Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6021,2,Mod(1,6021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6021, 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("6021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6021 = 3^{3} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6021.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: | \(48.0779270570\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 20x^{8} + 139x^{6} - 384x^{4} + 331x^{2} - 63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.513295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.513295 | −0.362954 | −0.181477 | − | 0.983395i | \(-0.558088\pi\) | ||||
−0.181477 | + | 0.983395i | \(0.558088\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73653 | −0.868264 | ||||||||
\(5\) | −3.39171 | −1.51682 | −0.758408 | − | 0.651780i | \(-0.774023\pi\) | ||||
−0.758408 | + | 0.651780i | \(0.774023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.33725 | −0.883397 | −0.441699 | − | 0.897164i | \(-0.645624\pi\) | ||||
−0.441699 | + | 0.897164i | \(0.645624\pi\) | |||||||
\(8\) | 1.91794 | 0.678094 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.74095 | 0.550535 | ||||||||
\(11\) | 6.00138 | 1.80948 | 0.904741 | − | 0.425961i | \(-0.140064\pi\) | ||||
0.904741 | + | 0.425961i | \(0.140064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.529519 | −0.146862 | −0.0734311 | − | 0.997300i | \(-0.523395\pi\) | ||||
−0.0734311 | + | 0.997300i | \(0.523395\pi\) | |||||||
\(14\) | 1.19970 | 0.320633 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.48859 | 0.622147 | ||||||||
\(17\) | 3.47145 | 0.841950 | 0.420975 | − | 0.907072i | \(-0.361688\pi\) | ||||
0.420975 | + | 0.907072i | \(0.361688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.60072 | 0.367231 | 0.183615 | − | 0.982998i | \(-0.441220\pi\) | ||||
0.183615 | + | 0.982998i | \(0.441220\pi\) | |||||||
\(20\) | 5.88979 | 1.31700 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.08048 | −0.656759 | ||||||||
\(23\) | −4.78346 | −0.997420 | −0.498710 | − | 0.866769i | \(-0.666193\pi\) | ||||
−0.498710 | + | 0.866769i | \(0.666193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.50367 | 1.30073 | ||||||||
\(26\) | 0.271799 | 0.0533043 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.05870 | 0.767022 | ||||||||
\(29\) | 0.564435 | 0.104813 | 0.0524065 | − | 0.998626i | \(-0.483311\pi\) | ||||
0.0524065 | + | 0.998626i | \(0.483311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.16166 | −0.567851 | −0.283926 | − | 0.958846i | \(-0.591637\pi\) | ||||
−0.283926 | + | 0.958846i | \(0.591637\pi\) | |||||||
\(32\) | −5.11326 | −0.903905 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.78188 | −0.305589 | ||||||||
\(35\) | 7.92726 | 1.33995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.70734 | −1.10268 | −0.551340 | − | 0.834280i | \(-0.685883\pi\) | ||||
−0.551340 | + | 0.834280i | \(0.685883\pi\) | |||||||
\(38\) | −0.821642 | −0.133288 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.50509 | −1.02855 | ||||||||
\(41\) | 1.61963 | 0.252943 | 0.126472 | − | 0.991970i | \(-0.459635\pi\) | ||||
0.126472 | + | 0.991970i | \(0.459635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24461 | 1.10479 | 0.552396 | − | 0.833582i | \(-0.313713\pi\) | ||||
0.552396 | + | 0.833582i | \(0.313713\pi\) | |||||||
\(44\) | −10.4216 | −1.57111 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.45533 | 0.362018 | ||||||||
\(47\) | −3.63167 | −0.529733 | −0.264866 | − | 0.964285i | \(-0.585328\pi\) | ||||
−0.264866 | + | 0.964285i | \(0.585328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.53727 | −0.219609 | ||||||||
\(50\) | −3.33830 | −0.472107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.919525 | 0.127515 | ||||||||
\(53\) | −0.415335 | −0.0570507 | −0.0285253 | − | 0.999593i | \(-0.509081\pi\) | ||||
−0.0285253 | + | 0.999593i | \(0.509081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.3549 | −2.74465 | ||||||||
\(56\) | −4.48271 | −0.599027 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.289722 | −0.0380423 | ||||||||
\(59\) | −8.45889 | −1.10125 | −0.550627 | − | 0.834752i | \(-0.685611\pi\) | ||||
−0.550627 | + | 0.834752i | \(0.685611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.30107 | 0.550696 | 0.275348 | − | 0.961345i | \(-0.411207\pi\) | ||||
0.275348 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(62\) | 1.62286 | 0.206104 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.35256 | −0.294071 | ||||||||
\(65\) | 1.79597 | 0.222763 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.14056 | 0.872359 | 0.436179 | − | 0.899860i | \(-0.356331\pi\) | ||||
0.436179 | + | 0.899860i | \(0.356331\pi\) | |||||||
\(68\) | −6.02827 | −0.731035 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.06902 | −0.486341 | ||||||||
\(71\) | −9.02792 | −1.07142 | −0.535708 | − | 0.844403i | \(-0.679955\pi\) | ||||
−0.535708 | + | 0.844403i | \(0.679955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.46165 | 0.522196 | 0.261098 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261098 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(74\) | 3.44285 | 0.400223 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.77970 | −0.318853 | ||||||||
\(77\) | −14.0267 | −1.59849 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.33392 | 0.262586 | 0.131293 | − | 0.991344i | \(-0.458087\pi\) | ||||
0.131293 | + | 0.991344i | \(0.458087\pi\) | |||||||
\(80\) | −8.44056 | −0.943683 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.831346 | −0.0918069 | ||||||||
\(83\) | −1.10162 | −0.120919 | −0.0604595 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604595 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7741 | −1.27708 | ||||||||
\(86\) | −3.71862 | −0.400989 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.5103 | 1.22700 | ||||||||
\(89\) | 7.97816 | 0.845684 | 0.422842 | − | 0.906204i | \(-0.361033\pi\) | ||||
0.422842 | + | 0.906204i | \(0.361033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23762 | 0.129738 | ||||||||
\(92\) | 8.30661 | 0.866024 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.86412 | 0.192269 | ||||||||
\(95\) | −5.42917 | −0.557021 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.18700 | −0.932798 | −0.466399 | − | 0.884574i | \(-0.654449\pi\) | ||||
−0.466399 | + | 0.884574i | \(0.654449\pi\) | |||||||
\(98\) | 0.789071 | 0.0797082 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.2938 | −1.12938 | ||||||||
\(101\) | −14.4635 | −1.43917 | −0.719586 | − | 0.694403i | \(-0.755668\pi\) | ||||
−0.719586 | + | 0.694403i | \(0.755668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3653 | 1.31693 | 0.658463 | − | 0.752613i | \(-0.271207\pi\) | ||||
0.658463 | + | 0.752613i | \(0.271207\pi\) | |||||||
\(104\) | −1.01559 | −0.0995864 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.213189 | 0.0207068 | ||||||||
\(107\) | 1.80141 | 0.174149 | 0.0870745 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870745 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.60886 | −0.920362 | −0.460181 | − | 0.887825i | \(-0.652216\pi\) | ||||
−0.460181 | + | 0.887825i | \(0.652216\pi\) | |||||||
\(110\) | 10.4481 | 0.996184 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.81645 | −0.549603 | ||||||||
\(113\) | −4.85776 | −0.456980 | −0.228490 | − | 0.973546i | \(-0.573379\pi\) | ||||
−0.228490 | + | 0.973546i | \(0.573379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.2241 | 1.51290 | ||||||||
\(116\) | −0.980157 | −0.0910053 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.34190 | 0.399705 | ||||||||
\(119\) | −8.11364 | −0.743776 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0165 | 2.27423 | ||||||||
\(122\) | −2.20772 | −0.199877 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.49031 | 0.493045 | ||||||||
\(125\) | −5.09999 | −0.456157 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.03893 | 0.0921902 | 0.0460951 | − | 0.998937i | \(-0.485322\pi\) | ||||
0.0460951 | + | 0.998937i | \(0.485322\pi\) | |||||||
\(128\) | 11.4341 | 1.01064 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.921864 | −0.0808528 | ||||||||
\(131\) | −13.4193 | −1.17245 | −0.586226 | − | 0.810148i | \(-0.699387\pi\) | ||||
−0.586226 | + | 0.810148i | \(0.699387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.74128 | −0.324410 | ||||||||
\(134\) | −3.66521 | −0.316626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.65803 | 0.570922 | ||||||||
\(137\) | −22.4434 | −1.91747 | −0.958733 | − | 0.284307i | \(-0.908236\pi\) | ||||
−0.958733 | + | 0.284307i | \(0.908236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.185572 | −0.0157400 | −0.00787002 | − | 0.999969i | \(-0.502505\pi\) | ||||
−0.00787002 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(140\) | −13.7659 | −1.16343 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.63398 | 0.388875 | ||||||||
\(143\) | −3.17784 | −0.265745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.91440 | −0.158982 | ||||||||
\(146\) | −2.29014 | −0.189533 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.6475 | 0.957418 | ||||||||
\(149\) | 15.7053 | 1.28663 | 0.643314 | − | 0.765602i | \(-0.277559\pi\) | ||||
0.643314 | + | 0.765602i | \(0.277559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1211 | 0.823641 | 0.411820 | − | 0.911265i | \(-0.364893\pi\) | ||||
0.411820 | + | 0.911265i | \(0.364893\pi\) | |||||||
\(152\) | 3.07009 | 0.249017 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.19984 | 0.580179 | ||||||||
\(155\) | 10.7234 | 0.861326 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.84167 | 0.226790 | 0.113395 | − | 0.993550i | \(-0.463827\pi\) | ||||
0.113395 | + | 0.993550i | \(0.463827\pi\) | |||||||
\(158\) | −1.19799 | −0.0953069 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.3427 | 1.37106 | ||||||||
\(161\) | 11.1801 | 0.881118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.03794 | 0.237950 | 0.118975 | − | 0.992897i | \(-0.462039\pi\) | ||||
0.118975 | + | 0.992897i | \(0.462039\pi\) | |||||||
\(164\) | −2.81253 | −0.219622 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.565458 | 0.0438881 | ||||||||
\(167\) | 2.86625 | 0.221797 | 0.110899 | − | 0.993832i | \(-0.464627\pi\) | ||||
0.110899 | + | 0.993832i | \(0.464627\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7196 | −0.978432 | ||||||||
\(170\) | 6.04360 | 0.463523 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.5805 | −0.959252 | ||||||||
\(173\) | 1.37172 | 0.104290 | 0.0521451 | − | 0.998640i | \(-0.483394\pi\) | ||||
0.0521451 | + | 0.998640i | \(0.483394\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.2007 | −1.14906 | ||||||||
\(176\) | 14.9349 | 1.12576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.09515 | −0.306944 | ||||||||
\(179\) | −22.0927 | −1.65128 | −0.825642 | − | 0.564194i | \(-0.809187\pi\) | ||||
−0.825642 | + | 0.564194i | \(0.809187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.30691 | 0.691777 | 0.345889 | − | 0.938276i | \(-0.387577\pi\) | ||||
0.345889 | + | 0.938276i | \(0.387577\pi\) | |||||||
\(182\) | −0.635263 | −0.0470888 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.17439 | −0.676345 | ||||||||
\(185\) | 22.7493 | 1.67256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.8335 | 1.52349 | ||||||||
\(188\) | 6.30649 | 0.459948 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.78677 | 0.202173 | ||||||||
\(191\) | 3.18205 | 0.230245 | 0.115123 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115123 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7508 | 1.06178 | 0.530892 | − | 0.847439i | \(-0.321857\pi\) | ||||
0.530892 | + | 0.847439i | \(0.321857\pi\) | |||||||
\(194\) | 4.71564 | 0.338563 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.66951 | 0.190679 | ||||||||
\(197\) | −4.18236 | −0.297981 | −0.148991 | − | 0.988839i | \(-0.547602\pi\) | ||||
−0.148991 | + | 0.988839i | \(0.547602\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.83782 | 0.626497 | 0.313248 | − | 0.949671i | \(-0.398583\pi\) | ||||
0.313248 | + | 0.949671i | \(0.398583\pi\) | |||||||
\(200\) | 12.4736 | 0.882020 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.42404 | 0.522354 | ||||||||
\(203\) | −1.31923 | −0.0925915 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.49330 | −0.383669 | ||||||||
\(206\) | −6.86036 | −0.477984 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.31775 | −0.0913698 | ||||||||
\(209\) | 9.60653 | 0.664497 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.97482 | −0.204795 | −0.102397 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102397 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(212\) | 0.721241 | 0.0495351 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.924656 | −0.0632082 | ||||||||
\(215\) | −24.5716 | −1.67577 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.38959 | 0.501638 | ||||||||
\(218\) | 4.93218 | 0.334049 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 35.3469 | 2.38308 | ||||||||
\(221\) | −1.83820 | −0.123651 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 11.9510 | 0.798507 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.49347 | 0.165863 | ||||||||
\(227\) | 7.61794 | 0.505621 | 0.252810 | − | 0.967516i | \(-0.418645\pi\) | ||||
0.252810 | + | 0.967516i | \(0.418645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.83725 | −0.583982 | −0.291991 | − | 0.956421i | \(-0.594318\pi\) | ||||
−0.291991 | + | 0.956421i | \(0.594318\pi\) | |||||||
\(230\) | −8.32774 | −0.549115 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08255 | 0.0710731 | ||||||||
\(233\) | 13.3252 | 0.872964 | 0.436482 | − | 0.899713i | \(-0.356224\pi\) | ||||
0.436482 | + | 0.899713i | \(0.356224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3175 | 0.803508 | ||||||||
\(236\) | 14.6891 | 0.956179 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.16469 | 0.269957 | ||||||||
\(239\) | 14.0347 | 0.907830 | 0.453915 | − | 0.891045i | \(-0.350027\pi\) | ||||
0.453915 | + | 0.891045i | \(0.350027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0863 | 1.48712 | 0.743561 | − | 0.668668i | \(-0.233135\pi\) | ||||
0.743561 | + | 0.668668i | \(0.233135\pi\) | |||||||
\(242\) | −12.8408 | −0.825441 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.46894 | −0.478150 | ||||||||
\(245\) | 5.21395 | 0.333107 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.847612 | −0.0539323 | ||||||||
\(248\) | −6.06388 | −0.385057 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.61780 | 0.165564 | ||||||||
\(251\) | 17.9910 | 1.13558 | 0.567792 | − | 0.823172i | \(-0.307798\pi\) | ||||
0.567792 | + | 0.823172i | \(0.307798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.7073 | −1.80481 | ||||||||
\(254\) | −0.533278 | −0.0334608 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.16393 | −0.0727454 | ||||||||
\(257\) | 2.89339 | 0.180485 | 0.0902424 | − | 0.995920i | \(-0.471236\pi\) | ||||
0.0902424 | + | 0.995920i | \(0.471236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.6767 | 0.974105 | ||||||||
\(260\) | −3.11876 | −0.193417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.88807 | 0.425546 | ||||||||
\(263\) | −8.25888 | −0.509265 | −0.254632 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254632 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.40869 | 0.0865354 | ||||||||
\(266\) | 1.92038 | 0.117746 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.3998 | −0.757438 | ||||||||
\(269\) | 27.4532 | 1.67385 | 0.836927 | − | 0.547315i | \(-0.184350\pi\) | ||||
0.836927 | + | 0.547315i | \(0.184350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5102 | 1.30665 | 0.653325 | − | 0.757077i | \(-0.273373\pi\) | ||||
0.653325 | + | 0.757077i | \(0.273373\pi\) | |||||||
\(272\) | 8.63900 | 0.523816 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5201 | 0.695953 | ||||||||
\(275\) | 39.0309 | 2.35365 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7081 | 0.763556 | 0.381778 | − | 0.924254i | \(-0.375312\pi\) | ||||
0.381778 | + | 0.924254i | \(0.375312\pi\) | |||||||
\(278\) | 0.0952533 | 0.00571292 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.2040 | 0.908614 | ||||||||
\(281\) | 3.18529 | 0.190018 | 0.0950091 | − | 0.995476i | \(-0.469712\pi\) | ||||
0.0950091 | + | 0.995476i | \(0.469712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8124 | −1.17773 | −0.588864 | − | 0.808232i | \(-0.700425\pi\) | ||||
−0.588864 | + | 0.808232i | \(0.700425\pi\) | |||||||
\(284\) | 15.6772 | 0.930273 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.63117 | 0.0964531 | ||||||||
\(287\) | −3.78547 | −0.223449 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.94905 | −0.291120 | ||||||||
\(290\) | 0.982650 | 0.0577032 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.74778 | −0.453404 | ||||||||
\(293\) | −16.4181 | −0.959156 | −0.479578 | − | 0.877499i | \(-0.659210\pi\) | ||||
−0.479578 | + | 0.877499i | \(0.659210\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.6901 | 1.67040 | ||||||||
\(296\) | −12.8643 | −0.747722 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.06145 | −0.466988 | ||||||||
\(299\) | 2.53293 | 0.146483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.9325 | −0.975971 | ||||||||
\(302\) | −5.19509 | −0.298944 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.98353 | 0.228471 | ||||||||
\(305\) | −14.5880 | −0.835305 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.61879 | 0.320681 | 0.160341 | − | 0.987062i | \(-0.448741\pi\) | ||||
0.160341 | + | 0.987062i | \(0.448741\pi\) | |||||||
\(308\) | 24.3578 | 1.38791 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.50428 | −0.312622 | ||||||||
\(311\) | 12.9632 | 0.735077 | 0.367539 | − | 0.930008i | \(-0.380201\pi\) | ||||
0.367539 | + | 0.930008i | \(0.380201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.5913 | 1.72912 | 0.864561 | − | 0.502528i | \(-0.167597\pi\) | ||||
0.864561 | + | 0.502528i | \(0.167597\pi\) | |||||||
\(314\) | −1.45861 | −0.0823144 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.05292 | −0.227994 | ||||||||
\(317\) | 0.145803 | 0.00818910 | 0.00409455 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409455 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.38739 | 0.189657 | ||||||||
\(320\) | 7.97921 | 0.446051 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.73871 | −0.319806 | ||||||||
\(323\) | 5.55682 | 0.309190 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.44382 | −0.191028 | ||||||||
\(326\) | −1.55936 | −0.0863649 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.10635 | 0.171519 | ||||||||
\(329\) | 8.48811 | 0.467964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.06165 | 0.168284 | 0.0841419 | − | 0.996454i | \(-0.473185\pi\) | ||||
0.0841419 | + | 0.996454i | \(0.473185\pi\) | |||||||
\(332\) | 1.91300 | 0.104990 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.47123 | −0.0805022 | ||||||||
\(335\) | −24.2187 | −1.32321 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.7483 | −1.07576 | −0.537879 | − | 0.843022i | \(-0.680774\pi\) | ||||
−0.537879 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(338\) | 6.52891 | 0.355126 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.4461 | 1.10885 | ||||||||
\(341\) | −18.9743 | −1.02752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9537 | 1.07740 | ||||||||
\(344\) | 13.8947 | 0.749154 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.704098 | −0.0378526 | ||||||||
\(347\) | −28.1298 | −1.51009 | −0.755043 | − | 0.655675i | \(-0.772384\pi\) | ||||
−0.755043 | + | 0.655675i | \(0.772384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0056 | 1.49911 | 0.749553 | − | 0.661944i | \(-0.230268\pi\) | ||||
0.749553 | + | 0.661944i | \(0.230268\pi\) | |||||||
\(350\) | 7.80243 | 0.417058 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.6866 | −1.63560 | ||||||||
\(353\) | 25.9135 | 1.37923 | 0.689617 | − | 0.724174i | \(-0.257779\pi\) | ||||
0.689617 | + | 0.724174i | \(0.257779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.6200 | 1.62514 | ||||||||
\(356\) | −13.8543 | −0.734277 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3401 | 0.599341 | ||||||||
\(359\) | 7.00993 | 0.369970 | 0.184985 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184985 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4377 | −0.865142 | ||||||||
\(362\) | −4.77719 | −0.251084 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.14916 | −0.112647 | ||||||||
\(365\) | −15.1326 | −0.792076 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.8727 | −1.14174 | −0.570872 | − | 0.821039i | \(-0.693395\pi\) | ||||
−0.570872 | + | 0.821039i | \(0.693395\pi\) | |||||||
\(368\) | −11.9041 | −0.620542 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.6771 | −0.607064 | ||||||||
\(371\) | 0.970742 | 0.0503984 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.41439 | −0.0732345 | −0.0366173 | − | 0.999329i | \(-0.511658\pi\) | ||||
−0.0366173 | + | 0.999329i | \(0.511658\pi\) | |||||||
\(374\) | −10.6937 | −0.552959 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.96532 | −0.359209 | ||||||||
\(377\) | −0.298879 | −0.0153931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.4270 | 1.51156 | 0.755782 | − | 0.654823i | \(-0.227257\pi\) | ||||
0.755782 | + | 0.654823i | \(0.227257\pi\) | |||||||
\(380\) | 9.42791 | 0.483642 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.63333 | −0.0835684 | ||||||||
\(383\) | −8.41983 | −0.430233 | −0.215117 | − | 0.976588i | \(-0.569013\pi\) | ||||
−0.215117 | + | 0.976588i | \(0.569013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47.5745 | 2.42462 | ||||||||
\(386\) | −7.57150 | −0.385379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.9535 | 0.809915 | ||||||||
\(389\) | 15.0428 | 0.762700 | 0.381350 | − | 0.924431i | \(-0.375459\pi\) | ||||
0.381350 | + | 0.924431i | \(0.375459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.6055 | −0.839778 | ||||||||
\(392\) | −2.94839 | −0.148916 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.14679 | 0.108154 | ||||||||
\(395\) | −7.91597 | −0.398295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2828 | 1.51985 | 0.759925 | − | 0.650011i | \(-0.225236\pi\) | ||||
0.759925 | + | 0.650011i | \(0.225236\pi\) | |||||||
\(398\) | −4.53641 | −0.227390 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.1849 | 0.809247 | ||||||||
\(401\) | 21.9421 | 1.09574 | 0.547869 | − | 0.836564i | \(-0.315439\pi\) | ||||
0.547869 | + | 0.836564i | \(0.315439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.67416 | 0.0833958 | ||||||||
\(404\) | 25.1163 | 1.24958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.677152 | 0.0336065 | ||||||||
\(407\) | −40.2533 | −1.99528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.4944 | 1.90343 | 0.951713 | − | 0.306989i | \(-0.0993215\pi\) | ||||
0.951713 | + | 0.306989i | \(0.0993215\pi\) | |||||||
\(410\) | 2.81968 | 0.139254 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −23.2093 | −1.14344 | ||||||||
\(413\) | 19.7705 | 0.972844 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.73639 | 0.183412 | ||||||||
\(416\) | 2.70757 | 0.132750 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.93098 | −0.241182 | ||||||||
\(419\) | −9.68878 | −0.473328 | −0.236664 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236664 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0991 | −1.36946 | −0.684732 | − | 0.728795i | \(-0.740081\pi\) | ||||
−0.684732 | + | 0.728795i | \(0.740081\pi\) | |||||||
\(422\) | 1.52696 | 0.0743312 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.796588 | −0.0386857 | ||||||||
\(425\) | 22.5771 | 1.09515 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0527 | −0.486483 | ||||||||
\(428\) | −3.12820 | −0.151207 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.6125 | 0.608227 | ||||||||
\(431\) | 7.94768 | 0.382826 | 0.191413 | − | 0.981510i | \(-0.438693\pi\) | ||||
0.191413 | + | 0.981510i | \(0.438693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.8345 | −0.809012 | −0.404506 | − | 0.914535i | \(-0.632557\pi\) | ||||
−0.404506 | + | 0.914535i | \(0.632557\pi\) | |||||||
\(434\) | −3.79304 | −0.182072 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.6861 | 0.799118 | ||||||||
\(437\) | −7.65698 | −0.366283 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.63085 | −0.0778362 | −0.0389181 | − | 0.999242i | \(-0.512391\pi\) | ||||
−0.0389181 | + | 0.999242i | \(0.512391\pi\) | |||||||
\(440\) | −39.0395 | −1.86113 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.943538 | 0.0448795 | ||||||||
\(443\) | −8.13294 | −0.386408 | −0.193204 | − | 0.981159i | \(-0.561888\pi\) | ||||
−0.193204 | + | 0.981159i | \(0.561888\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0596 | −1.28275 | ||||||||
\(446\) | 0.513295 | 0.0243052 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.49853 | 0.259781 | ||||||||
\(449\) | −8.35560 | −0.394325 | −0.197163 | − | 0.980371i | \(-0.563173\pi\) | ||||
−0.197163 | + | 0.980371i | \(0.563173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.71999 | 0.457697 | ||||||||
\(452\) | 8.43564 | 0.396779 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.91025 | −0.183517 | ||||||||
\(455\) | −4.19764 | −0.196788 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7900 | 1.06607 | 0.533036 | − | 0.846093i | \(-0.321051\pi\) | ||||
0.533036 | + | 0.846093i | \(0.321051\pi\) | |||||||
\(458\) | 4.53612 | 0.211959 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.1736 | −1.31360 | ||||||||
\(461\) | −34.1572 | −1.59086 | −0.795430 | − | 0.606045i | \(-0.792755\pi\) | ||||
−0.795430 | + | 0.606045i | \(0.792755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.71082 | 0.172456 | 0.0862281 | − | 0.996275i | \(-0.472519\pi\) | ||||
0.0862281 | + | 0.996275i | \(0.472519\pi\) | |||||||
\(464\) | 1.40465 | 0.0652091 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.83976 | −0.316846 | ||||||||
\(467\) | 14.9207 | 0.690446 | 0.345223 | − | 0.938521i | \(-0.387803\pi\) | ||||
0.345223 | + | 0.938521i | \(0.387803\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.6893 | −0.770639 | ||||||||
\(470\) | −6.32253 | −0.291637 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.2236 | −0.746754 | ||||||||
\(473\) | 43.4776 | 1.99910 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.4106 | 0.477669 | ||||||||
\(476\) | 14.0896 | 0.645794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.20395 | −0.329501 | ||||||||
\(479\) | −29.0217 | −1.32604 | −0.663018 | − | 0.748603i | \(-0.730725\pi\) | ||||
−0.663018 | + | 0.748603i | \(0.730725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.55167 | 0.161942 | ||||||||
\(482\) | −11.8501 | −0.539757 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −43.4419 | −1.97463 | ||||||||
\(485\) | 31.1596 | 1.41488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8875 | −0.765246 | −0.382623 | − | 0.923905i | \(-0.624979\pi\) | ||||
−0.382623 | + | 0.923905i | \(0.624979\pi\) | |||||||
\(488\) | 8.24920 | 0.373424 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.67630 | −0.120903 | ||||||||
\(491\) | 25.5037 | 1.15097 | 0.575484 | − | 0.817813i | \(-0.304814\pi\) | ||||
0.575484 | + | 0.817813i | \(0.304814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.95941 | 0.0882473 | ||||||||
\(494\) | 0.435075 | 0.0195750 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.86807 | −0.353287 | ||||||||
\(497\) | 21.1005 | 0.946486 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0031 | −0.537335 | −0.268667 | − | 0.963233i | \(-0.586583\pi\) | ||||
−0.268667 | + | 0.963233i | \(0.586583\pi\) | |||||||
\(500\) | 8.85628 | 0.396065 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.23471 | −0.412165 | ||||||||
\(503\) | −35.0040 | −1.56075 | −0.780375 | − | 0.625312i | \(-0.784972\pi\) | ||||
−0.780375 | + | 0.625312i | \(0.784972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.0559 | 2.18296 | ||||||||
\(506\) | 14.7353 | 0.655065 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.80413 | −0.0800455 | ||||||||
\(509\) | 35.9815 | 1.59485 | 0.797426 | − | 0.603417i | \(-0.206195\pi\) | ||||
0.797426 | + | 0.603417i | \(0.206195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4280 | −0.461307 | ||||||||
\(512\) | −22.2707 | −0.984236 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.48516 | −0.0655077 | ||||||||
\(515\) | −45.3313 | −1.99754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.7950 | −0.958542 | ||||||||
\(518\) | −8.04679 | −0.353556 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.44457 | 0.151054 | ||||||||
\(521\) | −21.9220 | −0.960418 | −0.480209 | − | 0.877154i | \(-0.659439\pi\) | ||||
−0.480209 | + | 0.877154i | \(0.659439\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.8296 | 1.21690 | 0.608451 | − | 0.793592i | \(-0.291791\pi\) | ||||
0.608451 | + | 0.793592i | \(0.291791\pi\) | |||||||
\(524\) | 23.3030 | 1.01800 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.23924 | 0.184840 | ||||||||
\(527\) | −10.9755 | −0.478102 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.118510 | −0.00515259 | ||||||||
\(530\) | −0.723076 | −0.0314084 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.49685 | 0.281674 | ||||||||
\(533\) | −0.857624 | −0.0371478 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.10986 | −0.264152 | ||||||||
\(536\) | 13.6952 | 0.591542 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.0916 | −0.607532 | ||||||||
\(539\) | −9.22571 | −0.397379 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2815 | 0.785982 | 0.392991 | − | 0.919542i | \(-0.371440\pi\) | ||||
0.392991 | + | 0.919542i | \(0.371440\pi\) | |||||||
\(542\) | −11.0411 | −0.474254 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.7504 | −0.761043 | ||||||||
\(545\) | 32.5904 | 1.39602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.5937 | −1.30809 | −0.654047 | − | 0.756454i | \(-0.726930\pi\) | ||||
−0.654047 | + | 0.756454i | \(0.726930\pi\) | |||||||
\(548\) | 38.9735 | 1.66487 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.0344 | −0.854269 | ||||||||
\(551\) | 0.903503 | 0.0384905 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.45495 | −0.231968 | ||||||||
\(554\) | −6.52300 | −0.277136 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.322252 | 0.0136665 | ||||||||
\(557\) | −41.3981 | −1.75409 | −0.877046 | − | 0.480406i | \(-0.840489\pi\) | ||||
−0.877046 | + | 0.480406i | \(0.840489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.83616 | −0.162252 | ||||||||
\(560\) | 19.7277 | 0.833647 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.63499 | −0.0689679 | ||||||||
\(563\) | −32.0399 | −1.35032 | −0.675161 | − | 0.737670i | \(-0.735926\pi\) | ||||
−0.675161 | + | 0.737670i | \(0.735926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.4761 | 0.693155 | ||||||||
\(566\) | 10.1696 | 0.427461 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.3150 | −0.726522 | ||||||||
\(569\) | −23.8638 | −1.00042 | −0.500211 | − | 0.865903i | \(-0.666744\pi\) | ||||
−0.500211 | + | 0.865903i | \(0.666744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0209 | 0.503058 | 0.251529 | − | 0.967850i | \(-0.419067\pi\) | ||||
0.251529 | + | 0.967850i | \(0.419067\pi\) | |||||||
\(572\) | 5.51841 | 0.230736 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.94306 | 0.0811019 | ||||||||
\(575\) | −31.1100 | −1.29738 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.61611 | 0.0672795 | 0.0336398 | − | 0.999434i | \(-0.489290\pi\) | ||||
0.0336398 | + | 0.999434i | \(0.489290\pi\) | |||||||
\(578\) | 2.54032 | 0.105663 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.32441 | 0.138038 | ||||||||
\(581\) | 2.57477 | 0.106820 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.49258 | −0.103232 | ||||||||
\(584\) | 8.55718 | 0.354098 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.42733 | 0.348130 | ||||||||
\(587\) | 8.53142 | 0.352130 | 0.176065 | − | 0.984379i | \(-0.443663\pi\) | ||||
0.176065 | + | 0.984379i | \(0.443663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.06094 | −0.208532 | ||||||||
\(590\) | −14.7265 | −0.606279 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.6918 | −0.686029 | ||||||||
\(593\) | 6.80889 | 0.279608 | 0.139804 | − | 0.990179i | \(-0.455353\pi\) | ||||
0.139804 | + | 0.990179i | \(0.455353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.5191 | 1.12817 | ||||||||
\(596\) | −27.2727 | −1.11713 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.30014 | −0.0531667 | ||||||||
\(599\) | 3.33538 | 0.136280 | 0.0681400 | − | 0.997676i | \(-0.478294\pi\) | ||||
0.0681400 | + | 0.997676i | \(0.478294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.4736 | 1.81412 | 0.907059 | − | 0.421004i | \(-0.138322\pi\) | ||||
0.907059 | + | 0.421004i | \(0.138322\pi\) | |||||||
\(602\) | 8.69135 | 0.354233 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.5755 | −0.715138 | ||||||||
\(605\) | −84.8486 | −3.44959 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.74043 | −0.232997 | −0.116498 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116498 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(608\) | −8.18490 | −0.331942 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.48793 | 0.303177 | ||||||||
\(611\) | 1.92304 | 0.0777977 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.3585 | −1.46851 | −0.734253 | − | 0.678875i | \(-0.762468\pi\) | ||||
−0.734253 | + | 0.678875i | \(0.762468\pi\) | |||||||
\(614\) | −2.88410 | −0.116393 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.9024 | −1.08393 | ||||||||
\(617\) | 14.2699 | 0.574486 | 0.287243 | − | 0.957858i | \(-0.407261\pi\) | ||||
0.287243 | + | 0.957858i | \(0.407261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1753 | 1.33343 | 0.666713 | − | 0.745314i | \(-0.267701\pi\) | ||||
0.666713 | + | 0.745314i | \(0.267701\pi\) | |||||||
\(620\) | −18.6215 | −0.747859 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.65396 | −0.266799 | ||||||||
\(623\) | −18.6470 | −0.747074 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.2207 | −0.608826 | ||||||||
\(626\) | −15.7024 | −0.627592 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.93464 | −0.196914 | ||||||||
\(629\) | −23.2842 | −0.928402 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7317 | 0.865124 | 0.432562 | − | 0.901604i | \(-0.357610\pi\) | ||||
0.432562 | + | 0.901604i | \(0.357610\pi\) | |||||||
\(632\) | 4.47632 | 0.178058 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.0748398 | −0.00297227 | ||||||||
\(635\) | −3.52375 | −0.139836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.814012 | 0.0322523 | ||||||||
\(638\) | −1.73873 | −0.0688369 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −38.7810 | −1.53296 | ||||||||
\(641\) | −23.6805 | −0.935322 | −0.467661 | − | 0.883908i | \(-0.654903\pi\) | ||||
−0.467661 | + | 0.883908i | \(0.654903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.6117 | 0.970591 | 0.485296 | − | 0.874350i | \(-0.338712\pi\) | ||||
0.485296 | + | 0.874350i | \(0.338712\pi\) | |||||||
\(644\) | −19.4146 | −0.765043 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.85229 | −0.112222 | ||||||||
\(647\) | −0.956553 | −0.0376060 | −0.0188030 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188030 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.7649 | −1.99270 | ||||||||
\(650\) | 1.76769 | 0.0693346 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.27547 | −0.206603 | ||||||||
\(653\) | 20.9835 | 0.821150 | 0.410575 | − | 0.911827i | \(-0.365328\pi\) | ||||
0.410575 | + | 0.911827i | \(0.365328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.5144 | 1.77839 | ||||||||
\(656\) | 4.03058 | 0.157368 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.35690 | −0.169850 | ||||||||
\(659\) | −10.8250 | −0.421681 | −0.210841 | − | 0.977520i | \(-0.567620\pi\) | ||||
−0.210841 | + | 0.977520i | \(0.567620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.544481 | 0.0211779 | 0.0105889 | − | 0.999944i | \(-0.496629\pi\) | ||||
0.0105889 | + | 0.999944i | \(0.496629\pi\) | |||||||
\(662\) | −1.57153 | −0.0610793 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.11285 | −0.0819945 | ||||||||
\(665\) | 12.6893 | 0.492071 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.69995 | −0.104543 | ||||||||
\(668\) | −4.97733 | −0.192579 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.4313 | 0.480264 | ||||||||
\(671\) | 25.8124 | 0.996475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.5504 | 0.637971 | 0.318985 | − | 0.947760i | \(-0.396658\pi\) | ||||
0.318985 | + | 0.947760i | \(0.396658\pi\) | |||||||
\(674\) | 10.1367 | 0.390451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.0880 | 0.849537 | ||||||||
\(677\) | −0.0522237 | −0.00200712 | −0.00100356 | − | 0.999999i | \(-0.500319\pi\) | ||||
−0.00100356 | + | 0.999999i | \(0.500319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.4723 | 0.824031 | ||||||||
\(680\) | −22.5821 | −0.865983 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.73942 | 0.372942 | ||||||||
\(683\) | −5.32927 | −0.203919 | −0.101959 | − | 0.994789i | \(-0.532511\pi\) | ||||
−0.101959 | + | 0.994789i | \(0.532511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 76.1213 | 2.90845 | ||||||||
\(686\) | −10.2421 | −0.391047 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.0288 | 0.687343 | ||||||||
\(689\) | 0.219928 | 0.00837858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4960 | 0.437327 | 0.218663 | − | 0.975800i | \(-0.429830\pi\) | ||||
0.218663 | + | 0.975800i | \(0.429830\pi\) | |||||||
\(692\) | −2.38204 | −0.0905514 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4389 | 0.548093 | ||||||||
\(695\) | 0.629407 | 0.0238748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.62245 | 0.212966 | ||||||||
\(698\) | −14.3751 | −0.544107 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26.3964 | 0.997691 | ||||||||
\(701\) | 15.6919 | 0.592673 | 0.296337 | − | 0.955084i | \(-0.404235\pi\) | ||||
0.296337 | + | 0.955084i | \(0.404235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7366 | −0.404938 | ||||||||
\(704\) | −14.1186 | −0.532116 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.3012 | −0.500599 | ||||||||
\(707\) | 33.8048 | 1.27136 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.1458 | 1.43259 | 0.716297 | − | 0.697795i | \(-0.245836\pi\) | ||||
0.716297 | + | 0.697795i | \(0.245836\pi\) | |||||||
\(710\) | −15.7171 | −0.589852 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.3016 | 0.573453 | ||||||||
\(713\) | 15.1237 | 0.566386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7783 | 0.403086 | ||||||||
\(716\) | 38.3646 | 1.43375 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.59816 | −0.134282 | ||||||||
\(719\) | 15.4177 | 0.574983 | 0.287491 | − | 0.957783i | \(-0.407179\pi\) | ||||
0.287491 | + | 0.957783i | \(0.407179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.2381 | −1.16337 | ||||||||
\(722\) | 8.43738 | 0.314007 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.1617 | −0.600646 | ||||||||
\(725\) | 3.67090 | 0.136334 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.3341 | −1.16212 | −0.581058 | − | 0.813862i | \(-0.697361\pi\) | ||||
−0.581058 | + | 0.813862i | \(0.697361\pi\) | |||||||
\(728\) | 2.37368 | 0.0879744 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.76748 | 0.287487 | ||||||||
\(731\) | 25.1493 | 0.930180 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.2871 | −0.601576 | −0.300788 | − | 0.953691i | \(-0.597250\pi\) | ||||
−0.300788 | + | 0.953691i | \(0.597250\pi\) | |||||||
\(734\) | 11.2271 | 0.414401 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.4591 | 0.901574 | ||||||||
\(737\) | 42.8532 | 1.57852 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.9825 | −1.02935 | −0.514677 | − | 0.857384i | \(-0.672088\pi\) | ||||
−0.514677 | + | 0.857384i | \(0.672088\pi\) | |||||||
\(740\) | −39.5049 | −1.45223 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.498277 | −0.0182923 | ||||||||
\(743\) | −19.8961 | −0.729916 | −0.364958 | − | 0.931024i | \(-0.618917\pi\) | ||||
−0.364958 | + | 0.931024i | \(0.618917\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.2678 | −1.95158 | ||||||||
\(746\) | 0.726001 | 0.0265808 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.1779 | −1.32279 | ||||||||
\(749\) | −4.21035 | −0.153843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2940 | 1.47035 | 0.735175 | − | 0.677878i | \(-0.237100\pi\) | ||||
0.735175 | + | 0.677878i | \(0.237100\pi\) | |||||||
\(752\) | −9.03772 | −0.329572 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.153413 | 0.00558698 | ||||||||
\(755\) | −34.3277 | −1.24931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.8159 | −1.73790 | −0.868949 | − | 0.494901i | \(-0.835204\pi\) | ||||
−0.868949 | + | 0.494901i | \(0.835204\pi\) | |||||||
\(758\) | −15.1047 | −0.548629 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.4128 | −0.377713 | ||||||||
\(761\) | 14.3712 | 0.520956 | 0.260478 | − | 0.965480i | \(-0.416120\pi\) | ||||
0.260478 | + | 0.965480i | \(0.416120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.4583 | 0.813045 | ||||||||
\(764\) | −5.52572 | −0.199914 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.32186 | 0.156155 | ||||||||
\(767\) | 4.47914 | 0.161732 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.40950 | 0.231132 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(770\) | −24.4197 | −0.880026 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.6152 | −0.921910 | ||||||||
\(773\) | −15.5035 | −0.557624 | −0.278812 | − | 0.960346i | \(-0.589941\pi\) | ||||
−0.278812 | + | 0.960346i | \(0.589941\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.5624 | −0.738623 | ||||||||
\(776\) | −17.6201 | −0.632525 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.72139 | −0.276825 | ||||||||
\(779\) | 2.59257 | 0.0928885 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1799 | −1.93871 | ||||||||
\(782\) | 8.52354 | 0.304801 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.82562 | −0.136629 | ||||||||
\(785\) | −9.63810 | −0.343999 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −55.2404 | −1.96911 | −0.984554 | − | 0.175082i | \(-0.943981\pi\) | ||||
−0.984554 | + | 0.175082i | \(0.943981\pi\) | |||||||
\(788\) | 7.26279 | 0.258726 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.06322 | 0.144563 | ||||||||
\(791\) | 11.3538 | 0.403695 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.27750 | −0.0808764 | ||||||||
\(794\) | −15.5440 | −0.551636 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.3471 | −0.543965 | ||||||||
\(797\) | −13.1924 | −0.467299 | −0.233650 | − | 0.972321i | \(-0.575067\pi\) | ||||
−0.233650 | + | 0.972321i | \(0.575067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6071 | −0.446008 | ||||||||
\(800\) | −33.2549 | −1.17574 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.2628 | −0.397703 | ||||||||
\(803\) | 26.7760 | 0.944905 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.9197 | −1.33650 | ||||||||
\(806\) | −0.859338 | −0.0302689 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.7401 | −0.975895 | ||||||||
\(809\) | 14.0518 | 0.494035 | 0.247017 | − | 0.969011i | \(-0.420550\pi\) | ||||
0.247017 | + | 0.969011i | \(0.420550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.7981 | −1.92422 | −0.962111 | − | 0.272657i | \(-0.912097\pi\) | ||||
−0.962111 | + | 0.272657i | \(0.912097\pi\) | |||||||
\(812\) | 2.29087 | 0.0803939 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.6618 | 0.724196 | ||||||||
\(815\) | −10.3038 | −0.360926 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5966 | 0.405714 | ||||||||
\(818\) | −19.7590 | −0.690857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.53927 | 0.333126 | ||||||||
\(821\) | −9.96717 | −0.347857 | −0.173928 | − | 0.984758i | \(-0.555646\pi\) | ||||
−0.173928 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.2593 | 1.64735 | 0.823677 | − | 0.567059i | \(-0.191919\pi\) | ||||
0.823677 | + | 0.567059i | \(0.191919\pi\) | |||||||
\(824\) | 25.6339 | 0.893000 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.1481 | −0.353098 | ||||||||
\(827\) | 2.83027 | 0.0984181 | 0.0492090 | − | 0.998789i | \(-0.484330\pi\) | ||||
0.0492090 | + | 0.998789i | \(0.484330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.814307 | 0.0282820 | 0.0141410 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141410 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(830\) | −1.91787 | −0.0665702 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.24573 | 0.0431878 | ||||||||
\(833\) | −5.33654 | −0.184900 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.72148 | −0.336426 | ||||||||
\(836\) | −16.6820 | −0.576959 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.97320 | 0.171796 | ||||||||
\(839\) | 32.6993 | 1.12891 | 0.564453 | − | 0.825465i | \(-0.309087\pi\) | ||||
0.564453 | + | 0.825465i | \(0.309087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6814 | −0.989014 | ||||||||
\(842\) | 14.4231 | 0.497053 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.16585 | 0.177816 | ||||||||
\(845\) | 43.1412 | 1.48410 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −58.4698 | −2.00905 | ||||||||
\(848\) | −1.03360 | −0.0354939 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.5887 | −0.397490 | ||||||||
\(851\) | 32.0843 | 1.09984 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6427 | 0.398638 | 0.199319 | − | 0.979935i | \(-0.436127\pi\) | ||||
0.199319 | + | 0.979935i | \(0.436127\pi\) | |||||||
\(854\) | 5.15999 | 0.176571 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.45500 | 0.118090 | ||||||||
\(857\) | 53.6791 | 1.83364 | 0.916822 | − | 0.399295i | \(-0.130745\pi\) | ||||
0.916822 | + | 0.399295i | \(0.130745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9481 | 1.73833 | 0.869164 | − | 0.494524i | \(-0.164658\pi\) | ||||
0.869164 | + | 0.494524i | \(0.164658\pi\) | |||||||
\(860\) | 42.6693 | 1.45501 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.07950 | −0.138948 | ||||||||
\(863\) | 28.8475 | 0.981979 | 0.490990 | − | 0.871165i | \(-0.336635\pi\) | ||||
0.490990 | + | 0.871165i | \(0.336635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.65248 | −0.158189 | ||||||||
\(866\) | 8.64104 | 0.293634 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8322 | −0.435554 | ||||||||
\(869\) | 14.0067 | 0.475146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.78106 | −0.128116 | ||||||||
\(872\) | −18.4292 | −0.624093 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.93029 | 0.132944 | ||||||||
\(875\) | 11.9199 | 0.402968 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6543 | 0.697445 | 0.348722 | − | 0.937226i | \(-0.386616\pi\) | ||||
0.348722 | + | 0.937226i | \(0.386616\pi\) | |||||||
\(878\) | 0.837106 | 0.0282510 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −50.6549 | −1.70758 | ||||||||
\(881\) | 42.9046 | 1.44549 | 0.722746 | − | 0.691114i | \(-0.242880\pi\) | ||||
0.722746 | + | 0.691114i | \(0.242880\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8240 | 0.431561 | 0.215781 | − | 0.976442i | \(-0.430770\pi\) | ||||
0.215781 | + | 0.976442i | \(0.430770\pi\) | |||||||
\(884\) | 3.19208 | 0.107361 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.17460 | 0.140248 | ||||||||
\(887\) | −23.4296 | −0.786689 | −0.393345 | − | 0.919391i | \(-0.628682\pi\) | ||||
−0.393345 | + | 0.919391i | \(0.628682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.42824 | −0.0814406 | ||||||||
\(890\) | 13.8895 | 0.465579 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.73653 | 0.0581433 | ||||||||
\(893\) | −5.81328 | −0.194534 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74.9319 | 2.50470 | ||||||||
\(896\) | −26.7243 | −0.892796 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.28889 | 0.143122 | ||||||||
\(899\) | −1.78455 | −0.0595182 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.44181 | −0.0480338 | ||||||||
\(902\) | −4.98922 | −0.166123 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.31690 | −0.309876 | ||||||||
\(905\) | −31.5663 | −1.04930 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.1109 | 1.96275 | 0.981373 | − | 0.192113i | \(-0.0615340\pi\) | ||||
0.981373 | + | 0.192113i | \(0.0615340\pi\) | |||||||
\(908\) | −13.2288 | −0.439012 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.15462 | 0.0714251 | ||||||||
\(911\) | 12.0703 | 0.399907 | 0.199954 | − | 0.979805i | \(-0.435921\pi\) | ||||
0.199954 | + | 0.979805i | \(0.435921\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.61126 | −0.218801 | ||||||||
\(914\) | −11.6980 | −0.386935 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.3461 | 0.507051 | ||||||||
\(917\) | 31.3643 | 1.03574 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.6172 | 0.614125 | 0.307062 | − | 0.951689i | \(-0.400654\pi\) | ||||
0.307062 | + | 0.951689i | \(0.400654\pi\) | |||||||
\(920\) | 31.1168 | 1.02589 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.5327 | 0.577409 | ||||||||
\(923\) | 4.78045 | 0.157351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.6223 | −1.43429 | ||||||||
\(926\) | −1.90474 | −0.0625937 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.88610 | −0.0947410 | ||||||||
\(929\) | 17.7819 | 0.583406 | 0.291703 | − | 0.956509i | \(-0.405778\pi\) | ||||
0.291703 | + | 0.956509i | \(0.405778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.46073 | −0.0806473 | ||||||||
\(932\) | −23.1396 | −0.757963 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.65870 | −0.250600 | ||||||||
\(935\) | −70.6610 | −2.31086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.2425 | −0.922643 | −0.461322 | − | 0.887233i | \(-0.652625\pi\) | ||||
−0.461322 | + | 0.887233i | \(0.652625\pi\) | |||||||
\(938\) | 8.56652 | 0.279707 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.3898 | −0.697657 | ||||||||
\(941\) | 56.3982 | 1.83853 | 0.919265 | − | 0.393640i | \(-0.128784\pi\) | ||||
0.919265 | + | 0.393640i | \(0.128784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.74742 | −0.252291 | ||||||||
\(944\) | −21.0507 | −0.685141 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.3168 | −0.725583 | ||||||||
\(947\) | 24.1789 | 0.785708 | 0.392854 | − | 0.919601i | \(-0.371488\pi\) | ||||
0.392854 | + | 0.919601i | \(0.371488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.36253 | −0.0766909 | ||||||||
\(950\) | −5.34368 | −0.173372 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.5615 | −0.504350 | ||||||||
\(953\) | 25.7051 | 0.832670 | 0.416335 | − | 0.909211i | \(-0.363314\pi\) | ||||
0.416335 | + | 0.909211i | \(0.363314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7926 | −0.349240 | ||||||||
\(956\) | −24.3717 | −0.788236 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.8967 | 0.481291 | ||||||||
\(959\) | 52.4557 | 1.69388 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0039 | −0.677545 | ||||||||
\(962\) | −1.82305 | −0.0587776 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.0901 | −1.29121 | ||||||||
\(965\) | −50.0303 | −1.61053 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4596 | −0.464991 | −0.232495 | − | 0.972597i | \(-0.574689\pi\) | ||||
−0.232495 | + | 0.972597i | \(0.574689\pi\) | |||||||
\(968\) | 47.9802 | 1.54214 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.9941 | −0.513538 | ||||||||
\(971\) | 49.3477 | 1.58364 | 0.791822 | − | 0.610752i | \(-0.209133\pi\) | ||||
0.791822 | + | 0.610752i | \(0.209133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.433729 | 0.0139047 | ||||||||
\(974\) | 8.66827 | 0.277749 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7036 | 0.342614 | ||||||||
\(977\) | 35.6884 | 1.14177 | 0.570886 | − | 0.821029i | \(-0.306600\pi\) | ||||
0.570886 | + | 0.821029i | \(0.306600\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.8799 | 1.53025 | ||||||||
\(980\) | −9.05418 | −0.289225 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.0909 | −0.417748 | ||||||||
\(983\) | 9.33759 | 0.297823 | 0.148911 | − | 0.988851i | \(-0.452423\pi\) | ||||
0.148911 | + | 0.988851i | \(0.452423\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1853 | 0.451983 | ||||||||
\(986\) | −1.00575 | −0.0320297 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.47190 | 0.0468275 | ||||||||
\(989\) | −34.6543 | −1.10194 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.1586 | 1.05332 | 0.526659 | − | 0.850077i | \(-0.323444\pi\) | ||||
0.526659 | + | 0.850077i | \(0.323444\pi\) | |||||||
\(992\) | 16.1664 | 0.513284 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.8308 | −0.343531 | ||||||||
\(995\) | −29.9753 | −0.950280 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.2727 | 1.46547 | 0.732736 | − | 0.680513i | \(-0.238243\pi\) | ||||
0.732736 | + | 0.680513i | \(0.238243\pi\) | |||||||
\(998\) | 6.16115 | 0.195028 | ||||||||
\(999\) | 0 | 0 |
(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 | 6021.2.a.l.1.5 | ✓ | 10 | |
3.2 | odd | 2 | inner | 6021.2.a.l.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6021.2.a.l.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6021.2.a.l.1.6 | yes | 10 | 3.2 | odd | 2 | inner |