Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7232.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 5x^{2} + 4x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.63640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.222191 | −0.157113 | −0.0785565 | − | 0.996910i | \(-0.525031\pi\) | ||||
−0.0785565 | + | 0.996910i | \(0.525031\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.95063 | −0.975315 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.222191 | 0.0907092 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.877796 | 0.310348 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.222191 | −0.0702631 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.95063 | 0.563099 | ||||||||
\(13\) | 0.900012 | 0.249619 | 0.124809 | − | 0.992181i | \(-0.460168\pi\) | ||||
0.124809 | + | 0.992181i | \(0.460168\pi\) | |||||||
\(14\) | −0.222191 | −0.0593831 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 3.70622 | 0.926556 | ||||||||
\(17\) | −0.506248 | −0.122783 | −0.0613916 | − | 0.998114i | \(-0.519554\pi\) | ||||
−0.0613916 | + | 0.998114i | \(0.519554\pi\) | |||||||
\(18\) | −0.222191 | −0.0523710 | ||||||||
\(19\) | −4.95063 | −1.13575 | −0.567876 | − | 0.823114i | \(-0.692235\pi\) | ||||
−0.567876 | + | 0.823114i | \(0.692235\pi\) | |||||||
\(20\) | −1.95063 | −0.436174 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.222191 | −0.0473714 | ||||||||
\(23\) | −6.60749 | −1.37776 | −0.688878 | − | 0.724877i | \(-0.741896\pi\) | ||||
−0.688878 | + | 0.724877i | \(0.741896\pi\) | |||||||
\(24\) | −0.877796 | −0.179179 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.199975 | −0.0392183 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.95063 | −0.368635 | ||||||||
\(29\) | 3.40626 | 0.632527 | 0.316263 | − | 0.948671i | \(-0.397572\pi\) | ||||
0.316263 | + | 0.948671i | \(0.397572\pi\) | |||||||
\(30\) | 0.222191 | 0.0405664 | ||||||||
\(31\) | −3.54437 | −0.636588 | −0.318294 | − | 0.947992i | \(-0.603110\pi\) | ||||
−0.318294 | + | 0.947992i | \(0.603110\pi\) | |||||||
\(32\) | −2.57908 | −0.455922 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.112484 | 0.0192908 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.95063 | −0.325105 | ||||||||
\(37\) | 11.4456 | 1.88165 | 0.940825 | − | 0.338892i | \(-0.110052\pi\) | ||||
0.940825 | + | 0.338892i | \(0.110052\pi\) | |||||||
\(38\) | 1.09999 | 0.178442 | ||||||||
\(39\) | −0.900012 | −0.144117 | ||||||||
\(40\) | 0.877796 | 0.138792 | ||||||||
\(41\) | 6.80127 | 1.06218 | 0.531090 | − | 0.847315i | \(-0.321782\pi\) | ||||
0.531090 | + | 0.847315i | \(0.321782\pi\) | |||||||
\(42\) | 0.222191 | 0.0342849 | ||||||||
\(43\) | 9.26309 | 1.41261 | 0.706304 | − | 0.707909i | \(-0.250361\pi\) | ||||
0.706304 | + | 0.707909i | \(0.250361\pi\) | |||||||
\(44\) | −1.95063 | −0.294069 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.46813 | 0.216463 | ||||||||
\(47\) | 12.6581 | 1.84637 | 0.923187 | − | 0.384351i | \(-0.125575\pi\) | ||||
0.923187 | + | 0.384351i | \(0.125575\pi\) | |||||||
\(48\) | −3.70622 | −0.534947 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.222191 | −0.0314226 | ||||||||
\(51\) | 0.506248 | 0.0708889 | ||||||||
\(52\) | −1.75559 | −0.243457 | ||||||||
\(53\) | −1.39501 | −0.191620 | −0.0958099 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958099 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(54\) | 0.222191 | 0.0302364 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0.877796 | 0.117300 | ||||||||
\(57\) | 4.95063 | 0.655727 | ||||||||
\(58\) | −0.756842 | −0.0993782 | ||||||||
\(59\) | 6.93938 | 0.903431 | 0.451715 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451715 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(60\) | 1.95063 | 0.251825 | ||||||||
\(61\) | 5.39501 | 0.690761 | 0.345380 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345380 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(62\) | 0.787529 | 0.100016 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −6.83940 | −0.854925 | ||||||||
\(65\) | 0.900012 | 0.111633 | ||||||||
\(66\) | 0.222191 | 0.0273499 | ||||||||
\(67\) | −10.3012 | −1.25849 | −0.629247 | − | 0.777206i | \(-0.716636\pi\) | ||||
−0.629247 | + | 0.777206i | \(0.716636\pi\) | |||||||
\(68\) | 0.987504 | 0.119752 | ||||||||
\(69\) | 6.60749 | 0.795448 | ||||||||
\(70\) | −0.222191 | −0.0265569 | ||||||||
\(71\) | 6.35689 | 0.754424 | 0.377212 | − | 0.926127i | \(-0.376883\pi\) | ||||
0.377212 | + | 0.926127i | \(0.376883\pi\) | |||||||
\(72\) | 0.877796 | 0.103449 | ||||||||
\(73\) | 3.55562 | 0.416154 | 0.208077 | − | 0.978112i | \(-0.433280\pi\) | ||||
0.208077 | + | 0.978112i | \(0.433280\pi\) | |||||||
\(74\) | −2.54312 | −0.295632 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 9.65685 | 1.10772 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0.199975 | 0.0226427 | ||||||||
\(79\) | 1.98875 | 0.223752 | 0.111876 | − | 0.993722i | \(-0.464314\pi\) | ||||
0.111876 | + | 0.993722i | \(0.464314\pi\) | |||||||
\(80\) | 3.70622 | 0.414368 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.51118 | −0.166882 | ||||||||
\(83\) | −4.16310 | −0.456960 | −0.228480 | − | 0.973549i | \(-0.573376\pi\) | ||||
−0.228480 | + | 0.973549i | \(0.573376\pi\) | |||||||
\(84\) | 1.95063 | 0.212831 | ||||||||
\(85\) | −0.506248 | −0.0549103 | ||||||||
\(86\) | −2.05818 | −0.221939 | ||||||||
\(87\) | −3.40626 | −0.365189 | ||||||||
\(88\) | 0.877796 | 0.0935734 | ||||||||
\(89\) | 2.25059 | 0.238562 | 0.119281 | − | 0.992861i | \(-0.461941\pi\) | ||||
0.119281 | + | 0.992861i | \(0.461941\pi\) | |||||||
\(90\) | −0.222191 | −0.0234210 | ||||||||
\(91\) | 0.900012 | 0.0943469 | ||||||||
\(92\) | 12.8888 | 1.34375 | ||||||||
\(93\) | 3.54437 | 0.367534 | ||||||||
\(94\) | −2.81252 | −0.290089 | ||||||||
\(95\) | −4.95063 | −0.507924 | ||||||||
\(96\) | 2.57908 | 0.263227 | ||||||||
\(97\) | 0.0506185 | 0.00513953 | 0.00256976 | − | 0.999997i | \(-0.499182\pi\) | ||||
0.00256976 | + | 0.999997i | \(0.499182\pi\) | |||||||
\(98\) | −0.222191 | −0.0224447 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.95063 | −0.195063 | ||||||||
\(101\) | −3.25690 | −0.324074 | −0.162037 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162037 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(102\) | −0.112484 | −0.0111376 | ||||||||
\(103\) | −0.0481195 | −0.00474136 | −0.00237068 | − | 0.999997i | \(-0.500755\pi\) | ||||
−0.00237068 | + | 0.999997i | \(0.500755\pi\) | |||||||
\(104\) | 0.790027 | 0.0774686 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0.309960 | 0.0301060 | ||||||||
\(107\) | 15.8900 | 1.53615 | 0.768073 | − | 0.640362i | \(-0.221216\pi\) | ||||
0.768073 | + | 0.640362i | \(0.221216\pi\) | |||||||
\(108\) | 1.95063 | 0.187700 | ||||||||
\(109\) | −17.4706 | −1.67338 | −0.836691 | − | 0.547675i | \(-0.815513\pi\) | ||||
−0.836691 | + | 0.547675i | \(0.815513\pi\) | |||||||
\(110\) | −0.222191 | −0.0211851 | ||||||||
\(111\) | −11.4456 | −1.08637 | ||||||||
\(112\) | 3.70622 | 0.350205 | ||||||||
\(113\) | 19.4200 | 1.82688 | 0.913440 | − | 0.406973i | \(-0.133416\pi\) | ||||
0.913440 | + | 0.406973i | \(0.133416\pi\) | |||||||
\(114\) | −1.09999 | −0.103023 | ||||||||
\(115\) | −6.60749 | −0.616151 | ||||||||
\(116\) | −6.64436 | −0.616913 | ||||||||
\(117\) | 0.900012 | 0.0832062 | ||||||||
\(118\) | −1.54187 | −0.141941 | ||||||||
\(119\) | −0.506248 | −0.0464077 | ||||||||
\(120\) | −0.877796 | −0.0801315 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.19873 | −0.108528 | ||||||||
\(123\) | −6.80127 | −0.613250 | ||||||||
\(124\) | 6.91376 | 0.620874 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.222191 | −0.0197944 | ||||||||
\(127\) | 10.9394 | 0.970713 | 0.485357 | − | 0.874316i | \(-0.338690\pi\) | ||||
0.485357 | + | 0.874316i | \(0.338690\pi\) | |||||||
\(128\) | 6.67782 | 0.590242 | ||||||||
\(129\) | −9.26309 | −0.815570 | ||||||||
\(130\) | −0.199975 | −0.0175390 | ||||||||
\(131\) | 11.3469 | 0.991383 | 0.495691 | − | 0.868499i | \(-0.334915\pi\) | ||||
0.495691 | + | 0.868499i | \(0.334915\pi\) | |||||||
\(132\) | 1.95063 | 0.169781 | ||||||||
\(133\) | −4.95063 | −0.429274 | ||||||||
\(134\) | 2.28884 | 0.197726 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −0.444383 | −0.0381055 | ||||||||
\(137\) | 13.1900 | 1.12690 | 0.563448 | − | 0.826152i | \(-0.309475\pi\) | ||||
0.563448 | + | 0.826152i | \(0.309475\pi\) | |||||||
\(138\) | −1.46813 | −0.124975 | ||||||||
\(139\) | −19.5581 | −1.65890 | −0.829449 | − | 0.558583i | \(-0.811345\pi\) | ||||
−0.829449 | + | 0.558583i | \(0.811345\pi\) | |||||||
\(140\) | −1.95063 | −0.164858 | ||||||||
\(141\) | −12.6581 | −1.06600 | ||||||||
\(142\) | −1.41245 | −0.118530 | ||||||||
\(143\) | 0.900012 | 0.0752628 | ||||||||
\(144\) | 3.70622 | 0.308852 | ||||||||
\(145\) | 3.40626 | 0.282875 | ||||||||
\(146\) | −0.790027 | −0.0653831 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −22.3262 | −1.83520 | ||||||||
\(149\) | −0.568114 | −0.0465417 | −0.0232708 | − | 0.999729i | \(-0.507408\pi\) | ||||
−0.0232708 | + | 0.999729i | \(0.507408\pi\) | |||||||
\(150\) | 0.222191 | 0.0181418 | ||||||||
\(151\) | 4.44688 | 0.361882 | 0.180941 | − | 0.983494i | \(-0.442086\pi\) | ||||
0.180941 | + | 0.983494i | \(0.442086\pi\) | |||||||
\(152\) | −4.34564 | −0.352478 | ||||||||
\(153\) | −0.506248 | −0.0409277 | ||||||||
\(154\) | −0.222191 | −0.0179047 | ||||||||
\(155\) | −3.54437 | −0.284691 | ||||||||
\(156\) | 1.75559 | 0.140560 | ||||||||
\(157\) | 8.15186 | 0.650589 | 0.325294 | − | 0.945613i | \(-0.394537\pi\) | ||||
0.325294 | + | 0.945613i | \(0.394537\pi\) | |||||||
\(158\) | −0.441884 | −0.0351544 | ||||||||
\(159\) | 1.39501 | 0.110632 | ||||||||
\(160\) | −2.57908 | −0.203894 | ||||||||
\(161\) | −6.60749 | −0.520743 | ||||||||
\(162\) | −0.222191 | −0.0174570 | ||||||||
\(163\) | 6.63311 | 0.519545 | 0.259773 | − | 0.965670i | \(-0.416352\pi\) | ||||
0.259773 | + | 0.965670i | \(0.416352\pi\) | |||||||
\(164\) | −13.2668 | −1.03596 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 0.925005 | 0.0717943 | ||||||||
\(167\) | 3.75559 | 0.290616 | 0.145308 | − | 0.989386i | \(-0.453583\pi\) | ||||
0.145308 | + | 0.989386i | \(0.453583\pi\) | |||||||
\(168\) | −0.877796 | −0.0677234 | ||||||||
\(169\) | −12.1900 | −0.937691 | ||||||||
\(170\) | 0.112484 | 0.00862713 | ||||||||
\(171\) | −4.95063 | −0.378584 | ||||||||
\(172\) | −18.0689 | −1.37774 | ||||||||
\(173\) | −15.7038 | −1.19394 | −0.596968 | − | 0.802265i | \(-0.703628\pi\) | ||||
−0.596968 | + | 0.802265i | \(0.703628\pi\) | |||||||
\(174\) | 0.756842 | 0.0573760 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 3.70622 | 0.279367 | ||||||||
\(177\) | −6.93938 | −0.521596 | ||||||||
\(178\) | −0.500062 | −0.0374813 | ||||||||
\(179\) | −8.95682 | −0.669464 | −0.334732 | − | 0.942313i | \(-0.608646\pi\) | ||||
−0.334732 | + | 0.942313i | \(0.608646\pi\) | |||||||
\(180\) | −1.95063 | −0.145391 | ||||||||
\(181\) | −13.8025 | −1.02593 | −0.512967 | − | 0.858408i | \(-0.671454\pi\) | ||||
−0.512967 | + | 0.858408i | \(0.671454\pi\) | |||||||
\(182\) | −0.199975 | −0.0148231 | ||||||||
\(183\) | −5.39501 | −0.398811 | ||||||||
\(184\) | −5.80002 | −0.427584 | ||||||||
\(185\) | 11.4456 | 0.841500 | ||||||||
\(186\) | −0.787529 | −0.0577444 | ||||||||
\(187\) | −0.506248 | −0.0370205 | ||||||||
\(188\) | −24.6913 | −1.80080 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.09999 | 0.0798015 | ||||||||
\(191\) | 6.91376 | 0.500262 | 0.250131 | − | 0.968212i | \(-0.419526\pi\) | ||||
0.250131 | + | 0.968212i | \(0.419526\pi\) | |||||||
\(192\) | 6.83940 | 0.493591 | ||||||||
\(193\) | 2.14317 | 0.154269 | 0.0771344 | − | 0.997021i | \(-0.475423\pi\) | ||||
0.0771344 | + | 0.997021i | \(0.475423\pi\) | |||||||
\(194\) | −0.0112470 | −0.000807487 0 | ||||||||
\(195\) | −0.900012 | −0.0644512 | ||||||||
\(196\) | −1.95063 | −0.139331 | ||||||||
\(197\) | 18.5901 | 1.32449 | 0.662243 | − | 0.749289i | \(-0.269605\pi\) | ||||
0.662243 | + | 0.749289i | \(0.269605\pi\) | |||||||
\(198\) | −0.222191 | −0.0157905 | ||||||||
\(199\) | −3.60005 | −0.255201 | −0.127600 | − | 0.991826i | \(-0.540727\pi\) | ||||
−0.127600 | + | 0.991826i | \(0.540727\pi\) | |||||||
\(200\) | 0.877796 | 0.0620696 | ||||||||
\(201\) | 10.3012 | 0.726591 | ||||||||
\(202\) | 0.723656 | 0.0509163 | ||||||||
\(203\) | 3.40626 | 0.239073 | ||||||||
\(204\) | −0.987504 | −0.0691391 | ||||||||
\(205\) | 6.80127 | 0.475022 | ||||||||
\(206\) | 0.0106917 | 0.000744929 0 | ||||||||
\(207\) | −6.60749 | −0.459252 | ||||||||
\(208\) | 3.33565 | 0.231286 | ||||||||
\(209\) | −4.95063 | −0.342442 | ||||||||
\(210\) | 0.222191 | 0.0153327 | ||||||||
\(211\) | −4.22191 | −0.290649 | −0.145324 | − | 0.989384i | \(-0.546423\pi\) | ||||
−0.145324 | + | 0.989384i | \(0.546423\pi\) | |||||||
\(212\) | 2.72116 | 0.186890 | ||||||||
\(213\) | −6.35689 | −0.435567 | ||||||||
\(214\) | −3.53062 | −0.241349 | ||||||||
\(215\) | 9.26309 | 0.631737 | ||||||||
\(216\) | −0.877796 | −0.0597265 | ||||||||
\(217\) | −3.54437 | −0.240608 | ||||||||
\(218\) | 3.88182 | 0.262910 | ||||||||
\(219\) | −3.55562 | −0.240266 | ||||||||
\(220\) | −1.95063 | −0.131512 | ||||||||
\(221\) | −0.455630 | −0.0306490 | ||||||||
\(222\) | 2.54312 | 0.170683 | ||||||||
\(223\) | −9.94938 | −0.666260 | −0.333130 | − | 0.942881i | \(-0.608105\pi\) | ||||
−0.333130 | + | 0.942881i | \(0.608105\pi\) | |||||||
\(224\) | −2.57908 | −0.172322 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −4.31496 | −0.287027 | ||||||||
\(227\) | 14.8519 | 0.985755 | 0.492877 | − | 0.870099i | \(-0.335945\pi\) | ||||
0.492877 | + | 0.870099i | \(0.335945\pi\) | |||||||
\(228\) | −9.65685 | −0.639541 | ||||||||
\(229\) | 3.24316 | 0.214314 | 0.107157 | − | 0.994242i | \(-0.465825\pi\) | ||||
0.107157 | + | 0.994242i | \(0.465825\pi\) | |||||||
\(230\) | 1.46813 | 0.0968054 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 2.99000 | 0.196303 | ||||||||
\(233\) | 11.1694 | 0.731733 | 0.365866 | − | 0.930667i | \(-0.380773\pi\) | ||||
0.365866 | + | 0.930667i | \(0.380773\pi\) | |||||||
\(234\) | −0.199975 | −0.0130728 | ||||||||
\(235\) | 12.6581 | 0.825724 | ||||||||
\(236\) | −13.5362 | −0.881130 | ||||||||
\(237\) | −1.98875 | −0.129183 | ||||||||
\(238\) | 0.112484 | 0.00729125 | ||||||||
\(239\) | 2.45057 | 0.158514 | 0.0792571 | − | 0.996854i | \(-0.474745\pi\) | ||||
0.0792571 | + | 0.996854i | \(0.474745\pi\) | |||||||
\(240\) | −3.70622 | −0.239236 | ||||||||
\(241\) | −26.1012 | −1.68133 | −0.840664 | − | 0.541557i | \(-0.817835\pi\) | ||||
−0.840664 | + | 0.541557i | \(0.817835\pi\) | |||||||
\(242\) | −0.222191 | −0.0142830 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.5237 | −0.673710 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 1.51118 | 0.0963496 | ||||||||
\(247\) | −4.45563 | −0.283505 | ||||||||
\(248\) | −3.11123 | −0.197564 | ||||||||
\(249\) | 4.16310 | 0.263826 | ||||||||
\(250\) | −0.222191 | −0.0140526 | ||||||||
\(251\) | −9.37758 | −0.591908 | −0.295954 | − | 0.955202i | \(-0.595637\pi\) | ||||
−0.295954 | + | 0.955202i | \(0.595637\pi\) | |||||||
\(252\) | −1.95063 | −0.122878 | ||||||||
\(253\) | −6.60749 | −0.415409 | ||||||||
\(254\) | −2.43064 | −0.152512 | ||||||||
\(255\) | 0.506248 | 0.0317025 | ||||||||
\(256\) | 12.1950 | 0.762190 | ||||||||
\(257\) | −13.9718 | −0.871538 | −0.435769 | − | 0.900059i | \(-0.643523\pi\) | ||||
−0.435769 | + | 0.900059i | \(0.643523\pi\) | |||||||
\(258\) | 2.05818 | 0.128137 | ||||||||
\(259\) | 11.4456 | 0.711197 | ||||||||
\(260\) | −1.75559 | −0.108877 | ||||||||
\(261\) | 3.40626 | 0.210842 | ||||||||
\(262\) | −2.52118 | −0.155759 | ||||||||
\(263\) | −18.1232 | −1.11752 | −0.558761 | − | 0.829328i | \(-0.688723\pi\) | ||||
−0.558761 | + | 0.829328i | \(0.688723\pi\) | |||||||
\(264\) | −0.877796 | −0.0540246 | ||||||||
\(265\) | −1.39501 | −0.0856950 | ||||||||
\(266\) | 1.09999 | 0.0674446 | ||||||||
\(267\) | −2.25059 | −0.137734 | ||||||||
\(268\) | 20.0939 | 1.22743 | ||||||||
\(269\) | 32.1793 | 1.96201 | 0.981005 | − | 0.193984i | \(-0.0621409\pi\) | ||||
0.981005 | + | 0.193984i | \(0.0621409\pi\) | |||||||
\(270\) | 0.222191 | 0.0135221 | ||||||||
\(271\) | −24.0669 | −1.46196 | −0.730979 | − | 0.682400i | \(-0.760936\pi\) | ||||
−0.730979 | + | 0.682400i | \(0.760936\pi\) | |||||||
\(272\) | −1.87627 | −0.113766 | ||||||||
\(273\) | −0.900012 | −0.0544712 | ||||||||
\(274\) | −2.93070 | −0.177050 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −12.8888 | −0.775813 | ||||||||
\(277\) | 16.8443 | 1.01208 | 0.506039 | − | 0.862511i | \(-0.331109\pi\) | ||||
0.506039 | + | 0.862511i | \(0.331109\pi\) | |||||||
\(278\) | 4.34564 | 0.260634 | ||||||||
\(279\) | −3.54437 | −0.212196 | ||||||||
\(280\) | 0.877796 | 0.0524584 | ||||||||
\(281\) | −0.0444327 | −0.00265063 | −0.00132532 | − | 0.999999i | \(-0.500422\pi\) | ||||
−0.00132532 | + | 0.999999i | \(0.500422\pi\) | |||||||
\(282\) | 2.81252 | 0.167483 | ||||||||
\(283\) | −0.455630 | −0.0270844 | −0.0135422 | − | 0.999908i | \(-0.504311\pi\) | ||||
−0.0135422 | + | 0.999908i | \(0.504311\pi\) | |||||||
\(284\) | −12.4000 | −0.735802 | ||||||||
\(285\) | 4.95063 | 0.293250 | ||||||||
\(286\) | −0.199975 | −0.0118248 | ||||||||
\(287\) | 6.80127 | 0.401467 | ||||||||
\(288\) | −2.57908 | −0.151974 | ||||||||
\(289\) | −16.7437 | −0.984924 | ||||||||
\(290\) | −0.756842 | −0.0444433 | ||||||||
\(291\) | −0.0506185 | −0.00296731 | ||||||||
\(292\) | −6.93570 | −0.405881 | ||||||||
\(293\) | 31.1337 | 1.81885 | 0.909424 | − | 0.415870i | \(-0.136523\pi\) | ||||
0.909424 | + | 0.415870i | \(0.136523\pi\) | |||||||
\(294\) | 0.222191 | 0.0129585 | ||||||||
\(295\) | 6.93938 | 0.404027 | ||||||||
\(296\) | 10.0469 | 0.583966 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0.126230 | 0.00731231 | ||||||||
\(299\) | −5.94682 | −0.343913 | ||||||||
\(300\) | 1.95063 | 0.112620 | ||||||||
\(301\) | 9.26309 | 0.533916 | ||||||||
\(302\) | −0.988059 | −0.0568564 | ||||||||
\(303\) | 3.25690 | 0.187104 | ||||||||
\(304\) | −18.3481 | −1.05234 | ||||||||
\(305\) | 5.39501 | 0.308918 | ||||||||
\(306\) | 0.112484 | 0.00643028 | ||||||||
\(307\) | −27.9038 | −1.59255 | −0.796276 | − | 0.604934i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604934i | \(0.793200\pi\) | |||||||
\(308\) | −1.95063 | −0.111148 | ||||||||
\(309\) | 0.0481195 | 0.00273742 | ||||||||
\(310\) | 0.787529 | 0.0447286 | ||||||||
\(311\) | −20.4274 | −1.15833 | −0.579167 | − | 0.815209i | \(-0.696622\pi\) | ||||
−0.579167 | + | 0.815209i | \(0.696622\pi\) | |||||||
\(312\) | −0.790027 | −0.0447265 | ||||||||
\(313\) | 22.0531 | 1.24652 | 0.623258 | − | 0.782016i | \(-0.285809\pi\) | ||||
0.623258 | + | 0.782016i | \(0.285809\pi\) | |||||||
\(314\) | −1.81127 | −0.102216 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −3.87932 | −0.218229 | ||||||||
\(317\) | −17.9038 | −1.00558 | −0.502788 | − | 0.864410i | \(-0.667692\pi\) | ||||
−0.502788 | + | 0.864410i | \(0.667692\pi\) | |||||||
\(318\) | −0.309960 | −0.0173817 | ||||||||
\(319\) | 3.40626 | 0.190714 | ||||||||
\(320\) | −6.83940 | −0.382334 | ||||||||
\(321\) | −15.8900 | −0.886894 | ||||||||
\(322\) | 1.46813 | 0.0818155 | ||||||||
\(323\) | 2.50625 | 0.139451 | ||||||||
\(324\) | −1.95063 | −0.108368 | ||||||||
\(325\) | 0.900012 | 0.0499237 | ||||||||
\(326\) | −1.47382 | −0.0816273 | ||||||||
\(327\) | 17.4706 | 0.966128 | ||||||||
\(328\) | 5.97013 | 0.329645 | ||||||||
\(329\) | 12.6581 | 0.697864 | ||||||||
\(330\) | 0.222191 | 0.0122312 | ||||||||
\(331\) | 18.5112 | 1.01747 | 0.508735 | − | 0.860923i | \(-0.330113\pi\) | ||||
0.508735 | + | 0.860923i | \(0.330113\pi\) | |||||||
\(332\) | 8.12068 | 0.445680 | ||||||||
\(333\) | 11.4456 | 0.627217 | ||||||||
\(334\) | −0.834460 | −0.0456596 | ||||||||
\(335\) | −10.3012 | −0.562815 | ||||||||
\(336\) | −3.70622 | −0.202191 | ||||||||
\(337\) | 24.8187 | 1.35196 | 0.675981 | − | 0.736919i | \(-0.263720\pi\) | ||||
0.675981 | + | 0.736919i | \(0.263720\pi\) | |||||||
\(338\) | 2.70851 | 0.147323 | ||||||||
\(339\) | −19.4200 | −1.05475 | ||||||||
\(340\) | 0.987504 | 0.0535549 | ||||||||
\(341\) | −3.54437 | −0.191938 | ||||||||
\(342\) | 1.09999 | 0.0594805 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.13110 | 0.438400 | ||||||||
\(345\) | 6.60749 | 0.355735 | ||||||||
\(346\) | 3.48925 | 0.187583 | ||||||||
\(347\) | 1.03194 | 0.0553972 | 0.0276986 | − | 0.999616i | \(-0.491182\pi\) | ||||
0.0276986 | + | 0.999616i | \(0.491182\pi\) | |||||||
\(348\) | 6.64436 | 0.356175 | ||||||||
\(349\) | 18.6100 | 0.996170 | 0.498085 | − | 0.867128i | \(-0.334037\pi\) | ||||
0.498085 | + | 0.867128i | \(0.334037\pi\) | |||||||
\(350\) | −0.222191 | −0.0118766 | ||||||||
\(351\) | −0.900012 | −0.0480391 | ||||||||
\(352\) | −2.57908 | −0.137466 | ||||||||
\(353\) | −8.89126 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(354\) | 1.54187 | 0.0819495 | ||||||||
\(355\) | 6.35689 | 0.337389 | ||||||||
\(356\) | −4.39008 | −0.232674 | ||||||||
\(357\) | 0.506248 | 0.0267935 | ||||||||
\(358\) | 1.99013 | 0.105182 | ||||||||
\(359\) | −10.1395 | −0.535141 | −0.267571 | − | 0.963538i | \(-0.586221\pi\) | ||||
−0.267571 | + | 0.963538i | \(0.586221\pi\) | |||||||
\(360\) | 0.877796 | 0.0462639 | ||||||||
\(361\) | 5.50875 | 0.289934 | ||||||||
\(362\) | 3.06680 | 0.161188 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.75559 | −0.0920180 | ||||||||
\(365\) | 3.55562 | 0.186110 | ||||||||
\(366\) | 1.19873 | 0.0626584 | ||||||||
\(367\) | −15.4631 | −0.807165 | −0.403583 | − | 0.914943i | \(-0.632235\pi\) | ||||
−0.403583 | + | 0.914943i | \(0.632235\pi\) | |||||||
\(368\) | −24.4888 | −1.27657 | ||||||||
\(369\) | 6.80127 | 0.354060 | ||||||||
\(370\) | −2.54312 | −0.132211 | ||||||||
\(371\) | −1.39501 | −0.0724255 | ||||||||
\(372\) | −6.91376 | −0.358462 | ||||||||
\(373\) | 0.470008 | 0.0243361 | 0.0121681 | − | 0.999926i | \(-0.496127\pi\) | ||||
0.0121681 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(374\) | 0.112484 | 0.00581641 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 11.1112 | 0.573018 | ||||||||
\(377\) | 3.06568 | 0.157890 | ||||||||
\(378\) | 0.222191 | 0.0114283 | ||||||||
\(379\) | −25.2225 | −1.29559 | −0.647797 | − | 0.761813i | \(-0.724310\pi\) | ||||
−0.647797 | + | 0.761813i | \(0.724310\pi\) | |||||||
\(380\) | 9.65685 | 0.495386 | ||||||||
\(381\) | −10.9394 | −0.560442 | ||||||||
\(382\) | −1.53618 | −0.0785977 | ||||||||
\(383\) | −21.2257 | −1.08458 | −0.542290 | − | 0.840191i | \(-0.682443\pi\) | ||||
−0.542290 | + | 0.840191i | \(0.682443\pi\) | |||||||
\(384\) | −6.67782 | −0.340776 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | −0.476194 | −0.0242376 | ||||||||
\(387\) | 9.26309 | 0.470869 | ||||||||
\(388\) | −0.0987380 | −0.00501266 | ||||||||
\(389\) | 8.93182 | 0.452861 | 0.226431 | − | 0.974027i | \(-0.427294\pi\) | ||||
0.226431 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(390\) | 0.199975 | 0.0101261 | ||||||||
\(391\) | 3.34503 | 0.169165 | ||||||||
\(392\) | 0.877796 | 0.0443354 | ||||||||
\(393\) | −11.3469 | −0.572375 | ||||||||
\(394\) | −4.13055 | −0.208094 | ||||||||
\(395\) | 1.98875 | 0.100065 | ||||||||
\(396\) | −1.95063 | −0.0980229 | ||||||||
\(397\) | −17.6563 | −0.886144 | −0.443072 | − | 0.896486i | \(-0.646111\pi\) | ||||
−0.443072 | + | 0.896486i | \(0.646111\pi\) | |||||||
\(398\) | 0.799900 | 0.0400954 | ||||||||
\(399\) | 4.95063 | 0.247842 | ||||||||
\(400\) | 3.70622 | 0.185311 | ||||||||
\(401\) | −25.1494 | −1.25590 | −0.627951 | − | 0.778253i | \(-0.716106\pi\) | ||||
−0.627951 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(402\) | −2.28884 | −0.114157 | ||||||||
\(403\) | −3.18998 | −0.158904 | ||||||||
\(404\) | 6.35302 | 0.316074 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −0.756842 | −0.0375614 | ||||||||
\(407\) | 11.4456 | 0.567339 | ||||||||
\(408\) | 0.444383 | 0.0220002 | ||||||||
\(409\) | 29.0150 | 1.43470 | 0.717350 | − | 0.696713i | \(-0.245355\pi\) | ||||
0.717350 | + | 0.696713i | \(0.245355\pi\) | |||||||
\(410\) | −1.51118 | −0.0746321 | ||||||||
\(411\) | −13.1900 | −0.650614 | ||||||||
\(412\) | 0.0938634 | 0.00462432 | ||||||||
\(413\) | 6.93938 | 0.341465 | ||||||||
\(414\) | 1.46813 | 0.0721545 | ||||||||
\(415\) | −4.16310 | −0.204359 | ||||||||
\(416\) | −2.32121 | −0.113807 | ||||||||
\(417\) | 19.5581 | 0.957765 | ||||||||
\(418\) | 1.09999 | 0.0538021 | ||||||||
\(419\) | −26.1294 | −1.27650 | −0.638251 | − | 0.769828i | \(-0.720342\pi\) | ||||
−0.638251 | + | 0.769828i | \(0.720342\pi\) | |||||||
\(420\) | 1.95063 | 0.0951810 | ||||||||
\(421\) | 37.0963 | 1.80796 | 0.903982 | − | 0.427571i | \(-0.140631\pi\) | ||||
0.903982 | + | 0.427571i | \(0.140631\pi\) | |||||||
\(422\) | 0.938073 | 0.0456647 | ||||||||
\(423\) | 12.6581 | 0.615458 | ||||||||
\(424\) | −1.22454 | −0.0594688 | ||||||||
\(425\) | −0.506248 | −0.0245566 | ||||||||
\(426\) | 1.41245 | 0.0684333 | ||||||||
\(427\) | 5.39501 | 0.261083 | ||||||||
\(428\) | −30.9956 | −1.49823 | ||||||||
\(429\) | −0.900012 | −0.0434530 | ||||||||
\(430\) | −2.05818 | −0.0992542 | ||||||||
\(431\) | 9.60255 | 0.462539 | 0.231269 | − | 0.972890i | \(-0.425712\pi\) | ||||
0.231269 | + | 0.972890i | \(0.425712\pi\) | |||||||
\(432\) | −3.70622 | −0.178316 | ||||||||
\(433\) | −31.1137 | −1.49523 | −0.747615 | − | 0.664132i | \(-0.768801\pi\) | ||||
−0.747615 | + | 0.664132i | \(0.768801\pi\) | |||||||
\(434\) | 0.787529 | 0.0378026 | ||||||||
\(435\) | −3.40626 | −0.163318 | ||||||||
\(436\) | 34.0787 | 1.63208 | ||||||||
\(437\) | 32.7112 | 1.56479 | ||||||||
\(438\) | 0.790027 | 0.0377490 | ||||||||
\(439\) | −34.0644 | −1.62580 | −0.812902 | − | 0.582401i | \(-0.802113\pi\) | ||||
−0.812902 | + | 0.582401i | \(0.802113\pi\) | |||||||
\(440\) | 0.877796 | 0.0418473 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.101237 | 0.00481535 | ||||||||
\(443\) | 19.0375 | 0.904498 | 0.452249 | − | 0.891892i | \(-0.350622\pi\) | ||||
0.452249 | + | 0.891892i | \(0.350622\pi\) | |||||||
\(444\) | 22.3262 | 1.05955 | ||||||||
\(445\) | 2.25059 | 0.106688 | ||||||||
\(446\) | 2.21067 | 0.104678 | ||||||||
\(447\) | 0.568114 | 0.0268709 | ||||||||
\(448\) | −6.83940 | −0.323131 | ||||||||
\(449\) | 18.6806 | 0.881592 | 0.440796 | − | 0.897607i | \(-0.354696\pi\) | ||||
0.440796 | + | 0.897607i | \(0.354696\pi\) | |||||||
\(450\) | −0.222191 | −0.0104742 | ||||||||
\(451\) | 6.80127 | 0.320260 | ||||||||
\(452\) | −37.8813 | −1.78178 | ||||||||
\(453\) | −4.44688 | −0.208933 | ||||||||
\(454\) | −3.29996 | −0.154875 | ||||||||
\(455\) | 0.900012 | 0.0421932 | ||||||||
\(456\) | 4.34564 | 0.203503 | ||||||||
\(457\) | 27.2875 | 1.27646 | 0.638228 | − | 0.769847i | \(-0.279668\pi\) | ||||
0.638228 | + | 0.769847i | \(0.279668\pi\) | |||||||
\(458\) | −0.720602 | −0.0336715 | ||||||||
\(459\) | 0.506248 | 0.0236296 | ||||||||
\(460\) | 12.8888 | 0.600942 | ||||||||
\(461\) | −37.2644 | −1.73558 | −0.867788 | − | 0.496934i | \(-0.834459\pi\) | ||||
−0.867788 | + | 0.496934i | \(0.834459\pi\) | |||||||
\(462\) | 0.222191 | 0.0103373 | ||||||||
\(463\) | −8.50119 | −0.395084 | −0.197542 | − | 0.980294i | \(-0.563296\pi\) | ||||
−0.197542 | + | 0.980294i | \(0.563296\pi\) | |||||||
\(464\) | 12.6244 | 0.586071 | ||||||||
\(465\) | 3.54437 | 0.164366 | ||||||||
\(466\) | −2.48175 | −0.114965 | ||||||||
\(467\) | −20.5163 | −0.949381 | −0.474691 | − | 0.880153i | \(-0.657440\pi\) | ||||
−0.474691 | + | 0.880153i | \(0.657440\pi\) | |||||||
\(468\) | −1.75559 | −0.0811523 | ||||||||
\(469\) | −10.3012 | −0.475666 | ||||||||
\(470\) | −2.81252 | −0.129732 | ||||||||
\(471\) | −8.15186 | −0.375618 | ||||||||
\(472\) | 6.09136 | 0.280378 | ||||||||
\(473\) | 9.26309 | 0.425917 | ||||||||
\(474\) | 0.441884 | 0.0202964 | ||||||||
\(475\) | −4.95063 | −0.227151 | ||||||||
\(476\) | 0.987504 | 0.0452621 | ||||||||
\(477\) | −1.39501 | −0.0638733 | ||||||||
\(478\) | −0.544495 | −0.0249046 | ||||||||
\(479\) | 12.2806 | 0.561117 | 0.280559 | − | 0.959837i | \(-0.409480\pi\) | ||||
0.280559 | + | 0.959837i | \(0.409480\pi\) | |||||||
\(480\) | 2.57908 | 0.117718 | ||||||||
\(481\) | 10.3012 | 0.469695 | ||||||||
\(482\) | 5.79947 | 0.264159 | ||||||||
\(483\) | 6.60749 | 0.300651 | ||||||||
\(484\) | −1.95063 | −0.0886650 | ||||||||
\(485\) | 0.0506185 | 0.00229847 | ||||||||
\(486\) | 0.222191 | 0.0100788 | ||||||||
\(487\) | −20.5901 | −0.933024 | −0.466512 | − | 0.884515i | \(-0.654490\pi\) | ||||
−0.466512 | + | 0.884515i | \(0.654490\pi\) | |||||||
\(488\) | 4.73572 | 0.214376 | ||||||||
\(489\) | −6.63311 | −0.299960 | ||||||||
\(490\) | −0.222191 | −0.0100376 | ||||||||
\(491\) | 6.32684 | 0.285526 | 0.142763 | − | 0.989757i | \(-0.454401\pi\) | ||||
0.142763 | + | 0.989757i | \(0.454401\pi\) | |||||||
\(492\) | 13.2668 | 0.598112 | ||||||||
\(493\) | −1.72441 | −0.0776637 | ||||||||
\(494\) | 0.990002 | 0.0445423 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | −13.1362 | −0.589834 | ||||||||
\(497\) | 6.35689 | 0.285146 | ||||||||
\(498\) | −0.925005 | −0.0414505 | ||||||||
\(499\) | −0.627480 | −0.0280899 | −0.0140449 | − | 0.999901i | \(-0.504471\pi\) | ||||
−0.0140449 | + | 0.999901i | \(0.504471\pi\) | |||||||
\(500\) | −1.95063 | −0.0872349 | ||||||||
\(501\) | −3.75559 | −0.167787 | ||||||||
\(502\) | 2.08362 | 0.0929964 | ||||||||
\(503\) | −7.07686 | −0.315542 | −0.157771 | − | 0.987476i | \(-0.550431\pi\) | ||||
−0.157771 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(504\) | 0.877796 | 0.0391001 | ||||||||
\(505\) | −3.25690 | −0.144930 | ||||||||
\(506\) | 1.46813 | 0.0652662 | ||||||||
\(507\) | 12.1900 | 0.541376 | ||||||||
\(508\) | −21.3387 | −0.946752 | ||||||||
\(509\) | 3.06062 | 0.135659 | 0.0678297 | − | 0.997697i | \(-0.478393\pi\) | ||||
0.0678297 | + | 0.997697i | \(0.478393\pi\) | |||||||
\(510\) | −0.112484 | −0.00498087 | ||||||||
\(511\) | 3.55562 | 0.157291 | ||||||||
\(512\) | −16.0653 | −0.709992 | ||||||||
\(513\) | 4.95063 | 0.218576 | ||||||||
\(514\) | 3.10442 | 0.136930 | ||||||||
\(515\) | −0.0481195 | −0.00212040 | ||||||||
\(516\) | 18.0689 | 0.795438 | ||||||||
\(517\) | 12.6581 | 0.556703 | ||||||||
\(518\) | −2.54312 | −0.111738 | ||||||||
\(519\) | 15.7038 | 0.689320 | ||||||||
\(520\) | 0.790027 | 0.0346450 | ||||||||
\(521\) | −36.2018 | −1.58603 | −0.793016 | − | 0.609201i | \(-0.791490\pi\) | ||||
−0.793016 | + | 0.609201i | \(0.791490\pi\) | |||||||
\(522\) | −0.756842 | −0.0331261 | ||||||||
\(523\) | 35.7412 | 1.56285 | 0.781426 | − | 0.623998i | \(-0.214493\pi\) | ||||
0.781426 | + | 0.623998i | \(0.214493\pi\) | |||||||
\(524\) | −22.1336 | −0.966911 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 4.02681 | 0.175577 | ||||||||
\(527\) | 1.79433 | 0.0781623 | ||||||||
\(528\) | −3.70622 | −0.161293 | ||||||||
\(529\) | 20.6589 | 0.898211 | ||||||||
\(530\) | 0.309960 | 0.0134638 | ||||||||
\(531\) | 6.93938 | 0.301144 | ||||||||
\(532\) | 9.65685 | 0.418678 | ||||||||
\(533\) | 6.12123 | 0.265140 | ||||||||
\(534\) | 0.500062 | 0.0216398 | ||||||||
\(535\) | 15.8900 | 0.686985 | ||||||||
\(536\) | −9.04236 | −0.390571 | ||||||||
\(537\) | 8.95682 | 0.386515 | ||||||||
\(538\) | −7.14997 | −0.308257 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 1.95063 | 0.0839418 | ||||||||
\(541\) | 44.1644 | 1.89878 | 0.949388 | − | 0.314105i | \(-0.101704\pi\) | ||||
0.949388 | + | 0.314105i | \(0.101704\pi\) | |||||||
\(542\) | 5.34745 | 0.229693 | ||||||||
\(543\) | 13.8025 | 0.592323 | ||||||||
\(544\) | 1.30566 | 0.0559796 | ||||||||
\(545\) | −17.4706 | −0.748359 | ||||||||
\(546\) | 0.199975 | 0.00855814 | ||||||||
\(547\) | −11.1644 | −0.477353 | −0.238677 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238677 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(548\) | −25.7288 | −1.09908 | ||||||||
\(549\) | 5.39501 | 0.230254 | ||||||||
\(550\) | −0.222191 | −0.00947427 | ||||||||
\(551\) | −16.8631 | −0.718394 | ||||||||
\(552\) | 5.80002 | 0.246865 | ||||||||
\(553\) | 1.98875 | 0.0845704 | ||||||||
\(554\) | −3.74267 | −0.159011 | ||||||||
\(555\) | −11.4456 | −0.485840 | ||||||||
\(556\) | 38.1507 | 1.61795 | ||||||||
\(557\) | −15.5137 | −0.657336 | −0.328668 | − | 0.944446i | \(-0.606600\pi\) | ||||
−0.328668 | + | 0.944446i | \(0.606600\pi\) | |||||||
\(558\) | 0.787529 | 0.0333387 | ||||||||
\(559\) | 8.33690 | 0.352613 | ||||||||
\(560\) | 3.70622 | 0.156617 | ||||||||
\(561\) | 0.506248 | 0.0213738 | ||||||||
\(562\) | 0.00987257 | 0.000416449 0 | ||||||||
\(563\) | 29.7581 | 1.25415 | 0.627077 | − | 0.778957i | \(-0.284251\pi\) | ||||
0.627077 | + | 0.778957i | \(0.284251\pi\) | |||||||
\(564\) | 24.6913 | 1.03969 | ||||||||
\(565\) | 19.4200 | 0.817006 | ||||||||
\(566\) | 0.101237 | 0.00425531 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 5.58005 | 0.234134 | ||||||||
\(569\) | −11.2949 | −0.473507 | −0.236753 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236753 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(570\) | −1.09999 | −0.0460734 | ||||||||
\(571\) | 33.3300 | 1.39482 | 0.697408 | − | 0.716675i | \(-0.254337\pi\) | ||||
0.697408 | + | 0.716675i | \(0.254337\pi\) | |||||||
\(572\) | −1.75559 | −0.0734050 | ||||||||
\(573\) | −6.91376 | −0.288826 | ||||||||
\(574\) | −1.51118 | −0.0630756 | ||||||||
\(575\) | −6.60749 | −0.275551 | ||||||||
\(576\) | −6.83940 | −0.284975 | ||||||||
\(577\) | −47.6300 | −1.98286 | −0.991432 | − | 0.130622i | \(-0.958303\pi\) | ||||
−0.991432 | + | 0.130622i | \(0.958303\pi\) | |||||||
\(578\) | 3.72031 | 0.154744 | ||||||||
\(579\) | −2.14317 | −0.0890671 | ||||||||
\(580\) | −6.64436 | −0.275892 | ||||||||
\(581\) | −4.16310 | −0.172715 | ||||||||
\(582\) | 0.0112470 | 0.000466203 0 | ||||||||
\(583\) | −1.39501 | −0.0577756 | ||||||||
\(584\) | 3.12111 | 0.129152 | ||||||||
\(585\) | 0.900012 | 0.0372109 | ||||||||
\(586\) | −6.91763 | −0.285765 | ||||||||
\(587\) | 20.5844 | 0.849607 | 0.424804 | − | 0.905285i | \(-0.360343\pi\) | ||||
0.424804 | + | 0.905285i | \(0.360343\pi\) | |||||||
\(588\) | 1.95063 | 0.0804427 | ||||||||
\(589\) | 17.5469 | 0.723006 | ||||||||
\(590\) | −1.54187 | −0.0634778 | ||||||||
\(591\) | −18.5901 | −0.764693 | ||||||||
\(592\) | 42.4201 | 1.74345 | ||||||||
\(593\) | −7.47882 | −0.307118 | −0.153559 | − | 0.988139i | \(-0.549074\pi\) | ||||
−0.153559 | + | 0.988139i | \(0.549074\pi\) | |||||||
\(594\) | 0.222191 | 0.00911662 | ||||||||
\(595\) | −0.506248 | −0.0207542 | ||||||||
\(596\) | 1.10818 | 0.0453928 | ||||||||
\(597\) | 3.60005 | 0.147340 | ||||||||
\(598\) | 1.32133 | 0.0540333 | ||||||||
\(599\) | −28.5512 | −1.16657 | −0.583285 | − | 0.812268i | \(-0.698233\pi\) | ||||
−0.583285 | + | 0.812268i | \(0.698233\pi\) | |||||||
\(600\) | −0.877796 | −0.0358359 | ||||||||
\(601\) | −23.5950 | −0.962460 | −0.481230 | − | 0.876594i | \(-0.659810\pi\) | ||||
−0.481230 | + | 0.876594i | \(0.659810\pi\) | |||||||
\(602\) | −2.05818 | −0.0838851 | ||||||||
\(603\) | −10.3012 | −0.419498 | ||||||||
\(604\) | −8.67423 | −0.352949 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −0.723656 | −0.0293965 | ||||||||
\(607\) | 20.2401 | 0.821520 | 0.410760 | − | 0.911744i | \(-0.365263\pi\) | ||||
0.410760 | + | 0.911744i | \(0.365263\pi\) | |||||||
\(608\) | 12.7681 | 0.517814 | ||||||||
\(609\) | −3.40626 | −0.138029 | ||||||||
\(610\) | −1.19873 | −0.0485350 | ||||||||
\(611\) | 11.3925 | 0.460889 | ||||||||
\(612\) | 0.987504 | 0.0399175 | ||||||||
\(613\) | −31.4644 | −1.27083 | −0.635417 | − | 0.772169i | \(-0.719172\pi\) | ||||
−0.635417 | + | 0.772169i | \(0.719172\pi\) | |||||||
\(614\) | 6.19998 | 0.250211 | ||||||||
\(615\) | −6.80127 | −0.274254 | ||||||||
\(616\) | 0.877796 | 0.0353674 | ||||||||
\(617\) | 35.6813 | 1.43647 | 0.718237 | − | 0.695798i | \(-0.244949\pi\) | ||||
0.718237 | + | 0.695798i | \(0.244949\pi\) | |||||||
\(618\) | −0.0106917 | −0.000430085 0 | ||||||||
\(619\) | 5.41245 | 0.217545 | 0.108772 | − | 0.994067i | \(-0.465308\pi\) | ||||
0.108772 | + | 0.994067i | \(0.465308\pi\) | |||||||
\(620\) | 6.91376 | 0.277663 | ||||||||
\(621\) | 6.60749 | 0.265149 | ||||||||
\(622\) | 4.53880 | 0.181989 | ||||||||
\(623\) | 2.25059 | 0.0901681 | ||||||||
\(624\) | −3.33565 | −0.133533 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.90001 | −0.195844 | ||||||||
\(627\) | 4.95063 | 0.197709 | ||||||||
\(628\) | −15.9013 | −0.634529 | ||||||||
\(629\) | −5.79433 | −0.231035 | ||||||||
\(630\) | −0.222191 | −0.00885232 | ||||||||
\(631\) | −32.0863 | −1.27734 | −0.638668 | − | 0.769483i | \(-0.720514\pi\) | ||||
−0.638668 | + | 0.769483i | \(0.720514\pi\) | |||||||
\(632\) | 1.74572 | 0.0694410 | ||||||||
\(633\) | 4.22191 | 0.167806 | ||||||||
\(634\) | 3.97806 | 0.157989 | ||||||||
\(635\) | 10.9394 | 0.434116 | ||||||||
\(636\) | −2.72116 | −0.107901 | ||||||||
\(637\) | 0.900012 | 0.0356598 | ||||||||
\(638\) | −0.756842 | −0.0299637 | ||||||||
\(639\) | 6.35689 | 0.251475 | ||||||||
\(640\) | 6.67782 | 0.263964 | ||||||||
\(641\) | 33.8075 | 1.33532 | 0.667658 | − | 0.744468i | \(-0.267297\pi\) | ||||
0.667658 | + | 0.744468i | \(0.267297\pi\) | |||||||
\(642\) | 3.53062 | 0.139343 | ||||||||
\(643\) | −1.26309 | −0.0498114 | −0.0249057 | − | 0.999690i | \(-0.507929\pi\) | ||||
−0.0249057 | + | 0.999690i | \(0.507929\pi\) | |||||||
\(644\) | 12.8888 | 0.507889 | ||||||||
\(645\) | −9.26309 | −0.364734 | ||||||||
\(646\) | −0.556867 | −0.0219096 | ||||||||
\(647\) | −21.8000 | −0.857047 | −0.428524 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428524 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(648\) | 0.877796 | 0.0344831 | ||||||||
\(649\) | 6.93938 | 0.272395 | ||||||||
\(650\) | −0.199975 | −0.00784367 | ||||||||
\(651\) | 3.54437 | 0.138915 | ||||||||
\(652\) | −12.9388 | −0.506721 | ||||||||
\(653\) | −0.827455 | −0.0323808 | −0.0161904 | − | 0.999869i | \(-0.505154\pi\) | ||||
−0.0161904 | + | 0.999869i | \(0.505154\pi\) | |||||||
\(654\) | −3.88182 | −0.151791 | ||||||||
\(655\) | 11.3469 | 0.443360 | ||||||||
\(656\) | 25.2070 | 0.984170 | ||||||||
\(657\) | 3.55562 | 0.138718 | ||||||||
\(658\) | −2.81252 | −0.109644 | ||||||||
\(659\) | 19.7769 | 0.770399 | 0.385199 | − | 0.922833i | \(-0.374133\pi\) | ||||
0.385199 | + | 0.922833i | \(0.374133\pi\) | |||||||
\(660\) | 1.95063 | 0.0759282 | ||||||||
\(661\) | −2.73185 | −0.106257 | −0.0531283 | − | 0.998588i | \(-0.516919\pi\) | ||||
−0.0531283 | + | 0.998588i | \(0.516919\pi\) | |||||||
\(662\) | −4.11304 | −0.159858 | ||||||||
\(663\) | 0.455630 | 0.0176952 | ||||||||
\(664\) | −3.65436 | −0.141816 | ||||||||
\(665\) | −4.95063 | −0.191977 | ||||||||
\(666\) | −2.54312 | −0.0985439 | ||||||||
\(667\) | −22.5068 | −0.871467 | ||||||||
\(668\) | −7.32577 | −0.283443 | ||||||||
\(669\) | 9.94938 | 0.384665 | ||||||||
\(670\) | 2.28884 | 0.0884256 | ||||||||
\(671\) | 5.39501 | 0.208272 | ||||||||
\(672\) | 2.57908 | 0.0994903 | ||||||||
\(673\) | 43.2212 | 1.66605 | 0.833027 | − | 0.553233i | \(-0.186606\pi\) | ||||
0.833027 | + | 0.553233i | \(0.186606\pi\) | |||||||
\(674\) | −5.51450 | −0.212411 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 23.7781 | 0.914544 | ||||||||
\(677\) | 2.20504 | 0.0847464 | 0.0423732 | − | 0.999102i | \(-0.486508\pi\) | ||||
0.0423732 | + | 0.999102i | \(0.486508\pi\) | |||||||
\(678\) | 4.31496 | 0.165715 | ||||||||
\(679\) | 0.0506185 | 0.00194256 | ||||||||
\(680\) | −0.444383 | −0.0170413 | ||||||||
\(681\) | −14.8519 | −0.569126 | ||||||||
\(682\) | 0.787529 | 0.0301560 | ||||||||
\(683\) | −5.42757 | −0.207680 | −0.103840 | − | 0.994594i | \(-0.533113\pi\) | ||||
−0.103840 | + | 0.994594i | \(0.533113\pi\) | |||||||
\(684\) | 9.65685 | 0.369239 | ||||||||
\(685\) | 13.1900 | 0.503963 | ||||||||
\(686\) | −0.222191 | −0.00848331 | ||||||||
\(687\) | −3.24316 | −0.123734 | ||||||||
\(688\) | 34.3311 | 1.30886 | ||||||||
\(689\) | −1.25553 | −0.0478319 | ||||||||
\(690\) | −1.46813 | −0.0558906 | ||||||||
\(691\) | 7.72378 | 0.293826 | 0.146913 | − | 0.989149i | \(-0.453066\pi\) | ||||
0.146913 | + | 0.989149i | \(0.453066\pi\) | |||||||
\(692\) | 30.6323 | 1.16447 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | −0.229287 | −0.00870363 | ||||||||
\(695\) | −19.5581 | −0.741882 | ||||||||
\(696\) | −2.99000 | −0.113336 | ||||||||
\(697\) | −3.44313 | −0.130418 | ||||||||
\(698\) | −4.13498 | −0.156511 | ||||||||
\(699\) | −11.1694 | −0.422466 | ||||||||
\(700\) | −1.95063 | −0.0737269 | ||||||||
\(701\) | 32.1988 | 1.21613 | 0.608066 | − | 0.793887i | \(-0.291946\pi\) | ||||
0.608066 | + | 0.793887i | \(0.291946\pi\) | |||||||
\(702\) | 0.199975 | 0.00754757 | ||||||||
\(703\) | −56.6631 | −2.13709 | ||||||||
\(704\) | −6.83940 | −0.257769 | ||||||||
\(705\) | −12.6581 | −0.476732 | ||||||||
\(706\) | 1.97556 | 0.0743513 | ||||||||
\(707\) | −3.25690 | −0.122488 | ||||||||
\(708\) | 13.5362 | 0.508721 | ||||||||
\(709\) | −25.0963 | −0.942511 | −0.471256 | − | 0.881997i | \(-0.656199\pi\) | ||||
−0.471256 | + | 0.881997i | \(0.656199\pi\) | |||||||
\(710\) | −1.41245 | −0.0530082 | ||||||||
\(711\) | 1.98875 | 0.0745841 | ||||||||
\(712\) | 1.97556 | 0.0740373 | ||||||||
\(713\) | 23.4194 | 0.877062 | ||||||||
\(714\) | −0.112484 | −0.00420961 | ||||||||
\(715\) | 0.900012 | 0.0336586 | ||||||||
\(716\) | 17.4714 | 0.652939 | ||||||||
\(717\) | −2.45057 | −0.0915182 | ||||||||
\(718\) | 2.25291 | 0.0840777 | ||||||||
\(719\) | 9.36433 | 0.349230 | 0.174615 | − | 0.984637i | \(-0.444132\pi\) | ||||
0.174615 | + | 0.984637i | \(0.444132\pi\) | |||||||
\(720\) | 3.70622 | 0.138123 | ||||||||
\(721\) | −0.0481195 | −0.00179206 | ||||||||
\(722\) | −1.22400 | −0.0455524 | ||||||||
\(723\) | 26.1012 | 0.970715 | ||||||||
\(724\) | 26.9236 | 1.00061 | ||||||||
\(725\) | 3.40626 | 0.126505 | ||||||||
\(726\) | 0.222191 | 0.00824630 | ||||||||
\(727\) | −13.9145 | −0.516061 | −0.258030 | − | 0.966137i | \(-0.583073\pi\) | ||||
−0.258030 | + | 0.966137i | \(0.583073\pi\) | |||||||
\(728\) | 0.790027 | 0.0292804 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.790027 | −0.0292402 | ||||||||
\(731\) | −4.68942 | −0.173445 | ||||||||
\(732\) | 10.5237 | 0.388966 | ||||||||
\(733\) | −1.16554 | −0.0430502 | −0.0215251 | − | 0.999768i | \(-0.506852\pi\) | ||||
−0.0215251 | + | 0.999768i | \(0.506852\pi\) | |||||||
\(734\) | 3.43576 | 0.126816 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 17.0413 | 0.628149 | ||||||||
\(737\) | −10.3012 | −0.379450 | ||||||||
\(738\) | −1.51118 | −0.0556275 | ||||||||
\(739\) | 43.5856 | 1.60332 | 0.801661 | − | 0.597779i | \(-0.203950\pi\) | ||||
0.801661 | + | 0.597779i | \(0.203950\pi\) | |||||||
\(740\) | −22.3262 | −0.820728 | ||||||||
\(741\) | 4.45563 | 0.163682 | ||||||||
\(742\) | 0.309960 | 0.0113790 | ||||||||
\(743\) | 0.508255 | 0.0186461 | 0.00932304 | − | 0.999957i | \(-0.497032\pi\) | ||||
0.00932304 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(744\) | 3.11123 | 0.114063 | ||||||||
\(745\) | −0.568114 | −0.0208141 | ||||||||
\(746\) | −0.104432 | −0.00382352 | ||||||||
\(747\) | −4.16310 | −0.152320 | ||||||||
\(748\) | 0.987504 | 0.0361067 | ||||||||
\(749\) | 15.8900 | 0.580609 | ||||||||
\(750\) | 0.222191 | 0.00811328 | ||||||||
\(751\) | −11.1188 | −0.405731 | −0.202865 | − | 0.979207i | \(-0.565025\pi\) | ||||
−0.202865 | + | 0.979207i | \(0.565025\pi\) | |||||||
\(752\) | 46.9138 | 1.71077 | ||||||||
\(753\) | 9.37758 | 0.341738 | ||||||||
\(754\) | −0.681167 | −0.0248066 | ||||||||
\(755\) | 4.44688 | 0.161839 | ||||||||
\(756\) | 1.95063 | 0.0709438 | ||||||||
\(757\) | −3.60255 | −0.130937 | −0.0654684 | − | 0.997855i | \(-0.520854\pi\) | ||||
−0.0654684 | + | 0.997855i | \(0.520854\pi\) | |||||||
\(758\) | 5.60423 | 0.203555 | ||||||||
\(759\) | 6.60749 | 0.239837 | ||||||||
\(760\) | −4.34564 | −0.157633 | ||||||||
\(761\) | 41.5980 | 1.50793 | 0.753963 | − | 0.656917i | \(-0.228140\pi\) | ||||
0.753963 | + | 0.656917i | \(0.228140\pi\) | |||||||
\(762\) | 2.43064 | 0.0880527 | ||||||||
\(763\) | −17.4706 | −0.632479 | ||||||||
\(764\) | −13.4862 | −0.487913 | ||||||||
\(765\) | −0.506248 | −0.0183034 | ||||||||
\(766\) | 4.71616 | 0.170402 | ||||||||
\(767\) | 6.24553 | 0.225513 | ||||||||
\(768\) | −12.1950 | −0.440051 | ||||||||
\(769\) | −27.7113 | −0.999297 | −0.499648 | − | 0.866228i | \(-0.666537\pi\) | ||||
−0.499648 | + | 0.866228i | \(0.666537\pi\) | |||||||
\(770\) | −0.222191 | −0.00800722 | ||||||||
\(771\) | 13.9718 | 0.503183 | ||||||||
\(772\) | −4.18054 | −0.150461 | ||||||||
\(773\) | −10.8663 | −0.390833 | −0.195416 | − | 0.980720i | \(-0.562606\pi\) | ||||
−0.195416 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(774\) | −2.05818 | −0.0739797 | ||||||||
\(775\) | −3.54437 | −0.127318 | ||||||||
\(776\) | 0.0444327 | 0.00159504 | ||||||||
\(777\) | −11.4456 | −0.410610 | ||||||||
\(778\) | −1.98457 | −0.0711504 | ||||||||
\(779\) | −33.6706 | −1.20637 | ||||||||
\(780\) | 1.75559 | 0.0628603 | ||||||||
\(781\) | 6.35689 | 0.227467 | ||||||||
\(782\) | −0.743236 | −0.0265781 | ||||||||
\(783\) | −3.40626 | −0.121730 | ||||||||
\(784\) | 3.70622 | 0.132365 | ||||||||
\(785\) | 8.15186 | 0.290952 | ||||||||
\(786\) | 2.52118 | 0.0899276 | ||||||||
\(787\) | −52.8938 | −1.88546 | −0.942730 | − | 0.333558i | \(-0.891751\pi\) | ||||
−0.942730 | + | 0.333558i | \(0.891751\pi\) | |||||||
\(788\) | −36.2623 | −1.29179 | ||||||||
\(789\) | 18.1232 | 0.645202 | ||||||||
\(790\) | −0.441884 | −0.0157215 | ||||||||
\(791\) | 19.4200 | 0.690496 | ||||||||
\(792\) | 0.877796 | 0.0311911 | ||||||||
\(793\) | 4.85558 | 0.172427 | ||||||||
\(794\) | 3.92308 | 0.139225 | ||||||||
\(795\) | 1.39501 | 0.0494760 | ||||||||
\(796\) | 7.02237 | 0.248901 | ||||||||
\(797\) | 7.31621 | 0.259153 | 0.129577 | − | 0.991569i | \(-0.458638\pi\) | ||||
0.129577 | + | 0.991569i | \(0.458638\pi\) | |||||||
\(798\) | −1.09999 | −0.0389391 | ||||||||
\(799\) | −6.40814 | −0.226704 | ||||||||
\(800\) | −2.57908 | −0.0911844 | ||||||||
\(801\) | 2.25059 | 0.0795208 | ||||||||
\(802\) | 5.58798 | 0.197319 | ||||||||
\(803\) | 3.55562 | 0.125475 | ||||||||
\(804\) | −20.0939 | −0.708656 | ||||||||
\(805\) | −6.60749 | −0.232883 | ||||||||
\(806\) | 0.708785 | 0.0249659 | ||||||||
\(807\) | −32.1793 | −1.13277 | ||||||||
\(808\) | −2.85890 | −0.100576 | ||||||||
\(809\) | −44.1282 | −1.55146 | −0.775732 | − | 0.631063i | \(-0.782619\pi\) | ||||
−0.775732 | + | 0.631063i | \(0.782619\pi\) | |||||||
\(810\) | −0.222191 | −0.00780701 | ||||||||
\(811\) | 43.0394 | 1.51132 | 0.755659 | − | 0.654965i | \(-0.227317\pi\) | ||||
0.755659 | + | 0.654965i | \(0.227317\pi\) | |||||||
\(812\) | −6.64436 | −0.233171 | ||||||||
\(813\) | 24.0669 | 0.844062 | ||||||||
\(814\) | −2.54312 | −0.0891363 | ||||||||
\(815\) | 6.63311 | 0.232348 | ||||||||
\(816\) | 1.87627 | 0.0656826 | ||||||||
\(817\) | −45.8581 | −1.60437 | ||||||||
\(818\) | −6.44688 | −0.225410 | ||||||||
\(819\) | 0.900012 | 0.0314490 | ||||||||
\(820\) | −13.2668 | −0.463296 | ||||||||
\(821\) | −45.9099 | −1.60227 | −0.801134 | − | 0.598485i | \(-0.795770\pi\) | ||||
−0.801134 | + | 0.598485i | \(0.795770\pi\) | |||||||
\(822\) | 2.93070 | 0.102220 | ||||||||
\(823\) | 1.96931 | 0.0686459 | 0.0343230 | − | 0.999411i | \(-0.489073\pi\) | ||||
0.0343230 | + | 0.999411i | \(0.489073\pi\) | |||||||
\(824\) | −0.0422391 | −0.00147147 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −1.54187 | −0.0536486 | ||||||||
\(827\) | 3.60937 | 0.125510 | 0.0627550 | − | 0.998029i | \(-0.480011\pi\) | ||||
0.0627550 | + | 0.998029i | \(0.480011\pi\) | |||||||
\(828\) | 12.8888 | 0.447916 | ||||||||
\(829\) | −5.28622 | −0.183598 | −0.0917989 | − | 0.995778i | \(-0.529262\pi\) | ||||
−0.0917989 | + | 0.995778i | \(0.529262\pi\) | |||||||
\(830\) | 0.925005 | 0.0321074 | ||||||||
\(831\) | −16.8443 | −0.584323 | ||||||||
\(832\) | −6.15554 | −0.213405 | ||||||||
\(833\) | −0.506248 | −0.0175405 | ||||||||
\(834\) | −4.34564 | −0.150477 | ||||||||
\(835\) | 3.75559 | 0.129968 | ||||||||
\(836\) | 9.65685 | 0.333989 | ||||||||
\(837\) | 3.54437 | 0.122511 | ||||||||
\(838\) | 5.80572 | 0.200555 | ||||||||
\(839\) | 18.3268 | 0.632713 | 0.316356 | − | 0.948640i | \(-0.397540\pi\) | ||||
0.316356 | + | 0.948640i | \(0.397540\pi\) | |||||||
\(840\) | −0.877796 | −0.0302868 | ||||||||
\(841\) | −17.3974 | −0.599910 | ||||||||
\(842\) | −8.24248 | −0.284055 | ||||||||
\(843\) | 0.0444327 | 0.00153034 | ||||||||
\(844\) | 8.23540 | 0.283474 | ||||||||
\(845\) | −12.1900 | −0.419348 | ||||||||
\(846\) | −2.81252 | −0.0966965 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −5.17023 | −0.177547 | ||||||||
\(849\) | 0.455630 | 0.0156372 | ||||||||
\(850\) | 0.112484 | 0.00385817 | ||||||||
\(851\) | −75.6268 | −2.59245 | ||||||||
\(852\) | 12.4000 | 0.424815 | ||||||||
\(853\) | 38.1150 | 1.30503 | 0.652516 | − | 0.757775i | \(-0.273713\pi\) | ||||
0.652516 | + | 0.757775i | \(0.273713\pi\) | |||||||
\(854\) | −1.19873 | −0.0410195 | ||||||||
\(855\) | −4.95063 | −0.169308 | ||||||||
\(856\) | 13.9482 | 0.476739 | ||||||||
\(857\) | −19.0912 | −0.652144 | −0.326072 | − | 0.945345i | \(-0.605725\pi\) | ||||
−0.326072 | + | 0.945345i | \(0.605725\pi\) | |||||||
\(858\) | 0.199975 | 0.00682703 | ||||||||
\(859\) | 16.2357 | 0.553954 | 0.276977 | − | 0.960877i | \(-0.410667\pi\) | ||||
0.276977 | + | 0.960877i | \(0.410667\pi\) | |||||||
\(860\) | −18.0689 | −0.616143 | ||||||||
\(861\) | −6.80127 | −0.231787 | ||||||||
\(862\) | −2.13360 | −0.0726708 | ||||||||
\(863\) | 32.0076 | 1.08955 | 0.544775 | − | 0.838582i | \(-0.316615\pi\) | ||||
0.544775 | + | 0.838582i | \(0.316615\pi\) | |||||||
\(864\) | 2.57908 | 0.0877422 | ||||||||
\(865\) | −15.7038 | −0.533945 | ||||||||
\(866\) | 6.91320 | 0.234920 | ||||||||
\(867\) | 16.7437 | 0.568646 | ||||||||
\(868\) | 6.91376 | 0.234668 | ||||||||
\(869\) | 1.98875 | 0.0674638 | ||||||||
\(870\) | 0.756842 | 0.0256593 | ||||||||
\(871\) | −9.27122 | −0.314143 | ||||||||
\(872\) | −15.3356 | −0.519331 | ||||||||
\(873\) | 0.0506185 | 0.00171318 | ||||||||
\(874\) | −7.26815 | −0.245849 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 6.93570 | 0.234335 | ||||||||
\(877\) | −3.88495 | −0.131186 | −0.0655928 | − | 0.997846i | \(-0.520894\pi\) | ||||
−0.0655928 | + | 0.997846i | \(0.520894\pi\) | |||||||
\(878\) | 7.56881 | 0.255435 | ||||||||
\(879\) | −31.1337 | −1.05011 | ||||||||
\(880\) | 3.70622 | 0.124937 | ||||||||
\(881\) | 26.2331 | 0.883816 | 0.441908 | − | 0.897060i | \(-0.354302\pi\) | ||||
0.441908 | + | 0.897060i | \(0.354302\pi\) | |||||||
\(882\) | −0.222191 | −0.00748157 | ||||||||
\(883\) | −9.26622 | −0.311833 | −0.155917 | − | 0.987770i | \(-0.549833\pi\) | ||||
−0.155917 | + | 0.987770i | \(0.549833\pi\) | |||||||
\(884\) | 0.888765 | 0.0298924 | ||||||||
\(885\) | −6.93938 | −0.233265 | ||||||||
\(886\) | −4.22997 | −0.142108 | ||||||||
\(887\) | −16.2593 | −0.545935 | −0.272968 | − | 0.962023i | \(-0.588005\pi\) | ||||
−0.272968 | + | 0.962023i | \(0.588005\pi\) | |||||||
\(888\) | −10.0469 | −0.337153 | ||||||||
\(889\) | 10.9394 | 0.366895 | ||||||||
\(890\) | −0.500062 | −0.0167621 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 19.4076 | 0.649814 | ||||||||
\(893\) | −62.6656 | −2.09702 | ||||||||
\(894\) | −0.126230 | −0.00422176 | ||||||||
\(895\) | −8.95682 | −0.299393 | ||||||||
\(896\) | 6.67782 | 0.223090 | ||||||||
\(897\) | 5.94682 | 0.198559 | ||||||||
\(898\) | −4.15067 | −0.138510 | ||||||||
\(899\) | −12.0730 | −0.402659 | ||||||||
\(900\) | −1.95063 | −0.0650210 | ||||||||
\(901\) | 0.706223 | 0.0235277 | ||||||||
\(902\) | −1.51118 | −0.0503169 | ||||||||
\(903\) | −9.26309 | −0.308256 | ||||||||
\(904\) | 17.0468 | 0.566968 | ||||||||
\(905\) | −13.8025 | −0.458811 | ||||||||
\(906\) | 0.988059 | 0.0328261 | ||||||||
\(907\) | −44.6806 | −1.48359 | −0.741797 | − | 0.670624i | \(-0.766026\pi\) | ||||
−0.741797 | + | 0.670624i | \(0.766026\pi\) | |||||||
\(908\) | −28.9706 | −0.961422 | ||||||||
\(909\) | −3.25690 | −0.108025 | ||||||||
\(910\) | −0.199975 | −0.00662911 | ||||||||
\(911\) | −53.3601 | −1.76790 | −0.883949 | − | 0.467583i | \(-0.845125\pi\) | ||||
−0.883949 | + | 0.467583i | \(0.845125\pi\) | |||||||
\(912\) | 18.3481 | 0.607568 | ||||||||
\(913\) | −4.16310 | −0.137779 | ||||||||
\(914\) | −6.06305 | −0.200548 | ||||||||
\(915\) | −5.39501 | −0.178354 | ||||||||
\(916\) | −6.32620 | −0.209024 | ||||||||
\(917\) | 11.3469 | 0.374707 | ||||||||
\(918\) | −0.112484 | −0.00371252 | ||||||||
\(919\) | 42.4769 | 1.40118 | 0.700591 | − | 0.713563i | \(-0.252920\pi\) | ||||
0.700591 | + | 0.713563i | \(0.252920\pi\) | |||||||
\(920\) | −5.80002 | −0.191221 | ||||||||
\(921\) | 27.9038 | 0.919460 | ||||||||
\(922\) | 8.27983 | 0.272682 | ||||||||
\(923\) | 5.72128 | 0.188318 | ||||||||
\(924\) | 1.95063 | 0.0641710 | ||||||||
\(925\) | 11.4456 | 0.376330 | ||||||||
\(926\) | 1.88889 | 0.0620728 | ||||||||
\(927\) | −0.0481195 | −0.00158045 | ||||||||
\(928\) | −8.78503 | −0.288383 | ||||||||
\(929\) | 36.4812 | 1.19691 | 0.598455 | − | 0.801157i | \(-0.295782\pi\) | ||||
0.598455 | + | 0.801157i | \(0.295782\pi\) | |||||||
\(930\) | −0.787529 | −0.0258241 | ||||||||
\(931\) | −4.95063 | −0.162250 | ||||||||
\(932\) | −21.7874 | −0.713670 | ||||||||
\(933\) | 20.4274 | 0.668764 | ||||||||
\(934\) | 4.55855 | 0.149160 | ||||||||
\(935\) | −0.506248 | −0.0165561 | ||||||||
\(936\) | 0.790027 | 0.0258229 | ||||||||
\(937\) | −35.4087 | −1.15675 | −0.578376 | − | 0.815770i | \(-0.696313\pi\) | ||||
−0.578376 | + | 0.815770i | \(0.696313\pi\) | |||||||
\(938\) | 2.28884 | 0.0747333 | ||||||||
\(939\) | −22.0531 | −0.719676 | ||||||||
\(940\) | −24.6913 | −0.805341 | ||||||||
\(941\) | 16.8161 | 0.548191 | 0.274095 | − | 0.961703i | \(-0.411622\pi\) | ||||
0.274095 | + | 0.961703i | \(0.411622\pi\) | |||||||
\(942\) | 1.81127 | 0.0590144 | ||||||||
\(943\) | −44.9393 | −1.46343 | ||||||||
\(944\) | 25.7189 | 0.837079 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −2.05818 | −0.0669172 | ||||||||
\(947\) | −58.8375 | −1.91196 | −0.955980 | − | 0.293431i | \(-0.905203\pi\) | ||||
−0.955980 | + | 0.293431i | \(0.905203\pi\) | |||||||
\(948\) | 3.87932 | 0.125995 | ||||||||
\(949\) | 3.20010 | 0.103880 | ||||||||
\(950\) | 1.09999 | 0.0356883 | ||||||||
\(951\) | 17.9038 | 0.580569 | ||||||||
\(952\) | −0.444383 | −0.0144025 | ||||||||
\(953\) | 13.7575 | 0.445650 | 0.222825 | − | 0.974858i | \(-0.428472\pi\) | ||||
0.222825 | + | 0.974858i | \(0.428472\pi\) | |||||||
\(954\) | 0.309960 | 0.0100353 | ||||||||
\(955\) | 6.91376 | 0.223724 | ||||||||
\(956\) | −4.78015 | −0.154601 | ||||||||
\(957\) | −3.40626 | −0.110109 | ||||||||
\(958\) | −2.72865 | −0.0881588 | ||||||||
\(959\) | 13.1900 | 0.425927 | ||||||||
\(960\) | 6.83940 | 0.220741 | ||||||||
\(961\) | −18.4374 | −0.594756 | ||||||||
\(962\) | −2.28884 | −0.0737952 | ||||||||
\(963\) | 15.8900 | 0.512049 | ||||||||
\(964\) | 50.9139 | 1.63983 | ||||||||
\(965\) | 2.14317 | 0.0689911 | ||||||||
\(966\) | −1.46813 | −0.0472362 | ||||||||
\(967\) | 28.8681 | 0.928337 | 0.464168 | − | 0.885747i | \(-0.346353\pi\) | ||||
0.464168 | + | 0.885747i | \(0.346353\pi\) | |||||||
\(968\) | 0.877796 | 0.0282134 | ||||||||
\(969\) | −2.50625 | −0.0805123 | ||||||||
\(970\) | −0.0112470 | −0.000361119 0 | ||||||||
\(971\) | −39.4282 | −1.26531 | −0.632656 | − | 0.774433i | \(-0.718035\pi\) | ||||
−0.632656 | + | 0.774433i | \(0.718035\pi\) | |||||||
\(972\) | 1.95063 | 0.0625665 | ||||||||
\(973\) | −19.5581 | −0.627004 | ||||||||
\(974\) | 4.57493 | 0.146590 | ||||||||
\(975\) | −0.900012 | −0.0288235 | ||||||||
\(976\) | 19.9951 | 0.640028 | ||||||||
\(977\) | −2.81758 | −0.0901425 | −0.0450712 | − | 0.998984i | \(-0.514351\pi\) | ||||
−0.0450712 | + | 0.998984i | \(0.514351\pi\) | |||||||
\(978\) | 1.47382 | 0.0471276 | ||||||||
\(979\) | 2.25059 | 0.0719293 | ||||||||
\(980\) | −1.95063 | −0.0623106 | ||||||||
\(981\) | −17.4706 | −0.557794 | ||||||||
\(982\) | −1.40577 | −0.0448599 | ||||||||
\(983\) | 49.0000 | 1.56286 | 0.781429 | − | 0.623995i | \(-0.214491\pi\) | ||||
0.781429 | + | 0.623995i | \(0.214491\pi\) | |||||||
\(984\) | −5.97013 | −0.190321 | ||||||||
\(985\) | 18.5901 | 0.592328 | ||||||||
\(986\) | 0.383150 | 0.0122020 | ||||||||
\(987\) | −12.6581 | −0.402912 | ||||||||
\(988\) | 8.69129 | 0.276507 | ||||||||
\(989\) | −61.2057 | −1.94623 | ||||||||
\(990\) | −0.222191 | −0.00706171 | ||||||||
\(991\) | 7.64874 | 0.242970 | 0.121485 | − | 0.992593i | \(-0.461234\pi\) | ||||
0.121485 | + | 0.992593i | \(0.461234\pi\) | |||||||
\(992\) | 9.14123 | 0.290234 | ||||||||
\(993\) | −18.5112 | −0.587437 | ||||||||
\(994\) | −1.41245 | −0.0448001 | ||||||||
\(995\) | −3.60005 | −0.114129 | ||||||||
\(996\) | −8.12068 | −0.257313 | ||||||||
\(997\) | 32.7092 | 1.03591 | 0.517956 | − | 0.855408i | \(-0.326693\pi\) | ||||
0.517956 | + | 0.855408i | \(0.326693\pi\) | |||||||
\(998\) | 0.139421 | 0.00441329 | ||||||||
\(999\) | −11.4456 | −0.362124 |
(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 | 1155.2.a.v.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 3465.2.a.bj.1.3 | 4 | |||
5.4 | even | 2 | 5775.2.a.by.1.3 | 4 | |||
7.6 | odd | 2 | 8085.2.a.bq.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.v.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3465.2.a.bj.1.3 | 4 | 3.2 | odd | 2 | |||
5775.2.a.by.1.3 | 4 | 5.4 | even | 2 | |||
8085.2.a.bq.1.2 | 4 | 7.6 | odd | 2 |