Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.731229 | 0.422175 | 0.211088 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211088 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.24153 | 1.44966 | 0.724829 | − | 0.688929i | \(-0.241919\pi\) | ||||
0.724829 | + | 0.688929i | \(0.241919\pi\) | |||||||
\(6\) | 0.731229 | 0.298523 | ||||||||
\(7\) | 4.02612 | 1.52173 | 0.760866 | − | 0.648909i | \(-0.224774\pi\) | ||||
0.760866 | + | 0.648909i | \(0.224774\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.46530 | −0.821768 | ||||||||
\(10\) | 3.24153 | 1.02506 | ||||||||
\(11\) | 1.64443 | 0.495815 | 0.247907 | − | 0.968784i | \(-0.420257\pi\) | ||||
0.247907 | + | 0.968784i | \(0.420257\pi\) | |||||||
\(12\) | 0.731229 | 0.211088 | ||||||||
\(13\) | 2.18437 | 0.605836 | 0.302918 | − | 0.953017i | \(-0.402039\pi\) | ||||
0.302918 | + | 0.953017i | \(0.402039\pi\) | |||||||
\(14\) | 4.02612 | 1.07603 | ||||||||
\(15\) | 2.37030 | 0.612010 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.11672 | −0.513379 | −0.256690 | − | 0.966494i | \(-0.582632\pi\) | ||||
−0.256690 | + | 0.966494i | \(0.582632\pi\) | |||||||
\(18\) | −2.46530 | −0.581078 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.24153 | 0.724829 | ||||||||
\(21\) | 2.94402 | 0.642438 | ||||||||
\(22\) | 1.64443 | 0.350594 | ||||||||
\(23\) | 7.93136 | 1.65380 | 0.826902 | − | 0.562346i | \(-0.190101\pi\) | ||||
0.826902 | + | 0.562346i | \(0.190101\pi\) | |||||||
\(24\) | 0.731229 | 0.149261 | ||||||||
\(25\) | 5.50755 | 1.10151 | ||||||||
\(26\) | 2.18437 | 0.428391 | ||||||||
\(27\) | −3.99639 | −0.769105 | ||||||||
\(28\) | 4.02612 | 0.760866 | ||||||||
\(29\) | −7.04227 | −1.30772 | −0.653858 | − | 0.756617i | \(-0.726851\pi\) | ||||
−0.653858 | + | 0.756617i | \(0.726851\pi\) | |||||||
\(30\) | 2.37030 | 0.432756 | ||||||||
\(31\) | 2.96493 | 0.532516 | 0.266258 | − | 0.963902i | \(-0.414213\pi\) | ||||
0.266258 | + | 0.963902i | \(0.414213\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.20246 | 0.209321 | ||||||||
\(34\) | −2.11672 | −0.363014 | ||||||||
\(35\) | 13.0508 | 2.20599 | ||||||||
\(36\) | −2.46530 | −0.410884 | ||||||||
\(37\) | −1.09154 | −0.179448 | −0.0897240 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897240 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 1.59728 | 0.255769 | ||||||||
\(40\) | 3.24153 | 0.512532 | ||||||||
\(41\) | 5.86384 | 0.915778 | 0.457889 | − | 0.889009i | \(-0.348606\pi\) | ||||
0.457889 | + | 0.889009i | \(0.348606\pi\) | |||||||
\(42\) | 2.94402 | 0.454272 | ||||||||
\(43\) | −10.0819 | −1.53748 | −0.768741 | − | 0.639560i | \(-0.779116\pi\) | ||||
−0.768741 | + | 0.639560i | \(0.779116\pi\) | |||||||
\(44\) | 1.64443 | 0.247907 | ||||||||
\(45\) | −7.99137 | −1.19128 | ||||||||
\(46\) | 7.93136 | 1.16942 | ||||||||
\(47\) | 7.44446 | 1.08589 | 0.542943 | − | 0.839769i | \(-0.317310\pi\) | ||||
0.542943 | + | 0.839769i | \(0.317310\pi\) | |||||||
\(48\) | 0.731229 | 0.105544 | ||||||||
\(49\) | 9.20968 | 1.31567 | ||||||||
\(50\) | 5.50755 | 0.778885 | ||||||||
\(51\) | −1.54780 | −0.216736 | ||||||||
\(52\) | 2.18437 | 0.302918 | ||||||||
\(53\) | −1.80240 | −0.247579 | −0.123789 | − | 0.992309i | \(-0.539505\pi\) | ||||
−0.123789 | + | 0.992309i | \(0.539505\pi\) | |||||||
\(54\) | −3.99639 | −0.543840 | ||||||||
\(55\) | 5.33048 | 0.718762 | ||||||||
\(56\) | 4.02612 | 0.538014 | ||||||||
\(57\) | −0.731229 | −0.0968536 | ||||||||
\(58\) | −7.04227 | −0.924695 | ||||||||
\(59\) | −8.17643 | −1.06448 | −0.532240 | − | 0.846593i | \(-0.678650\pi\) | ||||
−0.532240 | + | 0.846593i | \(0.678650\pi\) | |||||||
\(60\) | 2.37030 | 0.306005 | ||||||||
\(61\) | −9.55710 | −1.22366 | −0.611831 | − | 0.790989i | \(-0.709567\pi\) | ||||
−0.611831 | + | 0.790989i | \(0.709567\pi\) | |||||||
\(62\) | 2.96493 | 0.376546 | ||||||||
\(63\) | −9.92562 | −1.25051 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.08072 | 0.878255 | ||||||||
\(66\) | 1.20246 | 0.148012 | ||||||||
\(67\) | 10.0295 | 1.22529 | 0.612647 | − | 0.790356i | \(-0.290105\pi\) | ||||
0.612647 | + | 0.790356i | \(0.290105\pi\) | |||||||
\(68\) | −2.11672 | −0.256690 | ||||||||
\(69\) | 5.79964 | 0.698195 | ||||||||
\(70\) | 13.0508 | 1.55987 | ||||||||
\(71\) | 2.43109 | 0.288518 | 0.144259 | − | 0.989540i | \(-0.453920\pi\) | ||||
0.144259 | + | 0.989540i | \(0.453920\pi\) | |||||||
\(72\) | −2.46530 | −0.290539 | ||||||||
\(73\) | 0.129250 | 0.0151276 | 0.00756380 | − | 0.999971i | \(-0.497592\pi\) | ||||
0.00756380 | + | 0.999971i | \(0.497592\pi\) | |||||||
\(74\) | −1.09154 | −0.126889 | ||||||||
\(75\) | 4.02728 | 0.465030 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 6.62069 | 0.754497 | ||||||||
\(78\) | 1.59728 | 0.180856 | ||||||||
\(79\) | 2.09468 | 0.235670 | 0.117835 | − | 0.993033i | \(-0.462405\pi\) | ||||
0.117835 | + | 0.993033i | \(0.462405\pi\) | |||||||
\(80\) | 3.24153 | 0.362415 | ||||||||
\(81\) | 4.47364 | 0.497071 | ||||||||
\(82\) | 5.86384 | 0.647553 | ||||||||
\(83\) | −1.41701 | −0.155537 | −0.0777684 | − | 0.996971i | \(-0.524779\pi\) | ||||
−0.0777684 | + | 0.996971i | \(0.524779\pi\) | |||||||
\(84\) | 2.94402 | 0.321219 | ||||||||
\(85\) | −6.86141 | −0.744224 | ||||||||
\(86\) | −10.0819 | −1.08716 | ||||||||
\(87\) | −5.14951 | −0.552085 | ||||||||
\(88\) | 1.64443 | 0.175297 | ||||||||
\(89\) | −7.58566 | −0.804078 | −0.402039 | − | 0.915622i | \(-0.631698\pi\) | ||||
−0.402039 | + | 0.915622i | \(0.631698\pi\) | |||||||
\(90\) | −7.99137 | −0.842364 | ||||||||
\(91\) | 8.79456 | 0.921920 | ||||||||
\(92\) | 7.93136 | 0.826902 | ||||||||
\(93\) | 2.16804 | 0.224815 | ||||||||
\(94\) | 7.44446 | 0.767838 | ||||||||
\(95\) | −3.24153 | −0.332574 | ||||||||
\(96\) | 0.731229 | 0.0746307 | ||||||||
\(97\) | 1.83031 | 0.185840 | 0.0929201 | − | 0.995674i | \(-0.470380\pi\) | ||||
0.0929201 | + | 0.995674i | \(0.470380\pi\) | |||||||
\(98\) | 9.20968 | 0.930318 | ||||||||
\(99\) | −4.05402 | −0.407445 | ||||||||
\(100\) | 5.50755 | 0.550755 | ||||||||
\(101\) | −17.2151 | −1.71297 | −0.856483 | − | 0.516175i | \(-0.827356\pi\) | ||||
−0.856483 | + | 0.516175i | \(0.827356\pi\) | |||||||
\(102\) | −1.54780 | −0.153255 | ||||||||
\(103\) | −16.4725 | −1.62309 | −0.811544 | − | 0.584292i | \(-0.801372\pi\) | ||||
−0.811544 | + | 0.584292i | \(0.801372\pi\) | |||||||
\(104\) | 2.18437 | 0.214195 | ||||||||
\(105\) | 9.54314 | 0.931315 | ||||||||
\(106\) | −1.80240 | −0.175065 | ||||||||
\(107\) | 17.0663 | 1.64986 | 0.824929 | − | 0.565236i | \(-0.191215\pi\) | ||||
0.824929 | + | 0.565236i | \(0.191215\pi\) | |||||||
\(108\) | −3.99639 | −0.384553 | ||||||||
\(109\) | 14.2864 | 1.36839 | 0.684194 | − | 0.729300i | \(-0.260154\pi\) | ||||
0.684194 | + | 0.729300i | \(0.260154\pi\) | |||||||
\(110\) | 5.33048 | 0.508242 | ||||||||
\(111\) | −0.798165 | −0.0757585 | ||||||||
\(112\) | 4.02612 | 0.380433 | ||||||||
\(113\) | 15.5876 | 1.46636 | 0.733178 | − | 0.680037i | \(-0.238036\pi\) | ||||
0.733178 | + | 0.680037i | \(0.238036\pi\) | |||||||
\(114\) | −0.731229 | −0.0684859 | ||||||||
\(115\) | 25.7098 | 2.39745 | ||||||||
\(116\) | −7.04227 | −0.653858 | ||||||||
\(117\) | −5.38514 | −0.497857 | ||||||||
\(118\) | −8.17643 | −0.752702 | ||||||||
\(119\) | −8.52216 | −0.781226 | ||||||||
\(120\) | 2.37030 | 0.216378 | ||||||||
\(121\) | −8.29584 | −0.754168 | ||||||||
\(122\) | −9.55710 | −0.865259 | ||||||||
\(123\) | 4.28781 | 0.386619 | ||||||||
\(124\) | 2.96493 | 0.266258 | ||||||||
\(125\) | 1.64523 | 0.147153 | ||||||||
\(126\) | −9.92562 | −0.884245 | ||||||||
\(127\) | −0.381396 | −0.0338434 | −0.0169217 | − | 0.999857i | \(-0.505387\pi\) | ||||
−0.0169217 | + | 0.999857i | \(0.505387\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.37221 | −0.649087 | ||||||||
\(130\) | 7.08072 | 0.621020 | ||||||||
\(131\) | −0.745467 | −0.0651318 | −0.0325659 | − | 0.999470i | \(-0.510368\pi\) | ||||
−0.0325659 | + | 0.999470i | \(0.510368\pi\) | |||||||
\(132\) | 1.20246 | 0.104660 | ||||||||
\(133\) | −4.02612 | −0.349109 | ||||||||
\(134\) | 10.0295 | 0.866414 | ||||||||
\(135\) | −12.9544 | −1.11494 | ||||||||
\(136\) | −2.11672 | −0.181507 | ||||||||
\(137\) | −8.61574 | −0.736093 | −0.368046 | − | 0.929807i | \(-0.619973\pi\) | ||||
−0.368046 | + | 0.929807i | \(0.619973\pi\) | |||||||
\(138\) | 5.79964 | 0.493698 | ||||||||
\(139\) | 10.8967 | 0.924244 | 0.462122 | − | 0.886816i | \(-0.347088\pi\) | ||||
0.462122 | + | 0.886816i | \(0.347088\pi\) | |||||||
\(140\) | 13.0508 | 1.10300 | ||||||||
\(141\) | 5.44361 | 0.458434 | ||||||||
\(142\) | 2.43109 | 0.204013 | ||||||||
\(143\) | 3.59205 | 0.300383 | ||||||||
\(144\) | −2.46530 | −0.205442 | ||||||||
\(145\) | −22.8278 | −1.89574 | ||||||||
\(146\) | 0.129250 | 0.0106968 | ||||||||
\(147\) | 6.73438 | 0.555443 | ||||||||
\(148\) | −1.09154 | −0.0897240 | ||||||||
\(149\) | −7.19939 | −0.589797 | −0.294899 | − | 0.955529i | \(-0.595286\pi\) | ||||
−0.294899 | + | 0.955529i | \(0.595286\pi\) | |||||||
\(150\) | 4.02728 | 0.328826 | ||||||||
\(151\) | 2.39938 | 0.195259 | 0.0976294 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976294 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.21835 | 0.421879 | ||||||||
\(154\) | 6.62069 | 0.533510 | ||||||||
\(155\) | 9.61091 | 0.771967 | ||||||||
\(156\) | 1.59728 | 0.127884 | ||||||||
\(157\) | 12.9233 | 1.03139 | 0.515696 | − | 0.856772i | \(-0.327533\pi\) | ||||
0.515696 | + | 0.856772i | \(0.327533\pi\) | |||||||
\(158\) | 2.09468 | 0.166644 | ||||||||
\(159\) | −1.31797 | −0.104522 | ||||||||
\(160\) | 3.24153 | 0.256266 | ||||||||
\(161\) | 31.9327 | 2.51665 | ||||||||
\(162\) | 4.47364 | 0.351482 | ||||||||
\(163\) | −17.2184 | −1.34865 | −0.674325 | − | 0.738434i | \(-0.735566\pi\) | ||||
−0.674325 | + | 0.738434i | \(0.735566\pi\) | |||||||
\(164\) | 5.86384 | 0.457889 | ||||||||
\(165\) | 3.89780 | 0.303444 | ||||||||
\(166\) | −1.41701 | −0.109981 | ||||||||
\(167\) | 7.66193 | 0.592898 | 0.296449 | − | 0.955049i | \(-0.404198\pi\) | ||||
0.296449 | + | 0.955049i | \(0.404198\pi\) | |||||||
\(168\) | 2.94402 | 0.227136 | ||||||||
\(169\) | −8.22852 | −0.632963 | ||||||||
\(170\) | −6.86141 | −0.526246 | ||||||||
\(171\) | 2.46530 | 0.188527 | ||||||||
\(172\) | −10.0819 | −0.768741 | ||||||||
\(173\) | −0.850469 | −0.0646600 | −0.0323300 | − | 0.999477i | \(-0.510293\pi\) | ||||
−0.0323300 | + | 0.999477i | \(0.510293\pi\) | |||||||
\(174\) | −5.14951 | −0.390383 | ||||||||
\(175\) | 22.1741 | 1.67620 | ||||||||
\(176\) | 1.64443 | 0.123954 | ||||||||
\(177\) | −5.97884 | −0.449397 | ||||||||
\(178\) | −7.58566 | −0.568569 | ||||||||
\(179\) | 8.77509 | 0.655881 | 0.327940 | − | 0.944698i | \(-0.393645\pi\) | ||||
0.327940 | + | 0.944698i | \(0.393645\pi\) | |||||||
\(180\) | −7.99137 | −0.595641 | ||||||||
\(181\) | −14.3582 | −1.06724 | −0.533620 | − | 0.845724i | \(-0.679169\pi\) | ||||
−0.533620 | + | 0.845724i | \(0.679169\pi\) | |||||||
\(182\) | 8.79456 | 0.651896 | ||||||||
\(183\) | −6.98843 | −0.516600 | ||||||||
\(184\) | 7.93136 | 0.584708 | ||||||||
\(185\) | −3.53826 | −0.260138 | ||||||||
\(186\) | 2.16804 | 0.158968 | ||||||||
\(187\) | −3.48080 | −0.254541 | ||||||||
\(188\) | 7.44446 | 0.542943 | ||||||||
\(189\) | −16.0900 | −1.17037 | ||||||||
\(190\) | −3.24153 | −0.235166 | ||||||||
\(191\) | 17.3329 | 1.25417 | 0.627083 | − | 0.778953i | \(-0.284249\pi\) | ||||
0.627083 | + | 0.778953i | \(0.284249\pi\) | |||||||
\(192\) | 0.731229 | 0.0527719 | ||||||||
\(193\) | −25.1710 | −1.81185 | −0.905923 | − | 0.423443i | \(-0.860821\pi\) | ||||
−0.905923 | + | 0.423443i | \(0.860821\pi\) | |||||||
\(194\) | 1.83031 | 0.131409 | ||||||||
\(195\) | 5.17763 | 0.370778 | ||||||||
\(196\) | 9.20968 | 0.657834 | ||||||||
\(197\) | 2.39308 | 0.170500 | 0.0852498 | − | 0.996360i | \(-0.472831\pi\) | ||||
0.0852498 | + | 0.996360i | \(0.472831\pi\) | |||||||
\(198\) | −4.05402 | −0.288107 | ||||||||
\(199\) | −11.6350 | −0.824786 | −0.412393 | − | 0.911006i | \(-0.635307\pi\) | ||||
−0.412393 | + | 0.911006i | \(0.635307\pi\) | |||||||
\(200\) | 5.50755 | 0.389442 | ||||||||
\(201\) | 7.33384 | 0.517289 | ||||||||
\(202\) | −17.2151 | −1.21125 | ||||||||
\(203\) | −28.3530 | −1.98999 | ||||||||
\(204\) | −1.54780 | −0.108368 | ||||||||
\(205\) | 19.0078 | 1.32757 | ||||||||
\(206\) | −16.4725 | −1.14770 | ||||||||
\(207\) | −19.5532 | −1.35904 | ||||||||
\(208\) | 2.18437 | 0.151459 | ||||||||
\(209\) | −1.64443 | −0.113748 | ||||||||
\(210\) | 9.54314 | 0.658539 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −1.80240 | −0.123789 | ||||||||
\(213\) | 1.77768 | 0.121805 | ||||||||
\(214\) | 17.0663 | 1.16663 | ||||||||
\(215\) | −32.6810 | −2.22882 | ||||||||
\(216\) | −3.99639 | −0.271920 | ||||||||
\(217\) | 11.9372 | 0.810347 | ||||||||
\(218\) | 14.2864 | 0.967596 | ||||||||
\(219\) | 0.0945115 | 0.00638650 | ||||||||
\(220\) | 5.33048 | 0.359381 | ||||||||
\(221\) | −4.62370 | −0.311024 | ||||||||
\(222\) | −0.798165 | −0.0535694 | ||||||||
\(223\) | 12.6046 | 0.844063 | 0.422032 | − | 0.906581i | \(-0.361317\pi\) | ||||
0.422032 | + | 0.906581i | \(0.361317\pi\) | |||||||
\(224\) | 4.02612 | 0.269007 | ||||||||
\(225\) | −13.5778 | −0.905185 | ||||||||
\(226\) | 15.5876 | 1.03687 | ||||||||
\(227\) | −0.152605 | −0.0101288 | −0.00506439 | − | 0.999987i | \(-0.501612\pi\) | ||||
−0.00506439 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(228\) | −0.731229 | −0.0484268 | ||||||||
\(229\) | −0.343084 | −0.0226716 | −0.0113358 | − | 0.999936i | \(-0.503608\pi\) | ||||
−0.0113358 | + | 0.999936i | \(0.503608\pi\) | |||||||
\(230\) | 25.7098 | 1.69525 | ||||||||
\(231\) | 4.84124 | 0.318530 | ||||||||
\(232\) | −7.04227 | −0.462348 | ||||||||
\(233\) | −24.5919 | −1.61107 | −0.805533 | − | 0.592551i | \(-0.798121\pi\) | ||||
−0.805533 | + | 0.592551i | \(0.798121\pi\) | |||||||
\(234\) | −5.38514 | −0.352038 | ||||||||
\(235\) | 24.1315 | 1.57416 | ||||||||
\(236\) | −8.17643 | −0.532240 | ||||||||
\(237\) | 1.53169 | 0.0994940 | ||||||||
\(238\) | −8.52216 | −0.552410 | ||||||||
\(239\) | 15.2818 | 0.988497 | 0.494249 | − | 0.869321i | \(-0.335443\pi\) | ||||
0.494249 | + | 0.869321i | \(0.335443\pi\) | |||||||
\(240\) | 2.37030 | 0.153002 | ||||||||
\(241\) | −3.76817 | −0.242729 | −0.121365 | − | 0.992608i | \(-0.538727\pi\) | ||||
−0.121365 | + | 0.992608i | \(0.538727\pi\) | |||||||
\(242\) | −8.29584 | −0.533277 | ||||||||
\(243\) | 15.2604 | 0.978956 | ||||||||
\(244\) | −9.55710 | −0.611831 | ||||||||
\(245\) | 29.8535 | 1.90727 | ||||||||
\(246\) | 4.28781 | 0.273381 | ||||||||
\(247\) | −2.18437 | −0.138988 | ||||||||
\(248\) | 2.96493 | 0.188273 | ||||||||
\(249\) | −1.03616 | −0.0656638 | ||||||||
\(250\) | 1.64523 | 0.104053 | ||||||||
\(251\) | 18.9149 | 1.19390 | 0.596950 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596950 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(252\) | −9.92562 | −0.625255 | ||||||||
\(253\) | 13.0426 | 0.819980 | ||||||||
\(254\) | −0.381396 | −0.0239309 | ||||||||
\(255\) | −5.01726 | −0.314193 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.4598 | −1.71289 | −0.856447 | − | 0.516234i | \(-0.827333\pi\) | ||||
−0.856447 | + | 0.516234i | \(0.827333\pi\) | |||||||
\(258\) | −7.37221 | −0.458974 | ||||||||
\(259\) | −4.39467 | −0.273072 | ||||||||
\(260\) | 7.08072 | 0.439128 | ||||||||
\(261\) | 17.3613 | 1.07464 | ||||||||
\(262\) | −0.745467 | −0.0460551 | ||||||||
\(263\) | −21.2240 | −1.30873 | −0.654365 | − | 0.756179i | \(-0.727064\pi\) | ||||
−0.654365 | + | 0.756179i | \(0.727064\pi\) | |||||||
\(264\) | 1.20246 | 0.0740061 | ||||||||
\(265\) | −5.84255 | −0.358905 | ||||||||
\(266\) | −4.02612 | −0.246858 | ||||||||
\(267\) | −5.54685 | −0.339462 | ||||||||
\(268\) | 10.0295 | 0.612647 | ||||||||
\(269\) | 14.6404 | 0.892639 | 0.446319 | − | 0.894874i | \(-0.352735\pi\) | ||||
0.446319 | + | 0.894874i | \(0.352735\pi\) | |||||||
\(270\) | −12.9544 | −0.788382 | ||||||||
\(271\) | −8.05587 | −0.489359 | −0.244680 | − | 0.969604i | \(-0.578683\pi\) | ||||
−0.244680 | + | 0.969604i | \(0.578683\pi\) | |||||||
\(272\) | −2.11672 | −0.128345 | ||||||||
\(273\) | 6.43083 | 0.389212 | ||||||||
\(274\) | −8.61574 | −0.520496 | ||||||||
\(275\) | 9.05678 | 0.546145 | ||||||||
\(276\) | 5.79964 | 0.349098 | ||||||||
\(277\) | 9.22890 | 0.554511 | 0.277255 | − | 0.960796i | \(-0.410575\pi\) | ||||
0.277255 | + | 0.960796i | \(0.410575\pi\) | |||||||
\(278\) | 10.8967 | 0.653539 | ||||||||
\(279\) | −7.30944 | −0.437605 | ||||||||
\(280\) | 13.0508 | 0.779936 | ||||||||
\(281\) | −23.5180 | −1.40297 | −0.701483 | − | 0.712686i | \(-0.747478\pi\) | ||||
−0.701483 | + | 0.712686i | \(0.747478\pi\) | |||||||
\(282\) | 5.44361 | 0.324162 | ||||||||
\(283\) | 11.7905 | 0.700871 | 0.350435 | − | 0.936587i | \(-0.386034\pi\) | ||||
0.350435 | + | 0.936587i | \(0.386034\pi\) | |||||||
\(284\) | 2.43109 | 0.144259 | ||||||||
\(285\) | −2.37030 | −0.140405 | ||||||||
\(286\) | 3.59205 | 0.212403 | ||||||||
\(287\) | 23.6086 | 1.39357 | ||||||||
\(288\) | −2.46530 | −0.145269 | ||||||||
\(289\) | −12.5195 | −0.736442 | ||||||||
\(290\) | −22.8278 | −1.34049 | ||||||||
\(291\) | 1.33838 | 0.0784571 | ||||||||
\(292\) | 0.129250 | 0.00756380 | ||||||||
\(293\) | −5.50119 | −0.321383 | −0.160691 | − | 0.987005i | \(-0.551372\pi\) | ||||
−0.160691 | + | 0.987005i | \(0.551372\pi\) | |||||||
\(294\) | 6.73438 | 0.392757 | ||||||||
\(295\) | −26.5042 | −1.54313 | ||||||||
\(296\) | −1.09154 | −0.0634445 | ||||||||
\(297\) | −6.57179 | −0.381334 | ||||||||
\(298\) | −7.19939 | −0.417049 | ||||||||
\(299\) | 17.3251 | 1.00193 | ||||||||
\(300\) | 4.02728 | 0.232515 | ||||||||
\(301\) | −40.5912 | −2.33964 | ||||||||
\(302\) | 2.39938 | 0.138069 | ||||||||
\(303\) | −12.5882 | −0.723172 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −30.9797 | −1.77389 | ||||||||
\(306\) | 5.21835 | 0.298313 | ||||||||
\(307\) | −3.32632 | −0.189843 | −0.0949215 | − | 0.995485i | \(-0.530260\pi\) | ||||
−0.0949215 | + | 0.995485i | \(0.530260\pi\) | |||||||
\(308\) | 6.62069 | 0.377249 | ||||||||
\(309\) | −12.0452 | −0.685227 | ||||||||
\(310\) | 9.61091 | 0.545863 | ||||||||
\(311\) | −18.7637 | −1.06399 | −0.531995 | − | 0.846748i | \(-0.678557\pi\) | ||||
−0.531995 | + | 0.846748i | \(0.678557\pi\) | |||||||
\(312\) | 1.59728 | 0.0904280 | ||||||||
\(313\) | −6.41053 | −0.362345 | −0.181172 | − | 0.983451i | \(-0.557989\pi\) | ||||
−0.181172 | + | 0.983451i | \(0.557989\pi\) | |||||||
\(314\) | 12.9233 | 0.729304 | ||||||||
\(315\) | −32.1742 | −1.81281 | ||||||||
\(316\) | 2.09468 | 0.117835 | ||||||||
\(317\) | 30.6899 | 1.72372 | 0.861858 | − | 0.507150i | \(-0.169301\pi\) | ||||
0.861858 | + | 0.507150i | \(0.169301\pi\) | |||||||
\(318\) | −1.31797 | −0.0739080 | ||||||||
\(319\) | −11.5805 | −0.648385 | ||||||||
\(320\) | 3.24153 | 0.181207 | ||||||||
\(321\) | 12.4793 | 0.696529 | ||||||||
\(322\) | 31.9327 | 1.77954 | ||||||||
\(323\) | 2.11672 | 0.117777 | ||||||||
\(324\) | 4.47364 | 0.248535 | ||||||||
\(325\) | 12.0305 | 0.667334 | ||||||||
\(326\) | −17.2184 | −0.953640 | ||||||||
\(327\) | 10.4466 | 0.577699 | ||||||||
\(328\) | 5.86384 | 0.323777 | ||||||||
\(329\) | 29.9723 | 1.65243 | ||||||||
\(330\) | 3.89780 | 0.214567 | ||||||||
\(331\) | 1.32964 | 0.0730837 | 0.0365419 | − | 0.999332i | \(-0.488366\pi\) | ||||
0.0365419 | + | 0.999332i | \(0.488366\pi\) | |||||||
\(332\) | −1.41701 | −0.0777684 | ||||||||
\(333\) | 2.69098 | 0.147465 | ||||||||
\(334\) | 7.66193 | 0.419242 | ||||||||
\(335\) | 32.5109 | 1.77626 | ||||||||
\(336\) | 2.94402 | 0.160609 | ||||||||
\(337\) | −3.74910 | −0.204226 | −0.102113 | − | 0.994773i | \(-0.532560\pi\) | ||||
−0.102113 | + | 0.994773i | \(0.532560\pi\) | |||||||
\(338\) | −8.22852 | −0.447572 | ||||||||
\(339\) | 11.3981 | 0.619059 | ||||||||
\(340\) | −6.86141 | −0.372112 | ||||||||
\(341\) | 4.87562 | 0.264030 | ||||||||
\(342\) | 2.46530 | 0.133308 | ||||||||
\(343\) | 8.89644 | 0.480363 | ||||||||
\(344\) | −10.0819 | −0.543582 | ||||||||
\(345\) | 18.7997 | 1.01214 | ||||||||
\(346\) | −0.850469 | −0.0457215 | ||||||||
\(347\) | −29.8884 | −1.60449 | −0.802246 | − | 0.596994i | \(-0.796362\pi\) | ||||
−0.802246 | + | 0.596994i | \(0.796362\pi\) | |||||||
\(348\) | −5.14951 | −0.276043 | ||||||||
\(349\) | 11.4539 | 0.613114 | 0.306557 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306557 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(350\) | 22.1741 | 1.18525 | ||||||||
\(351\) | −8.72960 | −0.465952 | ||||||||
\(352\) | 1.64443 | 0.0876485 | ||||||||
\(353\) | −32.0552 | −1.70613 | −0.853063 | − | 0.521809i | \(-0.825257\pi\) | ||||
−0.853063 | + | 0.521809i | \(0.825257\pi\) | |||||||
\(354\) | −5.97884 | −0.317772 | ||||||||
\(355\) | 7.88047 | 0.418252 | ||||||||
\(356\) | −7.58566 | −0.402039 | ||||||||
\(357\) | −6.23165 | −0.329814 | ||||||||
\(358\) | 8.77509 | 0.463778 | ||||||||
\(359\) | −19.8681 | −1.04860 | −0.524299 | − | 0.851534i | \(-0.675673\pi\) | ||||
−0.524299 | + | 0.851534i | \(0.675673\pi\) | |||||||
\(360\) | −7.99137 | −0.421182 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.3582 | −0.754652 | ||||||||
\(363\) | −6.06616 | −0.318391 | ||||||||
\(364\) | 8.79456 | 0.460960 | ||||||||
\(365\) | 0.418969 | 0.0219299 | ||||||||
\(366\) | −6.98843 | −0.365291 | ||||||||
\(367\) | 8.49405 | 0.443386 | 0.221693 | − | 0.975117i | \(-0.428842\pi\) | ||||
0.221693 | + | 0.975117i | \(0.428842\pi\) | |||||||
\(368\) | 7.93136 | 0.413451 | ||||||||
\(369\) | −14.4562 | −0.752557 | ||||||||
\(370\) | −3.53826 | −0.183946 | ||||||||
\(371\) | −7.25670 | −0.376749 | ||||||||
\(372\) | 2.16804 | 0.112408 | ||||||||
\(373\) | 23.7991 | 1.23227 | 0.616136 | − | 0.787640i | \(-0.288697\pi\) | ||||
0.616136 | + | 0.787640i | \(0.288697\pi\) | |||||||
\(374\) | −3.48080 | −0.179988 | ||||||||
\(375\) | 1.20304 | 0.0621245 | ||||||||
\(376\) | 7.44446 | 0.383919 | ||||||||
\(377\) | −15.3829 | −0.792262 | ||||||||
\(378\) | −16.0900 | −0.827578 | ||||||||
\(379\) | 29.6559 | 1.52332 | 0.761660 | − | 0.647977i | \(-0.224385\pi\) | ||||
0.761660 | + | 0.647977i | \(0.224385\pi\) | |||||||
\(380\) | −3.24153 | −0.166287 | ||||||||
\(381\) | −0.278888 | −0.0142878 | ||||||||
\(382\) | 17.3329 | 0.886829 | ||||||||
\(383\) | −2.71447 | −0.138703 | −0.0693514 | − | 0.997592i | \(-0.522093\pi\) | ||||
−0.0693514 | + | 0.997592i | \(0.522093\pi\) | |||||||
\(384\) | 0.731229 | 0.0373154 | ||||||||
\(385\) | 21.4612 | 1.09376 | ||||||||
\(386\) | −25.1710 | −1.28117 | ||||||||
\(387\) | 24.8551 | 1.26345 | ||||||||
\(388\) | 1.83031 | 0.0929201 | ||||||||
\(389\) | 30.6576 | 1.55440 | 0.777202 | − | 0.629251i | \(-0.216638\pi\) | ||||
0.777202 | + | 0.629251i | \(0.216638\pi\) | |||||||
\(390\) | 5.17763 | 0.262179 | ||||||||
\(391\) | −16.7884 | −0.849028 | ||||||||
\(392\) | 9.20968 | 0.465159 | ||||||||
\(393\) | −0.545107 | −0.0274970 | ||||||||
\(394\) | 2.39308 | 0.120561 | ||||||||
\(395\) | 6.78997 | 0.341641 | ||||||||
\(396\) | −4.05402 | −0.203722 | ||||||||
\(397\) | 2.17022 | 0.108920 | 0.0544600 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544600 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(398\) | −11.6350 | −0.583212 | ||||||||
\(399\) | −2.94402 | −0.147385 | ||||||||
\(400\) | 5.50755 | 0.275377 | ||||||||
\(401\) | 18.6126 | 0.929468 | 0.464734 | − | 0.885450i | \(-0.346150\pi\) | ||||
0.464734 | + | 0.885450i | \(0.346150\pi\) | |||||||
\(402\) | 7.33384 | 0.365779 | ||||||||
\(403\) | 6.47650 | 0.322618 | ||||||||
\(404\) | −17.2151 | −0.856483 | ||||||||
\(405\) | 14.5014 | 0.720583 | ||||||||
\(406\) | −28.3530 | −1.40714 | ||||||||
\(407\) | −1.79496 | −0.0889730 | ||||||||
\(408\) | −1.54780 | −0.0766277 | ||||||||
\(409\) | 12.3470 | 0.610522 | 0.305261 | − | 0.952269i | \(-0.401256\pi\) | ||||
0.305261 | + | 0.952269i | \(0.401256\pi\) | |||||||
\(410\) | 19.0078 | 0.938731 | ||||||||
\(411\) | −6.30008 | −0.310760 | ||||||||
\(412\) | −16.4725 | −0.811544 | ||||||||
\(413\) | −32.9193 | −1.61985 | ||||||||
\(414\) | −19.5532 | −0.960989 | ||||||||
\(415\) | −4.59328 | −0.225475 | ||||||||
\(416\) | 2.18437 | 0.107098 | ||||||||
\(417\) | 7.96796 | 0.390193 | ||||||||
\(418\) | −1.64443 | −0.0804318 | ||||||||
\(419\) | −34.3591 | −1.67855 | −0.839275 | − | 0.543706i | \(-0.817020\pi\) | ||||
−0.839275 | + | 0.543706i | \(0.817020\pi\) | |||||||
\(420\) | 9.54314 | 0.465657 | ||||||||
\(421\) | −31.1637 | −1.51883 | −0.759413 | − | 0.650609i | \(-0.774514\pi\) | ||||
−0.759413 | + | 0.650609i | \(0.774514\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −18.3529 | −0.892347 | ||||||||
\(424\) | −1.80240 | −0.0875324 | ||||||||
\(425\) | −11.6579 | −0.565492 | ||||||||
\(426\) | 1.77768 | 0.0861291 | ||||||||
\(427\) | −38.4781 | −1.86208 | ||||||||
\(428\) | 17.0663 | 0.824929 | ||||||||
\(429\) | 2.62661 | 0.126814 | ||||||||
\(430\) | −32.6810 | −1.57602 | ||||||||
\(431\) | −15.7166 | −0.757044 | −0.378522 | − | 0.925592i | \(-0.623568\pi\) | ||||
−0.378522 | + | 0.925592i | \(0.623568\pi\) | |||||||
\(432\) | −3.99639 | −0.192276 | ||||||||
\(433\) | 35.8497 | 1.72282 | 0.861412 | − | 0.507906i | \(-0.169580\pi\) | ||||
0.861412 | + | 0.507906i | \(0.169580\pi\) | |||||||
\(434\) | 11.9372 | 0.573002 | ||||||||
\(435\) | −16.6923 | −0.800335 | ||||||||
\(436\) | 14.2864 | 0.684194 | ||||||||
\(437\) | −7.93136 | −0.379409 | ||||||||
\(438\) | 0.0945115 | 0.00451594 | ||||||||
\(439\) | 8.77697 | 0.418902 | 0.209451 | − | 0.977819i | \(-0.432832\pi\) | ||||
0.209451 | + | 0.977819i | \(0.432832\pi\) | |||||||
\(440\) | 5.33048 | 0.254121 | ||||||||
\(441\) | −22.7047 | −1.08117 | ||||||||
\(442\) | −4.62370 | −0.219927 | ||||||||
\(443\) | 13.3669 | 0.635080 | 0.317540 | − | 0.948245i | \(-0.397143\pi\) | ||||
0.317540 | + | 0.948245i | \(0.397143\pi\) | |||||||
\(444\) | −0.798165 | −0.0378793 | ||||||||
\(445\) | −24.5892 | −1.16564 | ||||||||
\(446\) | 12.6046 | 0.596843 | ||||||||
\(447\) | −5.26440 | −0.248998 | ||||||||
\(448\) | 4.02612 | 0.190217 | ||||||||
\(449\) | −2.35505 | −0.111142 | −0.0555708 | − | 0.998455i | \(-0.517698\pi\) | ||||
−0.0555708 | + | 0.998455i | \(0.517698\pi\) | |||||||
\(450\) | −13.5778 | −0.640062 | ||||||||
\(451\) | 9.64269 | 0.454056 | ||||||||
\(452\) | 15.5876 | 0.733178 | ||||||||
\(453\) | 1.75450 | 0.0824335 | ||||||||
\(454\) | −0.152605 | −0.00716213 | ||||||||
\(455\) | 28.5079 | 1.33647 | ||||||||
\(456\) | −0.731229 | −0.0342429 | ||||||||
\(457\) | −2.75822 | −0.129024 | −0.0645121 | − | 0.997917i | \(-0.520549\pi\) | ||||
−0.0645121 | + | 0.997917i | \(0.520549\pi\) | |||||||
\(458\) | −0.343084 | −0.0160312 | ||||||||
\(459\) | 8.45922 | 0.394843 | ||||||||
\(460\) | 25.7098 | 1.19873 | ||||||||
\(461\) | −32.4649 | −1.51204 | −0.756020 | − | 0.654549i | \(-0.772859\pi\) | ||||
−0.756020 | + | 0.654549i | \(0.772859\pi\) | |||||||
\(462\) | 4.84124 | 0.225235 | ||||||||
\(463\) | 33.8729 | 1.57421 | 0.787104 | − | 0.616821i | \(-0.211580\pi\) | ||||
0.787104 | + | 0.616821i | \(0.211580\pi\) | |||||||
\(464\) | −7.04227 | −0.326929 | ||||||||
\(465\) | 7.02778 | 0.325905 | ||||||||
\(466\) | −24.5919 | −1.13920 | ||||||||
\(467\) | −28.8638 | −1.33566 | −0.667828 | − | 0.744315i | \(-0.732776\pi\) | ||||
−0.667828 | + | 0.744315i | \(0.732776\pi\) | |||||||
\(468\) | −5.38514 | −0.248928 | ||||||||
\(469\) | 40.3799 | 1.86457 | ||||||||
\(470\) | 24.1315 | 1.11310 | ||||||||
\(471\) | 9.44990 | 0.435428 | ||||||||
\(472\) | −8.17643 | −0.376351 | ||||||||
\(473\) | −16.5791 | −0.762306 | ||||||||
\(474\) | 1.53169 | 0.0703529 | ||||||||
\(475\) | −5.50755 | −0.252704 | ||||||||
\(476\) | −8.52216 | −0.390613 | ||||||||
\(477\) | 4.44347 | 0.203453 | ||||||||
\(478\) | 15.2818 | 0.698973 | ||||||||
\(479\) | 12.6792 | 0.579327 | 0.289663 | − | 0.957129i | \(-0.406457\pi\) | ||||
0.289663 | + | 0.957129i | \(0.406457\pi\) | |||||||
\(480\) | 2.37030 | 0.108189 | ||||||||
\(481\) | −2.38433 | −0.108716 | ||||||||
\(482\) | −3.76817 | −0.171636 | ||||||||
\(483\) | 23.3501 | 1.06247 | ||||||||
\(484\) | −8.29584 | −0.377084 | ||||||||
\(485\) | 5.93302 | 0.269405 | ||||||||
\(486\) | 15.2604 | 0.692227 | ||||||||
\(487\) | 18.3562 | 0.831798 | 0.415899 | − | 0.909411i | \(-0.363467\pi\) | ||||
0.415899 | + | 0.909411i | \(0.363467\pi\) | |||||||
\(488\) | −9.55710 | −0.432630 | ||||||||
\(489\) | −12.5906 | −0.569367 | ||||||||
\(490\) | 29.8535 | 1.34864 | ||||||||
\(491\) | −7.73203 | −0.348942 | −0.174471 | − | 0.984662i | \(-0.555821\pi\) | ||||
−0.174471 | + | 0.984662i | \(0.555821\pi\) | |||||||
\(492\) | 4.28781 | 0.193309 | ||||||||
\(493\) | 14.9065 | 0.671354 | ||||||||
\(494\) | −2.18437 | −0.0982796 | ||||||||
\(495\) | −13.1413 | −0.590656 | ||||||||
\(496\) | 2.96493 | 0.133129 | ||||||||
\(497\) | 9.78788 | 0.439046 | ||||||||
\(498\) | −1.03616 | −0.0464313 | ||||||||
\(499\) | −7.68285 | −0.343932 | −0.171966 | − | 0.985103i | \(-0.555012\pi\) | ||||
−0.171966 | + | 0.985103i | \(0.555012\pi\) | |||||||
\(500\) | 1.64523 | 0.0735767 | ||||||||
\(501\) | 5.60263 | 0.250307 | ||||||||
\(502\) | 18.9149 | 0.844215 | ||||||||
\(503\) | −2.08396 | −0.0929190 | −0.0464595 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464595 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(504\) | −9.92562 | −0.442122 | ||||||||
\(505\) | −55.8033 | −2.48322 | ||||||||
\(506\) | 13.0426 | 0.579814 | ||||||||
\(507\) | −6.01693 | −0.267221 | ||||||||
\(508\) | −0.381396 | −0.0169217 | ||||||||
\(509\) | 31.7306 | 1.40643 | 0.703217 | − | 0.710975i | \(-0.251746\pi\) | ||||
0.703217 | + | 0.710975i | \(0.251746\pi\) | |||||||
\(510\) | −5.01726 | −0.222168 | ||||||||
\(511\) | 0.520378 | 0.0230202 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.99639 | 0.176445 | ||||||||
\(514\) | −27.4598 | −1.21120 | ||||||||
\(515\) | −53.3963 | −2.35292 | ||||||||
\(516\) | −7.37221 | −0.324543 | ||||||||
\(517\) | 12.2419 | 0.538399 | ||||||||
\(518\) | −4.39467 | −0.193091 | ||||||||
\(519\) | −0.621888 | −0.0272978 | ||||||||
\(520\) | 7.08072 | 0.310510 | ||||||||
\(521\) | −16.9267 | −0.741572 | −0.370786 | − | 0.928718i | \(-0.620912\pi\) | ||||
−0.370786 | + | 0.928718i | \(0.620912\pi\) | |||||||
\(522\) | 17.3613 | 0.759885 | ||||||||
\(523\) | 9.27600 | 0.405611 | 0.202806 | − | 0.979219i | \(-0.434994\pi\) | ||||
0.202806 | + | 0.979219i | \(0.434994\pi\) | |||||||
\(524\) | −0.745467 | −0.0325659 | ||||||||
\(525\) | 16.2143 | 0.707651 | ||||||||
\(526\) | −21.2240 | −0.925412 | ||||||||
\(527\) | −6.27591 | −0.273383 | ||||||||
\(528\) | 1.20246 | 0.0523302 | ||||||||
\(529\) | 39.9065 | 1.73507 | ||||||||
\(530\) | −5.84255 | −0.253784 | ||||||||
\(531\) | 20.1574 | 0.874756 | ||||||||
\(532\) | −4.02612 | −0.174555 | ||||||||
\(533\) | 12.8088 | 0.554811 | ||||||||
\(534\) | −5.54685 | −0.240036 | ||||||||
\(535\) | 55.3209 | 2.39173 | ||||||||
\(536\) | 10.0295 | 0.433207 | ||||||||
\(537\) | 6.41660 | 0.276897 | ||||||||
\(538\) | 14.6404 | 0.631191 | ||||||||
\(539\) | 15.1447 | 0.652328 | ||||||||
\(540\) | −12.9544 | −0.557470 | ||||||||
\(541\) | 24.7005 | 1.06196 | 0.530979 | − | 0.847385i | \(-0.321824\pi\) | ||||
0.530979 | + | 0.847385i | \(0.321824\pi\) | |||||||
\(542\) | −8.05587 | −0.346029 | ||||||||
\(543\) | −10.4992 | −0.450562 | ||||||||
\(544\) | −2.11672 | −0.0907535 | ||||||||
\(545\) | 46.3098 | 1.98369 | ||||||||
\(546\) | 6.43083 | 0.275214 | ||||||||
\(547\) | −15.5522 | −0.664964 | −0.332482 | − | 0.943110i | \(-0.607886\pi\) | ||||
−0.332482 | + | 0.943110i | \(0.607886\pi\) | |||||||
\(548\) | −8.61574 | −0.368046 | ||||||||
\(549\) | 23.5612 | 1.00557 | ||||||||
\(550\) | 9.05678 | 0.386183 | ||||||||
\(551\) | 7.04227 | 0.300011 | ||||||||
\(552\) | 5.79964 | 0.246849 | ||||||||
\(553\) | 8.43344 | 0.358626 | ||||||||
\(554\) | 9.22890 | 0.392098 | ||||||||
\(555\) | −2.58728 | −0.109824 | ||||||||
\(556\) | 10.8967 | 0.462122 | ||||||||
\(557\) | 45.7360 | 1.93790 | 0.968949 | − | 0.247262i | \(-0.0795307\pi\) | ||||
0.968949 | + | 0.247262i | \(0.0795307\pi\) | |||||||
\(558\) | −7.30944 | −0.309433 | ||||||||
\(559\) | −22.0227 | −0.931462 | ||||||||
\(560\) | 13.0508 | 0.551498 | ||||||||
\(561\) | −2.54526 | −0.107461 | ||||||||
\(562\) | −23.5180 | −0.992047 | ||||||||
\(563\) | 0.429964 | 0.0181208 | 0.00906040 | − | 0.999959i | \(-0.497116\pi\) | ||||
0.00906040 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(564\) | 5.44361 | 0.229217 | ||||||||
\(565\) | 50.5277 | 2.12571 | ||||||||
\(566\) | 11.7905 | 0.495590 | ||||||||
\(567\) | 18.0114 | 0.756409 | ||||||||
\(568\) | 2.43109 | 0.102006 | ||||||||
\(569\) | 18.6866 | 0.783385 | 0.391693 | − | 0.920096i | \(-0.371890\pi\) | ||||
0.391693 | + | 0.920096i | \(0.371890\pi\) | |||||||
\(570\) | −2.37030 | −0.0992811 | ||||||||
\(571\) | −31.7284 | −1.32779 | −0.663897 | − | 0.747824i | \(-0.731099\pi\) | ||||
−0.663897 | + | 0.747824i | \(0.731099\pi\) | |||||||
\(572\) | 3.59205 | 0.150191 | ||||||||
\(573\) | 12.6743 | 0.529477 | ||||||||
\(574\) | 23.6086 | 0.985402 | ||||||||
\(575\) | 43.6823 | 1.82168 | ||||||||
\(576\) | −2.46530 | −0.102721 | ||||||||
\(577\) | −9.91499 | −0.412766 | −0.206383 | − | 0.978471i | \(-0.566169\pi\) | ||||
−0.206383 | + | 0.978471i | \(0.566169\pi\) | |||||||
\(578\) | −12.5195 | −0.520743 | ||||||||
\(579\) | −18.4057 | −0.764916 | ||||||||
\(580\) | −22.8278 | −0.947871 | ||||||||
\(581\) | −5.70505 | −0.236685 | ||||||||
\(582\) | 1.33838 | 0.0554776 | ||||||||
\(583\) | −2.96393 | −0.122753 | ||||||||
\(584\) | 0.129250 | 0.00534841 | ||||||||
\(585\) | −17.4561 | −0.721722 | ||||||||
\(586\) | −5.50119 | −0.227252 | ||||||||
\(587\) | −12.4239 | −0.512790 | −0.256395 | − | 0.966572i | \(-0.582535\pi\) | ||||
−0.256395 | + | 0.966572i | \(0.582535\pi\) | |||||||
\(588\) | 6.73438 | 0.277721 | ||||||||
\(589\) | −2.96493 | −0.122168 | ||||||||
\(590\) | −26.5042 | −1.09116 | ||||||||
\(591\) | 1.74989 | 0.0719807 | ||||||||
\(592\) | −1.09154 | −0.0448620 | ||||||||
\(593\) | −45.8510 | −1.88288 | −0.941438 | − | 0.337186i | \(-0.890525\pi\) | ||||
−0.941438 | + | 0.337186i | \(0.890525\pi\) | |||||||
\(594\) | −6.57179 | −0.269644 | ||||||||
\(595\) | −27.6249 | −1.13251 | ||||||||
\(596\) | −7.19939 | −0.294899 | ||||||||
\(597\) | −8.50788 | −0.348204 | ||||||||
\(598\) | 17.3251 | 0.708474 | ||||||||
\(599\) | 11.2392 | 0.459220 | 0.229610 | − | 0.973283i | \(-0.426255\pi\) | ||||
0.229610 | + | 0.973283i | \(0.426255\pi\) | |||||||
\(600\) | 4.02728 | 0.164413 | ||||||||
\(601\) | −27.9883 | −1.14167 | −0.570833 | − | 0.821066i | \(-0.693380\pi\) | ||||
−0.570833 | + | 0.821066i | \(0.693380\pi\) | |||||||
\(602\) | −40.5912 | −1.65437 | ||||||||
\(603\) | −24.7257 | −1.00691 | ||||||||
\(604\) | 2.39938 | 0.0976294 | ||||||||
\(605\) | −26.8913 | −1.09329 | ||||||||
\(606\) | −12.5882 | −0.511360 | ||||||||
\(607\) | 39.7790 | 1.61458 | 0.807289 | − | 0.590156i | \(-0.200934\pi\) | ||||
0.807289 | + | 0.590156i | \(0.200934\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −20.7326 | −0.840126 | ||||||||
\(610\) | −30.9797 | −1.25433 | ||||||||
\(611\) | 16.2615 | 0.657869 | ||||||||
\(612\) | 5.21835 | 0.210939 | ||||||||
\(613\) | 1.31277 | 0.0530223 | 0.0265111 | − | 0.999649i | \(-0.491560\pi\) | ||||
0.0265111 | + | 0.999649i | \(0.491560\pi\) | |||||||
\(614\) | −3.32632 | −0.134239 | ||||||||
\(615\) | 13.8991 | 0.560465 | ||||||||
\(616\) | 6.62069 | 0.266755 | ||||||||
\(617\) | 28.8387 | 1.16100 | 0.580501 | − | 0.814260i | \(-0.302857\pi\) | ||||
0.580501 | + | 0.814260i | \(0.302857\pi\) | |||||||
\(618\) | −12.0452 | −0.484529 | ||||||||
\(619\) | 31.8027 | 1.27826 | 0.639129 | − | 0.769100i | \(-0.279295\pi\) | ||||
0.639129 | + | 0.769100i | \(0.279295\pi\) | |||||||
\(620\) | 9.61091 | 0.385983 | ||||||||
\(621\) | −31.6968 | −1.27195 | ||||||||
\(622\) | −18.7637 | −0.752354 | ||||||||
\(623\) | −30.5408 | −1.22359 | ||||||||
\(624\) | 1.59728 | 0.0639422 | ||||||||
\(625\) | −22.2047 | −0.888187 | ||||||||
\(626\) | −6.41053 | −0.256216 | ||||||||
\(627\) | −1.20246 | −0.0480215 | ||||||||
\(628\) | 12.9233 | 0.515696 | ||||||||
\(629\) | 2.31048 | 0.0921249 | ||||||||
\(630\) | −32.1742 | −1.28185 | ||||||||
\(631\) | −31.9630 | −1.27243 | −0.636214 | − | 0.771512i | \(-0.719501\pi\) | ||||
−0.636214 | + | 0.771512i | \(0.719501\pi\) | |||||||
\(632\) | 2.09468 | 0.0833219 | ||||||||
\(633\) | −0.731229 | −0.0290637 | ||||||||
\(634\) | 30.6899 | 1.21885 | ||||||||
\(635\) | −1.23631 | −0.0490614 | ||||||||
\(636\) | −1.31797 | −0.0522609 | ||||||||
\(637\) | 20.1174 | 0.797079 | ||||||||
\(638\) | −11.5805 | −0.458478 | ||||||||
\(639\) | −5.99338 | −0.237094 | ||||||||
\(640\) | 3.24153 | 0.128133 | ||||||||
\(641\) | −3.51583 | −0.138867 | −0.0694335 | − | 0.997587i | \(-0.522119\pi\) | ||||
−0.0694335 | + | 0.997587i | \(0.522119\pi\) | |||||||
\(642\) | 12.4793 | 0.492521 | ||||||||
\(643\) | 12.0885 | 0.476722 | 0.238361 | − | 0.971177i | \(-0.423390\pi\) | ||||
0.238361 | + | 0.971177i | \(0.423390\pi\) | |||||||
\(644\) | 31.9327 | 1.25832 | ||||||||
\(645\) | −23.8973 | −0.940954 | ||||||||
\(646\) | 2.11672 | 0.0832811 | ||||||||
\(647\) | −19.6176 | −0.771249 | −0.385624 | − | 0.922656i | \(-0.626014\pi\) | ||||
−0.385624 | + | 0.922656i | \(0.626014\pi\) | |||||||
\(648\) | 4.47364 | 0.175741 | ||||||||
\(649\) | −13.4456 | −0.527785 | ||||||||
\(650\) | 12.0305 | 0.471876 | ||||||||
\(651\) | 8.72880 | 0.342109 | ||||||||
\(652\) | −17.2184 | −0.674325 | ||||||||
\(653\) | 21.3444 | 0.835273 | 0.417636 | − | 0.908614i | \(-0.362859\pi\) | ||||
0.417636 | + | 0.908614i | \(0.362859\pi\) | |||||||
\(654\) | 10.4466 | 0.408495 | ||||||||
\(655\) | −2.41646 | −0.0944188 | ||||||||
\(656\) | 5.86384 | 0.228945 | ||||||||
\(657\) | −0.318641 | −0.0124314 | ||||||||
\(658\) | 29.9723 | 1.16844 | ||||||||
\(659\) | −6.63518 | −0.258470 | −0.129235 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129235 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(660\) | 3.89780 | 0.151722 | ||||||||
\(661\) | −5.44306 | −0.211710 | −0.105855 | − | 0.994382i | \(-0.533758\pi\) | ||||
−0.105855 | + | 0.994382i | \(0.533758\pi\) | |||||||
\(662\) | 1.32964 | 0.0516780 | ||||||||
\(663\) | −3.38098 | −0.131306 | ||||||||
\(664\) | −1.41701 | −0.0549906 | ||||||||
\(665\) | −13.0508 | −0.506089 | ||||||||
\(666\) | 2.69098 | 0.104273 | ||||||||
\(667\) | −55.8548 | −2.16271 | ||||||||
\(668\) | 7.66193 | 0.296449 | ||||||||
\(669\) | 9.21681 | 0.356343 | ||||||||
\(670\) | 32.5109 | 1.25600 | ||||||||
\(671\) | −15.7160 | −0.606710 | ||||||||
\(672\) | 2.94402 | 0.113568 | ||||||||
\(673\) | −28.0842 | −1.08257 | −0.541283 | − | 0.840840i | \(-0.682061\pi\) | ||||
−0.541283 | + | 0.840840i | \(0.682061\pi\) | |||||||
\(674\) | −3.74910 | −0.144410 | ||||||||
\(675\) | −22.0103 | −0.847177 | ||||||||
\(676\) | −8.22852 | −0.316481 | ||||||||
\(677\) | 30.7617 | 1.18227 | 0.591134 | − | 0.806574i | \(-0.298681\pi\) | ||||
0.591134 | + | 0.806574i | \(0.298681\pi\) | |||||||
\(678\) | 11.3981 | 0.437741 | ||||||||
\(679\) | 7.36907 | 0.282799 | ||||||||
\(680\) | −6.86141 | −0.263123 | ||||||||
\(681\) | −0.111590 | −0.00427612 | ||||||||
\(682\) | 4.87562 | 0.186697 | ||||||||
\(683\) | 37.1331 | 1.42086 | 0.710429 | − | 0.703769i | \(-0.248501\pi\) | ||||
0.710429 | + | 0.703769i | \(0.248501\pi\) | |||||||
\(684\) | 2.46530 | 0.0942633 | ||||||||
\(685\) | −27.9282 | −1.06708 | ||||||||
\(686\) | 8.89644 | 0.339668 | ||||||||
\(687\) | −0.250873 | −0.00957139 | ||||||||
\(688\) | −10.0819 | −0.384370 | ||||||||
\(689\) | −3.93712 | −0.149992 | ||||||||
\(690\) | 18.7997 | 0.715694 | ||||||||
\(691\) | 27.4658 | 1.04485 | 0.522424 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522424 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(692\) | −0.850469 | −0.0323300 | ||||||||
\(693\) | −16.3220 | −0.620022 | ||||||||
\(694\) | −29.8884 | −1.13455 | ||||||||
\(695\) | 35.3219 | 1.33984 | ||||||||
\(696\) | −5.14951 | −0.195192 | ||||||||
\(697\) | −12.4121 | −0.470141 | ||||||||
\(698\) | 11.4539 | 0.433537 | ||||||||
\(699\) | −17.9823 | −0.680152 | ||||||||
\(700\) | 22.1741 | 0.838101 | ||||||||
\(701\) | −11.2595 | −0.425267 | −0.212633 | − | 0.977132i | \(-0.568204\pi\) | ||||
−0.212633 | + | 0.977132i | \(0.568204\pi\) | |||||||
\(702\) | −8.72960 | −0.329478 | ||||||||
\(703\) | 1.09154 | 0.0411682 | ||||||||
\(704\) | 1.64443 | 0.0619769 | ||||||||
\(705\) | 17.6456 | 0.664573 | ||||||||
\(706\) | −32.0552 | −1.20641 | ||||||||
\(707\) | −69.3101 | −2.60668 | ||||||||
\(708\) | −5.97884 | −0.224699 | ||||||||
\(709\) | −20.5576 | −0.772058 | −0.386029 | − | 0.922487i | \(-0.626154\pi\) | ||||
−0.386029 | + | 0.922487i | \(0.626154\pi\) | |||||||
\(710\) | 7.88047 | 0.295749 | ||||||||
\(711\) | −5.16402 | −0.193666 | ||||||||
\(712\) | −7.58566 | −0.284285 | ||||||||
\(713\) | 23.5159 | 0.880678 | ||||||||
\(714\) | −6.23165 | −0.233214 | ||||||||
\(715\) | 11.6438 | 0.435452 | ||||||||
\(716\) | 8.77509 | 0.327940 | ||||||||
\(717\) | 11.1745 | 0.417319 | ||||||||
\(718\) | −19.8681 | −0.741471 | ||||||||
\(719\) | −27.4192 | −1.02256 | −0.511281 | − | 0.859413i | \(-0.670829\pi\) | ||||
−0.511281 | + | 0.859413i | \(0.670829\pi\) | |||||||
\(720\) | −7.99137 | −0.297821 | ||||||||
\(721\) | −66.3205 | −2.46990 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −2.75540 | −0.102474 | ||||||||
\(724\) | −14.3582 | −0.533620 | ||||||||
\(725\) | −38.7856 | −1.44046 | ||||||||
\(726\) | −6.06616 | −0.225136 | ||||||||
\(727\) | 25.9929 | 0.964024 | 0.482012 | − | 0.876165i | \(-0.339906\pi\) | ||||
0.482012 | + | 0.876165i | \(0.339906\pi\) | |||||||
\(728\) | 8.79456 | 0.325948 | ||||||||
\(729\) | −2.26205 | −0.0837796 | ||||||||
\(730\) | 0.418969 | 0.0155067 | ||||||||
\(731\) | 21.3406 | 0.789311 | ||||||||
\(732\) | −6.98843 | −0.258300 | ||||||||
\(733\) | −28.0599 | −1.03642 | −0.518209 | − | 0.855254i | \(-0.673401\pi\) | ||||
−0.518209 | + | 0.855254i | \(0.673401\pi\) | |||||||
\(734\) | 8.49405 | 0.313521 | ||||||||
\(735\) | 21.8297 | 0.805202 | ||||||||
\(736\) | 7.93136 | 0.292354 | ||||||||
\(737\) | 16.4928 | 0.607519 | ||||||||
\(738\) | −14.4562 | −0.532138 | ||||||||
\(739\) | −7.29777 | −0.268453 | −0.134226 | − | 0.990951i | \(-0.542855\pi\) | ||||
−0.134226 | + | 0.990951i | \(0.542855\pi\) | |||||||
\(740\) | −3.53826 | −0.130069 | ||||||||
\(741\) | −1.59728 | −0.0586774 | ||||||||
\(742\) | −7.25670 | −0.266402 | ||||||||
\(743\) | −32.4781 | −1.19151 | −0.595753 | − | 0.803168i | \(-0.703146\pi\) | ||||
−0.595753 | + | 0.803168i | \(0.703146\pi\) | |||||||
\(744\) | 2.16804 | 0.0794842 | ||||||||
\(745\) | −23.3371 | −0.855004 | ||||||||
\(746\) | 23.7991 | 0.871348 | ||||||||
\(747\) | 3.49336 | 0.127815 | ||||||||
\(748\) | −3.48080 | −0.127271 | ||||||||
\(749\) | 68.7109 | 2.51064 | ||||||||
\(750\) | 1.20304 | 0.0439287 | ||||||||
\(751\) | 51.0438 | 1.86261 | 0.931307 | − | 0.364234i | \(-0.118669\pi\) | ||||
0.931307 | + | 0.364234i | \(0.118669\pi\) | |||||||
\(752\) | 7.44446 | 0.271472 | ||||||||
\(753\) | 13.8311 | 0.504035 | ||||||||
\(754\) | −15.3829 | −0.560214 | ||||||||
\(755\) | 7.77768 | 0.283059 | ||||||||
\(756\) | −16.0900 | −0.585186 | ||||||||
\(757\) | −34.6026 | −1.25765 | −0.628827 | − | 0.777545i | \(-0.716465\pi\) | ||||
−0.628827 | + | 0.777545i | \(0.716465\pi\) | |||||||
\(758\) | 29.6559 | 1.07715 | ||||||||
\(759\) | 9.53712 | 0.346175 | ||||||||
\(760\) | −3.24153 | −0.117583 | ||||||||
\(761\) | 22.2985 | 0.808321 | 0.404160 | − | 0.914688i | \(-0.367564\pi\) | ||||
0.404160 | + | 0.914688i | \(0.367564\pi\) | |||||||
\(762\) | −0.278888 | −0.0101030 | ||||||||
\(763\) | 57.5188 | 2.08232 | ||||||||
\(764\) | 17.3329 | 0.627083 | ||||||||
\(765\) | 16.9155 | 0.611580 | ||||||||
\(766\) | −2.71447 | −0.0980777 | ||||||||
\(767\) | −17.8604 | −0.644901 | ||||||||
\(768\) | 0.731229 | 0.0263860 | ||||||||
\(769\) | −16.4702 | −0.593932 | −0.296966 | − | 0.954888i | \(-0.595975\pi\) | ||||
−0.296966 | + | 0.954888i | \(0.595975\pi\) | |||||||
\(770\) | 21.4612 | 0.773407 | ||||||||
\(771\) | −20.0794 | −0.723142 | ||||||||
\(772\) | −25.1710 | −0.905923 | ||||||||
\(773\) | −7.44134 | −0.267646 | −0.133823 | − | 0.991005i | \(-0.542725\pi\) | ||||
−0.133823 | + | 0.991005i | \(0.542725\pi\) | |||||||
\(774\) | 24.8551 | 0.893396 | ||||||||
\(775\) | 16.3295 | 0.586572 | ||||||||
\(776\) | 1.83031 | 0.0657044 | ||||||||
\(777\) | −3.21351 | −0.115284 | ||||||||
\(778\) | 30.6576 | 1.09913 | ||||||||
\(779\) | −5.86384 | −0.210094 | ||||||||
\(780\) | 5.17763 | 0.185389 | ||||||||
\(781\) | 3.99777 | 0.143051 | ||||||||
\(782\) | −16.7884 | −0.600354 | ||||||||
\(783\) | 28.1436 | 1.00577 | ||||||||
\(784\) | 9.20968 | 0.328917 | ||||||||
\(785\) | 41.8913 | 1.49517 | ||||||||
\(786\) | −0.545107 | −0.0194433 | ||||||||
\(787\) | 1.16450 | 0.0415099 | 0.0207549 | − | 0.999785i | \(-0.493393\pi\) | ||||
0.0207549 | + | 0.999785i | \(0.493393\pi\) | |||||||
\(788\) | 2.39308 | 0.0852498 | ||||||||
\(789\) | −15.5196 | −0.552513 | ||||||||
\(790\) | 6.78997 | 0.241576 | ||||||||
\(791\) | 62.7575 | 2.23140 | ||||||||
\(792\) | −4.05402 | −0.144054 | ||||||||
\(793\) | −20.8763 | −0.741338 | ||||||||
\(794\) | 2.17022 | 0.0770181 | ||||||||
\(795\) | −4.27224 | −0.151521 | ||||||||
\(796\) | −11.6350 | −0.412393 | ||||||||
\(797\) | 27.2896 | 0.966647 | 0.483324 | − | 0.875442i | \(-0.339429\pi\) | ||||
0.483324 | + | 0.875442i | \(0.339429\pi\) | |||||||
\(798\) | −2.94402 | −0.104217 | ||||||||
\(799\) | −15.7578 | −0.557471 | ||||||||
\(800\) | 5.50755 | 0.194721 | ||||||||
\(801\) | 18.7010 | 0.660766 | ||||||||
\(802\) | 18.6126 | 0.657233 | ||||||||
\(803\) | 0.212543 | 0.00750049 | ||||||||
\(804\) | 7.33384 | 0.258645 | ||||||||
\(805\) | 103.511 | 3.64828 | ||||||||
\(806\) | 6.47650 | 0.228125 | ||||||||
\(807\) | 10.7055 | 0.376850 | ||||||||
\(808\) | −17.2151 | −0.605625 | ||||||||
\(809\) | 9.36235 | 0.329163 | 0.164581 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164581 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(810\) | 14.5014 | 0.509529 | ||||||||
\(811\) | −41.7318 | −1.46540 | −0.732701 | − | 0.680550i | \(-0.761741\pi\) | ||||
−0.732701 | + | 0.680550i | \(0.761741\pi\) | |||||||
\(812\) | −28.3530 | −0.994997 | ||||||||
\(813\) | −5.89069 | −0.206595 | ||||||||
\(814\) | −1.79496 | −0.0629134 | ||||||||
\(815\) | −55.8141 | −1.95508 | ||||||||
\(816\) | −1.54780 | −0.0541840 | ||||||||
\(817\) | 10.0819 | 0.352723 | ||||||||
\(818\) | 12.3470 | 0.431704 | ||||||||
\(819\) | −21.6813 | −0.757604 | ||||||||
\(820\) | 19.0078 | 0.663783 | ||||||||
\(821\) | 55.5967 | 1.94034 | 0.970169 | − | 0.242431i | \(-0.0779449\pi\) | ||||
0.970169 | + | 0.242431i | \(0.0779449\pi\) | |||||||
\(822\) | −6.30008 | −0.219741 | ||||||||
\(823\) | 15.5036 | 0.540420 | 0.270210 | − | 0.962801i | \(-0.412907\pi\) | ||||
0.270210 | + | 0.962801i | \(0.412907\pi\) | |||||||
\(824\) | −16.4725 | −0.573848 | ||||||||
\(825\) | 6.62258 | 0.230569 | ||||||||
\(826\) | −32.9193 | −1.14541 | ||||||||
\(827\) | −11.3875 | −0.395984 | −0.197992 | − | 0.980204i | \(-0.563442\pi\) | ||||
−0.197992 | + | 0.980204i | \(0.563442\pi\) | |||||||
\(828\) | −19.5532 | −0.679522 | ||||||||
\(829\) | 46.7508 | 1.62372 | 0.811861 | − | 0.583851i | \(-0.198455\pi\) | ||||
0.811861 | + | 0.583851i | \(0.198455\pi\) | |||||||
\(830\) | −4.59328 | −0.159435 | ||||||||
\(831\) | 6.74844 | 0.234101 | ||||||||
\(832\) | 2.18437 | 0.0757295 | ||||||||
\(833\) | −19.4943 | −0.675437 | ||||||||
\(834\) | 7.96796 | 0.275908 | ||||||||
\(835\) | 24.8364 | 0.859500 | ||||||||
\(836\) | −1.64443 | −0.0568739 | ||||||||
\(837\) | −11.8490 | −0.409561 | ||||||||
\(838\) | −34.3591 | −1.18691 | ||||||||
\(839\) | 3.90182 | 0.134706 | 0.0673528 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673528 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(840\) | 9.54314 | 0.329270 | ||||||||
\(841\) | 20.5935 | 0.710122 | ||||||||
\(842\) | −31.1637 | −1.07397 | ||||||||
\(843\) | −17.1970 | −0.592298 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −26.6730 | −0.917580 | ||||||||
\(846\) | −18.3529 | −0.630984 | ||||||||
\(847\) | −33.4001 | −1.14764 | ||||||||
\(848\) | −1.80240 | −0.0618947 | ||||||||
\(849\) | 8.62153 | 0.295890 | ||||||||
\(850\) | −11.6579 | −0.399863 | ||||||||
\(851\) | −8.65740 | −0.296772 | ||||||||
\(852\) | 1.77768 | 0.0609025 | ||||||||
\(853\) | −6.80197 | −0.232895 | −0.116448 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116448 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(854\) | −38.4781 | −1.31669 | ||||||||
\(855\) | 7.99137 | 0.273299 | ||||||||
\(856\) | 17.0663 | 0.583313 | ||||||||
\(857\) | −7.46206 | −0.254899 | −0.127450 | − | 0.991845i | \(-0.540679\pi\) | ||||
−0.127450 | + | 0.991845i | \(0.540679\pi\) | |||||||
\(858\) | 2.62661 | 0.0896711 | ||||||||
\(859\) | 40.6587 | 1.38726 | 0.693629 | − | 0.720332i | \(-0.256011\pi\) | ||||
0.693629 | + | 0.720332i | \(0.256011\pi\) | |||||||
\(860\) | −32.6810 | −1.11441 | ||||||||
\(861\) | 17.2633 | 0.588330 | ||||||||
\(862\) | −15.7166 | −0.535311 | ||||||||
\(863\) | −19.9143 | −0.677890 | −0.338945 | − | 0.940806i | \(-0.610070\pi\) | ||||
−0.338945 | + | 0.940806i | \(0.610070\pi\) | |||||||
\(864\) | −3.99639 | −0.135960 | ||||||||
\(865\) | −2.75682 | −0.0937349 | ||||||||
\(866\) | 35.8497 | 1.21822 | ||||||||
\(867\) | −9.15463 | −0.310908 | ||||||||
\(868\) | 11.9372 | 0.405174 | ||||||||
\(869\) | 3.44456 | 0.116849 | ||||||||
\(870\) | −16.6923 | −0.565923 | ||||||||
\(871\) | 21.9081 | 0.742328 | ||||||||
\(872\) | 14.2864 | 0.483798 | ||||||||
\(873\) | −4.51228 | −0.152718 | ||||||||
\(874\) | −7.93136 | −0.268282 | ||||||||
\(875\) | 6.62388 | 0.223928 | ||||||||
\(876\) | 0.0945115 | 0.00319325 | ||||||||
\(877\) | 25.5496 | 0.862749 | 0.431375 | − | 0.902173i | \(-0.358029\pi\) | ||||
0.431375 | + | 0.902173i | \(0.358029\pi\) | |||||||
\(878\) | 8.77697 | 0.296209 | ||||||||
\(879\) | −4.02263 | −0.135680 | ||||||||
\(880\) | 5.33048 | 0.179691 | ||||||||
\(881\) | 47.4187 | 1.59758 | 0.798788 | − | 0.601613i | \(-0.205475\pi\) | ||||
0.798788 | + | 0.601613i | \(0.205475\pi\) | |||||||
\(882\) | −22.7047 | −0.764506 | ||||||||
\(883\) | −45.8201 | −1.54197 | −0.770985 | − | 0.636854i | \(-0.780236\pi\) | ||||
−0.770985 | + | 0.636854i | \(0.780236\pi\) | |||||||
\(884\) | −4.62370 | −0.155512 | ||||||||
\(885\) | −19.3806 | −0.651473 | ||||||||
\(886\) | 13.3669 | 0.449069 | ||||||||
\(887\) | −25.2259 | −0.847002 | −0.423501 | − | 0.905896i | \(-0.639199\pi\) | ||||
−0.423501 | + | 0.905896i | \(0.639199\pi\) | |||||||
\(888\) | −0.798165 | −0.0267847 | ||||||||
\(889\) | −1.53555 | −0.0515006 | ||||||||
\(890\) | −24.5892 | −0.824231 | ||||||||
\(891\) | 7.35659 | 0.246455 | ||||||||
\(892\) | 12.6046 | 0.422032 | ||||||||
\(893\) | −7.44446 | −0.249119 | ||||||||
\(894\) | −5.26440 | −0.176068 | ||||||||
\(895\) | 28.4447 | 0.950803 | ||||||||
\(896\) | 4.02612 | 0.134503 | ||||||||
\(897\) | 12.6686 | 0.422992 | ||||||||
\(898\) | −2.35505 | −0.0785890 | ||||||||
\(899\) | −20.8798 | −0.696380 | ||||||||
\(900\) | −13.5778 | −0.452592 | ||||||||
\(901\) | 3.81517 | 0.127102 | ||||||||
\(902\) | 9.64269 | 0.321066 | ||||||||
\(903\) | −29.6814 | −0.987736 | ||||||||
\(904\) | 15.5876 | 0.518435 | ||||||||
\(905\) | −46.5427 | −1.54713 | ||||||||
\(906\) | 1.75450 | 0.0582893 | ||||||||
\(907\) | −11.4744 | −0.381000 | −0.190500 | − | 0.981687i | \(-0.561011\pi\) | ||||
−0.190500 | + | 0.981687i | \(0.561011\pi\) | |||||||
\(908\) | −0.152605 | −0.00506439 | ||||||||
\(909\) | 42.4405 | 1.40766 | ||||||||
\(910\) | 28.5079 | 0.945026 | ||||||||
\(911\) | 15.4063 | 0.510432 | 0.255216 | − | 0.966884i | \(-0.417853\pi\) | ||||
0.255216 | + | 0.966884i | \(0.417853\pi\) | |||||||
\(912\) | −0.731229 | −0.0242134 | ||||||||
\(913\) | −2.33017 | −0.0771175 | ||||||||
\(914\) | −2.75822 | −0.0912338 | ||||||||
\(915\) | −22.6532 | −0.748893 | ||||||||
\(916\) | −0.343084 | −0.0113358 | ||||||||
\(917\) | −3.00134 | −0.0991131 | ||||||||
\(918\) | 8.45922 | 0.279196 | ||||||||
\(919\) | 2.74438 | 0.0905286 | 0.0452643 | − | 0.998975i | \(-0.485587\pi\) | ||||
0.0452643 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(920\) | 25.7098 | 0.847627 | ||||||||
\(921\) | −2.43230 | −0.0801470 | ||||||||
\(922\) | −32.4649 | −1.06917 | ||||||||
\(923\) | 5.31041 | 0.174794 | ||||||||
\(924\) | 4.84124 | 0.159265 | ||||||||
\(925\) | −6.01170 | −0.197664 | ||||||||
\(926\) | 33.8729 | 1.11313 | ||||||||
\(927\) | 40.6098 | 1.33380 | ||||||||
\(928\) | −7.04227 | −0.231174 | ||||||||
\(929\) | 40.7179 | 1.33591 | 0.667955 | − | 0.744201i | \(-0.267170\pi\) | ||||
0.667955 | + | 0.744201i | \(0.267170\pi\) | |||||||
\(930\) | 7.02778 | 0.230450 | ||||||||
\(931\) | −9.20968 | −0.301835 | ||||||||
\(932\) | −24.5919 | −0.805533 | ||||||||
\(933\) | −13.7205 | −0.449190 | ||||||||
\(934\) | −28.8638 | −0.944452 | ||||||||
\(935\) | −11.2831 | −0.368998 | ||||||||
\(936\) | −5.38514 | −0.176019 | ||||||||
\(937\) | −3.78336 | −0.123597 | −0.0617985 | − | 0.998089i | \(-0.519684\pi\) | ||||
−0.0617985 | + | 0.998089i | \(0.519684\pi\) | |||||||
\(938\) | 40.3799 | 1.31845 | ||||||||
\(939\) | −4.68757 | −0.152973 | ||||||||
\(940\) | 24.1315 | 0.787082 | ||||||||
\(941\) | 33.5344 | 1.09319 | 0.546594 | − | 0.837398i | \(-0.315924\pi\) | ||||
0.546594 | + | 0.837398i | \(0.315924\pi\) | |||||||
\(942\) | 9.44990 | 0.307894 | ||||||||
\(943\) | 46.5083 | 1.51452 | ||||||||
\(944\) | −8.17643 | −0.266120 | ||||||||
\(945\) | −52.1562 | −1.69664 | ||||||||
\(946\) | −16.5791 | −0.539032 | ||||||||
\(947\) | 11.7566 | 0.382038 | 0.191019 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191019 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(948\) | 1.53169 | 0.0497470 | ||||||||
\(949\) | 0.282331 | 0.00916485 | ||||||||
\(950\) | −5.50755 | −0.178688 | ||||||||
\(951\) | 22.4413 | 0.727710 | ||||||||
\(952\) | −8.52216 | −0.276205 | ||||||||
\(953\) | 27.4805 | 0.890181 | 0.445090 | − | 0.895486i | \(-0.353172\pi\) | ||||
0.445090 | + | 0.895486i | \(0.353172\pi\) | |||||||
\(954\) | 4.44347 | 0.143863 | ||||||||
\(955\) | 56.1852 | 1.81811 | ||||||||
\(956\) | 15.2818 | 0.494249 | ||||||||
\(957\) | −8.46802 | −0.273732 | ||||||||
\(958\) | 12.6792 | 0.409646 | ||||||||
\(959\) | −34.6881 | −1.12014 | ||||||||
\(960\) | 2.37030 | 0.0765012 | ||||||||
\(961\) | −22.2092 | −0.716426 | ||||||||
\(962\) | −2.38433 | −0.0768739 | ||||||||
\(963\) | −42.0735 | −1.35580 | ||||||||
\(964\) | −3.76817 | −0.121365 | ||||||||
\(965\) | −81.5925 | −2.62656 | ||||||||
\(966\) | 23.3501 | 0.751277 | ||||||||
\(967\) | 38.4447 | 1.23630 | 0.618148 | − | 0.786061i | \(-0.287883\pi\) | ||||
0.618148 | + | 0.786061i | \(0.287883\pi\) | |||||||
\(968\) | −8.29584 | −0.266639 | ||||||||
\(969\) | 1.54780 | 0.0497226 | ||||||||
\(970\) | 5.93302 | 0.190498 | ||||||||
\(971\) | 52.6254 | 1.68883 | 0.844414 | − | 0.535691i | \(-0.179949\pi\) | ||||
0.844414 | + | 0.535691i | \(0.179949\pi\) | |||||||
\(972\) | 15.2604 | 0.489478 | ||||||||
\(973\) | 43.8714 | 1.40645 | ||||||||
\(974\) | 18.3562 | 0.588170 | ||||||||
\(975\) | 8.79707 | 0.281732 | ||||||||
\(976\) | −9.55710 | −0.305915 | ||||||||
\(977\) | −38.2740 | −1.22449 | −0.612247 | − | 0.790667i | \(-0.709734\pi\) | ||||
−0.612247 | + | 0.790667i | \(0.709734\pi\) | |||||||
\(978\) | −12.5906 | −0.402603 | ||||||||
\(979\) | −12.4741 | −0.398674 | ||||||||
\(980\) | 29.8535 | 0.953635 | ||||||||
\(981\) | −35.2203 | −1.12450 | ||||||||
\(982\) | −7.73203 | −0.246739 | ||||||||
\(983\) | −35.6313 | −1.13646 | −0.568230 | − | 0.822869i | \(-0.692372\pi\) | ||||
−0.568230 | + | 0.822869i | \(0.692372\pi\) | |||||||
\(984\) | 4.28781 | 0.136690 | ||||||||
\(985\) | 7.75724 | 0.247166 | ||||||||
\(986\) | 14.9065 | 0.474719 | ||||||||
\(987\) | 21.9166 | 0.697614 | ||||||||
\(988\) | −2.18437 | −0.0694942 | ||||||||
\(989\) | −79.9636 | −2.54269 | ||||||||
\(990\) | −13.1413 | −0.417657 | ||||||||
\(991\) | 7.57125 | 0.240509 | 0.120254 | − | 0.992743i | \(-0.461629\pi\) | ||||
0.120254 | + | 0.992743i | \(0.461629\pi\) | |||||||
\(992\) | 2.96493 | 0.0941365 | ||||||||
\(993\) | 0.972273 | 0.0308541 | ||||||||
\(994\) | 9.78788 | 0.310453 | ||||||||
\(995\) | −37.7154 | −1.19566 | ||||||||
\(996\) | −1.03616 | −0.0328319 | ||||||||
\(997\) | 23.4970 | 0.744158 | 0.372079 | − | 0.928201i | \(-0.378645\pi\) | ||||
0.372079 | + | 0.928201i | \(0.378645\pi\) | |||||||
\(998\) | −7.68285 | −0.243196 | ||||||||
\(999\) | 4.36222 | 0.138014 |
(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 | 8018.2.a.j.1.25 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.25 | ✓ | 47 | 1.1 | even | 1 | trivial |