 | −1.02334 | −0.511669 | − | 0.859183i | \(-0.670972\pi\) | ||||
−0.511669 | + | 0.859183i | \(0.670972\pi\) | |||||||
\(258\) | 1.97103 | 0.122711 | ||||||||
\(259\) | −45.6929 | −2.83922 | ||||||||
\(260\) | 4.59884 | 0.285208 | ||||||||
\(261\) | 2.23358 | 0.138255 | ||||||||
\(262\) | −9.98937 | −0.617146 | ||||||||
\(263\) | −27.1776 | −1.67584 | −0.837920 | − | 0.545793i | \(-0.816228\pi\) | ||||
−0.837920 | + | 0.545793i | \(0.816228\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.88345 | −0.484277 | ||||||||
\(266\) | −4.90325 | −0.300638 | ||||||||
\(267\) | 8.72423 | 0.533915 | ||||||||
\(268\) | −11.8731 | −0.725268 | ||||||||
\(269\) | 9.23922 | 0.563325 | 0.281663 | − | 0.959514i | \(-0.409114\pi\) | ||||
0.281663 | + | 0.959514i | \(0.409114\pi\) | |||||||
\(270\) | −0.696398 | −0.0423814 | ||||||||
\(271\) | 17.0613 | 1.03640 | 0.518201 | − | 0.855259i | \(-0.326602\pi\) | ||||
0.518201 | + | 0.855259i | \(0.326602\pi\) | |||||||
\(272\) | 5.90325 | 0.357937 | ||||||||
\(273\) | −37.7074 | −2.28215 | ||||||||
\(274\) | −10.6956 | −0.646144 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.20267 | 0.313164 | ||||||||
\(277\) | 21.6705 | 1.30205 | 0.651026 | − | 0.759055i | \(-0.274339\pi\) | ||||
0.651026 | + | 0.759055i | \(0.274339\pi\) | |||||||
\(278\) | −8.32680 | −0.499408 | ||||||||
\(279\) | 15.8619 | 0.949627 | ||||||||
\(280\) | 7.29411 | 0.435906 | ||||||||
\(281\) | −0.675793 | −0.0403144 | −0.0201572 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201572 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(282\) | 5.44335 | 0.324147 | ||||||||
\(283\) | 2.64841 | 0.157432 | 0.0787160 | − | 0.996897i | \(-0.474918\pi\) | ||||
0.0787160 | + | 0.996897i | \(0.474918\pi\) | |||||||
\(284\) | 9.45751 | 0.561200 | ||||||||
\(285\) | −3.70058 | −0.219203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.7843 | −1.87617 | ||||||||
\(288\) | −3.18819 | −0.187866 | ||||||||
\(289\) | 17.8484 | 1.04990 | ||||||||
\(290\) | −1.04219 | −0.0611993 | ||||||||
\(291\) | −24.8761 | −1.45826 | ||||||||
\(292\) | −1.90325 | −0.111379 | ||||||||
\(293\) | −1.70589 | −0.0996593 | −0.0498297 | − | 0.998758i | \(-0.515868\pi\) | ||||
−0.0498297 | + | 0.998758i | \(0.515868\pi\) | |||||||
\(294\) | −42.3934 | −2.47244 | ||||||||
\(295\) | −0.898261 | −0.0522988 | ||||||||
\(296\) | −9.31889 | −0.541650 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.3410 | −1.35211 | ||||||||
\(299\) | 6.46554 | 0.373912 | ||||||||
\(300\) | −6.93303 | −0.400278 | ||||||||
\(301\) | 3.88504 | 0.223930 | ||||||||
\(302\) | −3.32421 | −0.191287 | ||||||||
\(303\) | 15.1407 | 0.869810 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −7.60351 | −0.435375 | ||||||||
\(306\) | −18.8207 | −1.07591 | ||||||||
\(307\) | −14.3136 | −0.816919 | −0.408460 | − | 0.912776i | \(-0.633934\pi\) | ||||
−0.408460 | + | 0.912776i | \(0.633934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 43.5507 | 2.47751 | ||||||||
\(310\) | −7.40116 | −0.420358 | ||||||||
\(311\) | 22.1805 | 1.25774 | 0.628870 | − | 0.777511i | \(-0.283518\pi\) | ||||
0.628870 | + | 0.777511i | \(0.283518\pi\) | |||||||
\(312\) | −7.69028 | −0.435376 | ||||||||
\(313\) | 10.4873 | 0.592776 | 0.296388 | − | 0.955068i | \(-0.404218\pi\) | ||||
0.296388 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(314\) | −22.9177 | −1.29332 | ||||||||
\(315\) | −23.2550 | −1.31027 | ||||||||
\(316\) | −14.4823 | −0.814693 | ||||||||
\(317\) | 30.2785 | 1.70061 | 0.850305 | − | 0.526291i | \(-0.176418\pi\) | ||||
0.850305 | + | 0.526291i | \(0.176418\pi\) | |||||||
\(318\) | 13.1829 | 0.739259 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.48761 | 0.0831597 | ||||||||
\(321\) | 29.2106 | 1.63038 | ||||||||
\(322\) | 10.2548 | 0.571480 | ||||||||
\(323\) | −5.90325 | −0.328466 | ||||||||
\(324\) | −8.40003 | −0.466668 | ||||||||
\(325\) | −8.61592 | −0.477925 | ||||||||
\(326\) | 20.4053 | 1.13015 | ||||||||
\(327\) | −6.47730 | −0.358196 | ||||||||
\(328\) | −6.48229 | −0.357925 | ||||||||
\(329\) | 10.7292 | 0.591521 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.62330 | 0.254120 | 0.127060 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127060 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(332\) | 7.48761 | 0.410936 | ||||||||
\(333\) | 29.7104 | 1.62812 | ||||||||
\(334\) | −14.7817 | −0.808819 | ||||||||
\(335\) | −17.6626 | −0.965010 | ||||||||
\(336\) | −12.1974 | −0.665420 | ||||||||
\(337\) | −25.8728 | −1.40938 | −0.704691 | − | 0.709514i | \(-0.748914\pi\) | ||||
−0.704691 | + | 0.709514i | \(0.748914\pi\) | |||||||
\(338\) | 3.44302 | 0.187276 | ||||||||
\(339\) | 31.0510 | 1.68646 | ||||||||
\(340\) | 8.78171 | 0.476255 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.18819 | 0.172397 | ||||||||
\(343\) | −49.2378 | −2.65859 | ||||||||
\(344\) | 0.792340 | 0.0427201 | ||||||||
\(345\) | 7.73953 | 0.416682 | ||||||||
\(346\) | −18.2640 | −0.981879 | ||||||||
\(347\) | −30.4911 | −1.63685 | −0.818425 | − | 0.574613i | \(-0.805152\pi\) | ||||
−0.818425 | + | 0.574613i | \(0.805152\pi\) | |||||||
\(348\) | 1.74277 | 0.0934221 | ||||||||
\(349\) | −29.6967 | −1.58963 | −0.794815 | − | 0.606852i | \(-0.792432\pi\) | ||||
−0.794815 | + | 0.606852i | \(0.792432\pi\) | |||||||
\(350\) | −13.6655 | −0.730451 | ||||||||
\(351\) | 1.44720 | 0.0772460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.53977 | −0.507751 | −0.253875 | − | 0.967237i | \(-0.581705\pi\) | ||||
−0.253875 | + | 0.967237i | \(0.581705\pi\) | |||||||
\(354\) | 1.50209 | 0.0798352 | ||||||||
\(355\) | 14.0690 | 0.746708 | ||||||||
\(356\) | 3.50708 | 0.185875 | ||||||||
\(357\) | −72.0041 | −3.81086 | ||||||||
\(358\) | 15.6262 | 0.825871 | ||||||||
\(359\) | −16.6956 | −0.881160 | −0.440580 | − | 0.897713i | \(-0.645227\pi\) | ||||
−0.440580 | + | 0.897713i | \(0.645227\pi\) | |||||||
\(360\) | −4.74277 | −0.249966 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −22.6378 | −1.18982 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.1581 | −0.794500 | ||||||||
\(365\) | −2.83129 | −0.148196 | ||||||||
\(366\) | 12.7147 | 0.664610 | ||||||||
\(367\) | 0.198813 | 0.0103780 | 0.00518898 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00518898 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(368\) | 2.09144 | 0.109024 | ||||||||
\(369\) | 20.6668 | 1.07587 | ||||||||
\(370\) | −13.8628 | −0.720695 | ||||||||
\(371\) | 25.9844 | 1.34904 | ||||||||
\(372\) | 12.3764 | 0.641685 | ||||||||
\(373\) | −15.4427 | −0.799593 | −0.399796 | − | 0.916604i | \(-0.630919\pi\) | ||||
−0.399796 | + | 0.916604i | \(0.630919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.8165 | −1.48808 | ||||||||
\(376\) | 2.18819 | 0.112847 | ||||||||
\(377\) | 2.16580 | 0.111544 | ||||||||
\(378\) | 2.29537 | 0.118061 | ||||||||
\(379\) | 20.9791 | 1.07762 | 0.538811 | − | 0.842427i | \(-0.318874\pi\) | ||||
0.538811 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(380\) | −1.48761 | −0.0763126 | ||||||||
\(381\) | 46.7215 | 2.39362 | ||||||||
\(382\) | −13.5021 | −0.690827 | ||||||||
\(383\) | −25.3310 | −1.29435 | −0.647176 | − | 0.762340i | \(-0.724050\pi\) | ||||
−0.647176 | + | 0.762340i | \(0.724050\pi\) | |||||||
\(384\) | −2.48761 | −0.126945 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | −2.52613 | −0.128410 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | −4.46282 | −0.226274 | −0.113137 | − | 0.993579i | \(-0.536090\pi\) | ||||
−0.113137 | + | 0.993579i | \(0.536090\pi\) | |||||||
\(390\) | −11.4401 | −0.579292 | ||||||||
\(391\) | 12.3463 | 0.624378 | ||||||||
\(392\) | −17.0419 | −0.860744 | ||||||||
\(393\) | 24.8496 | 1.25350 | ||||||||
\(394\) | 13.3806 | 0.674103 | ||||||||
\(395\) | −21.5440 | −1.08399 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.9398 | 1.50264 | 0.751318 | − | 0.659941i | \(-0.229419\pi\) | ||||
0.751318 | + | 0.659941i | \(0.229419\pi\) | |||||||
\(398\) | 24.6354 | 1.23486 | ||||||||
\(399\) | 12.1974 | 0.610632 | ||||||||
\(400\) | −2.78703 | −0.139351 | ||||||||
\(401\) | −18.2888 | −0.913299 | −0.456649 | − | 0.889647i | \(-0.650951\pi\) | ||||
−0.456649 | + | 0.889647i | \(0.650951\pi\) | |||||||
\(402\) | 29.5357 | 1.47311 | ||||||||
\(403\) | 15.3806 | 0.766160 | ||||||||
\(404\) | 6.08645 | 0.302812 | ||||||||
\(405\) | −12.4959 | −0.620928 | ||||||||
\(406\) | 3.43512 | 0.170482 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.6850 | −0.727014 | ||||||||
\(409\) | −25.5634 | −1.26403 | −0.632015 | − | 0.774956i | \(-0.717772\pi\) | ||||
−0.632015 | + | 0.774956i | \(0.717772\pi\) | |||||||
\(410\) | −9.64310 | −0.476239 | ||||||||
\(411\) | 26.6064 | 1.31240 | ||||||||
\(412\) | 17.5071 | 0.862512 | ||||||||
\(413\) | 2.96073 | 0.145688 | ||||||||
\(414\) | −6.66789 | −0.327709 | ||||||||
\(415\) | 11.1386 | 0.546773 | ||||||||
\(416\) | −3.09144 | −0.151570 | ||||||||
\(417\) | 20.7138 | 1.01436 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.6103 | −1.34885 | −0.674425 | − | 0.738343i | \(-0.735608\pi\) | ||||
−0.674425 | + | 0.738343i | \(0.735608\pi\) | |||||||
\(420\) | −18.1449 | −0.885379 | ||||||||
\(421\) | −18.5242 | −0.902812 | −0.451406 | − | 0.892319i | \(-0.649077\pi\) | ||||
−0.451406 | + | 0.892319i | \(0.649077\pi\) | |||||||
\(422\) | −21.4522 | −1.04428 | ||||||||
\(423\) | −6.97634 | −0.339201 | ||||||||
\(424\) | 5.29942 | 0.257363 | ||||||||
\(425\) | −16.4525 | −0.798064 | ||||||||
\(426\) | −23.5266 | −1.13987 | ||||||||
\(427\) | 25.0617 | 1.21282 | ||||||||
\(428\) | 11.7424 | 0.567592 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.17869 | 0.0568415 | ||||||||
\(431\) | −13.8835 | −0.668742 | −0.334371 | − | 0.942441i | \(-0.608524\pi\) | ||||
−0.334371 | + | 0.942441i | \(0.608524\pi\) | |||||||
\(432\) | 0.468133 | 0.0225231 | ||||||||
\(433\) | 5.02479 | 0.241476 | 0.120738 | − | 0.992684i | \(-0.461474\pi\) | ||||
0.120738 | + | 0.992684i | \(0.461474\pi\) | |||||||
\(434\) | 24.3947 | 1.17098 | ||||||||
\(435\) | 2.59255 | 0.124303 | ||||||||
\(436\) | −2.60383 | −0.124701 | ||||||||
\(437\) | −2.09144 | −0.100047 | ||||||||
\(438\) | 4.73454 | 0.226225 | ||||||||
\(439\) | 8.23245 | 0.392913 | 0.196457 | − | 0.980513i | \(-0.437057\pi\) | ||||
0.196457 | + | 0.980513i | \(0.437057\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 54.3326 | 2.58727 | ||||||||
\(442\) | −18.2495 | −0.868041 | ||||||||
\(443\) | −20.1722 | −0.958412 | −0.479206 | − | 0.877702i | \(-0.659075\pi\) | ||||
−0.479206 | + | 0.877702i | \(0.659075\pi\) | |||||||
\(444\) | 23.1817 | 1.10016 | ||||||||
\(445\) | 5.21715 | 0.247317 | ||||||||
\(446\) | 7.26401 | 0.343961 | ||||||||
\(447\) | 58.0631 | 2.74629 | ||||||||
\(448\) | −4.90325 | −0.231657 | ||||||||
\(449\) | −10.7923 | −0.509322 | −0.254661 | − | 0.967030i | \(-0.581964\pi\) | ||||
−0.254661 | + | 0.967030i | \(0.581964\pi\) | |||||||
\(450\) | 8.88556 | 0.418869 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.4823 | 0.587118 | ||||||||
\(453\) | 8.26932 | 0.388527 | ||||||||
\(454\) | 6.44302 | 0.302386 | ||||||||
\(455\) | −22.5493 | −1.05713 | ||||||||
\(456\) | 2.48761 | 0.116493 | ||||||||
\(457\) | −8.27431 | −0.387056 | −0.193528 | − | 0.981095i | \(-0.561993\pi\) | ||||
−0.193528 | + | 0.981095i | \(0.561993\pi\) | |||||||
\(458\) | 14.1333 | 0.660406 | ||||||||
\(459\) | 2.76351 | 0.128989 | ||||||||
\(460\) | 3.11123 | 0.145062 | ||||||||
\(461\) | −17.6209 | −0.820687 | −0.410344 | − | 0.911931i | \(-0.634591\pi\) | ||||
−0.410344 | + | 0.911931i | \(0.634591\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.53977 | 0.118033 | 0.0590166 | − | 0.998257i | \(-0.481204\pi\) | ||||
0.0590166 | + | 0.998257i | \(0.481204\pi\) | |||||||
\(464\) | 0.700580 | 0.0325236 | ||||||||
\(465\) | 18.4112 | 0.853798 | ||||||||
\(466\) | −24.1776 | −1.12000 | ||||||||
\(467\) | −10.8213 | −0.500750 | −0.250375 | − | 0.968149i | \(-0.580554\pi\) | ||||
−0.250375 | + | 0.968149i | \(0.580554\pi\) | |||||||
\(468\) | 9.85607 | 0.455597 | ||||||||
\(469\) | 58.2170 | 2.68821 | ||||||||
\(470\) | 3.25516 | 0.150149 | ||||||||
\(471\) | 57.0103 | 2.62690 | ||||||||
\(472\) | 0.603830 | 0.0277935 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 36.0262 | 1.65474 | ||||||||
\(475\) | 2.78703 | 0.127878 | ||||||||
\(476\) | −28.9451 | −1.32670 | ||||||||
\(477\) | −16.8955 | −0.773594 | ||||||||
\(478\) | 28.1581 | 1.28792 | ||||||||
\(479\) | −9.96459 | −0.455294 | −0.227647 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227647 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(480\) | −3.70058 | −0.168908 | ||||||||
\(481\) | 28.8088 | 1.31357 | ||||||||
\(482\) | −17.7843 | −0.810053 | ||||||||
\(483\) | −25.5100 | −1.16074 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.8761 | −0.675487 | ||||||||
\(486\) | 22.3004 | 1.01156 | ||||||||
\(487\) | 8.36639 | 0.379118 | 0.189559 | − | 0.981869i | \(-0.439294\pi\) | ||||
0.189559 | + | 0.981869i | \(0.439294\pi\) | |||||||
\(488\) | 5.11123 | 0.231375 | ||||||||
\(489\) | −50.7605 | −2.29547 | ||||||||
\(490\) | −25.3516 | −1.14527 | ||||||||
\(491\) | 4.27722 | 0.193028 | 0.0965142 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965142 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(492\) | 16.1254 | 0.726989 | ||||||||
\(493\) | 4.13570 | 0.186262 | ||||||||
\(494\) | 3.09144 | 0.139090 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.97521 | 0.223394 | ||||||||
\(497\) | −46.3725 | −2.08009 | ||||||||
\(498\) | −18.6262 | −0.834661 | ||||||||
\(499\) | 2.08645 | 0.0934022 | 0.0467011 | − | 0.998909i | \(-0.485129\pi\) | ||||
0.0467011 | + | 0.998909i | \(0.485129\pi\) | |||||||
\(500\) | −11.5840 | −0.518054 | ||||||||
\(501\) | 36.7711 | 1.64281 | ||||||||
\(502\) | −1.20766 | −0.0539005 | ||||||||
\(503\) | −7.55166 | −0.336712 | −0.168356 | − | 0.985726i | \(-0.553846\pi\) | ||||
−0.168356 | + | 0.985726i | \(0.553846\pi\) | |||||||
\(504\) | 15.6325 | 0.696326 | ||||||||
\(505\) | 9.05424 | 0.402908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.56488 | −0.380380 | ||||||||
\(508\) | 18.7817 | 0.833304 | ||||||||
\(509\) | −23.3578 | −1.03532 | −0.517659 | − | 0.855587i | \(-0.673196\pi\) | ||||
−0.517659 | + | 0.855587i | \(0.673196\pi\) | |||||||
\(510\) | −21.8454 | −0.967333 | ||||||||
\(511\) | 9.33211 | 0.412828 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.468133 | −0.0206686 | ||||||||
\(514\) | 16.4053 | 0.723609 | ||||||||
\(515\) | 26.0436 | 1.14762 | ||||||||
\(516\) | −1.97103 | −0.0867698 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 45.6929 | 2.00763 | ||||||||
\(519\) | 45.4337 | 1.99432 | ||||||||
\(520\) | −4.59884 | −0.201673 | ||||||||
\(521\) | −15.0538 | −0.659517 | −0.329759 | − | 0.944065i | \(-0.606967\pi\) | ||||
−0.329759 | + | 0.944065i | \(0.606967\pi\) | |||||||
\(522\) | −2.23358 | −0.0977611 | ||||||||
\(523\) | 18.6027 | 0.813439 | 0.406720 | − | 0.913553i | \(-0.366673\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366673\pi\) | |||||||
\(524\) | 9.98937 | 0.436388 | ||||||||
\(525\) | 33.9944 | 1.48364 | ||||||||
\(526\) | 27.1776 | 1.18500 | ||||||||
\(527\) | 29.3699 | 1.27937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6259 | −0.809821 | ||||||||
\(530\) | 7.88345 | 0.342435 | ||||||||
\(531\) | −1.92512 | −0.0835432 | ||||||||
\(532\) | 4.90325 | 0.212583 | ||||||||
\(533\) | 20.0396 | 0.868011 | ||||||||
\(534\) | −8.72423 | −0.377535 | ||||||||
\(535\) | 17.4681 | 0.755213 | ||||||||
\(536\) | 11.8731 | 0.512842 | ||||||||
\(537\) | −38.8719 | −1.67745 | ||||||||
\(538\) | −9.23922 | −0.398331 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.696398 | 0.0299682 | ||||||||
\(541\) | −0.549267 | −0.0236148 | −0.0118074 | − | 0.999930i | \(-0.503759\pi\) | ||||
−0.0118074 | + | 0.999930i | \(0.503759\pi\) | |||||||
\(542\) | −17.0613 | −0.732847 | ||||||||
\(543\) | 56.3139 | 2.41666 | ||||||||
\(544\) | −5.90325 | −0.253100 | ||||||||
\(545\) | −3.87347 | −0.165921 | ||||||||
\(546\) | 37.7074 | 1.61373 | ||||||||
\(547\) | −40.5059 | −1.73191 | −0.865955 | − | 0.500123i | \(-0.833288\pi\) | ||||
−0.865955 | + | 0.500123i | \(0.833288\pi\) | |||||||
\(548\) | 10.6956 | 0.456893 | ||||||||
\(549\) | −16.2956 | −0.695478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.700580 | −0.0298457 | ||||||||
\(552\) | −5.20267 | −0.221440 | ||||||||
\(553\) | 71.0103 | 3.01967 | ||||||||
\(554\) | −21.6705 | −0.920690 | ||||||||
\(555\) | 34.4853 | 1.46382 | ||||||||
\(556\) | 8.32680 | 0.353135 | ||||||||
\(557\) | −41.5924 | −1.76233 | −0.881163 | − | 0.472812i | \(-0.843239\pi\) | ||||
−0.881163 | + | 0.472812i | \(0.843239\pi\) | |||||||
\(558\) | −15.8619 | −0.671488 | ||||||||
\(559\) | −2.44947 | −0.103602 | ||||||||
\(560\) | −7.29411 | −0.308232 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.675793 | 0.0285066 | ||||||||
\(563\) | −7.87879 | −0.332051 | −0.166026 | − | 0.986121i | \(-0.553093\pi\) | ||||
−0.166026 | + | 0.986121i | \(0.553093\pi\) | |||||||
\(564\) | −5.44335 | −0.229206 | ||||||||
\(565\) | 18.5687 | 0.781193 | ||||||||
\(566\) | −2.64841 | −0.111321 | ||||||||
\(567\) | 41.1874 | 1.72971 | ||||||||
\(568\) | −9.45751 | −0.396828 | ||||||||
\(569\) | −7.38055 | −0.309409 | −0.154704 | − | 0.987961i | \(-0.549443\pi\) | ||||
−0.154704 | + | 0.987961i | \(0.549443\pi\) | |||||||
\(570\) | 3.70058 | 0.155000 | ||||||||
\(571\) | −2.68464 | −0.112349 | −0.0561743 | − | 0.998421i | \(-0.517890\pi\) | ||||
−0.0561743 | + | 0.998421i | \(0.517890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.5879 | 1.40315 | ||||||||
\(574\) | 31.7843 | 1.32665 | ||||||||
\(575\) | −5.82889 | −0.243081 | ||||||||
\(576\) | 3.18819 | 0.132841 | ||||||||
\(577\) | 6.42355 | 0.267416 | 0.133708 | − | 0.991021i | \(-0.457312\pi\) | ||||
0.133708 | + | 0.991021i | \(0.457312\pi\) | |||||||
\(578\) | −17.8484 | −0.742394 | ||||||||
\(579\) | −19.9009 | −0.827051 | ||||||||
\(580\) | 1.04219 | 0.0432745 | ||||||||
\(581\) | −36.7136 | −1.52314 | ||||||||
\(582\) | 24.8761 | 1.03115 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.90325 | 0.0787571 | ||||||||
\(585\) | 14.6620 | 0.606197 | ||||||||
\(586\) | 1.70589 | 0.0704698 | ||||||||
\(587\) | −20.8392 | −0.860125 | −0.430063 | − | 0.902799i | \(-0.641509\pi\) | ||||
−0.430063 | + | 0.902799i | \(0.641509\pi\) | |||||||
\(588\) | 42.3934 | 1.74828 | ||||||||
\(589\) | −4.97521 | −0.205000 | ||||||||
\(590\) | 0.898261 | 0.0369808 | ||||||||
\(591\) | −33.2856 | −1.36918 | ||||||||
\(592\) | 9.31889 | 0.383004 | ||||||||
\(593\) | −5.11383 | −0.210000 | −0.105000 | − | 0.994472i | \(-0.533484\pi\) | ||||
−0.105000 | + | 0.994472i | \(0.533484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −43.0589 | −1.76524 | ||||||||
\(596\) | 23.3410 | 0.956083 | ||||||||
\(597\) | −61.2832 | −2.50815 | ||||||||
\(598\) | −6.46554 | −0.264396 | ||||||||
\(599\) | −19.4797 | −0.795919 | −0.397960 | − | 0.917403i | \(-0.630282\pi\) | ||||
−0.397960 | + | 0.917403i | \(0.630282\pi\) | |||||||
\(600\) | 6.93303 | 0.283040 | ||||||||
\(601\) | −33.3020 | −1.35842 | −0.679209 | − | 0.733945i | \(-0.737677\pi\) | ||||
−0.679209 | + | 0.733945i | \(0.737677\pi\) | |||||||
\(602\) | −3.88504 | −0.158343 | ||||||||
\(603\) | −37.8538 | −1.54153 | ||||||||
\(604\) | 3.32421 | 0.135260 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.1407 | −0.615048 | ||||||||
\(607\) | 7.07051 | 0.286983 | 0.143492 | − | 0.989652i | \(-0.454167\pi\) | ||||
0.143492 | + | 0.989652i | \(0.454167\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −8.54522 | −0.346270 | ||||||||
\(610\) | 7.60351 | 0.307857 | ||||||||
\(611\) | −6.76464 | −0.273668 | ||||||||
\(612\) | 18.8207 | 0.760780 | ||||||||
\(613\) | 31.2552 | 1.26238 | 0.631192 | − | 0.775627i | \(-0.282566\pi\) | ||||
0.631192 | + | 0.775627i | \(0.282566\pi\) | |||||||
\(614\) | 14.3136 | 0.577649 | ||||||||
\(615\) | 23.9882 | 0.967299 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.7410 | 1.68043 | 0.840214 | − | 0.542254i | \(-0.182429\pi\) | ||||
0.840214 | + | 0.542254i | \(0.182429\pi\) | |||||||
\(618\) | −43.5507 | −1.75187 | ||||||||
\(619\) | −8.82131 | −0.354558 | −0.177279 | − | 0.984161i | \(-0.556730\pi\) | ||||
−0.177279 | + | 0.984161i | \(0.556730\pi\) | |||||||
\(620\) | 7.40116 | 0.297238 | ||||||||
\(621\) | 0.979070 | 0.0392887 | ||||||||
\(622\) | −22.1805 | −0.889356 | ||||||||
\(623\) | −17.1961 | −0.688947 | ||||||||
\(624\) | 7.69028 | 0.307857 | ||||||||
\(625\) | −3.29735 | −0.131894 | ||||||||
\(626\) | −10.4873 | −0.419156 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.9177 | 0.914517 | ||||||||
\(629\) | 55.0118 | 2.19346 | ||||||||
\(630\) | 23.2550 | 0.926500 | ||||||||
\(631\) | −29.1623 | −1.16093 | −0.580466 | − | 0.814285i | \(-0.697129\pi\) | ||||
−0.580466 | + | 0.814285i | \(0.697129\pi\) | |||||||
\(632\) | 14.4823 | 0.576075 | ||||||||
\(633\) | 53.3646 | 2.12105 | ||||||||
\(634\) | −30.2785 | −1.20251 | ||||||||
\(635\) | 27.9398 | 1.10876 | ||||||||
\(636\) | −13.1829 | −0.522735 | ||||||||
\(637\) | 52.6838 | 2.08741 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.1523 | 1.19281 | ||||||||
\(640\) | −1.48761 | −0.0588028 | ||||||||
\(641\) | −39.8735 | −1.57491 | −0.787454 | − | 0.616374i | \(-0.788601\pi\) | ||||
−0.787454 | + | 0.616374i | \(0.788601\pi\) | |||||||
\(642\) | −29.2106 | −1.15285 | ||||||||
\(643\) | −11.2366 | −0.443129 | −0.221565 | − | 0.975146i | \(-0.571116\pi\) | ||||
−0.221565 | + | 0.975146i | \(0.571116\pi\) | |||||||
\(644\) | −10.2548 | −0.404097 | ||||||||
\(645\) | −2.93212 | −0.115452 | ||||||||
\(646\) | 5.90325 | 0.232260 | ||||||||
\(647\) | −10.7022 | −0.420746 | −0.210373 | − | 0.977621i | \(-0.567468\pi\) | ||||
−0.210373 | + | 0.977621i | \(0.567468\pi\) | |||||||
\(648\) | 8.40003 | 0.329984 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.61592 | 0.337944 | ||||||||
\(651\) | −60.6844 | −2.37841 | ||||||||
\(652\) | −20.4053 | −0.799135 | ||||||||
\(653\) | −33.6024 | −1.31496 | −0.657481 | − | 0.753471i | \(-0.728378\pi\) | ||||
−0.657481 | + | 0.753471i | \(0.728378\pi\) | |||||||
\(654\) | 6.47730 | 0.253283 | ||||||||
\(655\) | 14.8603 | 0.580638 | ||||||||
\(656\) | 6.48229 | 0.253091 | ||||||||
\(657\) | −6.06792 | −0.236732 | ||||||||
\(658\) | −10.7292 | −0.418269 | ||||||||
\(659\) | −6.17529 | −0.240555 | −0.120278 | − | 0.992740i | \(-0.538378\pi\) | ||||
−0.120278 | + | 0.992740i | \(0.538378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0114 | 0.856146 | 0.428073 | − | 0.903744i | \(-0.359193\pi\) | ||||
0.428073 | + | 0.903744i | \(0.359193\pi\) | |||||||
\(662\) | −4.62330 | −0.179690 | ||||||||
\(663\) | 45.3976 | 1.76310 | ||||||||
\(664\) | −7.48761 | −0.290575 | ||||||||
\(665\) | 7.29411 | 0.282853 | ||||||||
\(666\) | −29.7104 | −1.15125 | ||||||||
\(667\) | 1.46522 | 0.0567335 | ||||||||
\(668\) | 14.7817 | 0.571922 | ||||||||
\(669\) | −18.0700 | −0.698626 | ||||||||
\(670\) | 17.6626 | 0.682365 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 12.1974 | 0.470523 | ||||||||
\(673\) | −6.63620 | −0.255807 | −0.127903 | − | 0.991787i | \(-0.540825\pi\) | ||||
−0.127903 | + | 0.991787i | \(0.540825\pi\) | |||||||
\(674\) | 25.8728 | 0.996584 | ||||||||
\(675\) | −1.30470 | −0.0502179 | ||||||||
\(676\) | −3.44302 | −0.132424 | ||||||||
\(677\) | −26.2521 | −1.00895 | −0.504475 | − | 0.863426i | \(-0.668314\pi\) | ||||
−0.504475 | + | 0.863426i | \(0.668314\pi\) | |||||||
\(678\) | −31.0510 | −1.19251 | ||||||||
\(679\) | 49.0325 | 1.88169 | ||||||||
\(680\) | −8.78171 | −0.336763 | ||||||||
\(681\) | −16.0277 | −0.614183 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.5776 | 1.39960 | 0.699801 | − | 0.714338i | \(-0.253272\pi\) | ||||
0.699801 | + | 0.714338i | \(0.253272\pi\) | |||||||
\(684\) | −3.18819 | −0.121903 | ||||||||
\(685\) | 15.9108 | 0.607922 | ||||||||
\(686\) | 49.2378 | 1.87991 | ||||||||
\(687\) | −35.1581 | −1.34136 | ||||||||
\(688\) | −0.792340 | −0.0302077 | ||||||||
\(689\) | −16.3828 | −0.624136 | ||||||||
\(690\) | −7.73953 | −0.294639 | ||||||||
\(691\) | −17.1660 | −0.653025 | −0.326513 | − | 0.945193i | \(-0.605874\pi\) | ||||
−0.326513 | + | 0.945193i | \(0.605874\pi\) | |||||||
\(692\) | 18.2640 | 0.694293 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.4911 | 1.15743 | ||||||||
\(695\) | 12.3870 | 0.469866 | ||||||||
\(696\) | −1.74277 | −0.0660594 | ||||||||
\(697\) | 38.2666 | 1.44945 | ||||||||
\(698\) | 29.6967 | 1.12404 | ||||||||
\(699\) | 60.1443 | 2.27486 | ||||||||
\(700\) | 13.6655 | 0.516507 | ||||||||
\(701\) | −5.67838 | −0.214470 | −0.107235 | − | 0.994234i | \(-0.534200\pi\) | ||||
−0.107235 | + | 0.994234i | \(0.534200\pi\) | |||||||
\(702\) | −1.44720 | −0.0546212 | ||||||||
\(703\) | −9.31889 | −0.351469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.09756 | −0.304972 | ||||||||
\(706\) | 9.53977 | 0.359034 | ||||||||
\(707\) | −29.8434 | −1.12238 | ||||||||
\(708\) | −1.50209 | −0.0564520 | ||||||||
\(709\) | 5.39118 | 0.202470 | 0.101235 | − | 0.994863i | \(-0.467721\pi\) | ||||
0.101235 | + | 0.994863i | \(0.467721\pi\) | |||||||
\(710\) | −14.0690 | −0.528002 | ||||||||
\(711\) | −46.1722 | −1.73159 | ||||||||
\(712\) | −3.50708 | −0.131433 | ||||||||
\(713\) | 10.4053 | 0.389683 | ||||||||
\(714\) | 72.0041 | 2.69468 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.6262 | −0.583979 | ||||||||
\(717\) | −70.0462 | −2.61592 | ||||||||
\(718\) | 16.6956 | 0.623074 | ||||||||
\(719\) | −44.4507 | −1.65773 | −0.828866 | − | 0.559447i | \(-0.811014\pi\) | ||||
−0.828866 | + | 0.559447i | \(0.811014\pi\) | |||||||
\(720\) | 4.74277 | 0.176752 | ||||||||
\(721\) | −85.8416 | −3.19691 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 44.2404 | 1.64532 | ||||||||
\(724\) | 22.6378 | 0.841327 | ||||||||
\(725\) | −1.95253 | −0.0725153 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.35690 | −0.347028 | −0.173514 | − | 0.984831i | \(-0.555512\pi\) | ||||
−0.173514 | + | 0.984831i | \(0.555512\pi\) | |||||||
\(728\) | 15.1581 | 0.561796 | ||||||||
\(729\) | −30.2744 | −1.12128 | ||||||||
\(730\) | 2.83129 | 0.104791 | ||||||||
\(731\) | −4.67738 | −0.172999 | ||||||||
\(732\) | −12.7147 | −0.469950 | ||||||||
\(733\) | −5.76690 | −0.213005 | −0.106503 | − | 0.994312i | \(-0.533965\pi\) | ||||
−0.106503 | + | 0.994312i | \(0.533965\pi\) | |||||||
\(734\) | −0.198813 | −0.00733833 | ||||||||
\(735\) | 63.0648 | 2.32618 | ||||||||
\(736\) | −2.09144 | −0.0770914 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −20.6668 | −0.760754 | ||||||||
\(739\) | 21.1843 | 0.779278 | 0.389639 | − | 0.920968i | \(-0.372600\pi\) | ||||
0.389639 | + | 0.920968i | \(0.372600\pi\) | |||||||
\(740\) | 13.8628 | 0.509608 | ||||||||
\(741\) | −7.69028 | −0.282509 | ||||||||
\(742\) | −25.9844 | −0.953917 | ||||||||
\(743\) | 21.8117 | 0.800193 | 0.400097 | − | 0.916473i | \(-0.368977\pi\) | ||||
0.400097 | + | 0.916473i | \(0.368977\pi\) | |||||||
\(744\) | −12.3764 | −0.453740 | ||||||||
\(745\) | 34.7222 | 1.27212 | ||||||||
\(746\) | 15.4427 | 0.565397 | ||||||||
\(747\) | 23.8719 | 0.873427 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −57.5761 | −2.10379 | ||||||||
\(750\) | 28.8165 | 1.05223 | ||||||||
\(751\) | −0.530276 | −0.0193500 | −0.00967502 | − | 0.999953i | \(-0.503080\pi\) | ||||
−0.00967502 | + | 0.999953i | \(0.503080\pi\) | |||||||
\(752\) | −2.18819 | −0.0797949 | ||||||||
\(753\) | 3.00418 | 0.109478 | ||||||||
\(754\) | −2.16580 | −0.0788737 | ||||||||
\(755\) | 4.94511 | 0.179971 | ||||||||
\(756\) | −2.29537 | −0.0834819 | ||||||||
\(757\) | 6.70589 | 0.243730 | 0.121865 | − | 0.992547i | \(-0.461113\pi\) | ||||
0.121865 | + | 0.992547i | \(0.461113\pi\) | |||||||
\(758\) | −20.9791 | −0.761994 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.48761 | 0.0539612 | ||||||||
\(761\) | 46.5357 | 1.68692 | 0.843459 | − | 0.537193i | \(-0.180515\pi\) | ||||
0.843459 | + | 0.537193i | \(0.180515\pi\) | |||||||
\(762\) | −46.7215 | −1.69254 | ||||||||
\(763\) | 12.7672 | 0.462205 | ||||||||
\(764\) | 13.5021 | 0.488489 | ||||||||
\(765\) | 27.9977 | 1.01226 | ||||||||
\(766\) | 25.3310 | 0.915246 | ||||||||
\(767\) | −1.86670 | −0.0674027 | ||||||||
\(768\) | 2.48761 | 0.0897638 | ||||||||
\(769\) | −19.5882 | −0.706369 | −0.353185 | − | 0.935554i | \(-0.614901\pi\) | ||||
−0.353185 | + | 0.935554i | \(0.614901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.8100 | −1.46974 | ||||||||
\(772\) | −8.00000 | −0.287926 | ||||||||
\(773\) | 28.5348 | 1.02632 | 0.513162 | − | 0.858292i | \(-0.328474\pi\) | ||||
0.513162 | + | 0.858292i | \(0.328474\pi\) | |||||||
\(774\) | 2.52613 | 0.0907998 | ||||||||
\(775\) | −13.8661 | −0.498083 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | −113.666 | −4.07774 | ||||||||
\(778\) | 4.46282 | 0.160000 | ||||||||
\(779\) | −6.48229 | −0.232252 | ||||||||
\(780\) | 11.4401 | 0.409622 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −12.3463 | −0.441502 | ||||||||
\(783\) | 0.327964 | 0.0117205 | ||||||||
\(784\) | 17.0419 | 0.608638 | ||||||||
\(785\) | 34.0926 | 1.21682 | ||||||||
\(786\) | −24.8496 | −0.886357 | ||||||||
\(787\) | −22.0811 | −0.787107 | −0.393554 | − | 0.919302i | \(-0.628754\pi\) | ||||
−0.393554 | + | 0.919302i | \(0.628754\pi\) | |||||||
\(788\) | −13.3806 | −0.476663 | ||||||||
\(789\) | −67.6071 | −2.40688 | ||||||||
\(790\) | 21.5440 | 0.766499 | ||||||||
\(791\) | −61.2038 | −2.17616 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.8011 | −0.561112 | ||||||||
\(794\) | −29.9398 | −1.06252 | ||||||||
\(795\) | −19.6109 | −0.695528 | ||||||||
\(796\) | −24.6354 | −0.873178 | ||||||||
\(797\) | 40.8484 | 1.44692 | 0.723462 | − | 0.690365i | \(-0.242550\pi\) | ||||
0.723462 | + | 0.690365i | \(0.242550\pi\) | |||||||
\(798\) | −12.1974 | −0.431782 | ||||||||
\(799\) | −12.9174 | −0.456985 | ||||||||
\(800\) | 2.78703 | 0.0985363 | ||||||||
\(801\) | 11.1812 | 0.395069 | ||||||||
\(802\) | 18.2888 | 0.645800 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −29.5357 | −1.04164 | ||||||||
\(805\) | −15.2552 | −0.537674 | ||||||||
\(806\) | −15.3806 | −0.541757 | ||||||||
\(807\) | 22.9835 | 0.809059 | ||||||||
\(808\) | −6.08645 | −0.214120 | ||||||||
\(809\) | −5.16340 | −0.181535 | −0.0907677 | − | 0.995872i | \(-0.528932\pi\) | ||||
−0.0907677 | + | 0.995872i | \(0.528932\pi\) | |||||||
\(810\) | 12.4959 | 0.439062 | ||||||||
\(811\) | 33.6162 | 1.18043 | 0.590213 | − | 0.807248i | \(-0.299044\pi\) | ||||
0.590213 | + | 0.807248i | \(0.299044\pi\) | |||||||
\(812\) | −3.43512 | −0.120549 | ||||||||
\(813\) | 42.4419 | 1.48850 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.3551 | −1.06329 | ||||||||
\(816\) | 14.6850 | 0.514077 | ||||||||
\(817\) | 0.792340 | 0.0277205 | ||||||||
\(818\) | 25.5634 | 0.893804 | ||||||||
\(819\) | −48.3268 | −1.68867 | ||||||||
\(820\) | 9.64310 | 0.336752 | ||||||||
\(821\) | −38.4026 | −1.34026 | −0.670130 | − | 0.742243i | \(-0.733762\pi\) | ||||
−0.670130 | + | 0.742243i | \(0.733762\pi\) | |||||||
\(822\) | −26.6064 | −0.928005 | ||||||||
\(823\) | 42.0589 | 1.46608 | 0.733041 | − | 0.680184i | \(-0.238100\pi\) | ||||
0.733041 | + | 0.680184i | \(0.238100\pi\) | |||||||
\(824\) | −17.5071 | −0.609888 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.96073 | −0.103017 | ||||||||
\(827\) | −46.2094 | −1.60686 | −0.803430 | − | 0.595399i | \(-0.796994\pi\) | ||||
−0.803430 | + | 0.595399i | \(0.796994\pi\) | |||||||
\(828\) | 6.66789 | 0.231725 | ||||||||
\(829\) | −20.8484 | −0.724094 | −0.362047 | − | 0.932160i | \(-0.617922\pi\) | ||||
−0.362047 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(830\) | −11.1386 | −0.386627 | ||||||||
\(831\) | 53.9076 | 1.87003 | ||||||||
\(832\) | 3.09144 | 0.107176 | ||||||||
\(833\) | 100.602 | 3.48567 | ||||||||
\(834\) | −20.7138 | −0.717260 | ||||||||
\(835\) | 21.9894 | 0.760974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.32906 | 0.0805041 | ||||||||
\(838\) | 27.6103 | 0.953781 | ||||||||
\(839\) | 53.8522 | 1.85919 | 0.929593 | − | 0.368589i | \(-0.120159\pi\) | ||||
0.929593 | + | 0.368589i | \(0.120159\pi\) | |||||||
\(840\) | 18.1449 | 0.626057 | ||||||||
\(841\) | −28.5092 | −0.983075 | ||||||||
\(842\) | 18.5242 | 0.638385 | ||||||||
\(843\) | −1.68111 | −0.0579004 | ||||||||
\(844\) | 21.4522 | 0.738415 | ||||||||
\(845\) | −5.12186 | −0.176197 | ||||||||
\(846\) | 6.97634 | 0.239852 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.29942 | −0.181983 | ||||||||
\(849\) | 6.58821 | 0.226107 | ||||||||
\(850\) | 16.4525 | 0.564317 | ||||||||
\(851\) | 19.4899 | 0.668104 | ||||||||
\(852\) | 23.5266 | 0.806006 | ||||||||
\(853\) | −7.61300 | −0.260664 | −0.130332 | − | 0.991470i | \(-0.541604\pi\) | ||||
−0.130332 | + | 0.991470i | \(0.541604\pi\) | |||||||
\(854\) | −25.0617 | −0.857592 | ||||||||
\(855\) | −4.74277 | −0.162199 | ||||||||
\(856\) | −11.7424 | −0.401348 | ||||||||
\(857\) | 45.9688 | 1.57026 | 0.785132 | − | 0.619329i | \(-0.212595\pi\) | ||||
0.785132 | + | 0.619329i | \(0.212595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.5813 | 1.21402 | 0.607009 | − | 0.794695i | \(-0.292369\pi\) | ||||
0.607009 | + | 0.794695i | \(0.292369\pi\) | |||||||
\(860\) | −1.17869 | −0.0401930 | ||||||||
\(861\) | −79.0668 | −2.69459 | ||||||||
\(862\) | 13.8835 | 0.472872 | ||||||||
\(863\) | 4.29783 | 0.146300 | 0.0731499 | − | 0.997321i | \(-0.476695\pi\) | ||||
0.0731499 | + | 0.997321i | \(0.476695\pi\) | |||||||
\(864\) | −0.468133 | −0.0159262 | ||||||||
\(865\) | 27.1697 | 0.923796 | ||||||||
\(866\) | −5.02479 | −0.170749 | ||||||||
\(867\) | 44.3997 | 1.50789 | ||||||||
\(868\) | −24.3947 | −0.828011 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.59255 | −0.0878957 | ||||||||
\(871\) | −36.7051 | −1.24370 | ||||||||
\(872\) | 2.60383 | 0.0881768 | ||||||||
\(873\) | −31.8819 | −1.07904 | ||||||||
\(874\) | 2.09144 | 0.0707439 | ||||||||
\(875\) | 56.7994 | 1.92017 | ||||||||
\(876\) | −4.73454 | −0.159965 | ||||||||
\(877\) | 7.43836 | 0.251175 | 0.125588 | − | 0.992083i | \(-0.459918\pi\) | ||||
0.125588 | + | 0.992083i | \(0.459918\pi\) | |||||||
\(878\) | −8.23245 | −0.277832 | ||||||||
\(879\) | −4.24359 | −0.143133 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.71380 | 0.0577393 | 0.0288697 | − | 0.999583i | \(-0.490809\pi\) | ||||
0.0288697 | + | 0.999583i | \(0.490809\pi\) | |||||||
\(882\) | −54.3326 | −1.82947 | ||||||||
\(883\) | 9.92418 | 0.333975 | 0.166988 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166988 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(884\) | 18.2495 | 0.613798 | ||||||||
\(885\) | −2.23452 | −0.0751126 | ||||||||
\(886\) | 20.1722 | 0.677700 | ||||||||
\(887\) | 7.22441 | 0.242572 | 0.121286 | − | 0.992618i | \(-0.461298\pi\) | ||||
0.121286 | + | 0.992618i | \(0.461298\pi\) | |||||||
\(888\) | −23.1817 | −0.777928 | ||||||||
\(889\) | −92.0914 | −3.08865 | ||||||||
\(890\) | −5.21715 | −0.174879 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.26401 | −0.243217 | ||||||||
\(893\) | 2.18819 | 0.0732249 | ||||||||
\(894\) | −58.0631 | −1.94192 | ||||||||
\(895\) | −23.2457 | −0.777017 | ||||||||
\(896\) | 4.90325 | 0.163806 | ||||||||
\(897\) | 16.0837 | 0.537020 | ||||||||
\(898\) | 10.7923 | 0.360145 | ||||||||
\(899\) | 3.48553 | 0.116249 | ||||||||
\(900\) | −8.88556 | −0.296185 | ||||||||
\(901\) | −31.2838 | −1.04221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.66446 | 0.321613 | ||||||||
\(904\) | −12.4823 | −0.415155 | ||||||||
\(905\) | 33.6761 | 1.11943 | ||||||||
\(906\) | −8.26932 | −0.274730 | ||||||||
\(907\) | 26.1673 | 0.868869 | 0.434435 | − | 0.900703i | \(-0.356948\pi\) | ||||
0.434435 | + | 0.900703i | \(0.356948\pi\) | |||||||
\(908\) | −6.44302 | −0.213819 | ||||||||
\(909\) | 19.4047 | 0.643614 | ||||||||
\(910\) | 22.5493 | 0.747501 | ||||||||
\(911\) | 45.0705 | 1.49325 | 0.746626 | − | 0.665244i | \(-0.231672\pi\) | ||||
0.746626 | + | 0.665244i | \(0.231672\pi\) | |||||||
\(912\) | −2.48761 | −0.0823729 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.27431 | 0.273690 | ||||||||
\(915\) | −18.9145 | −0.625295 | ||||||||
\(916\) | −14.1333 | −0.466977 | ||||||||
\(917\) | −48.9804 | −1.61748 | ||||||||
\(918\) | −2.76351 | −0.0912093 | ||||||||
\(919\) | 25.4024 | 0.837949 | 0.418974 | − | 0.907998i | \(-0.362390\pi\) | ||||
0.418974 | + | 0.907998i | \(0.362390\pi\) | |||||||
\(920\) | −3.11123 | −0.102574 | ||||||||
\(921\) | −35.6066 | −1.17328 | ||||||||
\(922\) | 17.6209 | 0.580314 | ||||||||
\(923\) | 29.2373 | 0.962357 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.9720 | −0.853954 | ||||||||
\(926\) | −2.53977 | −0.0834621 | ||||||||
\(927\) | 55.8158 | 1.83323 | ||||||||
\(928\) | −0.700580 | −0.0229977 | ||||||||
\(929\) | 24.9398 | 0.818248 | 0.409124 | − | 0.912479i | \(-0.365834\pi\) | ||||
0.409124 | + | 0.912479i | \(0.365834\pi\) | |||||||
\(930\) | −18.4112 | −0.603726 | ||||||||
\(931\) | −17.0419 | −0.558524 | ||||||||
\(932\) | 24.1776 | 0.791962 | ||||||||
\(933\) | 55.1763 | 1.80639 | ||||||||
\(934\) | 10.8213 | 0.354084 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.85607 | −0.322156 | ||||||||
\(937\) | 16.0288 | 0.523639 | 0.261820 | − | 0.965117i | \(-0.415677\pi\) | ||||
0.261820 | + | 0.965117i | \(0.415677\pi\) | |||||||
\(938\) | −58.2170 | −1.90085 | ||||||||
\(939\) | 26.0882 | 0.851357 | ||||||||
\(940\) | −3.25516 | −0.106172 | ||||||||
\(941\) | 35.9569 | 1.17216 | 0.586080 | − | 0.810253i | \(-0.300670\pi\) | ||||
0.586080 | + | 0.810253i | \(0.300670\pi\) | |||||||
\(942\) | −57.0103 | −1.85750 | ||||||||
\(943\) | 13.5573 | 0.441487 | ||||||||
\(944\) | −0.603830 | −0.0196530 | ||||||||
\(945\) | −3.41461 | −0.111077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.1771 | −1.27308 | −0.636542 | − | 0.771242i | \(-0.719636\pi\) | ||||
−0.636542 | + | 0.771242i | \(0.719636\pi\) | |||||||
\(948\) | −36.0262 | −1.17008 | ||||||||
\(949\) | −5.88378 | −0.190995 | ||||||||
\(950\) | −2.78703 | −0.0904231 | ||||||||
\(951\) | 75.3210 | 2.44245 | ||||||||
\(952\) | 28.9451 | 0.938116 | ||||||||
\(953\) | −34.0670 | −1.10354 | −0.551769 | − | 0.833997i | \(-0.686047\pi\) | ||||
−0.551769 | + | 0.833997i | \(0.686047\pi\) | |||||||
\(954\) | 16.8955 | 0.547013 | ||||||||
\(955\) | 20.0858 | 0.649961 | ||||||||
\(956\) | −28.1581 | −0.910698 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.96459 | 0.321941 | ||||||||
\(959\) | −52.4432 | −1.69348 | ||||||||
\(960\) | 3.70058 | 0.119436 | ||||||||
\(961\) | −6.24726 | −0.201524 | ||||||||
\(962\) | −28.8088 | −0.928832 | ||||||||
\(963\) | 37.4371 | 1.20639 | ||||||||
\(964\) | 17.7843 | 0.572794 | ||||||||
\(965\) | −11.9009 | −0.383102 | ||||||||
\(966\) | 25.5100 | 0.820771 | ||||||||
\(967\) | −4.50980 | −0.145025 | −0.0725127 | − | 0.997367i | \(-0.523102\pi\) | ||||
−0.0725127 | + | 0.997367i | \(0.523102\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.6850 | −0.471749 | ||||||||
\(970\) | 14.8761 | 0.477642 | ||||||||
\(971\) | −1.82970 | −0.0587178 | −0.0293589 | − | 0.999569i | \(-0.509347\pi\) | ||||
−0.0293589 | + | 0.999569i | \(0.509347\pi\) | |||||||
\(972\) | −22.3004 | −0.715284 | ||||||||
\(973\) | −40.8284 | −1.30890 | ||||||||
\(974\) | −8.36639 | −0.268077 | ||||||||
\(975\) | −21.4330 | −0.686406 | ||||||||
\(976\) | −5.11123 | −0.163607 | ||||||||
\(977\) | −27.8902 | −0.892287 | −0.446144 | − | 0.894961i | \(-0.647203\pi\) | ||||
−0.446144 | + | 0.894961i | \(0.647203\pi\) | |||||||
\(978\) | 50.7605 | 1.62314 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 25.3516 | 0.809827 | ||||||||
\(981\) | −8.30149 | −0.265046 | ||||||||
\(982\) | −4.27722 | −0.136492 | ||||||||
\(983\) | 46.1790 | 1.47288 | 0.736441 | − | 0.676502i | \(-0.236505\pi\) | ||||
0.736441 | + | 0.676502i | \(0.236505\pi\) | |||||||
\(984\) | −16.1254 | −0.514059 | ||||||||
\(985\) | −19.9050 | −0.634226 | ||||||||
\(986\) | −4.13570 | −0.131707 | ||||||||
\(987\) | 26.6901 | 0.849555 | ||||||||
\(988\) | −3.09144 | −0.0983517 | ||||||||
\(989\) | −1.65713 | −0.0526937 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2782 | 1.15241 | 0.576207 | − | 0.817304i | \(-0.304532\pi\) | ||||
0.576207 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(992\) | −4.97521 | −0.157963 | ||||||||
\(993\) | 11.5010 | 0.364972 | ||||||||
\(994\) | 46.3725 | 1.47085 | ||||||||
\(995\) | −36.6478 | −1.16181 | ||||||||
\(996\) | 18.6262 | 0.590194 | ||||||||
\(997\) | 44.0469 | 1.39498 | 0.697489 | − | 0.716596i | \(-0.254301\pi\) | ||||
0.697489 | + | 0.716596i | \(0.254301\pi\) | |||||||
\(998\) | −2.08645 | −0.0660453 | ||||||||
\(999\) | 4.36248 | 0.138023 |
(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 | 4598.2.a.bs.1.3 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bv.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bs.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bv.1.3 | yes | 4 | 11.10 | odd | 2 |