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 | 1.22 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.829924 | 0.586845 | 0.293423 | − | 0.955983i | \(-0.405206\pi\) | ||||
0.293423 | + | 0.955983i | \(0.405206\pi\) | |||||||
\(3\) | 2.15264 | 1.24283 | 0.621413 | − | 0.783483i | \(-0.286559\pi\) | ||||
0.621413 | + | 0.783483i | \(0.286559\pi\) | |||||||
\(4\) | −1.31123 | −0.655613 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.78653 | 0.729347 | ||||||||
\(7\) | −1.04291 | −0.394181 | −0.197091 | − | 0.980385i | \(-0.563149\pi\) | ||||
−0.197091 | + | 0.980385i | \(0.563149\pi\) | |||||||
\(8\) | −2.74807 | −0.971588 | ||||||||
\(9\) | 1.63385 | 0.544618 | ||||||||
\(10\) | 0.829924 | 0.262445 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.82259 | −0.814813 | ||||||||
\(13\) | −4.99996 | −1.38674 | −0.693370 | − | 0.720582i | \(-0.743875\pi\) | ||||
−0.693370 | + | 0.720582i | \(0.743875\pi\) | |||||||
\(14\) | −0.865533 | −0.231323 | ||||||||
\(15\) | 2.15264 | 0.555809 | ||||||||
\(16\) | 0.341763 | 0.0854407 | ||||||||
\(17\) | 2.47904 | 0.601255 | 0.300627 | − | 0.953742i | \(-0.402804\pi\) | ||||
0.300627 | + | 0.953742i | \(0.402804\pi\) | |||||||
\(18\) | 1.35597 | 0.319606 | ||||||||
\(19\) | 2.20828 | 0.506615 | 0.253308 | − | 0.967386i | \(-0.418482\pi\) | ||||
0.253308 | + | 0.967386i | \(0.418482\pi\) | |||||||
\(20\) | −1.31123 | −0.293199 | ||||||||
\(21\) | −2.24500 | −0.489899 | ||||||||
\(22\) | 0.829924 | 0.176940 | ||||||||
\(23\) | 5.73620 | 1.19608 | 0.598040 | − | 0.801466i | \(-0.295946\pi\) | ||||
0.598040 | + | 0.801466i | \(0.295946\pi\) | |||||||
\(24\) | −5.91560 | −1.20752 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.14959 | −0.813802 | ||||||||
\(27\) | −2.94082 | −0.565961 | ||||||||
\(28\) | 1.36748 | 0.258430 | ||||||||
\(29\) | 7.55345 | 1.40264 | 0.701320 | − | 0.712846i | \(-0.252594\pi\) | ||||
0.701320 | + | 0.712846i | \(0.252594\pi\) | |||||||
\(30\) | 1.78653 | 0.326174 | ||||||||
\(31\) | 10.9263 | 1.96242 | 0.981212 | − | 0.192930i | \(-0.0617991\pi\) | ||||
0.981212 | + | 0.192930i | \(0.0617991\pi\) | |||||||
\(32\) | 5.77977 | 1.02173 | ||||||||
\(33\) | 2.15264 | 0.374726 | ||||||||
\(34\) | 2.05741 | 0.352843 | ||||||||
\(35\) | −1.04291 | −0.176283 | ||||||||
\(36\) | −2.14235 | −0.357058 | ||||||||
\(37\) | −2.81683 | −0.463083 | −0.231542 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231542 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(38\) | 1.83271 | 0.297305 | ||||||||
\(39\) | −10.7631 | −1.72348 | ||||||||
\(40\) | −2.74807 | −0.434508 | ||||||||
\(41\) | 4.54516 | 0.709834 | 0.354917 | − | 0.934898i | \(-0.384509\pi\) | ||||
0.354917 | + | 0.934898i | \(0.384509\pi\) | |||||||
\(42\) | −1.86318 | −0.287495 | ||||||||
\(43\) | 6.23420 | 0.950707 | 0.475354 | − | 0.879795i | \(-0.342320\pi\) | ||||
0.475354 | + | 0.879795i | \(0.342320\pi\) | |||||||
\(44\) | −1.31123 | −0.197675 | ||||||||
\(45\) | 1.63385 | 0.243560 | ||||||||
\(46\) | 4.76061 | 0.701914 | ||||||||
\(47\) | −7.66300 | −1.11776 | −0.558881 | − | 0.829248i | \(-0.688769\pi\) | ||||
−0.558881 | + | 0.829248i | \(0.688769\pi\) | |||||||
\(48\) | 0.735691 | 0.106188 | ||||||||
\(49\) | −5.91235 | −0.844621 | ||||||||
\(50\) | 0.829924 | 0.117369 | ||||||||
\(51\) | 5.33647 | 0.747255 | ||||||||
\(52\) | 6.55608 | 0.909164 | ||||||||
\(53\) | −4.99682 | −0.686366 | −0.343183 | − | 0.939269i | \(-0.611505\pi\) | ||||
−0.343183 | + | 0.939269i | \(0.611505\pi\) | |||||||
\(54\) | −2.44066 | −0.332132 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.86598 | 0.382982 | ||||||||
\(57\) | 4.75364 | 0.629635 | ||||||||
\(58\) | 6.26880 | 0.823133 | ||||||||
\(59\) | 12.1875 | 1.58668 | 0.793339 | − | 0.608780i | \(-0.208341\pi\) | ||||
0.793339 | + | 0.608780i | \(0.208341\pi\) | |||||||
\(60\) | −2.82259 | −0.364395 | ||||||||
\(61\) | −1.05992 | −0.135709 | −0.0678544 | − | 0.997695i | \(-0.521615\pi\) | ||||
−0.0678544 | + | 0.997695i | \(0.521615\pi\) | |||||||
\(62\) | 9.06802 | 1.15164 | ||||||||
\(63\) | −1.70396 | −0.214678 | ||||||||
\(64\) | 4.11325 | 0.514156 | ||||||||
\(65\) | −4.99996 | −0.620169 | ||||||||
\(66\) | 1.78653 | 0.219906 | ||||||||
\(67\) | 7.00699 | 0.856040 | 0.428020 | − | 0.903769i | \(-0.359211\pi\) | ||||
0.428020 | + | 0.903769i | \(0.359211\pi\) | |||||||
\(68\) | −3.25058 | −0.394190 | ||||||||
\(69\) | 12.3480 | 1.48652 | ||||||||
\(70\) | −0.865533 | −0.103451 | ||||||||
\(71\) | 13.6462 | 1.61951 | 0.809753 | − | 0.586770i | \(-0.199601\pi\) | ||||
0.809753 | + | 0.586770i | \(0.199601\pi\) | |||||||
\(72\) | −4.48994 | −0.529144 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −2.33775 | −0.271758 | ||||||||
\(75\) | 2.15264 | 0.248565 | ||||||||
\(76\) | −2.89556 | −0.332143 | ||||||||
\(77\) | −1.04291 | −0.118850 | ||||||||
\(78\) | −8.93257 | −1.01141 | ||||||||
\(79\) | 15.2672 | 1.71769 | 0.858845 | − | 0.512236i | \(-0.171183\pi\) | ||||
0.858845 | + | 0.512236i | \(0.171183\pi\) | |||||||
\(80\) | 0.341763 | 0.0382102 | ||||||||
\(81\) | −11.2321 | −1.24801 | ||||||||
\(82\) | 3.77214 | 0.416563 | ||||||||
\(83\) | 3.03747 | 0.333406 | 0.166703 | − | 0.986007i | \(-0.446688\pi\) | ||||
0.166703 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(84\) | 2.94370 | 0.321184 | ||||||||
\(85\) | 2.47904 | 0.268889 | ||||||||
\(86\) | 5.17392 | 0.557918 | ||||||||
\(87\) | 16.2599 | 1.74324 | ||||||||
\(88\) | −2.74807 | −0.292945 | ||||||||
\(89\) | −16.0244 | −1.69859 | −0.849293 | − | 0.527922i | \(-0.822972\pi\) | ||||
−0.849293 | + | 0.527922i | \(0.822972\pi\) | |||||||
\(90\) | 1.35597 | 0.142932 | ||||||||
\(91\) | 5.21449 | 0.546627 | ||||||||
\(92\) | −7.52145 | −0.784165 | ||||||||
\(93\) | 23.5204 | 2.43895 | ||||||||
\(94\) | −6.35971 | −0.655954 | ||||||||
\(95\) | 2.20828 | 0.226565 | ||||||||
\(96\) | 12.4418 | 1.26983 | ||||||||
\(97\) | 2.92528 | 0.297017 | 0.148508 | − | 0.988911i | \(-0.452553\pi\) | ||||
0.148508 | + | 0.988911i | \(0.452553\pi\) | |||||||
\(98\) | −4.90680 | −0.495662 | ||||||||
\(99\) | 1.63385 | 0.164208 | ||||||||
\(100\) | −1.31123 | −0.131123 | ||||||||
\(101\) | 10.6303 | 1.05775 | 0.528875 | − | 0.848700i | \(-0.322614\pi\) | ||||
0.528875 | + | 0.848700i | \(0.322614\pi\) | |||||||
\(102\) | 4.42887 | 0.438523 | ||||||||
\(103\) | −13.6587 | −1.34584 | −0.672918 | − | 0.739717i | \(-0.734959\pi\) | ||||
−0.672918 | + | 0.739717i | \(0.734959\pi\) | |||||||
\(104\) | 13.7402 | 1.34734 | ||||||||
\(105\) | −2.24500 | −0.219090 | ||||||||
\(106\) | −4.14698 | −0.402790 | ||||||||
\(107\) | −6.82896 | −0.660181 | −0.330090 | − | 0.943949i | \(-0.607079\pi\) | ||||
−0.330090 | + | 0.943949i | \(0.607079\pi\) | |||||||
\(108\) | 3.85608 | 0.371051 | ||||||||
\(109\) | 12.6156 | 1.20836 | 0.604178 | − | 0.796849i | \(-0.293502\pi\) | ||||
0.604178 | + | 0.796849i | \(0.293502\pi\) | |||||||
\(110\) | 0.829924 | 0.0791302 | ||||||||
\(111\) | −6.06361 | −0.575532 | ||||||||
\(112\) | −0.356426 | −0.0336791 | ||||||||
\(113\) | 1.50690 | 0.141757 | 0.0708784 | − | 0.997485i | \(-0.477420\pi\) | ||||
0.0708784 | + | 0.997485i | \(0.477420\pi\) | |||||||
\(114\) | 3.94516 | 0.369498 | ||||||||
\(115\) | 5.73620 | 0.534903 | ||||||||
\(116\) | −9.90428 | −0.919589 | ||||||||
\(117\) | −8.16920 | −0.755243 | ||||||||
\(118\) | 10.1147 | 0.931134 | ||||||||
\(119\) | −2.58540 | −0.237003 | ||||||||
\(120\) | −5.91560 | −0.540018 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.879653 | −0.0796401 | ||||||||
\(123\) | 9.78408 | 0.882201 | ||||||||
\(124\) | −14.3269 | −1.28659 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.41415 | −0.125983 | ||||||||
\(127\) | −4.36742 | −0.387546 | −0.193773 | − | 0.981046i | \(-0.562072\pi\) | ||||
−0.193773 | + | 0.981046i | \(0.562072\pi\) | |||||||
\(128\) | −8.14586 | −0.719999 | ||||||||
\(129\) | 13.4200 | 1.18156 | ||||||||
\(130\) | −4.14959 | −0.363943 | ||||||||
\(131\) | 16.7683 | 1.46505 | 0.732525 | − | 0.680741i | \(-0.238342\pi\) | ||||
0.732525 | + | 0.680741i | \(0.238342\pi\) | |||||||
\(132\) | −2.82259 | −0.245675 | ||||||||
\(133\) | −2.30303 | −0.199698 | ||||||||
\(134\) | 5.81528 | 0.502363 | ||||||||
\(135\) | −2.94082 | −0.253105 | ||||||||
\(136\) | −6.81256 | −0.584172 | ||||||||
\(137\) | −20.5287 | −1.75388 | −0.876942 | − | 0.480596i | \(-0.840420\pi\) | ||||
−0.876942 | + | 0.480596i | \(0.840420\pi\) | |||||||
\(138\) | 10.2479 | 0.872357 | ||||||||
\(139\) | 0.205962 | 0.0174694 | 0.00873472 | − | 0.999962i | \(-0.497220\pi\) | ||||
0.00873472 | + | 0.999962i | \(0.497220\pi\) | |||||||
\(140\) | 1.36748 | 0.115574 | ||||||||
\(141\) | −16.4957 | −1.38919 | ||||||||
\(142\) | 11.3253 | 0.950400 | ||||||||
\(143\) | −4.99996 | −0.418118 | ||||||||
\(144\) | 0.558390 | 0.0465325 | ||||||||
\(145\) | 7.55345 | 0.627280 | ||||||||
\(146\) | 0.829924 | 0.0686850 | ||||||||
\(147\) | −12.7271 | −1.04972 | ||||||||
\(148\) | 3.69349 | 0.303603 | ||||||||
\(149\) | 0.357433 | 0.0292821 | 0.0146410 | − | 0.999893i | \(-0.495339\pi\) | ||||
0.0146410 | + | 0.999893i | \(0.495339\pi\) | |||||||
\(150\) | 1.78653 | 0.145869 | ||||||||
\(151\) | −5.41786 | −0.440900 | −0.220450 | − | 0.975398i | \(-0.570753\pi\) | ||||
−0.220450 | + | 0.975398i | \(0.570753\pi\) | |||||||
\(152\) | −6.06851 | −0.492221 | ||||||||
\(153\) | 4.05038 | 0.327454 | ||||||||
\(154\) | −0.865533 | −0.0697466 | ||||||||
\(155\) | 10.9263 | 0.877623 | ||||||||
\(156\) | 14.1129 | 1.12993 | ||||||||
\(157\) | −12.3225 | −0.983441 | −0.491720 | − | 0.870753i | \(-0.663632\pi\) | ||||
−0.491720 | + | 0.870753i | \(0.663632\pi\) | |||||||
\(158\) | 12.6706 | 1.00802 | ||||||||
\(159\) | −10.7563 | −0.853034 | ||||||||
\(160\) | 5.77977 | 0.456931 | ||||||||
\(161\) | −5.98231 | −0.471472 | ||||||||
\(162\) | −9.32178 | −0.732388 | ||||||||
\(163\) | 7.40490 | 0.579997 | 0.289998 | − | 0.957027i | \(-0.406345\pi\) | ||||
0.289998 | + | 0.957027i | \(0.406345\pi\) | |||||||
\(164\) | −5.95972 | −0.465376 | ||||||||
\(165\) | 2.15264 | 0.167583 | ||||||||
\(166\) | 2.52087 | 0.195658 | ||||||||
\(167\) | −18.2133 | −1.40939 | −0.704695 | − | 0.709510i | \(-0.748916\pi\) | ||||
−0.704695 | + | 0.709510i | \(0.748916\pi\) | |||||||
\(168\) | 6.16941 | 0.475980 | ||||||||
\(169\) | 11.9996 | 0.923047 | ||||||||
\(170\) | 2.05741 | 0.157796 | ||||||||
\(171\) | 3.60801 | 0.275912 | ||||||||
\(172\) | −8.17445 | −0.623296 | ||||||||
\(173\) | −11.0730 | −0.841866 | −0.420933 | − | 0.907092i | \(-0.638297\pi\) | ||||
−0.420933 | + | 0.907092i | \(0.638297\pi\) | |||||||
\(174\) | 13.4945 | 1.02301 | ||||||||
\(175\) | −1.04291 | −0.0788363 | ||||||||
\(176\) | 0.341763 | 0.0257613 | ||||||||
\(177\) | 26.2353 | 1.97196 | ||||||||
\(178\) | −13.2991 | −0.996807 | ||||||||
\(179\) | −25.4658 | −1.90340 | −0.951700 | − | 0.307029i | \(-0.900665\pi\) | ||||
−0.951700 | + | 0.307029i | \(0.900665\pi\) | |||||||
\(180\) | −2.14235 | −0.159681 | ||||||||
\(181\) | 17.9896 | 1.33716 | 0.668579 | − | 0.743641i | \(-0.266903\pi\) | ||||
0.668579 | + | 0.743641i | \(0.266903\pi\) | |||||||
\(182\) | 4.32763 | 0.320785 | ||||||||
\(183\) | −2.28162 | −0.168662 | ||||||||
\(184\) | −15.7635 | −1.16210 | ||||||||
\(185\) | −2.81683 | −0.207097 | ||||||||
\(186\) | 19.5202 | 1.43129 | ||||||||
\(187\) | 2.47904 | 0.181285 | ||||||||
\(188\) | 10.0479 | 0.732820 | ||||||||
\(189\) | 3.06700 | 0.223091 | ||||||||
\(190\) | 1.83271 | 0.132959 | ||||||||
\(191\) | −0.0991286 | −0.00717269 | −0.00358635 | − | 0.999994i | \(-0.501142\pi\) | ||||
−0.00358635 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(192\) | 8.85434 | 0.639007 | ||||||||
\(193\) | −7.35857 | −0.529681 | −0.264841 | − | 0.964292i | \(-0.585319\pi\) | ||||
−0.264841 | + | 0.964292i | \(0.585319\pi\) | |||||||
\(194\) | 2.42776 | 0.174303 | ||||||||
\(195\) | −10.7631 | −0.770762 | ||||||||
\(196\) | 7.75242 | 0.553744 | ||||||||
\(197\) | 6.49007 | 0.462398 | 0.231199 | − | 0.972906i | \(-0.425735\pi\) | ||||
0.231199 | + | 0.972906i | \(0.425735\pi\) | |||||||
\(198\) | 1.35597 | 0.0963649 | ||||||||
\(199\) | −0.161833 | −0.0114720 | −0.00573600 | − | 0.999984i | \(-0.501826\pi\) | ||||
−0.00573600 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(200\) | −2.74807 | −0.194318 | ||||||||
\(201\) | 15.0835 | 1.06391 | ||||||||
\(202\) | 8.82231 | 0.620736 | ||||||||
\(203\) | −7.87754 | −0.552895 | ||||||||
\(204\) | −6.99731 | −0.489910 | ||||||||
\(205\) | 4.54516 | 0.317448 | ||||||||
\(206\) | −11.3357 | −0.789797 | ||||||||
\(207\) | 9.37210 | 0.651406 | ||||||||
\(208\) | −1.70880 | −0.118484 | ||||||||
\(209\) | 2.20828 | 0.152750 | ||||||||
\(210\) | −1.86318 | −0.128572 | ||||||||
\(211\) | 22.5360 | 1.55144 | 0.775720 | − | 0.631078i | \(-0.217387\pi\) | ||||
0.775720 | + | 0.631078i | \(0.217387\pi\) | |||||||
\(212\) | 6.55195 | 0.449990 | ||||||||
\(213\) | 29.3753 | 2.01277 | ||||||||
\(214\) | −5.66752 | −0.387424 | ||||||||
\(215\) | 6.23420 | 0.425169 | ||||||||
\(216\) | 8.08157 | 0.549881 | ||||||||
\(217\) | −11.3951 | −0.773551 | ||||||||
\(218\) | 10.4700 | 0.709118 | ||||||||
\(219\) | 2.15264 | 0.145462 | ||||||||
\(220\) | −1.31123 | −0.0884028 | ||||||||
\(221\) | −12.3951 | −0.833784 | ||||||||
\(222\) | −5.03234 | −0.337748 | ||||||||
\(223\) | −16.7780 | −1.12354 | −0.561771 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561771 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(224\) | −6.02776 | −0.402746 | ||||||||
\(225\) | 1.63385 | 0.108924 | ||||||||
\(226\) | 1.25061 | 0.0831893 | ||||||||
\(227\) | 20.4542 | 1.35759 | 0.678797 | − | 0.734326i | \(-0.262501\pi\) | ||||
0.678797 | + | 0.734326i | \(0.262501\pi\) | |||||||
\(228\) | −6.23309 | −0.412797 | ||||||||
\(229\) | −9.16392 | −0.605569 | −0.302784 | − | 0.953059i | \(-0.597916\pi\) | ||||
−0.302784 | + | 0.953059i | \(0.597916\pi\) | |||||||
\(230\) | 4.76061 | 0.313905 | ||||||||
\(231\) | −2.24500 | −0.147710 | ||||||||
\(232\) | −20.7574 | −1.36279 | ||||||||
\(233\) | −21.2588 | −1.39271 | −0.696356 | − | 0.717696i | \(-0.745197\pi\) | ||||
−0.696356 | + | 0.717696i | \(0.745197\pi\) | |||||||
\(234\) | −6.77982 | −0.443211 | ||||||||
\(235\) | −7.66300 | −0.499879 | ||||||||
\(236\) | −15.9806 | −1.04025 | ||||||||
\(237\) | 32.8647 | 2.13479 | ||||||||
\(238\) | −2.14569 | −0.139084 | ||||||||
\(239\) | −13.2380 | −0.856295 | −0.428148 | − | 0.903709i | \(-0.640834\pi\) | ||||
−0.428148 | + | 0.903709i | \(0.640834\pi\) | |||||||
\(240\) | 0.735691 | 0.0474887 | ||||||||
\(241\) | −6.99142 | −0.450357 | −0.225178 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225178 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(242\) | 0.829924 | 0.0533496 | ||||||||
\(243\) | −15.3562 | −0.985098 | ||||||||
\(244\) | 1.38979 | 0.0889724 | ||||||||
\(245\) | −5.91235 | −0.377726 | ||||||||
\(246\) | 8.12005 | 0.517715 | ||||||||
\(247\) | −11.0413 | −0.702543 | ||||||||
\(248\) | −30.0263 | −1.90667 | ||||||||
\(249\) | 6.53858 | 0.414365 | ||||||||
\(250\) | 0.829924 | 0.0524890 | ||||||||
\(251\) | 5.49663 | 0.346944 | 0.173472 | − | 0.984839i | \(-0.444501\pi\) | ||||
0.173472 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(252\) | 2.23427 | 0.140746 | ||||||||
\(253\) | 5.73620 | 0.360632 | ||||||||
\(254\) | −3.62463 | −0.227429 | ||||||||
\(255\) | 5.33647 | 0.334183 | ||||||||
\(256\) | −14.9869 | −0.936684 | ||||||||
\(257\) | 7.03141 | 0.438608 | 0.219304 | − | 0.975657i | \(-0.429621\pi\) | ||||
0.219304 | + | 0.975657i | \(0.429621\pi\) | |||||||
\(258\) | 11.1376 | 0.693395 | ||||||||
\(259\) | 2.93768 | 0.182539 | ||||||||
\(260\) | 6.55608 | 0.406591 | ||||||||
\(261\) | 12.3412 | 0.763903 | ||||||||
\(262\) | 13.9164 | 0.859757 | ||||||||
\(263\) | 20.0010 | 1.23331 | 0.616656 | − | 0.787233i | \(-0.288487\pi\) | ||||
0.616656 | + | 0.787233i | \(0.288487\pi\) | |||||||
\(264\) | −5.91560 | −0.364080 | ||||||||
\(265\) | −4.99682 | −0.306952 | ||||||||
\(266\) | −1.91134 | −0.117192 | ||||||||
\(267\) | −34.4948 | −2.11105 | ||||||||
\(268\) | −9.18775 | −0.561231 | ||||||||
\(269\) | −25.2922 | −1.54209 | −0.771046 | − | 0.636779i | \(-0.780266\pi\) | ||||
−0.771046 | + | 0.636779i | \(0.780266\pi\) | |||||||
\(270\) | −2.44066 | −0.148534 | ||||||||
\(271\) | 12.3769 | 0.751844 | 0.375922 | − | 0.926651i | \(-0.377326\pi\) | ||||
0.375922 | + | 0.926651i | \(0.377326\pi\) | |||||||
\(272\) | 0.847242 | 0.0513716 | ||||||||
\(273\) | 11.2249 | 0.679362 | ||||||||
\(274\) | −17.0373 | −1.02926 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −16.1910 | −0.974581 | ||||||||
\(277\) | −15.2397 | −0.915667 | −0.457833 | − | 0.889038i | \(-0.651374\pi\) | ||||
−0.457833 | + | 0.889038i | \(0.651374\pi\) | |||||||
\(278\) | 0.170933 | 0.0102519 | ||||||||
\(279\) | 17.8520 | 1.06877 | ||||||||
\(280\) | 2.86598 | 0.171275 | ||||||||
\(281\) | 26.7685 | 1.59687 | 0.798437 | − | 0.602078i | \(-0.205660\pi\) | ||||
0.798437 | + | 0.602078i | \(0.205660\pi\) | |||||||
\(282\) | −13.6902 | −0.815237 | ||||||||
\(283\) | 18.6758 | 1.11016 | 0.555082 | − | 0.831796i | \(-0.312687\pi\) | ||||
0.555082 | + | 0.831796i | \(0.312687\pi\) | |||||||
\(284\) | −17.8933 | −1.06177 | ||||||||
\(285\) | 4.75364 | 0.281581 | ||||||||
\(286\) | −4.14959 | −0.245370 | ||||||||
\(287\) | −4.74017 | −0.279803 | ||||||||
\(288\) | 9.44330 | 0.556452 | ||||||||
\(289\) | −10.8544 | −0.638493 | ||||||||
\(290\) | 6.26880 | 0.368116 | ||||||||
\(291\) | 6.29706 | 0.369140 | ||||||||
\(292\) | −1.31123 | −0.0767337 | ||||||||
\(293\) | −12.6535 | −0.739226 | −0.369613 | − | 0.929186i | \(-0.620510\pi\) | ||||
−0.369613 | + | 0.929186i | \(0.620510\pi\) | |||||||
\(294\) | −10.5626 | −0.616022 | ||||||||
\(295\) | 12.1875 | 0.709584 | ||||||||
\(296\) | 7.74083 | 0.449926 | ||||||||
\(297\) | −2.94082 | −0.170644 | ||||||||
\(298\) | 0.296643 | 0.0171840 | ||||||||
\(299\) | −28.6808 | −1.65865 | ||||||||
\(300\) | −2.82259 | −0.162963 | ||||||||
\(301\) | −6.50169 | −0.374751 | ||||||||
\(302\) | −4.49642 | −0.258740 | ||||||||
\(303\) | 22.8831 | 1.31460 | ||||||||
\(304\) | 0.754709 | 0.0432855 | ||||||||
\(305\) | −1.05992 | −0.0606908 | ||||||||
\(306\) | 3.36151 | 0.192165 | ||||||||
\(307\) | 10.1608 | 0.579905 | 0.289953 | − | 0.957041i | \(-0.406360\pi\) | ||||
0.289953 | + | 0.957041i | \(0.406360\pi\) | |||||||
\(308\) | 1.36748 | 0.0779197 | ||||||||
\(309\) | −29.4023 | −1.67264 | ||||||||
\(310\) | 9.06802 | 0.515029 | ||||||||
\(311\) | 9.06810 | 0.514205 | 0.257102 | − | 0.966384i | \(-0.417232\pi\) | ||||
0.257102 | + | 0.966384i | \(0.417232\pi\) | |||||||
\(312\) | 29.5777 | 1.67451 | ||||||||
\(313\) | 9.61319 | 0.543369 | 0.271685 | − | 0.962386i | \(-0.412419\pi\) | ||||
0.271685 | + | 0.962386i | \(0.412419\pi\) | |||||||
\(314\) | −10.2267 | −0.577127 | ||||||||
\(315\) | −1.70396 | −0.0960070 | ||||||||
\(316\) | −20.0187 | −1.12614 | ||||||||
\(317\) | −3.81576 | −0.214315 | −0.107157 | − | 0.994242i | \(-0.534175\pi\) | ||||
−0.107157 | + | 0.994242i | \(0.534175\pi\) | |||||||
\(318\) | −8.92695 | −0.500599 | ||||||||
\(319\) | 7.55345 | 0.422912 | ||||||||
\(320\) | 4.11325 | 0.229938 | ||||||||
\(321\) | −14.7003 | −0.820490 | ||||||||
\(322\) | −4.96487 | −0.276681 | ||||||||
\(323\) | 5.47442 | 0.304605 | ||||||||
\(324\) | 14.7278 | 0.818211 | ||||||||
\(325\) | −4.99996 | −0.277348 | ||||||||
\(326\) | 6.14551 | 0.340368 | ||||||||
\(327\) | 27.1568 | 1.50178 | ||||||||
\(328\) | −12.4904 | −0.689667 | ||||||||
\(329\) | 7.99178 | 0.440601 | ||||||||
\(330\) | 1.78653 | 0.0983451 | ||||||||
\(331\) | 3.71474 | 0.204180 | 0.102090 | − | 0.994775i | \(-0.467447\pi\) | ||||
0.102090 | + | 0.994775i | \(0.467447\pi\) | |||||||
\(332\) | −3.98281 | −0.218585 | ||||||||
\(333\) | −4.60228 | −0.252203 | ||||||||
\(334\) | −15.1157 | −0.827094 | ||||||||
\(335\) | 7.00699 | 0.382833 | ||||||||
\(336\) | −0.767257 | −0.0418573 | ||||||||
\(337\) | 17.0084 | 0.926504 | 0.463252 | − | 0.886227i | \(-0.346682\pi\) | ||||
0.463252 | + | 0.886227i | \(0.346682\pi\) | |||||||
\(338\) | 9.95877 | 0.541686 | ||||||||
\(339\) | 3.24380 | 0.176179 | ||||||||
\(340\) | −3.25058 | −0.176287 | ||||||||
\(341\) | 10.9263 | 0.591693 | ||||||||
\(342\) | 2.99438 | 0.161917 | ||||||||
\(343\) | 13.4664 | 0.727115 | ||||||||
\(344\) | −17.1320 | −0.923696 | ||||||||
\(345\) | 12.3480 | 0.664792 | ||||||||
\(346\) | −9.18977 | −0.494045 | ||||||||
\(347\) | 30.3558 | 1.62959 | 0.814793 | − | 0.579751i | \(-0.196850\pi\) | ||||
0.814793 | + | 0.579751i | \(0.196850\pi\) | |||||||
\(348\) | −21.3203 | −1.14289 | ||||||||
\(349\) | 14.6584 | 0.784647 | 0.392323 | − | 0.919827i | \(-0.371671\pi\) | ||||
0.392323 | + | 0.919827i | \(0.371671\pi\) | |||||||
\(350\) | −0.865533 | −0.0462647 | ||||||||
\(351\) | 14.7040 | 0.784841 | ||||||||
\(352\) | 5.77977 | 0.308063 | ||||||||
\(353\) | 5.37992 | 0.286344 | 0.143172 | − | 0.989698i | \(-0.454270\pi\) | ||||
0.143172 | + | 0.989698i | \(0.454270\pi\) | |||||||
\(354\) | 21.7733 | 1.15724 | ||||||||
\(355\) | 13.6462 | 0.724265 | ||||||||
\(356\) | 21.0116 | 1.11361 | ||||||||
\(357\) | −5.56544 | −0.294554 | ||||||||
\(358\) | −21.1347 | −1.11700 | ||||||||
\(359\) | −37.1141 | −1.95881 | −0.979403 | − | 0.201917i | \(-0.935283\pi\) | ||||
−0.979403 | + | 0.201917i | \(0.935283\pi\) | |||||||
\(360\) | −4.48994 | −0.236641 | ||||||||
\(361\) | −14.1235 | −0.743341 | ||||||||
\(362\) | 14.9300 | 0.784705 | ||||||||
\(363\) | 2.15264 | 0.112984 | ||||||||
\(364\) | −6.83737 | −0.358376 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −1.89358 | −0.0989788 | ||||||||
\(367\) | −7.98776 | −0.416957 | −0.208479 | − | 0.978027i | \(-0.566851\pi\) | ||||
−0.208479 | + | 0.978027i | \(0.566851\pi\) | |||||||
\(368\) | 1.96042 | 0.102194 | ||||||||
\(369\) | 7.42612 | 0.386588 | ||||||||
\(370\) | −2.33775 | −0.121534 | ||||||||
\(371\) | 5.21121 | 0.270553 | ||||||||
\(372\) | −30.8406 | −1.59901 | ||||||||
\(373\) | 5.56022 | 0.287897 | 0.143949 | − | 0.989585i | \(-0.454020\pi\) | ||||
0.143949 | + | 0.989585i | \(0.454020\pi\) | |||||||
\(374\) | 2.05741 | 0.106386 | ||||||||
\(375\) | 2.15264 | 0.111162 | ||||||||
\(376\) | 21.0584 | 1.08601 | ||||||||
\(377\) | −37.7670 | −1.94510 | ||||||||
\(378\) | 2.54538 | 0.130920 | ||||||||
\(379\) | −9.54987 | −0.490544 | −0.245272 | − | 0.969454i | \(-0.578877\pi\) | ||||
−0.245272 | + | 0.969454i | \(0.578877\pi\) | |||||||
\(380\) | −2.89556 | −0.148539 | ||||||||
\(381\) | −9.40147 | −0.481652 | ||||||||
\(382\) | −0.0822692 | −0.00420926 | ||||||||
\(383\) | 29.5944 | 1.51220 | 0.756102 | − | 0.654453i | \(-0.227101\pi\) | ||||
0.756102 | + | 0.654453i | \(0.227101\pi\) | |||||||
\(384\) | −17.5351 | −0.894834 | ||||||||
\(385\) | −1.04291 | −0.0531514 | ||||||||
\(386\) | −6.10705 | −0.310841 | ||||||||
\(387\) | 10.1858 | 0.517772 | ||||||||
\(388\) | −3.83570 | −0.194728 | ||||||||
\(389\) | 6.65207 | 0.337274 | 0.168637 | − | 0.985678i | \(-0.446064\pi\) | ||||
0.168637 | + | 0.985678i | \(0.446064\pi\) | |||||||
\(390\) | −8.93257 | −0.452318 | ||||||||
\(391\) | 14.2202 | 0.719148 | ||||||||
\(392\) | 16.2475 | 0.820624 | ||||||||
\(393\) | 36.0960 | 1.82080 | ||||||||
\(394\) | 5.38627 | 0.271356 | ||||||||
\(395\) | 15.2672 | 0.768174 | ||||||||
\(396\) | −2.14235 | −0.107657 | ||||||||
\(397\) | 21.4150 | 1.07479 | 0.537394 | − | 0.843331i | \(-0.319409\pi\) | ||||
0.537394 | + | 0.843331i | \(0.319409\pi\) | |||||||
\(398\) | −0.134309 | −0.00673229 | ||||||||
\(399\) | −4.95760 | −0.248190 | ||||||||
\(400\) | 0.341763 | 0.0170881 | ||||||||
\(401\) | −4.03434 | −0.201465 | −0.100733 | − | 0.994914i | \(-0.532119\pi\) | ||||
−0.100733 | + | 0.994914i | \(0.532119\pi\) | |||||||
\(402\) | 12.5182 | 0.624350 | ||||||||
\(403\) | −54.6312 | −2.72137 | ||||||||
\(404\) | −13.9387 | −0.693474 | ||||||||
\(405\) | −11.2321 | −0.558127 | ||||||||
\(406\) | −6.53776 | −0.324464 | ||||||||
\(407\) | −2.81683 | −0.139625 | ||||||||
\(408\) | −14.6650 | −0.726024 | ||||||||
\(409\) | 21.6220 | 1.06914 | 0.534570 | − | 0.845124i | \(-0.320474\pi\) | ||||
0.534570 | + | 0.845124i | \(0.320474\pi\) | |||||||
\(410\) | 3.77214 | 0.186293 | ||||||||
\(411\) | −44.1909 | −2.17977 | ||||||||
\(412\) | 17.9097 | 0.882347 | ||||||||
\(413\) | −12.7104 | −0.625439 | ||||||||
\(414\) | 7.77814 | 0.382275 | ||||||||
\(415\) | 3.03747 | 0.149104 | ||||||||
\(416\) | −28.8986 | −1.41687 | ||||||||
\(417\) | 0.443361 | 0.0217115 | ||||||||
\(418\) | 1.83271 | 0.0896407 | ||||||||
\(419\) | 15.0268 | 0.734106 | 0.367053 | − | 0.930200i | \(-0.380367\pi\) | ||||
0.367053 | + | 0.930200i | \(0.380367\pi\) | |||||||
\(420\) | 2.94370 | 0.143638 | ||||||||
\(421\) | −1.89690 | −0.0924490 | −0.0462245 | − | 0.998931i | \(-0.514719\pi\) | ||||
−0.0462245 | + | 0.998931i | \(0.514719\pi\) | |||||||
\(422\) | 18.7031 | 0.910455 | ||||||||
\(423\) | −12.5202 | −0.608754 | ||||||||
\(424\) | 13.7316 | 0.666865 | ||||||||
\(425\) | 2.47904 | 0.120251 | ||||||||
\(426\) | 24.3793 | 1.18118 | ||||||||
\(427\) | 1.10540 | 0.0534939 | ||||||||
\(428\) | 8.95431 | 0.432823 | ||||||||
\(429\) | −10.7631 | −0.519648 | ||||||||
\(430\) | 5.17392 | 0.249509 | ||||||||
\(431\) | −13.3293 | −0.642052 | −0.321026 | − | 0.947070i | \(-0.604028\pi\) | ||||
−0.321026 | + | 0.947070i | \(0.604028\pi\) | |||||||
\(432\) | −1.00506 | −0.0483561 | ||||||||
\(433\) | 14.0683 | 0.676077 | 0.338039 | − | 0.941132i | \(-0.390237\pi\) | ||||
0.338039 | + | 0.941132i | \(0.390237\pi\) | |||||||
\(434\) | −9.45709 | −0.453955 | ||||||||
\(435\) | 16.2599 | 0.779600 | ||||||||
\(436\) | −16.5419 | −0.792214 | ||||||||
\(437\) | 12.6672 | 0.605952 | ||||||||
\(438\) | 1.78653 | 0.0853636 | ||||||||
\(439\) | 8.53521 | 0.407363 | 0.203682 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203682 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(440\) | −2.74807 | −0.131009 | ||||||||
\(441\) | −9.65991 | −0.459996 | ||||||||
\(442\) | −10.2870 | −0.489302 | ||||||||
\(443\) | 6.33871 | 0.301161 | 0.150581 | − | 0.988598i | \(-0.451886\pi\) | ||||
0.150581 | + | 0.988598i | \(0.451886\pi\) | |||||||
\(444\) | 7.95076 | 0.377326 | ||||||||
\(445\) | −16.0244 | −0.759631 | ||||||||
\(446\) | −13.9245 | −0.659345 | ||||||||
\(447\) | 0.769425 | 0.0363925 | ||||||||
\(448\) | −4.28973 | −0.202671 | ||||||||
\(449\) | −20.5376 | −0.969230 | −0.484615 | − | 0.874727i | \(-0.661040\pi\) | ||||
−0.484615 | + | 0.874727i | \(0.661040\pi\) | |||||||
\(450\) | 1.35597 | 0.0639213 | ||||||||
\(451\) | 4.54516 | 0.214023 | ||||||||
\(452\) | −1.97588 | −0.0929375 | ||||||||
\(453\) | −11.6627 | −0.547962 | ||||||||
\(454\) | 16.9755 | 0.796698 | ||||||||
\(455\) | 5.21449 | 0.244459 | ||||||||
\(456\) | −13.0633 | −0.611746 | ||||||||
\(457\) | −16.5418 | −0.773792 | −0.386896 | − | 0.922123i | \(-0.626453\pi\) | ||||
−0.386896 | + | 0.922123i | \(0.626453\pi\) | |||||||
\(458\) | −7.60536 | −0.355375 | ||||||||
\(459\) | −7.29040 | −0.340287 | ||||||||
\(460\) | −7.52145 | −0.350689 | ||||||||
\(461\) | −10.7185 | −0.499212 | −0.249606 | − | 0.968348i | \(-0.580301\pi\) | ||||
−0.249606 | + | 0.968348i | \(0.580301\pi\) | |||||||
\(462\) | −1.86318 | −0.0866830 | ||||||||
\(463\) | 3.22102 | 0.149693 | 0.0748467 | − | 0.997195i | \(-0.476153\pi\) | ||||
0.0748467 | + | 0.997195i | \(0.476153\pi\) | |||||||
\(464\) | 2.58149 | 0.119843 | ||||||||
\(465\) | 23.5204 | 1.09073 | ||||||||
\(466\) | −17.6432 | −0.817307 | ||||||||
\(467\) | 12.9028 | 0.597069 | 0.298534 | − | 0.954399i | \(-0.403502\pi\) | ||||
0.298534 | + | 0.954399i | \(0.403502\pi\) | |||||||
\(468\) | 10.7117 | 0.495147 | ||||||||
\(469\) | −7.30763 | −0.337435 | ||||||||
\(470\) | −6.35971 | −0.293351 | ||||||||
\(471\) | −26.5258 | −1.22225 | ||||||||
\(472\) | −33.4921 | −1.54160 | ||||||||
\(473\) | 6.23420 | 0.286649 | ||||||||
\(474\) | 27.2752 | 1.25279 | ||||||||
\(475\) | 2.20828 | 0.101323 | ||||||||
\(476\) | 3.39004 | 0.155382 | ||||||||
\(477\) | −8.16407 | −0.373807 | ||||||||
\(478\) | −10.9865 | −0.502513 | ||||||||
\(479\) | −38.6171 | −1.76446 | −0.882229 | − | 0.470820i | \(-0.843958\pi\) | ||||
−0.882229 | + | 0.470820i | \(0.843958\pi\) | |||||||
\(480\) | 12.4418 | 0.567886 | ||||||||
\(481\) | 14.0840 | 0.642176 | ||||||||
\(482\) | −5.80235 | −0.264290 | ||||||||
\(483\) | −12.8778 | −0.585958 | ||||||||
\(484\) | −1.31123 | −0.0596012 | ||||||||
\(485\) | 2.92528 | 0.132830 | ||||||||
\(486\) | −12.7445 | −0.578100 | ||||||||
\(487\) | −15.9532 | −0.722907 | −0.361453 | − | 0.932390i | \(-0.617719\pi\) | ||||
−0.361453 | + | 0.932390i | \(0.617719\pi\) | |||||||
\(488\) | 2.91273 | 0.131853 | ||||||||
\(489\) | 15.9401 | 0.720835 | ||||||||
\(490\) | −4.90680 | −0.221667 | ||||||||
\(491\) | −27.1032 | −1.22315 | −0.611576 | − | 0.791186i | \(-0.709464\pi\) | ||||
−0.611576 | + | 0.791186i | \(0.709464\pi\) | |||||||
\(492\) | −12.8291 | −0.578382 | ||||||||
\(493\) | 18.7253 | 0.843344 | ||||||||
\(494\) | −9.16348 | −0.412284 | ||||||||
\(495\) | 1.63385 | 0.0734363 | ||||||||
\(496\) | 3.73421 | 0.167671 | ||||||||
\(497\) | −14.2317 | −0.638379 | ||||||||
\(498\) | 5.42653 | 0.243168 | ||||||||
\(499\) | −16.7500 | −0.749834 | −0.374917 | − | 0.927058i | \(-0.622329\pi\) | ||||
−0.374917 | + | 0.927058i | \(0.622329\pi\) | |||||||
\(500\) | −1.31123 | −0.0586398 | ||||||||
\(501\) | −39.2068 | −1.75163 | ||||||||
\(502\) | 4.56179 | 0.203603 | ||||||||
\(503\) | −19.2636 | −0.858923 | −0.429462 | − | 0.903085i | \(-0.641297\pi\) | ||||
−0.429462 | + | 0.903085i | \(0.641297\pi\) | |||||||
\(504\) | 4.68258 | 0.208579 | ||||||||
\(505\) | 10.6303 | 0.473040 | ||||||||
\(506\) | 4.76061 | 0.211635 | ||||||||
\(507\) | 25.8308 | 1.14719 | ||||||||
\(508\) | 5.72667 | 0.254080 | ||||||||
\(509\) | −36.7666 | −1.62965 | −0.814827 | − | 0.579705i | \(-0.803168\pi\) | ||||
−0.814827 | + | 0.579705i | \(0.803168\pi\) | |||||||
\(510\) | 4.42887 | 0.196114 | ||||||||
\(511\) | −1.04291 | −0.0461354 | ||||||||
\(512\) | 3.85368 | 0.170310 | ||||||||
\(513\) | −6.49417 | −0.286724 | ||||||||
\(514\) | 5.83554 | 0.257395 | ||||||||
\(515\) | −13.6587 | −0.601876 | ||||||||
\(516\) | −17.5966 | −0.774649 | ||||||||
\(517\) | −7.66300 | −0.337018 | ||||||||
\(518\) | 2.43806 | 0.107122 | ||||||||
\(519\) | −23.8362 | −1.04629 | ||||||||
\(520\) | 13.7402 | 0.602549 | ||||||||
\(521\) | 34.6661 | 1.51875 | 0.759374 | − | 0.650655i | \(-0.225505\pi\) | ||||
0.759374 | + | 0.650655i | \(0.225505\pi\) | |||||||
\(522\) | 10.2423 | 0.448293 | ||||||||
\(523\) | 6.25512 | 0.273517 | 0.136759 | − | 0.990604i | \(-0.456332\pi\) | ||||
0.136759 | + | 0.990604i | \(0.456332\pi\) | |||||||
\(524\) | −21.9870 | −0.960505 | ||||||||
\(525\) | −2.24500 | −0.0979798 | ||||||||
\(526\) | 16.5993 | 0.723763 | ||||||||
\(527\) | 27.0867 | 1.17992 | ||||||||
\(528\) | 0.735691 | 0.0320169 | ||||||||
\(529\) | 9.90395 | 0.430606 | ||||||||
\(530\) | −4.14698 | −0.180133 | ||||||||
\(531\) | 19.9126 | 0.864133 | ||||||||
\(532\) | 3.01980 | 0.130925 | ||||||||
\(533\) | −22.7256 | −0.984355 | ||||||||
\(534\) | −28.6281 | −1.23886 | ||||||||
\(535\) | −6.82896 | −0.295242 | ||||||||
\(536\) | −19.2557 | −0.831719 | ||||||||
\(537\) | −54.8186 | −2.36560 | ||||||||
\(538\) | −20.9906 | −0.904970 | ||||||||
\(539\) | −5.91235 | −0.254663 | ||||||||
\(540\) | 3.85608 | 0.165939 | ||||||||
\(541\) | −23.6234 | −1.01565 | −0.507824 | − | 0.861461i | \(-0.669550\pi\) | ||||
−0.507824 | + | 0.861461i | \(0.669550\pi\) | |||||||
\(542\) | 10.2719 | 0.441216 | ||||||||
\(543\) | 38.7252 | 1.66186 | ||||||||
\(544\) | 14.3283 | 0.614319 | ||||||||
\(545\) | 12.6156 | 0.540393 | ||||||||
\(546\) | 9.31583 | 0.398681 | ||||||||
\(547\) | −12.1926 | −0.521320 | −0.260660 | − | 0.965431i | \(-0.583940\pi\) | ||||
−0.260660 | + | 0.965431i | \(0.583940\pi\) | |||||||
\(548\) | 26.9177 | 1.14987 | ||||||||
\(549\) | −1.73175 | −0.0739094 | ||||||||
\(550\) | 0.829924 | 0.0353881 | ||||||||
\(551\) | 16.6802 | 0.710599 | ||||||||
\(552\) | −33.9330 | −1.44429 | ||||||||
\(553\) | −15.9222 | −0.677081 | ||||||||
\(554\) | −12.6478 | −0.537355 | ||||||||
\(555\) | −6.06361 | −0.257386 | ||||||||
\(556\) | −0.270062 | −0.0114532 | ||||||||
\(557\) | 12.6831 | 0.537399 | 0.268700 | − | 0.963224i | \(-0.413406\pi\) | ||||
0.268700 | + | 0.963224i | \(0.413406\pi\) | |||||||
\(558\) | 14.8158 | 0.627204 | ||||||||
\(559\) | −31.1708 | −1.31838 | ||||||||
\(560\) | −0.356426 | −0.0150618 | ||||||||
\(561\) | 5.33647 | 0.225306 | ||||||||
\(562\) | 22.2158 | 0.937118 | ||||||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 21.6295 | 0.910768 | ||||||||
\(565\) | 1.50690 | 0.0633956 | ||||||||
\(566\) | 15.4995 | 0.651494 | ||||||||
\(567\) | 11.7140 | 0.491942 | ||||||||
\(568\) | −37.5007 | −1.57349 | ||||||||
\(569\) | −4.29859 | −0.180206 | −0.0901032 | − | 0.995932i | \(-0.528720\pi\) | ||||
−0.0901032 | + | 0.995932i | \(0.528720\pi\) | |||||||
\(570\) | 3.94516 | 0.165245 | ||||||||
\(571\) | −9.46649 | −0.396160 | −0.198080 | − | 0.980186i | \(-0.563471\pi\) | ||||
−0.198080 | + | 0.980186i | \(0.563471\pi\) | |||||||
\(572\) | 6.55608 | 0.274123 | ||||||||
\(573\) | −0.213388 | −0.00891441 | ||||||||
\(574\) | −3.93398 | −0.164201 | ||||||||
\(575\) | 5.73620 | 0.239216 | ||||||||
\(576\) | 6.72044 | 0.280019 | ||||||||
\(577\) | −34.7090 | −1.44495 | −0.722477 | − | 0.691395i | \(-0.756997\pi\) | ||||
−0.722477 | + | 0.691395i | \(0.756997\pi\) | |||||||
\(578\) | −9.00832 | −0.374697 | ||||||||
\(579\) | −15.8403 | −0.658302 | ||||||||
\(580\) | −9.90428 | −0.411253 | ||||||||
\(581\) | −3.16780 | −0.131422 | ||||||||
\(582\) | 5.22608 | 0.216628 | ||||||||
\(583\) | −4.99682 | −0.206947 | ||||||||
\(584\) | −2.74807 | −0.113716 | ||||||||
\(585\) | −8.16920 | −0.337755 | ||||||||
\(586\) | −10.5015 | −0.433811 | ||||||||
\(587\) | 21.1630 | 0.873489 | 0.436744 | − | 0.899586i | \(-0.356131\pi\) | ||||
0.436744 | + | 0.899586i | \(0.356131\pi\) | |||||||
\(588\) | 16.6882 | 0.688208 | ||||||||
\(589\) | 24.1284 | 0.994194 | ||||||||
\(590\) | 10.1147 | 0.416416 | ||||||||
\(591\) | 13.9708 | 0.574681 | ||||||||
\(592\) | −0.962686 | −0.0395661 | ||||||||
\(593\) | 40.2295 | 1.65203 | 0.826014 | − | 0.563649i | \(-0.190603\pi\) | ||||
0.826014 | + | 0.563649i | \(0.190603\pi\) | |||||||
\(594\) | −2.44066 | −0.100141 | ||||||||
\(595\) | −2.58540 | −0.105991 | ||||||||
\(596\) | −0.468676 | −0.0191977 | ||||||||
\(597\) | −0.348367 | −0.0142577 | ||||||||
\(598\) | −23.8029 | −0.973371 | ||||||||
\(599\) | 22.3013 | 0.911206 | 0.455603 | − | 0.890183i | \(-0.349424\pi\) | ||||
0.455603 | + | 0.890183i | \(0.349424\pi\) | |||||||
\(600\) | −5.91560 | −0.241503 | ||||||||
\(601\) | 16.6444 | 0.678939 | 0.339470 | − | 0.940617i | \(-0.389752\pi\) | ||||
0.339470 | + | 0.940617i | \(0.389752\pi\) | |||||||
\(602\) | −5.39591 | −0.219921 | ||||||||
\(603\) | 11.4484 | 0.466215 | ||||||||
\(604\) | 7.10404 | 0.289059 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 18.9912 | 0.771467 | ||||||||
\(607\) | 17.8779 | 0.725641 | 0.362821 | − | 0.931859i | \(-0.381814\pi\) | ||||
0.362821 | + | 0.931859i | \(0.381814\pi\) | |||||||
\(608\) | 12.7634 | 0.517623 | ||||||||
\(609\) | −16.9575 | −0.687152 | ||||||||
\(610\) | −0.879653 | −0.0356161 | ||||||||
\(611\) | 38.3147 | 1.55005 | ||||||||
\(612\) | −5.31096 | −0.214683 | ||||||||
\(613\) | 35.5502 | 1.43586 | 0.717930 | − | 0.696115i | \(-0.245090\pi\) | ||||
0.717930 | + | 0.696115i | \(0.245090\pi\) | |||||||
\(614\) | 8.43266 | 0.340315 | ||||||||
\(615\) | 9.78408 | 0.394532 | ||||||||
\(616\) | 2.86598 | 0.115473 | ||||||||
\(617\) | 2.87315 | 0.115669 | 0.0578343 | − | 0.998326i | \(-0.481580\pi\) | ||||
0.0578343 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(618\) | −24.4017 | −0.981581 | ||||||||
\(619\) | −1.78215 | −0.0716308 | −0.0358154 | − | 0.999358i | \(-0.511403\pi\) | ||||
−0.0358154 | + | 0.999358i | \(0.511403\pi\) | |||||||
\(620\) | −14.3269 | −0.575381 | ||||||||
\(621\) | −16.8691 | −0.676934 | ||||||||
\(622\) | 7.52584 | 0.301758 | ||||||||
\(623\) | 16.7120 | 0.669551 | ||||||||
\(624\) | −3.67843 | −0.147255 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.97822 | 0.318874 | ||||||||
\(627\) | 4.75364 | 0.189842 | ||||||||
\(628\) | 16.1575 | 0.644756 | ||||||||
\(629\) | −6.98301 | −0.278431 | ||||||||
\(630\) | −1.41415 | −0.0563413 | ||||||||
\(631\) | 11.5434 | 0.459537 | 0.229768 | − | 0.973245i | \(-0.426203\pi\) | ||||
0.229768 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(632\) | −41.9552 | −1.66889 | ||||||||
\(633\) | 48.5118 | 1.92817 | ||||||||
\(634\) | −3.16680 | −0.125770 | ||||||||
\(635\) | −4.36742 | −0.173316 | ||||||||
\(636\) | 14.1040 | 0.559260 | ||||||||
\(637\) | 29.5615 | 1.17127 | ||||||||
\(638\) | 6.26880 | 0.248184 | ||||||||
\(639\) | 22.2959 | 0.882012 | ||||||||
\(640\) | −8.14586 | −0.321993 | ||||||||
\(641\) | −11.8352 | −0.467461 | −0.233730 | − | 0.972301i | \(-0.575093\pi\) | ||||
−0.233730 | + | 0.972301i | \(0.575093\pi\) | |||||||
\(642\) | −12.2001 | −0.481501 | ||||||||
\(643\) | −20.2651 | −0.799177 | −0.399589 | − | 0.916695i | \(-0.630847\pi\) | ||||
−0.399589 | + | 0.916695i | \(0.630847\pi\) | |||||||
\(644\) | 7.84416 | 0.309103 | ||||||||
\(645\) | 13.4200 | 0.528412 | ||||||||
\(646\) | 4.54335 | 0.178756 | ||||||||
\(647\) | 7.94946 | 0.312526 | 0.156263 | − | 0.987716i | \(-0.450055\pi\) | ||||
0.156263 | + | 0.987716i | \(0.450055\pi\) | |||||||
\(648\) | 30.8665 | 1.21255 | ||||||||
\(649\) | 12.1875 | 0.478401 | ||||||||
\(650\) | −4.14959 | −0.162760 | ||||||||
\(651\) | −24.5296 | −0.961390 | ||||||||
\(652\) | −9.70949 | −0.380253 | ||||||||
\(653\) | −18.0772 | −0.707416 | −0.353708 | − | 0.935356i | \(-0.615079\pi\) | ||||
−0.353708 | + | 0.935356i | \(0.615079\pi\) | |||||||
\(654\) | 22.5381 | 0.881311 | ||||||||
\(655\) | 16.7683 | 0.655190 | ||||||||
\(656\) | 1.55336 | 0.0606487 | ||||||||
\(657\) | 1.63385 | 0.0637427 | ||||||||
\(658\) | 6.63258 | 0.258565 | ||||||||
\(659\) | −44.4468 | −1.73140 | −0.865701 | − | 0.500561i | \(-0.833127\pi\) | ||||
−0.865701 | + | 0.500561i | \(0.833127\pi\) | |||||||
\(660\) | −2.82259 | −0.109869 | ||||||||
\(661\) | −29.1686 | −1.13453 | −0.567264 | − | 0.823536i | \(-0.691998\pi\) | ||||
−0.567264 | + | 0.823536i | \(0.691998\pi\) | |||||||
\(662\) | 3.08295 | 0.119822 | ||||||||
\(663\) | −26.6821 | −1.03625 | ||||||||
\(664\) | −8.34717 | −0.323933 | ||||||||
\(665\) | −2.30303 | −0.0893078 | ||||||||
\(666\) | −3.81954 | −0.148004 | ||||||||
\(667\) | 43.3281 | 1.67767 | ||||||||
\(668\) | 23.8818 | 0.924015 | ||||||||
\(669\) | −36.1171 | −1.39637 | ||||||||
\(670\) | 5.81528 | 0.224664 | ||||||||
\(671\) | −1.05992 | −0.0409177 | ||||||||
\(672\) | −12.9756 | −0.500544 | ||||||||
\(673\) | 12.7086 | 0.489880 | 0.244940 | − | 0.969538i | \(-0.421232\pi\) | ||||
0.244940 | + | 0.969538i | \(0.421232\pi\) | |||||||
\(674\) | 14.1157 | 0.543715 | ||||||||
\(675\) | −2.94082 | −0.113192 | ||||||||
\(676\) | −15.7342 | −0.605161 | ||||||||
\(677\) | 6.19998 | 0.238285 | 0.119142 | − | 0.992877i | \(-0.461986\pi\) | ||||
0.119142 | + | 0.992877i | \(0.461986\pi\) | |||||||
\(678\) | 2.69211 | 0.103390 | ||||||||
\(679\) | −3.05079 | −0.117078 | ||||||||
\(680\) | −6.81256 | −0.261250 | ||||||||
\(681\) | 44.0306 | 1.68725 | ||||||||
\(682\) | 9.06802 | 0.347232 | ||||||||
\(683\) | 19.4045 | 0.742492 | 0.371246 | − | 0.928534i | \(-0.378931\pi\) | ||||
0.371246 | + | 0.928534i | \(0.378931\pi\) | |||||||
\(684\) | −4.73092 | −0.180891 | ||||||||
\(685\) | −20.5287 | −0.784361 | ||||||||
\(686\) | 11.1761 | 0.426704 | ||||||||
\(687\) | −19.7266 | −0.752617 | ||||||||
\(688\) | 2.13062 | 0.0812291 | ||||||||
\(689\) | 24.9839 | 0.951811 | ||||||||
\(690\) | 10.2479 | 0.390130 | ||||||||
\(691\) | 38.2011 | 1.45324 | 0.726620 | − | 0.687040i | \(-0.241090\pi\) | ||||
0.726620 | + | 0.687040i | \(0.241090\pi\) | |||||||
\(692\) | 14.5192 | 0.551938 | ||||||||
\(693\) | −1.70396 | −0.0647279 | ||||||||
\(694\) | 25.1931 | 0.956315 | ||||||||
\(695\) | 0.205962 | 0.00781257 | ||||||||
\(696\) | −44.6832 | −1.69371 | ||||||||
\(697\) | 11.2676 | 0.426791 | ||||||||
\(698\) | 12.1654 | 0.460466 | ||||||||
\(699\) | −45.7626 | −1.73090 | ||||||||
\(700\) | 1.36748 | 0.0516861 | ||||||||
\(701\) | 7.88516 | 0.297818 | 0.148909 | − | 0.988851i | \(-0.452424\pi\) | ||||
0.148909 | + | 0.988851i | \(0.452424\pi\) | |||||||
\(702\) | 12.2032 | 0.460580 | ||||||||
\(703\) | −6.22035 | −0.234605 | ||||||||
\(704\) | 4.11325 | 0.155024 | ||||||||
\(705\) | −16.4957 | −0.621263 | ||||||||
\(706\) | 4.46493 | 0.168040 | ||||||||
\(707\) | −11.0864 | −0.416945 | ||||||||
\(708\) | −34.4004 | −1.29285 | ||||||||
\(709\) | 16.2668 | 0.610913 | 0.305457 | − | 0.952206i | \(-0.401191\pi\) | ||||
0.305457 | + | 0.952206i | \(0.401191\pi\) | |||||||
\(710\) | 11.3253 | 0.425032 | ||||||||
\(711\) | 24.9443 | 0.935485 | ||||||||
\(712\) | 44.0362 | 1.65033 | ||||||||
\(713\) | 62.6755 | 2.34722 | ||||||||
\(714\) | −4.61889 | −0.172858 | ||||||||
\(715\) | −4.99996 | −0.186988 | ||||||||
\(716\) | 33.3914 | 1.24789 | ||||||||
\(717\) | −28.4966 | −1.06423 | ||||||||
\(718\) | −30.8019 | −1.14952 | ||||||||
\(719\) | 10.4846 | 0.391009 | 0.195504 | − | 0.980703i | \(-0.437366\pi\) | ||||
0.195504 | + | 0.980703i | \(0.437366\pi\) | |||||||
\(720\) | 0.558390 | 0.0208100 | ||||||||
\(721\) | 14.2448 | 0.530503 | ||||||||
\(722\) | −11.7214 | −0.436226 | ||||||||
\(723\) | −15.0500 | −0.559715 | ||||||||
\(724\) | −23.5884 | −0.876658 | ||||||||
\(725\) | 7.55345 | 0.280528 | ||||||||
\(726\) | 1.78653 | 0.0663043 | ||||||||
\(727\) | −28.6795 | −1.06367 | −0.531833 | − | 0.846850i | \(-0.678496\pi\) | ||||
−0.531833 | + | 0.846850i | \(0.678496\pi\) | |||||||
\(728\) | −14.3298 | −0.531096 | ||||||||
\(729\) | 0.639991 | 0.0237034 | ||||||||
\(730\) | 0.829924 | 0.0307169 | ||||||||
\(731\) | 15.4548 | 0.571617 | ||||||||
\(732\) | 2.99172 | 0.110577 | ||||||||
\(733\) | 9.41565 | 0.347775 | 0.173887 | − | 0.984766i | \(-0.444367\pi\) | ||||
0.173887 | + | 0.984766i | \(0.444367\pi\) | |||||||
\(734\) | −6.62923 | −0.244690 | ||||||||
\(735\) | −12.7271 | −0.469448 | ||||||||
\(736\) | 33.1539 | 1.22207 | ||||||||
\(737\) | 7.00699 | 0.258106 | ||||||||
\(738\) | 6.16312 | 0.226868 | ||||||||
\(739\) | −28.5927 | −1.05180 | −0.525900 | − | 0.850546i | \(-0.676271\pi\) | ||||
−0.525900 | + | 0.850546i | \(0.676271\pi\) | |||||||
\(740\) | 3.69349 | 0.135776 | ||||||||
\(741\) | −23.7680 | −0.873140 | ||||||||
\(742\) | 4.32491 | 0.158772 | ||||||||
\(743\) | −13.3726 | −0.490593 | −0.245297 | − | 0.969448i | \(-0.578885\pi\) | ||||
−0.245297 | + | 0.969448i | \(0.578885\pi\) | |||||||
\(744\) | −64.6357 | −2.36966 | ||||||||
\(745\) | 0.357433 | 0.0130953 | ||||||||
\(746\) | 4.61456 | 0.168951 | ||||||||
\(747\) | 4.96278 | 0.181579 | ||||||||
\(748\) | −3.25058 | −0.118853 | ||||||||
\(749\) | 7.12197 | 0.260231 | ||||||||
\(750\) | 1.78653 | 0.0652348 | ||||||||
\(751\) | 7.16088 | 0.261304 | 0.130652 | − | 0.991428i | \(-0.458293\pi\) | ||||
0.130652 | + | 0.991428i | \(0.458293\pi\) | |||||||
\(752\) | −2.61893 | −0.0955024 | ||||||||
\(753\) | 11.8323 | 0.431192 | ||||||||
\(754\) | −31.3437 | −1.14147 | ||||||||
\(755\) | −5.41786 | −0.197176 | ||||||||
\(756\) | −4.02153 | −0.146261 | ||||||||
\(757\) | −29.6488 | −1.07760 | −0.538802 | − | 0.842433i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842433i | \(0.681123\pi\) | |||||||
\(758\) | −7.92567 | −0.287873 | ||||||||
\(759\) | 12.3480 | 0.448202 | ||||||||
\(760\) | −6.06851 | −0.220128 | ||||||||
\(761\) | −38.1278 | −1.38213 | −0.691066 | − | 0.722791i | \(-0.742859\pi\) | ||||
−0.691066 | + | 0.722791i | \(0.742859\pi\) | |||||||
\(762\) | −7.80251 | −0.282655 | ||||||||
\(763\) | −13.1569 | −0.476312 | ||||||||
\(764\) | 0.129980 | 0.00470251 | ||||||||
\(765\) | 4.05038 | 0.146442 | ||||||||
\(766\) | 24.5611 | 0.887430 | ||||||||
\(767\) | −60.9370 | −2.20031 | ||||||||
\(768\) | −32.2615 | −1.16414 | ||||||||
\(769\) | 7.37680 | 0.266014 | 0.133007 | − | 0.991115i | \(-0.457537\pi\) | ||||
0.133007 | + | 0.991115i | \(0.457537\pi\) | |||||||
\(770\) | −0.865533 | −0.0311916 | ||||||||
\(771\) | 15.1361 | 0.545113 | ||||||||
\(772\) | 9.64874 | 0.347266 | ||||||||
\(773\) | −46.2555 | −1.66369 | −0.831847 | − | 0.555004i | \(-0.812717\pi\) | ||||
−0.831847 | + | 0.555004i | \(0.812717\pi\) | |||||||
\(774\) | 8.45343 | 0.303852 | ||||||||
\(775\) | 10.9263 | 0.392485 | ||||||||
\(776\) | −8.03885 | −0.288578 | ||||||||
\(777\) | 6.32377 | 0.226864 | ||||||||
\(778\) | 5.52072 | 0.197927 | ||||||||
\(779\) | 10.0370 | 0.359613 | ||||||||
\(780\) | 14.1129 | 0.505322 | ||||||||
\(781\) | 13.6462 | 0.488300 | ||||||||
\(782\) | 11.8017 | 0.422029 | ||||||||
\(783\) | −22.2133 | −0.793840 | ||||||||
\(784\) | −2.02062 | −0.0721650 | ||||||||
\(785\) | −12.3225 | −0.439808 | ||||||||
\(786\) | 29.9569 | 1.06853 | ||||||||
\(787\) | −35.5094 | −1.26577 | −0.632886 | − | 0.774245i | \(-0.718130\pi\) | ||||
−0.632886 | + | 0.774245i | \(0.718130\pi\) | |||||||
\(788\) | −8.50994 | −0.303154 | ||||||||
\(789\) | 43.0548 | 1.53279 | ||||||||
\(790\) | 12.6706 | 0.450799 | ||||||||
\(791\) | −1.57155 | −0.0558779 | ||||||||
\(792\) | −4.48994 | −0.159543 | ||||||||
\(793\) | 5.29956 | 0.188193 | ||||||||
\(794\) | 17.7728 | 0.630734 | ||||||||
\(795\) | −10.7563 | −0.381488 | ||||||||
\(796\) | 0.212199 | 0.00752119 | ||||||||
\(797\) | −35.0553 | −1.24172 | −0.620861 | − | 0.783920i | \(-0.713217\pi\) | ||||
−0.620861 | + | 0.783920i | \(0.713217\pi\) | |||||||
\(798\) | −4.11443 | −0.145649 | ||||||||
\(799\) | −18.9968 | −0.672060 | ||||||||
\(800\) | 5.77977 | 0.204346 | ||||||||
\(801\) | −26.1816 | −0.925080 | ||||||||
\(802\) | −3.34820 | −0.118229 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −19.7779 | −0.697513 | ||||||||
\(805\) | −5.98231 | −0.210849 | ||||||||
\(806\) | −45.3398 | −1.59702 | ||||||||
\(807\) | −54.4450 | −1.91655 | ||||||||
\(808\) | −29.2127 | −1.02770 | ||||||||
\(809\) | 42.7463 | 1.50288 | 0.751440 | − | 0.659802i | \(-0.229360\pi\) | ||||
0.751440 | + | 0.659802i | \(0.229360\pi\) | |||||||
\(810\) | −9.32178 | −0.327534 | ||||||||
\(811\) | 7.93399 | 0.278600 | 0.139300 | − | 0.990250i | \(-0.455515\pi\) | ||||
0.139300 | + | 0.990250i | \(0.455515\pi\) | |||||||
\(812\) | 10.3292 | 0.362485 | ||||||||
\(813\) | 26.6430 | 0.934412 | ||||||||
\(814\) | −2.33775 | −0.0819382 | ||||||||
\(815\) | 7.40490 | 0.259382 | ||||||||
\(816\) | 1.82381 | 0.0638460 | ||||||||
\(817\) | 13.7669 | 0.481643 | ||||||||
\(818\) | 17.9446 | 0.627420 | ||||||||
\(819\) | 8.51971 | 0.297703 | ||||||||
\(820\) | −5.95972 | −0.208123 | ||||||||
\(821\) | −38.7862 | −1.35365 | −0.676824 | − | 0.736145i | \(-0.736644\pi\) | ||||
−0.676824 | + | 0.736145i | \(0.736644\pi\) | |||||||
\(822\) | −36.6751 | −1.27919 | ||||||||
\(823\) | −23.8084 | −0.829908 | −0.414954 | − | 0.909842i | \(-0.636202\pi\) | ||||
−0.414954 | + | 0.909842i | \(0.636202\pi\) | |||||||
\(824\) | 37.5351 | 1.30760 | ||||||||
\(825\) | 2.15264 | 0.0749453 | ||||||||
\(826\) | −10.5487 | −0.367036 | ||||||||
\(827\) | 21.2728 | 0.739728 | 0.369864 | − | 0.929086i | \(-0.379404\pi\) | ||||
0.369864 | + | 0.929086i | \(0.379404\pi\) | |||||||
\(828\) | −12.2889 | −0.427070 | ||||||||
\(829\) | 32.2902 | 1.12148 | 0.560742 | − | 0.827991i | \(-0.310516\pi\) | ||||
0.560742 | + | 0.827991i | \(0.310516\pi\) | |||||||
\(830\) | 2.52087 | 0.0875007 | ||||||||
\(831\) | −32.8056 | −1.13801 | ||||||||
\(832\) | −20.5661 | −0.713001 | ||||||||
\(833\) | −14.6569 | −0.507832 | ||||||||
\(834\) | 0.367956 | 0.0127413 | ||||||||
\(835\) | −18.2133 | −0.630299 | ||||||||
\(836\) | −2.89556 | −0.100145 | ||||||||
\(837\) | −32.1323 | −1.11066 | ||||||||
\(838\) | 12.4711 | 0.430807 | ||||||||
\(839\) | −3.75627 | −0.129681 | −0.0648404 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648404 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(840\) | 6.16941 | 0.212865 | ||||||||
\(841\) | 28.0546 | 0.967402 | ||||||||
\(842\) | −1.57428 | −0.0542533 | ||||||||
\(843\) | 57.6229 | 1.98464 | ||||||||
\(844\) | −29.5497 | −1.01714 | ||||||||
\(845\) | 11.9996 | 0.412799 | ||||||||
\(846\) | −10.3908 | −0.357244 | ||||||||
\(847\) | −1.04291 | −0.0358347 | ||||||||
\(848\) | −1.70773 | −0.0586435 | ||||||||
\(849\) | 40.2023 | 1.37974 | ||||||||
\(850\) | 2.05741 | 0.0705687 | ||||||||
\(851\) | −16.1579 | −0.553884 | ||||||||
\(852\) | −38.5177 | −1.31959 | ||||||||
\(853\) | 14.0599 | 0.481401 | 0.240701 | − | 0.970599i | \(-0.422623\pi\) | ||||
0.240701 | + | 0.970599i | \(0.422623\pi\) | |||||||
\(854\) | 0.917396 | 0.0313926 | ||||||||
\(855\) | 3.60801 | 0.123391 | ||||||||
\(856\) | 18.7665 | 0.641424 | ||||||||
\(857\) | −47.6535 | −1.62781 | −0.813906 | − | 0.580997i | \(-0.802663\pi\) | ||||
−0.813906 | + | 0.580997i | \(0.802663\pi\) | |||||||
\(858\) | −8.93257 | −0.304953 | ||||||||
\(859\) | 36.8435 | 1.25708 | 0.628542 | − | 0.777775i | \(-0.283652\pi\) | ||||
0.628542 | + | 0.777775i | \(0.283652\pi\) | |||||||
\(860\) | −8.17445 | −0.278746 | ||||||||
\(861\) | −10.2039 | −0.347747 | ||||||||
\(862\) | −11.0623 | −0.376785 | ||||||||
\(863\) | −39.9755 | −1.36078 | −0.680391 | − | 0.732850i | \(-0.738190\pi\) | ||||
−0.680391 | + | 0.732850i | \(0.738190\pi\) | |||||||
\(864\) | −16.9973 | −0.578259 | ||||||||
\(865\) | −11.0730 | −0.376494 | ||||||||
\(866\) | 11.6756 | 0.396753 | ||||||||
\(867\) | −23.3656 | −0.793536 | ||||||||
\(868\) | 14.9416 | 0.507150 | ||||||||
\(869\) | 15.2672 | 0.517903 | ||||||||
\(870\) | 13.4945 | 0.457505 | ||||||||
\(871\) | −35.0347 | −1.18711 | ||||||||
\(872\) | −34.6685 | −1.17402 | ||||||||
\(873\) | 4.77947 | 0.161761 | ||||||||
\(874\) | 10.5128 | 0.355600 | ||||||||
\(875\) | −1.04291 | −0.0352567 | ||||||||
\(876\) | −2.82259 | −0.0953666 | ||||||||
\(877\) | 43.9928 | 1.48553 | 0.742766 | − | 0.669551i | \(-0.233513\pi\) | ||||
0.742766 | + | 0.669551i | \(0.233513\pi\) | |||||||
\(878\) | 7.08358 | 0.239059 | ||||||||
\(879\) | −27.2385 | −0.918730 | ||||||||
\(880\) | 0.341763 | 0.0115208 | ||||||||
\(881\) | 34.0757 | 1.14804 | 0.574019 | − | 0.818842i | \(-0.305383\pi\) | ||||
0.574019 | + | 0.818842i | \(0.305383\pi\) | |||||||
\(882\) | −8.01699 | −0.269946 | ||||||||
\(883\) | 0.550601 | 0.0185292 | 0.00926460 | − | 0.999957i | \(-0.497051\pi\) | ||||
0.00926460 | + | 0.999957i | \(0.497051\pi\) | |||||||
\(884\) | 16.2527 | 0.546639 | ||||||||
\(885\) | 26.2353 | 0.881889 | ||||||||
\(886\) | 5.26065 | 0.176735 | ||||||||
\(887\) | 39.0533 | 1.31128 | 0.655642 | − | 0.755072i | \(-0.272398\pi\) | ||||
0.655642 | + | 0.755072i | \(0.272398\pi\) | |||||||
\(888\) | 16.6632 | 0.559180 | ||||||||
\(889\) | 4.55481 | 0.152763 | ||||||||
\(890\) | −13.2991 | −0.445786 | ||||||||
\(891\) | −11.2321 | −0.376289 | ||||||||
\(892\) | 21.9998 | 0.736608 | ||||||||
\(893\) | −16.9221 | −0.566276 | ||||||||
\(894\) | 0.638565 | 0.0213568 | ||||||||
\(895\) | −25.4658 | −0.851226 | ||||||||
\(896\) | 8.49536 | 0.283810 | ||||||||
\(897\) | −61.7393 | −2.06142 | ||||||||
\(898\) | −17.0447 | −0.568788 | ||||||||
\(899\) | 82.5314 | 2.75258 | ||||||||
\(900\) | −2.14235 | −0.0714117 | ||||||||
\(901\) | −12.3873 | −0.412681 | ||||||||
\(902\) | 3.77214 | 0.125598 | ||||||||
\(903\) | −13.9958 | −0.465751 | ||||||||
\(904\) | −4.14105 | −0.137729 | ||||||||
\(905\) | 17.9896 | 0.597995 | ||||||||
\(906\) | −9.67916 | −0.321569 | ||||||||
\(907\) | 27.2645 | 0.905304 | 0.452652 | − | 0.891687i | \(-0.350478\pi\) | ||||
0.452652 | + | 0.891687i | \(0.350478\pi\) | |||||||
\(908\) | −26.8201 | −0.890056 | ||||||||
\(909\) | 17.3683 | 0.576070 | ||||||||
\(910\) | 4.32763 | 0.143460 | ||||||||
\(911\) | −46.5648 | −1.54276 | −0.771380 | − | 0.636375i | \(-0.780433\pi\) | ||||
−0.771380 | + | 0.636375i | \(0.780433\pi\) | |||||||
\(912\) | 1.62462 | 0.0537964 | ||||||||
\(913\) | 3.03747 | 0.100526 | ||||||||
\(914\) | −13.7284 | −0.454096 | ||||||||
\(915\) | −2.28162 | −0.0754282 | ||||||||
\(916\) | 12.0160 | 0.397019 | ||||||||
\(917\) | −17.4877 | −0.577495 | ||||||||
\(918\) | −6.05048 | −0.199696 | ||||||||
\(919\) | −50.4399 | −1.66386 | −0.831930 | − | 0.554880i | \(-0.812764\pi\) | ||||
−0.831930 | + | 0.554880i | \(0.812764\pi\) | |||||||
\(920\) | −15.7635 | −0.519706 | ||||||||
\(921\) | 21.8724 | 0.720721 | ||||||||
\(922\) | −8.89557 | −0.292960 | ||||||||
\(923\) | −68.2305 | −2.24583 | ||||||||
\(924\) | 2.94370 | 0.0968406 | ||||||||
\(925\) | −2.81683 | −0.0926167 | ||||||||
\(926\) | 2.67320 | 0.0878469 | ||||||||
\(927\) | −22.3164 | −0.732966 | ||||||||
\(928\) | 43.6572 | 1.43312 | ||||||||
\(929\) | 44.4410 | 1.45806 | 0.729032 | − | 0.684480i | \(-0.239971\pi\) | ||||
0.729032 | + | 0.684480i | \(0.239971\pi\) | |||||||
\(930\) | 19.5202 | 0.640092 | ||||||||
\(931\) | −13.0561 | −0.427898 | ||||||||
\(932\) | 27.8751 | 0.913080 | ||||||||
\(933\) | 19.5203 | 0.639067 | ||||||||
\(934\) | 10.7083 | 0.350387 | ||||||||
\(935\) | 2.47904 | 0.0810732 | ||||||||
\(936\) | 22.4495 | 0.733785 | ||||||||
\(937\) | −48.3906 | −1.58085 | −0.790427 | − | 0.612557i | \(-0.790141\pi\) | ||||
−0.790427 | + | 0.612557i | \(0.790141\pi\) | |||||||
\(938\) | −6.06478 | −0.198022 | ||||||||
\(939\) | 20.6937 | 0.675314 | ||||||||
\(940\) | 10.0479 | 0.327727 | ||||||||
\(941\) | 14.2855 | 0.465694 | 0.232847 | − | 0.972513i | \(-0.425196\pi\) | ||||
0.232847 | + | 0.972513i | \(0.425196\pi\) | |||||||
\(942\) | −22.0144 | −0.717269 | ||||||||
\(943\) | 26.0719 | 0.849018 | ||||||||
\(944\) | 4.16523 | 0.135567 | ||||||||
\(945\) | 3.06700 | 0.0997695 | ||||||||
\(946\) | 5.17392 | 0.168219 | ||||||||
\(947\) | 31.6845 | 1.02961 | 0.514805 | − | 0.857308i | \(-0.327864\pi\) | ||||
0.514805 | + | 0.857308i | \(0.327864\pi\) | |||||||
\(948\) | −43.0930 | −1.39960 | ||||||||
\(949\) | −4.99996 | −0.162306 | ||||||||
\(950\) | 1.83271 | 0.0594609 | ||||||||
\(951\) | −8.21396 | −0.266356 | ||||||||
\(952\) | 7.10486 | 0.230270 | ||||||||
\(953\) | −40.1753 | −1.30141 | −0.650704 | − | 0.759332i | \(-0.725526\pi\) | ||||
−0.650704 | + | 0.759332i | \(0.725526\pi\) | |||||||
\(954\) | −6.77556 | −0.219367 | ||||||||
\(955\) | −0.0991286 | −0.00320772 | ||||||||
\(956\) | 17.3580 | 0.561398 | ||||||||
\(957\) | 16.2599 | 0.525606 | ||||||||
\(958\) | −32.0492 | −1.03546 | ||||||||
\(959\) | 21.4095 | 0.691349 | ||||||||
\(960\) | 8.85434 | 0.285773 | ||||||||
\(961\) | 88.3845 | 2.85111 | ||||||||
\(962\) | 11.6887 | 0.376858 | ||||||||
\(963\) | −11.1575 | −0.359546 | ||||||||
\(964\) | 9.16732 | 0.295260 | ||||||||
\(965\) | −7.35857 | −0.236881 | ||||||||
\(966\) | −10.6876 | −0.343867 | ||||||||
\(967\) | 1.86766 | 0.0600597 | 0.0300299 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300299 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(968\) | −2.74807 | −0.0883262 | ||||||||
\(969\) | 11.7844 | 0.378571 | ||||||||
\(970\) | 2.42776 | 0.0779506 | ||||||||
\(971\) | 42.4601 | 1.36261 | 0.681305 | − | 0.732000i | \(-0.261413\pi\) | ||||
0.681305 | + | 0.732000i | \(0.261413\pi\) | |||||||
\(972\) | 20.1354 | 0.645843 | ||||||||
\(973\) | −0.214799 | −0.00688613 | ||||||||
\(974\) | −13.2399 | −0.424235 | ||||||||
\(975\) | −10.7631 | −0.344695 | ||||||||
\(976\) | −0.362241 | −0.0115950 | ||||||||
\(977\) | 6.35485 | 0.203310 | 0.101655 | − | 0.994820i | \(-0.467586\pi\) | ||||
0.101655 | + | 0.994820i | \(0.467586\pi\) | |||||||
\(978\) | 13.2291 | 0.423019 | ||||||||
\(979\) | −16.0244 | −0.512143 | ||||||||
\(980\) | 7.75242 | 0.247642 | ||||||||
\(981\) | 20.6121 | 0.658092 | ||||||||
\(982\) | −22.4936 | −0.717801 | ||||||||
\(983\) | 57.0468 | 1.81951 | 0.909755 | − | 0.415146i | \(-0.136270\pi\) | ||||
0.909755 | + | 0.415146i | \(0.136270\pi\) | |||||||
\(984\) | −26.8873 | −0.857136 | ||||||||
\(985\) | 6.49007 | 0.206791 | ||||||||
\(986\) | 15.5406 | 0.494913 | ||||||||
\(987\) | 17.2034 | 0.547591 | ||||||||
\(988\) | 14.4777 | 0.460596 | ||||||||
\(989\) | 35.7606 | 1.13712 | ||||||||
\(990\) | 1.35597 | 0.0430957 | ||||||||
\(991\) | −6.94726 | −0.220687 | −0.110343 | − | 0.993894i | \(-0.535195\pi\) | ||||
−0.110343 | + | 0.993894i | \(0.535195\pi\) | |||||||
\(992\) | 63.1516 | 2.00507 | ||||||||
\(993\) | 7.99649 | 0.253761 | ||||||||
\(994\) | −11.8112 | −0.374630 | ||||||||
\(995\) | −0.161833 | −0.00513044 | ||||||||
\(996\) | −8.57355 | −0.271663 | ||||||||
\(997\) | −35.7252 | −1.13143 | −0.565714 | − | 0.824602i | \(-0.691399\pi\) | ||||
−0.565714 | + | 0.824602i | \(0.691399\pi\) | |||||||
\(998\) | −13.9012 | −0.440036 | ||||||||
\(999\) | 8.28378 | 0.262087 |
(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.1.22 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.22 | ✓ | 37 | 1.1 | even | 1 | trivial |