Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(1,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53113 | −1.24844 | −0.624221 | − | 0.781248i | \(-0.714584\pi\) | ||||
−0.624221 | + | 0.781248i | \(0.714584\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.46887 | 0.558609 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −10.5934 | −0.720789 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 12.4689 | 0.551051 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −17.6556 | −0.558320 | ||||||||
\(11\) | −2.93774 | −0.0805239 | −0.0402619 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402619 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(12\) | 13.4066 | 0.322513 | ||||||||
\(13\) | −19.0623 | −0.406686 | −0.203343 | − | 0.979108i | \(-0.565181\pi\) | ||||
−0.203343 | + | 0.979108i | \(0.565181\pi\) | |||||||
\(14\) | 24.7179 | 0.471867 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −79.7802 | −1.24656 | ||||||||
\(17\) | 122.498 | 1.74766 | 0.873828 | − | 0.486236i | \(-0.161630\pi\) | ||||
0.873828 | + | 0.486236i | \(0.161630\pi\) | |||||||
\(18\) | −31.7802 | −0.416148 | ||||||||
\(19\) | 107.436 | 1.29723 | 0.648617 | − | 0.761115i | \(-0.275348\pi\) | ||||
0.648617 | + | 0.761115i | \(0.275348\pi\) | |||||||
\(20\) | 22.3444 | 0.249817 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 10.3735 | 0.100529 | ||||||||
\(23\) | 210.623 | 1.90947 | 0.954736 | − | 0.297455i | \(-0.0961379\pi\) | ||||
0.954736 | + | 0.297455i | \(0.0961379\pi\) | |||||||
\(24\) | 37.4066 | 0.318150 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 67.3113 | 0.507724 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −31.2821 | −0.211134 | ||||||||
\(29\) | 95.4942 | 0.611477 | 0.305738 | − | 0.952116i | \(-0.401097\pi\) | ||||
0.305738 | + | 0.952116i | \(0.401097\pi\) | |||||||
\(30\) | −52.9669 | −0.322346 | ||||||||
\(31\) | −94.3074 | −0.546391 | −0.273195 | − | 0.961959i | \(-0.588081\pi\) | ||||
−0.273195 | + | 0.961959i | \(0.588081\pi\) | |||||||
\(32\) | 181.963 | 1.00521 | ||||||||
\(33\) | −8.81323 | −0.0464905 | ||||||||
\(34\) | −432.556 | −2.18185 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 40.2198 | 0.186203 | ||||||||
\(37\) | 97.1206 | 0.431528 | 0.215764 | − | 0.976446i | \(-0.430776\pi\) | ||||
0.215764 | + | 0.976446i | \(0.430776\pi\) | |||||||
\(38\) | −379.370 | −1.61952 | ||||||||
\(39\) | −57.1868 | −0.234800 | ||||||||
\(40\) | 62.3444 | 0.246438 | ||||||||
\(41\) | −491.113 | −1.87071 | −0.935353 | − | 0.353716i | \(-0.884918\pi\) | ||||
−0.935353 | + | 0.353716i | \(0.884918\pi\) | |||||||
\(42\) | 74.1537 | 0.272433 | ||||||||
\(43\) | −43.0039 | −0.152512 | −0.0762562 | − | 0.997088i | \(-0.524297\pi\) | ||||
−0.0762562 | + | 0.997088i | \(0.524297\pi\) | |||||||
\(44\) | −13.1284 | −0.0449814 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −743.735 | −2.38387 | ||||||||
\(47\) | 473.494 | 1.46949 | 0.734747 | − | 0.678341i | \(-0.237301\pi\) | ||||
0.734747 | + | 0.678341i | \(0.237301\pi\) | |||||||
\(48\) | −239.340 | −0.719705 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −88.2782 | −0.249689 | ||||||||
\(51\) | 367.494 | 1.00901 | ||||||||
\(52\) | −85.1868 | −0.227178 | ||||||||
\(53\) | −183.677 | −0.476038 | −0.238019 | − | 0.971261i | \(-0.576498\pi\) | ||||
−0.238019 | + | 0.971261i | \(0.576498\pi\) | |||||||
\(54\) | −95.3405 | −0.240263 | ||||||||
\(55\) | −14.6887 | −0.0360114 | ||||||||
\(56\) | −87.2821 | −0.208278 | ||||||||
\(57\) | 322.307 | 0.748959 | ||||||||
\(58\) | −337.202 | −0.763394 | ||||||||
\(59\) | −760.615 | −1.67837 | −0.839183 | − | 0.543849i | \(-0.816966\pi\) | ||||
−0.839183 | + | 0.543849i | \(0.816966\pi\) | |||||||
\(60\) | 67.0331 | 0.144232 | ||||||||
\(61\) | −198.747 | −0.417163 | −0.208582 | − | 0.978005i | \(-0.566885\pi\) | ||||
−0.208582 | + | 0.978005i | \(0.566885\pi\) | |||||||
\(62\) | 333.012 | 0.682137 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −4.29373 | −0.00838618 | ||||||||
\(65\) | −95.3113 | −0.181876 | ||||||||
\(66\) | 31.1206 | 0.0580407 | ||||||||
\(67\) | −309.992 | −0.565247 | −0.282624 | − | 0.959231i | \(-0.591205\pi\) | ||||
−0.282624 | + | 0.959231i | \(0.591205\pi\) | |||||||
\(68\) | 547.428 | 0.976256 | ||||||||
\(69\) | 631.868 | 1.10243 | ||||||||
\(70\) | 123.590 | 0.211025 | ||||||||
\(71\) | 665.693 | 1.11272 | 0.556360 | − | 0.830941i | \(-0.312197\pi\) | ||||
0.556360 | + | 0.830941i | \(0.312197\pi\) | |||||||
\(72\) | 112.220 | 0.183684 | ||||||||
\(73\) | 621.288 | 0.996113 | 0.498057 | − | 0.867145i | \(-0.334047\pi\) | ||||
0.498057 | + | 0.867145i | \(0.334047\pi\) | |||||||
\(74\) | −342.945 | −0.538738 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 480.117 | 0.724647 | ||||||||
\(77\) | 20.5642 | 0.0304352 | ||||||||
\(78\) | 201.934 | 0.293135 | ||||||||
\(79\) | −24.7626 | −0.0352659 | −0.0176330 | − | 0.999845i | \(-0.505613\pi\) | ||||
−0.0176330 | + | 0.999845i | \(0.505613\pi\) | |||||||
\(80\) | −398.901 | −0.557481 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1734.18 | 2.33547 | ||||||||
\(83\) | −406.724 | −0.537876 | −0.268938 | − | 0.963157i | \(-0.586673\pi\) | ||||
−0.268938 | + | 0.963157i | \(0.586673\pi\) | |||||||
\(84\) | −93.8463 | −0.121898 | ||||||||
\(85\) | 612.490 | 0.781575 | ||||||||
\(86\) | 151.852 | 0.190403 | ||||||||
\(87\) | 286.483 | 0.353036 | ||||||||
\(88\) | −36.6303 | −0.0443728 | ||||||||
\(89\) | 261.751 | 0.311748 | 0.155874 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155874 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(90\) | −158.901 | −0.186107 | ||||||||
\(91\) | 133.436 | 0.153713 | ||||||||
\(92\) | 941.245 | 1.06665 | ||||||||
\(93\) | −282.922 | −0.315459 | ||||||||
\(94\) | −1671.97 | −1.83458 | ||||||||
\(95\) | 537.179 | 0.580141 | ||||||||
\(96\) | 545.889 | 0.580360 | ||||||||
\(97\) | −1004.77 | −1.05175 | −0.525873 | − | 0.850563i | \(-0.676261\pi\) | ||||
−0.525873 | + | 0.850563i | \(0.676261\pi\) | |||||||
\(98\) | −173.025 | −0.178349 | ||||||||
\(99\) | −26.4397 | −0.0268413 | ||||||||
\(100\) | 111.722 | 0.111722 | ||||||||
\(101\) | −128.872 | −0.126962 | −0.0634812 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634812 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(102\) | −1297.67 | −1.25969 | ||||||||
\(103\) | 806.008 | 0.771051 | 0.385526 | − | 0.922697i | \(-0.374020\pi\) | ||||
0.385526 | + | 0.922697i | \(0.374020\pi\) | |||||||
\(104\) | −237.685 | −0.224105 | ||||||||
\(105\) | −105.000 | −0.0975900 | ||||||||
\(106\) | 648.587 | 0.594305 | ||||||||
\(107\) | −769.712 | −0.695429 | −0.347714 | − | 0.937600i | \(-0.613042\pi\) | ||||
−0.347714 | + | 0.937600i | \(0.613042\pi\) | |||||||
\(108\) | 120.660 | 0.107504 | ||||||||
\(109\) | −780.856 | −0.686169 | −0.343085 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343085 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(110\) | 51.8677 | 0.0449581 | ||||||||
\(111\) | 291.362 | 0.249143 | ||||||||
\(112\) | 558.461 | 0.471157 | ||||||||
\(113\) | −1115.65 | −0.928771 | −0.464386 | − | 0.885633i | \(-0.653725\pi\) | ||||
−0.464386 | + | 0.885633i | \(0.653725\pi\) | |||||||
\(114\) | −1138.11 | −0.935032 | ||||||||
\(115\) | 1053.11 | 0.853942 | ||||||||
\(116\) | 426.751 | 0.341576 | ||||||||
\(117\) | −171.560 | −0.135562 | ||||||||
\(118\) | 2685.83 | 2.09534 | ||||||||
\(119\) | −857.486 | −0.660552 | ||||||||
\(120\) | 187.033 | 0.142281 | ||||||||
\(121\) | −1322.37 | −0.993516 | ||||||||
\(122\) | 701.802 | 0.520804 | ||||||||
\(123\) | −1473.34 | −1.08005 | ||||||||
\(124\) | −421.448 | −0.305219 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 222.461 | 0.157289 | ||||||||
\(127\) | −1875.98 | −1.31076 | −0.655381 | − | 0.755299i | \(-0.727492\pi\) | ||||
−0.655381 | + | 0.755299i | \(0.727492\pi\) | |||||||
\(128\) | −1440.54 | −0.994744 | ||||||||
\(129\) | −129.012 | −0.0880530 | ||||||||
\(130\) | 336.556 | 0.227061 | ||||||||
\(131\) | 364.203 | 0.242905 | 0.121452 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121452 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(132\) | −39.3852 | −0.0259700 | ||||||||
\(133\) | −752.051 | −0.490309 | ||||||||
\(134\) | 1094.62 | 0.705679 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 1527.41 | 0.963048 | ||||||||
\(137\) | 1603.13 | 0.999743 | 0.499872 | − | 0.866099i | \(-0.333380\pi\) | ||||
0.499872 | + | 0.866099i | \(0.333380\pi\) | |||||||
\(138\) | −2231.21 | −1.37633 | ||||||||
\(139\) | 2431.12 | 1.48349 | 0.741746 | − | 0.670681i | \(-0.233998\pi\) | ||||
0.741746 | + | 0.670681i | \(0.233998\pi\) | |||||||
\(140\) | −156.410 | −0.0944221 | ||||||||
\(141\) | 1420.48 | 0.848413 | ||||||||
\(142\) | −2350.65 | −1.38917 | ||||||||
\(143\) | 56.0000 | 0.0327479 | ||||||||
\(144\) | −718.021 | −0.415522 | ||||||||
\(145\) | 477.471 | 0.273461 | ||||||||
\(146\) | −2193.85 | −1.24359 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 434.020 | 0.241055 | ||||||||
\(149\) | 2341.57 | 1.28744 | 0.643722 | − | 0.765260i | \(-0.277389\pi\) | ||||
0.643722 | + | 0.765260i | \(0.277389\pi\) | |||||||
\(150\) | −264.835 | −0.144158 | ||||||||
\(151\) | −2104.07 | −1.13395 | −0.566976 | − | 0.823734i | \(-0.691887\pi\) | ||||
−0.566976 | + | 0.823734i | \(0.691887\pi\) | |||||||
\(152\) | 1339.60 | 0.714843 | ||||||||
\(153\) | 1102.48 | 0.582552 | ||||||||
\(154\) | −72.6148 | −0.0379966 | ||||||||
\(155\) | −471.537 | −0.244353 | ||||||||
\(156\) | −255.560 | −0.131162 | ||||||||
\(157\) | −593.467 | −0.301680 | −0.150840 | − | 0.988558i | \(-0.548198\pi\) | ||||
−0.150840 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(158\) | 87.4399 | 0.0440275 | ||||||||
\(159\) | −551.031 | −0.274840 | ||||||||
\(160\) | 909.815 | 0.449545 | ||||||||
\(161\) | −1474.36 | −0.721712 | ||||||||
\(162\) | −286.021 | −0.138716 | ||||||||
\(163\) | 2178.71 | 1.04693 | 0.523465 | − | 0.852047i | \(-0.324639\pi\) | ||||
0.523465 | + | 0.852047i | \(0.324639\pi\) | |||||||
\(164\) | −2194.72 | −1.04499 | ||||||||
\(165\) | −44.0661 | −0.0207912 | ||||||||
\(166\) | 1436.19 | 0.671508 | ||||||||
\(167\) | 799.502 | 0.370463 | 0.185231 | − | 0.982695i | \(-0.440697\pi\) | ||||
0.185231 | + | 0.982695i | \(0.440697\pi\) | |||||||
\(168\) | −261.846 | −0.120249 | ||||||||
\(169\) | −1833.63 | −0.834606 | ||||||||
\(170\) | −2162.78 | −0.975752 | ||||||||
\(171\) | 966.922 | 0.432412 | ||||||||
\(172\) | −192.179 | −0.0851947 | ||||||||
\(173\) | −1444.36 | −0.634754 | −0.317377 | − | 0.948299i | \(-0.602802\pi\) | ||||
−0.317377 | + | 0.948299i | \(0.602802\pi\) | |||||||
\(174\) | −1011.61 | −0.440745 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | 234.374 | 0.100378 | ||||||||
\(177\) | −2281.84 | −0.969005 | ||||||||
\(178\) | −924.276 | −0.389199 | ||||||||
\(179\) | 3343.49 | 1.39611 | 0.698056 | − | 0.716043i | \(-0.254048\pi\) | ||||
0.698056 | + | 0.716043i | \(0.254048\pi\) | |||||||
\(180\) | 201.099 | 0.0832725 | ||||||||
\(181\) | 2251.81 | 0.924729 | 0.462365 | − | 0.886690i | \(-0.347001\pi\) | ||||
0.462365 | + | 0.886690i | \(0.347001\pi\) | |||||||
\(182\) | −471.179 | −0.191902 | ||||||||
\(183\) | −596.241 | −0.240849 | ||||||||
\(184\) | 2626.23 | 1.05222 | ||||||||
\(185\) | 485.603 | 0.192985 | ||||||||
\(186\) | 999.035 | 0.393832 | ||||||||
\(187\) | −359.868 | −0.140728 | ||||||||
\(188\) | 2115.98 | 0.820873 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | −1896.85 | −0.724273 | ||||||||
\(191\) | −1001.93 | −0.379565 | −0.189782 | − | 0.981826i | \(-0.560778\pi\) | ||||
−0.189782 | + | 0.981826i | \(0.560778\pi\) | |||||||
\(192\) | −12.8812 | −0.00484177 | ||||||||
\(193\) | −4054.97 | −1.51235 | −0.756173 | − | 0.654372i | \(-0.772933\pi\) | ||||
−0.756173 | + | 0.654372i | \(0.772933\pi\) | |||||||
\(194\) | 3547.99 | 1.31304 | ||||||||
\(195\) | −285.934 | −0.105006 | ||||||||
\(196\) | 218.975 | 0.0798013 | ||||||||
\(197\) | −5140.23 | −1.85902 | −0.929508 | − | 0.368802i | \(-0.879768\pi\) | ||||
−0.929508 | + | 0.368802i | \(0.879768\pi\) | |||||||
\(198\) | 93.3619 | 0.0335098 | ||||||||
\(199\) | 585.631 | 0.208614 | 0.104307 | − | 0.994545i | \(-0.466737\pi\) | ||||
0.104307 | + | 0.994545i | \(0.466737\pi\) | |||||||
\(200\) | 311.722 | 0.110210 | ||||||||
\(201\) | −929.977 | −0.326346 | ||||||||
\(202\) | 455.062 | 0.158505 | ||||||||
\(203\) | −668.459 | −0.231116 | ||||||||
\(204\) | 1642.28 | 0.563642 | ||||||||
\(205\) | −2455.56 | −0.836605 | ||||||||
\(206\) | −2846.12 | −0.962614 | ||||||||
\(207\) | 1895.60 | 0.636490 | ||||||||
\(208\) | 1520.79 | 0.506961 | ||||||||
\(209\) | −315.619 | −0.104458 | ||||||||
\(210\) | 370.769 | 0.121836 | ||||||||
\(211\) | −1055.16 | −0.344266 | −0.172133 | − | 0.985074i | \(-0.555066\pi\) | ||||
−0.172133 | + | 0.985074i | \(0.555066\pi\) | |||||||
\(212\) | −820.829 | −0.265919 | ||||||||
\(213\) | 1997.08 | 0.642430 | ||||||||
\(214\) | 2717.95 | 0.868203 | ||||||||
\(215\) | −215.019 | −0.0682056 | ||||||||
\(216\) | 336.660 | 0.106050 | ||||||||
\(217\) | 660.152 | 0.206516 | ||||||||
\(218\) | 2757.30 | 0.856643 | ||||||||
\(219\) | 1863.86 | 0.575106 | ||||||||
\(220\) | −65.6420 | −0.0201163 | ||||||||
\(221\) | −2335.09 | −0.710747 | ||||||||
\(222\) | −1028.84 | −0.311040 | ||||||||
\(223\) | 4675.85 | 1.40412 | 0.702059 | − | 0.712119i | \(-0.252264\pi\) | ||||
0.702059 | + | 0.712119i | \(0.252264\pi\) | |||||||
\(224\) | −1273.74 | −0.379935 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 3939.49 | 1.15952 | ||||||||
\(227\) | 5443.11 | 1.59151 | 0.795754 | − | 0.605621i | \(-0.207075\pi\) | ||||
0.795754 | + | 0.605621i | \(0.207075\pi\) | |||||||
\(228\) | 1440.35 | 0.418375 | ||||||||
\(229\) | −536.303 | −0.154759 | −0.0773797 | − | 0.997002i | \(-0.524655\pi\) | ||||
−0.0773797 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(230\) | −3718.68 | −1.06610 | ||||||||
\(231\) | 61.6926 | 0.0175717 | ||||||||
\(232\) | 1190.70 | 0.336955 | ||||||||
\(233\) | −183.490 | −0.0515916 | −0.0257958 | − | 0.999667i | \(-0.508212\pi\) | ||||
−0.0257958 | + | 0.999667i | \(0.508212\pi\) | |||||||
\(234\) | 605.802 | 0.169241 | ||||||||
\(235\) | 2367.47 | 0.657178 | ||||||||
\(236\) | −3399.09 | −0.937550 | ||||||||
\(237\) | −74.2878 | −0.0203608 | ||||||||
\(238\) | 3027.90 | 0.824661 | ||||||||
\(239\) | 643.218 | 0.174085 | 0.0870425 | − | 0.996205i | \(-0.472258\pi\) | ||||
0.0870425 | + | 0.996205i | \(0.472258\pi\) | |||||||
\(240\) | −1196.70 | −0.321862 | ||||||||
\(241\) | −5755.61 | −1.53839 | −0.769194 | − | 0.639015i | \(-0.779342\pi\) | ||||
−0.769194 | + | 0.639015i | \(0.779342\pi\) | |||||||
\(242\) | 4669.46 | 1.24035 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −888.175 | −0.233031 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 5202.55 | 1.34838 | ||||||||
\(247\) | −2047.97 | −0.527567 | ||||||||
\(248\) | −1175.91 | −0.301089 | ||||||||
\(249\) | −1220.17 | −0.310543 | ||||||||
\(250\) | −441.391 | −0.111664 | ||||||||
\(251\) | −5132.27 | −1.29062 | −0.645311 | − | 0.763920i | \(-0.723272\pi\) | ||||
−0.645311 | + | 0.763920i | \(0.723272\pi\) | |||||||
\(252\) | −281.539 | −0.0703781 | ||||||||
\(253\) | −618.755 | −0.153758 | ||||||||
\(254\) | 6624.34 | 1.63641 | ||||||||
\(255\) | 1837.47 | 0.451243 | ||||||||
\(256\) | 5121.09 | 1.25027 | ||||||||
\(257\) | 5041.74 | 1.22372 | 0.611859 | − | 0.790967i | \(-0.290422\pi\) | ||||
0.611859 | + | 0.790967i | \(0.290422\pi\) | |||||||
\(258\) | 455.557 | 0.109929 | ||||||||
\(259\) | −679.844 | −0.163102 | ||||||||
\(260\) | −425.934 | −0.101597 | ||||||||
\(261\) | 859.448 | 0.203826 | ||||||||
\(262\) | −1286.05 | −0.303253 | ||||||||
\(263\) | 7577.00 | 1.77649 | 0.888246 | − | 0.459367i | \(-0.151924\pi\) | ||||
0.888246 | + | 0.459367i | \(0.151924\pi\) | |||||||
\(264\) | −109.891 | −0.0256186 | ||||||||
\(265\) | −918.385 | −0.212890 | ||||||||
\(266\) | 2655.59 | 0.612122 | ||||||||
\(267\) | 785.253 | 0.179988 | ||||||||
\(268\) | −1385.32 | −0.315752 | ||||||||
\(269\) | 1023.10 | 0.231893 | 0.115947 | − | 0.993255i | \(-0.463010\pi\) | ||||
0.115947 | + | 0.993255i | \(0.463010\pi\) | |||||||
\(270\) | −476.702 | −0.107449 | ||||||||
\(271\) | −2251.98 | −0.504790 | −0.252395 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252395 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(272\) | −9772.91 | −2.17857 | ||||||||
\(273\) | 400.307 | 0.0887462 | ||||||||
\(274\) | −5660.87 | −1.24812 | ||||||||
\(275\) | −73.4436 | −0.0161048 | ||||||||
\(276\) | 2823.74 | 0.615829 | ||||||||
\(277\) | −8630.72 | −1.87209 | −0.936047 | − | 0.351875i | \(-0.885544\pi\) | ||||
−0.936047 | + | 0.351875i | \(0.885544\pi\) | |||||||
\(278\) | −8584.61 | −1.85205 | ||||||||
\(279\) | −848.767 | −0.182130 | ||||||||
\(280\) | −436.410 | −0.0931447 | ||||||||
\(281\) | −7521.62 | −1.59680 | −0.798402 | − | 0.602124i | \(-0.794321\pi\) | ||||
−0.798402 | + | 0.602124i | \(0.794321\pi\) | |||||||
\(282\) | −5015.91 | −1.05919 | ||||||||
\(283\) | 14.8169 | 0.00311226 | 0.00155613 | − | 0.999999i | \(-0.499505\pi\) | ||||
0.00155613 | + | 0.999999i | \(0.499505\pi\) | |||||||
\(284\) | 2974.89 | 0.621576 | ||||||||
\(285\) | 1611.54 | 0.334945 | ||||||||
\(286\) | −197.743 | −0.0408839 | ||||||||
\(287\) | 3437.79 | 0.707060 | ||||||||
\(288\) | 1637.67 | 0.335071 | ||||||||
\(289\) | 10092.8 | 2.05430 | ||||||||
\(290\) | −1686.01 | −0.341400 | ||||||||
\(291\) | −3014.32 | −0.607226 | ||||||||
\(292\) | 2776.46 | 0.556438 | ||||||||
\(293\) | 6913.39 | 1.37844 | 0.689222 | − | 0.724550i | \(-0.257952\pi\) | ||||
0.689222 | + | 0.724550i | \(0.257952\pi\) | |||||||
\(294\) | −519.076 | −0.102970 | ||||||||
\(295\) | −3803.07 | −0.750588 | ||||||||
\(296\) | 1210.98 | 0.237794 | ||||||||
\(297\) | −79.3190 | −0.0154968 | ||||||||
\(298\) | −8268.39 | −1.60730 | ||||||||
\(299\) | −4014.94 | −0.776555 | ||||||||
\(300\) | 335.165 | 0.0645026 | ||||||||
\(301\) | 301.027 | 0.0576442 | ||||||||
\(302\) | 7429.74 | 1.41567 | ||||||||
\(303\) | −386.615 | −0.0733018 | ||||||||
\(304\) | −8571.25 | −1.61709 | ||||||||
\(305\) | −993.735 | −0.186561 | ||||||||
\(306\) | −3893.01 | −0.727283 | ||||||||
\(307\) | −7644.12 | −1.42108 | −0.710542 | − | 0.703655i | \(-0.751550\pi\) | ||||
−0.710542 | + | 0.703655i | \(0.751550\pi\) | |||||||
\(308\) | 91.8987 | 0.0170014 | ||||||||
\(309\) | 2418.02 | 0.445167 | ||||||||
\(310\) | 1665.06 | 0.305061 | ||||||||
\(311\) | 7593.99 | 1.38462 | 0.692308 | − | 0.721602i | \(-0.256594\pi\) | ||||
0.692308 | + | 0.721602i | \(0.256594\pi\) | |||||||
\(312\) | −713.055 | −0.129387 | ||||||||
\(313\) | −9127.84 | −1.64836 | −0.824179 | − | 0.566329i | \(-0.808363\pi\) | ||||
−0.824179 | + | 0.566329i | \(0.808363\pi\) | |||||||
\(314\) | 2095.61 | 0.376631 | ||||||||
\(315\) | −315.000 | −0.0563436 | ||||||||
\(316\) | −110.661 | −0.0196999 | ||||||||
\(317\) | −4929.81 | −0.873456 | −0.436728 | − | 0.899593i | \(-0.643863\pi\) | ||||
−0.436728 | + | 0.899593i | \(0.643863\pi\) | |||||||
\(318\) | 1945.76 | 0.343122 | ||||||||
\(319\) | −280.537 | −0.0492385 | ||||||||
\(320\) | −21.4686 | −0.00375042 | ||||||||
\(321\) | −2309.14 | −0.401506 | ||||||||
\(322\) | 5206.15 | 0.901016 | ||||||||
\(323\) | 13160.7 | 2.26712 | ||||||||
\(324\) | 361.979 | 0.0620677 | ||||||||
\(325\) | −476.556 | −0.0813372 | ||||||||
\(326\) | −7693.30 | −1.30703 | ||||||||
\(327\) | −2342.57 | −0.396160 | ||||||||
\(328\) | −6123.62 | −1.03086 | ||||||||
\(329\) | −3314.46 | −0.555417 | ||||||||
\(330\) | 155.603 | 0.0259566 | ||||||||
\(331\) | 1221.67 | 0.202867 | 0.101433 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101433 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(332\) | −1817.60 | −0.300463 | ||||||||
\(333\) | 874.086 | 0.143843 | ||||||||
\(334\) | −2823.14 | −0.462502 | ||||||||
\(335\) | −1549.96 | −0.252786 | ||||||||
\(336\) | 1675.38 | 0.272023 | ||||||||
\(337\) | −8744.83 | −1.41354 | −0.706768 | − | 0.707446i | \(-0.749847\pi\) | ||||
−0.706768 | + | 0.707446i | \(0.749847\pi\) | |||||||
\(338\) | 6474.79 | 1.04196 | ||||||||
\(339\) | −3346.94 | −0.536226 | ||||||||
\(340\) | 2737.14 | 0.436595 | ||||||||
\(341\) | 277.051 | 0.0439975 | ||||||||
\(342\) | −3414.33 | −0.539841 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −536.210 | −0.0840421 | ||||||||
\(345\) | 3159.34 | 0.493023 | ||||||||
\(346\) | 5100.21 | 0.792454 | ||||||||
\(347\) | 4589.56 | 0.710031 | 0.355015 | − | 0.934860i | \(-0.384476\pi\) | ||||
0.355015 | + | 0.934860i | \(0.384476\pi\) | |||||||
\(348\) | 1280.25 | 0.197209 | ||||||||
\(349\) | −3989.89 | −0.611960 | −0.305980 | − | 0.952038i | \(-0.598984\pi\) | ||||
−0.305980 | + | 0.952038i | \(0.598984\pi\) | |||||||
\(350\) | 617.948 | 0.0943734 | ||||||||
\(351\) | −514.681 | −0.0782668 | ||||||||
\(352\) | −534.561 | −0.0809437 | ||||||||
\(353\) | 2416.35 | 0.364333 | 0.182166 | − | 0.983268i | \(-0.441689\pi\) | ||||
0.182166 | + | 0.983268i | \(0.441689\pi\) | |||||||
\(354\) | 8057.49 | 1.20975 | ||||||||
\(355\) | 3328.46 | 0.497624 | ||||||||
\(356\) | 1169.73 | 0.174145 | ||||||||
\(357\) | −2572.46 | −0.381370 | ||||||||
\(358\) | −11806.3 | −1.74297 | ||||||||
\(359\) | −2756.24 | −0.405206 | −0.202603 | − | 0.979261i | \(-0.564940\pi\) | ||||
−0.202603 | + | 0.979261i | \(0.564940\pi\) | |||||||
\(360\) | 561.099 | 0.0821459 | ||||||||
\(361\) | 4683.45 | 0.682818 | ||||||||
\(362\) | −7951.44 | −1.15447 | ||||||||
\(363\) | −3967.11 | −0.573607 | ||||||||
\(364\) | 596.307 | 0.0858654 | ||||||||
\(365\) | 3106.44 | 0.445475 | ||||||||
\(366\) | 2105.40 | 0.300687 | ||||||||
\(367\) | 11112.8 | 1.58061 | 0.790307 | − | 0.612711i | \(-0.209921\pi\) | ||||
0.790307 | + | 0.612711i | \(0.209921\pi\) | |||||||
\(368\) | −16803.5 | −2.38028 | ||||||||
\(369\) | −4420.02 | −0.623569 | ||||||||
\(370\) | −1714.73 | −0.240931 | ||||||||
\(371\) | 1285.74 | 0.179925 | ||||||||
\(372\) | −1264.34 | −0.176218 | ||||||||
\(373\) | 6091.09 | 0.845535 | 0.422768 | − | 0.906238i | \(-0.361059\pi\) | ||||
0.422768 | + | 0.906238i | \(0.361059\pi\) | |||||||
\(374\) | 1270.74 | 0.175691 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 5903.94 | 0.809767 | ||||||||
\(377\) | −1820.33 | −0.248679 | ||||||||
\(378\) | 667.383 | 0.0908108 | ||||||||
\(379\) | 3984.29 | 0.539998 | 0.269999 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269999 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(380\) | 2400.58 | 0.324072 | ||||||||
\(381\) | −5627.95 | −0.756768 | ||||||||
\(382\) | 3537.93 | 0.473865 | ||||||||
\(383\) | 318.475 | 0.0424890 | 0.0212445 | − | 0.999774i | \(-0.493237\pi\) | ||||
0.0212445 | + | 0.999774i | \(0.493237\pi\) | |||||||
\(384\) | −4321.63 | −0.574316 | ||||||||
\(385\) | 102.821 | 0.0136110 | ||||||||
\(386\) | 14318.6 | 1.88808 | ||||||||
\(387\) | −387.035 | −0.0508374 | ||||||||
\(388\) | −4490.21 | −0.587515 | ||||||||
\(389\) | 3885.46 | 0.506429 | 0.253214 | − | 0.967410i | \(-0.418512\pi\) | ||||
0.253214 | + | 0.967410i | \(0.418512\pi\) | |||||||
\(390\) | 1009.67 | 0.131094 | ||||||||
\(391\) | 25800.9 | 3.33710 | ||||||||
\(392\) | 610.975 | 0.0787216 | ||||||||
\(393\) | 1092.61 | 0.140241 | ||||||||
\(394\) | 18150.8 | 2.32088 | ||||||||
\(395\) | −123.813 | −0.0157714 | ||||||||
\(396\) | −118.156 | −0.0149938 | ||||||||
\(397\) | 4806.04 | 0.607578 | 0.303789 | − | 0.952739i | \(-0.401748\pi\) | ||||
0.303789 | + | 0.952739i | \(0.401748\pi\) | |||||||
\(398\) | −2067.94 | −0.260443 | ||||||||
\(399\) | −2256.15 | −0.283080 | ||||||||
\(400\) | −1994.50 | −0.249313 | ||||||||
\(401\) | 3618.59 | 0.450633 | 0.225316 | − | 0.974286i | \(-0.427658\pi\) | ||||
0.225316 | + | 0.974286i | \(0.427658\pi\) | |||||||
\(402\) | 3283.87 | 0.407424 | ||||||||
\(403\) | 1797.71 | 0.222209 | ||||||||
\(404\) | −575.911 | −0.0709223 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 2360.42 | 0.288536 | ||||||||
\(407\) | −285.315 | −0.0347483 | ||||||||
\(408\) | 4582.24 | 0.556016 | ||||||||
\(409\) | −2109.05 | −0.254978 | −0.127489 | − | 0.991840i | \(-0.540692\pi\) | ||||
−0.127489 | + | 0.991840i | \(0.540692\pi\) | |||||||
\(410\) | 8670.91 | 1.04445 | ||||||||
\(411\) | 4809.40 | 0.577202 | ||||||||
\(412\) | 3601.94 | 0.430716 | ||||||||
\(413\) | 5324.30 | 0.634363 | ||||||||
\(414\) | −6693.62 | −0.794622 | ||||||||
\(415\) | −2033.62 | −0.240546 | ||||||||
\(416\) | −3468.63 | −0.408806 | ||||||||
\(417\) | 7293.37 | 0.856494 | ||||||||
\(418\) | 1114.49 | 0.130410 | ||||||||
\(419\) | −6905.91 | −0.805193 | −0.402597 | − | 0.915377i | \(-0.631892\pi\) | ||||
−0.402597 | + | 0.915377i | \(0.631892\pi\) | |||||||
\(420\) | −469.231 | −0.0545146 | ||||||||
\(421\) | −9647.54 | −1.11685 | −0.558423 | − | 0.829556i | \(-0.688593\pi\) | ||||
−0.558423 | + | 0.829556i | \(0.688593\pi\) | |||||||
\(422\) | 3725.91 | 0.429797 | ||||||||
\(423\) | 4261.45 | 0.489831 | ||||||||
\(424\) | −2290.25 | −0.262321 | ||||||||
\(425\) | 3062.45 | 0.349531 | ||||||||
\(426\) | −7051.94 | −0.802037 | ||||||||
\(427\) | 1391.23 | 0.157673 | ||||||||
\(428\) | −3439.74 | −0.388473 | ||||||||
\(429\) | 168.000 | 0.0189070 | ||||||||
\(430\) | 759.261 | 0.0851508 | ||||||||
\(431\) | −13002.7 | −1.45318 | −0.726589 | − | 0.687073i | \(-0.758895\pi\) | ||||
−0.726589 | + | 0.687073i | \(0.758895\pi\) | |||||||
\(432\) | −2154.06 | −0.239902 | ||||||||
\(433\) | 7356.07 | 0.816420 | 0.408210 | − | 0.912888i | \(-0.366153\pi\) | ||||
0.408210 | + | 0.912888i | \(0.366153\pi\) | |||||||
\(434\) | −2331.08 | −0.257824 | ||||||||
\(435\) | 1432.41 | 0.157883 | ||||||||
\(436\) | −3489.55 | −0.383300 | ||||||||
\(437\) | 22628.4 | 2.47703 | ||||||||
\(438\) | −6581.54 | −0.717987 | ||||||||
\(439\) | 6909.21 | 0.751159 | 0.375579 | − | 0.926790i | \(-0.377444\pi\) | ||||
0.375579 | + | 0.926790i | \(0.377444\pi\) | |||||||
\(440\) | −183.152 | −0.0198441 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 8245.50 | 0.887327 | ||||||||
\(443\) | −14812.6 | −1.58864 | −0.794318 | − | 0.607502i | \(-0.792172\pi\) | ||||
−0.794318 | + | 0.607502i | \(0.792172\pi\) | |||||||
\(444\) | 1302.06 | 0.139173 | ||||||||
\(445\) | 1308.75 | 0.139418 | ||||||||
\(446\) | −16511.0 | −1.75296 | ||||||||
\(447\) | 7024.72 | 0.743306 | ||||||||
\(448\) | 30.0561 | 0.00316968 | ||||||||
\(449\) | −10654.5 | −1.11986 | −0.559932 | − | 0.828538i | \(-0.689173\pi\) | ||||
−0.559932 | + | 0.828538i | \(0.689173\pi\) | |||||||
\(450\) | −794.504 | −0.0832295 | ||||||||
\(451\) | 1442.76 | 0.150636 | ||||||||
\(452\) | −4985.68 | −0.518820 | ||||||||
\(453\) | −6312.21 | −0.654688 | ||||||||
\(454\) | −19220.3 | −1.98691 | ||||||||
\(455\) | 667.179 | 0.0687425 | ||||||||
\(456\) | 4018.81 | 0.412715 | ||||||||
\(457\) | −5855.16 | −0.599328 | −0.299664 | − | 0.954045i | \(-0.596875\pi\) | ||||
−0.299664 | + | 0.954045i | \(0.596875\pi\) | |||||||
\(458\) | 1893.76 | 0.193208 | ||||||||
\(459\) | 3307.45 | 0.336336 | ||||||||
\(460\) | 4706.23 | 0.477019 | ||||||||
\(461\) | 3204.74 | 0.323774 | 0.161887 | − | 0.986809i | \(-0.448242\pi\) | ||||
0.161887 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(462\) | −217.844 | −0.0219373 | ||||||||
\(463\) | 371.658 | 0.0373054 | 0.0186527 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186527 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(464\) | −7618.54 | −0.762245 | ||||||||
\(465\) | −1414.61 | −0.141077 | ||||||||
\(466\) | 647.927 | 0.0644091 | ||||||||
\(467\) | −19752.3 | −1.95723 | −0.978614 | − | 0.205703i | \(-0.934052\pi\) | ||||
−0.978614 | + | 0.205703i | \(0.934052\pi\) | |||||||
\(468\) | −766.681 | −0.0757262 | ||||||||
\(469\) | 2169.95 | 0.213643 | ||||||||
\(470\) | −8359.84 | −0.820449 | ||||||||
\(471\) | −1780.40 | −0.174175 | ||||||||
\(472\) | −9484.01 | −0.924866 | ||||||||
\(473\) | 126.334 | 0.0122809 | ||||||||
\(474\) | 262.320 | 0.0254193 | ||||||||
\(475\) | 2685.90 | 0.259447 | ||||||||
\(476\) | −3832.00 | −0.368990 | ||||||||
\(477\) | −1653.09 | −0.158679 | ||||||||
\(478\) | −2271.28 | −0.217335 | ||||||||
\(479\) | −20762.0 | −1.98046 | −0.990232 | − | 0.139433i | \(-0.955472\pi\) | ||||
−0.990232 | + | 0.139433i | \(0.955472\pi\) | |||||||
\(480\) | 2729.45 | 0.259545 | ||||||||
\(481\) | −1851.34 | −0.175496 | ||||||||
\(482\) | 20323.8 | 1.92059 | ||||||||
\(483\) | −4423.07 | −0.416681 | ||||||||
\(484\) | −5909.50 | −0.554987 | ||||||||
\(485\) | −5023.87 | −0.470355 | ||||||||
\(486\) | −858.064 | −0.0800876 | ||||||||
\(487\) | 17647.6 | 1.64207 | 0.821035 | − | 0.570878i | \(-0.193397\pi\) | ||||
0.821035 | + | 0.570878i | \(0.193397\pi\) | |||||||
\(488\) | −2478.15 | −0.229878 | ||||||||
\(489\) | 6536.12 | 0.604445 | ||||||||
\(490\) | −865.127 | −0.0797601 | ||||||||
\(491\) | −5637.46 | −0.518157 | −0.259078 | − | 0.965856i | \(-0.583419\pi\) | ||||
−0.259078 | + | 0.965856i | \(0.583419\pi\) | |||||||
\(492\) | −6584.16 | −0.603327 | ||||||||
\(493\) | 11697.9 | 1.06865 | ||||||||
\(494\) | 7231.64 | 0.658638 | ||||||||
\(495\) | −132.198 | −0.0120038 | ||||||||
\(496\) | 7523.86 | 0.681112 | ||||||||
\(497\) | −4659.85 | −0.420569 | ||||||||
\(498\) | 4308.58 | 0.387695 | ||||||||
\(499\) | −17474.1 | −1.56764 | −0.783818 | − | 0.620991i | \(-0.786730\pi\) | ||||
−0.783818 | + | 0.620991i | \(0.786730\pi\) | |||||||
\(500\) | 558.609 | 0.0499635 | ||||||||
\(501\) | 2398.51 | 0.213887 | ||||||||
\(502\) | 18122.7 | 1.61127 | ||||||||
\(503\) | 7444.81 | 0.659936 | 0.329968 | − | 0.943992i | \(-0.392962\pi\) | ||||
0.329968 | + | 0.943992i | \(0.392962\pi\) | |||||||
\(504\) | −785.539 | −0.0694260 | ||||||||
\(505\) | −644.358 | −0.0567793 | ||||||||
\(506\) | 2184.90 | 0.191958 | ||||||||
\(507\) | −5500.89 | −0.481860 | ||||||||
\(508\) | −8383.53 | −0.732203 | ||||||||
\(509\) | −3384.48 | −0.294724 | −0.147362 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147362 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(510\) | −6488.35 | −0.563351 | ||||||||
\(511\) | −4349.02 | −0.376495 | ||||||||
\(512\) | −6558.89 | −0.566142 | ||||||||
\(513\) | 2900.77 | 0.249653 | ||||||||
\(514\) | −17803.0 | −1.52774 | ||||||||
\(515\) | 4030.04 | 0.344825 | ||||||||
\(516\) | −576.536 | −0.0491872 | ||||||||
\(517\) | −1391.00 | −0.118329 | ||||||||
\(518\) | 2400.62 | 0.203624 | ||||||||
\(519\) | −4333.07 | −0.366476 | ||||||||
\(520\) | −1188.42 | −0.100223 | ||||||||
\(521\) | 2973.12 | 0.250009 | 0.125005 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125005 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(522\) | −3034.82 | −0.254465 | ||||||||
\(523\) | 2689.02 | 0.224823 | 0.112412 | − | 0.993662i | \(-0.464142\pi\) | ||||
0.112412 | + | 0.993662i | \(0.464142\pi\) | |||||||
\(524\) | 1627.57 | 0.135689 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | −26755.3 | −2.21785 | ||||||||
\(527\) | −11552.5 | −0.954903 | ||||||||
\(528\) | 703.121 | 0.0579534 | ||||||||
\(529\) | 32194.9 | 2.64608 | ||||||||
\(530\) | 3242.94 | 0.265781 | ||||||||
\(531\) | −6845.53 | −0.559455 | ||||||||
\(532\) | −3360.82 | −0.273891 | ||||||||
\(533\) | 9361.72 | 0.760790 | ||||||||
\(534\) | −2772.83 | −0.224704 | ||||||||
\(535\) | −3848.56 | −0.311005 | ||||||||
\(536\) | −3865.25 | −0.311480 | ||||||||
\(537\) | 10030.5 | 0.806046 | ||||||||
\(538\) | −3612.69 | −0.289506 | ||||||||
\(539\) | −143.949 | −0.0115034 | ||||||||
\(540\) | 603.298 | 0.0480774 | ||||||||
\(541\) | −14429.5 | −1.14671 | −0.573356 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573356 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(542\) | 7952.03 | 0.630201 | ||||||||
\(543\) | 6755.44 | 0.533893 | ||||||||
\(544\) | 22290.1 | 1.75677 | ||||||||
\(545\) | −3904.28 | −0.306864 | ||||||||
\(546\) | −1413.54 | −0.110795 | ||||||||
\(547\) | 13811.2 | 1.07957 | 0.539784 | − | 0.841804i | \(-0.318506\pi\) | ||||
0.539784 | + | 0.841804i | \(0.318506\pi\) | |||||||
\(548\) | 7164.19 | 0.558466 | ||||||||
\(549\) | −1788.72 | −0.139054 | ||||||||
\(550\) | 259.339 | 0.0201059 | ||||||||
\(551\) | 10259.5 | 0.793229 | ||||||||
\(552\) | 7878.68 | 0.607498 | ||||||||
\(553\) | 173.338 | 0.0133293 | ||||||||
\(554\) | 30476.2 | 2.33720 | ||||||||
\(555\) | 1456.81 | 0.111420 | ||||||||
\(556\) | 10864.4 | 0.828692 | ||||||||
\(557\) | −6033.26 | −0.458954 | −0.229477 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229477 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(558\) | 2997.10 | 0.227379 | ||||||||
\(559\) | 819.751 | 0.0620246 | ||||||||
\(560\) | 2792.31 | 0.210708 | ||||||||
\(561\) | −1079.60 | −0.0812493 | ||||||||
\(562\) | 26559.8 | 1.99352 | ||||||||
\(563\) | −6958.47 | −0.520896 | −0.260448 | − | 0.965488i | \(-0.583870\pi\) | ||||
−0.260448 | + | 0.965488i | \(0.583870\pi\) | |||||||
\(564\) | 6347.95 | 0.473931 | ||||||||
\(565\) | −5578.23 | −0.415359 | ||||||||
\(566\) | −52.3202 | −0.00388548 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 8300.44 | 0.613166 | ||||||||
\(569\) | −13396.4 | −0.987009 | −0.493505 | − | 0.869743i | \(-0.664284\pi\) | ||||
−0.493505 | + | 0.869743i | \(0.664284\pi\) | |||||||
\(570\) | −5690.55 | −0.418159 | ||||||||
\(571\) | −8055.84 | −0.590414 | −0.295207 | − | 0.955433i | \(-0.595389\pi\) | ||||
−0.295207 | + | 0.955433i | \(0.595389\pi\) | |||||||
\(572\) | 250.257 | 0.0182933 | ||||||||
\(573\) | −3005.78 | −0.219142 | ||||||||
\(574\) | −12139.3 | −0.882724 | ||||||||
\(575\) | 5265.56 | 0.381894 | ||||||||
\(576\) | −38.6435 | −0.00279539 | ||||||||
\(577\) | −21456.9 | −1.54812 | −0.774059 | − | 0.633114i | \(-0.781777\pi\) | ||||
−0.774059 | + | 0.633114i | \(0.781777\pi\) | |||||||
\(578\) | −35638.9 | −2.56468 | ||||||||
\(579\) | −12164.9 | −0.873153 | ||||||||
\(580\) | 2133.76 | 0.152758 | ||||||||
\(581\) | 2847.07 | 0.203298 | ||||||||
\(582\) | 10644.0 | 0.758087 | ||||||||
\(583\) | 539.596 | 0.0383324 | ||||||||
\(584\) | 7746.76 | 0.548910 | ||||||||
\(585\) | −857.802 | −0.0606252 | ||||||||
\(586\) | −24412.1 | −1.72091 | ||||||||
\(587\) | 20156.3 | 1.41728 | 0.708638 | − | 0.705572i | \(-0.249310\pi\) | ||||
0.708638 | + | 0.705572i | \(0.249310\pi\) | |||||||
\(588\) | 656.924 | 0.0460733 | ||||||||
\(589\) | −10132.0 | −0.708797 | ||||||||
\(590\) | 13429.1 | 0.937066 | ||||||||
\(591\) | −15420.7 | −1.07330 | ||||||||
\(592\) | −7748.30 | −0.537928 | ||||||||
\(593\) | 599.307 | 0.0415018 | 0.0207509 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207509 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(594\) | 280.086 | 0.0193469 | ||||||||
\(595\) | −4287.43 | −0.295408 | ||||||||
\(596\) | 10464.2 | 0.719177 | ||||||||
\(597\) | 1756.89 | 0.120444 | ||||||||
\(598\) | 14177.3 | 0.969485 | ||||||||
\(599\) | −5493.05 | −0.374691 | −0.187346 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187346 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(600\) | 935.165 | 0.0636299 | ||||||||
\(601\) | 24292.8 | 1.64879 | 0.824396 | − | 0.566014i | \(-0.191515\pi\) | ||||
0.824396 | + | 0.566014i | \(0.191515\pi\) | |||||||
\(602\) | −1062.97 | −0.0719655 | ||||||||
\(603\) | −2789.93 | −0.188416 | ||||||||
\(604\) | −9402.82 | −0.633436 | ||||||||
\(605\) | −6611.85 | −0.444314 | ||||||||
\(606\) | 1365.19 | 0.0915131 | ||||||||
\(607\) | 3029.50 | 0.202576 | 0.101288 | − | 0.994857i | \(-0.467704\pi\) | ||||
0.101288 | + | 0.994857i | \(0.467704\pi\) | |||||||
\(608\) | 19549.3 | 1.30400 | ||||||||
\(609\) | −2005.38 | −0.133435 | ||||||||
\(610\) | 3509.01 | 0.232911 | ||||||||
\(611\) | −9025.87 | −0.597623 | ||||||||
\(612\) | 4926.85 | 0.325419 | ||||||||
\(613\) | −19339.6 | −1.27426 | −0.637129 | − | 0.770757i | \(-0.719878\pi\) | ||||
−0.637129 | + | 0.770757i | \(0.719878\pi\) | |||||||
\(614\) | 26992.4 | 1.77414 | ||||||||
\(615\) | −7366.69 | −0.483014 | ||||||||
\(616\) | 256.412 | 0.0167713 | ||||||||
\(617\) | −5743.91 | −0.374783 | −0.187391 | − | 0.982285i | \(-0.560003\pi\) | ||||
−0.187391 | + | 0.982285i | \(0.560003\pi\) | |||||||
\(618\) | −8538.35 | −0.555765 | ||||||||
\(619\) | −8243.35 | −0.535264 | −0.267632 | − | 0.963521i | \(-0.586241\pi\) | ||||
−0.267632 | + | 0.963521i | \(0.586241\pi\) | |||||||
\(620\) | −2107.24 | −0.136498 | ||||||||
\(621\) | 5686.81 | 0.367478 | ||||||||
\(622\) | −26815.4 | −1.72861 | ||||||||
\(623\) | −1832.26 | −0.117830 | ||||||||
\(624\) | 4562.37 | 0.292694 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 32231.6 | 2.05788 | ||||||||
\(627\) | −946.856 | −0.0603091 | ||||||||
\(628\) | −2652.13 | −0.168521 | ||||||||
\(629\) | 11897.1 | 0.754162 | ||||||||
\(630\) | 1112.31 | 0.0703418 | ||||||||
\(631\) | −4376.56 | −0.276114 | −0.138057 | − | 0.990424i | \(-0.544086\pi\) | ||||
−0.138057 | + | 0.990424i | \(0.544086\pi\) | |||||||
\(632\) | −308.762 | −0.0194334 | ||||||||
\(633\) | −3165.48 | −0.198762 | ||||||||
\(634\) | 17407.8 | 1.09046 | ||||||||
\(635\) | −9379.92 | −0.586190 | ||||||||
\(636\) | −2462.49 | −0.153528 | ||||||||
\(637\) | −934.051 | −0.0580980 | ||||||||
\(638\) | 990.613 | 0.0614714 | ||||||||
\(639\) | 5991.23 | 0.370907 | ||||||||
\(640\) | −7202.71 | −0.444863 | ||||||||
\(641\) | 11836.6 | 0.729357 | 0.364678 | − | 0.931133i | \(-0.381179\pi\) | ||||
0.364678 | + | 0.931133i | \(0.381179\pi\) | |||||||
\(642\) | 8153.86 | 0.501257 | ||||||||
\(643\) | 1448.21 | 0.0888209 | 0.0444104 | − | 0.999013i | \(-0.485859\pi\) | ||||
0.0444104 | + | 0.999013i | \(0.485859\pi\) | |||||||
\(644\) | −6588.72 | −0.403155 | ||||||||
\(645\) | −645.058 | −0.0393785 | ||||||||
\(646\) | −46472.0 | −2.83037 | ||||||||
\(647\) | −8732.95 | −0.530646 | −0.265323 | − | 0.964160i | \(-0.585479\pi\) | ||||
−0.265323 | + | 0.964160i | \(0.585479\pi\) | |||||||
\(648\) | 1009.98 | 0.0612279 | ||||||||
\(649\) | 2234.49 | 0.135149 | ||||||||
\(650\) | 1682.78 | 0.101545 | ||||||||
\(651\) | 1980.46 | 0.119232 | ||||||||
\(652\) | 9736.37 | 0.584824 | ||||||||
\(653\) | −21978.4 | −1.31712 | −0.658562 | − | 0.752527i | \(-0.728835\pi\) | ||||
−0.658562 | + | 0.752527i | \(0.728835\pi\) | |||||||
\(654\) | 8271.91 | 0.494583 | ||||||||
\(655\) | 1821.01 | 0.108630 | ||||||||
\(656\) | 39181.1 | 2.33196 | ||||||||
\(657\) | 5591.59 | 0.332038 | ||||||||
\(658\) | 11703.8 | 0.693406 | ||||||||
\(659\) | −27761.7 | −1.64103 | −0.820516 | − | 0.571623i | \(-0.806314\pi\) | ||||
−0.820516 | + | 0.571623i | \(0.806314\pi\) | |||||||
\(660\) | −196.926 | −0.0116141 | ||||||||
\(661\) | −8573.72 | −0.504507 | −0.252254 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252254 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(662\) | −4313.86 | −0.253267 | ||||||||
\(663\) | −7005.27 | −0.410350 | ||||||||
\(664\) | −5071.39 | −0.296398 | ||||||||
\(665\) | −3760.25 | −0.219273 | ||||||||
\(666\) | −3086.51 | −0.179579 | ||||||||
\(667\) | 20113.2 | 1.16760 | ||||||||
\(668\) | 3572.87 | 0.206944 | ||||||||
\(669\) | 14027.6 | 0.810668 | ||||||||
\(670\) | 5473.11 | 0.315589 | ||||||||
\(671\) | 583.868 | 0.0335916 | ||||||||
\(672\) | −3821.22 | −0.219356 | ||||||||
\(673\) | 27159.2 | 1.55559 | 0.777795 | − | 0.628518i | \(-0.216338\pi\) | ||||
0.777795 | + | 0.628518i | \(0.216338\pi\) | |||||||
\(674\) | 30879.1 | 1.76472 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −8194.26 | −0.466219 | ||||||||
\(677\) | −1392.30 | −0.0790404 | −0.0395202 | − | 0.999219i | \(-0.512583\pi\) | ||||
−0.0395202 | + | 0.999219i | \(0.512583\pi\) | |||||||
\(678\) | 11818.5 | 0.669448 | ||||||||
\(679\) | 7033.42 | 0.397523 | ||||||||
\(680\) | 7637.06 | 0.430688 | ||||||||
\(681\) | 16329.3 | 0.918857 | ||||||||
\(682\) | −978.302 | −0.0549283 | ||||||||
\(683\) | −8675.09 | −0.486007 | −0.243004 | − | 0.970025i | \(-0.578133\pi\) | ||||
−0.243004 | + | 0.970025i | \(0.578133\pi\) | |||||||
\(684\) | 4321.05 | 0.241549 | ||||||||
\(685\) | 8015.66 | 0.447099 | ||||||||
\(686\) | 1211.18 | 0.0674096 | ||||||||
\(687\) | −1608.91 | −0.0893504 | ||||||||
\(688\) | 3430.86 | 0.190117 | ||||||||
\(689\) | 3501.30 | 0.193598 | ||||||||
\(690\) | −11156.0 | −0.615511 | ||||||||
\(691\) | −21426.0 | −1.17957 | −0.589785 | − | 0.807561i | \(-0.700787\pi\) | ||||
−0.589785 | + | 0.807561i | \(0.700787\pi\) | |||||||
\(692\) | −6454.65 | −0.354579 | ||||||||
\(693\) | 185.078 | 0.0101451 | ||||||||
\(694\) | −16206.3 | −0.886433 | ||||||||
\(695\) | 12155.6 | 0.663438 | ||||||||
\(696\) | 3572.11 | 0.194541 | ||||||||
\(697\) | −60160.4 | −3.26935 | ||||||||
\(698\) | 14088.8 | 0.763997 | ||||||||
\(699\) | −550.470 | −0.0297864 | ||||||||
\(700\) | −782.052 | −0.0422269 | ||||||||
\(701\) | 24840.5 | 1.33839 | 0.669197 | − | 0.743085i | \(-0.266638\pi\) | ||||
0.669197 | + | 0.743085i | \(0.266638\pi\) | |||||||
\(702\) | 1817.40 | 0.0977116 | ||||||||
\(703\) | 10434.2 | 0.559793 | ||||||||
\(704\) | 12.6139 | 0.000675288 0 | ||||||||
\(705\) | 7102.41 | 0.379422 | ||||||||
\(706\) | −8532.45 | −0.454848 | ||||||||
\(707\) | 902.101 | 0.0479873 | ||||||||
\(708\) | −10197.3 | −0.541295 | ||||||||
\(709\) | 12525.0 | 0.663450 | 0.331725 | − | 0.943376i | \(-0.392369\pi\) | ||||
0.331725 | + | 0.943376i | \(0.392369\pi\) | |||||||
\(710\) | −11753.2 | −0.621255 | ||||||||
\(711\) | −222.863 | −0.0117553 | ||||||||
\(712\) | 3263.74 | 0.171789 | ||||||||
\(713\) | −19863.3 | −1.04332 | ||||||||
\(714\) | 9083.69 | 0.476118 | ||||||||
\(715\) | 280.000 | 0.0146453 | ||||||||
\(716\) | 14941.6 | 0.779881 | ||||||||
\(717\) | 1929.65 | 0.100508 | ||||||||
\(718\) | 9732.66 | 0.505877 | ||||||||
\(719\) | 28085.0 | 1.45674 | 0.728369 | − | 0.685185i | \(-0.240279\pi\) | ||||
0.728369 | + | 0.685185i | \(0.240279\pi\) | |||||||
\(720\) | −3590.11 | −0.185827 | ||||||||
\(721\) | −5642.05 | −0.291430 | ||||||||
\(722\) | −16537.9 | −0.852460 | ||||||||
\(723\) | −17266.8 | −0.888189 | ||||||||
\(724\) | 10063.1 | 0.516562 | ||||||||
\(725\) | 2387.35 | 0.122295 | ||||||||
\(726\) | 14008.4 | 0.716115 | ||||||||
\(727\) | −14326.2 | −0.730851 | −0.365426 | − | 0.930841i | \(-0.619077\pi\) | ||||
−0.365426 | + | 0.930841i | \(0.619077\pi\) | |||||||
\(728\) | 1663.79 | 0.0847037 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −10969.2 | −0.556150 | ||||||||
\(731\) | −5267.89 | −0.266539 | ||||||||
\(732\) | −2664.53 | −0.134541 | ||||||||
\(733\) | 6727.85 | 0.339016 | 0.169508 | − | 0.985529i | \(-0.445782\pi\) | ||||
0.169508 | + | 0.985529i | \(0.445782\pi\) | |||||||
\(734\) | −39240.8 | −1.97331 | ||||||||
\(735\) | 735.000 | 0.0368856 | ||||||||
\(736\) | 38325.5 | 1.91943 | ||||||||
\(737\) | 910.677 | 0.0455159 | ||||||||
\(738\) | 15607.6 | 0.778490 | ||||||||
\(739\) | −3418.51 | −0.170165 | −0.0850826 | − | 0.996374i | \(-0.527115\pi\) | ||||
−0.0850826 | + | 0.996374i | \(0.527115\pi\) | |||||||
\(740\) | 2170.10 | 0.107803 | ||||||||
\(741\) | −6143.91 | −0.304591 | ||||||||
\(742\) | −4540.11 | −0.224626 | ||||||||
\(743\) | 8095.50 | 0.399724 | 0.199862 | − | 0.979824i | \(-0.435951\pi\) | ||||
0.199862 | + | 0.979824i | \(0.435951\pi\) | |||||||
\(744\) | −3527.72 | −0.173834 | ||||||||
\(745\) | 11707.9 | 0.575762 | ||||||||
\(746\) | −21508.4 | −1.05560 | ||||||||
\(747\) | −3660.51 | −0.179292 | ||||||||
\(748\) | −1608.20 | −0.0786119 | ||||||||
\(749\) | 5387.99 | 0.262847 | ||||||||
\(750\) | −1324.17 | −0.0644693 | ||||||||
\(751\) | 13446.8 | 0.653371 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(752\) | −37775.4 | −1.83182 | ||||||||
\(753\) | −15396.8 | −0.745141 | ||||||||
\(754\) | 6427.84 | 0.310462 | ||||||||
\(755\) | −10520.4 | −0.507119 | ||||||||
\(756\) | −844.617 | −0.0406328 | ||||||||
\(757\) | −2593.24 | −0.124508 | −0.0622541 | − | 0.998060i | \(-0.519829\pi\) | ||||
−0.0622541 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(758\) | −14069.0 | −0.674156 | ||||||||
\(759\) | −1856.26 | −0.0887722 | ||||||||
\(760\) | 6698.02 | 0.319688 | ||||||||
\(761\) | 27079.4 | 1.28992 | 0.644959 | − | 0.764217i | \(-0.276875\pi\) | ||||
0.644959 | + | 0.764217i | \(0.276875\pi\) | |||||||
\(762\) | 19873.0 | 0.944782 | ||||||||
\(763\) | 5465.99 | 0.259348 | ||||||||
\(764\) | −4477.48 | −0.212028 | ||||||||
\(765\) | 5512.41 | 0.260525 | ||||||||
\(766\) | −1124.58 | −0.0530451 | ||||||||
\(767\) | 14499.0 | 0.682568 | ||||||||
\(768\) | 15363.3 | 0.721842 | ||||||||
\(769\) | 2138.72 | 0.100292 | 0.0501458 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501458 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(770\) | −363.074 | −0.0169926 | ||||||||
\(771\) | 15125.2 | 0.706513 | ||||||||
\(772\) | −18121.1 | −0.844810 | ||||||||
\(773\) | 25864.0 | 1.20345 | 0.601724 | − | 0.798704i | \(-0.294481\pi\) | ||||
0.601724 | + | 0.798704i | \(0.294481\pi\) | |||||||
\(774\) | 1366.67 | 0.0634676 | ||||||||
\(775\) | −2357.69 | −0.109278 | ||||||||
\(776\) | −12528.4 | −0.579566 | ||||||||
\(777\) | −2039.53 | −0.0941671 | ||||||||
\(778\) | −13720.1 | −0.632247 | ||||||||
\(779\) | −52763.1 | −2.42675 | ||||||||
\(780\) | −1277.80 | −0.0586572 | ||||||||
\(781\) | −1955.63 | −0.0896006 | ||||||||
\(782\) | −91106.2 | −4.16618 | ||||||||
\(783\) | 2578.34 | 0.117679 | ||||||||
\(784\) | −3909.23 | −0.178081 | ||||||||
\(785\) | −2967.33 | −0.134916 | ||||||||
\(786\) | −3858.14 | −0.175083 | ||||||||
\(787\) | −32371.3 | −1.46621 | −0.733107 | − | 0.680113i | \(-0.761931\pi\) | ||||
−0.733107 | + | 0.680113i | \(0.761931\pi\) | |||||||
\(788\) | −22971.0 | −1.03846 | ||||||||
\(789\) | 22731.0 | 1.02566 | ||||||||
\(790\) | 437.200 | 0.0196897 | ||||||||
\(791\) | 7809.52 | 0.351043 | ||||||||
\(792\) | −329.673 | −0.0147909 | ||||||||
\(793\) | 3788.57 | 0.169654 | ||||||||
\(794\) | −16970.8 | −0.758526 | ||||||||
\(795\) | −2755.16 | −0.122912 | ||||||||
\(796\) | 2617.11 | 0.116534 | ||||||||
\(797\) | 2024.33 | 0.0899691 | 0.0449845 | − | 0.998988i | \(-0.485676\pi\) | ||||
0.0449845 | + | 0.998988i | \(0.485676\pi\) | |||||||
\(798\) | 7966.76 | 0.353409 | ||||||||
\(799\) | 58002.1 | 2.56817 | ||||||||
\(800\) | 4549.08 | 0.201043 | ||||||||
\(801\) | 2355.76 | 0.103916 | ||||||||
\(802\) | −12777.7 | −0.562589 | ||||||||
\(803\) | −1825.18 | −0.0802109 | ||||||||
\(804\) | −4155.95 | −0.182300 | ||||||||
\(805\) | −7371.79 | −0.322760 | ||||||||
\(806\) | −6347.95 | −0.277416 | ||||||||
\(807\) | 3069.29 | 0.133884 | ||||||||
\(808\) | −1606.88 | −0.0699628 | ||||||||
\(809\) | 12391.7 | 0.538526 | 0.269263 | − | 0.963067i | \(-0.413220\pi\) | ||||
0.269263 | + | 0.963067i | \(0.413220\pi\) | |||||||
\(810\) | −1430.11 | −0.0620356 | ||||||||
\(811\) | 14654.5 | 0.634511 | 0.317256 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(812\) | −2987.26 | −0.129104 | ||||||||
\(813\) | −6755.94 | −0.291441 | ||||||||
\(814\) | 1007.49 | 0.0433813 | ||||||||
\(815\) | 10893.5 | 0.468201 | ||||||||
\(816\) | −29318.7 | −1.25780 | ||||||||
\(817\) | −4620.16 | −0.197844 | ||||||||
\(818\) | 7447.33 | 0.318325 | ||||||||
\(819\) | 1200.92 | 0.0512376 | ||||||||
\(820\) | −10973.6 | −0.467335 | ||||||||
\(821\) | 23887.9 | 1.01546 | 0.507731 | − | 0.861516i | \(-0.330485\pi\) | ||||
0.507731 | + | 0.861516i | \(0.330485\pi\) | |||||||
\(822\) | −16982.6 | −0.720604 | ||||||||
\(823\) | −4008.41 | −0.169774 | −0.0848871 | − | 0.996391i | \(-0.527053\pi\) | ||||
−0.0848871 | + | 0.996391i | \(0.527053\pi\) | |||||||
\(824\) | 10050.0 | 0.424889 | ||||||||
\(825\) | −220.331 | −0.00929810 | ||||||||
\(826\) | −18800.8 | −0.791966 | ||||||||
\(827\) | −45110.4 | −1.89679 | −0.948394 | − | 0.317096i | \(-0.897292\pi\) | ||||
−0.948394 | + | 0.317096i | \(0.897292\pi\) | |||||||
\(828\) | 8471.21 | 0.355549 | ||||||||
\(829\) | 16165.4 | 0.677260 | 0.338630 | − | 0.940920i | \(-0.390036\pi\) | ||||
0.338630 | + | 0.940920i | \(0.390036\pi\) | |||||||
\(830\) | 7180.97 | 0.300307 | ||||||||
\(831\) | −25892.2 | −1.08085 | ||||||||
\(832\) | 81.8481 | 0.00341054 | ||||||||
\(833\) | 6002.41 | 0.249665 | ||||||||
\(834\) | −25753.8 | −1.06928 | ||||||||
\(835\) | 3997.51 | 0.165676 | ||||||||
\(836\) | −1410.46 | −0.0583514 | ||||||||
\(837\) | −2546.30 | −0.105153 | ||||||||
\(838\) | 24385.7 | 1.00524 | ||||||||
\(839\) | −25244.4 | −1.03878 | −0.519388 | − | 0.854538i | \(-0.673840\pi\) | ||||
−0.519388 | + | 0.854538i | \(0.673840\pi\) | |||||||
\(840\) | −1309.23 | −0.0537771 | ||||||||
\(841\) | −15269.9 | −0.626096 | ||||||||
\(842\) | 34066.7 | 1.39432 | ||||||||
\(843\) | −22564.9 | −0.921916 | ||||||||
\(844\) | −4715.37 | −0.192310 | ||||||||
\(845\) | −9168.15 | −0.373247 | ||||||||
\(846\) | −15047.7 | −0.611526 | ||||||||
\(847\) | 9256.59 | 0.375514 | ||||||||
\(848\) | 14653.8 | 0.593412 | ||||||||
\(849\) | 44.4506 | 0.00179687 | ||||||||
\(850\) | −10813.9 | −0.436370 | ||||||||
\(851\) | 20455.8 | 0.823990 | ||||||||
\(852\) | 8924.68 | 0.358867 | ||||||||
\(853\) | −30168.1 | −1.21094 | −0.605472 | − | 0.795867i | \(-0.707016\pi\) | ||||
−0.605472 | + | 0.795867i | \(0.707016\pi\) | |||||||
\(854\) | −4912.61 | −0.196846 | ||||||||
\(855\) | 4834.61 | 0.193380 | ||||||||
\(856\) | −9597.44 | −0.383217 | ||||||||
\(857\) | −13393.6 | −0.533857 | −0.266929 | − | 0.963716i | \(-0.586009\pi\) | ||||
−0.266929 | + | 0.963716i | \(0.586009\pi\) | |||||||
\(858\) | −593.230 | −0.0236043 | ||||||||
\(859\) | 19060.4 | 0.757081 | 0.378541 | − | 0.925585i | \(-0.376426\pi\) | ||||
0.378541 | + | 0.925585i | \(0.376426\pi\) | |||||||
\(860\) | −960.894 | −0.0381002 | ||||||||
\(861\) | 10313.4 | 0.408222 | ||||||||
\(862\) | 45914.3 | 1.81421 | ||||||||
\(863\) | −9466.86 | −0.373413 | −0.186707 | − | 0.982416i | \(-0.559781\pi\) | ||||
−0.186707 | + | 0.982416i | \(0.559781\pi\) | |||||||
\(864\) | 4913.00 | 0.193453 | ||||||||
\(865\) | −7221.79 | −0.283871 | ||||||||
\(866\) | −25975.2 | −1.01925 | ||||||||
\(867\) | 30278.3 | 1.18605 | ||||||||
\(868\) | 2950.13 | 0.115362 | ||||||||
\(869\) | 72.7461 | 0.00283975 | ||||||||
\(870\) | −5058.03 | −0.197107 | ||||||||
\(871\) | 5909.15 | 0.229878 | ||||||||
\(872\) | −9736.39 | −0.378115 | ||||||||
\(873\) | −9042.97 | −0.350582 | ||||||||
\(874\) | −79903.8 | −3.09243 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | 8329.37 | 0.321259 | ||||||||
\(877\) | 37740.6 | 1.45315 | 0.726573 | − | 0.687090i | \(-0.241112\pi\) | ||||
0.726573 | + | 0.687090i | \(0.241112\pi\) | |||||||
\(878\) | −24397.3 | −0.937778 | ||||||||
\(879\) | 20740.2 | 0.795845 | ||||||||
\(880\) | 1171.87 | 0.0448905 | ||||||||
\(881\) | 25991.5 | 0.993957 | 0.496979 | − | 0.867763i | \(-0.334443\pi\) | ||||
0.496979 | + | 0.867763i | \(0.334443\pi\) | |||||||
\(882\) | −1557.23 | −0.0594496 | ||||||||
\(883\) | 39420.3 | 1.50238 | 0.751189 | − | 0.660087i | \(-0.229481\pi\) | ||||
0.751189 | + | 0.660087i | \(0.229481\pi\) | |||||||
\(884\) | −10435.2 | −0.397030 | ||||||||
\(885\) | −11409.2 | −0.433352 | ||||||||
\(886\) | 52305.0 | 1.98332 | ||||||||
\(887\) | 46005.2 | 1.74149 | 0.870745 | − | 0.491735i | \(-0.163637\pi\) | ||||
0.870745 | + | 0.491735i | \(0.163637\pi\) | |||||||
\(888\) | 3632.95 | 0.137290 | ||||||||
\(889\) | 13131.9 | 0.495421 | ||||||||
\(890\) | −4621.38 | −0.174055 | ||||||||
\(891\) | −237.957 | −0.00894710 | ||||||||
\(892\) | 20895.8 | 0.784353 | ||||||||
\(893\) | 50870.2 | 1.90628 | ||||||||
\(894\) | −24805.2 | −0.927975 | ||||||||
\(895\) | 16717.5 | 0.624361 | ||||||||
\(896\) | 10083.8 | 0.375978 | ||||||||
\(897\) | −12044.8 | −0.448345 | ||||||||
\(898\) | 37622.6 | 1.39809 | ||||||||
\(899\) | −9005.81 | −0.334105 | ||||||||
\(900\) | 1005.50 | 0.0372406 | ||||||||
\(901\) | −22500.1 | −0.831950 | ||||||||
\(902\) | −5094.58 | −0.188061 | ||||||||
\(903\) | 903.081 | 0.0332809 | ||||||||
\(904\) | −13910.8 | −0.511801 | ||||||||
\(905\) | 11259.1 | 0.413551 | ||||||||
\(906\) | 22289.2 | 0.817340 | ||||||||
\(907\) | −2838.97 | −0.103932 | −0.0519661 | − | 0.998649i | \(-0.516549\pi\) | ||||
−0.0519661 | + | 0.998649i | \(0.516549\pi\) | |||||||
\(908\) | 24324.6 | 0.889030 | ||||||||
\(909\) | −1159.84 | −0.0423208 | ||||||||
\(910\) | −2355.90 | −0.0858211 | ||||||||
\(911\) | 39890.9 | 1.45076 | 0.725382 | − | 0.688347i | \(-0.241663\pi\) | ||||
0.725382 | + | 0.688347i | \(0.241663\pi\) | |||||||
\(912\) | −25713.7 | −0.933626 | ||||||||
\(913\) | 1194.85 | 0.0433119 | ||||||||
\(914\) | 20675.3 | 0.748226 | ||||||||
\(915\) | −2981.21 | −0.107711 | ||||||||
\(916\) | −2396.67 | −0.0864500 | ||||||||
\(917\) | −2549.42 | −0.0918094 | ||||||||
\(918\) | −11679.0 | −0.419897 | ||||||||
\(919\) | −646.475 | −0.0232048 | −0.0116024 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116024 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(920\) | 13131.1 | 0.470566 | ||||||||
\(921\) | −22932.4 | −0.820463 | ||||||||
\(922\) | −11316.3 | −0.404213 | ||||||||
\(923\) | −12689.6 | −0.452528 | ||||||||
\(924\) | 275.696 | 0.00981574 | ||||||||
\(925\) | 2428.02 | 0.0863056 | ||||||||
\(926\) | −1312.37 | −0.0465737 | ||||||||
\(927\) | 7254.07 | 0.257017 | ||||||||
\(928\) | 17376.4 | 0.614665 | ||||||||
\(929\) | 51188.2 | 1.80778 | 0.903892 | − | 0.427760i | \(-0.140697\pi\) | ||||
0.903892 | + | 0.427760i | \(0.140697\pi\) | |||||||
\(930\) | 4995.17 | 0.176127 | ||||||||
\(931\) | 5264.35 | 0.185319 | ||||||||
\(932\) | −819.993 | −0.0288195 | ||||||||
\(933\) | 22782.0 | 0.799409 | ||||||||
\(934\) | 69747.8 | 2.44349 | ||||||||
\(935\) | −1799.34 | −0.0629355 | ||||||||
\(936\) | −2139.16 | −0.0747017 | ||||||||
\(937\) | 29786.1 | 1.03849 | 0.519247 | − | 0.854624i | \(-0.326212\pi\) | ||||
0.519247 | + | 0.854624i | \(0.326212\pi\) | |||||||
\(938\) | −7662.36 | −0.266722 | ||||||||
\(939\) | −27383.5 | −0.951680 | ||||||||
\(940\) | 10579.9 | 0.367105 | ||||||||
\(941\) | −44817.4 | −1.55261 | −0.776304 | − | 0.630358i | \(-0.782908\pi\) | ||||
−0.776304 | + | 0.630358i | \(0.782908\pi\) | |||||||
\(942\) | 6286.82 | 0.217448 | ||||||||
\(943\) | −103439. | −3.57206 | ||||||||
\(944\) | 60682.0 | 2.09219 | ||||||||
\(945\) | −945.000 | −0.0325300 | ||||||||
\(946\) | −446.103 | −0.0153320 | ||||||||
\(947\) | 54697.1 | 1.87689 | 0.938446 | − | 0.345425i | \(-0.112265\pi\) | ||||
0.938446 | + | 0.345425i | \(0.112265\pi\) | |||||||
\(948\) | −331.983 | −0.0113737 | ||||||||
\(949\) | −11843.2 | −0.405105 | ||||||||
\(950\) | −9484.24 | −0.323905 | ||||||||
\(951\) | −14789.4 | −0.504290 | ||||||||
\(952\) | −10691.9 | −0.363998 | ||||||||
\(953\) | −7577.51 | −0.257565 | −0.128783 | − | 0.991673i | \(-0.541107\pi\) | ||||
−0.128783 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(954\) | 5837.29 | 0.198102 | ||||||||
\(955\) | −5009.63 | −0.169746 | ||||||||
\(956\) | 2874.46 | 0.0972454 | ||||||||
\(957\) | −841.612 | −0.0284278 | ||||||||
\(958\) | 73313.4 | 2.47249 | ||||||||
\(959\) | −11221.9 | −0.377868 | ||||||||
\(960\) | −64.4059 | −0.00216530 | ||||||||
\(961\) | −20897.1 | −0.701457 | ||||||||
\(962\) | 6537.32 | 0.219097 | ||||||||
\(963\) | −6927.41 | −0.231810 | ||||||||
\(964\) | −25721.1 | −0.859357 | ||||||||
\(965\) | −20274.8 | −0.676342 | ||||||||
\(966\) | 15618.4 | 0.520202 | ||||||||
\(967\) | 50779.0 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(968\) | −16488.5 | −0.547478 | ||||||||
\(969\) | 39482.0 | 1.30892 | ||||||||
\(970\) | 17739.9 | 0.587212 | ||||||||
\(971\) | −15313.2 | −0.506102 | −0.253051 | − | 0.967453i | \(-0.581434\pi\) | ||||
−0.253051 | + | 0.967453i | \(0.581434\pi\) | |||||||
\(972\) | 1085.94 | 0.0358348 | ||||||||
\(973\) | −17017.9 | −0.560707 | ||||||||
\(974\) | −62315.9 | −2.05003 | ||||||||
\(975\) | −1429.67 | −0.0469601 | ||||||||
\(976\) | 15856.1 | 0.520021 | ||||||||
\(977\) | 46620.4 | 1.52663 | 0.763316 | − | 0.646025i | \(-0.223570\pi\) | ||||
0.763316 | + | 0.646025i | \(0.223570\pi\) | |||||||
\(978\) | −23079.9 | −0.754615 | ||||||||
\(979\) | −768.957 | −0.0251031 | ||||||||
\(980\) | 1094.87 | 0.0356882 | ||||||||
\(981\) | −7027.70 | −0.228723 | ||||||||
\(982\) | 19906.6 | 0.646889 | ||||||||
\(983\) | −2824.37 | −0.0916414 | −0.0458207 | − | 0.998950i | \(-0.514590\pi\) | ||||
−0.0458207 | + | 0.998950i | \(0.514590\pi\) | |||||||
\(984\) | −18370.9 | −0.595165 | ||||||||
\(985\) | −25701.1 | −0.831377 | ||||||||
\(986\) | −41306.6 | −1.33415 | ||||||||
\(987\) | −9943.38 | −0.320670 | ||||||||
\(988\) | −9152.11 | −0.294704 | ||||||||
\(989\) | −9057.59 | −0.291218 | ||||||||
\(990\) | 466.810 | 0.0149860 | ||||||||
\(991\) | 16951.4 | 0.543370 | 0.271685 | − | 0.962386i | \(-0.412419\pi\) | ||||
0.271685 | + | 0.962386i | \(0.412419\pi\) | |||||||
\(992\) | −17160.5 | −0.549239 | ||||||||
\(993\) | 3665.00 | 0.117125 | ||||||||
\(994\) | 16454.5 | 0.525056 | ||||||||
\(995\) | 2928.15 | 0.0932952 | ||||||||
\(996\) | −5452.79 | −0.173472 | ||||||||
\(997\) | 23847.8 | 0.757540 | 0.378770 | − | 0.925491i | \(-0.376347\pi\) | ||||
0.378770 | + | 0.925491i | \(0.376347\pi\) | |||||||
\(998\) | 61703.4 | 1.95710 | ||||||||
\(999\) | 2622.26 | 0.0830476 |
(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 | 105.4.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.4.a.i.1.2 | 2 | |||
4.3 | odd | 2 | 1680.4.a.bg.1.1 | 2 | |||
5.2 | odd | 4 | 525.4.d.h.274.2 | 4 | |||
5.3 | odd | 4 | 525.4.d.h.274.3 | 4 | |||
5.4 | even | 2 | 525.4.a.k.1.2 | 2 | |||
7.6 | odd | 2 | 735.4.a.p.1.1 | 2 | |||
15.14 | odd | 2 | 1575.4.a.w.1.1 | 2 | |||
21.20 | even | 2 | 2205.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.4.a.i.1.2 | 2 | 3.2 | odd | 2 | |||
525.4.a.k.1.2 | 2 | 5.4 | even | 2 | |||
525.4.d.h.274.2 | 4 | 5.2 | odd | 4 | |||
525.4.d.h.274.3 | 4 | 5.3 | odd | 4 | |||
735.4.a.p.1.1 | 2 | 7.6 | odd | 2 | |||
1575.4.a.w.1.1 | 2 | 15.14 | odd | 2 | |||
1680.4.a.bg.1.1 | 2 | 4.3 | odd | 2 | |||
2205.4.a.z.1.2 | 2 | 21.20 | even | 2 |