Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,4,Mod(1,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, 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("2304.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.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: | \(135.940400653\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.5830 | −0.946573 | −0.473286 | − | 0.880909i | \(-0.656932\pi\) | ||||
−0.473286 | + | 0.880909i | \(0.656932\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.8745 | −0.435122 | −0.217561 | − | 0.976047i | \(-0.569810\pi\) | ||||
−0.217561 | + | 0.976047i | \(0.569810\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9150 | 1.12892 | 0.564461 | − | 0.825460i | \(-0.309084\pi\) | ||||
0.564461 | + | 0.825460i | \(0.309084\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −37.0405 | −0.447246 | −0.223623 | − | 0.974676i | \(-0.571788\pi\) | ||||
−0.223623 | + | 0.974676i | \(0.571788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −152.000 | −1.37801 | −0.689004 | − | 0.724757i | \(-0.741952\pi\) | ||||
−0.689004 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.0000 | −0.104000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.745 | 1.01649 | 0.508245 | − | 0.861212i | \(-0.330294\pi\) | ||||
0.508245 | + | 0.861212i | \(0.330294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 224.000 | 1.29779 | 0.648897 | − | 0.760877i | \(-0.275231\pi\) | ||||
0.648897 | + | 0.760877i | \(0.275231\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −84.6640 | −0.408881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −243.409 | −1.08152 | −0.540760 | − | 0.841177i | \(-0.681863\pi\) | ||||
−0.540760 | + | 0.841177i | \(0.681863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.0000 | −0.266638 | −0.133319 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133319 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 439.195 | 1.55759 | 0.778797 | − | 0.627276i | \(-0.215830\pi\) | ||||
0.778797 | + | 0.627276i | \(0.215830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −336.000 | −1.04278 | −0.521390 | − | 0.853319i | \(-0.674586\pi\) | ||||
−0.521390 | + | 0.853319i | \(0.674586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 31.7490 | 0.0822842 | 0.0411421 | − | 0.999153i | \(-0.486900\pi\) | ||||
0.0411421 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 168.000 | 0.411875 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 534.442 | 1.17929 | 0.589647 | − | 0.807661i | \(-0.299267\pi\) | ||||
0.589647 | + | 0.807661i | \(0.299267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 95.2470 | 0.199920 | 0.0999601 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999601 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −560.000 | −1.06861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 174.620 | 0.318406 | 0.159203 | − | 0.987246i | \(-0.449108\pi\) | ||||
0.159203 | + | 0.987246i | \(0.449108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.0000 | −0.120350 | −0.0601748 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601748 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 294.000 | 0.471371 | 0.235686 | − | 0.971829i | \(-0.424266\pi\) | ||||
0.235686 | + | 0.971829i | \(0.424266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −126.996 | −0.187955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −464.000 | −0.660811 | −0.330406 | − | 0.943839i | \(-0.607186\pi\) | ||||
−0.330406 | + | 0.943839i | \(0.607186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 545.025 | 0.720774 | 0.360387 | − | 0.932803i | \(-0.382645\pi\) | ||||
0.360387 | + | 0.932803i | \(0.382645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −148.162 | −0.189064 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 266.000 | 0.316808 | 0.158404 | − | 0.987374i | \(-0.449365\pi\) | ||||
0.158404 | + | 0.987374i | \(0.449365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 423.320 | 0.487649 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 392.000 | 0.423351 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 994.000 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 751.393 | 0.740262 | 0.370131 | − | 0.928980i | \(-0.379313\pi\) | ||||
0.370131 | + | 0.928980i | \(0.379313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1176.00 | −1.12500 | −0.562499 | − | 0.826798i | \(-0.690160\pi\) | ||||
−0.562499 | + | 0.826798i | \(0.690160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −269.867 | −0.243822 | −0.121911 | − | 0.992541i | \(-0.538902\pi\) | ||||
−0.121911 | + | 0.992541i | \(0.538902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1894.36 | −1.66465 | −0.832324 | − | 0.554290i | \(-0.812990\pi\) | ||||
−0.832324 | + | 0.554290i | \(0.812990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1710.00 | 1.42357 | 0.711784 | − | 0.702398i | \(-0.247887\pi\) | ||||
0.711784 | + | 0.702398i | \(0.247887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1608.62 | 1.30439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.000 | 0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1079.00 | −0.810669 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1460.45 | 1.04502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1664.00 | −1.16265 | −0.581323 | − | 0.813673i | \(-0.697465\pi\) | ||||
−0.581323 | + | 0.813673i | \(0.697465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 672.021 | 0.448204 | 0.224102 | − | 0.974566i | \(-0.428055\pi\) | ||||
0.224102 | + | 0.974566i | \(0.428055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −296.324 | −0.193192 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1062.00 | −0.662283 | −0.331142 | − | 0.943581i | \(-0.607434\pi\) | ||||
−0.331142 | + | 0.943581i | \(0.607434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2693.37 | −1.64352 | −0.821759 | − | 0.569835i | \(-0.807007\pi\) | ||||
−0.821759 | + | 0.569835i | \(0.807007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −840.000 | −0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1680.00 | −0.962182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 793.725 | 0.436406 | 0.218203 | − | 0.975903i | \(-0.429980\pi\) | ||||
0.218203 | + | 0.975903i | \(0.429980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −744.000 | −0.400966 | −0.200483 | − | 0.979697i | \(-0.564251\pi\) | ||||
−0.200483 | + | 0.979697i | \(0.564251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2370.59 | −1.22846 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 179.911 | 0.0914552 | 0.0457276 | − | 0.998954i | \(-0.485439\pi\) | ||||
0.0457276 | + | 0.998954i | \(0.485439\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1216.00 | −0.595244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1772.65 | −0.851809 | −0.425905 | − | 0.904768i | \(-0.640044\pi\) | ||||
−0.425905 | + | 0.904768i | \(0.640044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1960.00 | −0.908200 | −0.454100 | − | 0.890951i | \(-0.650039\pi\) | ||||
−0.454100 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 603.000 | 0.274465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2000.19 | −0.879026 | −0.439513 | − | 0.898236i | \(-0.644849\pi\) | ||||
−0.439513 | + | 0.898236i | \(0.644849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −104.000 | −0.0449238 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3264.86 | −1.36328 | −0.681639 | − | 0.731688i | \(-0.738733\pi\) | ||||
−0.681639 | + | 0.731688i | \(0.738733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2338.84 | 0.960469 | 0.480235 | − | 0.877140i | \(-0.340552\pi\) | ||||
0.480235 | + | 0.877140i | \(0.340552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2576.00 | 1.02374 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −222.243 | −0.0869092 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3904.00 | −1.47897 | −0.739486 | − | 0.673172i | \(-0.764931\pi\) | ||||
−0.739486 | + | 0.673172i | \(0.764931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3330.00 | 1.24196 | 0.620981 | − | 0.783826i | \(-0.286734\pi\) | ||||
0.620981 | + | 0.783826i | \(0.286734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1195.88 | −0.432502 | −0.216251 | − | 0.976338i | \(-0.569383\pi\) | ||||
−0.216251 | + | 0.976338i | \(0.569383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1736.00 | 0.618401 | 0.309200 | − | 0.950997i | \(-0.399939\pi\) | ||||
0.309200 | + | 0.950997i | \(0.399939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1269.96 | 0.439083 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 740.810 | 0.252392 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 588.000 | 0.194607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2915.62 | −0.951277 | −0.475638 | − | 0.879641i | \(-0.657783\pi\) | ||||
−0.475638 | + | 0.879641i | \(0.657783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4648.00 | −1.47438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1792.00 | 0.560594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 740.810 | 0.225486 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1568.00 | 0.470857 | 0.235428 | − | 0.971892i | \(-0.424351\pi\) | ||||
0.235428 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1264.67 | 0.369775 | 0.184888 | − | 0.982760i | \(-0.440808\pi\) | ||||
0.184888 | + | 0.982760i | \(0.440808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5153.92 | −1.48725 | −0.743626 | − | 0.668595i | \(-0.766896\pi\) | ||||
−0.743626 | + | 0.668595i | \(0.766896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −838.000 | −0.235619 | −0.117809 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117809 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3555.89 | 0.987067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6288.00 | −1.70183 | −0.850914 | − | 0.525305i | \(-0.823951\pi\) | ||||
−0.850914 | + | 0.525305i | \(0.823951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2926.00 | −0.782076 | −0.391038 | − | 0.920375i | \(-0.627884\pi\) | ||||
−0.391038 | + | 0.920375i | \(0.627884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2952.66 | 0.769953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1960.00 | −0.504906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5444.96 | 1.36925 | 0.684627 | − | 0.728894i | \(-0.259965\pi\) | ||||
0.684627 | + | 0.728894i | \(0.259965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2412.93 | 0.599602 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2562.00 | −0.621841 | −0.310921 | − | 0.950436i | \(-0.600637\pi\) | ||||
−0.310921 | + | 0.950436i | \(0.600637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1947.27 | −0.467172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5896.00 | −1.38237 | −0.691184 | − | 0.722679i | \(-0.742911\pi\) | ||||
−0.691184 | + | 0.722679i | \(0.742911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −336.000 | −0.0778880 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5365.58 | 1.21615 | 0.608077 | − | 0.793878i | \(-0.291941\pi\) | ||||
0.608077 | + | 0.793878i | \(0.291941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1680.00 | −0.376578 | −0.188289 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188289 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 206.369 | 0.0452527 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1576.87 | 0.342039 | 0.171019 | − | 0.985268i | \(-0.445294\pi\) | ||||
0.171019 | + | 0.985268i | \(0.445294\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2742.00 | −0.582114 | −0.291057 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291057 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2989.70 | −0.627983 | −0.313991 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313991 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −560.000 | −0.115177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9238.96 | −1.84214 | −0.921068 | − | 0.389401i | \(-0.872682\pi\) | ||||
−0.921068 | + | 0.389401i | \(0.872682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5656.00 | −1.11629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8043.08 | −1.55566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3513.56 | 0.672818 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1008.00 | −0.189239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2587.54 | 0.481039 | 0.240520 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240520 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2744.00 | −0.500315 | −0.250157 | − | 0.968205i | \(-0.580482\pi\) | ||||
−0.250157 | + | 0.968205i | \(0.580482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2282.00 | −0.412097 | −0.206048 | − | 0.978542i | \(-0.566060\pi\) | ||||
−0.206048 | + | 0.978542i | \(0.566060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9577.62 | −1.69695 | −0.848474 | − | 0.529237i | \(-0.822478\pi\) | ||||
−0.848474 | + | 0.529237i | \(0.822478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2520.00 | −0.442298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −518.567 | −0.0893308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −687.895 | −0.117408 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2688.00 | −0.450438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4249.08 | 0.705590 | 0.352795 | − | 0.935701i | \(-0.385231\pi\) | ||||
0.352795 | + | 0.935701i | \(0.385231\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1848.00 | −0.301394 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6130.00 | 0.990868 | 0.495434 | − | 0.868646i | \(-0.335009\pi\) | ||||
0.495434 | + | 0.868646i | \(0.335009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3555.89 | −0.564699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2481.71 | 0.383935 | 0.191967 | − | 0.981401i | \(-0.438513\pi\) | ||||
0.191967 | + | 0.981401i | \(0.438513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −328.073 | −0.0503191 | −0.0251595 | − | 0.999683i | \(-0.508009\pi\) | ||||
−0.0251595 | + | 0.999683i | \(0.508009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10206.0 | 1.53884 | 0.769420 | − | 0.638743i | \(-0.220545\pi\) | ||||
0.769420 | + | 0.638743i | \(0.220545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 761.976 | 0.113920 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3176.00 | −0.466916 | −0.233458 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233458 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5487.00 | −0.799971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3111.40 | −0.446187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11760.0 | −1.67266 | −0.836331 | − | 0.548225i | \(-0.815304\pi\) | ||||
−0.836331 | + | 0.548225i | \(0.815304\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 253.992 | 0.0355434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10974.6 | 1.52344 | 0.761719 | − | 0.647908i | \(-0.224356\pi\) | ||||
0.761719 | + | 0.647908i | \(0.224356\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8400.00 | 1.14754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3074.36 | −0.416674 | −0.208337 | − | 0.978057i | \(-0.566805\pi\) | ||||
−0.208337 | + | 0.978057i | \(0.566805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2688.00 | −0.358617 | −0.179309 | − | 0.983793i | \(-0.557386\pi\) | ||||
−0.179309 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1344.00 | 0.177913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10487.8 | 1.36697 | 0.683484 | − | 0.729966i | \(-0.260464\pi\) | ||||
0.683484 | + | 0.729966i | \(0.260464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2128.00 | −0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4910.51 | 0.625506 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5704.24 | −0.721127 | −0.360564 | − | 0.932735i | \(-0.617416\pi\) | ||||
−0.360564 | + | 0.932735i | \(0.617416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12402.0 | −1.54445 | −0.772227 | − | 0.635346i | \(-0.780857\pi\) | ||||
−0.772227 | + | 0.635346i | \(0.780857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11853.0 | 1.46511 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3864.00 | 0.470593 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12278.0 | 1.48437 | 0.742186 | − | 0.670194i | \(-0.233789\pi\) | ||||
0.742186 | + | 0.670194i | \(0.233789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4275.53 | 0.509407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5768.00 | −0.682265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8207.12 | 0.956907 | 0.478454 | − | 0.878113i | \(-0.341198\pi\) | ||||
0.478454 | + | 0.878113i | \(0.341198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1449.87 | 0.167844 | 0.0839221 | − | 0.996472i | \(-0.473255\pi\) | ||||
0.0839221 | + | 0.996472i | \(0.473255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −182.000 | −0.0207725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 761.976 | 0.0863574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7632.00 | −0.852948 | −0.426474 | − | 0.904500i | \(-0.640244\pi\) | ||||
−0.426474 | + | 0.904500i | \(0.640244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3794.00 | 0.421081 | 0.210540 | − | 0.977585i | \(-0.432478\pi\) | ||||
0.210540 | + | 0.977585i | \(0.432478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5630.16 | 0.616309 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1848.00 | 0.200912 | 0.100456 | − | 0.994942i | \(-0.467970\pi\) | ||||
0.100456 | + | 0.994942i | \(0.467970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12334.5 | −1.32287 | −0.661433 | − | 0.750004i | \(-0.730051\pi\) | ||||
−0.661433 | + | 0.750004i | \(0.730051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2815.08 | −0.299882 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3582.00 | 0.376492 | 0.188246 | − | 0.982122i | \(-0.439720\pi\) | ||||
0.188246 | + | 0.982122i | \(0.439720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1111.22 | 0.116020 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4480.00 | −0.461595 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2714.00 | −0.277802 | −0.138901 | − | 0.990306i | \(-0.544357\pi\) | ||||
−0.138901 | + | 0.990306i | \(0.544357\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8349.99 | −0.843596 | −0.421798 | − | 0.906690i | \(-0.638601\pi\) | ||||
−0.421798 | + | 0.906690i | \(0.638601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2224.00 | 0.223236 | 0.111618 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111618 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10292.0 | −1.01982 | −0.509910 | − | 0.860228i | \(-0.670321\pi\) | ||||
−0.509910 | + | 0.860228i | \(0.670321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1396.96 | 0.137538 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6972.00 | −0.677744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 481.527 | 0.0465136 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17696.0 | −1.68800 | −0.843999 | − | 0.536345i | \(-0.819805\pi\) | ||||
−0.843999 | + | 0.536345i | \(0.819805\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12880.0 | −1.22095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10519.5 | −0.984879 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1304.00 | −0.121334 | −0.0606672 | − | 0.998158i | \(-0.519323\pi\) | ||||
−0.0606672 | + | 0.998158i | \(0.519323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16662.9 | 1.53154 | 0.765772 | − | 0.643112i | \(-0.222357\pi\) | ||||
0.765772 | + | 0.643112i | \(0.222357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2222.43 | 0.203029 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −576.000 | −0.0519862 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3095.53 | 0.277705 | 0.138853 | − | 0.990313i | \(-0.455659\pi\) | ||||
0.138853 | + | 0.990313i | \(0.455659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19320.0 | −1.71260 | −0.856298 | − | 0.516481i | \(-0.827242\pi\) | ||||
−0.856298 | + | 0.516481i | \(0.827242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7952.00 | −0.700712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4476.61 | 0.389828 | 0.194914 | − | 0.980820i | \(-0.437557\pi\) | ||||
0.194914 | + | 0.980820i | \(0.437557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2352.00 | 0.203613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12445.6 | 1.06489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5333.83 | 0.453737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2982.00 | −0.250756 | −0.125378 | − | 0.992109i | \(-0.540014\pi\) | ||||
−0.125378 | + | 0.992109i | \(0.540014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2016.06 | −0.168559 | −0.0842794 | − | 0.996442i | \(-0.526859\pi\) | ||||
−0.0842794 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3136.00 | 0.259215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3704.05 | −0.301014 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2856.00 | 0.230796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4428.99 | 0.353933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15419.4 | 1.22539 | 0.612693 | − | 0.790321i | \(-0.290086\pi\) | ||||
0.612693 | + | 0.790321i | \(0.290086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20048.0 | 1.57571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12609.7 | −0.985649 | −0.492824 | − | 0.870129i | \(-0.664035\pi\) | ||||
−0.492824 | + | 0.870129i | \(0.664035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3712.00 | −0.285444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7143.53 | 0.543413 | 0.271706 | − | 0.962380i | \(-0.412412\pi\) | ||||
0.271706 | + | 0.962380i | \(0.412412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23240.0 | 1.75840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7572.14 | 0.566834 | 0.283417 | − | 0.958997i | \(-0.408532\pi\) | ||||
0.283417 | + | 0.958997i | \(0.408532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18096.9 | −1.34751 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15594.0 | 1.14892 | 0.574459 | − | 0.818533i | \(-0.305212\pi\) | ||||
0.574459 | + | 0.818533i | \(0.305212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16737.0 | 1.22666 | 0.613330 | − | 0.789827i | \(-0.289830\pi\) | ||||
0.613330 | + | 0.789827i | \(0.289830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1976.00 | 0.143313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6594.00 | 0.475757 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4360.20 | 0.311345 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −504.000 | −0.0358037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23213.8 | −1.63226 | −0.816130 | − | 0.577868i | \(-0.803885\pi\) | ||||
−0.816130 | + | 0.577868i | \(0.803885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8297.08 | −0.580433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14322.0 | −0.991794 | −0.495897 | − | 0.868381i | \(-0.665161\pi\) | ||||
−0.495897 | + | 0.868381i | \(0.665161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1185.30 | −0.0816679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16088.0 | −1.09739 | −0.548696 | − | 0.836022i | \(-0.684876\pi\) | ||||
−0.548696 | + | 0.836022i | \(0.684876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21238.0 | 1.44146 | 0.720729 | − | 0.693217i | \(-0.243807\pi\) | ||||
0.720729 | + | 0.693217i | \(0.243807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11419.1 | 0.767357 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13664.0 | −0.913681 | −0.456841 | − | 0.889549i | \(-0.651019\pi\) | ||||
−0.456841 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17779.4 | −1.17722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20393.5 | −1.34369 | −0.671846 | − | 0.740690i | \(-0.734499\pi\) | ||||
−0.671846 | + | 0.740690i | \(0.734499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3782.00 | −0.246771 | −0.123385 | − | 0.992359i | \(-0.539375\pi\) | ||||
−0.123385 | + | 0.992359i | \(0.539375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5825.94 | −0.378295 | −0.189147 | − | 0.981949i | \(-0.560572\pi\) | ||||
−0.189147 | + | 0.981949i | \(0.560572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2128.00 | 0.136848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3407.73 | −0.216017 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2056.00 | −0.129712 | −0.0648558 | − | 0.997895i | \(-0.520659\pi\) | ||||
−0.0648558 | + | 0.997895i | \(0.520659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17610.1 | 1.10053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14763.3 | −0.918278 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11842.0 | −0.729689 | −0.364845 | − | 0.931068i | \(-0.618878\pi\) | ||||
−0.364845 | + | 0.931068i | \(0.618878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16250.2 | −0.996649 | −0.498325 | − | 0.866991i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866991i | \(0.666051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19320.0 | 1.17395 | 0.586976 | − | 0.809604i | \(-0.300318\pi\) | ||||
0.586976 | + | 0.809604i | \(0.300318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8484.00 | −0.513137 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2317.68 | 0.138894 | 0.0694470 | − | 0.997586i | \(-0.477877\pi\) | ||||
0.0694470 | + | 0.997586i | \(0.477877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7112.00 | −0.424258 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27732.8 | −1.63932 | −0.819662 | − | 0.572847i | \(-0.805839\pi\) | ||||
−0.819662 | + | 0.572847i | \(0.805839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22467.7 | −1.32208 | −0.661039 | − | 0.750352i | \(-0.729884\pi\) | ||||
−0.661039 | + | 0.750352i | \(0.729884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3136.00 | 0.182870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24129.3 | −1.40073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1512.00 | −0.0869897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10078.0 | −0.577234 | −0.288617 | − | 0.957445i | \(-0.593195\pi\) | ||||
−0.288617 | + | 0.957445i | \(0.593195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16160.2 | 0.917413 | 0.458707 | − | 0.888588i | \(-0.348313\pi\) | ||||
0.458707 | + | 0.888588i | \(0.348313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7952.00 | 0.449440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16356.0 | −0.916320 | −0.458160 | − | 0.888870i | \(-0.651491\pi\) | ||||
−0.458160 | + | 0.888870i | \(0.651491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11239.2 | 0.626899 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1680.00 | 0.0928925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29246.1 | −1.61009 | −0.805047 | − | 0.593211i | \(-0.797860\pi\) | ||||
−0.805047 | + | 0.593211i | \(0.797860\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28504.0 | 1.55571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −980.000 | −0.0532570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2465.84 | −0.132858 | −0.0664290 | − | 0.997791i | \(-0.521161\pi\) | ||||
−0.0664290 | + | 0.997791i | \(0.521161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9016.00 | 0.483705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6011.15 | 0.319763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31674.9 | 1.67782 | 0.838912 | − | 0.544267i | \(-0.183192\pi\) | ||||
0.838912 | + | 0.544267i | \(0.183192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34048.0 | −1.78837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8889.72 | 0.464975 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9296.00 | 0.482173 | 0.241086 | − | 0.970504i | \(-0.422496\pi\) | ||||
0.241086 | + | 0.970504i | \(0.422496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9408.00 | −0.485953 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2063.69 | −0.105715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21672.0 | −1.10560 | −0.552799 | − | 0.833315i | \(-0.686440\pi\) | ||||
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6148.73 | 0.311106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9471.79 | −0.477283 | −0.238642 | − | 0.971108i | \(-0.576702\pi\) | ||||
−0.238642 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2772.00 | −0.138545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6863.08 | 0.341627 | 0.170814 | − | 0.985303i | \(-0.445360\pi\) | ||||
0.170814 | + | 0.985303i | \(0.445360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17432.0 | 0.860724 | 0.430362 | − | 0.902656i | \(-0.358386\pi\) | ||||
0.430362 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8400.00 | −0.413090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2158.93 | −0.105321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11632.0 | −0.565190 | −0.282595 | − | 0.959239i | \(-0.591195\pi\) | ||||
−0.282595 | + | 0.959239i | \(0.591195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7873.76 | 0.379543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16731.7 | 0.803336 | 0.401668 | − | 0.915785i | \(-0.368431\pi\) | ||||
0.401668 | + | 0.915785i | \(0.368431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39466.0 | 1.87995 | 0.939975 | − | 0.341244i | \(-0.110848\pi\) | ||||
0.939975 | + | 0.341244i | \(0.110848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15154.9 | −0.719060 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28280.0 | 1.33133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35266.0 | 1.65374 | 0.826869 | − | 0.562395i | \(-0.190120\pi\) | ||||
0.826869 | + | 0.562395i | \(0.190120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16244.9 | 0.755872 | 0.377936 | − | 0.925832i | \(-0.376634\pi\) | ||||
0.377936 | + | 0.925832i | \(0.376634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2912.00 | −0.134970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2592.84 | 0.119253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1142.96 | 0.0523668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1904.00 | −0.0865690 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34844.5 | 1.57824 | 0.789119 | − | 0.614240i | \(-0.210537\pi\) | ||||
0.789119 | + | 0.614240i | \(0.210537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13680.0 | 0.614924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5040.00 | 0.225694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2550.50 | −0.113354 | −0.0566772 | − | 0.998393i | \(-0.518051\pi\) | ||||
−0.0566772 | + | 0.998393i | \(0.518051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4704.00 | −0.208280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4667.11 | −0.205104 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12868.9 | 0.563441 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24390.0 | −1.05996 | −0.529979 | − | 0.848010i | \(-0.677800\pi\) | ||||
−0.529979 | + | 0.848010i | \(0.677800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9582.91 | 0.414922 | 0.207461 | − | 0.978243i | \(-0.433480\pi\) | ||||
0.207461 | + | 0.978243i | \(0.433480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18760.0 | 0.806300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16268.0 | −0.696628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8773.31 | −0.372948 | −0.186474 | − | 0.982460i | \(-0.559706\pi\) | ||||
−0.186474 | + | 0.982460i | \(0.559706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21688.0 | 0.918586 | 0.459293 | − | 0.888285i | \(-0.348103\pi\) | ||||
0.459293 | + | 0.888285i | \(0.348103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19446.3 | −0.817670 | −0.408835 | − | 0.912608i | \(-0.634065\pi\) | ||||
−0.408835 | + | 0.912608i | \(0.634065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19546.8 | −0.818925 | −0.409462 | − | 0.912327i | \(-0.634284\pi\) | ||||
−0.409462 | + | 0.912327i | \(0.634284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3906.00 | −0.162467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20742.7 | 0.859677 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18760.0 | −0.771951 | −0.385976 | − | 0.922509i | \(-0.626135\pi\) | ||||
−0.385976 | + | 0.922509i | \(0.626135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 811.000 | 0.0332527 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6381.55 | −0.259801 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8632.00 | −0.350176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36998.2 | 1.49034 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28732.9 | −1.15333 | −0.576667 | − | 0.816979i | \(-0.695647\pi\) | ||||
−0.576667 | + | 0.816979i | \(0.695647\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8778.00 | 0.349884 | 0.174942 | − | 0.984579i | \(-0.444026\pi\) | ||||
0.174942 | + | 0.984579i | \(0.444026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5646.03 | 0.224261 | 0.112130 | − | 0.993693i | \(-0.464233\pi\) | ||||
0.112130 | + | 0.993693i | \(0.464233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9312.00 | 0.367305 | 0.183652 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183652 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21168.0 | 0.832062 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7365.77 | 0.287534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9240.00 | 0.359455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11683.6 | 0.451405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 137.579 | 0.00529728 | 0.00264864 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264864 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31150.0 | 1.19123 | 0.595613 | − | 0.803272i | \(-0.296909\pi\) | ||||
0.595613 | + | 0.803272i | \(0.296909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12577.9 | 0.479366 | 0.239683 | − | 0.970851i | \(-0.422957\pi\) | ||||
0.239683 | + | 0.970851i | \(0.422957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37128.0 | 1.40545 | 0.702726 | − | 0.711460i | \(-0.251966\pi\) | ||||
0.702726 | + | 0.711460i | \(0.251966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13312.0 | −0.502216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12445.6 | 0.466379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34552.0 | 1.29044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35558.9 | 1.31919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 444.486 | 0.0164351 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24752.0 | −0.909154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35204.4 | −1.28880 | −0.644400 | − | 0.764688i | \(-0.722893\pi\) | ||||
−0.644400 | + | 0.764688i | \(0.722893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10512.0 | 0.382303 | 0.191152 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191152 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8652.00 | −0.313625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5376.17 | 0.193606 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46104.0 | 1.65488 | 0.827438 | − | 0.561557i | \(-0.189798\pi\) | ||||
0.827438 | + | 0.561557i | \(0.189798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3809.88 | −0.135865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3164.32 | 0.112478 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5726.00 | 0.202222 | 0.101111 | − | 0.994875i | \(-0.467760\pi\) | ||||
0.101111 | + | 0.994875i | \(0.467760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10334.3 | 0.363795 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2352.00 | 0.0822659 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1274.00 | −0.0444181 | −0.0222091 | − | 0.999753i | \(-0.507070\pi\) | ||||
−0.0222091 | + | 0.999753i | \(0.507070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26446.9 | 0.916201 | 0.458101 | − | 0.888900i | \(-0.348530\pi\) | ||||
0.458101 | + | 0.888900i | \(0.348530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10640.0 | 0.367430 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23922.9 | −0.820897 | −0.410448 | − | 0.911884i | \(-0.634628\pi\) | ||||
−0.410448 | + | 0.911884i | \(0.634628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15557.0 | 0.532141 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38250.0 | 1.30015 | 0.650073 | − | 0.759872i | \(-0.274738\pi\) | ||||
0.650073 | + | 0.759872i | \(0.274738\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41316.1 | 1.39995 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8496.00 | −0.286079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35241.4 | −1.17561 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4664.00 | −0.155103 | −0.0775513 | − | 0.996988i | \(-0.524710\pi\) | ||||
−0.0775513 | + | 0.996988i | \(0.524710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30971.2 | 1.02360 | 0.511798 | − | 0.859106i | \(-0.328980\pi\) | ||||
0.511798 | + | 0.859106i | \(0.328980\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21547.0 | −0.709933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4814.00 | 0.157639 | 0.0788196 | − | 0.996889i | \(-0.474885\pi\) | ||||
0.0788196 | + | 0.996889i | \(0.474885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4222.62 | −0.137850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12376.0 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12656.0 | 0.409395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −66757.6 | −2.14638 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45344.0 | 1.45348 | 0.726740 | − | 0.686912i | \(-0.241034\pi\) | ||||
0.726740 | + | 0.686912i | \(0.241034\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18372.1 | −0.585361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26002.4 | 0.825984 | 0.412992 | − | 0.910735i | \(-0.364484\pi\) | ||||
0.412992 | + | 0.910735i | \(0.364484\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.4.a.bn.1.1 | 2 | ||
3.2 | odd | 2 | 256.4.a.l.1.2 | 2 | |||
4.3 | odd | 2 | 2304.4.a.v.1.1 | 2 | |||
8.3 | odd | 2 | 2304.4.a.v.1.2 | 2 | |||
8.5 | even | 2 | inner | 2304.4.a.bn.1.2 | 2 | ||
12.11 | even | 2 | 256.4.a.j.1.1 | 2 | |||
16.3 | odd | 4 | 288.4.d.a.145.2 | 2 | |||
16.5 | even | 4 | 72.4.d.b.37.1 | 2 | |||
16.11 | odd | 4 | 288.4.d.a.145.1 | 2 | |||
16.13 | even | 4 | 72.4.d.b.37.2 | 2 | |||
24.5 | odd | 2 | 256.4.a.l.1.1 | 2 | |||
24.11 | even | 2 | 256.4.a.j.1.2 | 2 | |||
48.5 | odd | 4 | 8.4.b.a.5.2 | yes | 2 | ||
48.11 | even | 4 | 32.4.b.a.17.2 | 2 | |||
48.29 | odd | 4 | 8.4.b.a.5.1 | ✓ | 2 | ||
48.35 | even | 4 | 32.4.b.a.17.1 | 2 | |||
240.29 | odd | 4 | 200.4.d.a.101.2 | 2 | |||
240.53 | even | 4 | 200.4.f.a.149.4 | 4 | |||
240.59 | even | 4 | 800.4.d.a.401.1 | 2 | |||
240.77 | even | 4 | 200.4.f.a.149.3 | 4 | |||
240.83 | odd | 4 | 800.4.f.a.49.3 | 4 | |||
240.107 | odd | 4 | 800.4.f.a.49.4 | 4 | |||
240.149 | odd | 4 | 200.4.d.a.101.1 | 2 | |||
240.173 | even | 4 | 200.4.f.a.149.2 | 4 | |||
240.179 | even | 4 | 800.4.d.a.401.2 | 2 | |||
240.197 | even | 4 | 200.4.f.a.149.1 | 4 | |||
240.203 | odd | 4 | 800.4.f.a.49.1 | 4 | |||
240.227 | odd | 4 | 800.4.f.a.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.4.b.a.5.1 | ✓ | 2 | 48.29 | odd | 4 | ||
8.4.b.a.5.2 | yes | 2 | 48.5 | odd | 4 | ||
32.4.b.a.17.1 | 2 | 48.35 | even | 4 | |||
32.4.b.a.17.2 | 2 | 48.11 | even | 4 | |||
72.4.d.b.37.1 | 2 | 16.5 | even | 4 | |||
72.4.d.b.37.2 | 2 | 16.13 | even | 4 | |||
200.4.d.a.101.1 | 2 | 240.149 | odd | 4 | |||
200.4.d.a.101.2 | 2 | 240.29 | odd | 4 | |||
200.4.f.a.149.1 | 4 | 240.197 | even | 4 | |||
200.4.f.a.149.2 | 4 | 240.173 | even | 4 | |||
200.4.f.a.149.3 | 4 | 240.77 | even | 4 | |||
200.4.f.a.149.4 | 4 | 240.53 | even | 4 | |||
256.4.a.j.1.1 | 2 | 12.11 | even | 2 | |||
256.4.a.j.1.2 | 2 | 24.11 | even | 2 | |||
256.4.a.l.1.1 | 2 | 24.5 | odd | 2 | |||
256.4.a.l.1.2 | 2 | 3.2 | odd | 2 | |||
288.4.d.a.145.1 | 2 | 16.11 | odd | 4 | |||
288.4.d.a.145.2 | 2 | 16.3 | odd | 4 | |||
800.4.d.a.401.1 | 2 | 240.59 | even | 4 | |||
800.4.d.a.401.2 | 2 | 240.179 | even | 4 | |||
800.4.f.a.49.1 | 4 | 240.203 | odd | 4 | |||
800.4.f.a.49.2 | 4 | 240.227 | odd | 4 | |||
800.4.f.a.49.3 | 4 | 240.83 | odd | 4 | |||
800.4.f.a.49.4 | 4 | 240.107 | odd | 4 | |||
2304.4.a.v.1.1 | 2 | 4.3 | odd | 2 | |||
2304.4.a.v.1.2 | 2 | 8.3 | odd | 2 | |||
2304.4.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2304.4.a.bn.1.2 | 2 | 8.5 | even | 2 | inner |