Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
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: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.40552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.40552 | 1.38883 | 0.694415 | − | 0.719575i | \(-0.255663\pi\) | ||||
0.694415 | + | 0.719575i | \(0.255663\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.590303 | 0.263991 | 0.131996 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131996 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.95900 | −0.740431 | −0.370216 | − | 0.928946i | \(-0.620716\pi\) | ||||
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.78655 | 0.928849 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.52746 | 0.460546 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.67738 | −1.29727 | −0.648636 | − | 0.761099i | \(-0.724660\pi\) | ||||
−0.648636 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41999 | 0.366639 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.04913 | −0.739523 | −0.369761 | − | 0.929127i | \(-0.620561\pi\) | ||||
−0.369761 | + | 0.929127i | \(0.620561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.338159 | −0.0775789 | −0.0387895 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387895 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.71242 | −1.02833 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.98874 | 1.66577 | 0.832884 | − | 0.553448i | \(-0.186688\pi\) | ||||
0.832884 | + | 0.553448i | \(0.186688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65154 | −0.930309 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.513468 | −0.0988170 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.01794 | 1.11750 | 0.558751 | − | 0.829335i | \(-0.311281\pi\) | ||||
0.558751 | + | 0.829335i | \(0.311281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.17447 | 0.749758 | 0.374879 | − | 0.927074i | \(-0.377684\pi\) | ||||
0.374879 | + | 0.927074i | \(0.377684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.67434 | 0.639621 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.15640 | −0.195468 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0654 | −1.81914 | −0.909569 | − | 0.415553i | \(-0.863588\pi\) | ||||
−0.909569 | + | 0.415553i | \(0.863588\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.2515 | −1.80169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.82359 | −0.753319 | −0.376659 | − | 0.926352i | \(-0.622927\pi\) | ||||
−0.376659 | + | 0.926352i | \(0.622927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.4475 | −1.89822 | −0.949111 | − | 0.314941i | \(-0.898015\pi\) | ||||
−0.949111 | + | 0.314941i | \(0.898015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.64491 | 0.245208 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0094 | −1.60589 | −0.802945 | − | 0.596052i | \(-0.796735\pi\) | ||||
−0.802945 | + | 0.596052i | \(0.796735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16233 | −0.451761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.33476 | −1.02707 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.43684 | −0.472087 | −0.236043 | − | 0.971743i | \(-0.575851\pi\) | ||||
−0.236043 | + | 0.971743i | \(0.575851\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.901664 | 0.121580 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.813449 | −0.107744 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.63490 | −0.343034 | −0.171517 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171517 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4908 | 1.47125 | 0.735625 | − | 0.677389i | \(-0.236889\pi\) | ||||
0.735625 | + | 0.677389i | \(0.236889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.45884 | −0.687749 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.76107 | −0.342469 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2554 | 1.25289 | 0.626445 | − | 0.779465i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779465i | \(0.284509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.2171 | 2.31347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.66931 | −1.14754 | −0.573768 | − | 0.819018i | \(-0.694519\pi\) | ||||
−0.573768 | + | 0.819018i | \(0.694519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.33688 | −0.741676 | −0.370838 | − | 0.928698i | \(-0.620929\pi\) | ||||
−0.370838 | + | 0.928698i | \(0.620929\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1894 | −1.29204 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.99229 | −0.341003 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.667323 | 0.0750798 | 0.0375399 | − | 0.999295i | \(-0.488048\pi\) | ||||
0.0375399 | + | 0.999295i | \(0.488048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.59480 | −1.06609 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.26231 | 0.248321 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.79991 | −0.195228 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.4763 | 1.55202 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.21979 | 0.235297 | 0.117649 | − | 0.993055i | \(-0.462464\pi\) | ||||
0.117649 | + | 0.993055i | \(0.462464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.16297 | 0.960541 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0418 | 1.04129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.199616 | −0.0204802 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2878 | 1.45070 | 0.725352 | − | 0.688378i | \(-0.241677\pi\) | ||||
0.725352 | + | 0.688378i | \(0.241677\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.25634 | 0.427778 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.629834 | −0.0626708 | −0.0313354 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313354 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.51410 | 0.444788 | 0.222394 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222394 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.78175 | −0.271471 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.43562 | −0.332134 | −0.166067 | − | 0.986115i | \(-0.553107\pi\) | ||||
−0.166067 | + | 0.986115i | \(0.553107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.90039 | 0.948285 | 0.474142 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474142 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.6180 | −2.52647 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.47684 | −0.891506 | −0.445753 | − | 0.895156i | \(-0.647064\pi\) | ||||
−0.445753 | + | 0.895156i | \(0.647064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.71578 | 0.439748 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.0337 | −1.20497 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.97324 | 0.547566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.66687 | −0.787897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.6033 | −1.04623 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.69733 | −0.509585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3574 | 1.00781 | 0.503904 | − | 0.863760i | \(-0.331896\pi\) | ||||
0.503904 | + | 0.863760i | \(0.331896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29.9427 | −2.63631 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.9119 | −1.39023 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.662452 | 0.0574419 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.303102 | −0.0260868 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0390 | −1.28486 | −0.642432 | − | 0.766343i | \(-0.722075\pi\) | ||||
−0.642432 | + | 0.766343i | \(0.722075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6486 | 1.41212 | 0.706059 | − | 0.708153i | \(-0.250471\pi\) | ||||
0.706059 | + | 0.708153i | \(0.250471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −26.4835 | −2.23031 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.14451 | −0.597454 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.55241 | 0.295011 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.60706 | −0.627420 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0657 | −0.988463 | −0.494232 | − | 0.869330i | \(-0.664550\pi\) | ||||
−0.494232 | + | 0.869330i | \(0.664550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4897 | 1.34192 | 0.670958 | − | 0.741495i | \(-0.265883\pi\) | ||||
0.670958 | + | 0.741495i | \(0.265883\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.49655 | −0.686905 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.46420 | 0.197930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.10607 | 0.327700 | 0.163850 | − | 0.986485i | \(-0.447609\pi\) | ||||
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.26741 | −0.655648 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.6499 | −1.23339 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2459 | −1.66411 | −0.832053 | − | 0.554696i | \(-0.812835\pi\) | ||||
−0.832053 | + | 0.554696i | \(0.812835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.16897 | 0.168854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.96545 | 0.461620 | 0.230810 | − | 0.972999i | \(-0.425862\pi\) | ||||
0.230810 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.87787 | 0.682913 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.942295 | −0.0720591 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.2621 | −1.23638 | −0.618192 | − | 0.786027i | \(-0.712135\pi\) | ||||
−0.618192 | + | 0.786027i | \(0.712135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.11236 | 0.688830 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.33831 | −0.476416 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.36724 | −0.700140 | −0.350070 | − | 0.936723i | \(-0.613842\pi\) | ||||
−0.350070 | + | 0.936723i | \(0.613842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.62885 | 0.121072 | 0.0605358 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605358 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.6415 | 2.04332 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.53193 | −0.480237 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.65742 | −0.340585 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00588 | 0.0731672 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.41952 | 0.609215 | 0.304607 | − | 0.952478i | \(-0.401475\pi\) | ||||
0.304607 | + | 0.952478i | \(0.401475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9514 | −1.79604 | −0.898022 | − | 0.439950i | \(-0.854996\pi\) | ||||
−0.898022 | + | 0.439950i | \(0.854996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.64182 | −0.475631 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.36559 | 0.168541 | 0.0842705 | − | 0.996443i | \(-0.473144\pi\) | ||||
0.0842705 | + | 0.996443i | \(0.473144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7817 | −0.835180 | −0.417590 | − | 0.908636i | \(-0.637125\pi\) | ||||
−0.417590 | + | 0.908636i | \(0.637125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.6695 | 1.74005 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.7891 | −0.827434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.84738 | −0.198870 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.2610 | 1.54725 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.516524 | −0.0357287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8124 | 1.15742 | 0.578708 | − | 0.815535i | \(-0.303557\pi\) | ||||
0.578708 | + | 0.815535i | \(0.303557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.2597 | −1.59373 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.34778 | −0.501115 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.17778 | −0.555144 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2435 | −1.03006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2619 | 0.959362 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.32490 | −0.557476 | −0.278738 | − | 0.960367i | \(-0.589916\pi\) | ||||
−0.278738 | + | 0.960367i | \(0.589916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.9617 | −0.864116 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.35919 | −0.422074 | −0.211037 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211037 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4619 | 0.757426 | 0.378713 | − | 0.925514i | \(-0.376367\pi\) | ||||
0.378713 | + | 0.925514i | \(0.376367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.19802 | −0.473595 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5891 | 1.41435 | 0.707175 | − | 0.707039i | \(-0.249969\pi\) | ||||
0.707175 | + | 0.707039i | \(0.249969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.49890 | −0.423941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.60526 | 0.104273 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.52568 | 0.292742 | 0.146371 | − | 0.989230i | \(-0.453241\pi\) | ||||
0.146371 | + | 0.989230i | \(0.453241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.84982 | −0.634483 | −0.317241 | − | 0.948345i | \(-0.602757\pi\) | ||||
−0.317241 | + | 0.948345i | \(0.602757\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.5401 | −1.38180 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.86673 | −0.119261 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.58170 | 0.100641 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.44205 | 0.344876 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0558 | −1.39215 | −0.696075 | − | 0.717969i | \(-0.745072\pi\) | ||||
−0.696075 | + | 0.717969i | \(0.745072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2025 | 0.767163 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.32973 | −0.271138 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3211 | 1.57948 | 0.789742 | − | 0.613439i | \(-0.210214\pi\) | ||||
0.789742 | + | 0.613439i | \(0.210214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6771 | 1.34695 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.7693 | 1.03799 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.7243 | −0.661289 | −0.330644 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330644 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.02878 | −0.124627 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.33975 | 0.326788 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9609 | −0.729266 | −0.364633 | − | 0.931151i | \(-0.618806\pi\) | ||||
−0.364633 | + | 0.931151i | \(0.618806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7258 | 0.712295 | 0.356147 | − | 0.934430i | \(-0.384090\pi\) | ||||
0.356147 | + | 0.934430i | \(0.384090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.0418 | 1.33403 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.10504 | −0.428450 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.916745 | −0.0550819 | −0.0275409 | − | 0.999621i | \(-0.508768\pi\) | ||||
−0.0275409 | + | 0.999621i | \(0.508768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.6324 | 0.696411 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7464 | 1.29728 | 0.648640 | − | 0.761096i | \(-0.275338\pi\) | ||||
0.648640 | + | 0.761096i | \(0.275338\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.06684 | 0.479524 | 0.239762 | − | 0.970832i | \(-0.422931\pi\) | ||||
0.239762 | + | 0.970832i | \(0.422931\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.480181 | −0.0284435 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.44941 | 0.557781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.70280 | −0.453106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.3696 | 2.01478 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.16609 | −0.126544 | −0.0632722 | − | 0.997996i | \(-0.520154\pi\) | ||||
−0.0632722 | + | 0.997996i | \(0.520154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.55539 | −0.0905581 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.784302 | −0.0455098 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.3664 | −2.16095 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3846 | 1.40550 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.51508 | −0.0870391 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.78307 | 0.388397 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.60523 | −0.376980 | −0.188490 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188490 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8588 | 0.617735 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.84184 | −0.217851 | −0.108925 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108925 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4617 | −1.43918 | −0.719591 | − | 0.694398i | \(-0.755671\pi\) | ||||
−0.719591 | + | 0.694398i | \(0.755671\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.22237 | −0.181560 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.23817 | −0.462702 | −0.231351 | − | 0.972870i | \(-0.574314\pi\) | ||||
−0.231351 | + | 0.972870i | \(0.574314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.19216 | 0.514662 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.26446 | −0.461277 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.03109 | 0.0573714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.7570 | 1.20686 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.8156 | 1.31701 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.5675 | 1.18905 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.68597 | 0.367494 | 0.183747 | − | 0.982974i | \(-0.441177\pi\) | ||||
0.183747 | + | 0.982974i | \(0.441177\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30.8342 | −1.68970 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.05376 | 0.330752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.9491 | −1.90380 | −0.951899 | − | 0.306411i | \(-0.900872\pi\) | ||||
−0.951899 | + | 0.306411i | \(0.900872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.7968 | −1.23815 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.37634 | 0.345298 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9080 | 1.07493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.3439 | 0.610736 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1317 | 0.865998 | 0.432999 | − | 0.901394i | \(-0.357455\pi\) | ||||
0.432999 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.2651 | −0.870653 | −0.435326 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435326 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.40169 | 0.128192 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5427 | 0.827254 | 0.413627 | − | 0.910446i | \(-0.364262\pi\) | ||||
0.413627 | + | 0.910446i | \(0.364262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.70782 | −0.302940 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.3688 | 0.760476 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.5339 | 0.872625 | 0.436312 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436312 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8856 | −0.993982 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.8484 | −1.09425 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.74068 | −0.195796 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.62500 | −0.293623 | −0.146811 | − | 0.989165i | \(-0.546901\pi\) | ||||
−0.146811 | + | 0.989165i | \(0.546901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.4412 | −0.699719 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.73277 | 0.349548 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0602 | −0.935122 | −0.467561 | − | 0.883961i | \(-0.654867\pi\) | ||||
−0.467561 | + | 0.883961i | \(0.654867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7051 | −0.707727 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.1482 | −1.44970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.42773 | 0.124704 | 0.0623521 | − | 0.998054i | \(-0.480140\pi\) | ||||
0.0623521 | + | 0.998054i | \(0.480140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.3206 | 1.39967 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2778 | 0.831757 | 0.415878 | − | 0.909420i | \(-0.363474\pi\) | ||||
0.415878 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.76636 | −0.0900219 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −34.6855 | −1.76316 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0862 | −0.764899 | −0.382450 | − | 0.923976i | \(-0.624919\pi\) | ||||
−0.382450 | + | 0.923976i | \(0.624919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.3587 | −1.23187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −38.2764 | −1.93079 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.393923 | 0.0198204 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7523 | −1.34266 | −0.671329 | − | 0.741160i | \(-0.734276\pi\) | ||||
−0.671329 | + | 0.741160i | \(0.734276\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.59354 | 0.0797770 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.1930 | −1.05833 | −0.529165 | − | 0.848519i | \(-0.677495\pi\) | ||||
−0.529165 | + | 0.848519i | \(0.677495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5256 | −0.972639 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.66384 | −0.281438 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9019 | −0.837797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.2178 | 0.703023 | 0.351511 | − | 0.936184i | \(-0.385668\pi\) | ||||
0.351511 | + | 0.936184i | \(0.385668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.1766 | −1.78446 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.16176 | 0.253993 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.33545 | 0.0655547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.0487 | 1.96119 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.7220 | −1.98940 | −0.994700 | − | 0.102818i | \(-0.967214\pi\) | ||||
−0.994700 | + | 0.102818i | \(0.967214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2685 | 1.47519 | 0.737597 | − | 0.675241i | \(-0.235960\pi\) | ||||
0.737597 | + | 0.675241i | \(0.235960\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.6783 | −1.49163 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.1832 | 0.687984 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.5105 | −1.08936 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.1863 | −0.829762 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3367 | −0.690572 | −0.345286 | − | 0.938497i | \(-0.612218\pi\) | ||||
−0.345286 | + | 0.938497i | \(0.612218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4985 | −1.27344 | −0.636719 | − | 0.771096i | \(-0.719709\pi\) | ||||
−0.636719 | + | 0.771096i | \(0.719709\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.54540 | 0.409720 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.70146 | −0.129228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2176 | −0.917208 | −0.458604 | − | 0.888641i | \(-0.651650\pi\) | ||||
−0.458604 | + | 0.888641i | \(0.651650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.81198 | −0.419618 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.97322 | 0.283796 | 0.141898 | − | 0.989881i | \(-0.454679\pi\) | ||||
0.141898 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.31035 | 0.0621164 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.0244 | −1.37281 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.84304 | 0.0869784 | 0.0434892 | − | 0.999054i | \(-0.486153\pi\) | ||||
0.0434892 | + | 0.999054i | \(0.486153\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.36785 | −0.346938 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 39.6665 | 1.86369 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.40893 | 0.253575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.3399 | 1.27891 | 0.639453 | − | 0.768830i | \(-0.279161\pi\) | ||||
0.639453 | + | 0.768830i | \(0.279161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.56563 | 0.0730774 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.1434 | 1.63679 | 0.818395 | − | 0.574656i | \(-0.194864\pi\) | ||||
0.818395 | + | 0.574656i | \(0.194864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6765 | 0.867969 | 0.433984 | − | 0.900920i | \(-0.357107\pi\) | ||||
0.433984 | + | 0.900920i | \(0.357107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.92770 | 0.274891 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.9925 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0902 | −0.927680 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.87725 | 0.455120 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.0130 | −0.874220 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.57296 | 0.0721723 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.57692 | −0.438497 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4554 | 0.523409 | 0.261705 | − | 0.965148i | \(-0.415715\pi\) | ||||
0.261705 | + | 0.965148i | \(0.415715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.7570 | 2.35992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.6463 | −1.71296 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.43411 | 0.382973 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.2183 | 0.644295 | 0.322147 | − | 0.946690i | \(-0.395595\pi\) | ||||
0.322147 | + | 0.946690i | \(0.395595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −51.1075 | −2.31116 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.53402 | 0.204617 | 0.102309 | − | 0.994753i | \(-0.467377\pi\) | ||||
0.102309 | + | 0.994753i | \(0.467377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.3495 | −0.826419 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.51253 | 0.112930 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.9421 | 0.849671 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.1411 | 1.70743 | 0.853715 | − | 0.520741i | \(-0.174344\pi\) | ||||
0.853715 | + | 0.520741i | \(0.174344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.3500 | 0.641112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.371793 | −0.0165446 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.3559 | 0.948451 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.3114 | 1.52083 | 0.760413 | − | 0.649440i | \(-0.224997\pi\) | ||||
0.760413 | + | 0.649440i | \(0.224997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4139 | 0.549160 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.173634 | 0.00766612 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.66469 | 0.117420 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.8165 | −0.739587 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.1189 | −1.71713 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.8175 | 1.04346 | 0.521732 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521732 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.16718 | 0.0947643 | 0.0473821 | − | 0.998877i | \(-0.484912\pi\) | ||||
0.0473821 | + | 0.998877i | \(0.484912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.9200 | 0.956667 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.7285 | −0.554463 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.8200 | 1.77478 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.34226 | −0.318627 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.5618 | 0.977259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.02805 | −0.0876804 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.5331 | −0.972376 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.83033 | −0.208057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5019 | 0.580493 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.91824 | 0.168148 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.84423 | 0.250339 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.05880 | 0.0452710 | 0.0226355 | − | 0.999744i | \(-0.492794\pi\) | ||||
0.0226355 | + | 0.999744i | \(0.492794\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.0197 | 1.36657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.03502 | −0.0866947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.30728 | −0.0555914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.7127 | −0.666967 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.20176 | −0.389891 | −0.194946 | − | 0.980814i | \(-0.562453\pi\) | ||||
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.2216 | 2.46251 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2035 | −0.473014 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.6502 | 1.24961 | 0.624804 | − | 0.780782i | \(-0.285179\pi\) | ||||
0.624804 | + | 0.780782i | \(0.285179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.59420 | −0.235350 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.7962 | 0.789366 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.6715 | 0.950439 | 0.475220 | − | 0.879867i | \(-0.342369\pi\) | ||||
0.475220 | + | 0.879867i | \(0.342369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.2013 | 1.30573 | 0.652866 | − | 0.757473i | \(-0.273566\pi\) | ||||
0.652866 | + | 0.757473i | \(0.273566\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.2533 | 0.846096 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.1600 | −1.54968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.98191 | −0.165769 | −0.0828845 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828845 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −60.0213 | −2.49440 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.43187 | −0.183865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.24964 | −0.217418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.69385 | −0.318102 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.7494 | 0.526225 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.41163 | −0.0581654 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.69048 | 0.234075 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.27771 | −0.134600 | −0.0672998 | − | 0.997733i | \(-0.521438\pi\) | ||||
−0.0672998 | + | 0.997733i | \(0.521438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.52602 | 0.144553 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.3411 | −1.15992 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9237 | −0.446332 | −0.223166 | − | 0.974780i | \(-0.571639\pi\) | ||||
−0.223166 | + | 0.974780i | \(0.571639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7446 | −1.21331 | −0.606653 | − | 0.794967i | \(-0.707488\pi\) | ||||
−0.606653 | + | 0.794967i | \(0.707488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.5770 | 1.16375 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.11608 | −0.207998 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.8414 | 1.77947 | 0.889735 | − | 0.456478i | \(-0.150889\pi\) | ||||
0.889735 | + | 0.456478i | \(0.150889\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.3590 | −1.14917 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51.4953 | 2.08328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3195 | −1.30537 | −0.652687 | − | 0.757628i | \(-0.726358\pi\) | ||||
−0.652687 | + | 0.757628i | \(0.726358\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.84945 | −0.276196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.9696 | 1.64937 | 0.824687 | − | 0.565589i | \(-0.191351\pi\) | ||||
0.824687 | + | 0.565589i | \(0.191351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5775 | −0.907466 | −0.453733 | − | 0.891138i | \(-0.649908\pi\) | ||||
−0.453733 | + | 0.891138i | \(0.649908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.10196 | −0.164606 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.34856 | −0.174221 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8946 | 0.795782 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.24251 | −0.0496211 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.7398 | 1.34529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.9719 | −1.35240 | −0.676199 | − | 0.736719i | \(-0.736374\pi\) | ||||
−0.676199 | + | 0.736719i | \(0.736374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40.4427 | 1.60745 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.70432 | 0.266053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7914 | 0.586057 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.9440 | −1.06589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.53431 | −0.179095 | −0.0895473 | − | 0.995983i | \(-0.528542\pi\) | ||||
−0.0895473 | + | 0.995983i | \(0.528542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.3929 | −1.51407 | −0.757033 | − | 0.653376i | \(-0.773352\pi\) | ||||
−0.757033 | + | 0.653376i | \(0.773352\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.6753 | −0.695963 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.255028 | 0.0100262 | 0.00501309 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501309 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.02470 | −0.157983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.6719 | −0.771001 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.04379 | −0.0799797 | −0.0399898 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399898 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.39282 | −0.367008 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.6580 | −0.688904 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0768 | −0.392534 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.53010 | −0.215096 | −0.107548 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107548 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.3074 | 1.33239 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.391047 | 0.0151642 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0757 | 1.86150 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.0257 | −0.774240 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5518 | 0.677579 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16280 | −0.121917 | −0.0609585 | − | 0.998140i | \(-0.519416\pi\) | ||||
−0.0609585 | + | 0.998140i | \(0.519416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.38842 | 0.0919303 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.8219 | −1.83794 | −0.918972 | − | 0.394323i | \(-0.870979\pi\) | ||||
−0.918972 | + | 0.394323i | \(0.870979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.9897 | −1.07415 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.2972 | −0.586190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.2468 | −0.506873 | −0.253437 | − | 0.967352i | \(-0.581561\pi\) | ||||
−0.253437 | + | 0.967352i | \(0.581561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87754 | −0.339193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.5720 | 1.05194 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0754 | 0.612425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.80850 | 0.297049 | 0.148525 | − | 0.988909i | \(-0.452548\pi\) | ||||
0.148525 | + | 0.988909i | \(0.452548\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.33815 | −0.316740 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.82774 | 0.372787 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7078 | 0.557097 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.9331 | 1.96429 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.68972 | 0.290437 | 0.145218 | − | 0.989400i | \(-0.453612\pi\) | ||||
0.145218 | + | 0.989400i | \(0.453612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.74185 | 0.141127 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6333 | −0.588783 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.23384 | 0.0464034 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0522 | 1.16619 | 0.583096 | − | 0.812403i | \(-0.301841\pi\) | ||||
0.583096 | + | 0.812403i | \(0.301841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.85953 | 0.0697377 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.3488 | 1.24892 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.21742 | −0.157723 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.8866 | 0.406569 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.4494 | 1.13557 | 0.567786 | − | 0.823176i | \(-0.307800\pi\) | ||||
0.567786 | + | 0.823176i | \(0.307800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.84312 | −0.329335 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.6940 | −0.881189 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27.9927 | −1.03962 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.14587 | 0.227938 | 0.113969 | − | 0.993484i | \(-0.463644\pi\) | ||||
0.113969 | + | 0.993484i | \(0.463644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0309 | −0.852995 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.9540 | 1.40378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4237 | −0.939046 | −0.469523 | − | 0.882920i | \(-0.655574\pi\) | ||||
−0.469523 | + | 0.882920i | \(0.655574\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.49047 | −0.165633 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.6646 | 0.577014 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8464 | 0.730063 | 0.365032 | − | 0.930995i | \(-0.381058\pi\) | ||||
0.365032 | + | 0.930995i | \(0.381058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.80481 | 0.139773 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.7154 | 1.05346 | 0.526732 | − | 0.850031i | \(-0.323417\pi\) | ||||
0.526732 | + | 0.850031i | \(0.323417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.12243 | −0.260946 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.30404 | 0.230653 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.73036 | 0.245922 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0374 | −0.877139 | −0.438569 | − | 0.898697i | \(-0.644515\pi\) | ||||
−0.438569 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −53.0558 | −1.93346 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.73394 | 0.354254 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.2463 | −0.844902 | −0.422451 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422451 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.3534 | 1.06546 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.3555 | 1.60789 | 0.803943 | − | 0.594706i | \(-0.202732\pi\) | ||||
0.803943 | + | 0.594706i | \(0.202732\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.3948 | −0.702140 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.01553 | −0.181337 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.3244 | 0.445009 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4534 | −0.629385 | −0.314693 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314693 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.9104 | 2.19364 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.73607 | −0.0624422 | −0.0312211 | − | 0.999513i | \(-0.509940\pi\) | ||||
−0.0312211 | + | 0.999513i | \(0.509940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.4177 | −0.697506 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 52.1447 | 1.87068 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.63114 | 0.0584417 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7695 | −0.528493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.09002 | −0.110428 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.42383 | 0.0865100 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1636 | 0.576169 | 0.288085 | − | 0.957605i | \(-0.406982\pi\) | ||||
0.288085 | + | 0.957605i | \(0.406982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.7976 | −0.918418 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.5651 | 0.660099 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.7469 | −1.90861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.88028 | −0.173086 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.8208 | −0.950040 | −0.475020 | − | 0.879975i | \(-0.657559\pi\) | ||||
−0.475020 | + | 0.879975i | \(0.657559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.5692 | 1.18759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.18554 | 0.218555 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.67933 | −0.341576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.23819 | −0.325603 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.7721 | −1.01283 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.4065 | 1.17451 | 0.587255 | − | 0.809402i | \(-0.300209\pi\) | ||||
0.587255 | + | 0.809402i | \(0.300209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8499 | −1.22375 | −0.611873 | − | 0.790956i | \(-0.709584\pi\) | ||||
−0.611873 | + | 0.790956i | \(0.709584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2068 | 0.989256 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.5415 | −0.439310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.20922 | 0.147262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.5330 | 0.892197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.4182 | −0.852201 | −0.426101 | − | 0.904676i | \(-0.640113\pi\) | ||||
−0.426101 | + | 0.904676i | \(0.640113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.51039 | −0.157222 | −0.0786112 | − | 0.996905i | \(-0.525049\pi\) | ||||
−0.0786112 | + | 0.996905i | \(0.525049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.0914 | −0.595045 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.91499 | 0.101364 | 0.0506821 | − | 0.998715i | \(-0.483860\pi\) | ||||
0.0506821 | + | 0.998715i | \(0.483860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.2382 | 1.22387 | 0.611937 | − | 0.790906i | \(-0.290390\pi\) | ||||
0.611937 | + | 0.790906i | \(0.290390\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.20525 | −0.0764994 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.64236 | 0.334088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.52142 | 0.121864 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.14346 | −0.0740888 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.4876 | 0.500166 | 0.250083 | − | 0.968224i | \(-0.419542\pi\) | ||||
0.250083 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.21557 | 0.248813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52.3114 | 1.80170 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.24063 | 0.180283 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9784 | 0.583384 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.4050 | 0.665977 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −88.3985 | −3.03026 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.92917 | 0.168772 | 0.0843858 | − | 0.996433i | \(-0.473107\pi\) | ||||
0.0843858 | + | 0.996433i | \(0.473107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.556239 | −0.0190230 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.5344 | 1.79454 | 0.897270 | − | 0.441482i | \(-0.145547\pi\) | ||||
0.897270 | + | 0.441482i | \(0.145547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5431 | −1.11036 | −0.555179 | − | 0.831731i | \(-0.687350\pi\) | ||||
−0.555179 | + | 0.831731i | \(0.687350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.7308 | 0.774663 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.5604 | −1.75514 | −0.877568 | − | 0.479451i | \(-0.840836\pi\) | ||||
−0.877568 | + | 0.479451i | \(0.840836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.59956 | −0.326395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.5293 | −0.629287 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.01931 | 0.0345777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.9682 | −1.62534 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.8135 | 1.34748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1611 | 0.377313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8616 | 1.21096 | 0.605481 | − | 0.795860i | \(-0.292981\pi\) | ||||
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.21058 | −0.175749 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2432 | −1.38952 | −0.694759 | − | 0.719243i | \(-0.744489\pi\) | ||||
−0.694759 | + | 0.719243i | \(0.744489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3041 | −0.817898 | −0.408949 | − | 0.912557i | \(-0.634105\pi\) | ||||
−0.408949 | + | 0.912557i | \(0.634105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.74152 | −0.125770 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.7010 | −1.73595 | −0.867975 | − | 0.496608i | \(-0.834579\pi\) | ||||
−0.867975 | + | 0.496608i | \(0.834579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2492 | −0.746213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.6557 | −0.490983 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.72294 | 0.124583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.52951 | −0.184831 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −89.8857 | −3.00120 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.1217 | 0.837856 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.4794 | 0.349119 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 58.6577 | 1.95201 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.961515 | 0.0319618 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.06194 | 0.168079 | 0.0840395 | − | 0.996462i | \(-0.473218\pi\) | ||||
0.0840395 | + | 0.996462i | \(0.473218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.75506 | −0.0582117 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.4144 | 1.33899 | 0.669495 | − | 0.742817i | \(-0.266511\pi\) | ||||
0.669495 | + | 0.742817i | \(0.266511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.45559 | 0.114363 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.3168 | 0.539418 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.1713 | 1.02937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.2276 | −1.03010 | −0.515052 | − | 0.857159i | \(-0.672227\pi\) | ||||
−0.515052 | + | 0.857159i | \(0.672227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8890 | −0.523562 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.2270 | 1.48867 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.4711 | 1.69236 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.5788 | 0.413141 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.3773 | −1.68563 | −0.842817 | − | 0.538201i | \(-0.819104\pi\) | ||||
−0.842817 | + | 0.538201i | \(0.819104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.06937 | 0.0350472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.24164 | −0.302558 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.74929 | −0.0899114 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6093 | 0.738614 | 0.369307 | − | 0.929307i | \(-0.379595\pi\) | ||||
0.369307 | + | 0.929307i | \(0.379595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −61.2488 | −1.99878 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.2485 | −1.67065 | −0.835326 | − | 0.549754i | \(-0.814721\pi\) | ||||
−0.835326 | + | 0.549754i | \(0.814721\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −38.5344 | −1.25485 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.593776 | 0.0193155 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.1474 | 1.75955 | 0.879777 | − | 0.475387i | \(-0.157692\pi\) | ||||
0.879777 | + | 0.475387i | \(0.157692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.6400 | 0.962155 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.8171 | −0.642614 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0986 | −1.10456 | −0.552281 | − | 0.833658i | \(-0.686242\pi\) | ||||
−0.552281 | + | 0.833658i | \(0.686242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.97006 | 0.160827 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.1120 | 0.714778 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.4613 | 0.951354 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5738 | −0.437863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.57350 | −0.308502 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.7289 | −0.474140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9385 | −0.673336 | −0.336668 | − | 0.941623i | \(-0.609300\pi\) | ||||
−0.336668 | + | 0.941623i | \(0.609300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.48031 | 0.0796791 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00722 | 0.160689 | 0.0803447 | − | 0.996767i | \(-0.474398\pi\) | ||||
0.0803447 | + | 0.996767i | \(0.474398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6146 | −1.04558 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.3371 | 1.67613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5547 | 0.401662 | 0.200831 | − | 0.979626i | \(-0.435636\pi\) | ||||
0.200831 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.39064 | 0.108365 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.5879 | 0.880813 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.43810 | −0.0458683 | −0.0229341 | − | 0.999737i | \(-0.507301\pi\) | ||||
−0.0229341 | + | 0.999737i | \(0.507301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39641 | 0.0444934 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.8810 | 1.65139 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −99.4397 | −3.16200 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.6595 | 1.32336 | 0.661678 | − | 0.749788i | \(-0.269845\pi\) | ||||
0.661678 | + | 0.749788i | \(0.269845\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.0833 | 0.510387 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.95475 | −0.220480 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.5145 | 1.47313 | 0.736564 | − | 0.676367i | \(-0.236447\pi\) | ||||
0.736564 | + | 0.676367i | \(0.236447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.68172 | 0.179762 |
(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 | 8048.2.a.p.1.9 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.9 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.9 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.2 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.9 | 10 | 1.1 | even | 1 | trivial |