Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −0.423572 | −0.244549 | −0.122275 | − | 0.992496i | \(-0.539019\pi\) | ||||
−0.122275 | + | 0.992496i | \(0.539019\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.487122 | −0.217847 | −0.108924 | − | 0.994050i | \(-0.534740\pi\) | ||||
−0.108924 | + | 0.994050i | \(0.534740\pi\) | |||||||
\(6\) | −0.423572 | −0.172922 | ||||||||
\(7\) | 2.40385 | 0.908569 | 0.454285 | − | 0.890857i | \(-0.349895\pi\) | ||||
0.454285 | + | 0.890857i | \(0.349895\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.82059 | −0.940196 | ||||||||
\(10\) | −0.487122 | −0.154041 | ||||||||
\(11\) | 1.38245 | 0.416824 | 0.208412 | − | 0.978041i | \(-0.433171\pi\) | ||||
0.208412 | + | 0.978041i | \(0.433171\pi\) | |||||||
\(12\) | −0.423572 | −0.122275 | ||||||||
\(13\) | −1.29945 | −0.360402 | −0.180201 | − | 0.983630i | \(-0.557675\pi\) | ||||
−0.180201 | + | 0.983630i | \(0.557675\pi\) | |||||||
\(14\) | 2.40385 | 0.642455 | ||||||||
\(15\) | 0.206331 | 0.0532744 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.88437 | −0.699562 | −0.349781 | − | 0.936832i | \(-0.613744\pi\) | ||||
−0.349781 | + | 0.936832i | \(0.613744\pi\) | |||||||
\(18\) | −2.82059 | −0.664819 | ||||||||
\(19\) | 0.654438 | 0.150138 | 0.0750692 | − | 0.997178i | \(-0.476082\pi\) | ||||
0.0750692 | + | 0.997178i | \(0.476082\pi\) | |||||||
\(20\) | −0.487122 | −0.108924 | ||||||||
\(21\) | −1.01820 | −0.222190 | ||||||||
\(22\) | 1.38245 | 0.294739 | ||||||||
\(23\) | −8.21328 | −1.71259 | −0.856293 | − | 0.516490i | \(-0.827238\pi\) | ||||
−0.856293 | + | 0.516490i | \(0.827238\pi\) | |||||||
\(24\) | −0.423572 | −0.0864612 | ||||||||
\(25\) | −4.76271 | −0.952543 | ||||||||
\(26\) | −1.29945 | −0.254843 | ||||||||
\(27\) | 2.46544 | 0.474473 | ||||||||
\(28\) | 2.40385 | 0.454285 | ||||||||
\(29\) | 4.28186 | 0.795121 | 0.397560 | − | 0.917576i | \(-0.369857\pi\) | ||||
0.397560 | + | 0.917576i | \(0.369857\pi\) | |||||||
\(30\) | 0.206331 | 0.0376707 | ||||||||
\(31\) | −10.7659 | −1.93362 | −0.966811 | − | 0.255494i | \(-0.917762\pi\) | ||||
−0.966811 | + | 0.255494i | \(0.917762\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.585566 | −0.101934 | ||||||||
\(34\) | −2.88437 | −0.494665 | ||||||||
\(35\) | −1.17097 | −0.197929 | ||||||||
\(36\) | −2.82059 | −0.470098 | ||||||||
\(37\) | −8.21314 | −1.35023 | −0.675116 | − | 0.737712i | \(-0.735906\pi\) | ||||
−0.675116 | + | 0.737712i | \(0.735906\pi\) | |||||||
\(38\) | 0.654438 | 0.106164 | ||||||||
\(39\) | 0.550409 | 0.0881360 | ||||||||
\(40\) | −0.487122 | −0.0770207 | ||||||||
\(41\) | −0.313899 | −0.0490228 | −0.0245114 | − | 0.999700i | \(-0.507803\pi\) | ||||
−0.0245114 | + | 0.999700i | \(0.507803\pi\) | |||||||
\(42\) | −1.01820 | −0.157112 | ||||||||
\(43\) | 4.40071 | 0.671102 | 0.335551 | − | 0.942022i | \(-0.391078\pi\) | ||||
0.335551 | + | 0.942022i | \(0.391078\pi\) | |||||||
\(44\) | 1.38245 | 0.208412 | ||||||||
\(45\) | 1.37397 | 0.204819 | ||||||||
\(46\) | −8.21328 | −1.21098 | ||||||||
\(47\) | −5.56192 | −0.811290 | −0.405645 | − | 0.914031i | \(-0.632953\pi\) | ||||
−0.405645 | + | 0.914031i | \(0.632953\pi\) | |||||||
\(48\) | −0.423572 | −0.0611373 | ||||||||
\(49\) | −1.22152 | −0.174502 | ||||||||
\(50\) | −4.76271 | −0.673549 | ||||||||
\(51\) | 1.22174 | 0.171077 | ||||||||
\(52\) | −1.29945 | −0.180201 | ||||||||
\(53\) | 8.99732 | 1.23588 | 0.617938 | − | 0.786227i | \(-0.287968\pi\) | ||||
0.617938 | + | 0.786227i | \(0.287968\pi\) | |||||||
\(54\) | 2.46544 | 0.335503 | ||||||||
\(55\) | −0.673421 | −0.0908040 | ||||||||
\(56\) | 2.40385 | 0.321228 | ||||||||
\(57\) | −0.277201 | −0.0367162 | ||||||||
\(58\) | 4.28186 | 0.562235 | ||||||||
\(59\) | 0.393777 | 0.0512654 | 0.0256327 | − | 0.999671i | \(-0.491840\pi\) | ||||
0.0256327 | + | 0.999671i | \(0.491840\pi\) | |||||||
\(60\) | 0.206331 | 0.0266372 | ||||||||
\(61\) | 8.49444 | 1.08760 | 0.543801 | − | 0.839214i | \(-0.316985\pi\) | ||||
0.543801 | + | 0.839214i | \(0.316985\pi\) | |||||||
\(62\) | −10.7659 | −1.36728 | ||||||||
\(63\) | −6.78026 | −0.854233 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.632989 | 0.0785126 | ||||||||
\(66\) | −0.585566 | −0.0720782 | ||||||||
\(67\) | 3.95326 | 0.482968 | 0.241484 | − | 0.970405i | \(-0.422366\pi\) | ||||
0.241484 | + | 0.970405i | \(0.422366\pi\) | |||||||
\(68\) | −2.88437 | −0.349781 | ||||||||
\(69\) | 3.47891 | 0.418812 | ||||||||
\(70\) | −1.17097 | −0.139957 | ||||||||
\(71\) | 0.756879 | 0.0898251 | 0.0449125 | − | 0.998991i | \(-0.485699\pi\) | ||||
0.0449125 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(72\) | −2.82059 | −0.332409 | ||||||||
\(73\) | −9.00288 | −1.05371 | −0.526854 | − | 0.849956i | \(-0.676628\pi\) | ||||
−0.526854 | + | 0.849956i | \(0.676628\pi\) | |||||||
\(74\) | −8.21314 | −0.954758 | ||||||||
\(75\) | 2.01735 | 0.232943 | ||||||||
\(76\) | 0.654438 | 0.0750692 | ||||||||
\(77\) | 3.32320 | 0.378713 | ||||||||
\(78\) | 0.550409 | 0.0623216 | ||||||||
\(79\) | 10.9266 | 1.22934 | 0.614671 | − | 0.788784i | \(-0.289289\pi\) | ||||
0.614671 | + | 0.788784i | \(0.289289\pi\) | |||||||
\(80\) | −0.487122 | −0.0544618 | ||||||||
\(81\) | 7.41747 | 0.824164 | ||||||||
\(82\) | −0.313899 | −0.0346644 | ||||||||
\(83\) | −10.0973 | −1.10832 | −0.554160 | − | 0.832410i | \(-0.686961\pi\) | ||||
−0.554160 | + | 0.832410i | \(0.686961\pi\) | |||||||
\(84\) | −1.01820 | −0.111095 | ||||||||
\(85\) | 1.40504 | 0.152398 | ||||||||
\(86\) | 4.40071 | 0.474541 | ||||||||
\(87\) | −1.81367 | −0.194446 | ||||||||
\(88\) | 1.38245 | 0.147370 | ||||||||
\(89\) | −12.2322 | −1.29661 | −0.648304 | − | 0.761382i | \(-0.724521\pi\) | ||||
−0.648304 | + | 0.761382i | \(0.724521\pi\) | |||||||
\(90\) | 1.37397 | 0.144829 | ||||||||
\(91\) | −3.12368 | −0.327450 | ||||||||
\(92\) | −8.21328 | −0.856293 | ||||||||
\(93\) | 4.56015 | 0.472865 | ||||||||
\(94\) | −5.56192 | −0.573669 | ||||||||
\(95\) | −0.318791 | −0.0327072 | ||||||||
\(96\) | −0.423572 | −0.0432306 | ||||||||
\(97\) | 16.8496 | 1.71082 | 0.855408 | − | 0.517955i | \(-0.173306\pi\) | ||||
0.855408 | + | 0.517955i | \(0.173306\pi\) | |||||||
\(98\) | −1.22152 | −0.123392 | ||||||||
\(99\) | −3.89932 | −0.391896 | ||||||||
\(100\) | −4.76271 | −0.476271 | ||||||||
\(101\) | −8.18914 | −0.814850 | −0.407425 | − | 0.913239i | \(-0.633573\pi\) | ||||
−0.407425 | + | 0.913239i | \(0.633573\pi\) | |||||||
\(102\) | 1.22174 | 0.120970 | ||||||||
\(103\) | −17.2804 | −1.70269 | −0.851345 | − | 0.524606i | \(-0.824213\pi\) | ||||
−0.851345 | + | 0.524606i | \(0.824213\pi\) | |||||||
\(104\) | −1.29945 | −0.127421 | ||||||||
\(105\) | 0.495988 | 0.0484035 | ||||||||
\(106\) | 8.99732 | 0.873897 | ||||||||
\(107\) | −5.92372 | −0.572668 | −0.286334 | − | 0.958130i | \(-0.592437\pi\) | ||||
−0.286334 | + | 0.958130i | \(0.592437\pi\) | |||||||
\(108\) | 2.46544 | 0.237237 | ||||||||
\(109\) | −14.5587 | −1.39447 | −0.697234 | − | 0.716843i | \(-0.745586\pi\) | ||||
−0.697234 | + | 0.716843i | \(0.745586\pi\) | |||||||
\(110\) | −0.673421 | −0.0642081 | ||||||||
\(111\) | 3.47885 | 0.330198 | ||||||||
\(112\) | 2.40385 | 0.227142 | ||||||||
\(113\) | 13.2666 | 1.24801 | 0.624007 | − | 0.781419i | \(-0.285504\pi\) | ||||
0.624007 | + | 0.781419i | \(0.285504\pi\) | |||||||
\(114\) | −0.277201 | −0.0259623 | ||||||||
\(115\) | 4.00086 | 0.373083 | ||||||||
\(116\) | 4.28186 | 0.397560 | ||||||||
\(117\) | 3.66521 | 0.338848 | ||||||||
\(118\) | 0.393777 | 0.0362501 | ||||||||
\(119\) | −6.93358 | −0.635600 | ||||||||
\(120\) | 0.206331 | 0.0188353 | ||||||||
\(121\) | −9.08883 | −0.826258 | ||||||||
\(122\) | 8.49444 | 0.769050 | ||||||||
\(123\) | 0.132959 | 0.0119885 | ||||||||
\(124\) | −10.7659 | −0.966811 | ||||||||
\(125\) | 4.75563 | 0.425356 | ||||||||
\(126\) | −6.78026 | −0.604034 | ||||||||
\(127\) | 2.02739 | 0.179902 | 0.0899510 | − | 0.995946i | \(-0.471329\pi\) | ||||
0.0899510 | + | 0.995946i | \(0.471329\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.86402 | −0.164117 | ||||||||
\(130\) | 0.632989 | 0.0555168 | ||||||||
\(131\) | −1.55630 | −0.135975 | −0.0679874 | − | 0.997686i | \(-0.521658\pi\) | ||||
−0.0679874 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(132\) | −0.585566 | −0.0509670 | ||||||||
\(133\) | 1.57317 | 0.136411 | ||||||||
\(134\) | 3.95326 | 0.341510 | ||||||||
\(135\) | −1.20097 | −0.103363 | ||||||||
\(136\) | −2.88437 | −0.247332 | ||||||||
\(137\) | −17.9866 | −1.53670 | −0.768350 | − | 0.640030i | \(-0.778922\pi\) | ||||
−0.768350 | + | 0.640030i | \(0.778922\pi\) | |||||||
\(138\) | 3.47891 | 0.296145 | ||||||||
\(139\) | −19.2869 | −1.63590 | −0.817948 | − | 0.575292i | \(-0.804888\pi\) | ||||
−0.817948 | + | 0.575292i | \(0.804888\pi\) | |||||||
\(140\) | −1.17097 | −0.0989647 | ||||||||
\(141\) | 2.35587 | 0.198400 | ||||||||
\(142\) | 0.756879 | 0.0635159 | ||||||||
\(143\) | −1.79642 | −0.150224 | ||||||||
\(144\) | −2.82059 | −0.235049 | ||||||||
\(145\) | −2.08578 | −0.173215 | ||||||||
\(146\) | −9.00288 | −0.745083 | ||||||||
\(147\) | 0.517399 | 0.0426744 | ||||||||
\(148\) | −8.21314 | −0.675116 | ||||||||
\(149\) | 5.69382 | 0.466456 | 0.233228 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233228 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(150\) | 2.01735 | 0.164716 | ||||||||
\(151\) | 15.0185 | 1.22219 | 0.611093 | − | 0.791559i | \(-0.290730\pi\) | ||||
0.611093 | + | 0.791559i | \(0.290730\pi\) | |||||||
\(152\) | 0.654438 | 0.0530819 | ||||||||
\(153\) | 8.13561 | 0.657725 | ||||||||
\(154\) | 3.32320 | 0.267791 | ||||||||
\(155\) | 5.24433 | 0.421234 | ||||||||
\(156\) | 0.550409 | 0.0440680 | ||||||||
\(157\) | 22.5572 | 1.80026 | 0.900129 | − | 0.435624i | \(-0.143472\pi\) | ||||
0.900129 | + | 0.435624i | \(0.143472\pi\) | |||||||
\(158\) | 10.9266 | 0.869276 | ||||||||
\(159\) | −3.81101 | −0.302233 | ||||||||
\(160\) | −0.487122 | −0.0385103 | ||||||||
\(161\) | −19.7435 | −1.55600 | ||||||||
\(162\) | 7.41747 | 0.582772 | ||||||||
\(163\) | −6.69948 | −0.524744 | −0.262372 | − | 0.964967i | \(-0.584505\pi\) | ||||
−0.262372 | + | 0.964967i | \(0.584505\pi\) | |||||||
\(164\) | −0.313899 | −0.0245114 | ||||||||
\(165\) | 0.285242 | 0.0222060 | ||||||||
\(166\) | −10.0973 | −0.783701 | ||||||||
\(167\) | 9.77539 | 0.756442 | 0.378221 | − | 0.925715i | \(-0.376536\pi\) | ||||
0.378221 | + | 0.925715i | \(0.376536\pi\) | |||||||
\(168\) | −1.01820 | −0.0785560 | ||||||||
\(169\) | −11.3114 | −0.870110 | ||||||||
\(170\) | 1.40504 | 0.107761 | ||||||||
\(171\) | −1.84590 | −0.141159 | ||||||||
\(172\) | 4.40071 | 0.335551 | ||||||||
\(173\) | 6.39981 | 0.486568 | 0.243284 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243284 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(174\) | −1.81367 | −0.137494 | ||||||||
\(175\) | −11.4488 | −0.865451 | ||||||||
\(176\) | 1.38245 | 0.104206 | ||||||||
\(177\) | −0.166793 | −0.0125369 | ||||||||
\(178\) | −12.2322 | −0.916840 | ||||||||
\(179\) | −2.76473 | −0.206646 | −0.103323 | − | 0.994648i | \(-0.532947\pi\) | ||||
−0.103323 | + | 0.994648i | \(0.532947\pi\) | |||||||
\(180\) | 1.37397 | 0.102410 | ||||||||
\(181\) | −9.51712 | −0.707402 | −0.353701 | − | 0.935359i | \(-0.615077\pi\) | ||||
−0.353701 | + | 0.935359i | \(0.615077\pi\) | |||||||
\(182\) | −3.12368 | −0.231542 | ||||||||
\(183\) | −3.59800 | −0.265972 | ||||||||
\(184\) | −8.21328 | −0.605491 | ||||||||
\(185\) | 4.00080 | 0.294145 | ||||||||
\(186\) | 4.56015 | 0.334366 | ||||||||
\(187\) | −3.98749 | −0.291594 | ||||||||
\(188\) | −5.56192 | −0.405645 | ||||||||
\(189\) | 5.92653 | 0.431092 | ||||||||
\(190\) | −0.318791 | −0.0231275 | ||||||||
\(191\) | −26.5851 | −1.92363 | −0.961816 | − | 0.273698i | \(-0.911753\pi\) | ||||
−0.961816 | + | 0.273698i | \(0.911753\pi\) | |||||||
\(192\) | −0.423572 | −0.0305686 | ||||||||
\(193\) | 6.55798 | 0.472054 | 0.236027 | − | 0.971747i | \(-0.424155\pi\) | ||||
0.236027 | + | 0.971747i | \(0.424155\pi\) | |||||||
\(194\) | 16.8496 | 1.20973 | ||||||||
\(195\) | −0.268116 | −0.0192002 | ||||||||
\(196\) | −1.22152 | −0.0872512 | ||||||||
\(197\) | 3.97806 | 0.283425 | 0.141712 | − | 0.989908i | \(-0.454739\pi\) | ||||
0.141712 | + | 0.989908i | \(0.454739\pi\) | |||||||
\(198\) | −3.89932 | −0.277112 | ||||||||
\(199\) | −13.0404 | −0.924409 | −0.462204 | − | 0.886773i | \(-0.652941\pi\) | ||||
−0.462204 | + | 0.886773i | \(0.652941\pi\) | |||||||
\(200\) | −4.76271 | −0.336775 | ||||||||
\(201\) | −1.67449 | −0.118109 | ||||||||
\(202\) | −8.18914 | −0.576186 | ||||||||
\(203\) | 10.2929 | 0.722422 | ||||||||
\(204\) | 1.22174 | 0.0855386 | ||||||||
\(205\) | 0.152907 | 0.0106795 | ||||||||
\(206\) | −17.2804 | −1.20398 | ||||||||
\(207\) | 23.1663 | 1.61017 | ||||||||
\(208\) | −1.29945 | −0.0901005 | ||||||||
\(209\) | 0.904727 | 0.0625813 | ||||||||
\(210\) | 0.495988 | 0.0342264 | ||||||||
\(211\) | 22.1547 | 1.52519 | 0.762597 | − | 0.646874i | \(-0.223924\pi\) | ||||
0.762597 | + | 0.646874i | \(0.223924\pi\) | |||||||
\(212\) | 8.99732 | 0.617938 | ||||||||
\(213\) | −0.320593 | −0.0219666 | ||||||||
\(214\) | −5.92372 | −0.404937 | ||||||||
\(215\) | −2.14368 | −0.146198 | ||||||||
\(216\) | 2.46544 | 0.167752 | ||||||||
\(217\) | −25.8797 | −1.75683 | ||||||||
\(218\) | −14.5587 | −0.986038 | ||||||||
\(219\) | 3.81336 | 0.257683 | ||||||||
\(220\) | −0.673421 | −0.0454020 | ||||||||
\(221\) | 3.74809 | 0.252124 | ||||||||
\(222\) | 3.47885 | 0.233485 | ||||||||
\(223\) | −27.2023 | −1.82160 | −0.910800 | − | 0.412848i | \(-0.864534\pi\) | ||||
−0.910800 | + | 0.412848i | \(0.864534\pi\) | |||||||
\(224\) | 2.40385 | 0.160614 | ||||||||
\(225\) | 13.4336 | 0.895576 | ||||||||
\(226\) | 13.2666 | 0.882479 | ||||||||
\(227\) | 18.8854 | 1.25347 | 0.626735 | − | 0.779233i | \(-0.284391\pi\) | ||||
0.626735 | + | 0.779233i | \(0.284391\pi\) | |||||||
\(228\) | −0.277201 | −0.0183581 | ||||||||
\(229\) | 4.97064 | 0.328469 | 0.164234 | − | 0.986421i | \(-0.447485\pi\) | ||||
0.164234 | + | 0.986421i | \(0.447485\pi\) | |||||||
\(230\) | 4.00086 | 0.263809 | ||||||||
\(231\) | −1.40761 | −0.0926141 | ||||||||
\(232\) | 4.28186 | 0.281118 | ||||||||
\(233\) | −2.23009 | −0.146098 | −0.0730490 | − | 0.997328i | \(-0.523273\pi\) | ||||
−0.0730490 | + | 0.997328i | \(0.523273\pi\) | |||||||
\(234\) | 3.66521 | 0.239602 | ||||||||
\(235\) | 2.70933 | 0.176737 | ||||||||
\(236\) | 0.393777 | 0.0256327 | ||||||||
\(237\) | −4.62821 | −0.300634 | ||||||||
\(238\) | −6.93358 | −0.449437 | ||||||||
\(239\) | −3.30765 | −0.213954 | −0.106977 | − | 0.994261i | \(-0.534117\pi\) | ||||
−0.106977 | + | 0.994261i | \(0.534117\pi\) | |||||||
\(240\) | 0.206331 | 0.0133186 | ||||||||
\(241\) | −16.5056 | −1.06322 | −0.531608 | − | 0.846990i | \(-0.678412\pi\) | ||||
−0.531608 | + | 0.846990i | \(0.678412\pi\) | |||||||
\(242\) | −9.08883 | −0.584252 | ||||||||
\(243\) | −10.5381 | −0.676022 | ||||||||
\(244\) | 8.49444 | 0.543801 | ||||||||
\(245\) | 0.595027 | 0.0380149 | ||||||||
\(246\) | 0.132959 | 0.00847714 | ||||||||
\(247\) | −0.850408 | −0.0541102 | ||||||||
\(248\) | −10.7659 | −0.683638 | ||||||||
\(249\) | 4.27692 | 0.271039 | ||||||||
\(250\) | 4.75563 | 0.300772 | ||||||||
\(251\) | −5.28350 | −0.333492 | −0.166746 | − | 0.986000i | \(-0.553326\pi\) | ||||
−0.166746 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(252\) | −6.78026 | −0.427116 | ||||||||
\(253\) | −11.3544 | −0.713847 | ||||||||
\(254\) | 2.02739 | 0.127210 | ||||||||
\(255\) | −0.595134 | −0.0372687 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.6201 | 1.59814 | 0.799068 | − | 0.601240i | \(-0.205326\pi\) | ||||
0.799068 | + | 0.601240i | \(0.205326\pi\) | |||||||
\(258\) | −1.86402 | −0.116049 | ||||||||
\(259\) | −19.7431 | −1.22678 | ||||||||
\(260\) | 0.632989 | 0.0392563 | ||||||||
\(261\) | −12.0773 | −0.747569 | ||||||||
\(262\) | −1.55630 | −0.0961487 | ||||||||
\(263\) | −4.54683 | −0.280370 | −0.140185 | − | 0.990125i | \(-0.544770\pi\) | ||||
−0.140185 | + | 0.990125i | \(0.544770\pi\) | |||||||
\(264\) | −0.585566 | −0.0360391 | ||||||||
\(265\) | −4.38279 | −0.269232 | ||||||||
\(266\) | 1.57317 | 0.0964572 | ||||||||
\(267\) | 5.18120 | 0.317084 | ||||||||
\(268\) | 3.95326 | 0.241484 | ||||||||
\(269\) | 27.4647 | 1.67455 | 0.837275 | − | 0.546781i | \(-0.184147\pi\) | ||||
0.837275 | + | 0.546781i | \(0.184147\pi\) | |||||||
\(270\) | −1.20097 | −0.0730885 | ||||||||
\(271\) | 11.0589 | 0.671782 | 0.335891 | − | 0.941901i | \(-0.390963\pi\) | ||||
0.335891 | + | 0.941901i | \(0.390963\pi\) | |||||||
\(272\) | −2.88437 | −0.174890 | ||||||||
\(273\) | 1.32310 | 0.0800777 | ||||||||
\(274\) | −17.9866 | −1.08661 | ||||||||
\(275\) | −6.58421 | −0.397043 | ||||||||
\(276\) | 3.47891 | 0.209406 | ||||||||
\(277\) | −9.96389 | −0.598672 | −0.299336 | − | 0.954148i | \(-0.596765\pi\) | ||||
−0.299336 | + | 0.954148i | \(0.596765\pi\) | |||||||
\(278\) | −19.2869 | −1.15675 | ||||||||
\(279\) | 30.3663 | 1.81798 | ||||||||
\(280\) | −1.17097 | −0.0699786 | ||||||||
\(281\) | 13.9946 | 0.834847 | 0.417423 | − | 0.908712i | \(-0.362933\pi\) | ||||
0.417423 | + | 0.908712i | \(0.362933\pi\) | |||||||
\(282\) | 2.35587 | 0.140290 | ||||||||
\(283\) | −6.74061 | −0.400688 | −0.200344 | − | 0.979726i | \(-0.564206\pi\) | ||||
−0.200344 | + | 0.979726i | \(0.564206\pi\) | |||||||
\(284\) | 0.756879 | 0.0449125 | ||||||||
\(285\) | 0.135031 | 0.00799853 | ||||||||
\(286\) | −1.79642 | −0.106225 | ||||||||
\(287\) | −0.754566 | −0.0445406 | ||||||||
\(288\) | −2.82059 | −0.166205 | ||||||||
\(289\) | −8.68042 | −0.510613 | ||||||||
\(290\) | −2.08578 | −0.122481 | ||||||||
\(291\) | −7.13700 | −0.418379 | ||||||||
\(292\) | −9.00288 | −0.526854 | ||||||||
\(293\) | 30.9651 | 1.80900 | 0.904501 | − | 0.426471i | \(-0.140243\pi\) | ||||
0.904501 | + | 0.426471i | \(0.140243\pi\) | |||||||
\(294\) | 0.517399 | 0.0301754 | ||||||||
\(295\) | −0.191817 | −0.0111680 | ||||||||
\(296\) | −8.21314 | −0.477379 | ||||||||
\(297\) | 3.40834 | 0.197772 | ||||||||
\(298\) | 5.69382 | 0.329834 | ||||||||
\(299\) | 10.6727 | 0.617220 | ||||||||
\(300\) | 2.01735 | 0.116472 | ||||||||
\(301\) | 10.5786 | 0.609743 | ||||||||
\(302\) | 15.0185 | 0.864216 | ||||||||
\(303\) | 3.46869 | 0.199271 | ||||||||
\(304\) | 0.654438 | 0.0375346 | ||||||||
\(305\) | −4.13782 | −0.236931 | ||||||||
\(306\) | 8.13561 | 0.465082 | ||||||||
\(307\) | 23.8326 | 1.36020 | 0.680099 | − | 0.733120i | \(-0.261937\pi\) | ||||
0.680099 | + | 0.733120i | \(0.261937\pi\) | |||||||
\(308\) | 3.32320 | 0.189357 | ||||||||
\(309\) | 7.31949 | 0.416391 | ||||||||
\(310\) | 5.24433 | 0.297858 | ||||||||
\(311\) | 0.0857955 | 0.00486502 | 0.00243251 | − | 0.999997i | \(-0.499226\pi\) | ||||
0.00243251 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(312\) | 0.550409 | 0.0311608 | ||||||||
\(313\) | −20.5342 | −1.16066 | −0.580332 | − | 0.814380i | \(-0.697077\pi\) | ||||
−0.580332 | + | 0.814380i | \(0.697077\pi\) | |||||||
\(314\) | 22.5572 | 1.27297 | ||||||||
\(315\) | 3.30281 | 0.186092 | ||||||||
\(316\) | 10.9266 | 0.614671 | ||||||||
\(317\) | −21.9701 | −1.23396 | −0.616981 | − | 0.786978i | \(-0.711645\pi\) | ||||
−0.616981 | + | 0.786978i | \(0.711645\pi\) | |||||||
\(318\) | −3.81101 | −0.213711 | ||||||||
\(319\) | 5.91945 | 0.331425 | ||||||||
\(320\) | −0.487122 | −0.0272309 | ||||||||
\(321\) | 2.50912 | 0.140045 | ||||||||
\(322\) | −19.7435 | −1.10026 | ||||||||
\(323\) | −1.88764 | −0.105031 | ||||||||
\(324\) | 7.41747 | 0.412082 | ||||||||
\(325\) | 6.18890 | 0.343298 | ||||||||
\(326\) | −6.69948 | −0.371050 | ||||||||
\(327\) | 6.16664 | 0.341016 | ||||||||
\(328\) | −0.313899 | −0.0173322 | ||||||||
\(329\) | −13.3700 | −0.737113 | ||||||||
\(330\) | 0.285242 | 0.0157020 | ||||||||
\(331\) | 2.54722 | 0.140008 | 0.0700040 | − | 0.997547i | \(-0.477699\pi\) | ||||
0.0700040 | + | 0.997547i | \(0.477699\pi\) | |||||||
\(332\) | −10.0973 | −0.554160 | ||||||||
\(333\) | 23.1659 | 1.26948 | ||||||||
\(334\) | 9.77539 | 0.534886 | ||||||||
\(335\) | −1.92572 | −0.105213 | ||||||||
\(336\) | −1.01820 | −0.0555474 | ||||||||
\(337\) | 9.68168 | 0.527395 | 0.263697 | − | 0.964605i | \(-0.415058\pi\) | ||||
0.263697 | + | 0.964605i | \(0.415058\pi\) | |||||||
\(338\) | −11.3114 | −0.615261 | ||||||||
\(339\) | −5.61934 | −0.305201 | ||||||||
\(340\) | 1.40504 | 0.0761989 | ||||||||
\(341\) | −14.8834 | −0.805980 | ||||||||
\(342\) | −1.84590 | −0.0998148 | ||||||||
\(343\) | −19.7633 | −1.06712 | ||||||||
\(344\) | 4.40071 | 0.237270 | ||||||||
\(345\) | −1.69465 | −0.0912370 | ||||||||
\(346\) | 6.39981 | 0.344056 | ||||||||
\(347\) | −20.5598 | −1.10371 | −0.551855 | − | 0.833940i | \(-0.686080\pi\) | ||||
−0.551855 | + | 0.833940i | \(0.686080\pi\) | |||||||
\(348\) | −1.81367 | −0.0972230 | ||||||||
\(349\) | −12.5526 | −0.671924 | −0.335962 | − | 0.941876i | \(-0.609061\pi\) | ||||
−0.335962 | + | 0.941876i | \(0.609061\pi\) | |||||||
\(350\) | −11.4488 | −0.611966 | ||||||||
\(351\) | −3.20370 | −0.171001 | ||||||||
\(352\) | 1.38245 | 0.0736848 | ||||||||
\(353\) | 0.944759 | 0.0502845 | 0.0251422 | − | 0.999684i | \(-0.491996\pi\) | ||||
0.0251422 | + | 0.999684i | \(0.491996\pi\) | |||||||
\(354\) | −0.166793 | −0.00886493 | ||||||||
\(355\) | −0.368692 | −0.0195682 | ||||||||
\(356\) | −12.2322 | −0.648304 | ||||||||
\(357\) | 2.93687 | 0.155436 | ||||||||
\(358\) | −2.76473 | −0.146121 | ||||||||
\(359\) | 14.5533 | 0.768095 | 0.384047 | − | 0.923313i | \(-0.374530\pi\) | ||||
0.384047 | + | 0.923313i | \(0.374530\pi\) | |||||||
\(360\) | 1.37397 | 0.0724145 | ||||||||
\(361\) | −18.5717 | −0.977458 | ||||||||
\(362\) | −9.51712 | −0.500209 | ||||||||
\(363\) | 3.84977 | 0.202061 | ||||||||
\(364\) | −3.12368 | −0.163725 | ||||||||
\(365\) | 4.38550 | 0.229547 | ||||||||
\(366\) | −3.59800 | −0.188071 | ||||||||
\(367\) | −18.8279 | −0.982809 | −0.491405 | − | 0.870931i | \(-0.663516\pi\) | ||||
−0.491405 | + | 0.870931i | \(0.663516\pi\) | |||||||
\(368\) | −8.21328 | −0.428147 | ||||||||
\(369\) | 0.885380 | 0.0460910 | ||||||||
\(370\) | 4.00080 | 0.207992 | ||||||||
\(371\) | 21.6282 | 1.12288 | ||||||||
\(372\) | 4.56015 | 0.236433 | ||||||||
\(373\) | −30.3593 | −1.57194 | −0.785972 | − | 0.618262i | \(-0.787837\pi\) | ||||
−0.785972 | + | 0.618262i | \(0.787837\pi\) | |||||||
\(374\) | −3.98749 | −0.206188 | ||||||||
\(375\) | −2.01435 | −0.104021 | ||||||||
\(376\) | −5.56192 | −0.286834 | ||||||||
\(377\) | −5.56405 | −0.286563 | ||||||||
\(378\) | 5.92653 | 0.304828 | ||||||||
\(379\) | 22.6287 | 1.16236 | 0.581179 | − | 0.813775i | \(-0.302591\pi\) | ||||
0.581179 | + | 0.813775i | \(0.302591\pi\) | |||||||
\(380\) | −0.318791 | −0.0163536 | ||||||||
\(381\) | −0.858746 | −0.0439949 | ||||||||
\(382\) | −26.5851 | −1.36021 | ||||||||
\(383\) | 14.6831 | 0.750273 | 0.375136 | − | 0.926970i | \(-0.377596\pi\) | ||||
0.375136 | + | 0.926970i | \(0.377596\pi\) | |||||||
\(384\) | −0.423572 | −0.0216153 | ||||||||
\(385\) | −1.61880 | −0.0825017 | ||||||||
\(386\) | 6.55798 | 0.333792 | ||||||||
\(387\) | −12.4126 | −0.630967 | ||||||||
\(388\) | 16.8496 | 0.855408 | ||||||||
\(389\) | 24.9705 | 1.26605 | 0.633026 | − | 0.774130i | \(-0.281812\pi\) | ||||
0.633026 | + | 0.774130i | \(0.281812\pi\) | |||||||
\(390\) | −0.268116 | −0.0135766 | ||||||||
\(391\) | 23.6901 | 1.19806 | ||||||||
\(392\) | −1.22152 | −0.0616959 | ||||||||
\(393\) | 0.659206 | 0.0332525 | ||||||||
\(394\) | 3.97806 | 0.200412 | ||||||||
\(395\) | −5.32260 | −0.267809 | ||||||||
\(396\) | −3.89932 | −0.195948 | ||||||||
\(397\) | 10.3228 | 0.518086 | 0.259043 | − | 0.965866i | \(-0.416593\pi\) | ||||
0.259043 | + | 0.965866i | \(0.416593\pi\) | |||||||
\(398\) | −13.0404 | −0.653656 | ||||||||
\(399\) | −0.666349 | −0.0333592 | ||||||||
\(400\) | −4.76271 | −0.238136 | ||||||||
\(401\) | −25.3580 | −1.26632 | −0.633158 | − | 0.774022i | \(-0.718242\pi\) | ||||
−0.633158 | + | 0.774022i | \(0.718242\pi\) | |||||||
\(402\) | −1.67449 | −0.0835159 | ||||||||
\(403\) | 13.9898 | 0.696881 | ||||||||
\(404\) | −8.18914 | −0.407425 | ||||||||
\(405\) | −3.61321 | −0.179542 | ||||||||
\(406\) | 10.2929 | 0.510829 | ||||||||
\(407\) | −11.3542 | −0.562809 | ||||||||
\(408\) | 1.22174 | 0.0604849 | ||||||||
\(409\) | 5.90920 | 0.292191 | 0.146096 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146096 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(410\) | 0.152907 | 0.00755154 | ||||||||
\(411\) | 7.61862 | 0.375799 | ||||||||
\(412\) | −17.2804 | −0.851345 | ||||||||
\(413\) | 0.946580 | 0.0465781 | ||||||||
\(414\) | 23.1663 | 1.13856 | ||||||||
\(415\) | 4.91860 | 0.241445 | ||||||||
\(416\) | −1.29945 | −0.0637107 | ||||||||
\(417\) | 8.16939 | 0.400057 | ||||||||
\(418\) | 0.904727 | 0.0442516 | ||||||||
\(419\) | −30.4294 | −1.48657 | −0.743286 | − | 0.668974i | \(-0.766734\pi\) | ||||
−0.743286 | + | 0.668974i | \(0.766734\pi\) | |||||||
\(420\) | 0.495988 | 0.0242017 | ||||||||
\(421\) | 15.2300 | 0.742265 | 0.371133 | − | 0.928580i | \(-0.378970\pi\) | ||||
0.371133 | + | 0.928580i | \(0.378970\pi\) | |||||||
\(422\) | 22.1547 | 1.07847 | ||||||||
\(423\) | 15.6879 | 0.762771 | ||||||||
\(424\) | 8.99732 | 0.436948 | ||||||||
\(425\) | 13.7374 | 0.666362 | ||||||||
\(426\) | −0.320593 | −0.0155328 | ||||||||
\(427\) | 20.4193 | 0.988161 | ||||||||
\(428\) | −5.92372 | −0.286334 | ||||||||
\(429\) | 0.760913 | 0.0367372 | ||||||||
\(430\) | −2.14368 | −0.103377 | ||||||||
\(431\) | 6.07512 | 0.292628 | 0.146314 | − | 0.989238i | \(-0.453259\pi\) | ||||
0.146314 | + | 0.989238i | \(0.453259\pi\) | |||||||
\(432\) | 2.46544 | 0.118618 | ||||||||
\(433\) | 10.3216 | 0.496026 | 0.248013 | − | 0.968757i | \(-0.420222\pi\) | ||||
0.248013 | + | 0.968757i | \(0.420222\pi\) | |||||||
\(434\) | −25.8797 | −1.24227 | ||||||||
\(435\) | 0.883479 | 0.0423596 | ||||||||
\(436\) | −14.5587 | −0.697234 | ||||||||
\(437\) | −5.37508 | −0.257125 | ||||||||
\(438\) | 3.81336 | 0.182210 | ||||||||
\(439\) | −13.4776 | −0.643251 | −0.321626 | − | 0.946867i | \(-0.604229\pi\) | ||||
−0.321626 | + | 0.946867i | \(0.604229\pi\) | |||||||
\(440\) | −0.673421 | −0.0321041 | ||||||||
\(441\) | 3.44539 | 0.164066 | ||||||||
\(442\) | 3.74809 | 0.178278 | ||||||||
\(443\) | −18.8787 | −0.896955 | −0.448478 | − | 0.893794i | \(-0.648034\pi\) | ||||
−0.448478 | + | 0.893794i | \(0.648034\pi\) | |||||||
\(444\) | 3.47885 | 0.165099 | ||||||||
\(445\) | 5.95855 | 0.282463 | ||||||||
\(446\) | −27.2023 | −1.28807 | ||||||||
\(447\) | −2.41174 | −0.114071 | ||||||||
\(448\) | 2.40385 | 0.113571 | ||||||||
\(449\) | 2.22579 | 0.105041 | 0.0525207 | − | 0.998620i | \(-0.483274\pi\) | ||||
0.0525207 | + | 0.998620i | \(0.483274\pi\) | |||||||
\(450\) | 13.4336 | 0.633268 | ||||||||
\(451\) | −0.433950 | −0.0204339 | ||||||||
\(452\) | 13.2666 | 0.624007 | ||||||||
\(453\) | −6.36140 | −0.298885 | ||||||||
\(454\) | 18.8854 | 0.886337 | ||||||||
\(455\) | 1.52161 | 0.0713342 | ||||||||
\(456\) | −0.277201 | −0.0129811 | ||||||||
\(457\) | −26.8389 | −1.25547 | −0.627736 | − | 0.778426i | \(-0.716018\pi\) | ||||
−0.627736 | + | 0.778426i | \(0.716018\pi\) | |||||||
\(458\) | 4.97064 | 0.232263 | ||||||||
\(459\) | −7.11122 | −0.331923 | ||||||||
\(460\) | 4.00086 | 0.186541 | ||||||||
\(461\) | −30.5674 | −1.42367 | −0.711833 | − | 0.702348i | \(-0.752135\pi\) | ||||
−0.711833 | + | 0.702348i | \(0.752135\pi\) | |||||||
\(462\) | −1.40761 | −0.0654880 | ||||||||
\(463\) | 18.6703 | 0.867682 | 0.433841 | − | 0.900989i | \(-0.357158\pi\) | ||||
0.433841 | + | 0.900989i | \(0.357158\pi\) | |||||||
\(464\) | 4.28186 | 0.198780 | ||||||||
\(465\) | −2.22135 | −0.103013 | ||||||||
\(466\) | −2.23009 | −0.103307 | ||||||||
\(467\) | 32.9483 | 1.52467 | 0.762333 | − | 0.647185i | \(-0.224054\pi\) | ||||
0.762333 | + | 0.647185i | \(0.224054\pi\) | |||||||
\(468\) | 3.66521 | 0.169424 | ||||||||
\(469\) | 9.50304 | 0.438810 | ||||||||
\(470\) | 2.70933 | 0.124972 | ||||||||
\(471\) | −9.55457 | −0.440251 | ||||||||
\(472\) | 0.393777 | 0.0181251 | ||||||||
\(473\) | 6.08376 | 0.279731 | ||||||||
\(474\) | −4.62821 | −0.212581 | ||||||||
\(475\) | −3.11690 | −0.143013 | ||||||||
\(476\) | −6.93358 | −0.317800 | ||||||||
\(477\) | −25.3777 | −1.16197 | ||||||||
\(478\) | −3.30765 | −0.151288 | ||||||||
\(479\) | 20.0398 | 0.915642 | 0.457821 | − | 0.889044i | \(-0.348630\pi\) | ||||
0.457821 | + | 0.889044i | \(0.348630\pi\) | |||||||
\(480\) | 0.206331 | 0.00941767 | ||||||||
\(481\) | 10.6726 | 0.486626 | ||||||||
\(482\) | −16.5056 | −0.751808 | ||||||||
\(483\) | 8.36277 | 0.380519 | ||||||||
\(484\) | −9.08883 | −0.413129 | ||||||||
\(485\) | −8.20779 | −0.372697 | ||||||||
\(486\) | −10.5381 | −0.478020 | ||||||||
\(487\) | −18.9345 | −0.858006 | −0.429003 | − | 0.903303i | \(-0.641135\pi\) | ||||
−0.429003 | + | 0.903303i | \(0.641135\pi\) | |||||||
\(488\) | 8.49444 | 0.384525 | ||||||||
\(489\) | 2.83771 | 0.128326 | ||||||||
\(490\) | 0.595027 | 0.0268806 | ||||||||
\(491\) | −1.35404 | −0.0611071 | −0.0305535 | − | 0.999533i | \(-0.509727\pi\) | ||||
−0.0305535 | + | 0.999533i | \(0.509727\pi\) | |||||||
\(492\) | 0.132959 | 0.00599424 | ||||||||
\(493\) | −12.3504 | −0.556236 | ||||||||
\(494\) | −0.850408 | −0.0382617 | ||||||||
\(495\) | 1.89944 | 0.0853736 | ||||||||
\(496\) | −10.7659 | −0.483405 | ||||||||
\(497\) | 1.81942 | 0.0816123 | ||||||||
\(498\) | 4.27692 | 0.191653 | ||||||||
\(499\) | 38.2002 | 1.71008 | 0.855038 | − | 0.518566i | \(-0.173534\pi\) | ||||
0.855038 | + | 0.518566i | \(0.173534\pi\) | |||||||
\(500\) | 4.75563 | 0.212678 | ||||||||
\(501\) | −4.14058 | −0.184987 | ||||||||
\(502\) | −5.28350 | −0.235814 | ||||||||
\(503\) | 14.2520 | 0.635467 | 0.317734 | − | 0.948180i | \(-0.397078\pi\) | ||||
0.317734 | + | 0.948180i | \(0.397078\pi\) | |||||||
\(504\) | −6.78026 | −0.302017 | ||||||||
\(505\) | 3.98911 | 0.177513 | ||||||||
\(506\) | −11.3544 | −0.504766 | ||||||||
\(507\) | 4.79120 | 0.212785 | ||||||||
\(508\) | 2.02739 | 0.0899510 | ||||||||
\(509\) | 18.5447 | 0.821980 | 0.410990 | − | 0.911640i | \(-0.365183\pi\) | ||||
0.410990 | + | 0.911640i | \(0.365183\pi\) | |||||||
\(510\) | −0.595134 | −0.0263530 | ||||||||
\(511\) | −21.6415 | −0.957366 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.61347 | 0.0712366 | ||||||||
\(514\) | 25.6201 | 1.13005 | ||||||||
\(515\) | 8.41766 | 0.370927 | ||||||||
\(516\) | −1.86402 | −0.0820587 | ||||||||
\(517\) | −7.68908 | −0.338165 | ||||||||
\(518\) | −19.7431 | −0.867464 | ||||||||
\(519\) | −2.71078 | −0.118990 | ||||||||
\(520\) | 0.632989 | 0.0277584 | ||||||||
\(521\) | 5.87186 | 0.257251 | 0.128626 | − | 0.991693i | \(-0.458943\pi\) | ||||
0.128626 | + | 0.991693i | \(0.458943\pi\) | |||||||
\(522\) | −12.0773 | −0.528611 | ||||||||
\(523\) | 34.3254 | 1.50094 | 0.750472 | − | 0.660902i | \(-0.229826\pi\) | ||||
0.750472 | + | 0.660902i | \(0.229826\pi\) | |||||||
\(524\) | −1.55630 | −0.0679874 | ||||||||
\(525\) | 4.84940 | 0.211645 | ||||||||
\(526\) | −4.54683 | −0.198251 | ||||||||
\(527\) | 31.0530 | 1.35269 | ||||||||
\(528\) | −0.585566 | −0.0254835 | ||||||||
\(529\) | 44.4579 | 1.93295 | ||||||||
\(530\) | −4.38279 | −0.190376 | ||||||||
\(531\) | −1.11068 | −0.0481995 | ||||||||
\(532\) | 1.57317 | 0.0682055 | ||||||||
\(533\) | 0.407896 | 0.0176679 | ||||||||
\(534\) | 5.18120 | 0.224212 | ||||||||
\(535\) | 2.88557 | 0.124754 | ||||||||
\(536\) | 3.95326 | 0.170755 | ||||||||
\(537\) | 1.17106 | 0.0505350 | ||||||||
\(538\) | 27.4647 | 1.18409 | ||||||||
\(539\) | −1.68868 | −0.0727368 | ||||||||
\(540\) | −1.20097 | −0.0516814 | ||||||||
\(541\) | −31.4902 | −1.35387 | −0.676936 | − | 0.736042i | \(-0.736692\pi\) | ||||
−0.676936 | + | 0.736042i | \(0.736692\pi\) | |||||||
\(542\) | 11.0589 | 0.475022 | ||||||||
\(543\) | 4.03118 | 0.172995 | ||||||||
\(544\) | −2.88437 | −0.123666 | ||||||||
\(545\) | 7.09184 | 0.303781 | ||||||||
\(546\) | 1.32310 | 0.0566235 | ||||||||
\(547\) | 5.58889 | 0.238963 | 0.119482 | − | 0.992836i | \(-0.461877\pi\) | ||||
0.119482 | + | 0.992836i | \(0.461877\pi\) | |||||||
\(548\) | −17.9866 | −0.768350 | ||||||||
\(549\) | −23.9593 | −1.02256 | ||||||||
\(550\) | −6.58421 | −0.280752 | ||||||||
\(551\) | 2.80221 | 0.119378 | ||||||||
\(552\) | 3.47891 | 0.148072 | ||||||||
\(553\) | 26.2659 | 1.11694 | ||||||||
\(554\) | −9.96389 | −0.423325 | ||||||||
\(555\) | −1.69462 | −0.0719328 | ||||||||
\(556\) | −19.2869 | −0.817948 | ||||||||
\(557\) | 5.18623 | 0.219748 | 0.109874 | − | 0.993946i | \(-0.464955\pi\) | ||||
0.109874 | + | 0.993946i | \(0.464955\pi\) | |||||||
\(558\) | 30.3663 | 1.28551 | ||||||||
\(559\) | −5.71849 | −0.241867 | ||||||||
\(560\) | −1.17097 | −0.0494823 | ||||||||
\(561\) | 1.68899 | 0.0713091 | ||||||||
\(562\) | 13.9946 | 0.590326 | ||||||||
\(563\) | 11.3474 | 0.478237 | 0.239118 | − | 0.970990i | \(-0.423142\pi\) | ||||
0.239118 | + | 0.970990i | \(0.423142\pi\) | |||||||
\(564\) | 2.35587 | 0.0992001 | ||||||||
\(565\) | −6.46243 | −0.271877 | ||||||||
\(566\) | −6.74061 | −0.283329 | ||||||||
\(567\) | 17.8305 | 0.748810 | ||||||||
\(568\) | 0.756879 | 0.0317580 | ||||||||
\(569\) | 19.9578 | 0.836673 | 0.418337 | − | 0.908292i | \(-0.362613\pi\) | ||||
0.418337 | + | 0.908292i | \(0.362613\pi\) | |||||||
\(570\) | 0.135031 | 0.00565581 | ||||||||
\(571\) | 23.8226 | 0.996947 | 0.498473 | − | 0.866905i | \(-0.333894\pi\) | ||||
0.498473 | + | 0.866905i | \(0.333894\pi\) | |||||||
\(572\) | −1.79642 | −0.0751121 | ||||||||
\(573\) | 11.2607 | 0.470422 | ||||||||
\(574\) | −0.754566 | −0.0314950 | ||||||||
\(575\) | 39.1175 | 1.63131 | ||||||||
\(576\) | −2.82059 | −0.117524 | ||||||||
\(577\) | −32.6655 | −1.35988 | −0.679942 | − | 0.733266i | \(-0.737995\pi\) | ||||
−0.679942 | + | 0.733266i | \(0.737995\pi\) | |||||||
\(578\) | −8.68042 | −0.361058 | ||||||||
\(579\) | −2.77777 | −0.115440 | ||||||||
\(580\) | −2.08578 | −0.0866075 | ||||||||
\(581\) | −24.2723 | −1.00699 | ||||||||
\(582\) | −7.13700 | −0.295838 | ||||||||
\(583\) | 12.4383 | 0.515143 | ||||||||
\(584\) | −9.00288 | −0.372542 | ||||||||
\(585\) | −1.78540 | −0.0738172 | ||||||||
\(586\) | 30.9651 | 1.27916 | ||||||||
\(587\) | −32.4538 | −1.33951 | −0.669755 | − | 0.742582i | \(-0.733601\pi\) | ||||
−0.669755 | + | 0.742582i | \(0.733601\pi\) | |||||||
\(588\) | 0.517399 | 0.0213372 | ||||||||
\(589\) | −7.04564 | −0.290311 | ||||||||
\(590\) | −0.191817 | −0.00789699 | ||||||||
\(591\) | −1.68499 | −0.0693113 | ||||||||
\(592\) | −8.21314 | −0.337558 | ||||||||
\(593\) | 9.52629 | 0.391198 | 0.195599 | − | 0.980684i | \(-0.437335\pi\) | ||||
0.195599 | + | 0.980684i | \(0.437335\pi\) | |||||||
\(594\) | 3.40834 | 0.139846 | ||||||||
\(595\) | 3.37750 | 0.138464 | ||||||||
\(596\) | 5.69382 | 0.233228 | ||||||||
\(597\) | 5.52354 | 0.226063 | ||||||||
\(598\) | 10.6727 | 0.436440 | ||||||||
\(599\) | 22.3459 | 0.913028 | 0.456514 | − | 0.889716i | \(-0.349098\pi\) | ||||
0.456514 | + | 0.889716i | \(0.349098\pi\) | |||||||
\(600\) | 2.01735 | 0.0823580 | ||||||||
\(601\) | −37.1680 | −1.51611 | −0.758057 | − | 0.652188i | \(-0.773851\pi\) | ||||
−0.758057 | + | 0.652188i | \(0.773851\pi\) | |||||||
\(602\) | 10.5786 | 0.431153 | ||||||||
\(603\) | −11.1505 | −0.454084 | ||||||||
\(604\) | 15.0185 | 0.611093 | ||||||||
\(605\) | 4.42737 | 0.179998 | ||||||||
\(606\) | 3.46869 | 0.140906 | ||||||||
\(607\) | 34.0379 | 1.38156 | 0.690778 | − | 0.723067i | \(-0.257268\pi\) | ||||
0.690778 | + | 0.723067i | \(0.257268\pi\) | |||||||
\(608\) | 0.654438 | 0.0265410 | ||||||||
\(609\) | −4.35979 | −0.176668 | ||||||||
\(610\) | −4.13782 | −0.167536 | ||||||||
\(611\) | 7.22743 | 0.292391 | ||||||||
\(612\) | 8.13561 | 0.328863 | ||||||||
\(613\) | −16.7046 | −0.674694 | −0.337347 | − | 0.941380i | \(-0.609529\pi\) | ||||
−0.337347 | + | 0.941380i | \(0.609529\pi\) | |||||||
\(614\) | 23.8326 | 0.961806 | ||||||||
\(615\) | −0.0647671 | −0.00261166 | ||||||||
\(616\) | 3.32320 | 0.133895 | ||||||||
\(617\) | 47.8658 | 1.92700 | 0.963502 | − | 0.267702i | \(-0.0862642\pi\) | ||||
0.963502 | + | 0.267702i | \(0.0862642\pi\) | |||||||
\(618\) | 7.31949 | 0.294433 | ||||||||
\(619\) | 2.54991 | 0.102490 | 0.0512448 | − | 0.998686i | \(-0.483681\pi\) | ||||
0.0512448 | + | 0.998686i | \(0.483681\pi\) | |||||||
\(620\) | 5.24433 | 0.210617 | ||||||||
\(621\) | −20.2493 | −0.812576 | ||||||||
\(622\) | 0.0857955 | 0.00344009 | ||||||||
\(623\) | −29.4043 | −1.17806 | ||||||||
\(624\) | 0.550409 | 0.0220340 | ||||||||
\(625\) | 21.4970 | 0.859880 | ||||||||
\(626\) | −20.5342 | −0.820713 | ||||||||
\(627\) | −0.383217 | −0.0153042 | ||||||||
\(628\) | 22.5572 | 0.900129 | ||||||||
\(629\) | 23.6897 | 0.944571 | ||||||||
\(630\) | 3.30281 | 0.131587 | ||||||||
\(631\) | 44.7184 | 1.78021 | 0.890106 | − | 0.455754i | \(-0.150630\pi\) | ||||
0.890106 | + | 0.455754i | \(0.150630\pi\) | |||||||
\(632\) | 10.9266 | 0.434638 | ||||||||
\(633\) | −9.38411 | −0.372985 | ||||||||
\(634\) | −21.9701 | −0.872543 | ||||||||
\(635\) | −0.987586 | −0.0391912 | ||||||||
\(636\) | −3.81101 | −0.151116 | ||||||||
\(637\) | 1.58730 | 0.0628910 | ||||||||
\(638\) | 5.91945 | 0.234353 | ||||||||
\(639\) | −2.13484 | −0.0844531 | ||||||||
\(640\) | −0.487122 | −0.0192552 | ||||||||
\(641\) | 35.2092 | 1.39068 | 0.695340 | − | 0.718681i | \(-0.255254\pi\) | ||||
0.695340 | + | 0.718681i | \(0.255254\pi\) | |||||||
\(642\) | 2.50912 | 0.0990270 | ||||||||
\(643\) | 19.0321 | 0.750553 | 0.375276 | − | 0.926913i | \(-0.377548\pi\) | ||||
0.375276 | + | 0.926913i | \(0.377548\pi\) | |||||||
\(644\) | −19.7435 | −0.778002 | ||||||||
\(645\) | 0.908002 | 0.0357525 | ||||||||
\(646\) | −1.88764 | −0.0742682 | ||||||||
\(647\) | −2.69643 | −0.106008 | −0.0530039 | − | 0.998594i | \(-0.516880\pi\) | ||||
−0.0530039 | + | 0.998594i | \(0.516880\pi\) | |||||||
\(648\) | 7.41747 | 0.291386 | ||||||||
\(649\) | 0.544377 | 0.0213686 | ||||||||
\(650\) | 6.18890 | 0.242749 | ||||||||
\(651\) | 10.9619 | 0.429631 | ||||||||
\(652\) | −6.69948 | −0.262372 | ||||||||
\(653\) | −41.4605 | −1.62247 | −0.811237 | − | 0.584718i | \(-0.801205\pi\) | ||||
−0.811237 | + | 0.584718i | \(0.801205\pi\) | |||||||
\(654\) | 6.16664 | 0.241135 | ||||||||
\(655\) | 0.758109 | 0.0296218 | ||||||||
\(656\) | −0.313899 | −0.0122557 | ||||||||
\(657\) | 25.3934 | 0.990691 | ||||||||
\(658\) | −13.3700 | −0.521217 | ||||||||
\(659\) | 28.5503 | 1.11216 | 0.556082 | − | 0.831128i | \(-0.312304\pi\) | ||||
0.556082 | + | 0.831128i | \(0.312304\pi\) | |||||||
\(660\) | 0.285242 | 0.0111030 | ||||||||
\(661\) | −33.3936 | −1.29886 | −0.649430 | − | 0.760421i | \(-0.724993\pi\) | ||||
−0.649430 | + | 0.760421i | \(0.724993\pi\) | |||||||
\(662\) | 2.54722 | 0.0990006 | ||||||||
\(663\) | −1.58758 | −0.0616566 | ||||||||
\(664\) | −10.0973 | −0.391850 | ||||||||
\(665\) | −0.766324 | −0.0297168 | ||||||||
\(666\) | 23.1659 | 0.897660 | ||||||||
\(667\) | −35.1681 | −1.36171 | ||||||||
\(668\) | 9.77539 | 0.378221 | ||||||||
\(669\) | 11.5221 | 0.445471 | ||||||||
\(670\) | −1.92572 | −0.0743970 | ||||||||
\(671\) | 11.7431 | 0.453338 | ||||||||
\(672\) | −1.01820 | −0.0392780 | ||||||||
\(673\) | −27.4679 | −1.05881 | −0.529406 | − | 0.848369i | \(-0.677585\pi\) | ||||
−0.529406 | + | 0.848369i | \(0.677585\pi\) | |||||||
\(674\) | 9.68168 | 0.372924 | ||||||||
\(675\) | −11.7422 | −0.451956 | ||||||||
\(676\) | −11.3114 | −0.435055 | ||||||||
\(677\) | 9.97285 | 0.383288 | 0.191644 | − | 0.981465i | \(-0.438618\pi\) | ||||
0.191644 | + | 0.981465i | \(0.438618\pi\) | |||||||
\(678\) | −5.61934 | −0.215810 | ||||||||
\(679\) | 40.5038 | 1.55439 | ||||||||
\(680\) | 1.40504 | 0.0538807 | ||||||||
\(681\) | −7.99933 | −0.306535 | ||||||||
\(682\) | −14.8834 | −0.569914 | ||||||||
\(683\) | 33.4102 | 1.27840 | 0.639202 | − | 0.769039i | \(-0.279265\pi\) | ||||
0.639202 | + | 0.769039i | \(0.279265\pi\) | |||||||
\(684\) | −1.84590 | −0.0705797 | ||||||||
\(685\) | 8.76167 | 0.334766 | ||||||||
\(686\) | −19.7633 | −0.754565 | ||||||||
\(687\) | −2.10542 | −0.0803268 | ||||||||
\(688\) | 4.40071 | 0.167776 | ||||||||
\(689\) | −11.6915 | −0.445412 | ||||||||
\(690\) | −1.69465 | −0.0645143 | ||||||||
\(691\) | −38.0915 | −1.44907 | −0.724534 | − | 0.689239i | \(-0.757945\pi\) | ||||
−0.724534 | + | 0.689239i | \(0.757945\pi\) | |||||||
\(692\) | 6.39981 | 0.243284 | ||||||||
\(693\) | −9.37337 | −0.356065 | ||||||||
\(694\) | −20.5598 | −0.780441 | ||||||||
\(695\) | 9.39508 | 0.356376 | ||||||||
\(696\) | −1.81367 | −0.0687471 | ||||||||
\(697\) | 0.905400 | 0.0342945 | ||||||||
\(698\) | −12.5526 | −0.475122 | ||||||||
\(699\) | 0.944602 | 0.0357281 | ||||||||
\(700\) | −11.4488 | −0.432725 | ||||||||
\(701\) | −12.8284 | −0.484522 | −0.242261 | − | 0.970211i | \(-0.577889\pi\) | ||||
−0.242261 | + | 0.970211i | \(0.577889\pi\) | |||||||
\(702\) | −3.20370 | −0.120916 | ||||||||
\(703\) | −5.37499 | −0.202722 | ||||||||
\(704\) | 1.38245 | 0.0521030 | ||||||||
\(705\) | −1.14760 | −0.0432210 | ||||||||
\(706\) | 0.944759 | 0.0355565 | ||||||||
\(707\) | −19.6855 | −0.740348 | ||||||||
\(708\) | −0.166793 | −0.00626845 | ||||||||
\(709\) | 15.4241 | 0.579264 | 0.289632 | − | 0.957138i | \(-0.406467\pi\) | ||||
0.289632 | + | 0.957138i | \(0.406467\pi\) | |||||||
\(710\) | −0.368692 | −0.0138368 | ||||||||
\(711\) | −30.8195 | −1.15582 | ||||||||
\(712\) | −12.2322 | −0.458420 | ||||||||
\(713\) | 88.4237 | 3.31149 | ||||||||
\(714\) | 2.93687 | 0.109909 | ||||||||
\(715\) | 0.875075 | 0.0327260 | ||||||||
\(716\) | −2.76473 | −0.103323 | ||||||||
\(717\) | 1.40103 | 0.0523223 | ||||||||
\(718\) | 14.5533 | 0.543125 | ||||||||
\(719\) | −13.0923 | −0.488261 | −0.244130 | − | 0.969742i | \(-0.578502\pi\) | ||||
−0.244130 | + | 0.969742i | \(0.578502\pi\) | |||||||
\(720\) | 1.37397 | 0.0512048 | ||||||||
\(721\) | −41.5395 | −1.54701 | ||||||||
\(722\) | −18.5717 | −0.691168 | ||||||||
\(723\) | 6.99129 | 0.260009 | ||||||||
\(724\) | −9.51712 | −0.353701 | ||||||||
\(725\) | −20.3932 | −0.757386 | ||||||||
\(726\) | 3.84977 | 0.142878 | ||||||||
\(727\) | −15.9120 | −0.590145 | −0.295072 | − | 0.955475i | \(-0.595344\pi\) | ||||
−0.295072 | + | 0.955475i | \(0.595344\pi\) | |||||||
\(728\) | −3.12368 | −0.115771 | ||||||||
\(729\) | −17.7888 | −0.658843 | ||||||||
\(730\) | 4.38550 | 0.162314 | ||||||||
\(731\) | −12.6933 | −0.469477 | ||||||||
\(732\) | −3.59800 | −0.132986 | ||||||||
\(733\) | 8.45503 | 0.312294 | 0.156147 | − | 0.987734i | \(-0.450093\pi\) | ||||
0.156147 | + | 0.987734i | \(0.450093\pi\) | |||||||
\(734\) | −18.8279 | −0.694951 | ||||||||
\(735\) | −0.252036 | −0.00929650 | ||||||||
\(736\) | −8.21328 | −0.302745 | ||||||||
\(737\) | 5.46518 | 0.201313 | ||||||||
\(738\) | 0.885380 | 0.0325913 | ||||||||
\(739\) | 19.5251 | 0.718243 | 0.359122 | − | 0.933291i | \(-0.383076\pi\) | ||||
0.359122 | + | 0.933291i | \(0.383076\pi\) | |||||||
\(740\) | 4.00080 | 0.147072 | ||||||||
\(741\) | 0.360209 | 0.0132326 | ||||||||
\(742\) | 21.6282 | 0.793996 | ||||||||
\(743\) | 36.0117 | 1.32114 | 0.660570 | − | 0.750765i | \(-0.270315\pi\) | ||||
0.660570 | + | 0.750765i | \(0.270315\pi\) | |||||||
\(744\) | 4.56015 | 0.167183 | ||||||||
\(745\) | −2.77358 | −0.101616 | ||||||||
\(746\) | −30.3593 | −1.11153 | ||||||||
\(747\) | 28.4803 | 1.04204 | ||||||||
\(748\) | −3.98749 | −0.145797 | ||||||||
\(749\) | −14.2397 | −0.520308 | ||||||||
\(750\) | −2.01435 | −0.0735536 | ||||||||
\(751\) | 17.0215 | 0.621123 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(752\) | −5.56192 | −0.202822 | ||||||||
\(753\) | 2.23794 | 0.0815551 | ||||||||
\(754\) | −5.56405 | −0.202631 | ||||||||
\(755\) | −7.31582 | −0.266250 | ||||||||
\(756\) | 5.92653 | 0.215546 | ||||||||
\(757\) | −8.52782 | −0.309949 | −0.154974 | − | 0.987918i | \(-0.549530\pi\) | ||||
−0.154974 | + | 0.987918i | \(0.549530\pi\) | |||||||
\(758\) | 22.6287 | 0.821912 | ||||||||
\(759\) | 4.80942 | 0.174571 | ||||||||
\(760\) | −0.318791 | −0.0115638 | ||||||||
\(761\) | −14.3668 | −0.520795 | −0.260397 | − | 0.965502i | \(-0.583854\pi\) | ||||
−0.260397 | + | 0.965502i | \(0.583854\pi\) | |||||||
\(762\) | −0.858746 | −0.0311091 | ||||||||
\(763\) | −34.9968 | −1.26697 | ||||||||
\(764\) | −26.5851 | −0.961816 | ||||||||
\(765\) | −3.96303 | −0.143284 | ||||||||
\(766\) | 14.6831 | 0.530523 | ||||||||
\(767\) | −0.511693 | −0.0184762 | ||||||||
\(768\) | −0.423572 | −0.0152843 | ||||||||
\(769\) | −6.08620 | −0.219474 | −0.109737 | − | 0.993961i | \(-0.535001\pi\) | ||||
−0.109737 | + | 0.993961i | \(0.535001\pi\) | |||||||
\(770\) | −1.61880 | −0.0583375 | ||||||||
\(771\) | −10.8519 | −0.390823 | ||||||||
\(772\) | 6.55798 | 0.236027 | ||||||||
\(773\) | −16.6883 | −0.600236 | −0.300118 | − | 0.953902i | \(-0.597026\pi\) | ||||
−0.300118 | + | 0.953902i | \(0.597026\pi\) | |||||||
\(774\) | −12.4126 | −0.446161 | ||||||||
\(775\) | 51.2751 | 1.84186 | ||||||||
\(776\) | 16.8496 | 0.604865 | ||||||||
\(777\) | 8.36263 | 0.300008 | ||||||||
\(778\) | 24.9705 | 0.895234 | ||||||||
\(779\) | −0.205427 | −0.00736020 | ||||||||
\(780\) | −0.268116 | −0.00960010 | ||||||||
\(781\) | 1.04635 | 0.0374412 | ||||||||
\(782\) | 23.6901 | 0.847157 | ||||||||
\(783\) | 10.5566 | 0.377263 | ||||||||
\(784\) | −1.22152 | −0.0436256 | ||||||||
\(785\) | −10.9881 | −0.392181 | ||||||||
\(786\) | 0.659206 | 0.0235131 | ||||||||
\(787\) | −29.3303 | −1.04551 | −0.522756 | − | 0.852482i | \(-0.675096\pi\) | ||||
−0.522756 | + | 0.852482i | \(0.675096\pi\) | |||||||
\(788\) | 3.97806 | 0.141712 | ||||||||
\(789\) | 1.92591 | 0.0685641 | ||||||||
\(790\) | −5.32260 | −0.189369 | ||||||||
\(791\) | 31.8908 | 1.13391 | ||||||||
\(792\) | −3.89932 | −0.138556 | ||||||||
\(793\) | −11.0381 | −0.391974 | ||||||||
\(794\) | 10.3228 | 0.366342 | ||||||||
\(795\) | 1.85642 | 0.0658406 | ||||||||
\(796\) | −13.0404 | −0.462204 | ||||||||
\(797\) | −7.13508 | −0.252737 | −0.126369 | − | 0.991983i | \(-0.540332\pi\) | ||||
−0.126369 | + | 0.991983i | \(0.540332\pi\) | |||||||
\(798\) | −0.666349 | −0.0235885 | ||||||||
\(799\) | 16.0426 | 0.567547 | ||||||||
\(800\) | −4.76271 | −0.168387 | ||||||||
\(801\) | 34.5019 | 1.21906 | ||||||||
\(802\) | −25.3580 | −0.895421 | ||||||||
\(803\) | −12.4460 | −0.439210 | ||||||||
\(804\) | −1.67449 | −0.0590547 | ||||||||
\(805\) | 9.61747 | 0.338971 | ||||||||
\(806\) | 13.9898 | 0.492769 | ||||||||
\(807\) | −11.6333 | −0.409510 | ||||||||
\(808\) | −8.18914 | −0.288093 | ||||||||
\(809\) | −24.6870 | −0.867948 | −0.433974 | − | 0.900925i | \(-0.642889\pi\) | ||||
−0.433974 | + | 0.900925i | \(0.642889\pi\) | |||||||
\(810\) | −3.61321 | −0.126955 | ||||||||
\(811\) | −4.22066 | −0.148207 | −0.0741037 | − | 0.997251i | \(-0.523610\pi\) | ||||
−0.0741037 | + | 0.997251i | \(0.523610\pi\) | |||||||
\(812\) | 10.2929 | 0.361211 | ||||||||
\(813\) | −4.68425 | −0.164284 | ||||||||
\(814\) | −11.3542 | −0.397966 | ||||||||
\(815\) | 3.26346 | 0.114314 | ||||||||
\(816\) | 1.22174 | 0.0427693 | ||||||||
\(817\) | 2.87999 | 0.100758 | ||||||||
\(818\) | 5.90920 | 0.206610 | ||||||||
\(819\) | 8.81060 | 0.307867 | ||||||||
\(820\) | 0.152907 | 0.00533975 | ||||||||
\(821\) | −38.8041 | −1.35427 | −0.677136 | − | 0.735858i | \(-0.736779\pi\) | ||||
−0.677136 | + | 0.735858i | \(0.736779\pi\) | |||||||
\(822\) | 7.61862 | 0.265730 | ||||||||
\(823\) | 2.28375 | 0.0796064 | 0.0398032 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398032 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(824\) | −17.2804 | −0.601992 | ||||||||
\(825\) | 2.78888 | 0.0970964 | ||||||||
\(826\) | 0.946580 | 0.0329357 | ||||||||
\(827\) | 42.5631 | 1.48006 | 0.740032 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740032 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(828\) | 23.1663 | 0.805083 | ||||||||
\(829\) | 0.0647099 | 0.00224747 | 0.00112373 | − | 0.999999i | \(-0.499642\pi\) | ||||
0.00112373 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(830\) | 4.91860 | 0.170727 | ||||||||
\(831\) | 4.22042 | 0.146405 | ||||||||
\(832\) | −1.29945 | −0.0450503 | ||||||||
\(833\) | 3.52330 | 0.122075 | ||||||||
\(834\) | 8.16939 | 0.282883 | ||||||||
\(835\) | −4.76180 | −0.164789 | ||||||||
\(836\) | 0.904727 | 0.0312906 | ||||||||
\(837\) | −26.5427 | −0.917452 | ||||||||
\(838\) | −30.4294 | −1.05116 | ||||||||
\(839\) | 54.5046 | 1.88171 | 0.940853 | − | 0.338815i | \(-0.110026\pi\) | ||||
0.940853 | + | 0.338815i | \(0.110026\pi\) | |||||||
\(840\) | 0.495988 | 0.0171132 | ||||||||
\(841\) | −10.6657 | −0.367783 | ||||||||
\(842\) | 15.2300 | 0.524861 | ||||||||
\(843\) | −5.92771 | −0.204161 | ||||||||
\(844\) | 22.1547 | 0.762597 | ||||||||
\(845\) | 5.51004 | 0.189551 | ||||||||
\(846\) | 15.6879 | 0.539361 | ||||||||
\(847\) | −21.8482 | −0.750712 | ||||||||
\(848\) | 8.99732 | 0.308969 | ||||||||
\(849\) | 2.85513 | 0.0979878 | ||||||||
\(850\) | 13.7374 | 0.471189 | ||||||||
\(851\) | 67.4568 | 2.31239 | ||||||||
\(852\) | −0.320593 | −0.0109833 | ||||||||
\(853\) | 20.6397 | 0.706690 | 0.353345 | − | 0.935493i | \(-0.385044\pi\) | ||||
0.353345 | + | 0.935493i | \(0.385044\pi\) | |||||||
\(854\) | 20.4193 | 0.698735 | ||||||||
\(855\) | 0.899177 | 0.0307512 | ||||||||
\(856\) | −5.92372 | −0.202469 | ||||||||
\(857\) | 35.8205 | 1.22361 | 0.611803 | − | 0.791010i | \(-0.290445\pi\) | ||||
0.611803 | + | 0.791010i | \(0.290445\pi\) | |||||||
\(858\) | 0.760913 | 0.0259771 | ||||||||
\(859\) | −5.99497 | −0.204546 | −0.102273 | − | 0.994756i | \(-0.532611\pi\) | ||||
−0.102273 | + | 0.994756i | \(0.532611\pi\) | |||||||
\(860\) | −2.14368 | −0.0730989 | ||||||||
\(861\) | 0.319613 | 0.0108924 | ||||||||
\(862\) | 6.07512 | 0.206919 | ||||||||
\(863\) | 21.1282 | 0.719211 | 0.359606 | − | 0.933104i | \(-0.382911\pi\) | ||||
0.359606 | + | 0.933104i | \(0.382911\pi\) | |||||||
\(864\) | 2.46544 | 0.0838758 | ||||||||
\(865\) | −3.11748 | −0.105998 | ||||||||
\(866\) | 10.3216 | 0.350743 | ||||||||
\(867\) | 3.67678 | 0.124870 | ||||||||
\(868\) | −25.8797 | −0.878414 | ||||||||
\(869\) | 15.1055 | 0.512419 | ||||||||
\(870\) | 0.883479 | 0.0299527 | ||||||||
\(871\) | −5.13706 | −0.174063 | ||||||||
\(872\) | −14.5587 | −0.493019 | ||||||||
\(873\) | −47.5257 | −1.60850 | ||||||||
\(874\) | −5.37508 | −0.181815 | ||||||||
\(875\) | 11.4318 | 0.386466 | ||||||||
\(876\) | 3.81336 | 0.128842 | ||||||||
\(877\) | −32.1630 | −1.08607 | −0.543034 | − | 0.839711i | \(-0.682725\pi\) | ||||
−0.543034 | + | 0.839711i | \(0.682725\pi\) | |||||||
\(878\) | −13.4776 | −0.454847 | ||||||||
\(879\) | −13.1160 | −0.442390 | ||||||||
\(880\) | −0.673421 | −0.0227010 | ||||||||
\(881\) | 11.8744 | 0.400059 | 0.200029 | − | 0.979790i | \(-0.435896\pi\) | ||||
0.200029 | + | 0.979790i | \(0.435896\pi\) | |||||||
\(882\) | 3.44539 | 0.116012 | ||||||||
\(883\) | 44.6036 | 1.50103 | 0.750515 | − | 0.660854i | \(-0.229806\pi\) | ||||
0.750515 | + | 0.660854i | \(0.229806\pi\) | |||||||
\(884\) | 3.74809 | 0.126062 | ||||||||
\(885\) | 0.0812483 | 0.00273113 | ||||||||
\(886\) | −18.8787 | −0.634243 | ||||||||
\(887\) | 18.9436 | 0.636064 | 0.318032 | − | 0.948080i | \(-0.396978\pi\) | ||||
0.318032 | + | 0.948080i | \(0.396978\pi\) | |||||||
\(888\) | 3.47885 | 0.116743 | ||||||||
\(889\) | 4.87354 | 0.163453 | ||||||||
\(890\) | 5.95855 | 0.199731 | ||||||||
\(891\) | 10.2543 | 0.343531 | ||||||||
\(892\) | −27.2023 | −0.910800 | ||||||||
\(893\) | −3.63993 | −0.121806 | ||||||||
\(894\) | −2.41174 | −0.0806606 | ||||||||
\(895\) | 1.34676 | 0.0450172 | ||||||||
\(896\) | 2.40385 | 0.0803069 | ||||||||
\(897\) | −4.52066 | −0.150941 | ||||||||
\(898\) | 2.22579 | 0.0742755 | ||||||||
\(899\) | −46.0982 | −1.53746 | ||||||||
\(900\) | 13.4336 | 0.447788 | ||||||||
\(901\) | −25.9516 | −0.864572 | ||||||||
\(902\) | −0.433950 | −0.0144489 | ||||||||
\(903\) | −4.48081 | −0.149112 | ||||||||
\(904\) | 13.2666 | 0.441240 | ||||||||
\(905\) | 4.63600 | 0.154106 | ||||||||
\(906\) | −6.36140 | −0.211343 | ||||||||
\(907\) | −9.60532 | −0.318939 | −0.159470 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159470 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(908\) | 18.8854 | 0.626735 | ||||||||
\(909\) | 23.0982 | 0.766119 | ||||||||
\(910\) | 1.52161 | 0.0504409 | ||||||||
\(911\) | −29.1899 | −0.967104 | −0.483552 | − | 0.875316i | \(-0.660654\pi\) | ||||
−0.483552 | + | 0.875316i | \(0.660654\pi\) | |||||||
\(912\) | −0.277201 | −0.00917905 | ||||||||
\(913\) | −13.9590 | −0.461975 | ||||||||
\(914\) | −26.8389 | −0.887752 | ||||||||
\(915\) | 1.75266 | 0.0579413 | ||||||||
\(916\) | 4.97064 | 0.164234 | ||||||||
\(917\) | −3.74111 | −0.123542 | ||||||||
\(918\) | −7.11122 | −0.234705 | ||||||||
\(919\) | −17.7538 | −0.585644 | −0.292822 | − | 0.956167i | \(-0.594594\pi\) | ||||
−0.292822 | + | 0.956167i | \(0.594594\pi\) | |||||||
\(920\) | 4.00086 | 0.131905 | ||||||||
\(921\) | −10.0948 | −0.332635 | ||||||||
\(922\) | −30.5674 | −1.00668 | ||||||||
\(923\) | −0.983525 | −0.0323731 | ||||||||
\(924\) | −1.40761 | −0.0463070 | ||||||||
\(925\) | 39.1168 | 1.28615 | ||||||||
\(926\) | 18.6703 | 0.613544 | ||||||||
\(927\) | 48.7409 | 1.60086 | ||||||||
\(928\) | 4.28186 | 0.140559 | ||||||||
\(929\) | −23.2601 | −0.763138 | −0.381569 | − | 0.924340i | \(-0.624616\pi\) | ||||
−0.381569 | + | 0.924340i | \(0.624616\pi\) | |||||||
\(930\) | −2.22135 | −0.0728408 | ||||||||
\(931\) | −0.799406 | −0.0261995 | ||||||||
\(932\) | −2.23009 | −0.0730490 | ||||||||
\(933\) | −0.0363406 | −0.00118974 | ||||||||
\(934\) | 32.9483 | 1.07810 | ||||||||
\(935\) | 1.94239 | 0.0635230 | ||||||||
\(936\) | 3.66521 | 0.119801 | ||||||||
\(937\) | 39.2108 | 1.28096 | 0.640481 | − | 0.767974i | \(-0.278735\pi\) | ||||
0.640481 | + | 0.767974i | \(0.278735\pi\) | |||||||
\(938\) | 9.50304 | 0.310285 | ||||||||
\(939\) | 8.69772 | 0.283839 | ||||||||
\(940\) | 2.70933 | 0.0883687 | ||||||||
\(941\) | −25.7206 | −0.838467 | −0.419233 | − | 0.907878i | \(-0.637701\pi\) | ||||
−0.419233 | + | 0.907878i | \(0.637701\pi\) | |||||||
\(942\) | −9.55457 | −0.311305 | ||||||||
\(943\) | 2.57814 | 0.0839558 | ||||||||
\(944\) | 0.393777 | 0.0128163 | ||||||||
\(945\) | −2.88694 | −0.0939122 | ||||||||
\(946\) | 6.08376 | 0.197800 | ||||||||
\(947\) | 33.9661 | 1.10375 | 0.551874 | − | 0.833927i | \(-0.313913\pi\) | ||||
0.551874 | + | 0.833927i | \(0.313913\pi\) | |||||||
\(948\) | −4.62821 | −0.150317 | ||||||||
\(949\) | 11.6988 | 0.379758 | ||||||||
\(950\) | −3.11690 | −0.101126 | ||||||||
\(951\) | 9.30590 | 0.301765 | ||||||||
\(952\) | −6.93358 | −0.224719 | ||||||||
\(953\) | −53.5320 | −1.73407 | −0.867035 | − | 0.498247i | \(-0.833977\pi\) | ||||
−0.867035 | + | 0.498247i | \(0.833977\pi\) | |||||||
\(954\) | −25.3777 | −0.821634 | ||||||||
\(955\) | 12.9502 | 0.419058 | ||||||||
\(956\) | −3.30765 | −0.106977 | ||||||||
\(957\) | −2.50731 | −0.0810498 | ||||||||
\(958\) | 20.0398 | 0.647457 | ||||||||
\(959\) | −43.2371 | −1.39620 | ||||||||
\(960\) | 0.206331 | 0.00665930 | ||||||||
\(961\) | 84.9056 | 2.73889 | ||||||||
\(962\) | 10.6726 | 0.344097 | ||||||||
\(963\) | 16.7084 | 0.538420 | ||||||||
\(964\) | −16.5056 | −0.531608 | ||||||||
\(965\) | −3.19453 | −0.102836 | ||||||||
\(966\) | 8.36277 | 0.269068 | ||||||||
\(967\) | 19.0347 | 0.612114 | 0.306057 | − | 0.952013i | \(-0.400990\pi\) | ||||
0.306057 | + | 0.952013i | \(0.400990\pi\) | |||||||
\(968\) | −9.08883 | −0.292126 | ||||||||
\(969\) | 0.799550 | 0.0256852 | ||||||||
\(970\) | −8.20779 | −0.263536 | ||||||||
\(971\) | −1.60381 | −0.0514686 | −0.0257343 | − | 0.999669i | \(-0.508192\pi\) | ||||
−0.0257343 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(972\) | −10.5381 | −0.338011 | ||||||||
\(973\) | −46.3628 | −1.48632 | ||||||||
\(974\) | −18.9345 | −0.606702 | ||||||||
\(975\) | −2.62144 | −0.0839533 | ||||||||
\(976\) | 8.49444 | 0.271900 | ||||||||
\(977\) | −50.1436 | −1.60424 | −0.802119 | − | 0.597165i | \(-0.796294\pi\) | ||||
−0.802119 | + | 0.597165i | \(0.796294\pi\) | |||||||
\(978\) | 2.83771 | 0.0907399 | ||||||||
\(979\) | −16.9104 | −0.540457 | ||||||||
\(980\) | 0.595027 | 0.0190074 | ||||||||
\(981\) | 41.0640 | 1.31107 | ||||||||
\(982\) | −1.35404 | −0.0432092 | ||||||||
\(983\) | −21.8946 | −0.698330 | −0.349165 | − | 0.937061i | \(-0.613535\pi\) | ||||
−0.349165 | + | 0.937061i | \(0.613535\pi\) | |||||||
\(984\) | 0.132959 | 0.00423857 | ||||||||
\(985\) | −1.93780 | −0.0617434 | ||||||||
\(986\) | −12.3504 | −0.393318 | ||||||||
\(987\) | 5.66316 | 0.180260 | ||||||||
\(988\) | −0.850408 | −0.0270551 | ||||||||
\(989\) | −36.1443 | −1.14932 | ||||||||
\(990\) | 1.89944 | 0.0603682 | ||||||||
\(991\) | −2.00108 | −0.0635665 | −0.0317832 | − | 0.999495i | \(-0.510119\pi\) | ||||
−0.0317832 | + | 0.999495i | \(0.510119\pi\) | |||||||
\(992\) | −10.7659 | −0.341819 | ||||||||
\(993\) | −1.07893 | −0.0342388 | ||||||||
\(994\) | 1.81942 | 0.0577086 | ||||||||
\(995\) | 6.35226 | 0.201380 | ||||||||
\(996\) | 4.27692 | 0.135519 | ||||||||
\(997\) | −51.3334 | −1.62575 | −0.812873 | − | 0.582441i | \(-0.802098\pi\) | ||||
−0.812873 | + | 0.582441i | \(0.802098\pi\) | |||||||
\(998\) | 38.2002 | 1.20921 | ||||||||
\(999\) | −20.2490 | −0.640649 |
(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 | 4034.2.a.a.1.16 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.a.1.16 | ✓ | 33 | 1.1 | even | 1 | trivial |