Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.135076.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 3192) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.15154\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.30308 | −1.92439 | −0.962197 | − | 0.272354i | \(-0.912198\pi\) | ||||
−0.962197 | + | 0.272354i | \(0.912198\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56627 | 0.773759 | 0.386880 | − | 0.922130i | \(-0.373553\pi\) | ||||
0.386880 | + | 0.922130i | \(0.373553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81429 | 0.780544 | 0.390272 | − | 0.920700i | \(-0.372381\pi\) | ||||
0.390272 | + | 0.920700i | \(0.372381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.96536 | 1.93188 | 0.965942 | − | 0.258757i | \(-0.0833130\pi\) | ||||
0.965942 | + | 0.258757i | \(0.0833130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.814291 | 0.169791 | 0.0848957 | − | 0.996390i | \(-0.472944\pi\) | ||||
0.0848957 | + | 0.996390i | \(0.472944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.5165 | 2.70329 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.48879 | −0.647851 | −0.323926 | − | 0.946083i | \(-0.605003\pi\) | ||||
−0.323926 | + | 0.946083i | \(0.605003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.38056 | 0.607166 | 0.303583 | − | 0.952805i | \(-0.401817\pi\) | ||||
0.303583 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.30308 | −0.727353 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75198 | 0.616821 | 0.308411 | − | 0.951253i | \(-0.400203\pi\) | ||||
0.308411 | + | 0.951253i | \(0.400203\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.60615 | −1.03171 | −0.515854 | − | 0.856677i | \(-0.672525\pi\) | ||||
−0.515854 | + | 0.856677i | \(0.672525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2533 | −1.49559 | −0.747797 | − | 0.663928i | \(-0.768888\pi\) | ||||
−0.747797 | + | 0.663928i | \(0.768888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.511215 | −0.0702207 | −0.0351104 | − | 0.999383i | \(-0.511178\pi\) | ||||
−0.0351104 | + | 0.999383i | \(0.511178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.0428 | −1.48902 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.9901 | 1.82135 | 0.910677 | − | 0.413120i | \(-0.135561\pi\) | ||||
0.910677 | + | 0.413120i | \(0.135561\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.1101 | −1.50207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9805 | 1.46366 | 0.731828 | − | 0.681490i | \(-0.238668\pi\) | ||||
0.731828 | + | 0.681490i | \(0.238668\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.02768 | −0.596676 | −0.298338 | − | 0.954460i | \(-0.596432\pi\) | ||||
−0.298338 | + | 0.954460i | \(0.596432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0204 | 1.87505 | 0.937524 | − | 0.347920i | \(-0.113112\pi\) | ||||
0.937524 | + | 0.347920i | \(0.113112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.56627 | 0.292453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8347 | −1.66904 | −0.834518 | − | 0.550981i | \(-0.814254\pi\) | ||||
−0.834518 | + | 0.550981i | \(0.814254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.01517 | 0.221194 | 0.110597 | − | 0.993865i | \(-0.464724\pi\) | ||||
0.110597 | + | 0.993865i | \(0.464724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.2756 | −3.71771 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.6490 | −1.87079 | −0.935395 | − | 0.353604i | \(-0.884956\pi\) | ||||
−0.935395 | + | 0.353604i | \(0.884956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.81429 | 0.295018 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.30308 | −0.441486 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.66847 | −0.575545 | −0.287773 | − | 0.957699i | \(-0.592915\pi\) | ||||
−0.287773 | + | 0.957699i | \(0.592915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.90923 | 0.488486 | 0.244243 | − | 0.969714i | \(-0.421460\pi\) | ||||
0.244243 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.47025 | 0.144868 | 0.0724339 | − | 0.997373i | \(-0.476923\pi\) | ||||
0.0724339 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3767 | 1.00315 | 0.501575 | − | 0.865114i | \(-0.332754\pi\) | ||||
0.501575 | + | 0.865114i | \(0.332754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.98671 | −0.573423 | −0.286711 | − | 0.958017i | \(-0.592562\pi\) | ||||
−0.286711 | + | 0.958017i | \(0.592562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.14771 | 0.860544 | 0.430272 | − | 0.902699i | \(-0.358418\pi\) | ||||
0.430272 | + | 0.902699i | \(0.358418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.50396 | −0.326746 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.96536 | 0.730184 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.41427 | −0.401297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −36.6470 | −3.27781 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.599976 | 0.0532392 | 0.0266196 | − | 0.999646i | \(-0.491526\pi\) | ||||
0.0266196 | + | 0.999646i | \(0.491526\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.14771 | −0.624498 | −0.312249 | − | 0.950000i | \(-0.601082\pi\) | ||||
−0.312249 | + | 0.950000i | \(0.601082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6286 | −0.993497 | −0.496748 | − | 0.867895i | \(-0.665473\pi\) | ||||
−0.496748 | + | 0.867895i | \(0.665473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.01251 | −0.255518 | −0.127759 | − | 0.991805i | \(-0.540778\pi\) | ||||
−0.127759 | + | 0.991805i | \(0.540778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.22223 | 0.603953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0125 | 1.24672 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8542 | −1.05306 | −0.526528 | − | 0.850158i | \(-0.676506\pi\) | ||||
−0.526528 | + | 0.850158i | \(0.676506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8123 | −1.44954 | −0.724771 | − | 0.688989i | \(-0.758055\pi\) | ||||
−0.724771 | + | 0.688989i | \(0.758055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5468 | −1.16843 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.92023 | 0.153251 | 0.0766256 | − | 0.997060i | \(-0.475585\pi\) | ||||
0.0766256 | + | 0.997060i | \(0.475585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.814291 | 0.0641751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5468 | 1.76600 | 0.883001 | − | 0.469371i | \(-0.155519\pi\) | ||||
0.883001 | + | 0.469371i | \(0.155519\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5165 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.07977 | −0.390751 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.4101 | 1.85587 | 0.927933 | − | 0.372746i | \(-0.121584\pi\) | ||||
0.927933 | + | 0.372746i | \(0.121584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.5165 | 1.02175 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.08703 | −0.529709 | −0.264855 | − | 0.964288i | \(-0.585324\pi\) | ||||
−0.264855 | + | 0.964288i | \(0.585324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.56964 | 0.191000 | 0.0954998 | − | 0.995429i | \(-0.469555\pi\) | ||||
0.0954998 | + | 0.995429i | \(0.469555\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.1450 | −1.18701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.4413 | 1.49481 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.2265 | −1.97004 | −0.985022 | − | 0.172429i | \(-0.944838\pi\) | ||||
−0.985022 | + | 0.172429i | \(0.944838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5369 | −1.04639 | −0.523194 | − | 0.852214i | \(-0.675260\pi\) | ||||
−0.523194 | + | 0.852214i | \(0.675260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.32779 | 0.593330 | 0.296665 | − | 0.954982i | \(-0.404125\pi\) | ||||
0.296665 | + | 0.954982i | \(0.404125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0204 | 0.993881 | 0.496941 | − | 0.867785i | \(-0.334457\pi\) | ||||
0.496941 | + | 0.867785i | \(0.334457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.48879 | −0.244865 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.4268 | 1.98541 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.56627 | 0.177512 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.44624 | 0.306092 | 0.153046 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153046 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.38056 | 0.229487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4169 | 1.50792 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0238 | 1.07303 | 0.536516 | − | 0.843890i | \(-0.319740\pi\) | ||||
0.536516 | + | 0.843890i | \(0.319740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.25930 | −0.216327 | −0.108164 | − | 0.994133i | \(-0.534497\pi\) | ||||
−0.108164 | + | 0.994133i | \(0.534497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7387 | 1.56870 | 0.784348 | − | 0.620321i | \(-0.212998\pi\) | ||||
0.784348 | + | 0.620321i | \(0.212998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.3673 | −1.39982 | −0.699908 | − | 0.714233i | \(-0.746776\pi\) | ||||
−0.699908 | + | 0.714233i | \(0.746776\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44.1206 | 2.87811 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3208 | 1.89661 | 0.948303 | − | 0.317365i | \(-0.102798\pi\) | ||||
0.948303 | + | 0.317365i | \(0.102798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6216 | −0.941862 | −0.470931 | − | 0.882170i | \(-0.656082\pi\) | ||||
−0.470931 | + | 0.882170i | \(0.656082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.30308 | −0.274913 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.81429 | 0.179069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8931 | 1.31876 | 0.659381 | − | 0.751809i | \(-0.270818\pi\) | ||||
0.659381 | + | 0.751809i | \(0.270818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.08969 | 0.131378 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.54680 | −0.533135 | −0.266567 | − | 0.963816i | \(-0.585890\pi\) | ||||
−0.266567 | + | 0.963816i | \(0.585890\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.75198 | 0.233137 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.24107 | 0.0765274 | 0.0382637 | − | 0.999268i | \(-0.487817\pi\) | ||||
0.0382637 | + | 0.999268i | \(0.487817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.19980 | 0.135132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.6266 | 1.25762 | 0.628812 | − | 0.777557i | \(-0.283541\pi\) | ||||
0.628812 | + | 0.777557i | \(0.283541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7758 | −1.07980 | −0.539900 | − | 0.841729i | \(-0.681538\pi\) | ||||
−0.539900 | + | 0.841729i | \(0.681538\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.6869 | 2.09170 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.8613 | −1.37360 | −0.686801 | − | 0.726845i | \(-0.740986\pi\) | ||||
−0.686801 | + | 0.726845i | \(0.740986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0949 | 0.960143 | 0.480072 | − | 0.877229i | \(-0.340611\pi\) | ||||
0.480072 | + | 0.877229i | \(0.340611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4042 | 0.975128 | 0.487564 | − | 0.873087i | \(-0.337886\pi\) | ||||
0.487564 | + | 0.873087i | \(0.337886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.60615 | −0.389949 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.4470 | 2.73218 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3918 | 0.840780 | 0.420390 | − | 0.907343i | \(-0.361893\pi\) | ||||
0.420390 | + | 0.907343i | \(0.361893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −60.2004 | −3.50500 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.29165 | 0.132530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.8185 | −1.47836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9901 | 1.02675 | 0.513374 | − | 0.858165i | \(-0.328395\pi\) | ||||
0.513374 | + | 0.858165i | \(0.328395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0916 | 0.685650 | 0.342825 | − | 0.939399i | \(-0.388616\pi\) | ||||
0.342825 | + | 0.939399i | \(0.388616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2024 | −1.42452 | −0.712261 | − | 0.701914i | \(-0.752329\pi\) | ||||
−0.712261 | + | 0.701914i | \(0.752329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.8806 | 0.667282 | 0.333641 | − | 0.942700i | \(-0.391723\pi\) | ||||
0.333641 | + | 0.942700i | \(0.391723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.95316 | −0.501281 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.96536 | 0.443205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.0393 | 2.11004 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.2533 | −0.565281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.28454 | 0.345429 | 0.172715 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172715 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −51.5532 | −2.81665 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.1430 | 1.69647 | 0.848235 | − | 0.529621i | \(-0.177666\pi\) | ||||
0.848235 | + | 0.529621i | \(0.177666\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.67542 | 0.469800 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.3196 | −1.68132 | −0.840662 | − | 0.541560i | \(-0.817834\pi\) | ||||
−0.840662 | + | 0.541560i | \(0.817834\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.6432 | −0.783834 | −0.391917 | − | 0.920001i | \(-0.628188\pi\) | ||||
−0.391917 | + | 0.920001i | \(0.628188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.85309 | 0.524427 | 0.262214 | − | 0.965010i | \(-0.415548\pi\) | ||||
0.262214 | + | 0.965010i | \(0.415548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.6345 | 1.14824 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.26548 | −0.172345 | −0.0861726 | − | 0.996280i | \(-0.527464\pi\) | ||||
−0.0861726 | + | 0.996280i | \(0.527464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −68.9371 | −3.60833 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.03034 | −0.210382 | −0.105191 | − | 0.994452i | \(-0.533545\pi\) | ||||
−0.105191 | + | 0.994452i | \(0.533545\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.511215 | −0.0265409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6194 | 0.756966 | 0.378483 | − | 0.925608i | \(-0.376446\pi\) | ||||
0.378483 | + | 0.925608i | \(0.376446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.81846 | −0.505676 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3175 | 0.992272 | 0.496136 | − | 0.868245i | \(-0.334752\pi\) | ||||
0.496136 | + | 0.868245i | \(0.334752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.2954 | 0.730462 | 0.365231 | − | 0.930917i | \(-0.380990\pi\) | ||||
0.365231 | + | 0.930917i | \(0.380990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0428 | −0.562796 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9946 | 1.06447 | 0.532235 | − | 0.846597i | \(-0.321352\pi\) | ||||
0.532235 | + | 0.846597i | \(0.321352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.48612 | 0.328017 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 63.8349 | 3.21188 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6365 | −0.533830 | −0.266915 | − | 0.963720i | \(-0.586004\pi\) | ||||
−0.266915 | + | 0.963720i | \(0.586004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.0011 | 1.74787 | 0.873936 | − | 0.486041i | \(-0.161560\pi\) | ||||
0.873936 | + | 0.486041i | \(0.161560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.51388 | 0.473920 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.62858 | 0.477271 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.98845 | 0.246663 | 0.123331 | − | 0.992366i | \(-0.460642\pi\) | ||||
0.123331 | + | 0.992366i | \(0.460642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.9901 | 0.688407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.67143 | −0.425664 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6991 | −0.669245 | −0.334623 | − | 0.942352i | \(-0.608609\pi\) | ||||
−0.334623 | + | 0.942352i | \(0.608609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9399 | 0.923073 | 0.461536 | − | 0.887121i | \(-0.347298\pi\) | ||||
0.461536 | + | 0.887121i | \(0.347298\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 107.664 | 5.22245 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.20706 | −0.443488 | −0.221744 | − | 0.975105i | \(-0.571175\pi\) | ||||
−0.221744 | + | 0.975105i | \(0.571175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6236 | −0.558595 | −0.279297 | − | 0.960205i | \(-0.590102\pi\) | ||||
−0.279297 | + | 0.960205i | \(0.590102\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.814291 | 0.0389528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.43333 | 0.211591 | 0.105796 | − | 0.994388i | \(-0.466261\pi\) | ||||
0.105796 | + | 0.994388i | \(0.466261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.2847 | −0.631175 | −0.315587 | − | 0.948897i | \(-0.602202\pi\) | ||||
−0.315587 | + | 0.948897i | \(0.602202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 75.9450 | 3.60014 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.9213 | 1.83681 | 0.918406 | − | 0.395640i | \(-0.129477\pi\) | ||||
0.918406 | + | 0.395640i | \(0.129477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.9532 | −0.798293 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.1101 | −0.567731 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1820 | 0.897294 | 0.448647 | − | 0.893709i | \(-0.351906\pi\) | ||||
0.448647 | + | 0.893709i | \(0.351906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6356 | −0.495348 | −0.247674 | − | 0.968843i | \(-0.579666\pi\) | ||||
−0.247674 | + | 0.968843i | \(0.579666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1794 | −0.566024 | −0.283012 | − | 0.959116i | \(-0.591334\pi\) | ||||
−0.283012 | + | 0.959116i | \(0.591334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3765 | 0.896638 | 0.448319 | − | 0.893874i | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.9805 | 0.553210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.5165 | 0.620178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.65503 | −0.212694 | −0.106347 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106347 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5592 | 0.481456 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.3918 | 1.10758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5431 | 1.29341 | 0.646705 | − | 0.762740i | \(-0.276147\pi\) | ||||
0.646705 | + | 0.762740i | \(0.276147\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.2443 | −0.913611 | −0.456806 | − | 0.889566i | \(-0.651007\pi\) | ||||
−0.456806 | + | 0.889566i | \(0.651007\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.7894 | −1.25157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.02768 | −0.225522 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.6345 | −1.32662 | −0.663311 | − | 0.748344i | \(-0.730849\pi\) | ||||
−0.663311 | + | 0.748344i | \(0.730849\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.03089 | 0.179729 | 0.0898643 | − | 0.995954i | \(-0.471357\pi\) | ||||
0.0898643 | + | 0.995954i | \(0.471357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.1248 | −0.940040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5409 | 0.644513 | 0.322256 | − | 0.946652i | \(-0.395559\pi\) | ||||
0.322256 | + | 0.946652i | \(0.395559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0204 | 0.708702 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.32659 | −0.278783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.3126 | −1.15723 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0631 | 1.40471 | 0.702355 | − | 0.711827i | \(-0.252132\pi\) | ||||
0.702355 | + | 0.711827i | \(0.252132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.0837 | −1.70901 | −0.854505 | − | 0.519443i | \(-0.826139\pi\) | ||||
−0.854505 | + | 0.519443i | \(0.826139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.9274 | 1.17298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3369 | −0.971171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.5916 | −0.805293 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.6516 | −1.93046 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.56627 | 0.110537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.3166 | 1.21743 | 0.608714 | − | 0.793390i | \(-0.291686\pi\) | ||||
0.608714 | + | 0.793390i | \(0.291686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.7613 | 1.10349 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.2621 | −1.08013 | −0.540065 | − | 0.841623i | \(-0.681600\pi\) | ||||
−0.540065 | + | 0.841623i | \(0.681600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.48879 | −0.148627 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8347 | −0.630836 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.67480 | −0.367563 | −0.183781 | − | 0.982967i | \(-0.558834\pi\) | ||||
−0.183781 | + | 0.982967i | \(0.558834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.97958 | 0.252009 | 0.126005 | − | 0.992030i | \(-0.459785\pi\) | ||||
0.126005 | + | 0.992030i | \(0.459785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.3633 | −1.65603 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.7830 | 1.29049 | 0.645246 | − | 0.763975i | \(-0.276755\pi\) | ||||
0.645246 | + | 0.763975i | \(0.276755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5389 | 0.482888 | 0.241444 | − | 0.970415i | \(-0.422379\pi\) | ||||
0.241444 | + | 0.970415i | \(0.422379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.0063 | 0.458996 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7345 | 1.02971 | 0.514856 | − | 0.857277i | \(-0.327845\pi\) | ||||
0.514856 | + | 0.857277i | \(0.327845\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.01517 | 0.0836033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.31191 | −0.0543339 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.5745 | 0.973023 | 0.486511 | − | 0.873674i | \(-0.338269\pi\) | ||||
0.486511 | + | 0.873674i | \(0.338269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.38056 | 0.139294 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0608 | 0.536344 | 0.268172 | − | 0.963371i | \(-0.413580\pi\) | ||||
0.268172 | + | 0.963371i | \(0.413580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.2756 | −1.40516 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.38643 | 0.220084 | 0.110042 | − | 0.993927i | \(-0.464902\pi\) | ||||
0.110042 | + | 0.993927i | \(0.464902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8213 | −1.05327 | −0.526636 | − | 0.850091i | \(-0.676547\pi\) | ||||
−0.526636 | + | 0.850091i | \(0.676547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.9949 | 0.772253 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.6095 | −1.08005 | −0.540024 | − | 0.841650i | \(-0.681585\pi\) | ||||
−0.540024 | + | 0.841650i | \(0.681585\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.8557 | −1.16738 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4101 | −0.501240 | −0.250620 | − | 0.968086i | \(-0.580634\pi\) | ||||
−0.250620 | + | 0.968086i | \(0.580634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.3448 | 1.46319 | 0.731594 | − | 0.681740i | \(-0.238777\pi\) | ||||
0.731594 | + | 0.681740i | \(0.238777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3371 | −1.05858 | −0.529288 | − | 0.848442i | \(-0.677541\pi\) | ||||
−0.529288 | + | 0.848442i | \(0.677541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.6490 | −0.707092 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 90.1125 | 3.60450 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.8859 | 1.19163 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2024 | −0.923672 | −0.461836 | − | 0.886965i | \(-0.652809\pi\) | ||||
−0.461836 | + | 0.886965i | \(0.652809\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.58174 | −0.102453 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.81429 | 0.111506 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.8540 | −1.10017 | −0.550084 | − | 0.835109i | \(-0.685404\pi\) | ||||
−0.550084 | + | 0.835109i | \(0.685404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.5593 | 1.32345 | 0.661725 | − | 0.749747i | \(-0.269825\pi\) | ||||
0.661725 | + | 0.749747i | \(0.269825\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0534 | 0.867010 | 0.433505 | − | 0.901151i | \(-0.357277\pi\) | ||||
0.433505 | + | 0.901151i | \(0.357277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9023 | 1.40929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.41949 | 0.0555489 | 0.0277745 | − | 0.999614i | \(-0.491158\pi\) | ||||
0.0277745 | + | 0.999614i | \(0.491158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.7571 | 1.20178 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.46852 | 0.0961600 | 0.0480800 | − | 0.998843i | \(-0.484690\pi\) | ||||
0.0480800 | + | 0.998843i | \(0.484690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.78771 | −0.264011 | −0.132006 | − | 0.991249i | \(-0.542142\pi\) | ||||
−0.132006 | + | 0.991249i | \(0.542142\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.30308 | −0.166866 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.84089 | −0.110000 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3976 | 0.594418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6087 | 0.910050 | 0.455025 | − | 0.890479i | \(-0.349630\pi\) | ||||
0.455025 | + | 0.890479i | \(0.349630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2817 | 0.548891 | 0.274446 | − | 0.961603i | \(-0.411506\pi\) | ||||
0.274446 | + | 0.961603i | \(0.411506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.66847 | −0.217536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.0560 | −1.45617 | −0.728086 | − | 0.685485i | \(-0.759590\pi\) | ||||
−0.728086 | + | 0.685485i | \(0.759590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.0387 | 1.91188 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.43871 | −0.0548104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3838 | −0.699352 | −0.349676 | − | 0.936871i | \(-0.613708\pi\) | ||||
−0.349676 | + | 0.936871i | \(0.613708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9631 | 0.491717 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.6204 | −1.99314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7583 | −1.23726 | −0.618632 | − | 0.785681i | \(-0.712313\pi\) | ||||
−0.618632 | + | 0.785681i | \(0.712313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.75198 | 0.141509 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.90923 | 0.184631 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.39583 | 0.0899773 | 0.0449886 | − | 0.998987i | \(-0.485675\pi\) | ||||
0.0449886 | + | 0.998987i | \(0.485675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.75276 | 0.103092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.0778 | −1.16224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.7999 | −0.663825 | −0.331912 | − | 0.943310i | \(-0.607694\pi\) | ||||
−0.331912 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.47025 | 0.0547549 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −47.1560 | −1.75133 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0921 | −0.745175 | −0.372588 | − | 0.927997i | \(-0.621529\pi\) | ||||
−0.372588 | + | 0.927997i | \(0.621529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.3474 | 1.67495 | 0.837473 | − | 0.546479i | \(-0.184032\pi\) | ||||
0.837473 | + | 0.546479i | \(0.184032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.7453 | 1.13252 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.15710 | −0.226493 | −0.113246 | − | 0.993567i | \(-0.536125\pi\) | ||||
−0.113246 | + | 0.993567i | \(0.536125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.5785 | −1.15850 | −0.579251 | − | 0.815149i | \(-0.696655\pi\) | ||||
−0.579251 | + | 0.815149i | \(0.696655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.3125 | 2.02649 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3767 | 0.379155 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.3207 | −1.39834 | −0.699171 | − | 0.714955i | \(-0.746447\pi\) | ||||
−0.699171 | + | 0.714955i | \(0.746447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 76.6476 | 2.78949 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0924 | −1.02104 | −0.510518 | − | 0.859867i | \(-0.670546\pi\) | ||||
−0.510518 | + | 0.859867i | \(0.670546\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4348 | −0.595762 | −0.297881 | − | 0.954603i | \(-0.596280\pi\) | ||||
−0.297881 | + | 0.954603i | \(0.596280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.98671 | −0.216733 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3721 | 1.42165 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0679 | 0.399117 | 0.199559 | − | 0.979886i | \(-0.436049\pi\) | ||||
0.199559 | + | 0.979886i | \(0.436049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.596231 | 0.0214449 | 0.0107225 | − | 0.999943i | \(-0.496587\pi\) | ||||
0.0107225 | + | 0.999943i | \(0.496587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.6932 | 1.64135 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.60615 | −0.236690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.9024 | −0.461683 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.26291 | −0.294916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8567 | −0.957339 | −0.478670 | − | 0.877995i | \(-0.658881\pi\) | ||||
−0.478670 | + | 0.877995i | \(0.658881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.14771 | 0.325255 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8857 | 0.599630 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.04742 | −0.249632 | −0.124816 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124816 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −81.6710 | −2.88931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.1127 | 1.45084 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.50396 | −0.123498 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.1531 | −0.989811 | −0.494905 | − | 0.868947i | \(-0.664797\pi\) | ||||
−0.494905 | + | 0.868947i | \(0.664797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.75550 | −0.237218 | −0.118609 | − | 0.992941i | \(-0.537843\pi\) | ||||
−0.118609 | + | 0.992941i | \(0.537843\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −97.0206 | −3.39848 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.1260 | −1.22591 | −0.612953 | − | 0.790120i | \(-0.710018\pi\) | ||||
−0.612953 | + | 0.790120i | \(0.710018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4393 | −0.398748 | −0.199374 | − | 0.979923i | \(-0.563891\pi\) | ||||
−0.199374 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.7134 | −0.650730 | −0.325365 | − | 0.945588i | \(-0.605487\pi\) | ||||
−0.325365 | + | 0.945588i | \(0.605487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.2244 | 1.29286 | 0.646429 | − | 0.762974i | \(-0.276262\pi\) | ||||
0.646429 | + | 0.762974i | \(0.276262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.96536 | 0.275984 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −45.2531 | −1.56605 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.6127 | 1.12591 | 0.562957 | − | 0.826486i | \(-0.309664\pi\) | ||||
0.562957 | + | 0.826486i | \(0.309664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8284 | −0.580289 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.8586 | 0.751960 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.41427 | −0.151676 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.05520 | 0.104731 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.56346 | 0.224729 | 0.112364 | − | 0.993667i | \(-0.464158\pi\) | ||||
0.112364 | + | 0.993667i | \(0.464158\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.6939 | −0.672729 | −0.336365 | − | 0.941732i | \(-0.609197\pi\) | ||||
−0.336365 | + | 0.941732i | \(0.609197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.41988 | −0.0484458 | −0.0242229 | − | 0.999707i | \(-0.507711\pi\) | ||||
−0.0242229 | + | 0.999707i | \(0.507711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.9991 | 1.08926 | 0.544631 | − | 0.838676i | \(-0.316670\pi\) | ||||
0.544631 | + | 0.838676i | \(0.316670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −105.039 | −3.57142 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.0698 | −1.29143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.7167 | 1.14245 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.6470 | −1.23889 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4933 | −0.894614 | −0.447307 | − | 0.894381i | \(-0.647617\pi\) | ||||
−0.447307 | + | 0.894381i | \(0.647617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5630 | 0.591713 | 0.295856 | − | 0.955232i | \(-0.404395\pi\) | ||||
0.295856 | + | 0.955232i | \(0.404395\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.05551 | −0.170132 | −0.0850658 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850658 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.7390 | 0.528464 | 0.264232 | − | 0.964459i | \(-0.414882\pi\) | ||||
0.264232 | + | 0.964459i | \(0.414882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.599976 | 0.0201225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2533 | −0.343113 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.4960 | 1.01937 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.7940 | −0.393353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.07201 | −0.135658 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0573 | −0.367558 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0379 | 0.632142 | 0.316071 | − | 0.948736i | \(-0.397636\pi\) | ||||
0.316071 | + | 0.948736i | \(0.397636\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.9775 | −1.75522 | −0.877611 | − | 0.479373i | \(-0.840864\pi\) | ||||
−0.877611 | + | 0.479373i | \(0.840864\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.17147 | 0.171151 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.14771 | −0.236038 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.5222 | −1.23774 | −0.618872 | − | 0.785492i | \(-0.712410\pi\) | ||||
−0.618872 | + | 0.785492i | \(0.712410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.1493 | −0.465731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.7135 | 1.66745 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.3372 | 1.88117 | 0.940586 | − | 0.339555i | \(-0.110276\pi\) | ||||
0.940586 | + | 0.339555i | \(0.110276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −87.9603 | −2.87661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.3469 | −0.370685 | −0.185343 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185343 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.7123 | 1.13159 | 0.565794 | − | 0.824547i | \(-0.308570\pi\) | ||||
0.565794 | + | 0.824547i | \(0.308570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.37933 | −0.175175 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.2357 | 0.527589 | 0.263794 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263794 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.0861 | 1.46356 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.4158 | 0.628938 | 0.314469 | − | 0.949268i | \(-0.398174\pi\) | ||||
0.314469 | + | 0.949268i | \(0.398174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 117.158 | 3.79114 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6286 | −0.375506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5718 | −0.631349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 62.5533 | 2.01366 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.38578 | −0.0445638 | −0.0222819 | − | 0.999752i | \(-0.507093\pi\) | ||||
−0.0222819 | + | 0.999752i | \(0.507093\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.33450 | 0.0428261 | 0.0214131 | − | 0.999771i | \(-0.493183\pi\) | ||||
0.0214131 | + | 0.999771i | \(0.493183\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.01251 | −0.0965766 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0460 | 0.417377 | 0.208689 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208689 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.2921 | −1.44754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0877 | −0.417433 | −0.208717 | − | 0.977976i | \(-0.566929\pi\) | ||||
−0.208717 | + | 0.977976i | \(0.566929\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.8351 | −1.14180 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.81643 | −0.152999 | −0.0764994 | − | 0.997070i | \(-0.524374\pi\) | ||||
−0.0764994 | + | 0.997070i | \(0.524374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −60.3309 | −1.91262 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.1127 | −0.351943 | −0.175971 | − | 0.984395i | \(-0.556307\pi\) | ||||
−0.175971 | + | 0.984395i | \(0.556307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 9576.2.a.co.1.1 | 5 | ||
3.2 | odd | 2 | 3192.2.a.ba.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 6384.2.a.ce.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.ba.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
6384.2.a.ce.1.5 | 5 | 12.11 | even | 2 | |||
9576.2.a.co.1.1 | 5 | 1.1 | even | 1 | trivial |