Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [841,4,Mod(1,841)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(841, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("841.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 841 = 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 841.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: | \(49.6206063148\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.03898\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 841.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.49488 | 1.94273 | 0.971367 | − | 0.237584i | \(-0.0763557\pi\) | ||||
0.971367 | + | 0.237584i | \(0.0763557\pi\) | |||||||
\(3\) | 6.46343 | 1.24389 | 0.621944 | − | 0.783062i | \(-0.286343\pi\) | ||||
0.621944 | + | 0.783062i | \(0.286343\pi\) | |||||||
\(4\) | 22.1937 | 2.77421 | ||||||||
\(5\) | 2.14270 | 0.191649 | 0.0958246 | − | 0.995398i | \(-0.469451\pi\) | ||||
0.0958246 | + | 0.995398i | \(0.469451\pi\) | |||||||
\(6\) | 35.5158 | 2.41654 | ||||||||
\(7\) | 20.3573 | 1.09919 | 0.549595 | − | 0.835431i | \(-0.314782\pi\) | ||||
0.549595 | + | 0.835431i | \(0.314782\pi\) | |||||||
\(8\) | 77.9928 | 3.44683 | ||||||||
\(9\) | 14.7760 | 0.547258 | ||||||||
\(10\) | 11.7739 | 0.372323 | ||||||||
\(11\) | −52.0703 | −1.42725 | −0.713627 | − | 0.700526i | \(-0.752949\pi\) | ||||
−0.713627 | + | 0.700526i | \(0.752949\pi\) | |||||||
\(12\) | 143.448 | 3.45081 | ||||||||
\(13\) | 7.04574 | 0.150318 | 0.0751591 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751591 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(14\) | 111.861 | 2.13544 | ||||||||
\(15\) | 13.8492 | 0.238390 | ||||||||
\(16\) | 251.011 | 3.92205 | ||||||||
\(17\) | −28.7724 | −0.410490 | −0.205245 | − | 0.978711i | \(-0.565799\pi\) | ||||
−0.205245 | + | 0.978711i | \(0.565799\pi\) | |||||||
\(18\) | 81.1922 | 1.06318 | ||||||||
\(19\) | −76.4208 | −0.922744 | −0.461372 | − | 0.887207i | \(-0.652643\pi\) | ||||
−0.461372 | + | 0.887207i | \(0.652643\pi\) | |||||||
\(20\) | 47.5545 | 0.531676 | ||||||||
\(21\) | 131.578 | 1.36727 | ||||||||
\(22\) | −286.120 | −2.77277 | ||||||||
\(23\) | 59.7251 | 0.541458 | 0.270729 | − | 0.962656i | \(-0.412735\pi\) | ||||
0.270729 | + | 0.962656i | \(0.412735\pi\) | |||||||
\(24\) | 504.101 | 4.28747 | ||||||||
\(25\) | −120.409 | −0.963271 | ||||||||
\(26\) | 38.7155 | 0.292028 | ||||||||
\(27\) | −79.0092 | −0.563160 | ||||||||
\(28\) | 451.804 | 3.04939 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 76.0998 | 0.463128 | ||||||||
\(31\) | 3.25229 | 0.0188428 | 0.00942142 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00942142 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(32\) | 755.335 | 4.17268 | ||||||||
\(33\) | −336.553 | −1.77534 | ||||||||
\(34\) | −158.101 | −0.797473 | ||||||||
\(35\) | 43.6196 | 0.210659 | ||||||||
\(36\) | 327.934 | 1.51821 | ||||||||
\(37\) | −150.673 | −0.669471 | −0.334736 | − | 0.942312i | \(-0.608647\pi\) | ||||
−0.334736 | + | 0.942312i | \(0.608647\pi\) | |||||||
\(38\) | −419.923 | −1.79265 | ||||||||
\(39\) | 45.5397 | 0.186979 | ||||||||
\(40\) | 167.115 | 0.660581 | ||||||||
\(41\) | 92.3254 | 0.351678 | 0.175839 | − | 0.984419i | \(-0.443736\pi\) | ||||
0.175839 | + | 0.984419i | \(0.443736\pi\) | |||||||
\(42\) | 723.006 | 2.65624 | ||||||||
\(43\) | 100.703 | 0.357142 | 0.178571 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178571 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(44\) | −1155.63 | −3.95951 | ||||||||
\(45\) | 31.6605 | 0.104882 | ||||||||
\(46\) | 328.182 | 1.05191 | ||||||||
\(47\) | −324.003 | −1.00555 | −0.502774 | − | 0.864418i | \(-0.667687\pi\) | ||||
−0.502774 | + | 0.864418i | \(0.667687\pi\) | |||||||
\(48\) | 1622.39 | 4.87859 | ||||||||
\(49\) | 71.4197 | 0.208221 | ||||||||
\(50\) | −661.632 | −1.87138 | ||||||||
\(51\) | −185.969 | −0.510604 | ||||||||
\(52\) | 156.371 | 0.417015 | ||||||||
\(53\) | 374.774 | 0.971305 | 0.485653 | − | 0.874152i | \(-0.338582\pi\) | ||||
0.485653 | + | 0.874152i | \(0.338582\pi\) | |||||||
\(54\) | −434.146 | −1.09407 | ||||||||
\(55\) | −111.571 | −0.273532 | ||||||||
\(56\) | 1587.72 | 3.78872 | ||||||||
\(57\) | −493.941 | −1.14779 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 489.567 | 1.08027 | 0.540137 | − | 0.841577i | \(-0.318372\pi\) | ||||
0.540137 | + | 0.841577i | \(0.318372\pi\) | |||||||
\(60\) | 307.365 | 0.661345 | ||||||||
\(61\) | −221.508 | −0.464937 | −0.232468 | − | 0.972604i | \(-0.574680\pi\) | ||||
−0.232468 | + | 0.972604i | \(0.574680\pi\) | |||||||
\(62\) | 17.8709 | 0.0366066 | ||||||||
\(63\) | 300.799 | 0.601541 | ||||||||
\(64\) | 2142.39 | 4.18435 | ||||||||
\(65\) | 15.0969 | 0.0288083 | ||||||||
\(66\) | −1849.32 | −3.44902 | ||||||||
\(67\) | −427.538 | −0.779584 | −0.389792 | − | 0.920903i | \(-0.627453\pi\) | ||||
−0.389792 | + | 0.920903i | \(0.627453\pi\) | |||||||
\(68\) | −638.567 | −1.13879 | ||||||||
\(69\) | 386.029 | 0.673514 | ||||||||
\(70\) | 239.685 | 0.409254 | ||||||||
\(71\) | −898.999 | −1.50270 | −0.751349 | − | 0.659905i | \(-0.770596\pi\) | ||||
−0.751349 | + | 0.659905i | \(0.770596\pi\) | |||||||
\(72\) | 1152.42 | 1.88630 | ||||||||
\(73\) | 1087.35 | 1.74335 | 0.871673 | − | 0.490087i | \(-0.163035\pi\) | ||||
0.871673 | + | 0.490087i | \(0.163035\pi\) | |||||||
\(74\) | −827.929 | −1.30060 | ||||||||
\(75\) | −778.254 | −1.19820 | ||||||||
\(76\) | −1696.06 | −2.55989 | ||||||||
\(77\) | −1060.01 | −1.56882 | ||||||||
\(78\) | 250.235 | 0.363250 | ||||||||
\(79\) | 798.018 | 1.13651 | 0.568253 | − | 0.822854i | \(-0.307619\pi\) | ||||
0.568253 | + | 0.822854i | \(0.307619\pi\) | |||||||
\(80\) | 537.842 | 0.751658 | ||||||||
\(81\) | −909.622 | −1.24777 | ||||||||
\(82\) | 507.317 | 0.683217 | ||||||||
\(83\) | −436.713 | −0.577536 | −0.288768 | − | 0.957399i | \(-0.593246\pi\) | ||||
−0.288768 | + | 0.957399i | \(0.593246\pi\) | |||||||
\(84\) | 2920.21 | 3.79310 | ||||||||
\(85\) | −61.6507 | −0.0786701 | ||||||||
\(86\) | 553.353 | 0.693833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4061.11 | −4.91950 | ||||||||
\(89\) | −456.763 | −0.544009 | −0.272004 | − | 0.962296i | \(-0.587687\pi\) | ||||
−0.272004 | + | 0.962296i | \(0.587687\pi\) | |||||||
\(90\) | 173.971 | 0.203757 | ||||||||
\(91\) | 143.432 | 0.165228 | ||||||||
\(92\) | 1325.52 | 1.50212 | ||||||||
\(93\) | 21.0209 | 0.0234384 | ||||||||
\(94\) | −1780.36 | −1.95351 | ||||||||
\(95\) | −163.747 | −0.176843 | ||||||||
\(96\) | 4882.06 | 5.19034 | ||||||||
\(97\) | −803.714 | −0.841287 | −0.420643 | − | 0.907226i | \(-0.638196\pi\) | ||||
−0.420643 | + | 0.907226i | \(0.638196\pi\) | |||||||
\(98\) | 392.442 | 0.404517 | ||||||||
\(99\) | −769.390 | −0.781077 | ||||||||
\(100\) | −2672.32 | −2.67232 | ||||||||
\(101\) | 738.800 | 0.727855 | 0.363928 | − | 0.931427i | \(-0.381436\pi\) | ||||
0.363928 | + | 0.931427i | \(0.381436\pi\) | |||||||
\(102\) | −1021.87 | −0.991967 | ||||||||
\(103\) | 2031.60 | 1.94349 | 0.971743 | − | 0.236042i | \(-0.0758501\pi\) | ||||
0.971743 | + | 0.236042i | \(0.0758501\pi\) | |||||||
\(104\) | 549.517 | 0.518121 | ||||||||
\(105\) | 281.933 | 0.262036 | ||||||||
\(106\) | 2059.34 | 1.88699 | ||||||||
\(107\) | 1594.33 | 1.44047 | 0.720233 | − | 0.693732i | \(-0.244035\pi\) | ||||
0.720233 | + | 0.693732i | \(0.244035\pi\) | |||||||
\(108\) | −1753.51 | −1.56233 | ||||||||
\(109\) | −229.668 | −0.201818 | −0.100909 | − | 0.994896i | \(-0.532175\pi\) | ||||
−0.100909 | + | 0.994896i | \(0.532175\pi\) | |||||||
\(110\) | −613.071 | −0.531400 | ||||||||
\(111\) | −973.863 | −0.832748 | ||||||||
\(112\) | 5109.91 | 4.31108 | ||||||||
\(113\) | 1584.73 | 1.31928 | 0.659640 | − | 0.751582i | \(-0.270709\pi\) | ||||
0.659640 | + | 0.751582i | \(0.270709\pi\) | |||||||
\(114\) | −2714.15 | −2.22985 | ||||||||
\(115\) | 127.973 | 0.103770 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104.108 | 0.0822629 | ||||||||
\(118\) | 2690.11 | 2.09869 | ||||||||
\(119\) | −585.728 | −0.451207 | ||||||||
\(120\) | 1080.14 | 0.821689 | ||||||||
\(121\) | 1380.32 | 1.03705 | ||||||||
\(122\) | −1217.16 | −0.903248 | ||||||||
\(123\) | 596.739 | 0.437448 | ||||||||
\(124\) | 72.1803 | 0.0522741 | ||||||||
\(125\) | −525.838 | −0.376259 | ||||||||
\(126\) | 1652.85 | 1.16863 | ||||||||
\(127\) | −621.184 | −0.434025 | −0.217013 | − | 0.976169i | \(-0.569631\pi\) | ||||
−0.217013 | + | 0.976169i | \(0.569631\pi\) | |||||||
\(128\) | 5729.47 | 3.95639 | ||||||||
\(129\) | 650.890 | 0.444245 | ||||||||
\(130\) | 82.9558 | 0.0559669 | ||||||||
\(131\) | 1504.34 | 1.00332 | 0.501659 | − | 0.865066i | \(-0.332723\pi\) | ||||
0.501659 | + | 0.865066i | \(0.332723\pi\) | |||||||
\(132\) | −7469.36 | −4.92519 | ||||||||
\(133\) | −1555.72 | −1.01427 | ||||||||
\(134\) | −2349.27 | −1.51452 | ||||||||
\(135\) | −169.293 | −0.107929 | ||||||||
\(136\) | −2244.04 | −1.41489 | ||||||||
\(137\) | 29.3812 | 0.0183227 | 0.00916135 | − | 0.999958i | \(-0.497084\pi\) | ||||
0.00916135 | + | 0.999958i | \(0.497084\pi\) | |||||||
\(138\) | 2121.18 | 1.30846 | ||||||||
\(139\) | 1262.60 | 0.770450 | 0.385225 | − | 0.922823i | \(-0.374124\pi\) | ||||
0.385225 | + | 0.922823i | \(0.374124\pi\) | |||||||
\(140\) | 968.082 | 0.584413 | ||||||||
\(141\) | −2094.17 | −1.25079 | ||||||||
\(142\) | −4939.89 | −2.91934 | ||||||||
\(143\) | −366.874 | −0.214542 | ||||||||
\(144\) | 3708.94 | 2.14637 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5974.84 | 3.38686 | ||||||||
\(147\) | 461.616 | 0.259003 | ||||||||
\(148\) | −3343.99 | −1.85726 | ||||||||
\(149\) | 826.526 | 0.454441 | 0.227220 | − | 0.973843i | \(-0.427036\pi\) | ||||
0.227220 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(150\) | −4276.42 | −2.32779 | ||||||||
\(151\) | −2632.03 | −1.41849 | −0.709243 | − | 0.704964i | \(-0.750963\pi\) | ||||
−0.709243 | + | 0.704964i | \(0.750963\pi\) | |||||||
\(152\) | −5960.27 | −3.18054 | ||||||||
\(153\) | −425.140 | −0.224644 | ||||||||
\(154\) | −5824.64 | −3.04781 | ||||||||
\(155\) | 6.96868 | 0.00361121 | ||||||||
\(156\) | 1010.69 | 0.518720 | ||||||||
\(157\) | −234.540 | −0.119225 | −0.0596124 | − | 0.998222i | \(-0.518986\pi\) | ||||
−0.0596124 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(158\) | 4385.01 | 2.20793 | ||||||||
\(159\) | 2422.33 | 1.20820 | ||||||||
\(160\) | 1618.46 | 0.799689 | ||||||||
\(161\) | 1215.84 | 0.595166 | ||||||||
\(162\) | −4998.26 | −2.42408 | ||||||||
\(163\) | 1650.78 | 0.793246 | 0.396623 | − | 0.917982i | \(-0.370182\pi\) | ||||
0.396623 | + | 0.917982i | \(0.370182\pi\) | |||||||
\(164\) | 2049.04 | 0.975631 | ||||||||
\(165\) | −721.133 | −0.340243 | ||||||||
\(166\) | −2399.69 | −1.12200 | ||||||||
\(167\) | −3684.28 | −1.70717 | −0.853587 | − | 0.520950i | \(-0.825578\pi\) | ||||
−0.853587 | + | 0.520950i | \(0.825578\pi\) | |||||||
\(168\) | 10262.1 | 4.71274 | ||||||||
\(169\) | −2147.36 | −0.977404 | ||||||||
\(170\) | −338.763 | −0.152835 | ||||||||
\(171\) | −1129.19 | −0.504979 | ||||||||
\(172\) | 2234.98 | 0.990790 | ||||||||
\(173\) | −3073.58 | −1.35075 | −0.675375 | − | 0.737474i | \(-0.736018\pi\) | ||||
−0.675375 | + | 0.737474i | \(0.736018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2451.20 | −1.05882 | ||||||||
\(176\) | −13070.2 | −5.59776 | ||||||||
\(177\) | 3164.28 | 1.34374 | ||||||||
\(178\) | −2509.86 | −1.05686 | ||||||||
\(179\) | 2980.70 | 1.24463 | 0.622313 | − | 0.782769i | \(-0.286193\pi\) | ||||
0.622313 | + | 0.782769i | \(0.286193\pi\) | |||||||
\(180\) | 702.664 | 0.290964 | ||||||||
\(181\) | 3145.07 | 1.29155 | 0.645777 | − | 0.763526i | \(-0.276533\pi\) | ||||
0.645777 | + | 0.763526i | \(0.276533\pi\) | |||||||
\(182\) | 788.143 | 0.320995 | ||||||||
\(183\) | −1431.70 | −0.578329 | ||||||||
\(184\) | 4658.13 | 1.86631 | ||||||||
\(185\) | −322.847 | −0.128304 | ||||||||
\(186\) | 115.508 | 0.0455346 | ||||||||
\(187\) | 1498.19 | 0.585874 | ||||||||
\(188\) | −7190.84 | −2.78960 | ||||||||
\(189\) | −1608.41 | −0.619021 | ||||||||
\(190\) | −899.771 | −0.343559 | ||||||||
\(191\) | 2125.56 | 0.805236 | 0.402618 | − | 0.915368i | \(-0.368100\pi\) | ||||
0.402618 | + | 0.915368i | \(0.368100\pi\) | |||||||
\(192\) | 13847.2 | 5.20486 | ||||||||
\(193\) | −3085.29 | −1.15069 | −0.575347 | − | 0.817909i | \(-0.695133\pi\) | ||||
−0.575347 | + | 0.817909i | \(0.695133\pi\) | |||||||
\(194\) | −4416.31 | −1.63440 | ||||||||
\(195\) | 97.5779 | 0.0358344 | ||||||||
\(196\) | 1585.07 | 0.577649 | ||||||||
\(197\) | −2484.45 | −0.898526 | −0.449263 | − | 0.893400i | \(-0.648313\pi\) | ||||
−0.449263 | + | 0.893400i | \(0.648313\pi\) | |||||||
\(198\) | −4227.70 | −1.51742 | ||||||||
\(199\) | 5489.57 | 1.95550 | 0.977752 | − | 0.209764i | \(-0.0672696\pi\) | ||||
0.977752 | + | 0.209764i | \(0.0672696\pi\) | |||||||
\(200\) | −9391.02 | −3.32023 | ||||||||
\(201\) | −2763.37 | −0.969715 | ||||||||
\(202\) | 4059.62 | 1.41403 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4127.33 | −1.41652 | ||||||||
\(205\) | 197.826 | 0.0673988 | ||||||||
\(206\) | 11163.4 | 3.77568 | ||||||||
\(207\) | 882.496 | 0.296318 | ||||||||
\(208\) | 1768.56 | 0.589556 | ||||||||
\(209\) | 3979.26 | 1.31699 | ||||||||
\(210\) | 1549.19 | 0.509067 | ||||||||
\(211\) | 1884.64 | 0.614902 | 0.307451 | − | 0.951564i | \(-0.400524\pi\) | ||||
0.307451 | + | 0.951564i | \(0.400524\pi\) | |||||||
\(212\) | 8317.63 | 2.69461 | ||||||||
\(213\) | −5810.62 | −1.86919 | ||||||||
\(214\) | 8760.67 | 2.79844 | ||||||||
\(215\) | 215.777 | 0.0684460 | ||||||||
\(216\) | −6162.15 | −1.94112 | ||||||||
\(217\) | 66.2078 | 0.0207119 | ||||||||
\(218\) | −1262.00 | −0.392079 | ||||||||
\(219\) | 7027.99 | 2.16853 | ||||||||
\(220\) | −2476.18 | −0.758836 | ||||||||
\(221\) | −202.723 | −0.0617041 | ||||||||
\(222\) | −5351.26 | −1.61781 | ||||||||
\(223\) | −5208.50 | −1.56407 | −0.782033 | − | 0.623237i | \(-0.785817\pi\) | ||||
−0.782033 | + | 0.623237i | \(0.785817\pi\) | |||||||
\(224\) | 15376.6 | 4.58657 | ||||||||
\(225\) | −1779.16 | −0.527158 | ||||||||
\(226\) | 8707.89 | 2.56301 | ||||||||
\(227\) | −5243.29 | −1.53308 | −0.766540 | − | 0.642196i | \(-0.778023\pi\) | ||||
−0.766540 | + | 0.642196i | \(0.778023\pi\) | |||||||
\(228\) | −10962.4 | −3.18422 | ||||||||
\(229\) | 846.348 | 0.244228 | 0.122114 | − | 0.992516i | \(-0.461033\pi\) | ||||
0.122114 | + | 0.992516i | \(0.461033\pi\) | |||||||
\(230\) | 703.197 | 0.201597 | ||||||||
\(231\) | −6851.31 | −1.95144 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 823.620 | 0.231576 | 0.115788 | − | 0.993274i | \(-0.463061\pi\) | ||||
0.115788 | + | 0.993274i | \(0.463061\pi\) | |||||||
\(234\) | 572.059 | 0.159815 | ||||||||
\(235\) | −694.243 | −0.192712 | ||||||||
\(236\) | 10865.3 | 2.99691 | ||||||||
\(237\) | 5157.93 | 1.41369 | ||||||||
\(238\) | −3218.51 | −0.876575 | ||||||||
\(239\) | −2471.50 | −0.668903 | −0.334452 | − | 0.942413i | \(-0.608551\pi\) | ||||
−0.334452 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(240\) | 3476.31 | 0.934978 | ||||||||
\(241\) | −1148.79 | −0.307055 | −0.153527 | − | 0.988144i | \(-0.549063\pi\) | ||||
−0.153527 | + | 0.988144i | \(0.549063\pi\) | |||||||
\(242\) | 7584.69 | 2.01472 | ||||||||
\(243\) | −3746.03 | −0.988922 | ||||||||
\(244\) | −4916.08 | −1.28983 | ||||||||
\(245\) | 153.031 | 0.0399053 | ||||||||
\(246\) | 3279.01 | 0.849846 | ||||||||
\(247\) | −538.441 | −0.138705 | ||||||||
\(248\) | 253.655 | 0.0649480 | ||||||||
\(249\) | −2822.67 | −0.718391 | ||||||||
\(250\) | −2889.42 | −0.730971 | ||||||||
\(251\) | 1686.20 | 0.424032 | 0.212016 | − | 0.977266i | \(-0.431997\pi\) | ||||
0.212016 | + | 0.977266i | \(0.431997\pi\) | |||||||
\(252\) | 6675.84 | 1.66880 | ||||||||
\(253\) | −3109.91 | −0.772799 | ||||||||
\(254\) | −3413.33 | −0.843195 | ||||||||
\(255\) | −398.475 | −0.0978568 | ||||||||
\(256\) | 14343.7 | 3.50188 | ||||||||
\(257\) | 3593.97 | 0.872318 | 0.436159 | − | 0.899870i | \(-0.356338\pi\) | ||||
0.436159 | + | 0.899870i | \(0.356338\pi\) | |||||||
\(258\) | 3576.56 | 0.863051 | ||||||||
\(259\) | −3067.29 | −0.735877 | ||||||||
\(260\) | 335.057 | 0.0799205 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8266.15 | 1.94918 | ||||||||
\(263\) | 2321.87 | 0.544382 | 0.272191 | − | 0.962243i | \(-0.412252\pi\) | ||||
0.272191 | + | 0.962243i | \(0.412252\pi\) | |||||||
\(264\) | −26248.7 | −6.11931 | ||||||||
\(265\) | 803.029 | 0.186150 | ||||||||
\(266\) | −8548.51 | −1.97046 | ||||||||
\(267\) | −2952.26 | −0.676686 | ||||||||
\(268\) | −9488.66 | −2.16273 | ||||||||
\(269\) | −2365.41 | −0.536140 | −0.268070 | − | 0.963399i | \(-0.586386\pi\) | ||||
−0.268070 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(270\) | −930.246 | −0.209678 | ||||||||
\(271\) | −1732.51 | −0.388348 | −0.194174 | − | 0.980967i | \(-0.562203\pi\) | ||||
−0.194174 | + | 0.980967i | \(0.562203\pi\) | |||||||
\(272\) | −7222.20 | −1.60996 | ||||||||
\(273\) | 927.065 | 0.205526 | ||||||||
\(274\) | 161.446 | 0.0355961 | ||||||||
\(275\) | 6269.73 | 1.37483 | ||||||||
\(276\) | 8567.42 | 1.86847 | ||||||||
\(277\) | −688.616 | −0.149368 | −0.0746839 | − | 0.997207i | \(-0.523795\pi\) | ||||
−0.0746839 | + | 0.997207i | \(0.523795\pi\) | |||||||
\(278\) | 6937.85 | 1.49678 | ||||||||
\(279\) | 48.0557 | 0.0103119 | ||||||||
\(280\) | 3402.02 | 0.726105 | ||||||||
\(281\) | 2224.44 | 0.472238 | 0.236119 | − | 0.971724i | \(-0.424125\pi\) | ||||
0.236119 | + | 0.971724i | \(0.424125\pi\) | |||||||
\(282\) | −11507.2 | −2.42995 | ||||||||
\(283\) | 5037.52 | 1.05813 | 0.529063 | − | 0.848582i | \(-0.322543\pi\) | ||||
0.529063 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(284\) | −19952.1 | −4.16881 | ||||||||
\(285\) | −1058.37 | −0.219973 | ||||||||
\(286\) | −2015.93 | −0.416798 | ||||||||
\(287\) | 1879.50 | 0.386561 | ||||||||
\(288\) | 11160.8 | 2.28353 | ||||||||
\(289\) | −4085.15 | −0.831498 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5194.75 | −1.04647 | ||||||||
\(292\) | 24132.3 | 4.83642 | ||||||||
\(293\) | 6761.01 | 1.34806 | 0.674032 | − | 0.738702i | \(-0.264561\pi\) | ||||
0.674032 | + | 0.738702i | \(0.264561\pi\) | |||||||
\(294\) | 2536.53 | 0.503174 | ||||||||
\(295\) | 1049.00 | 0.207034 | ||||||||
\(296\) | −11751.4 | −2.30755 | ||||||||
\(297\) | 4114.03 | 0.803773 | ||||||||
\(298\) | 4541.66 | 0.882857 | ||||||||
\(299\) | 420.807 | 0.0813910 | ||||||||
\(300\) | −17272.4 | −3.32407 | ||||||||
\(301\) | 2050.05 | 0.392568 | ||||||||
\(302\) | −14462.7 | −2.75574 | ||||||||
\(303\) | 4775.19 | 0.905371 | ||||||||
\(304\) | −19182.5 | −3.61905 | ||||||||
\(305\) | −474.625 | −0.0891047 | ||||||||
\(306\) | −2336.09 | −0.436424 | ||||||||
\(307\) | −8860.99 | −1.64731 | −0.823653 | − | 0.567093i | \(-0.808068\pi\) | ||||
−0.823653 | + | 0.567093i | \(0.808068\pi\) | |||||||
\(308\) | −23525.6 | −4.35226 | ||||||||
\(309\) | 13131.1 | 2.41748 | ||||||||
\(310\) | 38.2921 | 0.00701563 | ||||||||
\(311\) | −4127.77 | −0.752619 | −0.376309 | − | 0.926494i | \(-0.622807\pi\) | ||||
−0.376309 | + | 0.926494i | \(0.622807\pi\) | |||||||
\(312\) | 3551.76 | 0.644484 | ||||||||
\(313\) | −5384.53 | −0.972369 | −0.486184 | − | 0.873856i | \(-0.661612\pi\) | ||||
−0.486184 | + | 0.873856i | \(0.661612\pi\) | |||||||
\(314\) | −1288.77 | −0.231622 | ||||||||
\(315\) | 644.522 | 0.115285 | ||||||||
\(316\) | 17711.0 | 3.15291 | ||||||||
\(317\) | 5379.49 | 0.953129 | 0.476565 | − | 0.879139i | \(-0.341882\pi\) | ||||
0.476565 | + | 0.879139i | \(0.341882\pi\) | |||||||
\(318\) | 13310.4 | 2.34720 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4590.49 | 0.801926 | ||||||||
\(321\) | 10304.9 | 1.79178 | ||||||||
\(322\) | 6680.90 | 1.15625 | ||||||||
\(323\) | 2198.81 | 0.378778 | ||||||||
\(324\) | −20187.9 | −3.46157 | ||||||||
\(325\) | −848.369 | −0.144797 | ||||||||
\(326\) | 9070.84 | 1.54106 | ||||||||
\(327\) | −1484.44 | −0.251039 | ||||||||
\(328\) | 7200.71 | 1.21217 | ||||||||
\(329\) | −6595.83 | −1.10529 | ||||||||
\(330\) | −3962.54 | −0.661002 | ||||||||
\(331\) | −5825.09 | −0.967298 | −0.483649 | − | 0.875262i | \(-0.660689\pi\) | ||||
−0.483649 | + | 0.875262i | \(0.660689\pi\) | |||||||
\(332\) | −9692.29 | −1.60221 | ||||||||
\(333\) | −2226.34 | −0.366374 | ||||||||
\(334\) | −20244.7 | −3.31658 | ||||||||
\(335\) | −916.087 | −0.149407 | ||||||||
\(336\) | 33027.6 | 5.36251 | ||||||||
\(337\) | 3627.26 | 0.586318 | 0.293159 | − | 0.956064i | \(-0.405293\pi\) | ||||
0.293159 | + | 0.956064i | \(0.405293\pi\) | |||||||
\(338\) | −11799.5 | −1.89884 | ||||||||
\(339\) | 10242.8 | 1.64104 | ||||||||
\(340\) | −1368.26 | −0.218248 | ||||||||
\(341\) | −169.348 | −0.0268935 | ||||||||
\(342\) | −6204.78 | −0.981041 | ||||||||
\(343\) | −5528.64 | −0.870317 | ||||||||
\(344\) | 7854.14 | 1.23101 | ||||||||
\(345\) | 827.145 | 0.129078 | ||||||||
\(346\) | −16889.0 | −2.62415 | ||||||||
\(347\) | 1172.68 | 0.181421 | 0.0907104 | − | 0.995877i | \(-0.471086\pi\) | ||||
0.0907104 | + | 0.995877i | \(0.471086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −173.078 | −0.0265463 | −0.0132731 | − | 0.999912i | \(-0.504225\pi\) | ||||
−0.0132731 | + | 0.999912i | \(0.504225\pi\) | |||||||
\(350\) | −13469.0 | −2.05700 | ||||||||
\(351\) | −556.678 | −0.0846532 | ||||||||
\(352\) | −39330.5 | −5.95547 | ||||||||
\(353\) | 13008.4 | 1.96137 | 0.980687 | − | 0.195582i | \(-0.0626596\pi\) | ||||
0.980687 | + | 0.195582i | \(0.0626596\pi\) | |||||||
\(354\) | 17387.4 | 2.61053 | ||||||||
\(355\) | −1926.29 | −0.287991 | ||||||||
\(356\) | −10137.3 | −1.50920 | ||||||||
\(357\) | −3785.82 | −0.561251 | ||||||||
\(358\) | 16378.6 | 2.41798 | ||||||||
\(359\) | 4487.40 | 0.659710 | 0.329855 | − | 0.944032i | \(-0.393000\pi\) | ||||
0.329855 | + | 0.944032i | \(0.393000\pi\) | |||||||
\(360\) | 2469.29 | 0.361508 | ||||||||
\(361\) | −1018.85 | −0.148543 | ||||||||
\(362\) | 17281.8 | 2.50915 | ||||||||
\(363\) | 8921.60 | 1.28998 | ||||||||
\(364\) | 3183.29 | 0.458379 | ||||||||
\(365\) | 2329.86 | 0.334111 | ||||||||
\(366\) | −7867.02 | −1.12354 | ||||||||
\(367\) | −1674.11 | −0.238114 | −0.119057 | − | 0.992887i | \(-0.537987\pi\) | ||||
−0.119057 | + | 0.992887i | \(0.537987\pi\) | |||||||
\(368\) | 14991.7 | 2.12363 | ||||||||
\(369\) | 1364.20 | 0.192459 | ||||||||
\(370\) | −1774.00 | −0.249260 | ||||||||
\(371\) | 7629.39 | 1.06765 | ||||||||
\(372\) | 466.533 | 0.0650231 | ||||||||
\(373\) | −6800.89 | −0.944066 | −0.472033 | − | 0.881581i | \(-0.656480\pi\) | ||||
−0.472033 | + | 0.881581i | \(0.656480\pi\) | |||||||
\(374\) | 8232.37 | 1.13820 | ||||||||
\(375\) | −3398.72 | −0.468024 | ||||||||
\(376\) | −25269.9 | −3.46595 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8838.04 | −1.20259 | ||||||||
\(379\) | −10216.7 | −1.38468 | −0.692341 | − | 0.721571i | \(-0.743421\pi\) | ||||
−0.692341 | + | 0.721571i | \(0.743421\pi\) | |||||||
\(380\) | −3634.16 | −0.490601 | ||||||||
\(381\) | −4014.98 | −0.539879 | ||||||||
\(382\) | 11679.7 | 1.56436 | ||||||||
\(383\) | −7184.47 | −0.958509 | −0.479255 | − | 0.877676i | \(-0.659093\pi\) | ||||
−0.479255 | + | 0.877676i | \(0.659093\pi\) | |||||||
\(384\) | 37032.1 | 4.92131 | ||||||||
\(385\) | −2271.29 | −0.300664 | ||||||||
\(386\) | −16953.3 | −2.23549 | ||||||||
\(387\) | 1487.99 | 0.195449 | ||||||||
\(388\) | −17837.4 | −2.33391 | ||||||||
\(389\) | 3848.67 | 0.501633 | 0.250817 | − | 0.968035i | \(-0.419301\pi\) | ||||
0.250817 | + | 0.968035i | \(0.419301\pi\) | |||||||
\(390\) | 536.179 | 0.0696166 | ||||||||
\(391\) | −1718.43 | −0.222263 | ||||||||
\(392\) | 5570.22 | 0.717700 | ||||||||
\(393\) | 9723.18 | 1.24801 | ||||||||
\(394\) | −13651.7 | −1.74560 | ||||||||
\(395\) | 1709.91 | 0.217810 | ||||||||
\(396\) | −17075.6 | −2.16687 | ||||||||
\(397\) | −1622.51 | −0.205117 | −0.102559 | − | 0.994727i | \(-0.532703\pi\) | ||||
−0.102559 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(398\) | 30164.5 | 3.79902 | ||||||||
\(399\) | −10055.3 | −1.26164 | ||||||||
\(400\) | −30224.0 | −3.77800 | ||||||||
\(401\) | 13842.9 | 1.72389 | 0.861947 | − | 0.506999i | \(-0.169245\pi\) | ||||
0.861947 | + | 0.506999i | \(0.169245\pi\) | |||||||
\(402\) | −15184.4 | −1.88390 | ||||||||
\(403\) | 22.9148 | 0.00283242 | ||||||||
\(404\) | 16396.7 | 2.01923 | ||||||||
\(405\) | −1949.05 | −0.239133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7845.58 | 0.955506 | ||||||||
\(408\) | −14504.2 | −1.75996 | ||||||||
\(409\) | −3357.24 | −0.405880 | −0.202940 | − | 0.979191i | \(-0.565050\pi\) | ||||
−0.202940 | + | 0.979191i | \(0.565050\pi\) | |||||||
\(410\) | 1087.03 | 0.130938 | ||||||||
\(411\) | 189.904 | 0.0227914 | ||||||||
\(412\) | 45088.7 | 5.39165 | ||||||||
\(413\) | 9966.26 | 1.18743 | ||||||||
\(414\) | 4849.21 | 0.575666 | ||||||||
\(415\) | −935.746 | −0.110684 | ||||||||
\(416\) | 5321.89 | 0.627229 | ||||||||
\(417\) | 8160.74 | 0.958353 | ||||||||
\(418\) | 21865.6 | 2.55856 | ||||||||
\(419\) | 1652.11 | 0.192627 | 0.0963134 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963134 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(420\) | 6257.13 | 0.726945 | ||||||||
\(421\) | 6405.13 | 0.741490 | 0.370745 | − | 0.928735i | \(-0.379102\pi\) | ||||
0.370745 | + | 0.928735i | \(0.379102\pi\) | |||||||
\(422\) | 10355.9 | 1.19459 | ||||||||
\(423\) | −4787.46 | −0.550294 | ||||||||
\(424\) | 29229.7 | 3.34792 | ||||||||
\(425\) | 3464.45 | 0.395413 | ||||||||
\(426\) | −31928.7 | −3.63133 | ||||||||
\(427\) | −4509.30 | −0.511054 | ||||||||
\(428\) | 35384.2 | 3.99616 | ||||||||
\(429\) | −2371.27 | −0.266867 | ||||||||
\(430\) | 1185.67 | 0.132972 | ||||||||
\(431\) | 252.536 | 0.0282233 | 0.0141116 | − | 0.999900i | \(-0.495508\pi\) | ||||
0.0141116 | + | 0.999900i | \(0.495508\pi\) | |||||||
\(432\) | −19832.2 | −2.20874 | ||||||||
\(433\) | 12779.1 | 1.41831 | 0.709153 | − | 0.705055i | \(-0.249078\pi\) | ||||
0.709153 | + | 0.705055i | \(0.249078\pi\) | |||||||
\(434\) | 363.804 | 0.0402377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5097.18 | −0.559887 | ||||||||
\(437\) | −4564.24 | −0.499628 | ||||||||
\(438\) | 38618.0 | 4.21287 | ||||||||
\(439\) | −3760.84 | −0.408873 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(440\) | −8701.75 | −0.942817 | ||||||||
\(441\) | 1055.29 | 0.113950 | ||||||||
\(442\) | −1113.94 | −0.119875 | ||||||||
\(443\) | −3713.77 | −0.398299 | −0.199149 | − | 0.979969i | \(-0.563818\pi\) | ||||
−0.199149 | + | 0.979969i | \(0.563818\pi\) | |||||||
\(444\) | −21613.6 | −2.31022 | ||||||||
\(445\) | −978.707 | −0.104259 | ||||||||
\(446\) | −28620.1 | −3.03856 | ||||||||
\(447\) | 5342.20 | 0.565274 | ||||||||
\(448\) | 43613.2 | 4.59939 | ||||||||
\(449\) | 12043.9 | 1.26589 | 0.632947 | − | 0.774195i | \(-0.281845\pi\) | ||||
0.632947 | + | 0.774195i | \(0.281845\pi\) | |||||||
\(450\) | −9776.26 | −1.02413 | ||||||||
\(451\) | −4807.41 | −0.501934 | ||||||||
\(452\) | 35171.0 | 3.65997 | ||||||||
\(453\) | −17011.9 | −1.76444 | ||||||||
\(454\) | −28811.2 | −2.97837 | ||||||||
\(455\) | 307.333 | 0.0316659 | ||||||||
\(456\) | −38523.8 | −3.95624 | ||||||||
\(457\) | −12995.7 | −1.33023 | −0.665113 | − | 0.746743i | \(-0.731617\pi\) | ||||
−0.665113 | + | 0.746743i | \(0.731617\pi\) | |||||||
\(458\) | 4650.58 | 0.474470 | ||||||||
\(459\) | 2273.28 | 0.231172 | ||||||||
\(460\) | 2840.20 | 0.287880 | ||||||||
\(461\) | −7874.30 | −0.795538 | −0.397769 | − | 0.917486i | \(-0.630215\pi\) | ||||
−0.397769 | + | 0.917486i | \(0.630215\pi\) | |||||||
\(462\) | −37647.1 | −3.79113 | ||||||||
\(463\) | −3466.08 | −0.347910 | −0.173955 | − | 0.984754i | \(-0.555655\pi\) | ||||
−0.173955 | + | 0.984754i | \(0.555655\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.0416 | 0.00449195 | ||||||||
\(466\) | 4525.69 | 0.449890 | ||||||||
\(467\) | −14835.9 | −1.47007 | −0.735034 | − | 0.678030i | \(-0.762834\pi\) | ||||
−0.735034 | + | 0.678030i | \(0.762834\pi\) | |||||||
\(468\) | 2310.54 | 0.228215 | ||||||||
\(469\) | −8703.53 | −0.856912 | ||||||||
\(470\) | −3814.78 | −0.374389 | ||||||||
\(471\) | −1515.93 | −0.148302 | ||||||||
\(472\) | 38182.7 | 3.72352 | ||||||||
\(473\) | −5243.66 | −0.509733 | ||||||||
\(474\) | 28342.2 | 2.74642 | ||||||||
\(475\) | 9201.74 | 0.888853 | ||||||||
\(476\) | −12999.5 | −1.25175 | ||||||||
\(477\) | 5537.65 | 0.531555 | ||||||||
\(478\) | −13580.6 | −1.29950 | ||||||||
\(479\) | −8119.86 | −0.774542 | −0.387271 | − | 0.921966i | \(-0.626582\pi\) | ||||
−0.387271 | + | 0.921966i | \(0.626582\pi\) | |||||||
\(480\) | 10460.8 | 0.994724 | ||||||||
\(481\) | −1061.60 | −0.100634 | ||||||||
\(482\) | −6312.48 | −0.596526 | ||||||||
\(483\) | 7858.51 | 0.740320 | ||||||||
\(484\) | 30634.4 | 2.87701 | ||||||||
\(485\) | −1722.12 | −0.161232 | ||||||||
\(486\) | −20584.0 | −1.92121 | ||||||||
\(487\) | 9698.92 | 0.902464 | 0.451232 | − | 0.892407i | \(-0.350985\pi\) | ||||
0.451232 | + | 0.892407i | \(0.350985\pi\) | |||||||
\(488\) | −17276.0 | −1.60256 | ||||||||
\(489\) | 10669.7 | 0.986709 | ||||||||
\(490\) | 840.887 | 0.0775253 | ||||||||
\(491\) | 6844.25 | 0.629076 | 0.314538 | − | 0.949245i | \(-0.398150\pi\) | ||||
0.314538 | + | 0.949245i | \(0.398150\pi\) | |||||||
\(492\) | 13243.9 | 1.21358 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2958.67 | −0.269467 | ||||||||
\(495\) | −1648.57 | −0.149693 | ||||||||
\(496\) | 816.361 | 0.0739026 | ||||||||
\(497\) | −18301.2 | −1.65175 | ||||||||
\(498\) | −15510.2 | −1.39564 | ||||||||
\(499\) | −18603.4 | −1.66895 | −0.834473 | − | 0.551049i | \(-0.814228\pi\) | ||||
−0.834473 | + | 0.551049i | \(0.814228\pi\) | |||||||
\(500\) | −11670.3 | −1.04382 | ||||||||
\(501\) | −23813.1 | −2.12353 | ||||||||
\(502\) | 9265.47 | 0.823781 | ||||||||
\(503\) | −10624.8 | −0.941822 | −0.470911 | − | 0.882181i | \(-0.656075\pi\) | ||||
−0.470911 | + | 0.882181i | \(0.656075\pi\) | |||||||
\(504\) | 23460.1 | 2.07341 | ||||||||
\(505\) | 1583.03 | 0.139493 | ||||||||
\(506\) | −17088.6 | −1.50134 | ||||||||
\(507\) | −13879.3 | −1.21578 | ||||||||
\(508\) | −13786.4 | −1.20408 | ||||||||
\(509\) | −7931.22 | −0.690658 | −0.345329 | − | 0.938482i | \(-0.612233\pi\) | ||||
−0.345329 | + | 0.938482i | \(0.612233\pi\) | |||||||
\(510\) | −2189.57 | −0.190110 | ||||||||
\(511\) | 22135.4 | 1.91627 | ||||||||
\(512\) | 32981.1 | 2.84682 | ||||||||
\(513\) | 6037.95 | 0.519653 | ||||||||
\(514\) | 19748.4 | 1.69468 | ||||||||
\(515\) | 4353.10 | 0.372467 | ||||||||
\(516\) | 14445.7 | 1.23243 | ||||||||
\(517\) | 16871.0 | 1.43517 | ||||||||
\(518\) | −16854.4 | −1.42961 | ||||||||
\(519\) | −19865.9 | −1.68018 | ||||||||
\(520\) | 1177.45 | 0.0992974 | ||||||||
\(521\) | 13771.1 | 1.15801 | 0.579005 | − | 0.815324i | \(-0.303441\pi\) | ||||
0.579005 | + | 0.815324i | \(0.303441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20397.1 | 1.70536 | 0.852680 | − | 0.522433i | \(-0.174976\pi\) | ||||
0.852680 | + | 0.522433i | \(0.174976\pi\) | |||||||
\(524\) | 33386.8 | 2.78342 | ||||||||
\(525\) | −15843.2 | −1.31705 | ||||||||
\(526\) | 12758.4 | 1.05759 | ||||||||
\(527\) | −93.5761 | −0.00773480 | ||||||||
\(528\) | −84478.6 | −6.96299 | ||||||||
\(529\) | −8599.91 | −0.706823 | ||||||||
\(530\) | 4412.55 | 0.361640 | ||||||||
\(531\) | 7233.83 | 0.591189 | ||||||||
\(532\) | −34527.3 | −2.81381 | ||||||||
\(533\) | 650.501 | 0.0528636 | ||||||||
\(534\) | −16222.3 | −1.31462 | ||||||||
\(535\) | 3416.18 | 0.276064 | ||||||||
\(536\) | −33344.9 | −2.68709 | ||||||||
\(537\) | 19265.6 | 1.54817 | ||||||||
\(538\) | −12997.7 | −1.04158 | ||||||||
\(539\) | −3718.85 | −0.297184 | ||||||||
\(540\) | −3757.24 | −0.299419 | ||||||||
\(541\) | −1883.72 | −0.149699 | −0.0748496 | − | 0.997195i | \(-0.523848\pi\) | ||||
−0.0748496 | + | 0.997195i | \(0.523848\pi\) | |||||||
\(542\) | −9519.92 | −0.754457 | ||||||||
\(543\) | 20328.0 | 1.60655 | ||||||||
\(544\) | −21732.8 | −1.71284 | ||||||||
\(545\) | −492.110 | −0.0386783 | ||||||||
\(546\) | 5094.11 | 0.399282 | ||||||||
\(547\) | −9079.06 | −0.709676 | −0.354838 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354838 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(548\) | 652.079 | 0.0508311 | ||||||||
\(549\) | −3272.99 | −0.254440 | ||||||||
\(550\) | 34451.4 | 2.67093 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 30107.5 | 2.32148 | ||||||||
\(553\) | 16245.5 | 1.24924 | ||||||||
\(554\) | −3783.86 | −0.290182 | ||||||||
\(555\) | −2086.70 | −0.159595 | ||||||||
\(556\) | 28021.8 | 2.13739 | ||||||||
\(557\) | −5982.38 | −0.455084 | −0.227542 | − | 0.973768i | \(-0.573069\pi\) | ||||
−0.227542 | + | 0.973768i | \(0.573069\pi\) | |||||||
\(558\) | 264.060 | 0.0200333 | ||||||||
\(559\) | 709.530 | 0.0536850 | ||||||||
\(560\) | 10949.0 | 0.826215 | ||||||||
\(561\) | 9683.44 | 0.728762 | ||||||||
\(562\) | 12223.0 | 0.917432 | ||||||||
\(563\) | 7837.88 | 0.586727 | 0.293363 | − | 0.956001i | \(-0.405225\pi\) | ||||
0.293363 | + | 0.956001i | \(0.405225\pi\) | |||||||
\(564\) | −46477.5 | −3.46996 | ||||||||
\(565\) | 3395.60 | 0.252839 | ||||||||
\(566\) | 27680.6 | 2.05566 | ||||||||
\(567\) | −18517.4 | −1.37153 | ||||||||
\(568\) | −70115.4 | −5.17954 | ||||||||
\(569\) | −10019.2 | −0.738182 | −0.369091 | − | 0.929393i | \(-0.620331\pi\) | ||||
−0.369091 | + | 0.929393i | \(0.620331\pi\) | |||||||
\(570\) | −5815.61 | −0.427349 | ||||||||
\(571\) | 8832.38 | 0.647327 | 0.323663 | − | 0.946172i | \(-0.395085\pi\) | ||||
0.323663 | + | 0.946172i | \(0.395085\pi\) | |||||||
\(572\) | −8142.30 | −0.595186 | ||||||||
\(573\) | 13738.4 | 1.00162 | ||||||||
\(574\) | 10327.6 | 0.750986 | ||||||||
\(575\) | −7191.43 | −0.521571 | ||||||||
\(576\) | 31655.8 | 2.28992 | ||||||||
\(577\) | 17583.3 | 1.26863 | 0.634317 | − | 0.773073i | \(-0.281281\pi\) | ||||
0.634317 | + | 0.773073i | \(0.281281\pi\) | |||||||
\(578\) | −22447.4 | −1.61538 | ||||||||
\(579\) | −19941.6 | −1.43133 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8890.30 | −0.634823 | ||||||||
\(582\) | −28544.6 | −2.03301 | ||||||||
\(583\) | −19514.6 | −1.38630 | ||||||||
\(584\) | 84805.2 | 6.00901 | ||||||||
\(585\) | 223.072 | 0.0157656 | ||||||||
\(586\) | 37151.0 | 2.61893 | ||||||||
\(587\) | −10120.7 | −0.711630 | −0.355815 | − | 0.934556i | \(-0.615797\pi\) | ||||
−0.355815 | + | 0.934556i | \(0.615797\pi\) | |||||||
\(588\) | 10245.0 | 0.718530 | ||||||||
\(589\) | −248.543 | −0.0173871 | ||||||||
\(590\) | 5764.11 | 0.402211 | ||||||||
\(591\) | −16058.1 | −1.11767 | ||||||||
\(592\) | −37820.6 | −2.62570 | ||||||||
\(593\) | 3597.06 | 0.249095 | 0.124548 | − | 0.992214i | \(-0.460252\pi\) | ||||
0.124548 | + | 0.992214i | \(0.460252\pi\) | |||||||
\(594\) | 22606.1 | 1.56152 | ||||||||
\(595\) | −1255.04 | −0.0864734 | ||||||||
\(596\) | 18343.7 | 1.26072 | ||||||||
\(597\) | 35481.5 | 2.43243 | ||||||||
\(598\) | 2312.29 | 0.158121 | ||||||||
\(599\) | 7987.90 | 0.544870 | 0.272435 | − | 0.962174i | \(-0.412171\pi\) | ||||
0.272435 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(600\) | −60698.2 | −4.12999 | ||||||||
\(601\) | −2646.60 | −0.179629 | −0.0898147 | − | 0.995958i | \(-0.528627\pi\) | ||||
−0.0898147 | + | 0.995958i | \(0.528627\pi\) | |||||||
\(602\) | 11264.8 | 0.762655 | ||||||||
\(603\) | −6317.29 | −0.426634 | ||||||||
\(604\) | −58414.5 | −3.93518 | ||||||||
\(605\) | 2957.61 | 0.198751 | ||||||||
\(606\) | 26239.1 | 1.75889 | ||||||||
\(607\) | 15181.8 | 1.01517 | 0.507587 | − | 0.861600i | \(-0.330537\pi\) | ||||
0.507587 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(608\) | −57723.3 | −3.85031 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2608.01 | −0.173107 | ||||||||
\(611\) | −2282.84 | −0.151152 | ||||||||
\(612\) | −9435.44 | −0.623211 | ||||||||
\(613\) | −9721.86 | −0.640558 | −0.320279 | − | 0.947323i | \(-0.603777\pi\) | ||||
−0.320279 | + | 0.947323i | \(0.603777\pi\) | |||||||
\(614\) | −48690.1 | −3.20028 | ||||||||
\(615\) | 1278.63 | 0.0838366 | ||||||||
\(616\) | −82673.2 | −5.40747 | ||||||||
\(617\) | 14150.2 | 0.923282 | 0.461641 | − | 0.887067i | \(-0.347261\pi\) | ||||
0.461641 | + | 0.887067i | \(0.347261\pi\) | |||||||
\(618\) | 72153.7 | 4.69652 | ||||||||
\(619\) | 10804.4 | 0.701560 | 0.350780 | − | 0.936458i | \(-0.385917\pi\) | ||||
0.350780 | + | 0.936458i | \(0.385917\pi\) | |||||||
\(620\) | 154.661 | 0.0100183 | ||||||||
\(621\) | −4718.83 | −0.304928 | ||||||||
\(622\) | −22681.6 | −1.46214 | ||||||||
\(623\) | −9298.46 | −0.597970 | ||||||||
\(624\) | 11431.0 | 0.733341 | ||||||||
\(625\) | 13924.4 | 0.891161 | ||||||||
\(626\) | −29587.3 | −1.88905 | ||||||||
\(627\) | 25719.7 | 1.63819 | ||||||||
\(628\) | −5205.30 | −0.330755 | ||||||||
\(629\) | 4335.22 | 0.274811 | ||||||||
\(630\) | 3541.57 | 0.223968 | ||||||||
\(631\) | 20692.1 | 1.30545 | 0.652725 | − | 0.757595i | \(-0.273626\pi\) | ||||
0.652725 | + | 0.757595i | \(0.273626\pi\) | |||||||
\(632\) | 62239.6 | 3.91734 | ||||||||
\(633\) | 12181.3 | 0.764869 | ||||||||
\(634\) | 29559.6 | 1.85168 | ||||||||
\(635\) | −1331.01 | −0.0831805 | ||||||||
\(636\) | 53760.5 | 3.35179 | ||||||||
\(637\) | 503.204 | 0.0312993 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13283.6 | −0.822364 | ||||||||
\(640\) | 12276.6 | 0.758239 | ||||||||
\(641\) | 1995.59 | 0.122966 | 0.0614828 | − | 0.998108i | \(-0.480417\pi\) | ||||
0.0614828 | + | 0.998108i | \(0.480417\pi\) | |||||||
\(642\) | 56624.0 | 3.48095 | ||||||||
\(643\) | 10911.2 | 0.669203 | 0.334602 | − | 0.942360i | \(-0.391398\pi\) | ||||
0.334602 | + | 0.942360i | \(0.391398\pi\) | |||||||
\(644\) | 26984.0 | 1.65112 | ||||||||
\(645\) | 1394.66 | 0.0851392 | ||||||||
\(646\) | 12082.2 | 0.735864 | ||||||||
\(647\) | 20046.3 | 1.21808 | 0.609042 | − | 0.793138i | \(-0.291554\pi\) | ||||
0.609042 | + | 0.793138i | \(0.291554\pi\) | |||||||
\(648\) | −70943.9 | −4.30083 | ||||||||
\(649\) | −25491.9 | −1.54183 | ||||||||
\(650\) | −4661.69 | −0.281302 | ||||||||
\(651\) | 427.930 | 0.0257633 | ||||||||
\(652\) | 36636.9 | 2.20063 | ||||||||
\(653\) | −20205.6 | −1.21088 | −0.605441 | − | 0.795890i | \(-0.707003\pi\) | ||||
−0.605441 | + | 0.795890i | \(0.707003\pi\) | |||||||
\(654\) | −8156.84 | −0.487703 | ||||||||
\(655\) | 3223.35 | 0.192285 | ||||||||
\(656\) | 23174.7 | 1.37930 | ||||||||
\(657\) | 16066.6 | 0.954061 | ||||||||
\(658\) | −36243.3 | −2.14728 | ||||||||
\(659\) | 9268.73 | 0.547888 | 0.273944 | − | 0.961746i | \(-0.411672\pi\) | ||||
0.273944 | + | 0.961746i | \(0.411672\pi\) | |||||||
\(660\) | −16004.6 | −0.943908 | ||||||||
\(661\) | −18209.9 | −1.07153 | −0.535765 | − | 0.844367i | \(-0.679977\pi\) | ||||
−0.535765 | + | 0.844367i | \(0.679977\pi\) | |||||||
\(662\) | −32008.1 | −1.87920 | ||||||||
\(663\) | −1310.29 | −0.0767531 | ||||||||
\(664\) | −34060.5 | −1.99067 | ||||||||
\(665\) | −3333.45 | −0.194384 | ||||||||
\(666\) | −12233.4 | −0.711767 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −81767.8 | −4.73607 | ||||||||
\(669\) | −33664.8 | −1.94552 | ||||||||
\(670\) | −5033.79 | −0.290257 | ||||||||
\(671\) | 11534.0 | 0.663583 | ||||||||
\(672\) | 99385.5 | 5.70518 | ||||||||
\(673\) | −63.9154 | −0.00366086 | −0.00183043 | − | 0.999998i | \(-0.500583\pi\) | ||||
−0.00183043 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(674\) | 19931.3 | 1.13906 | ||||||||
\(675\) | 9513.40 | 0.542476 | ||||||||
\(676\) | −47657.8 | −2.71153 | ||||||||
\(677\) | −11436.2 | −0.649231 | −0.324616 | − | 0.945846i | \(-0.605235\pi\) | ||||
−0.324616 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(678\) | 56282.9 | 3.18810 | ||||||||
\(679\) | −16361.5 | −0.924735 | ||||||||
\(680\) | −4808.31 | −0.271162 | ||||||||
\(681\) | −33889.6 | −1.90698 | ||||||||
\(682\) | −930.545 | −0.0522470 | ||||||||
\(683\) | −22719.5 | −1.27282 | −0.636410 | − | 0.771351i | \(-0.719581\pi\) | ||||
−0.636410 | + | 0.771351i | \(0.719581\pi\) | |||||||
\(684\) | −25061.0 | −1.40092 | ||||||||
\(685\) | 62.9553 | 0.00351153 | ||||||||
\(686\) | −30379.2 | −1.69079 | ||||||||
\(687\) | 5470.31 | 0.303793 | ||||||||
\(688\) | 25277.7 | 1.40073 | ||||||||
\(689\) | 2640.56 | 0.146005 | ||||||||
\(690\) | 4545.07 | 0.250765 | ||||||||
\(691\) | 10495.0 | 0.577783 | 0.288891 | − | 0.957362i | \(-0.406713\pi\) | ||||
0.288891 | + | 0.957362i | \(0.406713\pi\) | |||||||
\(692\) | −68214.1 | −3.74727 | ||||||||
\(693\) | −15662.7 | −0.858552 | ||||||||
\(694\) | 6443.76 | 0.352452 | ||||||||
\(695\) | 2705.38 | 0.147656 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2656.42 | −0.144360 | ||||||||
\(698\) | −951.043 | −0.0515723 | ||||||||
\(699\) | 5323.41 | 0.288054 | ||||||||
\(700\) | −54401.2 | −2.93739 | ||||||||
\(701\) | −6530.49 | −0.351859 | −0.175930 | − | 0.984403i | \(-0.556293\pi\) | ||||
−0.175930 | + | 0.984403i | \(0.556293\pi\) | |||||||
\(702\) | −3058.88 | −0.164459 | ||||||||
\(703\) | 11514.5 | 0.617751 | ||||||||
\(704\) | −111555. | −5.97212 | ||||||||
\(705\) | −4487.19 | −0.239713 | ||||||||
\(706\) | 71479.4 | 3.81043 | ||||||||
\(707\) | 15040.0 | 0.800052 | ||||||||
\(708\) | 70227.2 | 3.72782 | ||||||||
\(709\) | −16597.7 | −0.879183 | −0.439591 | − | 0.898198i | \(-0.644877\pi\) | ||||
−0.439591 | + | 0.898198i | \(0.644877\pi\) | |||||||
\(710\) | −10584.7 | −0.559489 | ||||||||
\(711\) | 11791.5 | 0.621962 | ||||||||
\(712\) | −35624.2 | −1.87510 | ||||||||
\(713\) | 194.243 | 0.0102026 | ||||||||
\(714\) | −20802.6 | −1.09036 | ||||||||
\(715\) | −786.102 | −0.0411168 | ||||||||
\(716\) | 66152.8 | 3.45286 | ||||||||
\(717\) | −15974.4 | −0.832041 | ||||||||
\(718\) | 24657.7 | 1.28164 | ||||||||
\(719\) | 6525.25 | 0.338457 | 0.169229 | − | 0.985577i | \(-0.445872\pi\) | ||||
0.169229 | + | 0.985577i | \(0.445872\pi\) | |||||||
\(720\) | 7947.14 | 0.411351 | ||||||||
\(721\) | 41357.8 | 2.13626 | ||||||||
\(722\) | −5598.48 | −0.288579 | ||||||||
\(723\) | −7425.14 | −0.381942 | ||||||||
\(724\) | 69800.8 | 3.58305 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 49023.1 | 2.50609 | ||||||||
\(727\) | −1066.84 | −0.0544249 | −0.0272125 | − | 0.999630i | \(-0.508663\pi\) | ||||
−0.0272125 | + | 0.999630i | \(0.508663\pi\) | |||||||
\(728\) | 11186.7 | 0.569514 | ||||||||
\(729\) | 347.561 | 0.0176579 | ||||||||
\(730\) | 12802.3 | 0.649088 | ||||||||
\(731\) | −2897.48 | −0.146603 | ||||||||
\(732\) | −31774.7 | −1.60441 | ||||||||
\(733\) | 6226.75 | 0.313765 | 0.156883 | − | 0.987617i | \(-0.449856\pi\) | ||||
0.156883 | + | 0.987617i | \(0.449856\pi\) | |||||||
\(734\) | −9199.02 | −0.462592 | ||||||||
\(735\) | 989.106 | 0.0496377 | ||||||||
\(736\) | 45112.4 | 2.25933 | ||||||||
\(737\) | 22262.1 | 1.11266 | ||||||||
\(738\) | 7496.10 | 0.373896 | ||||||||
\(739\) | −31226.3 | −1.55437 | −0.777183 | − | 0.629274i | \(-0.783352\pi\) | ||||
−0.777183 | + | 0.629274i | \(0.783352\pi\) | |||||||
\(740\) | −7165.17 | −0.355942 | ||||||||
\(741\) | −3480.18 | −0.172534 | ||||||||
\(742\) | 41922.6 | 2.07416 | ||||||||
\(743\) | 30790.4 | 1.52031 | 0.760156 | − | 0.649741i | \(-0.225123\pi\) | ||||
0.760156 | + | 0.649741i | \(0.225123\pi\) | |||||||
\(744\) | 1639.48 | 0.0807881 | ||||||||
\(745\) | 1771.00 | 0.0870932 | ||||||||
\(746\) | −37370.1 | −1.83407 | ||||||||
\(747\) | −6452.86 | −0.316061 | ||||||||
\(748\) | 33250.4 | 1.62534 | ||||||||
\(749\) | 32456.3 | 1.58335 | ||||||||
\(750\) | −18675.6 | −0.909247 | ||||||||
\(751\) | −11908.0 | −0.578598 | −0.289299 | − | 0.957239i | \(-0.593422\pi\) | ||||
−0.289299 | + | 0.957239i | \(0.593422\pi\) | |||||||
\(752\) | −81328.5 | −3.94381 | ||||||||
\(753\) | 10898.6 | 0.527448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5639.65 | −0.271852 | ||||||||
\(756\) | −35696.7 | −1.71730 | ||||||||
\(757\) | 7197.74 | 0.345583 | 0.172792 | − | 0.984958i | \(-0.444721\pi\) | ||||
0.172792 | + | 0.984958i | \(0.444721\pi\) | |||||||
\(758\) | −56139.3 | −2.69007 | ||||||||
\(759\) | −20100.7 | −0.961275 | ||||||||
\(760\) | −12771.1 | −0.609548 | ||||||||
\(761\) | 9185.20 | 0.437534 | 0.218767 | − | 0.975777i | \(-0.429797\pi\) | ||||
0.218767 | + | 0.975777i | \(0.429797\pi\) | |||||||
\(762\) | −22061.9 | −1.04884 | ||||||||
\(763\) | −4675.42 | −0.221837 | ||||||||
\(764\) | 47174.1 | 2.23390 | ||||||||
\(765\) | −910.949 | −0.0430528 | ||||||||
\(766\) | −39477.8 | −1.86213 | ||||||||
\(767\) | 3449.36 | 0.162385 | ||||||||
\(768\) | 92709.4 | 4.35594 | ||||||||
\(769\) | −32791.1 | −1.53768 | −0.768840 | − | 0.639441i | \(-0.779166\pi\) | ||||
−0.768840 | + | 0.639441i | \(0.779166\pi\) | |||||||
\(770\) | −12480.5 | −0.584110 | ||||||||
\(771\) | 23229.4 | 1.08507 | ||||||||
\(772\) | −68474.0 | −3.19227 | ||||||||
\(773\) | 28237.1 | 1.31386 | 0.656932 | − | 0.753950i | \(-0.271854\pi\) | ||||
0.656932 | + | 0.753950i | \(0.271854\pi\) | |||||||
\(774\) | 8176.33 | 0.379706 | ||||||||
\(775\) | −391.604 | −0.0181508 | ||||||||
\(776\) | −62683.9 | −2.89977 | ||||||||
\(777\) | −19825.2 | −0.915349 | ||||||||
\(778\) | 21148.0 | 0.974540 | ||||||||
\(779\) | −7055.58 | −0.324509 | ||||||||
\(780\) | 2165.62 | 0.0994122 | ||||||||
\(781\) | 46811.2 | 2.14473 | ||||||||
\(782\) | −9442.59 | −0.431798 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17927.1 | 0.816652 | ||||||||
\(785\) | −502.548 | −0.0228493 | ||||||||
\(786\) | 53427.7 | 2.42456 | ||||||||
\(787\) | 12082.3 | 0.547254 | 0.273627 | − | 0.961836i | \(-0.411777\pi\) | ||||
0.273627 | + | 0.961836i | \(0.411777\pi\) | |||||||
\(788\) | −55139.1 | −2.49270 | ||||||||
\(789\) | 15007.2 | 0.677151 | ||||||||
\(790\) | 9395.77 | 0.423148 | ||||||||
\(791\) | 32260.8 | 1.45014 | ||||||||
\(792\) | −60006.8 | −2.69224 | ||||||||
\(793\) | −1560.68 | −0.0698884 | ||||||||
\(794\) | −8915.52 | −0.398489 | ||||||||
\(795\) | 5190.33 | 0.231550 | ||||||||
\(796\) | 121834. | 5.42499 | ||||||||
\(797\) | 1248.33 | 0.0554807 | 0.0277404 | − | 0.999615i | \(-0.491169\pi\) | ||||
0.0277404 | + | 0.999615i | \(0.491169\pi\) | |||||||
\(798\) | −55252.7 | −2.45103 | ||||||||
\(799\) | 9322.35 | 0.412767 | ||||||||
\(800\) | −90949.0 | −4.01942 | ||||||||
\(801\) | −6749.12 | −0.297713 | ||||||||
\(802\) | 76065.1 | 3.34907 | ||||||||
\(803\) | −56618.5 | −2.48820 | ||||||||
\(804\) | −61329.4 | −2.69020 | ||||||||
\(805\) | 2605.19 | 0.114063 | ||||||||
\(806\) | 125.914 | 0.00550264 | ||||||||
\(807\) | −15288.7 | −0.666898 | ||||||||
\(808\) | 57621.1 | 2.50879 | ||||||||
\(809\) | 23512.6 | 1.02183 | 0.510914 | − | 0.859632i | \(-0.329307\pi\) | ||||
0.510914 | + | 0.859632i | \(0.329307\pi\) | |||||||
\(810\) | −10709.8 | −0.464572 | ||||||||
\(811\) | 23248.4 | 1.00661 | 0.503306 | − | 0.864108i | \(-0.332117\pi\) | ||||
0.503306 | + | 0.864108i | \(0.332117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11197.9 | −0.483062 | ||||||||
\(814\) | 43110.5 | 1.85629 | ||||||||
\(815\) | 3537.13 | 0.152025 | ||||||||
\(816\) | −46680.2 | −2.00261 | ||||||||
\(817\) | −7695.84 | −0.329551 | ||||||||
\(818\) | −18447.6 | −0.788516 | ||||||||
\(819\) | 2119.35 | 0.0904226 | ||||||||
\(820\) | 4390.49 | 0.186979 | ||||||||
\(821\) | 26898.0 | 1.14342 | 0.571708 | − | 0.820457i | \(-0.306281\pi\) | ||||
0.571708 | + | 0.820457i | \(0.306281\pi\) | |||||||
\(822\) | 1043.50 | 0.0442776 | ||||||||
\(823\) | −12422.7 | −0.526158 | −0.263079 | − | 0.964774i | \(-0.584738\pi\) | ||||
−0.263079 | + | 0.964774i | \(0.584738\pi\) | |||||||
\(824\) | 158450. | 6.69886 | ||||||||
\(825\) | 40524.0 | 1.71014 | ||||||||
\(826\) | 54763.4 | 2.30686 | ||||||||
\(827\) | 4915.14 | 0.206670 | 0.103335 | − | 0.994647i | \(-0.467049\pi\) | ||||
0.103335 | + | 0.994647i | \(0.467049\pi\) | |||||||
\(828\) | 19585.9 | 0.822048 | ||||||||
\(829\) | 45226.4 | 1.89478 | 0.947392 | − | 0.320074i | \(-0.103708\pi\) | ||||
0.947392 | + | 0.320074i | \(0.103708\pi\) | |||||||
\(830\) | −5141.81 | −0.215030 | ||||||||
\(831\) | −4450.82 | −0.185797 | ||||||||
\(832\) | 15094.7 | 0.628983 | ||||||||
\(833\) | −2054.92 | −0.0854725 | ||||||||
\(834\) | 44842.3 | 1.86183 | ||||||||
\(835\) | −7894.31 | −0.327178 | ||||||||
\(836\) | 88314.5 | 3.65362 | ||||||||
\(837\) | −256.961 | −0.0106115 | ||||||||
\(838\) | 9078.13 | 0.374223 | ||||||||
\(839\) | −3982.56 | −0.163877 | −0.0819387 | − | 0.996637i | \(-0.526111\pi\) | ||||
−0.0819387 | + | 0.996637i | \(0.526111\pi\) | |||||||
\(840\) | 21988.7 | 0.903193 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 35195.5 | 1.44052 | ||||||||
\(843\) | 14377.5 | 0.587411 | ||||||||
\(844\) | 41827.3 | 1.70587 | ||||||||
\(845\) | −4601.15 | −0.187319 | ||||||||
\(846\) | −26306.5 | −1.06907 | ||||||||
\(847\) | 28099.6 | 1.13992 | ||||||||
\(848\) | 94072.5 | 3.80951 | ||||||||
\(849\) | 32559.7 | 1.31619 | ||||||||
\(850\) | 19036.7 | 0.768182 | ||||||||
\(851\) | −8998.94 | −0.362491 | ||||||||
\(852\) | −128959. | −5.18553 | ||||||||
\(853\) | 37142.6 | 1.49090 | 0.745450 | − | 0.666562i | \(-0.232235\pi\) | ||||
0.745450 | + | 0.666562i | \(0.232235\pi\) | |||||||
\(854\) | −24778.0 | −0.992842 | ||||||||
\(855\) | −2419.52 | −0.0967789 | ||||||||
\(856\) | 124346. | 4.96504 | ||||||||
\(857\) | 18690.5 | 0.744990 | 0.372495 | − | 0.928034i | \(-0.378502\pi\) | ||||
0.372495 | + | 0.928034i | \(0.378502\pi\) | |||||||
\(858\) | −13029.8 | −0.518451 | ||||||||
\(859\) | 22852.1 | 0.907687 | 0.453843 | − | 0.891081i | \(-0.350053\pi\) | ||||
0.453843 | + | 0.891081i | \(0.350053\pi\) | |||||||
\(860\) | 4788.90 | 0.189884 | ||||||||
\(861\) | 12148.0 | 0.480839 | ||||||||
\(862\) | 1387.65 | 0.0548303 | ||||||||
\(863\) | 41976.4 | 1.65573 | 0.827865 | − | 0.560928i | \(-0.189555\pi\) | ||||
0.827865 | + | 0.560928i | \(0.189555\pi\) | |||||||
\(864\) | −59678.4 | −2.34988 | ||||||||
\(865\) | −6585.77 | −0.258870 | ||||||||
\(866\) | 70219.9 | 2.75539 | ||||||||
\(867\) | −26404.1 | −1.03429 | ||||||||
\(868\) | 1469.40 | 0.0574592 | ||||||||
\(869\) | −41553.0 | −1.62208 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3012.32 | −0.117186 | ||||||||
\(872\) | −17912.4 | −0.695633 | ||||||||
\(873\) | −11875.7 | −0.460401 | ||||||||
\(874\) | −25080.0 | −0.970644 | ||||||||
\(875\) | −10704.6 | −0.413581 | ||||||||
\(876\) | 155977. | 6.01596 | ||||||||
\(877\) | 44394.0 | 1.70932 | 0.854662 | − | 0.519184i | \(-0.173764\pi\) | ||||
0.854662 | + | 0.519184i | \(0.173764\pi\) | |||||||
\(878\) | −20665.4 | −0.794331 | ||||||||
\(879\) | 43699.4 | 1.67684 | ||||||||
\(880\) | −28005.6 | −1.07281 | ||||||||
\(881\) | 6337.13 | 0.242342 | 0.121171 | − | 0.992632i | \(-0.461335\pi\) | ||||
0.121171 | + | 0.992632i | \(0.461335\pi\) | |||||||
\(882\) | 5798.72 | 0.221375 | ||||||||
\(883\) | −2834.24 | −0.108018 | −0.0540090 | − | 0.998540i | \(-0.517200\pi\) | ||||
−0.0540090 | + | 0.998540i | \(0.517200\pi\) | |||||||
\(884\) | −4499.17 | −0.171181 | ||||||||
\(885\) | 6780.12 | 0.257527 | ||||||||
\(886\) | −20406.7 | −0.773788 | ||||||||
\(887\) | −76.3532 | −0.00289029 | −0.00144515 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144515 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(888\) | −75954.3 | −2.87034 | ||||||||
\(889\) | −12645.6 | −0.477077 | ||||||||
\(890\) | −5377.88 | −0.202547 | ||||||||
\(891\) | 47364.3 | 1.78088 | ||||||||
\(892\) | −115596. | −4.33905 | ||||||||
\(893\) | 24760.6 | 0.927863 | ||||||||
\(894\) | 29354.7 | 1.09818 | ||||||||
\(895\) | 6386.75 | 0.238531 | ||||||||
\(896\) | 116637. | 4.34883 | ||||||||
\(897\) | 2719.86 | 0.101241 | ||||||||
\(898\) | 66179.7 | 2.45929 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −39486.1 | −1.46245 | ||||||||
\(901\) | −10783.2 | −0.398711 | ||||||||
\(902\) | −26416.2 | −0.975124 | ||||||||
\(903\) | 13250.4 | 0.488310 | ||||||||
\(904\) | 123597. | 4.54733 | ||||||||
\(905\) | 6738.95 | 0.247525 | ||||||||
\(906\) | −93478.6 | −3.42783 | ||||||||
\(907\) | −18209.7 | −0.666641 | −0.333320 | − | 0.942814i | \(-0.608169\pi\) | ||||
−0.333320 | + | 0.942814i | \(0.608169\pi\) | |||||||
\(908\) | −116368. | −4.25309 | ||||||||
\(909\) | 10916.5 | 0.398325 | ||||||||
\(910\) | 1688.76 | 0.0615184 | ||||||||
\(911\) | −33348.8 | −1.21284 | −0.606419 | − | 0.795145i | \(-0.707395\pi\) | ||||
−0.606419 | + | 0.795145i | \(0.707395\pi\) | |||||||
\(912\) | −123985. | −4.50170 | ||||||||
\(913\) | 22739.8 | 0.824291 | ||||||||
\(914\) | −71409.8 | −2.58427 | ||||||||
\(915\) | −3067.71 | −0.110836 | ||||||||
\(916\) | 18783.6 | 0.677541 | ||||||||
\(917\) | 30624.2 | 1.10284 | ||||||||
\(918\) | 12491.4 | 0.449105 | ||||||||
\(919\) | 20190.6 | 0.724730 | 0.362365 | − | 0.932036i | \(-0.381969\pi\) | ||||
0.362365 | + | 0.932036i | \(0.381969\pi\) | |||||||
\(920\) | 9980.98 | 0.357677 | ||||||||
\(921\) | −57272.4 | −2.04907 | ||||||||
\(922\) | −43268.4 | −1.54552 | ||||||||
\(923\) | −6334.11 | −0.225883 | ||||||||
\(924\) | −152056. | −5.41372 | ||||||||
\(925\) | 18142.3 | 0.644882 | ||||||||
\(926\) | −19045.7 | −0.675897 | ||||||||
\(927\) | 30018.8 | 1.06359 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9089.58 | 0.321011 | 0.160506 | − | 0.987035i | \(-0.448688\pi\) | ||||
0.160506 | + | 0.987035i | \(0.448688\pi\) | |||||||
\(930\) | 247.498 | 0.00872666 | ||||||||
\(931\) | −5457.95 | −0.192134 | ||||||||
\(932\) | 18279.2 | 0.642440 | ||||||||
\(933\) | −26679.6 | −0.936173 | ||||||||
\(934\) | −81521.3 | −2.85595 | ||||||||
\(935\) | 3210.17 | 0.112282 | ||||||||
\(936\) | 8119.64 | 0.283546 | ||||||||
\(937\) | 39646.5 | 1.38228 | 0.691140 | − | 0.722721i | \(-0.257109\pi\) | ||||
0.691140 | + | 0.722721i | \(0.257109\pi\) | |||||||
\(938\) | −47824.8 | −1.66475 | ||||||||
\(939\) | −34802.5 | −1.20952 | ||||||||
\(940\) | −15407.8 | −0.534625 | ||||||||
\(941\) | −51013.4 | −1.76726 | −0.883629 | − | 0.468188i | \(-0.844907\pi\) | ||||
−0.883629 | + | 0.468188i | \(0.844907\pi\) | |||||||
\(942\) | −8329.86 | −0.288112 | ||||||||
\(943\) | 5514.14 | 0.190419 | ||||||||
\(944\) | 122887. | 4.23689 | ||||||||
\(945\) | −3446.35 | −0.118635 | ||||||||
\(946\) | −28813.3 | −0.990276 | ||||||||
\(947\) | −43867.1 | −1.50527 | −0.752634 | − | 0.658439i | \(-0.771217\pi\) | ||||
−0.752634 | + | 0.658439i | \(0.771217\pi\) | |||||||
\(948\) | 114474. | 3.92187 | ||||||||
\(949\) | 7661.16 | 0.262057 | ||||||||
\(950\) | 50562.5 | 1.72680 | ||||||||
\(951\) | 34769.9 | 1.18559 | ||||||||
\(952\) | −45682.6 | −1.55523 | ||||||||
\(953\) | −4167.10 | −0.141643 | −0.0708214 | − | 0.997489i | \(-0.522562\pi\) | ||||
−0.0708214 | + | 0.997489i | \(0.522562\pi\) | |||||||
\(954\) | 30428.7 | 1.03267 | ||||||||
\(955\) | 4554.44 | 0.154323 | ||||||||
\(956\) | −54851.7 | −1.85568 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −44617.6 | −1.50473 | ||||||||
\(959\) | 598.123 | 0.0201401 | ||||||||
\(960\) | 29670.3 | 0.997507 | ||||||||
\(961\) | −29780.4 | −0.999645 | ||||||||
\(962\) | −5833.37 | −0.195505 | ||||||||
\(963\) | 23557.8 | 0.788307 | ||||||||
\(964\) | −25496.0 | −0.851836 | ||||||||
\(965\) | −6610.85 | −0.220529 | ||||||||
\(966\) | 43181.6 | 1.43824 | ||||||||
\(967\) | 21935.0 | 0.729454 | 0.364727 | − | 0.931115i | \(-0.381162\pi\) | ||||
0.364727 | + | 0.931115i | \(0.381162\pi\) | |||||||
\(968\) | 107655. | 3.57455 | ||||||||
\(969\) | 14211.9 | 0.471157 | ||||||||
\(970\) | −9462.85 | −0.313231 | ||||||||
\(971\) | 24169.6 | 0.798805 | 0.399403 | − | 0.916776i | \(-0.369218\pi\) | ||||
0.399403 | + | 0.916776i | \(0.369218\pi\) | |||||||
\(972\) | −83138.4 | −2.74348 | ||||||||
\(973\) | 25703.2 | 0.846871 | ||||||||
\(974\) | 53294.4 | 1.75325 | ||||||||
\(975\) | −5483.38 | −0.180111 | ||||||||
\(976\) | −55600.9 | −1.82351 | ||||||||
\(977\) | 16106.2 | 0.527415 | 0.263707 | − | 0.964603i | \(-0.415055\pi\) | ||||
0.263707 | + | 0.964603i | \(0.415055\pi\) | |||||||
\(978\) | 58628.7 | 1.91691 | ||||||||
\(979\) | 23783.8 | 0.776439 | ||||||||
\(980\) | 3396.33 | 0.110706 | ||||||||
\(981\) | −3393.57 | −0.110447 | ||||||||
\(982\) | 37608.3 | 1.22213 | ||||||||
\(983\) | 22527.2 | 0.730933 | 0.365466 | − | 0.930825i | \(-0.380910\pi\) | ||||
0.365466 | + | 0.930825i | \(0.380910\pi\) | |||||||
\(984\) | 46541.3 | 1.50781 | ||||||||
\(985\) | −5323.43 | −0.172202 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −42631.7 | −1.37486 | ||||||||
\(988\) | −11950.0 | −0.384798 | ||||||||
\(989\) | 6014.52 | 0.193378 | ||||||||
\(990\) | −9058.71 | −0.290813 | ||||||||
\(991\) | 8337.94 | 0.267269 | 0.133634 | − | 0.991031i | \(-0.457335\pi\) | ||||
0.133634 | + | 0.991031i | \(0.457335\pi\) | |||||||
\(992\) | 2456.57 | 0.0786251 | ||||||||
\(993\) | −37650.1 | −1.20321 | ||||||||
\(994\) | −100563. | −3.20891 | ||||||||
\(995\) | 11762.5 | 0.374771 | ||||||||
\(996\) | −62645.5 | −1.99297 | ||||||||
\(997\) | 18827.2 | 0.598058 | 0.299029 | − | 0.954244i | \(-0.403337\pi\) | ||||
0.299029 | + | 0.954244i | \(0.403337\pi\) | |||||||
\(998\) | −102224. | −3.24232 | ||||||||
\(999\) | 11904.5 | 0.377020 |
(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 | 841.4.a.b.1.5 | 5 | ||
29.28 | even | 2 | 29.4.a.b.1.1 | ✓ | 5 | ||
87.86 | odd | 2 | 261.4.a.f.1.5 | 5 | |||
116.115 | odd | 2 | 464.4.a.l.1.5 | 5 | |||
145.144 | even | 2 | 725.4.a.c.1.5 | 5 | |||
203.202 | odd | 2 | 1421.4.a.e.1.1 | 5 | |||
232.115 | odd | 2 | 1856.4.a.bb.1.1 | 5 | |||
232.173 | even | 2 | 1856.4.a.y.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.1 | ✓ | 5 | 29.28 | even | 2 | ||
261.4.a.f.1.5 | 5 | 87.86 | odd | 2 | |||
464.4.a.l.1.5 | 5 | 116.115 | odd | 2 | |||
725.4.a.c.1.5 | 5 | 145.144 | even | 2 | |||
841.4.a.b.1.5 | 5 | 1.1 | even | 1 | trivial | ||
1421.4.a.e.1.1 | 5 | 203.202 | odd | 2 | |||
1856.4.a.y.1.5 | 5 | 232.173 | even | 2 | |||
1856.4.a.bb.1.1 | 5 | 232.115 | odd | 2 |