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 | 1.4 | ||
Root | \(6.81072\) 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 | \(-0.0776716\pi\) | ||||
0.970376 | + | 0.241598i | \(0.0776716\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.1322 | 2.76652 | ||||||||
\(5\) | −14.0859 | −1.25989 | −0.629943 | − | 0.776642i | \(-0.716922\pi\) | ||||
−0.629943 | + | 0.776642i | \(0.716922\pi\) | |||||||
\(6\) | 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 | \(-0.513560\pi\) | ||||
−0.0425870 | + | 0.999093i | \(0.513560\pi\) | |||||||
\(12\) | 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 | \(-0.398580\pi\) | ||||
0.313258 | + | 0.949668i | \(0.398580\pi\) | |||||||
\(18\) | 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 | \(-0.124950\pi\) | ||||
0.923940 | + | 0.382537i | \(0.124950\pi\) | |||||||
\(24\) | 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 | \(-0.531720\pi\) | ||||
−0.0994877 | + | 0.995039i | \(0.531720\pi\) | |||||||
\(30\) | 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 | \(-0.408582\pi\) | ||||
0.283266 | + | 0.959041i | \(0.408582\pi\) | |||||||
\(42\) | 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 | \(-0.385949\pi\) | ||||
0.350683 | + | 0.936494i | \(0.385949\pi\) | |||||||
\(48\) | 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 | \(-0.428132\pi\) | ||||
0.223865 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(54\) | 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 | \(-0.485520\pi\) | ||||
0.0454751 | + | 0.998965i | \(0.485520\pi\) | |||||||
\(60\) | 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 | \(-0.790439\pi\) | ||||
−0.791000 | + | 0.611816i | \(0.790439\pi\) | |||||||
\(72\) | 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 | \(-0.512516\pi\) | ||||
−0.0393109 | + | 0.999227i | \(0.512516\pi\) | |||||||
\(84\) | 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 | \(-0.241576\pi\) | ||||
0.725571 | + | 0.688147i | \(0.241576\pi\) | |||||||
\(90\) | 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 | \(-0.540188\pi\) | ||||
−0.125920 | + | 0.992040i | \(0.540188\pi\) | |||||||
\(102\) | 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 | \(-0.620197\pi\) | ||||
−0.368699 | + | 0.929549i | \(0.620197\pi\) | |||||||
\(108\) | 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 | \(-0.526486\pi\) | ||||
−0.0831112 | + | 0.996540i | \(0.526486\pi\) | |||||||
\(114\) | 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 | \(-0.758689\pi\) | ||||
−0.726143 | + | 0.687544i | \(0.758689\pi\) | |||||||
\(132\) | 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 | \(-0.572458\pi\) | ||||
−0.225672 | + | 0.974203i | \(0.572458\pi\) | |||||||
\(138\) | 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 | \(-0.311805\pi\) | ||||
0.557384 | + | 0.830255i | \(0.311805\pi\) | |||||||
\(150\) | 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 | \(-0.564805\pi\) | ||||
−0.202187 | + | 0.979347i | \(0.564805\pi\) | |||||||
\(168\) | 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 | \(-0.448515\pi\) | ||||
0.161040 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(174\) | 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 | \(-0.603550\pi\) | ||||
−0.319604 | + | 0.947551i | \(0.603550\pi\) | |||||||
\(180\) | 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 | \(-0.345336\pi\) | ||||
0.466997 | + | 0.884259i | \(0.345336\pi\) | |||||||
\(192\) | 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 | \(-0.746155\pi\) | ||||
−0.698514 | + | 0.715596i | \(0.746155\pi\) | |||||||
\(198\) | 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 | \(-0.644842\pi\) | ||||
−0.439493 | + | 0.898246i | \(0.644842\pi\) | |||||||
\(228\) | 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 | \(-0.812428\pi\) | ||||
−0.831344 | + | 0.555759i | \(0.812428\pi\) | |||||||
\(234\) | 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 | \(-0.510790\pi\) | ||||
−0.0338904 | + | 0.999426i | \(0.510790\pi\) | |||||||
\(240\) | 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 | \(-0.644879\pi\) | ||||
−0.439597 | + | 0.898195i | \(0.644879\pi\) | |||||||
\(252\) | 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 | \(-0.690589\pi\) | ||||
−0.563614 | + | 0.826039i | \(0.690589\pi\) | |||||||
\(258\) | 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 | \(-0.303838\pi\) | ||||
0.577989 | + | 0.816045i | \(0.303838\pi\) | |||||||
\(264\) | 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 | \(-0.453792\pi\) | ||||
0.144658 | + | 0.989482i | \(0.453792\pi\) | |||||||
\(270\) | 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 | \(-0.319594\pi\) | ||||
0.536904 | + | 0.843643i | \(0.319594\pi\) | |||||||
\(282\) | 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 | \(-0.170469\pi\) | ||||
0.859990 | + | 0.510310i | \(0.170469\pi\) | |||||||
\(294\) | 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 | \(-0.588912\pi\) | ||||
−0.275707 | + | 0.961242i | \(0.588912\pi\) | |||||||
\(312\) | 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 | \(-0.771341\pi\) | ||||
−0.752891 | + | 0.658145i | \(0.771341\pi\) | |||||||
\(318\) | 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 | \(-0.653343\pi\) | ||||
−0.463323 | + | 0.886189i | \(0.653343\pi\) | |||||||
\(348\) | 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 | \(-0.195767\pi\) | ||||
0.816761 | + | 0.576976i | \(0.195767\pi\) | |||||||
\(354\) | 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 | \(-0.397244\pi\) | ||||
0.317239 | + | 0.948346i | \(0.397244\pi\) | |||||||
\(360\) | 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 | \(-0.655672\pi\) | ||||
−0.469795 | + | 0.882775i | \(0.655672\pi\) | |||||||
\(384\) | 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 | \(-0.264655\pi\) | ||||
0.673815 | + | 0.738900i | \(0.264655\pi\) | |||||||
\(390\) | 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 | \(-0.564344\pi\) | ||||
−0.200770 | + | 0.979638i | \(0.564344\pi\) | |||||||
\(402\) | 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 | \(-0.212694\pi\) | ||||
0.784938 | + | 0.619574i | \(0.212694\pi\) | |||||||
\(420\) | 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 | \(-0.321889\pi\) | ||||
0.530806 | + | 0.847493i | \(0.321889\pi\) | |||||||
\(432\) | 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 | \(-0.696208\pi\) | ||||
−0.578105 | + | 0.815962i | \(0.696208\pi\) | |||||||
\(444\) | 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 | \(-0.716328\pi\) | ||||
−0.628493 | + | 0.777815i | \(0.716328\pi\) | |||||||
\(450\) | 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 | \(-0.785343\pi\) | ||||
−0.781103 | + | 0.624402i | \(0.785343\pi\) | |||||||
\(462\) | 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 | \(-0.699649\pi\) | ||||
−0.586893 | + | 0.809664i | \(0.699649\pi\) | |||||||
\(468\) | 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 | \(-0.710561\pi\) | ||||
−0.614299 | + | 0.789074i | \(0.710561\pi\) | |||||||
\(480\) | 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 | \(-0.269992\pi\) | ||||
0.661330 | + | 0.750095i | \(0.269992\pi\) | |||||||
\(492\) | 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 | \(-0.794787\pi\) | ||||
−0.799283 | + | 0.600955i | \(0.794787\pi\) | |||||||
\(504\) | 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 | \(-0.606071\pi\) | ||||
−0.327099 | + | 0.944990i | \(0.606071\pi\) | |||||||
\(510\) | 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 | \(-0.145092\pi\) | ||||
0.897901 | + | 0.440198i | \(0.145092\pi\) | |||||||
\(522\) | 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 | \(-0.842460\pi\) | ||||
−0.880004 | + | 0.474967i | \(0.842460\pi\) | |||||||
\(558\) | 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 | \(-0.547574\pi\) | ||||
−0.148903 | + | 0.988852i | \(0.547574\pi\) | |||||||
\(564\) | 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 | \(-0.902090\pi\) | ||||
−0.953065 | + | 0.302764i | \(0.902090\pi\) | |||||||
\(570\) | 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 | \(-0.692815\pi\) | ||||
−0.569376 | + | 0.822078i | \(0.692815\pi\) | |||||||
\(588\) | 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 | \(-0.327638\pi\) | ||||
0.515413 | + | 0.856942i | \(0.327638\pi\) | |||||||
\(594\) | 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 | \(-0.762269\pi\) | ||||
−0.733829 | + | 0.679334i | \(0.762269\pi\) | |||||||
\(600\) | 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 | \(-0.483010\pi\) | ||||
0.0533506 | + | 0.998576i | \(0.483010\pi\) | |||||||
\(618\) | 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 | \(-0.485457\pi\) | ||||
0.0456720 | + | 0.998956i | \(0.485457\pi\) | |||||||
\(642\) | 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 | \(-0.338509\pi\) | ||||
0.485854 | + | 0.874040i | \(0.338509\pi\) | |||||||
\(648\) | 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 | \(-0.291608\pi\) | ||||
0.608907 | + | 0.793242i | \(0.291608\pi\) | |||||||
\(654\) | 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 | \(-0.720369\pi\) | ||||
−0.638318 | + | 0.769773i | \(0.720369\pi\) | |||||||
\(660\) | 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 | \(-0.713257\pi\) | ||||
−0.620960 | + | 0.783842i | \(0.713257\pi\) | |||||||
\(678\) | 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 | \(-0.522767\pi\) | ||||
−0.0714625 | + | 0.997443i | \(0.522767\pi\) | |||||||
\(684\) | 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 | \(-0.495212\pi\) | ||||
0.0150401 | + | 0.999887i | \(0.495212\pi\) | |||||||
\(702\) | 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 | \(-0.624261\pi\) | ||||
−0.380536 | + | 0.924766i | \(0.624261\pi\) | |||||||
\(720\) | 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 | \(-0.600107\pi\) | ||||
−0.309336 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(744\) | 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 | \(-0.543429\pi\) | ||||
−0.136012 | + | 0.990707i | \(0.543429\pi\) | |||||||
\(762\) | 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 | \(-0.504392\pi\) | ||||
−0.0137985 | + | 0.999905i | \(0.504392\pi\) | |||||||
\(774\) | 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 | \(-0.462942\pi\) | ||||
0.116158 | + | 0.993231i | \(0.462942\pi\) | |||||||
\(798\) | 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 | \(-0.562000\pi\) | ||||
−0.193551 | + | 0.981090i | \(0.562000\pi\) | |||||||
\(810\) | 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 | \(-0.411805\pi\) | ||||
0.273540 | + | 0.961861i | \(0.411805\pi\) | |||||||
\(822\) | 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 | \(-0.855883\pi\) | ||||
−0.899245 | + | 0.437446i | \(0.855883\pi\) | |||||||
\(828\) | 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 | \(-0.838888\pi\) | ||||
−0.874619 | + | 0.484811i | \(0.838888\pi\) | |||||||
\(840\) | 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 | \(-0.216972\pi\) | ||||
0.776542 | + | 0.630065i | \(0.216972\pi\) | |||||||
\(858\) | 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 | \(-0.268217\pi\) | ||||
0.665504 | + | 0.746395i | \(0.268217\pi\) | |||||||
\(864\) | 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 | \(-0.489341\pi\) | ||||
0.0334786 | + | 0.999439i | \(0.489341\pi\) | |||||||
\(882\) | 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 | \(-0.692203\pi\) | ||||
−0.567794 | + | 0.823171i | \(0.692203\pi\) | |||||||
\(888\) | 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 | \(-0.457395\pi\) | ||||
0.133448 | + | 0.991056i | \(0.457395\pi\) | |||||||
\(912\) | 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 | \(-0.463508\pi\) | ||||
0.114391 | + | 0.993436i | \(0.463508\pi\) | |||||||
\(930\) | 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 | \(-0.803552\pi\) | ||||
−0.815525 | + | 0.578722i | \(0.803552\pi\) | |||||||
\(942\) | 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 | \(-0.523311\pi\) | ||||
−0.0731688 | + | 0.997320i | \(0.523311\pi\) | |||||||
\(948\) | 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 | \(-0.364080\pi\) | ||||
0.414146 | + | 0.910211i | \(0.364080\pi\) | |||||||
\(954\) | 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 | \(-0.484087\pi\) | ||||
0.0499726 | + | 0.998751i | \(0.484087\pi\) | |||||||
\(972\) | 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 | \(-0.735803\pi\) | ||||
−0.674877 | + | 0.737930i | \(0.735803\pi\) | |||||||
\(978\) | 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 | \(-0.386152\pi\) | ||||
0.350088 | + | 0.936717i | \(0.386152\pi\) | |||||||
\(984\) | 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.1.4 | 4 | ||
3.2 | odd | 2 | inner | 1521.4.a.ba.1.1 | 4 | ||
13.12 | even | 2 | 117.4.a.g.1.1 | ✓ | 4 | ||
39.38 | odd | 2 | 117.4.a.g.1.4 | yes | 4 | ||
52.51 | odd | 2 | 1872.4.a.bo.1.3 | 4 | |||
156.155 | even | 2 | 1872.4.a.bo.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.a.g.1.1 | ✓ | 4 | 13.12 | even | 2 | ||
117.4.a.g.1.4 | yes | 4 | 39.38 | odd | 2 | ||
1521.4.a.ba.1.1 | 4 | 3.2 | odd | 2 | inner | ||
1521.4.a.ba.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1872.4.a.bo.1.2 | 4 | 156.155 | even | 2 | |||
1872.4.a.bo.1.3 | 4 | 52.51 | odd | 2 |