Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(521,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.521");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.10 | ||
Character | \(\chi\) | \(=\) | 1764.521 |
Dual form | 1764.4.t.c.1097.10 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.27916 | − | 5.67967i | −0.293297 | − | 0.508005i | 0.681290 | − | 0.732013i | \(-0.261419\pi\) |
−0.974587 | + | 0.224008i | \(0.928086\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.2427 | − | 19.7700i | −0.938596 | − | 0.541899i | −0.0490760 | − | 0.998795i | \(-0.515628\pi\) |
−0.889520 | + | 0.456896i | \(0.848961\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 79.8324i | − | 1.70319i | −0.524197 | − | 0.851597i | \(-0.675635\pi\) | ||
0.524197 | − | 0.851597i | \(-0.324365\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −34.1569 | + | 59.1615i | −0.487310 | + | 0.844045i | −0.999894 | − | 0.0145918i | \(-0.995355\pi\) |
0.512584 | + | 0.858637i | \(0.328688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.89034 | − | 5.71019i | 0.119421 | − | 0.0689478i | −0.439100 | − | 0.898438i | \(-0.644702\pi\) |
0.558521 | + | 0.829491i | \(0.311369\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 118.003 | − | 68.1289i | 1.06979 | − | 0.617646i | 0.141669 | − | 0.989914i | \(-0.454753\pi\) |
0.928125 | + | 0.372268i | \(0.121420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.9942 | − | 71.0040i | 0.327954 | − | 0.568032i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.32277i | 0.0596964i | 0.999554 | + | 0.0298482i | \(0.00950239\pi\) | ||||
−0.999554 | + | 0.0298482i | \(0.990498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −69.9858 | − | 40.4063i | −0.405478 | − | 0.234103i | 0.283367 | − | 0.959012i | \(-0.408549\pi\) |
−0.688845 | + | 0.724909i | \(0.741882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −117.636 | − | 203.751i | −0.522681 | − | 0.905309i | −0.999652 | − | 0.0263904i | \(-0.991599\pi\) |
0.476971 | − | 0.878919i | \(-0.341735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 50.7669 | 0.193377 | 0.0966886 | − | 0.995315i | \(-0.469175\pi\) | ||||
0.0966886 | + | 0.995315i | \(0.469175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.3676 | −0.0864191 | −0.0432096 | − | 0.999066i | \(-0.513758\pi\) | ||||
−0.0432096 | + | 0.999066i | \(0.513758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −114.479 | − | 198.284i | −0.355287 | − | 0.615376i | 0.631880 | − | 0.775066i | \(-0.282284\pi\) |
−0.987167 | + | 0.159691i | \(0.948950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 413.578 | + | 238.780i | 1.07187 | + | 0.618847i | 0.928693 | − | 0.370849i | \(-0.120933\pi\) |
0.143182 | + | 0.989696i | \(0.454267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 259.316i | 0.635749i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 194.591 | − | 337.042i | 0.429384 | − | 0.743714i | −0.567435 | − | 0.823418i | \(-0.692064\pi\) |
0.996819 | + | 0.0797038i | \(0.0253975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −345.404 | + | 199.419i | −0.724992 | + | 0.418574i | −0.816587 | − | 0.577222i | \(-0.804137\pi\) |
0.0915953 | + | 0.995796i | \(0.470803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −453.422 | + | 261.783i | −0.865232 | + | 0.499542i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −377.437 | + | 653.740i | −0.688228 | + | 1.19205i | 0.284182 | + | 0.958770i | \(0.408278\pi\) |
−0.972411 | + | 0.233276i | \(0.925055\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 799.714i | 1.33674i | 0.743829 | + | 0.668370i | \(0.233008\pi\) | ||||
−0.743829 | + | 0.668370i | \(0.766992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −523.232 | − | 302.088i | −0.838900 | − | 0.484339i | 0.0179900 | − | 0.999838i | \(-0.494273\pi\) |
−0.856890 | + | 0.515499i | \(0.827607\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −22.9193 | − | 39.6975i | −0.0326408 | − | 0.0565356i | 0.849244 | − | 0.528001i | \(-0.177058\pi\) |
−0.881884 | + | 0.471466i | \(0.843725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 45.6855 | 0.0604172 | 0.0302086 | − | 0.999544i | \(-0.490383\pi\) | ||||
0.0302086 | + | 0.999544i | \(0.490383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 448.024 | 0.571706 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −163.313 | − | 282.867i | −0.194508 | − | 0.336897i | 0.752231 | − | 0.658899i | \(-0.228978\pi\) |
−0.946739 | + | 0.322002i | \(0.895644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −64.8640 | − | 37.4493i | −0.0700517 | − | 0.0404444i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 109.900i | − | 0.115038i | −0.998344 | − | 0.0575191i | \(-0.981681\pi\) | ||
0.998344 | − | 0.0575191i | \(-0.0183190\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −988.707 | + | 1712.49i | −0.974059 | + | 1.68712i | −0.291054 | + | 0.956707i | \(0.594006\pi\) |
−0.683005 | + | 0.730414i | \(0.739327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1519.02 | − | 877.006i | 1.45314 | − | 0.838971i | 0.454481 | − | 0.890756i | \(-0.349825\pi\) |
0.998658 | + | 0.0517856i | \(0.0164912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 628.349 | − | 362.777i | 0.567708 | − | 0.327767i | −0.188525 | − | 0.982068i | \(-0.560371\pi\) |
0.756234 | + | 0.654302i | \(0.227037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 297.498 | − | 515.281i | 0.261423 | − | 0.452798i | −0.705197 | − | 0.709011i | \(-0.749142\pi\) |
0.966620 | + | 0.256213i | \(0.0824748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 311.261i | 0.259123i | 0.991571 | + | 0.129562i | \(0.0413570\pi\) | ||||
−0.991571 | + | 0.129562i | \(0.958643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −773.900 | − | 446.811i | −0.627535 | − | 0.362308i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 116.207 | + | 201.277i | 0.0873082 | + | 0.151222i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1357.50 | −0.971346 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2397.08 | −1.67485 | −0.837426 | − | 0.546551i | \(-0.815940\pi\) | ||||
−0.837426 | + | 0.546551i | \(0.815940\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −667.091 | − | 1155.44i | −0.444916 | − | 0.770618i | 0.553130 | − | 0.833095i | \(-0.313433\pi\) |
−0.998046 | + | 0.0624773i | \(0.980100\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 983.475 | + | 567.809i | 0.613313 | + | 0.354097i | 0.774261 | − | 0.632866i | \(-0.218122\pi\) |
−0.160948 | + | 0.986963i | \(0.551455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1869.35i | − | 1.14069i | −0.821404 | − | 0.570347i | \(-0.806809\pi\) | ||
0.821404 | − | 0.570347i | \(-0.193191\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1578.29 | + | 2733.67i | −0.922958 | + | 1.59861i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 52.9503 | − | 30.5709i | 0.0303261 | − | 0.0175088i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −846.445 | + | 488.695i | −0.465392 | + | 0.268694i | −0.714309 | − | 0.699830i | \(-0.753259\pi\) |
0.248916 | + | 0.968525i | \(0.419926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −517.459 | + | 896.266i | −0.278876 | + | 0.483027i | −0.971106 | − | 0.238650i | \(-0.923295\pi\) |
0.692230 | + | 0.721677i | \(0.256628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 529.995i | 0.274647i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −54.0241 | − | 31.1908i | −0.0274624 | − | 0.0158554i | 0.486206 | − | 0.873844i | \(-0.338380\pi\) |
−0.513668 | + | 0.857989i | \(0.671714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −198.891 | − | 344.489i | −0.0955725 | − | 0.165536i | 0.814275 | − | 0.580479i | \(-0.197135\pi\) |
−0.909847 | + | 0.414943i | \(0.863802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2001.69 | 0.927519 | 0.463759 | − | 0.885961i | \(-0.346500\pi\) | ||||
0.463759 | + | 0.885961i | \(0.346500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4176.21 | −1.90087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −999.942 | − | 1731.95i | −0.439446 | − | 0.761143i | 0.558201 | − | 0.829706i | \(-0.311492\pi\) |
−0.997647 | + | 0.0685630i | \(0.978159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3289.27 | + | 1899.06i | 1.37347 | + | 0.792975i | 0.991363 | − | 0.131143i | \(-0.0418647\pi\) |
0.382109 | + | 0.924117i | \(0.375198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2540.89i | 1.04344i | 0.853116 | + | 0.521720i | \(0.174710\pi\) | ||||
−0.853116 | + | 0.521720i | \(0.825290\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −771.493 | + | 1336.26i | −0.306601 | + | 0.531049i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2339.25 | − | 1350.57i | 0.914774 | − | 0.528145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4534.50 | + | 2618.00i | −1.71783 | + | 0.991789i | −0.794970 | + | 0.606649i | \(0.792513\pi\) |
−0.922858 | + | 0.385140i | \(0.874153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2557.59 | + | 4429.88i | −0.953883 | + | 1.65217i | −0.216980 | + | 0.976176i | \(0.569621\pi\) |
−0.736903 | + | 0.675998i | \(0.763713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3849.94i | 1.39237i | 0.717862 | + | 0.696186i | \(0.245121\pi\) | ||||
−0.717862 | + | 0.696186i | \(0.754879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2104.82 | − | 1215.22i | −0.749782 | − | 0.432887i | 0.0758329 | − | 0.997121i | \(-0.475838\pi\) |
−0.825615 | + | 0.564233i | \(0.809172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −166.473 | − | 288.340i | −0.0567170 | − | 0.0982366i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −451.562 | −0.149451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4284.81 | 1.39800 | 0.699000 | − | 0.715121i | \(-0.253629\pi\) | ||||
0.699000 | + | 0.715121i | \(0.253629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 79.9053 | + | 138.400i | 0.0253465 | + | 0.0439014i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4723.00 | + | 2726.83i | 1.43757 | + | 0.829983i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1484.34i | 0.445735i | 0.974849 | + | 0.222868i | \(0.0715418\pi\) | ||||
−0.974849 | + | 0.222868i | \(0.928458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2355.84 | + | 4080.44i | −0.688823 | + | 1.19308i | 0.283396 | + | 0.959003i | \(0.408539\pi\) |
−0.972219 | + | 0.234073i | \(0.924794\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3382.78 | − | 1953.05i | 0.976160 | − | 0.563586i | 0.0750511 | − | 0.997180i | \(-0.476088\pi\) |
0.901108 | + | 0.433594i | \(0.142755\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2409.55 | − | 1391.15i | 0.677489 | − | 0.391148i | −0.121419 | − | 0.992601i | \(-0.538745\pi\) |
0.798908 | + | 0.601453i | \(0.205411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −750.791 | + | 1300.41i | −0.208409 | + | 0.360976i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6237.16i | 1.68807i | 0.536289 | + | 0.844034i | \(0.319826\pi\) | ||||
−0.536289 | + | 0.844034i | \(0.680174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5102.67 | − | 2946.03i | −1.36387 | − | 0.787429i | −0.373732 | − | 0.927537i | \(-0.621922\pi\) |
−0.990136 | + | 0.140107i | \(0.955255\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −455.858 | − | 789.569i | −0.117431 | − | 0.203397i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4252.57 | −1.06940 | −0.534701 | − | 0.845041i | \(-0.679576\pi\) | ||||
−0.534701 | + | 0.845041i | \(0.679576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5387.64 | −1.33881 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3188.99 | − | 5523.49i | −0.774022 | − | 1.34065i | −0.935342 | − | 0.353744i | \(-0.884908\pi\) |
0.161320 | − | 0.986902i | \(-0.448425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2608.95 | − | 1506.28i | −0.611692 | − | 0.353160i | 0.161936 | − | 0.986801i | \(-0.448226\pi\) |
−0.773627 | + | 0.633641i | \(0.781560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3131.99i | − | 0.726024i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2392.65 | + | 4144.19i | −0.542314 | + | 0.939315i | 0.456457 | + | 0.889746i | \(0.349118\pi\) |
−0.998771 | + | 0.0495695i | \(0.984215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −880.131 | + | 508.144i | −0.197285 | + | 0.113902i | −0.595388 | − | 0.803438i | \(-0.703002\pi\) |
0.398104 | + | 0.917340i | \(0.369668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2807.50 | + | 1620.91i | −0.615632 | + | 0.355435i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 334.462 | − | 579.305i | 0.0725483 | − | 0.125657i | −0.827469 | − | 0.561511i | \(-0.810220\pi\) |
0.900017 | + | 0.435854i | \(0.143554\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2593.65i | 0.550620i | 0.961355 | + | 0.275310i | \(0.0887805\pi\) | ||||
−0.961355 | + | 0.275310i | \(0.911219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5494.58 | − | 3172.30i | −1.15413 | − | 0.666338i | −0.204240 | − | 0.978921i | \(-0.565472\pi\) |
−0.949890 | + | 0.312583i | \(0.898806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 123.111 | + | 213.234i | 0.0250582 | + | 0.0434021i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1039.64 | −0.207292 | −0.103646 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103646 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2552.39 | −0.503748 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5438.89 | − | 9420.44i | −1.05197 | − | 1.82207i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2265.27 | + | 1307.86i | 0.425276 | + | 0.245533i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3398.31i | − | 0.631765i | −0.948798 | − | 0.315882i | \(-0.897699\pi\) | ||
0.948798 | − | 0.315882i | \(-0.102301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4756.89 | + | 8239.17i | −0.867326 | + | 1.50225i | −0.00260717 | + | 0.999997i | \(0.500830\pi\) |
−0.864719 | + | 0.502256i | \(0.832503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −823.587 | + | 475.498i | −0.148728 | + | 0.0858682i | −0.572517 | − | 0.819893i | \(-0.694033\pi\) |
0.423789 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6249.91 | − | 3608.39i | 1.10735 | − | 0.639329i | 0.169209 | − | 0.985580i | \(-0.445879\pi\) |
0.938142 | + | 0.346251i | \(0.112546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 184.311 | − | 319.237i | 0.0323494 | − | 0.0560308i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 780.170i | 0.134396i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5668.42 | − | 3272.67i | −0.967469 | − | 0.558569i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4365.53 | − | 7561.32i | −0.724928 | − | 1.25561i | −0.959003 | − | 0.283394i | \(-0.908540\pi\) |
0.234075 | − | 0.972219i | \(-0.424794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4950.71 | 0.807421 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5333.20 | −0.862071 | −0.431035 | − | 0.902335i | \(-0.641852\pi\) | ||||
−0.431035 | + | 0.902335i | \(0.641852\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1597.67 | + | 2767.24i | 0.253720 | + | 0.439456i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9172.37 | + | 5295.67i | 1.41902 | + | 0.819270i | 0.996213 | − | 0.0869514i | \(-0.0277125\pi\) |
0.422804 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4590.04i | − | 0.704009i | −0.935998 | − | 0.352005i | \(-0.885500\pi\) | ||
0.935998 | − | 0.352005i | \(-0.114500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −779.032 | + | 1349.32i | −0.117461 | + | 0.203448i | −0.918761 | − | 0.394815i | \(-0.870809\pi\) |
0.801300 | + | 0.598263i | \(0.204142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4542.11 | − | 2622.39i | 0.679071 | − | 0.392062i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −137.428 | + | 79.3440i | −0.0202038 | + | 0.0116647i | −0.510068 | − | 0.860134i | \(-0.670380\pi\) |
0.489864 | + | 0.871799i | \(0.337046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3364.29 | + | 5827.12i | −0.490492 | + | 0.849558i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3962.39i | 0.568221i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5680.46 | + | 3279.61i | 0.807950 | + | 0.466470i | 0.846243 | − | 0.532797i | \(-0.178859\pi\) |
−0.0382936 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2182.12 | − | 3779.53i | −0.302911 | − | 0.524656i | 0.673883 | − | 0.738838i | \(-0.264625\pi\) |
−0.976794 | + | 0.214181i | \(0.931292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 744.259 | 0.101675 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2376.69 | 0.322117 | 0.161058 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161058 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −647.067 | − | 1120.75i | −0.0863279 | − | 0.149524i | 0.819628 | − | 0.572896i | \(-0.194180\pi\) |
−0.905956 | + | 0.423371i | \(0.860847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8314.04 | + | 4800.11i | 1.08365 | + | 0.625644i | 0.931878 | − | 0.362772i | \(-0.118170\pi\) |
0.151769 | + | 0.988416i | \(0.451503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9308.29i | 1.20394i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −150.312 | + | 260.349i | −0.0191469 | + | 0.0331635i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2834.36 | − | 1636.42i | 0.358318 | − | 0.206875i | −0.310025 | − | 0.950728i | \(-0.600337\pi\) |
0.668343 | + | 0.743854i | \(0.267004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12659.5 | + | 7308.97i | −1.57652 | + | 0.910205i | −0.581182 | + | 0.813773i | \(0.697410\pi\) |
−0.995340 | + | 0.0964319i | \(0.969257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3225.73 | + | 5587.13i | −0.398722 | + | 0.690607i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9302.64i | 1.13296i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2613.35 | − | 1508.82i | −0.315945 | − | 0.182411i | 0.333639 | − | 0.942701i | \(-0.391723\pi\) |
−0.649584 | + | 0.760290i | \(0.725057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −149.810 | − | 259.479i | −0.0177202 | − | 0.0306923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7955.52 | 0.927572 | 0.463786 | − | 0.885947i | \(-0.346491\pi\) | ||||
0.463786 | + | 0.885947i | \(0.346491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4238.67 | 0.490689 | 0.245344 | − | 0.969436i | \(-0.421099\pi\) | ||||
0.245344 | + | 0.969436i | \(0.421099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2800.47 | + | 4850.56i | 0.319630 | + | 0.553616i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7717.51 | − | 4455.71i | −0.862504 | − | 0.497967i | 0.00234585 | − | 0.999997i | \(-0.499253\pi\) |
−0.864850 | + | 0.502030i | \(0.832587\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 427.546i | − | 0.0474517i | −0.999719 | − | 0.0237258i | \(-0.992447\pi\) | ||
0.999719 | − | 0.0237258i | \(-0.00755287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 778.058 | − | 1347.64i | 0.0851707 | − | 0.147520i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5009.56 | − | 2892.27i | 0.544631 | − | 0.314443i | −0.202323 | − | 0.979319i | \(-0.564849\pi\) |
0.746954 | + | 0.664876i | \(0.231516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 175.946 | − | 101.583i | 0.0188701 | − | 0.0108947i | −0.490535 | − | 0.871421i | \(-0.663199\pi\) |
0.509405 | + | 0.860527i | \(0.329865\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1071.06 | + | 1855.13i | −0.114097 | + | 0.197622i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 609.140i | 0.0640247i | 0.999487 | + | 0.0320124i | \(0.0101916\pi\) | ||||
−0.999487 | + | 0.0320124i | \(0.989808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1738.40 | − | 1003.66i | −0.181503 | − | 0.104791i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6135.29 | + | 10626.6i | 0.628001 | + | 1.08773i | 0.987952 | + | 0.154759i | \(0.0494601\pi\) |
−0.359951 | + | 0.932971i | \(0.617207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15165.2 | −1.53213 | −0.766066 | − | 0.642762i | \(-0.777788\pi\) | ||||
−0.766066 | + | 0.642762i | \(0.777788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14315.9 | −1.43697 | −0.718485 | − | 0.695542i | \(-0.755164\pi\) | ||||
−0.718485 | + | 0.695542i | \(0.755164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8482.12 | − | 14691.5i | −0.840483 | − | 1.45576i | −0.889487 | − | 0.456961i | \(-0.848938\pi\) |
0.0490032 | − | 0.998799i | \(-0.484396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 834.411 | + | 481.748i | 0.0811126 | + | 0.0468304i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 936.339i | − | 0.0904467i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1799.92 | − | 3117.55i | 0.171692 | − | 0.297379i | −0.767320 | − | 0.641265i | \(-0.778410\pi\) |
0.939011 | + | 0.343886i | \(0.111743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16265.9 | + | 9391.14i | −1.54192 | + | 0.890226i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −624.199 | + | 360.381i | −0.0584400 | + | 0.0337404i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2752.29 | − | 4767.10i | 0.256094 | − | 0.443569i | −0.709098 | − | 0.705110i | \(-0.750898\pi\) |
0.965192 | + | 0.261542i | \(0.0842309\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13643.7i | − | 1.25404i | −0.779003 | − | 0.627020i | \(-0.784274\pi\) | ||
0.779003 | − | 0.627020i | \(-0.215726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −551.549 | − | 318.437i | −0.0503865 | − | 0.0290906i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8536.31 | + | 14785.3i | 0.765807 | + | 1.32642i | 0.939819 | + | 0.341674i | \(0.110994\pi\) |
−0.174011 | + | 0.984744i | \(0.555673\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7574.12 | −0.671398 | −0.335699 | − | 0.941969i | \(-0.608972\pi\) | ||||
−0.335699 | + | 0.941969i | \(0.608972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12968.5 | 1.14275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8460.09 | + | 14653.3i | 0.736713 | + | 1.27602i | 0.953968 | + | 0.299909i | \(0.0969564\pi\) |
−0.217255 | + | 0.976115i | \(0.569710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9962.22 | − | 5751.69i | −0.852403 | − | 0.492135i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9053.02i | 0.770119i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10540.2 | + | 18256.2i | −0.886326 | + | 1.53516i | −0.0421406 | + | 0.999112i | \(0.513418\pi\) |
−0.844186 | + | 0.536051i | \(0.819916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15348.8 | − | 8861.62i | 1.28328 | − | 0.740902i | 0.305833 | − | 0.952085i | \(-0.401065\pi\) |
0.977446 | + | 0.211183i | \(0.0677317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4780.99 | − | 2760.31i | 0.395187 | − | 0.228161i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3199.60 | − | 5541.87i | 0.262974 | − | 0.455484i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4052.85i | − | 0.329359i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4120.91 | − | 2379.21i | −0.333014 | − | 0.192266i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 383.271 | + | 663.844i | 0.0304586 | + | 0.0527558i | 0.880853 | − | 0.473390i | \(-0.156970\pi\) |
−0.850394 | + | 0.526146i | \(0.823637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3902.17 | −0.306699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6579.52 | −0.514296 | −0.257148 | − | 0.966372i | \(-0.582783\pi\) | ||||
−0.257148 | + | 0.966372i | \(0.582783\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.2348 | + | 92.2054i | 0.00411593 | + | 0.00712901i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7811.71 | − | 4510.09i | −0.594242 | − | 0.343086i | 0.172531 | − | 0.985004i | \(-0.444806\pi\) |
−0.766773 | + | 0.641918i | \(0.778139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1945.32i | 0.147189i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10544.4 | − | 18263.4i | 0.789328 | − | 1.36716i | −0.137051 | − | 0.990564i | \(-0.543763\pi\) |
0.926379 | − | 0.376592i | \(-0.122904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1767.86 | − | 1020.67i | 0.131636 | − | 0.0760001i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13686.2 | − | 7901.71i | 1.00835 | − | 0.582174i | 0.0976451 | − | 0.995221i | \(-0.468869\pi\) |
0.910709 | + | 0.413048i | \(0.135536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13091.9 | − | 22675.8i | 0.959505 | − | 1.66191i | 0.235799 | − | 0.971802i | \(-0.424229\pi\) |
0.723706 | − | 0.690109i | \(-0.242437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 11171.6i | − | 0.810237i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20391.8 | + | 11773.2i | 1.47127 | + | 0.849439i | 0.999479 | − | 0.0322714i | \(-0.0102741\pi\) |
0.471792 | + | 0.881710i | \(0.343607\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9441.35 | − | 16352.9i | −0.670705 | − | 1.16169i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12296.8 | 0.864640 | 0.432320 | − | 0.901720i | \(-0.357695\pi\) | ||||
0.432320 | + | 0.901720i | \(0.357695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −922.911 | −0.0645634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4871.98 | + | 8438.52i | 0.337383 | + | 0.584365i | 0.983940 | − | 0.178501i | \(-0.0571248\pi\) |
−0.646556 | + | 0.762866i | \(0.723791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3700.30 | − | 2136.37i | −0.252404 | − | 0.145726i | 0.368460 | − | 0.929643i | \(-0.379885\pi\) |
−0.620865 | + | 0.783918i | \(0.713218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28823.5i | − | 1.95630i | −0.207903 | − | 0.978149i | \(-0.566664\pi\) | ||
0.207903 | − | 0.978149i | \(-0.433336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 762.124 | − | 1320.04i | 0.0512145 | − | 0.0887060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7006.35 | + | 4045.12i | −0.468499 | + | 0.270488i | −0.715611 | − | 0.698499i | \(-0.753852\pi\) |
0.247112 | + | 0.968987i | \(0.420518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15829.5 | + | 9139.14i | −1.04810 | + | 0.605123i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8498.69 | + | 14720.2i | −0.559966 | + | 0.969889i | 0.437533 | + | 0.899202i | \(0.355852\pi\) |
−0.997499 | + | 0.0706867i | \(0.977481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4408.19i | 0.287629i | 0.989605 | + | 0.143815i | \(0.0459369\pi\) | ||||
−0.989605 | + | 0.143815i | \(0.954063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13169.9 | + | 7603.66i | 0.855160 | + | 0.493727i | 0.862389 | − | 0.506247i | \(-0.168968\pi\) |
−0.00722832 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −672.826 | − | 1165.37i | −0.0430608 | − | 0.0745836i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16072.3 | 1.01883 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17710.9 | 1.11737 | 0.558685 | − | 0.829380i | \(-0.311306\pi\) | ||||
0.558685 | + | 0.829380i | \(0.311306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7860.40 | + | 13614.6i | 0.491229 | + | 0.850834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9213.97 | + | 5319.69i | 0.567753 | + | 0.327793i | 0.756252 | − | 0.654281i | \(-0.227029\pi\) |
−0.188498 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14402.2i | 0.883306i | 0.897186 | + | 0.441653i | \(0.145608\pi\) | ||||
−0.897186 | + | 0.441653i | \(0.854392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13769.9 | − | 23850.2i | 0.836710 | − | 1.44922i | −0.0559201 | − | 0.998435i | \(-0.517809\pi\) |
0.892630 | − | 0.450789i | \(-0.148857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13326.7 | + | 7694.15i | −0.806036 | + | 0.465365i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13163.2 | − | 7599.77i | 0.788845 | − | 0.455440i | −0.0507109 | − | 0.998713i | \(-0.516149\pi\) |
0.839556 | + | 0.543274i | \(0.182815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4375.00 | + | 7577.72i | −0.260985 | + | 0.452040i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17308.4i | − | 1.02313i | −0.859246 | − | 0.511563i | \(-0.829067\pi\) | ||
0.859246 | − | 0.511563i | \(-0.170933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16408.1 | + | 9473.20i | 0.965507 | + | 0.557436i | 0.897863 | − | 0.440274i | \(-0.145119\pi\) |
0.0676432 | + | 0.997710i | \(0.478452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 635.151 | + | 1100.11i | 0.0368713 | + | 0.0638629i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15770.1 | 0.907299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 992.154 | 0.0568273 | 0.0284136 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284136 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10190.7 | + | 17650.9i | 0.578526 | + | 1.00204i | 0.995649 | + | 0.0931857i | \(0.0297050\pi\) |
−0.417123 | + | 0.908850i | \(0.636962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14531.3 | − | 8389.63i | −0.814090 | − | 0.470015i | 0.0342842 | − | 0.999412i | \(-0.489085\pi\) |
−0.848374 | + | 0.529397i | \(0.822418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7447.75i | − | 0.415422i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19062.3 | − | 33017.0i | 1.05402 | − | 1.82561i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13082.6 | + | 7553.27i | −0.720242 | + | 0.415832i | −0.814842 | − | 0.579684i | \(-0.803176\pi\) |
0.0945999 | + | 0.995515i | \(0.469843\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10617.3 | + | 6129.91i | −0.579479 | + | 0.334562i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1734.04 | + | 3003.45i | −0.0942346 | + | 0.163219i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4771.58i | − | 0.257090i | −0.991704 | − | 0.128545i | \(-0.958969\pi\) | ||
0.991704 | − | 0.128545i | \(-0.0410306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2326.91 | − | 1343.44i | −0.124838 | − | 0.0720753i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3189.38 | + | 5524.17i | 0.168942 | + | 0.292616i | 0.938048 | − | 0.346505i | \(-0.112632\pi\) |
−0.769106 | + | 0.639121i | \(0.779298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11011.4 | −0.578371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20701.8 | 1.08280 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13420.0 | − | 23244.1i | −0.696079 | − | 1.20564i | −0.969815 | − | 0.243840i | \(-0.921593\pi\) |
0.273736 | − | 0.961805i | \(-0.411741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 661.955 | + | 382.180i | 0.0339095 | + | 0.0195777i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13222.5i | 0.674547i | 0.941407 | + | 0.337273i | \(0.109505\pi\) | ||||
−0.941407 | + | 0.337273i | \(0.890495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 832.322 | − | 1441.62i | 0.0421129 | − | 0.0729417i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18543.8 | + | 10706.2i | −0.934420 | + | 0.539488i | −0.888207 | − | 0.459444i | \(-0.848049\pi\) |
−0.0462131 | + | 0.998932i | \(0.514715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25848.9 | − | 14923.9i | 1.29194 | − | 0.745900i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17088.5 | − | 29598.2i | 0.850624 | − | 1.47332i | −0.0300220 | − | 0.999549i | \(-0.509558\pi\) |
0.880646 | − | 0.473775i | \(-0.157109\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23205.8i | − | 1.14581i | −0.819621 | − | 0.572906i | \(-0.805816\pi\) | ||
0.819621 | − | 0.572906i | \(-0.194184\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5551.26 | + | 3205.02i | 0.272996 | + | 0.157615i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9232.97 | − | 15992.0i | −0.448623 | − | 0.777038i | 0.549674 | − | 0.835379i | \(-0.314752\pi\) |
−0.998297 | + | 0.0583418i | \(0.981419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6787.33 | 0.327174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13606.4 | 0.653280 | 0.326640 | − | 0.945149i | \(-0.394084\pi\) | ||||
0.326640 | + | 0.945149i | \(0.394084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9008.18 | + | 15602.6i | 0.429101 | + | 0.743225i | 0.996794 | − | 0.0800155i | \(-0.0254970\pi\) |
−0.567692 | + | 0.823241i | \(0.692164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26906.9 | − | 15534.7i | −1.26669 | − | 0.731324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21716.1i | 1.01834i | 0.860666 | + | 0.509169i | \(0.170047\pi\) | ||||
−0.860666 | + | 0.509169i | \(0.829953\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18105.0 | − | 31358.7i | 0.842420 | − | 1.45911i | −0.0454230 | − | 0.998968i | \(-0.514464\pi\) |
0.887843 | − | 0.460146i | \(-0.152203\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5738.02 | + | 3312.85i | −0.265956 | + | 0.153550i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 502.102 | − | 289.889i | 0.0230933 | − | 0.0133329i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15810.4 | − | 27384.3i | 0.724378 | − | 1.25466i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 409.119i | 0.0186014i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13622.5 | − | 7864.94i | −0.617012 | − | 0.356232i | 0.158693 | − | 0.987328i | \(-0.449272\pi\) |
−0.775705 | + | 0.631096i | \(0.782605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15920.1 | + | 27574.5i | 0.712913 | + | 1.23480i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31098.5 | −1.38214 | −0.691070 | − | 0.722787i | \(-0.742861\pi\) | ||||
−0.691070 | + | 0.722787i | \(0.742861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15641.0 | 0.692540 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11944.6 | + | 20688.6i | 0.524926 | + | 0.909198i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22218.0 | − | 12827.6i | −0.965568 | − | 0.557471i | −0.0676861 | − | 0.997707i | \(-0.521562\pi\) |
−0.897882 | + | 0.440235i | \(0.854895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17351.0i | 0.751263i | 0.926769 | + | 0.375632i | \(0.122574\pi\) | ||||
−0.926769 | + | 0.375632i | \(0.877426\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1304.39 | + | 2259.27i | −0.0560623 | + | 0.0971027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −241.004 | + | 139.144i | −0.0103203 | + | 0.00595841i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20178.2 | − | 11649.9i | 0.857765 | − | 0.495231i | −0.00549814 | − | 0.999985i | \(-0.501750\pi\) |
0.863263 | + | 0.504754i | \(0.168417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7212.13 | − | 12491.8i | 0.305466 | − | 0.529083i | −0.671899 | − | 0.740643i | \(-0.734521\pi\) |
0.977365 | + | 0.211560i | \(0.0678543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11516.8i | − | 0.484255i | −0.970244 | − | 0.242127i | \(-0.922155\pi\) | ||
0.970244 | − | 0.242127i | \(-0.0778452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8122.14 | − | 4689.32i | −0.340282 | − | 0.196462i | 0.320115 | − | 0.947379i | \(-0.396278\pi\) |
−0.660397 | + | 0.750917i | \(0.729612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6563.87 | − | 11369.0i | −0.272039 | − | 0.471185i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31050.7 | −1.27770 | −0.638848 | − | 0.769333i | \(-0.720589\pi\) | ||||
−0.638848 | + | 0.769333i | \(0.720589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24302.1 | 0.996436 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13694.5 | + | 23719.5i | 0.557519 | + | 0.965652i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27762.7 | − | 16028.8i | −1.11832 | − | 0.645663i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 41308.2i | − | 1.65811i | −0.559170 | − | 0.829053i | \(-0.688880\pi\) | ||
0.559170 | − | 0.829053i | \(-0.311120\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13700.1 | − | 23729.3i | 0.546077 | − | 0.945832i | −0.452462 | − | 0.891784i | \(-0.649454\pi\) |
0.998538 | − | 0.0540486i | \(-0.0172126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3112.62 | − | 1797.07i | 0.123633 | − | 0.0713798i | −0.436908 | − | 0.899506i | \(-0.643926\pi\) |
0.560541 | + | 0.828126i | \(0.310593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3029.24 | + | 1748.93i | −0.119486 | + | 0.0689852i | −0.558552 | − | 0.829470i | \(-0.688643\pi\) |
0.439066 | + | 0.898455i | \(0.355309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6557.94 | + | 11358.7i | −0.257776 | + | 0.446482i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1812.46i | 0.0707521i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52189.6 | + | 30131.7i | 2.03029 | + | 1.17219i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21247.7 | + | 36802.1i | 0.818111 | + | 1.41701i | 0.907072 | + | 0.420974i | \(0.138312\pi\) |
−0.0889617 | + | 0.996035i | \(0.528355\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5554.52 | 0.212414 | 0.106207 | − | 0.994344i | \(-0.466129\pi\) | ||||
0.106207 | + | 0.994344i | \(0.466129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1152.28 | −0.0439154 | −0.0219577 | − | 0.999759i | \(-0.506990\pi\) | ||||
−0.0219577 | + | 0.999759i | \(0.506990\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18868.8 | − | 32681.7i | −0.714264 | − | 1.23714i | −0.963243 | − | 0.268632i | \(-0.913428\pi\) |
0.248979 | − | 0.968509i | \(-0.419905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2264.48 | − | 1307.40i | −0.0848575 | − | 0.0489925i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 24909.3i | − | 0.930308i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 376.699 | − | 652.461i | 0.0139751 | − | 0.0242056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28253.1 | + | 16311.9i | −1.04467 | + | 0.603141i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14431.4 | − | 8331.99i | 0.530074 | − | 0.306038i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14064.8 | − | 24360.9i | 0.514900 | − | 0.891832i | −0.484951 | − | 0.874541i | \(-0.661163\pi\) |
0.999851 | − | 0.0172909i | \(-0.00550414\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35517.2i | − | 1.29170i | −0.763465 | − | 0.645849i | \(-0.776503\pi\) | ||
0.763465 | − | 0.645849i | \(-0.223497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1564.39 | − | 903.202i | −0.0567074 | − | 0.0327400i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9544.14 | − | 16530.9i | −0.342581 | − | 0.593368i | 0.642330 | − | 0.766428i | \(-0.277968\pi\) |
−0.984911 | + | 0.173060i | \(0.944634\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 63843.1 | 2.27673 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19289.5 | −0.685660 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22986.0 | + | 39813.0i | 0.811784 | + | 1.40605i | 0.911614 | + | 0.411046i | \(0.134837\pi\) |
−0.0998306 | + | 0.995004i | \(0.531830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15341.5 | − | 8857.44i | −0.536601 | − | 0.309807i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10653.2i | 0.371423i | 0.982604 | + | 0.185712i | \(0.0594591\pi\) | ||||
−0.982604 | + | 0.185712i | \(0.940541\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3480.93 | − | 6029.15i | 0.120590 | − | 0.208868i | −0.799411 | − | 0.600785i | \(-0.794855\pi\) |
0.920000 | + | 0.391917i | \(0.128188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5990.64 | − | 3458.70i | 0.206874 | − | 0.119439i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28060.9 | + | 16200.9i | −0.962889 | + | 0.555924i | −0.897061 | − | 0.441907i | \(-0.854302\pi\) |
−0.0658278 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24116.4 | + | 41770.9i | −0.824924 | + | 1.42881i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 27432.4i | − | 0.932448i | −0.884667 | − | 0.466224i | \(-0.845614\pi\) | ||
0.884667 | − | 0.466224i | \(-0.154386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29738.7 | + | 17169.7i | 1.00767 | + | 0.581777i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11630.2 | − | 20144.0i | −0.390392 | − | 0.676178i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33547.0 | 1.11908 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43449.7 | 1.44493 | 0.722465 | − | 0.691408i | \(-0.243009\pi\) | ||||
0.722465 | + | 0.691408i | \(0.243009\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5273.30 | + | 9133.63i | 0.174283 | + | 0.301866i | 0.939913 | − | 0.341415i | \(-0.110906\pi\) |
−0.765630 | + | 0.643281i | \(0.777573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30648.2 | + | 17694.8i | 1.00361 | + | 0.579433i | 0.909313 | − | 0.416112i | \(-0.136608\pi\) |
0.0942933 | + | 0.995544i | \(0.469941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12914.8i | 0.421614i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13990.4 | − | 24232.1i | 0.453942 | − | 0.786251i | −0.544684 | − | 0.838641i | \(-0.683351\pi\) |
0.998627 | + | 0.0523900i | \(0.0166839\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21866.4 | − | 12624.6i | 0.707332 | − | 0.408378i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2875.44 | + | 1660.14i | −0.0924507 | + | 0.0533765i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5288.79 | − | 9160.46i | 0.169530 | − | 0.293634i | −0.768725 | − | 0.639580i | \(-0.779108\pi\) |
0.938255 | + | 0.345945i | \(0.112442\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15939.6i | 0.507858i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23948.3 | + | 13826.6i | 0.760734 | + | 0.439210i | 0.829559 | − | 0.558419i | \(-0.188592\pi\) |
−0.0688254 | + | 0.997629i | \(0.521925\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.4.t.c.521.10 | 48 | ||
3.2 | odd | 2 | inner | 1764.4.t.c.521.15 | 48 | ||
7.2 | even | 3 | inner | 1764.4.t.c.1097.9 | 48 | ||
7.3 | odd | 6 | 1764.4.f.b.881.9 | ✓ | 24 | ||
7.4 | even | 3 | 1764.4.f.b.881.15 | yes | 24 | ||
7.5 | odd | 6 | inner | 1764.4.t.c.1097.15 | 48 | ||
7.6 | odd | 2 | inner | 1764.4.t.c.521.16 | 48 | ||
21.2 | odd | 6 | inner | 1764.4.t.c.1097.16 | 48 | ||
21.5 | even | 6 | inner | 1764.4.t.c.1097.10 | 48 | ||
21.11 | odd | 6 | 1764.4.f.b.881.10 | yes | 24 | ||
21.17 | even | 6 | 1764.4.f.b.881.16 | yes | 24 | ||
21.20 | even | 2 | inner | 1764.4.t.c.521.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.4.f.b.881.9 | ✓ | 24 | 7.3 | odd | 6 | ||
1764.4.f.b.881.10 | yes | 24 | 21.11 | odd | 6 | ||
1764.4.f.b.881.15 | yes | 24 | 7.4 | even | 3 | ||
1764.4.f.b.881.16 | yes | 24 | 21.17 | even | 6 | ||
1764.4.t.c.521.9 | 48 | 21.20 | even | 2 | inner | ||
1764.4.t.c.521.10 | 48 | 1.1 | even | 1 | trivial | ||
1764.4.t.c.521.15 | 48 | 3.2 | odd | 2 | inner | ||
1764.4.t.c.521.16 | 48 | 7.6 | odd | 2 | inner | ||
1764.4.t.c.1097.9 | 48 | 7.2 | even | 3 | inner | ||
1764.4.t.c.1097.10 | 48 | 21.5 | even | 6 | inner | ||
1764.4.t.c.1097.15 | 48 | 7.5 | odd | 6 | inner | ||
1764.4.t.c.1097.16 | 48 | 21.2 | odd | 6 | inner |