Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,3,Mod(127,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.m (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.6213475300\) |
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: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-0.895644 - 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.127 |
Dual form | 1344.3.m.a.127.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.58258 | −1.11652 | −0.558258 | − | 0.829668i | \(-0.688530\pi\) | ||||
−0.558258 | + | 0.829668i | \(0.688530\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.37780i | − 0.397982i | −0.980001 | − | 0.198991i | \(-0.936234\pi\) | ||||
0.980001 | − | 0.198991i | \(-0.0637665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.1652 | −1.32040 | −0.660198 | − | 0.751091i | \(-0.729528\pi\) | ||||
−0.660198 | + | 0.751091i | \(0.729528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.66930i | 0.644620i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.747727 | 0.0439839 | 0.0219920 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219920 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.65480i | − 0.192358i | −0.995364 | − | 0.0961790i | \(-0.969338\pi\) | ||||
0.995364 | − | 0.0961790i | \(-0.0306621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.86001i | 0.428696i | 0.976757 | + | 0.214348i | \(0.0687626\pi\) | ||||
−0.976757 | + | 0.214348i | \(0.931237\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.16515 | 0.246606 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.0689655 | 0.0344828 | − | 0.999405i | \(-0.489022\pi\) | ||||
0.0344828 | + | 0.999405i | \(0.489022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17.8926i | 0.577181i | 0.957453 | + | 0.288590i | \(0.0931866\pi\) | ||||
−0.957453 | + | 0.288590i | \(0.906813\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.58258 | −0.229775 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 14.7701i | − 0.422003i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.49545 | 0.202580 | 0.101290 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101290 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 29.7309i | 0.762331i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 76.5735 | 1.86765 | 0.933823 | − | 0.357735i | \(-0.116451\pi\) | ||||
0.933823 | + | 0.357735i | \(0.116451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 70.0448i | − 1.62895i | −0.580199 | − | 0.814475i | \(-0.697025\pi\) | ||||
0.580199 | − | 0.814475i | \(-0.302975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.7477 | 0.372172 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.1232i | 0.853686i | 0.904326 | + | 0.426843i | \(0.140374\pi\) | ||||
−0.904326 | + | 0.426843i | \(0.859626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.29510i | − 0.0253941i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −49.8258 | −0.940109 | −0.470054 | − | 0.882637i | \(-0.655766\pi\) | ||||
−0.470054 | + | 0.882637i | \(0.655766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.4394i | 0.444353i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.33030 | −0.111058 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 89.3834i | 1.51497i | 0.652850 | + | 0.757487i | \(0.273573\pi\) | ||||
−0.652850 | + | 0.757487i | \(0.726427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 120.991 | 1.98346 | 0.991729 | − | 0.128351i | \(-0.0409685\pi\) | ||||
0.991729 | + | 0.128351i | \(0.0409685\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 7.93725i | − 0.125988i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 95.8258 | 1.47424 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.3748i | 0.348878i | 0.984668 | + | 0.174439i | \(0.0558112\pi\) | ||||
−0.984668 | + | 0.174439i | \(0.944189\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.0780 | 0.247508 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 66.0484i | − 0.930260i | −0.885242 | − | 0.465130i | \(-0.846008\pi\) | ||||
0.885242 | − | 0.465130i | \(-0.153992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −40.5045 | −0.554857 | −0.277428 | − | 0.960746i | \(-0.589482\pi\) | ||||
−0.277428 | + | 0.960746i | \(0.589482\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 10.6784i | − 0.142378i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.5826 | 0.150423 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 95.5488i | − 1.20948i | −0.796423 | − | 0.604740i | \(-0.793277\pi\) | ||||
0.796423 | − | 0.604740i | \(-0.206723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 115.650i | 1.39338i | 0.717374 | + | 0.696688i | \(0.245344\pi\) | ||||
−0.717374 | + | 0.696688i | \(0.754656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.17424 | −0.0491087 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3.46410i | − 0.0398173i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34.9038 | 0.392177 | 0.196089 | − | 0.980586i | \(-0.437176\pi\) | ||||
0.196089 | + | 0.980586i | \(0.437176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 45.4147i | − 0.499063i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30.9909 | 0.333236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.4032i | 0.214771i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 52.5045 | 0.541284 | 0.270642 | − | 0.962680i | \(-0.412764\pi\) | ||||
0.270642 | + | 0.962680i | \(0.412764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.1334i | 0.132661i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 113.583 | 1.12458 | 0.562290 | − | 0.826940i | \(-0.309920\pi\) | ||||
0.562290 | + | 0.826940i | \(0.309920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 50.0230i | − 0.485660i | −0.970069 | − | 0.242830i | \(-0.921924\pi\) | ||||
0.970069 | − | 0.242830i | \(-0.0780758\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.5826 | −0.243644 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 160.533i | 1.50031i | 0.661265 | + | 0.750153i | \(0.270020\pi\) | ||||
−0.661265 | + | 0.750153i | \(0.729980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 205.303 | 1.88351 | 0.941757 | − | 0.336294i | \(-0.109174\pi\) | ||||
0.941757 | + | 0.336294i | \(0.109174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 12.9825i | − 0.116960i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 179.321 | 1.58691 | 0.793457 | − | 0.608627i | \(-0.208279\pi\) | ||||
0.793457 | + | 0.608627i | \(0.208279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 55.0442i | − 0.478645i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 51.4955 | 0.440132 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.97830i | 0.0166244i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.835 | 0.841610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 132.629i | − 1.07829i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 105.147 | 0.841176 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 130.571i | − 1.02812i | −0.857754 | − | 0.514060i | \(-0.828141\pi\) | ||||
0.857754 | − | 0.514060i | \(-0.171859\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −121.321 | −0.940475 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 71.1890i | 0.543428i | 0.962378 | + | 0.271714i | \(0.0875904\pi\) | ||||
−0.962378 | + | 0.271714i | \(0.912410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.66970 | 0.0727045 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 29.0079i | − 0.214873i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −99.8439 | −0.728788 | −0.364394 | − | 0.931245i | \(-0.618724\pi\) | ||||
−0.364394 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 162.400i | − 1.16834i | −0.811630 | − | 0.584172i | \(-0.801419\pi\) | ||||
0.811630 | − | 0.584172i | \(-0.198581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 69.4955 | 0.492876 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 75.1456i | 0.525494i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1652 | −0.0770010 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1244i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −293.165 | −1.96755 | −0.983776 | − | 0.179403i | \(-0.942583\pi\) | ||||
−0.983776 | + | 0.179403i | \(0.942583\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 120.449i | − 0.797677i | −0.917021 | − | 0.398839i | \(-0.869413\pi\) | ||||
0.917021 | − | 0.398839i | \(-0.130587\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.24318 | −0.0146613 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 99.8868i | − 0.644431i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 163.982 | 1.04447 | 0.522235 | − | 0.852802i | \(-0.325098\pi\) | ||||
0.522235 | + | 0.852802i | \(0.325098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 86.3007i | 0.542772i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.0871 | −0.162032 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 226.803i | 1.39143i | 0.718317 | + | 0.695716i | \(0.244913\pi\) | ||||
−0.718317 | + | 0.695716i | \(0.755087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 42.3303 | 0.256547 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 226.803i | − 1.35810i | −0.734090 | − | 0.679052i | \(-0.762391\pi\) | ||||
0.734090 | − | 0.679052i | \(-0.237609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 125.642 | 0.743446 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.9644i | 0.0641193i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 108.922 | 0.629607 | 0.314803 | − | 0.949157i | \(-0.398061\pi\) | ||||
0.314803 | + | 0.949157i | \(0.398061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.3115i | 0.0932083i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 154.817 | 0.874670 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 91.2506i | − 0.509780i | −0.966970 | − | 0.254890i | \(-0.917961\pi\) | ||||
0.966970 | − | 0.254890i | \(-0.0820393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −135.495 | −0.748594 | −0.374297 | − | 0.927309i | \(-0.622116\pi\) | ||||
−0.374297 | + | 0.927309i | \(0.622116\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 209.562i | − 1.14515i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −41.8439 | −0.226183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.27340i | − 0.0175048i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.7477 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 106.934i | 0.559866i | 0.960020 | + | 0.279933i | \(0.0903123\pi\) | ||||
−0.960020 | + | 0.279933i | \(0.909688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −116.505 | −0.603650 | −0.301825 | − | 0.953363i | \(-0.597596\pi\) | ||||
−0.301825 | + | 0.953363i | \(0.597596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 165.975i | − 0.851154i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −38.8348 | −0.197131 | −0.0985656 | − | 0.995131i | \(-0.531425\pi\) | ||||
−0.0985656 | + | 0.995131i | \(0.531425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 353.116i | 1.77445i | 0.461334 | + | 0.887227i | \(0.347371\pi\) | ||||
−0.461334 | + | 0.887227i | \(0.652629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.4864 | 0.201425 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.29150i | 0.0260665i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −427.477 | −2.08525 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 29.5800i | − 0.142899i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −0.0765550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 54.0592i | − 0.256205i | −0.991761 | − | 0.128102i | \(-0.959111\pi\) | ||||
0.991761 | − | 0.128102i | \(-0.0408886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −114.399 | −0.537086 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 391.031i | 1.81875i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −47.3394 | −0.218154 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 70.1559i | 0.320347i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.8348 | −0.0580762 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 93.3400i | 0.418565i | 0.977855 | + | 0.209283i | \(0.0671129\pi\) | ||||
−0.977855 | + | 0.209283i | \(0.932887\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.4955 | −0.0822020 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 170.233i | − 0.749927i | −0.927040 | − | 0.374964i | \(-0.877655\pi\) | ||||
0.927040 | − | 0.374964i | \(-0.122345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 227.844 | 0.994952 | 0.497476 | − | 0.867478i | \(-0.334260\pi\) | ||||
0.497476 | + | 0.867478i | \(0.334260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 20.0616i | − 0.0868468i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 378.486 | 1.62440 | 0.812202 | − | 0.583376i | \(-0.198268\pi\) | ||||
0.812202 | + | 0.583376i | \(0.198268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 223.991i | − 0.953153i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −165.495 | −0.698293 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 205.535i | 0.859977i | 0.902834 | + | 0.429989i | \(0.141482\pi\) | ||||
−0.902834 | + | 0.429989i | \(0.858518\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40.4682 | 0.167918 | 0.0839589 | − | 0.996469i | \(-0.473244\pi\) | ||||
0.0839589 | + | 0.996469i | \(0.473244\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.0780 | 0.159502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.7352i | 0.253989i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 200.312 | 0.804466 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 332.856i | 1.32612i | 0.748567 | + | 0.663059i | \(0.230742\pi\) | ||||
−0.748567 | + | 0.663059i | \(0.769258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 43.1652 | 0.170613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.23000i | 0.0283529i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −205.372 | −0.799113 | −0.399556 | − | 0.916709i | \(-0.630836\pi\) | ||||
−0.399556 | + | 0.916709i | \(0.630836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.8311i | 0.0765680i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.0229885 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 45.4064i | − 0.172648i | −0.996267 | − | 0.0863240i | \(-0.972488\pi\) | ||||
0.996267 | − | 0.0863240i | \(-0.0275120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 278.156 | 1.04965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 60.4551i | − 0.226424i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 202.069 | 0.751186 | 0.375593 | − | 0.926785i | \(-0.377439\pi\) | ||||
0.375593 | + | 0.926785i | \(0.377439\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 279.798i | 1.03246i | 0.856449 | + | 0.516232i | \(0.172666\pi\) | ||||
−0.856449 | + | 0.516232i | \(0.827334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −78.6606 | −0.288134 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 26.9898i | − 0.0981448i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −135.459 | −0.489022 | −0.244511 | − | 0.969647i | \(-0.578627\pi\) | ||||
−0.244511 | + | 0.969647i | \(0.578627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 53.6778i | − 0.192394i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.8530 | 0.0742101 | 0.0371050 | − | 0.999311i | \(-0.488186\pi\) | ||||
0.0371050 | + | 0.999311i | \(0.488186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 113.743i | − 0.401920i | −0.979599 | − | 0.200960i | \(-0.935594\pi\) | ||||
0.979599 | − | 0.200960i | \(-0.0644061\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 35.3394 | 0.123998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 202.594i | 0.705904i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.441 | −0.998065 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 90.9405i | − 0.312510i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 121.931 | 0.416147 | 0.208073 | − | 0.978113i | \(-0.433281\pi\) | ||||
0.208073 | + | 0.978113i | \(0.433281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 498.990i | − 1.69149i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.7477 | 0.0765917 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 169.248i | − 0.566048i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 185.321 | 0.615685 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 196.731i | − 0.649277i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −675.441 | −2.21456 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 337.131i | 1.09815i | 0.835775 | + | 0.549073i | \(0.185019\pi\) | ||||
−0.835775 | + | 0.549073i | \(0.814981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −86.6424 | −0.280396 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 246.762i | 0.793447i | 0.917938 | + | 0.396724i | \(0.129853\pi\) | ||||
−0.917938 | + | 0.396724i | \(0.870147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 274.624 | 0.877394 | 0.438697 | − | 0.898635i | \(-0.355440\pi\) | ||||
0.438697 | + | 0.898635i | \(0.355440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 44.3103i | 0.140668i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 129.441 | 0.408331 | 0.204165 | − | 0.978936i | \(-0.434552\pi\) | ||||
0.204165 | + | 0.978936i | \(0.434552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8.75560i | − 0.0274470i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 278.051 | 0.866202 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.73279i | − 0.00846066i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −105.826 | −0.325618 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 355.595i | − 1.08745i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −106.156 | −0.322663 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 219.573i | 0.663363i | 0.943391 | + | 0.331682i | \(0.107616\pi\) | ||||
−0.943391 | + | 0.331682i | \(0.892384\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.4864 | −0.0675266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 130.492i | − 0.389527i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −132.955 | −0.394524 | −0.197262 | − | 0.980351i | \(-0.563205\pi\) | ||||
−0.197262 | + | 0.980351i | \(0.563205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 310.593i | − 0.916205i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 78.3303 | 0.229708 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −95.3394 | −0.276346 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 453.282i | 1.30629i | 0.757234 | + | 0.653144i | \(0.226550\pi\) | ||||
−0.757234 | + | 0.653144i | \(0.773450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −525.615 | −1.50606 | −0.753030 | − | 0.657986i | \(-0.771409\pi\) | ||||
−0.753030 | + | 0.657986i | \(0.771409\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 89.1927i | − 0.254110i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −389.858 | −1.10441 | −0.552207 | − | 0.833707i | \(-0.686214\pi\) | ||||
−0.552207 | + | 0.833707i | \(0.686214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 368.720i | 1.03865i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.42652 | 0.00959808 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 692.718i | 1.92958i | 0.263030 | + | 0.964788i | \(0.415278\pi\) | ||||
−0.263030 | + | 0.964788i | \(0.584722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 347.642 | 0.962998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 176.383i | − 0.485904i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 226.120 | 0.619506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 556.863i | − 1.51734i | −0.651476 | − | 0.758669i | \(-0.725850\pi\) | ||||
0.651476 | − | 0.758669i | \(-0.274150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −229.720 | −0.622549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 131.827i | − 0.355328i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −549.267 | −1.47256 | −0.736282 | − | 0.676674i | \(-0.763420\pi\) | ||||
−0.736282 | + | 0.676674i | \(0.763420\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 182.120i | − 0.485653i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.3303 | −0.0910618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 232.667i | − 0.613897i | −0.951726 | − | 0.306948i | \(-0.900692\pi\) | ||||
0.951726 | − | 0.306948i | \(-0.0993079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −226.156 | −0.593585 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 394.526i | 1.03009i | 0.857162 | + | 0.515047i | \(0.172226\pi\) | ||||
−0.857162 | + | 0.515047i | \(0.827774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −64.6606 | −0.167950 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 210.135i | 0.542983i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.98182 | −0.0102360 | −0.00511802 | − | 0.999987i | \(-0.501629\pi\) | ||||
−0.00511802 | + | 0.999987i | \(0.501629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.37259i | 0.0188557i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 123.303 | 0.313748 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 533.409i | 1.35040i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 476.606 | 1.20052 | 0.600260 | − | 0.799805i | \(-0.295064\pi\) | ||||
0.600260 | + | 0.799805i | \(0.295064\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 16.7484i | − 0.0419760i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −157.441 | −0.392621 | −0.196310 | − | 0.980542i | \(-0.562896\pi\) | ||||
−0.196310 | + | 0.980542i | \(0.562896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 307.129i | − 0.762108i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −50.2432 | −0.124057 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 32.8136i | − 0.0806231i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −112.156 | −0.274220 | −0.137110 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137110 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 172.935i | 0.420766i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −236.486 | −0.572606 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 645.626i | − 1.55573i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −281.285 | −0.674544 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 699.065i | 1.66841i | 0.551452 | + | 0.834207i | \(0.314074\pi\) | ||||
−0.551452 | + | 0.834207i | \(0.685926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −198.762 | −0.472119 | −0.236060 | − | 0.971739i | \(-0.575856\pi\) | ||||
−0.236060 | + | 0.971739i | \(0.575856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 120.370i | − 0.284562i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.60985 | 0.0108467 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 320.112i | 0.749676i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 130.156 | 0.303394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 513.871i | − 1.19228i | −0.802882 | − | 0.596138i | \(-0.796701\pi\) | ||||
0.802882 | − | 0.596138i | \(-0.203299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −654.900 | −1.51247 | −0.756236 | − | 0.654299i | \(-0.772964\pi\) | ||||
−0.756236 | + | 0.654299i | \(0.772964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.3386i | 0.0444566i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.0364 | 0.0824631 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 143.141i | − 0.326061i | −0.986621 | − | 0.163031i | \(-0.947873\pi\) | ||||
0.986621 | − | 0.163031i | \(-0.0521269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 46.8690i | 0.105799i | 0.998600 | + | 0.0528996i | \(0.0168463\pi\) | ||||
−0.998600 | + | 0.0528996i | \(0.983154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −194.853 | −0.437872 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 507.777i | 1.13597i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −292.955 | −0.652460 | −0.326230 | − | 0.945290i | \(-0.605778\pi\) | ||||
−0.326230 | + | 0.945290i | \(0.605778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 335.224i | − 0.743289i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −208.624 | −0.460539 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 253.531i | 0.557211i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −424.018 | −0.927830 | −0.463915 | − | 0.885880i | \(-0.653556\pi\) | ||||
−0.463915 | + | 0.885880i | \(0.653556\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.88530i | 0.00846471i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 344.886 | 0.748125 | 0.374062 | − | 0.927404i | \(-0.377965\pi\) | ||||
0.374062 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 319.381i | − 0.689807i | −0.938638 | − | 0.344903i | \(-0.887912\pi\) | ||||
0.938638 | − | 0.344903i | \(-0.112088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −173.009 | −0.372063 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 306.065i | 0.655385i | 0.944784 | + | 0.327692i | \(0.106271\pi\) | ||||
−0.944784 | + | 0.327692i | \(0.893729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −61.8439 | −0.131863 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 284.025i | − 0.603025i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −306.642 | −0.648293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 22.5324i | − 0.0474366i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 149.477 | 0.313370 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 355.769i | − 0.742734i | −0.928486 | − | 0.371367i | \(-0.878889\pi\) | ||||
0.928486 | − | 0.371367i | \(-0.121111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −128.661 | −0.267486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 45.1842i | 0.0935491i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −293.111 | −0.604352 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 765.313i | 1.57148i | 0.618554 | + | 0.785742i | \(0.287719\pi\) | ||||
−0.618554 | + | 0.785742i | \(0.712281\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 392.835 | 0.803343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 975.169i | − 1.98609i | −0.117749 | − | 0.993043i | \(-0.537568\pi\) | ||||
0.117749 | − | 0.993043i | \(-0.462432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.49545 | 0.00303338 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 73.3182i | − 0.148118i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 174.748 | 0.351605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 472.358i | − 0.946610i | −0.880899 | − | 0.473305i | \(-0.843061\pi\) | ||||
0.880899 | − | 0.473305i | \(-0.156939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −392.835 | −0.784101 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 513.165i | 1.02021i | 0.860113 | + | 0.510104i | \(0.170393\pi\) | ||||
−0.860113 | + | 0.510104i | \(0.829607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −634.083 | −1.25561 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 217.619i | − 0.429229i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −361.546 | −0.710307 | −0.355153 | − | 0.934808i | \(-0.615571\pi\) | ||||
−0.355153 | + | 0.934808i | \(0.615571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 107.165i | − 0.209716i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9909 | 0.0370193 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 279.257i | 0.542247i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 175.652 | 0.339751 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 188.658i | − 0.363504i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 71.4265 | 0.137095 | 0.0685475 | − | 0.997648i | \(-0.478164\pi\) | ||||
0.0685475 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 587.246i | − 1.12284i | −0.827531 | − | 0.561420i | \(-0.810255\pi\) | ||||
0.827531 | − | 0.561420i | \(-0.189745\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.2523 | 0.0538139 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.3788i | 0.0253867i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 431.780 | 0.816220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 268.150i | − 0.504991i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1314.40 | −2.46603 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 896.186i | − 1.67511i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −158.051 | −0.294322 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.6446i | 0.0568546i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 436.505 | 0.806848 | 0.403424 | − | 0.915013i | \(-0.367820\pi\) | ||||
0.403424 | + | 0.915013i | \(0.367820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 234.685i | 0.432201i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1146.12 | −2.10297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.2188i | 0.0461039i | 0.999734 | + | 0.0230519i | \(0.00733831\pi\) | ||||
−0.999734 | + | 0.0230519i | \(0.992662\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −362.973 | −0.661153 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 7.30960i | − 0.0132661i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 252.798 | 0.457140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 72.4758i | 0.130587i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −58.1742 | −0.104442 | −0.0522210 | − | 0.998636i | \(-0.516630\pi\) | ||||
−0.0522210 | + | 0.998636i | \(0.516630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1202.33i | 2.15086i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.66970 | −0.0101064 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 565.396i | − 1.00426i | −0.864793 | − | 0.502128i | \(-0.832551\pi\) | ||||
0.864793 | − | 0.502128i | \(-0.167449\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1001.07 | −1.77181 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 573.056 | 1.00713 | 0.503564 | − | 0.863958i | \(-0.332022\pi\) | ||||
0.503564 | + | 0.863958i | \(0.332022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 685.750i | − 1.20096i | −0.799639 | − | 0.600481i | \(-0.794976\pi\) | ||||
0.799639 | − | 0.600481i | \(-0.205024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 185.216 | 0.323239 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 60.7884i | 0.105719i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −278.900 | −0.483362 | −0.241681 | − | 0.970356i | \(-0.577699\pi\) | ||||
−0.241681 | + | 0.970356i | \(0.577699\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 201.792i | 0.348518i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −305.982 | −0.526647 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 218.127i | 0.374146i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −287.477 | −0.491414 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1169.74i | 1.99274i | 0.0851245 | + | 0.996370i | \(0.472871\pi\) | ||||
−0.0851245 | + | 0.996370i | \(0.527129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 65.3939 | 0.111025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 67.2639i | 0.113814i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 969.023 | 1.63410 | 0.817052 | − | 0.576564i | \(-0.195607\pi\) | ||||
0.817052 | + | 0.576564i | \(0.195607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 11.0440i | − 0.0185614i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 611.615 | 1.02448 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 656.488i | 1.09597i | 0.836487 | + | 0.547987i | \(0.184606\pi\) | ||||
−0.836487 | + | 0.547987i | \(0.815394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 312.955 | 0.520723 | 0.260362 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260362 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 70.1244i | − 0.116293i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −568.501 | −0.939671 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 113.584i | − 0.187124i | −0.995613 | − | 0.0935618i | \(-0.970175\pi\) | ||||
0.995613 | − | 0.0935618i | \(-0.0298253\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.16515 | 0.0150495 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 688.721i | − 1.12720i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.0000 | −0.0163132 | −0.00815661 | − | 0.999967i | \(-0.502596\pi\) | ||||
−0.00815661 | + | 0.999967i | \(0.502596\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 740.412i | 1.20392i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 984.323 | 1.59534 | 0.797668 | − | 0.603096i | \(-0.206067\pi\) | ||||
0.797668 | + | 0.603096i | \(0.206067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 266.864i | − 0.431120i | −0.976491 | − | 0.215560i | \(-0.930842\pi\) | ||||
0.976491 | − | 0.215560i | \(-0.0691578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −51.2341 | −0.0825026 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 92.3467i | 0.148229i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −741.120 | −1.18579 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.7128i | 0.0441991i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.60455 | 0.00891026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 609.443i | − 0.965837i | −0.875665 | − | 0.482918i | \(-0.839577\pi\) | ||||
0.875665 | − | 0.482918i | \(-0.160423\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −93.6333 | −0.147920 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 728.924i | 1.14791i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 120.156 | 0.188628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 198.145i | 0.310087i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 528.120 | 0.823900 | 0.411950 | − | 0.911207i | \(-0.364848\pi\) | ||||
0.411950 | + | 0.911207i | \(0.364848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 812.666i | − 1.26387i | −0.775023 | − | 0.631933i | \(-0.782262\pi\) | ||||
0.775023 | − | 0.631933i | \(-0.217738\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 677.285 | 1.05005 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1153.37i | − 1.78265i | −0.453369 | − | 0.891323i | \(-0.649778\pi\) | ||||
0.453369 | − | 0.891323i | \(-0.350222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 391.303 | 0.602932 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 81.9942i | 0.125951i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 994.000 | 1.52221 | 0.761103 | − | 0.648632i | \(-0.224658\pi\) | ||||
0.761103 | + | 0.648632i | \(0.224658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 397.418i | − 0.606745i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 121.514 | 0.184952 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1223.14i | − 1.85605i | −0.372516 | − | 0.928026i | \(-0.621505\pi\) | ||||
0.372516 | − | 0.928026i | \(-0.378495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0545 | −0.0363911 | −0.0181956 | − | 0.999834i | \(-0.505792\pi\) | ||||
−0.0181956 | + | 0.999834i | \(0.505792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.2306i | 0.0335303i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −53.9818 | −0.0811757 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.7200i | 0.0295652i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 161.670 | 0.241659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 529.674i | − 0.789380i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 653.789 | 0.971455 | 0.485728 | − | 0.874110i | \(-0.338555\pi\) | ||||
0.485728 | + | 0.874110i | \(0.338555\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 32.0351i | 0.0474594i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −366.069 | −0.540722 | −0.270361 | − | 0.962759i | \(-0.587143\pi\) | ||||
−0.270361 | + | 0.962759i | \(0.587143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 138.914i | 0.204586i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −294.853 | −0.432971 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 971.912i | 1.42300i | 0.702684 | + | 0.711502i | \(0.251985\pi\) | ||||
−0.702684 | + | 0.711502i | \(0.748015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 557.386 | 0.813703 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 394.637i | − 0.574436i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 855.267 | 1.24132 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1028.20i | 1.48799i | 0.668184 | + | 0.743996i | \(0.267072\pi\) | ||||
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −34.7477 | −0.0501410 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 906.610i | 1.30447i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 57.2561 | 0.0821464 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 655.558i | − 0.937851i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 276.918 | 0.395033 | 0.197517 | − | 0.980300i | \(-0.436712\pi\) | ||||
0.197517 | + | 0.980300i | \(0.436712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 27.3944i | − 0.0389679i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −387.964 | −0.550303 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 300.511i | 0.425051i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.2485 | −0.0722828 | −0.0361414 | − | 0.999347i | \(-0.511507\pi\) | ||||
−0.0361414 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 286.647i | 0.403160i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −176.421 | −0.247435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 419.506i | − 0.586722i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 355.996 | 0.496508 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 898.093i | 1.24909i | 0.780990 | + | 0.624543i | \(0.214715\pi\) | ||||
−0.780990 | + | 0.624543i | \(0.785285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 132.348 | 0.183562 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 70.0929i | − 0.0969474i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.3303 | 0.0170073 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 107.100i | 0.147318i | 0.997283 | + | 0.0736590i | \(0.0234677\pi\) | ||||
−0.997283 | + | 0.0736590i | \(0.976532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 52.3744i | − 0.0716476i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 541.368 | 0.738565 | 0.369283 | − | 0.929317i | \(-0.379603\pi\) | ||||
0.369283 | + | 0.929317i | \(0.379603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 67.6851i | − 0.0920886i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 102.330 | 0.138847 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 241.423i | 0.326688i | 0.986569 | + | 0.163344i | \(0.0522281\pi\) | ||||
−0.986569 | + | 0.163344i | \(0.947772\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 108.661 | 0.146640 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 593.753i | 0.799129i | 0.916705 | + | 0.399564i | \(0.130839\pi\) | ||||
−0.916705 | + | 0.399564i | \(0.869161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1636.62 | 2.19680 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 346.951i | − 0.464459i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −424.730 | −0.567062 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 918.781i | 1.22341i | 0.791086 | + | 0.611705i | \(0.209516\pi\) | ||||
−0.791086 | + | 0.611705i | \(0.790484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 576.523 | 0.765634 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 672.417i | 0.890619i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1407.80 | 1.85971 | 0.929855 | − | 0.367927i | \(-0.119932\pi\) | ||||
0.929855 | + | 0.367927i | \(0.119932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 74.7642i | − 0.0985036i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −295.042 | −0.387703 | −0.193851 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193851 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 543.181i | 0.711901i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.5227 | 0.0163696 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1534.28i | − 2.00037i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 116.991 | 0.152134 | 0.0760669 | − | 0.997103i | \(-0.475764\pi\) | ||||
0.0760669 | + | 0.997103i | \(0.475764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 355.715i | 0.461368i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −105.408 | −0.136363 | −0.0681813 | − | 0.997673i | \(-0.521720\pi\) | ||||
−0.0681813 | + | 0.997673i | \(0.521720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 110.311i | 0.142336i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.3485 | 0.0442065 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 279.861i | − 0.359257i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −289.147 | −0.370227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.3923i | 0.0132724i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −915.441 | −1.16617 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 542.148i | − 0.688879i | −0.938809 | − | 0.344439i | \(-0.888069\pi\) | ||||
0.938809 | − | 0.344439i | \(-0.111931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.6462 | −0.0996783 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 474.439i | 0.599797i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2076.83 | −2.61895 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 481.780i | − 0.606013i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 296.886 | 0.372504 | 0.186252 | − | 0.982502i | \(-0.440366\pi\) | ||||
0.186252 | + | 0.982502i | \(0.440366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0012i | 0.0375485i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −104.711 | −0.130726 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 177.321i | 0.220823i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 145.633 | 0.180911 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 349.994i | − 0.433697i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1066.83 | 1.31870 | 0.659349 | − | 0.751837i | \(-0.270832\pi\) | ||||
0.659349 | + | 0.751837i | \(0.270832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.82020i | 0.0121088i | 0.999982 | + | 0.00605438i | \(0.00192718\pi\) | ||||
−0.999982 | + | 0.00605438i | \(0.998073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 484.624 | 0.596094 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1266.15i | − 1.55355i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −256.000 | −0.313341 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 136.244i | 0.166354i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 928.395 | 1.13081 | 0.565405 | − | 0.824813i | \(-0.308720\pi\) | ||||
0.565405 | + | 0.824813i | \(0.308720\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 396.291i | − 0.481520i | −0.970585 | − | 0.240760i | \(-0.922603\pi\) | ||||
0.970585 | − | 0.240760i | \(-0.0773966\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −46.7477 | −0.0566639 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1094.28i | 1.32320i | 0.749858 | + | 0.661599i | \(0.230122\pi\) | ||||
−0.749858 | + | 0.661599i | \(0.769878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 107.074 | 0.129161 | 0.0645804 | − | 0.997913i | \(-0.479429\pi\) | ||||
0.0645804 | + | 0.997913i | \(0.479429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 234.622i | 0.282337i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.23409 | −0.00628342 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1266.15i | 1.51634i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −92.9727 | −0.111079 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1110.28i | − 1.32333i | −0.749798 | − | 0.661667i | \(-0.769849\pi\) | ||||
0.749798 | − | 0.661667i | \(-0.230151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.000 | −0.995244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 36.1185i | − 0.0428452i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −701.408 | −0.830069 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 269.430i | 0.318099i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −197.009 | −0.232048 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 73.9052i | 0.0868451i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −657.506 | −0.770816 | −0.385408 | − | 0.922746i | \(-0.625939\pi\) | ||||
−0.385408 | + | 0.922746i | \(0.625939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 61.2096i | − 0.0715902i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 664.958 | 0.775914 | 0.387957 | − | 0.921677i | \(-0.373181\pi\) | ||||
0.387957 | + | 0.921677i | \(0.373181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1071.96i | 1.24792i | 0.781456 | + | 0.623961i | \(0.214477\pi\) | ||||
−0.781456 | + | 0.623961i | \(0.785523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 350.904 | 0.407554 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 612.073i | 0.709239i | 0.935011 | + | 0.354619i | \(0.115390\pi\) | ||||
−0.935011 | + | 0.354619i | \(0.884610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −608.065 | −0.702965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 499.594i | 0.576233i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −418.294 | −0.481351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 401.232i | − 0.460657i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −157.514 | −0.180428 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 278.193i | 0.317935i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1385.19 | 1.57947 | 0.789734 | − | 0.613449i | \(-0.210218\pi\) | ||||
0.789734 | + | 0.613449i | \(0.210218\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 211.191i | − 0.240263i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −623.325 | −0.707520 | −0.353760 | − | 0.935336i | \(-0.615097\pi\) | ||||
−0.353760 | + | 0.935336i | \(0.615097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 636.791i | − 0.721168i | −0.932727 | − | 0.360584i | \(-0.882577\pi\) | ||||
0.932727 | − | 0.360584i | \(-0.117423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −864.276 | −0.976583 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 282.866i | − 0.318902i | −0.987206 | − | 0.159451i | \(-0.949028\pi\) | ||||
0.987206 | − | 0.159451i | \(-0.0509723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 345.459 | 0.388593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 39.4002i | − 0.0442202i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 146.642 | 0.164213 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 509.414i | 0.569177i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −293.147 | −0.326808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.7852i | 0.0398056i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.2561 | −0.0413497 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 320.986i | − 0.355466i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 756.414 | 0.835816 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1419.65i | 1.56521i | 0.622517 | + | 0.782607i | \(0.286110\pi\) | ||||
−0.622517 | + | 0.782607i | \(0.713890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −340.748 | −0.374860 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1170.46i | − 1.28481i | −0.766365 | − | 0.642405i | \(-0.777937\pi\) | ||||
0.766365 | − | 0.642405i | \(-0.222063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 506.294 | 0.554539 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1169.90i | 1.27858i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −188.348 | −0.205396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 944.239i | 1.02746i | 0.857951 | + | 0.513732i | \(0.171737\pi\) | ||||
−0.857951 | + | 0.513732i | \(0.828263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 583.927 | 0.634014 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1133.73i | 1.22831i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.2106 | 0.0499574 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 150.069i | 0.161887i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1253.20 | 1.34897 | 0.674487 | − | 0.738286i | \(-0.264365\pi\) | ||||
0.674487 | + | 0.738286i | \(0.264365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.5836i | 0.0274797i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 427.405 | 0.458097 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.2740i | 0.0195444i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 470.936 | 0.502600 | 0.251300 | − | 0.967909i | \(-0.419142\pi\) | ||||
0.251300 | + | 0.967909i | \(0.419142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 475.663i | − 0.506564i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 816.951 | 0.868173 | 0.434086 | − | 0.900871i | \(-0.357071\pi\) | ||||
0.434086 | + | 0.900871i | \(0.357071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 755.015i | 0.800652i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 76.7477 | 0.0812145 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 994.889i | − 1.05057i | −0.850927 | − | 0.525284i | \(-0.823959\pi\) | ||||
0.850927 | − | 0.525284i | \(-0.176041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 695.267 | 0.732631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 224.198i | − 0.235750i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1293.85 | −1.35766 | −0.678832 | − | 0.734293i | \(-0.737514\pi\) | ||||
−0.678832 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 596.970i | − 0.625099i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.1652 | −0.0158466 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 264.162i | − 0.275456i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 640.855 | 0.666862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 481.598i | − 0.500102i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 650.395 | 0.673985 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1071.60i | − 1.10817i | −0.832460 | − | 0.554085i | \(-0.813068\pi\) | ||||
0.832460 | − | 0.554085i | \(-0.186932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.73334 | −0.00488477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1433.12i | − 1.47593i | −0.674842 | − | 0.737963i | \(-0.735788\pi\) | ||||
0.674842 | − | 0.737963i | \(-0.264212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 429.670 | 0.441593 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 183.296i | 0.187995i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −126.559 | −0.129538 | −0.0647692 | − | 0.997900i | \(-0.520631\pi\) | ||||
−0.0647692 | + | 0.997900i | \(0.520631\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 152.802i | − 0.156080i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −615.909 | −0.627838 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.1480i | 0.0184619i | 0.999957 | + | 0.00923094i | \(0.00293834\pi\) | ||||
−0.999957 | + | 0.00923094i | \(0.997062\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 216.798 | 0.220100 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 183.868i | 0.186289i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 690.642 | 0.698324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 643.338i | − 0.649181i | −0.945855 | − | 0.324590i | \(-0.894774\pi\) | ||||
0.945855 | − | 0.324590i | \(-0.105226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 380.312 | 0.382993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1971.30i | − 1.98120i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −631.358 | −0.633257 | −0.316629 | − | 0.948550i | \(-0.602551\pi\) | ||||
−0.316629 | + | 0.948550i | \(0.602551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.9475i | 0.0389865i |
(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 | 1344.3.m.a.127.1 | 4 | ||
4.3 | odd | 2 | inner | 1344.3.m.a.127.3 | 4 | ||
8.3 | odd | 2 | 336.3.m.c.127.2 | ✓ | 4 | ||
8.5 | even | 2 | 336.3.m.c.127.4 | yes | 4 | ||
24.5 | odd | 2 | 1008.3.m.b.127.2 | 4 | |||
24.11 | even | 2 | 1008.3.m.b.127.1 | 4 | |||
56.13 | odd | 2 | 2352.3.m.f.1471.1 | 4 | |||
56.27 | even | 2 | 2352.3.m.f.1471.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.m.c.127.2 | ✓ | 4 | 8.3 | odd | 2 | ||
336.3.m.c.127.4 | yes | 4 | 8.5 | even | 2 | ||
1008.3.m.b.127.1 | 4 | 24.11 | even | 2 | |||
1008.3.m.b.127.2 | 4 | 24.5 | odd | 2 | |||
1344.3.m.a.127.1 | 4 | 1.1 | even | 1 | trivial | ||
1344.3.m.a.127.3 | 4 | 4.3 | odd | 2 | inner | ||
2352.3.m.f.1471.1 | 4 | 56.13 | odd | 2 | |||
2352.3.m.f.1471.3 | 4 | 56.27 | even | 2 |