Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,4,Mod(401,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.401");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.2015280046\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.3 | ||
Root | \(-1.86176 - 0.730647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.401 |
Dual form | 800.4.d.d.401.10 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 6.25785i | − 1.20432i | −0.798374 | − | 0.602161i | \(-0.794306\pi\) | ||||
0.798374 | − | 0.602161i | \(-0.205694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −34.6280 | −1.86973 | −0.934867 | − | 0.354998i | \(-0.884482\pi\) | ||||
−0.934867 | + | 0.354998i | \(0.884482\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −12.1606 | −0.450394 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.91595i | 0.216977i | 0.994098 | + | 0.108489i | \(0.0346011\pi\) | ||||
−0.994098 | + | 0.108489i | \(0.965399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.0346i | 0.235420i | 0.993048 | + | 0.117710i | \(0.0375553\pi\) | ||||
−0.993048 | + | 0.117710i | \(0.962445\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −57.6152 | −0.821985 | −0.410992 | − | 0.911639i | \(-0.634818\pi\) | ||||
−0.410992 | + | 0.911639i | \(0.634818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 141.133i | 1.70411i | 0.523453 | + | 0.852055i | \(0.324644\pi\) | ||||
−0.523453 | + | 0.852055i | \(0.675356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 216.696i | 2.25176i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 129.328 | 1.17247 | 0.586233 | − | 0.810143i | \(-0.300610\pi\) | ||||
0.586233 | + | 0.810143i | \(0.300610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 92.8625i | − 0.661903i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 89.1664i | − 0.570958i | −0.958385 | − | 0.285479i | \(-0.907847\pi\) | ||||
0.958385 | − | 0.285479i | \(-0.0921527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 78.3307 | 0.453826 | 0.226913 | − | 0.973915i | \(-0.427137\pi\) | ||||
0.226913 | + | 0.973915i | \(0.427137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.5368 | 0.261310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 249.332i | − 1.10783i | −0.832572 | − | 0.553917i | \(-0.813132\pi\) | ||||
0.832572 | − | 0.553917i | \(-0.186868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 69.0530 | 0.283521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 91.8705 | 0.349946 | 0.174973 | − | 0.984573i | \(-0.444016\pi\) | ||||
0.174973 | + | 0.984573i | \(0.444016\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 194.184i | 0.688668i | 0.938847 | + | 0.344334i | \(0.111895\pi\) | ||||
−0.938847 | + | 0.344334i | \(0.888105\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −72.6149 | −0.225361 | −0.112680 | − | 0.993631i | \(-0.535944\pi\) | ||||
−0.112680 | + | 0.993631i | \(0.535944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 856.096 | 2.49591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 360.547i | 0.989935i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 456.782i | 1.18385i | 0.805995 | + | 0.591923i | \(0.201631\pi\) | ||||
−0.805995 | + | 0.591923i | \(0.798369\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 883.187 | 2.05230 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 341.098i | − 0.752664i | −0.926485 | − | 0.376332i | \(-0.877185\pi\) | ||||
0.926485 | − | 0.376332i | \(-0.122815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 217.067i | − 0.455616i | −0.973706 | − | 0.227808i | \(-0.926844\pi\) | ||||
0.973706 | − | 0.227808i | \(-0.0731559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 421.098 | 0.842117 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 529.237i | 0.965024i | 0.875889 | + | 0.482512i | \(0.160276\pi\) | ||||
−0.875889 | + | 0.482512i | \(0.839724\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 809.314i | − 1.41203i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −381.540 | −0.637754 | −0.318877 | − | 0.947796i | \(-0.603306\pi\) | ||||
−0.318877 | + | 0.947796i | \(0.603306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 876.902 | 1.40594 | 0.702970 | − | 0.711220i | \(-0.251857\pi\) | ||||
0.702970 | + | 0.711220i | \(0.251857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 274.113i | − 0.405690i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 203.950 | 0.290458 | 0.145229 | − | 0.989398i | \(-0.453608\pi\) | ||||
0.145229 | + | 0.989398i | \(0.453608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −909.456 | −1.24754 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 996.654i | − 1.31804i | −0.752127 | − | 0.659018i | \(-0.770972\pi\) | ||||
0.752127 | − | 0.659018i | \(-0.229028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −557.989 | −0.687618 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 172.456 | 0.205396 | 0.102698 | − | 0.994713i | \(-0.467252\pi\) | ||||
0.102698 | + | 0.994713i | \(0.467252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 382.107i | − 0.440172i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 490.182i | − 0.546553i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1058.49 | −1.10797 | −0.553984 | − | 0.832527i | \(-0.686893\pi\) | ||||
−0.553984 | + | 0.832527i | \(0.686893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 96.2629i | − 0.0977251i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 689.992i | − 0.679770i | −0.940467 | − | 0.339885i | \(-0.889612\pi\) | ||||
0.940467 | − | 0.339885i | \(-0.110388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1289.96 | 1.23402 | 0.617009 | − | 0.786956i | \(-0.288344\pi\) | ||||
0.617009 | + | 0.786956i | \(0.288344\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1843.74i | 1.66580i | 0.553420 | + | 0.832902i | \(0.313322\pi\) | ||||
−0.553420 | + | 0.832902i | \(0.686678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 340.598i | 0.299297i | 0.988739 | + | 0.149648i | \(0.0478142\pi\) | ||||
−0.988739 | + | 0.149648i | \(0.952186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1560.28 | −1.33419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −157.831 | −0.131393 | −0.0656967 | − | 0.997840i | \(-0.520927\pi\) | ||||
−0.0656967 | + | 0.997840i | \(0.520927\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 134.188i | − 0.106031i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1995.10 | 1.53689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1268.34 | 0.952921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 574.912i | − 0.421447i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 494.704 | 0.345652 | 0.172826 | − | 0.984952i | \(-0.444710\pi\) | ||||
0.172826 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1215.17 | 0.829379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 488.783i | 0.325993i | 0.986627 | + | 0.162997i | \(0.0521160\pi\) | ||||
−0.986627 | + | 0.162997i | \(0.947884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4887.14i | − 3.18623i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1532.13 | 0.955464 | 0.477732 | − | 0.878506i | \(-0.341459\pi\) | ||||
0.477732 | + | 0.878506i | \(0.341459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 755.095i | − 0.460765i | −0.973100 | − | 0.230382i | \(-0.926002\pi\) | ||||
0.973100 | − | 0.230382i | \(-0.0739977\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 454.413i | 0.271407i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −87.3495 | −0.0510807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 5357.32i | − 3.00588i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1446.67i | − 0.795410i | −0.917513 | − | 0.397705i | \(-0.869807\pi\) | ||||
0.917513 | − | 0.397705i | \(-0.130193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1230.20 | 0.662998 | 0.331499 | − | 0.943456i | \(-0.392446\pi\) | ||||
0.331499 | + | 0.943456i | \(0.392446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 700.637 | 0.370217 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1773.74i | 0.901657i | 0.892611 | + | 0.450828i | \(0.148871\pi\) | ||||
−0.892611 | + | 0.450828i | \(0.851129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2858.47 | 1.42573 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4478.36 | −2.19220 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1711.28i | − 0.822319i | −0.911563 | − | 0.411159i | \(-0.865124\pi\) | ||||
0.911563 | − | 0.411159i | \(-0.134876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3913.26 | 1.81328 | 0.906638 | − | 0.421909i | \(-0.138640\pi\) | ||||
0.906638 | + | 0.421909i | \(0.138640\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2075.24 | 0.944578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1716.26i | − 0.767520i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3985.34i | 1.75144i | 0.482815 | + | 0.875722i | \(0.339614\pi\) | ||||
−0.482815 | + | 0.875722i | \(0.660386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2134.54 | −0.906450 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 884.734i | − 0.369431i | −0.982792 | − | 0.184715i | \(-0.940864\pi\) | ||||
0.982792 | − | 0.184715i | \(-0.0591363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2810.77i | 1.15427i | 0.816649 | + | 0.577134i | \(0.195829\pi\) | ||||
−0.816649 | + | 0.577134i | \(0.804171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1358.37 | −0.548709 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 456.079i | − 0.178352i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3215.64i | 1.23758i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 749.321 | 0.283869 | 0.141935 | − | 0.989876i | \(-0.454668\pi\) | ||||
0.141935 | + | 0.989876i | \(0.454668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3969.83 | 1.48060 | 0.740298 | − | 0.672279i | \(-0.234685\pi\) | ||||
0.740298 | + | 0.672279i | \(0.234685\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2243.20i | 0.811275i | 0.914034 | + | 0.405638i | \(0.132951\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 672.030 | 0.239392 | 0.119696 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119696 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3311.89 | 1.16220 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3087.65i | 1.06754i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1572.71 | −0.528071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1117.20 | −0.369753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1935.07i | 0.631356i | 0.948866 | + | 0.315678i | \(0.102232\pi\) | ||||
−0.948866 | + | 0.315678i | \(0.897768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2387.62i | 0.768061i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2712.43 | −0.848535 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 5487.52i | − 1.69321i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 635.762i | − 0.193511i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2492.56 | 0.748494 | 0.374247 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374247 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3155.27i | 0.922567i | 0.887253 | + | 0.461283i | \(0.152611\pi\) | ||||
−0.887253 | + | 0.461283i | \(0.847389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2299.43i | − 0.663539i | −0.943360 | − | 0.331770i | \(-0.892354\pi\) | ||||
0.943360 | − | 0.331770i | \(-0.107646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1715.36 | −0.488581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −741.991 | −0.208624 | −0.104312 | − | 0.994545i | \(-0.533264\pi\) | ||||
−0.104312 | + | 0.994545i | \(0.533264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1276.29i | − 0.349806i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5786.01 | −1.56597 | −0.782984 | − | 0.622042i | \(-0.786303\pi\) | ||||
−0.782984 | + | 0.622042i | \(0.786303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 265.054 | 0.0708449 | 0.0354224 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354224 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3183.95i | 0.840537i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1557.35 | −0.401181 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6236.91 | −1.58734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1762.02i | − 0.443098i | −0.975149 | − | 0.221549i | \(-0.928889\pi\) | ||||
0.975149 | − | 0.221549i | \(-0.0711113\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1023.75i | 0.254398i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1507.84 | 0.365980 | 0.182990 | − | 0.983115i | \(-0.441422\pi\) | ||||
0.182990 | + | 0.983115i | \(0.441422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8633.85i | 2.07136i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1084.32i | 0.257156i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2772.54 | 0.650046 | 0.325023 | − | 0.945706i | \(-0.394628\pi\) | ||||
0.325023 | + | 0.945706i | \(0.394628\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1079.20i | − 0.247364i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5166.61i | 1.17106i | 0.810652 | + | 0.585528i | \(0.199113\pi\) | ||||
−0.810652 | + | 0.585528i | \(0.800887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1458.79 | 0.326994 | 0.163497 | − | 0.986544i | \(-0.447723\pi\) | ||||
0.163497 | + | 0.986544i | \(0.447723\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2391.16 | −0.530109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1994.60i | − 0.432650i | −0.976321 | − | 0.216325i | \(-0.930593\pi\) | ||||
0.976321 | − | 0.216325i | \(-0.0694070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −952.551 | −0.204400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −311.583 | −0.0661477 | −0.0330739 | − | 0.999453i | \(-0.510530\pi\) | ||||
−0.0330739 | + | 0.999453i | \(0.510530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6072.33i | 1.27549i | 0.770249 | + | 0.637743i | \(0.220132\pi\) | ||||
−0.770249 | + | 0.637743i | \(0.779868\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3181.29 | −0.654305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1593.49 | −0.324341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6623.84i | 1.33435i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2321.06i | − 0.462791i | −0.972860 | − | 0.231395i | \(-0.925671\pi\) | ||||
0.972860 | − | 0.231395i | \(-0.0743291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 735.095 | 0.143618 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1427.08i | 0.276021i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 6724.19i | − 1.28763i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4317.86 | −0.818662 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2499.43i | 0.464658i | 0.972637 | + | 0.232329i | \(0.0746347\pi\) | ||||
−0.972637 | + | 0.232329i | \(0.925365\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8072.39i | − 1.48616i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3052.83 | 0.556624 | 0.278312 | − | 0.960491i | \(-0.410225\pi\) | ||||
0.278312 | + | 0.960491i | \(0.410225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6179.23 | −1.11588 | −0.557941 | − | 0.829881i | \(-0.688408\pi\) | ||||
−0.557941 | + | 0.829881i | \(0.688408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3116.20i | − 0.552124i | −0.961140 | − | 0.276062i | \(-0.910971\pi\) | ||||
0.961140 | − | 0.276062i | \(-0.0890295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 705.836 | 0.123885 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11537.8 | 2.00617 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 8131.39i | − 1.40075i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2131.41 | 0.360450 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2514.51 | 0.421365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4157.26i | 0.690343i | 0.938540 | + | 0.345171i | \(0.112179\pi\) | ||||
−0.938540 | + | 0.345171i | \(0.887821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3032.03i | 0.498962i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8123.42 | 1.31309 | 0.656544 | − | 0.754287i | \(-0.272017\pi\) | ||||
0.656544 | + | 0.754287i | \(0.272017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 987.679i | 0.158240i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 620.062i | 0.0984699i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17767.5 | −2.79695 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4620.55i | 0.714824i | 0.933947 | + | 0.357412i | \(0.116341\pi\) | ||||
−0.933947 | + | 0.357412i | \(0.883659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5560.98i | 0.852929i | 0.904504 | + | 0.426465i | \(0.140241\pi\) | ||||
−0.904504 | + | 0.426465i | \(0.859759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1024.70 | 0.155825 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12031.8 | −1.81413 | −0.907066 | − | 0.420989i | \(-0.861683\pi\) | ||||
−0.907066 | + | 0.420989i | \(0.861683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 12485.0i | − 1.85092i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1533.24 | −0.225408 | −0.112704 | − | 0.993629i | \(-0.535951\pi\) | ||||
−0.112704 | + | 0.993629i | \(0.535951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13059.5 | −1.90399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7937.06i | − 1.14762i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5480.04 | −0.779444 | −0.389722 | − | 0.920933i | \(-0.627429\pi\) | ||||
−0.389722 | + | 0.920933i | \(0.627429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1117.20 | −0.157613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 15817.4i | − 2.21348i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6225.70i | − 0.864221i | −0.901821 | − | 0.432111i | \(-0.857769\pi\) | ||||
0.901821 | − | 0.432111i | \(-0.142231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 983.917 | 0.134415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11172.0i | 1.51416i | 0.653325 | + | 0.757078i | \(0.273374\pi\) | ||||
−0.653325 | + | 0.757078i | \(0.726626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3095.78i | − 0.416277i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7621.03 | 1.01675 | 0.508376 | − | 0.861135i | \(-0.330246\pi\) | ||||
0.508376 | + | 0.861135i | \(0.330246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2361.40i | − 0.310172i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5546.31i | 0.722903i | 0.932391 | + | 0.361451i | \(0.117719\pi\) | ||||
−0.932391 | + | 0.361451i | \(0.882281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7451.25 | −0.963749 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3058.73 | 0.392601 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11025.2i | 1.39380i | 0.717169 | + | 0.696900i | \(0.245438\pi\) | ||||
−0.717169 | + | 0.696900i | \(0.754562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30583.0 | −3.83725 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10522.3 | 1.31037 | 0.655186 | − | 0.755467i | \(-0.272590\pi\) | ||||
0.655186 | + | 0.755467i | \(0.272590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 864.350i | 0.106840i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1973.70 | 0.240375 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2320.17 | 0.280502 | 0.140251 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140251 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 9587.82i | − 1.15069i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11811.5i | 1.40728i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4725.27 | −0.554910 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 9212.17i | − 1.07409i | −0.843554 | − | 0.537045i | \(-0.819541\pi\) | ||||
0.843554 | − | 0.537045i | \(-0.180459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6967.70i | 0.806615i | 0.915064 | + | 0.403308i | \(0.132140\pi\) | ||||
−0.915064 | + | 0.403308i | \(0.867860\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 883.042 | 0.101501 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7516.59i | 0.851882i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 546.620i | 0.0615176i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11247.1 | 1.25697 | 0.628486 | − | 0.777821i | \(-0.283675\pi\) | ||||
0.628486 | + | 0.777821i | \(0.283675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2589.27 | −0.287372 | −0.143686 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18252.4i | 1.99801i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4220.01 | −0.458793 | −0.229396 | − | 0.973333i | \(-0.573675\pi\) | ||||
−0.229396 | + | 0.973333i | \(0.573675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10410.7 | −1.12414 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9764.04i | − 1.04719i | −0.851969 | − | 0.523593i | \(-0.824591\pi\) | ||||
0.851969 | − | 0.523593i | \(-0.175409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9053.06 | −0.957931 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17159.3 | −1.80355 | −0.901777 | − | 0.432202i | \(-0.857737\pi\) | ||||
−0.901777 | + | 0.432202i | \(0.857737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 727.242i | 0.0759302i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7698.43i | − 0.798463i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13027.3 | −1.33346 | −0.666730 | − | 0.745299i | \(-0.732307\pi\) | ||||
−0.666730 | + | 0.745299i | \(0.732307\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5350.29i | 0.544075i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 313.396i | − 0.0316623i | −0.999875 | − | 0.0158312i | \(-0.994961\pi\) | ||||
0.999875 | − | 0.0158312i | \(-0.00503943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12166.5 | −1.22123 | −0.610613 | − | 0.791930i | \(-0.709077\pi\) | ||||
−0.610613 | + | 0.791930i | \(0.709077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1844.42i | − 0.182761i | −0.995816 | − | 0.0913806i | \(-0.970872\pi\) | ||||
0.995816 | − | 0.0913806i | \(-0.0291280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 18326.4i | − 1.80434i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11099.8 | 1.08589 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1537.15 | −0.149425 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5554.75i | − 0.533196i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16355.9 | 1.56017 | 0.780084 | − | 0.625675i | \(-0.215176\pi\) | ||||
0.780084 | + | 0.625675i | \(0.215176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2751.28 | 0.260806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28024.9i | 2.64012i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11824.6 | 1.10025 | 0.550126 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550126 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10708.9 | −0.990337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7931.40i | 0.729000i | 0.931203 | + | 0.364500i | \(0.118760\pi\) | ||||
−0.931203 | + | 0.364500i | \(0.881240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5137.34i | 0.469319i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13212.0 | 1.19243 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 2734.69i | − 0.245333i | −0.992448 | − | 0.122667i | \(-0.960855\pi\) | ||||
0.992448 | − | 0.122667i | \(-0.0391446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 24488.6i | − 2.18377i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7297.64 | 0.646890 | 0.323445 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323445 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 12986.5i | − 1.13758i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10972.4i | 0.955486i | 0.878500 | + | 0.477743i | \(0.158545\pi\) | ||||
−0.878500 | + | 0.477743i | \(0.841455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30365.3 | −2.62873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13105.9 | 1.12796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 574.815i | − 0.0488982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24939.7 | 2.10931 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7693.43 | 0.646939 | 0.323470 | − | 0.946239i | \(-0.395151\pi\) | ||||
0.323470 | + | 0.946239i | \(0.395151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14535.3i | 1.21527i | 0.794217 | + | 0.607634i | \(0.207881\pi\) | ||||
−0.794217 | + | 0.607634i | \(0.792119\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4513.04 | −0.373038 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4558.69 | 0.374676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4147.97i | 0.338995i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1013.76i | 0.0823840i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5536.53 | −0.444914 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6776.81i | 0.541555i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19131.8i | 1.52040i | 0.649686 | + | 0.760202i | \(0.274900\pi\) | ||||
−0.649686 | + | 0.760202i | \(0.725100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17589.3 | 1.39011 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7142.78i | 0.558324i | 0.960244 | + | 0.279162i | \(0.0900566\pi\) | ||||
−0.960244 | + | 0.279162i | \(0.909943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2639.67i | 0.205207i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12584.3 | 0.972974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7062.39 | −0.543080 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11347.8i | − 0.863236i | −0.902057 | − | 0.431618i | \(-0.857943\pi\) | ||||
0.902057 | − | 0.431618i | \(-0.142057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2142.74 | −0.162126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2854.07 | −0.214793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8802.19i | − 0.658913i | −0.944171 | − | 0.329456i | \(-0.893135\pi\) | ||||
0.944171 | − | 0.329456i | \(-0.106865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31492.6 | 2.33257 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16714.7 | 1.23149 | 0.615744 | − | 0.787946i | \(-0.288855\pi\) | ||||
0.615744 | + | 0.787946i | \(0.288855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17386.8i | 1.27428i | 0.770746 | + | 0.637142i | \(0.219884\pi\) | ||||
−0.770746 | + | 0.637142i | \(0.780116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4689.14i | − 0.341870i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2260.52 | −0.163097 | −0.0815483 | − | 0.996669i | \(-0.525986\pi\) | ||||
−0.0815483 | + | 0.996669i | \(0.525986\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 24842.6i | − 1.78311i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34512.1i | 2.46438i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3615.86 | −0.256867 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 25591.0i | − 1.79941i | −0.436498 | − | 0.899705i | \(-0.643781\pi\) | ||||
0.436498 | − | 0.899705i | \(-0.356219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11055.0i | 0.773369i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14037.6 | 0.977037 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10053.7 | 0.696218 | 0.348109 | − | 0.937454i | \(-0.386824\pi\) | ||||
0.348109 | + | 0.937454i | \(0.386824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4205.46i | − 0.288305i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7086.68 | 0.483395 | 0.241698 | − | 0.970352i | \(-0.422296\pi\) | ||||
0.241698 | + | 0.970352i | \(0.422296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6673.11 | 0.452915 | 0.226458 | − | 0.974021i | \(-0.427286\pi\) | ||||
0.226458 | + | 0.974021i | \(0.427286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6435.86i | − 0.434641i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15205.6 | −1.01677 | −0.508383 | − | 0.861131i | \(-0.669757\pi\) | ||||
−0.508383 | + | 0.861131i | \(0.669757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19322.0 | 1.28566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 801.278i | − 0.0530544i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8147.64i | 0.536836i | 0.963303 | + | 0.268418i | \(0.0865008\pi\) | ||||
−0.963303 | + | 0.268418i | \(0.913499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −449.110 | −0.0293039 | −0.0146519 | − | 0.999893i | \(-0.504664\pi\) | ||||
−0.0146519 | + | 0.999893i | \(0.504664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 27800.4i | − 1.80516i | −0.430524 | − | 0.902579i | \(-0.641671\pi\) | ||||
0.430524 | − | 0.902579i | \(-0.358329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 12009.7i | − 0.776059i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5971.79 | −0.384037 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6991.26i | 0.445302i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14365.3i | 0.910623i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14793.5 | −0.933315 | −0.466657 | − | 0.884438i | \(-0.654542\pi\) | ||||
−0.466657 | + | 0.884438i | \(0.654542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12109.4 | 0.760356 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9446.70i | 0.587585i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4639.77 | 0.287240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13853.8 | −0.853655 | −0.426828 | − | 0.904333i | \(-0.640369\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4978.60i | − 0.305345i | −0.988277 | − | 0.152672i | \(-0.951212\pi\) | ||||
0.988277 | − | 0.152672i | \(-0.0487880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1903.39 | −0.115657 | −0.0578284 | − | 0.998327i | \(-0.518418\pi\) | ||||
−0.0578284 | + | 0.998327i | \(0.518418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2700.11 | 0.163311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16974.0i | 1.02191i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 10877.0i | − 0.651839i | −0.945397 | − | 0.325920i | \(-0.894326\pi\) | ||||
0.945397 | − | 0.325920i | \(-0.105674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10663.7 | −0.633226 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30611.3i | 1.80948i | 0.425965 | + | 0.904739i | \(0.359935\pi\) | ||||
−0.425965 | + | 0.904739i | \(0.640065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 16098.8i | − 0.947310i | −0.880710 | − | 0.473655i | \(-0.842934\pi\) | ||||
0.880710 | − | 0.473655i | \(-0.157066\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3978.50 | −0.233050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11531.7i | − 0.669429i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 15598.0i | − 0.901428i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1718.29 | 0.0988583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23837.8 | 1.36535 | 0.682673 | − | 0.730724i | \(-0.260817\pi\) | ||||
0.682673 | + | 0.730724i | \(0.260817\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 25235.3i | − 1.43260i | −0.697791 | − | 0.716302i | \(-0.745833\pi\) | ||||
0.697791 | − | 0.716302i | \(-0.254167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36653.2 | 2.07161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19745.2 | 1.11107 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 19975.3i | − 1.11909i | −0.828802 | − | 0.559543i | \(-0.810977\pi\) | ||||
0.828802 | − | 0.559543i | \(-0.189023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14389.5 | −0.799115 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5040.42 | −0.278700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13772.3i | − 0.758209i | −0.925354 | − | 0.379104i | \(-0.876232\pi\) | ||||
0.925354 | − | 0.379104i | \(-0.123768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3333.39i | 0.182720i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5293.14 | −0.287650 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4643.26i | 0.251251i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 6347.90i | − 0.342021i | −0.985269 | − | 0.171011i | \(-0.945297\pi\) | ||||
0.985269 | − | 0.171011i | \(-0.0547032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35188.9 | 1.88787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23893.0i | 1.27099i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17910.5i | 0.948719i | 0.880331 | + | 0.474360i | \(0.157320\pi\) | ||||
−0.880331 | + | 0.474360i | \(0.842680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2480.16 | −0.130821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10130.3 | 0.532096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36208.0i | 1.88593i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36601.6 | −1.89849 | −0.949243 | − | 0.314545i | \(-0.898148\pi\) | ||||
−0.949243 | + | 0.314545i | \(0.898148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44668.8 | −2.30728 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1658.67i | − 0.0853201i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2644.18 | 0.134893 | 0.0674466 | − | 0.997723i | \(-0.478515\pi\) | ||||
0.0674466 | + | 0.997723i | \(0.478515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4630.66 | −0.235262 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 11187.9i | − 0.566075i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 33452.1i | − 1.68565i | −0.538188 | − | 0.842825i | \(-0.680891\pi\) | ||||
0.538188 | − | 0.842825i | \(-0.319109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4189.42 | −0.209388 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 25834.9i | − 1.28600i | −0.765867 | − | 0.642999i | \(-0.777690\pi\) | ||||
0.765867 | − | 0.642999i | \(-0.222310\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9745.64i | 0.483151i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7625.09 | 0.376497 | 0.188249 | − | 0.982121i | \(-0.439719\pi\) | ||||
0.188249 | + | 0.982121i | \(0.439719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12119.9i | 0.593635i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 63845.0i | − 3.11461i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25362.7 | −1.23235 | −0.616177 | − | 0.787607i | \(-0.711320\pi\) | ||||
−0.616177 | + | 0.787607i | \(0.711320\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11026.4 | −0.533633 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38948.0i | 1.87000i | 0.354648 | + | 0.935000i | \(0.384601\pi\) | ||||
−0.354648 | + | 0.935000i | \(0.615399\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6406.48 | 0.306378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13722.2 | −0.653654 | −0.326827 | − | 0.945084i | \(-0.605979\pi\) | ||||
−0.326827 | + | 0.945084i | \(0.605979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11794.2i | − 0.559606i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3763.89 | 0.177192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18689.5 | 0.876414 | 0.438207 | − | 0.898874i | \(-0.355614\pi\) | ||||
0.438207 | + | 0.898874i | \(0.355614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 9435.86i | − 0.440758i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6386.49i | − 0.297162i | −0.988900 | − | 0.148581i | \(-0.952529\pi\) | ||||
0.988900 | − | 0.148581i | \(-0.0474705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54029.3 | 2.49458 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12965.9i | 0.596345i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3020.25i | − 0.138378i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8280.21 | −0.377919 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 19410.3i | − 0.879167i | −0.898202 | − | 0.439583i | \(-0.855126\pi\) | ||||
0.898202 | − | 0.439583i | \(-0.144874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 17350.1i | − 0.782865i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5465.35 | 0.245671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2395.25 | 0.107261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 30740.8i | − 1.36624i | −0.730305 | − | 0.683121i | \(-0.760622\pi\) | ||||
0.730305 | − | 0.683121i | \(-0.239378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4183.72 | 0.185243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2097.17 | −0.0925092 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6941.51i | 0.305057i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32331.9 | 1.41033 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31805.5 | 1.38223 | 0.691114 | − | 0.722746i | \(-0.257120\pi\) | ||||
0.691114 | + | 0.722746i | \(0.257120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 31014.7i | − 1.34288i | −0.741060 | − | 0.671439i | \(-0.765677\pi\) | ||||
0.741060 | − | 0.671439i | \(-0.234323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 9128.90i | − 0.393806i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27405.7 | −1.17357 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4646.66i | 0.198251i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 12021.4i | − 0.511021i | −0.966806 | − | 0.255511i | \(-0.917756\pi\) | ||||
0.966806 | − | 0.255511i | \(-0.0822436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15489.0 | 0.656032 | 0.328016 | − | 0.944672i | \(-0.393620\pi\) | ||||
0.328016 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17097.2i | 0.718898i | 0.933165 | + | 0.359449i | \(0.117035\pi\) | ||||
−0.933165 | + | 0.359449i | \(0.882965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 9885.97i | − 0.414178i | −0.978322 | − | 0.207089i | \(-0.933601\pi\) | ||||
0.978322 | − | 0.207089i | \(-0.0663990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12481.9 | −0.521050 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49324.2 | −2.05160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7273.99i | − 0.300389i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39204.3 | 1.61321 | 0.806606 | − | 0.591090i | \(-0.201302\pi\) | ||||
0.806606 | + | 0.591090i | \(0.201302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16438.4 | 0.674007 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1949.84i | 0.0796632i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43920.0 | −1.78171 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37999.7 | 1.53610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 32245.5i | − 1.29890i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45054.1i | 1.80847i | 0.427038 | + | 0.904234i | \(0.359557\pi\) | ||||
−0.427038 | + | 0.904234i | \(0.640443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48464.2 | 1.93174 | 0.965872 | − | 0.259021i | \(-0.0834000\pi\) | ||||
0.965872 | + | 0.259021i | \(0.0834000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1000.76i | − 0.0397503i | −0.999802 | − | 0.0198751i | \(-0.993673\pi\) | ||||
0.999802 | − | 0.0198751i | \(-0.00632687\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19908.0i | 0.787995i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22485.5 | 0.886922 | 0.443461 | − | 0.896294i | \(-0.353750\pi\) | ||||
0.443461 | + | 0.896294i | \(0.353750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9971.79i | 0.390611i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1614.46i | 0.0630228i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5839.94 | −0.227186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12871.9 | 0.499022 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 43726.2i | − 1.68361i | −0.539780 | − | 0.841806i | \(-0.681493\pi\) | ||||
0.539780 | − | 0.841806i | \(-0.318507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14524.8 | −0.557349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20290.0 | 0.775923 | 0.387962 | − | 0.921675i | \(-0.373179\pi\) | ||||
0.387962 | + | 0.921675i | \(0.373179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 14887.3i | − 0.567382i | −0.958916 | − | 0.283691i | \(-0.908441\pi\) | ||||
0.958916 | − | 0.283691i | \(-0.0915590\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34359.3 | 1.30065 | 0.650323 | − | 0.759658i | \(-0.274633\pi\) | ||||
0.650323 | + | 0.759658i | \(0.274633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17130.6 | −0.646278 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 7199.21i | − 0.270687i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 10248.3i | − 0.384040i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8930.47 | 0.332419 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 6984.47i | − 0.259116i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 26317.6i | − 0.973103i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42078.9 | −1.55072 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53363.9i | 1.95360i | 0.214144 | + | 0.976802i | \(0.431304\pi\) | ||||
−0.214144 | + | 0.976802i | \(0.568696\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8390.73i | 0.306164i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25213.9 | 0.916984 | 0.458492 | − | 0.888699i | \(-0.348390\pi\) | ||||
0.458492 | + | 0.888699i | \(0.348390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7889.46 | 0.285984 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 16925.5i | − 0.609521i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3747.02 | −0.134497 | −0.0672485 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672485 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15641.1 | 0.559599 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4210.15i | − 0.150140i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15686.8 | −0.555794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27726.7 | −0.979209 | −0.489604 | − | 0.871945i | \(-0.662859\pi\) | ||||
−0.489604 | + | 0.871945i | \(0.662859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 120823.i | 4.25330i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 19104.1i | − 0.670355i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29333.2 | −1.02270 | −0.511352 | − | 0.859371i | \(-0.670855\pi\) | ||||
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38668.7i | 1.34388i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24218.4i | 0.838998i | 0.907756 | + | 0.419499i | \(0.137794\pi\) | ||||
−0.907756 | + | 0.419499i | \(0.862206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11881.4 | 0.410299 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 50824.6i | − 1.74401i | −0.489497 | − | 0.872005i | \(-0.662820\pi\) | ||||
0.489497 | − | 0.872005i | \(-0.337180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9676.28i | 0.330986i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19500.7 | −0.664935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10155.1 | 0.345180 | 0.172590 | − | 0.984994i | \(-0.444786\pi\) | ||||
0.172590 | + | 0.984994i | \(0.444786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 4417.01i | − 0.149197i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −53054.5 | −1.78646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23655.3 | −0.794042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 22421.0i | − 0.750268i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28225.7 | −0.938652 | −0.469326 | − | 0.883025i | \(-0.655503\pi\) | ||||
−0.469326 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50885.0 | −1.68696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47631.4i | 1.57422i | 0.616814 | + | 0.787109i | \(0.288423\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26147.4i | 0.861508i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13542.4 | −0.443460 | −0.221730 | − | 0.975108i | \(-0.571170\pi\) | ||||
−0.221730 | + | 0.975108i | \(0.571170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1365.15i | 0.0445663i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 4141.88i | − 0.134801i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35108.5 | −1.13915 | −0.569576 | − | 0.821938i | \(-0.692893\pi\) | ||||
−0.569576 | + | 0.821938i | \(0.692893\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 15735.4i | − 0.507460i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25113.4i | 0.807440i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42816.1 | 1.37245 | 0.686225 | − | 0.727390i | \(-0.259267\pi\) | ||||
0.686225 | + | 0.727390i | \(0.259267\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26015.5 | 0.831396 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13029.0i | 0.413873i | 0.978354 | + | 0.206936i | \(0.0663493\pi\) | ||||
−0.978354 | + | 0.206936i | \(0.933651\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23153.6 | −0.733280 |
(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 | 800.4.d.d.401.3 | 12 | ||
4.3 | odd | 2 | 200.4.d.b.101.12 | 12 | |||
5.2 | odd | 4 | 800.4.f.b.49.3 | 12 | |||
5.3 | odd | 4 | 800.4.f.c.49.10 | 12 | |||
5.4 | even | 2 | 160.4.d.a.81.10 | 12 | |||
8.3 | odd | 2 | 200.4.d.b.101.11 | 12 | |||
8.5 | even | 2 | inner | 800.4.d.d.401.10 | 12 | ||
15.14 | odd | 2 | 1440.4.k.c.721.12 | 12 | |||
20.3 | even | 4 | 200.4.f.b.149.9 | 12 | |||
20.7 | even | 4 | 200.4.f.c.149.4 | 12 | |||
20.19 | odd | 2 | 40.4.d.a.21.1 | ✓ | 12 | ||
40.3 | even | 4 | 200.4.f.c.149.3 | 12 | |||
40.13 | odd | 4 | 800.4.f.b.49.4 | 12 | |||
40.19 | odd | 2 | 40.4.d.a.21.2 | yes | 12 | ||
40.27 | even | 4 | 200.4.f.b.149.10 | 12 | |||
40.29 | even | 2 | 160.4.d.a.81.3 | 12 | |||
40.37 | odd | 4 | 800.4.f.c.49.9 | 12 | |||
60.59 | even | 2 | 360.4.k.c.181.12 | 12 | |||
80.19 | odd | 4 | 1280.4.a.bc.1.5 | 6 | |||
80.29 | even | 4 | 1280.4.a.ba.1.2 | 6 | |||
80.59 | odd | 4 | 1280.4.a.bb.1.2 | 6 | |||
80.69 | even | 4 | 1280.4.a.bd.1.5 | 6 | |||
120.29 | odd | 2 | 1440.4.k.c.721.6 | 12 | |||
120.59 | even | 2 | 360.4.k.c.181.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.d.a.21.1 | ✓ | 12 | 20.19 | odd | 2 | ||
40.4.d.a.21.2 | yes | 12 | 40.19 | odd | 2 | ||
160.4.d.a.81.3 | 12 | 40.29 | even | 2 | |||
160.4.d.a.81.10 | 12 | 5.4 | even | 2 | |||
200.4.d.b.101.11 | 12 | 8.3 | odd | 2 | |||
200.4.d.b.101.12 | 12 | 4.3 | odd | 2 | |||
200.4.f.b.149.9 | 12 | 20.3 | even | 4 | |||
200.4.f.b.149.10 | 12 | 40.27 | even | 4 | |||
200.4.f.c.149.3 | 12 | 40.3 | even | 4 | |||
200.4.f.c.149.4 | 12 | 20.7 | even | 4 | |||
360.4.k.c.181.11 | 12 | 120.59 | even | 2 | |||
360.4.k.c.181.12 | 12 | 60.59 | even | 2 | |||
800.4.d.d.401.3 | 12 | 1.1 | even | 1 | trivial | ||
800.4.d.d.401.10 | 12 | 8.5 | even | 2 | inner | ||
800.4.f.b.49.3 | 12 | 5.2 | odd | 4 | |||
800.4.f.b.49.4 | 12 | 40.13 | odd | 4 | |||
800.4.f.c.49.9 | 12 | 40.37 | odd | 4 | |||
800.4.f.c.49.10 | 12 | 5.3 | odd | 4 | |||
1280.4.a.ba.1.2 | 6 | 80.29 | even | 4 | |||
1280.4.a.bb.1.2 | 6 | 80.59 | odd | 4 | |||
1280.4.a.bc.1.5 | 6 | 80.19 | odd | 4 | |||
1280.4.a.bd.1.5 | 6 | 80.69 | even | 4 | |||
1440.4.k.c.721.6 | 12 | 120.29 | odd | 2 | |||
1440.4.k.c.721.12 | 12 | 15.14 | odd | 2 |