Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1587,4,Mod(1,1587)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1587, 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("1587.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1587 = 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1587.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: | \(93.6360311791\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1587.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.23607 | −1.49768 | −0.748838 | − | 0.662753i | \(-0.769388\pi\) | ||||
−0.748838 | + | 0.662753i | \(0.769388\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 9.94427 | 1.24303 | ||||||||
\(5\) | 10.7639 | 0.962755 | 0.481378 | − | 0.876513i | \(-0.340137\pi\) | ||||
0.481378 | + | 0.876513i | \(0.340137\pi\) | |||||||
\(6\) | −12.7082 | −0.864684 | ||||||||
\(7\) | −10.6525 | −0.575180 | −0.287590 | − | 0.957754i | \(-0.592854\pi\) | ||||
−0.287590 | + | 0.957754i | \(0.592854\pi\) | |||||||
\(8\) | −8.23607 | −0.363986 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −45.5967 | −1.44190 | ||||||||
\(11\) | 52.3607 | 1.43521 | 0.717606 | − | 0.696449i | \(-0.245238\pi\) | ||||
0.717606 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(12\) | 29.8328 | 0.717666 | ||||||||
\(13\) | −79.0820 | −1.68719 | −0.843593 | − | 0.536984i | \(-0.819564\pi\) | ||||
−0.843593 | + | 0.536984i | \(0.819564\pi\) | |||||||
\(14\) | 45.1246 | 0.861433 | ||||||||
\(15\) | 32.2918 | 0.555847 | ||||||||
\(16\) | −44.6656 | −0.697900 | ||||||||
\(17\) | 77.2361 | 1.10191 | 0.550956 | − | 0.834534i | \(-0.314263\pi\) | ||||
0.550956 | + | 0.834534i | \(0.314263\pi\) | |||||||
\(18\) | −38.1246 | −0.499225 | ||||||||
\(19\) | −50.7902 | −0.613267 | −0.306634 | − | 0.951828i | \(-0.599203\pi\) | ||||
−0.306634 | + | 0.951828i | \(0.599203\pi\) | |||||||
\(20\) | 107.039 | 1.19674 | ||||||||
\(21\) | −31.9574 | −0.332080 | ||||||||
\(22\) | −221.803 | −2.14948 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −24.7082 | −0.210148 | ||||||||
\(25\) | −9.13777 | −0.0731021 | ||||||||
\(26\) | 334.997 | 2.52686 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −105.931 | −0.714968 | ||||||||
\(29\) | 12.7477 | 0.0816270 | 0.0408135 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408135 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(30\) | −136.790 | −0.832479 | ||||||||
\(31\) | −12.4133 | −0.0719192 | −0.0359596 | − | 0.999353i | \(-0.511449\pi\) | ||||
−0.0359596 | + | 0.999353i | \(0.511449\pi\) | |||||||
\(32\) | 255.095 | 1.40922 | ||||||||
\(33\) | 157.082 | 0.828620 | ||||||||
\(34\) | −327.177 | −1.65031 | ||||||||
\(35\) | −114.663 | −0.553757 | ||||||||
\(36\) | 89.4984 | 0.414345 | ||||||||
\(37\) | 73.1084 | 0.324836 | 0.162418 | − | 0.986722i | \(-0.448071\pi\) | ||||
0.162418 | + | 0.986722i | \(0.448071\pi\) | |||||||
\(38\) | 215.151 | 0.918476 | ||||||||
\(39\) | −237.246 | −0.974097 | ||||||||
\(40\) | −88.6525 | −0.350430 | ||||||||
\(41\) | −38.8916 | −0.148143 | −0.0740714 | − | 0.997253i | \(-0.523599\pi\) | ||||
−0.0740714 | + | 0.997253i | \(0.523599\pi\) | |||||||
\(42\) | 135.374 | 0.497348 | ||||||||
\(43\) | −171.787 | −0.609239 | −0.304620 | − | 0.952474i | \(-0.598529\pi\) | ||||
−0.304620 | + | 0.952474i | \(0.598529\pi\) | |||||||
\(44\) | 520.689 | 1.78402 | ||||||||
\(45\) | 96.8754 | 0.320918 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 614.545 | 1.90725 | 0.953623 | − | 0.301003i | \(-0.0973214\pi\) | ||||
0.953623 | + | 0.301003i | \(0.0973214\pi\) | |||||||
\(48\) | −133.997 | −0.402933 | ||||||||
\(49\) | −229.525 | −0.669168 | ||||||||
\(50\) | 38.7082 | 0.109483 | ||||||||
\(51\) | 231.708 | 0.636189 | ||||||||
\(52\) | −786.413 | −2.09723 | ||||||||
\(53\) | −269.597 | −0.698716 | −0.349358 | − | 0.936989i | \(-0.613600\pi\) | ||||
−0.349358 | + | 0.936989i | \(0.613600\pi\) | |||||||
\(54\) | −114.374 | −0.288228 | ||||||||
\(55\) | 563.607 | 1.38176 | ||||||||
\(56\) | 87.7345 | 0.209357 | ||||||||
\(57\) | −152.371 | −0.354070 | ||||||||
\(58\) | −54.0000 | −0.122251 | ||||||||
\(59\) | −534.768 | −1.18001 | −0.590007 | − | 0.807398i | \(-0.700875\pi\) | ||||
−0.590007 | + | 0.807398i | \(0.700875\pi\) | |||||||
\(60\) | 321.118 | 0.690937 | ||||||||
\(61\) | 838.604 | 1.76020 | 0.880100 | − | 0.474788i | \(-0.157475\pi\) | ||||
0.880100 | + | 0.474788i | \(0.157475\pi\) | |||||||
\(62\) | 52.5836 | 0.107712 | ||||||||
\(63\) | −95.8723 | −0.191727 | ||||||||
\(64\) | −723.276 | −1.41265 | ||||||||
\(65\) | −851.234 | −1.62435 | ||||||||
\(66\) | −665.410 | −1.24101 | ||||||||
\(67\) | 448.180 | 0.817223 | 0.408612 | − | 0.912708i | \(-0.366013\pi\) | ||||
0.408612 | + | 0.912708i | \(0.366013\pi\) | |||||||
\(68\) | 768.056 | 1.36971 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 485.718 | 0.829349 | ||||||||
\(71\) | 628.604 | 1.05073 | 0.525363 | − | 0.850878i | \(-0.323930\pi\) | ||||
0.525363 | + | 0.850878i | \(0.323930\pi\) | |||||||
\(72\) | −74.1246 | −0.121329 | ||||||||
\(73\) | 925.266 | 1.48348 | 0.741741 | − | 0.670686i | \(-0.234000\pi\) | ||||
0.741741 | + | 0.670686i | \(0.234000\pi\) | |||||||
\(74\) | −309.692 | −0.486499 | ||||||||
\(75\) | −27.4133 | −0.0422055 | ||||||||
\(76\) | −505.072 | −0.762312 | ||||||||
\(77\) | −557.771 | −0.825505 | ||||||||
\(78\) | 1004.99 | 1.45888 | ||||||||
\(79\) | 963.479 | 1.37215 | 0.686075 | − | 0.727531i | \(-0.259332\pi\) | ||||
0.686075 | + | 0.727531i | \(0.259332\pi\) | |||||||
\(80\) | −480.778 | −0.671907 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 164.748 | 0.221870 | ||||||||
\(83\) | −133.358 | −0.176360 | −0.0881801 | − | 0.996105i | \(-0.528105\pi\) | ||||
−0.0881801 | + | 0.996105i | \(0.528105\pi\) | |||||||
\(84\) | −317.793 | −0.412787 | ||||||||
\(85\) | 831.364 | 1.06087 | ||||||||
\(86\) | 727.702 | 0.912443 | ||||||||
\(87\) | 38.2430 | 0.0471274 | ||||||||
\(88\) | −431.246 | −0.522398 | ||||||||
\(89\) | 778.581 | 0.927297 | 0.463649 | − | 0.886019i | \(-0.346540\pi\) | ||||
0.463649 | + | 0.886019i | \(0.346540\pi\) | |||||||
\(90\) | −410.371 | −0.480632 | ||||||||
\(91\) | 842.420 | 0.970435 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −37.2399 | −0.0415226 | ||||||||
\(94\) | −2603.25 | −2.85644 | ||||||||
\(95\) | −546.703 | −0.590426 | ||||||||
\(96\) | 765.286 | 0.813611 | ||||||||
\(97\) | −1603.57 | −1.67853 | −0.839266 | − | 0.543721i | \(-0.817015\pi\) | ||||
−0.839266 | + | 0.543721i | \(0.817015\pi\) | |||||||
\(98\) | 972.282 | 1.00220 | ||||||||
\(99\) | 471.246 | 0.478404 | ||||||||
\(100\) | −90.8684 | −0.0908684 | ||||||||
\(101\) | 1229.04 | 1.21084 | 0.605418 | − | 0.795908i | \(-0.293006\pi\) | ||||
0.605418 | + | 0.795908i | \(0.293006\pi\) | |||||||
\(102\) | −981.532 | −0.952805 | ||||||||
\(103\) | −215.066 | −0.205738 | −0.102869 | − | 0.994695i | \(-0.532802\pi\) | ||||
−0.102869 | + | 0.994695i | \(0.532802\pi\) | |||||||
\(104\) | 651.325 | 0.614112 | ||||||||
\(105\) | −343.988 | −0.319712 | ||||||||
\(106\) | 1142.03 | 1.04645 | ||||||||
\(107\) | 1586.58 | 1.43346 | 0.716730 | − | 0.697351i | \(-0.245638\pi\) | ||||
0.716730 | + | 0.697351i | \(0.245638\pi\) | |||||||
\(108\) | 268.495 | 0.239222 | ||||||||
\(109\) | −822.255 | −0.722549 | −0.361274 | − | 0.932460i | \(-0.617658\pi\) | ||||
−0.361274 | + | 0.932460i | \(0.617658\pi\) | |||||||
\(110\) | −2387.48 | −2.06943 | ||||||||
\(111\) | 219.325 | 0.187544 | ||||||||
\(112\) | 475.800 | 0.401418 | ||||||||
\(113\) | −19.7005 | −0.0164006 | −0.00820031 | − | 0.999966i | \(-0.502610\pi\) | ||||
−0.00820031 | + | 0.999966i | \(0.502610\pi\) | |||||||
\(114\) | 645.453 | 0.530282 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 126.766 | 0.101465 | ||||||||
\(117\) | −711.738 | −0.562395 | ||||||||
\(118\) | 2265.31 | 1.76728 | ||||||||
\(119\) | −822.755 | −0.633797 | ||||||||
\(120\) | −265.957 | −0.202321 | ||||||||
\(121\) | 1410.64 | 1.05984 | ||||||||
\(122\) | −3552.38 | −2.63621 | ||||||||
\(123\) | −116.675 | −0.0855303 | ||||||||
\(124\) | −123.441 | −0.0893980 | ||||||||
\(125\) | −1443.85 | −1.03313 | ||||||||
\(126\) | 406.122 | 0.287144 | ||||||||
\(127\) | 1143.23 | 0.798784 | 0.399392 | − | 0.916780i | \(-0.369221\pi\) | ||||
0.399392 | + | 0.916780i | \(0.369221\pi\) | |||||||
\(128\) | 1023.08 | 0.706473 | ||||||||
\(129\) | −515.361 | −0.351745 | ||||||||
\(130\) | 3605.88 | 2.43275 | ||||||||
\(131\) | 1154.64 | 0.770085 | 0.385043 | − | 0.922899i | \(-0.374187\pi\) | ||||
0.385043 | + | 0.922899i | \(0.374187\pi\) | |||||||
\(132\) | 1562.07 | 1.03000 | ||||||||
\(133\) | 541.042 | 0.352739 | ||||||||
\(134\) | −1898.52 | −1.22394 | ||||||||
\(135\) | 290.626 | 0.185282 | ||||||||
\(136\) | −636.122 | −0.401081 | ||||||||
\(137\) | 2153.10 | 1.34271 | 0.671356 | − | 0.741135i | \(-0.265712\pi\) | ||||
0.671356 | + | 0.741135i | \(0.265712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2392.16 | −1.45971 | −0.729857 | − | 0.683600i | \(-0.760413\pi\) | ||||
−0.729857 | + | 0.683600i | \(0.760413\pi\) | |||||||
\(140\) | −1140.24 | −0.688339 | ||||||||
\(141\) | 1843.63 | 1.10115 | ||||||||
\(142\) | −2662.81 | −1.57365 | ||||||||
\(143\) | −4140.79 | −2.42147 | ||||||||
\(144\) | −401.991 | −0.232633 | ||||||||
\(145\) | 137.215 | 0.0785868 | ||||||||
\(146\) | −3919.49 | −2.22178 | ||||||||
\(147\) | −688.574 | −0.386345 | ||||||||
\(148\) | 727.009 | 0.403782 | ||||||||
\(149\) | 2259.80 | 1.24248 | 0.621242 | − | 0.783619i | \(-0.286628\pi\) | ||||
0.621242 | + | 0.783619i | \(0.286628\pi\) | |||||||
\(150\) | 116.125 | 0.0632102 | ||||||||
\(151\) | −2410.84 | −1.29928 | −0.649639 | − | 0.760243i | \(-0.725080\pi\) | ||||
−0.649639 | + | 0.760243i | \(0.725080\pi\) | |||||||
\(152\) | 418.312 | 0.223221 | ||||||||
\(153\) | 695.125 | 0.367304 | ||||||||
\(154\) | 2362.76 | 1.23634 | ||||||||
\(155\) | −133.616 | −0.0692406 | ||||||||
\(156\) | −2359.24 | −1.21084 | ||||||||
\(157\) | 614.960 | 0.312606 | 0.156303 | − | 0.987709i | \(-0.450042\pi\) | ||||
0.156303 | + | 0.987709i | \(0.450042\pi\) | |||||||
\(158\) | −4081.36 | −2.05504 | ||||||||
\(159\) | −808.790 | −0.403404 | ||||||||
\(160\) | 2745.83 | 1.35673 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −343.122 | −0.166408 | ||||||||
\(163\) | −50.8127 | −0.0244169 | −0.0122085 | − | 0.999925i | \(-0.503886\pi\) | ||||
−0.0122085 | + | 0.999925i | \(0.503886\pi\) | |||||||
\(164\) | −386.749 | −0.184147 | ||||||||
\(165\) | 1690.82 | 0.797759 | ||||||||
\(166\) | 564.912 | 0.264130 | ||||||||
\(167\) | −2000.84 | −0.927125 | −0.463562 | − | 0.886064i | \(-0.653429\pi\) | ||||
−0.463562 | + | 0.886064i | \(0.653429\pi\) | |||||||
\(168\) | 263.204 | 0.120873 | ||||||||
\(169\) | 4056.97 | 1.84659 | ||||||||
\(170\) | −3521.71 | −1.58884 | ||||||||
\(171\) | −457.112 | −0.204422 | ||||||||
\(172\) | −1708.30 | −0.757305 | ||||||||
\(173\) | −3796.78 | −1.66858 | −0.834288 | − | 0.551330i | \(-0.814121\pi\) | ||||
−0.834288 | + | 0.551330i | \(0.814121\pi\) | |||||||
\(174\) | −162.000 | −0.0705815 | ||||||||
\(175\) | 97.3398 | 0.0420469 | ||||||||
\(176\) | −2338.72 | −1.00164 | ||||||||
\(177\) | −1604.30 | −0.681281 | ||||||||
\(178\) | −3298.12 | −1.38879 | ||||||||
\(179\) | −3084.16 | −1.28783 | −0.643913 | − | 0.765099i | \(-0.722690\pi\) | ||||
−0.643913 | + | 0.765099i | \(0.722690\pi\) | |||||||
\(180\) | 963.355 | 0.398913 | ||||||||
\(181\) | −4733.12 | −1.94370 | −0.971851 | − | 0.235597i | \(-0.924295\pi\) | ||||
−0.971851 | + | 0.235597i | \(0.924295\pi\) | |||||||
\(182\) | −3568.55 | −1.45340 | ||||||||
\(183\) | 2515.81 | 1.01625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 786.933 | 0.312738 | ||||||||
\(186\) | 157.751 | 0.0621874 | ||||||||
\(187\) | 4044.13 | 1.58148 | ||||||||
\(188\) | 6111.20 | 2.37077 | ||||||||
\(189\) | −287.617 | −0.110693 | ||||||||
\(190\) | 2315.87 | 0.884268 | ||||||||
\(191\) | 1293.13 | 0.489885 | 0.244942 | − | 0.969538i | \(-0.421231\pi\) | ||||
0.244942 | + | 0.969538i | \(0.421231\pi\) | |||||||
\(192\) | −2169.83 | −0.815592 | ||||||||
\(193\) | −1171.75 | −0.437019 | −0.218510 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218510 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(194\) | 6792.82 | 2.51390 | ||||||||
\(195\) | −2553.70 | −0.937817 | ||||||||
\(196\) | −2282.46 | −0.831799 | ||||||||
\(197\) | 4559.19 | 1.64888 | 0.824438 | − | 0.565952i | \(-0.191491\pi\) | ||||
0.824438 | + | 0.565952i | \(0.191491\pi\) | |||||||
\(198\) | −1996.23 | −0.716495 | ||||||||
\(199\) | 473.721 | 0.168750 | 0.0843748 | − | 0.996434i | \(-0.473111\pi\) | ||||
0.0843748 | + | 0.996434i | \(0.473111\pi\) | |||||||
\(200\) | 75.2593 | 0.0266082 | ||||||||
\(201\) | 1344.54 | 0.471824 | ||||||||
\(202\) | −5206.31 | −1.81344 | ||||||||
\(203\) | −135.794 | −0.0469502 | ||||||||
\(204\) | 2304.17 | 0.790805 | ||||||||
\(205\) | −418.627 | −0.142625 | ||||||||
\(206\) | 911.033 | 0.308130 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3532.25 | 1.17749 | ||||||||
\(209\) | −2659.41 | −0.880169 | ||||||||
\(210\) | 1457.15 | 0.478825 | ||||||||
\(211\) | −1423.56 | −0.464465 | −0.232232 | − | 0.972660i | \(-0.574603\pi\) | ||||
−0.232232 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(212\) | −2680.94 | −0.868528 | ||||||||
\(213\) | 1885.81 | 0.606637 | ||||||||
\(214\) | −6720.85 | −2.14686 | ||||||||
\(215\) | −1849.11 | −0.586548 | ||||||||
\(216\) | −222.374 | −0.0700492 | ||||||||
\(217\) | 132.232 | 0.0413665 | ||||||||
\(218\) | 3483.13 | 1.08214 | ||||||||
\(219\) | 2775.80 | 0.856489 | ||||||||
\(220\) | 5604.66 | 1.71757 | ||||||||
\(221\) | −6107.99 | −1.85913 | ||||||||
\(222\) | −929.076 | −0.280881 | ||||||||
\(223\) | 6088.63 | 1.82836 | 0.914181 | − | 0.405305i | \(-0.132835\pi\) | ||||
0.914181 | + | 0.405305i | \(0.132835\pi\) | |||||||
\(224\) | −2717.40 | −0.810552 | ||||||||
\(225\) | −82.2399 | −0.0243674 | ||||||||
\(226\) | 83.4528 | 0.0245628 | ||||||||
\(227\) | 4463.66 | 1.30513 | 0.652563 | − | 0.757734i | \(-0.273694\pi\) | ||||
0.652563 | + | 0.757734i | \(0.273694\pi\) | |||||||
\(228\) | −1515.22 | −0.440121 | ||||||||
\(229\) | −1298.87 | −0.374812 | −0.187406 | − | 0.982283i | \(-0.560008\pi\) | ||||
−0.187406 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1673.31 | −0.476606 | ||||||||
\(232\) | −104.991 | −0.0297111 | ||||||||
\(233\) | −1257.41 | −0.353544 | −0.176772 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176772 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(234\) | 3014.97 | 0.842286 | ||||||||
\(235\) | 6614.92 | 1.83621 | ||||||||
\(236\) | −5317.88 | −1.46680 | ||||||||
\(237\) | 2890.44 | 0.792211 | ||||||||
\(238\) | 3485.25 | 0.949223 | ||||||||
\(239\) | 3473.96 | 0.940217 | 0.470108 | − | 0.882609i | \(-0.344215\pi\) | ||||
0.470108 | + | 0.882609i | \(0.344215\pi\) | |||||||
\(240\) | −1442.33 | −0.387926 | ||||||||
\(241\) | 2140.92 | 0.572235 | 0.286118 | − | 0.958195i | \(-0.407635\pi\) | ||||
0.286118 | + | 0.958195i | \(0.407635\pi\) | |||||||
\(242\) | −5975.57 | −1.58729 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 8339.30 | 2.18799 | ||||||||
\(245\) | −2470.59 | −0.644245 | ||||||||
\(246\) | 494.243 | 0.128097 | ||||||||
\(247\) | 4016.60 | 1.03470 | ||||||||
\(248\) | 102.237 | 0.0261776 | ||||||||
\(249\) | −400.073 | −0.101822 | ||||||||
\(250\) | 6116.25 | 1.54730 | ||||||||
\(251\) | 5613.17 | 1.41155 | 0.705777 | − | 0.708434i | \(-0.250598\pi\) | ||||
0.705777 | + | 0.708434i | \(0.250598\pi\) | |||||||
\(252\) | −953.380 | −0.238323 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4842.82 | −1.19632 | ||||||||
\(255\) | 2494.09 | 0.612494 | ||||||||
\(256\) | 1452.36 | 0.354579 | ||||||||
\(257\) | 1017.98 | 0.247082 | 0.123541 | − | 0.992339i | \(-0.460575\pi\) | ||||
0.123541 | + | 0.992339i | \(0.460575\pi\) | |||||||
\(258\) | 2183.11 | 0.526799 | ||||||||
\(259\) | −778.785 | −0.186839 | ||||||||
\(260\) | −8464.90 | −2.01912 | ||||||||
\(261\) | 114.729 | 0.0272090 | ||||||||
\(262\) | −4891.12 | −1.15334 | ||||||||
\(263\) | 995.531 | 0.233411 | 0.116705 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116705 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(264\) | −1293.74 | −0.301606 | ||||||||
\(265\) | −2901.92 | −0.672693 | ||||||||
\(266\) | −2291.89 | −0.528289 | ||||||||
\(267\) | 2335.74 | 0.535375 | ||||||||
\(268\) | 4456.83 | 1.01584 | ||||||||
\(269\) | −3568.95 | −0.808932 | −0.404466 | − | 0.914553i | \(-0.632543\pi\) | ||||
−0.404466 | + | 0.914553i | \(0.632543\pi\) | |||||||
\(270\) | −1231.11 | −0.277493 | ||||||||
\(271\) | −6294.26 | −1.41088 | −0.705441 | − | 0.708768i | \(-0.749251\pi\) | ||||
−0.705441 | + | 0.708768i | \(0.749251\pi\) | |||||||
\(272\) | −3449.80 | −0.769025 | ||||||||
\(273\) | 2527.26 | 0.560281 | ||||||||
\(274\) | −9120.67 | −2.01095 | ||||||||
\(275\) | −478.460 | −0.104917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2263.65 | −0.491009 | −0.245505 | − | 0.969395i | \(-0.578954\pi\) | ||||
−0.245505 | + | 0.969395i | \(0.578954\pi\) | |||||||
\(278\) | 10133.3 | 2.18618 | ||||||||
\(279\) | −111.720 | −0.0239731 | ||||||||
\(280\) | 944.368 | 0.201560 | ||||||||
\(281\) | 505.900 | 0.107400 | 0.0537001 | − | 0.998557i | \(-0.482898\pi\) | ||||
0.0537001 | + | 0.998557i | \(0.482898\pi\) | |||||||
\(282\) | −7809.76 | −1.64916 | ||||||||
\(283\) | 7018.20 | 1.47417 | 0.737083 | − | 0.675802i | \(-0.236203\pi\) | ||||
0.737083 | + | 0.675802i | \(0.236203\pi\) | |||||||
\(284\) | 6251.01 | 1.30609 | ||||||||
\(285\) | −1640.11 | −0.340883 | ||||||||
\(286\) | 17540.7 | 3.62658 | ||||||||
\(287\) | 414.292 | 0.0852087 | ||||||||
\(288\) | 2295.86 | 0.469738 | ||||||||
\(289\) | 1052.41 | 0.214209 | ||||||||
\(290\) | −581.252 | −0.117698 | ||||||||
\(291\) | −4810.70 | −0.969101 | ||||||||
\(292\) | 9201.10 | 1.84402 | ||||||||
\(293\) | 9488.82 | 1.89196 | 0.945978 | − | 0.324232i | \(-0.105106\pi\) | ||||
0.945978 | + | 0.324232i | \(0.105106\pi\) | |||||||
\(294\) | 2916.85 | 0.578619 | ||||||||
\(295\) | −5756.20 | −1.13606 | ||||||||
\(296\) | −602.125 | −0.118236 | ||||||||
\(297\) | 1413.74 | 0.276207 | ||||||||
\(298\) | −9572.67 | −1.86084 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −272.605 | −0.0524629 | ||||||||
\(301\) | 1829.96 | 0.350422 | ||||||||
\(302\) | 10212.5 | 1.94590 | ||||||||
\(303\) | 3687.13 | 0.699076 | ||||||||
\(304\) | 2268.58 | 0.428000 | ||||||||
\(305\) | 9026.67 | 1.69464 | ||||||||
\(306\) | −2944.60 | −0.550102 | ||||||||
\(307\) | 4660.58 | 0.866427 | 0.433214 | − | 0.901291i | \(-0.357380\pi\) | ||||
0.433214 | + | 0.901291i | \(0.357380\pi\) | |||||||
\(308\) | −5546.63 | −1.02613 | ||||||||
\(309\) | −645.197 | −0.118783 | ||||||||
\(310\) | 566.006 | 0.103700 | ||||||||
\(311\) | 4378.51 | 0.798336 | 0.399168 | − | 0.916878i | \(-0.369299\pi\) | ||||
0.399168 | + | 0.916878i | \(0.369299\pi\) | |||||||
\(312\) | 1953.98 | 0.354558 | ||||||||
\(313\) | 4444.17 | 0.802553 | 0.401277 | − | 0.915957i | \(-0.368567\pi\) | ||||
0.401277 | + | 0.915957i | \(0.368567\pi\) | |||||||
\(314\) | −2605.01 | −0.468182 | ||||||||
\(315\) | −1031.96 | −0.184586 | ||||||||
\(316\) | 9581.10 | 1.70563 | ||||||||
\(317\) | 7881.61 | 1.39645 | 0.698226 | − | 0.715878i | \(-0.253973\pi\) | ||||
0.698226 | + | 0.715878i | \(0.253973\pi\) | |||||||
\(318\) | 3426.09 | 0.604169 | ||||||||
\(319\) | 667.477 | 0.117152 | ||||||||
\(320\) | −7785.29 | −1.36003 | ||||||||
\(321\) | 4759.73 | 0.827609 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3922.84 | −0.675767 | ||||||||
\(324\) | 805.486 | 0.138115 | ||||||||
\(325\) | 722.633 | 0.123337 | ||||||||
\(326\) | 215.246 | 0.0365686 | ||||||||
\(327\) | −2466.77 | −0.417164 | ||||||||
\(328\) | 320.314 | 0.0539219 | ||||||||
\(329\) | −6546.42 | −1.09701 | ||||||||
\(330\) | −7162.43 | −1.19478 | ||||||||
\(331\) | −127.060 | −0.0210993 | −0.0105497 | − | 0.999944i | \(-0.503358\pi\) | ||||
−0.0105497 | + | 0.999944i | \(0.503358\pi\) | |||||||
\(332\) | −1326.14 | −0.219222 | ||||||||
\(333\) | 657.975 | 0.108279 | ||||||||
\(334\) | 8475.70 | 1.38853 | ||||||||
\(335\) | 4824.18 | 0.786786 | ||||||||
\(336\) | 1427.40 | 0.231759 | ||||||||
\(337\) | 1739.07 | 0.281107 | 0.140554 | − | 0.990073i | \(-0.455112\pi\) | ||||
0.140554 | + | 0.990073i | \(0.455112\pi\) | |||||||
\(338\) | −17185.6 | −2.76560 | ||||||||
\(339\) | −59.1016 | −0.00946890 | ||||||||
\(340\) | 8267.31 | 1.31870 | ||||||||
\(341\) | −649.969 | −0.103219 | ||||||||
\(342\) | 1936.36 | 0.306159 | ||||||||
\(343\) | 6098.81 | 0.960072 | ||||||||
\(344\) | 1414.85 | 0.221755 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16083.4 | 2.49899 | ||||||||
\(347\) | 7551.30 | 1.16823 | 0.584114 | − | 0.811672i | \(-0.301442\pi\) | ||||
0.584114 | + | 0.811672i | \(0.301442\pi\) | |||||||
\(348\) | 380.299 | 0.0585809 | ||||||||
\(349\) | −6237.28 | −0.956659 | −0.478329 | − | 0.878180i | \(-0.658758\pi\) | ||||
−0.478329 | + | 0.878180i | \(0.658758\pi\) | |||||||
\(350\) | −412.338 | −0.0629726 | ||||||||
\(351\) | −2135.22 | −0.324699 | ||||||||
\(352\) | 13357.0 | 2.02252 | ||||||||
\(353\) | 1788.57 | 0.269678 | 0.134839 | − | 0.990868i | \(-0.456948\pi\) | ||||
0.134839 | + | 0.990868i | \(0.456948\pi\) | |||||||
\(354\) | 6795.94 | 1.02034 | ||||||||
\(355\) | 6766.25 | 1.01159 | ||||||||
\(356\) | 7742.42 | 1.15266 | ||||||||
\(357\) | −2468.27 | −0.365923 | ||||||||
\(358\) | 13064.7 | 1.92875 | ||||||||
\(359\) | −2234.70 | −0.328531 | −0.164266 | − | 0.986416i | \(-0.552525\pi\) | ||||
−0.164266 | + | 0.986416i | \(0.552525\pi\) | |||||||
\(360\) | −797.872 | −0.116810 | ||||||||
\(361\) | −4279.35 | −0.623903 | ||||||||
\(362\) | 20049.8 | 2.91104 | ||||||||
\(363\) | 4231.92 | 0.611896 | ||||||||
\(364\) | 8377.25 | 1.20628 | ||||||||
\(365\) | 9959.50 | 1.42823 | ||||||||
\(366\) | −10657.1 | −1.52202 | ||||||||
\(367\) | −10551.7 | −1.50080 | −0.750399 | − | 0.660985i | \(-0.770139\pi\) | ||||
−0.750399 | + | 0.660985i | \(0.770139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −350.025 | −0.0493809 | ||||||||
\(370\) | −3333.50 | −0.468380 | ||||||||
\(371\) | 2871.87 | 0.401887 | ||||||||
\(372\) | −370.324 | −0.0516140 | ||||||||
\(373\) | 996.068 | 0.138269 | 0.0691347 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691347 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(374\) | −17131.2 | −2.36854 | ||||||||
\(375\) | −4331.55 | −0.596481 | ||||||||
\(376\) | −5061.43 | −0.694211 | ||||||||
\(377\) | −1008.11 | −0.137720 | ||||||||
\(378\) | 1218.36 | 0.165783 | ||||||||
\(379\) | 11117.0 | 1.50670 | 0.753351 | − | 0.657619i | \(-0.228436\pi\) | ||||
0.753351 | + | 0.657619i | \(0.228436\pi\) | |||||||
\(380\) | −5436.56 | −0.733920 | ||||||||
\(381\) | 3429.70 | 0.461178 | ||||||||
\(382\) | −5477.81 | −0.733688 | ||||||||
\(383\) | −5315.09 | −0.709108 | −0.354554 | − | 0.935035i | \(-0.615367\pi\) | ||||
−0.354554 | + | 0.935035i | \(0.615367\pi\) | |||||||
\(384\) | 3069.25 | 0.407883 | ||||||||
\(385\) | −6003.81 | −0.794759 | ||||||||
\(386\) | 4963.63 | 0.654513 | ||||||||
\(387\) | −1546.08 | −0.203080 | ||||||||
\(388\) | −15946.3 | −2.08647 | ||||||||
\(389\) | 8438.06 | 1.09981 | 0.549906 | − | 0.835227i | \(-0.314664\pi\) | ||||
0.549906 | + | 0.835227i | \(0.314664\pi\) | |||||||
\(390\) | 10817.7 | 1.40455 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1890.38 | 0.243568 | ||||||||
\(393\) | 3463.91 | 0.444609 | ||||||||
\(394\) | −19313.0 | −2.46948 | ||||||||
\(395\) | 10370.8 | 1.32104 | ||||||||
\(396\) | 4686.20 | 0.594673 | ||||||||
\(397\) | 11582.0 | 1.46419 | 0.732094 | − | 0.681204i | \(-0.238543\pi\) | ||||
0.732094 | + | 0.681204i | \(0.238543\pi\) | |||||||
\(398\) | −2006.71 | −0.252732 | ||||||||
\(399\) | 1623.13 | 0.203654 | ||||||||
\(400\) | 408.144 | 0.0510180 | ||||||||
\(401\) | −4267.85 | −0.531487 | −0.265744 | − | 0.964044i | \(-0.585617\pi\) | ||||
−0.265744 | + | 0.964044i | \(0.585617\pi\) | |||||||
\(402\) | −5695.57 | −0.706639 | ||||||||
\(403\) | 981.669 | 0.121341 | ||||||||
\(404\) | 12221.9 | 1.50511 | ||||||||
\(405\) | 871.878 | 0.106973 | ||||||||
\(406\) | 575.234 | 0.0703162 | ||||||||
\(407\) | 3828.00 | 0.466209 | ||||||||
\(408\) | −1908.36 | −0.231564 | ||||||||
\(409\) | 6902.51 | 0.834491 | 0.417246 | − | 0.908794i | \(-0.362995\pi\) | ||||
0.417246 | + | 0.908794i | \(0.362995\pi\) | |||||||
\(410\) | 1773.33 | 0.213606 | ||||||||
\(411\) | 6459.29 | 0.775215 | ||||||||
\(412\) | −2138.67 | −0.255740 | ||||||||
\(413\) | 5696.60 | 0.678720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1435.45 | −0.169792 | ||||||||
\(416\) | −20173.4 | −2.37761 | ||||||||
\(417\) | −7176.47 | −0.842766 | ||||||||
\(418\) | 11265.4 | 1.31821 | ||||||||
\(419\) | 2241.24 | 0.261316 | 0.130658 | − | 0.991427i | \(-0.458291\pi\) | ||||
0.130658 | + | 0.991427i | \(0.458291\pi\) | |||||||
\(420\) | −3420.71 | −0.397413 | ||||||||
\(421\) | −9117.52 | −1.05549 | −0.527744 | − | 0.849403i | \(-0.676962\pi\) | ||||
−0.527744 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(422\) | 6030.30 | 0.695618 | ||||||||
\(423\) | 5530.90 | 0.635749 | ||||||||
\(424\) | 2220.42 | 0.254323 | ||||||||
\(425\) | −705.765 | −0.0805521 | ||||||||
\(426\) | −7988.42 | −0.908546 | ||||||||
\(427\) | −8933.21 | −1.01243 | ||||||||
\(428\) | 15777.4 | 1.78184 | ||||||||
\(429\) | −12422.4 | −1.39804 | ||||||||
\(430\) | 7832.93 | 0.878460 | ||||||||
\(431\) | 1366.55 | 0.152725 | 0.0763623 | − | 0.997080i | \(-0.475669\pi\) | ||||
0.0763623 | + | 0.997080i | \(0.475669\pi\) | |||||||
\(432\) | −1205.97 | −0.134311 | ||||||||
\(433\) | −3511.21 | −0.389695 | −0.194848 | − | 0.980834i | \(-0.562421\pi\) | ||||
−0.194848 | + | 0.980834i | \(0.562421\pi\) | |||||||
\(434\) | −560.145 | −0.0619536 | ||||||||
\(435\) | 411.645 | 0.0453721 | ||||||||
\(436\) | −8176.73 | −0.898152 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −11758.5 | −1.28274 | ||||||||
\(439\) | 7032.17 | 0.764526 | 0.382263 | − | 0.924054i | \(-0.375145\pi\) | ||||
0.382263 | + | 0.924054i | \(0.375145\pi\) | |||||||
\(440\) | −4641.90 | −0.502941 | ||||||||
\(441\) | −2065.72 | −0.223056 | ||||||||
\(442\) | 25873.8 | 2.78437 | ||||||||
\(443\) | 8748.68 | 0.938289 | 0.469145 | − | 0.883121i | \(-0.344562\pi\) | ||||
0.469145 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(444\) | 2181.03 | 0.233124 | ||||||||
\(445\) | 8380.60 | 0.892760 | ||||||||
\(446\) | −25791.9 | −2.73830 | ||||||||
\(447\) | 6779.40 | 0.717348 | ||||||||
\(448\) | 7704.68 | 0.812526 | ||||||||
\(449\) | −805.208 | −0.0846327 | −0.0423164 | − | 0.999104i | \(-0.513474\pi\) | ||||
−0.0423164 | + | 0.999104i | \(0.513474\pi\) | |||||||
\(450\) | 348.374 | 0.0364944 | ||||||||
\(451\) | −2036.39 | −0.212616 | ||||||||
\(452\) | −195.907 | −0.0203865 | ||||||||
\(453\) | −7232.51 | −0.750139 | ||||||||
\(454\) | −18908.4 | −1.95466 | ||||||||
\(455\) | 9067.75 | 0.934291 | ||||||||
\(456\) | 1254.94 | 0.128877 | ||||||||
\(457\) | 10496.9 | 1.07445 | 0.537226 | − | 0.843438i | \(-0.319472\pi\) | ||||
0.537226 | + | 0.843438i | \(0.319472\pi\) | |||||||
\(458\) | 5502.12 | 0.561348 | ||||||||
\(459\) | 2085.37 | 0.212063 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3325.68 | −0.335992 | −0.167996 | − | 0.985788i | \(-0.553730\pi\) | ||||
−0.167996 | + | 0.985788i | \(0.553730\pi\) | |||||||
\(462\) | 7088.27 | 0.713801 | ||||||||
\(463\) | −840.876 | −0.0844035 | −0.0422018 | − | 0.999109i | \(-0.513437\pi\) | ||||
−0.0422018 | + | 0.999109i | \(0.513437\pi\) | |||||||
\(464\) | −569.383 | −0.0569675 | ||||||||
\(465\) | −400.848 | −0.0399761 | ||||||||
\(466\) | 5326.48 | 0.529495 | ||||||||
\(467\) | −8450.82 | −0.837382 | −0.418691 | − | 0.908129i | \(-0.637511\pi\) | ||||
−0.418691 | + | 0.908129i | \(0.637511\pi\) | |||||||
\(468\) | −7077.72 | −0.699076 | ||||||||
\(469\) | −4774.23 | −0.470050 | ||||||||
\(470\) | −28021.2 | −2.75005 | ||||||||
\(471\) | 1844.88 | 0.180483 | ||||||||
\(472\) | 4404.38 | 0.429509 | ||||||||
\(473\) | −8994.89 | −0.874388 | ||||||||
\(474\) | −12244.1 | −1.18648 | ||||||||
\(475\) | 464.109 | 0.0448312 | ||||||||
\(476\) | −8181.70 | −0.787831 | ||||||||
\(477\) | −2426.37 | −0.232905 | ||||||||
\(478\) | −14715.9 | −1.40814 | ||||||||
\(479\) | 5686.86 | 0.542462 | 0.271231 | − | 0.962514i | \(-0.412569\pi\) | ||||
0.271231 | + | 0.962514i | \(0.412569\pi\) | |||||||
\(480\) | 8237.48 | 0.783308 | ||||||||
\(481\) | −5781.56 | −0.548059 | ||||||||
\(482\) | −9069.07 | −0.857023 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14027.8 | 1.31741 | ||||||||
\(485\) | −17260.7 | −1.61602 | ||||||||
\(486\) | −1029.36 | −0.0960760 | ||||||||
\(487\) | −13768.2 | −1.28110 | −0.640551 | − | 0.767916i | \(-0.721294\pi\) | ||||
−0.640551 | + | 0.767916i | \(0.721294\pi\) | |||||||
\(488\) | −6906.80 | −0.640689 | ||||||||
\(489\) | −152.438 | −0.0140971 | ||||||||
\(490\) | 10465.6 | 0.964871 | ||||||||
\(491\) | 8480.14 | 0.779436 | 0.389718 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389718 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(492\) | −1160.25 | −0.106317 | ||||||||
\(493\) | 984.580 | 0.0899457 | ||||||||
\(494\) | −17014.6 | −1.54964 | ||||||||
\(495\) | 5072.46 | 0.460586 | ||||||||
\(496\) | 554.448 | 0.0501924 | ||||||||
\(497\) | −6696.19 | −0.604356 | ||||||||
\(498\) | 1694.74 | 0.152496 | ||||||||
\(499\) | 12472.5 | 1.11893 | 0.559466 | − | 0.828853i | \(-0.311006\pi\) | ||||
0.559466 | + | 0.828853i | \(0.311006\pi\) | |||||||
\(500\) | −14358.0 | −1.28422 | ||||||||
\(501\) | −6002.53 | −0.535276 | ||||||||
\(502\) | −23777.8 | −2.11405 | ||||||||
\(503\) | 4676.36 | 0.414530 | 0.207265 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207265 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(504\) | 789.611 | 0.0697858 | ||||||||
\(505\) | 13229.3 | 1.16574 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12170.9 | 1.06613 | ||||||||
\(508\) | 11368.6 | 0.992916 | ||||||||
\(509\) | 5925.58 | 0.516005 | 0.258003 | − | 0.966144i | \(-0.416936\pi\) | ||||
0.258003 | + | 0.966144i | \(0.416936\pi\) | |||||||
\(510\) | −10565.1 | −0.917318 | ||||||||
\(511\) | −9856.38 | −0.853269 | ||||||||
\(512\) | −14336.9 | −1.23752 | ||||||||
\(513\) | −1371.34 | −0.118023 | ||||||||
\(514\) | −4312.25 | −0.370049 | ||||||||
\(515\) | −2314.95 | −0.198076 | ||||||||
\(516\) | −5124.89 | −0.437230 | ||||||||
\(517\) | 32178.0 | 2.73730 | ||||||||
\(518\) | 3298.99 | 0.279825 | ||||||||
\(519\) | −11390.3 | −0.963352 | ||||||||
\(520\) | 7010.82 | 0.591240 | ||||||||
\(521\) | −2626.25 | −0.220841 | −0.110421 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110421 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(522\) | −486.000 | −0.0407503 | ||||||||
\(523\) | −372.504 | −0.0311443 | −0.0155721 | − | 0.999879i | \(-0.504957\pi\) | ||||
−0.0155721 | + | 0.999879i | \(0.504957\pi\) | |||||||
\(524\) | 11482.0 | 0.957242 | ||||||||
\(525\) | 292.020 | 0.0242758 | ||||||||
\(526\) | −4217.14 | −0.349574 | ||||||||
\(527\) | −958.755 | −0.0792486 | ||||||||
\(528\) | −7016.17 | −0.578295 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 12292.7 | 1.00748 | ||||||||
\(531\) | −4812.91 | −0.393338 | ||||||||
\(532\) | 5380.27 | 0.438466 | ||||||||
\(533\) | 3075.63 | 0.249944 | ||||||||
\(534\) | −9894.37 | −0.801819 | ||||||||
\(535\) | 17077.8 | 1.38007 | ||||||||
\(536\) | −3691.24 | −0.297458 | ||||||||
\(537\) | −9252.47 | −0.743526 | ||||||||
\(538\) | 15118.3 | 1.21152 | ||||||||
\(539\) | −12018.1 | −0.960399 | ||||||||
\(540\) | 2890.07 | 0.230312 | ||||||||
\(541\) | 12899.2 | 1.02510 | 0.512550 | − | 0.858657i | \(-0.328701\pi\) | ||||
0.512550 | + | 0.858657i | \(0.328701\pi\) | |||||||
\(542\) | 26662.9 | 2.11305 | ||||||||
\(543\) | −14199.4 | −1.12220 | ||||||||
\(544\) | 19702.5 | 1.55283 | ||||||||
\(545\) | −8850.70 | −0.695637 | ||||||||
\(546\) | −10705.6 | −0.839119 | ||||||||
\(547\) | −22144.7 | −1.73097 | −0.865485 | − | 0.500936i | \(-0.832989\pi\) | ||||
−0.865485 | + | 0.500936i | \(0.832989\pi\) | |||||||
\(548\) | 21411.0 | 1.66904 | ||||||||
\(549\) | 7547.43 | 0.586733 | ||||||||
\(550\) | 2026.79 | 0.157132 | ||||||||
\(551\) | −647.457 | −0.0500592 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10263.4 | −0.789233 | ||||||||
\(554\) | 9588.98 | 0.735373 | ||||||||
\(555\) | 2360.80 | 0.180559 | ||||||||
\(556\) | −23788.3 | −1.81447 | ||||||||
\(557\) | 10236.7 | 0.778716 | 0.389358 | − | 0.921086i | \(-0.372697\pi\) | ||||
0.389358 | + | 0.921086i | \(0.372697\pi\) | |||||||
\(558\) | 473.252 | 0.0359039 | ||||||||
\(559\) | 13585.3 | 1.02790 | ||||||||
\(560\) | 5121.47 | 0.386467 | ||||||||
\(561\) | 12132.4 | 0.913066 | ||||||||
\(562\) | −2143.03 | −0.160851 | ||||||||
\(563\) | −5750.83 | −0.430495 | −0.215247 | − | 0.976560i | \(-0.569056\pi\) | ||||
−0.215247 | + | 0.976560i | \(0.569056\pi\) | |||||||
\(564\) | 18333.6 | 1.36877 | ||||||||
\(565\) | −212.055 | −0.0157898 | ||||||||
\(566\) | −29729.6 | −2.20782 | ||||||||
\(567\) | −862.851 | −0.0639088 | ||||||||
\(568\) | −5177.22 | −0.382450 | ||||||||
\(569\) | 8285.10 | 0.610421 | 0.305210 | − | 0.952285i | \(-0.401273\pi\) | ||||
0.305210 | + | 0.952285i | \(0.401273\pi\) | |||||||
\(570\) | 6947.61 | 0.510532 | ||||||||
\(571\) | 19799.8 | 1.45113 | 0.725565 | − | 0.688154i | \(-0.241579\pi\) | ||||
0.725565 | + | 0.688154i | \(0.241579\pi\) | |||||||
\(572\) | −41177.1 | −3.00997 | ||||||||
\(573\) | 3879.40 | 0.282835 | ||||||||
\(574\) | −1754.97 | −0.127615 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6509.48 | −0.470883 | ||||||||
\(577\) | −250.868 | −0.0181001 | −0.00905006 | − | 0.999959i | \(-0.502881\pi\) | ||||
−0.00905006 | + | 0.999959i | \(0.502881\pi\) | |||||||
\(578\) | −4458.08 | −0.320816 | ||||||||
\(579\) | −3515.26 | −0.252313 | ||||||||
\(580\) | 1364.50 | 0.0976861 | ||||||||
\(581\) | 1420.59 | 0.101439 | ||||||||
\(582\) | 20378.5 | 1.45140 | ||||||||
\(583\) | −14116.3 | −1.00281 | ||||||||
\(584\) | −7620.56 | −0.539967 | ||||||||
\(585\) | −7661.10 | −0.541449 | ||||||||
\(586\) | −40195.3 | −2.83354 | ||||||||
\(587\) | −9767.11 | −0.686766 | −0.343383 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343383 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(588\) | −6847.37 | −0.480239 | ||||||||
\(589\) | 630.475 | 0.0441057 | ||||||||
\(590\) | 24383.7 | 1.70146 | ||||||||
\(591\) | 13677.6 | 0.951979 | ||||||||
\(592\) | −3265.43 | −0.226703 | ||||||||
\(593\) | −18853.8 | −1.30562 | −0.652810 | − | 0.757521i | \(-0.726410\pi\) | ||||
−0.652810 | + | 0.757521i | \(0.726410\pi\) | |||||||
\(594\) | −5988.69 | −0.413668 | ||||||||
\(595\) | −8856.08 | −0.610192 | ||||||||
\(596\) | 22472.1 | 1.54445 | ||||||||
\(597\) | 1421.16 | 0.0974276 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11356.0 | −0.774615 | −0.387307 | − | 0.921951i | \(-0.626595\pi\) | ||||
−0.387307 | + | 0.921951i | \(0.626595\pi\) | |||||||
\(600\) | 225.778 | 0.0153622 | ||||||||
\(601\) | 20359.1 | 1.38180 | 0.690902 | − | 0.722948i | \(-0.257213\pi\) | ||||
0.690902 | + | 0.722948i | \(0.257213\pi\) | |||||||
\(602\) | −7751.83 | −0.524819 | ||||||||
\(603\) | 4033.62 | 0.272408 | ||||||||
\(604\) | −23974.0 | −1.61505 | ||||||||
\(605\) | 15184.0 | 1.02036 | ||||||||
\(606\) | −15618.9 | −1.04699 | ||||||||
\(607\) | 5975.14 | 0.399545 | 0.199772 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199772 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(608\) | −12956.3 | −0.864226 | ||||||||
\(609\) | −407.383 | −0.0271067 | ||||||||
\(610\) | −38237.6 | −2.53802 | ||||||||
\(611\) | −48599.5 | −3.21788 | ||||||||
\(612\) | 6912.51 | 0.456571 | ||||||||
\(613\) | −16997.4 | −1.11993 | −0.559967 | − | 0.828515i | \(-0.689186\pi\) | ||||
−0.559967 | + | 0.828515i | \(0.689186\pi\) | |||||||
\(614\) | −19742.5 | −1.29763 | ||||||||
\(615\) | −1255.88 | −0.0823447 | ||||||||
\(616\) | 4593.84 | 0.300472 | ||||||||
\(617\) | 13096.0 | 0.854497 | 0.427249 | − | 0.904134i | \(-0.359483\pi\) | ||||
0.427249 | + | 0.904134i | \(0.359483\pi\) | |||||||
\(618\) | 2733.10 | 0.177899 | ||||||||
\(619\) | −702.058 | −0.0455866 | −0.0227933 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227933 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(620\) | −1328.71 | −0.0860684 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18547.7 | −1.19565 | ||||||||
\(623\) | −8293.82 | −0.533362 | ||||||||
\(624\) | 10596.7 | 0.679823 | ||||||||
\(625\) | −14399.3 | −0.921554 | ||||||||
\(626\) | −18825.8 | −1.20196 | ||||||||
\(627\) | −7978.23 | −0.508166 | ||||||||
\(628\) | 6115.33 | 0.388580 | ||||||||
\(629\) | 5646.60 | 0.357941 | ||||||||
\(630\) | 4371.46 | 0.276450 | ||||||||
\(631\) | −23871.5 | −1.50604 | −0.753019 | − | 0.657999i | \(-0.771403\pi\) | ||||
−0.753019 | + | 0.657999i | \(0.771403\pi\) | |||||||
\(632\) | −7935.28 | −0.499444 | ||||||||
\(633\) | −4270.69 | −0.268159 | ||||||||
\(634\) | −33387.0 | −2.09143 | ||||||||
\(635\) | 12305.7 | 0.769034 | ||||||||
\(636\) | −8042.83 | −0.501445 | ||||||||
\(637\) | 18151.3 | 1.12901 | ||||||||
\(638\) | −2827.48 | −0.175456 | ||||||||
\(639\) | 5657.43 | 0.350242 | ||||||||
\(640\) | 11012.4 | 0.680161 | ||||||||
\(641\) | −24172.6 | −1.48949 | −0.744743 | − | 0.667351i | \(-0.767428\pi\) | ||||
−0.744743 | + | 0.667351i | \(0.767428\pi\) | |||||||
\(642\) | −20162.5 | −1.23949 | ||||||||
\(643\) | −13648.6 | −0.837090 | −0.418545 | − | 0.908196i | \(-0.637460\pi\) | ||||
−0.418545 | + | 0.908196i | \(0.637460\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5547.32 | −0.338644 | ||||||||
\(646\) | 16617.4 | 1.01208 | ||||||||
\(647\) | −7009.18 | −0.425903 | −0.212952 | − | 0.977063i | \(-0.568308\pi\) | ||||
−0.212952 | + | 0.977063i | \(0.568308\pi\) | |||||||
\(648\) | −667.122 | −0.0404429 | ||||||||
\(649\) | −28000.8 | −1.69357 | ||||||||
\(650\) | −3061.12 | −0.184719 | ||||||||
\(651\) | 396.697 | 0.0238829 | ||||||||
\(652\) | −505.295 | −0.0303511 | ||||||||
\(653\) | 4533.57 | 0.271688 | 0.135844 | − | 0.990730i | \(-0.456625\pi\) | ||||
0.135844 | + | 0.990730i | \(0.456625\pi\) | |||||||
\(654\) | 10449.4 | 0.624776 | ||||||||
\(655\) | 12428.4 | 0.741404 | ||||||||
\(656\) | 1737.12 | 0.103389 | ||||||||
\(657\) | 8327.40 | 0.494494 | ||||||||
\(658\) | 27731.1 | 1.64296 | ||||||||
\(659\) | 7112.62 | 0.420438 | 0.210219 | − | 0.977654i | \(-0.432582\pi\) | ||||
0.210219 | + | 0.977654i | \(0.432582\pi\) | |||||||
\(660\) | 16814.0 | 0.991641 | ||||||||
\(661\) | −16088.6 | −0.946709 | −0.473354 | − | 0.880872i | \(-0.656957\pi\) | ||||
−0.473354 | + | 0.880872i | \(0.656957\pi\) | |||||||
\(662\) | 538.237 | 0.0316000 | ||||||||
\(663\) | −18324.0 | −1.07337 | ||||||||
\(664\) | 1098.34 | 0.0641927 | ||||||||
\(665\) | 5823.74 | 0.339601 | ||||||||
\(666\) | −2787.23 | −0.162166 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −19896.9 | −1.15245 | ||||||||
\(669\) | 18265.9 | 1.05561 | ||||||||
\(670\) | −20435.6 | −1.17835 | ||||||||
\(671\) | 43909.9 | 2.52626 | ||||||||
\(672\) | −8152.19 | −0.467972 | ||||||||
\(673\) | 22629.7 | 1.29615 | 0.648076 | − | 0.761576i | \(-0.275574\pi\) | ||||
0.648076 | + | 0.761576i | \(0.275574\pi\) | |||||||
\(674\) | −7366.82 | −0.421008 | ||||||||
\(675\) | −246.720 | −0.0140685 | ||||||||
\(676\) | 40343.6 | 2.29538 | ||||||||
\(677\) | 15444.0 | 0.876749 | 0.438375 | − | 0.898792i | \(-0.355554\pi\) | ||||
0.438375 | + | 0.898792i | \(0.355554\pi\) | |||||||
\(678\) | 250.358 | 0.0141813 | ||||||||
\(679\) | 17082.0 | 0.965458 | ||||||||
\(680\) | −6847.17 | −0.386143 | ||||||||
\(681\) | 13391.0 | 0.753515 | ||||||||
\(682\) | 2753.31 | 0.154589 | ||||||||
\(683\) | 834.894 | 0.0467736 | 0.0233868 | − | 0.999726i | \(-0.492555\pi\) | ||||
0.0233868 | + | 0.999726i | \(0.492555\pi\) | |||||||
\(684\) | −4545.65 | −0.254104 | ||||||||
\(685\) | 23175.8 | 1.29270 | ||||||||
\(686\) | −25835.0 | −1.43788 | ||||||||
\(687\) | −3896.62 | −0.216398 | ||||||||
\(688\) | 7672.98 | 0.425188 | ||||||||
\(689\) | 21320.3 | 1.17886 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4982.99 | 0.274330 | 0.137165 | − | 0.990548i | \(-0.456201\pi\) | ||||
0.137165 | + | 0.990548i | \(0.456201\pi\) | |||||||
\(692\) | −37756.2 | −2.07410 | ||||||||
\(693\) | −5019.94 | −0.275168 | ||||||||
\(694\) | −31987.8 | −1.74963 | ||||||||
\(695\) | −25749.0 | −1.40535 | ||||||||
\(696\) | −314.972 | −0.0171537 | ||||||||
\(697\) | −3003.84 | −0.163240 | ||||||||
\(698\) | 26421.5 | 1.43277 | ||||||||
\(699\) | −3772.23 | −0.204119 | ||||||||
\(700\) | 967.974 | 0.0522657 | ||||||||
\(701\) | −21916.9 | −1.18087 | −0.590436 | − | 0.807084i | \(-0.701044\pi\) | ||||
−0.590436 | + | 0.807084i | \(0.701044\pi\) | |||||||
\(702\) | 9044.92 | 0.486294 | ||||||||
\(703\) | −3713.19 | −0.199211 | ||||||||
\(704\) | −37871.2 | −2.02745 | ||||||||
\(705\) | 19844.8 | 1.06014 | ||||||||
\(706\) | −7576.52 | −0.403890 | ||||||||
\(707\) | −13092.4 | −0.696448 | ||||||||
\(708\) | −15953.6 | −0.846856 | ||||||||
\(709\) | 30858.3 | 1.63456 | 0.817282 | − | 0.576237i | \(-0.195480\pi\) | ||||
0.817282 | + | 0.576237i | \(0.195480\pi\) | |||||||
\(710\) | −28662.3 | −1.51504 | ||||||||
\(711\) | 8671.31 | 0.457383 | ||||||||
\(712\) | −6412.45 | −0.337523 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 10455.7 | 0.548034 | ||||||||
\(715\) | −44571.2 | −2.33128 | ||||||||
\(716\) | −30669.7 | −1.60081 | ||||||||
\(717\) | 10421.9 | 0.542834 | ||||||||
\(718\) | 9466.32 | 0.492033 | ||||||||
\(719\) | 19500.3 | 1.01146 | 0.505728 | − | 0.862693i | \(-0.331224\pi\) | ||||
0.505728 | + | 0.862693i | \(0.331224\pi\) | |||||||
\(720\) | −4327.00 | −0.223969 | ||||||||
\(721\) | 2290.98 | 0.118337 | ||||||||
\(722\) | 18127.6 | 0.934405 | ||||||||
\(723\) | 6422.75 | 0.330380 | ||||||||
\(724\) | −47067.4 | −2.41609 | ||||||||
\(725\) | −116.485 | −0.00596711 | ||||||||
\(726\) | −17926.7 | −0.916422 | ||||||||
\(727\) | −26922.8 | −1.37347 | −0.686735 | − | 0.726908i | \(-0.740957\pi\) | ||||
−0.686735 | + | 0.726908i | \(0.740957\pi\) | |||||||
\(728\) | −6938.22 | −0.353225 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −42189.1 | −2.13903 | ||||||||
\(731\) | −13268.2 | −0.671328 | ||||||||
\(732\) | 25017.9 | 1.26324 | ||||||||
\(733\) | 22120.5 | 1.11465 | 0.557326 | − | 0.830294i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830294i | \(0.311827\pi\) | |||||||
\(734\) | 44697.6 | 2.24771 | ||||||||
\(735\) | −7411.77 | −0.371955 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23467.0 | 1.17289 | ||||||||
\(738\) | 1482.73 | 0.0739567 | ||||||||
\(739\) | −27225.8 | −1.35523 | −0.677617 | − | 0.735415i | \(-0.736987\pi\) | ||||
−0.677617 | + | 0.735415i | \(0.736987\pi\) | |||||||
\(740\) | 7825.48 | 0.388744 | ||||||||
\(741\) | 12049.8 | 0.597382 | ||||||||
\(742\) | −12165.4 | −0.601897 | ||||||||
\(743\) | 191.429 | 0.00945201 | 0.00472600 | − | 0.999989i | \(-0.498496\pi\) | ||||
0.00472600 | + | 0.999989i | \(0.498496\pi\) | |||||||
\(744\) | 306.710 | 0.0151136 | ||||||||
\(745\) | 24324.3 | 1.19621 | ||||||||
\(746\) | −4219.41 | −0.207083 | ||||||||
\(747\) | −1200.22 | −0.0587867 | ||||||||
\(748\) | 40216.0 | 1.96583 | ||||||||
\(749\) | −16901.0 | −0.824497 | ||||||||
\(750\) | 18348.7 | 0.893335 | ||||||||
\(751\) | 876.709 | 0.0425986 | 0.0212993 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212993 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(752\) | −27449.0 | −1.33107 | ||||||||
\(753\) | 16839.5 | 0.814961 | ||||||||
\(754\) | 4270.43 | 0.206260 | ||||||||
\(755\) | −25950.1 | −1.25089 | ||||||||
\(756\) | −2860.14 | −0.137596 | ||||||||
\(757\) | 26681.0 | 1.28103 | 0.640513 | − | 0.767948i | \(-0.278722\pi\) | ||||
0.640513 | + | 0.767948i | \(0.278722\pi\) | |||||||
\(758\) | −47092.2 | −2.25655 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4502.68 | 0.214907 | ||||||||
\(761\) | −6947.99 | −0.330965 | −0.165483 | − | 0.986213i | \(-0.552918\pi\) | ||||
−0.165483 | + | 0.986213i | \(0.552918\pi\) | |||||||
\(762\) | −14528.4 | −0.690696 | ||||||||
\(763\) | 8759.06 | 0.415595 | ||||||||
\(764\) | 12859.3 | 0.608943 | ||||||||
\(765\) | 7482.27 | 0.353624 | ||||||||
\(766\) | 22515.1 | 1.06201 | ||||||||
\(767\) | 42290.5 | 1.99090 | ||||||||
\(768\) | 4357.07 | 0.204716 | ||||||||
\(769\) | −7189.91 | −0.337159 | −0.168579 | − | 0.985688i | \(-0.553918\pi\) | ||||
−0.168579 | + | 0.985688i | \(0.553918\pi\) | |||||||
\(770\) | 25432.5 | 1.19029 | ||||||||
\(771\) | 3053.95 | 0.142653 | ||||||||
\(772\) | −11652.2 | −0.543230 | ||||||||
\(773\) | 27591.1 | 1.28381 | 0.641904 | − | 0.766785i | \(-0.278145\pi\) | ||||
0.641904 | + | 0.766785i | \(0.278145\pi\) | |||||||
\(774\) | 6549.32 | 0.304148 | ||||||||
\(775\) | 113.430 | 0.00525745 | ||||||||
\(776\) | 13207.1 | 0.610963 | ||||||||
\(777\) | −2336.35 | −0.107872 | ||||||||
\(778\) | −35744.2 | −1.64716 | ||||||||
\(779\) | 1975.32 | 0.0908512 | ||||||||
\(780\) | −25394.7 | −1.16574 | ||||||||
\(781\) | 32914.1 | 1.50801 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 344.187 | 0.0157091 | ||||||||
\(784\) | 10251.9 | 0.467013 | ||||||||
\(785\) | 6619.38 | 0.300963 | ||||||||
\(786\) | −14673.4 | −0.665880 | ||||||||
\(787\) | −10322.4 | −0.467541 | −0.233770 | − | 0.972292i | \(-0.575106\pi\) | ||||
−0.233770 | + | 0.972292i | \(0.575106\pi\) | |||||||
\(788\) | 45337.8 | 2.04961 | ||||||||
\(789\) | 2986.59 | 0.134760 | ||||||||
\(790\) | −43931.5 | −1.97850 | ||||||||
\(791\) | 209.859 | 0.00943330 | ||||||||
\(792\) | −3881.22 | −0.174133 | ||||||||
\(793\) | −66318.5 | −2.96978 | ||||||||
\(794\) | −49062.0 | −2.19288 | ||||||||
\(795\) | −8705.76 | −0.388379 | ||||||||
\(796\) | 4710.81 | 0.209761 | ||||||||
\(797\) | −40205.9 | −1.78691 | −0.893455 | − | 0.449153i | \(-0.851726\pi\) | ||||
−0.893455 | + | 0.449153i | \(0.851726\pi\) | |||||||
\(798\) | −6875.67 | −0.305008 | ||||||||
\(799\) | 47465.0 | 2.10162 | ||||||||
\(800\) | −2331.00 | −0.103017 | ||||||||
\(801\) | 7007.23 | 0.309099 | ||||||||
\(802\) | 18078.9 | 0.795995 | ||||||||
\(803\) | 48447.6 | 2.12911 | ||||||||
\(804\) | 13370.5 | 0.586493 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4158.42 | −0.181730 | ||||||||
\(807\) | −10706.8 | −0.467037 | ||||||||
\(808\) | −10122.5 | −0.440727 | ||||||||
\(809\) | −42375.9 | −1.84160 | −0.920802 | − | 0.390031i | \(-0.872464\pi\) | ||||
−0.920802 | + | 0.390031i | \(0.872464\pi\) | |||||||
\(810\) | −3693.34 | −0.160211 | ||||||||
\(811\) | 7082.68 | 0.306667 | 0.153333 | − | 0.988175i | \(-0.450999\pi\) | ||||
0.153333 | + | 0.988175i | \(0.450999\pi\) | |||||||
\(812\) | −1350.37 | −0.0583607 | ||||||||
\(813\) | −18882.8 | −0.814573 | ||||||||
\(814\) | −16215.7 | −0.698230 | ||||||||
\(815\) | −546.945 | −0.0235075 | ||||||||
\(816\) | −10349.4 | −0.443997 | ||||||||
\(817\) | 8725.11 | 0.373627 | ||||||||
\(818\) | −29239.5 | −1.24980 | ||||||||
\(819\) | 7581.78 | 0.323478 | ||||||||
\(820\) | −4162.94 | −0.177288 | ||||||||
\(821\) | 18154.3 | 0.771728 | 0.385864 | − | 0.922556i | \(-0.373903\pi\) | ||||
0.385864 | + | 0.922556i | \(0.373903\pi\) | |||||||
\(822\) | −27362.0 | −1.16102 | ||||||||
\(823\) | 10437.1 | 0.442058 | 0.221029 | − | 0.975267i | \(-0.429059\pi\) | ||||
0.221029 | + | 0.975267i | \(0.429059\pi\) | |||||||
\(824\) | 1771.30 | 0.0748860 | ||||||||
\(825\) | −1435.38 | −0.0605739 | ||||||||
\(826\) | −24131.2 | −1.01650 | ||||||||
\(827\) | 1486.57 | 0.0625068 | 0.0312534 | − | 0.999511i | \(-0.490050\pi\) | ||||
0.0312534 | + | 0.999511i | \(0.490050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9987.68 | −0.418440 | −0.209220 | − | 0.977869i | \(-0.567092\pi\) | ||||
−0.209220 | + | 0.977869i | \(0.567092\pi\) | |||||||
\(830\) | 6080.67 | 0.254293 | ||||||||
\(831\) | −6790.95 | −0.283484 | ||||||||
\(832\) | 57198.1 | 2.38340 | ||||||||
\(833\) | −17727.6 | −0.737364 | ||||||||
\(834\) | 30400.0 | 1.26219 | ||||||||
\(835\) | −21536.9 | −0.892594 | ||||||||
\(836\) | −26445.9 | −1.09408 | ||||||||
\(837\) | −335.159 | −0.0138409 | ||||||||
\(838\) | −9494.03 | −0.391367 | ||||||||
\(839\) | 2835.68 | 0.116685 | 0.0583424 | − | 0.998297i | \(-0.481418\pi\) | ||||
0.0583424 | + | 0.998297i | \(0.481418\pi\) | |||||||
\(840\) | 2833.11 | 0.116371 | ||||||||
\(841\) | −24226.5 | −0.993337 | ||||||||
\(842\) | 38622.4 | 1.58078 | ||||||||
\(843\) | 1517.70 | 0.0620076 | ||||||||
\(844\) | −14156.3 | −0.577345 | ||||||||
\(845\) | 43668.9 | 1.77782 | ||||||||
\(846\) | −23429.3 | −0.952146 | ||||||||
\(847\) | −15026.8 | −0.609596 | ||||||||
\(848\) | 12041.7 | 0.487634 | ||||||||
\(849\) | 21054.6 | 0.851110 | ||||||||
\(850\) | 2989.67 | 0.120641 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 18753.0 | 0.754070 | ||||||||
\(853\) | 17544.2 | 0.704223 | 0.352111 | − | 0.935958i | \(-0.385464\pi\) | ||||
0.352111 | + | 0.935958i | \(0.385464\pi\) | |||||||
\(854\) | 37841.7 | 1.51629 | ||||||||
\(855\) | −4920.32 | −0.196809 | ||||||||
\(856\) | −13067.2 | −0.521760 | ||||||||
\(857\) | 12827.7 | 0.511301 | 0.255651 | − | 0.966769i | \(-0.417710\pi\) | ||||
0.255651 | + | 0.966769i | \(0.417710\pi\) | |||||||
\(858\) | 52622.0 | 2.09381 | ||||||||
\(859\) | −35061.5 | −1.39265 | −0.696324 | − | 0.717728i | \(-0.745182\pi\) | ||||
−0.696324 | + | 0.717728i | \(0.745182\pi\) | |||||||
\(860\) | −18388.0 | −0.729100 | ||||||||
\(861\) | 1242.88 | 0.0491953 | ||||||||
\(862\) | −5788.79 | −0.228732 | ||||||||
\(863\) | −4222.11 | −0.166538 | −0.0832691 | − | 0.996527i | \(-0.526536\pi\) | ||||
−0.0832691 | + | 0.996527i | \(0.526536\pi\) | |||||||
\(864\) | 6887.57 | 0.271204 | ||||||||
\(865\) | −40868.2 | −1.60643 | ||||||||
\(866\) | 14873.7 | 0.583637 | ||||||||
\(867\) | 3157.23 | 0.123674 | ||||||||
\(868\) | 1314.95 | 0.0514199 | ||||||||
\(869\) | 50448.4 | 1.96933 | ||||||||
\(870\) | −1743.76 | −0.0679528 | ||||||||
\(871\) | −35443.0 | −1.37881 | ||||||||
\(872\) | 6772.15 | 0.262998 | ||||||||
\(873\) | −14432.1 | −0.559511 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15380.6 | 0.594238 | ||||||||
\(876\) | 27603.3 | 1.06464 | ||||||||
\(877\) | 17535.0 | 0.675159 | 0.337579 | − | 0.941297i | \(-0.390392\pi\) | ||||
0.337579 | + | 0.941297i | \(0.390392\pi\) | |||||||
\(878\) | −29788.7 | −1.14501 | ||||||||
\(879\) | 28466.5 | 1.09232 | ||||||||
\(880\) | −25173.9 | −0.964330 | ||||||||
\(881\) | −9116.63 | −0.348634 | −0.174317 | − | 0.984690i | \(-0.555772\pi\) | ||||
−0.174317 | + | 0.984690i | \(0.555772\pi\) | |||||||
\(882\) | 8750.54 | 0.334066 | ||||||||
\(883\) | −41050.4 | −1.56450 | −0.782251 | − | 0.622963i | \(-0.785929\pi\) | ||||
−0.782251 | + | 0.622963i | \(0.785929\pi\) | |||||||
\(884\) | −60739.5 | −2.31096 | ||||||||
\(885\) | −17268.6 | −0.655907 | ||||||||
\(886\) | −37060.0 | −1.40525 | ||||||||
\(887\) | 22519.5 | 0.852461 | 0.426230 | − | 0.904615i | \(-0.359841\pi\) | ||||
0.426230 | + | 0.904615i | \(0.359841\pi\) | |||||||
\(888\) | −1806.38 | −0.0682635 | ||||||||
\(889\) | −12178.3 | −0.459444 | ||||||||
\(890\) | −35500.8 | −1.33707 | ||||||||
\(891\) | 4241.22 | 0.159468 | ||||||||
\(892\) | 60547.0 | 2.27272 | ||||||||
\(893\) | −31212.9 | −1.16965 | ||||||||
\(894\) | −28718.0 | −1.07436 | ||||||||
\(895\) | −33197.7 | −1.23986 | ||||||||
\(896\) | −10898.4 | −0.406349 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3410.91 | 0.126752 | ||||||||
\(899\) | −158.241 | −0.00587055 | ||||||||
\(900\) | −817.816 | −0.0302895 | ||||||||
\(901\) | −20822.6 | −0.769924 | ||||||||
\(902\) | 8626.30 | 0.318431 | ||||||||
\(903\) | 5489.88 | 0.202316 | ||||||||
\(904\) | 162.255 | 0.00596960 | ||||||||
\(905\) | −50947.0 | −1.87131 | ||||||||
\(906\) | 30637.4 | 1.12346 | ||||||||
\(907\) | 32037.9 | 1.17288 | 0.586439 | − | 0.809993i | \(-0.300529\pi\) | ||||
0.586439 | + | 0.809993i | \(0.300529\pi\) | |||||||
\(908\) | 44387.9 | 1.62232 | ||||||||
\(909\) | 11061.4 | 0.403612 | ||||||||
\(910\) | −38411.6 | −1.39927 | ||||||||
\(911\) | 12881.7 | 0.468485 | 0.234242 | − | 0.972178i | \(-0.424739\pi\) | ||||
0.234242 | + | 0.972178i | \(0.424739\pi\) | |||||||
\(912\) | 6805.73 | 0.247106 | ||||||||
\(913\) | −6982.69 | −0.253114 | ||||||||
\(914\) | −44465.6 | −1.60918 | ||||||||
\(915\) | 27080.0 | 0.978402 | ||||||||
\(916\) | −12916.4 | −0.465905 | ||||||||
\(917\) | −12299.8 | −0.442937 | ||||||||
\(918\) | −8833.79 | −0.317602 | ||||||||
\(919\) | 7311.92 | 0.262457 | 0.131229 | − | 0.991352i | \(-0.458108\pi\) | ||||
0.131229 | + | 0.991352i | \(0.458108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13981.7 | 0.500232 | ||||||||
\(922\) | 14087.8 | 0.503207 | ||||||||
\(923\) | −49711.3 | −1.77277 | ||||||||
\(924\) | −16639.9 | −0.592437 | ||||||||
\(925\) | −668.047 | −0.0237462 | ||||||||
\(926\) | 3562.01 | 0.126409 | ||||||||
\(927\) | −1935.59 | −0.0685795 | ||||||||
\(928\) | 3251.87 | 0.115030 | ||||||||
\(929\) | 35059.5 | 1.23817 | 0.619087 | − | 0.785322i | \(-0.287503\pi\) | ||||
0.619087 | + | 0.785322i | \(0.287503\pi\) | |||||||
\(930\) | 1698.02 | 0.0598712 | ||||||||
\(931\) | 11657.6 | 0.410379 | ||||||||
\(932\) | −12504.0 | −0.439467 | ||||||||
\(933\) | 13135.5 | 0.460919 | ||||||||
\(934\) | 35798.2 | 1.25413 | ||||||||
\(935\) | 43530.8 | 1.52258 | ||||||||
\(936\) | 5861.93 | 0.204704 | ||||||||
\(937\) | −25471.7 | −0.888072 | −0.444036 | − | 0.896009i | \(-0.646454\pi\) | ||||
−0.444036 | + | 0.896009i | \(0.646454\pi\) | |||||||
\(938\) | 20224.0 | 0.703983 | ||||||||
\(939\) | 13332.5 | 0.463354 | ||||||||
\(940\) | 65780.6 | 2.28247 | ||||||||
\(941\) | −22426.5 | −0.776923 | −0.388461 | − | 0.921465i | \(-0.626993\pi\) | ||||
−0.388461 | + | 0.921465i | \(0.626993\pi\) | |||||||
\(942\) | −7815.03 | −0.270305 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 23885.7 | 0.823532 | ||||||||
\(945\) | −3095.89 | −0.106571 | ||||||||
\(946\) | 38103.0 | 1.30955 | ||||||||
\(947\) | −36090.9 | −1.23843 | −0.619216 | − | 0.785220i | \(-0.712550\pi\) | ||||
−0.619216 | + | 0.785220i | \(0.712550\pi\) | |||||||
\(948\) | 28743.3 | 0.984746 | ||||||||
\(949\) | −73171.9 | −2.50291 | ||||||||
\(950\) | −1966.00 | −0.0671426 | ||||||||
\(951\) | 23644.8 | 0.806242 | ||||||||
\(952\) | 6776.27 | 0.230693 | ||||||||
\(953\) | 16379.8 | 0.556762 | 0.278381 | − | 0.960471i | \(-0.410202\pi\) | ||||
0.278381 | + | 0.960471i | \(0.410202\pi\) | |||||||
\(954\) | 10278.3 | 0.348817 | ||||||||
\(955\) | 13919.2 | 0.471639 | ||||||||
\(956\) | 34546.0 | 1.16872 | ||||||||
\(957\) | 2002.43 | 0.0676378 | ||||||||
\(958\) | −24089.9 | −0.812432 | ||||||||
\(959\) | −22935.8 | −0.772301 | ||||||||
\(960\) | −23355.9 | −0.785216 | ||||||||
\(961\) | −29636.9 | −0.994828 | ||||||||
\(962\) | 24491.1 | 0.820815 | ||||||||
\(963\) | 14279.2 | 0.477820 | ||||||||
\(964\) | 21289.9 | 0.711308 | ||||||||
\(965\) | −12612.7 | −0.420742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22686.2 | −0.754434 | −0.377217 | − | 0.926125i | \(-0.623119\pi\) | ||||
−0.377217 | + | 0.926125i | \(0.623119\pi\) | |||||||
\(968\) | −11618.1 | −0.385765 | ||||||||
\(969\) | −11768.5 | −0.390154 | ||||||||
\(970\) | 73117.5 | 2.42027 | ||||||||
\(971\) | −53773.7 | −1.77722 | −0.888610 | − | 0.458663i | \(-0.848328\pi\) | ||||
−0.888610 | + | 0.458663i | \(0.848328\pi\) | |||||||
\(972\) | 2416.46 | 0.0797407 | ||||||||
\(973\) | 25482.4 | 0.839597 | ||||||||
\(974\) | 58323.0 | 1.91867 | ||||||||
\(975\) | 2167.90 | 0.0712086 | ||||||||
\(976\) | −37456.8 | −1.22844 | ||||||||
\(977\) | 20398.6 | 0.667972 | 0.333986 | − | 0.942578i | \(-0.391606\pi\) | ||||
0.333986 | + | 0.942578i | \(0.391606\pi\) | |||||||
\(978\) | 645.738 | 0.0211129 | ||||||||
\(979\) | 40767.0 | 1.33087 | ||||||||
\(980\) | −24568.2 | −0.800819 | ||||||||
\(981\) | −7400.30 | −0.240850 | ||||||||
\(982\) | −35922.4 | −1.16734 | ||||||||
\(983\) | 12118.6 | 0.393208 | 0.196604 | − | 0.980483i | \(-0.437009\pi\) | ||||
0.196604 | + | 0.980483i | \(0.437009\pi\) | |||||||
\(984\) | 960.943 | 0.0311318 | ||||||||
\(985\) | 49074.8 | 1.58746 | ||||||||
\(986\) | −4170.75 | −0.134710 | ||||||||
\(987\) | −19639.3 | −0.633359 | ||||||||
\(988\) | 39942.1 | 1.28616 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −21487.3 | −0.689809 | ||||||||
\(991\) | −26885.7 | −0.861809 | −0.430904 | − | 0.902398i | \(-0.641805\pi\) | ||||
−0.430904 | + | 0.902398i | \(0.641805\pi\) | |||||||
\(992\) | −3166.57 | −0.101350 | ||||||||
\(993\) | −381.181 | −0.0121817 | ||||||||
\(994\) | 28365.5 | 0.905130 | ||||||||
\(995\) | 5099.10 | 0.162465 | ||||||||
\(996\) | −3978.43 | −0.126568 | ||||||||
\(997\) | 21022.7 | 0.667797 | 0.333899 | − | 0.942609i | \(-0.391636\pi\) | ||||
0.333899 | + | 0.942609i | \(0.391636\pi\) | |||||||
\(998\) | −52834.5 | −1.67580 | ||||||||
\(999\) | 1973.93 | 0.0625148 |
(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 | 1587.4.a.b.1.1 | 2 | ||
23.22 | odd | 2 | 69.4.a.a.1.1 | ✓ | 2 | ||
69.68 | even | 2 | 207.4.a.c.1.2 | 2 | |||
92.91 | even | 2 | 1104.4.a.h.1.2 | 2 | |||
115.114 | odd | 2 | 1725.4.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.4.a.a.1.1 | ✓ | 2 | 23.22 | odd | 2 | ||
207.4.a.c.1.2 | 2 | 69.68 | even | 2 | |||
1104.4.a.h.1.2 | 2 | 92.91 | even | 2 | |||
1587.4.a.b.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1725.4.a.n.1.2 | 2 | 115.114 | odd | 2 |