Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(1,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("256.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(15.1044889615\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.1 |
$q$-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 | ||||||||
\(3\) | 5.29150 | 1.01835 | 0.509175 | − | 0.860663i | \(-0.329951\pi\) | ||||
0.509175 | + | 0.860663i | \(0.329951\pi\) | |||||||
\(4\) | 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 | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.0370370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8745 | 0.435122 | 0.217561 | − | 0.976047i | \(-0.430190\pi\) | ||||
0.217561 | + | 0.976047i | \(0.430190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −52.9150 | −1.12892 | −0.564461 | − | 0.825460i | \(-0.690916\pi\) | ||||
−0.564461 | + | 0.825460i | \(0.690916\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −56.0000 | −0.963943 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.0000 | −0.199735 | −0.0998676 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998676 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −37.0405 | −0.447246 | −0.223623 | − | 0.974676i | \(-0.571788\pi\) | ||||
−0.223623 | + | 0.974676i | \(0.571788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −42.3320 | −0.439886 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | −137.579 | −0.980633 | ||||||||
\(28\) | 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 | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 84.0000 | 0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 84.6640 | 0.408881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 243.409 | 1.08152 | 0.540760 | − | 0.841177i | \(-0.318137\pi\) | ||||
0.540760 | + | 0.841177i | \(0.318137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −280.000 | −1.14964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.0000 | 0.266638 | 0.133319 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133319 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 439.195 | 1.55759 | 0.778797 | − | 0.627276i | \(-0.215830\pi\) | ||||
0.778797 | + | 0.627276i | \(0.215830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5830 | −0.0350583 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | −74.0810 | −0.203400 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | −196.000 | −0.455453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −534.442 | −1.17929 | −0.589647 | − | 0.807661i | \(-0.700733\pi\) | ||||
−0.589647 | + | 0.807661i | \(0.700733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.2470 | −0.199920 | −0.0999601 | − | 0.994991i | \(-0.531872\pi\) | ||||
−0.0999601 | + | 0.994991i | \(0.531872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.00000 | −0.0159985 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | −804.308 | −1.40329 | ||||||||
\(70\) | 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 | ||||||||
\(75\) | −68.7895 | −0.105908 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −126.996 | −0.187955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 464.000 | 0.660811 | 0.330406 | − | 0.943839i | \(-0.392814\pi\) | ||||
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −755.000 | −1.03567 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −545.025 | −0.720774 | −0.360387 | − | 0.932803i | \(-0.617355\pi\) | ||||
−0.360387 | + | 0.932803i | \(0.617355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 148.162 | 0.189064 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 840.000 | 1.03514 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −266.000 | −0.316808 | −0.158404 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158404 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 423.320 | 0.487649 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1185.30 | −1.32161 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 15.8745 | 0.0161156 | ||||||||
\(100\) | 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 | \(-0.309840\pi\) | ||||
0.562499 | + | 0.826798i | \(0.309840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 448.000 | 0.416384 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 269.867 | 0.243822 | 0.121911 | − | 0.992541i | \(-0.461098\pi\) | ||||
0.121911 | + | 0.992541i | \(0.461098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1894.36 | 1.66465 | 0.832324 | − | 0.554290i | \(-0.187010\pi\) | ||||
0.832324 | + | 0.554290i | \(0.187010\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1288.00 | 1.10137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1710.00 | −1.42357 | −0.711784 | − | 0.702398i | \(-0.752113\pi\) | ||||
−0.711784 | + | 0.702398i | \(0.752113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1608.62 | 1.30439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −52.9150 | −0.0418119 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.000 | 0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1079.00 | −0.810669 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 370.405 | 0.271531 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1460.45 | 1.04502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1664.00 | 1.16265 | 0.581323 | − | 0.813673i | \(-0.302535\pi\) | ||||
0.581323 | + | 0.813673i | \(0.302535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2324.00 | 1.58618 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −672.021 | −0.448204 | −0.224102 | − | 0.974566i | \(-0.571945\pi\) | ||||
−0.224102 | + | 0.974566i | \(0.571945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 296.324 | 0.193192 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1456.00 | 0.928241 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1062.00 | 0.662283 | 0.331142 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331142 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2693.37 | −1.64352 | −0.821759 | − | 0.569835i | \(-0.807007\pi\) | ||||
−0.821759 | + | 0.569835i | \(0.807007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1777.94 | −1.06191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −840.000 | −0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1680.00 | −0.962182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1476.33 | −0.828337 | ||||||||
\(148\) | 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 | \(-0.435749\pi\) | ||||
0.200483 | + | 0.979697i | \(0.435749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.0000 | −0.00739760 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2370.59 | 1.22846 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −179.911 | −0.0914552 | −0.0457276 | − | 0.998954i | \(-0.514561\pi\) | ||||
−0.0457276 | + | 0.998954i | \(0.514561\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 168.000 | 0.0837941 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | −888.972 | −0.419433 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | −37.0405 | −0.0165647 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | −2828.00 | −1.20094 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3264.86 | 1.36328 | 0.681639 | − | 0.731688i | \(-0.261267\pi\) | ||||
0.681639 | + | 0.731688i | \(0.261267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2338.84 | −0.960469 | −0.480235 | − | 0.877140i | \(-0.659448\pi\) | ||||
−0.480235 | + | 0.877140i | \(0.659448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −504.000 | −0.203589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2576.00 | −1.02374 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −222.243 | −0.0869092 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1100.63 | 0.423594 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 2963.24 | 1.08822 | ||||||||
\(196\) | 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 | \(-0.600061\pi\) | ||||
−0.309200 | + | 0.950997i | \(0.600061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 924.000 | 0.324248 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1269.96 | −0.439083 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −740.810 | −0.252392 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −152.000 | −0.0510373 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | −380.988 | −0.122558 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4648.00 | −1.47438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1792.00 | 0.560594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1555.70 | 0.480021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 740.810 | 0.225486 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1568.00 | −0.470857 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.00385185 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1264.67 | −0.369775 | −0.184888 | − | 0.982760i | \(-0.559192\pi\) | ||||
−0.184888 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5153.92 | 1.48725 | 0.743626 | − | 0.668595i | \(-0.233104\pi\) | ||||
0.743626 | + | 0.668595i | \(0.233104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −672.000 | −0.191404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 838.000 | 0.235619 | 0.117809 | − | 0.993036i | \(-0.462413\pi\) | ||||
0.117809 | + | 0.993036i | \(0.462413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3555.89 | 0.987067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2455.26 | 0.672937 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | −280.450 | −0.0740364 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2952.66 | 0.769953 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1960.00 | 0.504906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2884.00 | −0.734000 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5444.96 | −1.36925 | −0.684627 | − | 0.728894i | \(-0.740035\pi\) | ||||
−0.684627 | + | 0.728894i | \(0.740035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2412.93 | −0.599602 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 784.000 | 0.192533 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2562.00 | 0.621841 | 0.310921 | − | 0.950436i | \(-0.399363\pi\) | ||||
0.310921 | + | 0.950436i | \(0.399363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1947.27 | −0.467172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 158.745 | 0.0376478 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −1407.54 | −0.322622 | ||||||||
\(268\) | 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 | \(-0.439706\pi\) | ||||
0.188289 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2240.00 | 0.496597 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −206.369 | −0.0452527 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1576.87 | −0.342039 | −0.171019 | − | 0.985268i | \(-0.554706\pi\) | ||||
−0.171019 | + | 0.985268i | \(0.554706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −224.000 | −0.0480664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2742.00 | 0.582114 | 0.291057 | − | 0.956706i | \(-0.405993\pi\) | ||||
0.291057 | + | 0.956706i | \(0.405993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2989.70 | −0.627983 | −0.313991 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313991 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2074.27 | 0.431120 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −560.000 | −0.115177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5259.75 | 1.05956 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | −2184.00 | −0.426695 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8043.08 | 1.55566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3513.56 | −0.672818 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3976.00 | 0.753846 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 6222.81 | 1.14564 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 84.6640 | 0.0151437 | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 1428.00 | 0.248297 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 518.567 | 0.0893308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 687.895 | 0.117408 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10024.0 | 1.69519 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 243.409 | 0.0400563 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −9048.47 | −1.44969 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3555.89 | −0.564699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8512.00 | 1.32832 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2481.71 | −0.383935 | −0.191967 | − | 0.981401i | \(-0.561487\pi\) | ||||
−0.191967 | + | 0.981401i | \(0.561487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 328.073 | 0.0503191 | 0.0251595 | − | 0.999683i | \(-0.491991\pi\) | ||||
0.0251595 | + | 0.999683i | \(0.491991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7280.00 | 1.10706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10206.0 | −1.53884 | −0.769420 | − | 0.638743i | \(-0.779455\pi\) | ||||
−0.769420 | + | 0.638743i | \(0.779455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 761.976 | 0.113920 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 592.648 | 0.0878607 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | −5709.53 | −0.825545 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3111.40 | −0.446187 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11760.0 | 1.67266 | 0.836331 | − | 0.548225i | \(-0.184696\pi\) | ||||
0.836331 | + | 0.548225i | \(0.184696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 70.0000 | 0.00987549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −253.992 | −0.0355434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10974.6 | −1.52344 | −0.761719 | − | 0.647908i | \(-0.775644\pi\) | ||||
−0.761719 | + | 0.647908i | \(0.775644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7728.00 | 1.06419 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 8805.06 | 1.18398 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 439.195 | 0.0576887 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | −3556.00 | −0.456429 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4910.51 | −0.625506 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5704.24 | 0.721127 | 0.360564 | − | 0.932735i | \(-0.382584\pi\) | ||||
0.360564 | + | 0.932735i | \(0.382584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1568.00 | 0.196737 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12402.0 | 1.54445 | 0.772227 | − | 0.635346i | \(-0.219143\pi\) | ||||
0.772227 | + | 0.635346i | \(0.219143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11853.0 | 1.46511 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7990.17 | 0.980333 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 5619.58 | 0.674436 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4275.53 | 0.509407 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5768.00 | 0.682265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14252.0 | −1.67368 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8207.12 | −0.956907 | −0.478454 | − | 0.878113i | \(-0.658802\pi\) | ||||
−0.478454 | + | 0.878113i | \(0.658802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1449.87 | −0.167844 | −0.0839221 | − | 0.996472i | \(-0.526745\pi\) | ||||
−0.0839221 | + | 0.996472i | \(0.526745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −336.000 | −0.0386215 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 182.000 | 0.0207725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 761.976 | 0.0863574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4444.86 | −0.500233 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | −8889.72 | −0.979838 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5630.16 | 0.616309 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1848.00 | −0.200912 | −0.100456 | − | 0.994942i | \(-0.532030\pi\) | ||||
−0.100456 | + | 0.994942i | \(0.532030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −279.000 | −0.0301263 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12334.5 | 1.32287 | 0.661433 | − | 0.750004i | \(-0.269949\pi\) | ||||
0.661433 | + | 0.750004i | \(0.269949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2815.08 | 0.299882 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4200.00 | 0.444414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3582.00 | −0.376492 | −0.188246 | − | 0.982122i | \(-0.560280\pi\) | ||||
−0.188246 | + | 0.982122i | \(0.560280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1111.22 | 0.116020 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3936.88 | 0.408324 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 1926.11 | 0.195867 | ||||||||
\(460\) | 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 | \(-0.535603\pi\) | ||||
−0.111618 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12544.0 | 1.25100 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10292.0 | 1.01982 | 0.509910 | − | 0.860228i | \(-0.329679\pi\) | ||||
0.509910 | + | 0.860228i | \(0.329679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1396.96 | −0.137538 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −952.000 | −0.0931334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6972.00 | 0.677744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 481.527 | 0.0465136 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.7490 | 0.00304756 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 6434.47 | 0.606166 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10519.5 | −0.984879 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1304.00 | 0.121334 | 0.0606672 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606672 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9380.00 | −0.867440 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16662.9 | −1.53154 | −0.765772 | − | 0.643112i | \(-0.777643\pi\) | ||||
−0.765772 | + | 0.643112i | \(0.777643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2222.43 | −0.203029 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −168.000 | −0.0152546 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | −10371.3 | −0.924865 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 3190.78 | 0.279502 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 5096.00 | 0.438585 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12445.6 | −1.06489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5333.83 | −0.453737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10584.0 | −0.895156 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2982.00 | 0.250756 | 0.125378 | − | 0.992109i | \(-0.459986\pi\) | ||||
0.125378 | + | 0.992109i | \(0.459986\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2016.06 | −0.168559 | −0.0842794 | − | 0.996442i | \(-0.526859\pi\) | ||||
−0.0842794 | + | 0.996442i | \(0.526859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 550.316 | 0.0457481 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3136.00 | 0.259215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −534.442 | −0.0436776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3704.05 | −0.301014 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2856.00 | −0.230796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17276.0 | 1.38830 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4428.99 | −0.353933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15419.4 | −1.22539 | −0.612693 | − | 0.790321i | \(-0.709914\pi\) | ||||
−0.612693 | + | 0.790321i | \(0.709914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12376.0 | −0.978094 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | −95.2470 | −0.00740445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3712.00 | −0.285444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13630.9 | −1.04252 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | −1176.00 | −0.0885040 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7572.14 | −0.566834 | −0.283417 | − | 0.958997i | \(-0.591468\pi\) | ||||
−0.283417 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18096.9 | 1.34751 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6040.00 | 0.447365 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15594.0 | −1.14892 | −0.574459 | − | 0.818533i | \(-0.694788\pi\) | ||||
−0.574459 | + | 0.818533i | \(0.694788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16737.0 | 1.22666 | 0.613330 | − | 0.789827i | \(-0.289830\pi\) | ||||
0.613330 | + | 0.789827i | \(0.289830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20658.0 | −1.50611 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 17620.7 | 1.26475 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4360.20 | 0.311345 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 504.000 | 0.0358037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 560.000 | 0.0395780 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23213.8 | 1.63226 | 0.816130 | − | 0.577868i | \(-0.196115\pi\) | ||||
0.816130 | + | 0.577868i | \(0.196115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8297.08 | 0.580433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6328.00 | −0.440438 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14322.0 | 0.991794 | 0.495897 | − | 0.868381i | \(-0.334839\pi\) | ||||
0.495897 | + | 0.868381i | \(0.334839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1185.30 | −0.0816679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9186.05 | −0.629749 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 174.620 | 0.0117928 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11419.1 | 0.767357 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13664.0 | 0.913681 | 0.456841 | − | 0.889549i | \(-0.348981\pi\) | ||||
0.456841 | + | 0.889549i | \(0.348981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6720.00 | −0.447140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17779.4 | 1.17722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20393.5 | 1.34369 | 0.671846 | − | 0.740690i | \(-0.265501\pi\) | ||||
0.671846 | + | 0.740690i | \(0.265501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3920.00 | −0.257024 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3782.00 | 0.246771 | 0.123385 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123385 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5825.94 | −0.378295 | −0.189147 | − | 0.981949i | \(-0.560572\pi\) | ||||
−0.189147 | + | 0.981949i | \(0.560572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20912.0 | 1.35132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2128.00 | 0.136848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3111.40 | −0.198178 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3407.73 | −0.216017 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2056.00 | 0.129712 | 0.0648558 | − | 0.997895i | \(-0.479341\pi\) | ||||
0.0648558 | + | 0.997895i | \(0.479341\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15428.0 | −0.968733 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17610.1 | −1.10053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14763.3 | 0.918278 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −72.0000 | −0.00445740 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11842.0 | 0.729689 | 0.364845 | − | 0.931068i | \(-0.381122\pi\) | ||||
0.364845 | + | 0.931068i | \(0.381122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16250.2 | −0.996649 | −0.498325 | − | 0.866991i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866991i | \(0.666051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24594.9 | −1.50143 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 9482.37 | 0.570881 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | 294.000 | 0.0174582 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27732.8 | 1.63932 | 0.819662 | − | 0.572847i | \(-0.194161\pi\) | ||||
0.819662 | + | 0.572847i | \(0.194161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22467.7 | 1.32208 | 0.661039 | − | 0.750352i | \(-0.270116\pi\) | ||||
0.661039 | + | 0.750352i | \(0.270116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3920.00 | 0.229623 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3136.00 | −0.182870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24129.3 | −1.40073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8297.08 | −0.479497 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 1788.53 | 0.101986 | ||||||||
\(676\) | 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 | ||||||||
\(681\) | −6692.00 | −0.376561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16356.0 | 0.916320 | 0.458160 | − | 0.888870i | \(-0.348509\pi\) | ||||
0.458160 | + | 0.888870i | \(0.348509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11239.2 | −0.626899 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27272.0 | 1.51454 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −126.996 | −0.00696130 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28504.0 | 1.55571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −980.000 | −0.0532570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4434.28 | 0.239943 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 18816.0 | 1.00518 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6011.15 | −0.319763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31674.9 | −1.67782 | −0.838912 | − | 0.544267i | \(-0.816808\pi\) | ||||
−0.838912 | + | 0.544267i | \(0.816808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 464.000 | 0.0244745 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34048.0 | 1.78837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8889.72 | 0.464975 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33273.0 | −1.73306 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | −15482.9 | −0.796427 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2063.69 | −0.105715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21672.0 | 1.10560 | 0.552799 | − | 0.833315i | \(-0.313560\pi\) | ||||
0.552799 | + | 0.833315i | \(0.313560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18901.0 | 0.960270 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6148.73 | −0.311106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9471.79 | 0.477283 | 0.238642 | − | 0.971108i | \(-0.423298\pi\) | ||||
0.238642 | + | 0.971108i | \(0.423298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15624.0 | 0.784082 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 10371.3 | 0.514171 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | −545.025 | −0.0266953 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2158.93 | −0.105321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11632.0 | 0.565190 | 0.282595 | − | 0.959239i | \(-0.408805\pi\) | ||||
0.282595 | + | 0.959239i | \(0.408805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28812.0 | −1.39438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7873.76 | −0.379543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16731.7 | −0.803336 | −0.401668 | − | 0.915785i | \(-0.631569\pi\) | ||||
−0.401668 | + | 0.915785i | \(0.631569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12768.0 | −0.610605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39466.0 | −1.87995 | −0.939975 | − | 0.341244i | \(-0.889152\pi\) | ||||
−0.939975 | + | 0.341244i | \(0.889152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15154.9 | −0.719060 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 148.162 | 0.00700237 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 13556.8 | 0.633252 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | −10304.0 | −0.475745 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2592.84 | −0.119253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1142.96 | −0.0523668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21840.0 | −0.996805 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | −31198.7 | −1.40774 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13680.0 | 0.614924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5040.00 | 0.225694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1777.94 | −0.0793172 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | −266.000 | −0.0117336 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4667.11 | 0.205104 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12868.9 | −0.563441 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28392.0 | 1.23847 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24390.0 | 1.05996 | 0.529979 | − | 0.848010i | \(-0.322200\pi\) | ||||
0.529979 | + | 0.848010i | \(0.322200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9582.91 | 0.414922 | 0.207461 | − | 0.978243i | \(-0.433480\pi\) | ||||
0.207461 | + | 0.978243i | \(0.433480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8889.72 | 0.383489 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18760.0 | 0.806300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16268.0 | −0.696628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 423.320 | 0.0180611 | ||||||||
\(820\) | 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 | \(-0.651897\pi\) | ||||
−0.459293 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1092.00 | −0.0460831 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19446.3 | 0.817670 | 0.408835 | − | 0.912608i | \(-0.365935\pi\) | ||||
0.408835 | + | 0.912608i | \(0.365935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19546.8 | 0.818925 | 0.409462 | − | 0.912327i | \(-0.365716\pi\) | ||||
0.409462 | + | 0.912327i | \(0.365716\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8344.00 | −0.348315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3906.00 | 0.162467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20742.7 | 0.859677 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30817.7 | 1.27266 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 14509.3 | 0.592796 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6381.55 | −0.259801 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8632.00 | 0.350176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15820.0 | −0.639506 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36998.2 | −1.49034 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28732.9 | 1.15333 | 0.576667 | − | 0.816979i | \(-0.304353\pi\) | ||||
0.576667 | + | 0.816979i | \(0.304353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 392.000 | 0.0156797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8778.00 | −0.349884 | −0.174942 | − | 0.984579i | \(-0.555974\pi\) | ||||
−0.174942 | + | 0.984579i | \(0.555974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5646.03 | 0.224261 | 0.112130 | − | 0.993693i | \(-0.464233\pi\) | ||||
0.112130 | + | 0.993693i | \(0.464233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2963.24 | −0.117290 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | −24960.0 | −0.977724 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7365.77 | 0.287534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9240.00 | −0.359455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 994.000 | 0.0385359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11683.6 | −0.451405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −137.579 | −0.00529728 | −0.00264864 | − | 0.999996i | \(-0.500843\pi\) | ||||
−0.00264864 | + | 0.999996i | \(0.500843\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48888.0 | −1.87594 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31150.0 | −1.19123 | −0.595613 | − | 0.803272i | \(-0.703091\pi\) | ||||
−0.595613 | + | 0.803272i | \(0.703091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12577.9 | 0.479366 | 0.239683 | − | 0.970851i | \(-0.422957\pi\) | ||||
0.239683 | + | 0.970851i | \(0.422957\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29928.7 | 1.13677 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | −11985.3 | −0.450641 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12445.6 | 0.466379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34552.0 | −1.29044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42560.0 | 1.58421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35558.9 | −1.31919 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −444.486 | −0.0164351 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18592.0 | −0.685164 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | 751.393 | 0.0274171 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 5333.83 | 0.192712 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5376.17 | 0.193606 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46104.0 | −1.65488 | −0.827438 | − | 0.561557i | \(-0.810202\pi\) | ||||
−0.827438 | + | 0.561557i | \(0.810202\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13692.0 | 0.489866 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3809.88 | 0.135865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3164.32 | −0.112478 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1176.00 | 0.0416666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5726.00 | −0.202222 | −0.101111 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101111 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10334.3 | 0.363795 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14519.9 | −0.509496 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −12075.2 | −0.419659 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | −11648.0 | −0.400962 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23922.9 | 0.820897 | 0.410448 | − | 0.911884i | \(-0.365372\pi\) | ||||
0.410448 | + | 0.911884i | \(0.365372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15557.0 | −0.532141 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −50680.0 | −1.72809 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38250.0 | −1.30015 | −0.650073 | − | 0.759872i | \(-0.725262\pi\) | ||||
−0.650073 | + | 0.759872i | \(0.725262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41316.1 | 1.39995 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13334.6 | 0.450414 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8496.00 | −0.286079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 269.867 | 0.00903046 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35241.4 | −1.17561 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4664.00 | 0.155103 | 0.0775513 | − | 0.996988i | \(-0.475290\pi\) | ||||
0.0775513 | + | 0.996988i | \(0.475290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2744.00 | 0.0909701 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30971.2 | −1.02360 | −0.511798 | − | 0.859106i | \(-0.671020\pi\) | ||||
−0.511798 | + | 0.859106i | \(0.671020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21547.0 | 0.709933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3640.00 | 0.119562 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4814.00 | −0.157639 | −0.0788196 | − | 0.996889i | \(-0.525115\pi\) | ||||
−0.0788196 | + | 0.996889i | \(0.525115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4222.62 | −0.137850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1894.36 | 0.0616536 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 14223.6 | 0.458704 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −66757.6 | −2.14638 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45344.0 | −1.45348 | −0.726740 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726740 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22484.0 | 0.718538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18372.1 | 0.585361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26002.4 | −0.825984 | −0.412992 | − | 0.910735i | \(-0.635516\pi\) | ||||
−0.412992 | + | 0.910735i | \(0.635516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33488.0 | −1.06057 |
(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 | 256.4.a.j.1.2 | 2 | ||
3.2 | odd | 2 | 2304.4.a.v.1.2 | 2 | |||
4.3 | odd | 2 | 256.4.a.l.1.1 | 2 | |||
8.3 | odd | 2 | 256.4.a.l.1.2 | 2 | |||
8.5 | even | 2 | inner | 256.4.a.j.1.1 | 2 | ||
12.11 | even | 2 | 2304.4.a.bn.1.2 | 2 | |||
16.3 | odd | 4 | 8.4.b.a.5.2 | yes | 2 | ||
16.5 | even | 4 | 32.4.b.a.17.1 | 2 | |||
16.11 | odd | 4 | 8.4.b.a.5.1 | ✓ | 2 | ||
16.13 | even | 4 | 32.4.b.a.17.2 | 2 | |||
24.5 | odd | 2 | 2304.4.a.v.1.1 | 2 | |||
24.11 | even | 2 | 2304.4.a.bn.1.1 | 2 | |||
48.5 | odd | 4 | 288.4.d.a.145.2 | 2 | |||
48.11 | even | 4 | 72.4.d.b.37.2 | 2 | |||
48.29 | odd | 4 | 288.4.d.a.145.1 | 2 | |||
48.35 | even | 4 | 72.4.d.b.37.1 | 2 | |||
80.3 | even | 4 | 200.4.f.a.149.4 | 4 | |||
80.13 | odd | 4 | 800.4.f.a.49.1 | 4 | |||
80.19 | odd | 4 | 200.4.d.a.101.1 | 2 | |||
80.27 | even | 4 | 200.4.f.a.149.3 | 4 | |||
80.29 | even | 4 | 800.4.d.a.401.1 | 2 | |||
80.37 | odd | 4 | 800.4.f.a.49.2 | 4 | |||
80.43 | even | 4 | 200.4.f.a.149.2 | 4 | |||
80.53 | odd | 4 | 800.4.f.a.49.3 | 4 | |||
80.59 | odd | 4 | 200.4.d.a.101.2 | 2 | |||
80.67 | even | 4 | 200.4.f.a.149.1 | 4 | |||
80.69 | even | 4 | 800.4.d.a.401.2 | 2 | |||
80.77 | odd | 4 | 800.4.f.a.49.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.4.b.a.5.1 | ✓ | 2 | 16.11 | odd | 4 | ||
8.4.b.a.5.2 | yes | 2 | 16.3 | odd | 4 | ||
32.4.b.a.17.1 | 2 | 16.5 | even | 4 | |||
32.4.b.a.17.2 | 2 | 16.13 | even | 4 | |||
72.4.d.b.37.1 | 2 | 48.35 | even | 4 | |||
72.4.d.b.37.2 | 2 | 48.11 | even | 4 | |||
200.4.d.a.101.1 | 2 | 80.19 | odd | 4 | |||
200.4.d.a.101.2 | 2 | 80.59 | odd | 4 | |||
200.4.f.a.149.1 | 4 | 80.67 | even | 4 | |||
200.4.f.a.149.2 | 4 | 80.43 | even | 4 | |||
200.4.f.a.149.3 | 4 | 80.27 | even | 4 | |||
200.4.f.a.149.4 | 4 | 80.3 | even | 4 | |||
256.4.a.j.1.1 | 2 | 8.5 | even | 2 | inner | ||
256.4.a.j.1.2 | 2 | 1.1 | even | 1 | trivial | ||
256.4.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
256.4.a.l.1.2 | 2 | 8.3 | odd | 2 | |||
288.4.d.a.145.1 | 2 | 48.29 | odd | 4 | |||
288.4.d.a.145.2 | 2 | 48.5 | odd | 4 | |||
800.4.d.a.401.1 | 2 | 80.29 | even | 4 | |||
800.4.d.a.401.2 | 2 | 80.69 | even | 4 | |||
800.4.f.a.49.1 | 4 | 80.13 | odd | 4 | |||
800.4.f.a.49.2 | 4 | 80.37 | odd | 4 | |||
800.4.f.a.49.3 | 4 | 80.53 | odd | 4 | |||
800.4.f.a.49.4 | 4 | 80.77 | odd | 4 | |||
2304.4.a.v.1.1 | 2 | 24.5 | odd | 2 | |||
2304.4.a.v.1.2 | 2 | 3.2 | odd | 2 | |||
2304.4.a.bn.1.1 | 2 | 24.11 | even | 2 | |||
2304.4.a.bn.1.2 | 2 | 12.11 | even | 2 |