Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1520092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 40x^{2} - 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.32145\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.48928 | −1.94075 | −0.970376 | − | 0.241598i | \(-0.922328\pi\) | ||||
−0.970376 | + | 0.241598i | \(0.922328\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.1322 | 2.76652 | ||||||||
\(5\) | 14.0859 | 1.25989 | 0.629943 | − | 0.776642i | \(-0.283078\pi\) | ||||
0.629943 | + | 0.776642i | \(0.283078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.2643 | −1.31015 | −0.655076 | − | 0.755563i | \(-0.727363\pi\) | ||||
−0.655076 | + | 0.755563i | \(0.727363\pi\) | |||||||
\(8\) | −77.5754 | −3.42838 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −77.3217 | −2.44513 | ||||||||
\(11\) | 3.10739 | 0.0851741 | 0.0425870 | − | 0.999093i | \(-0.486440\pi\) | ||||
0.0425870 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 133.194 | 2.54268 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 248.776 | 3.88712 | ||||||||
\(17\) | −43.9142 | −0.626515 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 85.8504 | 1.03660 | 0.518301 | − | 0.855198i | \(-0.326565\pi\) | ||||
0.518301 | + | 0.855198i | \(0.326565\pi\) | |||||||
\(20\) | 311.753 | 3.48550 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17.0574 | −0.165302 | ||||||||
\(23\) | −203.829 | −1.84788 | −0.923940 | − | 0.382537i | \(-0.875050\pi\) | ||||
−0.923940 | + | 0.382537i | \(0.875050\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 73.4140 | 0.587312 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −537.022 | −3.62456 | ||||||||
\(29\) | 31.0739 | 0.198975 | 0.0994877 | − | 0.995039i | \(-0.468280\pi\) | ||||
0.0994877 | + | 0.995039i | \(0.468280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 135.736 | 0.786414 | 0.393207 | − | 0.919450i | \(-0.371366\pi\) | ||||
0.393207 | + | 0.919450i | \(0.371366\pi\) | |||||||
\(32\) | −744.995 | −4.11555 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 241.057 | 1.21591 | ||||||||
\(35\) | −341.786 | −1.65064 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −290.229 | −1.28955 | −0.644776 | − | 0.764372i | \(-0.723049\pi\) | ||||
−0.644776 | + | 0.764372i | \(0.723049\pi\) | |||||||
\(38\) | −471.256 | −2.01179 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1092.72 | −4.31937 | ||||||||
\(41\) | −148.731 | −0.566532 | −0.283266 | − | 0.959041i | \(-0.591418\pi\) | ||||
−0.283266 | + | 0.959041i | \(0.591418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 281.057 | 0.996764 | 0.498382 | − | 0.866958i | \(-0.333928\pi\) | ||||
0.498382 | + | 0.866958i | \(0.333928\pi\) | |||||||
\(44\) | 68.7734 | 0.235636 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1118.87 | 3.58628 | ||||||||
\(47\) | −225.991 | −0.701366 | −0.350683 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350683 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 245.758 | 0.716496 | ||||||||
\(50\) | −402.990 | −1.13983 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −172.755 | −0.447730 | −0.223865 | − | 0.974620i | \(-0.571868\pi\) | ||||
−0.223865 | + | 0.974620i | \(0.571868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.7706 | 0.107310 | ||||||||
\(56\) | 1882.32 | 4.49170 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −170.574 | −0.386162 | ||||||||
\(59\) | −41.2175 | −0.0909503 | −0.0454751 | − | 0.998965i | \(-0.514480\pi\) | ||||
−0.0454751 | + | 0.998965i | \(0.514480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 499.815 | 1.04910 | 0.524548 | − | 0.851381i | \(-0.324234\pi\) | ||||
0.524548 | + | 0.851381i | \(0.324234\pi\) | |||||||
\(62\) | −745.091 | −1.52624 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2099.28 | 4.10015 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −503.506 | −0.918106 | −0.459053 | − | 0.888409i | \(-0.651811\pi\) | ||||
−0.459053 | + | 0.888409i | \(0.651811\pi\) | |||||||
\(68\) | −971.917 | −1.73327 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1876.16 | 3.20349 | ||||||||
\(71\) | 946.442 | 1.58200 | 0.791000 | − | 0.611816i | \(-0.209561\pi\) | ||||
0.791000 | + | 0.611816i | \(0.209561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1115.97 | 1.78925 | 0.894623 | − | 0.446821i | \(-0.147444\pi\) | ||||
0.894623 | + | 0.446821i | \(0.147444\pi\) | |||||||
\(74\) | 1593.15 | 2.50270 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1900.05 | 2.86778 | ||||||||
\(77\) | −75.3989 | −0.111591 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 674.803 | 0.961029 | 0.480514 | − | 0.876987i | \(-0.340450\pi\) | ||||
0.480514 | + | 0.876987i | \(0.340450\pi\) | |||||||
\(80\) | 3504.24 | 4.89732 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 816.424 | 1.09950 | ||||||||
\(83\) | 59.4512 | 0.0786219 | 0.0393109 | − | 0.999227i | \(-0.487484\pi\) | ||||
0.0393109 | + | 0.999227i | \(0.487484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −618.574 | −0.789338 | ||||||||
\(86\) | −1542.80 | −1.93447 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −241.057 | −0.292009 | ||||||||
\(89\) | −1218.41 | −1.45114 | −0.725571 | − | 0.688147i | \(-0.758424\pi\) | ||||
−0.725571 | + | 0.688147i | \(0.758424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4511.17 | −5.11220 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1240.53 | 1.36118 | ||||||||
\(95\) | 1209.28 | 1.30600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 879.746 | 0.920872 | 0.460436 | − | 0.887693i | \(-0.347693\pi\) | ||||
0.460436 | + | 0.887693i | \(0.347693\pi\) | |||||||
\(98\) | −1349.03 | −1.39054 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1624.81 | 1.62481 | ||||||||
\(101\) | 255.628 | 0.251841 | 0.125920 | − | 0.992040i | \(-0.459812\pi\) | ||||
0.125920 | + | 0.992040i | \(0.459812\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 176.369 | 0.168720 | 0.0843600 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843600 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 948.299 | 0.868934 | ||||||||
\(107\) | 816.164 | 0.737397 | 0.368699 | − | 0.929549i | \(-0.379803\pi\) | ||||
0.368699 | + | 0.929549i | \(0.379803\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −174.369 | −0.153225 | −0.0766125 | − | 0.997061i | \(-0.524410\pi\) | ||||
−0.0766125 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(110\) | −240.269 | −0.208261 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6036.37 | −5.09271 | ||||||||
\(113\) | 199.667 | 0.166222 | 0.0831112 | − | 0.996540i | \(-0.473514\pi\) | ||||
0.0831112 | + | 0.996540i | \(0.473514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2871.12 | −2.32812 | ||||||||
\(116\) | 687.734 | 0.550470 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 226.254 | 0.176512 | ||||||||
\(119\) | 1065.55 | 0.820830 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1321.34 | −0.992745 | ||||||||
\(122\) | −2743.63 | −2.03603 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3004.12 | 2.17563 | ||||||||
\(125\) | −726.638 | −0.519940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 407.840 | 0.284961 | 0.142480 | − | 0.989798i | \(-0.454492\pi\) | ||||
0.142480 | + | 0.989798i | \(0.454492\pi\) | |||||||
\(128\) | −5563.57 | −3.84183 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2177.50 | 1.45229 | 0.726143 | − | 0.687544i | \(-0.241311\pi\) | ||||
0.726143 | + | 0.687544i | \(0.241311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2083.10 | −1.35810 | ||||||||
\(134\) | 2763.89 | 1.78182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3406.66 | 2.14793 | ||||||||
\(137\) | 723.750 | 0.451344 | 0.225672 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225672 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1520.85 | −0.928033 | −0.464017 | − | 0.885826i | \(-0.653592\pi\) | ||||
−0.464017 | + | 0.885826i | \(0.653592\pi\) | |||||||
\(140\) | −7564.47 | −4.56653 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5195.28 | −3.07027 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 437.706 | 0.250686 | ||||||||
\(146\) | −6125.90 | −3.47248 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6423.41 | −3.56757 | ||||||||
\(149\) | −2027.51 | −1.11477 | −0.557384 | − | 0.830255i | \(-0.688195\pi\) | ||||
−0.557384 | + | 0.830255i | \(0.688195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8952 | 0.00641071 | 0.00320535 | − | 0.999995i | \(-0.498980\pi\) | ||||
0.00320535 | + | 0.999995i | \(0.498980\pi\) | |||||||
\(152\) | −6659.88 | −3.55386 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 413.885 | 0.216570 | ||||||||
\(155\) | 1911.97 | 0.990792 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1369.10 | 0.695963 | 0.347982 | − | 0.937501i | \(-0.386867\pi\) | ||||
0.347982 | + | 0.937501i | \(0.386867\pi\) | |||||||
\(158\) | −3704.18 | −1.86512 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10494.0 | −5.18513 | ||||||||
\(161\) | 4945.77 | 2.42100 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1650.54 | −0.793130 | −0.396565 | − | 0.918007i | \(-0.629798\pi\) | ||||
−0.396565 | + | 0.918007i | \(0.629798\pi\) | |||||||
\(164\) | −3291.73 | −1.56732 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −326.344 | −0.152586 | ||||||||
\(167\) | 872.686 | 0.404374 | 0.202187 | − | 0.979347i | \(-0.435195\pi\) | ||||
0.202187 | + | 0.979347i | \(0.435195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3395.52 | 1.53191 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6220.41 | 2.75757 | ||||||||
\(173\) | −732.880 | −0.322080 | −0.161040 | − | 0.986948i | \(-0.551485\pi\) | ||||
−0.161040 | + | 0.986948i | \(0.551485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1781.34 | −0.769467 | ||||||||
\(176\) | 773.044 | 0.331082 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6688.21 | 2.81631 | ||||||||
\(179\) | 1530.81 | 0.639207 | 0.319604 | − | 0.947551i | \(-0.396450\pi\) | ||||
0.319604 | + | 0.947551i | \(0.396450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1198.21 | −0.492056 | −0.246028 | − | 0.969263i | \(-0.579126\pi\) | ||||
−0.246028 | + | 0.969263i | \(0.579126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15812.1 | 6.33524 | ||||||||
\(185\) | −4088.16 | −1.62469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −136.459 | −0.0533629 | ||||||||
\(188\) | −5001.68 | −1.94034 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6638.09 | −2.53462 | ||||||||
\(191\) | −2465.44 | −0.933994 | −0.466997 | − | 0.884259i | \(-0.654664\pi\) | ||||
−0.466997 | + | 0.884259i | \(0.654664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4588.52 | 1.71134 | 0.855671 | − | 0.517520i | \(-0.173145\pi\) | ||||
0.855671 | + | 0.517520i | \(0.173145\pi\) | |||||||
\(194\) | −4829.17 | −1.78719 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5439.16 | 1.98220 | ||||||||
\(197\) | 3862.82 | 1.39703 | 0.698514 | − | 0.715596i | \(-0.253845\pi\) | ||||
0.698514 | + | 0.715596i | \(0.253845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1434.59 | 0.511033 | 0.255517 | − | 0.966805i | \(-0.417754\pi\) | ||||
0.255517 | + | 0.966805i | \(0.417754\pi\) | |||||||
\(200\) | −5695.12 | −2.01353 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1403.21 | −0.488761 | ||||||||
\(203\) | −753.989 | −0.260688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2095.01 | −0.713766 | ||||||||
\(206\) | −968.139 | −0.327444 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 266.771 | 0.0882915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1577.24 | −0.514604 | −0.257302 | − | 0.966331i | \(-0.582834\pi\) | ||||
−0.257302 | + | 0.966331i | \(0.582834\pi\) | |||||||
\(212\) | −3823.44 | −1.23866 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4480.15 | −1.43111 | ||||||||
\(215\) | 3958.96 | 1.25581 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3293.54 | −1.03032 | ||||||||
\(218\) | 957.161 | 0.297372 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 968.738 | 0.296874 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3123.69 | 0.938016 | 0.469008 | − | 0.883194i | \(-0.344612\pi\) | ||||
0.469008 | + | 0.883194i | \(0.344612\pi\) | |||||||
\(224\) | 18076.8 | 5.39200 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1096.03 | −0.322597 | ||||||||
\(227\) | 3006.22 | 0.878987 | 0.439493 | − | 0.898246i | \(-0.355158\pi\) | ||||
0.439493 | + | 0.898246i | \(0.355158\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2344.43 | 0.676526 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(230\) | 15760.4 | 4.51830 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2410.57 | −0.682163 | ||||||||
\(233\) | 5913.50 | 1.66269 | 0.831344 | − | 0.555759i | \(-0.187572\pi\) | ||||
0.831344 | + | 0.555759i | \(0.187572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3183.30 | −0.883641 | ||||||||
\(236\) | −912.233 | −0.251616 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5849.10 | −1.59303 | ||||||||
\(239\) | 250.440 | 0.0677807 | 0.0338904 | − | 0.999426i | \(-0.489210\pi\) | ||||
0.0338904 | + | 0.999426i | \(0.489210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1112.43 | −0.297337 | −0.148668 | − | 0.988887i | \(-0.547499\pi\) | ||||
−0.148668 | + | 0.988887i | \(0.547499\pi\) | |||||||
\(242\) | 7253.22 | 1.92667 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11062.0 | 2.90234 | ||||||||
\(245\) | 3461.74 | 0.902703 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10529.7 | −2.69613 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3988.72 | 1.00907 | ||||||||
\(251\) | 3496.19 | 0.879194 | 0.439597 | − | 0.898195i | \(-0.355121\pi\) | ||||
0.439597 | + | 0.898195i | \(0.355121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −633.376 | −0.157391 | ||||||||
\(254\) | −2238.75 | −0.553038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13745.7 | 3.35589 | ||||||||
\(257\) | 4644.20 | 1.12723 | 0.563614 | − | 0.826039i | \(-0.309411\pi\) | ||||
0.563614 | + | 0.826039i | \(0.309411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7042.22 | 1.68951 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11952.9 | −2.81853 | ||||||||
\(263\) | −4930.41 | −1.15598 | −0.577989 | − | 0.816045i | \(-0.696162\pi\) | ||||
−0.577989 | + | 0.816045i | \(0.696162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2433.42 | −0.564089 | ||||||||
\(266\) | 11434.7 | 2.63574 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11143.7 | −2.53996 | ||||||||
\(269\) | −1276.44 | −0.289316 | −0.144658 | − | 0.989482i | \(-0.546208\pi\) | ||||
−0.144658 | + | 0.989482i | \(0.546208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2519.91 | 0.564848 | 0.282424 | − | 0.959290i | \(-0.408861\pi\) | ||||
0.282424 | + | 0.959290i | \(0.408861\pi\) | |||||||
\(272\) | −10924.8 | −2.43534 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3972.86 | −0.875947 | ||||||||
\(275\) | 228.126 | 0.0500237 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2462.00 | −0.534033 | −0.267017 | − | 0.963692i | \(-0.586038\pi\) | ||||
−0.267017 | + | 0.963692i | \(0.586038\pi\) | |||||||
\(278\) | 8348.36 | 1.80108 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 26514.2 | 5.65902 | ||||||||
\(281\) | −5058.09 | −1.07381 | −0.536904 | − | 0.843643i | \(-0.680406\pi\) | ||||
−0.536904 | + | 0.843643i | \(0.680406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3078.55 | 0.646647 | 0.323323 | − | 0.946289i | \(-0.395200\pi\) | ||||
0.323323 | + | 0.946289i | \(0.395200\pi\) | |||||||
\(284\) | 20946.8 | 4.37664 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3608.85 | 0.742243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2984.54 | −0.607478 | ||||||||
\(290\) | −2402.69 | −0.486520 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24698.9 | 4.94999 | ||||||||
\(293\) | −8626.31 | −1.71998 | −0.859990 | − | 0.510310i | \(-0.829531\pi\) | ||||
−0.859990 | + | 0.510310i | \(0.829531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −580.588 | −0.114587 | ||||||||
\(296\) | 22514.7 | 4.42107 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11129.6 | 2.16349 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6819.67 | −1.30591 | ||||||||
\(302\) | −65.2960 | −0.0124416 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21357.5 | 4.02939 | ||||||||
\(305\) | 7040.37 | 1.32174 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −545.591 | −0.101428 | −0.0507142 | − | 0.998713i | \(-0.516150\pi\) | ||||
−0.0507142 | + | 0.998713i | \(0.516150\pi\) | |||||||
\(308\) | −1668.74 | −0.308719 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10495.3 | −1.92288 | ||||||||
\(311\) | 3024.25 | 0.551413 | 0.275707 | − | 0.961242i | \(-0.411088\pi\) | ||||
0.275707 | + | 0.961242i | \(0.411088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10082.4 | −1.82074 | −0.910370 | − | 0.413796i | \(-0.864203\pi\) | ||||
−0.910370 | + | 0.413796i | \(0.864203\pi\) | |||||||
\(314\) | −7515.38 | −1.35069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14934.9 | 2.65871 | ||||||||
\(317\) | 8498.67 | 1.50578 | 0.752891 | − | 0.658145i | \(-0.228659\pi\) | ||||
0.752891 | + | 0.658145i | \(0.228659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.5590 | 0.0169475 | ||||||||
\(320\) | 29570.3 | 5.16573 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −27148.7 | −4.69857 | ||||||||
\(323\) | −3770.05 | −0.649447 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9060.26 | 1.53927 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11537.8 | 1.94229 | ||||||||
\(329\) | 5483.53 | 0.918896 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9969.94 | −1.65558 | −0.827791 | − | 0.561037i | \(-0.810403\pi\) | ||||
−0.827791 | + | 0.561037i | \(0.810403\pi\) | |||||||
\(332\) | 1315.78 | 0.217509 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4790.41 | −0.784790 | ||||||||
\(335\) | −7092.36 | −1.15671 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3231.96 | −0.522422 | −0.261211 | − | 0.965282i | \(-0.584122\pi\) | ||||
−0.261211 | + | 0.965282i | \(0.584122\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13690.4 | −2.18372 | ||||||||
\(341\) | 421.784 | 0.0669821 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2359.51 | 0.371433 | ||||||||
\(344\) | −21803.1 | −3.41729 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4022.98 | 0.625078 | ||||||||
\(347\) | 5989.75 | 0.926647 | 0.463323 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463323 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9974.91 | 1.52993 | 0.764964 | − | 0.644074i | \(-0.222757\pi\) | ||||
0.764964 | + | 0.644074i | \(0.222757\pi\) | |||||||
\(350\) | 9778.28 | 1.49335 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2314.99 | −0.350538 | ||||||||
\(353\) | −10834.0 | −1.63352 | −0.816761 | − | 0.576976i | \(-0.804233\pi\) | ||||
−0.816761 | + | 0.576976i | \(0.804233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13331.5 | 1.99314 | ||||||||
\(356\) | −26966.2 | −4.01462 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8403.04 | −1.24054 | ||||||||
\(359\) | −4315.76 | −0.634477 | −0.317239 | − | 0.948346i | \(-0.602756\pi\) | ||||
−0.317239 | + | 0.948346i | \(0.602756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 511.285 | 0.0745422 | ||||||||
\(362\) | 6577.31 | 0.954960 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15719.6 | 2.25425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10505.3 | 1.49420 | 0.747101 | − | 0.664711i | \(-0.231445\pi\) | ||||
0.747101 | + | 0.664711i | \(0.231445\pi\) | |||||||
\(368\) | −50707.6 | −7.18293 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22441.0 | 3.15312 | ||||||||
\(371\) | 4191.78 | 0.586594 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5869.44 | 0.814767 | 0.407384 | − | 0.913257i | \(-0.366441\pi\) | ||||
0.407384 | + | 0.913257i | \(0.366441\pi\) | |||||||
\(374\) | 749.060 | 0.103564 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17531.4 | 2.40455 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6525.75 | 0.884447 | 0.442223 | − | 0.896905i | \(-0.354190\pi\) | ||||
0.442223 | + | 0.896905i | \(0.354190\pi\) | |||||||
\(380\) | 26764.1 | 3.61307 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13533.5 | 1.81265 | ||||||||
\(383\) | 7042.66 | 0.939590 | 0.469795 | − | 0.882775i | \(-0.344328\pi\) | ||||
0.469795 | + | 0.882775i | \(0.344328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1062.06 | −0.140592 | ||||||||
\(386\) | −25187.7 | −3.32129 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19470.7 | 2.54761 | ||||||||
\(389\) | −10339.4 | −1.34763 | −0.673815 | − | 0.738900i | \(-0.735345\pi\) | ||||
−0.673815 | + | 0.738900i | \(0.735345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8950.98 | 1.15773 | ||||||||
\(392\) | −19064.8 | −2.45642 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21204.1 | −2.71129 | ||||||||
\(395\) | 9505.24 | 1.21079 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7465.86 | 0.943831 | 0.471915 | − | 0.881644i | \(-0.343563\pi\) | ||||
0.471915 | + | 0.881644i | \(0.343563\pi\) | |||||||
\(398\) | −7874.88 | −0.991789 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18263.6 | 2.28295 | ||||||||
\(401\) | 3224.37 | 0.401539 | 0.200770 | − | 0.979638i | \(-0.435656\pi\) | ||||
0.200770 | + | 0.979638i | \(0.435656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5657.60 | 0.696723 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4138.85 | 0.505931 | ||||||||
\(407\) | −901.857 | −0.109836 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12391.9 | −1.49814 | −0.749072 | − | 0.662489i | \(-0.769500\pi\) | ||||
−0.749072 | + | 0.662489i | \(0.769500\pi\) | |||||||
\(410\) | 11500.1 | 1.38524 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3903.43 | 0.466768 | ||||||||
\(413\) | 1000.12 | 0.119159 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 837.426 | 0.0990546 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1464.38 | −0.171352 | ||||||||
\(419\) | −13464.4 | −1.56988 | −0.784938 | − | 0.619574i | \(-0.787306\pi\) | ||||
−0.784938 | + | 0.619574i | \(0.787306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6265.49 | 0.725324 | 0.362662 | − | 0.931921i | \(-0.381868\pi\) | ||||
0.362662 | + | 0.931921i | \(0.381868\pi\) | |||||||
\(422\) | 8657.89 | 0.998719 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13401.5 | 1.53499 | ||||||||
\(425\) | −3223.92 | −0.367960 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12127.7 | −1.37447 | ||||||||
\(428\) | 18063.5 | 2.04003 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21731.8 | −2.43721 | ||||||||
\(431\) | −9499.09 | −1.06161 | −0.530806 | − | 0.847493i | \(-0.678111\pi\) | ||||
−0.530806 | + | 0.847493i | \(0.678111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5002.67 | 0.555226 | 0.277613 | − | 0.960693i | \(-0.410457\pi\) | ||||
0.277613 | + | 0.960693i | \(0.410457\pi\) | |||||||
\(434\) | 18079.1 | 1.99960 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3859.17 | −0.423900 | ||||||||
\(437\) | −17498.8 | −1.91551 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13664.9 | 1.48563 | 0.742816 | − | 0.669496i | \(-0.233490\pi\) | ||||
0.742816 | + | 0.669496i | \(0.233490\pi\) | |||||||
\(440\) | −3395.52 | −0.367898 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10780.6 | 1.15621 | 0.578105 | − | 0.815962i | \(-0.303792\pi\) | ||||
0.578105 | + | 0.815962i | \(0.303792\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17162.5 | −1.82827 | ||||||||
\(446\) | −17146.8 | −1.82046 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −50937.6 | −5.37182 | ||||||||
\(449\) | 11959.1 | 1.25699 | 0.628493 | − | 0.777815i | \(-0.283672\pi\) | ||||
0.628493 | + | 0.777815i | \(0.283672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −462.165 | −0.0482539 | ||||||||
\(452\) | 4419.07 | 0.459858 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16502.0 | −1.70590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2120.66 | 0.217069 | 0.108534 | − | 0.994093i | \(-0.465384\pi\) | ||||
0.108534 | + | 0.994093i | \(0.465384\pi\) | |||||||
\(458\) | −12869.2 | −1.31297 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −63544.2 | −6.44079 | ||||||||
\(461\) | 15462.9 | 1.56221 | 0.781103 | − | 0.624402i | \(-0.214657\pi\) | ||||
0.781103 | + | 0.624402i | \(0.214657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10395.4 | 1.04344 | 0.521722 | − | 0.853116i | \(-0.325290\pi\) | ||||
0.521722 | + | 0.853116i | \(0.325290\pi\) | |||||||
\(464\) | 7730.44 | 0.773441 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32460.8 | −3.22687 | ||||||||
\(467\) | 11845.8 | 1.17379 | 0.586893 | − | 0.809664i | \(-0.300351\pi\) | ||||
0.586893 | + | 0.809664i | \(0.300351\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12217.2 | 1.20286 | ||||||||
\(470\) | 17474.0 | 1.71493 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3197.47 | 0.311812 | ||||||||
\(473\) | 873.356 | 0.0848984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6302.62 | 0.608808 | ||||||||
\(476\) | 23582.9 | 2.27084 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1374.73 | −0.131546 | ||||||||
\(479\) | 12879.9 | 1.22860 | 0.614299 | − | 0.789074i | \(-0.289439\pi\) | ||||
0.614299 | + | 0.789074i | \(0.289439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6106.46 | 0.577057 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −29244.2 | −2.74645 | ||||||||
\(485\) | 12392.1 | 1.16019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4946.81 | 0.460290 | 0.230145 | − | 0.973156i | \(-0.426080\pi\) | ||||
0.230145 | + | 0.973156i | \(0.426080\pi\) | |||||||
\(488\) | −38773.4 | −3.59670 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19002.4 | −1.75192 | ||||||||
\(491\) | −14390.3 | −1.32266 | −0.661330 | − | 0.750095i | \(-0.730008\pi\) | ||||
−0.661330 | + | 0.750095i | \(0.730008\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1364.59 | −0.124661 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33767.7 | 3.05689 | ||||||||
\(497\) | −22964.8 | −2.07266 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1427.01 | 0.128019 | 0.0640096 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640096 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(500\) | −16082.1 | −1.43842 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19191.6 | −1.70630 | ||||||||
\(503\) | 18033.6 | 1.59857 | 0.799283 | − | 0.600955i | \(-0.205213\pi\) | ||||
0.799283 | + | 0.600955i | \(0.205213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3600.76 | 0.317290 | ||||||||
\(506\) | 3476.78 | 0.305458 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9026.39 | 0.788349 | ||||||||
\(509\) | 7512.52 | 0.654198 | 0.327099 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327099 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27078.4 | −2.34418 | ||||||||
\(512\) | −30945.6 | −2.67112 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25493.3 | −2.18767 | ||||||||
\(515\) | 2484.33 | 0.212568 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −702.244 | −0.0597382 | ||||||||
\(518\) | −38656.7 | −3.27892 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21355.8 | −1.79580 | −0.897901 | − | 0.440198i | \(-0.854908\pi\) | ||||
−0.897901 | + | 0.440198i | \(0.854908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3086.57 | 0.258062 | 0.129031 | − | 0.991641i | \(-0.458813\pi\) | ||||
0.129031 | + | 0.991641i | \(0.458813\pi\) | |||||||
\(524\) | 48192.9 | 4.01778 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27064.4 | 2.24347 | ||||||||
\(527\) | −5960.73 | −0.492701 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29379.2 | 2.41466 | ||||||||
\(530\) | 13357.7 | 1.09476 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −46103.6 | −3.75722 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11496.4 | 0.929036 | ||||||||
\(536\) | 39059.7 | 3.14762 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7006.74 | 0.561491 | ||||||||
\(539\) | 763.667 | 0.0610269 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2029.46 | 0.161282 | 0.0806408 | − | 0.996743i | \(-0.474303\pi\) | ||||
0.0806408 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(542\) | −13832.5 | −1.09623 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32715.9 | 2.57846 | ||||||||
\(545\) | −2456.16 | −0.193046 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22144.8 | 1.73098 | 0.865488 | − | 0.500929i | \(-0.167008\pi\) | ||||
0.865488 | + | 0.500929i | \(0.167008\pi\) | |||||||
\(548\) | 16018.1 | 1.24865 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1252.25 | −0.0970837 | ||||||||
\(551\) | 2667.71 | 0.206258 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16373.6 | −1.25909 | ||||||||
\(554\) | 13514.6 | 1.03643 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −33659.7 | −2.56742 | ||||||||
\(557\) | 23136.5 | 1.76001 | 0.880004 | − | 0.474967i | \(-0.157540\pi\) | ||||
0.880004 | + | 0.474967i | \(0.157540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −85028.1 | −6.41623 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27765.2 | 2.08400 | ||||||||
\(563\) | 3978.29 | 0.297806 | 0.148903 | − | 0.988852i | \(-0.452426\pi\) | ||||
0.148903 | + | 0.988852i | \(0.452426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2812.51 | 0.209421 | ||||||||
\(566\) | −16899.0 | −1.25498 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −73420.6 | −5.42370 | ||||||||
\(569\) | 25871.5 | 1.90613 | 0.953065 | − | 0.302764i | \(-0.0979095\pi\) | ||||
0.953065 | + | 0.302764i | \(0.0979095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7241.31 | −0.530717 | −0.265358 | − | 0.964150i | \(-0.585490\pi\) | ||||
−0.265358 | + | 0.964150i | \(0.585490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19810.0 | −1.44051 | ||||||||
\(575\) | −14963.9 | −1.08528 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11537.4 | −0.832426 | −0.416213 | − | 0.909267i | \(-0.636643\pi\) | ||||
−0.416213 | + | 0.909267i | \(0.636643\pi\) | |||||||
\(578\) | 16383.0 | 1.17897 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9687.38 | 0.693529 | ||||||||
\(581\) | −1442.54 | −0.103007 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −536.817 | −0.0381350 | ||||||||
\(584\) | −86572.2 | −6.13422 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 47352.2 | 3.33806 | ||||||||
\(587\) | 16195.2 | 1.13875 | 0.569376 | − | 0.822078i | \(-0.307185\pi\) | ||||
0.569376 | + | 0.822078i | \(0.307185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11653.0 | 0.815198 | ||||||||
\(590\) | 3187.01 | 0.222385 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −72202.0 | −5.01264 | ||||||||
\(593\) | −14885.6 | −1.03083 | −0.515413 | − | 0.856942i | \(-0.672362\pi\) | ||||
−0.515413 | + | 0.856942i | \(0.672362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15009.3 | 1.03415 | ||||||||
\(596\) | −44873.3 | −3.08403 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21516.2 | 1.46766 | 0.733829 | − | 0.679334i | \(-0.237731\pi\) | ||||
0.733829 | + | 0.679334i | \(0.237731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −675.727 | −0.0458627 | −0.0229313 | − | 0.999737i | \(-0.507300\pi\) | ||||
−0.0229313 | + | 0.999737i | \(0.507300\pi\) | |||||||
\(602\) | 37435.1 | 2.53445 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 263.266 | 0.0177354 | ||||||||
\(605\) | −18612.4 | −1.25075 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12166.0 | −0.813512 | −0.406756 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406756 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(608\) | −63958.1 | −4.26619 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −38646.6 | −2.56517 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22799.0 | 1.50219 | 0.751095 | − | 0.660194i | \(-0.229526\pi\) | ||||
0.751095 | + | 0.660194i | \(0.229526\pi\) | |||||||
\(614\) | 2994.90 | 0.196847 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5849.10 | 0.382576 | ||||||||
\(617\) | −1635.30 | −0.106701 | −0.0533506 | − | 0.998576i | \(-0.516990\pi\) | ||||
−0.0533506 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4435.20 | 0.287990 | 0.143995 | − | 0.989578i | \(-0.454005\pi\) | ||||
0.143995 | + | 0.989578i | \(0.454005\pi\) | |||||||
\(620\) | 42315.9 | 2.74105 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16600.9 | −1.07016 | ||||||||
\(623\) | 29564.0 | 1.90122 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19412.1 | −1.24238 | ||||||||
\(626\) | 55345.1 | 3.53360 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30301.2 | 1.92540 | ||||||||
\(629\) | 12745.2 | 0.807924 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17645.7 | 1.11325 | 0.556626 | − | 0.830763i | \(-0.312096\pi\) | ||||
0.556626 | + | 0.830763i | \(0.312096\pi\) | |||||||
\(632\) | −52348.1 | −3.29477 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −46651.6 | −2.92235 | ||||||||
\(635\) | 5744.82 | 0.359018 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −530.039 | −0.0328910 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −78368.1 | −4.84027 | ||||||||
\(641\) | −1482.41 | −0.0913440 | −0.0456720 | − | 0.998956i | \(-0.514543\pi\) | ||||
−0.0456720 | + | 0.998956i | \(0.514543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9629.03 | −0.590563 | −0.295281 | − | 0.955410i | \(-0.595413\pi\) | ||||
−0.295281 | + | 0.955410i | \(0.595413\pi\) | |||||||
\(644\) | 109461. | 6.69775 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20694.9 | 1.26042 | ||||||||
\(647\) | −15991.6 | −0.971709 | −0.485854 | − | 0.874040i | \(-0.661491\pi\) | ||||
−0.485854 | + | 0.874040i | \(0.661491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −128.079 | −0.00774660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −36530.0 | −2.19421 | ||||||||
\(653\) | −20321.2 | −1.21781 | −0.608907 | − | 0.793242i | \(-0.708392\pi\) | ||||
−0.608907 | + | 0.793242i | \(0.708392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30672.2 | 1.82971 | ||||||||
\(656\) | −37000.5 | −2.20218 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30100.6 | −1.78335 | ||||||||
\(659\) | 21597.1 | 1.27664 | 0.638318 | − | 0.769773i | \(-0.279631\pi\) | ||||
0.638318 | + | 0.769773i | \(0.279631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −513.172 | −0.0301968 | −0.0150984 | − | 0.999886i | \(-0.504806\pi\) | ||||
−0.0150984 | + | 0.999886i | \(0.504806\pi\) | |||||||
\(662\) | 54727.8 | 3.21307 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4611.95 | −0.269546 | ||||||||
\(665\) | −29342.5 | −1.71106 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6333.76 | −0.367683 | ||||||||
\(668\) | 19314.4 | 1.11871 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38932.0 | 2.24488 | ||||||||
\(671\) | 1553.12 | 0.0893557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11983.8 | 0.686389 | 0.343195 | − | 0.939264i | \(-0.388491\pi\) | ||||
0.343195 | + | 0.939264i | \(0.388491\pi\) | |||||||
\(674\) | 17741.1 | 1.01389 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21876.5 | 1.24192 | 0.620960 | − | 0.783842i | \(-0.286743\pi\) | ||||
0.620960 | + | 0.783842i | \(0.286743\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21346.4 | −1.20648 | ||||||||
\(680\) | 47986.1 | 2.70615 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2315.29 | −0.129996 | ||||||||
\(683\) | 2551.17 | 0.142925 | 0.0714625 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714625 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10194.7 | 0.568642 | ||||||||
\(686\) | −12952.0 | −0.720860 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 69920.2 | 3.87454 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15321.2 | 0.843481 | 0.421741 | − | 0.906717i | \(-0.361419\pi\) | ||||
0.421741 | + | 0.906717i | \(0.361419\pi\) | |||||||
\(692\) | −16220.2 | −0.891041 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32879.4 | −1.79839 | ||||||||
\(695\) | −21422.6 | −1.16922 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6531.39 | 0.354941 | ||||||||
\(698\) | −54755.0 | −2.96921 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −39424.9 | −2.12875 | ||||||||
\(701\) | −558.289 | −0.0300803 | −0.0150401 | − | 0.999887i | \(-0.504788\pi\) | ||||
−0.0150401 | + | 0.999887i | \(0.504788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24916.3 | −1.33675 | ||||||||
\(704\) | 6523.29 | 0.349227 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 59470.6 | 3.17026 | ||||||||
\(707\) | −6202.64 | −0.329949 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7058.31 | 0.373879 | 0.186940 | − | 0.982371i | \(-0.440143\pi\) | ||||
0.186940 | + | 0.982371i | \(0.440143\pi\) | |||||||
\(710\) | −73180.5 | −3.86819 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 94519.0 | 4.97507 | ||||||||
\(713\) | −27666.8 | −1.45320 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33880.1 | 1.76838 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23690.4 | 1.23136 | ||||||||
\(719\) | 14673.0 | 0.761073 | 0.380536 | − | 0.924766i | \(-0.375739\pi\) | ||||
0.380536 | + | 0.924766i | \(0.375739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4279.48 | −0.221049 | ||||||||
\(722\) | −2806.58 | −0.144668 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26519.0 | −1.36128 | ||||||||
\(725\) | 2281.26 | 0.116861 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35867.8 | 1.82980 | 0.914899 | − | 0.403684i | \(-0.132270\pi\) | ||||
0.914899 | + | 0.403684i | \(0.132270\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −86289.1 | −4.37493 | ||||||||
\(731\) | −12342.4 | −0.624488 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27817.7 | −1.40173 | −0.700865 | − | 0.713294i | \(-0.747203\pi\) | ||||
−0.700865 | + | 0.713294i | \(0.747203\pi\) | |||||||
\(734\) | −57666.5 | −2.89988 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 151851. | 7.60505 | ||||||||
\(737\) | −1564.59 | −0.0781988 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7162.20 | 0.356517 | 0.178258 | − | 0.983984i | \(-0.442954\pi\) | ||||
0.178258 | + | 0.983984i | \(0.442954\pi\) | |||||||
\(740\) | −90479.8 | −4.49473 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23009.9 | −1.13843 | ||||||||
\(743\) | 12529.8 | 0.618671 | 0.309336 | − | 0.950953i | \(-0.399893\pi\) | ||||
0.309336 | + | 0.950953i | \(0.399893\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28559.5 | −1.40448 | ||||||||
\(746\) | −32219.0 | −1.58126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3020.13 | −0.147629 | ||||||||
\(749\) | −19803.7 | −0.966102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8282.62 | 0.402446 | 0.201223 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201223 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(752\) | −56221.1 | −2.72629 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 167.555 | 0.00807676 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22044.3 | −1.05840 | −0.529202 | − | 0.848496i | \(-0.677509\pi\) | ||||
−0.529202 | + | 0.848496i | \(0.677509\pi\) | |||||||
\(758\) | −35821.7 | −1.71649 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −93810.7 | −4.47746 | ||||||||
\(761\) | 5710.64 | 0.272025 | 0.136012 | − | 0.990707i | \(-0.456571\pi\) | ||||
0.136012 | + | 0.990707i | \(0.456571\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4230.95 | 0.200748 | ||||||||
\(764\) | −54565.5 | −2.58391 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38659.1 | −1.82351 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16851.6 | −0.790228 | −0.395114 | − | 0.918632i | \(-0.629295\pi\) | ||||
−0.395114 | + | 0.918632i | \(0.629295\pi\) | |||||||
\(770\) | 5829.97 | 0.272854 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 101554. | 4.73447 | ||||||||
\(773\) | 593.103 | 0.0275970 | 0.0137985 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137985 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9964.89 | 0.461870 | ||||||||
\(776\) | −68246.6 | −3.15710 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56755.8 | 2.61542 | ||||||||
\(779\) | −12768.6 | −0.587268 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2940.97 | 0.134745 | ||||||||
\(782\) | −49134.4 | −2.24686 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 61138.6 | 2.78510 | ||||||||
\(785\) | 19285.1 | 0.876834 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18564.0 | −0.840834 | −0.420417 | − | 0.907331i | \(-0.638116\pi\) | ||||
−0.420417 | + | 0.907331i | \(0.638116\pi\) | |||||||
\(788\) | 85492.6 | 3.86491 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −52176.9 | −2.34984 | ||||||||
\(791\) | −4844.80 | −0.217777 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −40982.2 | −1.83174 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31750.7 | 1.41378 | ||||||||
\(797\) | −5227.16 | −0.232316 | −0.116158 | − | 0.993231i | \(-0.537058\pi\) | ||||
−0.116158 | + | 0.993231i | \(0.537058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9924.23 | 0.439417 | ||||||||
\(800\) | −54693.0 | −2.41711 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17699.5 | −0.779289 | ||||||||
\(803\) | 3467.77 | 0.152397 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69665.9 | 3.05019 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19830.4 | −0.863406 | ||||||||
\(809\) | 8907.33 | 0.387101 | 0.193551 | − | 0.981090i | \(-0.438000\pi\) | ||||
0.193551 | + | 0.981090i | \(0.438000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15352.3 | 0.664725 | 0.332363 | − | 0.943152i | \(-0.392154\pi\) | ||||
0.332363 | + | 0.943152i | \(0.392154\pi\) | |||||||
\(812\) | −16687.4 | −0.721198 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4950.54 | 0.213165 | ||||||||
\(815\) | −23249.4 | −0.999253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24128.9 | 1.03325 | ||||||||
\(818\) | 68022.7 | 2.90753 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46367.2 | −1.97465 | ||||||||
\(821\) | −12869.6 | −0.547080 | −0.273540 | − | 0.961861i | \(-0.588195\pi\) | ||||
−0.273540 | + | 0.961861i | \(0.588195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −402.065 | −0.0170293 | −0.00851464 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851464 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(824\) | −13681.9 | −0.578437 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5489.91 | −0.231257 | ||||||||
\(827\) | 42772.7 | 1.79849 | 0.899245 | − | 0.437446i | \(-0.144117\pi\) | ||||
0.899245 | + | 0.437446i | \(0.144117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22933.5 | −0.960814 | −0.480407 | − | 0.877046i | \(-0.659511\pi\) | ||||
−0.480407 | + | 0.877046i | \(0.659511\pi\) | |||||||
\(830\) | −4596.87 | −0.192240 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10792.3 | −0.448896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12292.6 | 0.509465 | ||||||||
\(836\) | 5904.22 | 0.244260 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 73909.8 | 3.04674 | ||||||||
\(839\) | 42510.1 | 1.74924 | 0.874619 | − | 0.484811i | \(-0.161112\pi\) | ||||
0.874619 | + | 0.484811i | \(0.161112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23423.4 | −0.960409 | ||||||||
\(842\) | −34393.0 | −1.40767 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34907.7 | −1.42366 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32061.5 | 1.30065 | ||||||||
\(848\) | −42977.2 | −1.74038 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17697.0 | 0.714119 | ||||||||
\(851\) | 59157.1 | 2.38294 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40464.6 | −1.62425 | −0.812123 | − | 0.583487i | \(-0.801688\pi\) | ||||
−0.812123 | + | 0.583487i | \(0.801688\pi\) | |||||||
\(854\) | 66572.3 | 2.66751 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −63314.2 | −2.52808 | ||||||||
\(857\) | −38964.3 | −1.55308 | −0.776542 | − | 0.630065i | \(-0.783028\pi\) | ||||
−0.776542 | + | 0.630065i | \(0.783028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6379.47 | −0.253393 | −0.126697 | − | 0.991942i | \(-0.540437\pi\) | ||||
−0.126697 | + | 0.991942i | \(0.540437\pi\) | |||||||
\(860\) | 87620.4 | 3.47422 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 52143.1 | 2.06033 | ||||||||
\(863\) | −33744.0 | −1.33101 | −0.665504 | − | 0.746395i | \(-0.731783\pi\) | ||||
−0.665504 | + | 0.746395i | \(0.731783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10323.3 | −0.405784 | ||||||||
\(866\) | −27461.0 | −1.07756 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −72893.1 | −2.85041 | ||||||||
\(869\) | 2096.88 | 0.0818547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 13526.8 | 0.525314 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 96055.6 | 3.71754 | ||||||||
\(875\) | 17631.4 | 0.681200 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42898.6 | −1.65175 | −0.825874 | − | 0.563854i | \(-0.809318\pi\) | ||||
−0.825874 | + | 0.563854i | \(0.809318\pi\) | |||||||
\(878\) | −75010.7 | −2.88324 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10889.1 | 0.417125 | ||||||||
\(881\) | −1750.90 | −0.0669572 | −0.0334786 | − | 0.999439i | \(-0.510659\pi\) | ||||
−0.0334786 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33196.7 | 1.26518 | 0.632591 | − | 0.774486i | \(-0.281991\pi\) | ||||
0.632591 | + | 0.774486i | \(0.281991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −59177.6 | −2.24392 | ||||||||
\(887\) | 29998.9 | 1.13559 | 0.567794 | − | 0.823171i | \(-0.307797\pi\) | ||||
0.567794 | + | 0.823171i | \(0.307797\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9895.98 | −0.373341 | ||||||||
\(890\) | 94209.8 | 3.54823 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 69133.9 | 2.59504 | ||||||||
\(893\) | −19401.4 | −0.727037 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21562.9 | 0.805328 | ||||||||
\(896\) | 134996. | 5.03338 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −65647.0 | −2.43950 | ||||||||
\(899\) | 4217.84 | 0.156477 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7586.39 | 0.280510 | ||||||||
\(902\) | 2536.95 | 0.0936488 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15489.3 | −0.569874 | ||||||||
\(905\) | −16877.9 | −0.619935 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24629.3 | 0.901657 | 0.450829 | − | 0.892611i | \(-0.351129\pi\) | ||||
0.450829 | + | 0.892611i | \(0.351129\pi\) | |||||||
\(908\) | 66534.2 | 2.43173 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7338.72 | −0.266896 | −0.133448 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133448 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 184.738 | 0.00669654 | ||||||||
\(914\) | −11640.9 | −0.421277 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 51887.4 | 1.87162 | ||||||||
\(917\) | −52835.7 | −1.90271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1449.13 | −0.0520155 | −0.0260078 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260078 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(920\) | 222728. | 7.98167 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −84879.9 | −3.03186 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21306.9 | −0.757369 | ||||||||
\(926\) | −57063.2 | −2.02507 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23149.9 | −0.818894 | ||||||||
\(929\) | −6478.07 | −0.228782 | −0.114391 | − | 0.993436i | \(-0.536492\pi\) | ||||
−0.114391 | + | 0.993436i | \(0.536492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21098.4 | 0.742720 | ||||||||
\(932\) | 130879. | 4.59986 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −65024.9 | −2.27803 | ||||||||
\(935\) | −1922.15 | −0.0672311 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4679.24 | 0.163142 | 0.0815710 | − | 0.996668i | \(-0.474006\pi\) | ||||
0.0815710 | + | 0.996668i | \(0.474006\pi\) | |||||||
\(938\) | −67063.9 | −2.33445 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −70453.4 | −2.44461 | ||||||||
\(941\) | 47081.7 | 1.63105 | 0.815525 | − | 0.578722i | \(-0.196448\pi\) | ||||
0.815525 | + | 0.578722i | \(0.196448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30315.6 | 1.04688 | ||||||||
\(944\) | −10253.9 | −0.353534 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4794.09 | −0.164767 | ||||||||
\(947\) | 4264.62 | 0.146338 | 0.0731688 | − | 0.997320i | \(-0.476689\pi\) | ||||
0.0731688 | + | 0.997320i | \(0.476689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −34596.8 | −1.18155 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −82660.4 | −2.81412 | ||||||||
\(953\) | −24368.1 | −0.828292 | −0.414146 | − | 0.910211i | \(-0.635920\pi\) | ||||
−0.414146 | + | 0.910211i | \(0.635920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34728.0 | −1.17673 | ||||||||
\(956\) | 5542.77 | 0.187517 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −70701.4 | −2.38440 | ||||||||
\(959\) | −17561.3 | −0.591329 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11366.8 | −0.381552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24620.6 | −0.822588 | ||||||||
\(965\) | 64633.7 | 2.15610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11355.1 | −0.377616 | −0.188808 | − | 0.982014i | \(-0.560462\pi\) | ||||
−0.188808 | + | 0.982014i | \(0.560462\pi\) | |||||||
\(968\) | 102504. | 3.40351 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −68023.4 | −2.25165 | ||||||||
\(971\) | −3024.06 | −0.0999451 | −0.0499726 | − | 0.998751i | \(-0.515913\pi\) | ||||
−0.0499726 | + | 0.998751i | \(0.515913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36902.4 | 1.21586 | ||||||||
\(974\) | −27154.4 | −0.893309 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 124342. | 4.07796 | ||||||||
\(977\) | 41218.9 | 1.34975 | 0.674877 | − | 0.737930i | \(-0.264197\pi\) | ||||
0.674877 | + | 0.737930i | \(0.264197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3786.09 | −0.123600 | ||||||||
\(980\) | 76615.7 | 2.49735 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 78992.4 | 2.56695 | ||||||||
\(983\) | −21579.3 | −0.700177 | −0.350088 | − | 0.936717i | \(-0.613848\pi\) | ||||
−0.350088 | + | 0.936717i | \(0.613848\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54411.5 | 1.76010 | ||||||||
\(986\) | 7490.60 | 0.241936 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57287.6 | −1.84190 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34613.5 | −1.10952 | −0.554760 | − | 0.832010i | \(-0.687190\pi\) | ||||
−0.554760 | + | 0.832010i | \(0.687190\pi\) | |||||||
\(992\) | −101122. | −3.23653 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 126060. | 4.02252 | ||||||||
\(995\) | 20207.6 | 0.643843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20841.5 | 0.662043 | 0.331021 | − | 0.943623i | \(-0.392607\pi\) | ||||
0.331021 | + | 0.943623i | \(0.392607\pi\) | |||||||
\(998\) | −7833.24 | −0.248454 | ||||||||
\(999\) | 0 | 0 |
(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 | 1521.4.a.ba.1.1 | 4 | ||
3.2 | odd | 2 | inner | 1521.4.a.ba.1.4 | 4 | ||
13.12 | even | 2 | 117.4.a.g.1.4 | yes | 4 | ||
39.38 | odd | 2 | 117.4.a.g.1.1 | ✓ | 4 | ||
52.51 | odd | 2 | 1872.4.a.bo.1.2 | 4 | |||
156.155 | even | 2 | 1872.4.a.bo.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.a.g.1.1 | ✓ | 4 | 39.38 | odd | 2 | ||
117.4.a.g.1.4 | yes | 4 | 13.12 | even | 2 | ||
1521.4.a.ba.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1521.4.a.ba.1.4 | 4 | 3.2 | odd | 2 | inner | ||
1872.4.a.bo.1.2 | 4 | 52.51 | odd | 2 | |||
1872.4.a.bo.1.3 | 4 | 156.155 | even | 2 |