Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.33 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.177306 | 0.125375 | 0.0626873 | − | 0.998033i | \(-0.480033\pi\) | ||||
0.0626873 | + | 0.998033i | \(0.480033\pi\) | |||||||
\(3\) | −1.77336 | −1.02385 | −0.511925 | − | 0.859030i | \(-0.671067\pi\) | ||||
−0.511925 | + | 0.859030i | \(0.671067\pi\) | |||||||
\(4\) | −1.96856 | −0.984281 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.314428 | −0.128365 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.703651 | −0.248778 | ||||||||
\(9\) | 0.144804 | 0.0482679 | ||||||||
\(10\) | −0.177306 | −0.0560692 | ||||||||
\(11\) | −0.639776 | −0.192900 | −0.0964499 | − | 0.995338i | \(-0.530749\pi\) | ||||
−0.0964499 | + | 0.995338i | \(0.530749\pi\) | |||||||
\(12\) | 3.49097 | 1.00776 | ||||||||
\(13\) | −2.64003 | −0.732212 | −0.366106 | − | 0.930573i | \(-0.619309\pi\) | ||||
−0.366106 | + | 0.930573i | \(0.619309\pi\) | |||||||
\(14\) | −0.177306 | −0.0473871 | ||||||||
\(15\) | 1.77336 | 0.457879 | ||||||||
\(16\) | 3.81236 | 0.953091 | ||||||||
\(17\) | 6.32556 | 1.53417 | 0.767087 | − | 0.641543i | \(-0.221705\pi\) | ||||
0.767087 | + | 0.641543i | \(0.221705\pi\) | |||||||
\(18\) | 0.0256746 | 0.00605156 | ||||||||
\(19\) | −6.95789 | −1.59625 | −0.798125 | − | 0.602492i | \(-0.794175\pi\) | ||||
−0.798125 | + | 0.602492i | \(0.794175\pi\) | |||||||
\(20\) | 1.96856 | 0.440184 | ||||||||
\(21\) | 1.77336 | 0.386979 | ||||||||
\(22\) | −0.113436 | −0.0241847 | ||||||||
\(23\) | −3.01957 | −0.629624 | −0.314812 | − | 0.949154i | \(-0.601942\pi\) | ||||
−0.314812 | + | 0.949154i | \(0.601942\pi\) | |||||||
\(24\) | 1.24783 | 0.254712 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.468094 | −0.0918007 | ||||||||
\(27\) | 5.06329 | 0.974430 | ||||||||
\(28\) | 1.96856 | 0.372023 | ||||||||
\(29\) | −1.66003 | −0.308260 | −0.154130 | − | 0.988051i | \(-0.549257\pi\) | ||||
−0.154130 | + | 0.988051i | \(0.549257\pi\) | |||||||
\(30\) | 0.314428 | 0.0574064 | ||||||||
\(31\) | −5.14184 | −0.923502 | −0.461751 | − | 0.887010i | \(-0.652779\pi\) | ||||
−0.461751 | + | 0.887010i | \(0.652779\pi\) | |||||||
\(32\) | 2.08326 | 0.368272 | ||||||||
\(33\) | 1.13455 | 0.197500 | ||||||||
\(34\) | 1.12156 | 0.192346 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.285055 | −0.0475092 | ||||||||
\(37\) | −0.896079 | −0.147314 | −0.0736572 | − | 0.997284i | \(-0.523467\pi\) | ||||
−0.0736572 | + | 0.997284i | \(0.523467\pi\) | |||||||
\(38\) | −1.23368 | −0.200129 | ||||||||
\(39\) | 4.68172 | 0.749675 | ||||||||
\(40\) | 0.703651 | 0.111257 | ||||||||
\(41\) | 1.25216 | 0.195554 | 0.0977770 | − | 0.995208i | \(-0.468827\pi\) | ||||
0.0977770 | + | 0.995208i | \(0.468827\pi\) | |||||||
\(42\) | 0.314428 | 0.0485173 | ||||||||
\(43\) | −9.47924 | −1.44557 | −0.722785 | − | 0.691073i | \(-0.757138\pi\) | ||||
−0.722785 | + | 0.691073i | \(0.757138\pi\) | |||||||
\(44\) | 1.25944 | 0.189868 | ||||||||
\(45\) | −0.144804 | −0.0215861 | ||||||||
\(46\) | −0.535389 | −0.0789388 | ||||||||
\(47\) | −7.01227 | −1.02284 | −0.511422 | − | 0.859330i | \(-0.670881\pi\) | ||||
−0.511422 | + | 0.859330i | \(0.670881\pi\) | |||||||
\(48\) | −6.76069 | −0.975822 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.177306 | 0.0250749 | ||||||||
\(51\) | −11.2175 | −1.57076 | ||||||||
\(52\) | 5.19706 | 0.720703 | ||||||||
\(53\) | −9.00910 | −1.23749 | −0.618747 | − | 0.785590i | \(-0.712360\pi\) | ||||
−0.618747 | + | 0.785590i | \(0.712360\pi\) | |||||||
\(54\) | 0.897753 | 0.122169 | ||||||||
\(55\) | 0.639776 | 0.0862674 | ||||||||
\(56\) | 0.703651 | 0.0940294 | ||||||||
\(57\) | 12.3388 | 1.63432 | ||||||||
\(58\) | −0.294334 | −0.0386480 | ||||||||
\(59\) | −10.4486 | −1.36029 | −0.680144 | − | 0.733079i | \(-0.738083\pi\) | ||||
−0.680144 | + | 0.733079i | \(0.738083\pi\) | |||||||
\(60\) | −3.49097 | −0.450682 | ||||||||
\(61\) | −4.57798 | −0.586150 | −0.293075 | − | 0.956090i | \(-0.594679\pi\) | ||||
−0.293075 | + | 0.956090i | \(0.594679\pi\) | |||||||
\(62\) | −0.911681 | −0.115784 | ||||||||
\(63\) | −0.144804 | −0.0182435 | ||||||||
\(64\) | −7.25535 | −0.906919 | ||||||||
\(65\) | 2.64003 | 0.327455 | ||||||||
\(66\) | 0.201163 | 0.0247615 | ||||||||
\(67\) | −5.16197 | −0.630635 | −0.315317 | − | 0.948986i | \(-0.602111\pi\) | ||||
−0.315317 | + | 0.948986i | \(0.602111\pi\) | |||||||
\(68\) | −12.4523 | −1.51006 | ||||||||
\(69\) | 5.35479 | 0.644641 | ||||||||
\(70\) | 0.177306 | 0.0211922 | ||||||||
\(71\) | 9.51234 | 1.12891 | 0.564454 | − | 0.825465i | \(-0.309087\pi\) | ||||
0.564454 | + | 0.825465i | \(0.309087\pi\) | |||||||
\(72\) | −0.101891 | −0.0120080 | ||||||||
\(73\) | 5.65625 | 0.662015 | 0.331007 | − | 0.943628i | \(-0.392612\pi\) | ||||
0.331007 | + | 0.943628i | \(0.392612\pi\) | |||||||
\(74\) | −0.158880 | −0.0184695 | ||||||||
\(75\) | −1.77336 | −0.204770 | ||||||||
\(76\) | 13.6971 | 1.57116 | ||||||||
\(77\) | 0.639776 | 0.0729093 | ||||||||
\(78\) | 0.830098 | 0.0939901 | ||||||||
\(79\) | 1.21962 | 0.137218 | 0.0686091 | − | 0.997644i | \(-0.478144\pi\) | ||||
0.0686091 | + | 0.997644i | \(0.478144\pi\) | |||||||
\(80\) | −3.81236 | −0.426235 | ||||||||
\(81\) | −9.41344 | −1.04594 | ||||||||
\(82\) | 0.222015 | 0.0245175 | ||||||||
\(83\) | −17.2730 | −1.89595 | −0.947977 | − | 0.318339i | \(-0.896875\pi\) | ||||
−0.947977 | + | 0.318339i | \(0.896875\pi\) | |||||||
\(84\) | −3.49097 | −0.380896 | ||||||||
\(85\) | −6.32556 | −0.686104 | ||||||||
\(86\) | −1.68073 | −0.181238 | ||||||||
\(87\) | 2.94383 | 0.315612 | ||||||||
\(88\) | 0.450179 | 0.0479893 | ||||||||
\(89\) | 7.76378 | 0.822959 | 0.411480 | − | 0.911419i | \(-0.365012\pi\) | ||||
0.411480 | + | 0.911419i | \(0.365012\pi\) | |||||||
\(90\) | −0.0256746 | −0.00270634 | ||||||||
\(91\) | 2.64003 | 0.276750 | ||||||||
\(92\) | 5.94422 | 0.619727 | ||||||||
\(93\) | 9.11834 | 0.945527 | ||||||||
\(94\) | −1.24332 | −0.128239 | ||||||||
\(95\) | 6.95789 | 0.713865 | ||||||||
\(96\) | −3.69437 | −0.377055 | ||||||||
\(97\) | −18.6292 | −1.89151 | −0.945753 | − | 0.324885i | \(-0.894674\pi\) | ||||
−0.945753 | + | 0.324885i | \(0.894674\pi\) | |||||||
\(98\) | 0.177306 | 0.0179106 | ||||||||
\(99\) | −0.0926419 | −0.00931086 | ||||||||
\(100\) | −1.96856 | −0.196856 | ||||||||
\(101\) | 9.10274 | 0.905756 | 0.452878 | − | 0.891572i | \(-0.350397\pi\) | ||||
0.452878 | + | 0.891572i | \(0.350397\pi\) | |||||||
\(102\) | −1.98893 | −0.196934 | ||||||||
\(103\) | −13.0303 | −1.28391 | −0.641957 | − | 0.766741i | \(-0.721877\pi\) | ||||
−0.641957 | + | 0.766741i | \(0.721877\pi\) | |||||||
\(104\) | 1.85766 | 0.182158 | ||||||||
\(105\) | −1.77336 | −0.173062 | ||||||||
\(106\) | −1.59737 | −0.155150 | ||||||||
\(107\) | −7.46844 | −0.722001 | −0.361001 | − | 0.932566i | \(-0.617565\pi\) | ||||
−0.361001 | + | 0.932566i | \(0.617565\pi\) | |||||||
\(108\) | −9.96740 | −0.959114 | ||||||||
\(109\) | −20.0020 | −1.91585 | −0.957923 | − | 0.287025i | \(-0.907334\pi\) | ||||
−0.957923 | + | 0.287025i | \(0.907334\pi\) | |||||||
\(110\) | 0.113436 | 0.0108157 | ||||||||
\(111\) | 1.58907 | 0.150828 | ||||||||
\(112\) | −3.81236 | −0.360234 | ||||||||
\(113\) | −13.3848 | −1.25914 | −0.629570 | − | 0.776944i | \(-0.716769\pi\) | ||||
−0.629570 | + | 0.776944i | \(0.716769\pi\) | |||||||
\(114\) | 2.18776 | 0.204902 | ||||||||
\(115\) | 3.01957 | 0.281577 | ||||||||
\(116\) | 3.26788 | 0.303415 | ||||||||
\(117\) | −0.382286 | −0.0353423 | ||||||||
\(118\) | −1.85260 | −0.170545 | ||||||||
\(119\) | −6.32556 | −0.579863 | ||||||||
\(120\) | −1.24783 | −0.113910 | ||||||||
\(121\) | −10.5907 | −0.962790 | ||||||||
\(122\) | −0.811704 | −0.0734882 | ||||||||
\(123\) | −2.22052 | −0.200218 | ||||||||
\(124\) | 10.1220 | 0.908986 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.0256746 | −0.00228728 | ||||||||
\(127\) | −9.93366 | −0.881469 | −0.440735 | − | 0.897637i | \(-0.645282\pi\) | ||||
−0.440735 | + | 0.897637i | \(0.645282\pi\) | |||||||
\(128\) | −5.45294 | −0.481976 | ||||||||
\(129\) | 16.8101 | 1.48005 | ||||||||
\(130\) | 0.468094 | 0.0410545 | ||||||||
\(131\) | 5.00799 | 0.437551 | 0.218775 | − | 0.975775i | \(-0.429794\pi\) | ||||
0.218775 | + | 0.975775i | \(0.429794\pi\) | |||||||
\(132\) | −2.23344 | −0.194396 | ||||||||
\(133\) | 6.95789 | 0.603326 | ||||||||
\(134\) | −0.915250 | −0.0790655 | ||||||||
\(135\) | −5.06329 | −0.435779 | ||||||||
\(136\) | −4.45099 | −0.381669 | ||||||||
\(137\) | 22.7945 | 1.94746 | 0.973731 | − | 0.227701i | \(-0.0731209\pi\) | ||||
0.973731 | + | 0.227701i | \(0.0731209\pi\) | |||||||
\(138\) | 0.949438 | 0.0808215 | ||||||||
\(139\) | 21.9719 | 1.86363 | 0.931815 | − | 0.362935i | \(-0.118225\pi\) | ||||
0.931815 | + | 0.362935i | \(0.118225\pi\) | |||||||
\(140\) | −1.96856 | −0.166374 | ||||||||
\(141\) | 12.4353 | 1.04724 | ||||||||
\(142\) | 1.68660 | 0.141536 | ||||||||
\(143\) | 1.68903 | 0.141244 | ||||||||
\(144\) | 0.552044 | 0.0460037 | ||||||||
\(145\) | 1.66003 | 0.137858 | ||||||||
\(146\) | 1.00289 | 0.0829997 | ||||||||
\(147\) | −1.77336 | −0.146264 | ||||||||
\(148\) | 1.76399 | 0.144999 | ||||||||
\(149\) | 6.86559 | 0.562451 | 0.281226 | − | 0.959642i | \(-0.409259\pi\) | ||||
0.281226 | + | 0.959642i | \(0.409259\pi\) | |||||||
\(150\) | −0.314428 | −0.0256729 | ||||||||
\(151\) | −1.72727 | −0.140564 | −0.0702818 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702818 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(152\) | 4.89593 | 0.397112 | ||||||||
\(153\) | 0.915965 | 0.0740514 | ||||||||
\(154\) | 0.113436 | 0.00914096 | ||||||||
\(155\) | 5.14184 | 0.413003 | ||||||||
\(156\) | −9.21626 | −0.737891 | ||||||||
\(157\) | 7.85732 | 0.627082 | 0.313541 | − | 0.949575i | \(-0.398485\pi\) | ||||
0.313541 | + | 0.949575i | \(0.398485\pi\) | |||||||
\(158\) | 0.216247 | 0.0172037 | ||||||||
\(159\) | 15.9764 | 1.26701 | ||||||||
\(160\) | −2.08326 | −0.164696 | ||||||||
\(161\) | 3.01957 | 0.237976 | ||||||||
\(162\) | −1.66906 | −0.131134 | ||||||||
\(163\) | 10.9697 | 0.859212 | 0.429606 | − | 0.903016i | \(-0.358652\pi\) | ||||
0.429606 | + | 0.903016i | \(0.358652\pi\) | |||||||
\(164\) | −2.46495 | −0.192480 | ||||||||
\(165\) | −1.13455 | −0.0883248 | ||||||||
\(166\) | −3.06261 | −0.237704 | ||||||||
\(167\) | −0.101144 | −0.00782677 | −0.00391339 | − | 0.999992i | \(-0.501246\pi\) | ||||
−0.00391339 | + | 0.999992i | \(0.501246\pi\) | |||||||
\(168\) | −1.24783 | −0.0962719 | ||||||||
\(169\) | −6.03025 | −0.463865 | ||||||||
\(170\) | −1.12156 | −0.0860199 | ||||||||
\(171\) | −1.00753 | −0.0770476 | ||||||||
\(172\) | 18.6605 | 1.42285 | ||||||||
\(173\) | −2.37379 | −0.180476 | −0.0902379 | − | 0.995920i | \(-0.528763\pi\) | ||||
−0.0902379 | + | 0.995920i | \(0.528763\pi\) | |||||||
\(174\) | 0.521960 | 0.0395697 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −2.43906 | −0.183851 | ||||||||
\(177\) | 18.5291 | 1.39273 | ||||||||
\(178\) | 1.37657 | 0.103178 | ||||||||
\(179\) | −16.7854 | −1.25460 | −0.627298 | − | 0.778779i | \(-0.715839\pi\) | ||||
−0.627298 | + | 0.778779i | \(0.715839\pi\) | |||||||
\(180\) | 0.285055 | 0.0212467 | ||||||||
\(181\) | −14.2181 | −1.05682 | −0.528410 | − | 0.848989i | \(-0.677212\pi\) | ||||
−0.528410 | + | 0.848989i | \(0.677212\pi\) | |||||||
\(182\) | 0.468094 | 0.0346974 | ||||||||
\(183\) | 8.11840 | 0.600129 | ||||||||
\(184\) | 2.12473 | 0.156637 | ||||||||
\(185\) | 0.896079 | 0.0658810 | ||||||||
\(186\) | 1.61674 | 0.118545 | ||||||||
\(187\) | −4.04694 | −0.295942 | ||||||||
\(188\) | 13.8041 | 1.00677 | ||||||||
\(189\) | −5.06329 | −0.368300 | ||||||||
\(190\) | 1.23368 | 0.0895005 | ||||||||
\(191\) | −9.13370 | −0.660892 | −0.330446 | − | 0.943825i | \(-0.607199\pi\) | ||||
−0.330446 | + | 0.943825i | \(0.607199\pi\) | |||||||
\(192\) | 12.8663 | 0.928549 | ||||||||
\(193\) | 22.3999 | 1.61238 | 0.806189 | − | 0.591658i | \(-0.201526\pi\) | ||||
0.806189 | + | 0.591658i | \(0.201526\pi\) | |||||||
\(194\) | −3.30307 | −0.237147 | ||||||||
\(195\) | −4.68172 | −0.335265 | ||||||||
\(196\) | −1.96856 | −0.140612 | ||||||||
\(197\) | −10.5228 | −0.749718 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(198\) | −0.0164260 | −0.00116734 | ||||||||
\(199\) | −22.9550 | −1.62724 | −0.813619 | − | 0.581399i | \(-0.802506\pi\) | ||||
−0.813619 | + | 0.581399i | \(0.802506\pi\) | |||||||
\(200\) | −0.703651 | −0.0497557 | ||||||||
\(201\) | 9.15403 | 0.645675 | ||||||||
\(202\) | 1.61397 | 0.113559 | ||||||||
\(203\) | 1.66003 | 0.116511 | ||||||||
\(204\) | 22.0823 | 1.54607 | ||||||||
\(205\) | −1.25216 | −0.0874544 | ||||||||
\(206\) | −2.31035 | −0.160970 | ||||||||
\(207\) | −0.437245 | −0.0303906 | ||||||||
\(208\) | −10.0647 | −0.697865 | ||||||||
\(209\) | 4.45149 | 0.307916 | ||||||||
\(210\) | −0.314428 | −0.0216976 | ||||||||
\(211\) | −21.4441 | −1.47627 | −0.738136 | − | 0.674651i | \(-0.764294\pi\) | ||||
−0.738136 | + | 0.674651i | \(0.764294\pi\) | |||||||
\(212\) | 17.7350 | 1.21804 | ||||||||
\(213\) | −16.8688 | −1.15583 | ||||||||
\(214\) | −1.32420 | −0.0905206 | ||||||||
\(215\) | 9.47924 | 0.646479 | ||||||||
\(216\) | −3.56279 | −0.242417 | ||||||||
\(217\) | 5.14184 | 0.349051 | ||||||||
\(218\) | −3.54648 | −0.240198 | ||||||||
\(219\) | −10.0306 | −0.677803 | ||||||||
\(220\) | −1.25944 | −0.0849114 | ||||||||
\(221\) | −16.6997 | −1.12334 | ||||||||
\(222\) | 0.281752 | 0.0189100 | ||||||||
\(223\) | −11.6626 | −0.780986 | −0.390493 | − | 0.920606i | \(-0.627695\pi\) | ||||
−0.390493 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(224\) | −2.08326 | −0.139194 | ||||||||
\(225\) | 0.144804 | 0.00965358 | ||||||||
\(226\) | −2.37322 | −0.157864 | ||||||||
\(227\) | 3.51032 | 0.232988 | 0.116494 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116494 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(228\) | −24.2898 | −1.60863 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 0.535389 | 0.0353025 | ||||||||
\(231\) | −1.13455 | −0.0746481 | ||||||||
\(232\) | 1.16808 | 0.0766884 | ||||||||
\(233\) | 14.0683 | 0.921643 | 0.460821 | − | 0.887493i | \(-0.347555\pi\) | ||||
0.460821 | + | 0.887493i | \(0.347555\pi\) | |||||||
\(234\) | −0.0677817 | −0.00443103 | ||||||||
\(235\) | 7.01227 | 0.457430 | ||||||||
\(236\) | 20.5687 | 1.33891 | ||||||||
\(237\) | −2.16283 | −0.140491 | ||||||||
\(238\) | −1.12156 | −0.0727001 | ||||||||
\(239\) | 6.38400 | 0.412947 | 0.206473 | − | 0.978452i | \(-0.433801\pi\) | ||||
0.206473 | + | 0.978452i | \(0.433801\pi\) | |||||||
\(240\) | 6.76069 | 0.436401 | ||||||||
\(241\) | 1.06088 | 0.0683375 | 0.0341687 | − | 0.999416i | \(-0.489122\pi\) | ||||
0.0341687 | + | 0.999416i | \(0.489122\pi\) | |||||||
\(242\) | −1.87780 | −0.120709 | ||||||||
\(243\) | 1.50355 | 0.0964528 | ||||||||
\(244\) | 9.01203 | 0.576936 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −0.393713 | −0.0251022 | ||||||||
\(247\) | 18.3690 | 1.16879 | ||||||||
\(248\) | 3.61806 | 0.229747 | ||||||||
\(249\) | 30.6312 | 1.94117 | ||||||||
\(250\) | −0.177306 | −0.0112138 | ||||||||
\(251\) | −26.1553 | −1.65091 | −0.825455 | − | 0.564468i | \(-0.809081\pi\) | ||||
−0.825455 | + | 0.564468i | \(0.809081\pi\) | |||||||
\(252\) | 0.285055 | 0.0179568 | ||||||||
\(253\) | 1.93185 | 0.121454 | ||||||||
\(254\) | −1.76130 | −0.110514 | ||||||||
\(255\) | 11.2175 | 0.702467 | ||||||||
\(256\) | 13.5439 | 0.846491 | ||||||||
\(257\) | −1.74763 | −0.109014 | −0.0545071 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545071 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(258\) | 2.98054 | 0.185560 | ||||||||
\(259\) | 0.896079 | 0.0556796 | ||||||||
\(260\) | −5.19706 | −0.322308 | ||||||||
\(261\) | −0.240379 | −0.0148791 | ||||||||
\(262\) | 0.887949 | 0.0548577 | ||||||||
\(263\) | 9.21353 | 0.568131 | 0.284065 | − | 0.958805i | \(-0.408317\pi\) | ||||
0.284065 | + | 0.958805i | \(0.408317\pi\) | |||||||
\(264\) | −0.798330 | −0.0491338 | ||||||||
\(265\) | 9.00910 | 0.553424 | ||||||||
\(266\) | 1.23368 | 0.0756417 | ||||||||
\(267\) | −13.7680 | −0.842586 | ||||||||
\(268\) | 10.1617 | 0.620722 | ||||||||
\(269\) | 18.3383 | 1.11811 | 0.559054 | − | 0.829131i | \(-0.311164\pi\) | ||||
0.559054 | + | 0.829131i | \(0.311164\pi\) | |||||||
\(270\) | −0.897753 | −0.0546355 | ||||||||
\(271\) | −22.9608 | −1.39477 | −0.697386 | − | 0.716696i | \(-0.745654\pi\) | ||||
−0.697386 | + | 0.716696i | \(0.745654\pi\) | |||||||
\(272\) | 24.1153 | 1.46221 | ||||||||
\(273\) | −4.68172 | −0.283351 | ||||||||
\(274\) | 4.04160 | 0.244162 | ||||||||
\(275\) | −0.639776 | −0.0385800 | ||||||||
\(276\) | −10.5412 | −0.634508 | ||||||||
\(277\) | −10.7662 | −0.646877 | −0.323439 | − | 0.946249i | \(-0.604839\pi\) | ||||
−0.323439 | + | 0.946249i | \(0.604839\pi\) | |||||||
\(278\) | 3.89575 | 0.233652 | ||||||||
\(279\) | −0.744558 | −0.0445755 | ||||||||
\(280\) | −0.703651 | −0.0420512 | ||||||||
\(281\) | 18.7391 | 1.11788 | 0.558940 | − | 0.829208i | \(-0.311208\pi\) | ||||
0.558940 | + | 0.829208i | \(0.311208\pi\) | |||||||
\(282\) | 2.20485 | 0.131297 | ||||||||
\(283\) | 24.7051 | 1.46857 | 0.734283 | − | 0.678843i | \(-0.237519\pi\) | ||||
0.734283 | + | 0.678843i | \(0.237519\pi\) | |||||||
\(284\) | −18.7256 | −1.11116 | ||||||||
\(285\) | −12.3388 | −0.730890 | ||||||||
\(286\) | 0.299475 | 0.0177083 | ||||||||
\(287\) | −1.25216 | −0.0739124 | ||||||||
\(288\) | 0.301663 | 0.0177757 | ||||||||
\(289\) | 23.0128 | 1.35369 | ||||||||
\(290\) | 0.294334 | 0.0172839 | ||||||||
\(291\) | 33.0362 | 1.93662 | ||||||||
\(292\) | −11.1347 | −0.651609 | ||||||||
\(293\) | 33.2001 | 1.93957 | 0.969784 | − | 0.243966i | \(-0.0784484\pi\) | ||||
0.969784 | + | 0.243966i | \(0.0784484\pi\) | |||||||
\(294\) | −0.314428 | −0.0183378 | ||||||||
\(295\) | 10.4486 | 0.608339 | ||||||||
\(296\) | 0.630527 | 0.0366486 | ||||||||
\(297\) | −3.23937 | −0.187967 | ||||||||
\(298\) | 1.21731 | 0.0705171 | ||||||||
\(299\) | 7.97176 | 0.461019 | ||||||||
\(300\) | 3.49097 | 0.201551 | ||||||||
\(301\) | 9.47924 | 0.546374 | ||||||||
\(302\) | −0.306257 | −0.0176231 | ||||||||
\(303\) | −16.1424 | −0.927358 | ||||||||
\(304\) | −26.5260 | −1.52137 | ||||||||
\(305\) | 4.57798 | 0.262134 | ||||||||
\(306\) | 0.162406 | 0.00928415 | ||||||||
\(307\) | 24.7066 | 1.41008 | 0.705039 | − | 0.709169i | \(-0.250930\pi\) | ||||
0.705039 | + | 0.709169i | \(0.250930\pi\) | |||||||
\(308\) | −1.25944 | −0.0717632 | ||||||||
\(309\) | 23.1074 | 1.31453 | ||||||||
\(310\) | 0.911681 | 0.0517800 | ||||||||
\(311\) | 18.8964 | 1.07152 | 0.535759 | − | 0.844371i | \(-0.320026\pi\) | ||||
0.535759 | + | 0.844371i | \(0.320026\pi\) | |||||||
\(312\) | −3.29430 | −0.186503 | ||||||||
\(313\) | −24.5126 | −1.38554 | −0.692768 | − | 0.721160i | \(-0.743609\pi\) | ||||
−0.692768 | + | 0.721160i | \(0.743609\pi\) | |||||||
\(314\) | 1.39315 | 0.0786201 | ||||||||
\(315\) | 0.144804 | 0.00815876 | ||||||||
\(316\) | −2.40090 | −0.135061 | ||||||||
\(317\) | 7.11436 | 0.399582 | 0.199791 | − | 0.979839i | \(-0.435974\pi\) | ||||
0.199791 | + | 0.979839i | \(0.435974\pi\) | |||||||
\(318\) | 2.83271 | 0.158851 | ||||||||
\(319\) | 1.06205 | 0.0594633 | ||||||||
\(320\) | 7.25535 | 0.405586 | ||||||||
\(321\) | 13.2442 | 0.739221 | ||||||||
\(322\) | 0.535389 | 0.0298361 | ||||||||
\(323\) | −44.0126 | −2.44893 | ||||||||
\(324\) | 18.5310 | 1.02950 | ||||||||
\(325\) | −2.64003 | −0.146442 | ||||||||
\(326\) | 1.94499 | 0.107723 | ||||||||
\(327\) | 35.4708 | 1.96154 | ||||||||
\(328\) | −0.881081 | −0.0486496 | ||||||||
\(329\) | 7.01227 | 0.386599 | ||||||||
\(330\) | −0.201163 | −0.0110737 | ||||||||
\(331\) | −26.6025 | −1.46221 | −0.731103 | − | 0.682267i | \(-0.760994\pi\) | ||||
−0.731103 | + | 0.682267i | \(0.760994\pi\) | |||||||
\(332\) | 34.0029 | 1.86615 | ||||||||
\(333\) | −0.129756 | −0.00711056 | ||||||||
\(334\) | −0.0179335 | −0.000981277 0 | ||||||||
\(335\) | 5.16197 | 0.282029 | ||||||||
\(336\) | 6.76069 | 0.368826 | ||||||||
\(337\) | −20.5741 | −1.12074 | −0.560371 | − | 0.828242i | \(-0.689342\pi\) | ||||
−0.560371 | + | 0.828242i | \(0.689342\pi\) | |||||||
\(338\) | −1.06920 | −0.0581569 | ||||||||
\(339\) | 23.7361 | 1.28917 | ||||||||
\(340\) | 12.4523 | 0.675319 | ||||||||
\(341\) | 3.28963 | 0.178143 | ||||||||
\(342\) | −0.178641 | −0.00965981 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.67008 | 0.359627 | ||||||||
\(345\) | −5.35479 | −0.288292 | ||||||||
\(346\) | −0.420888 | −0.0226271 | ||||||||
\(347\) | 19.1273 | 1.02681 | 0.513404 | − | 0.858147i | \(-0.328384\pi\) | ||||
0.513404 | + | 0.858147i | \(0.328384\pi\) | |||||||
\(348\) | −5.79512 | −0.310651 | ||||||||
\(349\) | −22.1849 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(350\) | −0.177306 | −0.00947742 | ||||||||
\(351\) | −13.3672 | −0.713490 | ||||||||
\(352\) | −1.33282 | −0.0710395 | ||||||||
\(353\) | 2.55318 | 0.135892 | 0.0679462 | − | 0.997689i | \(-0.478355\pi\) | ||||
0.0679462 | + | 0.997689i | \(0.478355\pi\) | |||||||
\(354\) | 3.28532 | 0.174613 | ||||||||
\(355\) | −9.51234 | −0.504863 | ||||||||
\(356\) | −15.2835 | −0.810023 | ||||||||
\(357\) | 11.2175 | 0.593693 | ||||||||
\(358\) | −2.97615 | −0.157294 | ||||||||
\(359\) | 14.3040 | 0.754938 | 0.377469 | − | 0.926022i | \(-0.376794\pi\) | ||||
0.377469 | + | 0.926022i | \(0.376794\pi\) | |||||||
\(360\) | 0.101891 | 0.00537014 | ||||||||
\(361\) | 29.4123 | 1.54802 | ||||||||
\(362\) | −2.52095 | −0.132498 | ||||||||
\(363\) | 18.7811 | 0.985752 | ||||||||
\(364\) | −5.19706 | −0.272400 | ||||||||
\(365\) | −5.65625 | −0.296062 | ||||||||
\(366\) | 1.43944 | 0.0752409 | ||||||||
\(367\) | 3.02815 | 0.158068 | 0.0790341 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790341 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(368\) | −11.5117 | −0.600089 | ||||||||
\(369\) | 0.181317 | 0.00943898 | ||||||||
\(370\) | 0.158880 | 0.00825980 | ||||||||
\(371\) | 9.00910 | 0.467729 | ||||||||
\(372\) | −17.9500 | −0.930665 | ||||||||
\(373\) | −20.0667 | −1.03901 | −0.519507 | − | 0.854466i | \(-0.673884\pi\) | ||||
−0.519507 | + | 0.854466i | \(0.673884\pi\) | |||||||
\(374\) | −0.717549 | −0.0371036 | ||||||||
\(375\) | 1.77336 | 0.0915759 | ||||||||
\(376\) | 4.93419 | 0.254461 | ||||||||
\(377\) | 4.38253 | 0.225712 | ||||||||
\(378\) | −0.897753 | −0.0461754 | ||||||||
\(379\) | −31.0196 | −1.59337 | −0.796686 | − | 0.604394i | \(-0.793415\pi\) | ||||
−0.796686 | + | 0.604394i | \(0.793415\pi\) | |||||||
\(380\) | −13.6971 | −0.702644 | ||||||||
\(381\) | 17.6159 | 0.902492 | ||||||||
\(382\) | −1.61946 | −0.0828590 | ||||||||
\(383\) | 28.4889 | 1.45572 | 0.727858 | − | 0.685728i | \(-0.240516\pi\) | ||||
0.727858 | + | 0.685728i | \(0.240516\pi\) | |||||||
\(384\) | 9.67002 | 0.493471 | ||||||||
\(385\) | −0.639776 | −0.0326060 | ||||||||
\(386\) | 3.97164 | 0.202151 | ||||||||
\(387\) | −1.37263 | −0.0697746 | ||||||||
\(388\) | 36.6727 | 1.86177 | ||||||||
\(389\) | −13.7177 | −0.695517 | −0.347759 | − | 0.937584i | \(-0.613057\pi\) | ||||
−0.347759 | + | 0.937584i | \(0.613057\pi\) | |||||||
\(390\) | −0.830098 | −0.0420337 | ||||||||
\(391\) | −19.1005 | −0.965954 | ||||||||
\(392\) | −0.703651 | −0.0355398 | ||||||||
\(393\) | −8.88097 | −0.447986 | ||||||||
\(394\) | −1.86576 | −0.0939955 | ||||||||
\(395\) | −1.21962 | −0.0613659 | ||||||||
\(396\) | 0.182371 | 0.00916451 | ||||||||
\(397\) | 14.8305 | 0.744323 | 0.372161 | − | 0.928168i | \(-0.378617\pi\) | ||||
0.372161 | + | 0.928168i | \(0.378617\pi\) | |||||||
\(398\) | −4.07007 | −0.204014 | ||||||||
\(399\) | −12.3388 | −0.617715 | ||||||||
\(400\) | 3.81236 | 0.190618 | ||||||||
\(401\) | 34.4861 | 1.72216 | 0.861078 | − | 0.508473i | \(-0.169790\pi\) | ||||
0.861078 | + | 0.508473i | \(0.169790\pi\) | |||||||
\(402\) | 1.62307 | 0.0809512 | ||||||||
\(403\) | 13.5746 | 0.676200 | ||||||||
\(404\) | −17.9193 | −0.891519 | ||||||||
\(405\) | 9.41344 | 0.467758 | ||||||||
\(406\) | 0.294334 | 0.0146076 | ||||||||
\(407\) | 0.573290 | 0.0284169 | ||||||||
\(408\) | 7.89321 | 0.390772 | ||||||||
\(409\) | 17.7653 | 0.878438 | 0.439219 | − | 0.898380i | \(-0.355255\pi\) | ||||
0.439219 | + | 0.898380i | \(0.355255\pi\) | |||||||
\(410\) | −0.222015 | −0.0109645 | ||||||||
\(411\) | −40.4228 | −1.99391 | ||||||||
\(412\) | 25.6509 | 1.26373 | ||||||||
\(413\) | 10.4486 | 0.514140 | ||||||||
\(414\) | −0.0775263 | −0.00381021 | ||||||||
\(415\) | 17.2730 | 0.847896 | ||||||||
\(416\) | −5.49986 | −0.269653 | ||||||||
\(417\) | −38.9640 | −1.90808 | ||||||||
\(418\) | 0.789278 | 0.0386049 | ||||||||
\(419\) | −14.0985 | −0.688758 | −0.344379 | − | 0.938831i | \(-0.611910\pi\) | ||||
−0.344379 | + | 0.938831i | \(0.611910\pi\) | |||||||
\(420\) | 3.49097 | 0.170342 | ||||||||
\(421\) | 2.43136 | 0.118497 | 0.0592485 | − | 0.998243i | \(-0.481130\pi\) | ||||
0.0592485 | + | 0.998243i | \(0.481130\pi\) | |||||||
\(422\) | −3.80217 | −0.185087 | ||||||||
\(423\) | −1.01540 | −0.0493705 | ||||||||
\(424\) | 6.33926 | 0.307862 | ||||||||
\(425\) | 6.32556 | 0.306835 | ||||||||
\(426\) | −2.99095 | −0.144912 | ||||||||
\(427\) | 4.57798 | 0.221544 | ||||||||
\(428\) | 14.7021 | 0.710652 | ||||||||
\(429\) | −2.99525 | −0.144612 | ||||||||
\(430\) | 1.68073 | 0.0810520 | ||||||||
\(431\) | 11.5551 | 0.556592 | 0.278296 | − | 0.960495i | \(-0.410230\pi\) | ||||
0.278296 | + | 0.960495i | \(0.410230\pi\) | |||||||
\(432\) | 19.3031 | 0.928721 | ||||||||
\(433\) | 35.1114 | 1.68735 | 0.843673 | − | 0.536858i | \(-0.180389\pi\) | ||||
0.843673 | + | 0.536858i | \(0.180389\pi\) | |||||||
\(434\) | 0.911681 | 0.0437621 | ||||||||
\(435\) | −2.94383 | −0.141146 | ||||||||
\(436\) | 39.3752 | 1.88573 | ||||||||
\(437\) | 21.0099 | 1.00504 | ||||||||
\(438\) | −1.77848 | −0.0849793 | ||||||||
\(439\) | 8.10691 | 0.386922 | 0.193461 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193461 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(440\) | −0.450179 | −0.0214615 | ||||||||
\(441\) | 0.144804 | 0.00689541 | ||||||||
\(442\) | −2.96096 | −0.140838 | ||||||||
\(443\) | 13.4712 | 0.640035 | 0.320018 | − | 0.947412i | \(-0.396311\pi\) | ||||
0.320018 | + | 0.947412i | \(0.396311\pi\) | |||||||
\(444\) | −3.12818 | −0.148457 | ||||||||
\(445\) | −7.76378 | −0.368038 | ||||||||
\(446\) | −2.06785 | −0.0979157 | ||||||||
\(447\) | −12.1752 | −0.575866 | ||||||||
\(448\) | 7.25535 | 0.342783 | ||||||||
\(449\) | −35.2371 | −1.66294 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(450\) | 0.0256746 | 0.00121031 | ||||||||
\(451\) | −0.801100 | −0.0377223 | ||||||||
\(452\) | 26.3489 | 1.23935 | ||||||||
\(453\) | 3.06308 | 0.143916 | ||||||||
\(454\) | 0.622402 | 0.0292108 | ||||||||
\(455\) | −2.64003 | −0.123766 | ||||||||
\(456\) | −8.68225 | −0.406583 | ||||||||
\(457\) | −24.5476 | −1.14829 | −0.574145 | − | 0.818754i | \(-0.694665\pi\) | ||||
−0.574145 | + | 0.818754i | \(0.694665\pi\) | |||||||
\(458\) | 0.177306 | 0.00828498 | ||||||||
\(459\) | 32.0282 | 1.49495 | ||||||||
\(460\) | −5.94422 | −0.277151 | ||||||||
\(461\) | 6.05338 | 0.281934 | 0.140967 | − | 0.990014i | \(-0.454979\pi\) | ||||
0.140967 | + | 0.990014i | \(0.454979\pi\) | |||||||
\(462\) | −0.201163 | −0.00935897 | ||||||||
\(463\) | −4.03738 | −0.187633 | −0.0938166 | − | 0.995590i | \(-0.529907\pi\) | ||||
−0.0938166 | + | 0.995590i | \(0.529907\pi\) | |||||||
\(464\) | −6.32864 | −0.293800 | ||||||||
\(465\) | −9.11834 | −0.422853 | ||||||||
\(466\) | 2.49439 | 0.115551 | ||||||||
\(467\) | −21.9718 | −1.01673 | −0.508366 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508366 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(468\) | 0.752553 | 0.0347868 | ||||||||
\(469\) | 5.16197 | 0.238358 | ||||||||
\(470\) | 1.24332 | 0.0573500 | ||||||||
\(471\) | −13.9338 | −0.642038 | ||||||||
\(472\) | 7.35215 | 0.338410 | ||||||||
\(473\) | 6.06459 | 0.278850 | ||||||||
\(474\) | −0.383483 | −0.0176140 | ||||||||
\(475\) | −6.95789 | −0.319250 | ||||||||
\(476\) | 12.4523 | 0.570749 | ||||||||
\(477\) | −1.30455 | −0.0597313 | ||||||||
\(478\) | 1.13192 | 0.0517730 | ||||||||
\(479\) | −6.64512 | −0.303623 | −0.151812 | − | 0.988409i | \(-0.548511\pi\) | ||||
−0.151812 | + | 0.988409i | \(0.548511\pi\) | |||||||
\(480\) | 3.69437 | 0.168624 | ||||||||
\(481\) | 2.36567 | 0.107865 | ||||||||
\(482\) | 0.188101 | 0.00856778 | ||||||||
\(483\) | −5.35479 | −0.243651 | ||||||||
\(484\) | 20.8484 | 0.947656 | ||||||||
\(485\) | 18.6292 | 0.845908 | ||||||||
\(486\) | 0.266589 | 0.0120927 | ||||||||
\(487\) | 12.7097 | 0.575933 | 0.287967 | − | 0.957640i | \(-0.407021\pi\) | ||||
0.287967 | + | 0.957640i | \(0.407021\pi\) | |||||||
\(488\) | 3.22130 | 0.145821 | ||||||||
\(489\) | −19.4532 | −0.879704 | ||||||||
\(490\) | −0.177306 | −0.00800988 | ||||||||
\(491\) | −27.5861 | −1.24494 | −0.622472 | − | 0.782642i | \(-0.713872\pi\) | ||||
−0.622472 | + | 0.782642i | \(0.713872\pi\) | |||||||
\(492\) | 4.37124 | 0.197071 | ||||||||
\(493\) | −10.5006 | −0.472925 | ||||||||
\(494\) | 3.25695 | 0.146537 | ||||||||
\(495\) | 0.0926419 | 0.00416394 | ||||||||
\(496\) | −19.6026 | −0.880181 | ||||||||
\(497\) | −9.51234 | −0.426687 | ||||||||
\(498\) | 5.43110 | 0.243373 | ||||||||
\(499\) | −37.3390 | −1.67152 | −0.835761 | − | 0.549094i | \(-0.814973\pi\) | ||||
−0.835761 | + | 0.549094i | \(0.814973\pi\) | |||||||
\(500\) | 1.96856 | 0.0880368 | ||||||||
\(501\) | 0.179365 | 0.00801344 | ||||||||
\(502\) | −4.63750 | −0.206982 | ||||||||
\(503\) | 24.5926 | 1.09653 | 0.548264 | − | 0.836305i | \(-0.315289\pi\) | ||||
0.548264 | + | 0.836305i | \(0.315289\pi\) | |||||||
\(504\) | 0.101891 | 0.00453860 | ||||||||
\(505\) | −9.10274 | −0.405067 | ||||||||
\(506\) | 0.342529 | 0.0152273 | ||||||||
\(507\) | 10.6938 | 0.474928 | ||||||||
\(508\) | 19.5550 | 0.867614 | ||||||||
\(509\) | −17.4789 | −0.774737 | −0.387369 | − | 0.921925i | \(-0.626616\pi\) | ||||
−0.387369 | + | 0.921925i | \(0.626616\pi\) | |||||||
\(510\) | 1.98893 | 0.0880714 | ||||||||
\(511\) | −5.65625 | −0.250218 | ||||||||
\(512\) | 13.3073 | 0.588105 | ||||||||
\(513\) | −35.2298 | −1.55544 | ||||||||
\(514\) | −0.309866 | −0.0136676 | ||||||||
\(515\) | 13.0303 | 0.574183 | ||||||||
\(516\) | −33.0917 | −1.45678 | ||||||||
\(517\) | 4.48628 | 0.197306 | ||||||||
\(518\) | 0.158880 | 0.00698081 | ||||||||
\(519\) | 4.20958 | 0.184780 | ||||||||
\(520\) | −1.85766 | −0.0814637 | ||||||||
\(521\) | −1.48819 | −0.0651990 | −0.0325995 | − | 0.999468i | \(-0.510379\pi\) | ||||
−0.0325995 | + | 0.999468i | \(0.510379\pi\) | |||||||
\(522\) | −0.0426207 | −0.00186546 | ||||||||
\(523\) | 2.09180 | 0.0914679 | 0.0457339 | − | 0.998954i | \(-0.485437\pi\) | ||||
0.0457339 | + | 0.998954i | \(0.485437\pi\) | |||||||
\(524\) | −9.85855 | −0.430673 | ||||||||
\(525\) | 1.77336 | 0.0773958 | ||||||||
\(526\) | 1.63362 | 0.0712291 | ||||||||
\(527\) | −32.5251 | −1.41681 | ||||||||
\(528\) | 4.32533 | 0.188236 | ||||||||
\(529\) | −13.8822 | −0.603573 | ||||||||
\(530\) | 1.59737 | 0.0693853 | ||||||||
\(531\) | −1.51299 | −0.0656582 | ||||||||
\(532\) | −13.6971 | −0.593842 | ||||||||
\(533\) | −3.30573 | −0.143187 | ||||||||
\(534\) | −2.44115 | −0.105639 | ||||||||
\(535\) | 7.46844 | 0.322889 | ||||||||
\(536\) | 3.63223 | 0.156888 | ||||||||
\(537\) | 29.7665 | 1.28452 | ||||||||
\(538\) | 3.25150 | 0.140182 | ||||||||
\(539\) | −0.639776 | −0.0275571 | ||||||||
\(540\) | 9.96740 | 0.428929 | ||||||||
\(541\) | −14.6748 | −0.630920 | −0.315460 | − | 0.948939i | \(-0.602159\pi\) | ||||
−0.315460 | + | 0.948939i | \(0.602159\pi\) | |||||||
\(542\) | −4.07110 | −0.174869 | ||||||||
\(543\) | 25.2137 | 1.08202 | ||||||||
\(544\) | 13.1778 | 0.564993 | ||||||||
\(545\) | 20.0020 | 0.856792 | ||||||||
\(546\) | −0.830098 | −0.0355249 | ||||||||
\(547\) | 39.9747 | 1.70920 | 0.854598 | − | 0.519290i | \(-0.173804\pi\) | ||||
0.854598 | + | 0.519290i | \(0.173804\pi\) | |||||||
\(548\) | −44.8723 | −1.91685 | ||||||||
\(549\) | −0.662908 | −0.0282922 | ||||||||
\(550\) | −0.113436 | −0.00483694 | ||||||||
\(551\) | 11.5503 | 0.492060 | ||||||||
\(552\) | −3.76790 | −0.160373 | ||||||||
\(553\) | −1.21962 | −0.0518636 | ||||||||
\(554\) | −1.90891 | −0.0811019 | ||||||||
\(555\) | −1.58907 | −0.0674523 | ||||||||
\(556\) | −43.2530 | −1.83434 | ||||||||
\(557\) | −25.7840 | −1.09250 | −0.546251 | − | 0.837621i | \(-0.683946\pi\) | ||||
−0.546251 | + | 0.837621i | \(0.683946\pi\) | |||||||
\(558\) | −0.132015 | −0.00558863 | ||||||||
\(559\) | 25.0255 | 1.05846 | ||||||||
\(560\) | 3.81236 | 0.161102 | ||||||||
\(561\) | 7.17669 | 0.303000 | ||||||||
\(562\) | 3.32256 | 0.140154 | ||||||||
\(563\) | 15.4832 | 0.652537 | 0.326269 | − | 0.945277i | \(-0.394209\pi\) | ||||
0.326269 | + | 0.945277i | \(0.394209\pi\) | |||||||
\(564\) | −24.4796 | −1.03078 | ||||||||
\(565\) | 13.3848 | 0.563104 | ||||||||
\(566\) | 4.38037 | 0.184121 | ||||||||
\(567\) | 9.41344 | 0.395327 | ||||||||
\(568\) | −6.69337 | −0.280848 | ||||||||
\(569\) | −26.5208 | −1.11181 | −0.555906 | − | 0.831245i | \(-0.687628\pi\) | ||||
−0.555906 | + | 0.831245i | \(0.687628\pi\) | |||||||
\(570\) | −2.18776 | −0.0916350 | ||||||||
\(571\) | 27.6779 | 1.15828 | 0.579142 | − | 0.815227i | \(-0.303388\pi\) | ||||
0.579142 | + | 0.815227i | \(0.303388\pi\) | |||||||
\(572\) | −3.32496 | −0.139023 | ||||||||
\(573\) | 16.1973 | 0.676654 | ||||||||
\(574\) | −0.222015 | −0.00926674 | ||||||||
\(575\) | −3.01957 | −0.125925 | ||||||||
\(576\) | −1.05060 | −0.0437751 | ||||||||
\(577\) | 19.0810 | 0.794352 | 0.397176 | − | 0.917743i | \(-0.369990\pi\) | ||||
0.397176 | + | 0.917743i | \(0.369990\pi\) | |||||||
\(578\) | 4.08031 | 0.169718 | ||||||||
\(579\) | −39.7230 | −1.65083 | ||||||||
\(580\) | −3.26788 | −0.135691 | ||||||||
\(581\) | 17.2730 | 0.716603 | ||||||||
\(582\) | 5.85753 | 0.242803 | ||||||||
\(583\) | 5.76381 | 0.238712 | ||||||||
\(584\) | −3.98003 | −0.164695 | ||||||||
\(585\) | 0.382286 | 0.0158056 | ||||||||
\(586\) | 5.88658 | 0.243172 | ||||||||
\(587\) | −34.9330 | −1.44184 | −0.720920 | − | 0.693018i | \(-0.756281\pi\) | ||||
−0.720920 | + | 0.693018i | \(0.756281\pi\) | |||||||
\(588\) | 3.49097 | 0.143965 | ||||||||
\(589\) | 35.7764 | 1.47414 | ||||||||
\(590\) | 1.85260 | 0.0762702 | ||||||||
\(591\) | 18.6607 | 0.767599 | ||||||||
\(592\) | −3.41618 | −0.140404 | ||||||||
\(593\) | −3.83915 | −0.157655 | −0.0788275 | − | 0.996888i | \(-0.525118\pi\) | ||||
−0.0788275 | + | 0.996888i | \(0.525118\pi\) | |||||||
\(594\) | −0.574361 | −0.0235663 | ||||||||
\(595\) | 6.32556 | 0.259323 | ||||||||
\(596\) | −13.5153 | −0.553610 | ||||||||
\(597\) | 40.7075 | 1.66605 | ||||||||
\(598\) | 1.41344 | 0.0578000 | ||||||||
\(599\) | 40.6855 | 1.66237 | 0.831183 | − | 0.555999i | \(-0.187664\pi\) | ||||
0.831183 | + | 0.555999i | \(0.187664\pi\) | |||||||
\(600\) | 1.24783 | 0.0509423 | ||||||||
\(601\) | 22.7544 | 0.928170 | 0.464085 | − | 0.885791i | \(-0.346383\pi\) | ||||
0.464085 | + | 0.885791i | \(0.346383\pi\) | |||||||
\(602\) | 1.68073 | 0.0685014 | ||||||||
\(603\) | −0.747472 | −0.0304394 | ||||||||
\(604\) | 3.40025 | 0.138354 | ||||||||
\(605\) | 10.5907 | 0.430573 | ||||||||
\(606\) | −2.86215 | −0.116267 | ||||||||
\(607\) | 23.9724 | 0.973010 | 0.486505 | − | 0.873678i | \(-0.338272\pi\) | ||||
0.486505 | + | 0.873678i | \(0.338272\pi\) | |||||||
\(608\) | −14.4951 | −0.587854 | ||||||||
\(609\) | −2.94383 | −0.119290 | ||||||||
\(610\) | 0.811704 | 0.0328649 | ||||||||
\(611\) | 18.5126 | 0.748939 | ||||||||
\(612\) | −1.80313 | −0.0728874 | ||||||||
\(613\) | 3.34662 | 0.135169 | 0.0675845 | − | 0.997714i | \(-0.478471\pi\) | ||||
0.0675845 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(614\) | 4.38063 | 0.176788 | ||||||||
\(615\) | 2.22052 | 0.0895401 | ||||||||
\(616\) | −0.450179 | −0.0181382 | ||||||||
\(617\) | −10.9995 | −0.442822 | −0.221411 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221411 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(618\) | 4.09709 | 0.164809 | ||||||||
\(619\) | 16.3619 | 0.657640 | 0.328820 | − | 0.944393i | \(-0.393349\pi\) | ||||
0.328820 | + | 0.944393i | \(0.393349\pi\) | |||||||
\(620\) | −10.1220 | −0.406511 | ||||||||
\(621\) | −15.2890 | −0.613525 | ||||||||
\(622\) | 3.35046 | 0.134341 | ||||||||
\(623\) | −7.76378 | −0.311049 | ||||||||
\(624\) | 17.8484 | 0.714508 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.34625 | −0.173711 | ||||||||
\(627\) | −7.89410 | −0.315260 | ||||||||
\(628\) | −15.4676 | −0.617225 | ||||||||
\(629\) | −5.66820 | −0.226006 | ||||||||
\(630\) | 0.0256746 | 0.00102290 | ||||||||
\(631\) | 36.1886 | 1.44065 | 0.720323 | − | 0.693639i | \(-0.243994\pi\) | ||||
0.720323 | + | 0.693639i | \(0.243994\pi\) | |||||||
\(632\) | −0.858189 | −0.0341369 | ||||||||
\(633\) | 38.0281 | 1.51148 | ||||||||
\(634\) | 1.26142 | 0.0500974 | ||||||||
\(635\) | 9.93366 | 0.394205 | ||||||||
\(636\) | −31.4505 | −1.24709 | ||||||||
\(637\) | −2.64003 | −0.104602 | ||||||||
\(638\) | 0.188308 | 0.00745518 | ||||||||
\(639\) | 1.37742 | 0.0544900 | ||||||||
\(640\) | 5.45294 | 0.215546 | ||||||||
\(641\) | −25.6413 | −1.01277 | −0.506385 | − | 0.862308i | \(-0.669018\pi\) | ||||
−0.506385 | + | 0.862308i | \(0.669018\pi\) | |||||||
\(642\) | 2.34829 | 0.0926794 | ||||||||
\(643\) | 0.144796 | 0.00571018 | 0.00285509 | − | 0.999996i | \(-0.499091\pi\) | ||||
0.00285509 | + | 0.999996i | \(0.499091\pi\) | |||||||
\(644\) | −5.94422 | −0.234235 | ||||||||
\(645\) | −16.8101 | −0.661897 | ||||||||
\(646\) | −7.80371 | −0.307033 | ||||||||
\(647\) | −14.2312 | −0.559486 | −0.279743 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279743 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(648\) | 6.62378 | 0.260207 | ||||||||
\(649\) | 6.68474 | 0.262399 | ||||||||
\(650\) | −0.468094 | −0.0183601 | ||||||||
\(651\) | −9.11834 | −0.357376 | ||||||||
\(652\) | −21.5945 | −0.845706 | ||||||||
\(653\) | −5.41349 | −0.211846 | −0.105923 | − | 0.994374i | \(-0.533780\pi\) | ||||
−0.105923 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(654\) | 6.28919 | 0.245927 | ||||||||
\(655\) | −5.00799 | −0.195679 | ||||||||
\(656\) | 4.77367 | 0.186381 | ||||||||
\(657\) | 0.819046 | 0.0319540 | ||||||||
\(658\) | 1.24332 | 0.0484696 | ||||||||
\(659\) | −32.2234 | −1.25524 | −0.627622 | − | 0.778518i | \(-0.715972\pi\) | ||||
−0.627622 | + | 0.778518i | \(0.715972\pi\) | |||||||
\(660\) | 2.23344 | 0.0869365 | ||||||||
\(661\) | −29.6861 | −1.15466 | −0.577328 | − | 0.816513i | \(-0.695904\pi\) | ||||
−0.577328 | + | 0.816513i | \(0.695904\pi\) | |||||||
\(662\) | −4.71679 | −0.183323 | ||||||||
\(663\) | 29.6145 | 1.15013 | ||||||||
\(664\) | 12.1541 | 0.471672 | ||||||||
\(665\) | −6.95789 | −0.269816 | ||||||||
\(666\) | −0.0230065 | −0.000891483 0 | ||||||||
\(667\) | 5.01259 | 0.194088 | ||||||||
\(668\) | 0.199109 | 0.00770374 | ||||||||
\(669\) | 20.6820 | 0.799612 | ||||||||
\(670\) | 0.915250 | 0.0353592 | ||||||||
\(671\) | 2.92888 | 0.113068 | ||||||||
\(672\) | 3.69437 | 0.142513 | ||||||||
\(673\) | −11.2206 | −0.432523 | −0.216262 | − | 0.976335i | \(-0.569386\pi\) | ||||
−0.216262 | + | 0.976335i | \(0.569386\pi\) | |||||||
\(674\) | −3.64792 | −0.140513 | ||||||||
\(675\) | 5.06329 | 0.194886 | ||||||||
\(676\) | 11.8709 | 0.456574 | ||||||||
\(677\) | 31.2202 | 1.19989 | 0.599944 | − | 0.800042i | \(-0.295189\pi\) | ||||
0.599944 | + | 0.800042i | \(0.295189\pi\) | |||||||
\(678\) | 4.20856 | 0.161629 | ||||||||
\(679\) | 18.6292 | 0.714922 | ||||||||
\(680\) | 4.45099 | 0.170688 | ||||||||
\(681\) | −6.22506 | −0.238545 | ||||||||
\(682\) | 0.583272 | 0.0223346 | ||||||||
\(683\) | 35.5516 | 1.36034 | 0.680172 | − | 0.733053i | \(-0.261905\pi\) | ||||
0.680172 | + | 0.733053i | \(0.261905\pi\) | |||||||
\(684\) | 1.98338 | 0.0758365 | ||||||||
\(685\) | −22.7945 | −0.870932 | ||||||||
\(686\) | −0.177306 | −0.00676959 | ||||||||
\(687\) | −1.77336 | −0.0676579 | ||||||||
\(688\) | −36.1383 | −1.37776 | ||||||||
\(689\) | 23.7843 | 0.906109 | ||||||||
\(690\) | −0.949438 | −0.0361445 | ||||||||
\(691\) | −21.0442 | −0.800560 | −0.400280 | − | 0.916393i | \(-0.631087\pi\) | ||||
−0.400280 | + | 0.916393i | \(0.631087\pi\) | |||||||
\(692\) | 4.67295 | 0.177639 | ||||||||
\(693\) | 0.0926419 | 0.00351918 | ||||||||
\(694\) | 3.39139 | 0.128735 | ||||||||
\(695\) | −21.9719 | −0.833440 | ||||||||
\(696\) | −2.07143 | −0.0785174 | ||||||||
\(697\) | 7.92059 | 0.300014 | ||||||||
\(698\) | −3.93352 | −0.148886 | ||||||||
\(699\) | −24.9481 | −0.943624 | ||||||||
\(700\) | 1.96856 | 0.0744047 | ||||||||
\(701\) | −22.3782 | −0.845212 | −0.422606 | − | 0.906313i | \(-0.638885\pi\) | ||||
−0.422606 | + | 0.906313i | \(0.638885\pi\) | |||||||
\(702\) | −2.37009 | −0.0894534 | ||||||||
\(703\) | 6.23482 | 0.235151 | ||||||||
\(704\) | 4.64180 | 0.174944 | ||||||||
\(705\) | −12.4353 | −0.468339 | ||||||||
\(706\) | 0.452696 | 0.0170374 | ||||||||
\(707\) | −9.10274 | −0.342344 | ||||||||
\(708\) | −36.4756 | −1.37084 | ||||||||
\(709\) | 45.5067 | 1.70904 | 0.854520 | − | 0.519419i | \(-0.173851\pi\) | ||||
0.854520 | + | 0.519419i | \(0.173851\pi\) | |||||||
\(710\) | −1.68660 | −0.0632969 | ||||||||
\(711\) | 0.176606 | 0.00662324 | ||||||||
\(712\) | −5.46299 | −0.204734 | ||||||||
\(713\) | 15.5262 | 0.581460 | ||||||||
\(714\) | 1.98893 | 0.0744340 | ||||||||
\(715\) | −1.68903 | −0.0631660 | ||||||||
\(716\) | 33.0430 | 1.23488 | ||||||||
\(717\) | −11.3211 | −0.422795 | ||||||||
\(718\) | 2.53620 | 0.0946500 | ||||||||
\(719\) | 18.7149 | 0.697950 | 0.348975 | − | 0.937132i | \(-0.386530\pi\) | ||||
0.348975 | + | 0.937132i | \(0.386530\pi\) | |||||||
\(720\) | −0.552044 | −0.0205735 | ||||||||
\(721\) | 13.0303 | 0.485274 | ||||||||
\(722\) | 5.21499 | 0.194082 | ||||||||
\(723\) | −1.88133 | −0.0699673 | ||||||||
\(724\) | 27.9891 | 1.04021 | ||||||||
\(725\) | −1.66003 | −0.0616520 | ||||||||
\(726\) | 3.33001 | 0.123588 | ||||||||
\(727\) | −20.3001 | −0.752888 | −0.376444 | − | 0.926439i | \(-0.622853\pi\) | ||||
−0.376444 | + | 0.926439i | \(0.622853\pi\) | |||||||
\(728\) | −1.85766 | −0.0688494 | ||||||||
\(729\) | 25.5740 | 0.947185 | ||||||||
\(730\) | −1.00289 | −0.0371186 | ||||||||
\(731\) | −59.9615 | −2.21776 | ||||||||
\(732\) | −15.9816 | −0.590696 | ||||||||
\(733\) | −5.90820 | −0.218224 | −0.109112 | − | 0.994029i | \(-0.534801\pi\) | ||||
−0.109112 | + | 0.994029i | \(0.534801\pi\) | |||||||
\(734\) | 0.536911 | 0.0198177 | ||||||||
\(735\) | 1.77336 | 0.0654113 | ||||||||
\(736\) | −6.29055 | −0.231873 | ||||||||
\(737\) | 3.30250 | 0.121649 | ||||||||
\(738\) | 0.0321486 | 0.00118341 | ||||||||
\(739\) | 25.3524 | 0.932604 | 0.466302 | − | 0.884625i | \(-0.345586\pi\) | ||||
0.466302 | + | 0.884625i | \(0.345586\pi\) | |||||||
\(740\) | −1.76399 | −0.0648455 | ||||||||
\(741\) | −32.5749 | −1.19667 | ||||||||
\(742\) | 1.59737 | 0.0586413 | ||||||||
\(743\) | 41.4168 | 1.51943 | 0.759717 | − | 0.650253i | \(-0.225337\pi\) | ||||
0.759717 | + | 0.650253i | \(0.225337\pi\) | |||||||
\(744\) | −6.41613 | −0.235227 | ||||||||
\(745\) | −6.86559 | −0.251536 | ||||||||
\(746\) | −3.55795 | −0.130266 | ||||||||
\(747\) | −2.50119 | −0.0915137 | ||||||||
\(748\) | 7.96666 | 0.291290 | ||||||||
\(749\) | 7.46844 | 0.272891 | ||||||||
\(750\) | 0.314428 | 0.0114813 | ||||||||
\(751\) | 11.5455 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(752\) | −26.7333 | −0.974863 | ||||||||
\(753\) | 46.3828 | 1.69028 | ||||||||
\(754\) | 0.777050 | 0.0282985 | ||||||||
\(755\) | 1.72727 | 0.0628620 | ||||||||
\(756\) | 9.96740 | 0.362511 | ||||||||
\(757\) | −14.3446 | −0.521363 | −0.260681 | − | 0.965425i | \(-0.583947\pi\) | ||||
−0.260681 | + | 0.965425i | \(0.583947\pi\) | |||||||
\(758\) | −5.49998 | −0.199768 | ||||||||
\(759\) | −3.42587 | −0.124351 | ||||||||
\(760\) | −4.89593 | −0.177594 | ||||||||
\(761\) | 3.31937 | 0.120327 | 0.0601635 | − | 0.998189i | \(-0.480838\pi\) | ||||
0.0601635 | + | 0.998189i | \(0.480838\pi\) | |||||||
\(762\) | 3.12342 | 0.113149 | ||||||||
\(763\) | 20.0020 | 0.724122 | ||||||||
\(764\) | 17.9803 | 0.650503 | ||||||||
\(765\) | −0.915965 | −0.0331168 | ||||||||
\(766\) | 5.05127 | 0.182510 | ||||||||
\(767\) | 27.5845 | 0.996019 | ||||||||
\(768\) | −24.0181 | −0.866680 | ||||||||
\(769\) | −3.61887 | −0.130500 | −0.0652499 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652499 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(770\) | −0.113436 | −0.00408796 | ||||||||
\(771\) | 3.09918 | 0.111614 | ||||||||
\(772\) | −44.0956 | −1.58703 | ||||||||
\(773\) | −43.6956 | −1.57162 | −0.785810 | − | 0.618468i | \(-0.787754\pi\) | ||||
−0.785810 | + | 0.618468i | \(0.787754\pi\) | |||||||
\(774\) | −0.243376 | −0.00874796 | ||||||||
\(775\) | −5.14184 | −0.184700 | ||||||||
\(776\) | 13.1084 | 0.470566 | ||||||||
\(777\) | −1.58907 | −0.0570076 | ||||||||
\(778\) | −2.43224 | −0.0872001 | ||||||||
\(779\) | −8.71237 | −0.312153 | ||||||||
\(780\) | 9.21626 | 0.329995 | ||||||||
\(781\) | −6.08577 | −0.217766 | ||||||||
\(782\) | −3.38664 | −0.121106 | ||||||||
\(783\) | −8.40522 | −0.300378 | ||||||||
\(784\) | 3.81236 | 0.136156 | ||||||||
\(785\) | −7.85732 | −0.280440 | ||||||||
\(786\) | −1.57465 | −0.0561660 | ||||||||
\(787\) | 22.2010 | 0.791379 | 0.395689 | − | 0.918384i | \(-0.370506\pi\) | ||||
0.395689 | + | 0.918384i | \(0.370506\pi\) | |||||||
\(788\) | 20.7148 | 0.737933 | ||||||||
\(789\) | −16.3389 | −0.581680 | ||||||||
\(790\) | −0.216247 | −0.00769372 | ||||||||
\(791\) | 13.3848 | 0.475910 | ||||||||
\(792\) | 0.0651876 | 0.00231634 | ||||||||
\(793\) | 12.0860 | 0.429186 | ||||||||
\(794\) | 2.62955 | 0.0933191 | ||||||||
\(795\) | −15.9764 | −0.566623 | ||||||||
\(796\) | 45.1884 | 1.60166 | ||||||||
\(797\) | 0.552766 | 0.0195800 | 0.00978999 | − | 0.999952i | \(-0.496884\pi\) | ||||
0.00978999 | + | 0.999952i | \(0.496884\pi\) | |||||||
\(798\) | −2.18776 | −0.0774457 | ||||||||
\(799\) | −44.3565 | −1.56922 | ||||||||
\(800\) | 2.08326 | 0.0736543 | ||||||||
\(801\) | 1.12422 | 0.0397225 | ||||||||
\(802\) | 6.11461 | 0.215914 | ||||||||
\(803\) | −3.61874 | −0.127702 | ||||||||
\(804\) | −18.0203 | −0.635526 | ||||||||
\(805\) | −3.01957 | −0.106426 | ||||||||
\(806\) | 2.40686 | 0.0847782 | ||||||||
\(807\) | −32.5205 | −1.14477 | ||||||||
\(808\) | −6.40515 | −0.225332 | ||||||||
\(809\) | −23.4047 | −0.822866 | −0.411433 | − | 0.911440i | \(-0.634972\pi\) | ||||
−0.411433 | + | 0.911440i | \(0.634972\pi\) | |||||||
\(810\) | 1.66906 | 0.0586449 | ||||||||
\(811\) | 30.7889 | 1.08115 | 0.540573 | − | 0.841297i | \(-0.318207\pi\) | ||||
0.540573 | + | 0.841297i | \(0.318207\pi\) | |||||||
\(812\) | −3.26788 | −0.114680 | ||||||||
\(813\) | 40.7178 | 1.42804 | ||||||||
\(814\) | 0.101648 | 0.00356276 | ||||||||
\(815\) | −10.9697 | −0.384251 | ||||||||
\(816\) | −42.7652 | −1.49708 | ||||||||
\(817\) | 65.9556 | 2.30749 | ||||||||
\(818\) | 3.14990 | 0.110134 | ||||||||
\(819\) | 0.382286 | 0.0133581 | ||||||||
\(820\) | 2.46495 | 0.0860797 | ||||||||
\(821\) | −53.9264 | −1.88204 | −0.941022 | − | 0.338344i | \(-0.890133\pi\) | ||||
−0.941022 | + | 0.338344i | \(0.890133\pi\) | |||||||
\(822\) | −7.16721 | −0.249985 | ||||||||
\(823\) | −20.4217 | −0.711856 | −0.355928 | − | 0.934513i | \(-0.615835\pi\) | ||||
−0.355928 | + | 0.934513i | \(0.615835\pi\) | |||||||
\(824\) | 9.16878 | 0.319410 | ||||||||
\(825\) | 1.13455 | 0.0395001 | ||||||||
\(826\) | 1.85260 | 0.0644601 | ||||||||
\(827\) | 32.6957 | 1.13694 | 0.568470 | − | 0.822704i | \(-0.307535\pi\) | ||||
0.568470 | + | 0.822704i | \(0.307535\pi\) | |||||||
\(828\) | 0.860744 | 0.0299129 | ||||||||
\(829\) | 37.3968 | 1.29884 | 0.649422 | − | 0.760428i | \(-0.275011\pi\) | ||||
0.649422 | + | 0.760428i | \(0.275011\pi\) | |||||||
\(830\) | 3.06261 | 0.106305 | ||||||||
\(831\) | 19.0923 | 0.662305 | ||||||||
\(832\) | 19.1543 | 0.664057 | ||||||||
\(833\) | 6.32556 | 0.219168 | ||||||||
\(834\) | −6.90857 | −0.239224 | ||||||||
\(835\) | 0.101144 | 0.00350024 | ||||||||
\(836\) | −8.76305 | −0.303076 | ||||||||
\(837\) | −26.0346 | −0.899889 | ||||||||
\(838\) | −2.49976 | −0.0863527 | ||||||||
\(839\) | −17.2708 | −0.596254 | −0.298127 | − | 0.954526i | \(-0.596362\pi\) | ||||
−0.298127 | + | 0.954526i | \(0.596362\pi\) | |||||||
\(840\) | 1.24783 | 0.0430541 | ||||||||
\(841\) | −26.2443 | −0.904976 | ||||||||
\(842\) | 0.431095 | 0.0148565 | ||||||||
\(843\) | −33.2311 | −1.14454 | ||||||||
\(844\) | 42.2141 | 1.45307 | ||||||||
\(845\) | 6.03025 | 0.207447 | ||||||||
\(846\) | −0.180037 | −0.00618981 | ||||||||
\(847\) | 10.5907 | 0.363900 | ||||||||
\(848\) | −34.3459 | −1.17944 | ||||||||
\(849\) | −43.8110 | −1.50359 | ||||||||
\(850\) | 1.12156 | 0.0384693 | ||||||||
\(851\) | 2.70578 | 0.0927528 | ||||||||
\(852\) | 33.2073 | 1.13766 | ||||||||
\(853\) | −26.6556 | −0.912672 | −0.456336 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456336 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(854\) | 0.811704 | 0.0277759 | ||||||||
\(855\) | 1.00753 | 0.0344568 | ||||||||
\(856\) | 5.25518 | 0.179618 | ||||||||
\(857\) | 44.4595 | 1.51871 | 0.759354 | − | 0.650678i | \(-0.225515\pi\) | ||||
0.759354 | + | 0.650678i | \(0.225515\pi\) | |||||||
\(858\) | −0.531077 | −0.0181307 | ||||||||
\(859\) | 14.5481 | 0.496375 | 0.248187 | − | 0.968712i | \(-0.420165\pi\) | ||||
0.248187 | + | 0.968712i | \(0.420165\pi\) | |||||||
\(860\) | −18.6605 | −0.636317 | ||||||||
\(861\) | 2.22052 | 0.0756752 | ||||||||
\(862\) | 2.04880 | 0.0697824 | ||||||||
\(863\) | −32.4779 | −1.10556 | −0.552780 | − | 0.833327i | \(-0.686433\pi\) | ||||
−0.552780 | + | 0.833327i | \(0.686433\pi\) | |||||||
\(864\) | 10.5481 | 0.358855 | ||||||||
\(865\) | 2.37379 | 0.0807112 | ||||||||
\(866\) | 6.22547 | 0.211550 | ||||||||
\(867\) | −40.8099 | −1.38598 | ||||||||
\(868\) | −10.1220 | −0.343564 | ||||||||
\(869\) | −0.780286 | −0.0264694 | ||||||||
\(870\) | −0.521960 | −0.0176961 | ||||||||
\(871\) | 13.6277 | 0.461759 | ||||||||
\(872\) | 14.0744 | 0.476621 | ||||||||
\(873\) | −2.69757 | −0.0912990 | ||||||||
\(874\) | 3.72518 | 0.126006 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 19.7458 | 0.667149 | ||||||||
\(877\) | 29.5104 | 0.996495 | 0.498247 | − | 0.867035i | \(-0.333977\pi\) | ||||
0.498247 | + | 0.867035i | \(0.333977\pi\) | |||||||
\(878\) | 1.43741 | 0.0485101 | ||||||||
\(879\) | −58.8756 | −1.98583 | ||||||||
\(880\) | 2.43906 | 0.0822207 | ||||||||
\(881\) | 28.8388 | 0.971605 | 0.485802 | − | 0.874069i | \(-0.338527\pi\) | ||||
0.485802 | + | 0.874069i | \(0.338527\pi\) | |||||||
\(882\) | 0.0256746 | 0.000864509 0 | ||||||||
\(883\) | −6.08332 | −0.204720 | −0.102360 | − | 0.994747i | \(-0.532639\pi\) | ||||
−0.102360 | + | 0.994747i | \(0.532639\pi\) | |||||||
\(884\) | 32.8743 | 1.10568 | ||||||||
\(885\) | −18.5291 | −0.622848 | ||||||||
\(886\) | 2.38853 | 0.0802441 | ||||||||
\(887\) | 4.67202 | 0.156871 | 0.0784355 | − | 0.996919i | \(-0.475008\pi\) | ||||
0.0784355 | + | 0.996919i | \(0.475008\pi\) | |||||||
\(888\) | −1.11815 | −0.0375227 | ||||||||
\(889\) | 9.93366 | 0.333164 | ||||||||
\(890\) | −1.37657 | −0.0461426 | ||||||||
\(891\) | 6.02250 | 0.201761 | ||||||||
\(892\) | 22.9586 | 0.768709 | ||||||||
\(893\) | 48.7906 | 1.63272 | ||||||||
\(894\) | −2.15873 | −0.0721989 | ||||||||
\(895\) | 16.7854 | 0.561073 | ||||||||
\(896\) | 5.45294 | 0.182170 | ||||||||
\(897\) | −14.1368 | −0.472014 | ||||||||
\(898\) | −6.24775 | −0.208490 | ||||||||
\(899\) | 8.53562 | 0.284679 | ||||||||
\(900\) | −0.285055 | −0.00950184 | ||||||||
\(901\) | −56.9876 | −1.89853 | ||||||||
\(902\) | −0.142040 | −0.00472942 | ||||||||
\(903\) | −16.8101 | −0.559405 | ||||||||
\(904\) | 9.41826 | 0.313247 | ||||||||
\(905\) | 14.2181 | 0.472624 | ||||||||
\(906\) | 0.543103 | 0.0180434 | ||||||||
\(907\) | 37.0421 | 1.22996 | 0.614981 | − | 0.788542i | \(-0.289164\pi\) | ||||
0.614981 | + | 0.788542i | \(0.289164\pi\) | |||||||
\(908\) | −6.91028 | −0.229326 | ||||||||
\(909\) | 1.31811 | 0.0437189 | ||||||||
\(910\) | −0.468094 | −0.0155172 | ||||||||
\(911\) | 3.87020 | 0.128226 | 0.0641128 | − | 0.997943i | \(-0.479578\pi\) | ||||
0.0641128 | + | 0.997943i | \(0.479578\pi\) | |||||||
\(912\) | 47.0402 | 1.55766 | ||||||||
\(913\) | 11.0508 | 0.365729 | ||||||||
\(914\) | −4.35245 | −0.143966 | ||||||||
\(915\) | −8.11840 | −0.268386 | ||||||||
\(916\) | −1.96856 | −0.0650431 | ||||||||
\(917\) | −5.00799 | −0.165379 | ||||||||
\(918\) | 5.67879 | 0.187428 | ||||||||
\(919\) | −42.9788 | −1.41774 | −0.708870 | − | 0.705339i | \(-0.750795\pi\) | ||||
−0.708870 | + | 0.705339i | \(0.750795\pi\) | |||||||
\(920\) | −2.12473 | −0.0700501 | ||||||||
\(921\) | −43.8136 | −1.44371 | ||||||||
\(922\) | 1.07330 | 0.0353473 | ||||||||
\(923\) | −25.1129 | −0.826600 | ||||||||
\(924\) | 2.23344 | 0.0734747 | ||||||||
\(925\) | −0.896079 | −0.0294629 | ||||||||
\(926\) | −0.715854 | −0.0235244 | ||||||||
\(927\) | −1.88683 | −0.0619718 | ||||||||
\(928\) | −3.45827 | −0.113523 | ||||||||
\(929\) | −17.7526 | −0.582445 | −0.291222 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291222 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(930\) | −1.61674 | −0.0530149 | ||||||||
\(931\) | −6.95789 | −0.228036 | ||||||||
\(932\) | −27.6943 | −0.907156 | ||||||||
\(933\) | −33.5101 | −1.09707 | ||||||||
\(934\) | −3.89573 | −0.127472 | ||||||||
\(935\) | 4.04694 | 0.132349 | ||||||||
\(936\) | 0.268996 | 0.00879240 | ||||||||
\(937\) | 45.9827 | 1.50219 | 0.751094 | − | 0.660195i | \(-0.229526\pi\) | ||||
0.751094 | + | 0.660195i | \(0.229526\pi\) | |||||||
\(938\) | 0.915250 | 0.0298840 | ||||||||
\(939\) | 43.4697 | 1.41858 | ||||||||
\(940\) | −13.8041 | −0.450240 | ||||||||
\(941\) | 18.7917 | 0.612591 | 0.306295 | − | 0.951937i | \(-0.400910\pi\) | ||||
0.306295 | + | 0.951937i | \(0.400910\pi\) | |||||||
\(942\) | −2.47056 | −0.0804952 | ||||||||
\(943\) | −3.78098 | −0.123126 | ||||||||
\(944\) | −39.8337 | −1.29648 | ||||||||
\(945\) | 5.06329 | 0.164709 | ||||||||
\(946\) | 1.07529 | 0.0349607 | ||||||||
\(947\) | −21.7088 | −0.705440 | −0.352720 | − | 0.935729i | \(-0.614743\pi\) | ||||
−0.352720 | + | 0.935729i | \(0.614743\pi\) | |||||||
\(948\) | 4.25767 | 0.138283 | ||||||||
\(949\) | −14.9327 | −0.484735 | ||||||||
\(950\) | −1.23368 | −0.0400258 | ||||||||
\(951\) | −12.6163 | −0.409112 | ||||||||
\(952\) | 4.45099 | 0.144257 | ||||||||
\(953\) | 14.7668 | 0.478344 | 0.239172 | − | 0.970977i | \(-0.423124\pi\) | ||||
0.239172 | + | 0.970977i | \(0.423124\pi\) | |||||||
\(954\) | −0.231305 | −0.00748878 | ||||||||
\(955\) | 9.13370 | 0.295560 | ||||||||
\(956\) | −12.5673 | −0.406456 | ||||||||
\(957\) | −1.88339 | −0.0608815 | ||||||||
\(958\) | −1.17822 | −0.0380666 | ||||||||
\(959\) | −22.7945 | −0.736071 | ||||||||
\(960\) | −12.8663 | −0.415260 | ||||||||
\(961\) | −4.56145 | −0.147144 | ||||||||
\(962\) | 0.419449 | 0.0135236 | ||||||||
\(963\) | −1.08146 | −0.0348495 | ||||||||
\(964\) | −2.08841 | −0.0672633 | ||||||||
\(965\) | −22.3999 | −0.721077 | ||||||||
\(966\) | −0.949438 | −0.0305477 | ||||||||
\(967\) | −47.7645 | −1.53600 | −0.768001 | − | 0.640449i | \(-0.778748\pi\) | ||||
−0.768001 | + | 0.640449i | \(0.778748\pi\) | |||||||
\(968\) | 7.45215 | 0.239521 | ||||||||
\(969\) | 78.0502 | 2.50733 | ||||||||
\(970\) | 3.30307 | 0.106055 | ||||||||
\(971\) | −44.0116 | −1.41240 | −0.706199 | − | 0.708013i | \(-0.749592\pi\) | ||||
−0.706199 | + | 0.708013i | \(0.749592\pi\) | |||||||
\(972\) | −2.95983 | −0.0949366 | ||||||||
\(973\) | −21.9719 | −0.704386 | ||||||||
\(974\) | 2.25352 | 0.0722074 | ||||||||
\(975\) | 4.68172 | 0.149935 | ||||||||
\(976\) | −17.4529 | −0.558654 | ||||||||
\(977\) | −3.25938 | −0.104277 | −0.0521384 | − | 0.998640i | \(-0.516604\pi\) | ||||
−0.0521384 | + | 0.998640i | \(0.516604\pi\) | |||||||
\(978\) | −3.44917 | −0.110292 | ||||||||
\(979\) | −4.96708 | −0.158749 | ||||||||
\(980\) | 1.96856 | 0.0628834 | ||||||||
\(981\) | −2.89637 | −0.0924738 | ||||||||
\(982\) | −4.89119 | −0.156084 | ||||||||
\(983\) | −52.0093 | −1.65884 | −0.829419 | − | 0.558627i | \(-0.811328\pi\) | ||||
−0.829419 | + | 0.558627i | \(0.811328\pi\) | |||||||
\(984\) | 1.56247 | 0.0498098 | ||||||||
\(985\) | 10.5228 | 0.335284 | ||||||||
\(986\) | −1.86183 | −0.0592927 | ||||||||
\(987\) | −12.4353 | −0.395819 | ||||||||
\(988\) | −36.1606 | −1.15042 | ||||||||
\(989\) | 28.6233 | 0.910166 | ||||||||
\(990\) | 0.0164260 | 0.000522053 0 | ||||||||
\(991\) | −59.0845 | −1.87688 | −0.938440 | − | 0.345441i | \(-0.887729\pi\) | ||||
−0.938440 | + | 0.345441i | \(0.887729\pi\) | |||||||
\(992\) | −10.7118 | −0.340100 | ||||||||
\(993\) | 47.1758 | 1.49708 | ||||||||
\(994\) | −1.68660 | −0.0534957 | ||||||||
\(995\) | 22.9550 | 0.727723 | ||||||||
\(996\) | −60.2994 | −1.91066 | ||||||||
\(997\) | 18.9426 | 0.599918 | 0.299959 | − | 0.953952i | \(-0.403027\pi\) | ||||
0.299959 | + | 0.953952i | \(0.403027\pi\) | |||||||
\(998\) | −6.62044 | −0.209566 | ||||||||
\(999\) | −4.53711 | −0.143548 |
(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 | 8015.2.a.l.1.33 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.33 | ✓ | 62 | 1.1 | even | 1 | trivial |