Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(127,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, 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("336.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.m (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: | \(9.15533688251\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.127 |
Dual form | 336.3.m.c.127.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | \(-0.311470\pi\) | ||||
0.558258 | + | 0.829668i | \(0.311470\pi\) | |||||||
\(6\) | 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 | \(-0.270472\pi\) | ||||
0.660198 | + | 0.751091i | \(0.270472\pi\) | |||||||
\(14\) | 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 | \(-0.931237\pi\) | ||||
0.976757 | − | 0.214348i | \(-0.0687626\pi\) | |||||||
\(24\) | 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 | \(-0.510978\pi\) | ||||
−0.0344828 | + | 0.999405i | \(0.510978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 17.8926i | − 0.577181i | −0.957453 | − | 0.288590i | \(-0.906813\pi\) | ||||
0.957453 | − | 0.288590i | \(-0.0931866\pi\) | |||||||
\(32\) | 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 | \(-0.532297\pi\) | ||||
−0.101290 | + | 0.994857i | \(0.532297\pi\) | |||||||
\(38\) | 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 | \(-0.859626\pi\) | ||||
0.904326 | − | 0.426843i | \(-0.140374\pi\) | |||||||
\(48\) | 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 | \(-0.344234\pi\) | ||||
0.470054 | + | 0.882637i | \(0.344234\pi\) | |||||||
\(54\) | 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 | \(-0.959031\pi\) | ||||
−0.991729 | + | 0.128351i | \(0.959031\pi\) | |||||||
\(62\) | 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 | \(0.153992\pi\) | ||||
−0.885242 | + | 0.465130i | \(0.846008\pi\) | |||||||
\(72\) | 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 | \(0.206723\pi\) | ||||
−0.796423 | + | 0.604740i | \(0.793277\pi\) | |||||||
\(80\) | 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 | \(-0.690080\pi\) | ||||
−0.562290 | + | 0.826940i | \(0.690080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50.0230i | 0.485660i | 0.970069 | + | 0.242830i | \(0.0780758\pi\) | ||||
−0.970069 | + | 0.242830i | \(0.921924\pi\) | |||||||
\(104\) | 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 | \(-0.890826\pi\) | ||||
−0.941757 | + | 0.336294i | \(0.890826\pi\) | |||||||
\(110\) | 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 | \(0.171859\pi\) | ||||
−0.857754 | + | 0.514060i | \(0.828141\pi\) | |||||||
\(128\) | 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 | \(-0.0574166\pi\) | ||||
0.983776 | + | 0.179403i | \(0.0574166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 120.449i | 0.797677i | 0.917021 | + | 0.398839i | \(0.130587\pi\) | ||||
−0.917021 | + | 0.398839i | \(0.869413\pi\) | |||||||
\(152\) | 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 | \(-0.674902\pi\) | ||||
−0.522235 | + | 0.852802i | \(0.674902\pi\) | |||||||
\(158\) | 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 | \(0.237609\pi\) | ||||
−0.734090 | + | 0.679052i | \(0.762391\pi\) | |||||||
\(168\) | 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 | \(-0.601939\pi\) | ||||
−0.314803 | + | 0.949157i | \(0.601939\pi\) | |||||||
\(174\) | 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 | \(-0.377884\pi\) | ||||
0.374297 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(182\) | 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 | \(-0.909688\pi\) | ||||
0.960020 | − | 0.279933i | \(-0.0903123\pi\) | |||||||
\(192\) | 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 | \(-0.468575\pi\) | ||||
0.0985656 | + | 0.995131i | \(0.468575\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 353.116i | − 1.77445i | −0.461334 | − | 0.887227i | \(-0.652629\pi\) | ||||
0.461334 | − | 0.887227i | \(-0.347371\pi\) | |||||||
\(200\) | 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 | \(-0.932887\pi\) | ||||
0.977855 | − | 0.209283i | \(-0.0671129\pi\) | |||||||
\(224\) | 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 | \(-0.665740\pi\) | ||||
−0.497476 | + | 0.867478i | \(0.665740\pi\) | |||||||
\(230\) | 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 | \(-0.858518\pi\) | ||||
0.902834 | − | 0.429989i | \(-0.141482\pi\) | |||||||
\(240\) | 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 | \(0.0275120\pi\) | ||||
−0.996267 | + | 0.0863240i | \(0.972488\pi\) | |||||||
\(264\) | 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 | \(-0.622561\pi\) | ||||
−0.375593 | + | 0.926785i | \(0.622561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 279.798i | − 1.03246i | −0.856449 | − | 0.516232i | \(-0.827334\pi\) | ||||
0.856449 | − | 0.516232i | \(-0.172666\pi\) | |||||||
\(272\) | 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 | \(-0.421373\pi\) | ||||
0.244511 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(278\) | 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 | \(-0.566719\pi\) | ||||
−0.208073 | + | 0.978113i | \(0.566719\pi\) | |||||||
\(294\) | 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 | \(-0.870147\pi\) | ||||
0.917938 | − | 0.396724i | \(-0.129853\pi\) | |||||||
\(312\) | 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 | \(-0.565448\pi\) | ||||
−0.204165 | + | 0.978936i | \(0.565448\pi\) | |||||||
\(318\) | 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 | \(-0.228591\pi\) | ||||
0.753030 | + | 0.657986i | \(0.228591\pi\) | |||||||
\(350\) | 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 | \(-0.584722\pi\) | ||||
0.263030 | − | 0.964788i | \(-0.415278\pi\) | |||||||
\(360\) | 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 | \(0.274150\pi\) | ||||
−0.651476 | + | 0.758669i | \(0.725850\pi\) | |||||||
\(368\) | 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 | \(-0.236580\pi\) | ||||
0.736282 | + | 0.676674i | \(0.236580\pi\) | |||||||
\(374\) | 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 | \(-0.827774\pi\) | ||||
0.857162 | − | 0.515047i | \(-0.172226\pi\) | |||||||
\(384\) | 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 | \(-0.498371\pi\) | ||||
0.00511802 | + | 0.999987i | \(0.498371\pi\) | |||||||
\(390\) | 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 | \(-0.704936\pi\) | ||||
−0.600260 | + | 0.799805i | \(0.704936\pi\) | |||||||
\(398\) | 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 | \(-0.424144\pi\) | ||||
0.236060 | + | 0.971739i | \(0.424144\pi\) | |||||||
\(422\) | 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 | \(0.203299\pi\) | ||||
−0.802882 | + | 0.596138i | \(0.796701\pi\) | |||||||
\(432\) | 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 | \(0.0521269\pi\) | ||||
−0.986621 | + | 0.163031i | \(0.947873\pi\) | |||||||
\(440\) | 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 | \(-0.622035\pi\) | ||||
−0.374062 | + | 0.927404i | \(0.622035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 319.381i | 0.689807i | 0.938638 | + | 0.344903i | \(0.112088\pi\) | ||||
−0.938638 | + | 0.344903i | \(0.887912\pi\) | |||||||
\(464\) | 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 | \(0.121111\pi\) | ||||
−0.928486 | + | 0.371367i | \(0.878889\pi\) | |||||||
\(480\) | 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 | \(-0.712281\pi\) | ||||
0.618554 | − | 0.785742i | \(-0.287719\pi\) | |||||||
\(488\) | 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 | \(-0.829607\pi\) | ||||
0.860113 | − | 0.510104i | \(-0.170393\pi\) | |||||||
\(504\) | 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 | \(-0.384429\pi\) | ||||
0.355153 | + | 0.934808i | \(0.384429\pi\) | |||||||
\(510\) | 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 | \(-0.632180\pi\) | ||||
−0.403424 | + | 0.915013i | \(0.632180\pi\) | |||||||
\(542\) | 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 | \(-0.483370\pi\) | ||||
0.0522210 | + | 0.998636i | \(0.483370\pi\) | |||||||
\(558\) | 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 | \(-0.815394\pi\) | ||||
0.836487 | − | 0.547987i | \(-0.184606\pi\) | |||||||
\(600\) | 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 | \(0.0298253\pi\) | ||||
−0.995613 | + | 0.0935618i | \(0.970175\pi\) | |||||||
\(608\) | 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 | \(-0.497404\pi\) | ||||
0.00815661 | + | 0.999967i | \(0.497404\pi\) | |||||||
\(614\) | 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 | \(0.160423\pi\) | ||||
−0.875665 | + | 0.482918i | \(0.839577\pi\) | |||||||
\(632\) | 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 | \(0.350222\pi\) | ||||
−0.453369 | + | 0.891323i | \(0.649778\pi\) | |||||||
\(648\) | 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 | \(-0.775342\pi\) | ||||
−0.761103 | + | 0.648632i | \(0.775342\pi\) | |||||||
\(654\) | 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 | \(-0.494208\pi\) | ||||
0.0181956 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(662\) | 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 | \(-0.412857\pi\) | ||||
0.270361 | + | 0.962759i | \(0.412857\pi\) | |||||||
\(678\) | 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 | \(-0.563288\pi\) | ||||
−0.197517 | + | 0.980300i | \(0.563288\pi\) | |||||||
\(702\) | 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 | \(-0.488493\pi\) | ||||
0.0361414 | + | 0.999347i | \(0.488493\pi\) | |||||||
\(710\) | 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 | \(-0.785285\pi\) | ||||
0.780990 | − | 0.624543i | \(-0.214715\pi\) | |||||||
\(720\) | 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 | \(-0.976532\pi\) | ||||
0.997283 | − | 0.0736590i | \(-0.0234677\pi\) | |||||||
\(728\) | 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 | \(-0.620397\pi\) | ||||
−0.369283 | + | 0.929317i | \(0.620397\pi\) | |||||||
\(734\) | 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 | \(-0.869161\pi\) | ||||
0.916705 | − | 0.399564i | \(-0.130839\pi\) | |||||||
\(744\) | 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 | \(-0.790484\pi\) | ||||
0.791086 | − | 0.611705i | \(-0.209516\pi\) | |||||||
\(752\) | 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 | \(-0.880068\pi\) | ||||
−0.929855 | + | 0.367927i | \(0.880068\pi\) | |||||||
\(758\) | 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 | \(-0.478280\pi\) | ||||
0.0681813 | + | 0.997673i | \(0.478280\pi\) | |||||||
\(774\) | 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 | \(-0.559634\pi\) | ||||
−0.186252 | + | 0.982502i | \(0.559634\pi\) | |||||||
\(798\) | 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 | \(-0.691280\pi\) | ||||
−0.565405 | + | 0.824813i | \(0.691280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 396.291i | 0.481520i | 0.970585 | + | 0.240760i | \(0.0773966\pi\) | ||||
−0.970585 | + | 0.240760i | \(0.922603\pi\) | |||||||
\(824\) | 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 | \(-0.520571\pi\) | ||||
−0.0645804 | + | 0.997913i | \(0.520571\pi\) | |||||||
\(830\) | 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 | \(0.230151\pi\) | ||||
−0.749798 | + | 0.661667i | \(0.769849\pi\) | |||||||
\(840\) | 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 | \(-0.374061\pi\) | ||||
0.385408 | + | 0.922746i | \(0.374061\pi\) | |||||||
\(854\) | 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 | \(-0.884610\pi\) | ||||
0.935011 | − | 0.354619i | \(-0.115390\pi\) | |||||||
\(864\) | 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 | \(-0.789782\pi\) | ||||
−0.789734 | + | 0.613449i | \(0.789782\pi\) | |||||||
\(878\) | 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 | \(0.0509723\pi\) | ||||
−0.987206 | + | 0.159451i | \(0.949028\pi\) | |||||||
\(888\) | 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 | \(0.222063\pi\) | ||||
−0.766365 | + | 0.642405i | \(0.777937\pi\) | |||||||
\(912\) | 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 | \(-0.828263\pi\) | ||||
0.857951 | − | 0.513732i | \(-0.171737\pi\) | |||||||
\(920\) | 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 | \(-0.642929\pi\) | ||||
−0.434086 | + | 0.900871i | \(0.642929\pi\) | |||||||
\(942\) | 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 | \(0.186932\pi\) | ||||
−0.832460 | + | 0.554085i | \(0.813068\pi\) | |||||||
\(968\) | 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 | \(-0.997062\pi\) | ||||
0.999957 | − | 0.00923094i | \(-0.00293834\pi\) | |||||||
\(984\) | 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 | \(0.105226\pi\) | ||||
−0.945855 | + | 0.324590i | \(0.894774\pi\) | |||||||
\(992\) | 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 | \(-0.397449\pi\) | ||||
0.316629 | + | 0.948550i | \(0.397449\pi\) | |||||||
\(998\) | 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 | 336.3.m.c.127.2 | ✓ | 4 | |
3.2 | odd | 2 | 1008.3.m.b.127.1 | 4 | |||
4.3 | odd | 2 | inner | 336.3.m.c.127.4 | yes | 4 | |
7.6 | odd | 2 | 2352.3.m.f.1471.3 | 4 | |||
8.3 | odd | 2 | 1344.3.m.a.127.1 | 4 | |||
8.5 | even | 2 | 1344.3.m.a.127.3 | 4 | |||
12.11 | even | 2 | 1008.3.m.b.127.2 | 4 | |||
28.27 | even | 2 | 2352.3.m.f.1471.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.m.c.127.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
336.3.m.c.127.4 | yes | 4 | 4.3 | odd | 2 | inner | |
1008.3.m.b.127.1 | 4 | 3.2 | odd | 2 | |||
1008.3.m.b.127.2 | 4 | 12.11 | even | 2 | |||
1344.3.m.a.127.1 | 4 | 8.3 | odd | 2 | |||
1344.3.m.a.127.3 | 4 | 8.5 | even | 2 | |||
2352.3.m.f.1471.1 | 4 | 28.27 | even | 2 | |||
2352.3.m.f.1471.3 | 4 | 7.6 | odd | 2 |