Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.851234 | −0.491460 | −0.245730 | − | 0.969338i | \(-0.579028\pi\) | ||||
−0.245730 | + | 0.969338i | \(0.579028\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.73591 | −1.22354 | −0.611769 | − | 0.791037i | \(-0.709542\pi\) | ||||
−0.611769 | + | 0.791037i | \(0.709542\pi\) | |||||||
\(6\) | −0.851234 | −0.347515 | ||||||||
\(7\) | 0.590237 | 0.223088 | 0.111544 | − | 0.993759i | \(-0.464420\pi\) | ||||
0.111544 | + | 0.993759i | \(0.464420\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.27540 | −0.758467 | ||||||||
\(10\) | −2.73591 | −0.865171 | ||||||||
\(11\) | −1.85097 | −0.558087 | −0.279044 | − | 0.960278i | \(-0.590017\pi\) | ||||
−0.279044 | + | 0.960278i | \(0.590017\pi\) | |||||||
\(12\) | −0.851234 | −0.245730 | ||||||||
\(13\) | 1.88529 | 0.522884 | 0.261442 | − | 0.965219i | \(-0.415802\pi\) | ||||
0.261442 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(14\) | 0.590237 | 0.157747 | ||||||||
\(15\) | 2.32890 | 0.601320 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.96288 | −1.20367 | −0.601837 | − | 0.798619i | \(-0.705564\pi\) | ||||
−0.601837 | + | 0.798619i | \(0.705564\pi\) | |||||||
\(18\) | −2.27540 | −0.536317 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.73591 | −0.611769 | ||||||||
\(21\) | −0.502429 | −0.109639 | ||||||||
\(22\) | −1.85097 | −0.394627 | ||||||||
\(23\) | 9.18427 | 1.91505 | 0.957526 | − | 0.288346i | \(-0.0931053\pi\) | ||||
0.957526 | + | 0.288346i | \(0.0931053\pi\) | |||||||
\(24\) | −0.851234 | −0.173757 | ||||||||
\(25\) | 2.48522 | 0.497043 | ||||||||
\(26\) | 1.88529 | 0.369735 | ||||||||
\(27\) | 4.49060 | 0.864217 | ||||||||
\(28\) | 0.590237 | 0.111544 | ||||||||
\(29\) | 5.21129 | 0.967712 | 0.483856 | − | 0.875148i | \(-0.339236\pi\) | ||||
0.483856 | + | 0.875148i | \(0.339236\pi\) | |||||||
\(30\) | 2.32890 | 0.425197 | ||||||||
\(31\) | 2.14709 | 0.385629 | 0.192814 | − | 0.981235i | \(-0.438238\pi\) | ||||
0.192814 | + | 0.981235i | \(0.438238\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.57561 | 0.274278 | ||||||||
\(34\) | −4.96288 | −0.851126 | ||||||||
\(35\) | −1.61484 | −0.272957 | ||||||||
\(36\) | −2.27540 | −0.379233 | ||||||||
\(37\) | 4.56743 | 0.750881 | 0.375440 | − | 0.926847i | \(-0.377491\pi\) | ||||
0.375440 | + | 0.926847i | \(0.377491\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −1.60482 | −0.256977 | ||||||||
\(40\) | −2.73591 | −0.432586 | ||||||||
\(41\) | 2.66253 | 0.415817 | 0.207909 | − | 0.978148i | \(-0.433334\pi\) | ||||
0.207909 | + | 0.978148i | \(0.433334\pi\) | |||||||
\(42\) | −0.502429 | −0.0775266 | ||||||||
\(43\) | −2.82781 | −0.431238 | −0.215619 | − | 0.976478i | \(-0.569177\pi\) | ||||
−0.215619 | + | 0.976478i | \(0.569177\pi\) | |||||||
\(44\) | −1.85097 | −0.279044 | ||||||||
\(45\) | 6.22530 | 0.928012 | ||||||||
\(46\) | 9.18427 | 1.35415 | ||||||||
\(47\) | −5.33483 | −0.778165 | −0.389083 | − | 0.921203i | \(-0.627208\pi\) | ||||
−0.389083 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(48\) | −0.851234 | −0.122865 | ||||||||
\(49\) | −6.65162 | −0.950232 | ||||||||
\(50\) | 2.48522 | 0.351463 | ||||||||
\(51\) | 4.22457 | 0.591558 | ||||||||
\(52\) | 1.88529 | 0.261442 | ||||||||
\(53\) | −4.12591 | −0.566737 | −0.283368 | − | 0.959011i | \(-0.591452\pi\) | ||||
−0.283368 | + | 0.959011i | \(0.591452\pi\) | |||||||
\(54\) | 4.49060 | 0.611093 | ||||||||
\(55\) | 5.06408 | 0.682841 | ||||||||
\(56\) | 0.590237 | 0.0788737 | ||||||||
\(57\) | −0.851234 | −0.112749 | ||||||||
\(58\) | 5.21129 | 0.684276 | ||||||||
\(59\) | −1.38390 | −0.180168 | −0.0900842 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900842 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(60\) | 2.32890 | 0.300660 | ||||||||
\(61\) | 2.88432 | 0.369299 | 0.184650 | − | 0.982804i | \(-0.440885\pi\) | ||||
0.184650 | + | 0.982804i | \(0.440885\pi\) | |||||||
\(62\) | 2.14709 | 0.272681 | ||||||||
\(63\) | −1.34302 | −0.169205 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.15798 | −0.639768 | ||||||||
\(66\) | 1.57561 | 0.193944 | ||||||||
\(67\) | −5.02573 | −0.613991 | −0.306995 | − | 0.951711i | \(-0.599324\pi\) | ||||
−0.306995 | + | 0.951711i | \(0.599324\pi\) | |||||||
\(68\) | −4.96288 | −0.601837 | ||||||||
\(69\) | −7.81796 | −0.941172 | ||||||||
\(70\) | −1.61484 | −0.193010 | ||||||||
\(71\) | 3.68758 | 0.437635 | 0.218817 | − | 0.975766i | \(-0.429780\pi\) | ||||
0.218817 | + | 0.975766i | \(0.429780\pi\) | |||||||
\(72\) | −2.27540 | −0.268159 | ||||||||
\(73\) | −2.34064 | −0.273951 | −0.136975 | − | 0.990574i | \(-0.543738\pi\) | ||||
−0.136975 | + | 0.990574i | \(0.543738\pi\) | |||||||
\(74\) | 4.56743 | 0.530953 | ||||||||
\(75\) | −2.11550 | −0.244277 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −1.09251 | −0.124503 | ||||||||
\(78\) | −1.60482 | −0.181710 | ||||||||
\(79\) | −5.28066 | −0.594121 | −0.297060 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297060 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(80\) | −2.73591 | −0.305884 | ||||||||
\(81\) | 3.00365 | 0.333739 | ||||||||
\(82\) | 2.66253 | 0.294027 | ||||||||
\(83\) | 4.69968 | 0.515857 | 0.257929 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257929 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(84\) | −0.502429 | −0.0548195 | ||||||||
\(85\) | 13.5780 | 1.47274 | ||||||||
\(86\) | −2.82781 | −0.304931 | ||||||||
\(87\) | −4.43603 | −0.475592 | ||||||||
\(88\) | −1.85097 | −0.197314 | ||||||||
\(89\) | 11.7557 | 1.24610 | 0.623051 | − | 0.782181i | \(-0.285893\pi\) | ||||
0.623051 | + | 0.782181i | \(0.285893\pi\) | |||||||
\(90\) | 6.22530 | 0.656204 | ||||||||
\(91\) | 1.11276 | 0.116649 | ||||||||
\(92\) | 9.18427 | 0.957526 | ||||||||
\(93\) | −1.82768 | −0.189521 | ||||||||
\(94\) | −5.33483 | −0.550246 | ||||||||
\(95\) | −2.73591 | −0.280699 | ||||||||
\(96\) | −0.851234 | −0.0868787 | ||||||||
\(97\) | 14.6135 | 1.48377 | 0.741887 | − | 0.670525i | \(-0.233931\pi\) | ||||
0.741887 | + | 0.670525i | \(0.233931\pi\) | |||||||
\(98\) | −6.65162 | −0.671915 | ||||||||
\(99\) | 4.21169 | 0.423291 | ||||||||
\(100\) | 2.48522 | 0.248522 | ||||||||
\(101\) | −12.8472 | −1.27835 | −0.639173 | − | 0.769063i | \(-0.720723\pi\) | ||||
−0.639173 | + | 0.769063i | \(0.720723\pi\) | |||||||
\(102\) | 4.22457 | 0.418295 | ||||||||
\(103\) | −16.3116 | −1.60723 | −0.803613 | − | 0.595152i | \(-0.797092\pi\) | ||||
−0.803613 | + | 0.595152i | \(0.797092\pi\) | |||||||
\(104\) | 1.88529 | 0.184867 | ||||||||
\(105\) | 1.37460 | 0.134148 | ||||||||
\(106\) | −4.12591 | −0.400743 | ||||||||
\(107\) | −14.6131 | −1.41270 | −0.706350 | − | 0.707862i | \(-0.749660\pi\) | ||||
−0.706350 | + | 0.707862i | \(0.749660\pi\) | |||||||
\(108\) | 4.49060 | 0.432108 | ||||||||
\(109\) | −13.7129 | −1.31345 | −0.656727 | − | 0.754128i | \(-0.728060\pi\) | ||||
−0.656727 | + | 0.754128i | \(0.728060\pi\) | |||||||
\(110\) | 5.06408 | 0.482841 | ||||||||
\(111\) | −3.88795 | −0.369028 | ||||||||
\(112\) | 0.590237 | 0.0557721 | ||||||||
\(113\) | 9.58561 | 0.901738 | 0.450869 | − | 0.892590i | \(-0.351114\pi\) | ||||
0.450869 | + | 0.892590i | \(0.351114\pi\) | |||||||
\(114\) | −0.851234 | −0.0797254 | ||||||||
\(115\) | −25.1274 | −2.34314 | ||||||||
\(116\) | 5.21129 | 0.483856 | ||||||||
\(117\) | −4.28978 | −0.396590 | ||||||||
\(118\) | −1.38390 | −0.127398 | ||||||||
\(119\) | −2.92927 | −0.268526 | ||||||||
\(120\) | 2.32890 | 0.212599 | ||||||||
\(121\) | −7.57392 | −0.688538 | ||||||||
\(122\) | 2.88432 | 0.261134 | ||||||||
\(123\) | −2.26643 | −0.204358 | ||||||||
\(124\) | 2.14709 | 0.192814 | ||||||||
\(125\) | 6.88023 | 0.615387 | ||||||||
\(126\) | −1.34302 | −0.119646 | ||||||||
\(127\) | −11.2005 | −0.993886 | −0.496943 | − | 0.867783i | \(-0.665544\pi\) | ||||
−0.496943 | + | 0.867783i | \(0.665544\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.40713 | 0.211936 | ||||||||
\(130\) | −5.15798 | −0.452384 | ||||||||
\(131\) | 22.0343 | 1.92515 | 0.962573 | − | 0.271023i | \(-0.0873619\pi\) | ||||
0.962573 | + | 0.271023i | \(0.0873619\pi\) | |||||||
\(132\) | 1.57561 | 0.137139 | ||||||||
\(133\) | 0.590237 | 0.0511800 | ||||||||
\(134\) | −5.02573 | −0.434157 | ||||||||
\(135\) | −12.2859 | −1.05740 | ||||||||
\(136\) | −4.96288 | −0.425563 | ||||||||
\(137\) | −12.8366 | −1.09670 | −0.548351 | − | 0.836248i | \(-0.684744\pi\) | ||||
−0.548351 | + | 0.836248i | \(0.684744\pi\) | |||||||
\(138\) | −7.81796 | −0.665509 | ||||||||
\(139\) | −13.2901 | −1.12725 | −0.563625 | − | 0.826031i | \(-0.690594\pi\) | ||||
−0.563625 | + | 0.826031i | \(0.690594\pi\) | |||||||
\(140\) | −1.61484 | −0.136478 | ||||||||
\(141\) | 4.54119 | 0.382437 | ||||||||
\(142\) | 3.68758 | 0.309454 | ||||||||
\(143\) | −3.48960 | −0.291815 | ||||||||
\(144\) | −2.27540 | −0.189617 | ||||||||
\(145\) | −14.2576 | −1.18403 | ||||||||
\(146\) | −2.34064 | −0.193713 | ||||||||
\(147\) | 5.66209 | 0.467001 | ||||||||
\(148\) | 4.56743 | 0.375440 | ||||||||
\(149\) | −9.18506 | −0.752469 | −0.376235 | − | 0.926524i | \(-0.622781\pi\) | ||||
−0.376235 | + | 0.926524i | \(0.622781\pi\) | |||||||
\(150\) | −2.11550 | −0.172730 | ||||||||
\(151\) | −18.1659 | −1.47832 | −0.739161 | − | 0.673529i | \(-0.764778\pi\) | ||||
−0.739161 | + | 0.673529i | \(0.764778\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 11.2925 | 0.912947 | ||||||||
\(154\) | −1.09251 | −0.0880368 | ||||||||
\(155\) | −5.87425 | −0.471831 | ||||||||
\(156\) | −1.60482 | −0.128488 | ||||||||
\(157\) | −6.86544 | −0.547921 | −0.273961 | − | 0.961741i | \(-0.588334\pi\) | ||||
−0.273961 | + | 0.961741i | \(0.588334\pi\) | |||||||
\(158\) | −5.28066 | −0.420107 | ||||||||
\(159\) | 3.51211 | 0.278529 | ||||||||
\(160\) | −2.73591 | −0.216293 | ||||||||
\(161\) | 5.42089 | 0.427226 | ||||||||
\(162\) | 3.00365 | 0.235989 | ||||||||
\(163\) | −7.85359 | −0.615141 | −0.307570 | − | 0.951525i | \(-0.599516\pi\) | ||||
−0.307570 | + | 0.951525i | \(0.599516\pi\) | |||||||
\(164\) | 2.66253 | 0.207909 | ||||||||
\(165\) | −4.31072 | −0.335589 | ||||||||
\(166\) | 4.69968 | 0.364766 | ||||||||
\(167\) | −3.06987 | −0.237554 | −0.118777 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118777 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(168\) | −0.502429 | −0.0387633 | ||||||||
\(169\) | −9.44570 | −0.726592 | ||||||||
\(170\) | 13.5780 | 1.04138 | ||||||||
\(171\) | −2.27540 | −0.174004 | ||||||||
\(172\) | −2.82781 | −0.215619 | ||||||||
\(173\) | 8.70636 | 0.661932 | 0.330966 | − | 0.943643i | \(-0.392625\pi\) | ||||
0.330966 | + | 0.943643i | \(0.392625\pi\) | |||||||
\(174\) | −4.43603 | −0.336294 | ||||||||
\(175\) | 1.46686 | 0.110885 | ||||||||
\(176\) | −1.85097 | −0.139522 | ||||||||
\(177\) | 1.17802 | 0.0885456 | ||||||||
\(178\) | 11.7557 | 0.881128 | ||||||||
\(179\) | −18.7136 | −1.39872 | −0.699360 | − | 0.714769i | \(-0.746532\pi\) | ||||
−0.699360 | + | 0.714769i | \(0.746532\pi\) | |||||||
\(180\) | 6.22530 | 0.464006 | ||||||||
\(181\) | −12.8415 | −0.954498 | −0.477249 | − | 0.878768i | \(-0.658366\pi\) | ||||
−0.477249 | + | 0.878768i | \(0.658366\pi\) | |||||||
\(182\) | 1.11276 | 0.0824836 | ||||||||
\(183\) | −2.45523 | −0.181496 | ||||||||
\(184\) | 9.18427 | 0.677073 | ||||||||
\(185\) | −12.4961 | −0.918731 | ||||||||
\(186\) | −1.82768 | −0.134012 | ||||||||
\(187\) | 9.18612 | 0.671755 | ||||||||
\(188\) | −5.33483 | −0.389083 | ||||||||
\(189\) | 2.65052 | 0.192797 | ||||||||
\(190\) | −2.73591 | −0.198484 | ||||||||
\(191\) | 18.4358 | 1.33396 | 0.666982 | − | 0.745074i | \(-0.267586\pi\) | ||||
0.666982 | + | 0.745074i | \(0.267586\pi\) | |||||||
\(192\) | −0.851234 | −0.0614325 | ||||||||
\(193\) | 1.16570 | 0.0839086 | 0.0419543 | − | 0.999120i | \(-0.486642\pi\) | ||||
0.0419543 | + | 0.999120i | \(0.486642\pi\) | |||||||
\(194\) | 14.6135 | 1.04919 | ||||||||
\(195\) | 4.39064 | 0.314421 | ||||||||
\(196\) | −6.65162 | −0.475116 | ||||||||
\(197\) | −0.461268 | −0.0328640 | −0.0164320 | − | 0.999865i | \(-0.505231\pi\) | ||||
−0.0164320 | + | 0.999865i | \(0.505231\pi\) | |||||||
\(198\) | 4.21169 | 0.299312 | ||||||||
\(199\) | −24.2470 | −1.71883 | −0.859413 | − | 0.511282i | \(-0.829171\pi\) | ||||
−0.859413 | + | 0.511282i | \(0.829171\pi\) | |||||||
\(200\) | 2.48522 | 0.175731 | ||||||||
\(201\) | 4.27807 | 0.301752 | ||||||||
\(202\) | −12.8472 | −0.903927 | ||||||||
\(203\) | 3.07589 | 0.215885 | ||||||||
\(204\) | 4.22457 | 0.295779 | ||||||||
\(205\) | −7.28444 | −0.508768 | ||||||||
\(206\) | −16.3116 | −1.13648 | ||||||||
\(207\) | −20.8979 | −1.45250 | ||||||||
\(208\) | 1.88529 | 0.130721 | ||||||||
\(209\) | −1.85097 | −0.128034 | ||||||||
\(210\) | 1.37460 | 0.0948566 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −4.12591 | −0.283368 | ||||||||
\(213\) | −3.13899 | −0.215080 | ||||||||
\(214\) | −14.6131 | −0.998930 | ||||||||
\(215\) | 7.73665 | 0.527635 | ||||||||
\(216\) | 4.49060 | 0.305547 | ||||||||
\(217\) | 1.26729 | 0.0860293 | ||||||||
\(218\) | −13.7129 | −0.928752 | ||||||||
\(219\) | 1.99243 | 0.134636 | ||||||||
\(220\) | 5.06408 | 0.341420 | ||||||||
\(221\) | −9.35644 | −0.629382 | ||||||||
\(222\) | −3.88795 | −0.260942 | ||||||||
\(223\) | 23.5388 | 1.57628 | 0.788138 | − | 0.615499i | \(-0.211045\pi\) | ||||
0.788138 | + | 0.615499i | \(0.211045\pi\) | |||||||
\(224\) | 0.590237 | 0.0394368 | ||||||||
\(225\) | −5.65486 | −0.376991 | ||||||||
\(226\) | 9.58561 | 0.637625 | ||||||||
\(227\) | −22.4844 | −1.49234 | −0.746172 | − | 0.665754i | \(-0.768110\pi\) | ||||
−0.746172 | + | 0.665754i | \(0.768110\pi\) | |||||||
\(228\) | −0.851234 | −0.0563744 | ||||||||
\(229\) | 14.6615 | 0.968857 | 0.484428 | − | 0.874831i | \(-0.339028\pi\) | ||||
0.484428 | + | 0.874831i | \(0.339028\pi\) | |||||||
\(230\) | −25.1274 | −1.65685 | ||||||||
\(231\) | 0.929980 | 0.0611882 | ||||||||
\(232\) | 5.21129 | 0.342138 | ||||||||
\(233\) | 6.87666 | 0.450505 | 0.225252 | − | 0.974300i | \(-0.427679\pi\) | ||||
0.225252 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(234\) | −4.28978 | −0.280432 | ||||||||
\(235\) | 14.5956 | 0.952114 | ||||||||
\(236\) | −1.38390 | −0.0900842 | ||||||||
\(237\) | 4.49508 | 0.291987 | ||||||||
\(238\) | −2.92927 | −0.189876 | ||||||||
\(239\) | −13.6353 | −0.881997 | −0.440998 | − | 0.897508i | \(-0.645376\pi\) | ||||
−0.440998 | + | 0.897508i | \(0.645376\pi\) | |||||||
\(240\) | 2.32890 | 0.150330 | ||||||||
\(241\) | 9.32981 | 0.600986 | 0.300493 | − | 0.953784i | \(-0.402849\pi\) | ||||
0.300493 | + | 0.953784i | \(0.402849\pi\) | |||||||
\(242\) | −7.57392 | −0.486870 | ||||||||
\(243\) | −16.0286 | −1.02824 | ||||||||
\(244\) | 2.88432 | 0.184650 | ||||||||
\(245\) | 18.1983 | 1.16264 | ||||||||
\(246\) | −2.26643 | −0.144503 | ||||||||
\(247\) | 1.88529 | 0.119958 | ||||||||
\(248\) | 2.14709 | 0.136340 | ||||||||
\(249\) | −4.00053 | −0.253523 | ||||||||
\(250\) | 6.88023 | 0.435144 | ||||||||
\(251\) | 4.53768 | 0.286416 | 0.143208 | − | 0.989693i | \(-0.454258\pi\) | ||||
0.143208 | + | 0.989693i | \(0.454258\pi\) | |||||||
\(252\) | −1.34302 | −0.0846026 | ||||||||
\(253\) | −16.9998 | −1.06877 | ||||||||
\(254\) | −11.2005 | −0.702784 | ||||||||
\(255\) | −11.5580 | −0.723793 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.6876 | −1.22808 | −0.614039 | − | 0.789276i | \(-0.710456\pi\) | ||||
−0.614039 | + | 0.789276i | \(0.710456\pi\) | |||||||
\(258\) | 2.40713 | 0.149862 | ||||||||
\(259\) | 2.69586 | 0.167513 | ||||||||
\(260\) | −5.15798 | −0.319884 | ||||||||
\(261\) | −11.8578 | −0.733977 | ||||||||
\(262\) | 22.0343 | 1.36128 | ||||||||
\(263\) | 7.31531 | 0.451081 | 0.225541 | − | 0.974234i | \(-0.427585\pi\) | ||||
0.225541 | + | 0.974234i | \(0.427585\pi\) | |||||||
\(264\) | 1.57561 | 0.0969719 | ||||||||
\(265\) | 11.2881 | 0.693424 | ||||||||
\(266\) | 0.590237 | 0.0361897 | ||||||||
\(267\) | −10.0069 | −0.612410 | ||||||||
\(268\) | −5.02573 | −0.306995 | ||||||||
\(269\) | 22.7402 | 1.38650 | 0.693248 | − | 0.720699i | \(-0.256179\pi\) | ||||
0.693248 | + | 0.720699i | \(0.256179\pi\) | |||||||
\(270\) | −12.2859 | −0.747695 | ||||||||
\(271\) | −0.653391 | −0.0396907 | −0.0198453 | − | 0.999803i | \(-0.506317\pi\) | ||||
−0.0198453 | + | 0.999803i | \(0.506317\pi\) | |||||||
\(272\) | −4.96288 | −0.300919 | ||||||||
\(273\) | −0.947223 | −0.0573285 | ||||||||
\(274\) | −12.8366 | −0.775486 | ||||||||
\(275\) | −4.60005 | −0.277394 | ||||||||
\(276\) | −7.81796 | −0.470586 | ||||||||
\(277\) | 3.66730 | 0.220347 | 0.110173 | − | 0.993912i | \(-0.464859\pi\) | ||||
0.110173 | + | 0.993912i | \(0.464859\pi\) | |||||||
\(278\) | −13.2901 | −0.797086 | ||||||||
\(279\) | −4.88549 | −0.292487 | ||||||||
\(280\) | −1.61484 | −0.0965049 | ||||||||
\(281\) | 14.2063 | 0.847478 | 0.423739 | − | 0.905784i | \(-0.360717\pi\) | ||||
0.423739 | + | 0.905784i | \(0.360717\pi\) | |||||||
\(282\) | 4.54119 | 0.270424 | ||||||||
\(283\) | 14.2527 | 0.847236 | 0.423618 | − | 0.905841i | \(-0.360760\pi\) | ||||
0.423618 | + | 0.905841i | \(0.360760\pi\) | |||||||
\(284\) | 3.68758 | 0.218817 | ||||||||
\(285\) | 2.32890 | 0.137952 | ||||||||
\(286\) | −3.48960 | −0.206344 | ||||||||
\(287\) | 1.57152 | 0.0927640 | ||||||||
\(288\) | −2.27540 | −0.134079 | ||||||||
\(289\) | 7.63013 | 0.448831 | ||||||||
\(290\) | −14.2576 | −0.837237 | ||||||||
\(291\) | −12.4395 | −0.729216 | ||||||||
\(292\) | −2.34064 | −0.136975 | ||||||||
\(293\) | −13.3014 | −0.777073 | −0.388537 | − | 0.921433i | \(-0.627019\pi\) | ||||
−0.388537 | + | 0.921433i | \(0.627019\pi\) | |||||||
\(294\) | 5.66209 | 0.330220 | ||||||||
\(295\) | 3.78623 | 0.220443 | ||||||||
\(296\) | 4.56743 | 0.265476 | ||||||||
\(297\) | −8.31195 | −0.482308 | ||||||||
\(298\) | −9.18506 | −0.532076 | ||||||||
\(299\) | 17.3150 | 1.00135 | ||||||||
\(300\) | −2.11550 | −0.122138 | ||||||||
\(301\) | −1.66908 | −0.0962041 | ||||||||
\(302\) | −18.1659 | −1.04533 | ||||||||
\(303\) | 10.9360 | 0.628256 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −7.89124 | −0.451851 | ||||||||
\(306\) | 11.2925 | 0.645551 | ||||||||
\(307\) | 27.9110 | 1.59297 | 0.796483 | − | 0.604661i | \(-0.206691\pi\) | ||||
0.796483 | + | 0.604661i | \(0.206691\pi\) | |||||||
\(308\) | −1.09251 | −0.0622514 | ||||||||
\(309\) | 13.8850 | 0.789888 | ||||||||
\(310\) | −5.87425 | −0.333635 | ||||||||
\(311\) | 12.2226 | 0.693078 | 0.346539 | − | 0.938036i | \(-0.387357\pi\) | ||||
0.346539 | + | 0.938036i | \(0.387357\pi\) | |||||||
\(312\) | −1.60482 | −0.0908550 | ||||||||
\(313\) | 23.3705 | 1.32098 | 0.660490 | − | 0.750835i | \(-0.270349\pi\) | ||||
0.660490 | + | 0.750835i | \(0.270349\pi\) | |||||||
\(314\) | −6.86544 | −0.387439 | ||||||||
\(315\) | 3.67440 | 0.207029 | ||||||||
\(316\) | −5.28066 | −0.297060 | ||||||||
\(317\) | −5.04135 | −0.283151 | −0.141575 | − | 0.989927i | \(-0.545217\pi\) | ||||
−0.141575 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(318\) | 3.51211 | 0.196949 | ||||||||
\(319\) | −9.64592 | −0.540068 | ||||||||
\(320\) | −2.73591 | −0.152942 | ||||||||
\(321\) | 12.4392 | 0.694286 | ||||||||
\(322\) | 5.42089 | 0.302094 | ||||||||
\(323\) | −4.96288 | −0.276142 | ||||||||
\(324\) | 3.00365 | 0.166869 | ||||||||
\(325\) | 4.68534 | 0.259896 | ||||||||
\(326\) | −7.85359 | −0.434970 | ||||||||
\(327\) | 11.6729 | 0.645511 | ||||||||
\(328\) | 2.66253 | 0.147014 | ||||||||
\(329\) | −3.14881 | −0.173600 | ||||||||
\(330\) | −4.31072 | −0.237297 | ||||||||
\(331\) | −27.5631 | −1.51500 | −0.757502 | − | 0.652833i | \(-0.773580\pi\) | ||||
−0.757502 | + | 0.652833i | \(0.773580\pi\) | |||||||
\(332\) | 4.69968 | 0.257929 | ||||||||
\(333\) | −10.3927 | −0.569518 | ||||||||
\(334\) | −3.06987 | −0.167976 | ||||||||
\(335\) | 13.7500 | 0.751241 | ||||||||
\(336\) | −0.502429 | −0.0274098 | ||||||||
\(337\) | −10.5707 | −0.575822 | −0.287911 | − | 0.957657i | \(-0.592961\pi\) | ||||
−0.287911 | + | 0.957657i | \(0.592961\pi\) | |||||||
\(338\) | −9.44570 | −0.513778 | ||||||||
\(339\) | −8.15960 | −0.443168 | ||||||||
\(340\) | 13.5780 | 0.736370 | ||||||||
\(341\) | −3.97419 | −0.215215 | ||||||||
\(342\) | −2.27540 | −0.123040 | ||||||||
\(343\) | −8.05769 | −0.435074 | ||||||||
\(344\) | −2.82781 | −0.152466 | ||||||||
\(345\) | 21.3893 | 1.15156 | ||||||||
\(346\) | 8.70636 | 0.468057 | ||||||||
\(347\) | 12.6630 | 0.679787 | 0.339894 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339894 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(348\) | −4.43603 | −0.237796 | ||||||||
\(349\) | −28.4933 | −1.52521 | −0.762606 | − | 0.646863i | \(-0.776081\pi\) | ||||
−0.762606 | + | 0.646863i | \(0.776081\pi\) | |||||||
\(350\) | 1.46686 | 0.0784072 | ||||||||
\(351\) | 8.46606 | 0.451885 | ||||||||
\(352\) | −1.85097 | −0.0986569 | ||||||||
\(353\) | −21.5746 | −1.14830 | −0.574150 | − | 0.818750i | \(-0.694667\pi\) | ||||
−0.574150 | + | 0.818750i | \(0.694667\pi\) | |||||||
\(354\) | 1.17802 | 0.0626112 | ||||||||
\(355\) | −10.0889 | −0.535462 | ||||||||
\(356\) | 11.7557 | 0.623051 | ||||||||
\(357\) | 2.49349 | 0.131970 | ||||||||
\(358\) | −18.7136 | −0.989045 | ||||||||
\(359\) | 23.0994 | 1.21914 | 0.609571 | − | 0.792731i | \(-0.291342\pi\) | ||||
0.609571 | + | 0.792731i | \(0.291342\pi\) | |||||||
\(360\) | 6.22530 | 0.328102 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −12.8415 | −0.674932 | ||||||||
\(363\) | 6.44718 | 0.338389 | ||||||||
\(364\) | 1.11276 | 0.0583247 | ||||||||
\(365\) | 6.40378 | 0.335189 | ||||||||
\(366\) | −2.45523 | −0.128337 | ||||||||
\(367\) | −13.3317 | −0.695910 | −0.347955 | − | 0.937511i | \(-0.613124\pi\) | ||||
−0.347955 | + | 0.937511i | \(0.613124\pi\) | |||||||
\(368\) | 9.18427 | 0.478763 | ||||||||
\(369\) | −6.05832 | −0.315383 | ||||||||
\(370\) | −12.4961 | −0.649641 | ||||||||
\(371\) | −2.43526 | −0.126432 | ||||||||
\(372\) | −1.82768 | −0.0947606 | ||||||||
\(373\) | −22.7148 | −1.17613 | −0.588063 | − | 0.808815i | \(-0.700109\pi\) | ||||
−0.588063 | + | 0.808815i | \(0.700109\pi\) | |||||||
\(374\) | 9.18612 | 0.475003 | ||||||||
\(375\) | −5.85669 | −0.302438 | ||||||||
\(376\) | −5.33483 | −0.275123 | ||||||||
\(377\) | 9.82476 | 0.506001 | ||||||||
\(378\) | 2.65052 | 0.136328 | ||||||||
\(379\) | 27.9622 | 1.43632 | 0.718162 | − | 0.695876i | \(-0.244984\pi\) | ||||
0.718162 | + | 0.695876i | \(0.244984\pi\) | |||||||
\(380\) | −2.73591 | −0.140349 | ||||||||
\(381\) | 9.53427 | 0.488456 | ||||||||
\(382\) | 18.4358 | 0.943255 | ||||||||
\(383\) | −4.12225 | −0.210637 | −0.105319 | − | 0.994439i | \(-0.533586\pi\) | ||||
−0.105319 | + | 0.994439i | \(0.533586\pi\) | |||||||
\(384\) | −0.851234 | −0.0434394 | ||||||||
\(385\) | 2.98901 | 0.152334 | ||||||||
\(386\) | 1.16570 | 0.0593324 | ||||||||
\(387\) | 6.43441 | 0.327079 | ||||||||
\(388\) | 14.6135 | 0.741887 | ||||||||
\(389\) | 13.2545 | 0.672028 | 0.336014 | − | 0.941857i | \(-0.390921\pi\) | ||||
0.336014 | + | 0.941857i | \(0.390921\pi\) | |||||||
\(390\) | 4.39064 | 0.222329 | ||||||||
\(391\) | −45.5804 | −2.30510 | ||||||||
\(392\) | −6.65162 | −0.335958 | ||||||||
\(393\) | −18.7563 | −0.946133 | ||||||||
\(394\) | −0.461268 | −0.0232383 | ||||||||
\(395\) | 14.4474 | 0.726929 | ||||||||
\(396\) | 4.21169 | 0.211645 | ||||||||
\(397\) | 9.35973 | 0.469751 | 0.234876 | − | 0.972025i | \(-0.424532\pi\) | ||||
0.234876 | + | 0.972025i | \(0.424532\pi\) | |||||||
\(398\) | −24.2470 | −1.21539 | ||||||||
\(399\) | −0.502429 | −0.0251529 | ||||||||
\(400\) | 2.48522 | 0.124261 | ||||||||
\(401\) | 23.9174 | 1.19438 | 0.597188 | − | 0.802101i | \(-0.296285\pi\) | ||||
0.597188 | + | 0.802101i | \(0.296285\pi\) | |||||||
\(402\) | 4.27807 | 0.213371 | ||||||||
\(403\) | 4.04788 | 0.201639 | ||||||||
\(404\) | −12.8472 | −0.639173 | ||||||||
\(405\) | −8.21772 | −0.408342 | ||||||||
\(406\) | 3.07589 | 0.152654 | ||||||||
\(407\) | −8.45416 | −0.419057 | ||||||||
\(408\) | 4.22457 | 0.209147 | ||||||||
\(409\) | −24.4329 | −1.20813 | −0.604065 | − | 0.796935i | \(-0.706453\pi\) | ||||
−0.604065 | + | 0.796935i | \(0.706453\pi\) | |||||||
\(410\) | −7.28444 | −0.359753 | ||||||||
\(411\) | 10.9269 | 0.538986 | ||||||||
\(412\) | −16.3116 | −0.803613 | ||||||||
\(413\) | −0.816828 | −0.0401935 | ||||||||
\(414\) | −20.8979 | −1.02708 | ||||||||
\(415\) | −12.8579 | −0.631170 | ||||||||
\(416\) | 1.88529 | 0.0924337 | ||||||||
\(417\) | 11.3130 | 0.553998 | ||||||||
\(418\) | −1.85097 | −0.0905337 | ||||||||
\(419\) | 7.08550 | 0.346149 | 0.173075 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173075 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(420\) | 1.37460 | 0.0670738 | ||||||||
\(421\) | −25.9286 | −1.26368 | −0.631841 | − | 0.775098i | \(-0.717701\pi\) | ||||
−0.631841 | + | 0.775098i | \(0.717701\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 12.1389 | 0.590213 | ||||||||
\(424\) | −4.12591 | −0.200372 | ||||||||
\(425\) | −12.3338 | −0.598278 | ||||||||
\(426\) | −3.13899 | −0.152085 | ||||||||
\(427\) | 1.70243 | 0.0823864 | ||||||||
\(428\) | −14.6131 | −0.706350 | ||||||||
\(429\) | 2.97047 | 0.143416 | ||||||||
\(430\) | 7.73665 | 0.373095 | ||||||||
\(431\) | −22.2780 | −1.07309 | −0.536546 | − | 0.843871i | \(-0.680271\pi\) | ||||
−0.536546 | + | 0.843871i | \(0.680271\pi\) | |||||||
\(432\) | 4.49060 | 0.216054 | ||||||||
\(433\) | −8.14495 | −0.391422 | −0.195711 | − | 0.980662i | \(-0.562701\pi\) | ||||
−0.195711 | + | 0.980662i | \(0.562701\pi\) | |||||||
\(434\) | 1.26729 | 0.0608319 | ||||||||
\(435\) | 12.1366 | 0.581904 | ||||||||
\(436\) | −13.7129 | −0.656727 | ||||||||
\(437\) | 9.18427 | 0.439343 | ||||||||
\(438\) | 1.99243 | 0.0952020 | ||||||||
\(439\) | −23.9146 | −1.14138 | −0.570692 | − | 0.821164i | \(-0.693325\pi\) | ||||
−0.570692 | + | 0.821164i | \(0.693325\pi\) | |||||||
\(440\) | 5.06408 | 0.241421 | ||||||||
\(441\) | 15.1351 | 0.720719 | ||||||||
\(442\) | −9.35644 | −0.445040 | ||||||||
\(443\) | −18.2748 | −0.868262 | −0.434131 | − | 0.900850i | \(-0.642944\pi\) | ||||
−0.434131 | + | 0.900850i | \(0.642944\pi\) | |||||||
\(444\) | −3.88795 | −0.184514 | ||||||||
\(445\) | −32.1626 | −1.52465 | ||||||||
\(446\) | 23.5388 | 1.11460 | ||||||||
\(447\) | 7.81864 | 0.369809 | ||||||||
\(448\) | 0.590237 | 0.0278861 | ||||||||
\(449\) | −32.7585 | −1.54597 | −0.772984 | − | 0.634426i | \(-0.781237\pi\) | ||||
−0.772984 | + | 0.634426i | \(0.781237\pi\) | |||||||
\(450\) | −5.65486 | −0.266573 | ||||||||
\(451\) | −4.92825 | −0.232062 | ||||||||
\(452\) | 9.58561 | 0.450869 | ||||||||
\(453\) | 15.4635 | 0.726537 | ||||||||
\(454\) | −22.4844 | −1.05525 | ||||||||
\(455\) | −3.04443 | −0.142725 | ||||||||
\(456\) | −0.851234 | −0.0398627 | ||||||||
\(457\) | −3.45841 | −0.161777 | −0.0808887 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808887 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(458\) | 14.6615 | 0.685085 | ||||||||
\(459\) | −22.2863 | −1.04024 | ||||||||
\(460\) | −25.1274 | −1.17157 | ||||||||
\(461\) | −30.8497 | −1.43681 | −0.718406 | − | 0.695624i | \(-0.755128\pi\) | ||||
−0.718406 | + | 0.695624i | \(0.755128\pi\) | |||||||
\(462\) | 0.929980 | 0.0432666 | ||||||||
\(463\) | −39.7861 | −1.84902 | −0.924508 | − | 0.381163i | \(-0.875524\pi\) | ||||
−0.924508 | + | 0.381163i | \(0.875524\pi\) | |||||||
\(464\) | 5.21129 | 0.241928 | ||||||||
\(465\) | 5.00036 | 0.231886 | ||||||||
\(466\) | 6.87666 | 0.318555 | ||||||||
\(467\) | −4.95261 | −0.229180 | −0.114590 | − | 0.993413i | \(-0.536555\pi\) | ||||
−0.114590 | + | 0.993413i | \(0.536555\pi\) | |||||||
\(468\) | −4.28978 | −0.198295 | ||||||||
\(469\) | −2.96637 | −0.136974 | ||||||||
\(470\) | 14.5956 | 0.673247 | ||||||||
\(471\) | 5.84409 | 0.269282 | ||||||||
\(472\) | −1.38390 | −0.0636991 | ||||||||
\(473\) | 5.23419 | 0.240668 | ||||||||
\(474\) | 4.49508 | 0.206466 | ||||||||
\(475\) | 2.48522 | 0.114029 | ||||||||
\(476\) | −2.92927 | −0.134263 | ||||||||
\(477\) | 9.38809 | 0.429851 | ||||||||
\(478\) | −13.6353 | −0.623666 | ||||||||
\(479\) | 1.34533 | 0.0614699 | 0.0307349 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307349 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(480\) | 2.32890 | 0.106299 | ||||||||
\(481\) | 8.61091 | 0.392624 | ||||||||
\(482\) | 9.32981 | 0.424961 | ||||||||
\(483\) | −4.61445 | −0.209965 | ||||||||
\(484\) | −7.57392 | −0.344269 | ||||||||
\(485\) | −39.9812 | −1.81545 | ||||||||
\(486\) | −16.0286 | −0.727073 | ||||||||
\(487\) | −32.4030 | −1.46832 | −0.734160 | − | 0.678977i | \(-0.762424\pi\) | ||||
−0.734160 | + | 0.678977i | \(0.762424\pi\) | |||||||
\(488\) | 2.88432 | 0.130567 | ||||||||
\(489\) | 6.68524 | 0.302317 | ||||||||
\(490\) | 18.1983 | 0.822113 | ||||||||
\(491\) | 3.96106 | 0.178760 | 0.0893800 | − | 0.995998i | \(-0.471511\pi\) | ||||
0.0893800 | + | 0.995998i | \(0.471511\pi\) | |||||||
\(492\) | −2.26643 | −0.102179 | ||||||||
\(493\) | −25.8630 | −1.16481 | ||||||||
\(494\) | 1.88529 | 0.0848230 | ||||||||
\(495\) | −11.5228 | −0.517912 | ||||||||
\(496\) | 2.14709 | 0.0964072 | ||||||||
\(497\) | 2.17654 | 0.0976312 | ||||||||
\(498\) | −4.00053 | −0.179268 | ||||||||
\(499\) | −14.9638 | −0.669871 | −0.334935 | − | 0.942241i | \(-0.608715\pi\) | ||||
−0.334935 | + | 0.942241i | \(0.608715\pi\) | |||||||
\(500\) | 6.88023 | 0.307693 | ||||||||
\(501\) | 2.61318 | 0.116748 | ||||||||
\(502\) | 4.53768 | 0.202526 | ||||||||
\(503\) | 2.73170 | 0.121801 | 0.0609003 | − | 0.998144i | \(-0.480603\pi\) | ||||
0.0609003 | + | 0.998144i | \(0.480603\pi\) | |||||||
\(504\) | −1.34302 | −0.0598231 | ||||||||
\(505\) | 35.1488 | 1.56410 | ||||||||
\(506\) | −16.9998 | −0.755732 | ||||||||
\(507\) | 8.04050 | 0.357091 | ||||||||
\(508\) | −11.2005 | −0.496943 | ||||||||
\(509\) | 8.11268 | 0.359588 | 0.179794 | − | 0.983704i | \(-0.442457\pi\) | ||||
0.179794 | + | 0.983704i | \(0.442457\pi\) | |||||||
\(510\) | −11.5580 | −0.511799 | ||||||||
\(511\) | −1.38153 | −0.0611153 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.49060 | 0.198265 | ||||||||
\(514\) | −19.6876 | −0.868383 | ||||||||
\(515\) | 44.6270 | 1.96650 | ||||||||
\(516\) | 2.40713 | 0.105968 | ||||||||
\(517\) | 9.87460 | 0.434284 | ||||||||
\(518\) | 2.69586 | 0.118449 | ||||||||
\(519\) | −7.41115 | −0.325313 | ||||||||
\(520\) | −5.15798 | −0.226192 | ||||||||
\(521\) | 25.4442 | 1.11473 | 0.557366 | − | 0.830267i | \(-0.311812\pi\) | ||||
0.557366 | + | 0.830267i | \(0.311812\pi\) | |||||||
\(522\) | −11.8578 | −0.519000 | ||||||||
\(523\) | −18.5770 | −0.812315 | −0.406157 | − | 0.913803i | \(-0.633132\pi\) | ||||
−0.406157 | + | 0.913803i | \(0.633132\pi\) | |||||||
\(524\) | 22.0343 | 0.962573 | ||||||||
\(525\) | −1.24865 | −0.0544954 | ||||||||
\(526\) | 7.31531 | 0.318962 | ||||||||
\(527\) | −10.6557 | −0.464171 | ||||||||
\(528\) | 1.57561 | 0.0685695 | ||||||||
\(529\) | 61.3508 | 2.66743 | ||||||||
\(530\) | 11.2881 | 0.490325 | ||||||||
\(531\) | 3.14893 | 0.136652 | ||||||||
\(532\) | 0.590237 | 0.0255900 | ||||||||
\(533\) | 5.01963 | 0.217424 | ||||||||
\(534\) | −10.0069 | −0.433039 | ||||||||
\(535\) | 39.9801 | 1.72849 | ||||||||
\(536\) | −5.02573 | −0.217079 | ||||||||
\(537\) | 15.9297 | 0.687415 | ||||||||
\(538\) | 22.7402 | 0.980400 | ||||||||
\(539\) | 12.3119 | 0.530312 | ||||||||
\(540\) | −12.2859 | −0.528701 | ||||||||
\(541\) | 9.21356 | 0.396122 | 0.198061 | − | 0.980190i | \(-0.436536\pi\) | ||||
0.198061 | + | 0.980190i | \(0.436536\pi\) | |||||||
\(542\) | −0.653391 | −0.0280656 | ||||||||
\(543\) | 10.9311 | 0.469098 | ||||||||
\(544\) | −4.96288 | −0.212782 | ||||||||
\(545\) | 37.5172 | 1.60706 | ||||||||
\(546\) | −0.947223 | −0.0405374 | ||||||||
\(547\) | 32.4664 | 1.38816 | 0.694082 | − | 0.719896i | \(-0.255810\pi\) | ||||
0.694082 | + | 0.719896i | \(0.255810\pi\) | |||||||
\(548\) | −12.8366 | −0.548351 | ||||||||
\(549\) | −6.56298 | −0.280101 | ||||||||
\(550\) | −4.60005 | −0.196147 | ||||||||
\(551\) | 5.21129 | 0.222008 | ||||||||
\(552\) | −7.81796 | −0.332755 | ||||||||
\(553\) | −3.11684 | −0.132541 | ||||||||
\(554\) | 3.66730 | 0.155809 | ||||||||
\(555\) | 10.6371 | 0.451520 | ||||||||
\(556\) | −13.2901 | −0.563625 | ||||||||
\(557\) | 22.9713 | 0.973325 | 0.486662 | − | 0.873590i | \(-0.338214\pi\) | ||||
0.486662 | + | 0.873590i | \(0.338214\pi\) | |||||||
\(558\) | −4.88549 | −0.206819 | ||||||||
\(559\) | −5.33124 | −0.225487 | ||||||||
\(560\) | −1.61484 | −0.0682392 | ||||||||
\(561\) | −7.81954 | −0.330141 | ||||||||
\(562\) | 14.2063 | 0.599258 | ||||||||
\(563\) | 46.2540 | 1.94937 | 0.974686 | − | 0.223577i | \(-0.0717734\pi\) | ||||
0.974686 | + | 0.223577i | \(0.0717734\pi\) | |||||||
\(564\) | 4.54119 | 0.191219 | ||||||||
\(565\) | −26.2254 | −1.10331 | ||||||||
\(566\) | 14.2527 | 0.599086 | ||||||||
\(567\) | 1.77286 | 0.0744533 | ||||||||
\(568\) | 3.68758 | 0.154727 | ||||||||
\(569\) | −44.3647 | −1.85987 | −0.929933 | − | 0.367730i | \(-0.880135\pi\) | ||||
−0.929933 | + | 0.367730i | \(0.880135\pi\) | |||||||
\(570\) | 2.32890 | 0.0975470 | ||||||||
\(571\) | −30.1679 | −1.26249 | −0.631244 | − | 0.775584i | \(-0.717455\pi\) | ||||
−0.631244 | + | 0.775584i | \(0.717455\pi\) | |||||||
\(572\) | −3.48960 | −0.145908 | ||||||||
\(573\) | −15.6931 | −0.655590 | ||||||||
\(574\) | 1.57152 | 0.0655940 | ||||||||
\(575\) | 22.8249 | 0.951864 | ||||||||
\(576\) | −2.27540 | −0.0948084 | ||||||||
\(577\) | 41.1781 | 1.71427 | 0.857133 | − | 0.515095i | \(-0.172243\pi\) | ||||
0.857133 | + | 0.515095i | \(0.172243\pi\) | |||||||
\(578\) | 7.63013 | 0.317372 | ||||||||
\(579\) | −0.992280 | −0.0412377 | ||||||||
\(580\) | −14.2576 | −0.592016 | ||||||||
\(581\) | 2.77392 | 0.115082 | ||||||||
\(582\) | −12.4395 | −0.515634 | ||||||||
\(583\) | 7.63692 | 0.316289 | ||||||||
\(584\) | −2.34064 | −0.0968563 | ||||||||
\(585\) | 11.7365 | 0.485243 | ||||||||
\(586\) | −13.3014 | −0.549474 | ||||||||
\(587\) | −23.0521 | −0.951462 | −0.475731 | − | 0.879591i | \(-0.657816\pi\) | ||||
−0.475731 | + | 0.879591i | \(0.657816\pi\) | |||||||
\(588\) | 5.66209 | 0.233501 | ||||||||
\(589\) | 2.14709 | 0.0884693 | ||||||||
\(590\) | 3.78623 | 0.155877 | ||||||||
\(591\) | 0.392647 | 0.0161513 | ||||||||
\(592\) | 4.56743 | 0.187720 | ||||||||
\(593\) | −10.5408 | −0.432861 | −0.216430 | − | 0.976298i | \(-0.569441\pi\) | ||||
−0.216430 | + | 0.976298i | \(0.569441\pi\) | |||||||
\(594\) | −8.31195 | −0.341044 | ||||||||
\(595\) | 8.01423 | 0.328551 | ||||||||
\(596\) | −9.18506 | −0.376235 | ||||||||
\(597\) | 20.6399 | 0.844735 | ||||||||
\(598\) | 17.3150 | 0.708062 | ||||||||
\(599\) | −27.4181 | −1.12027 | −0.560136 | − | 0.828400i | \(-0.689251\pi\) | ||||
−0.560136 | + | 0.828400i | \(0.689251\pi\) | |||||||
\(600\) | −2.11550 | −0.0863649 | ||||||||
\(601\) | 46.3625 | 1.89117 | 0.945583 | − | 0.325382i | \(-0.105493\pi\) | ||||
0.945583 | + | 0.325382i | \(0.105493\pi\) | |||||||
\(602\) | −1.66908 | −0.0680266 | ||||||||
\(603\) | 11.4356 | 0.465692 | ||||||||
\(604\) | −18.1659 | −0.739161 | ||||||||
\(605\) | 20.7216 | 0.842452 | ||||||||
\(606\) | 10.9360 | 0.444244 | ||||||||
\(607\) | −3.71754 | −0.150890 | −0.0754452 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754452 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −2.61830 | −0.106099 | ||||||||
\(610\) | −7.89124 | −0.319507 | ||||||||
\(611\) | −10.0577 | −0.406890 | ||||||||
\(612\) | 11.2925 | 0.456473 | ||||||||
\(613\) | −19.0907 | −0.771067 | −0.385534 | − | 0.922694i | \(-0.625983\pi\) | ||||
−0.385534 | + | 0.922694i | \(0.625983\pi\) | |||||||
\(614\) | 27.9110 | 1.12640 | ||||||||
\(615\) | 6.20077 | 0.250039 | ||||||||
\(616\) | −1.09251 | −0.0440184 | ||||||||
\(617\) | −3.08331 | −0.124130 | −0.0620648 | − | 0.998072i | \(-0.519769\pi\) | ||||
−0.0620648 | + | 0.998072i | \(0.519769\pi\) | |||||||
\(618\) | 13.8850 | 0.558535 | ||||||||
\(619\) | −20.1500 | −0.809898 | −0.404949 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404949 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(620\) | −5.87425 | −0.235915 | ||||||||
\(621\) | 41.2429 | 1.65502 | ||||||||
\(622\) | 12.2226 | 0.490080 | ||||||||
\(623\) | 6.93865 | 0.277991 | ||||||||
\(624\) | −1.60482 | −0.0642442 | ||||||||
\(625\) | −31.2498 | −1.24999 | ||||||||
\(626\) | 23.3705 | 0.934073 | ||||||||
\(627\) | 1.57561 | 0.0629236 | ||||||||
\(628\) | −6.86544 | −0.273961 | ||||||||
\(629\) | −22.6676 | −0.903816 | ||||||||
\(630\) | 3.67440 | 0.146391 | ||||||||
\(631\) | 22.4966 | 0.895576 | 0.447788 | − | 0.894140i | \(-0.352212\pi\) | ||||
0.447788 | + | 0.894140i | \(0.352212\pi\) | |||||||
\(632\) | −5.28066 | −0.210053 | ||||||||
\(633\) | 0.851234 | 0.0338335 | ||||||||
\(634\) | −5.04135 | −0.200218 | ||||||||
\(635\) | 30.6437 | 1.21606 | ||||||||
\(636\) | 3.51211 | 0.139264 | ||||||||
\(637\) | −12.5402 | −0.496861 | ||||||||
\(638\) | −9.64592 | −0.381886 | ||||||||
\(639\) | −8.39071 | −0.331931 | ||||||||
\(640\) | −2.73591 | −0.108146 | ||||||||
\(641\) | −33.6952 | −1.33088 | −0.665440 | − | 0.746452i | \(-0.731756\pi\) | ||||
−0.665440 | + | 0.746452i | \(0.731756\pi\) | |||||||
\(642\) | 12.4392 | 0.490935 | ||||||||
\(643\) | −0.279610 | −0.0110267 | −0.00551337 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551337 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(644\) | 5.42089 | 0.213613 | ||||||||
\(645\) | −6.58570 | −0.259312 | ||||||||
\(646\) | −4.96288 | −0.195262 | ||||||||
\(647\) | 35.1454 | 1.38171 | 0.690855 | − | 0.722994i | \(-0.257234\pi\) | ||||
0.690855 | + | 0.722994i | \(0.257234\pi\) | |||||||
\(648\) | 3.00365 | 0.117994 | ||||||||
\(649\) | 2.56155 | 0.100550 | ||||||||
\(650\) | 4.68534 | 0.183774 | ||||||||
\(651\) | −1.07876 | −0.0422800 | ||||||||
\(652\) | −7.85359 | −0.307570 | ||||||||
\(653\) | 43.4375 | 1.69984 | 0.849921 | − | 0.526910i | \(-0.176650\pi\) | ||||
0.849921 | + | 0.526910i | \(0.176650\pi\) | |||||||
\(654\) | 11.6729 | 0.456445 | ||||||||
\(655\) | −60.2839 | −2.35549 | ||||||||
\(656\) | 2.66253 | 0.103954 | ||||||||
\(657\) | 5.32589 | 0.207783 | ||||||||
\(658\) | −3.14881 | −0.122754 | ||||||||
\(659\) | 16.2510 | 0.633051 | 0.316525 | − | 0.948584i | \(-0.397484\pi\) | ||||
0.316525 | + | 0.948584i | \(0.397484\pi\) | |||||||
\(660\) | −4.31072 | −0.167795 | ||||||||
\(661\) | −37.3742 | −1.45369 | −0.726843 | − | 0.686803i | \(-0.759013\pi\) | ||||
−0.726843 | + | 0.686803i | \(0.759013\pi\) | |||||||
\(662\) | −27.5631 | −1.07127 | ||||||||
\(663\) | 7.96452 | 0.309316 | ||||||||
\(664\) | 4.69968 | 0.182383 | ||||||||
\(665\) | −1.61484 | −0.0626206 | ||||||||
\(666\) | −10.3927 | −0.402710 | ||||||||
\(667\) | 47.8619 | 1.85322 | ||||||||
\(668\) | −3.06987 | −0.118777 | ||||||||
\(669\) | −20.0370 | −0.774677 | ||||||||
\(670\) | 13.7500 | 0.531207 | ||||||||
\(671\) | −5.33878 | −0.206101 | ||||||||
\(672\) | −0.502429 | −0.0193816 | ||||||||
\(673\) | −21.8313 | −0.841534 | −0.420767 | − | 0.907169i | \(-0.638239\pi\) | ||||
−0.420767 | + | 0.907169i | \(0.638239\pi\) | |||||||
\(674\) | −10.5707 | −0.407168 | ||||||||
\(675\) | 11.1601 | 0.429553 | ||||||||
\(676\) | −9.44570 | −0.363296 | ||||||||
\(677\) | −30.7230 | −1.18078 | −0.590390 | − | 0.807118i | \(-0.701026\pi\) | ||||
−0.590390 | + | 0.807118i | \(0.701026\pi\) | |||||||
\(678\) | −8.15960 | −0.313367 | ||||||||
\(679\) | 8.62541 | 0.331013 | ||||||||
\(680\) | 13.5780 | 0.520692 | ||||||||
\(681\) | 19.1395 | 0.733427 | ||||||||
\(682\) | −3.97419 | −0.152180 | ||||||||
\(683\) | −50.1126 | −1.91750 | −0.958752 | − | 0.284245i | \(-0.908257\pi\) | ||||
−0.958752 | + | 0.284245i | \(0.908257\pi\) | |||||||
\(684\) | −2.27540 | −0.0870021 | ||||||||
\(685\) | 35.1197 | 1.34186 | ||||||||
\(686\) | −8.05769 | −0.307644 | ||||||||
\(687\) | −12.4803 | −0.476154 | ||||||||
\(688\) | −2.82781 | −0.107809 | ||||||||
\(689\) | −7.77851 | −0.296338 | ||||||||
\(690\) | 21.3893 | 0.814275 | ||||||||
\(691\) | −33.4120 | −1.27105 | −0.635526 | − | 0.772079i | \(-0.719217\pi\) | ||||
−0.635526 | + | 0.772079i | \(0.719217\pi\) | |||||||
\(692\) | 8.70636 | 0.330966 | ||||||||
\(693\) | 2.48589 | 0.0944313 | ||||||||
\(694\) | 12.6630 | 0.480682 | ||||||||
\(695\) | 36.3605 | 1.37923 | ||||||||
\(696\) | −4.43603 | −0.168147 | ||||||||
\(697\) | −13.2138 | −0.500508 | ||||||||
\(698\) | −28.4933 | −1.07849 | ||||||||
\(699\) | −5.85364 | −0.221405 | ||||||||
\(700\) | 1.46686 | 0.0554423 | ||||||||
\(701\) | −22.1771 | −0.837619 | −0.418809 | − | 0.908074i | \(-0.637552\pi\) | ||||
−0.418809 | + | 0.908074i | \(0.637552\pi\) | |||||||
\(702\) | 8.46606 | 0.319531 | ||||||||
\(703\) | 4.56743 | 0.172264 | ||||||||
\(704\) | −1.85097 | −0.0697609 | ||||||||
\(705\) | −12.4243 | −0.467926 | ||||||||
\(706\) | −21.5746 | −0.811970 | ||||||||
\(707\) | −7.58289 | −0.285184 | ||||||||
\(708\) | 1.17802 | 0.0442728 | ||||||||
\(709\) | 11.9572 | 0.449061 | 0.224531 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224531 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(710\) | −10.0889 | −0.378629 | ||||||||
\(711\) | 12.0156 | 0.450621 | ||||||||
\(712\) | 11.7557 | 0.440564 | ||||||||
\(713\) | 19.7194 | 0.738499 | ||||||||
\(714\) | 2.49349 | 0.0933167 | ||||||||
\(715\) | 9.54724 | 0.357047 | ||||||||
\(716\) | −18.7136 | −0.699360 | ||||||||
\(717\) | 11.6069 | 0.433466 | ||||||||
\(718\) | 23.0994 | 0.862064 | ||||||||
\(719\) | 29.3090 | 1.09304 | 0.546521 | − | 0.837445i | \(-0.315952\pi\) | ||||
0.546521 | + | 0.837445i | \(0.315952\pi\) | |||||||
\(720\) | 6.22530 | 0.232003 | ||||||||
\(721\) | −9.62768 | −0.358554 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −7.94186 | −0.295361 | ||||||||
\(724\) | −12.8415 | −0.477249 | ||||||||
\(725\) | 12.9512 | 0.480994 | ||||||||
\(726\) | 6.44718 | 0.239277 | ||||||||
\(727\) | 11.9179 | 0.442010 | 0.221005 | − | 0.975273i | \(-0.429066\pi\) | ||||
0.221005 | + | 0.975273i | \(0.429066\pi\) | |||||||
\(728\) | 1.11276 | 0.0412418 | ||||||||
\(729\) | 4.63315 | 0.171598 | ||||||||
\(730\) | 6.40378 | 0.237014 | ||||||||
\(731\) | 14.0341 | 0.519070 | ||||||||
\(732\) | −2.45523 | −0.0907480 | ||||||||
\(733\) | −15.5131 | −0.572991 | −0.286496 | − | 0.958082i | \(-0.592490\pi\) | ||||
−0.286496 | + | 0.958082i | \(0.592490\pi\) | |||||||
\(734\) | −13.3317 | −0.492083 | ||||||||
\(735\) | −15.4910 | −0.571393 | ||||||||
\(736\) | 9.18427 | 0.338537 | ||||||||
\(737\) | 9.30246 | 0.342661 | ||||||||
\(738\) | −6.05832 | −0.223010 | ||||||||
\(739\) | 11.6483 | 0.428490 | 0.214245 | − | 0.976780i | \(-0.431271\pi\) | ||||
0.214245 | + | 0.976780i | \(0.431271\pi\) | |||||||
\(740\) | −12.4961 | −0.459365 | ||||||||
\(741\) | −1.60482 | −0.0589545 | ||||||||
\(742\) | −2.43526 | −0.0894012 | ||||||||
\(743\) | 0.558624 | 0.0204939 | 0.0102470 | − | 0.999947i | \(-0.496738\pi\) | ||||
0.0102470 | + | 0.999947i | \(0.496738\pi\) | |||||||
\(744\) | −1.82768 | −0.0670059 | ||||||||
\(745\) | 25.1295 | 0.920674 | ||||||||
\(746\) | −22.7148 | −0.831647 | ||||||||
\(747\) | −10.6937 | −0.391261 | ||||||||
\(748\) | 9.18612 | 0.335878 | ||||||||
\(749\) | −8.62518 | −0.315157 | ||||||||
\(750\) | −5.85669 | −0.213856 | ||||||||
\(751\) | −14.6166 | −0.533368 | −0.266684 | − | 0.963784i | \(-0.585928\pi\) | ||||
−0.266684 | + | 0.963784i | \(0.585928\pi\) | |||||||
\(752\) | −5.33483 | −0.194541 | ||||||||
\(753\) | −3.86262 | −0.140762 | ||||||||
\(754\) | 9.82476 | 0.357797 | ||||||||
\(755\) | 49.7004 | 1.80878 | ||||||||
\(756\) | 2.65052 | 0.0963984 | ||||||||
\(757\) | −38.1142 | −1.38528 | −0.692642 | − | 0.721281i | \(-0.743554\pi\) | ||||
−0.692642 | + | 0.721281i | \(0.743554\pi\) | |||||||
\(758\) | 27.9622 | 1.01563 | ||||||||
\(759\) | 14.4708 | 0.525256 | ||||||||
\(760\) | −2.73591 | −0.0992420 | ||||||||
\(761\) | 11.4364 | 0.414568 | 0.207284 | − | 0.978281i | \(-0.433538\pi\) | ||||
0.207284 | + | 0.978281i | \(0.433538\pi\) | |||||||
\(762\) | 9.53427 | 0.345390 | ||||||||
\(763\) | −8.09383 | −0.293016 | ||||||||
\(764\) | 18.4358 | 0.666982 | ||||||||
\(765\) | −30.8954 | −1.11702 | ||||||||
\(766\) | −4.12225 | −0.148943 | ||||||||
\(767\) | −2.60905 | −0.0942072 | ||||||||
\(768\) | −0.851234 | −0.0307163 | ||||||||
\(769\) | −1.30181 | −0.0469444 | −0.0234722 | − | 0.999724i | \(-0.507472\pi\) | ||||
−0.0234722 | + | 0.999724i | \(0.507472\pi\) | |||||||
\(770\) | 2.98901 | 0.107716 | ||||||||
\(771\) | 16.7588 | 0.603552 | ||||||||
\(772\) | 1.16570 | 0.0419543 | ||||||||
\(773\) | −14.9282 | −0.536930 | −0.268465 | − | 0.963289i | \(-0.586516\pi\) | ||||
−0.268465 | + | 0.963289i | \(0.586516\pi\) | |||||||
\(774\) | 6.43441 | 0.231280 | ||||||||
\(775\) | 5.33598 | 0.191674 | ||||||||
\(776\) | 14.6135 | 0.524593 | ||||||||
\(777\) | −2.29481 | −0.0823259 | ||||||||
\(778\) | 13.2545 | 0.475196 | ||||||||
\(779\) | 2.66253 | 0.0953950 | ||||||||
\(780\) | 4.39064 | 0.157210 | ||||||||
\(781\) | −6.82558 | −0.244238 | ||||||||
\(782\) | −45.5804 | −1.62995 | ||||||||
\(783\) | 23.4018 | 0.836313 | ||||||||
\(784\) | −6.65162 | −0.237558 | ||||||||
\(785\) | 18.7832 | 0.670402 | ||||||||
\(786\) | −18.7563 | −0.669017 | ||||||||
\(787\) | 15.7775 | 0.562407 | 0.281203 | − | 0.959648i | \(-0.409266\pi\) | ||||
0.281203 | + | 0.959648i | \(0.409266\pi\) | |||||||
\(788\) | −0.461268 | −0.0164320 | ||||||||
\(789\) | −6.22704 | −0.221688 | ||||||||
\(790\) | 14.4474 | 0.514016 | ||||||||
\(791\) | 5.65778 | 0.201167 | ||||||||
\(792\) | 4.21169 | 0.149656 | ||||||||
\(793\) | 5.43777 | 0.193101 | ||||||||
\(794\) | 9.35973 | 0.332164 | ||||||||
\(795\) | −9.60883 | −0.340790 | ||||||||
\(796\) | −24.2470 | −0.859413 | ||||||||
\(797\) | 4.18880 | 0.148375 | 0.0741875 | − | 0.997244i | \(-0.476364\pi\) | ||||
0.0741875 | + | 0.997244i | \(0.476364\pi\) | |||||||
\(798\) | −0.502429 | −0.0177858 | ||||||||
\(799\) | 26.4761 | 0.936658 | ||||||||
\(800\) | 2.48522 | 0.0878656 | ||||||||
\(801\) | −26.7489 | −0.945127 | ||||||||
\(802\) | 23.9174 | 0.844551 | ||||||||
\(803\) | 4.33244 | 0.152889 | ||||||||
\(804\) | 4.27807 | 0.150876 | ||||||||
\(805\) | −14.8311 | −0.522727 | ||||||||
\(806\) | 4.04788 | 0.142580 | ||||||||
\(807\) | −19.3572 | −0.681407 | ||||||||
\(808\) | −12.8472 | −0.451963 | ||||||||
\(809\) | −32.8100 | −1.15354 | −0.576769 | − | 0.816907i | \(-0.695687\pi\) | ||||
−0.576769 | + | 0.816907i | \(0.695687\pi\) | |||||||
\(810\) | −8.21772 | −0.288741 | ||||||||
\(811\) | −23.5911 | −0.828394 | −0.414197 | − | 0.910187i | \(-0.635938\pi\) | ||||
−0.414197 | + | 0.910187i | \(0.635938\pi\) | |||||||
\(812\) | 3.07589 | 0.107943 | ||||||||
\(813\) | 0.556189 | 0.0195064 | ||||||||
\(814\) | −8.45416 | −0.296318 | ||||||||
\(815\) | 21.4867 | 0.752647 | ||||||||
\(816\) | 4.22457 | 0.147889 | ||||||||
\(817\) | −2.82781 | −0.0989327 | ||||||||
\(818\) | −24.4329 | −0.854277 | ||||||||
\(819\) | −2.53198 | −0.0884747 | ||||||||
\(820\) | −7.28444 | −0.254384 | ||||||||
\(821\) | 20.2176 | 0.705598 | 0.352799 | − | 0.935699i | \(-0.385230\pi\) | ||||
0.352799 | + | 0.935699i | \(0.385230\pi\) | |||||||
\(822\) | 10.9269 | 0.381120 | ||||||||
\(823\) | 33.7231 | 1.17551 | 0.587757 | − | 0.809038i | \(-0.300011\pi\) | ||||
0.587757 | + | 0.809038i | \(0.300011\pi\) | |||||||
\(824\) | −16.3116 | −0.568240 | ||||||||
\(825\) | 3.91572 | 0.136328 | ||||||||
\(826\) | −0.816828 | −0.0284211 | ||||||||
\(827\) | 44.8266 | 1.55877 | 0.779387 | − | 0.626542i | \(-0.215531\pi\) | ||||
0.779387 | + | 0.626542i | \(0.215531\pi\) | |||||||
\(828\) | −20.8979 | −0.726252 | ||||||||
\(829\) | 49.8577 | 1.73163 | 0.865816 | − | 0.500363i | \(-0.166800\pi\) | ||||
0.865816 | + | 0.500363i | \(0.166800\pi\) | |||||||
\(830\) | −12.8579 | −0.446305 | ||||||||
\(831\) | −3.12174 | −0.108292 | ||||||||
\(832\) | 1.88529 | 0.0653605 | ||||||||
\(833\) | 33.0112 | 1.14377 | ||||||||
\(834\) | 11.3130 | 0.391736 | ||||||||
\(835\) | 8.39890 | 0.290656 | ||||||||
\(836\) | −1.85097 | −0.0640170 | ||||||||
\(837\) | 9.64172 | 0.333267 | ||||||||
\(838\) | 7.08550 | 0.244765 | ||||||||
\(839\) | −50.0326 | −1.72732 | −0.863658 | − | 0.504078i | \(-0.831832\pi\) | ||||
−0.863658 | + | 0.504078i | \(0.831832\pi\) | |||||||
\(840\) | 1.37460 | 0.0474283 | ||||||||
\(841\) | −1.84248 | −0.0635340 | ||||||||
\(842\) | −25.9286 | −0.893558 | ||||||||
\(843\) | −12.0929 | −0.416502 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 25.8426 | 0.889013 | ||||||||
\(846\) | 12.1389 | 0.417343 | ||||||||
\(847\) | −4.47041 | −0.153605 | ||||||||
\(848\) | −4.12591 | −0.141684 | ||||||||
\(849\) | −12.1324 | −0.416383 | ||||||||
\(850\) | −12.3338 | −0.423046 | ||||||||
\(851\) | 41.9485 | 1.43798 | ||||||||
\(852\) | −3.13899 | −0.107540 | ||||||||
\(853\) | −43.1050 | −1.47589 | −0.737944 | − | 0.674862i | \(-0.764203\pi\) | ||||
−0.737944 | + | 0.674862i | \(0.764203\pi\) | |||||||
\(854\) | 1.70243 | 0.0582560 | ||||||||
\(855\) | 6.22530 | 0.212901 | ||||||||
\(856\) | −14.6131 | −0.499465 | ||||||||
\(857\) | 8.23730 | 0.281381 | 0.140690 | − | 0.990054i | \(-0.455068\pi\) | ||||
0.140690 | + | 0.990054i | \(0.455068\pi\) | |||||||
\(858\) | 2.97047 | 0.101410 | ||||||||
\(859\) | 5.09199 | 0.173737 | 0.0868683 | − | 0.996220i | \(-0.472314\pi\) | ||||
0.0868683 | + | 0.996220i | \(0.472314\pi\) | |||||||
\(860\) | 7.73665 | 0.263818 | ||||||||
\(861\) | −1.33773 | −0.0455898 | ||||||||
\(862\) | −22.2780 | −0.758791 | ||||||||
\(863\) | 44.4564 | 1.51331 | 0.756657 | − | 0.653812i | \(-0.226831\pi\) | ||||
0.756657 | + | 0.653812i | \(0.226831\pi\) | |||||||
\(864\) | 4.49060 | 0.152773 | ||||||||
\(865\) | −23.8198 | −0.809899 | ||||||||
\(866\) | −8.14495 | −0.276777 | ||||||||
\(867\) | −6.49503 | −0.220583 | ||||||||
\(868\) | 1.26729 | 0.0430146 | ||||||||
\(869\) | 9.77433 | 0.331571 | ||||||||
\(870\) | 12.1366 | 0.411468 | ||||||||
\(871\) | −9.47494 | −0.321046 | ||||||||
\(872\) | −13.7129 | −0.464376 | ||||||||
\(873\) | −33.2515 | −1.12539 | ||||||||
\(874\) | 9.18427 | 0.310663 | ||||||||
\(875\) | 4.06096 | 0.137286 | ||||||||
\(876\) | 1.99243 | 0.0673180 | ||||||||
\(877\) | −20.3998 | −0.688853 | −0.344427 | − | 0.938813i | \(-0.611927\pi\) | ||||
−0.344427 | + | 0.938813i | \(0.611927\pi\) | |||||||
\(878\) | −23.9146 | −0.807080 | ||||||||
\(879\) | 11.3226 | 0.381901 | ||||||||
\(880\) | 5.06408 | 0.170710 | ||||||||
\(881\) | −18.0011 | −0.606473 | −0.303237 | − | 0.952915i | \(-0.598067\pi\) | ||||
−0.303237 | + | 0.952915i | \(0.598067\pi\) | |||||||
\(882\) | 15.1351 | 0.509625 | ||||||||
\(883\) | 18.3131 | 0.616283 | 0.308142 | − | 0.951340i | \(-0.400293\pi\) | ||||
0.308142 | + | 0.951340i | \(0.400293\pi\) | |||||||
\(884\) | −9.35644 | −0.314691 | ||||||||
\(885\) | −3.22297 | −0.108339 | ||||||||
\(886\) | −18.2748 | −0.613954 | ||||||||
\(887\) | −32.1648 | −1.07999 | −0.539994 | − | 0.841669i | \(-0.681574\pi\) | ||||
−0.539994 | + | 0.841669i | \(0.681574\pi\) | |||||||
\(888\) | −3.88795 | −0.130471 | ||||||||
\(889\) | −6.61096 | −0.221725 | ||||||||
\(890\) | −32.1626 | −1.07809 | ||||||||
\(891\) | −5.55965 | −0.186255 | ||||||||
\(892\) | 23.5388 | 0.788138 | ||||||||
\(893\) | −5.33483 | −0.178523 | ||||||||
\(894\) | 7.81864 | 0.261494 | ||||||||
\(895\) | 51.1988 | 1.71139 | ||||||||
\(896\) | 0.590237 | 0.0197184 | ||||||||
\(897\) | −14.7391 | −0.492124 | ||||||||
\(898\) | −32.7585 | −1.09316 | ||||||||
\(899\) | 11.1891 | 0.373177 | ||||||||
\(900\) | −5.65486 | −0.188495 | ||||||||
\(901\) | 20.4764 | 0.682166 | ||||||||
\(902\) | −4.92825 | −0.164093 | ||||||||
\(903\) | 1.42078 | 0.0472805 | ||||||||
\(904\) | 9.58561 | 0.318813 | ||||||||
\(905\) | 35.1331 | 1.16786 | ||||||||
\(906\) | 15.4635 | 0.513739 | ||||||||
\(907\) | −20.0049 | −0.664251 | −0.332125 | − | 0.943235i | \(-0.607766\pi\) | ||||
−0.332125 | + | 0.943235i | \(0.607766\pi\) | |||||||
\(908\) | −22.4844 | −0.746172 | ||||||||
\(909\) | 29.2326 | 0.969583 | ||||||||
\(910\) | −3.04443 | −0.100922 | ||||||||
\(911\) | −18.5493 | −0.614565 | −0.307283 | − | 0.951618i | \(-0.599420\pi\) | ||||
−0.307283 | + | 0.951618i | \(0.599420\pi\) | |||||||
\(912\) | −0.851234 | −0.0281872 | ||||||||
\(913\) | −8.69896 | −0.287893 | ||||||||
\(914\) | −3.45841 | −0.114394 | ||||||||
\(915\) | 6.71730 | 0.222067 | ||||||||
\(916\) | 14.6615 | 0.484428 | ||||||||
\(917\) | 13.0054 | 0.429478 | ||||||||
\(918\) | −22.2863 | −0.735557 | ||||||||
\(919\) | 23.9314 | 0.789423 | 0.394711 | − | 0.918805i | \(-0.370845\pi\) | ||||
0.394711 | + | 0.918805i | \(0.370845\pi\) | |||||||
\(920\) | −25.1274 | −0.828424 | ||||||||
\(921\) | −23.7588 | −0.782879 | ||||||||
\(922\) | −30.8497 | −1.01598 | ||||||||
\(923\) | 6.95213 | 0.228832 | ||||||||
\(924\) | 0.929980 | 0.0305941 | ||||||||
\(925\) | 11.3510 | 0.373220 | ||||||||
\(926\) | −39.7861 | −1.30745 | ||||||||
\(927\) | 37.1153 | 1.21903 | ||||||||
\(928\) | 5.21129 | 0.171069 | ||||||||
\(929\) | −27.6684 | −0.907770 | −0.453885 | − | 0.891060i | \(-0.649962\pi\) | ||||
−0.453885 | + | 0.891060i | \(0.649962\pi\) | |||||||
\(930\) | 5.00036 | 0.163968 | ||||||||
\(931\) | −6.65162 | −0.217998 | ||||||||
\(932\) | 6.87666 | 0.225252 | ||||||||
\(933\) | −10.4043 | −0.340620 | ||||||||
\(934\) | −4.95261 | −0.162054 | ||||||||
\(935\) | −25.1324 | −0.821918 | ||||||||
\(936\) | −4.28978 | −0.140216 | ||||||||
\(937\) | −30.6488 | −1.00125 | −0.500626 | − | 0.865664i | \(-0.666897\pi\) | ||||
−0.500626 | + | 0.865664i | \(0.666897\pi\) | |||||||
\(938\) | −2.96637 | −0.0968554 | ||||||||
\(939\) | −19.8938 | −0.649209 | ||||||||
\(940\) | 14.5956 | 0.476057 | ||||||||
\(941\) | −25.0236 | −0.815745 | −0.407873 | − | 0.913039i | \(-0.633729\pi\) | ||||
−0.407873 | + | 0.913039i | \(0.633729\pi\) | |||||||
\(942\) | 5.84409 | 0.190411 | ||||||||
\(943\) | 24.4534 | 0.796311 | ||||||||
\(944\) | −1.38390 | −0.0450421 | ||||||||
\(945\) | −7.25158 | −0.235894 | ||||||||
\(946\) | 5.23419 | 0.170178 | ||||||||
\(947\) | 35.9832 | 1.16930 | 0.584648 | − | 0.811287i | \(-0.301233\pi\) | ||||
0.584648 | + | 0.811287i | \(0.301233\pi\) | |||||||
\(948\) | 4.49508 | 0.145993 | ||||||||
\(949\) | −4.41277 | −0.143245 | ||||||||
\(950\) | 2.48522 | 0.0806310 | ||||||||
\(951\) | 4.29137 | 0.139157 | ||||||||
\(952\) | −2.92927 | −0.0949382 | ||||||||
\(953\) | 49.1700 | 1.59277 | 0.796386 | − | 0.604789i | \(-0.206743\pi\) | ||||
0.796386 | + | 0.604789i | \(0.206743\pi\) | |||||||
\(954\) | 9.38809 | 0.303951 | ||||||||
\(955\) | −50.4386 | −1.63215 | ||||||||
\(956\) | −13.6353 | −0.440998 | ||||||||
\(957\) | 8.21094 | 0.265422 | ||||||||
\(958\) | 1.34533 | 0.0434658 | ||||||||
\(959\) | −7.57661 | −0.244662 | ||||||||
\(960\) | 2.32890 | 0.0751650 | ||||||||
\(961\) | −26.3900 | −0.851291 | ||||||||
\(962\) | 8.61091 | 0.277627 | ||||||||
\(963\) | 33.2506 | 1.07149 | ||||||||
\(964\) | 9.32981 | 0.300493 | ||||||||
\(965\) | −3.18924 | −0.102665 | ||||||||
\(966\) | −4.61445 | −0.148467 | ||||||||
\(967\) | 27.1270 | 0.872345 | 0.436172 | − | 0.899863i | \(-0.356334\pi\) | ||||
0.436172 | + | 0.899863i | \(0.356334\pi\) | |||||||
\(968\) | −7.57392 | −0.243435 | ||||||||
\(969\) | 4.22457 | 0.135713 | ||||||||
\(970\) | −39.9812 | −1.28372 | ||||||||
\(971\) | 14.3827 | 0.461564 | 0.230782 | − | 0.973006i | \(-0.425872\pi\) | ||||
0.230782 | + | 0.973006i | \(0.425872\pi\) | |||||||
\(972\) | −16.0286 | −0.514118 | ||||||||
\(973\) | −7.84429 | −0.251476 | ||||||||
\(974\) | −32.4030 | −1.03826 | ||||||||
\(975\) | −3.98832 | −0.127729 | ||||||||
\(976\) | 2.88432 | 0.0923248 | ||||||||
\(977\) | 17.1218 | 0.547774 | 0.273887 | − | 0.961762i | \(-0.411691\pi\) | ||||
0.273887 | + | 0.961762i | \(0.411691\pi\) | |||||||
\(978\) | 6.68524 | 0.213770 | ||||||||
\(979\) | −21.7594 | −0.695434 | ||||||||
\(980\) | 18.1983 | 0.581322 | ||||||||
\(981\) | 31.2023 | 0.996211 | ||||||||
\(982\) | 3.96106 | 0.126402 | ||||||||
\(983\) | −14.0672 | −0.448675 | −0.224338 | − | 0.974512i | \(-0.572022\pi\) | ||||
−0.224338 | + | 0.974512i | \(0.572022\pi\) | |||||||
\(984\) | −2.26643 | −0.0722513 | ||||||||
\(985\) | 1.26199 | 0.0402103 | ||||||||
\(986\) | −25.8630 | −0.823645 | ||||||||
\(987\) | 2.68038 | 0.0853174 | ||||||||
\(988\) | 1.88529 | 0.0599789 | ||||||||
\(989\) | −25.9714 | −0.825843 | ||||||||
\(990\) | −11.5228 | −0.366219 | ||||||||
\(991\) | −2.44087 | −0.0775367 | −0.0387683 | − | 0.999248i | \(-0.512343\pi\) | ||||
−0.0387683 | + | 0.999248i | \(0.512343\pi\) | |||||||
\(992\) | 2.14709 | 0.0681702 | ||||||||
\(993\) | 23.4626 | 0.744564 | ||||||||
\(994\) | 2.17654 | 0.0690357 | ||||||||
\(995\) | 66.3377 | 2.10305 | ||||||||
\(996\) | −4.00053 | −0.126762 | ||||||||
\(997\) | 20.7114 | 0.655936 | 0.327968 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327968 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(998\) | −14.9638 | −0.473670 | ||||||||
\(999\) | 20.5105 | 0.648924 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.d.1.14 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.14 | ✓ | 30 | 1.1 | even | 1 | trivial |