Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\), degree \(1\), 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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.12258833328.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 29x^{4} - 20x^{3} + 808x^{2} - 672x + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.5 | ||
Root | \(-2.61524 - 4.52973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.h.783.6 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 9.29424 | 1.78868 | 0.894339 | − | 0.447390i | \(-0.147647\pi\) | ||||
0.894339 | + | 0.447390i | \(0.147647\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 19.8510i | − 1.77553i | −0.460300 | − | 0.887763i | \(-0.652258\pi\) | ||||
0.460300 | − | 0.887763i | \(-0.347742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59.3829 | 2.19937 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 11.8356i | − 0.324414i | −0.986757 | − | 0.162207i | \(-0.948139\pi\) | ||||
0.986757 | − | 0.162207i | \(-0.0518613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 19.9862i | − 0.426398i | −0.977009 | − | 0.213199i | \(-0.931612\pi\) | ||||
0.977009 | − | 0.213199i | \(-0.0683882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 184.500i | − 3.17584i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.81702i | − 0.0259231i | −0.999916 | − | 0.0129616i | \(-0.995874\pi\) | ||||
0.999916 | − | 0.0129616i | \(-0.00412591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.32284 | −0.0884197 | −0.0442098 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442098 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 106.472i | − 0.965258i | −0.875825 | − | 0.482629i | \(-0.839682\pi\) | ||||
0.875825 | − | 0.482629i | \(-0.160318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −269.062 | −2.15249 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 300.975 | 2.14528 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −191.679 | −1.22737 | −0.613687 | − | 0.789549i | \(-0.710315\pi\) | ||||
−0.613687 | + | 0.789549i | \(0.710315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 125.150 | 0.725087 | 0.362543 | − | 0.931967i | \(-0.381908\pi\) | ||||
0.362543 | + | 0.931967i | \(0.381908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 110.003i | − 0.580273i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 316.828 | 1.40773 | 0.703867 | − | 0.710332i | \(-0.251455\pi\) | ||||
0.703867 | + | 0.710332i | \(0.251455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 185.756i | − 0.762688i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 321.806i | 1.22580i | 0.790162 | + | 0.612898i | \(0.209997\pi\) | ||||
−0.790162 | + | 0.612898i | \(0.790003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.3089i | 0.263535i | 0.991281 | + | 0.131767i | \(0.0420652\pi\) | ||||
−0.991281 | + | 0.131767i | \(0.957935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1178.81i | − 3.90504i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 154.562 | 0.479685 | 0.239842 | − | 0.970812i | \(-0.422904\pi\) | ||||
0.239842 | + | 0.970812i | \(0.422904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 16.8879i | − 0.0463681i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −319.421 | −0.827847 | −0.413923 | − | 0.910312i | \(-0.635842\pi\) | ||||
−0.413923 | + | 0.910312i | \(0.635842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −234.948 | −0.576006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −68.0602 | −0.158154 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −61.1169 | −0.134860 | −0.0674300 | − | 0.997724i | \(-0.521480\pi\) | ||||
−0.0674300 | + | 0.997724i | \(0.521480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 309.324i | − 0.649260i | −0.945841 | − | 0.324630i | \(-0.894760\pi\) | ||||
0.945841 | − | 0.324630i | \(-0.105240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −396.745 | −0.757080 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 594.102i | − 1.08330i | −0.840604 | − | 0.541650i | \(-0.817800\pi\) | ||||
0.840604 | − | 0.541650i | \(-0.182200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 989.576i | − 1.72654i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.6774i | 0.0813654i | 0.999172 | + | 0.0406827i | \(0.0129533\pi\) | ||||
−0.999172 | + | 0.0406827i | \(0.987047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 770.269i | 1.23497i | 0.786581 | + | 0.617487i | \(0.211849\pi\) | ||||
−0.786581 | + | 0.617487i | \(0.788151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2500.73 | −3.85012 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 960.207i | − 1.36749i | −0.729721 | − | 0.683745i | \(-0.760350\pi\) | ||||
0.729721 | − | 0.683745i | \(-0.239650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1193.99 | 1.63785 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1064.55 | −1.40782 | −0.703912 | − | 0.710288i | \(-0.748565\pi\) | ||||
−0.703912 | + | 0.710288i | \(0.748565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −36.0697 | −0.0460272 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1781.51 | −2.19538 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 655.567i | − 0.780786i | −0.920648 | − | 0.390393i | \(-0.872339\pi\) | ||||
0.920648 | − | 0.390393i | \(-0.127661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1163.18 | 1.29695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 145.366i | 0.156991i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 704.225i | 0.737147i | 0.929599 | + | 0.368573i | \(0.120154\pi\) | ||||
−0.929599 | + | 0.368573i | \(0.879846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 702.830i | − 0.713506i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 690.058i | 0.679835i | 0.940455 | + | 0.339918i | \(0.110399\pi\) | ||||
−0.940455 | + | 0.339918i | \(0.889601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1398.27 | 1.33763 | 0.668814 | − | 0.743429i | \(-0.266802\pi\) | ||||
0.668814 | + | 0.743429i | \(0.266802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 31.1751i | 0.0281665i | 0.999901 | + | 0.0140832i | \(0.00448298\pi\) | ||||
−0.999901 | + | 0.0140832i | \(0.995517\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 478.157 | 0.420176 | 0.210088 | − | 0.977683i | \(-0.432625\pi\) | ||||
0.210088 | + | 0.977683i | \(0.432625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2944.67 | 2.51798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1861.07 | 1.54933 | 0.774666 | − | 0.632371i | \(-0.217918\pi\) | ||||
0.774666 | + | 0.632371i | \(0.217918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2113.57 | −1.71384 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1186.84i | − 0.937805i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1190.92 | 0.894755 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2990.94i | 2.19256i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2859.77i | 2.04628i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1583.04i | 1.10608i | 0.833155 | + | 0.553040i | \(0.186532\pi\) | ||||
−0.833155 | + | 0.553040i | \(0.813468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 690.645i | 0.471379i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2197.20 | −1.46542 | −0.732712 | − | 0.680539i | \(-0.761746\pi\) | ||||
−0.732712 | + | 0.680539i | \(0.761746\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5974.65i | − 3.80900i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2499.40 | 1.55867 | 0.779336 | − | 0.626607i | \(-0.215557\pi\) | ||||
0.779336 | + | 0.626607i | \(0.215557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2709.21 | 1.65318 | 0.826591 | − | 0.562804i | \(-0.190277\pi\) | ||||
0.826591 | + | 0.562804i | \(0.190277\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1436.54 | 0.858001 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −236.548 | −0.138329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3805.02i | 2.17924i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1687.58 | −0.927867 | −0.463933 | − | 0.885870i | \(-0.653562\pi\) | ||||
−0.463933 | + | 0.885870i | \(0.653562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2554.77i | − 1.37685i | −0.725309 | − | 0.688424i | \(-0.758303\pi\) | ||||
0.725309 | − | 0.688424i | \(-0.241697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 107.900i | − 0.0570145i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2484.36i | − 1.28741i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 288.483i | 0.146646i | 0.997308 | + | 0.0733230i | \(0.0233604\pi\) | ||||
−0.997308 | + | 0.0733230i | \(0.976640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2968.78 | −1.48075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 731.683i | − 0.351594i | −0.984426 | − | 0.175797i | \(-0.943750\pi\) | ||||
0.984426 | − | 0.175797i | \(-0.0562502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2183.66 | −1.03029 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2121.63 | −0.983092 | −0.491546 | − | 0.870852i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870852i | \(0.663568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1797.55 | 0.818185 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −434.851 | −0.194467 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3179.74i | − 1.39741i | −0.715412 | − | 0.698703i | \(-0.753761\pi\) | ||||
0.715412 | − | 0.698703i | \(-0.246239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −568.035 | −0.241221 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2198.12i | 0.917849i | 0.888475 | + | 0.458924i | \(0.151765\pi\) | ||||
−0.888475 | + | 0.458924i | \(0.848235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1266.98i | − 0.520299i | −0.965568 | − | 0.260150i | \(-0.916228\pi\) | ||||
0.965568 | − | 0.260150i | \(-0.0837719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2874.93i | − 1.16132i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 6289.34i | − 2.49947i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.5055 | −0.00840983 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1741.49i | 0.659737i | 0.944027 | + | 0.329869i | \(0.107004\pi\) | ||||
−0.944027 | + | 0.329869i | \(0.892996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1278.61 | −0.476874 | −0.238437 | − | 0.971158i | \(-0.576635\pi\) | ||||
−0.238437 | + | 0.971158i | \(0.576635\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3687.45 | −1.35417 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 760.622 | 0.275087 | 0.137543 | − | 0.990496i | \(-0.456079\pi\) | ||||
0.137543 | + | 0.990496i | \(0.456079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4438.89 | 1.58123 | 0.790615 | − | 0.612313i | \(-0.209761\pi\) | ||||
0.790615 | + | 0.612313i | \(0.209761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 5521.73i | − 1.93767i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6388.17 | 2.17643 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 6322.62i | − 2.12296i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 86.6699i | 0.0286846i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2084.90i | 0.680239i | 0.940382 | + | 0.340119i | \(0.110467\pi\) | ||||
−0.940382 | + | 0.340119i | \(0.889533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 452.420i | 0.145537i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1475.11 | 0.467913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7159.06i | 2.20897i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.3154 | −0.0110536 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 399.456 | 0.119953 | 0.0599766 | − | 0.998200i | \(-0.480897\pi\) | ||||
0.0599766 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15977.7 | −4.73413 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2932.62 | −0.857466 | −0.428733 | − | 0.903431i | \(-0.641040\pi\) | ||||
−0.428733 | + | 0.903431i | \(0.641040\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1505.24i | 0.434363i | 0.976131 | + | 0.217182i | \(0.0696864\pi\) | ||||
−0.976131 | + | 0.217182i | \(0.930314\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 934.190 | 0.262664 | 0.131332 | − | 0.991338i | \(-0.458075\pi\) | ||||
0.131332 | + | 0.991338i | \(0.458075\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 3068.21i | − 0.851693i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8924.39i | − 2.44600i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6859.78i | 1.85658i | 0.371860 | + | 0.928289i | \(0.378720\pi\) | ||||
−0.371860 | + | 0.928289i | \(0.621280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 1294.25i | − 0.345933i | −0.984928 | − | 0.172966i | \(-0.944665\pi\) | ||||
0.984928 | − | 0.172966i | \(-0.0553352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2970.94 | 0.784304 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 146.356i | 0.0377019i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9894.17 | −2.51814 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 178.426 | 0.0448691 | 0.0224345 | − | 0.999748i | \(-0.492858\pi\) | ||||
0.0224345 | + | 0.999748i | \(0.492858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1260.16 | −0.313144 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −335.241 | −0.0823278 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5899.74i | 1.43197i | 0.698117 | + | 0.715984i | \(0.254022\pi\) | ||||
−0.698117 | + | 0.715984i | \(0.745978\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11382.5 | −2.69945 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2019.42i | 0.473470i | 0.971574 | + | 0.236735i | \(0.0760774\pi\) | ||||
−0.971574 | + | 0.236735i | \(0.923923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6340.83i | 1.46986i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6092.99i | − 1.39657i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1849.77i | 0.419265i | 0.977780 | + | 0.209632i | \(0.0672267\pi\) | ||||
−0.977780 | + | 0.209632i | \(0.932773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7198.86 | 1.61365 | 0.806826 | − | 0.590790i | \(-0.201184\pi\) | ||||
0.806826 | + | 0.590790i | \(0.201184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3184.50i | 0.698300i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5534.83 | 1.20056 | 0.600281 | − | 0.799789i | \(-0.295056\pi\) | ||||
0.600281 | + | 0.799789i | \(0.295056\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7431.80 | 1.59473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 752.919 | 0.159841 | 0.0799207 | − | 0.996801i | \(-0.474533\pi\) | ||||
0.0799207 | + | 0.996801i | \(0.474533\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5623.58 | 1.18123 | 0.590614 | − | 0.806954i | \(-0.298886\pi\) | ||||
0.590614 | + | 0.806954i | \(0.298886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1351.06i | 0.280807i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4909.70 | 0.999328 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6545.24i | 1.31852i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 507.111i | − 0.101112i | −0.998721 | − | 0.0505559i | \(-0.983901\pi\) | ||||
0.998721 | − | 0.0505559i | \(-0.0160993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1213.23i | 0.239447i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 3562.21i | − 0.695960i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2127.97 | −0.411584 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6413.57i | 1.21601i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6140.38 | −1.15278 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7402.96 | −1.37625 | −0.688126 | − | 0.725591i | \(-0.741566\pi\) | ||||
−0.688126 | + | 0.725591i | \(0.741566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12995.9 | 2.39259 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4284.78 | 0.781245 | 0.390623 | − | 0.920551i | \(-0.372260\pi\) | ||||
0.390623 | + | 0.920551i | \(0.372260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1502.00i | − 0.271239i | −0.990761 | − | 0.135620i | \(-0.956698\pi\) | ||||
0.990761 | − | 0.135620i | \(-0.0433025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7097.55 | 1.25753 | 0.628767 | − | 0.777594i | \(-0.283560\pi\) | ||||
0.628767 | + | 0.777594i | \(0.283560\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2268.63i | 0.398178i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 289.749i | 0.0503808i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.3058i | 0.00229211i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5377.52i | 0.917818i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4444.11 | 0.751559 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 11497.2i | − 1.90919i | −0.297907 | − | 0.954595i | \(-0.596288\pi\) | ||||
0.297907 | − | 0.954595i | \(-0.403712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18814.2 | 3.09612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11793.5 | −1.92343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6020.26 | 0.973128 | 0.486564 | − | 0.873645i | \(-0.338250\pi\) | ||||
0.486564 | + | 0.873645i | \(0.338250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17297.2 | 2.77126 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1481.23i | − 0.235229i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19644.1 | −3.06551 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8890.39i | − 1.37539i | −0.725999 | − | 0.687696i | \(-0.758622\pi\) | ||||
0.725999 | − | 0.687696i | \(-0.241378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6396.47i | 0.981075i | 0.871420 | + | 0.490538i | \(0.163200\pi\) | ||||
−0.871420 | + | 0.490538i | \(0.836800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 6015.33i | − 0.914743i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11472.5i | 1.72981i | 0.501940 | + | 0.864903i | \(0.332620\pi\) | ||||
−0.501940 | + | 0.864903i | \(0.667380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 966.295 | 0.144466 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 195.405i | 0.0287272i | 0.999897 | + | 0.0143636i | \(0.00457224\pi\) | ||||
−0.999897 | + | 0.0143636i | \(0.995428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6805.38 | −0.992182 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11068.7 | 1.60043 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15290.6 | 2.19273 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10227.7 | −1.45472 | −0.727362 | − | 0.686254i | \(-0.759254\pi\) | ||||
−0.727362 | + | 0.686254i | \(0.759254\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19109.8i | 2.69598i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7734.15 | −1.07362 | −0.536808 | − | 0.843704i | \(-0.680370\pi\) | ||||
−0.536808 | + | 0.843704i | \(0.680370\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26579.4i | 3.66014i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3830.93i | 0.523350i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9739.99i | 1.32008i | 0.751231 | + | 0.660039i | \(0.229460\pi\) | ||||
−0.751231 | + | 0.660039i | \(0.770540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14713.2i | 1.97842i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2525.17 | −0.336894 | −0.168447 | − | 0.985711i | \(-0.553875\pi\) | ||||
−0.168447 | + | 0.985711i | \(0.553875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4412.68i | 0.579610i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2665.26 | −0.347388 | −0.173694 | − | 0.984800i | \(-0.555570\pi\) | ||||
−0.173694 | + | 0.984800i | \(0.555570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −193.462 | −0.0250225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20421.3 | −2.62117 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19061.1 | −2.42801 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7966.78i | 1.00716i | 0.863950 | + | 0.503578i | \(0.167983\pi\) | ||||
−0.863950 | + | 0.503578i | \(0.832017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2607.89 | 0.324768 | 0.162384 | − | 0.986728i | \(-0.448082\pi\) | ||||
0.162384 | + | 0.986728i | \(0.448082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2501.28i | − 0.309175i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 23701.9i | − 2.90805i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3749.83i | − 0.456689i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8794.35i | 1.06321i | 0.846993 | + | 0.531605i | \(0.178411\pi\) | ||||
−0.846993 | + | 0.531605i | \(0.821589\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23230.0 | 2.78796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21132.3i | 2.49963i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25180.0 | 2.95701 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −333.409 | −0.0388737 | −0.0194368 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194368 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1186.07 | −0.137305 | −0.0686526 | − | 0.997641i | \(-0.521870\pi\) | ||||
−0.0686526 | + | 0.997641i | \(0.521870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9178.34 | 1.05500 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 488.892i | 0.0557994i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2198.53 | −0.247427 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 12163.1i | − 1.35934i | −0.733519 | − | 0.679669i | \(-0.762124\pi\) | ||||
0.733519 | − | 0.679669i | \(-0.237876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14229.4i | 1.57926i | 0.613582 | + | 0.789631i | \(0.289728\pi\) | ||||
−0.613582 | + | 0.789631i | \(0.710272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 35364.7i | 3.89795i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 779.677i | 0.0853478i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7955.09 | −0.864865 | −0.432432 | − | 0.901666i | \(-0.642345\pi\) | ||||
−0.432432 | + | 0.901666i | \(0.642345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6411.91i | 0.687673i | 0.939030 | + | 0.343837i | \(0.111727\pi\) | ||||
−0.939030 | + | 0.343837i | \(0.888273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13013.6 | −1.38631 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15684.8 | −1.65965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5918.99 | −0.622125 | −0.311063 | − | 0.950389i | \(-0.600685\pi\) | ||||
−0.311063 | + | 0.950389i | \(0.600685\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3808.76 | 0.397666 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 23744.6i | − 2.46274i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 868.613 | 0.0889103 | 0.0444551 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444551 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 546.878i | − 0.0556124i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 4645.89i | − 0.469372i | −0.972071 | − | 0.234686i | \(-0.924594\pi\) | ||||
0.972071 | − | 0.234686i | \(-0.0754062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 288.831i | 0.0289916i | 0.999895 | + | 0.0144958i | \(0.00461433\pi\) | ||||
−0.999895 | + | 0.0144958i | \(0.995386\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 23090.2i | − 2.30276i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11317.4 | 1.12143 | 0.560716 | − | 0.828008i | \(-0.310526\pi\) | ||||
0.560716 | + | 0.828008i | \(0.310526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2681.23i | 0.262302i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 879.488 | 0.0854945 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1970.30 | 0.190323 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18968.2 | −1.82074 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4324.22 | −0.412482 | −0.206241 | − | 0.978501i | \(-0.566123\pi\) | ||||
−0.206241 | + | 0.978501i | \(0.566123\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 6332.17i | − 0.600254i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13979.6 | 1.30882 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11480.5i | 1.06824i | 0.845410 | + | 0.534119i | \(0.179356\pi\) | ||||
−0.845410 | + | 0.534119i | \(0.820644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 6800.44i | − 0.628888i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 10052.9i | − 0.923994i | −0.886881 | − | 0.461997i | \(-0.847133\pi\) | ||||
0.886881 | − | 0.461997i | \(-0.152867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 348.285i | 0.0318174i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13951.9 | −1.26685 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7204.13i | 0.646295i | 0.946349 | + | 0.323147i | \(0.104741\pi\) | ||||
−0.946349 | + | 0.323147i | \(0.895259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19718.9 | −1.75843 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6434.36 | −0.570366 | −0.285183 | − | 0.958473i | \(-0.592054\pi\) | ||||
−0.285183 | + | 0.958473i | \(0.592054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13698.3 | 1.20707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16706.9 | 1.46347 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13015.0i | 1.13336i | 0.823939 | + | 0.566679i | \(0.191772\pi\) | ||||
−0.823939 | + | 0.566679i | \(0.808228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2203.99 | −0.189685 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 27757.1i | − 2.37500i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1829.33i | − 0.155617i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 29553.3i | − 2.49951i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 5144.91i | − 0.432635i | −0.976323 | − | 0.216317i | \(-0.930595\pi\) | ||||
0.976323 | − | 0.216317i | \(-0.0694046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11197.7 | −0.936213 | −0.468106 | − | 0.883672i | \(-0.655064\pi\) | ||||
−0.468106 | + | 0.883672i | \(0.655064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 227.402i | − 0.0187965i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 830.726 | 0.0682769 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3629.30 | −0.296607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6431.67 | 0.522677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 618.857 | 0.0500104 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20429.8i | 1.64174i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21827.4 | −1.73463 | −0.867313 | − | 0.497762i | \(-0.834155\pi\) | ||||
−0.867313 | + | 0.497762i | \(0.834155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 11775.6i | − 0.930647i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 9491.89i | − 0.746033i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20005.0i | − 1.56371i | −0.623459 | − | 0.781856i | \(-0.714273\pi\) | ||||
0.623459 | − | 0.781856i | \(-0.285727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 18368.5i | − 1.42796i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1403.63 | 0.108524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 58454.7i | − 4.47074i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7400.91 | −0.562992 | −0.281496 | − | 0.959562i | \(-0.590831\pi\) | ||||
−0.281496 | + | 0.959562i | \(0.590831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1485.15 | 0.112371 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −199.877 | −0.0150425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1080.79 | −0.0809059 | −0.0404529 | − | 0.999181i | \(-0.512880\pi\) | ||||
−0.0404529 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 36944.0i | − 2.75088i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4208.13 | 0.310042 | 0.155021 | − | 0.987911i | \(-0.450455\pi\) | ||||
0.155021 | + | 0.987911i | \(0.450455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12881.7i | 0.944105i | 0.881570 | + | 0.472052i | \(0.156487\pi\) | ||||
−0.881570 | + | 0.472052i | \(0.843513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16185.8i | 1.18006i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28647.5i | 2.07771i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 13271.6i | − 0.957546i | −0.877939 | − | 0.478773i | \(-0.841082\pi\) | ||||
0.877939 | − | 0.478773i | \(-0.158918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11883.7 | −0.852974 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3780.53i | 0.268565i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23559.9 | −1.66510 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16892.3 | 1.18777 | 0.593885 | − | 0.804550i | \(-0.297593\pi\) | ||||
0.593885 | + | 0.804550i | \(0.297593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −916.456 | −0.0641119 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7069.40 | 0.492041 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10957.3i | 0.758787i | 0.925235 | + | 0.379394i | \(0.123867\pi\) | ||||
−0.925235 | + | 0.379394i | \(0.876133\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41256.1 | 2.82831 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 11575.6i | − 0.789596i | −0.918768 | − | 0.394798i | \(-0.870815\pi\) | ||||
0.918768 | − | 0.394798i | \(-0.129185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17612.6i | 1.19540i | 0.801721 | + | 0.597699i | \(0.203918\pi\) | ||||
−0.801721 | + | 0.597699i | \(0.796082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 35279.5i | − 2.38257i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23640.9i | − 1.58866i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16363.0 | −1.09416 | −0.547080 | − | 0.837080i | \(-0.684261\pi\) | ||||
−0.547080 | + | 0.837080i | \(0.684261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3089.10i | − 0.204536i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1007.72 | 0.0663974 | 0.0331987 | − | 0.999449i | \(-0.489431\pi\) | ||||
0.0331987 | + | 0.999449i | \(0.489431\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 59373.2 | 3.89294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14986.9 | −0.977876 | −0.488938 | − | 0.872318i | \(-0.662616\pi\) | ||||
−0.488938 | + | 0.872318i | \(0.662616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17668.2 | 1.14725 | 0.573624 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573624 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 32045.4i | − 2.07075i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23136.5 | 1.48074 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 805.531i | 0.0513075i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 575.684i | − 0.0364929i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3794.54i | 0.239395i | 0.992810 | + | 0.119698i | \(0.0381925\pi\) | ||||
−0.992810 | + | 0.119698i | \(0.961807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19377.6i | 1.21673i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31424.9 | 1.96387 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2890.61i | 0.178952i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14251.5 | 0.878157 | 0.439079 | − | 0.898449i | \(-0.355305\pi\) | ||||
0.439079 | + | 0.898449i | \(0.355305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10643.5 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13710.0 | 0.836946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18948.4 | −1.15137 | −0.575686 | − | 0.817671i | \(-0.695265\pi\) | ||||
−0.575686 | + | 0.817671i | \(0.695265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 723.353i | 0.0437505i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21346.3 | 1.27924 | 0.639620 | − | 0.768691i | \(-0.279092\pi\) | ||||
0.639620 | + | 0.768691i | \(0.279092\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43616.7i | 2.60190i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 45740.8i | 2.71616i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 3245.68i | − 0.191857i | −0.995388 | − | 0.0959284i | \(-0.969418\pi\) | ||||
0.995388 | − | 0.0959284i | \(-0.0305820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 15989.9i | − 0.940898i | −0.882427 | − | 0.470449i | \(-0.844092\pi\) | ||||
0.882427 | − | 0.470449i | \(-0.155908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −337.524 | −0.0197713 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20408.4i | 1.18473i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3712.64 | 0.214558 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3661.02 | −0.210629 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3473.65 | −0.198959 | −0.0994796 | − | 0.995040i | \(-0.531718\pi\) | ||||
−0.0994796 | + | 0.995040i | \(0.531718\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −80980.8 | −4.61771 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27077.2i | 1.53717i | 0.639750 | + | 0.768583i | \(0.279038\pi\) | ||||
−0.639750 | + | 0.768583i | \(0.720962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27256.5 | −1.53373 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6615.17i | 0.370604i | 0.982682 | + | 0.185302i | \(0.0593263\pi\) | ||||
−0.982682 | + | 0.185302i | \(0.940674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 49615.5i | − 2.76746i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13990.1i | 0.776936i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6384.01i | 0.352992i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15808.2 | −0.870294 | −0.435147 | − | 0.900359i | \(-0.643304\pi\) | ||||
−0.435147 | + | 0.900359i | \(0.643304\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 53780.5i | − 2.93527i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 584.730 | 0.0317765 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8682.59 | 0.469822 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9851.70 | 0.530804 | 0.265402 | − | 0.964138i | \(-0.414495\pi\) | ||||
0.265402 | + | 0.964138i | \(0.414495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2320.08 | −0.124471 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 28516.7i | − 1.52340i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10767.2 | −0.570342 | −0.285171 | − | 0.958477i | \(-0.592050\pi\) | ||||
−0.285171 | + | 0.958477i | \(0.592050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 57019.9i | − 3.00761i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 13325.0i | − 0.699896i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4695.71i | 0.245608i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63756.4i | 3.32082i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20738.0 | −1.07565 | −0.537827 | − | 0.843055i | \(-0.680755\pi\) | ||||
−0.537827 | + | 0.843055i | \(0.680755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 12029.0i | − 0.618762i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 51573.5 | 2.64192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2738.00 | 0.139679 | 0.0698396 | − | 0.997558i | \(-0.477751\pi\) | ||||
0.0698396 | + | 0.997558i | \(0.477751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4625.18 | −0.234984 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 135.021 | 0.00683165 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17216.1i | 0.867519i | 0.901029 | + | 0.433760i | \(0.142813\pi\) | ||||
−0.901029 | + | 0.433760i | \(0.857187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7031.53 | −0.351438 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 5523.75i | − 0.274959i | −0.990505 | − | 0.137479i | \(-0.956100\pi\) | ||||
0.990505 | − | 0.137479i | \(-0.0439001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1360.26i | 0.0674366i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20424.6i | − 1.00849i | −0.863561 | − | 0.504244i | \(-0.831771\pi\) | ||||
0.863561 | − | 0.504244i | \(-0.168229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33500.2i | 1.64745i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −63216.0 | −3.09632 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 10763.8i | − 0.523003i | −0.965203 | − | 0.261502i | \(-0.915782\pi\) | ||||
0.965203 | − | 0.261502i | \(-0.0842177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1658.33 | 0.0802563 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50714.7 | −2.44463 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8591.14 | 0.412484 | 0.206242 | − | 0.978501i | \(-0.433877\pi\) | ||||
0.206242 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11712.2 | −0.560113 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 29877.8i | − 1.42322i | −0.702575 | − | 0.711610i | \(-0.747966\pi\) | ||||
0.702575 | − | 0.711610i | \(-0.252034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2141.93 | −0.101231 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1221.49i | 0.0575040i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 3093.61i | − 0.145070i | −0.997366 | − | 0.0725348i | \(-0.976891\pi\) | ||||
0.997366 | − | 0.0725348i | \(-0.0231089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54833.6i | 2.56133i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 24031.7i | − 1.11819i | −0.829104 | − | 0.559095i | \(-0.811149\pi\) | ||||
0.829104 | − | 0.559095i | \(-0.188851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33673.2 | −1.56075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2356.53i | − 0.108385i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 576.125 | 0.0263961 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −57690.5 | −2.63307 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5726.67 | 0.260374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11593.2 | 0.525099 | 0.262550 | − | 0.964918i | \(-0.415437\pi\) | ||||
0.262550 | + | 0.964918i | \(0.415437\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18769.0i | 0.846886i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6182.20 | −0.276843 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 58933.2i | 2.62911i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11467.4i | 0.509658i | 0.966986 | + | 0.254829i | \(0.0820192\pi\) | ||||
−0.966986 | + | 0.254829i | \(0.917981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 280.843i | − 0.0124349i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 38929.5i | − 1.71723i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9116.57 | 0.400643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17192.2i | 0.749930i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36381.7 | 1.58110 | 0.790551 | − | 0.612396i | \(-0.209794\pi\) | ||||
0.790551 | + | 0.612396i | \(0.209794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35717.1 | 1.54648 | 0.773241 | − | 0.634113i | \(-0.218634\pi\) | ||||
0.773241 | + | 0.634113i | \(0.218634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66907.9 | 2.88630 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14524.6 | −0.624264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 544.152i | − 0.0233017i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31319.1 | −1.33136 | −0.665678 | − | 0.746239i | \(-0.731858\pi\) | ||||
−0.665678 | + | 0.746239i | \(0.731858\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 4176.34i | − 0.176887i | −0.996081 | − | 0.0884435i | \(-0.971811\pi\) | ||||
0.996081 | − | 0.0884435i | \(-0.0281893\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29597.5i | 1.24903i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 7930.70i | − 0.333467i | −0.986002 | − | 0.166734i | \(-0.946678\pi\) | ||||
0.986002 | − | 0.166734i | \(-0.0533220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2847.17i | − 0.119284i | −0.998220 | − | 0.0596419i | \(-0.981004\pi\) | ||||
0.998220 | − | 0.0596419i | \(-0.0189959\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 51442.0 | 2.14742 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42116.4i | 1.74551i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37667.1 | 1.55552 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25648.9 | −1.05542 | −0.527711 | − | 0.849424i | \(-0.676949\pi\) | ||||
−0.527711 | + | 0.849424i | \(0.676949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12351.8 | 0.506449 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6997.82 | 0.285905 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 35683.2i | − 1.45271i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 52266.9 | 2.11283 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 33733.3i | − 1.35883i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1004.85i | − 0.0403348i | −0.999797 | − | 0.0201674i | \(-0.993580\pi\) | ||||
0.999797 | − | 0.0201674i | \(-0.00641991\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8632.23i | 0.345282i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 35060.5i | − 1.39748i | −0.715374 | − | 0.698742i | \(-0.753744\pi\) | ||||
0.715374 | − | 0.698742i | \(-0.246256\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9006.42 | 0.357736 | 0.178868 | − | 0.983873i | \(-0.442757\pi\) | ||||
0.178868 | + | 0.983873i | \(0.442757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 43533.3i | − 1.71714i | −0.512696 | − | 0.858570i | \(-0.671353\pi\) | ||||
0.512696 | − | 0.858570i | \(-0.328647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −63121.0 | −2.48113 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45631.9 | 1.78748 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11364.6 | −0.443633 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11873.8 | −0.461916 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41818.9i | 1.62126i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23537.6 | −0.906280 | −0.453140 | − | 0.891439i | \(-0.649696\pi\) | ||||
−0.453140 | + | 0.891439i | \(0.649696\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 4713.21i | − 0.180856i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 41234.7i | − 1.57688i | −0.615111 | − | 0.788440i | \(-0.710889\pi\) | ||||
0.615111 | − | 0.788440i | \(-0.289111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2981.04i | − 0.113613i | −0.998385 | − | 0.0568063i | \(-0.981908\pi\) | ||||
0.998385 | − | 0.0568063i | \(-0.0180917\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11276.1i | 0.428294i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23841.2 | 0.902490 | 0.451245 | − | 0.892400i | \(-0.350980\pi\) | ||||
0.451245 | + | 0.892400i | \(0.350980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 14131.6i | − 0.531342i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1131.83 | −0.0424136 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43634.8 | 1.62967 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19777.8 | −0.736191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23988.7 | −0.889953 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 580.396i | 0.0214604i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25150.9 | −0.923805 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33942.4i | 1.24260i | 0.783572 | + | 0.621301i | \(0.213395\pi\) | ||||
−0.783572 | + | 0.621301i | \(0.786605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 40977.7i | 1.49521i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18217.3i | 0.662531i | 0.943538 | + | 0.331265i | \(0.107476\pi\) | ||||
−0.943538 | + | 0.331265i | \(0.892524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12599.5i | 0.456718i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −57070.2 | −2.06195 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 40860.7i | − 1.46667i | −0.679867 | − | 0.733335i | \(-0.737963\pi\) | ||||
0.679867 | − | 0.733335i | \(-0.262037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −68804.9 | −2.46167 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 972.875 | 0.0346940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −85246.2 | −3.03014 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 83033.4 | 2.94194 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30596.3i | 1.08055i | 0.841488 | + | 0.540276i | \(0.181680\pi\) | ||||
−0.841488 | + | 0.540276i | \(0.818320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39823.7 | 1.39740 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 426.906i | 0.0149319i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28125.2i | 0.980586i | 0.871558 | + | 0.490293i | \(0.163110\pi\) | ||||
−0.871558 | + | 0.490293i | \(0.836890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 13959.9i | − 0.485159i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30098.1i | 1.04269i | 0.853347 | + | 0.521344i | \(0.174569\pi\) | ||||
−0.853347 | + | 0.521344i | \(0.825431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34263.3 | 1.18321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41414.0i | 1.42109i | 0.703650 | + | 0.710547i | \(0.251552\pi\) | ||||
−0.703650 | + | 0.710547i | \(0.748448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15394.7 | 0.526590 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65966.3 | 2.24932 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33248.1 | −1.13013 | −0.565063 | − | 0.825047i | \(-0.691148\pi\) | ||||
−0.565063 | + | 0.825047i | \(0.691148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34570.3 | 1.17138 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21085.2i | 0.712212i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14128.4 | −0.474249 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1851.27i | 0.0619485i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25381.8i | 0.846702i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 39769.8i | − 1.32255i | −0.750142 | − | 0.661277i | \(-0.770015\pi\) | ||||
0.750142 | − | 0.661277i | \(-0.229985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 123.667i | 0.00409985i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26812.5 | 0.886153 | 0.443077 | − | 0.896484i | \(-0.353887\pi\) | ||||
0.443077 | + | 0.896484i | \(0.353887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49979.9i | 1.64168i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15822.0 | 0.518106 | 0.259053 | − | 0.965863i | \(-0.416590\pi\) | ||||
0.259053 | + | 0.965863i | \(0.416590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7759.00 | −0.253298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28394.4 | 0.924120 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35033.3 | −1.13671 | −0.568356 | − | 0.822783i | \(-0.692420\pi\) | ||||
−0.568356 | + | 0.822783i | \(0.692420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 15099.1i | − 0.488424i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7911.82 | 0.254379 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 25557.0i | − 0.819217i | −0.912261 | − | 0.409608i | \(-0.865665\pi\) | ||||
0.912261 | − | 0.409608i | \(-0.134335\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 106858.i | − 3.41493i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 88116.4i | − 2.80752i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29598.9i | 0.940226i | 0.882606 | + | 0.470113i | \(0.155787\pi\) | ||||
−0.882606 | + | 0.470113i | \(0.844213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 95357.1 | 3.01999 |
(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 | 784.4.f.h.783.5 | 6 | ||
4.3 | odd | 2 | 784.4.f.g.783.1 | 6 | |||
7.2 | even | 3 | 112.4.p.f.31.1 | ✓ | 6 | ||
7.3 | odd | 6 | 112.4.p.g.47.3 | yes | 6 | ||
7.6 | odd | 2 | 784.4.f.g.783.2 | 6 | |||
28.3 | even | 6 | 112.4.p.f.47.1 | yes | 6 | ||
28.23 | odd | 6 | 112.4.p.g.31.3 | yes | 6 | ||
28.27 | even | 2 | inner | 784.4.f.h.783.6 | 6 | ||
56.3 | even | 6 | 448.4.p.g.383.3 | 6 | |||
56.37 | even | 6 | 448.4.p.g.255.3 | 6 | |||
56.45 | odd | 6 | 448.4.p.f.383.1 | 6 | |||
56.51 | odd | 6 | 448.4.p.f.255.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.f.31.1 | ✓ | 6 | 7.2 | even | 3 | ||
112.4.p.f.47.1 | yes | 6 | 28.3 | even | 6 | ||
112.4.p.g.31.3 | yes | 6 | 28.23 | odd | 6 | ||
112.4.p.g.47.3 | yes | 6 | 7.3 | odd | 6 | ||
448.4.p.f.255.1 | 6 | 56.51 | odd | 6 | |||
448.4.p.f.383.1 | 6 | 56.45 | odd | 6 | |||
448.4.p.g.255.3 | 6 | 56.37 | even | 6 | |||
448.4.p.g.383.3 | 6 | 56.3 | even | 6 | |||
784.4.f.g.783.1 | 6 | 4.3 | odd | 2 | |||
784.4.f.g.783.2 | 6 | 7.6 | odd | 2 | |||
784.4.f.h.783.5 | 6 | 1.1 | even | 1 | trivial | ||
784.4.f.h.783.6 | 6 | 28.27 | even | 2 | inner |