Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(737,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bj (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1313.12 | ||
Character | \(\chi\) | \(=\) | 2880.1313 |
Dual form | 2880.2.bj.f.737.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.27770 | + | 1.83507i | 0.571406 | + | 0.820667i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.254252 | − | 0.254252i | 0.0960981 | − | 0.0960981i | −0.657423 | − | 0.753521i | \(-0.728354\pi\) |
0.753521 | + | 0.657423i | \(0.228354\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83080 | −0.552007 | −0.276003 | − | 0.961157i | \(-0.589010\pi\) | ||||
−0.276003 | + | 0.961157i | \(0.589010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.689567 | − | 0.689567i | 0.191252 | − | 0.191252i | −0.604985 | − | 0.796237i | \(-0.706821\pi\) |
0.796237 | + | 0.604985i | \(0.206821\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00475 | + | 2.00475i | 0.486224 | + | 0.486224i | 0.907113 | − | 0.420888i | \(-0.138281\pi\) |
−0.420888 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.78955 | −1.09880 | −0.549399 | − | 0.835560i | \(-0.685143\pi\) | ||||
−0.549399 | + | 0.835560i | \(0.685143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.64533 | + | 4.64533i | −0.968618 | + | 0.968618i | −0.999522 | − | 0.0309039i | \(-0.990161\pi\) |
0.0309039 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.73495 | + | 4.68935i | −0.346989 | + | 0.937869i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.83628i | 0.340988i | 0.985359 | + | 0.170494i | \(0.0545363\pi\) | ||||
−0.985359 | + | 0.170494i | \(0.945464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.61389 | 0.649074 | 0.324537 | − | 0.945873i | \(-0.394792\pi\) | ||||
0.324537 | + | 0.945873i | \(0.394792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.791427 | + | 0.141711i | 0.133776 | + | 0.0239535i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.09169 | − | 5.09169i | −0.837069 | − | 0.837069i | 0.151403 | − | 0.988472i | \(-0.451621\pi\) |
−0.988472 | + | 0.151403i | \(0.951621\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.516552i | − | 0.0806719i | −0.999186 | − | 0.0403360i | \(-0.987157\pi\) | ||
0.999186 | − | 0.0403360i | \(-0.0128428\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.20041 | + | 4.20041i | −0.640556 | + | 0.640556i | −0.950692 | − | 0.310136i | \(-0.899625\pi\) |
0.310136 | + | 0.950692i | \(0.399625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22065 | − | 1.22065i | −0.178049 | − | 0.178049i | 0.612456 | − | 0.790505i | \(-0.290182\pi\) |
−0.790505 | + | 0.612456i | \(0.790182\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.87071i | 0.981530i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.36642 | + | 3.36642i | 0.462413 | + | 0.462413i | 0.899446 | − | 0.437032i | \(-0.143971\pi\) |
−0.437032 | + | 0.899446i | \(0.643971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.33922 | − | 3.35964i | −0.315420 | − | 0.453014i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6782i | 1.65057i | 0.564719 | + | 0.825283i | \(0.308985\pi\) | ||||
−0.564719 | + | 0.825283i | \(0.691015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.95560i | 0.378426i | 0.981936 | + | 0.189213i | \(0.0605936\pi\) | ||||
−0.981936 | + | 0.189213i | \(0.939406\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.14647 | + | 0.384340i | 0.266236 | + | 0.0476715i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.25944 | − | 6.25944i | −0.764713 | − | 0.764713i | 0.212458 | − | 0.977170i | \(-0.431853\pi\) |
−0.977170 | + | 0.212458i | \(0.931853\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.95039i | − | 0.231469i | −0.993280 | − | 0.115734i | \(-0.963078\pi\) | ||
0.993280 | − | 0.115734i | \(-0.0369222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.15481 | + | 7.15481i | 0.837407 | + | 0.837407i | 0.988517 | − | 0.151110i | \(-0.0482848\pi\) |
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.465483 | + | 0.465483i | −0.0530468 | + | 0.0530468i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.76682i | − | 0.761327i | −0.924714 | − | 0.380663i | \(-0.875696\pi\) | ||
0.924714 | − | 0.380663i | \(-0.124304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.933138 | + | 0.933138i | 0.102425 | + | 0.102425i | 0.756462 | − | 0.654037i | \(-0.226926\pi\) |
−0.654037 | + | 0.756462i | \(0.726926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.11738 | + | 6.24034i | −0.121197 | + | 0.676860i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7800 | 1.46068 | 0.730340 | − | 0.683084i | \(-0.239362\pi\) | ||||
0.730340 | + | 0.683084i | \(0.239362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.350647i | − | 0.0367578i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.11963 | − | 8.78915i | −0.627860 | − | 0.901748i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.21384 | + | 7.21384i | −0.732455 | + | 0.732455i | −0.971105 | − | 0.238651i | \(-0.923295\pi\) |
0.238651 | + | 0.971105i | \(0.423295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.05879 | −0.702376 | −0.351188 | − | 0.936305i | \(-0.614222\pi\) | ||||
−0.351188 | + | 0.936305i | \(0.614222\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.08589 | − | 5.08589i | −0.501128 | − | 0.501128i | 0.410660 | − | 0.911788i | \(-0.365298\pi\) |
−0.911788 | + | 0.410660i | \(0.865298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.60425 | + | 8.60425i | −0.831804 | + | 0.831804i | −0.987763 | − | 0.155960i | \(-0.950153\pi\) |
0.155960 | + | 0.987763i | \(0.450153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3463 | −1.85304 | −0.926522 | − | 0.376241i | \(-0.877216\pi\) | ||||
−0.926522 | + | 0.376241i | \(0.877216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.36399 | − | 7.36399i | 0.692746 | − | 0.692746i | −0.270090 | − | 0.962835i | \(-0.587053\pi\) |
0.962835 | + | 0.270090i | \(0.0870533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.4599 | − | 2.58914i | −1.34839 | − | 0.241439i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.01942 | 0.0934505 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.64818 | −0.695289 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8220 | + | 2.80785i | −0.967950 | + | 0.251142i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0141 | − | 12.0141i | 1.06608 | − | 1.06608i | 0.0684223 | − | 0.997656i | \(-0.478203\pi\) |
0.997656 | − | 0.0684223i | \(-0.0217965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4279 | 1.17320 | 0.586602 | − | 0.809876i | \(-0.300465\pi\) | ||||
0.586602 | + | 0.809876i | \(0.300465\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.21775 | + | 1.21775i | −0.105592 | + | 0.105592i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.42848 | + | 7.42848i | 0.634658 | + | 0.634658i | 0.949233 | − | 0.314575i | \(-0.101862\pi\) |
−0.314575 | + | 0.949233i | \(0.601862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.77951 | −0.659849 | −0.329925 | − | 0.944007i | \(-0.607023\pi\) | ||||
−0.329925 | + | 0.944007i | \(0.607023\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26246 | + | 1.26246i | −0.105572 | + | 0.105572i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.36969 | + | 2.34622i | −0.279837 | + | 0.194843i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5.40869i | − | 0.443097i | −0.975149 | − | 0.221549i | \(-0.928889\pi\) | ||
0.975149 | − | 0.221549i | \(-0.0711112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4143 | −1.66129 | −0.830646 | − | 0.556801i | \(-0.812029\pi\) | ||||
−0.830646 | + | 0.556801i | \(0.812029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.61748 | + | 6.63174i | 0.370885 | + | 0.532674i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.47780 | − | 1.47780i | −0.117941 | − | 0.117941i | 0.645673 | − | 0.763614i | \(-0.276577\pi\) |
−0.763614 | + | 0.645673i | \(0.776577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.36217i | 0.186165i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.20041 | + | 6.20041i | −0.485654 | + | 0.485654i | −0.906932 | − | 0.421278i | \(-0.861582\pi\) |
0.421278 | + | 0.906932i | \(0.361582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.70865 | + | 8.70865i | 0.673895 | + | 0.673895i | 0.958612 | − | 0.284716i | \(-0.0918994\pi\) |
−0.284716 | + | 0.958612i | \(0.591899\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0490i | 0.926846i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2164 | + | 11.2164i | 0.852767 | + | 0.852767i | 0.990473 | − | 0.137706i | \(-0.0439729\pi\) |
−0.137706 | + | 0.990473i | \(0.543973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.751160 | + | 1.63339i | 0.0567824 | + | 0.123472i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.10948i | 0.307157i | 0.988136 | + | 0.153578i | \(0.0490797\pi\) | ||||
−0.988136 | + | 0.153578i | \(0.950920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.00341534i | − | 0.000253860i | −1.00000 | 0.000126930i | \(-0.999960\pi\) | |||
1.00000 | 0.000126930i | \(-4.04031e-5\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.83793 | − | 15.8493i | 0.208648 | − | 1.16526i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.67030 | − | 3.67030i | −0.268399 | − | 0.268399i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.3997i | − | 1.11428i | −0.830418 | − | 0.557141i | \(-0.811898\pi\) | ||
0.830418 | − | 0.557141i | \(-0.188102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7895 | + | 11.7895i | 0.848630 | + | 0.848630i | 0.989962 | − | 0.141332i | \(-0.0451385\pi\) |
−0.141332 | + | 0.989962i | \(0.545138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.0500670 | + | 0.0500670i | −0.00356713 | + | 0.00356713i | −0.708888 | − | 0.705321i | \(-0.750803\pi\) |
0.705321 | + | 0.708888i | \(0.250803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.0367i | − | 1.49125i | −0.666367 | − | 0.745624i | \(-0.732151\pi\) | ||
0.666367 | − | 0.745624i | \(-0.267849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.466876 | + | 0.466876i | 0.0327683 | + | 0.0327683i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.947908 | − | 0.660001i | 0.0662048 | − | 0.0460965i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.76870 | 0.606544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.97787i | − | 0.480377i | −0.970726 | − | 0.240188i | \(-0.922791\pi\) | ||
0.970726 | − | 0.240188i | \(-0.0772092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.0749 | − | 2.34116i | −0.891702 | − | 0.159666i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.918838 | − | 0.918838i | 0.0623748 | − | 0.0623748i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.76483 | 0.185982 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5156 | + | 17.5156i | 1.17293 | + | 1.17293i | 0.981507 | + | 0.191426i | \(0.0613112\pi\) |
0.191426 | + | 0.981507i | \(0.438689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.4948 | + | 12.4948i | −0.829308 | + | 0.829308i | −0.987421 | − | 0.158113i | \(-0.949459\pi\) |
0.158113 | + | 0.987421i | \(0.449459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.7394 | −0.709681 | −0.354841 | − | 0.934927i | \(-0.615465\pi\) | ||||
−0.354841 | + | 0.934927i | \(0.615465\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9848 | + | 14.9848i | −0.981687 | + | 0.981687i | −0.999835 | − | 0.0181481i | \(-0.994223\pi\) |
0.0181481 | + | 0.999835i | \(0.494223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.680344 | − | 3.79959i | 0.0443808 | − | 0.247858i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.22643 | 0.0793311 | 0.0396656 | − | 0.999213i | \(-0.487371\pi\) | ||||
0.0396656 | + | 0.999213i | \(0.487371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.90880 | 0.122956 | 0.0614782 | − | 0.998108i | \(-0.480419\pi\) | ||||
0.0614782 | + | 0.998108i | \(0.480419\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.6082 | + | 8.77873i | −0.805510 | + | 0.560853i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.30272 | + | 3.30272i | −0.210147 | + | 0.210147i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9617 | −0.818133 | −0.409067 | − | 0.912505i | \(-0.634146\pi\) | ||||
−0.409067 | + | 0.912505i | \(0.634146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.50467 | − | 8.50467i | 0.534684 | − | 0.534684i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.79714 | + | 6.79714i | 0.423994 | + | 0.423994i | 0.886576 | − | 0.462582i | \(-0.153077\pi\) |
−0.462582 | + | 0.886576i | \(0.653077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.58914 | −0.160881 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3880 | + | 21.3880i | −1.31884 | + | 1.31884i | −0.404142 | + | 0.914696i | \(0.632430\pi\) |
−0.914696 | + | 0.404142i | \(0.867570\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.87632 | + | 10.4789i | −0.115262 | + | 0.643713i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 8.79735i | − | 0.536384i | −0.963366 | − | 0.268192i | \(-0.913574\pi\) | ||
0.963366 | − | 0.268192i | \(-0.0864261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7139 | 1.25828 | 0.629139 | − | 0.777293i | \(-0.283407\pi\) | ||||
0.629139 | + | 0.777293i | \(0.283407\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.17634 | − | 8.58525i | 0.191540 | − | 0.517710i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.64175 | − | 3.64175i | −0.218812 | − | 0.218812i | 0.589186 | − | 0.807997i | \(-0.299449\pi\) |
−0.807997 | + | 0.589186i | \(0.799449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.96873i | − | 0.475375i | −0.971342 | − | 0.237687i | \(-0.923611\pi\) | ||
0.971342 | − | 0.237687i | \(-0.0763893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1783 | + | 15.1783i | −0.902255 | + | 0.902255i | −0.995631 | − | 0.0933758i | \(-0.970234\pi\) |
0.0933758 | + | 0.995631i | \(0.470234\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.131334 | − | 0.131334i | −0.00775241 | − | 0.00775241i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 8.96192i | − | 0.527172i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2504 | + | 19.2504i | 1.12462 | + | 1.12462i | 0.991038 | + | 0.133582i | \(0.0426479\pi\) |
0.133582 | + | 0.991038i | \(0.457352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.2654 | + | 16.1990i | −1.35457 | + | 0.943145i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.40654i | 0.370500i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.13592i | 0.123112i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.42372 | + | 3.77638i | −0.310561 | + | 0.216235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0590 | + | 14.0590i | 0.802391 | + | 0.802391i | 0.983469 | − | 0.181077i | \(-0.0579584\pi\) |
−0.181077 | + | 0.983469i | \(0.557958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3949i | 1.38331i | 0.722230 | + | 0.691653i | \(0.243117\pi\) | ||||
−0.722230 | + | 0.691653i | \(0.756883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.49794 | − | 3.49794i | −0.197715 | − | 0.197715i | 0.601305 | − | 0.799020i | \(-0.294648\pi\) |
−0.799020 | + | 0.601305i | \(0.794648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1877 | − | 16.1877i | 0.909191 | − | 0.909191i | −0.0870160 | − | 0.996207i | \(-0.527733\pi\) |
0.996207 | + | 0.0870160i | \(0.0277331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.36185i | − | 0.188228i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.60187 | − | 9.60187i | −0.534263 | − | 0.534263i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.03726 | + | 4.42998i | 0.113007 | + | 0.245731i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.620702 | −0.0342204 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.02804i | − | 0.386296i | −0.981170 | − | 0.193148i | \(-0.938130\pi\) | ||
0.981170 | − | 0.193148i | \(-0.0618698\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.48879 | − | 19.4842i | 0.190613 | − | 1.06454i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.44642 | − | 1.44642i | 0.0787915 | − | 0.0787915i | −0.666613 | − | 0.745404i | \(-0.732256\pi\) |
0.745404 | + | 0.666613i | \(0.232256\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.61631 | −0.358293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.52665 | + | 3.52665i | 0.190421 | + | 0.190421i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.9677 | − | 21.9677i | 1.17929 | − | 1.17929i | 0.199361 | − | 0.979926i | \(-0.436113\pi\) |
0.979926 | − | 0.199361i | \(-0.0638866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8467 | 1.06237 | 0.531184 | − | 0.847257i | \(-0.321747\pi\) | ||||
0.531184 | + | 0.847257i | \(0.321747\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.3280 | + | 17.3280i | −0.922275 | + | 0.922275i | −0.997190 | − | 0.0749150i | \(-0.976131\pi\) |
0.0749150 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.57910 | − | 2.49202i | 0.189959 | − | 0.132263i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.0838 | 1.00720 | 0.503602 | − | 0.863936i | \(-0.332008\pi\) | ||||
0.503602 | + | 0.863936i | \(0.332008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.93979 | 0.207357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.98783 | + | 22.2713i | −0.208733 | + | 1.16573i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9049 | − | 16.9049i | 0.882427 | − | 0.882427i | −0.111354 | − | 0.993781i | \(-0.535519\pi\) |
0.993781 | + | 0.111354i | \(0.0355186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71184 | 0.0888740 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1898 | − | 16.1898i | 0.838278 | − | 0.838278i | −0.150355 | − | 0.988632i | \(-0.548042\pi\) |
0.988632 | + | 0.150355i | \(0.0480415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.26624 | + | 1.26624i | 0.0652144 | + | 0.0652144i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0180 | 0.925523 | 0.462761 | − | 0.886483i | \(-0.346859\pi\) | ||||
0.462761 | + | 0.886483i | \(0.346859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.69204 | + | 9.69204i | −0.495240 | + | 0.495240i | −0.909953 | − | 0.414712i | \(-0.863882\pi\) |
0.414712 | + | 0.909953i | \(0.363882\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.44894 | − | 0.259444i | −0.0738450 | − | 0.0132225i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 12.0298i | − | 0.609937i | −0.952363 | − | 0.304968i | \(-0.901354\pi\) | ||
0.952363 | − | 0.304968i | \(-0.0986459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.6255 | −0.941932 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.4176 | − | 8.64599i | 0.624796 | − | 0.435027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2547 | − | 14.2547i | −0.715420 | − | 0.715420i | 0.252243 | − | 0.967664i | \(-0.418832\pi\) |
−0.967664 | + | 0.252243i | \(0.918832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.8873i | − | 1.39263i | −0.717739 | − | 0.696313i | \(-0.754823\pi\) | ||
0.717739 | − | 0.696313i | \(-0.245177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.49202 | − | 2.49202i | 0.124136 | − | 0.124136i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.32186 | + | 9.32186i | 0.462068 | + | 0.462068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.0490i | − | 1.23859i | −0.785157 | − | 0.619297i | \(-0.787418\pi\) | ||
0.785157 | − | 0.619297i | \(-0.212582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.22346 | + | 3.22346i | 0.158616 | + | 0.158616i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.520097 | + | 2.90464i | −0.0255306 | + | 0.142583i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.04215i | 0.295178i | 0.989049 | + | 0.147589i | \(0.0471513\pi\) | ||||
−0.989049 | + | 0.147589i | \(0.952849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2560i | 0.792267i | 0.918193 | + | 0.396134i | \(0.129648\pi\) | ||||
−0.918193 | + | 0.396134i | \(0.870352\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8791 | + | 5.92284i | −0.624730 | + | 0.287300i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.751466 | + | 0.751466i | 0.0363660 | + | 0.0363660i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.5991i | − | 1.90742i | −0.300725 | − | 0.953711i | \(-0.597229\pi\) | ||
0.300725 | − | 0.953711i | \(-0.402771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.87071 | − | 6.87071i | −0.330185 | − | 0.330185i | 0.522471 | − | 0.852657i | \(-0.325010\pi\) |
−0.852657 | + | 0.522471i | \(0.825010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.2490 | − | 22.2490i | 1.06432 | − | 1.06432i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.51705i | 0.215587i | 0.994173 | + | 0.107794i | \(0.0343786\pi\) | ||||
−0.994173 | + | 0.107794i | \(0.965621\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0369 | − | 28.0369i | −1.33208 | − | 1.33208i | −0.903512 | − | 0.428564i | \(-0.859020\pi\) |
−0.428564 | − | 0.903512i | \(-0.640980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.6068 | + | 25.2873i | 0.834642 | + | 1.19873i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00946 | 0.0948321 | 0.0474161 | − | 0.998875i | \(-0.484901\pi\) | ||||
0.0474161 | + | 0.998875i | \(0.484901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.945703i | 0.0445314i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.643461 | − | 0.448023i | 0.0301659 | − | 0.0210036i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6837 | − | 18.6837i | 0.873988 | − | 0.873988i | −0.118916 | − | 0.992904i | \(-0.537942\pi\) |
0.992904 | + | 0.118916i | \(0.0379419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8230 | −1.43557 | −0.717785 | − | 0.696265i | \(-0.754844\pi\) | ||||
−0.717785 | + | 0.696265i | \(0.754844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.6582 | + | 25.6582i | 1.19244 | + | 1.19244i | 0.976381 | + | 0.216055i | \(0.0693190\pi\) |
0.216055 | + | 0.976381i | \(0.430681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7321 | + | 20.7321i | −0.959368 | + | 0.959368i | −0.999206 | − | 0.0398377i | \(-0.987316\pi\) |
0.0398377 | + | 0.999206i | \(0.487316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.18295 | −0.146975 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.69010 | − | 7.69010i | 0.353591 | − | 0.353591i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.30961 | − | 22.4599i | 0.381271 | − | 1.03053i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4211 | 1.57274 | 0.786369 | − | 0.617757i | \(-0.211958\pi\) | ||||
0.786369 | + | 0.617757i | \(0.211958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.02213 | −0.320181 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.4550 | − | 4.02074i | −1.01963 | − | 0.182572i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4836 | + | 16.4836i | −0.746944 | + | 0.746944i | −0.973904 | − | 0.226960i | \(-0.927121\pi\) |
0.226960 | + | 0.973904i | \(0.427121\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.4583 | 1.28431 | 0.642153 | − | 0.766576i | \(-0.278041\pi\) | ||||
0.642153 | + | 0.766576i | \(0.278041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.68128 | + | 3.68128i | −0.165797 | + | 0.165797i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.495890 | − | 0.495890i | −0.0222437 | − | 0.0222437i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.7252 | 1.46498 | 0.732491 | − | 0.680777i | \(-0.238358\pi\) | ||||
0.732491 | + | 0.680777i | \(0.238358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.29645 | + | 9.29645i | −0.414508 | + | 0.414508i | −0.883306 | − | 0.468798i | \(-0.844687\pi\) |
0.468798 | + | 0.883306i | \(0.344687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.01904 | − | 12.9534i | −0.401342 | − | 0.576417i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 42.2217i | − | 1.87145i | −0.352736 | − | 0.935723i | \(-0.614749\pi\) | ||
0.352736 | − | 0.935723i | \(-0.385251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.63824 | 0.160946 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.83469 | − | 15.8312i | 0.124912 | − | 0.697607i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.23476 | + | 2.23476i | 0.0982845 | + | 0.0982845i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.2056i | 0.885222i | 0.896714 | + | 0.442611i | \(0.145948\pi\) | ||||
−0.896714 | + | 0.442611i | \(0.854052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0770 | − | 12.0770i | 0.528092 | − | 0.528092i | −0.391911 | − | 0.920003i | \(-0.628186\pi\) |
0.920003 | + | 0.391911i | \(0.128186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.24497 | + | 7.24497i | 0.315596 | + | 0.315596i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 20.1582i | − | 0.876443i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.356198 | − | 0.356198i | −0.0154286 | − | 0.0154286i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.7830 | − | 4.79570i | −1.15793 | − | 0.207336i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.5789i | − | 0.541811i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.64277i | 0.0706282i | 0.999376 | + | 0.0353141i | \(0.0112432\pi\) | ||||
−0.999376 | + | 0.0353141i | \(0.988757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.7189 | − | 35.5018i | −1.05884 | − | 1.52073i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1302 | + | 30.1302i | 1.28827 | + | 1.28827i | 0.935836 | + | 0.352437i | \(0.114647\pi\) |
0.352437 | + | 0.935836i | \(0.385353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.79493i | − | 0.374677i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.72047 | − | 1.72047i | −0.0731620 | − | 0.0731620i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.13608 | + | 6.13608i | −0.259994 | + | 0.259994i | −0.825051 | − | 0.565058i | \(-0.808854\pi\) |
0.565058 | + | 0.825051i | \(0.308854\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.79293i | 0.245015i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.8286 | + | 11.8286i | 0.498516 | + | 0.498516i | 0.910976 | − | 0.412460i | \(-0.135330\pi\) |
−0.412460 | + | 0.910976i | \(0.635330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.9224 | + | 4.10442i | 0.964353 | + | 0.172674i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00956 | −0.251934 | −0.125967 | − | 0.992034i | \(-0.540203\pi\) | ||||
−0.125967 | + | 0.992034i | \(0.540203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6691i | 0.948673i | 0.880344 | + | 0.474337i | \(0.157312\pi\) | ||||
−0.880344 | + | 0.474337i | \(0.842688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.7242 | − | 29.8430i | −0.572337 | − | 1.24454i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5469 | − | 22.5469i | 0.938641 | − | 0.938641i | −0.0595824 | − | 0.998223i | \(-0.518977\pi\) |
0.998223 | + | 0.0595824i | \(0.0189769\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.474503 | 0.0196857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.16324 | − | 6.16324i | −0.255255 | − | 0.255255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.28298 | − | 9.28298i | 0.383149 | − | 0.383149i | −0.489086 | − | 0.872236i | \(-0.662670\pi\) |
0.872236 | + | 0.489086i | \(0.162670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.3089 | −0.713201 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.4256 | + | 20.4256i | −0.838780 | + | 0.838780i | −0.988698 | − | 0.149919i | \(-0.952099\pi\) |
0.149919 | + | 0.988698i | \(0.452099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.30252 | + | 1.87071i | 0.0533982 | + | 0.0766917i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.3981 | 1.32375 | 0.661876 | − | 0.749613i | \(-0.269761\pi\) | ||||
0.661876 | + | 0.749613i | \(0.269761\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.6924 | −0.762480 | −0.381240 | − | 0.924476i | \(-0.624503\pi\) | ||||
−0.381240 | + | 0.924476i | \(0.624503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.77210 | − | 14.0349i | −0.397292 | − | 0.570601i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.49215 | − | 5.49215i | 0.222919 | − | 0.222919i | −0.586807 | − | 0.809727i | \(-0.699615\pi\) |
0.809727 | + | 0.586807i | \(0.199615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.68343 | −0.0681045 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.9411 | − | 23.9411i | 0.966973 | − | 0.966973i | −0.0324989 | − | 0.999472i | \(-0.510347\pi\) |
0.999472 | + | 0.0324989i | \(0.0103465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4369 | − | 25.4369i | −1.02405 | − | 1.02405i | −0.999704 | − | 0.0243492i | \(-0.992249\pi\) |
−0.0243492 | − | 0.999704i | \(-0.507751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.9418 | 1.20346 | 0.601732 | − | 0.798698i | \(-0.294478\pi\) | ||||
0.601732 | + | 0.798698i | \(0.294478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.50359 | − | 3.50359i | 0.140368 | − | 0.140368i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.9799 | − | 16.2715i | −0.759197 | − | 0.650861i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20.4152i | − | 0.814007i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.4833 | −1.85047 | −0.925236 | − | 0.379391i | \(-0.876133\pi\) | ||||
−0.925236 | + | 0.379391i | \(0.876133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.3971 | + | 6.69623i | 1.48406 | + | 0.265732i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.73782 | + | 4.73782i | 0.187719 | + | 0.187719i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9516i | 0.432562i | 0.976331 | + | 0.216281i | \(0.0693927\pi\) | ||||
−0.976331 | + | 0.216281i | \(0.930607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5469 | − | 23.5469i | 0.928600 | − | 0.928600i | −0.0690153 | − | 0.997616i | \(-0.521986\pi\) |
0.997616 | + | 0.0690153i | \(0.0219857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.3239 | + | 30.3239i | 1.19216 | + | 1.19216i | 0.976461 | + | 0.215694i | \(0.0692014\pi\) |
0.215694 | + | 0.976461i | \(0.430799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 23.2113i | − | 0.911124i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3657 | + | 21.3657i | 0.836106 | + | 0.836106i | 0.988344 | − | 0.152238i | \(-0.0486481\pi\) |
−0.152238 | + | 0.988344i | \(0.548648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1569 | + | 24.6412i | 0.670376 | + | 0.962810i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 16.9067i | − | 0.658591i | −0.944227 | − | 0.329295i | \(-0.893189\pi\) | ||
0.944227 | − | 0.329295i | \(-0.106811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.28919i | 0.205726i | 0.994696 | + | 0.102863i | \(0.0328003\pi\) | ||||
−0.994696 | + | 0.102863i | \(0.967200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.79058 | − | 0.678730i | −0.146992 | − | 0.0263200i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.53011 | − | 8.53011i | −0.330287 | − | 0.330287i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.41111i | − | 0.208893i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.93979 | + | 9.93979i | 0.383151 | + | 0.383151i | 0.872236 | − | 0.489085i | \(-0.162669\pi\) |
−0.489085 | + | 0.872236i | \(0.662669\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.23998 | − | 8.23998i | 0.316688 | − | 0.316688i | −0.530805 | − | 0.847494i | \(-0.678111\pi\) |
0.847494 | + | 0.530805i | \(0.178111\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.66826i | 0.140775i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.8299 | − | 30.8299i | −1.17967 | − | 1.17967i | −0.979827 | − | 0.199846i | \(-0.935956\pi\) |
−0.199846 | − | 0.979827i | \(-0.564044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.14037 | + | 23.1232i | −0.158195 | + | 0.883490i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.64275 | 0.176875 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.2506i | − | 0.846452i | −0.906024 | − | 0.423226i | \(-0.860898\pi\) | ||
0.906024 | − | 0.423226i | \(-0.139102\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.93991 | − | 14.2759i | −0.377042 | − | 0.541517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03556 | − | 1.03556i | 0.0392247 | − | 0.0392247i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.59065 | −0.248925 | −0.124463 | − | 0.992224i | \(-0.539721\pi\) | ||||
−0.124463 | + | 0.992224i | \(0.539721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.3869 | + | 24.3869i | 0.919770 | + | 0.919770i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.79471 | + | 1.79471i | −0.0674970 | + | 0.0674970i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.7255 | −0.778362 | −0.389181 | − | 0.921161i | \(-0.627242\pi\) | ||||
−0.389181 | + | 0.921161i | \(0.627242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.7877 | + | 16.7877i | −0.628705 | + | 0.628705i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.92975 | − | 0.703649i | −0.146964 | − | 0.0263150i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.2992 | 0.645152 | 0.322576 | − | 0.946543i | \(-0.395451\pi\) | ||||
0.322576 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.58619 | −0.0963149 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.61093 | − | 3.18584i | −0.319802 | − | 0.118319i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.70255 | − | 7.70255i | 0.285672 | − | 0.285672i | −0.549694 | − | 0.835366i | \(-0.685256\pi\) |
0.835366 | + | 0.549694i | \(0.185256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.8416 | −0.622908 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.9043 | − | 37.9043i | 1.40003 | − | 1.40003i | 0.600106 | − | 0.799920i | \(-0.295125\pi\) |
0.799920 | − | 0.600106i | \(-0.204875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4598 | + | 11.4598i | 0.422127 | + | 0.422127i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.01209 | 0.147587 | 0.0737935 | − | 0.997274i | \(-0.476489\pi\) | ||||
0.0737935 | + | 0.997274i | \(0.476489\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.0857 | + | 32.0857i | −1.17711 | + | 1.17711i | −0.196633 | + | 0.980477i | \(0.563001\pi\) |
−0.980477 | + | 0.196633i | \(0.936999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.92532 | − | 6.91070i | 0.363635 | − | 0.253189i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.37529i | 0.159869i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.1166 | 0.953007 | 0.476504 | − | 0.879172i | \(-0.341904\pi\) | ||||
0.476504 | + | 0.879172i | \(0.341904\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.0834 | − | 37.4616i | −0.949273 | − | 1.36337i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.7046 | + | 15.7046i | 0.570793 | + | 0.570793i | 0.932350 | − | 0.361557i | \(-0.117755\pi\) |
−0.361557 | + | 0.932350i | \(0.617755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 39.0720i | − | 1.41636i | −0.706032 | − | 0.708180i | \(-0.749517\pi\) | ||
0.706032 | − | 0.708180i | \(-0.250483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.91884 | + | 4.91884i | −0.178074 | + | 0.178074i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.74250 | + | 8.74250i | 0.315674 | + | 0.315674i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 43.8064i | − | 1.57970i | −0.613301 | − | 0.789849i | \(-0.710159\pi\) | ||
0.613301 | − | 0.789849i | \(-0.289841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.8154 | + | 12.8154i | 0.460939 | + | 0.460939i | 0.898963 | − | 0.438024i | \(-0.144322\pi\) |
−0.438024 | + | 0.898963i | \(0.644322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.26991 | + | 16.9468i | −0.225222 | + | 0.608746i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.47405i | 0.0886421i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.57077i | 0.127772i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.823672 | − | 4.60005i | 0.0293981 | − | 0.164183i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4879 | + | 21.4879i | 0.765961 | + | 0.765961i | 0.977393 | − | 0.211432i | \(-0.0678127\pi\) |
−0.211432 | + | 0.977393i | \(0.567813\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.74461i | − | 0.133143i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03808 | + | 2.03808i | 0.0723745 | + | 0.0723745i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.2719 | − | 23.2719i | 0.824333 | − | 0.824333i | −0.162393 | − | 0.986726i | \(-0.551921\pi\) |
0.986726 | + | 0.162393i | \(0.0519214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.89419i | − | 0.173144i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.0990 | − | 13.0990i | −0.462254 | − | 0.462254i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.33473 | + | 3.01815i | −0.152779 | + | 0.106376i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3594 | −0.504850 | −0.252425 | − | 0.967617i | \(-0.581228\pi\) | ||||
−0.252425 | + | 0.967617i | \(0.581228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.03808i | 0.141796i | 0.997484 | + | 0.0708982i | \(0.0225865\pi\) | ||||
−0.997484 | + | 0.0708982i | \(0.977413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.3005 | − | 3.45589i | −0.676065 | − | 0.121054i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.1181 | − | 20.1181i | 0.703842 | − | 0.703842i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.45799 | 0.190485 | 0.0952426 | − | 0.995454i | \(-0.469637\pi\) | ||||
0.0952426 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.0732 | + | 12.0732i | 0.420846 | + | 0.420846i | 0.885495 | − | 0.464649i | \(-0.153819\pi\) |
−0.464649 | + | 0.885495i | \(0.653819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.37343 | − | 5.37343i | 0.186853 | − | 0.186853i | −0.607481 | − | 0.794334i | \(-0.707820\pi\) |
0.794334 | + | 0.607481i | \(0.207820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2343 | 0.876425 | 0.438213 | − | 0.898871i | \(-0.355612\pi\) | ||||
0.438213 | + | 0.898871i | \(0.355612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.7741 | + | 13.7741i | −0.477244 | + | 0.477244i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.85389 | + | 27.1080i | −0.167976 | + | 0.938112i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.7466 | −0.750775 | −0.375388 | − | 0.926868i | \(-0.622490\pi\) | ||||
−0.375388 | + | 0.926868i | \(0.622490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6281 | 0.883727 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.1107 | + | 15.3950i | −0.760632 | + | 0.529606i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.94456 | + | 1.94456i | −0.0668159 | + | 0.0668159i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.3052 | 1.62160 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0763 | − | 13.0763i | 0.447723 | − | 0.447723i | −0.446874 | − | 0.894597i | \(-0.647463\pi\) |
0.894597 | + | 0.446874i | \(0.147463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.8777 | + | 17.8777i | 0.610691 | + | 0.610691i | 0.943126 | − | 0.332435i | \(-0.107870\pi\) |
−0.332435 | + | 0.943126i | \(0.607870\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9017 | 0.917874 | 0.458937 | − | 0.888469i | \(-0.348230\pi\) | ||||
0.458937 | + | 0.888469i | \(0.348230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.00388 | − | 2.00388i | 0.0682129 | − | 0.0682129i | −0.672177 | − | 0.740390i | \(-0.734641\pi\) |
0.740390 | + | 0.672177i | \(0.234641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.25162 | + | 34.9141i | −0.212561 | + | 1.18711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.3887i | 0.420257i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.63262 | −0.292505 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.03761 | + | 3.46541i | −0.0688839 | + | 0.117152i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.9778 | − | 12.9778i | −0.438228 | − | 0.438228i | 0.453187 | − | 0.891415i | \(-0.350287\pi\) |
−0.891415 | + | 0.453187i | \(0.850287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4446i | 0.823561i | 0.911283 | + | 0.411780i | \(0.135093\pi\) | ||||
−0.911283 | + | 0.411780i | \(0.864907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2583 | + | 25.2583i | −0.850008 | + | 0.850008i | −0.990134 | − | 0.140125i | \(-0.955249\pi\) |
0.140125 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8856 | + | 30.8856i | 1.03704 | + | 1.03704i | 0.999287 | + | 0.0377508i | \(0.0120193\pi\) |
0.0377508 | + | 0.999287i | \(0.487981\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.10921i | − | 0.204896i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.84634 | + | 5.84634i | 0.195640 | + | 0.195640i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.54117 | + | 5.25069i | −0.252073 | + | 0.175511i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.63610i | 0.221326i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4977i | 0.449673i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.00626738 | − | 0.00436379i | 0.000208335 | − | 0.000145057i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.41677 | + | 5.41677i | 0.179861 | + | 0.179861i | 0.791295 | − | 0.611434i | \(-0.209407\pi\) |
−0.611434 | + | 0.791295i | \(0.709407\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.68534i | − | 0.188364i | −0.995555 | − | 0.0941819i | \(-0.969976\pi\) | ||
0.995555 | − | 0.0941819i | \(-0.0300235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.70839 | − | 1.70839i | −0.0565394 | − | 0.0565394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.41407 | − | 3.41407i | 0.112743 | − | 0.112743i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 0.556042i | − | 0.0183421i | −0.999958 | − | 0.00917107i | \(-0.997081\pi\) | ||
0.999958 | − | 0.00917107i | \(-0.00291928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.34493 | − | 1.34493i | −0.0442688 | − | 0.0442688i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.7105 | − | 15.0429i | 1.07551 | − | 0.494607i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.82202 | −0.158205 | −0.0791026 | − | 0.996866i | \(-0.525205\pi\) | ||||
−0.0791026 | + | 0.996866i | \(0.525205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 32.9076i | − | 1.07850i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.04570 | − | 11.4248i | 0.0669014 | − | 0.373631i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.4658 | + | 21.4658i | −0.701256 | + | 0.701256i | −0.964680 | − | 0.263424i | \(-0.915148\pi\) |
0.263424 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.7844 | 1.45993 | 0.729965 | − | 0.683485i | \(-0.239536\pi\) | ||||
0.729965 | + | 0.683485i | \(0.239536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.39956 | + | 2.39956i | 0.0781403 | + | 0.0781403i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.2492 | + | 19.2492i | −0.625516 | + | 0.625516i | −0.946937 | − | 0.321420i | \(-0.895840\pi\) |
0.321420 | + | 0.946937i | \(0.395840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.86744 | 0.320311 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.3612 | + | 17.3612i | −0.562383 | + | 0.562383i | −0.929984 | − | 0.367600i | \(-0.880179\pi\) |
0.367600 | + | 0.929984i | \(0.380179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.2594 | − | 19.6762i | 0.914454 | − | 0.636707i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.77740 | 0.121979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.9398 | −0.578703 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.57107 | + | 36.6982i | −0.211530 | + | 1.18136i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.61454 | + | 9.61454i | −0.309183 | + | 0.309183i | −0.844592 | − | 0.535410i | \(-0.820157\pi\) |
0.535410 | + | 0.844592i | \(0.320157\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.6838 | −1.33770 | −0.668848 | − | 0.743399i | \(-0.733212\pi\) | ||||
−0.668848 | + | 0.743399i | \(0.733212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.97795 | + | 1.97795i | −0.0634102 | + | 0.0634102i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.3061 | − | 22.3061i | −0.713635 | − | 0.713635i | 0.253659 | − | 0.967294i | \(-0.418366\pi\) |
−0.967294 | + | 0.253659i | \(0.918366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.2285 | −0.806305 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.3658 | + | 15.3658i | −0.490093 | + | 0.490093i | −0.908336 | − | 0.418242i | \(-0.862646\pi\) |
0.418242 | + | 0.908336i | \(0.362646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.155847 | − | 0.0279056i | −0.00496571 | − | 0.000889145i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 39.0246i | − | 1.24091i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.1016 | 0.447953 | 0.223976 | − | 0.974595i | \(-0.428096\pi\) | ||||
0.223976 | + | 0.974595i | \(0.428096\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.6037 | − | 26.8786i | 1.22382 | − | 0.852109i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.5052 | − | 44.5052i | −1.40949 | − | 1.40949i | −0.762466 | − | 0.647029i | \(-0.776011\pi\) |
−0.647029 | − | 0.762466i | \(-0.723989\pi\) | |||||||
\(998\) | 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 | 2880.2.bj.f.1313.12 | yes | 32 | |
3.2 | odd | 2 | inner | 2880.2.bj.f.1313.6 | yes | 32 | |
4.3 | odd | 2 | 2880.2.bj.e.1313.11 | yes | 32 | ||
5.2 | odd | 4 | 2880.2.bj.e.737.12 | yes | 32 | ||
8.3 | odd | 2 | inner | 2880.2.bj.f.1313.5 | yes | 32 | |
8.5 | even | 2 | 2880.2.bj.e.1313.6 | yes | 32 | ||
12.11 | even | 2 | 2880.2.bj.e.1313.5 | yes | 32 | ||
15.2 | even | 4 | 2880.2.bj.e.737.6 | yes | 32 | ||
20.7 | even | 4 | inner | 2880.2.bj.f.737.11 | yes | 32 | |
24.5 | odd | 2 | 2880.2.bj.e.1313.12 | yes | 32 | ||
24.11 | even | 2 | inner | 2880.2.bj.f.1313.11 | yes | 32 | |
40.27 | even | 4 | 2880.2.bj.e.737.5 | ✓ | 32 | ||
40.37 | odd | 4 | inner | 2880.2.bj.f.737.6 | yes | 32 | |
60.47 | odd | 4 | inner | 2880.2.bj.f.737.5 | yes | 32 | |
120.77 | even | 4 | inner | 2880.2.bj.f.737.12 | yes | 32 | |
120.107 | odd | 4 | 2880.2.bj.e.737.11 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.bj.e.737.5 | ✓ | 32 | 40.27 | even | 4 | ||
2880.2.bj.e.737.6 | yes | 32 | 15.2 | even | 4 | ||
2880.2.bj.e.737.11 | yes | 32 | 120.107 | odd | 4 | ||
2880.2.bj.e.737.12 | yes | 32 | 5.2 | odd | 4 | ||
2880.2.bj.e.1313.5 | yes | 32 | 12.11 | even | 2 | ||
2880.2.bj.e.1313.6 | yes | 32 | 8.5 | even | 2 | ||
2880.2.bj.e.1313.11 | yes | 32 | 4.3 | odd | 2 | ||
2880.2.bj.e.1313.12 | yes | 32 | 24.5 | odd | 2 | ||
2880.2.bj.f.737.5 | yes | 32 | 60.47 | odd | 4 | inner | |
2880.2.bj.f.737.6 | yes | 32 | 40.37 | odd | 4 | inner | |
2880.2.bj.f.737.11 | yes | 32 | 20.7 | even | 4 | inner | |
2880.2.bj.f.737.12 | yes | 32 | 120.77 | even | 4 | inner | |
2880.2.bj.f.1313.5 | yes | 32 | 8.3 | odd | 2 | inner | |
2880.2.bj.f.1313.6 | yes | 32 | 3.2 | odd | 2 | inner | |
2880.2.bj.f.1313.11 | yes | 32 | 24.11 | even | 2 | inner | |
2880.2.bj.f.1313.12 | yes | 32 | 1.1 | even | 1 | trivial |