Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(23.6007640023\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.00000 | −1.34715 | −0.673575 | − | 0.739119i | \(-0.735242\pi\) | ||||
−0.673575 | + | 0.739119i | \(0.735242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 34.0000 | 1.83583 | 0.917914 | − | 0.396780i | \(-0.129872\pi\) | ||||
0.917914 | + | 0.396780i | \(0.129872\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.0000 | −0.740073 | −0.370037 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370037 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.0000 | 0.299603 | 0.149801 | − | 0.988716i | \(-0.452137\pi\) | ||||
0.149801 | + | 0.988716i | \(0.452137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0000 | −0.422608 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −238.000 | −2.47314 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 78.0000 | 0.707136 | 0.353568 | − | 0.935409i | \(-0.384968\pi\) | ||||
0.353568 | + | 0.935409i | \(0.384968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −120.000 | −0.768395 | −0.384197 | − | 0.923251i | \(-0.625522\pi\) | ||||
−0.384197 | + | 0.923251i | \(0.625522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −182.000 | −1.05446 | −0.527228 | − | 0.849724i | \(-0.676769\pi\) | ||||
−0.527228 | + | 0.849724i | \(0.676769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 189.000 | 0.996990 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 146.000 | 0.648710 | 0.324355 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324355 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 196.000 | 0.804747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 357.000 | 1.35985 | 0.679927 | − | 0.733280i | \(-0.262011\pi\) | ||||
0.679927 | + | 0.733280i | \(0.262011\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 148.000 | 0.524879 | 0.262439 | − | 0.964948i | \(-0.415473\pi\) | ||||
0.262439 | + | 0.964948i | \(0.415473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 84.0000 | 0.260695 | 0.130347 | − | 0.991468i | \(-0.458391\pi\) | ||||
0.130347 | + | 0.991468i | \(0.458391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 813.000 | 2.37026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −147.000 | −0.403610 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 702.000 | 1.81938 | 0.909690 | − | 0.415288i | \(-0.136319\pi\) | ||||
0.909690 | + | 0.415288i | \(0.136319\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 245.000 | 0.569317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 840.000 | 1.85354 | 0.926769 | − | 0.375633i | \(-0.122575\pi\) | ||||
0.926769 | + | 0.375633i | \(0.122575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −238.000 | −0.499554 | −0.249777 | − | 0.968303i | \(-0.580357\pi\) | ||||
−0.249777 | + | 0.968303i | \(0.580357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 748.000 | 1.49586 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −461.000 | −0.840599 | −0.420299 | − | 0.907386i | \(-0.638075\pi\) | ||||
−0.420299 | + | 0.907386i | \(0.638075\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −546.000 | −0.952618 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 708.000 | 1.18344 | 0.591719 | − | 0.806144i | \(-0.298449\pi\) | ||||
0.591719 | + | 0.806144i | \(0.298449\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −133.000 | −0.213239 | −0.106620 | − | 0.994300i | \(-0.534003\pi\) | ||||
−0.106620 | + | 0.994300i | \(0.534003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −918.000 | −1.35865 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −650.000 | −0.925705 | −0.462853 | − | 0.886435i | \(-0.653174\pi\) | ||||
−0.462853 | + | 0.886435i | \(0.653174\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 903.000 | 1.19418 | 0.597091 | − | 0.802173i | \(-0.296323\pi\) | ||||
0.597091 | + | 0.802173i | \(0.296323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 840.000 | 1.03514 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 735.000 | 0.875392 | 0.437696 | − | 0.899123i | \(-0.355795\pi\) | ||||
0.437696 | + | 0.899123i | \(0.355795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −952.000 | −1.09667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1274.00 | 1.42051 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1106.00 | 1.15770 | 0.578852 | − | 0.815433i | \(-0.303501\pi\) | ||||
0.578852 | + | 0.815433i | \(0.303501\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −594.000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 462.000 | 0.455156 | 0.227578 | − | 0.973760i | \(-0.426919\pi\) | ||||
0.227578 | + | 0.973760i | \(0.426919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −812.000 | −0.776784 | −0.388392 | − | 0.921494i | \(-0.626969\pi\) | ||||
−0.388392 | + | 0.921494i | \(0.626969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 789.000 | 0.712855 | 0.356428 | − | 0.934323i | \(-0.383995\pi\) | ||||
0.356428 | + | 0.934323i | \(0.383995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 230.000 | 0.202110 | 0.101055 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101055 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1022.00 | −0.873909 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2073.00 | −1.72576 | −0.862882 | − | 0.505405i | \(-0.831343\pi\) | ||||
−0.862882 | + | 0.505405i | \(0.831343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −616.000 | −0.486745 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 714.000 | 0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −602.000 | −0.452292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2499.00 | −1.83193 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1114.00 | 0.778358 | 0.389179 | − | 0.921162i | \(-0.372759\pi\) | ||||
0.389179 | + | 0.921162i | \(0.372759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1036.00 | −0.707091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −252.000 | −0.168071 | −0.0840357 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840357 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1190.00 | −0.775835 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1941.00 | 1.21044 | 0.605222 | − | 0.796057i | \(-0.293084\pi\) | ||||
0.605222 | + | 0.796057i | \(0.293084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1645.00 | 1.00379 | 0.501896 | − | 0.864928i | \(-0.332636\pi\) | ||||
0.501896 | + | 0.864928i | \(0.332636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −588.000 | −0.351195 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 756.000 | 0.442097 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5691.00 | −3.19310 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1800.00 | −0.989676 | −0.494838 | − | 0.868985i | \(-0.664773\pi\) | ||||
−0.494838 | + | 0.868985i | \(0.664773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3298.00 | 1.77740 | 0.888700 | − | 0.458489i | \(-0.151609\pi\) | ||||
0.888700 | + | 0.458489i | \(0.151609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 462.000 | 0.244121 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 266.000 | 0.135217 | 0.0676086 | − | 0.997712i | \(-0.478463\pi\) | ||||
0.0676086 | + | 0.997712i | \(0.478463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4914.00 | −2.45098 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2652.00 | 1.29818 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1157.00 | −0.555971 | −0.277985 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277985 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1764.00 | 0.817380 | 0.408690 | − | 0.912673i | \(-0.365986\pi\) | ||||
0.408690 | + | 0.912673i | \(0.365986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −770.000 | −0.344347 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1848.00 | −0.812144 | −0.406072 | − | 0.913841i | \(-0.633102\pi\) | ||||
−0.406072 | + | 0.913841i | \(0.633102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5880.00 | −2.49699 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −135.000 | −0.0563708 | −0.0281854 | − | 0.999603i | \(-0.508973\pi\) | ||||
−0.0281854 | + | 0.999603i | \(0.508973\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2282.00 | 0.937126 | 0.468563 | − | 0.883430i | \(-0.344772\pi\) | ||||
0.468563 | + | 0.883430i | \(0.344772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1666.00 | 0.672974 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −567.000 | −0.221728 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1190.00 | 0.457988 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1398.00 | 0.529611 | 0.264806 | − | 0.964302i | \(-0.414692\pi\) | ||||
0.264806 | + | 0.964302i | \(0.414692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3317.00 | 1.23711 | 0.618557 | − | 0.785740i | \(-0.287718\pi\) | ||||
0.618557 | + | 0.785740i | \(0.287718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1686.00 | 0.609759 | 0.304880 | − | 0.952391i | \(-0.401384\pi\) | ||||
0.304880 | + | 0.952391i | \(0.401384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1540.00 | 0.548581 | 0.274291 | − | 0.961647i | \(-0.411557\pi\) | ||||
0.274291 | + | 0.961647i | \(0.411557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3227.00 | 1.13241 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4080.00 | −1.41064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1716.00 | 0.576185 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 945.000 | 0.312761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3043.00 | 0.992838 | 0.496419 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496419 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4956.00 | −1.59427 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6188.00 | −1.93580 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 931.000 | 0.287266 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −588.000 | −0.178974 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3332.00 | −1.00057 | −0.500285 | − | 0.865861i | \(-0.666772\pi\) | ||||
−0.500285 | + | 0.865861i | \(0.666772\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1596.00 | −0.466653 | −0.233327 | − | 0.972398i | \(-0.574961\pi\) | ||||
−0.233327 | + | 0.972398i | \(0.574961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4340.00 | 1.25238 | 0.626191 | − | 0.779670i | \(-0.284613\pi\) | ||||
0.626191 | + | 0.779670i | \(0.284613\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6426.00 | 1.83030 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3018.00 | −0.848565 | −0.424283 | − | 0.905530i | \(-0.639474\pi\) | ||||
−0.424283 | + | 0.905530i | \(0.639474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4550.00 | 1.24706 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4440.00 | −1.20167 | −0.600836 | − | 0.799372i | \(-0.705166\pi\) | ||||
−0.600836 | + | 0.799372i | \(0.705166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3703.00 | −0.989756 | −0.494878 | − | 0.868962i | \(-0.664787\pi\) | ||||
−0.494878 | + | 0.868962i | \(0.664787\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4928.00 | 1.30095 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 980.000 | 0.252453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6321.00 | −1.60874 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7077.00 | −1.77967 | −0.889833 | − | 0.456286i | \(-0.849179\pi\) | ||||
−0.889833 | + | 0.456286i | \(0.849179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2106.00 | −0.523332 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6846.00 | 1.66164 | 0.830821 | − | 0.556540i | \(-0.187872\pi\) | ||||
0.830821 | + | 0.556540i | \(0.187872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4964.00 | 1.19092 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2640.00 | −0.626099 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3438.00 | 0.806069 | 0.403035 | − | 0.915185i | \(-0.367955\pi\) | ||||
0.403035 | + | 0.915185i | \(0.367955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5145.00 | −1.17928 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1680.00 | −0.380786 | −0.190393 | − | 0.981708i | \(-0.560976\pi\) | ||||
−0.190393 | + | 0.981708i | \(0.560976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5222.00 | −1.17053 | −0.585266 | − | 0.810842i | \(-0.699010\pi\) | ||||
−0.585266 | + | 0.810842i | \(0.699010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6664.00 | 1.47738 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1384.00 | −0.300204 | −0.150102 | − | 0.988671i | \(-0.547960\pi\) | ||||
−0.150102 | + | 0.988671i | \(0.547960\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4004.00 | −0.859187 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3858.00 | −0.819036 | −0.409518 | − | 0.912302i | \(-0.634303\pi\) | ||||
−0.409518 | + | 0.912302i | \(0.634303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4277.00 | −0.898379 | −0.449190 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449190 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12138.0 | 2.49646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4472.00 | −0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7742.00 | −1.55960 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6342.00 | 1.26452 | 0.632259 | − | 0.774757i | \(-0.282128\pi\) | ||||
0.632259 | + | 0.774757i | \(0.282128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −945.000 | −0.184628 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2184.00 | −0.422421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5032.00 | 0.963587 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3234.00 | −0.613163 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5831.00 | −1.08402 | −0.542008 | − | 0.840373i | \(-0.682336\pi\) | ||||
−0.542008 | + | 0.840373i | \(0.682336\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5684.00 | 1.04644 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2478.00 | 0.451815 | 0.225908 | − | 0.974149i | \(-0.427465\pi\) | ||||
0.225908 | + | 0.974149i | \(0.427465\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2758.00 | −0.498056 | −0.249028 | − | 0.968496i | \(-0.580111\pi\) | ||||
−0.249028 | + | 0.968496i | \(0.580111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 636.000 | 0.112686 | 0.0563428 | − | 0.998411i | \(-0.482056\pi\) | ||||
0.0563428 | + | 0.998411i | \(0.482056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3240.00 | 0.568668 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5523.00 | −0.960323 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −735.000 | −0.126615 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1610.00 | −0.272273 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2856.00 | 0.478591 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6887.00 | −1.14364 | −0.571818 | − | 0.820380i | \(-0.693762\pi\) | ||||
−0.571818 | + | 0.820380i | \(0.693762\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3212.00 | 0.528578 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7331.00 | 1.18500 | 0.592500 | − | 0.805570i | \(-0.298141\pi\) | ||||
0.592500 | + | 0.805570i | \(0.298141\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14511.0 | 2.32487 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4914.00 | 0.780375 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15980.0 | 2.51557 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5349.00 | 0.827520 | 0.413760 | − | 0.910386i | \(-0.364215\pi\) | ||||
0.413760 | + | 0.910386i | \(0.364215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11270.0 | 1.72857 | 0.864283 | − | 0.503007i | \(-0.167773\pi\) | ||||
0.864283 | + | 0.503007i | \(0.167773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −980.000 | −0.149027 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1302.00 | 0.196313 | 0.0981565 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981565 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4998.00 | −0.740959 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 750.000 | 0.110260 | 0.0551302 | − | 0.998479i | \(-0.482443\pi\) | ||||
0.0551302 | + | 0.998479i | \(0.482443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5634.00 | −0.821403 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4214.00 | 0.609305 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1204.00 | 0.171249 | 0.0856244 | − | 0.996327i | \(-0.472712\pi\) | ||||
0.0856244 | + | 0.996327i | \(0.472712\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7854.00 | 1.10803 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23868.0 | 3.34007 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1198.00 | −0.166301 | −0.0831503 | − | 0.996537i | \(-0.526498\pi\) | ||||
−0.0831503 | + | 0.996537i | \(0.526498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3360.00 | 0.459015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8105.00 | −1.09849 | −0.549243 | − | 0.835663i | \(-0.685084\pi\) | ||||
−0.549243 | + | 0.835663i | \(0.685084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7798.00 | −1.04857 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3318.00 | 0.442668 | 0.221334 | − | 0.975198i | \(-0.428959\pi\) | ||||
0.221334 | + | 0.975198i | \(0.428959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3256.00 | 0.427679 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13770.0 | −1.79477 | −0.897387 | − | 0.441245i | \(-0.854537\pi\) | ||||
−0.897387 | + | 0.441245i | \(0.854537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1638.00 | 0.211860 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1764.00 | 0.226417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3724.00 | −0.470786 | −0.235393 | − | 0.971900i | \(-0.575638\pi\) | ||||
−0.235393 | + | 0.971900i | \(0.575638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8330.00 | 1.04517 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6117.00 | 0.761767 | 0.380883 | − | 0.924623i | \(-0.375620\pi\) | ||||
0.380883 | + | 0.924623i | \(0.375620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5096.00 | 0.629900 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3942.00 | −0.480093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6125.00 | 0.740493 | 0.370247 | − | 0.928933i | \(-0.379273\pi\) | ||||
0.370247 | + | 0.928933i | \(0.379273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13587.0 | −1.63065 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28560.0 | 3.40277 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11515.0 | −1.35226 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1575.00 | −0.183637 | −0.0918184 | − | 0.995776i | \(-0.529268\pi\) | ||||
−0.0918184 | + | 0.995776i | \(0.529268\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −988.000 | −0.114376 | −0.0571879 | − | 0.998363i | \(-0.518213\pi\) | ||||
−0.0571879 | + | 0.998363i | \(0.518213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1848.00 | 0.212418 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8092.00 | −0.917094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5292.00 | −0.595571 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 558.000 | 0.0623617 | 0.0311809 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311809 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2443.00 | −0.271139 | −0.135569 | − | 0.990768i | \(-0.543286\pi\) | ||||
−0.135569 | + | 0.990768i | \(0.543286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2730.00 | −0.298841 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12320.0 | −1.33941 | −0.669706 | − | 0.742627i | \(-0.733580\pi\) | ||||
−0.669706 | + | 0.742627i | \(0.733580\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17886.0 | 1.93132 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2343.00 | 0.251285 | 0.125643 | − | 0.992076i | \(-0.459901\pi\) | ||||
0.125643 | + | 0.992076i | \(0.459901\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12600.0 | 1.33324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10905.0 | 1.14619 | 0.573094 | − | 0.819489i | \(-0.305743\pi\) | ||||
0.573094 | + | 0.819489i | \(0.305743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9639.00 | −1.00639 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23086.0 | −2.39443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3319.00 | −0.339729 | −0.169865 | − | 0.985467i | \(-0.554333\pi\) | ||||
−0.169865 | + | 0.985467i | \(0.554333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 735.000 | 0.0747426 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6468.00 | −0.653459 | −0.326730 | − | 0.945118i | \(-0.605947\pi\) | ||||
−0.326730 | + | 0.945118i | \(0.605947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11972.0 | −1.20170 | −0.600849 | − | 0.799363i | \(-0.705171\pi\) | ||||
−0.600849 | + | 0.799363i | \(0.705171\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6636.00 | −0.657553 | −0.328777 | − | 0.944408i | \(-0.606636\pi\) | ||||
−0.328777 | + | 0.944408i | \(0.606636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15674.0 | −1.54319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1862.00 | −0.182158 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3996.00 | −0.388449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15444.0 | 1.48246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 630.000 | 0.0600949 | 0.0300474 | − | 0.999548i | \(-0.490434\pi\) | ||||
0.0300474 | + | 0.999548i | \(0.490434\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4088.00 | −0.387519 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18564.0 | −1.74884 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10646.0 | −0.990588 | −0.495294 | − | 0.868725i | \(-0.664940\pi\) | ||||
−0.495294 | + | 0.868725i | \(0.664940\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8099.00 | 0.748976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2388.00 | 0.219489 | 0.109744 | − | 0.993960i | \(-0.464997\pi\) | ||||
0.109744 | + | 0.993960i | \(0.464997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2520.00 | −0.230213 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24072.0 | 2.17259 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10540.0 | 0.945562 | 0.472781 | − | 0.881180i | \(-0.343250\pi\) | ||||
0.472781 | + | 0.881180i | \(0.343250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12348.0 | −1.10113 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6972.00 | −0.618024 | −0.309012 | − | 0.951058i | \(-0.599998\pi\) | ||||
−0.309012 | + | 0.951058i | \(0.599998\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9891.00 | 0.866420 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9030.00 | −0.786341 | −0.393171 | − | 0.919466i | \(-0.628622\pi\) | ||||
−0.393171 | + | 0.919466i | \(0.628622\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4522.00 | −0.391471 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1225.00 | −0.105429 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2268.00 | −0.192933 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12936.0 | 1.09408 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10437.0 | 0.877645 | 0.438823 | − | 0.898574i | \(-0.355396\pi\) | ||||
0.438823 | + | 0.898574i | \(0.355396\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8113.00 | 0.678311 | 0.339156 | − | 0.940730i | \(-0.389859\pi\) | ||||
0.339156 | + | 0.940730i | \(0.389859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3822.00 | −0.315918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6083.00 | −0.499959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18480.0 | 1.51029 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9996.00 | −0.812336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 945.000 | 0.0759400 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21951.0 | −1.75417 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14848.0 | −1.17997 | −0.589986 | − | 0.807413i | \(-0.700867\pi\) | ||||
−0.589986 | + | 0.807413i | \(0.700867\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15974.0 | −1.26245 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20329.0 | 1.58904 | 0.794520 | − | 0.607238i | \(-0.207722\pi\) | ||||
0.794520 | + | 0.607238i | \(0.207722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5236.00 | −0.407044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4200.00 | 0.324730 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22100.0 | −1.69944 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15324.0 | −1.16571 | −0.582853 | − | 0.812577i | \(-0.698064\pi\) | ||||
−0.582853 | + | 0.812577i | \(0.698064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4144.00 | −0.313547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3969.00 | 0.298701 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9408.00 | 0.704263 | 0.352131 | − | 0.935951i | \(-0.385457\pi\) | ||||
0.352131 | + | 0.935951i | \(0.385457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28526.0 | −2.11284 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24375.0 | −1.79588 | −0.897938 | − | 0.440122i | \(-0.854935\pi\) | ||||
−0.897938 | + | 0.440122i | \(0.854935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 988.000 | 0.0724107 | 0.0362054 | − | 0.999344i | \(-0.488473\pi\) | ||||
0.0362054 | + | 0.999344i | \(0.488473\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9786.00 | −0.713466 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16429.0 | −1.18535 | −0.592676 | − | 0.805441i | \(-0.701929\pi\) | ||||
−0.592676 | + | 0.805441i | \(0.701929\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23219.0 | −1.66658 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30702.0 | 2.19231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18954.0 | −1.34647 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13839.0 | 0.973078 | 0.486539 | − | 0.873659i | \(-0.338259\pi\) | ||||
0.486539 | + | 0.873659i | \(0.338259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6370.00 | 0.445622 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11802.0 | −0.821437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14007.0 | 0.969981 | 0.484990 | − | 0.874520i | \(-0.338823\pi\) | ||||
0.484990 | + | 0.874520i | \(0.338823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10780.0 | −0.739022 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21090.0 | −1.43859 | −0.719294 | − | 0.694706i | \(-0.755535\pi\) | ||||
−0.719294 | + | 0.694706i | \(0.755535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5747.00 | 0.390058 | 0.195029 | − | 0.980797i | \(-0.437520\pi\) | ||||
0.195029 | + | 0.980797i | \(0.437520\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10142.0 | −0.684932 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17696.0 | −1.18329 | −0.591646 | − | 0.806198i | \(-0.701522\pi\) | ||||
−0.591646 | + | 0.806198i | \(0.701522\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28560.0 | 1.90034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2352.00 | −0.155731 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26102.0 | 1.71982 | 0.859910 | − | 0.510445i | \(-0.170519\pi\) | ||||
0.859910 | + | 0.510445i | \(0.170519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4194.00 | −0.273653 | −0.136827 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136827 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7420.00 | 0.481801 | 0.240901 | − | 0.970550i | \(-0.422557\pi\) | ||||
0.240901 | + | 0.970550i | \(0.422557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2730.00 | 0.176411 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24990.0 | 1.60707 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6615.00 | −0.421336 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3066.00 | 0.194355 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5818.00 | 0.367054 | 0.183527 | − | 0.983015i | \(-0.441249\pi\) | ||||
0.183527 | + | 0.983015i | \(0.441249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21301.0 | −1.33750 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22764.0 | −1.41592 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15576.0 | 0.964283 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29478.0 | −1.81640 | −0.908199 | − | 0.418539i | \(-0.862542\pi\) | ||||
−0.908199 | + | 0.418539i | \(0.862542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5852.00 | −0.358912 | −0.179456 | − | 0.983766i | \(-0.557434\pi\) | ||||
−0.179456 | + | 0.983766i | \(0.557434\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29484.0 | 1.79155 | 0.895777 | − | 0.444503i | \(-0.146620\pi\) | ||||
0.895777 | + | 0.444503i | \(0.146620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22680.0 | −1.37175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43316.0 | 2.60782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3498.00 | −0.209628 | −0.104814 | − | 0.994492i | \(-0.533425\pi\) | ||||
−0.104814 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2926.00 | −0.173751 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7905.00 | −0.467276 | −0.233638 | − | 0.972324i | \(-0.575063\pi\) | ||||
−0.233638 | + | 0.972324i | \(0.575063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27272.0 | 1.60478 | 0.802389 | − | 0.596802i | \(-0.203562\pi\) | ||||
0.802389 | + | 0.596802i | \(0.203562\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4116.00 | 0.241104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9360.00 | −0.543359 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23324.0 | 1.34792 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6426.00 | 0.369706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12602.0 | 0.721800 | 0.360900 | − | 0.932605i | \(-0.382470\pi\) | ||||
0.360900 | + | 0.932605i | \(0.382470\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25536.0 | 1.44967 | 0.724836 | − | 0.688921i | \(-0.241915\pi\) | ||||
0.724836 | + | 0.688921i | \(0.241915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37604.0 | 2.12534 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11172.0 | 0.628652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2127.00 | −0.119162 | −0.0595808 | − | 0.998223i | \(-0.518976\pi\) | ||||
−0.0595808 | + | 0.998223i | \(0.518976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30380.0 | −1.68715 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19656.0 | −1.08684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8953.00 | 0.492892 | 0.246446 | − | 0.969157i | \(-0.420737\pi\) | ||||
0.246446 | + | 0.969157i | \(0.420737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20196.0 | −1.10705 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7497.00 | 0.407416 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21126.0 | 1.14315 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23172.0 | 1.24849 | 0.624247 | − | 0.781227i | \(-0.285406\pi\) | ||||
0.624247 | + | 0.781227i | \(0.285406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5110.00 | −0.274150 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15708.0 | 0.835587 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9620.00 | 0.509572 | 0.254786 | − | 0.966997i | \(-0.417995\pi\) | ||||
0.254786 | + | 0.966997i | \(0.417995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14300.0 | −0.754278 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14196.0 | −0.745644 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31080.0 | 1.61883 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4830.00 | −0.250527 | −0.125263 | − | 0.992124i | \(-0.539978\pi\) | ||||
−0.125263 | + | 0.992124i | \(0.539978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27608.0 | −1.42604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25921.0 | 1.33335 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11816.0 | −0.602794 | −0.301397 | − | 0.953499i | \(-0.597453\pi\) | ||||
−0.301397 | + | 0.953499i | \(0.597453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3108.00 | 0.157255 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23492.0 | 1.18376 | 0.591881 | − | 0.806026i | \(-0.298386\pi\) | ||||
0.591881 | + | 0.806026i | \(0.298386\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12447.0 | 0.622105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35300.0 | −1.75715 | −0.878573 | − | 0.477607i | \(-0.841504\pi\) | ||||
−0.878573 | + | 0.477607i | \(0.841504\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6860.00 | −0.340092 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16242.0 | −0.801967 | −0.400983 | − | 0.916085i | \(-0.631331\pi\) | ||||
−0.400983 | + | 0.916085i | \(0.631331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19866.0 | 0.973037 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26826.0 | 1.30868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10712.0 | −0.520488 | −0.260244 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260244 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 49539.0 | 2.39748 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13504.0 | −0.648364 | −0.324182 | − | 0.945995i | \(-0.605089\pi\) | ||||
−0.324182 | + | 0.945995i | \(0.605089\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14742.0 | 0.705008 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18123.0 | −0.863283 | −0.431641 | − | 0.902045i | \(-0.642065\pi\) | ||||
−0.431641 | + | 0.902045i | \(0.642065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7820.00 | 0.371039 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23520.0 | −1.10725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9485.00 | 0.444783 | 0.222391 | − | 0.974957i | \(-0.428614\pi\) | ||||
0.222391 | + | 0.974957i | \(0.428614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −47922.0 | −2.23848 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31248.0 | −1.45396 | −0.726981 | − | 0.686658i | \(-0.759077\pi\) | ||||
−0.726981 | + | 0.686658i | \(0.759077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34748.0 | −1.60435 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12495.0 | −0.574685 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19116.0 | −0.875831 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4200.00 | −0.191693 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15484.0 | 0.701328 | 0.350664 | − | 0.936501i | \(-0.385956\pi\) | ||||
0.350664 | + | 0.936501i | \(0.385956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24066.0 | −1.08590 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −70482.0 | −3.16821 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6664.00 | 0.298418 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34146.0 | 1.51758 | 0.758791 | − | 0.651334i | \(-0.225790\pi\) | ||||
0.758791 | + | 0.651334i | \(0.225790\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1764.00 | 0.0781049 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16170.0 | 0.713282 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3591.00 | 0.157813 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11760.0 | 0.512976 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36030.0 | −1.56582 | −0.782909 | − | 0.622136i | \(-0.786265\pi\) | ||||
−0.782909 | + | 0.622136i | \(0.786265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6748.00 | 0.292175 | 0.146088 | − | 0.989272i | \(-0.453332\pi\) | ||||
0.146088 | + | 0.989272i | \(0.453332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36554.0 | 1.57688 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5180.00 | −0.221818 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20944.0 | −0.893581 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5598.00 | −0.237968 | −0.118984 | − | 0.992896i | \(-0.537964\pi\) | ||||
−0.118984 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5732.00 | −0.242776 | −0.121388 | − | 0.992605i | \(-0.538735\pi\) | ||||
−0.121388 | + | 0.992605i | \(0.538735\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39999.0 | 1.68186 | 0.840932 | − | 0.541141i | \(-0.182007\pi\) | ||||
0.840932 | + | 0.541141i | \(0.182007\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16940.0 | 0.709711 | 0.354856 | − | 0.934921i | \(-0.384530\pi\) | ||||
0.354856 | + | 0.934921i | \(0.384530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9688.00 | 0.404420 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17073.0 | 0.710137 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6370.00 | −0.263058 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45360.0 | 1.86651 | 0.933255 | − | 0.359216i | \(-0.116956\pi\) | ||||
0.933255 | + | 0.359216i | \(0.116956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9989.00 | −0.409570 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27006.0 | 1.10336 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20468.0 | −0.830329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29939.0 | 1.21025 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11388.0 | 0.458726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43918.0 | −1.76286 | −0.881432 | − | 0.472310i | \(-0.843420\pi\) | ||||
−0.881432 | + | 0.472310i | \(0.843420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3339.00 | −0.133090 | −0.0665450 | − | 0.997783i | \(-0.521198\pi\) | ||||
−0.0665450 | + | 0.997783i | \(0.521198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36925.0 | 1.46666 | 0.733332 | − | 0.679870i | \(-0.237964\pi\) | ||||
0.733332 | + | 0.679870i | \(0.237964\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −84966.0 | −3.36311 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40608.0 | 1.60175 | 0.800876 | − | 0.598830i | \(-0.204367\pi\) | ||||
0.800876 | + | 0.598830i | \(0.204367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31304.0 | 1.22623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17550.0 | 0.685090 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12908.0 | 0.502148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24332.0 | 0.943314 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35156.0 | 1.35363 | 0.676815 | − | 0.736153i | \(-0.263360\pi\) | ||||
0.676815 | + | 0.736153i | \(0.263360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −44394.0 | −1.70350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2142.00 | 0.0819135 | 0.0409568 | − | 0.999161i | \(-0.486959\pi\) | ||||
0.0409568 | + | 0.999161i | \(0.486959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19153.0 | 0.729954 | 0.364977 | − | 0.931016i | \(-0.381077\pi\) | ||||
0.364977 | + | 0.931016i | \(0.381077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24444.0 | 0.925309 | 0.462655 | − | 0.886539i | \(-0.346897\pi\) | ||||
0.462655 | + | 0.886539i | \(0.346897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37876.0 | 1.42893 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22653.0 | 0.851744 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2940.00 | −0.110172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15288.0 | 0.569065 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21840.0 | 0.810239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14742.0 | 0.545091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35224.0 | −1.29810 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20036.0 | −0.733500 | −0.366750 | − | 0.930320i | \(-0.619530\pi\) | ||||
−0.366750 | + | 0.930320i | \(0.619530\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10164.0 | 0.370868 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33468.0 | 1.21717 | 0.608586 | − | 0.793488i | \(-0.291737\pi\) | ||||
0.608586 | + | 0.793488i | \(0.291737\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24381.0 | −0.883782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8568.00 | −0.308550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35090.0 | −1.25953 | −0.629767 | − | 0.776784i | \(-0.716850\pi\) | ||||
−0.629767 | + | 0.776784i | \(0.716850\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40817.0 | 1.46033 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19824.0 | −0.706950 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17864.0 | −0.632935 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32130.0 | −1.13472 | −0.567358 | − | 0.823471i | \(-0.692034\pi\) | ||||
−0.567358 | + | 0.823471i | \(0.692034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28455.0 | −1.00169 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17346.0 | −0.608663 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20531.0 | 0.715815 | 0.357907 | − | 0.933757i | \(-0.383490\pi\) | ||||
0.357907 | + | 0.933757i | \(0.383490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19306.0 | 0.670956 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7812.00 | 0.270631 | 0.135316 | − | 0.990803i | \(-0.456795\pi\) | ||||
0.135316 | + | 0.990803i | \(0.456795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27846.0 | 0.961602 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23256.0 | −0.798013 | −0.399007 | − | 0.916948i | \(-0.630645\pi\) | ||||
−0.399007 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3724.00 | 0.127383 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4452.00 | −0.151804 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14097.0 | 0.479167 | 0.239584 | − | 0.970876i | \(-0.422989\pi\) | ||||
0.239584 | + | 0.970876i | \(0.422989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22680.0 | −0.766082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 65994.0 | 2.22217 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3333.00 | 0.111879 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17358.0 | 0.580845 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34144.0 | 1.13547 | 0.567734 | − | 0.823212i | \(-0.307820\pi\) | ||||
0.567734 | + | 0.823212i | \(0.307820\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5145.00 | 0.170569 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32613.0 | 1.07786 | 0.538929 | − | 0.842351i | \(-0.318829\pi\) | ||||
0.538929 | + | 0.842351i | \(0.318829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55930.0 | 1.84279 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43359.0 | −1.41983 | −0.709917 | − | 0.704286i | \(-0.751267\pi\) | ||||
−0.709917 | + | 0.704286i | \(0.751267\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19845.0 | −0.647854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5060.00 | 0.164682 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28518.0 | 0.925313 | 0.462657 | − | 0.886538i | \(-0.346896\pi\) | ||||
0.462657 | + | 0.886538i | \(0.346896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19992.0 | −0.644734 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11544.0 | 0.371161 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18122.0 | −0.580892 | −0.290446 | − | 0.956891i | \(-0.593804\pi\) | ||||
−0.290446 | + | 0.956891i | \(0.593804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48209.0 | 1.54065 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28924.0 | −0.918789 | −0.459394 | − | 0.888232i | \(-0.651934\pi\) | ||||
−0.459394 | + | 0.888232i | \(0.651934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5110.00 | 0.161835 |
(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 | 400.4.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 50.4.a.e.1.1 | yes | 1 | ||
5.2 | odd | 4 | 400.4.c.d.49.2 | 2 | |||
5.3 | odd | 4 | 400.4.c.d.49.1 | 2 | |||
5.4 | even | 2 | 400.4.a.r.1.1 | 1 | |||
8.3 | odd | 2 | 1600.4.a.f.1.1 | 1 | |||
8.5 | even | 2 | 1600.4.a.bv.1.1 | 1 | |||
12.11 | even | 2 | 450.4.a.a.1.1 | 1 | |||
20.3 | even | 4 | 50.4.b.b.49.1 | 2 | |||
20.7 | even | 4 | 50.4.b.b.49.2 | 2 | |||
20.19 | odd | 2 | 50.4.a.a.1.1 | ✓ | 1 | ||
28.27 | even | 2 | 2450.4.a.y.1.1 | 1 | |||
40.19 | odd | 2 | 1600.4.a.bu.1.1 | 1 | |||
40.29 | even | 2 | 1600.4.a.g.1.1 | 1 | |||
60.23 | odd | 4 | 450.4.c.c.199.2 | 2 | |||
60.47 | odd | 4 | 450.4.c.c.199.1 | 2 | |||
60.59 | even | 2 | 450.4.a.t.1.1 | 1 | |||
140.139 | even | 2 | 2450.4.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.4.a.a.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
50.4.a.e.1.1 | yes | 1 | 4.3 | odd | 2 | ||
50.4.b.b.49.1 | 2 | 20.3 | even | 4 | |||
50.4.b.b.49.2 | 2 | 20.7 | even | 4 | |||
400.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
400.4.a.r.1.1 | 1 | 5.4 | even | 2 | |||
400.4.c.d.49.1 | 2 | 5.3 | odd | 4 | |||
400.4.c.d.49.2 | 2 | 5.2 | odd | 4 | |||
450.4.a.a.1.1 | 1 | 12.11 | even | 2 | |||
450.4.a.t.1.1 | 1 | 60.59 | even | 2 | |||
450.4.c.c.199.1 | 2 | 60.47 | odd | 4 | |||
450.4.c.c.199.2 | 2 | 60.23 | odd | 4 | |||
1600.4.a.f.1.1 | 1 | 8.3 | odd | 2 | |||
1600.4.a.g.1.1 | 1 | 40.29 | even | 2 | |||
1600.4.a.bu.1.1 | 1 | 40.19 | odd | 2 | |||
1600.4.a.bv.1.1 | 1 | 8.5 | even | 2 | |||
2450.4.a.t.1.1 | 1 | 140.139 | even | 2 | |||
2450.4.a.y.1.1 | 1 | 28.27 | even | 2 |