Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{65})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 33x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(-3.53113i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.h.274.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.53113i | − 1.24844i | −0.781248 | − | 0.624221i | \(-0.785416\pi\) | ||||
0.781248 | − | 0.624221i | \(-0.214584\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −4.46887 | −0.558609 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.5934 | −0.720789 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | − 12.4689i | − 0.551051i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93774 | −0.0805239 | −0.0402619 | − | 0.999189i | \(-0.512819\pi\) | ||||
−0.0402619 | + | 0.999189i | \(0.512819\pi\) | |||||||
\(12\) | 13.4066i | 0.322513i | ||||||||
\(13\) | 19.0623i | 0.406686i | 0.979108 | + | 0.203343i | \(0.0651807\pi\) | ||||
−0.979108 | + | 0.203343i | \(0.934819\pi\) | |||||||
\(14\) | −24.7179 | −0.471867 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.7802 | −1.24656 | ||||||||
\(17\) | 122.498i | 1.74766i | 0.486236 | + | 0.873828i | \(0.338370\pi\) | ||||
−0.486236 | + | 0.873828i | \(0.661630\pi\) | |||||||
\(18\) | 31.7802i | 0.416148i | ||||||||
\(19\) | −107.436 | −1.29723 | −0.648617 | − | 0.761115i | \(-0.724652\pi\) | ||||
−0.648617 | + | 0.761115i | \(0.724652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 10.3735i | 0.100529i | ||||||||
\(23\) | − 210.623i | − 1.90947i | −0.297455 | − | 0.954736i | \(-0.596138\pi\) | ||||
0.297455 | − | 0.954736i | \(-0.403862\pi\) | |||||||
\(24\) | −37.4066 | −0.318150 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 67.3113 | 0.507724 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 31.2821i | 0.211134i | ||||||||
\(29\) | −95.4942 | −0.611477 | −0.305738 | − | 0.952116i | \(-0.598903\pi\) | ||||
−0.305738 | + | 0.952116i | \(0.598903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −94.3074 | −0.546391 | −0.273195 | − | 0.961959i | \(-0.588081\pi\) | ||||
−0.273195 | + | 0.961959i | \(0.588081\pi\) | |||||||
\(32\) | 181.963i | 1.00521i | ||||||||
\(33\) | 8.81323i | 0.0464905i | ||||||||
\(34\) | 432.556 | 2.18185 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 40.2198 | 0.186203 | ||||||||
\(37\) | 97.1206i | 0.431528i | 0.976446 | + | 0.215764i | \(0.0692242\pi\) | ||||
−0.976446 | + | 0.215764i | \(0.930776\pi\) | |||||||
\(38\) | 379.370i | 1.61952i | ||||||||
\(39\) | 57.1868 | 0.234800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −491.113 | −1.87071 | −0.935353 | − | 0.353716i | \(-0.884918\pi\) | ||||
−0.935353 | + | 0.353716i | \(0.884918\pi\) | |||||||
\(42\) | 74.1537i | 0.272433i | ||||||||
\(43\) | 43.0039i | 0.152512i | 0.997088 | + | 0.0762562i | \(0.0242967\pi\) | ||||
−0.997088 | + | 0.0762562i | \(0.975703\pi\) | |||||||
\(44\) | 13.1284 | 0.0449814 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −743.735 | −2.38387 | ||||||||
\(47\) | 473.494i | 1.46949i | 0.678341 | + | 0.734747i | \(0.262699\pi\) | ||||
−0.678341 | + | 0.734747i | \(0.737301\pi\) | |||||||
\(48\) | 239.340i | 0.719705i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 367.494 | 1.00901 | ||||||||
\(52\) | − 85.1868i | − 0.227178i | ||||||||
\(53\) | 183.677i | 0.476038i | 0.971261 | + | 0.238019i | \(0.0764980\pi\) | ||||
−0.971261 | + | 0.238019i | \(0.923502\pi\) | |||||||
\(54\) | 95.3405 | 0.240263 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −87.2821 | −0.208278 | ||||||||
\(57\) | 322.307i | 0.748959i | ||||||||
\(58\) | 337.202i | 0.763394i | ||||||||
\(59\) | 760.615 | 1.67837 | 0.839183 | − | 0.543849i | \(-0.183034\pi\) | ||||
0.839183 | + | 0.543849i | \(0.183034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −198.747 | −0.417163 | −0.208582 | − | 0.978005i | \(-0.566885\pi\) | ||||
−0.208582 | + | 0.978005i | \(0.566885\pi\) | |||||||
\(62\) | 333.012i | 0.682137i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 4.29373 | 0.00838618 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 31.1206 | 0.0580407 | ||||||||
\(67\) | − 309.992i | − 0.565247i | −0.959231 | − | 0.282624i | \(-0.908795\pi\) | ||||
0.959231 | − | 0.282624i | \(-0.0912048\pi\) | |||||||
\(68\) | − 547.428i | − 0.976256i | ||||||||
\(69\) | −631.868 | −1.10243 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 665.693 | 1.11272 | 0.556360 | − | 0.830941i | \(-0.312197\pi\) | ||||
0.556360 | + | 0.830941i | \(0.312197\pi\) | |||||||
\(72\) | 112.220i | 0.183684i | ||||||||
\(73\) | − 621.288i | − 0.996113i | −0.867145 | − | 0.498057i | \(-0.834047\pi\) | ||||
0.867145 | − | 0.498057i | \(-0.165953\pi\) | |||||||
\(74\) | 342.945 | 0.538738 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 480.117 | 0.724647 | ||||||||
\(77\) | 20.5642i | 0.0304352i | ||||||||
\(78\) | − 201.934i | − 0.293135i | ||||||||
\(79\) | 24.7626 | 0.0352659 | 0.0176330 | − | 0.999845i | \(-0.494387\pi\) | ||||
0.0176330 | + | 0.999845i | \(0.494387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1734.18i | 2.33547i | ||||||||
\(83\) | 406.724i | 0.537876i | 0.963157 | + | 0.268938i | \(0.0866727\pi\) | ||||
−0.963157 | + | 0.268938i | \(0.913327\pi\) | |||||||
\(84\) | 93.8463 | 0.121898 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 151.852 | 0.190403 | ||||||||
\(87\) | 286.483i | 0.353036i | ||||||||
\(88\) | 36.6303i | 0.0443728i | ||||||||
\(89\) | −261.751 | −0.311748 | −0.155874 | − | 0.987777i | \(-0.549819\pi\) | ||||
−0.155874 | + | 0.987777i | \(0.549819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133.436 | 0.153713 | ||||||||
\(92\) | 941.245i | 1.06665i | ||||||||
\(93\) | 282.922i | 0.315459i | ||||||||
\(94\) | 1671.97 | 1.83458 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 545.889 | 0.580360 | ||||||||
\(97\) | − 1004.77i | − 1.05175i | −0.850563 | − | 0.525873i | \(-0.823739\pi\) | ||||
0.850563 | − | 0.525873i | \(-0.176261\pi\) | |||||||
\(98\) | 173.025i | 0.178349i | ||||||||
\(99\) | 26.4397 | 0.0268413 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −128.872 | −0.126962 | −0.0634812 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634812 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(102\) | − 1297.67i | − 1.25969i | ||||||||
\(103\) | − 806.008i | − 0.771051i | −0.922697 | − | 0.385526i | \(-0.874020\pi\) | ||||
0.922697 | − | 0.385526i | \(-0.125980\pi\) | |||||||
\(104\) | 237.685 | 0.224105 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 648.587 | 0.594305 | ||||||||
\(107\) | − 769.712i | − 0.695429i | −0.937600 | − | 0.347714i | \(-0.886958\pi\) | ||||
0.937600 | − | 0.347714i | \(-0.113042\pi\) | |||||||
\(108\) | − 120.660i | − 0.107504i | ||||||||
\(109\) | 780.856 | 0.686169 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 291.362 | 0.249143 | ||||||||
\(112\) | 558.461i | 0.471157i | ||||||||
\(113\) | 1115.65i | 0.928771i | 0.885633 | + | 0.464386i | \(0.153725\pi\) | ||||
−0.885633 | + | 0.464386i | \(0.846275\pi\) | |||||||
\(114\) | 1138.11 | 0.935032 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 426.751 | 0.341576 | ||||||||
\(117\) | − 171.560i | − 0.135562i | ||||||||
\(118\) | − 2685.83i | − 2.09534i | ||||||||
\(119\) | 857.486 | 0.660552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1322.37 | −0.993516 | ||||||||
\(122\) | 701.802i | 0.520804i | ||||||||
\(123\) | 1473.34i | 1.08005i | ||||||||
\(124\) | 421.448 | 0.305219 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 222.461 | 0.157289 | ||||||||
\(127\) | − 1875.98i | − 1.31076i | −0.755299 | − | 0.655381i | \(-0.772508\pi\) | ||||
0.755299 | − | 0.655381i | \(-0.227492\pi\) | |||||||
\(128\) | 1440.54i | 0.994744i | ||||||||
\(129\) | 129.012 | 0.0880530 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 364.203 | 0.242905 | 0.121452 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121452 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(132\) | − 39.3852i | − 0.0259700i | ||||||||
\(133\) | 752.051i | 0.490309i | ||||||||
\(134\) | −1094.62 | −0.705679 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1527.41 | 0.963048 | ||||||||
\(137\) | 1603.13i | 0.999743i | 0.866099 | + | 0.499872i | \(0.166620\pi\) | ||||
−0.866099 | + | 0.499872i | \(0.833380\pi\) | |||||||
\(138\) | 2231.21i | 1.37633i | ||||||||
\(139\) | −2431.12 | −1.48349 | −0.741746 | − | 0.670681i | \(-0.766002\pi\) | ||||
−0.741746 | + | 0.670681i | \(0.766002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1420.48 | 0.848413 | ||||||||
\(142\) | − 2350.65i | − 1.38917i | ||||||||
\(143\) | − 56.0000i | − 0.0327479i | ||||||||
\(144\) | 718.021 | 0.415522 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2193.85 | −1.24359 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − 434.020i | − 0.241055i | ||||||||
\(149\) | −2341.57 | −1.28744 | −0.643722 | − | 0.765260i | \(-0.722611\pi\) | ||||
−0.643722 | + | 0.765260i | \(0.722611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2104.07 | −1.13395 | −0.566976 | − | 0.823734i | \(-0.691887\pi\) | ||||
−0.566976 | + | 0.823734i | \(0.691887\pi\) | |||||||
\(152\) | 1339.60i | 0.714843i | ||||||||
\(153\) | − 1102.48i | − 0.582552i | ||||||||
\(154\) | 72.6148 | 0.0379966 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −255.560 | −0.131162 | ||||||||
\(157\) | − 593.467i | − 0.301680i | −0.988558 | − | 0.150840i | \(-0.951802\pi\) | ||||
0.988558 | − | 0.150840i | \(-0.0481979\pi\) | |||||||
\(158\) | − 87.4399i | − 0.0440275i | ||||||||
\(159\) | 551.031 | 0.274840 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1474.36 | −0.721712 | ||||||||
\(162\) | − 286.021i | − 0.138716i | ||||||||
\(163\) | − 2178.71i | − 1.04693i | −0.852047 | − | 0.523465i | \(-0.824639\pi\) | ||||
0.852047 | − | 0.523465i | \(-0.175361\pi\) | |||||||
\(164\) | 2194.72 | 1.04499 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1436.19 | 0.671508 | ||||||||
\(167\) | 799.502i | 0.370463i | 0.982695 | + | 0.185231i | \(0.0593035\pi\) | ||||
−0.982695 | + | 0.185231i | \(0.940697\pi\) | |||||||
\(168\) | 261.846i | 0.120249i | ||||||||
\(169\) | 1833.63 | 0.834606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 966.922 | 0.432412 | ||||||||
\(172\) | − 192.179i | − 0.0851947i | ||||||||
\(173\) | 1444.36i | 0.634754i | 0.948299 | + | 0.317377i | \(0.102802\pi\) | ||||
−0.948299 | + | 0.317377i | \(0.897198\pi\) | |||||||
\(174\) | 1011.61 | 0.440745 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 234.374 | 0.100378 | ||||||||
\(177\) | − 2281.84i | − 0.969005i | ||||||||
\(178\) | 924.276i | 0.389199i | ||||||||
\(179\) | −3343.49 | −1.39611 | −0.698056 | − | 0.716043i | \(-0.745952\pi\) | ||||
−0.698056 | + | 0.716043i | \(0.745952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2251.81 | 0.924729 | 0.462365 | − | 0.886690i | \(-0.347001\pi\) | ||||
0.462365 | + | 0.886690i | \(0.347001\pi\) | |||||||
\(182\) | − 471.179i | − 0.191902i | ||||||||
\(183\) | 596.241i | 0.240849i | ||||||||
\(184\) | −2626.23 | −1.05222 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 999.035 | 0.393832 | ||||||||
\(187\) | − 359.868i | − 0.140728i | ||||||||
\(188\) | − 2115.98i | − 0.820873i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1001.93 | −0.379565 | −0.189782 | − | 0.981826i | \(-0.560778\pi\) | ||||
−0.189782 | + | 0.981826i | \(0.560778\pi\) | |||||||
\(192\) | − 12.8812i | − 0.00484177i | ||||||||
\(193\) | 4054.97i | 1.51235i | 0.654372 | + | 0.756173i | \(0.272933\pi\) | ||||
−0.654372 | + | 0.756173i | \(0.727067\pi\) | |||||||
\(194\) | −3547.99 | −1.31304 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 218.975 | 0.0798013 | ||||||||
\(197\) | − 5140.23i | − 1.85902i | −0.368802 | − | 0.929508i | \(-0.620232\pi\) | ||||
0.368802 | − | 0.929508i | \(-0.379768\pi\) | |||||||
\(198\) | − 93.3619i | − 0.0335098i | ||||||||
\(199\) | −585.631 | −0.208614 | −0.104307 | − | 0.994545i | \(-0.533263\pi\) | ||||
−0.104307 | + | 0.994545i | \(0.533263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −929.977 | −0.326346 | ||||||||
\(202\) | 455.062i | 0.158505i | ||||||||
\(203\) | 668.459i | 0.231116i | ||||||||
\(204\) | −1642.28 | −0.563642 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2846.12 | −0.962614 | ||||||||
\(207\) | 1895.60i | 0.636490i | ||||||||
\(208\) | − 1520.79i | − 0.506961i | ||||||||
\(209\) | 315.619 | 0.104458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1055.16 | −0.344266 | −0.172133 | − | 0.985074i | \(-0.555066\pi\) | ||||
−0.172133 | + | 0.985074i | \(0.555066\pi\) | |||||||
\(212\) | − 820.829i | − 0.265919i | ||||||||
\(213\) | − 1997.08i | − 0.642430i | ||||||||
\(214\) | −2717.95 | −0.868203 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 336.660 | 0.106050 | ||||||||
\(217\) | 660.152i | 0.206516i | ||||||||
\(218\) | − 2757.30i | − 0.856643i | ||||||||
\(219\) | −1863.86 | −0.575106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2335.09 | −0.710747 | ||||||||
\(222\) | − 1028.84i | − 0.311040i | ||||||||
\(223\) | − 4675.85i | − 1.40412i | −0.712119 | − | 0.702059i | \(-0.752264\pi\) | ||||
0.712119 | − | 0.702059i | \(-0.247736\pi\) | |||||||
\(224\) | 1273.74 | 0.379935 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3939.49 | 1.15952 | ||||||||
\(227\) | 5443.11i | 1.59151i | 0.605621 | + | 0.795754i | \(0.292925\pi\) | ||||
−0.605621 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(228\) | − 1440.35i | − 0.418375i | ||||||||
\(229\) | 536.303 | 0.154759 | 0.0773797 | − | 0.997002i | \(-0.475345\pi\) | ||||
0.0773797 | + | 0.997002i | \(0.475345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 61.6926 | 0.0175717 | ||||||||
\(232\) | 1190.70i | 0.336955i | ||||||||
\(233\) | 183.490i | 0.0515916i | 0.999667 | + | 0.0257958i | \(0.00821196\pi\) | ||||
−0.999667 | + | 0.0257958i | \(0.991788\pi\) | |||||||
\(234\) | −605.802 | −0.169241 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3399.09 | −0.937550 | ||||||||
\(237\) | − 74.2878i | − 0.0203608i | ||||||||
\(238\) | − 3027.90i | − 0.824661i | ||||||||
\(239\) | −643.218 | −0.174085 | −0.0870425 | − | 0.996205i | \(-0.527742\pi\) | ||||
−0.0870425 | + | 0.996205i | \(0.527742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5755.61 | −1.53839 | −0.769194 | − | 0.639015i | \(-0.779342\pi\) | ||||
−0.769194 | + | 0.639015i | \(0.779342\pi\) | |||||||
\(242\) | 4669.46i | 1.24035i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 888.175 | 0.233031 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5202.55 | 1.34838 | ||||||||
\(247\) | − 2047.97i | − 0.527567i | ||||||||
\(248\) | 1175.91i | 0.301089i | ||||||||
\(249\) | 1220.17 | 0.310543 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5132.27 | −1.29062 | −0.645311 | − | 0.763920i | \(-0.723272\pi\) | ||||
−0.645311 | + | 0.763920i | \(0.723272\pi\) | |||||||
\(252\) | − 281.539i | − 0.0703781i | ||||||||
\(253\) | 618.755i | 0.153758i | ||||||||
\(254\) | −6624.34 | −1.63641 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5121.09 | 1.25027 | ||||||||
\(257\) | 5041.74i | 1.22372i | 0.790967 | + | 0.611859i | \(0.209578\pi\) | ||||
−0.790967 | + | 0.611859i | \(0.790422\pi\) | |||||||
\(258\) | − 455.557i | − 0.109929i | ||||||||
\(259\) | 679.844 | 0.163102 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 859.448 | 0.203826 | ||||||||
\(262\) | − 1286.05i | − 0.303253i | ||||||||
\(263\) | − 7577.00i | − 1.77649i | −0.459367 | − | 0.888246i | \(-0.651924\pi\) | ||||
0.459367 | − | 0.888246i | \(-0.348076\pi\) | |||||||
\(264\) | 109.891 | 0.0256186 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2655.59 | 0.612122 | ||||||||
\(267\) | 785.253i | 0.179988i | ||||||||
\(268\) | 1385.32i | 0.315752i | ||||||||
\(269\) | −1023.10 | −0.231893 | −0.115947 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115947 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2251.98 | −0.504790 | −0.252395 | − | 0.967624i | \(-0.581218\pi\) | ||||
−0.252395 | + | 0.967624i | \(0.581218\pi\) | |||||||
\(272\) | − 9772.91i | − 2.17857i | ||||||||
\(273\) | − 400.307i | − 0.0887462i | ||||||||
\(274\) | 5660.87 | 1.24812 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2823.74 | 0.615829 | ||||||||
\(277\) | − 8630.72i | − 1.87209i | −0.351875 | − | 0.936047i | \(-0.614456\pi\) | ||||
0.351875 | − | 0.936047i | \(-0.385544\pi\) | |||||||
\(278\) | 8584.61i | 1.85205i | ||||||||
\(279\) | 848.767 | 0.182130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7521.62 | −1.59680 | −0.798402 | − | 0.602124i | \(-0.794321\pi\) | ||||
−0.798402 | + | 0.602124i | \(0.794321\pi\) | |||||||
\(282\) | − 5015.91i | − 1.05919i | ||||||||
\(283\) | − 14.8169i | − 0.00311226i | −0.999999 | − | 0.00155613i | \(-0.999505\pi\) | ||||
0.999999 | − | 0.00155613i | \(-0.000495333\pi\) | |||||||
\(284\) | −2974.89 | −0.621576 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −197.743 | −0.0408839 | ||||||||
\(287\) | 3437.79i | 0.707060i | ||||||||
\(288\) | − 1637.67i | − 0.335071i | ||||||||
\(289\) | −10092.8 | −2.05430 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3014.32 | −0.607226 | ||||||||
\(292\) | 2776.46i | 0.556438i | ||||||||
\(293\) | − 6913.39i | − 1.37844i | −0.724550 | − | 0.689222i | \(-0.757952\pi\) | ||||
0.724550 | − | 0.689222i | \(-0.242048\pi\) | |||||||
\(294\) | 519.076 | 0.102970 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1210.98 | 0.237794 | ||||||||
\(297\) | − 79.3190i | − 0.0154968i | ||||||||
\(298\) | 8268.39i | 1.60730i | ||||||||
\(299\) | 4014.94 | 0.776555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 301.027 | 0.0576442 | ||||||||
\(302\) | 7429.74i | 1.41567i | ||||||||
\(303\) | 386.615i | 0.0733018i | ||||||||
\(304\) | 8571.25 | 1.61709 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3893.01 | −0.727283 | ||||||||
\(307\) | − 7644.12i | − 1.42108i | −0.703655 | − | 0.710542i | \(-0.748450\pi\) | ||||
0.703655 | − | 0.710542i | \(-0.251550\pi\) | |||||||
\(308\) | − 91.8987i | − 0.0170014i | ||||||||
\(309\) | −2418.02 | −0.445167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7593.99 | 1.38462 | 0.692308 | − | 0.721602i | \(-0.256594\pi\) | ||||
0.692308 | + | 0.721602i | \(0.256594\pi\) | |||||||
\(312\) | − 713.055i | − 0.129387i | ||||||||
\(313\) | 9127.84i | 1.64836i | 0.566329 | + | 0.824179i | \(0.308363\pi\) | ||||
−0.566329 | + | 0.824179i | \(0.691637\pi\) | |||||||
\(314\) | −2095.61 | −0.376631 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −110.661 | −0.0196999 | ||||||||
\(317\) | − 4929.81i | − 0.873456i | −0.899593 | − | 0.436728i | \(-0.856137\pi\) | ||||
0.899593 | − | 0.436728i | \(-0.143863\pi\) | |||||||
\(318\) | − 1945.76i | − 0.343122i | ||||||||
\(319\) | 280.537 | 0.0492385 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2309.14 | −0.401506 | ||||||||
\(322\) | 5206.15i | 0.901016i | ||||||||
\(323\) | − 13160.7i | − 2.26712i | ||||||||
\(324\) | −361.979 | −0.0620677 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7693.30 | −1.30703 | ||||||||
\(327\) | − 2342.57i | − 0.396160i | ||||||||
\(328\) | 6123.62i | 1.03086i | ||||||||
\(329\) | 3314.46 | 0.555417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1221.67 | 0.202867 | 0.101433 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101433 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(332\) | − 1817.60i | − 0.300463i | ||||||||
\(333\) | − 874.086i | − 0.143843i | ||||||||
\(334\) | 2823.14 | 0.462502 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1675.38 | 0.272023 | ||||||||
\(337\) | − 8744.83i | − 1.41354i | −0.707446 | − | 0.706768i | \(-0.750153\pi\) | ||||
0.707446 | − | 0.706768i | \(-0.249847\pi\) | |||||||
\(338\) | − 6474.79i | − 1.04196i | ||||||||
\(339\) | 3346.94 | 0.536226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 277.051 | 0.0439975 | ||||||||
\(342\) | − 3414.33i | − 0.539841i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 536.210 | 0.0840421 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5100.21 | 0.792454 | ||||||||
\(347\) | 4589.56i | 0.710031i | 0.934860 | + | 0.355015i | \(0.115524\pi\) | ||||
−0.934860 | + | 0.355015i | \(0.884476\pi\) | |||||||
\(348\) | − 1280.25i | − 0.197209i | ||||||||
\(349\) | 3989.89 | 0.611960 | 0.305980 | − | 0.952038i | \(-0.401016\pi\) | ||||
0.305980 | + | 0.952038i | \(0.401016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −514.681 | −0.0782668 | ||||||||
\(352\) | − 534.561i | − 0.0809437i | ||||||||
\(353\) | − 2416.35i | − 0.364333i | −0.983268 | − | 0.182166i | \(-0.941689\pi\) | ||||
0.983268 | − | 0.182166i | \(-0.0583109\pi\) | |||||||
\(354\) | −8057.49 | −1.20975 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1169.73 | 0.174145 | ||||||||
\(357\) | − 2572.46i | − 0.381370i | ||||||||
\(358\) | 11806.3i | 1.74297i | ||||||||
\(359\) | 2756.24 | 0.405206 | 0.202603 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202603 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4683.45 | 0.682818 | ||||||||
\(362\) | − 7951.44i | − 1.15447i | ||||||||
\(363\) | 3967.11i | 0.573607i | ||||||||
\(364\) | −596.307 | −0.0858654 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2105.40 | 0.300687 | ||||||||
\(367\) | 11112.8i | 1.58061i | 0.612711 | + | 0.790307i | \(0.290079\pi\) | ||||
−0.612711 | + | 0.790307i | \(0.709921\pi\) | |||||||
\(368\) | 16803.5i | 2.38028i | ||||||||
\(369\) | 4420.02 | 0.623569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1285.74 | 0.179925 | ||||||||
\(372\) | − 1264.34i | − 0.176218i | ||||||||
\(373\) | − 6091.09i | − 0.845535i | −0.906238 | − | 0.422768i | \(-0.861059\pi\) | ||||
0.906238 | − | 0.422768i | \(-0.138941\pi\) | |||||||
\(374\) | −1270.74 | −0.175691 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5903.94 | 0.809767 | ||||||||
\(377\) | − 1820.33i | − 0.248679i | ||||||||
\(378\) | − 667.383i | − 0.0908108i | ||||||||
\(379\) | −3984.29 | −0.539998 | −0.269999 | − | 0.962861i | \(-0.587023\pi\) | ||||
−0.269999 | + | 0.962861i | \(0.587023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5627.95 | −0.756768 | ||||||||
\(382\) | 3537.93i | 0.473865i | ||||||||
\(383\) | − 318.475i | − 0.0424890i | −0.999774 | − | 0.0212445i | \(-0.993237\pi\) | ||||
0.999774 | − | 0.0212445i | \(-0.00676285\pi\) | |||||||
\(384\) | 4321.63 | 0.574316 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14318.6 | 1.88808 | ||||||||
\(387\) | − 387.035i | − 0.0508374i | ||||||||
\(388\) | 4490.21i | 0.587515i | ||||||||
\(389\) | −3885.46 | −0.506429 | −0.253214 | − | 0.967410i | \(-0.581488\pi\) | ||||
−0.253214 | + | 0.967410i | \(0.581488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25800.9 | 3.33710 | ||||||||
\(392\) | 610.975i | 0.0787216i | ||||||||
\(393\) | − 1092.61i | − 0.140241i | ||||||||
\(394\) | −18150.8 | −2.32088 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −118.156 | −0.0149938 | ||||||||
\(397\) | 4806.04i | 0.607578i | 0.952739 | + | 0.303789i | \(0.0982518\pi\) | ||||
−0.952739 | + | 0.303789i | \(0.901748\pi\) | |||||||
\(398\) | 2067.94i | 0.260443i | ||||||||
\(399\) | 2256.15 | 0.283080 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3618.59 | 0.450633 | 0.225316 | − | 0.974286i | \(-0.427658\pi\) | ||||
0.225316 | + | 0.974286i | \(0.427658\pi\) | |||||||
\(402\) | 3283.87i | 0.407424i | ||||||||
\(403\) | − 1797.71i | − 0.222209i | ||||||||
\(404\) | 575.911 | 0.0709223 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2360.42 | 0.288536 | ||||||||
\(407\) | − 285.315i | − 0.0347483i | ||||||||
\(408\) | − 4582.24i | − 0.556016i | ||||||||
\(409\) | 2109.05 | 0.254978 | 0.127489 | − | 0.991840i | \(-0.459308\pi\) | ||||
0.127489 | + | 0.991840i | \(0.459308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4809.40 | 0.577202 | ||||||||
\(412\) | 3601.94i | 0.430716i | ||||||||
\(413\) | − 5324.30i | − 0.634363i | ||||||||
\(414\) | 6693.62 | 0.794622 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3468.63 | −0.408806 | ||||||||
\(417\) | 7293.37i | 0.856494i | ||||||||
\(418\) | − 1114.49i | − 0.130410i | ||||||||
\(419\) | 6905.91 | 0.805193 | 0.402597 | − | 0.915377i | \(-0.368108\pi\) | ||||
0.402597 | + | 0.915377i | \(0.368108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9647.54 | −1.11685 | −0.558423 | − | 0.829556i | \(-0.688593\pi\) | ||||
−0.558423 | + | 0.829556i | \(0.688593\pi\) | |||||||
\(422\) | 3725.91i | 0.429797i | ||||||||
\(423\) | − 4261.45i | − 0.489831i | ||||||||
\(424\) | 2290.25 | 0.262321 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7051.94 | −0.802037 | ||||||||
\(427\) | 1391.23i | 0.157673i | ||||||||
\(428\) | 3439.74i | 0.388473i | ||||||||
\(429\) | −168.000 | −0.0189070 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13002.7 | −1.45318 | −0.726589 | − | 0.687073i | \(-0.758895\pi\) | ||||
−0.726589 | + | 0.687073i | \(0.758895\pi\) | |||||||
\(432\) | − 2154.06i | − 0.239902i | ||||||||
\(433\) | − 7356.07i | − 0.816420i | −0.912888 | − | 0.408210i | \(-0.866153\pi\) | ||||
0.912888 | − | 0.408210i | \(-0.133847\pi\) | |||||||
\(434\) | 2331.08 | 0.257824 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3489.55 | −0.383300 | ||||||||
\(437\) | 22628.4i | 2.47703i | ||||||||
\(438\) | 6581.54i | 0.717987i | ||||||||
\(439\) | −6909.21 | −0.751159 | −0.375579 | − | 0.926790i | \(-0.622556\pi\) | ||||
−0.375579 | + | 0.926790i | \(0.622556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 8245.50i | 0.887327i | ||||||||
\(443\) | 14812.6i | 1.58864i | 0.607502 | + | 0.794318i | \(0.292172\pi\) | ||||
−0.607502 | + | 0.794318i | \(0.707828\pi\) | |||||||
\(444\) | −1302.06 | −0.139173 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16511.0 | −1.75296 | ||||||||
\(447\) | 7024.72i | 0.743306i | ||||||||
\(448\) | − 30.0561i | − 0.00316968i | ||||||||
\(449\) | 10654.5 | 1.11986 | 0.559932 | − | 0.828538i | \(-0.310827\pi\) | ||||
0.559932 | + | 0.828538i | \(0.310827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1442.76 | 0.150636 | ||||||||
\(452\) | − 4985.68i | − 0.518820i | ||||||||
\(453\) | 6312.21i | 0.654688i | ||||||||
\(454\) | 19220.3 | 1.98691 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4018.81 | 0.412715 | ||||||||
\(457\) | − 5855.16i | − 0.599328i | −0.954045 | − | 0.299664i | \(-0.903125\pi\) | ||||
0.954045 | − | 0.299664i | \(-0.0968745\pi\) | |||||||
\(458\) | − 1893.76i | − 0.193208i | ||||||||
\(459\) | −3307.45 | −0.336336 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3204.74 | 0.323774 | 0.161887 | − | 0.986809i | \(-0.448242\pi\) | ||||
0.161887 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(462\) | − 217.844i | − 0.0219373i | ||||||||
\(463\) | − 371.658i | − 0.0373054i | −0.999826 | − | 0.0186527i | \(-0.994062\pi\) | ||||
0.999826 | − | 0.0186527i | \(-0.00593769\pi\) | |||||||
\(464\) | 7618.54 | 0.762245 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 647.927 | 0.0644091 | ||||||||
\(467\) | − 19752.3i | − 1.95723i | −0.205703 | − | 0.978614i | \(-0.565948\pi\) | ||||
0.205703 | − | 0.978614i | \(-0.434052\pi\) | |||||||
\(468\) | 766.681i | 0.0757262i | ||||||||
\(469\) | −2169.95 | −0.213643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1780.40 | −0.174175 | ||||||||
\(472\) | − 9484.01i | − 0.924866i | ||||||||
\(473\) | − 126.334i | − 0.0122809i | ||||||||
\(474\) | −262.320 | −0.0254193 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3832.00 | −0.368990 | ||||||||
\(477\) | − 1653.09i | − 0.158679i | ||||||||
\(478\) | 2271.28i | 0.217335i | ||||||||
\(479\) | 20762.0 | 1.98046 | 0.990232 | − | 0.139433i | \(-0.0445279\pi\) | ||||
0.990232 | + | 0.139433i | \(0.0445279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1851.34 | −0.175496 | ||||||||
\(482\) | 20323.8i | 1.92059i | ||||||||
\(483\) | 4423.07i | 0.416681i | ||||||||
\(484\) | 5909.50 | 0.554987 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −858.064 | −0.0800876 | ||||||||
\(487\) | 17647.6i | 1.64207i | 0.570878 | + | 0.821035i | \(0.306603\pi\) | ||||
−0.570878 | + | 0.821035i | \(0.693397\pi\) | |||||||
\(488\) | 2478.15i | 0.229878i | ||||||||
\(489\) | −6536.12 | −0.604445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5637.46 | −0.518157 | −0.259078 | − | 0.965856i | \(-0.583419\pi\) | ||||
−0.259078 | + | 0.965856i | \(0.583419\pi\) | |||||||
\(492\) | − 6584.16i | − 0.603327i | ||||||||
\(493\) | − 11697.9i | − 1.06865i | ||||||||
\(494\) | −7231.64 | −0.658638 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7523.86 | 0.681112 | ||||||||
\(497\) | − 4659.85i | − 0.420569i | ||||||||
\(498\) | − 4308.58i | − 0.387695i | ||||||||
\(499\) | 17474.1 | 1.56764 | 0.783818 | − | 0.620991i | \(-0.213270\pi\) | ||||
0.783818 | + | 0.620991i | \(0.213270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2398.51 | 0.213887 | ||||||||
\(502\) | 18122.7i | 1.61127i | ||||||||
\(503\) | − 7444.81i | − 0.659936i | −0.943992 | − | 0.329968i | \(-0.892962\pi\) | ||||
0.943992 | − | 0.329968i | \(-0.107038\pi\) | |||||||
\(504\) | 785.539 | 0.0694260 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2184.90 | 0.191958 | ||||||||
\(507\) | − 5500.89i | − 0.481860i | ||||||||
\(508\) | 8383.53i | 0.732203i | ||||||||
\(509\) | 3384.48 | 0.294724 | 0.147362 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147362 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4349.02 | −0.376495 | ||||||||
\(512\) | − 6558.89i | − 0.566142i | ||||||||
\(513\) | − 2900.77i | − 0.249653i | ||||||||
\(514\) | 17803.0 | 1.52774 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −576.536 | −0.0491872 | ||||||||
\(517\) | − 1391.00i | − 0.118329i | ||||||||
\(518\) | − 2400.62i | − 0.203624i | ||||||||
\(519\) | 4333.07 | 0.366476 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2973.12 | 0.250009 | 0.125005 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125005 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(522\) | − 3034.82i | − 0.254465i | ||||||||
\(523\) | − 2689.02i | − 0.224823i | −0.993662 | − | 0.112412i | \(-0.964142\pi\) | ||||
0.993662 | − | 0.112412i | \(-0.0358575\pi\) | |||||||
\(524\) | −1627.57 | −0.135689 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26755.3 | −2.21785 | ||||||||
\(527\) | − 11552.5i | − 0.954903i | ||||||||
\(528\) | − 703.121i | − 0.0579534i | ||||||||
\(529\) | −32194.9 | −2.64608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6845.53 | −0.559455 | ||||||||
\(532\) | − 3360.82i | − 0.273891i | ||||||||
\(533\) | − 9361.72i | − 0.760790i | ||||||||
\(534\) | 2772.83 | 0.224704 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3865.25 | −0.311480 | ||||||||
\(537\) | 10030.5i | 0.806046i | ||||||||
\(538\) | 3612.69i | 0.289506i | ||||||||
\(539\) | 143.949 | 0.0115034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14429.5 | −1.14671 | −0.573356 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573356 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(542\) | 7952.03i | 0.630201i | ||||||||
\(543\) | − 6755.44i | − 0.533893i | ||||||||
\(544\) | −22290.1 | −1.75677 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1413.54 | −0.110795 | ||||||||
\(547\) | 13811.2i | 1.07957i | 0.841804 | + | 0.539784i | \(0.181494\pi\) | ||||
−0.841804 | + | 0.539784i | \(0.818506\pi\) | |||||||
\(548\) | − 7164.19i | − 0.558466i | ||||||||
\(549\) | 1788.72 | 0.139054 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10259.5 | 0.793229 | ||||||||
\(552\) | 7878.68i | 0.607498i | ||||||||
\(553\) | − 173.338i | − 0.0133293i | ||||||||
\(554\) | −30476.2 | −2.33720 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10864.4 | 0.828692 | ||||||||
\(557\) | − 6033.26i | − 0.458954i | −0.973314 | − | 0.229477i | \(-0.926298\pi\) | ||||
0.973314 | − | 0.229477i | \(-0.0737016\pi\) | |||||||
\(558\) | − 2997.10i | − 0.227379i | ||||||||
\(559\) | −819.751 | −0.0620246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1079.60 | −0.0812493 | ||||||||
\(562\) | 26559.8i | 1.99352i | ||||||||
\(563\) | 6958.47i | 0.520896i | 0.965488 | + | 0.260448i | \(0.0838703\pi\) | ||||
−0.965488 | + | 0.260448i | \(0.916130\pi\) | |||||||
\(564\) | −6347.95 | −0.473931 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −52.3202 | −0.00388548 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | − 8300.44i | − 0.613166i | ||||||||
\(569\) | 13396.4 | 0.987009 | 0.493505 | − | 0.869743i | \(-0.335716\pi\) | ||||
0.493505 | + | 0.869743i | \(0.335716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8055.84 | −0.590414 | −0.295207 | − | 0.955433i | \(-0.595389\pi\) | ||||
−0.295207 | + | 0.955433i | \(0.595389\pi\) | |||||||
\(572\) | 250.257i | 0.0182933i | ||||||||
\(573\) | 3005.78i | 0.219142i | ||||||||
\(574\) | 12139.3 | 0.882724 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −38.6435 | −0.00279539 | ||||||||
\(577\) | − 21456.9i | − 1.54812i | −0.633114 | − | 0.774059i | \(-0.718223\pi\) | ||||
0.633114 | − | 0.774059i | \(-0.281777\pi\) | |||||||
\(578\) | 35638.9i | 2.56468i | ||||||||
\(579\) | 12164.9 | 0.873153 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2847.07 | 0.203298 | ||||||||
\(582\) | 10644.0i | 0.758087i | ||||||||
\(583\) | − 539.596i | − 0.0383324i | ||||||||
\(584\) | −7746.76 | −0.548910 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24412.1 | −1.72091 | ||||||||
\(587\) | 20156.3i | 1.41728i | 0.705572 | + | 0.708638i | \(0.250690\pi\) | ||||
−0.705572 | + | 0.708638i | \(0.749310\pi\) | |||||||
\(588\) | − 656.924i | − 0.0460733i | ||||||||
\(589\) | 10132.0 | 0.708797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15420.7 | −1.07330 | ||||||||
\(592\) | − 7748.30i | − 0.537928i | ||||||||
\(593\) | − 599.307i | − 0.0415018i | −0.999785 | − | 0.0207509i | \(-0.993394\pi\) | ||||
0.999785 | − | 0.0207509i | \(-0.00660570\pi\) | |||||||
\(594\) | −280.086 | −0.0193469 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10464.2 | 0.719177 | ||||||||
\(597\) | 1756.89i | 0.120444i | ||||||||
\(598\) | − 14177.3i | − 0.969485i | ||||||||
\(599\) | 5493.05 | 0.374691 | 0.187346 | − | 0.982294i | \(-0.440012\pi\) | ||||
0.187346 | + | 0.982294i | \(0.440012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24292.8 | 1.64879 | 0.824396 | − | 0.566014i | \(-0.191515\pi\) | ||||
0.824396 | + | 0.566014i | \(0.191515\pi\) | |||||||
\(602\) | − 1062.97i | − 0.0719655i | ||||||||
\(603\) | 2789.93i | 0.188416i | ||||||||
\(604\) | 9402.82 | 0.633436 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1365.19 | 0.0915131 | ||||||||
\(607\) | 3029.50i | 0.202576i | 0.994857 | + | 0.101288i | \(0.0322964\pi\) | ||||
−0.994857 | + | 0.101288i | \(0.967704\pi\) | |||||||
\(608\) | − 19549.3i | − 1.30400i | ||||||||
\(609\) | 2005.38 | 0.133435 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9025.87 | −0.597623 | ||||||||
\(612\) | 4926.85i | 0.325419i | ||||||||
\(613\) | 19339.6i | 1.27426i | 0.770757 | + | 0.637129i | \(0.219878\pi\) | ||||
−0.770757 | + | 0.637129i | \(0.780122\pi\) | |||||||
\(614\) | −26992.4 | −1.77414 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 256.412 | 0.0167713 | ||||||||
\(617\) | − 5743.91i | − 0.374783i | −0.982285 | − | 0.187391i | \(-0.939997\pi\) | ||||
0.982285 | − | 0.187391i | \(-0.0600033\pi\) | |||||||
\(618\) | 8538.35i | 0.555765i | ||||||||
\(619\) | 8243.35 | 0.535264 | 0.267632 | − | 0.963521i | \(-0.413759\pi\) | ||||
0.267632 | + | 0.963521i | \(0.413759\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5686.81 | 0.367478 | ||||||||
\(622\) | − 26815.4i | − 1.72861i | ||||||||
\(623\) | 1832.26i | 0.117830i | ||||||||
\(624\) | −4562.37 | −0.292694 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32231.6 | 2.05788 | ||||||||
\(627\) | − 946.856i | − 0.0603091i | ||||||||
\(628\) | 2652.13i | 0.168521i | ||||||||
\(629\) | −11897.1 | −0.754162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4376.56 | −0.276114 | −0.138057 | − | 0.990424i | \(-0.544086\pi\) | ||||
−0.138057 | + | 0.990424i | \(0.544086\pi\) | |||||||
\(632\) | − 308.762i | − 0.0194334i | ||||||||
\(633\) | 3165.48i | 0.198762i | ||||||||
\(634\) | −17407.8 | −1.09046 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2462.49 | −0.153528 | ||||||||
\(637\) | − 934.051i | − 0.0580980i | ||||||||
\(638\) | − 990.613i | − 0.0614714i | ||||||||
\(639\) | −5991.23 | −0.370907 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11836.6 | 0.729357 | 0.364678 | − | 0.931133i | \(-0.381179\pi\) | ||||
0.364678 | + | 0.931133i | \(0.381179\pi\) | |||||||
\(642\) | 8153.86i | 0.501257i | ||||||||
\(643\) | − 1448.21i | − 0.0888209i | −0.999013 | − | 0.0444104i | \(-0.985859\pi\) | ||||
0.999013 | − | 0.0444104i | \(-0.0141409\pi\) | |||||||
\(644\) | 6588.72 | 0.403155 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46472.0 | −2.83037 | ||||||||
\(647\) | − 8732.95i | − 0.530646i | −0.964160 | − | 0.265323i | \(-0.914521\pi\) | ||||
0.964160 | − | 0.265323i | \(-0.0854785\pi\) | |||||||
\(648\) | − 1009.98i | − 0.0612279i | ||||||||
\(649\) | −2234.49 | −0.135149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1980.46 | 0.119232 | ||||||||
\(652\) | 9736.37i | 0.584824i | ||||||||
\(653\) | 21978.4i | 1.31712i | 0.752527 | + | 0.658562i | \(0.228835\pi\) | ||||
−0.752527 | + | 0.658562i | \(0.771165\pi\) | |||||||
\(654\) | −8271.91 | −0.494583 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 39181.1 | 2.33196 | ||||||||
\(657\) | 5591.59i | 0.332038i | ||||||||
\(658\) | − 11703.8i | − 0.693406i | ||||||||
\(659\) | 27761.7 | 1.64103 | 0.820516 | − | 0.571623i | \(-0.193686\pi\) | ||||
0.820516 | + | 0.571623i | \(0.193686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8573.72 | −0.504507 | −0.252254 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252254 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(662\) | − 4313.86i | − 0.253267i | ||||||||
\(663\) | 7005.27i | 0.410350i | ||||||||
\(664\) | 5071.39 | 0.296398 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3086.51 | −0.179579 | ||||||||
\(667\) | 20113.2i | 1.16760i | ||||||||
\(668\) | − 3572.87i | − 0.206944i | ||||||||
\(669\) | −14027.6 | −0.810668 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 583.868 | 0.0335916 | ||||||||
\(672\) | − 3821.22i | − 0.219356i | ||||||||
\(673\) | − 27159.2i | − 1.55559i | −0.628518 | − | 0.777795i | \(-0.716338\pi\) | ||||
0.628518 | − | 0.777795i | \(-0.283662\pi\) | |||||||
\(674\) | −30879.1 | −1.76472 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8194.26 | −0.466219 | ||||||||
\(677\) | − 1392.30i | − 0.0790404i | −0.999219 | − | 0.0395202i | \(-0.987417\pi\) | ||||
0.999219 | − | 0.0395202i | \(-0.0125829\pi\) | |||||||
\(678\) | − 11818.5i | − 0.669448i | ||||||||
\(679\) | −7033.42 | −0.397523 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16329.3 | 0.918857 | ||||||||
\(682\) | − 978.302i | − 0.0549283i | ||||||||
\(683\) | 8675.09i | 0.486007i | 0.970025 | + | 0.243004i | \(0.0781327\pi\) | ||||
−0.970025 | + | 0.243004i | \(0.921867\pi\) | |||||||
\(684\) | −4321.05 | −0.241549 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1211.18 | 0.0674096 | ||||||||
\(687\) | − 1608.91i | − 0.0893504i | ||||||||
\(688\) | − 3430.86i | − 0.190117i | ||||||||
\(689\) | −3501.30 | −0.193598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21426.0 | −1.17957 | −0.589785 | − | 0.807561i | \(-0.700787\pi\) | ||||
−0.589785 | + | 0.807561i | \(0.700787\pi\) | |||||||
\(692\) | − 6454.65i | − 0.354579i | ||||||||
\(693\) | − 185.078i | − 0.0101451i | ||||||||
\(694\) | 16206.3 | 0.886433 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3572.11 | 0.194541 | ||||||||
\(697\) | − 60160.4i | − 3.26935i | ||||||||
\(698\) | − 14088.8i | − 0.763997i | ||||||||
\(699\) | 550.470 | 0.0297864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24840.5 | 1.33839 | 0.669197 | − | 0.743085i | \(-0.266638\pi\) | ||||
0.669197 | + | 0.743085i | \(0.266638\pi\) | |||||||
\(702\) | 1817.40i | 0.0977116i | ||||||||
\(703\) | − 10434.2i | − 0.559793i | ||||||||
\(704\) | −12.6139 | −0.000675288 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8532.45 | −0.454848 | ||||||||
\(707\) | 902.101i | 0.0479873i | ||||||||
\(708\) | 10197.3i | 0.541295i | ||||||||
\(709\) | −12525.0 | −0.663450 | −0.331725 | − | 0.943376i | \(-0.607631\pi\) | ||||
−0.331725 | + | 0.943376i | \(0.607631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −222.863 | −0.0117553 | ||||||||
\(712\) | 3263.74i | 0.171789i | ||||||||
\(713\) | 19863.3i | 1.04332i | ||||||||
\(714\) | −9083.69 | −0.476118 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14941.6 | 0.779881 | ||||||||
\(717\) | 1929.65i | 0.100508i | ||||||||
\(718\) | − 9732.66i | − 0.505877i | ||||||||
\(719\) | −28085.0 | −1.45674 | −0.728369 | − | 0.685185i | \(-0.759721\pi\) | ||||
−0.728369 | + | 0.685185i | \(0.759721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5642.05 | −0.291430 | ||||||||
\(722\) | − 16537.9i | − 0.852460i | ||||||||
\(723\) | 17266.8i | 0.888189i | ||||||||
\(724\) | −10063.1 | −0.516562 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14008.4 | 0.716115 | ||||||||
\(727\) | − 14326.2i | − 0.730851i | −0.930841 | − | 0.365426i | \(-0.880923\pi\) | ||||
0.930841 | − | 0.365426i | \(-0.119077\pi\) | |||||||
\(728\) | − 1663.79i | − 0.0847037i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5267.89 | −0.266539 | ||||||||
\(732\) | − 2664.53i | − 0.134541i | ||||||||
\(733\) | − 6727.85i | − 0.339016i | −0.985529 | − | 0.169508i | \(-0.945782\pi\) | ||||
0.985529 | − | 0.169508i | \(-0.0542179\pi\) | |||||||
\(734\) | 39240.8 | 1.97331 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38325.5 | 1.91943 | ||||||||
\(737\) | 910.677i | 0.0455159i | ||||||||
\(738\) | − 15607.6i | − 0.778490i | ||||||||
\(739\) | 3418.51 | 0.170165 | 0.0850826 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850826 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6143.91 | −0.304591 | ||||||||
\(742\) | − 4540.11i | − 0.224626i | ||||||||
\(743\) | − 8095.50i | − 0.399724i | −0.979824 | − | 0.199862i | \(-0.935951\pi\) | ||||
0.979824 | − | 0.199862i | \(-0.0640494\pi\) | |||||||
\(744\) | 3527.72 | 0.173834 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21508.4 | −1.05560 | ||||||||
\(747\) | − 3660.51i | − 0.179292i | ||||||||
\(748\) | 1608.20i | 0.0786119i | ||||||||
\(749\) | −5387.99 | −0.262847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13446.8 | 0.653371 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(752\) | − 37775.4i | − 1.83182i | ||||||||
\(753\) | 15396.8i | 0.745141i | ||||||||
\(754\) | −6427.84 | −0.310462 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −844.617 | −0.0406328 | ||||||||
\(757\) | − 2593.24i | − 0.124508i | −0.998060 | − | 0.0622541i | \(-0.980171\pi\) | ||||
0.998060 | − | 0.0622541i | \(-0.0198289\pi\) | |||||||
\(758\) | 14069.0i | 0.674156i | ||||||||
\(759\) | 1856.26 | 0.0887722 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27079.4 | 1.28992 | 0.644959 | − | 0.764217i | \(-0.276875\pi\) | ||||
0.644959 | + | 0.764217i | \(0.276875\pi\) | |||||||
\(762\) | 19873.0i | 0.944782i | ||||||||
\(763\) | − 5465.99i | − 0.259348i | ||||||||
\(764\) | 4477.48 | 0.212028 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1124.58 | −0.0530451 | ||||||||
\(767\) | 14499.0i | 0.682568i | ||||||||
\(768\) | − 15363.3i | − 0.721842i | ||||||||
\(769\) | −2138.72 | −0.100292 | −0.0501458 | − | 0.998742i | \(-0.515969\pi\) | ||||
−0.0501458 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15125.2 | 0.706513 | ||||||||
\(772\) | − 18121.1i | − 0.844810i | ||||||||
\(773\) | − 25864.0i | − 1.20345i | −0.798704 | − | 0.601724i | \(-0.794481\pi\) | ||||
0.798704 | − | 0.601724i | \(-0.205519\pi\) | |||||||
\(774\) | −1366.67 | −0.0634676 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12528.4 | −0.579566 | ||||||||
\(777\) | − 2039.53i | − 0.0941671i | ||||||||
\(778\) | 13720.1i | 0.632247i | ||||||||
\(779\) | 52763.1 | 2.42675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1955.63 | −0.0896006 | ||||||||
\(782\) | − 91106.2i | − 4.16618i | ||||||||
\(783\) | − 2578.34i | − 0.117679i | ||||||||
\(784\) | 3909.23 | 0.178081 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3858.14 | −0.175083 | ||||||||
\(787\) | − 32371.3i | − 1.46621i | −0.680113 | − | 0.733107i | \(-0.738069\pi\) | ||||
0.680113 | − | 0.733107i | \(-0.261931\pi\) | |||||||
\(788\) | 22971.0i | 1.03846i | ||||||||
\(789\) | −22731.0 | −1.02566 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7809.52 | 0.351043 | ||||||||
\(792\) | − 329.673i | − 0.0147909i | ||||||||
\(793\) | − 3788.57i | − 0.169654i | ||||||||
\(794\) | 16970.8 | 0.758526 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2617.11 | 0.116534 | ||||||||
\(797\) | 2024.33i | 0.0899691i | 0.998988 | + | 0.0449845i | \(0.0143239\pi\) | ||||
−0.998988 | + | 0.0449845i | \(0.985676\pi\) | |||||||
\(798\) | − 7966.76i | − 0.353409i | ||||||||
\(799\) | −58002.1 | −2.56817 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2355.76 | 0.103916 | ||||||||
\(802\) | − 12777.7i | − 0.562589i | ||||||||
\(803\) | 1825.18i | 0.0802109i | ||||||||
\(804\) | 4155.95 | 0.182300 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6347.95 | −0.277416 | ||||||||
\(807\) | 3069.29i | 0.133884i | ||||||||
\(808\) | 1606.88i | 0.0699628i | ||||||||
\(809\) | −12391.7 | −0.538526 | −0.269263 | − | 0.963067i | \(-0.586780\pi\) | ||||
−0.269263 | + | 0.963067i | \(0.586780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14654.5 | 0.634511 | 0.317256 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(812\) | − 2987.26i | − 0.129104i | ||||||||
\(813\) | 6755.94i | 0.291441i | ||||||||
\(814\) | −1007.49 | −0.0433813 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29318.7 | −1.25780 | ||||||||
\(817\) | − 4620.16i | − 0.197844i | ||||||||
\(818\) | − 7447.33i | − 0.318325i | ||||||||
\(819\) | −1200.92 | −0.0512376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23887.9 | 1.01546 | 0.507731 | − | 0.861516i | \(-0.330485\pi\) | ||||
0.507731 | + | 0.861516i | \(0.330485\pi\) | |||||||
\(822\) | − 16982.6i | − 0.720604i | ||||||||
\(823\) | 4008.41i | 0.169774i | 0.996391 | + | 0.0848871i | \(0.0270530\pi\) | ||||
−0.996391 | + | 0.0848871i | \(0.972947\pi\) | |||||||
\(824\) | −10050.0 | −0.424889 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18800.8 | −0.791966 | ||||||||
\(827\) | − 45110.4i | − 1.89679i | −0.317096 | − | 0.948394i | \(-0.602708\pi\) | ||||
0.317096 | − | 0.948394i | \(-0.397292\pi\) | |||||||
\(828\) | − 8471.21i | − 0.355549i | ||||||||
\(829\) | −16165.4 | −0.677260 | −0.338630 | − | 0.940920i | \(-0.609964\pi\) | ||||
−0.338630 | + | 0.940920i | \(0.609964\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25892.2 | −1.08085 | ||||||||
\(832\) | 81.8481i | 0.00341054i | ||||||||
\(833\) | − 6002.41i | − 0.249665i | ||||||||
\(834\) | 25753.8 | 1.06928 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1410.46 | −0.0583514 | ||||||||
\(837\) | − 2546.30i | − 0.105153i | ||||||||
\(838\) | − 24385.7i | − 1.00524i | ||||||||
\(839\) | 25244.4 | 1.03878 | 0.519388 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519388 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15269.9 | −0.626096 | ||||||||
\(842\) | 34066.7i | 1.39432i | ||||||||
\(843\) | 22564.9i | 0.921916i | ||||||||
\(844\) | 4715.37 | 0.192310 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15047.7 | −0.611526 | ||||||||
\(847\) | 9256.59i | 0.375514i | ||||||||
\(848\) | − 14653.8i | − 0.593412i | ||||||||
\(849\) | −44.4506 | −0.00179687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20455.8 | 0.823990 | ||||||||
\(852\) | 8924.68i | 0.358867i | ||||||||
\(853\) | 30168.1i | 1.21094i | 0.795867 | + | 0.605472i | \(0.207016\pi\) | ||||
−0.795867 | + | 0.605472i | \(0.792984\pi\) | |||||||
\(854\) | 4912.61 | 0.196846 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9597.44 | −0.383217 | ||||||||
\(857\) | − 13393.6i | − 0.533857i | −0.963716 | − | 0.266929i | \(-0.913991\pi\) | ||||
0.963716 | − | 0.266929i | \(-0.0860088\pi\) | |||||||
\(858\) | 593.230i | 0.0236043i | ||||||||
\(859\) | −19060.4 | −0.757081 | −0.378541 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378541 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10313.4 | 0.408222 | ||||||||
\(862\) | 45914.3i | 1.81421i | ||||||||
\(863\) | 9466.86i | 0.373413i | 0.982416 | + | 0.186707i | \(0.0597814\pi\) | ||||
−0.982416 | + | 0.186707i | \(0.940219\pi\) | |||||||
\(864\) | −4913.00 | −0.193453 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25975.2 | −1.01925 | ||||||||
\(867\) | 30278.3i | 1.18605i | ||||||||
\(868\) | − 2950.13i | − 0.115362i | ||||||||
\(869\) | −72.7461 | −0.00283975 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5909.15 | 0.229878 | ||||||||
\(872\) | − 9736.39i | − 0.378115i | ||||||||
\(873\) | 9042.97i | 0.350582i | ||||||||
\(874\) | 79903.8 | 3.09243 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8329.37 | 0.321259 | ||||||||
\(877\) | 37740.6i | 1.45315i | 0.687090 | + | 0.726573i | \(0.258888\pi\) | ||||
−0.687090 | + | 0.726573i | \(0.741112\pi\) | |||||||
\(878\) | 24397.3i | 0.937778i | ||||||||
\(879\) | −20740.2 | −0.795845 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25991.5 | 0.993957 | 0.496979 | − | 0.867763i | \(-0.334443\pi\) | ||||
0.496979 | + | 0.867763i | \(0.334443\pi\) | |||||||
\(882\) | − 1557.23i | − 0.0594496i | ||||||||
\(883\) | − 39420.3i | − 1.50238i | −0.660087 | − | 0.751189i | \(-0.729481\pi\) | ||||
0.660087 | − | 0.751189i | \(-0.270519\pi\) | |||||||
\(884\) | 10435.2 | 0.397030 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52305.0 | 1.98332 | ||||||||
\(887\) | 46005.2i | 1.74149i | 0.491735 | + | 0.870745i | \(0.336363\pi\) | ||||
−0.491735 | + | 0.870745i | \(0.663637\pi\) | |||||||
\(888\) | − 3632.95i | − 0.137290i | ||||||||
\(889\) | −13131.9 | −0.495421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −237.957 | −0.00894710 | ||||||||
\(892\) | 20895.8i | 0.784353i | ||||||||
\(893\) | − 50870.2i | − 1.90628i | ||||||||
\(894\) | 24805.2 | 0.927975 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10083.8 | 0.375978 | ||||||||
\(897\) | − 12044.8i | − 0.448345i | ||||||||
\(898\) | − 37622.6i | − 1.39809i | ||||||||
\(899\) | 9005.81 | 0.334105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22500.1 | −0.831950 | ||||||||
\(902\) | − 5094.58i | − 0.188061i | ||||||||
\(903\) | − 903.081i | − 0.0332809i | ||||||||
\(904\) | 13910.8 | 0.511801 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22289.2 | 0.817340 | ||||||||
\(907\) | − 2838.97i | − 0.103932i | −0.998649 | − | 0.0519661i | \(-0.983451\pi\) | ||||
0.998649 | − | 0.0519661i | \(-0.0165488\pi\) | |||||||
\(908\) | − 24324.6i | − 0.889030i | ||||||||
\(909\) | 1159.84 | 0.0423208 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39890.9 | 1.45076 | 0.725382 | − | 0.688347i | \(-0.241663\pi\) | ||||
0.725382 | + | 0.688347i | \(0.241663\pi\) | |||||||
\(912\) | − 25713.7i | − 0.933626i | ||||||||
\(913\) | − 1194.85i | − 0.0433119i | ||||||||
\(914\) | −20675.3 | −0.748226 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2396.67 | −0.0864500 | ||||||||
\(917\) | − 2549.42i | − 0.0918094i | ||||||||
\(918\) | 11679.0i | 0.419897i | ||||||||
\(919\) | 646.475 | 0.0232048 | 0.0116024 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116024 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22932.4 | −0.820463 | ||||||||
\(922\) | − 11316.3i | − 0.404213i | ||||||||
\(923\) | 12689.6i | 0.452528i | ||||||||
\(924\) | −275.696 | −0.00981574 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1312.37 | −0.0465737 | ||||||||
\(927\) | 7254.07i | 0.257017i | ||||||||
\(928\) | − 17376.4i | − 0.614665i | ||||||||
\(929\) | −51188.2 | −1.80778 | −0.903892 | − | 0.427760i | \(-0.859303\pi\) | ||||
−0.903892 | + | 0.427760i | \(0.859303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5264.35 | 0.185319 | ||||||||
\(932\) | − 819.993i | − 0.0288195i | ||||||||
\(933\) | − 22782.0i | − 0.799409i | ||||||||
\(934\) | −69747.8 | −2.44349 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2139.16 | −0.0747017 | ||||||||
\(937\) | 29786.1i | 1.03849i | 0.854624 | + | 0.519247i | \(0.173788\pi\) | ||||
−0.854624 | + | 0.519247i | \(0.826212\pi\) | |||||||
\(938\) | 7662.36i | 0.266722i | ||||||||
\(939\) | 27383.5 | 0.951680 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44817.4 | −1.55261 | −0.776304 | − | 0.630358i | \(-0.782908\pi\) | ||||
−0.776304 | + | 0.630358i | \(0.782908\pi\) | |||||||
\(942\) | 6286.82i | 0.217448i | ||||||||
\(943\) | 103439.i | 3.57206i | ||||||||
\(944\) | −60682.0 | −2.09219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −446.103 | −0.0153320 | ||||||||
\(947\) | 54697.1i | 1.87689i | 0.345425 | + | 0.938446i | \(0.387735\pi\) | ||||
−0.345425 | + | 0.938446i | \(0.612265\pi\) | |||||||
\(948\) | 331.983i | 0.0113737i | ||||||||
\(949\) | 11843.2 | 0.405105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14789.4 | −0.504290 | ||||||||
\(952\) | − 10691.9i | − 0.363998i | ||||||||
\(953\) | 7577.51i | 0.257565i | 0.991673 | + | 0.128783i | \(0.0411069\pi\) | ||||
−0.991673 | + | 0.128783i | \(0.958893\pi\) | |||||||
\(954\) | −5837.29 | −0.198102 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2874.46 | 0.0972454 | ||||||||
\(957\) | − 841.612i | − 0.0284278i | ||||||||
\(958\) | − 73313.4i | − 2.47249i | ||||||||
\(959\) | 11221.9 | 0.377868 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20897.1 | −0.701457 | ||||||||
\(962\) | 6537.32i | 0.219097i | ||||||||
\(963\) | 6927.41i | 0.231810i | ||||||||
\(964\) | 25721.1 | 0.859357 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15618.4 | 0.520202 | ||||||||
\(967\) | 50779.0i | 1.68867i | 0.535817 | + | 0.844334i | \(0.320004\pi\) | ||||
−0.535817 | + | 0.844334i | \(0.679996\pi\) | |||||||
\(968\) | 16488.5i | 0.547478i | ||||||||
\(969\) | −39482.0 | −1.30892 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15313.2 | −0.506102 | −0.253051 | − | 0.967453i | \(-0.581434\pi\) | ||||
−0.253051 | + | 0.967453i | \(0.581434\pi\) | |||||||
\(972\) | 1085.94i | 0.0358348i | ||||||||
\(973\) | 17017.9i | 0.560707i | ||||||||
\(974\) | 62315.9 | 2.05003 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15856.1 | 0.520021 | ||||||||
\(977\) | 46620.4i | 1.52663i | 0.646025 | + | 0.763316i | \(0.276430\pi\) | ||||
−0.646025 | + | 0.763316i | \(0.723570\pi\) | |||||||
\(978\) | 23079.9i | 0.754615i | ||||||||
\(979\) | 768.957 | 0.0251031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7027.70 | −0.228723 | ||||||||
\(982\) | 19906.6i | 0.646889i | ||||||||
\(983\) | 2824.37i | 0.0916414i | 0.998950 | + | 0.0458207i | \(0.0145903\pi\) | ||||
−0.998950 | + | 0.0458207i | \(0.985410\pi\) | |||||||
\(984\) | 18370.9 | 0.595165 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41306.6 | −1.33415 | ||||||||
\(987\) | − 9943.38i | − 0.320670i | ||||||||
\(988\) | 9152.11i | 0.294704i | ||||||||
\(989\) | 9057.59 | 0.291218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16951.4 | 0.543370 | 0.271685 | − | 0.962386i | \(-0.412419\pi\) | ||||
0.271685 | + | 0.962386i | \(0.412419\pi\) | |||||||
\(992\) | − 17160.5i | − 0.549239i | ||||||||
\(993\) | − 3665.00i | − 0.117125i | ||||||||
\(994\) | −16454.5 | −0.525056 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5452.79 | −0.173472 | ||||||||
\(997\) | 23847.8i | 0.757540i | 0.925491 | + | 0.378770i | \(0.123653\pi\) | ||||
−0.925491 | + | 0.378770i | \(0.876347\pi\) | |||||||
\(998\) | − 61703.4i | − 1.95710i | ||||||||
\(999\) | −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 | 525.4.d.h.274.2 | 4 | ||
5.2 | odd | 4 | 525.4.a.k.1.2 | 2 | |||
5.3 | odd | 4 | 105.4.a.f.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 525.4.d.h.274.3 | 4 | ||
15.2 | even | 4 | 1575.4.a.w.1.1 | 2 | |||
15.8 | even | 4 | 315.4.a.i.1.2 | 2 | |||
20.3 | even | 4 | 1680.4.a.bg.1.1 | 2 | |||
35.13 | even | 4 | 735.4.a.p.1.1 | 2 | |||
105.83 | odd | 4 | 2205.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
315.4.a.i.1.2 | 2 | 15.8 | even | 4 | |||
525.4.a.k.1.2 | 2 | 5.2 | odd | 4 | |||
525.4.d.h.274.2 | 4 | 1.1 | even | 1 | trivial | ||
525.4.d.h.274.3 | 4 | 5.4 | even | 2 | inner | ||
735.4.a.p.1.1 | 2 | 35.13 | even | 4 | |||
1575.4.a.w.1.1 | 2 | 15.2 | even | 4 | |||
1680.4.a.bg.1.1 | 2 | 20.3 | even | 4 | |||
2205.4.a.z.1.2 | 2 | 105.83 | odd | 4 |