Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,3,Mod(321,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.321");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.5340921606\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 64 x^{14} - 16 x^{13} + 2252 x^{12} + 648 x^{11} - 30106 x^{10} + 12360 x^{9} + \cdots + 1535848276 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.2 | ||
Root | \(-5.14043 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.321 |
Dual form | 460.3.f.a.321.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.14043 | −1.71348 | −0.856738 | − | 0.515752i | \(-0.827512\pi\) | ||||
−0.856738 | + | 0.515752i | \(0.827512\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.88014i | 1.12573i | 0.826547 | + | 0.562867i | \(0.190302\pi\) | ||||
−0.826547 | + | 0.562867i | \(0.809698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 17.4240 | 1.93600 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.98380i | − | 0.362163i | −0.983468 | − | 0.181082i | \(-0.942040\pi\) | ||
0.983468 | − | 0.181082i | \(-0.0579598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.5122 | 1.03940 | 0.519702 | − | 0.854348i | \(-0.326043\pi\) | ||||
0.519702 | + | 0.854348i | \(0.326043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11.4943i | − | 0.766290i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.06277i | 0.474280i | 0.971475 | + | 0.237140i | \(0.0762101\pi\) | ||||
−0.971475 | + | 0.237140i | \(0.923790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.96508i | − | 0.156057i | −0.996951 | − | 0.0780284i | \(-0.975138\pi\) | ||
0.996951 | − | 0.0780284i | \(-0.0248625\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 40.5073i | − | 1.92892i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.80075 | + | 22.4934i | −0.208728 | + | 0.977974i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −43.3029 | −1.60381 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.688711 | 0.0237487 | 0.0118743 | − | 0.999929i | \(-0.496220\pi\) | ||||
0.0118743 | + | 0.999929i | \(0.496220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.6485 | −1.18221 | −0.591105 | − | 0.806595i | \(-0.701308\pi\) | ||||
−0.591105 | + | 0.806595i | \(0.701308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.4784i | 0.620558i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.6205 | −0.503444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.63322i | − | 0.0981952i | −0.998794 | − | 0.0490976i | \(-0.984365\pi\) | ||
0.998794 | − | 0.0490976i | \(-0.0156345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −69.4587 | −1.78099 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.4636 | −0.791796 | −0.395898 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395898 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.5054i | 0.988497i | 0.869321 | + | 0.494248i | \(0.164557\pi\) | ||||
−0.869321 | + | 0.494248i | \(0.835443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 38.9612i | 0.865805i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −59.3870 | −1.26355 | −0.631777 | − | 0.775151i | \(-0.717674\pi\) | ||||
−0.631777 | + | 0.775151i | \(0.717674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.0966 | −0.267279 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 41.4461i | − | 0.812668i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 57.5176i | 1.08524i | 0.839979 | + | 0.542618i | \(0.182567\pi\) | ||||
−0.839979 | + | 0.542618i | \(0.817433\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.90804 | 0.161964 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.2418i | 0.267399i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.3686 | −0.429977 | −0.214989 | − | 0.976617i | \(-0.568971\pi\) | ||||
−0.214989 | + | 0.976617i | \(0.568971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 31.8220i | − | 0.521672i | −0.965383 | − | 0.260836i | \(-0.916002\pi\) | ||
0.965383 | − | 0.260836i | \(-0.0839981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 137.303i | 2.17942i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 30.2143i | 0.464835i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 108.405i | − | 1.61799i | −0.587819 | − | 0.808993i | \(-0.700013\pi\) | ||
0.587819 | − | 0.808993i | \(-0.299987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.6779 | − | 115.626i | 0.357651 | − | 1.67573i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −67.6191 | −0.952382 | −0.476191 | − | 0.879342i | \(-0.657983\pi\) | ||||
−0.476191 | + | 0.879342i | \(0.657983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −102.151 | −1.39933 | −0.699663 | − | 0.714473i | \(-0.746667\pi\) | ||||
−0.699663 | + | 0.714473i | \(0.746667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.7021 | 0.342695 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.3929 | 0.407700 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 48.5263i | − | 0.614257i | −0.951668 | − | 0.307128i | \(-0.900632\pi\) | ||
0.951668 | − | 0.307128i | \(-0.0993681\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 65.7793 | 0.812091 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.0389i | 0.879987i | 0.898001 | + | 0.439993i | \(0.145019\pi\) | ||||
−0.898001 | + | 0.439993i | \(0.854981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.0289 | −0.212105 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.54027 | −0.0406928 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 92.9465i | − | 1.04434i | −0.852840 | − | 0.522172i | \(-0.825122\pi\) | ||
0.852840 | − | 0.522172i | \(-0.174878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 106.478i | 1.17009i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 188.389 | 2.02569 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.63011 | 0.0697907 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 138.539i | − | 1.42824i | −0.700025 | − | 0.714119i | \(-0.746828\pi\) | ||
0.700025 | − | 0.714119i | \(-0.253172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 69.4136i | − | 0.701148i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 71.2312 | 0.705259 | 0.352630 | − | 0.935763i | \(-0.385288\pi\) | ||||
0.352630 | + | 0.935763i | \(0.385288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 173.582i | 1.68526i | 0.538492 | + | 0.842630i | \(0.318994\pi\) | ||||
−0.538492 | + | 0.842630i | \(0.681006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 90.5771 | 0.862639 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 88.3635i | − | 0.825827i | −0.910770 | − | 0.412914i | \(-0.864511\pi\) | ||
0.910770 | − | 0.412914i | \(-0.135489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 142.645i | 1.30867i | 0.756203 | + | 0.654337i | \(0.227052\pi\) | ||||
−0.756203 | + | 0.654337i | \(0.772948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.6763i | 0.168255i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 91.5083i | − | 0.809808i | −0.914359 | − | 0.404904i | \(-0.867305\pi\) | ||
0.914359 | − | 0.404904i | \(-0.132695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −50.2968 | − | 10.7348i | −0.437363 | − | 0.0933462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 235.437 | 2.01228 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −63.5358 | −0.533914 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 105.129 | 0.868838 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 166.877 | 1.35672 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 101.492 | 0.799147 | 0.399574 | − | 0.916701i | \(-0.369158\pi\) | ||||
0.399574 | + | 0.916701i | \(0.369158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 218.496i | − | 1.69377i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −43.9095 | −0.335187 | −0.167594 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167594 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.3652 | 0.175678 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 96.8282i | − | 0.717246i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 215.195i | 1.57077i | 0.619009 | + | 0.785384i | \(0.287535\pi\) | ||||
−0.619009 | + | 0.785384i | \(0.712465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 63.6545 | 0.457946 | 0.228973 | − | 0.973433i | \(-0.426463\pi\) | ||||
0.228973 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 305.275 | 2.16507 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 53.8300i | − | 0.376434i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.54001i | 0.0106207i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 67.3223 | 0.457975 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 97.7394i | 0.655969i | 0.944683 | + | 0.327985i | \(0.106369\pi\) | ||||
−0.944683 | + | 0.327985i | \(0.893631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −209.737 | −1.38899 | −0.694493 | − | 0.719500i | \(-0.744371\pi\) | ||||
−0.694493 | + | 0.719500i | \(0.744371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 140.486i | 0.918206i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 81.9485i | − | 0.528700i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 287.459i | 1.83095i | 0.402378 | + | 0.915474i | \(0.368184\pi\) | ||||
−0.402378 | + | 0.915474i | \(0.631816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 295.665i | − | 1.85953i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −177.251 | − | 37.8306i | −1.10094 | − | 0.234973i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 112.054 | 0.687446 | 0.343723 | − | 0.939071i | \(-0.388312\pi\) | ||||
0.343723 | + | 0.939071i | \(0.388312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −45.7911 | −0.277522 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −192.709 | −1.15394 | −0.576972 | − | 0.816764i | \(-0.695766\pi\) | ||||
−0.576972 | + | 0.816764i | \(0.695766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.5807 | 0.0803593 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 51.6635i | − | 0.302125i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −303.454 | −1.75407 | −0.877034 | − | 0.480429i | \(-0.840481\pi\) | ||||
−0.877034 | + | 0.480429i | \(0.840481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 39.4007i | − | 0.225147i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 130.406 | 0.736755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −94.6527 | −0.528786 | −0.264393 | − | 0.964415i | \(-0.585172\pi\) | ||||
−0.264393 | + | 0.964415i | \(0.585172\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 251.014i | − | 1.38682i | −0.720545 | − | 0.693408i | \(-0.756108\pi\) | ||
0.720545 | − | 0.693408i | \(-0.243892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 163.578i | 0.893871i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.12413 | 0.0439142 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.1204 | 0.171767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 341.233i | − | 1.80546i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 74.3125i | 0.389071i | 0.980895 | + | 0.194535i | \(0.0623199\pi\) | ||||
−0.980895 | + | 0.194535i | \(0.937680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −279.864 | −1.45007 | −0.725037 | − | 0.688710i | \(-0.758177\pi\) | ||||
−0.725037 | + | 0.688710i | \(0.758177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 155.314i | − | 0.796484i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −239.461 | −1.21554 | −0.607770 | − | 0.794113i | \(-0.707936\pi\) | ||||
−0.607770 | + | 0.794113i | \(0.707936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 302.424i | 1.51972i | 0.650087 | + | 0.759860i | \(0.274733\pi\) | ||||
−0.650087 | + | 0.759860i | \(0.725267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 557.248i | 2.77238i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.42714i | 0.0267347i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 72.5909i | − | 0.354102i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −83.6483 | + | 391.925i | −0.404098 | + | 1.89336i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.8123 | −0.0565180 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 313.131 | 1.48403 | 0.742016 | − | 0.670382i | \(-0.233870\pi\) | ||||
0.742016 | + | 0.670382i | \(0.233870\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 347.591 | 1.63188 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −95.0449 | −0.442069 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 288.795i | − | 1.33085i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 525.099 | 2.39771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 108.946i | 0.492969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −42.5933 | −0.191001 | −0.0955007 | − | 0.995429i | \(-0.530445\pi\) | ||||
−0.0955007 | + | 0.995429i | \(0.530445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −87.1199 | −0.387200 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 246.716i | − | 1.08686i | −0.839456 | − | 0.543428i | \(-0.817126\pi\) | ||
0.839456 | − | 0.543428i | \(-0.182874\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 192.536i | − | 0.840767i | −0.907347 | − | 0.420383i | \(-0.861896\pi\) | ||
0.907347 | − | 0.420383i | \(-0.138104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −161.373 | −0.698584 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 246.508 | 1.05797 | 0.528986 | − | 0.848630i | \(-0.322572\pi\) | ||||
0.528986 | + | 0.848630i | \(0.322572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 132.793i | − | 0.565078i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 249.446i | 1.05251i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −36.1050 | −0.151067 | −0.0755335 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755335 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 137.672i | 0.571253i | 0.958341 | + | 0.285627i | \(0.0922017\pi\) | ||||
−0.958341 | + | 0.285627i | \(0.907798\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 51.5919 | 0.212312 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 29.2850i | − | 0.119531i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 40.0648i | − | 0.162206i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 375.451i | − | 1.50784i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 60.0114i | − | 0.239089i | −0.992829 | − | 0.119545i | \(-0.961857\pi\) | ||
0.992829 | − | 0.119545i | \(-0.0381435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 89.6091 | + | 19.1252i | 0.354186 | + | 0.0755938i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 92.6762 | 0.363436 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −162.546 | −0.632475 | −0.316237 | − | 0.948680i | \(-0.602420\pi\) | ||||
−0.316237 | + | 0.948680i | \(0.602420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.6303 | 0.110542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0001 | 0.0459774 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 416.956i | − | 1.58539i | −0.609621 | − | 0.792693i | \(-0.708678\pi\) | ||
0.609621 | − | 0.792693i | \(-0.291322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −128.613 | −0.485333 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 477.785i | 1.78946i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −354.383 | −1.31741 | −0.658704 | − | 0.752402i | \(-0.728895\pi\) | ||||
−0.658704 | + | 0.752402i | \(0.728895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 430.921 | 1.59011 | 0.795056 | − | 0.606535i | \(-0.207441\pi\) | ||||
0.795056 | + | 0.606535i | \(0.207441\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 547.344i | − | 2.00492i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.9190i | 0.0724327i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8119 | −0.0643029 | −0.0321515 | − | 0.999483i | \(-0.510236\pi\) | ||||
−0.0321515 | + | 0.999483i | \(0.510236\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −638.563 | −2.28876 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 537.350i | 1.91228i | 0.292915 | + | 0.956138i | \(0.405375\pi\) | ||||
−0.292915 | + | 0.956138i | \(0.594625\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 227.251i | − | 0.803007i | −0.915858 | − | 0.401503i | \(-0.868488\pi\) | ||
0.915858 | − | 0.401503i | \(-0.131512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −34.0816 | −0.119585 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 255.818i | − | 0.891352i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 223.992 | 0.775058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 712.150i | 2.44725i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 570.580i | 1.94737i | 0.227896 | + | 0.973685i | \(0.426815\pi\) | ||||
−0.227896 | + | 0.973685i | \(0.573185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 56.7260i | − | 0.192292i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 172.510i | 0.580841i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −64.8690 | + | 303.936i | −0.216953 | + | 1.01651i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −334.948 | −1.11279 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −366.159 | −1.20844 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 71.1561 | 0.233299 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.4675 | −0.0568973 | −0.0284487 | − | 0.999595i | \(-0.509057\pi\) | ||||
−0.0284487 | + | 0.999595i | \(0.509057\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 892.285i | − | 2.88765i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −41.5565 | −0.133622 | −0.0668111 | − | 0.997766i | \(-0.521282\pi\) | ||||
−0.0668111 | + | 0.997766i | \(0.521282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 193.750i | − | 0.619011i | −0.950898 | − | 0.309505i | \(-0.899836\pi\) | ||
0.950898 | − | 0.309505i | \(-0.100164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −307.020 | −0.974666 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 292.088 | 0.921413 | 0.460707 | − | 0.887553i | \(-0.347596\pi\) | ||||
0.460707 | + | 0.887553i | \(0.347596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.74369i | − | 0.00860090i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 454.226i | 1.41503i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.9067 | 0.0740146 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −67.5612 | −0.207881 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 733.259i | − | 2.24238i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 467.978i | − | 1.42243i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 562.886 | 1.70056 | 0.850281 | − | 0.526329i | \(-0.176432\pi\) | ||||
0.850281 | + | 0.526329i | \(0.176432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 63.3052i | − | 0.190106i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 242.401 | 0.723585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 178.192i | 0.528759i | 0.964419 | + | 0.264379i | \(0.0851671\pi\) | ||||
−0.964419 | + | 0.264379i | \(0.914833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 470.392i | 1.38759i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 146.000i | 0.428153i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 282.924i | 0.824850i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 258.547 | + | 55.1815i | 0.749411 | + | 0.159946i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −462.453 | −1.33272 | −0.666359 | − | 0.745631i | \(-0.732148\pi\) | ||||
−0.666359 | + | 0.745631i | \(0.732148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 159.441 | 0.456850 | 0.228425 | − | 0.973562i | \(-0.426642\pi\) | ||||
0.228425 | + | 0.973562i | \(0.426642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −585.119 | −1.66701 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −474.031 | −1.34286 | −0.671432 | − | 0.741067i | \(-0.734320\pi\) | ||||
−0.671432 | + | 0.741067i | \(0.734320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 151.201i | − | 0.425918i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 326.601 | 0.914848 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 462.027i | 1.28698i | 0.765453 | + | 0.643492i | \(0.222515\pi\) | ||||
−0.765453 | + | 0.643492i | \(0.777485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 352.208 | 0.975646 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −540.410 | −1.48873 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 228.416i | − | 0.625798i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 215.737i | − | 0.587839i | −0.955830 | − | 0.293919i | \(-0.905040\pi\) | ||
0.955830 | − | 0.293919i | \(-0.0949597\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −565.646 | −1.53292 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −453.247 | −1.22169 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 137.933i | 0.369795i | 0.982758 | + | 0.184897i | \(0.0591952\pi\) | ||||
−0.982758 | + | 0.184897i | \(0.940805\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 57.4717i | 0.153258i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.30604 | 0.0246844 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4281i | 0.0407073i | 0.999793 | + | 0.0203536i | \(0.00647921\pi\) | ||||
−0.999793 | + | 0.0203536i | \(0.993521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −521.711 | −1.36932 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 713.842i | 1.86382i | 0.362694 | + | 0.931908i | \(0.381857\pi\) | ||||
−0.362694 | + | 0.931908i | \(0.618143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 70.1966i | 0.182329i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 740.613i | 1.91373i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 165.475i | 0.425385i | 0.977119 | + | 0.212692i | \(0.0682232\pi\) | ||||
−0.977119 | + | 0.212692i | \(0.931777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −181.359 | − | 38.7074i | −0.463834 | − | 0.0989958i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 225.714 | 0.574335 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 108.508 | 0.274704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −92.3570 | −0.232637 | −0.116319 | − | 0.993212i | \(-0.537109\pi\) | ||||
−0.116319 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −120.107 | −0.301021 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 162.145i | − | 0.404352i | −0.979349 | − | 0.202176i | \(-0.935199\pi\) | ||
0.979349 | − | 0.202176i | \(-0.0648013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −495.203 | −1.22879 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 147.087i | 0.363178i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.4740 | −0.0355627 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −91.8175 | −0.224493 | −0.112246 | − | 0.993680i | \(-0.535805\pi\) | ||||
−0.112246 | + | 0.993680i | \(0.535805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1106.20i | − | 2.69147i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 199.909i | − | 0.484040i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −163.320 | −0.393542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −327.211 | −0.784679 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 210.857i | − | 0.503238i | −0.967826 | − | 0.251619i | \(-0.919037\pi\) | ||
0.967826 | − | 0.251619i | \(-0.0809629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 557.635i | − | 1.32455i | −0.749261 | − | 0.662274i | \(-0.769591\pi\) | ||
0.749261 | − | 0.662274i | \(-0.230409\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1034.76 | −2.44624 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 40.3138i | − | 0.0948561i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 250.762 | 0.587264 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 276.709i | 0.645010i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 162.258i | − | 0.376469i | −0.982124 | − | 0.188234i | \(-0.939724\pi\) | ||
0.982124 | − | 0.188234i | \(-0.0602765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 465.859i | 1.07589i | 0.842981 | + | 0.537944i | \(0.180799\pi\) | ||||
−0.842981 | + | 0.537944i | \(0.819201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 7.91629i | − | 0.0181984i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 66.6947 | + | 14.2346i | 0.152619 | + | 0.0325735i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −112.072 | −0.255289 | −0.127644 | − | 0.991820i | \(-0.540742\pi\) | ||||
−0.127644 | + | 0.991820i | \(0.540742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −228.196 | −0.517451 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 765.565 | 1.72814 | 0.864069 | − | 0.503373i | \(-0.167908\pi\) | ||||
0.864069 | + | 0.503373i | \(0.167908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 207.835 | 0.467044 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 502.422i | − | 1.12399i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −167.225 | −0.372439 | −0.186220 | − | 0.982508i | \(-0.559624\pi\) | ||||
−0.186220 | + | 0.982508i | \(0.559624\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 129.329i | 0.286759i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1078.14 | 2.37999 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −238.093 | −0.523281 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 283.250i | − | 0.619804i | −0.950768 | − | 0.309902i | \(-0.899704\pi\) | ||
0.950768 | − | 0.309902i | \(-0.100296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 349.141i | − | 0.760656i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −98.1109 | −0.212822 | −0.106411 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106411 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 749.068 | 1.61786 | 0.808929 | − | 0.587907i | \(-0.200048\pi\) | ||||
0.808929 | + | 0.587907i | \(0.200048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 421.250i | 0.905915i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 71.8733i | − | 0.153904i | −0.997035 | − | 0.0769522i | \(-0.975481\pi\) | ||
0.997035 | − | 0.0769522i | \(-0.0245189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 854.247 | 1.82142 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1477.66i | − | 3.13728i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 169.333 | 0.357997 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8254i | 0.0312113i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1002.18i | 2.10102i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 624.966i | 1.30473i | 0.757905 | + | 0.652365i | \(0.226223\pi\) | ||||
−0.757905 | + | 0.652365i | \(0.773777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 49.0930i | − | 0.102064i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 911.146 | + | 194.466i | 1.88643 | + | 0.402620i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 309.783 | 0.638727 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 879.504 | 1.80596 | 0.902982 | − | 0.429679i | \(-0.141373\pi\) | ||||
0.902982 | + | 0.429679i | \(0.141373\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −576.004 | −1.17792 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 716.334 | 1.45893 | 0.729464 | − | 0.684019i | \(-0.239770\pi\) | ||||
0.729464 | + | 0.684019i | \(0.239770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.55292i | 0.0112635i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 155.214 | 0.313563 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 532.848i | − | 1.07213i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.6000 | −0.0693387 | −0.0346693 | − | 0.999399i | \(-0.511038\pi\) | ||||
−0.0346693 | + | 0.999399i | \(0.511038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 990.604 | 1.97725 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 287.726i | 0.572020i | 0.958227 | + | 0.286010i | \(0.0923291\pi\) | ||||
−0.958227 | + | 0.286010i | \(0.907671\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 159.278i | 0.315402i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −69.8107 | −0.137694 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 284.848 | 0.559624 | 0.279812 | − | 0.960055i | \(-0.409728\pi\) | ||||
0.279812 | + | 0.960055i | \(0.409728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 804.963i | − | 1.57527i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 128.396i | 0.250285i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −388.141 | −0.753672 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 236.586i | 0.457613i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1559.88 | 3.00555 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 195.190i | 0.374645i | 0.982298 | + | 0.187323i | \(0.0599810\pi\) | ||||
−0.982298 | + | 0.187323i | \(0.940019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.505041i | 0.000965661i | 1.00000 | 0.000482831i | \(0.000153690\pi\) | |||||
−1.00000 | 0.000482831i | \(0.999846\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 202.536i | 0.385784i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 295.488i | − | 0.560699i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −482.906 | − | 215.970i | −0.912865 | − | 0.408262i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −442.023 | −0.832435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −438.657 | −0.822995 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 197.587 | 0.369321 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 486.555 | 0.906062 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 52.1744i | 0.0967985i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 579.191 | 1.07059 | 0.535296 | − | 0.844664i | \(-0.320200\pi\) | ||||
0.535296 | + | 0.844664i | \(0.320200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1290.32i | 2.37628i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −318.965 | −0.585257 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 623.934 | 1.14065 | 0.570324 | − | 0.821420i | \(-0.306818\pi\) | ||||
0.570324 | + | 0.821420i | \(0.306818\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 554.465i | − | 1.00996i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.04208i | − | 0.00370614i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 382.394 | 0.691490 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −41.7615 | −0.0752460 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 445.491i | − | 0.799805i | −0.916558 | − | 0.399903i | \(-0.869044\pi\) | ||
0.916558 | − | 0.399903i | \(-0.130956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 574.343i | 1.02745i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −165.113 | −0.294319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 315.518i | − | 0.560422i | −0.959938 | − | 0.280211i | \(-0.909595\pi\) | ||
0.959938 | − | 0.280211i | \(-0.0904045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 204.619 | 0.362157 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 518.351i | 0.914199i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 954.594i | 1.67767i | 0.544386 | + | 0.838835i | \(0.316763\pi\) | ||||
−0.544386 | + | 0.838835i | \(0.683237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 266.616i | − | 0.466929i | −0.972365 | − | 0.233464i | \(-0.924994\pi\) | ||
0.972365 | − | 0.233464i | \(-0.0750062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 381.998i | − | 0.666663i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0038 | − | 112.467i | 0.0417457 | − | 0.195595i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1069.07 | −1.85280 | −0.926401 | − | 0.376539i | \(-0.877114\pi\) | ||||
−0.926401 | + | 0.376539i | \(0.877114\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1438.62 | 2.48466 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −575.557 | −0.990632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 229.138 | 0.393033 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 526.453i | 0.899920i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1065.52 | −1.81520 | −0.907600 | − | 0.419835i | \(-0.862088\pi\) | ||||
−0.907600 | + | 0.419835i | \(0.862088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 108.666i | 0.184492i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1230.93 | 2.08280 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −337.936 | −0.569875 | −0.284938 | − | 0.958546i | \(-0.591973\pi\) | ||||
−0.284938 | + | 0.958546i | \(0.591973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 142.070i | − | 0.238774i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1554.59i | − | 2.60400i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 549.708 | 0.917709 | 0.458854 | − | 0.888511i | \(-0.348260\pi\) | ||||
0.458854 | + | 0.888511i | \(0.348260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −375.387 | −0.624605 | −0.312302 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312302 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1888.85i | − | 3.13242i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 235.076i | 0.388556i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 440.263 | 0.725309 | 0.362654 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362654 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 27.8978i | − | 0.0458093i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −802.452 | −1.31334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 49.5676i | 0.0808607i | 0.999182 | + | 0.0404303i | \(0.0128729\pi\) | ||||
−0.999182 | + | 0.0404303i | \(0.987127\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 373.148i | 0.606745i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 785.550i | − | 1.27318i | −0.771204 | − | 0.636588i | \(-0.780345\pi\) | ||
0.771204 | − | 0.636588i | \(-0.219655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 693.014i | 1.11957i | 0.828638 | + | 0.559785i | \(0.189116\pi\) | ||||
−0.828638 | + | 0.559785i | \(0.810884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 207.886 | − | 974.028i | 0.334761 | − | 1.56848i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 732.432 | 1.17565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 60.7201 | 0.0968422 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.2938 | 0.0465721 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.68025i | 0.0153411i | 0.999971 | + | 0.00767056i | \(0.00244164\pi\) | ||||
−0.999971 | + | 0.00767056i | \(0.997558\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1609.63 | −2.54285 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 226.942i | 0.357389i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −176.965 | −0.277810 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1178.19 | −1.84381 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 174.812i | − | 0.272718i | −0.990659 | − | 0.136359i | \(-0.956460\pi\) | ||
0.990659 | − | 0.136359i | \(-0.0435401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 285.997i | 0.444785i | 0.974957 | + | 0.222393i | \(0.0713867\pi\) | ||||
−0.974957 | + | 0.222393i | \(0.928613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 488.571 | 0.757475 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 698.951 | 1.08030 | 0.540148 | − | 0.841570i | \(-0.318368\pi\) | ||||
0.540148 | + | 0.841570i | \(0.318368\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 101.064i | 0.155722i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1484.53i | 2.28039i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −639.144 | −0.978781 | −0.489390 | − | 0.872065i | \(-0.662781\pi\) | ||||
−0.489390 | + | 0.872065i | \(0.662781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 98.1846i | − | 0.149900i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1779.87 | −2.70909 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1204.48i | − | 1.82774i | −0.406004 | − | 0.913871i | \(-0.633078\pi\) | ||
0.406004 | − | 0.913871i | \(-0.366922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 442.012i | 0.668702i | 0.942449 | + | 0.334351i | \(0.108517\pi\) | ||||
−0.942449 | + | 0.334351i | \(0.891483\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 560.029i | − | 0.844690i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 52.2462i | 0.0785658i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.30633 | + | 15.4915i | −0.00495702 | + | 0.0232256i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 218.948 | 0.327276 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −126.772 | −0.188930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 401.763 | 0.596974 | 0.298487 | − | 0.954414i | \(-0.403518\pi\) | ||||
0.298487 | + | 0.954414i | \(0.403518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 216.514 | 0.320762 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 575.340i | − | 0.849838i | −0.905231 | − | 0.424919i | \(-0.860303\pi\) | ||
0.905231 | − | 0.424919i | \(-0.139697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1091.71 | 1.60782 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1268.23i | 1.86230i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −148.111 | −0.216854 | −0.108427 | − | 0.994104i | \(-0.534581\pi\) | ||||
−0.108427 | + | 0.994104i | \(0.534581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −481.191 | −0.702469 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 989.715i | 1.44063i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 777.191i | 1.12800i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −176.640 | −0.255629 | −0.127815 | − | 0.991798i | \(-0.540796\pi\) | ||||
−0.127815 | + | 0.991798i | \(0.540796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 546.989 | 0.789306 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 142.336i | 0.204800i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 261.747i | − | 0.375533i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1267.15 | −1.81281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 179.122i | 0.255524i | 0.991805 | + | 0.127762i | \(0.0407793\pi\) | ||||
−0.991805 | + | 0.127762i | \(0.959221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7728 | −0.0153240 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 682.615i | 0.968248i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 561.312i | 0.793935i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 612.124i | 0.863363i | 0.902026 | + | 0.431681i | \(0.142080\pi\) | ||||
−0.902026 | + | 0.431681i | \(0.857920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 845.521i | − | 1.18920i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 175.940 | − | 824.349i | 0.246761 | − | 1.15617i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 120.368 | 0.168346 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 185.595 | 0.258850 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −332.970 | −0.463102 | −0.231551 | − | 0.972823i | \(-0.574380\pi\) | ||||
−0.231551 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1367.85 | −1.89716 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 707.693i | − | 0.978829i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.44356 | −0.00474973 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 363.921i | − | 0.500579i | −0.968171 | − | 0.250290i | \(-0.919474\pi\) | ||
0.968171 | − | 0.250290i | \(-0.0805258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −857.219 | −1.17588 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −342.711 | −0.468825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 414.694i | − | 0.565749i | −0.959157 | − | 0.282875i | \(-0.908712\pi\) | ||
0.959157 | − | 0.282875i | \(-0.0912880\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 150.537i | 0.204813i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −431.864 | −0.585975 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −750.501 | −1.01556 | −0.507782 | − | 0.861486i | \(-0.669534\pi\) | ||||
−0.507782 | + | 0.861486i | \(0.669534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 205.950i | 0.277936i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1301.85i | 1.75215i | 0.482171 | + | 0.876077i | \(0.339848\pi\) | ||||
−0.482171 | + | 0.876077i | \(0.660152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −218.552 | −0.293358 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1272.63i | 1.70365i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 696.317 | 0.929662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 860.771i | − | 1.14617i | −0.819497 | − | 0.573083i | \(-0.805747\pi\) | ||
0.819497 | − | 0.573083i | \(-0.194253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 308.484i | 0.409674i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 468.986i | − | 0.621173i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 281.079i | 0.371306i | 0.982615 | + | 0.185653i | \(0.0594400\pi\) | ||||
−0.982615 | + | 0.185653i | \(0.940560\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −460.629 | − | 98.3118i | −0.606889 | − | 0.129528i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 155.150 | 0.203877 | 0.101938 | − | 0.994791i | \(-0.467496\pi\) | ||||
0.101938 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1124.07 | −1.47322 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −314.135 | −0.410634 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −342.787 | −0.446920 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1242.19i | 1.61533i | 0.589642 | + | 0.807665i | \(0.299269\pi\) | ||||
−0.589642 | + | 0.807665i | \(0.700731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 835.556 | 1.08373 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1105.56i | − | 1.43022i | −0.699014 | − | 0.715108i | \(-0.746377\pi\) | ||
0.699014 | − | 0.715108i | \(-0.253623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 183.242 | 0.236442 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −147.172 | −0.189411 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 96.2572i | 0.123565i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 269.381i | 0.344918i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.8232 | −0.0380884 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −642.777 | −0.818825 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 166.440i | 0.211486i | 0.994393 | + | 0.105743i | \(0.0337221\pi\) | ||||
−0.994393 | + | 0.105743i | \(0.966278\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2143.33i | 2.71652i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 721.098 | 0.911629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 429.986i | − | 0.542227i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 661.126 | 0.831606 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 702.946i | − | 0.881990i | −0.897510 | − | 0.440995i | \(-0.854626\pi\) | ||
0.897510 | − | 0.440995i | \(-0.145374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 478.824i | − | 0.599279i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1619.50i | − | 2.02185i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 406.948i | 0.506785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 84.5919 | − | 396.346i | 0.105083 | − | 0.492355i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1821.68 | 2.25735 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 612.933 | 0.757643 | 0.378822 | − | 0.925470i | \(-0.376329\pi\) | ||||
0.378822 | + | 0.925470i | \(0.376329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −664.035 | −0.818785 | −0.409393 | − | 0.912358i | \(-0.634259\pi\) | ||||
−0.409393 | + | 0.912358i | \(0.634259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2215.12 | −2.72462 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 250.560i | 0.307435i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 126.032 | 0.154262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1855.28i | 2.26530i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 598.546 | 0.729046 | 0.364523 | − | 0.931194i | \(-0.381232\pi\) | ||||
0.364523 | + | 0.931194i | \(0.381232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1216.57 | 1.47821 | 0.739105 | − | 0.673591i | \(-0.235249\pi\) | ||||
0.739105 | + | 0.673591i | \(0.235249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 102.392i | − | 0.124112i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 719.387i | − | 0.869875i | −0.900461 | − | 0.434937i | \(-0.856770\pi\) | ||
0.900461 | − | 0.434937i | \(-0.143230\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −340.645 | −0.410911 | −0.205455 | − | 0.978666i | \(-0.565868\pi\) | ||||
−0.205455 | + | 0.978666i | \(0.565868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 91.5608 | 0.110181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 105.595i | − | 0.126765i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 430.909i | − | 0.516059i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1586.98 | 1.89604 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.11326i | 0.0108621i | 0.999985 | + | 0.00543103i | \(0.00172876\pi\) | ||||
−0.999985 | + | 0.00543103i | \(0.998271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −840.526 | −0.999436 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2762.21i | − | 3.27664i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.3674i | 0.0359378i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 828.434i | 0.978081i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1168.17i | 1.37593i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 81.7235 | + | 17.4422i | 0.0960323 | + | 0.0204961i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1029.00 | −1.20633 | −0.603163 | − | 0.797618i | \(-0.706093\pi\) | ||||
−0.603163 | + | 0.797618i | \(0.706093\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 115.523 | 0.135115 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 606.460 | 0.707654 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1147.62 | 1.33600 | 0.668001 | − | 0.744161i | \(-0.267150\pi\) | ||||
0.668001 | + | 0.744161i | \(0.267150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1315.01i | 1.52731i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1299.38 | −1.50566 | −0.752829 | − | 0.658216i | \(-0.771311\pi\) | ||||
−0.752829 | + | 0.658216i | \(0.771311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 678.543i | − | 0.784443i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1151.41 | −1.32804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −193.319 | −0.222461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1464.80i | − | 1.68174i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2413.90i | − | 2.76507i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 88.1027 | 0.100689 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −869.529 | −0.991482 | −0.495741 | − | 0.868470i | \(-0.665103\pi\) | ||||
−0.495741 | + | 0.868470i | \(0.665103\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2933.02i | − | 3.33677i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1210.10i | 1.37355i | 0.726869 | + | 0.686776i | \(0.240975\pi\) | ||||
−0.726869 | + | 0.686776i | \(0.759025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 275.674 | 0.312202 | 0.156101 | − | 0.987741i | \(-0.450107\pi\) | ||||
0.156101 | + | 0.987741i | \(0.450107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 291.596i | 0.329487i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 742.524 | 0.837119 | 0.418559 | − | 0.908189i | \(-0.362535\pi\) | ||||
0.418559 | + | 0.908189i | \(0.362535\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 799.769i | 0.899628i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 262.052i | − | 0.294109i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 176.087i | 0.197186i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 211.650i | − | 0.236480i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 333.454 | − | 1562.36i | 0.371744 | − | 1.74176i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.2402 | −0.0280759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −463.751 | −0.514707 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1721.78 | 1.90673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 561.284 | 0.620203 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1335.53i | 1.47247i | 0.676727 | + | 0.736234i | \(0.263398\pi\) | ||||
−0.676727 | + | 0.736234i | \(0.736602\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1241.13 | 1.36538 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 511.312i | − | 0.561265i | −0.959815 | − | 0.280632i | \(-0.909456\pi\) | ||
0.959815 | − | 0.280632i | \(-0.0905442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 290.972 | 0.318699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −365.773 | −0.399751 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 346.013i | − | 0.377332i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 712.793i | 0.775618i | 0.921740 | + | 0.387809i | \(0.126768\pi\) | ||||
−0.921740 | + | 0.387809i | \(0.873232\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 89.7903 | 0.0974921 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −913.686 | −0.989909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.1661i | 0.0196390i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3024.49i | 3.26266i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 86.3665 | 0.0929672 | 0.0464836 | − | 0.998919i | \(-0.485198\pi\) | ||||
0.0464836 | + | 0.998919i | \(0.485198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.8326i | 0.0417106i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 213.618 | 0.228958 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 71.8235i | 0.0768165i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 994.559i | 1.06143i | 0.847551 | + | 0.530714i | \(0.178076\pi\) | ||||
−0.847551 | + | 0.530714i | \(0.821924\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 995.960i | 1.06066i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1456.29i | 1.54760i | 0.633429 | + | 0.773800i | \(0.281647\pi\) | ||||
−0.633429 | + | 0.773800i | \(0.718353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 155.850 | − | 730.217i | 0.165270 | − | 0.774356i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 763.020 | 0.807428 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −206.079 | −0.217613 | −0.108806 | − | 0.994063i | \(-0.534703\pi\) | ||||
−0.108806 | + | 0.994063i | \(0.534703\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1380.29 | −1.45446 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1501.46 | −1.57882 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 457.750i | 0.480325i | 0.970733 | + | 0.240163i | \(0.0772007\pi\) | ||||
−0.970733 | + | 0.240163i | \(0.922799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −166.168 | −0.173998 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.1037i | 0.0147374i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1695.77 | −1.76827 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 382.112 | 0.397619 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1539.64i | − | 1.59880i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 625.795i | − | 0.648492i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −942.336 | −0.974495 | −0.487247 | − | 0.873264i | \(-0.661999\pi\) | ||||
−0.487247 | + | 0.873264i | \(0.661999\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −122.891 | −0.126822 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 218.442i | 0.224966i | 0.993654 | + | 0.112483i | \(0.0358804\pi\) | ||||
−0.993654 | + | 0.112483i | \(0.964120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 501.607i | 0.515526i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 347.293 | 0.356198 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 378.433i | 0.387342i | 0.981067 | + | 0.193671i | \(0.0620394\pi\) | ||||
−0.981067 | + | 0.193671i | \(0.937961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −370.280 | −0.378223 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2485.45i | 2.53359i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1359.48i | − | 1.38299i | −0.722381 | − | 0.691495i | \(-0.756952\pi\) | ||
0.722381 | − | 0.691495i | \(-0.243048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 535.452i | − | 0.543606i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2405.61i | 2.43729i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −956.090 | − | 204.058i | −0.966724 | − | 0.206327i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −648.537 | −0.654426 | −0.327213 | − | 0.944951i | \(-0.606110\pi\) | ||||
−0.327213 | + | 0.944951i | \(0.606110\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2893.47 | −2.91387 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −676.241 | −0.679640 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −155.843 | −0.156312 | −0.0781562 | − | 0.996941i | \(-0.524903\pi\) | ||||
−0.0781562 | + | 0.996941i | \(0.524903\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 157.329i | 0.157486i |
(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 | 460.3.f.a.321.2 | yes | 16 | |
3.2 | odd | 2 | 4140.3.d.a.2161.7 | 16 | |||
4.3 | odd | 2 | 1840.3.k.c.321.16 | 16 | |||
5.2 | odd | 4 | 2300.3.d.b.1149.30 | 32 | |||
5.3 | odd | 4 | 2300.3.d.b.1149.3 | 32 | |||
5.4 | even | 2 | 2300.3.f.e.1701.15 | 16 | |||
23.22 | odd | 2 | inner | 460.3.f.a.321.1 | ✓ | 16 | |
69.68 | even | 2 | 4140.3.d.a.2161.10 | 16 | |||
92.91 | even | 2 | 1840.3.k.c.321.15 | 16 | |||
115.22 | even | 4 | 2300.3.d.b.1149.4 | 32 | |||
115.68 | even | 4 | 2300.3.d.b.1149.29 | 32 | |||
115.114 | odd | 2 | 2300.3.f.e.1701.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.3.f.a.321.1 | ✓ | 16 | 23.22 | odd | 2 | inner | |
460.3.f.a.321.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1840.3.k.c.321.15 | 16 | 92.91 | even | 2 | |||
1840.3.k.c.321.16 | 16 | 4.3 | odd | 2 | |||
2300.3.d.b.1149.3 | 32 | 5.3 | odd | 4 | |||
2300.3.d.b.1149.4 | 32 | 115.22 | even | 4 | |||
2300.3.d.b.1149.29 | 32 | 115.68 | even | 4 | |||
2300.3.d.b.1149.30 | 32 | 5.2 | odd | 4 | |||
2300.3.f.e.1701.15 | 16 | 5.4 | even | 2 | |||
2300.3.f.e.1701.16 | 16 | 115.114 | odd | 2 | |||
4140.3.d.a.2161.7 | 16 | 3.2 | odd | 2 | |||
4140.3.d.a.2161.10 | 16 | 69.68 | even | 2 |