Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.2 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.f.783.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.64575 | −0.509175 | −0.254588 | − | 0.967050i | \(-0.581940\pi\) | ||||
−0.254588 | + | 0.967050i | \(0.581940\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.66025i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.0000 | −0.740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 68.7386i | 1.88413i | 0.335424 | + | 0.942067i | \(0.391120\pi\) | ||||
−0.335424 | + | 0.942067i | \(0.608880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.9615i | 1.10858i | 0.832324 | + | 0.554290i | \(0.187010\pi\) | ||||
−0.832324 | + | 0.554290i | \(0.812990\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 22.9129i | − 0.394405i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 8.66025i | − 0.123554i | −0.998090 | − | 0.0617771i | \(-0.980323\pi\) | ||||
0.998090 | − | 0.0617771i | \(-0.0196768\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −66.1438 | −0.798654 | −0.399327 | − | 0.916809i | \(-0.630756\pi\) | ||||
−0.399327 | + | 0.916809i | \(0.630756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 50.4083i | − 0.456994i | −0.973545 | − | 0.228497i | \(-0.926619\pi\) | ||||
0.973545 | − | 0.228497i | \(-0.0733811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.0000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 124.350 | 0.886342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −168.000 | −1.07575 | −0.537876 | − | 0.843024i | \(-0.680773\pi\) | ||||
−0.537876 | + | 0.843024i | \(0.680773\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 224.889 | 1.30294 | 0.651471 | − | 0.758673i | \(-0.274152\pi\) | ||||
0.651471 | + | 0.758673i | \(0.274152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 181.865i | − 0.959354i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −245.000 | −1.08859 | −0.544294 | − | 0.838895i | \(-0.683202\pi\) | ||||
−0.544294 | + | 0.838895i | \(0.683202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 137.477i | − 0.564461i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.0333i | 0.171537i | 0.996315 | + | 0.0857686i | \(0.0273346\pi\) | ||||
−0.996315 | + | 0.0857686i | \(0.972665\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 302.450i | 1.07263i | 0.844017 | + | 0.536316i | \(0.180185\pi\) | ||||
−0.844017 | + | 0.536316i | \(0.819815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 173.205i | − 0.573775i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 420.674 | 1.30557 | 0.652784 | − | 0.757544i | \(-0.273601\pi\) | ||||
0.652784 | + | 0.757544i | \(0.273601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.9129i | 0.0629107i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −345.000 | −0.894140 | −0.447070 | − | 0.894499i | \(-0.647532\pi\) | ||||
−0.447070 | + | 0.894499i | \(0.647532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −595.294 | −1.45944 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 175.000 | 0.406655 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −436.549 | −0.963285 | −0.481643 | − | 0.876368i | \(-0.659960\pi\) | ||||
−0.481643 | + | 0.876368i | \(0.659960\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 396.640i | − 0.832533i | −0.909243 | − | 0.416266i | \(-0.863338\pi\) | ||||
0.909243 | − | 0.416266i | \(-0.136662\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −450.000 | −0.858702 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 444.510i | 0.810530i | 0.914199 | + | 0.405265i | \(0.132821\pi\) | ||||
−0.914199 | + | 0.405265i | \(0.867179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 133.368i | 0.232690i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.8258i | 0.0765988i | 0.999266 | + | 0.0382994i | \(0.0121941\pi\) | ||||
−0.999266 | + | 0.0382994i | \(0.987806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 961.288i | − 1.54124i | −0.637297 | − | 0.770618i | \(-0.719948\pi\) | ||||
0.637297 | − | 0.770618i | \(-0.280052\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −132.288 | −0.203670 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 206.216i | 0.293685i | 0.989160 | + | 0.146842i | \(0.0469110\pi\) | ||||
−0.989160 | + | 0.146842i | \(0.953089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 211.000 | 0.289438 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 888.972 | 1.17563 | 0.587816 | − | 0.808995i | \(-0.299988\pi\) | ||||
0.587816 | + | 0.808995i | \(0.299988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 75.0000 | 0.0957046 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 444.486 | 0.547746 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1512.08i | − 1.80090i | −0.434958 | − | 0.900451i | \(-0.643237\pi\) | ||||
0.434958 | − | 0.900451i | \(-0.356763\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −595.000 | −0.663426 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 572.822i | − 0.618635i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 433.013i | 0.453255i | 0.973981 | + | 0.226628i | \(0.0727701\pi\) | ||||
−0.973981 | + | 0.226628i | \(0.927230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 1374.77i | − 1.39566i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 833.116i | − 0.820774i | −0.911911 | − | 0.410387i | \(-0.865394\pi\) | ||||
0.911911 | − | 0.410387i | \(-0.134606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1934.04 | −1.85017 | −0.925083 | − | 0.379766i | \(-0.876005\pi\) | ||||
−0.925083 | + | 0.379766i | \(0.876005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 792.786i | − 0.716275i | −0.933669 | − | 0.358138i | \(-0.883412\pi\) | ||||
0.933669 | − | 0.358138i | \(-0.116588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −763.000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 648.209 | 0.554282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1500.00 | −1.24874 | −0.624372 | − | 0.781127i | \(-0.714645\pi\) | ||||
−0.624372 | + | 0.781127i | \(0.714645\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 436.549 | 0.353986 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1039.23i | − 0.821170i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3394.00 | −2.54996 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 119.147i | − 0.0873424i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1515.54i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 45.8258i | − 0.0320187i | −0.999872 | − | 0.0160094i | \(-0.994904\pi\) | ||||
0.999872 | − | 0.0160094i | \(-0.00509616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 800.207i | − 0.546158i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2024.00 | 1.34991 | 0.674953 | − | 0.737861i | \(-0.264164\pi\) | ||||
0.674953 | + | 0.737861i | \(0.264164\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1076.91i | 0.686557i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −315.000 | −0.196440 | −0.0982199 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982199 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2275.35 | −1.38843 | −0.694217 | − | 0.719766i | \(-0.744249\pi\) | ||||
−0.694217 | + | 0.719766i | \(0.744249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1113.00 | −0.664762 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3571.76 | −2.08871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 1454.92i | − 0.833274i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1563.00 | −0.859369 | −0.429684 | − | 0.902979i | \(-0.641375\pi\) | ||||
−0.429684 | + | 0.902979i | \(0.641375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 297.867i | − 0.160531i | −0.996774 | − | 0.0802653i | \(-0.974423\pi\) | ||||
0.996774 | − | 0.0802653i | \(-0.0255767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 173.205i | 0.0915216i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1947.59i | 1.00926i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 718.801i | − 0.365392i | −0.983169 | − | 0.182696i | \(-0.941518\pi\) | ||||
0.983169 | − | 0.182696i | \(-0.0584824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 912.784 | 0.455274 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2130.90i | 1.02396i | 0.858999 | + | 0.511978i | \(0.171087\pi\) | ||||
−0.858999 | + | 0.511978i | \(0.828913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1575.00 | 0.743113 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −746.102 | −0.345719 | −0.172860 | − | 0.984946i | \(-0.555301\pi\) | ||||
−0.172860 | + | 0.984946i | \(0.555301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −503.000 | −0.228949 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1322.88 | 0.591595 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1082.53i | − 0.475742i | −0.971297 | − | 0.237871i | \(-0.923550\pi\) | ||||
0.971297 | − | 0.237871i | \(-0.0764495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1155.00 | 0.490481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1489.34i | − 0.621890i | −0.950428 | − | 0.310945i | \(-0.899355\pi\) | ||||
0.950428 | − | 0.310945i | \(-0.100645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2833.64i | 1.16366i | 0.813310 | + | 0.581830i | \(0.197663\pi\) | ||||
−0.813310 | + | 0.581830i | \(0.802337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1049.41i | 0.423905i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2121.76i | − 0.843217i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 595.294 | 0.232793 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 4880.44i | − 1.84888i | −0.381325 | − | 0.924441i | \(-0.624532\pi\) | ||||
0.381325 | − | 0.924441i | \(-0.375468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1955.00 | −0.729140 | −0.364570 | − | 0.931176i | \(-0.618784\pi\) | ||||
−0.364570 | + | 0.931176i | \(0.618784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1190.59 | 0.437230 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3180.00 | 1.15008 | 0.575040 | − | 0.818126i | \(-0.304987\pi\) | ||||
0.575040 | + | 0.818126i | \(0.304987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3346.88 | 1.19223 | 0.596115 | − | 0.802899i | \(-0.296710\pi\) | ||||
0.596115 | + | 0.802899i | \(0.296710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 1176.06i | − 0.412702i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −390.000 | −0.132872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1008.17i | 0.338514i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 4546.63i | − 1.50477i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3803.54i | − 1.24098i | −0.784215 | − | 0.620489i | \(-0.786934\pi\) | ||||
0.784215 | − | 0.620489i | \(-0.213066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 121.244i | − 0.0390022i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2619.29 | −0.830857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2543.33i | 0.784759i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 450.000 | 0.136970 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4942.26 | 1.48412 | 0.742059 | − | 0.670334i | \(-0.233849\pi\) | ||||
0.742059 | + | 0.670334i | \(0.233849\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1000.00 | −0.296296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2246.24 | 0.656777 | 0.328388 | − | 0.944543i | \(-0.393494\pi\) | ||||
0.328388 | + | 0.944543i | \(0.393494\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4858.40i | 1.40198i | 0.713174 | + | 0.700988i | \(0.247257\pi\) | ||||
−0.713174 | + | 0.700988i | \(0.752743\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1365.00 | 0.383795 | 0.191897 | − | 0.981415i | \(-0.438536\pi\) | ||||
0.191897 | + | 0.981415i | \(0.438536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3643.15i | 1.01129i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 545.596i | − 0.149537i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1283.12i | 0.347273i | 0.984810 | + | 0.173636i | \(0.0555518\pi\) | ||||
−0.984810 | + | 0.173636i | \(0.944448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5689.79i | 1.52079i | 0.649458 | + | 0.760397i | \(0.274996\pi\) | ||||
−0.649458 | + | 0.760397i | \(0.725004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3915.71 | −1.03372 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3436.93i | − 0.885371i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2352.00 | −0.598602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1190.59 | −0.299399 | −0.149700 | − | 0.988732i | \(-0.547831\pi\) | ||||
−0.149700 | + | 0.988732i | \(0.547831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3465.00 | 0.861038 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −198.431 | −0.0487304 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1203.78i | − 0.292177i | −0.989272 | − | 0.146088i | \(-0.953332\pi\) | ||||
0.989272 | − | 0.146088i | \(-0.0466684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3360.00 | 0.796854 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5961.93i | 1.39783i | 0.715206 | + | 0.698913i | \(0.246333\pi\) | ||||
−0.715206 | + | 0.698913i | \(0.753667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 2987.79i | − 0.692597i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4000.59i | 0.916974i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3815.71i | − 0.864862i | −0.901667 | − | 0.432431i | \(-0.857656\pi\) | ||||
0.901667 | − | 0.432431i | \(-0.142344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4828.50 | 1.08233 | 0.541163 | − | 0.840918i | \(-0.317984\pi\) | ||||
0.541163 | + | 0.840918i | \(0.317984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3436.93i | 0.753654i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2515.00 | 0.545530 | 0.272765 | − | 0.962081i | \(-0.412062\pi\) | ||||
0.272765 | + | 0.962081i | \(0.412062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4497.78 | −0.965143 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5208.00 | −1.10563 | −0.552817 | − | 0.833303i | \(-0.686447\pi\) | ||||
−0.552817 | + | 0.833303i | \(0.686447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7098.55 | −1.49104 | −0.745521 | − | 0.666482i | \(-0.767799\pi\) | ||||
−0.745521 | + | 0.666482i | \(0.767799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1515.54i | 0.314993i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4838.00 | 0.984734 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1145.64i | − 0.230786i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 311.769i | − 0.0621630i | −0.999517 | − | 0.0310815i | \(-0.990105\pi\) | ||||
0.999517 | − | 0.0310815i | \(-0.00989514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3780.62i | − 0.746158i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8547.67i | 1.66999i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2619.29 | 0.506614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2204.22i | 0.417918i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3435.00 | 0.644877 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −391.571 | −0.0727953 | −0.0363976 | − | 0.999337i | \(-0.511588\pi\) | ||||
−0.0363976 | + | 0.999337i | \(0.511588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5117.00 | 0.942058 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2420.86 | 0.441397 | 0.220699 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220699 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6192.08i | 1.11820i | 0.829100 | + | 0.559101i | \(0.188854\pi\) | ||||
−0.829100 | + | 0.559101i | \(0.811146\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5595.00 | 0.991314 | 0.495657 | − | 0.868518i | \(-0.334927\pi\) | ||||
0.495657 | + | 0.868518i | \(0.334927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 11548.1i | − 2.02686i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2097.51i | 0.364710i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 572.822i | 0.0986770i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2598.08i | 0.443432i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2018.71 | 0.341391 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7675.81i | − 1.27463i | −0.770605 | − | 0.637313i | \(-0.780046\pi\) | ||||
0.770605 | − | 0.637313i | \(-0.219954\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4900.00 | 0.806361 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3849.57 | −0.627834 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3220.00 | −0.520488 | −0.260244 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260244 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3968.63 | 0.635830 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15458.6i | 2.45492i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1155.00 | −0.180241 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6997.59i | − 1.08257i | −0.840840 | − | 0.541283i | \(-0.817939\pi\) | ||||
0.840840 | − | 0.541283i | \(-0.182061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4021.82i | 0.616857i | 0.951247 | + | 0.308429i | \(0.0998031\pi\) | ||||
−0.951247 | + | 0.308429i | \(0.900197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6461.43i | 0.982580i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6434.57i | 0.970191i | 0.874461 | + | 0.485096i | \(0.161215\pi\) | ||||
−0.874461 | + | 0.485096i | \(0.838785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −396.863 | −0.0593332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10883.6i | 1.60004i | 0.599971 | + | 0.800021i | \(0.295179\pi\) | ||||
−0.599971 | + | 0.800021i | \(0.704821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2484.00 | −0.362152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8979.68 | 1.29838 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8325.00 | 1.19384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3368.04 | −0.479047 | −0.239524 | − | 0.970891i | \(-0.576991\pi\) | ||||
−0.239524 | + | 0.970891i | \(0.576991\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 900.666i | − 0.127065i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4835.00 | 0.671171 | 0.335586 | − | 0.942010i | \(-0.391066\pi\) | ||||
0.335586 | + | 0.942010i | \(0.391066\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 4009.75i | − 0.552167i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 8729.54i | − 1.19256i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3941.02i | − 0.534133i | −0.963678 | − | 0.267066i | \(-0.913946\pi\) | ||||
0.963678 | − | 0.267066i | \(-0.0860543\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 121.244i | 0.0163031i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8469.05 | −1.12989 | −0.564945 | − | 0.825128i | \(-0.691103\pi\) | ||||
−0.564945 | + | 0.825128i | \(0.691103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6049.00i | − 0.794542i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6951.00 | −0.905989 | −0.452994 | − | 0.891513i | \(-0.649644\pi\) | ||||
−0.452994 | + | 0.891513i | \(0.649644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −436.549 | −0.0564635 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5355.00 | −0.687338 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1785.88 | −0.227487 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4477.35i | 0.566025i | 0.959116 | + | 0.283012i | \(0.0913337\pi\) | ||||
−0.959116 | + | 0.283012i | \(0.908666\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6909.00 | 0.860396 | 0.430198 | − | 0.902734i | \(-0.358444\pi\) | ||||
0.430198 | + | 0.902734i | \(0.358444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11685.6i | 1.44442i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1827.31i | 0.224197i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 16841.0i | − 2.05105i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6725.55i | 0.813098i | 0.913629 | + | 0.406549i | \(0.133268\pi\) | ||||
−0.913629 | + | 0.406549i | \(0.866732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 833.412 | 0.100022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7698.73i | 0.910640i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6020.00 | 0.706956 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6508.55 | −0.758863 | −0.379431 | − | 0.925220i | \(-0.623880\pi\) | ||||
−0.379431 | + | 0.925220i | \(0.623880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7576.00 | 0.877035 | 0.438517 | − | 0.898723i | \(-0.355504\pi\) | ||||
0.438517 | + | 0.898723i | \(0.355504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8413.49 | −0.967087 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 433.013i | − 0.0494217i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9450.00 | 1.06352 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16382.7i | 1.83092i | 0.402407 | + | 0.915461i | \(0.368174\pi\) | ||||
−0.402407 | + | 0.915461i | \(0.631826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 15952.2i | − 1.77047i | −0.465145 | − | 0.885235i | \(-0.653998\pi\) | ||||
0.465145 | − | 0.885235i | \(-0.346002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3849.36i | 0.424282i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3334.20i | 0.364980i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −383.634 | −0.0417081 | −0.0208540 | − | 0.999783i | \(-0.506639\pi\) | ||||
−0.0208540 | + | 0.999783i | \(0.506639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10856.1i | − 1.16431i | −0.813077 | − | 0.582156i | \(-0.802209\pi\) | ||||
0.813077 | − | 0.582156i | \(-0.197791\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13095.0 | 1.39497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4135.31 | 0.437569 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5868.00 | −0.616766 | −0.308383 | − | 0.951262i | \(-0.599788\pi\) | ||||
−0.308383 | + | 0.951262i | \(0.599788\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3095.53 | −0.323199 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 788.083i | 0.0817381i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6935.00 | 0.709859 | 0.354930 | − | 0.934893i | \(-0.384505\pi\) | ||||
0.354930 | + | 0.934893i | \(0.384505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1076.91i | − 0.109511i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2961.81i | − 0.299230i | −0.988744 | − | 0.149615i | \(-0.952197\pi\) | ||||
0.988744 | − | 0.149615i | \(-0.0478034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11154.0i | 1.11959i | 0.828631 | + | 0.559795i | \(0.189120\pi\) | ||||
−0.828631 | + | 0.559795i | \(0.810880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 5152.85i | − 0.513888i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8643.67 | −0.856491 | −0.428246 | − | 0.903662i | \(-0.640868\pi\) | ||||
−0.428246 | + | 0.903662i | \(0.640868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1901.77i | 0.186049i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20790.0 | −2.02098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3307.19 | −0.319462 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6900.00 | 0.662326 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16231.7 | 1.54832 | 0.774159 | − | 0.632991i | \(-0.218173\pi\) | ||||
0.774159 | + | 0.632991i | \(0.218173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 12730.6i | − 1.20679i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3750.00 | −0.351090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3826.45i | − 0.356043i | −0.984027 | − | 0.178022i | \(-0.943030\pi\) | ||||
0.984027 | − | 0.178022i | \(-0.0569697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 5637.83i | − 0.521373i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8890.20i | − 0.817126i | −0.912730 | − | 0.408563i | \(-0.866030\pi\) | ||||
0.912730 | − | 0.408563i | \(-0.133970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1454.92i | 0.132914i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11905.9 | 1.08107 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3047.41i | 0.273389i | 0.990613 | + | 0.136694i | \(0.0436478\pi\) | ||||
−0.990613 | + | 0.136694i | \(0.956352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1974.00 | 0.176032 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7715.01 | 0.683887 | 0.341944 | − | 0.939720i | \(-0.388915\pi\) | ||||
0.341944 | + | 0.939720i | \(0.388915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7215.00 | 0.635769 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1330.81 | 0.116575 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16068.2i | 1.39924i | 0.714516 | + | 0.699619i | \(0.246647\pi\) | ||||
−0.714516 | + | 0.699619i | \(0.753353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8225.00 | −0.707880 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 16749.3i | − 1.43313i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28916.6i | 2.45986i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2864.11i | 0.242236i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 13328.1i | − 1.12076i | −0.828236 | − | 0.560380i | \(-0.810655\pi\) | ||||
0.828236 | − | 0.560380i | \(-0.189345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −775.205 | −0.0648133 | −0.0324066 | − | 0.999475i | \(-0.510317\pi\) | ||||
−0.0324066 | + | 0.999475i | \(0.510317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1947.59i | − 0.160984i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9626.00 | 0.791156 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8730.98 | 0.713545 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2340.00 | −0.190163 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6865.72 | 0.554825 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3940.42i | 0.316651i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −359.000 | −0.0285298 | −0.0142649 | − | 0.999898i | \(-0.504541\pi\) | ||||
−0.0142649 | + | 0.999898i | \(0.504541\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 7497.09i | − 0.592507i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 6607.77i | − 0.519350i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24984.2i | 1.95292i | 0.215698 | + | 0.976460i | \(0.430797\pi\) | ||||
−0.215698 | + | 0.976460i | \(0.569203\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7932.79i | 0.616691i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11112.2 | 0.859154 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5613.66i | 0.429345i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14775.0 | −1.12394 | −0.561972 | − | 0.827156i | \(-0.689957\pi\) | ||||
−0.561972 | + | 0.827156i | \(0.689957\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15715.8 | −1.18910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1575.00 | −0.118532 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2674.85 | 0.200234 | 0.100117 | − | 0.994976i | \(-0.468078\pi\) | ||||
0.100117 | + | 0.994976i | \(0.468078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 12990.4i | − 0.967273i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24381.0 | −1.79632 | −0.898159 | − | 0.439671i | \(-0.855095\pi\) | ||||
−0.898159 | + | 0.439671i | \(0.855095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4926.27i | 0.361047i | 0.983571 | + | 0.180524i | \(0.0577792\pi\) | ||||
−0.983571 | + | 0.180524i | \(0.942221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12912.4i | 0.941405i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2520.42i | − 0.182798i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1099.85i | − 0.0793543i | −0.999213 | − | 0.0396772i | \(-0.987367\pi\) | ||||
0.999213 | − | 0.0396772i | \(-0.0126330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5172.44 | 0.371260 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 23714.8i | − 1.68468i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9000.00 | 0.636076 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10064.4 | −0.707673 | −0.353836 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353836 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14875.0 | −1.04060 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8413.49 | −0.585592 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 20498.8i | − 1.41954i | −0.704435 | − | 0.709769i | \(-0.748799\pi\) | ||||
0.704435 | − | 0.709769i | \(-0.251201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8855.00 | −0.607054 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12120.9i | 0.826790i | 0.910552 | + | 0.413395i | \(0.135657\pi\) | ||||
−0.910552 | + | 0.413395i | \(0.864343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 2476.83i | − 0.168107i | −0.996461 | − | 0.0840533i | \(-0.973213\pi\) | ||||
0.996461 | − | 0.0840533i | \(-0.0267866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8890.20i | − 0.600393i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 29392.9i | − 1.97519i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5177.74 | −0.346224 | −0.173112 | − | 0.984902i | \(-0.555382\pi\) | ||||
−0.173112 | + | 0.984902i | \(0.555382\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21858.9i | 1.44733i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12845.0 | 0.846337 | 0.423169 | − | 0.906051i | \(-0.360918\pi\) | ||||
0.423169 | + | 0.906051i | \(0.360918\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1031.84 | 0.0676552 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24360.0 | −1.58946 | −0.794730 | − | 0.606963i | \(-0.792387\pi\) | ||||
−0.794730 | + | 0.606963i | \(0.792387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 463.006 | 0.0300643 | 0.0150321 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150321 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 6268.29i | − 0.405053i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6875.00 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12029.3i | 0.766192i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2121.76i | 0.134500i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2337.11i | 0.147447i | 0.997279 | + | 0.0737235i | \(0.0234882\pi\) | ||||
−0.997279 | + | 0.0737235i | \(0.976512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10063.2i | 0.631875i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 396.863 | 0.0248016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 916.515i | − 0.0567399i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11109.0 | −0.684523 | −0.342261 | − | 0.939605i | \(-0.611193\pi\) | ||||
−0.342261 | + | 0.939605i | \(0.611193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2772.75 | −0.170057 | −0.0850284 | − | 0.996379i | \(-0.527098\pi\) | ||||
−0.0850284 | + | 0.996379i | \(0.527098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6930.00 | 0.423052 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16184.1 | −0.983402 | −0.491701 | − | 0.870764i | \(-0.663625\pi\) | ||||
−0.491701 | + | 0.870764i | \(0.663625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 30007.8i | − 1.81496i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15225.0 | −0.912405 | −0.456202 | − | 0.889876i | \(-0.650791\pi\) | ||||
−0.456202 | + | 0.889876i | \(0.650791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17528.4i | 1.04563i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19225.8i | 1.14166i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1328.95i | 0.0785560i | 0.999228 | + | 0.0392780i | \(0.0125058\pi\) | ||||
−0.999228 | + | 0.0392780i | \(0.987494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6635.49i | − 0.390455i | −0.980758 | − | 0.195227i | \(-0.937456\pi\) | ||||
0.980758 | − | 0.195227i | \(-0.0625445\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1190.59 | −0.0697415 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8468.60i | 0.491612i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13076.0 | −0.755676 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27264.5 | 1.56860 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21980.0 | −1.25894 | −0.629470 | − | 0.777025i | \(-0.716728\pi\) | ||||
−0.629470 | + | 0.777025i | \(0.716728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6217.52 | 0.354537 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 961.288i | − 0.0545721i | −0.999628 | − | 0.0272860i | \(-0.991314\pi\) | ||||
0.999628 | − | 0.0272860i | \(-0.00868650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5943.00 | −0.334414 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3524.00i | − 0.197426i | −0.995116 | − | 0.0987131i | \(-0.968527\pi\) | ||||
0.995116 | − | 0.0987131i | \(-0.0314726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 2727.98i | − 0.152162i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 12854.1i | − 0.713851i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 17926.7i | − 0.991225i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15490.9 | −0.852823 | −0.426411 | − | 0.904529i | \(-0.640222\pi\) | ||||
−0.426411 | + | 0.904529i | \(0.640222\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 19705.1i | − 1.07548i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 390.000 | 0.0211941 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3611.45 | −0.195419 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22974.0 | 1.23783 | 0.618913 | − | 0.785460i | \(-0.287573\pi\) | ||||
0.618913 | + | 0.785460i | \(0.287573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16205.2 | 0.869405 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 9638.86i | − 0.514923i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10297.0 | −0.545433 | −0.272716 | − | 0.962094i | \(-0.587922\pi\) | ||||
−0.272716 | + | 0.962094i | \(0.587922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 4124.32i | − 0.217544i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 11336.3i | − 0.595437i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 30932.4i | − 1.61791i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3394.82i | − 0.176823i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21311.5 | −1.10540 | −0.552702 | − | 0.833379i | \(-0.686403\pi\) | ||||
−0.552702 | + | 0.833379i | \(0.686403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 15053.8i | − 0.774350i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8400.00 | −0.430301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10773.5 | 0.549611 | 0.274805 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274805 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4663.00 | 0.236905 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2619.29 | 0.132528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5932.27i | − 0.298927i | −0.988767 | − | 0.149464i | \(-0.952245\pi\) | ||||
0.988767 | − | 0.149464i | \(-0.0477547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30555.0 | −1.52715 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 31734.3i | − 1.57966i | −0.613328 | − | 0.789828i | \(-0.710170\pi\) | ||||
0.613328 | − | 0.789828i | \(-0.289830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9093.27i | 0.450809i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11575.6i | 0.571557i | 0.958296 | + | 0.285779i | \(0.0922522\pi\) | ||||
−0.958296 | + | 0.285779i | \(0.907748\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 13536.0i | − 0.665664i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17779.4 | −0.870838 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30130.4i | 1.46401i | 0.681297 | + | 0.732007i | \(0.261416\pi\) | ||||
−0.681297 | + | 0.732007i | \(0.738584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3150.00 | 0.152447 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2579.61 | 0.124346 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11900.0 | 0.571351 | 0.285676 | − | 0.958326i | \(-0.407782\pi\) | ||||
0.285676 | + | 0.958326i | \(0.407782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9167.53 | −0.438419 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11752.0i | 0.559801i | 0.960029 | + | 0.279900i | \(0.0903014\pi\) | ||||
−0.960029 | + | 0.279900i | \(0.909699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1500.00 | −0.0708923 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 22683.7i | − 1.06788i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23573.2i | 1.10542i | 0.833372 | + | 0.552712i | \(0.186407\pi\) | ||||
−0.833372 | + | 0.552712i | \(0.813593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3184.89i | 0.148769i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 38668.0i | − 1.79921i | −0.436700 | − | 0.899607i | \(-0.643853\pi\) | ||||
0.436700 | − | 0.899607i | \(-0.356147\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11244.4 | 0.521177 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2978.67i | − 0.136999i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3150.00 | −0.144322 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20890.9 | −0.953484 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6225.00 | 0.283032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10680.9 | −0.483778 | −0.241889 | − | 0.970304i | \(-0.577767\pi\) | ||||
−0.241889 | + | 0.970304i | \(0.577767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 15773.8i | − 0.711739i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20610.0 | 0.922929 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7904.94i | 0.352653i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 24196.7i | − 1.07540i | −0.843137 | − | 0.537699i | \(-0.819294\pi\) | ||||
0.843137 | − | 0.537699i | \(-0.180706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 3643.15i | − 0.161308i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30241.6i | 1.33400i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 66077.6 | 2.90390 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10095.4i | 0.440366i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18597.0 | −0.808202 | −0.404101 | − | 0.914714i | \(-0.632416\pi\) | ||||
−0.404101 | + | 0.914714i | \(0.632416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4339.03 | −0.187872 | −0.0939359 | − | 0.995578i | \(-0.529945\pi\) | ||||
−0.0939359 | + | 0.995578i | \(0.529945\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12775.0 | −0.551093 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18454.1 | −0.793153 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 20005.2i | − 0.856662i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4713.00 | 0.200347 | 0.100173 | − | 0.994970i | \(-0.468060\pi\) | ||||
0.100173 | + | 0.994970i | \(0.468060\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 14018.1i | − 0.593731i | −0.954919 | − | 0.296865i | \(-0.904059\pi\) | ||||
0.954919 | − | 0.296865i | \(-0.0959412\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 9093.27i | − 0.383742i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35111.7i | 1.47636i | 0.674601 | + | 0.738182i | \(0.264316\pi\) | ||||
−0.674601 | + | 0.738182i | \(0.735684\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9933.31i | 0.416162i | 0.978112 | + | 0.208081i | \(0.0667217\pi\) | ||||
−0.978112 | + | 0.208081i | \(0.933278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6654.06 | −0.277770 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 6461.43i | − 0.267793i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27965.0 | 1.15485 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24605.5 | −1.01249 | −0.506243 | − | 0.862391i | \(-0.668966\pi\) | ||||
−0.506243 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3835.00 | 0.157243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13779.1 | 0.562961 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4356.11i | − 0.177343i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18781.0 | 0.759202 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12350.0i | 0.497478i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13769.8i | 0.552719i | 0.961054 | + | 0.276359i | \(0.0891280\pi\) | ||||
−0.961054 | + | 0.276359i | \(0.910872\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11456.4i | 0.458248i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 39170.3i | − 1.56130i | −0.624969 | − | 0.780649i | \(-0.714889\pi\) | ||||
0.624969 | − | 0.780649i | \(-0.285111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11046.0 | 0.438749 | 0.219374 | − | 0.975641i | \(-0.429598\pi\) | ||||
0.219374 | + | 0.975641i | \(0.429598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5540.33i | 0.218534i | 0.994012 | + | 0.109267i | \(0.0348504\pi\) | ||||
−0.994012 | + | 0.109267i | \(0.965150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9375.00 | 0.368508 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12800.1 | −0.501402 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14175.0 | −0.553342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23097.4 | −0.898537 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 8660.25i | − 0.335745i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16555.0 | −0.637426 | −0.318713 | − | 0.947851i | \(-0.603251\pi\) | ||||
−0.318713 | + | 0.947851i | \(0.603251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 824.864i | 0.0316518i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 8701.82i | − 0.332772i | −0.986061 | − | 0.166386i | \(-0.946790\pi\) | ||||
0.986061 | − | 0.166386i | \(-0.0532097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24241.8i | − 0.923899i | −0.886906 | − | 0.461949i | \(-0.847150\pi\) | ||||
0.886906 | − | 0.461949i | \(-0.152850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10002.6i | 0.379925i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16819.0 | −0.636672 | −0.318336 | − | 0.947978i | \(-0.603124\pi\) | ||||
−0.318336 | + | 0.947978i | \(0.603124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14503.9i | 0.545339i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27825.0 | −1.04270 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12898.0 | 0.481714 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6930.00 | −0.257955 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37781.3 | −1.40164 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2987.79i | 0.110475i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24540.0 | −0.901367 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23522.4i | 0.861133i | 0.902559 | + | 0.430566i | \(0.141686\pi\) | ||||
−0.902559 | + | 0.430566i | \(0.858314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16662.3i | 0.607981i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7836.20i | 0.284989i | 0.989796 | + | 0.142495i | \(0.0455123\pi\) | ||||
−0.989796 | + | 0.142495i | \(0.954488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61106.8i | 2.21505i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9088.16 | −0.328355 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 3597.32i | − 0.129124i | −0.997914 | − | 0.0645619i | \(-0.979435\pi\) | ||||
0.997914 | − | 0.0645619i | \(-0.0205650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1036.00 | 0.0370655 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2381.18 | −0.0849159 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12250.0 | −0.435435 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38680.9 | 1.37049 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43833.0i | 1.54802i | 0.633171 | + | 0.774012i | \(0.281753\pi\) | ||||
−0.633171 | + | 0.774012i | \(0.718247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6405.00 | −0.224748 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5155.40i | 0.180320i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 13995.0i | − 0.487936i | −0.969783 | − | 0.243968i | \(-0.921551\pi\) | ||||
0.969783 | − | 0.243968i | \(-0.0784491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 16382.7i | − 0.569360i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11041.8i | − 0.382522i | −0.981539 | − | 0.191261i | \(-0.938742\pi\) | ||||
0.981539 | − | 0.191261i | \(-0.0612577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2270.05 | 0.0783915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 36876.0i | − 1.26537i | −0.774408 | − | 0.632687i | \(-0.781952\pi\) | ||||
0.774408 | − | 0.632687i | \(-0.218048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49950.0 | 1.70858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14803.0 | −0.504752 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16980.0 | −0.577163 | −0.288581 | − | 0.957455i | \(-0.593184\pi\) | ||||
−0.288581 | + | 0.957455i | \(0.593184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42265.9 | 1.43214 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30553.4i | 1.03203i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20784.0 | 0.697660 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15855.7i | 0.530574i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 16930.8i | − 0.564789i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 7982.85i | − 0.265472i | −0.991151 | − | 0.132736i | \(-0.957624\pi\) | ||||
0.991151 | − | 0.132736i | \(-0.0423762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 1515.54i | − 0.0502439i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29725.0 | −0.982411 | −0.491206 | − | 0.871044i | \(-0.663444\pi\) | ||||
−0.491206 | + | 0.871044i | \(0.663444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 6873.86i | − 0.225784i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43155.0 | −1.41315 | −0.706577 | − | 0.707637i | \(-0.749761\pi\) | ||||
−0.706577 | + | 0.707637i | \(0.749761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 103938. | 3.39314 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15260.0 | 0.496651 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49552.3 | 1.60780 | 0.803902 | − | 0.594761i | \(-0.202753\pi\) | ||||
0.803902 | + | 0.594761i | \(0.202753\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27539.6i | 0.890848i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15246.0 | 0.490187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 4559.66i | − 0.146158i | −0.997326 | − | 0.0730789i | \(-0.976717\pi\) | ||||
0.997326 | − | 0.0730789i | \(-0.0232825\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20308.3i | 0.649007i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28984.8i | 0.923497i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41716.4i | 1.32515i | 0.748996 | + | 0.662574i | \(0.230536\pi\) | ||||
−0.748996 | + | 0.662574i | \(0.769464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30465.8 | −0.964861 |
(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 | 784.4.f.f.783.2 | 4 | ||
4.3 | odd | 2 | inner | 784.4.f.f.783.4 | 4 | ||
7.4 | even | 3 | 112.4.p.e.47.2 | yes | 4 | ||
7.5 | odd | 6 | 112.4.p.e.31.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 784.4.f.f.783.3 | 4 | ||
28.11 | odd | 6 | 112.4.p.e.47.1 | yes | 4 | ||
28.19 | even | 6 | 112.4.p.e.31.2 | yes | 4 | ||
28.27 | even | 2 | inner | 784.4.f.f.783.1 | 4 | ||
56.5 | odd | 6 | 448.4.p.e.255.2 | 4 | |||
56.11 | odd | 6 | 448.4.p.e.383.2 | 4 | |||
56.19 | even | 6 | 448.4.p.e.255.1 | 4 | |||
56.53 | even | 6 | 448.4.p.e.383.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.e.31.1 | ✓ | 4 | 7.5 | odd | 6 | ||
112.4.p.e.31.2 | yes | 4 | 28.19 | even | 6 | ||
112.4.p.e.47.1 | yes | 4 | 28.11 | odd | 6 | ||
112.4.p.e.47.2 | yes | 4 | 7.4 | even | 3 | ||
448.4.p.e.255.1 | 4 | 56.19 | even | 6 | |||
448.4.p.e.255.2 | 4 | 56.5 | odd | 6 | |||
448.4.p.e.383.1 | 4 | 56.53 | even | 6 | |||
448.4.p.e.383.2 | 4 | 56.11 | odd | 6 | |||
784.4.f.f.783.1 | 4 | 28.27 | even | 2 | inner | ||
784.4.f.f.783.2 | 4 | 1.1 | even | 1 | trivial | ||
784.4.f.f.783.3 | 4 | 7.6 | odd | 2 | inner | ||
784.4.f.f.783.4 | 4 | 4.3 | odd | 2 | inner |