Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.745458 | −0.527118 | −0.263559 | − | 0.964643i | \(-0.584896\pi\) | ||||
−0.263559 | + | 0.964643i | \(0.584896\pi\) | |||||||
\(3\) | 3.05905 | 1.76614 | 0.883072 | − | 0.469238i | \(-0.155471\pi\) | ||||
0.883072 | + | 0.469238i | \(0.155471\pi\) | |||||||
\(4\) | −1.44429 | −0.722146 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.28039 | −0.930967 | ||||||||
\(7\) | −3.66055 | −1.38356 | −0.691779 | − | 0.722109i | \(-0.743173\pi\) | ||||
−0.691779 | + | 0.722109i | \(0.743173\pi\) | |||||||
\(8\) | 2.56757 | 0.907775 | ||||||||
\(9\) | 6.35779 | 2.11926 | ||||||||
\(10\) | −0.745458 | −0.235734 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.41817 | −1.27541 | ||||||||
\(13\) | 1.02611 | 0.284593 | 0.142296 | − | 0.989824i | \(-0.454551\pi\) | ||||
0.142296 | + | 0.989824i | \(0.454551\pi\) | |||||||
\(14\) | 2.72879 | 0.729298 | ||||||||
\(15\) | 3.05905 | 0.789844 | ||||||||
\(16\) | 0.974567 | 0.243642 | ||||||||
\(17\) | 7.92938 | 1.92316 | 0.961579 | − | 0.274529i | \(-0.0885219\pi\) | ||||
0.961579 | + | 0.274529i | \(0.0885219\pi\) | |||||||
\(18\) | −4.73947 | −1.11710 | ||||||||
\(19\) | −1.53458 | −0.352057 | −0.176029 | − | 0.984385i | \(-0.556325\pi\) | ||||
−0.176029 | + | 0.984385i | \(0.556325\pi\) | |||||||
\(20\) | −1.44429 | −0.322954 | ||||||||
\(21\) | −11.1978 | −2.44356 | ||||||||
\(22\) | −0.745458 | −0.158932 | ||||||||
\(23\) | −9.02592 | −1.88203 | −0.941017 | − | 0.338358i | \(-0.890129\pi\) | ||||
−0.941017 | + | 0.338358i | \(0.890129\pi\) | |||||||
\(24\) | 7.85434 | 1.60326 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.764924 | −0.150014 | ||||||||
\(27\) | 10.2717 | 1.97678 | ||||||||
\(28\) | 5.28691 | 0.999131 | ||||||||
\(29\) | 3.19396 | 0.593104 | 0.296552 | − | 0.955017i | \(-0.404163\pi\) | ||||
0.296552 | + | 0.955017i | \(0.404163\pi\) | |||||||
\(30\) | −2.28039 | −0.416341 | ||||||||
\(31\) | −7.54361 | −1.35487 | −0.677436 | − | 0.735582i | \(-0.736909\pi\) | ||||
−0.677436 | + | 0.735582i | \(0.736909\pi\) | |||||||
\(32\) | −5.86165 | −1.03620 | ||||||||
\(33\) | 3.05905 | 0.532512 | ||||||||
\(34\) | −5.91102 | −1.01373 | ||||||||
\(35\) | −3.66055 | −0.618746 | ||||||||
\(36\) | −9.18251 | −1.53042 | ||||||||
\(37\) | 6.07994 | 0.999535 | 0.499768 | − | 0.866159i | \(-0.333419\pi\) | ||||
0.499768 | + | 0.866159i | \(0.333419\pi\) | |||||||
\(38\) | 1.14397 | 0.185576 | ||||||||
\(39\) | 3.13893 | 0.502631 | ||||||||
\(40\) | 2.56757 | 0.405969 | ||||||||
\(41\) | 7.65235 | 1.19510 | 0.597548 | − | 0.801833i | \(-0.296142\pi\) | ||||
0.597548 | + | 0.801833i | \(0.296142\pi\) | |||||||
\(42\) | 8.34749 | 1.28805 | ||||||||
\(43\) | 8.29774 | 1.26539 | 0.632696 | − | 0.774400i | \(-0.281948\pi\) | ||||
0.632696 | + | 0.774400i | \(0.281948\pi\) | |||||||
\(44\) | −1.44429 | −0.217735 | ||||||||
\(45\) | 6.35779 | 0.947764 | ||||||||
\(46\) | 6.72844 | 0.992055 | ||||||||
\(47\) | 9.63324 | 1.40515 | 0.702576 | − | 0.711609i | \(-0.252033\pi\) | ||||
0.702576 | + | 0.711609i | \(0.252033\pi\) | |||||||
\(48\) | 2.98125 | 0.430307 | ||||||||
\(49\) | 6.39962 | 0.914232 | ||||||||
\(50\) | −0.745458 | −0.105424 | ||||||||
\(51\) | 24.2564 | 3.39657 | ||||||||
\(52\) | −1.48201 | −0.205518 | ||||||||
\(53\) | −3.09231 | −0.424762 | −0.212381 | − | 0.977187i | \(-0.568122\pi\) | ||||
−0.212381 | + | 0.977187i | \(0.568122\pi\) | |||||||
\(54\) | −7.65709 | −1.04200 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −9.39873 | −1.25596 | ||||||||
\(57\) | −4.69437 | −0.621784 | ||||||||
\(58\) | −2.38096 | −0.312636 | ||||||||
\(59\) | 8.32297 | 1.08356 | 0.541779 | − | 0.840521i | \(-0.317751\pi\) | ||||
0.541779 | + | 0.840521i | \(0.317751\pi\) | |||||||
\(60\) | −4.41817 | −0.570383 | ||||||||
\(61\) | −7.95140 | −1.01807 | −0.509036 | − | 0.860745i | \(-0.669998\pi\) | ||||
−0.509036 | + | 0.860745i | \(0.669998\pi\) | |||||||
\(62\) | 5.62344 | 0.714178 | ||||||||
\(63\) | −23.2730 | −2.93212 | ||||||||
\(64\) | 2.42048 | 0.302560 | ||||||||
\(65\) | 1.02611 | 0.127274 | ||||||||
\(66\) | −2.28039 | −0.280697 | ||||||||
\(67\) | −2.85577 | −0.348888 | −0.174444 | − | 0.984667i | \(-0.555813\pi\) | ||||
−0.174444 | + | 0.984667i | \(0.555813\pi\) | |||||||
\(68\) | −11.4523 | −1.38880 | ||||||||
\(69\) | −27.6108 | −3.32394 | ||||||||
\(70\) | 2.72879 | 0.326152 | ||||||||
\(71\) | −3.17918 | −0.377300 | −0.188650 | − | 0.982044i | \(-0.560411\pi\) | ||||
−0.188650 | + | 0.982044i | \(0.560411\pi\) | |||||||
\(72\) | 16.3241 | 1.92381 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −4.53234 | −0.526873 | ||||||||
\(75\) | 3.05905 | 0.353229 | ||||||||
\(76\) | 2.21639 | 0.254237 | ||||||||
\(77\) | −3.66055 | −0.417158 | ||||||||
\(78\) | −2.33994 | −0.264946 | ||||||||
\(79\) | 16.2070 | 1.82343 | 0.911717 | − | 0.410820i | \(-0.134757\pi\) | ||||
0.911717 | + | 0.410820i | \(0.134757\pi\) | |||||||
\(80\) | 0.974567 | 0.108960 | ||||||||
\(81\) | 12.3481 | 1.37202 | ||||||||
\(82\) | −5.70450 | −0.629957 | ||||||||
\(83\) | −1.77293 | −0.194604 | −0.0973021 | − | 0.995255i | \(-0.531021\pi\) | ||||
−0.0973021 | + | 0.995255i | \(0.531021\pi\) | |||||||
\(84\) | 16.1729 | 1.76461 | ||||||||
\(85\) | 7.92938 | 0.860062 | ||||||||
\(86\) | −6.18561 | −0.667012 | ||||||||
\(87\) | 9.77049 | 1.04751 | ||||||||
\(88\) | 2.56757 | 0.273704 | ||||||||
\(89\) | 0.725334 | 0.0768852 | 0.0384426 | − | 0.999261i | \(-0.487760\pi\) | ||||
0.0384426 | + | 0.999261i | \(0.487760\pi\) | |||||||
\(90\) | −4.73947 | −0.499584 | ||||||||
\(91\) | −3.75614 | −0.393750 | ||||||||
\(92\) | 13.0361 | 1.35910 | ||||||||
\(93\) | −23.0763 | −2.39290 | ||||||||
\(94\) | −7.18117 | −0.740681 | ||||||||
\(95\) | −1.53458 | −0.157445 | ||||||||
\(96\) | −17.9311 | −1.83008 | ||||||||
\(97\) | 18.9489 | 1.92397 | 0.961983 | − | 0.273110i | \(-0.0880524\pi\) | ||||
0.961983 | + | 0.273110i | \(0.0880524\pi\) | |||||||
\(98\) | −4.77065 | −0.481908 | ||||||||
\(99\) | 6.35779 | 0.638982 | ||||||||
\(100\) | −1.44429 | −0.144429 | ||||||||
\(101\) | 2.13994 | 0.212932 | 0.106466 | − | 0.994316i | \(-0.466046\pi\) | ||||
0.106466 | + | 0.994316i | \(0.466046\pi\) | |||||||
\(102\) | −18.0821 | −1.79040 | ||||||||
\(103\) | −5.76145 | −0.567693 | −0.283846 | − | 0.958870i | \(-0.591611\pi\) | ||||
−0.283846 | + | 0.958870i | \(0.591611\pi\) | |||||||
\(104\) | 2.63462 | 0.258346 | ||||||||
\(105\) | −11.1978 | −1.09279 | ||||||||
\(106\) | 2.30519 | 0.223900 | ||||||||
\(107\) | −17.7209 | −1.71314 | −0.856571 | − | 0.516029i | \(-0.827410\pi\) | ||||
−0.856571 | + | 0.516029i | \(0.827410\pi\) | |||||||
\(108\) | −14.8353 | −1.42753 | ||||||||
\(109\) | 10.8333 | 1.03764 | 0.518821 | − | 0.854883i | \(-0.326371\pi\) | ||||
0.518821 | + | 0.854883i | \(0.326371\pi\) | |||||||
\(110\) | −0.745458 | −0.0710766 | ||||||||
\(111\) | 18.5988 | 1.76532 | ||||||||
\(112\) | −3.56745 | −0.337093 | ||||||||
\(113\) | −12.3929 | −1.16583 | −0.582914 | − | 0.812534i | \(-0.698087\pi\) | ||||
−0.582914 | + | 0.812534i | \(0.698087\pi\) | |||||||
\(114\) | 3.49945 | 0.327754 | ||||||||
\(115\) | −9.02592 | −0.841672 | ||||||||
\(116\) | −4.61302 | −0.428308 | ||||||||
\(117\) | 6.52381 | 0.603127 | ||||||||
\(118\) | −6.20442 | −0.571164 | ||||||||
\(119\) | −29.0259 | −2.66080 | ||||||||
\(120\) | 7.85434 | 0.717000 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.92744 | 0.536645 | ||||||||
\(123\) | 23.4089 | 2.11071 | ||||||||
\(124\) | 10.8952 | 0.978416 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 17.3490 | 1.54558 | ||||||||
\(127\) | 16.4683 | 1.46133 | 0.730664 | − | 0.682737i | \(-0.239210\pi\) | ||||
0.730664 | + | 0.682737i | \(0.239210\pi\) | |||||||
\(128\) | 9.91893 | 0.876718 | ||||||||
\(129\) | 25.3832 | 2.23487 | ||||||||
\(130\) | −0.764924 | −0.0670883 | ||||||||
\(131\) | −0.222835 | −0.0194692 | −0.00973461 | − | 0.999953i | \(-0.503099\pi\) | ||||
−0.00973461 | + | 0.999953i | \(0.503099\pi\) | |||||||
\(132\) | −4.41817 | −0.384552 | ||||||||
\(133\) | 5.61742 | 0.487092 | ||||||||
\(134\) | 2.12886 | 0.183905 | ||||||||
\(135\) | 10.2717 | 0.884044 | ||||||||
\(136\) | 20.3593 | 1.74579 | ||||||||
\(137\) | 0.277250 | 0.0236871 | 0.0118435 | − | 0.999930i | \(-0.496230\pi\) | ||||
0.0118435 | + | 0.999930i | \(0.496230\pi\) | |||||||
\(138\) | 20.5827 | 1.75211 | ||||||||
\(139\) | 7.00548 | 0.594197 | 0.297098 | − | 0.954847i | \(-0.403981\pi\) | ||||
0.297098 | + | 0.954847i | \(0.403981\pi\) | |||||||
\(140\) | 5.28691 | 0.446825 | ||||||||
\(141\) | 29.4686 | 2.48170 | ||||||||
\(142\) | 2.36995 | 0.198882 | ||||||||
\(143\) | 1.02611 | 0.0858079 | ||||||||
\(144\) | 6.19610 | 0.516341 | ||||||||
\(145\) | 3.19396 | 0.265244 | ||||||||
\(146\) | −0.745458 | −0.0616945 | ||||||||
\(147\) | 19.5768 | 1.61467 | ||||||||
\(148\) | −8.78121 | −0.721811 | ||||||||
\(149\) | −0.618196 | −0.0506446 | −0.0253223 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253223 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(150\) | −2.28039 | −0.186193 | ||||||||
\(151\) | −8.77873 | −0.714403 | −0.357201 | − | 0.934027i | \(-0.616269\pi\) | ||||
−0.357201 | + | 0.934027i | \(0.616269\pi\) | |||||||
\(152\) | −3.94016 | −0.319589 | ||||||||
\(153\) | 50.4134 | 4.07568 | ||||||||
\(154\) | 2.72879 | 0.219892 | ||||||||
\(155\) | −7.54361 | −0.605917 | ||||||||
\(156\) | −4.53354 | −0.362974 | ||||||||
\(157\) | 5.14023 | 0.410235 | 0.205118 | − | 0.978737i | \(-0.434242\pi\) | ||||
0.205118 | + | 0.978737i | \(0.434242\pi\) | |||||||
\(158\) | −12.0817 | −0.961165 | ||||||||
\(159\) | −9.45954 | −0.750190 | ||||||||
\(160\) | −5.86165 | −0.463404 | ||||||||
\(161\) | 33.0398 | 2.60390 | ||||||||
\(162\) | −9.20502 | −0.723215 | ||||||||
\(163\) | −10.5410 | −0.825637 | −0.412818 | − | 0.910813i | \(-0.635456\pi\) | ||||
−0.412818 | + | 0.910813i | \(0.635456\pi\) | |||||||
\(164\) | −11.0522 | −0.863035 | ||||||||
\(165\) | 3.05905 | 0.238147 | ||||||||
\(166\) | 1.32164 | 0.102579 | ||||||||
\(167\) | 0.991594 | 0.0767319 | 0.0383659 | − | 0.999264i | \(-0.487785\pi\) | ||||
0.0383659 | + | 0.999264i | \(0.487785\pi\) | |||||||
\(168\) | −28.7512 | −2.21820 | ||||||||
\(169\) | −11.9471 | −0.919007 | ||||||||
\(170\) | −5.91102 | −0.453354 | ||||||||
\(171\) | −9.75656 | −0.746103 | ||||||||
\(172\) | −11.9844 | −0.913799 | ||||||||
\(173\) | −4.27659 | −0.325143 | −0.162572 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162572 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(174\) | −7.28349 | −0.552160 | ||||||||
\(175\) | −3.66055 | −0.276712 | ||||||||
\(176\) | 0.974567 | 0.0734608 | ||||||||
\(177\) | 25.4604 | 1.91372 | ||||||||
\(178\) | −0.540706 | −0.0405276 | ||||||||
\(179\) | 2.49969 | 0.186836 | 0.0934179 | − | 0.995627i | \(-0.470221\pi\) | ||||
0.0934179 | + | 0.995627i | \(0.470221\pi\) | |||||||
\(180\) | −9.18251 | −0.684424 | ||||||||
\(181\) | 3.30917 | 0.245969 | 0.122984 | − | 0.992409i | \(-0.460753\pi\) | ||||
0.122984 | + | 0.992409i | \(0.460753\pi\) | |||||||
\(182\) | 2.80004 | 0.207553 | ||||||||
\(183\) | −24.3237 | −1.79806 | ||||||||
\(184\) | −23.1747 | −1.70846 | ||||||||
\(185\) | 6.07994 | 0.447006 | ||||||||
\(186\) | 17.2024 | 1.26134 | ||||||||
\(187\) | 7.92938 | 0.579854 | ||||||||
\(188\) | −13.9132 | −1.01473 | ||||||||
\(189\) | −37.5999 | −2.73499 | ||||||||
\(190\) | 1.14397 | 0.0829920 | ||||||||
\(191\) | 23.7192 | 1.71626 | 0.858132 | − | 0.513429i | \(-0.171625\pi\) | ||||
0.858132 | + | 0.513429i | \(0.171625\pi\) | |||||||
\(192\) | 7.40436 | 0.534364 | ||||||||
\(193\) | 9.56799 | 0.688719 | 0.344359 | − | 0.938838i | \(-0.388096\pi\) | ||||
0.344359 | + | 0.938838i | \(0.388096\pi\) | |||||||
\(194\) | −14.1256 | −1.01416 | ||||||||
\(195\) | 3.13893 | 0.224784 | ||||||||
\(196\) | −9.24293 | −0.660209 | ||||||||
\(197\) | 13.1006 | 0.933380 | 0.466690 | − | 0.884421i | \(-0.345446\pi\) | ||||
0.466690 | + | 0.884421i | \(0.345446\pi\) | |||||||
\(198\) | −4.73947 | −0.336819 | ||||||||
\(199\) | −12.6096 | −0.893870 | −0.446935 | − | 0.894566i | \(-0.647485\pi\) | ||||
−0.446935 | + | 0.894566i | \(0.647485\pi\) | |||||||
\(200\) | 2.56757 | 0.181555 | ||||||||
\(201\) | −8.73595 | −0.616187 | ||||||||
\(202\) | −1.59524 | −0.112241 | ||||||||
\(203\) | −11.6917 | −0.820593 | ||||||||
\(204\) | −35.0333 | −2.45282 | ||||||||
\(205\) | 7.65235 | 0.534463 | ||||||||
\(206\) | 4.29492 | 0.299241 | ||||||||
\(207\) | −57.3849 | −3.98853 | ||||||||
\(208\) | 1.00002 | 0.0693387 | ||||||||
\(209\) | −1.53458 | −0.106149 | ||||||||
\(210\) | 8.34749 | 0.576032 | ||||||||
\(211\) | 13.6724 | 0.941245 | 0.470622 | − | 0.882335i | \(-0.344029\pi\) | ||||
0.470622 | + | 0.882335i | \(0.344029\pi\) | |||||||
\(212\) | 4.46620 | 0.306740 | ||||||||
\(213\) | −9.72529 | −0.666366 | ||||||||
\(214\) | 13.2102 | 0.903029 | ||||||||
\(215\) | 8.29774 | 0.565901 | ||||||||
\(216\) | 26.3733 | 1.79447 | ||||||||
\(217\) | 27.6137 | 1.87454 | ||||||||
\(218\) | −8.07577 | −0.546960 | ||||||||
\(219\) | 3.05905 | 0.206712 | ||||||||
\(220\) | −1.44429 | −0.0973742 | ||||||||
\(221\) | 8.13644 | 0.547316 | ||||||||
\(222\) | −13.8646 | −0.930534 | ||||||||
\(223\) | 17.2192 | 1.15308 | 0.576541 | − | 0.817068i | \(-0.304402\pi\) | ||||
0.576541 | + | 0.817068i | \(0.304402\pi\) | |||||||
\(224\) | 21.4569 | 1.43365 | ||||||||
\(225\) | 6.35779 | 0.423853 | ||||||||
\(226\) | 9.23839 | 0.614529 | ||||||||
\(227\) | 19.9155 | 1.32184 | 0.660918 | − | 0.750458i | \(-0.270167\pi\) | ||||
0.660918 | + | 0.750458i | \(0.270167\pi\) | |||||||
\(228\) | 6.78004 | 0.449019 | ||||||||
\(229\) | 2.12024 | 0.140109 | 0.0700547 | − | 0.997543i | \(-0.477683\pi\) | ||||
0.0700547 | + | 0.997543i | \(0.477683\pi\) | |||||||
\(230\) | 6.72844 | 0.443660 | ||||||||
\(231\) | −11.1978 | −0.736762 | ||||||||
\(232\) | 8.20073 | 0.538405 | ||||||||
\(233\) | 19.4593 | 1.27482 | 0.637410 | − | 0.770525i | \(-0.280006\pi\) | ||||
0.637410 | + | 0.770525i | \(0.280006\pi\) | |||||||
\(234\) | −4.86323 | −0.317919 | ||||||||
\(235\) | 9.63324 | 0.628403 | ||||||||
\(236\) | −12.0208 | −0.782488 | ||||||||
\(237\) | 49.5781 | 3.22045 | ||||||||
\(238\) | 21.6376 | 1.40256 | ||||||||
\(239\) | 1.35119 | 0.0874013 | 0.0437006 | − | 0.999045i | \(-0.486085\pi\) | ||||
0.0437006 | + | 0.999045i | \(0.486085\pi\) | |||||||
\(240\) | 2.98125 | 0.192439 | ||||||||
\(241\) | 19.4434 | 1.25246 | 0.626228 | − | 0.779640i | \(-0.284598\pi\) | ||||
0.626228 | + | 0.779640i | \(0.284598\pi\) | |||||||
\(242\) | −0.745458 | −0.0479198 | ||||||||
\(243\) | 6.95864 | 0.446397 | ||||||||
\(244\) | 11.4842 | 0.735198 | ||||||||
\(245\) | 6.39962 | 0.408857 | ||||||||
\(246\) | −17.4504 | −1.11259 | ||||||||
\(247\) | −1.57466 | −0.100193 | ||||||||
\(248\) | −19.3688 | −1.22992 | ||||||||
\(249\) | −5.42348 | −0.343699 | ||||||||
\(250\) | −0.745458 | −0.0471469 | ||||||||
\(251\) | 4.96317 | 0.313273 | 0.156636 | − | 0.987656i | \(-0.449935\pi\) | ||||
0.156636 | + | 0.987656i | \(0.449935\pi\) | |||||||
\(252\) | 33.6130 | 2.11742 | ||||||||
\(253\) | −9.02592 | −0.567455 | ||||||||
\(254\) | −12.2765 | −0.770293 | ||||||||
\(255\) | 24.2564 | 1.51899 | ||||||||
\(256\) | −12.2351 | −0.764694 | ||||||||
\(257\) | 6.95937 | 0.434113 | 0.217057 | − | 0.976159i | \(-0.430354\pi\) | ||||
0.217057 | + | 0.976159i | \(0.430354\pi\) | |||||||
\(258\) | −18.9221 | −1.17804 | ||||||||
\(259\) | −22.2559 | −1.38292 | ||||||||
\(260\) | −1.48201 | −0.0919102 | ||||||||
\(261\) | 20.3065 | 1.25694 | ||||||||
\(262\) | 0.166114 | 0.0102626 | ||||||||
\(263\) | −21.5934 | −1.33150 | −0.665752 | − | 0.746173i | \(-0.731889\pi\) | ||||
−0.665752 | + | 0.746173i | \(0.731889\pi\) | |||||||
\(264\) | 7.85434 | 0.483401 | ||||||||
\(265\) | −3.09231 | −0.189959 | ||||||||
\(266\) | −4.18755 | −0.256755 | ||||||||
\(267\) | 2.21883 | 0.135790 | ||||||||
\(268\) | 4.12457 | 0.251948 | ||||||||
\(269\) | −25.2542 | −1.53977 | −0.769887 | − | 0.638180i | \(-0.779688\pi\) | ||||
−0.769887 | + | 0.638180i | \(0.779688\pi\) | |||||||
\(270\) | −7.65709 | −0.465995 | ||||||||
\(271\) | −0.0873812 | −0.00530803 | −0.00265402 | − | 0.999996i | \(-0.500845\pi\) | ||||
−0.00265402 | + | 0.999996i | \(0.500845\pi\) | |||||||
\(272\) | 7.72772 | 0.468562 | ||||||||
\(273\) | −11.4902 | −0.695420 | ||||||||
\(274\) | −0.206678 | −0.0124859 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 39.8780 | 2.40037 | ||||||||
\(277\) | −15.5840 | −0.936350 | −0.468175 | − | 0.883636i | \(-0.655088\pi\) | ||||
−0.468175 | + | 0.883636i | \(0.655088\pi\) | |||||||
\(278\) | −5.22229 | −0.313212 | ||||||||
\(279\) | −47.9607 | −2.87133 | ||||||||
\(280\) | −9.39873 | −0.561682 | ||||||||
\(281\) | −23.2266 | −1.38558 | −0.692791 | − | 0.721138i | \(-0.743619\pi\) | ||||
−0.692791 | + | 0.721138i | \(0.743619\pi\) | |||||||
\(282\) | −21.9676 | −1.30815 | ||||||||
\(283\) | −2.22884 | −0.132491 | −0.0662453 | − | 0.997803i | \(-0.521102\pi\) | ||||
−0.0662453 | + | 0.997803i | \(0.521102\pi\) | |||||||
\(284\) | 4.59167 | 0.272466 | ||||||||
\(285\) | −4.69437 | −0.278070 | ||||||||
\(286\) | −0.764924 | −0.0452309 | ||||||||
\(287\) | −28.0118 | −1.65348 | ||||||||
\(288\) | −37.2671 | −2.19599 | ||||||||
\(289\) | 45.8751 | 2.69854 | ||||||||
\(290\) | −2.38096 | −0.139815 | ||||||||
\(291\) | 57.9655 | 3.39800 | ||||||||
\(292\) | −1.44429 | −0.0845208 | ||||||||
\(293\) | −0.867891 | −0.0507027 | −0.0253514 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253514 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(294\) | −14.5937 | −0.851119 | ||||||||
\(295\) | 8.32297 | 0.484582 | ||||||||
\(296\) | 15.6107 | 0.907353 | ||||||||
\(297\) | 10.2717 | 0.596022 | ||||||||
\(298\) | 0.460839 | 0.0266957 | ||||||||
\(299\) | −9.26162 | −0.535613 | ||||||||
\(300\) | −4.41817 | −0.255083 | ||||||||
\(301\) | −30.3743 | −1.75074 | ||||||||
\(302\) | 6.54417 | 0.376575 | ||||||||
\(303\) | 6.54620 | 0.376069 | ||||||||
\(304\) | −1.49555 | −0.0857759 | ||||||||
\(305\) | −7.95140 | −0.455296 | ||||||||
\(306\) | −37.5810 | −2.14836 | ||||||||
\(307\) | 21.7728 | 1.24264 | 0.621319 | − | 0.783558i | \(-0.286597\pi\) | ||||
0.621319 | + | 0.783558i | \(0.286597\pi\) | |||||||
\(308\) | 5.28691 | 0.301249 | ||||||||
\(309\) | −17.6246 | −1.00263 | ||||||||
\(310\) | 5.62344 | 0.319390 | ||||||||
\(311\) | −23.3048 | −1.32149 | −0.660747 | − | 0.750609i | \(-0.729760\pi\) | ||||
−0.660747 | + | 0.750609i | \(0.729760\pi\) | |||||||
\(312\) | 8.05944 | 0.456276 | ||||||||
\(313\) | 21.1142 | 1.19344 | 0.596722 | − | 0.802448i | \(-0.296469\pi\) | ||||
0.596722 | + | 0.802448i | \(0.296469\pi\) | |||||||
\(314\) | −3.83183 | −0.216242 | ||||||||
\(315\) | −23.2730 | −1.31129 | ||||||||
\(316\) | −23.4077 | −1.31679 | ||||||||
\(317\) | −0.318916 | −0.0179121 | −0.00895605 | − | 0.999960i | \(-0.502851\pi\) | ||||
−0.00895605 | + | 0.999960i | \(0.502851\pi\) | |||||||
\(318\) | 7.05169 | 0.395439 | ||||||||
\(319\) | 3.19396 | 0.178827 | ||||||||
\(320\) | 2.42048 | 0.135309 | ||||||||
\(321\) | −54.2091 | −3.02566 | ||||||||
\(322\) | −24.6298 | −1.37257 | ||||||||
\(323\) | −12.1683 | −0.677062 | ||||||||
\(324\) | −17.8343 | −0.990797 | ||||||||
\(325\) | 1.02611 | 0.0569185 | ||||||||
\(326\) | 7.85789 | 0.435208 | ||||||||
\(327\) | 33.1396 | 1.83263 | ||||||||
\(328\) | 19.6480 | 1.08488 | ||||||||
\(329\) | −35.2629 | −1.94411 | ||||||||
\(330\) | −2.28039 | −0.125532 | ||||||||
\(331\) | −27.0626 | −1.48749 | −0.743747 | − | 0.668462i | \(-0.766953\pi\) | ||||
−0.743747 | + | 0.668462i | \(0.766953\pi\) | |||||||
\(332\) | 2.56063 | 0.140533 | ||||||||
\(333\) | 38.6550 | 2.11828 | ||||||||
\(334\) | −0.739192 | −0.0404468 | ||||||||
\(335\) | −2.85577 | −0.156028 | ||||||||
\(336\) | −10.9130 | −0.595354 | ||||||||
\(337\) | 11.4837 | 0.625555 | 0.312778 | − | 0.949826i | \(-0.398741\pi\) | ||||
0.312778 | + | 0.949826i | \(0.398741\pi\) | |||||||
\(338\) | 8.90605 | 0.484425 | ||||||||
\(339\) | −37.9106 | −2.05902 | ||||||||
\(340\) | −11.4523 | −0.621091 | ||||||||
\(341\) | −7.54361 | −0.408509 | ||||||||
\(342\) | 7.27310 | 0.393284 | ||||||||
\(343\) | 2.19770 | 0.118665 | ||||||||
\(344\) | 21.3051 | 1.14869 | ||||||||
\(345\) | −27.6108 | −1.48651 | ||||||||
\(346\) | 3.18802 | 0.171389 | ||||||||
\(347\) | −13.5714 | −0.728550 | −0.364275 | − | 0.931291i | \(-0.618683\pi\) | ||||
−0.364275 | + | 0.931291i | \(0.618683\pi\) | |||||||
\(348\) | −14.1114 | −0.756453 | ||||||||
\(349\) | 18.2877 | 0.978917 | 0.489459 | − | 0.872026i | \(-0.337194\pi\) | ||||
0.489459 | + | 0.872026i | \(0.337194\pi\) | |||||||
\(350\) | 2.72879 | 0.145860 | ||||||||
\(351\) | 10.5399 | 0.562577 | ||||||||
\(352\) | −5.86165 | −0.312427 | ||||||||
\(353\) | −25.7020 | −1.36798 | −0.683989 | − | 0.729492i | \(-0.739757\pi\) | ||||
−0.683989 | + | 0.729492i | \(0.739757\pi\) | |||||||
\(354\) | −18.9797 | −1.00876 | ||||||||
\(355\) | −3.17918 | −0.168734 | ||||||||
\(356\) | −1.04759 | −0.0555224 | ||||||||
\(357\) | −88.7917 | −4.69936 | ||||||||
\(358\) | −1.86342 | −0.0984846 | ||||||||
\(359\) | −5.27668 | −0.278493 | −0.139246 | − | 0.990258i | \(-0.544468\pi\) | ||||
−0.139246 | + | 0.990258i | \(0.544468\pi\) | |||||||
\(360\) | 16.3241 | 0.860356 | ||||||||
\(361\) | −16.6451 | −0.876056 | ||||||||
\(362\) | −2.46685 | −0.129655 | ||||||||
\(363\) | 3.05905 | 0.160559 | ||||||||
\(364\) | 5.42496 | 0.284345 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 18.1323 | 0.947792 | ||||||||
\(367\) | −21.0497 | −1.09879 | −0.549393 | − | 0.835564i | \(-0.685141\pi\) | ||||
−0.549393 | + | 0.835564i | \(0.685141\pi\) | |||||||
\(368\) | −8.79637 | −0.458542 | ||||||||
\(369\) | 48.6521 | 2.53273 | ||||||||
\(370\) | −4.53234 | −0.235625 | ||||||||
\(371\) | 11.3196 | 0.587682 | ||||||||
\(372\) | 33.3289 | 1.72802 | ||||||||
\(373\) | 27.2340 | 1.41012 | 0.705062 | − | 0.709146i | \(-0.250919\pi\) | ||||
0.705062 | + | 0.709146i | \(0.250919\pi\) | |||||||
\(374\) | −5.91102 | −0.305652 | ||||||||
\(375\) | 3.05905 | 0.157969 | ||||||||
\(376\) | 24.7341 | 1.27556 | ||||||||
\(377\) | 3.27737 | 0.168793 | ||||||||
\(378\) | 28.0291 | 1.44166 | ||||||||
\(379\) | −3.29864 | −0.169440 | −0.0847200 | − | 0.996405i | \(-0.527000\pi\) | ||||
−0.0847200 | + | 0.996405i | \(0.527000\pi\) | |||||||
\(380\) | 2.21639 | 0.113698 | ||||||||
\(381\) | 50.3775 | 2.58092 | ||||||||
\(382\) | −17.6817 | −0.904674 | ||||||||
\(383\) | −5.14155 | −0.262721 | −0.131361 | − | 0.991335i | \(-0.541935\pi\) | ||||
−0.131361 | + | 0.991335i | \(0.541935\pi\) | |||||||
\(384\) | 30.3425 | 1.54841 | ||||||||
\(385\) | −3.66055 | −0.186559 | ||||||||
\(386\) | −7.13253 | −0.363036 | ||||||||
\(387\) | 52.7553 | 2.68170 | ||||||||
\(388\) | −27.3677 | −1.38938 | ||||||||
\(389\) | −5.42794 | −0.275207 | −0.137604 | − | 0.990487i | \(-0.543940\pi\) | ||||
−0.137604 | + | 0.990487i | \(0.543940\pi\) | |||||||
\(390\) | −2.33994 | −0.118488 | ||||||||
\(391\) | −71.5700 | −3.61945 | ||||||||
\(392\) | 16.4315 | 0.829917 | ||||||||
\(393\) | −0.681665 | −0.0343854 | ||||||||
\(394\) | −9.76595 | −0.492002 | ||||||||
\(395\) | 16.2070 | 0.815464 | ||||||||
\(396\) | −9.18251 | −0.461439 | ||||||||
\(397\) | −32.9788 | −1.65516 | −0.827580 | − | 0.561348i | \(-0.810283\pi\) | ||||
−0.827580 | + | 0.561348i | \(0.810283\pi\) | |||||||
\(398\) | 9.39992 | 0.471175 | ||||||||
\(399\) | 17.1840 | 0.860274 | ||||||||
\(400\) | 0.974567 | 0.0487284 | ||||||||
\(401\) | 16.3960 | 0.818775 | 0.409388 | − | 0.912361i | \(-0.365742\pi\) | ||||
0.409388 | + | 0.912361i | \(0.365742\pi\) | |||||||
\(402\) | 6.51228 | 0.324803 | ||||||||
\(403\) | −7.74060 | −0.385587 | ||||||||
\(404\) | −3.09071 | −0.153768 | ||||||||
\(405\) | 12.3481 | 0.613584 | ||||||||
\(406\) | 8.71563 | 0.432550 | ||||||||
\(407\) | 6.07994 | 0.301371 | ||||||||
\(408\) | 62.2801 | 3.08332 | ||||||||
\(409\) | −28.6106 | −1.41470 | −0.707351 | − | 0.706863i | \(-0.750110\pi\) | ||||
−0.707351 | + | 0.706863i | \(0.750110\pi\) | |||||||
\(410\) | −5.70450 | −0.281725 | ||||||||
\(411\) | 0.848122 | 0.0418348 | ||||||||
\(412\) | 8.32123 | 0.409957 | ||||||||
\(413\) | −30.4667 | −1.49917 | ||||||||
\(414\) | 42.7780 | 2.10243 | ||||||||
\(415\) | −1.77293 | −0.0870297 | ||||||||
\(416\) | −6.01471 | −0.294896 | ||||||||
\(417\) | 21.4301 | 1.04944 | ||||||||
\(418\) | 1.14397 | 0.0559532 | ||||||||
\(419\) | −30.1719 | −1.47400 | −0.736998 | − | 0.675895i | \(-0.763757\pi\) | ||||
−0.736998 | + | 0.675895i | \(0.763757\pi\) | |||||||
\(420\) | 16.1729 | 0.789157 | ||||||||
\(421\) | −15.5634 | −0.758512 | −0.379256 | − | 0.925292i | \(-0.623820\pi\) | ||||
−0.379256 | + | 0.925292i | \(0.623820\pi\) | |||||||
\(422\) | −10.1922 | −0.496147 | ||||||||
\(423\) | 61.2461 | 2.97789 | ||||||||
\(424\) | −7.93974 | −0.385588 | ||||||||
\(425\) | 7.92938 | 0.384632 | ||||||||
\(426\) | 7.24979 | 0.351254 | ||||||||
\(427\) | 29.1065 | 1.40856 | ||||||||
\(428\) | 25.5941 | 1.23714 | ||||||||
\(429\) | 3.13893 | 0.151549 | ||||||||
\(430\) | −6.18561 | −0.298297 | ||||||||
\(431\) | −30.5031 | −1.46928 | −0.734641 | − | 0.678456i | \(-0.762649\pi\) | ||||
−0.734641 | + | 0.678456i | \(0.762649\pi\) | |||||||
\(432\) | 10.0104 | 0.481627 | ||||||||
\(433\) | −28.0526 | −1.34812 | −0.674061 | − | 0.738676i | \(-0.735451\pi\) | ||||
−0.674061 | + | 0.738676i | \(0.735451\pi\) | |||||||
\(434\) | −20.5849 | −0.988106 | ||||||||
\(435\) | 9.77049 | 0.468459 | ||||||||
\(436\) | −15.6465 | −0.749330 | ||||||||
\(437\) | 13.8510 | 0.662584 | ||||||||
\(438\) | −2.28039 | −0.108961 | ||||||||
\(439\) | −6.29430 | −0.300411 | −0.150205 | − | 0.988655i | \(-0.547993\pi\) | ||||
−0.150205 | + | 0.988655i | \(0.547993\pi\) | |||||||
\(440\) | 2.56757 | 0.122404 | ||||||||
\(441\) | 40.6875 | 1.93750 | ||||||||
\(442\) | −6.06537 | −0.288500 | ||||||||
\(443\) | −26.4873 | −1.25845 | −0.629225 | − | 0.777223i | \(-0.716627\pi\) | ||||
−0.629225 | + | 0.777223i | \(0.716627\pi\) | |||||||
\(444\) | −26.8622 | −1.27482 | ||||||||
\(445\) | 0.725334 | 0.0343841 | ||||||||
\(446\) | −12.8362 | −0.607810 | ||||||||
\(447\) | −1.89109 | −0.0894457 | ||||||||
\(448\) | −8.86027 | −0.418609 | ||||||||
\(449\) | 29.1325 | 1.37485 | 0.687423 | − | 0.726257i | \(-0.258742\pi\) | ||||
0.687423 | + | 0.726257i | \(0.258742\pi\) | |||||||
\(450\) | −4.73947 | −0.223421 | ||||||||
\(451\) | 7.65235 | 0.360335 | ||||||||
\(452\) | 17.8990 | 0.841898 | ||||||||
\(453\) | −26.8546 | −1.26174 | ||||||||
\(454\) | −14.8461 | −0.696764 | ||||||||
\(455\) | −3.75614 | −0.176090 | ||||||||
\(456\) | −12.0531 | −0.564440 | ||||||||
\(457\) | 21.4931 | 1.00541 | 0.502703 | − | 0.864459i | \(-0.332339\pi\) | ||||
0.502703 | + | 0.864459i | \(0.332339\pi\) | |||||||
\(458\) | −1.58055 | −0.0738542 | ||||||||
\(459\) | 81.4479 | 3.80166 | ||||||||
\(460\) | 13.0361 | 0.607810 | ||||||||
\(461\) | −7.98018 | −0.371674 | −0.185837 | − | 0.982581i | \(-0.559500\pi\) | ||||
−0.185837 | + | 0.982581i | \(0.559500\pi\) | |||||||
\(462\) | 8.34749 | 0.388360 | ||||||||
\(463\) | 16.0042 | 0.743779 | 0.371889 | − | 0.928277i | \(-0.378710\pi\) | ||||
0.371889 | + | 0.928277i | \(0.378710\pi\) | |||||||
\(464\) | 3.11273 | 0.144505 | ||||||||
\(465\) | −23.0763 | −1.07014 | ||||||||
\(466\) | −14.5061 | −0.671980 | ||||||||
\(467\) | −32.8843 | −1.52170 | −0.760851 | − | 0.648926i | \(-0.775218\pi\) | ||||
−0.760851 | + | 0.648926i | \(0.775218\pi\) | |||||||
\(468\) | −9.42230 | −0.435546 | ||||||||
\(469\) | 10.4537 | 0.482707 | ||||||||
\(470\) | −7.18117 | −0.331243 | ||||||||
\(471\) | 15.7242 | 0.724534 | ||||||||
\(472\) | 21.3699 | 0.983627 | ||||||||
\(473\) | 8.29774 | 0.381530 | ||||||||
\(474\) | −36.9584 | −1.69756 | ||||||||
\(475\) | −1.53458 | −0.0704115 | ||||||||
\(476\) | 41.9219 | 1.92149 | ||||||||
\(477\) | −19.6603 | −0.900182 | ||||||||
\(478\) | −1.00726 | −0.0460708 | ||||||||
\(479\) | 26.6751 | 1.21882 | 0.609408 | − | 0.792857i | \(-0.291407\pi\) | ||||
0.609408 | + | 0.792857i | \(0.291407\pi\) | |||||||
\(480\) | −17.9311 | −0.818438 | ||||||||
\(481\) | 6.23870 | 0.284460 | ||||||||
\(482\) | −14.4942 | −0.660193 | ||||||||
\(483\) | 101.071 | 4.59887 | ||||||||
\(484\) | −1.44429 | −0.0656497 | ||||||||
\(485\) | 18.9489 | 0.860423 | ||||||||
\(486\) | −5.18737 | −0.235304 | ||||||||
\(487\) | −27.0336 | −1.22501 | −0.612504 | − | 0.790467i | \(-0.709838\pi\) | ||||
−0.612504 | + | 0.790467i | \(0.709838\pi\) | |||||||
\(488\) | −20.4158 | −0.924181 | ||||||||
\(489\) | −32.2455 | −1.45819 | ||||||||
\(490\) | −4.77065 | −0.215516 | ||||||||
\(491\) | 32.6940 | 1.47546 | 0.737731 | − | 0.675095i | \(-0.235898\pi\) | ||||
0.737731 | + | 0.675095i | \(0.235898\pi\) | |||||||
\(492\) | −33.8094 | −1.52424 | ||||||||
\(493\) | 25.3261 | 1.14063 | ||||||||
\(494\) | 1.17384 | 0.0528135 | ||||||||
\(495\) | 6.35779 | 0.285762 | ||||||||
\(496\) | −7.35175 | −0.330103 | ||||||||
\(497\) | 11.6376 | 0.522016 | ||||||||
\(498\) | 4.04298 | 0.181170 | ||||||||
\(499\) | 6.50850 | 0.291361 | 0.145680 | − | 0.989332i | \(-0.453463\pi\) | ||||
0.145680 | + | 0.989332i | \(0.453463\pi\) | |||||||
\(500\) | −1.44429 | −0.0645907 | ||||||||
\(501\) | 3.03334 | 0.135520 | ||||||||
\(502\) | −3.69984 | −0.165132 | ||||||||
\(503\) | 34.5960 | 1.54256 | 0.771280 | − | 0.636495i | \(-0.219617\pi\) | ||||
0.771280 | + | 0.636495i | \(0.219617\pi\) | |||||||
\(504\) | −59.7552 | −2.66171 | ||||||||
\(505\) | 2.13994 | 0.0952263 | ||||||||
\(506\) | 6.72844 | 0.299116 | ||||||||
\(507\) | −36.5468 | −1.62310 | ||||||||
\(508\) | −23.7851 | −1.05529 | ||||||||
\(509\) | 24.2189 | 1.07348 | 0.536741 | − | 0.843747i | \(-0.319655\pi\) | ||||
0.536741 | + | 0.843747i | \(0.319655\pi\) | |||||||
\(510\) | −18.0821 | −0.800689 | ||||||||
\(511\) | −3.66055 | −0.161933 | ||||||||
\(512\) | −10.7171 | −0.473634 | ||||||||
\(513\) | −15.7627 | −0.695941 | ||||||||
\(514\) | −5.18791 | −0.228829 | ||||||||
\(515\) | −5.76145 | −0.253880 | ||||||||
\(516\) | −36.6608 | −1.61390 | ||||||||
\(517\) | 9.63324 | 0.423669 | ||||||||
\(518\) | 16.5908 | 0.728960 | ||||||||
\(519\) | −13.0823 | −0.574250 | ||||||||
\(520\) | 2.63462 | 0.115536 | ||||||||
\(521\) | 24.2739 | 1.06346 | 0.531730 | − | 0.846914i | \(-0.321542\pi\) | ||||
0.531730 | + | 0.846914i | \(0.321542\pi\) | |||||||
\(522\) | −15.1377 | −0.662558 | ||||||||
\(523\) | −35.7848 | −1.56476 | −0.782380 | − | 0.622802i | \(-0.785994\pi\) | ||||
−0.782380 | + | 0.622802i | \(0.785994\pi\) | |||||||
\(524\) | 0.321840 | 0.0140596 | ||||||||
\(525\) | −11.1978 | −0.488712 | ||||||||
\(526\) | 16.0969 | 0.701860 | ||||||||
\(527\) | −59.8161 | −2.60563 | ||||||||
\(528\) | 2.98125 | 0.129742 | ||||||||
\(529\) | 58.4673 | 2.54206 | ||||||||
\(530\) | 2.30519 | 0.100131 | ||||||||
\(531\) | 52.9157 | 2.29635 | ||||||||
\(532\) | −8.11319 | −0.351752 | ||||||||
\(533\) | 7.85218 | 0.340116 | ||||||||
\(534\) | −1.65405 | −0.0715776 | ||||||||
\(535\) | −17.7209 | −0.766141 | ||||||||
\(536\) | −7.33241 | −0.316712 | ||||||||
\(537\) | 7.64669 | 0.329979 | ||||||||
\(538\) | 18.8259 | 0.811643 | ||||||||
\(539\) | 6.39962 | 0.275651 | ||||||||
\(540\) | −14.8353 | −0.638409 | ||||||||
\(541\) | −4.42411 | −0.190207 | −0.0951037 | − | 0.995467i | \(-0.530318\pi\) | ||||
−0.0951037 | + | 0.995467i | \(0.530318\pi\) | |||||||
\(542\) | 0.0651390 | 0.00279796 | ||||||||
\(543\) | 10.1229 | 0.434416 | ||||||||
\(544\) | −46.4792 | −1.99278 | ||||||||
\(545\) | 10.8333 | 0.464048 | ||||||||
\(546\) | 8.56547 | 0.366568 | ||||||||
\(547\) | −8.59061 | −0.367308 | −0.183654 | − | 0.982991i | \(-0.558793\pi\) | ||||
−0.183654 | + | 0.982991i | \(0.558793\pi\) | |||||||
\(548\) | −0.400430 | −0.0171055 | ||||||||
\(549\) | −50.5534 | −2.15757 | ||||||||
\(550\) | −0.745458 | −0.0317864 | ||||||||
\(551\) | −4.90140 | −0.208807 | ||||||||
\(552\) | −70.8927 | −3.01739 | ||||||||
\(553\) | −59.3266 | −2.52283 | ||||||||
\(554\) | 11.6172 | 0.493567 | ||||||||
\(555\) | 18.5988 | 0.789477 | ||||||||
\(556\) | −10.1180 | −0.429097 | ||||||||
\(557\) | −18.6859 | −0.791745 | −0.395873 | − | 0.918305i | \(-0.629558\pi\) | ||||
−0.395873 | + | 0.918305i | \(0.629558\pi\) | |||||||
\(558\) | 35.7527 | 1.51353 | ||||||||
\(559\) | 8.51442 | 0.360121 | ||||||||
\(560\) | −3.56745 | −0.150752 | ||||||||
\(561\) | 24.2564 | 1.02411 | ||||||||
\(562\) | 17.3144 | 0.730366 | ||||||||
\(563\) | −8.39664 | −0.353876 | −0.176938 | − | 0.984222i | \(-0.556619\pi\) | ||||
−0.176938 | + | 0.984222i | \(0.556619\pi\) | |||||||
\(564\) | −42.5612 | −1.79215 | ||||||||
\(565\) | −12.3929 | −0.521374 | ||||||||
\(566\) | 1.66150 | 0.0698382 | ||||||||
\(567\) | −45.2010 | −1.89826 | ||||||||
\(568\) | −8.16279 | −0.342503 | ||||||||
\(569\) | 32.4465 | 1.36023 | 0.680113 | − | 0.733107i | \(-0.261931\pi\) | ||||
0.680113 | + | 0.733107i | \(0.261931\pi\) | |||||||
\(570\) | 3.49945 | 0.146576 | ||||||||
\(571\) | 10.5141 | 0.440000 | 0.220000 | − | 0.975500i | \(-0.429394\pi\) | ||||
0.220000 | + | 0.975500i | \(0.429394\pi\) | |||||||
\(572\) | −1.48201 | −0.0619659 | ||||||||
\(573\) | 72.5584 | 3.03117 | ||||||||
\(574\) | 20.8816 | 0.871582 | ||||||||
\(575\) | −9.02592 | −0.376407 | ||||||||
\(576\) | 15.3889 | 0.641204 | ||||||||
\(577\) | −11.6334 | −0.484304 | −0.242152 | − | 0.970238i | \(-0.577853\pi\) | ||||
−0.242152 | + | 0.970238i | \(0.577853\pi\) | |||||||
\(578\) | −34.1980 | −1.42245 | ||||||||
\(579\) | 29.2690 | 1.21638 | ||||||||
\(580\) | −4.61302 | −0.191545 | ||||||||
\(581\) | 6.48990 | 0.269246 | ||||||||
\(582\) | −43.2109 | −1.79115 | ||||||||
\(583\) | −3.09231 | −0.128070 | ||||||||
\(584\) | 2.56757 | 0.106247 | ||||||||
\(585\) | 6.52381 | 0.269727 | ||||||||
\(586\) | 0.646976 | 0.0267263 | ||||||||
\(587\) | 0.883663 | 0.0364727 | 0.0182363 | − | 0.999834i | \(-0.494195\pi\) | ||||
0.0182363 | + | 0.999834i | \(0.494195\pi\) | |||||||
\(588\) | −28.2746 | −1.16602 | ||||||||
\(589\) | 11.5763 | 0.476993 | ||||||||
\(590\) | −6.20442 | −0.255432 | ||||||||
\(591\) | 40.0754 | 1.64848 | ||||||||
\(592\) | 5.92531 | 0.243529 | ||||||||
\(593\) | 2.67385 | 0.109802 | 0.0549008 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549008 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(594\) | −7.65709 | −0.314174 | ||||||||
\(595\) | −29.0259 | −1.18995 | ||||||||
\(596\) | 0.892856 | 0.0365728 | ||||||||
\(597\) | −38.5734 | −1.57870 | ||||||||
\(598\) | 6.90414 | 0.282331 | ||||||||
\(599\) | −4.46895 | −0.182596 | −0.0912982 | − | 0.995824i | \(-0.529102\pi\) | ||||
−0.0912982 | + | 0.995824i | \(0.529102\pi\) | |||||||
\(600\) | 7.85434 | 0.320652 | ||||||||
\(601\) | −25.3077 | −1.03232 | −0.516162 | − | 0.856491i | \(-0.672640\pi\) | ||||
−0.516162 | + | 0.856491i | \(0.672640\pi\) | |||||||
\(602\) | 22.6427 | 0.922849 | ||||||||
\(603\) | −18.1564 | −0.739386 | ||||||||
\(604\) | 12.6791 | 0.515903 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −4.87992 | −0.198233 | ||||||||
\(607\) | −26.9252 | −1.09286 | −0.546431 | − | 0.837504i | \(-0.684014\pi\) | ||||
−0.546431 | + | 0.837504i | \(0.684014\pi\) | |||||||
\(608\) | 8.99518 | 0.364803 | ||||||||
\(609\) | −35.7654 | −1.44929 | ||||||||
\(610\) | 5.92744 | 0.239995 | ||||||||
\(611\) | 9.88479 | 0.399896 | ||||||||
\(612\) | −72.8117 | −2.94324 | ||||||||
\(613\) | 5.84970 | 0.236267 | 0.118133 | − | 0.992998i | \(-0.462309\pi\) | ||||
0.118133 | + | 0.992998i | \(0.462309\pi\) | |||||||
\(614\) | −16.2307 | −0.655017 | ||||||||
\(615\) | 23.4089 | 0.943939 | ||||||||
\(616\) | −9.39873 | −0.378686 | ||||||||
\(617\) | 25.6742 | 1.03360 | 0.516802 | − | 0.856105i | \(-0.327122\pi\) | ||||
0.516802 | + | 0.856105i | \(0.327122\pi\) | |||||||
\(618\) | 13.1384 | 0.528503 | ||||||||
\(619\) | 28.5604 | 1.14794 | 0.573969 | − | 0.818877i | \(-0.305403\pi\) | ||||
0.573969 | + | 0.818877i | \(0.305403\pi\) | |||||||
\(620\) | 10.8952 | 0.437561 | ||||||||
\(621\) | −92.7112 | −3.72037 | ||||||||
\(622\) | 17.3727 | 0.696583 | ||||||||
\(623\) | −2.65512 | −0.106375 | ||||||||
\(624\) | 3.05910 | 0.122462 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.7397 | −0.629086 | ||||||||
\(627\) | −4.69437 | −0.187475 | ||||||||
\(628\) | −7.42400 | −0.296250 | ||||||||
\(629\) | 48.2101 | 1.92226 | ||||||||
\(630\) | 17.3490 | 0.691203 | ||||||||
\(631\) | −13.7548 | −0.547570 | −0.273785 | − | 0.961791i | \(-0.588276\pi\) | ||||
−0.273785 | + | 0.961791i | \(0.588276\pi\) | |||||||
\(632\) | 41.6128 | 1.65527 | ||||||||
\(633\) | 41.8245 | 1.66237 | ||||||||
\(634\) | 0.237738 | 0.00944179 | ||||||||
\(635\) | 16.4683 | 0.653526 | ||||||||
\(636\) | 13.6623 | 0.541747 | ||||||||
\(637\) | 6.56674 | 0.260184 | ||||||||
\(638\) | −2.38096 | −0.0942632 | ||||||||
\(639\) | −20.2126 | −0.799598 | ||||||||
\(640\) | 9.91893 | 0.392080 | ||||||||
\(641\) | −37.3178 | −1.47396 | −0.736982 | − | 0.675912i | \(-0.763750\pi\) | ||||
−0.736982 | + | 0.675912i | \(0.763750\pi\) | |||||||
\(642\) | 40.4106 | 1.59488 | ||||||||
\(643\) | −30.2238 | −1.19191 | −0.595956 | − | 0.803017i | \(-0.703227\pi\) | ||||
−0.595956 | + | 0.803017i | \(0.703227\pi\) | |||||||
\(644\) | −47.7192 | −1.88040 | ||||||||
\(645\) | 25.3832 | 0.999462 | ||||||||
\(646\) | 9.07095 | 0.356892 | ||||||||
\(647\) | 0.269979 | 0.0106140 | 0.00530699 | − | 0.999986i | \(-0.498311\pi\) | ||||
0.00530699 | + | 0.999986i | \(0.498311\pi\) | |||||||
\(648\) | 31.7048 | 1.24548 | ||||||||
\(649\) | 8.32297 | 0.326705 | ||||||||
\(650\) | −0.764924 | −0.0300028 | ||||||||
\(651\) | 84.4719 | 3.31071 | ||||||||
\(652\) | 15.2243 | 0.596231 | ||||||||
\(653\) | −36.8015 | −1.44016 | −0.720078 | − | 0.693893i | \(-0.755894\pi\) | ||||
−0.720078 | + | 0.693893i | \(0.755894\pi\) | |||||||
\(654\) | −24.7042 | −0.966010 | ||||||||
\(655\) | −0.222835 | −0.00870690 | ||||||||
\(656\) | 7.45773 | 0.291175 | ||||||||
\(657\) | 6.35779 | 0.248041 | ||||||||
\(658\) | 26.2870 | 1.02478 | ||||||||
\(659\) | −11.7704 | −0.458510 | −0.229255 | − | 0.973366i | \(-0.573629\pi\) | ||||
−0.229255 | + | 0.973366i | \(0.573629\pi\) | |||||||
\(660\) | −4.41817 | −0.171977 | ||||||||
\(661\) | −26.0057 | −1.01151 | −0.505753 | − | 0.862679i | \(-0.668785\pi\) | ||||
−0.505753 | + | 0.862679i | \(0.668785\pi\) | |||||||
\(662\) | 20.1740 | 0.784085 | ||||||||
\(663\) | 24.8898 | 0.966640 | ||||||||
\(664\) | −4.55213 | −0.176657 | ||||||||
\(665\) | 5.61742 | 0.217834 | ||||||||
\(666\) | −28.8157 | −1.11658 | ||||||||
\(667\) | −28.8284 | −1.11624 | ||||||||
\(668\) | −1.43215 | −0.0554117 | ||||||||
\(669\) | 52.6743 | 2.03651 | ||||||||
\(670\) | 2.12886 | 0.0822449 | ||||||||
\(671\) | −7.95140 | −0.306961 | ||||||||
\(672\) | 65.6376 | 2.53203 | ||||||||
\(673\) | −44.5215 | −1.71618 | −0.858088 | − | 0.513503i | \(-0.828348\pi\) | ||||
−0.858088 | + | 0.513503i | \(0.828348\pi\) | |||||||
\(674\) | −8.56059 | −0.329742 | ||||||||
\(675\) | 10.2717 | 0.395356 | ||||||||
\(676\) | 17.2551 | 0.663658 | ||||||||
\(677\) | −38.7167 | −1.48801 | −0.744003 | − | 0.668177i | \(-0.767075\pi\) | ||||
−0.744003 | + | 0.668177i | \(0.767075\pi\) | |||||||
\(678\) | 28.2607 | 1.08535 | ||||||||
\(679\) | −69.3632 | −2.66192 | ||||||||
\(680\) | 20.3593 | 0.780743 | ||||||||
\(681\) | 60.9224 | 2.33455 | ||||||||
\(682\) | 5.62344 | 0.215333 | ||||||||
\(683\) | 32.4364 | 1.24114 | 0.620572 | − | 0.784149i | \(-0.286900\pi\) | ||||
0.620572 | + | 0.784149i | \(0.286900\pi\) | |||||||
\(684\) | 14.0913 | 0.538795 | ||||||||
\(685\) | 0.277250 | 0.0105932 | ||||||||
\(686\) | −1.63830 | −0.0625504 | ||||||||
\(687\) | 6.48592 | 0.247453 | ||||||||
\(688\) | 8.08670 | 0.308303 | ||||||||
\(689\) | −3.17306 | −0.120884 | ||||||||
\(690\) | 20.5827 | 0.783568 | ||||||||
\(691\) | 9.99291 | 0.380148 | 0.190074 | − | 0.981770i | \(-0.439127\pi\) | ||||
0.190074 | + | 0.981770i | \(0.439127\pi\) | |||||||
\(692\) | 6.17665 | 0.234801 | ||||||||
\(693\) | −23.2730 | −0.884069 | ||||||||
\(694\) | 10.1169 | 0.384032 | ||||||||
\(695\) | 7.00548 | 0.265733 | ||||||||
\(696\) | 25.0865 | 0.950900 | ||||||||
\(697\) | 60.6784 | 2.29836 | ||||||||
\(698\) | −13.6327 | −0.516005 | ||||||||
\(699\) | 59.5269 | 2.25151 | ||||||||
\(700\) | 5.28691 | 0.199826 | ||||||||
\(701\) | −23.9841 | −0.905867 | −0.452934 | − | 0.891544i | \(-0.649623\pi\) | ||||
−0.452934 | + | 0.891544i | \(0.649623\pi\) | |||||||
\(702\) | −7.85704 | −0.296545 | ||||||||
\(703\) | −9.33017 | −0.351894 | ||||||||
\(704\) | 2.42048 | 0.0912251 | ||||||||
\(705\) | 29.4686 | 1.10985 | ||||||||
\(706\) | 19.1597 | 0.721087 | ||||||||
\(707\) | −7.83337 | −0.294604 | ||||||||
\(708\) | −36.7723 | −1.38199 | ||||||||
\(709\) | 17.0050 | 0.638637 | 0.319319 | − | 0.947647i | \(-0.396546\pi\) | ||||
0.319319 | + | 0.947647i | \(0.396546\pi\) | |||||||
\(710\) | 2.36995 | 0.0889426 | ||||||||
\(711\) | 103.041 | 3.86434 | ||||||||
\(712\) | 1.86235 | 0.0697945 | ||||||||
\(713\) | 68.0880 | 2.54992 | ||||||||
\(714\) | 66.1905 | 2.47712 | ||||||||
\(715\) | 1.02611 | 0.0383745 | ||||||||
\(716\) | −3.61029 | −0.134923 | ||||||||
\(717\) | 4.13336 | 0.154363 | ||||||||
\(718\) | 3.93354 | 0.146799 | ||||||||
\(719\) | 2.46818 | 0.0920478 | 0.0460239 | − | 0.998940i | \(-0.485345\pi\) | ||||
0.0460239 | + | 0.998940i | \(0.485345\pi\) | |||||||
\(720\) | 6.19610 | 0.230915 | ||||||||
\(721\) | 21.0901 | 0.785436 | ||||||||
\(722\) | 12.4082 | 0.461785 | ||||||||
\(723\) | 59.4782 | 2.21202 | ||||||||
\(724\) | −4.77941 | −0.177625 | ||||||||
\(725\) | 3.19396 | 0.118621 | ||||||||
\(726\) | −2.28039 | −0.0846333 | ||||||||
\(727\) | −18.8451 | −0.698924 | −0.349462 | − | 0.936950i | \(-0.613636\pi\) | ||||
−0.349462 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(728\) | −9.64417 | −0.357437 | ||||||||
\(729\) | −15.7576 | −0.583615 | ||||||||
\(730\) | −0.745458 | −0.0275906 | ||||||||
\(731\) | 65.7959 | 2.43355 | ||||||||
\(732\) | 35.1306 | 1.29846 | ||||||||
\(733\) | 8.26369 | 0.305226 | 0.152613 | − | 0.988286i | \(-0.451231\pi\) | ||||
0.152613 | + | 0.988286i | \(0.451231\pi\) | |||||||
\(734\) | 15.6917 | 0.579191 | ||||||||
\(735\) | 19.5768 | 0.722100 | ||||||||
\(736\) | 52.9068 | 1.95017 | ||||||||
\(737\) | −2.85577 | −0.105194 | ||||||||
\(738\) | −36.2681 | −1.33505 | ||||||||
\(739\) | −38.7957 | −1.42712 | −0.713562 | − | 0.700592i | \(-0.752919\pi\) | ||||
−0.713562 | + | 0.700592i | \(0.752919\pi\) | |||||||
\(740\) | −8.78121 | −0.322804 | ||||||||
\(741\) | −4.81695 | −0.176955 | ||||||||
\(742\) | −8.43826 | −0.309778 | ||||||||
\(743\) | −12.6764 | −0.465052 | −0.232526 | − | 0.972590i | \(-0.574699\pi\) | ||||
−0.232526 | + | 0.972590i | \(0.574699\pi\) | |||||||
\(744\) | −59.2501 | −2.17221 | ||||||||
\(745\) | −0.618196 | −0.0226490 | ||||||||
\(746\) | −20.3018 | −0.743302 | ||||||||
\(747\) | −11.2719 | −0.412418 | ||||||||
\(748\) | −11.4523 | −0.418739 | ||||||||
\(749\) | 64.8682 | 2.37023 | ||||||||
\(750\) | −2.28039 | −0.0832682 | ||||||||
\(751\) | −29.8876 | −1.09061 | −0.545307 | − | 0.838236i | \(-0.683587\pi\) | ||||
−0.545307 | + | 0.838236i | \(0.683587\pi\) | |||||||
\(752\) | 9.38824 | 0.342354 | ||||||||
\(753\) | 15.1826 | 0.553285 | ||||||||
\(754\) | −2.44314 | −0.0889738 | ||||||||
\(755\) | −8.77873 | −0.319491 | ||||||||
\(756\) | 54.3053 | 1.97506 | ||||||||
\(757\) | −19.8595 | −0.721807 | −0.360903 | − | 0.932603i | \(-0.617532\pi\) | ||||
−0.360903 | + | 0.932603i | \(0.617532\pi\) | |||||||
\(758\) | 2.45900 | 0.0893149 | ||||||||
\(759\) | −27.6108 | −1.00221 | ||||||||
\(760\) | −3.94016 | −0.142924 | ||||||||
\(761\) | −22.5344 | −0.816870 | −0.408435 | − | 0.912787i | \(-0.633925\pi\) | ||||
−0.408435 | + | 0.912787i | \(0.633925\pi\) | |||||||
\(762\) | −37.5543 | −1.36045 | ||||||||
\(763\) | −39.6558 | −1.43564 | ||||||||
\(764\) | −34.2575 | −1.23939 | ||||||||
\(765\) | 50.4134 | 1.82270 | ||||||||
\(766\) | 3.83281 | 0.138485 | ||||||||
\(767\) | 8.54031 | 0.308373 | ||||||||
\(768\) | −37.4278 | −1.35056 | ||||||||
\(769\) | −33.6335 | −1.21286 | −0.606428 | − | 0.795139i | \(-0.707398\pi\) | ||||
−0.606428 | + | 0.795139i | \(0.707398\pi\) | |||||||
\(770\) | 2.72879 | 0.0983386 | ||||||||
\(771\) | 21.2891 | 0.766707 | ||||||||
\(772\) | −13.8190 | −0.497356 | ||||||||
\(773\) | −3.81775 | −0.137315 | −0.0686575 | − | 0.997640i | \(-0.521872\pi\) | ||||
−0.0686575 | + | 0.997640i | \(0.521872\pi\) | |||||||
\(774\) | −39.3268 | −1.41357 | ||||||||
\(775\) | −7.54361 | −0.270974 | ||||||||
\(776\) | 48.6526 | 1.74653 | ||||||||
\(777\) | −68.0820 | −2.44243 | ||||||||
\(778\) | 4.04630 | 0.145067 | ||||||||
\(779\) | −11.7432 | −0.420743 | ||||||||
\(780\) | −4.53354 | −0.162327 | ||||||||
\(781\) | −3.17918 | −0.113760 | ||||||||
\(782\) | 53.3524 | 1.90788 | ||||||||
\(783\) | 32.8073 | 1.17244 | ||||||||
\(784\) | 6.23686 | 0.222745 | ||||||||
\(785\) | 5.14023 | 0.183463 | ||||||||
\(786\) | 0.508152 | 0.0181252 | ||||||||
\(787\) | −16.4419 | −0.586089 | −0.293045 | − | 0.956099i | \(-0.594668\pi\) | ||||
−0.293045 | + | 0.956099i | \(0.594668\pi\) | |||||||
\(788\) | −18.9211 | −0.674037 | ||||||||
\(789\) | −66.0552 | −2.35163 | ||||||||
\(790\) | −12.0817 | −0.429846 | ||||||||
\(791\) | 45.3649 | 1.61299 | ||||||||
\(792\) | 16.3241 | 0.580052 | ||||||||
\(793\) | −8.15904 | −0.289736 | ||||||||
\(794\) | 24.5843 | 0.872465 | ||||||||
\(795\) | −9.45954 | −0.335495 | ||||||||
\(796\) | 18.2119 | 0.645505 | ||||||||
\(797\) | 38.6822 | 1.37020 | 0.685098 | − | 0.728451i | \(-0.259760\pi\) | ||||
0.685098 | + | 0.728451i | \(0.259760\pi\) | |||||||
\(798\) | −12.8099 | −0.453466 | ||||||||
\(799\) | 76.3856 | 2.70233 | ||||||||
\(800\) | −5.86165 | −0.207241 | ||||||||
\(801\) | 4.61152 | 0.162940 | ||||||||
\(802\) | −12.2225 | −0.431591 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 12.6173 | 0.444977 | ||||||||
\(805\) | 33.0398 | 1.16450 | ||||||||
\(806\) | 5.77029 | 0.203250 | ||||||||
\(807\) | −77.2538 | −2.71946 | ||||||||
\(808\) | 5.49447 | 0.193295 | ||||||||
\(809\) | 28.5008 | 1.00203 | 0.501017 | − | 0.865438i | \(-0.332960\pi\) | ||||
0.501017 | + | 0.865438i | \(0.332960\pi\) | |||||||
\(810\) | −9.20502 | −0.323432 | ||||||||
\(811\) | −13.3390 | −0.468396 | −0.234198 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234198 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(812\) | 16.8862 | 0.592588 | ||||||||
\(813\) | −0.267304 | −0.00937475 | ||||||||
\(814\) | −4.53234 | −0.158858 | ||||||||
\(815\) | −10.5410 | −0.369236 | ||||||||
\(816\) | 23.6395 | 0.827547 | ||||||||
\(817\) | −12.7336 | −0.445491 | ||||||||
\(818\) | 21.3280 | 0.745715 | ||||||||
\(819\) | −23.8807 | −0.834461 | ||||||||
\(820\) | −11.0522 | −0.385961 | ||||||||
\(821\) | 22.4293 | 0.782787 | 0.391393 | − | 0.920223i | \(-0.371993\pi\) | ||||
0.391393 | + | 0.920223i | \(0.371993\pi\) | |||||||
\(822\) | −0.632239 | −0.0220519 | ||||||||
\(823\) | −7.55118 | −0.263218 | −0.131609 | − | 0.991302i | \(-0.542014\pi\) | ||||
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(824\) | −14.7930 | −0.515337 | ||||||||
\(825\) | 3.05905 | 0.106502 | ||||||||
\(826\) | 22.7116 | 0.790238 | ||||||||
\(827\) | −0.858475 | −0.0298521 | −0.0149260 | − | 0.999889i | \(-0.504751\pi\) | ||||
−0.0149260 | + | 0.999889i | \(0.504751\pi\) | |||||||
\(828\) | 82.8807 | 2.88030 | ||||||||
\(829\) | 46.3599 | 1.61015 | 0.805073 | − | 0.593175i | \(-0.202126\pi\) | ||||
0.805073 | + | 0.593175i | \(0.202126\pi\) | |||||||
\(830\) | 1.32164 | 0.0458749 | ||||||||
\(831\) | −47.6721 | −1.65373 | ||||||||
\(832\) | 2.48368 | 0.0861062 | ||||||||
\(833\) | 50.7451 | 1.75821 | ||||||||
\(834\) | −15.9752 | −0.553178 | ||||||||
\(835\) | 0.991594 | 0.0343155 | ||||||||
\(836\) | 2.21639 | 0.0766553 | ||||||||
\(837\) | −77.4854 | −2.67829 | ||||||||
\(838\) | 22.4919 | 0.776970 | ||||||||
\(839\) | 1.05196 | 0.0363178 | 0.0181589 | − | 0.999835i | \(-0.494220\pi\) | ||||
0.0181589 | + | 0.999835i | \(0.494220\pi\) | |||||||
\(840\) | −28.7512 | −0.992011 | ||||||||
\(841\) | −18.7986 | −0.648228 | ||||||||
\(842\) | 11.6018 | 0.399825 | ||||||||
\(843\) | −71.0513 | −2.44714 | ||||||||
\(844\) | −19.7469 | −0.679717 | ||||||||
\(845\) | −11.9471 | −0.410992 | ||||||||
\(846\) | −45.6564 | −1.56970 | ||||||||
\(847\) | −3.66055 | −0.125778 | ||||||||
\(848\) | −3.01367 | −0.103490 | ||||||||
\(849\) | −6.81813 | −0.233998 | ||||||||
\(850\) | −5.91102 | −0.202746 | ||||||||
\(851\) | −54.8770 | −1.88116 | ||||||||
\(852\) | 14.0462 | 0.481214 | ||||||||
\(853\) | −23.3445 | −0.799300 | −0.399650 | − | 0.916668i | \(-0.630868\pi\) | ||||
−0.399650 | + | 0.916668i | \(0.630868\pi\) | |||||||
\(854\) | −21.6977 | −0.742479 | ||||||||
\(855\) | −9.75656 | −0.333667 | ||||||||
\(856\) | −45.4997 | −1.55515 | ||||||||
\(857\) | −8.85205 | −0.302380 | −0.151190 | − | 0.988505i | \(-0.548311\pi\) | ||||
−0.151190 | + | 0.988505i | \(0.548311\pi\) | |||||||
\(858\) | −2.33994 | −0.0798843 | ||||||||
\(859\) | −15.5623 | −0.530977 | −0.265489 | − | 0.964114i | \(-0.585533\pi\) | ||||
−0.265489 | + | 0.964114i | \(0.585533\pi\) | |||||||
\(860\) | −11.9844 | −0.408663 | ||||||||
\(861\) | −85.6896 | −2.92029 | ||||||||
\(862\) | 22.7388 | 0.774485 | ||||||||
\(863\) | 28.5694 | 0.972515 | 0.486258 | − | 0.873816i | \(-0.338362\pi\) | ||||
0.486258 | + | 0.873816i | \(0.338362\pi\) | |||||||
\(864\) | −60.2088 | −2.04835 | ||||||||
\(865\) | −4.27659 | −0.145409 | ||||||||
\(866\) | 20.9120 | 0.710619 | ||||||||
\(867\) | 140.334 | 4.76600 | ||||||||
\(868\) | −39.8823 | −1.35369 | ||||||||
\(869\) | 16.2070 | 0.549786 | ||||||||
\(870\) | −7.28349 | −0.246933 | ||||||||
\(871\) | −2.93035 | −0.0992910 | ||||||||
\(872\) | 27.8153 | 0.941946 | ||||||||
\(873\) | 120.473 | 4.07739 | ||||||||
\(874\) | −10.3254 | −0.349260 | ||||||||
\(875\) | −3.66055 | −0.123749 | ||||||||
\(876\) | −4.41817 | −0.149276 | ||||||||
\(877\) | −51.3452 | −1.73380 | −0.866902 | − | 0.498479i | \(-0.833892\pi\) | ||||
−0.866902 | + | 0.498479i | \(0.833892\pi\) | |||||||
\(878\) | 4.69214 | 0.158352 | ||||||||
\(879\) | −2.65492 | −0.0895483 | ||||||||
\(880\) | 0.974567 | 0.0328527 | ||||||||
\(881\) | −31.6055 | −1.06482 | −0.532408 | − | 0.846488i | \(-0.678713\pi\) | ||||
−0.532408 | + | 0.846488i | \(0.678713\pi\) | |||||||
\(882\) | −30.3308 | −1.02129 | ||||||||
\(883\) | −53.5711 | −1.80281 | −0.901405 | − | 0.432977i | \(-0.857463\pi\) | ||||
−0.901405 | + | 0.432977i | \(0.857463\pi\) | |||||||
\(884\) | −11.7514 | −0.395243 | ||||||||
\(885\) | 25.4604 | 0.855842 | ||||||||
\(886\) | 19.7452 | 0.663352 | ||||||||
\(887\) | −20.1353 | −0.676077 | −0.338038 | − | 0.941132i | \(-0.609763\pi\) | ||||
−0.338038 | + | 0.941132i | \(0.609763\pi\) | |||||||
\(888\) | 47.7539 | 1.60252 | ||||||||
\(889\) | −60.2832 | −2.02183 | ||||||||
\(890\) | −0.540706 | −0.0181245 | ||||||||
\(891\) | 12.3481 | 0.413679 | ||||||||
\(892\) | −24.8695 | −0.832693 | ||||||||
\(893\) | −14.7830 | −0.494694 | ||||||||
\(894\) | 1.40973 | 0.0471484 | ||||||||
\(895\) | 2.49969 | 0.0835555 | ||||||||
\(896\) | −36.3087 | −1.21299 | ||||||||
\(897\) | −28.3318 | −0.945970 | ||||||||
\(898\) | −21.7170 | −0.724707 | ||||||||
\(899\) | −24.0940 | −0.803580 | ||||||||
\(900\) | −9.18251 | −0.306084 | ||||||||
\(901\) | −24.5201 | −0.816884 | ||||||||
\(902\) | −5.70450 | −0.189939 | ||||||||
\(903\) | −92.9164 | −3.09207 | ||||||||
\(904\) | −31.8197 | −1.05831 | ||||||||
\(905\) | 3.30917 | 0.110001 | ||||||||
\(906\) | 20.0189 | 0.665085 | ||||||||
\(907\) | 48.1956 | 1.60031 | 0.800154 | − | 0.599794i | \(-0.204751\pi\) | ||||
0.800154 | + | 0.599794i | \(0.204751\pi\) | |||||||
\(908\) | −28.7638 | −0.954559 | ||||||||
\(909\) | 13.6053 | 0.451260 | ||||||||
\(910\) | 2.80004 | 0.0928205 | ||||||||
\(911\) | 2.65861 | 0.0880838 | 0.0440419 | − | 0.999030i | \(-0.485976\pi\) | ||||
0.0440419 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(912\) | −4.57498 | −0.151493 | ||||||||
\(913\) | −1.77293 | −0.0586754 | ||||||||
\(914\) | −16.0222 | −0.529967 | ||||||||
\(915\) | −24.3237 | −0.804118 | ||||||||
\(916\) | −3.06225 | −0.101179 | ||||||||
\(917\) | 0.815700 | 0.0269368 | ||||||||
\(918\) | −60.7160 | −2.00393 | ||||||||
\(919\) | 34.0241 | 1.12235 | 0.561176 | − | 0.827696i | \(-0.310349\pi\) | ||||
0.561176 | + | 0.827696i | \(0.310349\pi\) | |||||||
\(920\) | −23.1747 | −0.764048 | ||||||||
\(921\) | 66.6040 | 2.19468 | ||||||||
\(922\) | 5.94889 | 0.195916 | ||||||||
\(923\) | −3.26220 | −0.107377 | ||||||||
\(924\) | 16.1729 | 0.532050 | ||||||||
\(925\) | 6.07994 | 0.199907 | ||||||||
\(926\) | −11.9305 | −0.392059 | ||||||||
\(927\) | −36.6301 | −1.20309 | ||||||||
\(928\) | −18.7219 | −0.614576 | ||||||||
\(929\) | 45.1410 | 1.48103 | 0.740514 | − | 0.672041i | \(-0.234582\pi\) | ||||
0.740514 | + | 0.672041i | \(0.234582\pi\) | |||||||
\(930\) | 17.2024 | 0.564089 | ||||||||
\(931\) | −9.82075 | −0.321862 | ||||||||
\(932\) | −28.1049 | −0.920606 | ||||||||
\(933\) | −71.2906 | −2.33395 | ||||||||
\(934\) | 24.5138 | 0.802117 | ||||||||
\(935\) | 7.92938 | 0.259319 | ||||||||
\(936\) | 16.7504 | 0.547503 | ||||||||
\(937\) | 23.6534 | 0.772721 | 0.386361 | − | 0.922348i | \(-0.373732\pi\) | ||||
0.386361 | + | 0.922348i | \(0.373732\pi\) | |||||||
\(938\) | −7.79279 | −0.254444 | ||||||||
\(939\) | 64.5894 | 2.10780 | ||||||||
\(940\) | −13.9132 | −0.453799 | ||||||||
\(941\) | −35.5296 | −1.15823 | −0.579116 | − | 0.815245i | \(-0.696602\pi\) | ||||
−0.579116 | + | 0.815245i | \(0.696602\pi\) | |||||||
\(942\) | −11.7218 | −0.381915 | ||||||||
\(943\) | −69.0695 | −2.24921 | ||||||||
\(944\) | 8.11130 | 0.264000 | ||||||||
\(945\) | −37.5999 | −1.22313 | ||||||||
\(946\) | −6.18561 | −0.201112 | ||||||||
\(947\) | 11.0303 | 0.358437 | 0.179219 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179219 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(948\) | −71.6053 | −2.32563 | ||||||||
\(949\) | 1.02611 | 0.0333090 | ||||||||
\(950\) | 1.14397 | 0.0371152 | ||||||||
\(951\) | −0.975580 | −0.0316353 | ||||||||
\(952\) | −74.5262 | −2.41541 | ||||||||
\(953\) | −39.0570 | −1.26518 | −0.632590 | − | 0.774487i | \(-0.718008\pi\) | ||||
−0.632590 | + | 0.774487i | \(0.718008\pi\) | |||||||
\(954\) | 14.6559 | 0.474503 | ||||||||
\(955\) | 23.7192 | 0.767537 | ||||||||
\(956\) | −1.95151 | −0.0631165 | ||||||||
\(957\) | 9.77049 | 0.315835 | ||||||||
\(958\) | −19.8851 | −0.642460 | ||||||||
\(959\) | −1.01489 | −0.0327724 | ||||||||
\(960\) | 7.40436 | 0.238975 | ||||||||
\(961\) | 25.9060 | 0.835678 | ||||||||
\(962\) | −4.65069 | −0.149944 | ||||||||
\(963\) | −112.666 | −3.63060 | ||||||||
\(964\) | −28.0819 | −0.904457 | ||||||||
\(965\) | 9.56799 | 0.308004 | ||||||||
\(966\) | −75.3438 | −2.42415 | ||||||||
\(967\) | −43.6286 | −1.40300 | −0.701500 | − | 0.712669i | \(-0.747486\pi\) | ||||
−0.701500 | + | 0.712669i | \(0.747486\pi\) | |||||||
\(968\) | 2.56757 | 0.0825250 | ||||||||
\(969\) | −37.2234 | −1.19579 | ||||||||
\(970\) | −14.1256 | −0.453545 | ||||||||
\(971\) | −29.7850 | −0.955847 | −0.477924 | − | 0.878401i | \(-0.658610\pi\) | ||||
−0.477924 | + | 0.878401i | \(0.658610\pi\) | |||||||
\(972\) | −10.0503 | −0.322364 | ||||||||
\(973\) | −25.6439 | −0.822106 | ||||||||
\(974\) | 20.1524 | 0.645724 | ||||||||
\(975\) | 3.13893 | 0.100526 | ||||||||
\(976\) | −7.74918 | −0.248045 | ||||||||
\(977\) | −42.9978 | −1.37562 | −0.687810 | − | 0.725890i | \(-0.741428\pi\) | ||||
−0.687810 | + | 0.725890i | \(0.741428\pi\) | |||||||
\(978\) | 24.0377 | 0.768640 | ||||||||
\(979\) | 0.725334 | 0.0231818 | ||||||||
\(980\) | −9.24293 | −0.295255 | ||||||||
\(981\) | 68.8759 | 2.19904 | ||||||||
\(982\) | −24.3720 | −0.777742 | ||||||||
\(983\) | 49.6405 | 1.58329 | 0.791643 | − | 0.610984i | \(-0.209226\pi\) | ||||
0.791643 | + | 0.610984i | \(0.209226\pi\) | |||||||
\(984\) | 60.1042 | 1.91605 | ||||||||
\(985\) | 13.1006 | 0.417420 | ||||||||
\(986\) | −18.8796 | −0.601248 | ||||||||
\(987\) | −107.871 | −3.43358 | ||||||||
\(988\) | 2.27426 | 0.0723540 | ||||||||
\(989\) | −74.8947 | −2.38151 | ||||||||
\(990\) | −4.73947 | −0.150630 | ||||||||
\(991\) | 48.0861 | 1.52751 | 0.763753 | − | 0.645509i | \(-0.223355\pi\) | ||||
0.763753 | + | 0.645509i | \(0.223355\pi\) | |||||||
\(992\) | 44.2180 | 1.40392 | ||||||||
\(993\) | −82.7858 | −2.62713 | ||||||||
\(994\) | −8.67531 | −0.275164 | ||||||||
\(995\) | −12.6096 | −0.399751 | ||||||||
\(996\) | 7.83310 | 0.248201 | ||||||||
\(997\) | −37.4483 | −1.18600 | −0.592999 | − | 0.805203i | \(-0.702056\pi\) | ||||
−0.592999 | + | 0.805203i | \(0.702056\pi\) | |||||||
\(998\) | −4.85181 | −0.153581 | ||||||||
\(999\) | 62.4510 | 1.97586 |
(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 | 4015.2.a.h.1.13 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.13 | ✓ | 37 | 1.1 | even | 1 | trivial |