Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, 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("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-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 | ||||||||
\(3\) | −5.46410 | −1.05157 | −0.525783 | − | 0.850618i | \(-0.676228\pi\) | ||||
−0.525783 | + | 0.850618i | \(0.676228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.9282 | 1.15633 | 0.578167 | − | 0.815919i | \(-0.303768\pi\) | ||||
0.578167 | + | 0.815919i | \(0.303768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 28.3923 | 1.53304 | 0.766520 | − | 0.642220i | \(-0.221987\pi\) | ||||
0.766520 | + | 0.642220i | \(0.221987\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.85641 | 0.105793 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 55.0333 | 1.50847 | 0.754235 | − | 0.656605i | \(-0.228008\pi\) | ||||
0.754235 | + | 0.656605i | \(0.228008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.430781 | −0.00919054 | −0.00459527 | − | 0.999989i | \(-0.501463\pi\) | ||||
−0.00459527 | + | 0.999989i | \(0.501463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −70.6410 | −1.21596 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 147.636 | 1.78263 | 0.891316 | − | 0.453384i | \(-0.149783\pi\) | ||||
0.891316 | + | 0.453384i | \(0.149783\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −155.138 | −1.61209 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −108.603 | −0.984574 | −0.492287 | − | 0.870433i | \(-0.663839\pi\) | ||||
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.1384 | 0.337108 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 131.923 | 0.940319 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 107.933 | 0.691128 | 0.345564 | − | 0.938395i | \(-0.387688\pi\) | ||||
0.345564 | + | 0.938395i | \(0.387688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 70.1718 | 0.406555 | 0.203278 | − | 0.979121i | \(-0.434841\pi\) | ||||
0.203278 | + | 0.979121i | \(0.434841\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −300.708 | −1.58626 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 367.061 | 1.77271 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 381.769 | 1.69628 | 0.848141 | − | 0.529770i | \(-0.177722\pi\) | ||||
0.848141 | + | 0.529770i | \(0.177722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.35383 | 0.00966447 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.1436 | 0.0614928 | 0.0307464 | − | 0.999527i | \(-0.490212\pi\) | ||||
0.0307464 | + | 0.999527i | \(0.490212\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 382.354 | 1.35601 | 0.678005 | − | 0.735057i | \(-0.262845\pi\) | ||||
0.678005 | + | 0.735057i | \(0.262845\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 36.9282 | 0.122332 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −455.846 | −1.41472 | −0.707362 | − | 0.706852i | \(-0.750115\pi\) | ||||
−0.707362 | + | 0.706852i | \(0.750115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 463.123 | 1.35021 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 21.0052 | 0.0544392 | 0.0272196 | − | 0.999629i | \(-0.491335\pi\) | ||||
0.0272196 | + | 0.999629i | \(0.491335\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 711.482 | 1.74429 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −806.697 | −1.87456 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.91274 | −0.0218734 | −0.0109367 | − | 0.999940i | \(-0.503481\pi\) | ||||
−0.0109367 | + | 0.999940i | \(0.503481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 679.759 | 1.42679 | 0.713395 | − | 0.700762i | \(-0.247157\pi\) | ||||
0.713395 | + | 0.700762i | \(0.247157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 81.1000 | 0.162185 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.56922 | −0.0106273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 708.574 | 1.29203 | 0.646016 | − | 0.763324i | \(-0.276434\pi\) | ||||
0.646016 | + | 0.763324i | \(0.276434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 593.415 | 1.03535 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −85.0793 | −0.142212 | −0.0711061 | − | 0.997469i | \(-0.522653\pi\) | ||||
−0.0711061 | + | 0.997469i | \(0.522653\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37.5795 | 0.0602514 | 0.0301257 | − | 0.999546i | \(-0.490409\pi\) | ||||
0.0301257 | + | 0.999546i | \(0.490409\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −230.249 | −0.354491 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1562.52 | 2.31255 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −685.290 | −0.975963 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −797.964 | −1.09460 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1294.89 | −1.71244 | −0.856219 | − | 0.516613i | \(-0.827192\pi\) | ||||
−0.856219 | + | 0.516613i | \(0.827192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −589.759 | −0.726768 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1572.08 | −1.87236 | −0.936182 | − | 0.351517i | \(-0.885666\pi\) | ||||
−0.936182 | + | 0.351517i | \(0.885666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2309 | −0.0140895 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −383.426 | −0.427520 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1908.67 | 2.06132 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 175.990 | 0.184217 | 0.0921085 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921085 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 157.198 | 0.159585 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 381.538 | 0.375886 | 0.187943 | − | 0.982180i | \(-0.439818\pi\) | ||||
0.187943 | + | 0.982180i | \(0.439818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 724.246 | 0.692836 | 0.346418 | − | 0.938080i | \(-0.387398\pi\) | ||||
0.346418 | + | 0.938080i | \(0.387398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2005.66 | −1.86412 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1132.23 | −1.02296 | −0.511482 | − | 0.859294i | \(-0.670903\pi\) | ||||
−0.511482 | + | 0.859294i | \(0.670903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −555.913 | −0.488503 | −0.244251 | − | 0.969712i | \(-0.578542\pi\) | ||||
−0.244251 | + | 0.969712i | \(0.578542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2086.03 | −1.78375 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1156.28 | 0.962596 | 0.481298 | − | 0.876557i | \(-0.340165\pi\) | ||||
0.481298 | + | 0.876557i | \(0.340165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1404.04 | −1.13850 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.23048 | −0.000972293 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1697.67 | 1.27548 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −88.2102 | −0.0646638 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1071.25 | −0.766525 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2071.22 | −1.44717 | −0.723585 | − | 0.690235i | \(-0.757507\pi\) | ||||
−0.723585 | + | 0.690235i | \(0.757507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2089.22 | −1.42593 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 498.690 | 0.332601 | 0.166300 | − | 0.986075i | \(-0.446818\pi\) | ||||
0.166300 | + | 0.986075i | \(0.446818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4191.72 | 2.73285 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1705.53 | 1.08732 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1500.66 | −0.935837 | −0.467919 | − | 0.883772i | \(-0.654996\pi\) | ||||
−0.467919 | + | 0.883772i | \(0.654996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 272.043 | 0.166003 | 0.0830015 | − | 0.996549i | \(-0.473549\pi\) | ||||
0.0830015 | + | 0.996549i | \(0.473549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2490.79 | 1.48768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.7073 | −0.0138637 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1395.38 | 0.799175 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2530.55 | −1.41984 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −122.349 | −0.0672700 | −0.0336350 | − | 0.999434i | \(-0.510708\pi\) | ||||
−0.0336350 | + | 0.999434i | \(0.510708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −703.944 | −0.379378 | −0.189689 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189689 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 907.195 | 0.470114 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1785.67 | 0.907720 | 0.453860 | − | 0.891073i | \(-0.350047\pi\) | ||||
0.453860 | + | 0.891073i | \(0.350047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −114.774 | −0.0572465 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3083.48 | −1.50939 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3588.11 | −1.72418 | −0.862092 | − | 0.506751i | \(-0.830846\pi\) | ||||
−0.862092 | + | 0.506751i | \(0.830846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3887.61 | −1.83424 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1659.15 | 0.768794 | 0.384397 | − | 0.923168i | \(-0.374409\pi\) | ||||
0.384397 | + | 0.923168i | \(0.374409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2196.81 | −0.999916 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 421.708 | 0.188590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 142.148 | 0.0624702 | 0.0312351 | − | 0.999512i | \(-0.490056\pi\) | ||||
0.0312351 | + | 0.999512i | \(0.490056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1196.41 | 0.516799 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 54.1642 | 0.0230013 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 387.749 | 0.161909 | 0.0809544 | − | 0.996718i | \(-0.474203\pi\) | ||||
0.0809544 | + | 0.996718i | \(0.474203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3683.64 | −1.51272 | −0.756360 | − | 0.654155i | \(-0.773024\pi\) | ||||
−0.756360 | + | 0.654155i | \(0.773024\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3714.27 | −1.50037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4935.59 | 1.96147 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3745.60 | 1.44155 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1308.05 | −0.495535 | −0.247768 | − | 0.968819i | \(-0.579697\pi\) | ||||
−0.247768 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3585.28 | 1.33717 | 0.668586 | − | 0.743635i | \(-0.266900\pi\) | ||||
0.668586 | + | 0.743635i | \(0.266900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30.4308 | 0.0111754 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1434.13 | 0.518667 | 0.259333 | − | 0.965788i | \(-0.416497\pi\) | ||||
0.259333 | + | 0.965788i | \(0.416497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1018.55 | −0.362828 | −0.181414 | − | 0.983407i | \(-0.558067\pi\) | ||||
−0.181414 | + | 0.983407i | \(0.558067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3871.72 | −1.35866 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3064.48 | 1.05953 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 208.708 | 0.0711062 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −310.213 | −0.104161 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8124.89 | 2.68905 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2888.47 | −0.942421 | −0.471210 | − | 0.882021i | \(-0.656183\pi\) | ||||
−0.471210 | + | 0.882021i | \(0.656183\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 464.882 | 0.149546 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4943.15 | 1.56800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1992.34 | 0.623266 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −205.338 | −0.0633584 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3641.74 | 1.09358 | 0.546791 | − | 0.837269i | \(-0.315849\pi\) | ||||
0.546791 | + | 0.837269i | \(0.315849\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 120.365 | 0.0356636 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5221.59 | −1.52674 | −0.763368 | − | 0.645963i | \(-0.776456\pi\) | ||||
−0.763368 | + | 0.645963i | \(0.776456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4186.66 | 1.20813 | 0.604065 | − | 0.796935i | \(-0.293547\pi\) | ||||
0.604065 | + | 0.796935i | \(0.293547\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8537.78 | −2.43180 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3420.08 | 0.961618 | 0.480809 | − | 0.876825i | \(-0.340343\pi\) | ||||
0.480809 | + | 0.876825i | \(0.340343\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5893.27 | −1.63589 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3744.49 | 1.02629 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2456.35 | −0.664803 | −0.332402 | − | 0.943138i | \(-0.607859\pi\) | ||||
−0.332402 | + | 0.943138i | \(0.607859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2967.19 | −0.793085 | −0.396542 | − | 0.918016i | \(-0.629790\pi\) | ||||
−0.396542 | + | 0.918016i | \(0.629790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 798.234 | 0.210727 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5987.35 | 1.56130 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −63.5987 | −0.0163833 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7075.39 | 1.80074 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5652.07 | −1.42134 | −0.710668 | − | 0.703527i | \(-0.751607\pi\) | ||||
−0.710668 | + | 0.703527i | \(0.751607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5976.76 | −1.48520 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1480.86 | −0.359430 | −0.179715 | − | 0.983719i | \(-0.557518\pi\) | ||||
−0.179715 | + | 0.983719i | \(0.557518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10839.3 | 2.60047 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 308.302 | 0.0731164 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1460.73 | −0.342482 | −0.171241 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171241 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 271.559 | 0.0629499 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8590.01 | 1.96892 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6260.73 | 1.41905 | 0.709523 | − | 0.704682i | \(-0.248910\pi\) | ||||
0.709523 | + | 0.704682i | \(0.248910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −269.538 | −0.0604179 | −0.0302089 | − | 0.999544i | \(-0.509617\pi\) | ||||
−0.0302089 | + | 0.999544i | \(0.509617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66.8306 | 0.0148160 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2319.02 | 0.508517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5097.56 | 1.10571 | 0.552857 | − | 0.833276i | \(-0.313537\pi\) | ||||
0.552857 | + | 0.833276i | \(0.313537\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 200.439 | 0.0430107 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1516.13 | −0.321868 | −0.160934 | − | 0.986965i | \(-0.551451\pi\) | ||||
−0.160934 | + | 0.986965i | \(0.551451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7668.88 | 1.61084 | 0.805420 | − | 0.592705i | \(-0.201940\pi\) | ||||
0.805420 | + | 0.592705i | \(0.201940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10429.1 | −2.16761 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 458.354 | 0.0942710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −961.626 | −0.193716 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2580.58 | 0.514537 | 0.257269 | − | 0.966340i | \(-0.417178\pi\) | ||||
0.257269 | + | 0.966340i | \(0.417178\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.154 | −0.0252929 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7260.16 | 1.41844 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 46.7839 | 0.00904877 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10855.9 | 2.07882 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2084.76 | −0.395269 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8788.06 | 1.64985 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −583.507 | −0.108477 | −0.0542386 | − | 0.998528i | \(-0.517273\pi\) | ||||
−0.0542386 | + | 0.998528i | \(0.517273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3957.35 | −0.728563 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 154.973 | 0.0282563 | 0.0141282 | − | 0.999900i | \(-0.495503\pi\) | ||||
0.0141282 | + | 0.999900i | \(0.495503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5835.86 | 1.05387 | 0.526936 | − | 0.849905i | \(-0.323341\pi\) | ||||
0.526936 | + | 0.849905i | \(0.323341\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1048.48 | 0.187540 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10586.1 | −1.87563 | −0.937817 | − | 0.347130i | \(-0.887156\pi\) | ||||
−0.937817 | + | 0.347130i | \(0.887156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5939.93 | 1.04255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6186.64 | 1.07571 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.1524 | −0.00309820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3037.56 | 0.513693 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12942.5 | −2.16883 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7094.38 | −1.17807 | −0.589037 | − | 0.808106i | \(-0.700493\pi\) | ||||
−0.589037 | + | 0.808106i | \(0.700493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1090.49 | 0.179455 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9160.59 | 1.49402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1579.48 | 0.255310 | 0.127655 | − | 0.991819i | \(-0.459255\pi\) | ||||
0.127655 | + | 0.991819i | \(0.459255\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6318.01 | −1.01223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3861.78 | 0.613277 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3410.57 | 0.536890 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7671.79 | 1.19720 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1717.38 | 0.265688 | 0.132844 | − | 0.991137i | \(-0.457589\pi\) | ||||
0.132844 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6237.70 | −0.956724 | −0.478362 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478362 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −56.8299 | −0.00864204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9900.99 | 1.49285 | 0.746426 | − | 0.665469i | \(-0.231768\pi\) | ||||
0.746426 | + | 0.665469i | \(0.231768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1099.92 | −0.164445 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7524.52 | −1.10621 | −0.553104 | − | 0.833112i | \(-0.686557\pi\) | ||||
−0.553104 | + | 0.833112i | \(0.686557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14937.3 | 2.17777 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9276.22 | −1.34125 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 485.836 | 0.0696707 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10169.2 | −1.44640 | −0.723199 | − | 0.690640i | \(-0.757329\pi\) | ||||
−0.723199 | + | 0.690640i | \(0.757329\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 46.1127 | 0.00650550 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 596.385 | 0.0834576 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14115.4 | 1.95943 | 0.979716 | − | 0.200393i | \(-0.0642219\pi\) | ||||
0.979716 | + | 0.200393i | \(0.0642219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5853.42 | 0.806052 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46.4956 | −0.00635184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10480.9 | 1.42050 | 0.710249 | − | 0.703951i | \(-0.248583\pi\) | ||||
0.710249 | + | 0.703951i | \(0.248583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11317.3 | 1.52180 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9726.14 | 1.29760 | 0.648802 | − | 0.760957i | \(-0.275270\pi\) | ||||
0.648802 | + | 0.760957i | \(0.275270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20200.6 | 2.67407 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1092.16 | 0.143456 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13217.9 | 1.72282 | 0.861409 | − | 0.507912i | \(-0.169583\pi\) | ||||
0.861409 | + | 0.507912i | \(0.169583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2724.89 | −0.349752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8859.56 | −1.12854 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5628.14 | −0.711507 | −0.355753 | − | 0.934580i | \(-0.615776\pi\) | ||||
−0.355753 | + | 0.934580i | \(0.615776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22904.0 | −2.87377 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8890.10 | −1.10711 | −0.553554 | − | 0.832813i | \(-0.686729\pi\) | ||||
−0.553554 | + | 0.832813i | \(0.686729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.2286 | −0.00373647 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10316.2 | −1.26572 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21010.0 | 2.55879 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 721.057 | 0.0871736 | 0.0435868 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435868 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8199.74 | 0.984095 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −281.446 | −0.0335328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16740.6 | −1.98015 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1486.47 | −0.174563 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16306.9 | 1.90129 | 0.950647 | − | 0.310275i | \(-0.100421\pi\) | ||||
0.950647 | + | 0.310275i | \(0.100421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11568.8 | −1.33926 | −0.669628 | − | 0.742697i | \(-0.733546\pi\) | ||||
−0.669628 | + | 0.742697i | \(0.733546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1302.08 | −0.149668 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19299.9 | 2.18733 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 129.539 | 0.0145786 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11733.2 | 1.31129 | 0.655647 | − | 0.755067i | \(-0.272396\pi\) | ||||
0.655647 | + | 0.755067i | \(0.272396\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8900.96 | −0.987882 | −0.493941 | − | 0.869495i | \(-0.664444\pi\) | ||||
−0.493941 | + | 0.869495i | \(0.664444\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7624.52 | −0.840386 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16033.6 | −1.75513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8857.07 | 0.962927 | 0.481464 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481464 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1322.87 | 0.142843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13328.1 | 1.42943 | 0.714716 | − | 0.699415i | \(-0.246556\pi\) | ||||
0.714716 | + | 0.699415i | \(0.246556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20324.2 | −2.16508 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 668.528 | 0.0707389 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8432.61 | 0.886323 | 0.443162 | − | 0.896442i | \(-0.353857\pi\) | ||||
0.443162 | + | 0.896442i | \(0.353857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 888.436 | 0.0927601 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3846.42 | 0.398942 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −158.123 | −0.0162921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6628.94 | 0.678531 | 0.339266 | − | 0.940691i | \(-0.389821\pi\) | ||||
0.339266 | + | 0.940691i | \(0.389821\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7327.69 | −0.740314 | −0.370157 | − | 0.928969i | \(-0.620696\pi\) | ||||
−0.370157 | + | 0.928969i | \(0.620696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8996.83 | −0.903063 | −0.451531 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451531 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4957.00 | −0.494356 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12138.4 | 1.20278 | 0.601388 | − | 0.798957i | \(-0.294614\pi\) | ||||
0.601388 | + | 0.798957i | \(0.294614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20118.1 | 1.98074 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9757.09 | −0.954529 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21042.2 | 2.04550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6221.14 | 0.600938 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 59.9993 | 0.00575928 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1644.47 | −0.156864 | −0.0784320 | − | 0.996919i | \(-0.524991\pi\) | ||||
−0.0784320 | + | 0.996919i | \(0.524991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −164.459 | −0.0155898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16848.4 | 1.58723 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2275.23 | 0.213016 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1761.78 | 0.163930 | 0.0819648 | − | 0.996635i | \(-0.473881\pi\) | ||||
0.0819648 | + | 0.996635i | \(0.473881\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19605.8 | 1.81310 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2471.08 | 0.227125 | 0.113562 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113562 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2032.28 | 0.184534 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2415.60 | −0.218017 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16582.5 | 1.48764 | 0.743821 | − | 0.668379i | \(-0.233012\pi\) | ||||
0.743821 | + | 0.668379i | \(0.233012\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9065.74 | −0.808438 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19067.9 | −1.69025 | −0.845126 | − | 0.534566i | \(-0.820475\pi\) | ||||
−0.845126 | + | 0.534566i | \(0.820475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4932.60 | 0.434650 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12003.6 | 1.05148 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9295.25 | −0.809439 | −0.404720 | − | 0.914441i | \(-0.632631\pi\) | ||||
−0.404720 | + | 0.914441i | \(0.632631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1066.97 | 0.0923678 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19476.6 | 1.67624 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9363.20 | 0.801149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25086.7 | −2.13407 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −776.713 | −0.0656916 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4907.38 | −0.412661 | −0.206330 | − | 0.978482i | \(-0.566152\pi\) | ||||
−0.206330 | + | 0.978482i | \(0.566152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11247.5 | −0.940381 | −0.470191 | − | 0.882565i | \(-0.655815\pi\) | ||||
−0.470191 | + | 0.882565i | \(0.655815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6537.29 | −0.543449 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −372.488 | −0.0306146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.3148 | −0.00231405 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.95435 | −0.000565152 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14637.7 | −1.18289 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2118.70 | −0.170258 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25487.2 | 2.03676 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3992.37 | 0.317274 | 0.158637 | − | 0.987337i | \(-0.449290\pi\) | ||||
0.158637 | + | 0.987337i | \(0.449290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20127.8 | 1.59073 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7186.95 | −0.564872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3014.39 | 0.235624 | 0.117812 | − | 0.993036i | \(-0.462412\pi\) | ||||
0.117812 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1941.67 | 0.150944 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15934.8 | 1.23203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19457.0 | −1.49619 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26968.6 | −2.06262 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16174.5 | −1.23041 | −0.615203 | − | 0.788369i | \(-0.710926\pi\) | ||||
−0.615203 | + | 0.788369i | \(0.710926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −164.711 | −0.0124625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6626.51 | −0.496047 | −0.248023 | − | 0.968754i | \(-0.579781\pi\) | ||||
−0.248023 | + | 0.968754i | \(0.579781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14948.6 | 1.11308 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22656.0 | −1.67807 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2651.54 | 0.195357 | 0.0976786 | − | 0.995218i | \(-0.468858\pi\) | ||||
0.0976786 | + | 0.995218i | \(0.468858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7663.21 | −0.561638 | −0.280819 | − | 0.959761i | \(-0.590606\pi\) | ||||
−0.280819 | + | 0.959761i | \(0.590606\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7147.32 | 0.521088 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4576.34 | −0.331907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22136.0 | −1.59711 | −0.798557 | − | 0.601919i | \(-0.794403\pi\) | ||||
−0.798557 | + | 0.601919i | \(0.794403\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19590.3 | −1.40613 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36764.8 | −2.62524 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1155.98 | 0.0821200 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.9080 | −0.00112430 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24994.8 | 1.75749 | 0.878744 | − | 0.477294i | \(-0.158382\pi\) | ||||
0.878744 | + | 0.477294i | \(0.158382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10359.9 | 0.724738 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7836.22 | −0.545413 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11985.7 | 0.830007 | 0.415004 | − | 0.909820i | \(-0.363780\pi\) | ||||
0.415004 | + | 0.909820i | \(0.363780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5565.44 | 0.381538 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2943.68 | 0.200794 | 0.100397 | − | 0.994947i | \(-0.467989\pi\) | ||||
0.100397 | + | 0.994947i | \(0.467989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4398.52 | 0.298535 | 0.149267 | − | 0.988797i | \(-0.452308\pi\) | ||||
0.149267 | + | 0.988797i | \(0.452308\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2023.98 | 0.136688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21947.8 | 1.47488 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19859.6 | −1.32797 | −0.663985 | − | 0.747746i | \(-0.731136\pi\) | ||||
−0.663985 | + | 0.747746i | \(0.731136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16744.6 | −1.11416 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 196.370 | 0.0130021 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5581.75 | 0.367773 | 0.183887 | − | 0.982947i | \(-0.441132\pi\) | ||||
0.183887 | + | 0.982947i | \(0.441132\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1140.40 | −0.0747729 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9888.18 | 0.645192 | 0.322596 | − | 0.946537i | \(-0.395445\pi\) | ||||
0.322596 | + | 0.946537i | \(0.395445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9547.62 | −0.619953 | −0.309977 | − | 0.950744i | \(-0.600321\pi\) | ||||
−0.309977 | + | 0.950744i | \(0.600321\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14327.2 | −0.925813 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44635.0 | −2.87041 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19116.7 | −1.22347 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −44395.2 | −2.82771 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −198.776 | −0.0125406 | −0.00627032 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00627032 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15782.9 | 0.991019 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26777.1 | −1.67341 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −199.504 | −0.0124092 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −243.021 | −0.0150450 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15596.6 | −0.961043 | −0.480522 | − | 0.876983i | \(-0.659553\pi\) | ||||
−0.480522 | + | 0.876983i | \(0.659553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18359.9 | −1.12604 | −0.563020 | − | 0.826443i | \(-0.690361\pi\) | ||||
−0.563020 | + | 0.826443i | \(0.690361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27009.9 | −1.64886 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23713.7 | −1.44093 | −0.720465 | − | 0.693491i | \(-0.756072\pi\) | ||||
−0.720465 | + | 0.693491i | \(0.756072\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −545.531 | −0.0329953 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10886.3 | −0.655406 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22829.6 | −1.36814 | −0.684068 | − | 0.729418i | \(-0.739791\pi\) | ||||
−0.684068 | + | 0.729418i | \(0.739791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6447.16 | 0.384598 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 107.342 | 0.00637416 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16979.9 | −1.00371 | −0.501853 | − | 0.864953i | \(-0.667348\pi\) | ||||
−0.501853 | + | 0.864953i | \(0.667348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15036.2 | −0.884782 | −0.442391 | − | 0.896822i | \(-0.645870\pi\) | ||||
−0.442391 | + | 0.896822i | \(0.645870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 54191.4 | 3.16008 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11721.8 | −0.680467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19898.8 | −1.14997 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37409.4 | 2.15227 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16935.7 | 0.970022 | 0.485011 | − | 0.874508i | \(-0.338816\pi\) | ||||
0.485011 | + | 0.874508i | \(0.338816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5559.03 | 0.316988 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6514.79 | −0.369843 | −0.184921 | − | 0.982753i | \(-0.559203\pi\) | ||||
−0.184921 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4996.75 | 0.282412 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28531.3 | 1.60547 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6261.11 | 0.350768 | 0.175384 | − | 0.984500i | \(-0.443883\pi\) | ||||
0.175384 | + | 0.984500i | \(0.443883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19400.8 | −1.08214 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22876.3 | −1.27043 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.04861 | −0.000500326 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12775.3 | −0.703320 | −0.351660 | − | 0.936128i | \(-0.614383\pi\) | ||||
−0.351660 | + | 0.936128i | \(0.614383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4463.20 | 0.244651 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3517.03 | 0.191955 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18687.7 | −1.01121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5939.18 | −0.320000 | −0.160000 | − | 0.987117i | \(-0.551149\pi\) | ||||
−0.160000 | + | 0.987117i | \(0.551149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56362.8 | 3.02385 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32201.4 | 1.72025 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10832.8 | 0.576248 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22029.4 | 1.16690 | 0.583450 | − | 0.812149i | \(-0.301702\pi\) | ||||
0.583450 | + | 0.812149i | \(0.301702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1957.47 | −0.103250 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7620.83 | −0.400284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −306.493 | −0.0160310 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13421.7 | 0.699085 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4477.22 | −0.232228 | −0.116114 | − | 0.993236i | \(-0.537044\pi\) | ||||
−0.116114 | + | 0.993236i | \(0.537044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20563.0 | 1.06215 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16213.0 | 0.833982 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4548.14 | 0.232985 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7878.08 | −0.401901 | −0.200950 | − | 0.979601i | \(-0.564403\pi\) | ||||
−0.200950 | + | 0.979601i | \(0.564403\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17183.4 | 0.873007 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11332.8 | 0.571060 | 0.285530 | − | 0.958370i | \(-0.407830\pi\) | ||||
0.285530 | + | 0.958370i | \(0.407830\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32715.5 | −1.64181 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38995.2 | 1.94899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20027.3 | 0.996908 | 0.498454 | − | 0.866916i | \(-0.333901\pi\) | ||||
0.498454 | + | 0.866916i | \(0.333901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 347.510 | 0.0172282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8839.83 | 0.436477 | 0.218238 | − | 0.975896i | \(-0.429969\pi\) | ||||
0.218238 | + | 0.975896i | \(0.429969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1581.75 | −0.0777865 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3698.72 | −0.181164 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32146.7 | −1.56824 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1533.58 | −0.0745156 | −0.0372578 | − | 0.999306i | \(-0.511862\pi\) | ||||
−0.0372578 | + | 0.999306i | \(0.511862\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30883.5 | 1.49463 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9100.73 | −0.438688 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16470.7 | 0.790801 | 0.395401 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395401 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32657.6 | 1.56179 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18629.7 | −0.887418 | −0.443709 | − | 0.896171i | \(-0.646338\pi\) | ||||
−0.443709 | + | 0.896171i | \(0.646338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15783.6 | −0.748894 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.27022 | 0.000201028 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6086.38 | −0.285410 | −0.142705 | − | 0.989765i | \(-0.545580\pi\) | ||||
−0.142705 | + | 0.989765i | \(0.545580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8091.57 | 0.377965 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7472.68 | 0.347702 | 0.173851 | − | 0.984772i | \(-0.444379\pi\) | ||||
0.173851 | + | 0.984772i | \(0.444379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2956.93 | 0.137053 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −59227.1 | −2.73457 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2383.37 | 0.109619 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4682.20 | −0.214523 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14238.9 | 0.649881 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23085.5 | 1.04963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28318.2 | −1.28263 | −0.641317 | − | 0.767276i | \(-0.721612\pi\) | ||||
−0.641317 | + | 0.767276i | \(0.721612\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7981.60 | 0.360142 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32829.4 | 1.47570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −292.827 | −0.0131130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1483.83 | −0.0661961 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29551.4 | 1.31338 | 0.656691 | − | 0.754160i | \(-0.271956\pi\) | ||||
0.656691 | + | 0.754160i | \(0.271956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4490.50 | −0.198083 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2068.13 | 0.0908874 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39863.8 | −1.74536 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34209.3 | −1.49222 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28511.0 | −1.23905 | −0.619527 | − | 0.784975i | \(-0.712676\pi\) | ||||
−0.619527 | + | 0.784975i | \(0.712676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29641.1 | 1.28340 | 0.641700 | − | 0.766955i | \(-0.278229\pi\) | ||||
0.641700 | + | 0.766955i | \(0.278229\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1472.78 | 0.0635334 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46387.8 | −1.99373 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56449.1 | 2.41726 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −34.9363 | −0.00149057 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8825.39 | −0.375162 | −0.187581 | − | 0.982249i | \(-0.560065\pi\) | ||||
−0.187581 | + | 0.982249i | \(0.560065\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19790.8 | 0.838233 | 0.419116 | − | 0.907933i | \(-0.362340\pi\) | ||||
0.419116 | + | 0.907933i | \(0.362340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12671.4 | −0.534739 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38948.7 | −1.63770 | −0.818850 | − | 0.574008i | \(-0.805388\pi\) | ||||
−0.818850 | + | 0.574008i | \(0.805388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34825.0 | 1.45901 | 0.729506 | − | 0.683974i | \(-0.239750\pi\) | ||||
0.729506 | + | 0.683974i | \(0.239750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27853.6 | −1.16273 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21449.8 | 0.888982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9257.27 | 0.382292 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17082.9 | 0.702941 | 0.351470 | − | 0.936199i | \(-0.385682\pi\) | ||||
0.351470 | + | 0.936199i | \(0.385682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12739.4 | −0.522342 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8284.31 | 0.338466 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28400.9 | −1.15624 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48200.7 | 1.95537 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41903.5 | −1.69391 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41461.1 | −1.67012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38982.3 | 1.56475 | 0.782373 | − | 0.622810i | \(-0.214009\pi\) | ||||
0.782373 | + | 0.622810i | \(0.214009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5451.93 | 0.218072 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6648.98 | 0.265023 | 0.132512 | − | 0.991181i | \(-0.457696\pi\) | ||||
0.132512 | + | 0.991181i | \(0.457696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1644.93 | −0.0653368 | −0.0326684 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326684 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2504.49 | −0.0991322 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24272.3 | 0.957402 | 0.478701 | − | 0.877978i | \(-0.341108\pi\) | ||||
0.478701 | + | 0.877978i | \(0.341108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1837.72 | 0.0722364 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37713.8 | −1.47221 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −305.240 | −0.0118745 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 502.698 | 0.0194888 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30415.3 | −1.17511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51065.8 | 1.96621 | 0.983107 | − | 0.183030i | \(-0.0585904\pi\) | ||||
0.983107 | + | 0.183030i | \(0.0585904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14100.6 | −0.541070 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10283.5 | 0.393258 | 0.196629 | − | 0.980478i | \(-0.437000\pi\) | ||||
0.196629 | + | 0.980478i | \(0.437000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5412.08 | −0.206264 | −0.103132 | − | 0.994668i | \(-0.532886\pi\) | ||||
−0.103132 | + | 0.994668i | \(0.532886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 700.246 | 0.0265972 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11306.0 | −0.427981 | −0.213991 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213991 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58806.6 | −2.21857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43914.6 | −1.65117 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −67299.2 | −2.52193 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5012.89 | 0.187221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −255.632 | −0.00951538 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7573.87 | 0.280982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −59317.8 | −2.18602 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47622.8 | −1.74921 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13122.6 | −0.480408 | −0.240204 | − | 0.970722i | \(-0.577214\pi\) | ||||
−0.240204 | + | 0.970722i | \(0.577214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1089.83 | 0.0397660 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24127.8 | 0.877485 | 0.438743 | − | 0.898613i | \(-0.355424\pi\) | ||||
0.438743 | + | 0.898613i | \(0.355424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71261.9 | −2.58316 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −48018.9 | −1.73492 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14159.0 | 0.509891 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10597.4 | −0.380387 | −0.190194 | − | 0.981747i | \(-0.560912\pi\) | ||||
−0.190194 | + | 0.981747i | \(0.560912\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3188.34 | 0.114071 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.6505 | 0.00130701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16087.2 | 0.571830 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2068.74 | 0.0732970 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16159.9 | −0.570711 | −0.285356 | − | 0.958422i | \(-0.592112\pi\) | ||||
−0.285356 | + | 0.958422i | \(0.592112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68373.6 | 2.40693 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −846.788 | −0.0297134 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12857.2 | 0.448267 | 0.224134 | − | 0.974558i | \(-0.428045\pi\) | ||||
0.224134 | + | 0.974558i | \(0.428045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31887.7 | −1.10822 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31043.6 | 1.07544 | 0.537722 | − | 0.843122i | \(-0.319285\pi\) | ||||
0.537722 | + | 0.843122i | \(0.319285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1753.24 | −0.0605442 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48423.9 | 1.66691 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39841.0 | 1.36712 | 0.683558 | − | 0.729896i | \(-0.260432\pi\) | ||||
0.683558 | + | 0.729896i | \(0.260432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.1885 | −0.000553743 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57843.7 | 1.97235 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26601.9 | −0.904217 | −0.452109 | − | 0.891963i | \(-0.649328\pi\) | ||||
−0.452109 | + | 0.891963i | \(0.649328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16910.7 | −0.573004 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −32456.4 | −1.09631 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42607.1 | −1.43468 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24866.9 | −0.834713 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3234.12 | −0.108222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46351.2 | 1.54622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15998.2 | 0.532024 | 0.266012 | − | 0.963970i | \(-0.414294\pi\) | ||||
0.266012 | + | 0.963970i | \(0.414294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21950.4 | −0.725461 | −0.362731 | − | 0.931894i | \(-0.618155\pi\) | ||||
−0.362731 | + | 0.931894i | \(0.618155\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7723.94 | 0.254489 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 99.1867 | 0.00325797 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24955.7 | −0.817198 | −0.408599 | − | 0.912714i | \(-0.633983\pi\) | ||||
−0.408599 | + | 0.912714i | \(0.633983\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −86516.9 | −2.82440 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1587.91 | −0.0516801 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35207.3 | −1.14236 | −0.571180 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18540.7 | 0.599752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 70719.3 | 2.28067 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41524.6 | −1.33509 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47633.5 | −1.52687 | −0.763435 | − | 0.645885i | \(-0.776489\pi\) | ||||
−0.763435 | + | 0.645885i | \(0.776489\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38764.4 | 1.23882 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13168.0 | −0.419550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6114.40 | −0.194228 | −0.0971139 | − | 0.995273i | \(-0.530961\pi\) | ||||
−0.0971139 | + | 0.995273i | \(0.530961\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50364.1 | 1.59505 |
(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 | 2312.4.a.b.1.1 | 2 | ||
17.16 | even | 2 | 136.4.a.a.1.2 | ✓ | 2 | ||
51.50 | odd | 2 | 1224.4.a.d.1.2 | 2 | |||
68.67 | odd | 2 | 272.4.a.f.1.1 | 2 | |||
136.67 | odd | 2 | 1088.4.a.p.1.2 | 2 | |||
136.101 | even | 2 | 1088.4.a.n.1.1 | 2 | |||
204.203 | even | 2 | 2448.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.a.a.1.2 | ✓ | 2 | 17.16 | even | 2 | ||
272.4.a.f.1.1 | 2 | 68.67 | odd | 2 | |||
1088.4.a.n.1.1 | 2 | 136.101 | even | 2 | |||
1088.4.a.p.1.2 | 2 | 136.67 | odd | 2 | |||
1224.4.a.d.1.2 | 2 | 51.50 | odd | 2 | |||
2312.4.a.b.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2448.4.a.z.1.2 | 2 | 204.203 | even | 2 |