Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.1 | ||
Root | \(-3.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.j.274.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.70156i | − 1.66225i | −0.556083 | − | 0.831127i | \(-0.687696\pi\) | ||||
0.556083 | − | 0.831127i | \(-0.312304\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −14.1047 | −1.76309 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.1047 | 0.959702 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 28.7016i | 1.26844i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.5969 | 0.674203 | 0.337102 | − | 0.941468i | \(-0.390553\pi\) | ||||
0.337102 | + | 0.941468i | \(0.390553\pi\) | |||||||
\(12\) | − 42.3141i | − 1.01792i | ||||||||
\(13\) | − 35.0156i | − 0.747045i | −0.927621 | − | 0.373523i | \(-0.878150\pi\) | ||||
0.927621 | − | 0.373523i | \(-0.121850\pi\) | |||||||
\(14\) | −32.9109 | −0.628273 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 22.1047 | 0.345386 | ||||||||
\(17\) | 18.4187i | 0.262777i | 0.991331 | + | 0.131388i | \(0.0419435\pi\) | ||||
−0.991331 | + | 0.131388i | \(0.958057\pi\) | |||||||
\(18\) | 42.3141i | 0.554084i | ||||||||
\(19\) | 67.4031 | 0.813860 | 0.406930 | − | 0.913459i | \(-0.366599\pi\) | ||||
0.406930 | + | 0.913459i | \(0.366599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | − 115.644i | − 1.12070i | ||||||||
\(23\) | − 145.675i | − 1.32067i | −0.750973 | − | 0.660333i | \(-0.770415\pi\) | ||||
0.750973 | − | 0.660333i | \(-0.229585\pi\) | |||||||
\(24\) | −86.1047 | −0.732335 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −164.628 | −1.24178 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 98.7328i | 0.666384i | ||||||||
\(29\) | −214.419 | −1.37298 | −0.686492 | − | 0.727137i | \(-0.740851\pi\) | ||||
−0.686492 | + | 0.727137i | \(0.740851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −88.6594 | −0.513667 | −0.256834 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256834 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(32\) | 125.686i | 0.694323i | ||||||||
\(33\) | 73.7906i | 0.389251i | ||||||||
\(34\) | 86.5969 | 0.436801 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 126.942 | 0.587695 | ||||||||
\(37\) | − 162.125i | − 0.720356i | −0.932884 | − | 0.360178i | \(-0.882716\pi\) | ||||
0.932884 | − | 0.360178i | \(-0.117284\pi\) | |||||||
\(38\) | − 316.900i | − 1.35284i | ||||||||
\(39\) | 105.047 | 0.431307 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −337.769 | −1.28660 | −0.643300 | − | 0.765614i | \(-0.722435\pi\) | ||||
−0.643300 | + | 0.765614i | \(0.722435\pi\) | |||||||
\(42\) | − 98.7328i | − 0.362733i | ||||||||
\(43\) | 122.156i | 0.433224i | 0.976258 | + | 0.216612i | \(0.0695007\pi\) | ||||
−0.976258 | + | 0.216612i | \(0.930499\pi\) | |||||||
\(44\) | −346.931 | −1.18868 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −684.900 | −2.19528 | ||||||||
\(47\) | − 354.219i | − 1.09932i | −0.835388 | − | 0.549661i | \(-0.814757\pi\) | ||||
0.835388 | − | 0.549661i | \(-0.185243\pi\) | |||||||
\(48\) | 66.3141i | 0.199409i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −55.2562 | −0.151714 | ||||||||
\(52\) | 493.884i | 1.31710i | ||||||||
\(53\) | 676.691i | 1.75378i | 0.480687 | + | 0.876892i | \(0.340387\pi\) | ||||
−0.480687 | + | 0.876892i | \(0.659613\pi\) | |||||||
\(54\) | −126.942 | −0.319901 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 200.911 | 0.479426 | ||||||||
\(57\) | 202.209i | 0.469882i | ||||||||
\(58\) | 1008.10i | 2.28225i | ||||||||
\(59\) | −501.319 | −1.10621 | −0.553103 | − | 0.833113i | \(-0.686556\pi\) | ||||
−0.553103 | + | 0.833113i | \(0.686556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −708.931 | −1.48802 | −0.744011 | − | 0.668167i | \(-0.767079\pi\) | ||||
−0.744011 | + | 0.668167i | \(0.767079\pi\) | |||||||
\(62\) | 416.837i | 0.853845i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 767.758 | 1.49953 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 346.931 | 0.647035 | ||||||||
\(67\) | 907.956i | 1.65559i | 0.561031 | + | 0.827795i | \(0.310405\pi\) | ||||
−0.561031 | + | 0.827795i | \(0.689595\pi\) | |||||||
\(68\) | − 259.791i | − 0.463298i | ||||||||
\(69\) | 437.025 | 0.762487 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 430.334 | 0.719314 | 0.359657 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359657 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(72\) | − 258.314i | − 0.422814i | ||||||||
\(73\) | 41.3406i | 0.0662816i | 0.999451 | + | 0.0331408i | \(0.0105510\pi\) | ||||
−0.999451 | + | 0.0331408i | \(0.989449\pi\) | |||||||
\(74\) | −762.241 | −1.19741 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −950.700 | −1.43490 | ||||||||
\(77\) | − 172.178i | − 0.254825i | ||||||||
\(78\) | − 493.884i | − 0.716941i | ||||||||
\(79\) | −890.388 | −1.26806 | −0.634028 | − | 0.773310i | \(-0.718600\pi\) | ||||
−0.634028 | + | 0.773310i | \(0.718600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1588.04i | 2.13866i | ||||||||
\(83\) | − 1057.15i | − 1.39804i | −0.715102 | − | 0.699020i | \(-0.753620\pi\) | ||||
0.715102 | − | 0.699020i | \(-0.246380\pi\) | |||||||
\(84\) | −296.198 | −0.384737 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 574.325 | 0.720129 | ||||||||
\(87\) | − 643.256i | − 0.792693i | ||||||||
\(88\) | 705.969i | 0.855188i | ||||||||
\(89\) | −1473.72 | −1.75522 | −0.877610 | − | 0.479376i | \(-0.840863\pi\) | ||||
−0.877610 | + | 0.479376i | \(0.840863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −245.109 | −0.282356 | ||||||||
\(92\) | 2054.70i | 2.32845i | ||||||||
\(93\) | − 265.978i | − 0.296566i | ||||||||
\(94\) | −1665.38 | −1.82735 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −377.058 | −0.400868 | ||||||||
\(97\) | − 555.034i | − 0.580981i | −0.956878 | − | 0.290491i | \(-0.906181\pi\) | ||||
0.956878 | − | 0.290491i | \(-0.0938185\pi\) | |||||||
\(98\) | 230.377i | 0.237465i | ||||||||
\(99\) | −221.372 | −0.224734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1890.14 | 1.86214 | 0.931071 | − | 0.364838i | \(-0.118876\pi\) | ||||
0.931071 | + | 0.364838i | \(0.118876\pi\) | |||||||
\(102\) | 259.791i | 0.252187i | ||||||||
\(103\) | 662.700i | 0.633959i | 0.948432 | + | 0.316979i | \(0.102669\pi\) | ||||
−0.948432 | + | 0.316979i | \(0.897331\pi\) | |||||||
\(104\) | 1005.00 | 0.947583 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3181.50 | 2.91523 | ||||||||
\(107\) | − 1614.53i | − 1.45872i | −0.684132 | − | 0.729358i | \(-0.739819\pi\) | ||||
0.684132 | − | 0.729358i | \(-0.260181\pi\) | |||||||
\(108\) | 380.827i | 0.339306i | ||||||||
\(109\) | −217.206 | −0.190868 | −0.0954339 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954339 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 486.375 | 0.415898 | ||||||||
\(112\) | − 154.733i | − 0.130544i | ||||||||
\(113\) | − 1658.20i | − 1.38044i | −0.723598 | − | 0.690221i | \(-0.757513\pi\) | ||||
0.723598 | − | 0.690221i | \(-0.242487\pi\) | |||||||
\(114\) | 950.700 | 0.781063 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3024.31 | 2.42069 | ||||||||
\(117\) | 315.141i | 0.249015i | ||||||||
\(118\) | 2356.98i | 1.83879i | ||||||||
\(119\) | 128.931 | 0.0993202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −725.994 | −0.545450 | ||||||||
\(122\) | 3333.08i | 2.47347i | ||||||||
\(123\) | − 1013.31i | − 0.742819i | ||||||||
\(124\) | 1250.51 | 0.905640 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 296.198 | 0.209424 | ||||||||
\(127\) | 1108.81i | 0.774734i | 0.921926 | + | 0.387367i | \(0.126615\pi\) | ||||
−0.921926 | + | 0.387367i | \(0.873385\pi\) | |||||||
\(128\) | − 2604.17i | − 1.79827i | ||||||||
\(129\) | −366.469 | −0.250122 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 185.488 | 0.123711 | 0.0618554 | − | 0.998085i | \(-0.480298\pi\) | ||||
0.0618554 | + | 0.998085i | \(0.480298\pi\) | |||||||
\(132\) | − 1040.79i | − 0.686284i | ||||||||
\(133\) | − 471.822i | − 0.307610i | ||||||||
\(134\) | 4268.81 | 2.75201 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −528.647 | −0.333317 | ||||||||
\(137\) | 37.9907i | 0.0236917i | 0.999930 | + | 0.0118458i | \(0.00377074\pi\) | ||||
−0.999930 | + | 0.0118458i | \(0.996229\pi\) | |||||||
\(138\) | − 2054.70i | − 1.26745i | ||||||||
\(139\) | −183.609 | −0.112040 | −0.0560199 | − | 0.998430i | \(-0.517841\pi\) | ||||
−0.0560199 | + | 0.998430i | \(0.517841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1062.66 | 0.634694 | ||||||||
\(142\) | − 2023.24i | − 1.19568i | ||||||||
\(143\) | − 861.275i | − 0.503660i | ||||||||
\(144\) | −198.942 | −0.115129 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 194.366 | 0.110177 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 2286.72i | 1.27005i | ||||||||
\(149\) | 1383.34 | 0.760587 | 0.380293 | − | 0.924866i | \(-0.375823\pi\) | ||||
0.380293 | + | 0.924866i | \(0.375823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 765.256 | 0.412422 | 0.206211 | − | 0.978508i | \(-0.433887\pi\) | ||||
0.206211 | + | 0.978508i | \(0.433887\pi\) | |||||||
\(152\) | 1934.57i | 1.03233i | ||||||||
\(153\) | − 165.769i | − 0.0875922i | ||||||||
\(154\) | −809.506 | −0.423584 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1481.65 | −0.760431 | ||||||||
\(157\) | 2366.76i | 1.20311i | 0.798832 | + | 0.601554i | \(0.205452\pi\) | ||||
−0.798832 | + | 0.601554i | \(0.794548\pi\) | |||||||
\(158\) | 4186.21i | 2.10783i | ||||||||
\(159\) | −2030.07 | −1.01255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1019.72 | −0.499165 | ||||||||
\(162\) | − 380.827i | − 0.184695i | ||||||||
\(163\) | − 3137.69i | − 1.50775i | −0.657018 | − | 0.753875i | \(-0.728183\pi\) | ||||
0.657018 | − | 0.753875i | \(-0.271817\pi\) | |||||||
\(164\) | 4764.12 | 2.26839 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4970.26 | −2.32390 | ||||||||
\(167\) | − 146.469i | − 0.0678688i | −0.999424 | − | 0.0339344i | \(-0.989196\pi\) | ||||
0.999424 | − | 0.0339344i | \(-0.0108037\pi\) | |||||||
\(168\) | 602.733i | 0.276797i | ||||||||
\(169\) | 970.906 | 0.441924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −606.628 | −0.271287 | ||||||||
\(172\) | − 1722.98i | − 0.763812i | ||||||||
\(173\) | − 1424.12i | − 0.625860i | −0.949776 | − | 0.312930i | \(-0.898689\pi\) | ||||
0.949776 | − | 0.312930i | \(-0.101311\pi\) | |||||||
\(174\) | −3024.31 | −1.31766 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 543.706 | 0.232860 | ||||||||
\(177\) | − 1503.96i | − 0.638668i | ||||||||
\(178\) | 6928.81i | 2.91762i | ||||||||
\(179\) | −1244.70 | −0.519737 | −0.259869 | − | 0.965644i | \(-0.583679\pi\) | ||||
−0.259869 | + | 0.965644i | \(0.583679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3879.09 | −1.59299 | −0.796493 | − | 0.604648i | \(-0.793314\pi\) | ||||
−0.796493 | + | 0.604648i | \(0.793314\pi\) | |||||||
\(182\) | 1152.40i | 0.469348i | ||||||||
\(183\) | − 2126.79i | − 0.859110i | ||||||||
\(184\) | 4181.10 | 1.67519 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1250.51 | −0.492968 | ||||||||
\(187\) | 453.044i | 0.177165i | ||||||||
\(188\) | 4996.14i | 1.93820i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1574.90 | 0.596628 | 0.298314 | − | 0.954468i | \(-0.403576\pi\) | ||||
0.298314 | + | 0.954468i | \(0.403576\pi\) | |||||||
\(192\) | 2303.27i | 0.865752i | ||||||||
\(193\) | − 4775.67i | − 1.78114i | −0.454843 | − | 0.890572i | \(-0.650305\pi\) | ||||
0.454843 | − | 0.890572i | \(-0.349695\pi\) | |||||||
\(194\) | −2609.53 | −0.965738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 691.130 | 0.251869 | ||||||||
\(197\) | 2803.58i | 1.01394i | 0.861963 | + | 0.506971i | \(0.169235\pi\) | ||||
−0.861963 | + | 0.506971i | \(0.830765\pi\) | |||||||
\(198\) | 1040.79i | 0.373566i | ||||||||
\(199\) | −4102.92 | −1.46155 | −0.730774 | − | 0.682620i | \(-0.760841\pi\) | ||||
−0.730774 | + | 0.682620i | \(0.760841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2723.87 | −0.955855 | ||||||||
\(202\) | − 8886.63i | − 3.09535i | ||||||||
\(203\) | 1500.93i | 0.518940i | ||||||||
\(204\) | 779.372 | 0.267485 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3115.72 | 1.05380 | ||||||||
\(207\) | 1311.07i | 0.440222i | ||||||||
\(208\) | − 774.009i | − 0.258019i | ||||||||
\(209\) | 1657.91 | 0.548707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −823.512 | −0.268687 | −0.134343 | − | 0.990935i | \(-0.542893\pi\) | ||||
−0.134343 | + | 0.990935i | \(0.542893\pi\) | |||||||
\(212\) | − 9544.51i | − 3.09207i | ||||||||
\(213\) | 1291.00i | 0.415296i | ||||||||
\(214\) | −7590.82 | −2.42476 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 774.942 | 0.244112 | ||||||||
\(217\) | 620.616i | 0.194148i | ||||||||
\(218\) | 1021.21i | 0.317271i | ||||||||
\(219\) | −124.022 | −0.0382677 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 644.944 | 0.196306 | ||||||||
\(222\) | − 2286.72i | − 0.691328i | ||||||||
\(223\) | 817.194i | 0.245396i | 0.992444 | + | 0.122698i | \(0.0391547\pi\) | ||||
−0.992444 | + | 0.122698i | \(0.960845\pi\) | |||||||
\(224\) | 879.802 | 0.262430 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7796.12 | −2.29465 | ||||||||
\(227\) | − 3655.85i | − 1.06893i | −0.845190 | − | 0.534465i | \(-0.820513\pi\) | ||||
0.845190 | − | 0.534465i | \(-0.179487\pi\) | |||||||
\(228\) | − 2852.10i | − 0.828443i | ||||||||
\(229\) | −939.393 | −0.271078 | −0.135539 | − | 0.990772i | \(-0.543277\pi\) | ||||
−0.135539 | + | 0.990772i | \(0.543277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 516.534 | 0.147123 | ||||||||
\(232\) | − 6154.15i | − 1.74155i | ||||||||
\(233\) | − 7.64701i | − 0.00215010i | −0.999999 | − | 0.00107505i | \(-0.999658\pi\) | ||||
0.999999 | − | 0.00107505i | \(-0.000342198\pi\) | |||||||
\(234\) | 1481.65 | 0.413926 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7070.94 | 1.95034 | ||||||||
\(237\) | − 2671.16i | − 0.732112i | ||||||||
\(238\) | − 606.178i | − 0.165095i | ||||||||
\(239\) | 889.115 | 0.240636 | 0.120318 | − | 0.992735i | \(-0.461609\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2140.23 | 0.572051 | 0.286026 | − | 0.958222i | \(-0.407666\pi\) | ||||
0.286026 | + | 0.958222i | \(0.407666\pi\) | |||||||
\(242\) | 3413.30i | 0.906676i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 9999.25 | 2.62351 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4764.12 | −1.23475 | ||||||||
\(247\) | − 2360.16i | − 0.607990i | ||||||||
\(248\) | − 2544.66i | − 0.651557i | ||||||||
\(249\) | 3171.45 | 0.807158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6749.81 | −1.69739 | −0.848693 | − | 0.528886i | \(-0.822610\pi\) | ||||
−0.848693 | + | 0.528886i | \(0.822610\pi\) | |||||||
\(252\) | − 888.595i | − 0.222128i | ||||||||
\(253\) | − 3583.15i | − 0.890398i | ||||||||
\(254\) | 5213.15 | 1.28780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6101.62 | −1.48965 | ||||||||
\(257\) | − 3068.64i | − 0.744811i | −0.928070 | − | 0.372405i | \(-0.878533\pi\) | ||||
0.928070 | − | 0.372405i | \(-0.121467\pi\) | |||||||
\(258\) | 1722.98i | 0.415766i | ||||||||
\(259\) | −1134.87 | −0.272269 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1929.77 | 0.457662 | ||||||||
\(262\) | − 872.081i | − 0.205639i | ||||||||
\(263\) | − 4674.12i | − 1.09589i | −0.836515 | − | 0.547944i | \(-0.815411\pi\) | ||||
0.836515 | − | 0.547944i | \(-0.184589\pi\) | |||||||
\(264\) | −2117.91 | −0.493743 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2218.30 | −0.511326 | ||||||||
\(267\) | − 4421.17i | − 1.01338i | ||||||||
\(268\) | − 12806.4i | − 2.91895i | ||||||||
\(269\) | −2417.38 | −0.547919 | −0.273960 | − | 0.961741i | \(-0.588333\pi\) | ||||
−0.273960 | + | 0.961741i | \(0.588333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7724.30 | 1.73143 | 0.865715 | − | 0.500537i | \(-0.166864\pi\) | ||||
0.865715 | + | 0.500537i | \(0.166864\pi\) | |||||||
\(272\) | 407.141i | 0.0907593i | ||||||||
\(273\) | − 735.328i | − 0.163019i | ||||||||
\(274\) | 178.616 | 0.0393816 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6164.10 | −1.34433 | ||||||||
\(277\) | 4576.17i | 0.992620i | 0.868145 | + | 0.496310i | \(0.165312\pi\) | ||||
−0.868145 | + | 0.496310i | \(0.834688\pi\) | |||||||
\(278\) | 863.250i | 0.186239i | ||||||||
\(279\) | 797.934 | 0.171222 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1358.56 | −0.288415 | −0.144208 | − | 0.989547i | \(-0.546063\pi\) | ||||
−0.144208 | + | 0.989547i | \(0.546063\pi\) | |||||||
\(282\) | − 4996.14i | − 1.05502i | ||||||||
\(283\) | 3885.04i | 0.816048i | 0.912971 | + | 0.408024i | \(0.133782\pi\) | ||||
−0.912971 | + | 0.408024i | \(0.866218\pi\) | |||||||
\(284\) | −6069.73 | −1.26821 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4049.34 | −0.837211 | ||||||||
\(287\) | 2364.38i | 0.486289i | ||||||||
\(288\) | − 1131.17i | − 0.231441i | ||||||||
\(289\) | 4573.75 | 0.930948 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1665.10 | 0.335430 | ||||||||
\(292\) | − 583.097i | − 0.116860i | ||||||||
\(293\) | − 4033.91i | − 0.804312i | −0.915571 | − | 0.402156i | \(-0.868261\pi\) | ||||
0.915571 | − | 0.402156i | \(-0.131739\pi\) | |||||||
\(294\) | −691.130 | −0.137100 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4653.24 | 0.913730 | ||||||||
\(297\) | − 664.116i | − 0.129750i | ||||||||
\(298\) | − 6503.85i | − 1.26429i | ||||||||
\(299\) | −5100.90 | −0.986598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 855.093 | 0.163743 | ||||||||
\(302\) | − 3597.90i | − 0.685549i | ||||||||
\(303\) | 5670.43i | 1.07511i | ||||||||
\(304\) | 1489.92 | 0.281096 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −779.372 | −0.145600 | ||||||||
\(307\) | 4620.36i | 0.858950i | 0.903079 | + | 0.429475i | \(0.141301\pi\) | ||||
−0.903079 | + | 0.429475i | \(0.858699\pi\) | |||||||
\(308\) | 2428.52i | 0.449278i | ||||||||
\(309\) | −1988.10 | −0.366016 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6675.89 | 1.21722 | 0.608609 | − | 0.793470i | \(-0.291728\pi\) | ||||
0.608609 | + | 0.793470i | \(0.291728\pi\) | |||||||
\(312\) | 3015.01i | 0.547087i | ||||||||
\(313\) | 2836.78i | 0.512283i | 0.966639 | + | 0.256141i | \(0.0824513\pi\) | ||||
−0.966639 | + | 0.256141i | \(0.917549\pi\) | |||||||
\(314\) | 11127.5 | 1.99987 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12558.6 | 2.23569 | ||||||||
\(317\) | − 4010.63i | − 0.710597i | −0.934753 | − | 0.355299i | \(-0.884379\pi\) | ||||
0.934753 | − | 0.355299i | \(-0.115621\pi\) | |||||||
\(318\) | 9544.51i | 1.68311i | ||||||||
\(319\) | −5274.03 | −0.925671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4843.59 | 0.842190 | ||||||||
\(322\) | 4794.30i | 0.829739i | ||||||||
\(323\) | 1241.48i | 0.213863i | ||||||||
\(324\) | −1142.48 | −0.195898 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14752.1 | −2.50626 | ||||||||
\(327\) | − 651.619i | − 0.110198i | ||||||||
\(328\) | − 9694.49i | − 1.63198i | ||||||||
\(329\) | −2479.53 | −0.415504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11087.5 | 1.84117 | 0.920583 | − | 0.390546i | \(-0.127714\pi\) | ||||
0.920583 | + | 0.390546i | \(0.127714\pi\) | |||||||
\(332\) | 14910.8i | 2.46486i | ||||||||
\(333\) | 1459.12i | 0.240119i | ||||||||
\(334\) | −688.631 | −0.112815 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 464.198 | 0.0753693 | ||||||||
\(337\) | − 12118.7i | − 1.95890i | −0.201689 | − | 0.979450i | \(-0.564643\pi\) | ||||
0.201689 | − | 0.979450i | \(-0.435357\pi\) | |||||||
\(338\) | − 4564.78i | − 0.734589i | ||||||||
\(339\) | 4974.59 | 0.796999 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2180.74 | −0.346316 | ||||||||
\(342\) | 2852.10i | 0.450947i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −3506.07 | −0.549520 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6695.58 | −1.04034 | ||||||||
\(347\) | 6361.22i | 0.984116i | 0.870562 | + | 0.492058i | \(0.163755\pi\) | ||||
−0.870562 | + | 0.492058i | \(0.836245\pi\) | |||||||
\(348\) | 9072.93i | 1.39759i | ||||||||
\(349\) | 3115.18 | 0.477799 | 0.238899 | − | 0.971044i | \(-0.423213\pi\) | ||||
0.238899 | + | 0.971044i | \(0.423213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −945.422 | −0.143769 | ||||||||
\(352\) | 3091.48i | 0.468115i | ||||||||
\(353\) | − 11927.4i | − 1.79839i | −0.437550 | − | 0.899194i | \(-0.644154\pi\) | ||||
0.437550 | − | 0.899194i | \(-0.355846\pi\) | |||||||
\(354\) | −7070.94 | −1.06163 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20786.4 | 3.09460 | ||||||||
\(357\) | 386.794i | 0.0573426i | ||||||||
\(358\) | 5852.02i | 0.863935i | ||||||||
\(359\) | 6143.95 | 0.903245 | 0.451623 | − | 0.892209i | \(-0.350845\pi\) | ||||
0.451623 | + | 0.892209i | \(0.350845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2315.82 | −0.337632 | ||||||||
\(362\) | 18237.8i | 2.64794i | ||||||||
\(363\) | − 2177.98i | − 0.314916i | ||||||||
\(364\) | 3457.19 | 0.497819 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9999.25 | −1.42806 | ||||||||
\(367\) | 1927.67i | 0.274178i | 0.990559 | + | 0.137089i | \(0.0437747\pi\) | ||||
−0.990559 | + | 0.137089i | \(0.956225\pi\) | |||||||
\(368\) | − 3220.10i | − 0.456139i | ||||||||
\(369\) | 3039.92 | 0.428867 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4736.83 | 0.662868 | ||||||||
\(372\) | 3751.54i | 0.522871i | ||||||||
\(373\) | 10452.0i | 1.45090i | 0.688276 | + | 0.725449i | \(0.258368\pi\) | ||||
−0.688276 | + | 0.725449i | \(0.741632\pi\) | |||||||
\(374\) | 2130.01 | 0.294493 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10166.6 | 1.39443 | ||||||||
\(377\) | 7508.01i | 1.02568i | ||||||||
\(378\) | 888.595i | 0.120911i | ||||||||
\(379\) | −7066.43 | −0.957726 | −0.478863 | − | 0.877890i | \(-0.658951\pi\) | ||||
−0.478863 | + | 0.877890i | \(0.658951\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3326.44 | −0.447293 | ||||||||
\(382\) | − 7404.51i | − 0.991747i | ||||||||
\(383\) | 7168.04i | 0.956318i | 0.878273 | + | 0.478159i | \(0.158696\pi\) | ||||
−0.878273 | + | 0.478159i | \(0.841304\pi\) | |||||||
\(384\) | 7812.52 | 1.03823 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22453.1 | −2.96071 | ||||||||
\(387\) | − 1099.41i | − 0.144408i | ||||||||
\(388\) | 7828.58i | 1.02432i | ||||||||
\(389\) | 7414.06 | 0.966344 | 0.483172 | − | 0.875525i | \(-0.339485\pi\) | ||||
0.483172 | + | 0.875525i | \(0.339485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2683.15 | 0.347040 | ||||||||
\(392\) | − 1406.38i | − 0.181206i | ||||||||
\(393\) | 556.463i | 0.0714245i | ||||||||
\(394\) | 13181.2 | 1.68543 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3122.38 | 0.396226 | ||||||||
\(397\) | 8936.01i | 1.12969i | 0.825198 | + | 0.564843i | \(0.191063\pi\) | ||||
−0.825198 | + | 0.564843i | \(0.808937\pi\) | |||||||
\(398\) | 19290.1i | 2.42946i | ||||||||
\(399\) | 1415.47 | 0.177599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1782.91 | 0.222031 | 0.111015 | − | 0.993819i | \(-0.464590\pi\) | ||||
0.111015 | + | 0.993819i | \(0.464590\pi\) | |||||||
\(402\) | 12806.4i | 1.58887i | ||||||||
\(403\) | 3104.46i | 0.383733i | ||||||||
\(404\) | −26659.9 | −3.28312 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7056.72 | 0.862609 | ||||||||
\(407\) | − 3987.77i | − 0.485667i | ||||||||
\(408\) | − 1585.94i | − 0.192441i | ||||||||
\(409\) | 8759.92 | 1.05905 | 0.529524 | − | 0.848295i | \(-0.322371\pi\) | ||||
0.529524 | + | 0.848295i | \(0.322371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −113.972 | −0.0136784 | ||||||||
\(412\) | − 9347.17i | − 1.11772i | ||||||||
\(413\) | 3509.23i | 0.418106i | ||||||||
\(414\) | 6164.10 | 0.731761 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4400.97 | 0.518691 | ||||||||
\(417\) | − 550.828i | − 0.0646862i | ||||||||
\(418\) | − 7794.75i | − 0.912090i | ||||||||
\(419\) | 3212.74 | 0.374588 | 0.187294 | − | 0.982304i | \(-0.440028\pi\) | ||||
0.187294 | + | 0.982304i | \(0.440028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15757.8 | 1.82420 | 0.912101 | − | 0.409965i | \(-0.134459\pi\) | ||||
0.912101 | + | 0.409965i | \(0.134459\pi\) | |||||||
\(422\) | 3871.79i | 0.446626i | ||||||||
\(423\) | 3187.97i | 0.366440i | ||||||||
\(424\) | −19422.1 | −2.22457 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6069.73 | 0.690327 | ||||||||
\(427\) | 4962.52i | 0.562419i | ||||||||
\(428\) | 22772.5i | 2.57184i | ||||||||
\(429\) | 2583.82 | 0.290788 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −405.917 | −0.0453650 | −0.0226825 | − | 0.999743i | \(-0.507221\pi\) | ||||
−0.0226825 | + | 0.999743i | \(0.507221\pi\) | |||||||
\(432\) | − 596.827i | − 0.0664695i | ||||||||
\(433\) | − 7845.25i | − 0.870713i | −0.900258 | − | 0.435357i | \(-0.856622\pi\) | ||||
0.900258 | − | 0.435357i | \(-0.143378\pi\) | |||||||
\(434\) | 2917.86 | 0.322723 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3063.63 | 0.336516 | ||||||||
\(437\) | − 9818.95i | − 1.07484i | ||||||||
\(438\) | 583.097i | 0.0636106i | ||||||||
\(439\) | −423.029 | −0.0459911 | −0.0229955 | − | 0.999736i | \(-0.507320\pi\) | ||||
−0.0229955 | + | 0.999736i | \(0.507320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 3032.24i | − 0.326310i | ||||||||
\(443\) | − 16058.7i | − 1.72229i | −0.508362 | − | 0.861143i | \(-0.669749\pi\) | ||||
0.508362 | − | 0.861143i | \(-0.330251\pi\) | |||||||
\(444\) | −6860.17 | −0.733264 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3842.09 | 0.407911 | ||||||||
\(447\) | 4150.01i | 0.439125i | ||||||||
\(448\) | − 5374.30i | − 0.566768i | ||||||||
\(449\) | −2186.75 | −0.229842 | −0.114921 | − | 0.993375i | \(-0.536662\pi\) | ||||
−0.114921 | + | 0.993375i | \(0.536662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8308.05 | −0.867430 | ||||||||
\(452\) | 23388.3i | 2.43384i | ||||||||
\(453\) | 2295.77i | 0.238112i | ||||||||
\(454\) | −17188.2 | −1.77683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5803.72 | −0.596018 | ||||||||
\(457\) | 5799.22i | 0.593602i | 0.954939 | + | 0.296801i | \(0.0959198\pi\) | ||||
−0.954939 | + | 0.296801i | \(0.904080\pi\) | |||||||
\(458\) | 4416.62i | 0.450600i | ||||||||
\(459\) | 497.306 | 0.0505714 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9873.35 | 0.997500 | 0.498750 | − | 0.866746i | \(-0.333793\pi\) | ||||
0.498750 | + | 0.866746i | \(0.333793\pi\) | |||||||
\(462\) | − 2428.52i | − 0.244556i | ||||||||
\(463\) | − 6181.84i | − 0.620506i | −0.950654 | − | 0.310253i | \(-0.899586\pi\) | ||||
0.950654 | − | 0.310253i | \(-0.100414\pi\) | |||||||
\(464\) | −4739.66 | −0.474209 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.9529 | −0.00357400 | ||||||||
\(467\) | − 6145.50i | − 0.608950i | −0.952520 | − | 0.304475i | \(-0.901519\pi\) | ||||
0.952520 | − | 0.304475i | \(-0.0984810\pi\) | |||||||
\(468\) | − 4444.96i | − 0.439035i | ||||||||
\(469\) | 6355.69 | 0.625754 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7100.28 | −0.694615 | ||||||||
\(472\) | − 14388.6i | − 1.40316i | ||||||||
\(473\) | 3004.66i | 0.292081i | ||||||||
\(474\) | −12558.6 | −1.21696 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1818.53 | −0.175110 | ||||||||
\(477\) | − 6090.22i | − 0.584595i | ||||||||
\(478\) | − 4180.23i | − 0.399999i | ||||||||
\(479\) | −10879.4 | −1.03777 | −0.518887 | − | 0.854843i | \(-0.673653\pi\) | ||||
−0.518887 | + | 0.854843i | \(0.673653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5676.91 | −0.538139 | ||||||||
\(482\) | − 10062.4i | − 0.950894i | ||||||||
\(483\) | − 3059.17i | − 0.288193i | ||||||||
\(484\) | 10239.9 | 0.961675 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1142.48 | 0.106634 | ||||||||
\(487\) | − 8087.51i | − 0.752526i | −0.926513 | − | 0.376263i | \(-0.877209\pi\) | ||||
0.926513 | − | 0.376263i | \(-0.122791\pi\) | |||||||
\(488\) | − 20347.4i | − 1.88747i | ||||||||
\(489\) | 9413.08 | 0.870499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6959.90 | −0.639707 | −0.319853 | − | 0.947467i | \(-0.603634\pi\) | ||||
−0.319853 | + | 0.947467i | \(0.603634\pi\) | |||||||
\(492\) | 14292.4i | 1.30965i | ||||||||
\(493\) | − 3949.32i | − 0.360788i | ||||||||
\(494\) | −11096.4 | −1.01063 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1959.79 | −0.177413 | ||||||||
\(497\) | − 3012.34i | − 0.271875i | ||||||||
\(498\) | − 14910.8i | − 1.34170i | ||||||||
\(499\) | −18632.0 | −1.67151 | −0.835756 | − | 0.549101i | \(-0.814970\pi\) | ||||
−0.835756 | + | 0.549101i | \(0.814970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 439.406 | 0.0391840 | ||||||||
\(502\) | 31734.6i | 2.82149i | ||||||||
\(503\) | 4627.62i | 0.410209i | 0.978740 | + | 0.205105i | \(0.0657535\pi\) | ||||
−0.978740 | + | 0.205105i | \(0.934247\pi\) | |||||||
\(504\) | −1808.20 | −0.159809 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −16846.4 | −1.48007 | ||||||||
\(507\) | 2912.72i | 0.255145i | ||||||||
\(508\) | − 15639.4i | − 1.36592i | ||||||||
\(509\) | 11351.8 | 0.988528 | 0.494264 | − | 0.869312i | \(-0.335438\pi\) | ||||
0.494264 | + | 0.869312i | \(0.335438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 289.384 | 0.0250521 | ||||||||
\(512\) | 7853.76i | 0.677911i | ||||||||
\(513\) | − 1819.88i | − 0.156627i | ||||||||
\(514\) | −14427.4 | −1.23806 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5168.93 | 0.440987 | ||||||||
\(517\) | − 8712.67i | − 0.741166i | ||||||||
\(518\) | 5335.68i | 0.452580i | ||||||||
\(519\) | 4272.36 | 0.361340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19096.1 | 1.60579 | 0.802893 | − | 0.596123i | \(-0.203293\pi\) | ||||
0.802893 | + | 0.596123i | \(0.203293\pi\) | |||||||
\(522\) | − 9072.93i | − 0.760750i | ||||||||
\(523\) | − 3145.11i | − 0.262956i | −0.991319 | − | 0.131478i | \(-0.958028\pi\) | ||||
0.991319 | − | 0.131478i | \(-0.0419723\pi\) | |||||||
\(524\) | −2616.24 | −0.218113 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21975.7 | −1.82164 | ||||||||
\(527\) | − 1632.99i | − 0.134980i | ||||||||
\(528\) | 1631.12i | 0.134442i | ||||||||
\(529\) | −9054.20 | −0.744160 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4511.87 | 0.368735 | ||||||||
\(532\) | 6654.90i | 0.542343i | ||||||||
\(533\) | 11827.2i | 0.961148i | ||||||||
\(534\) | −20786.4 | −1.68449 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26059.8 | −2.10002 | ||||||||
\(537\) | − 3734.09i | − 0.300071i | ||||||||
\(538\) | 11365.5i | 0.910781i | ||||||||
\(539\) | −1205.25 | −0.0963148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8776.12 | 0.697440 | 0.348720 | − | 0.937227i | \(-0.386616\pi\) | ||||
0.348720 | + | 0.937227i | \(0.386616\pi\) | |||||||
\(542\) | − 36316.3i | − 2.87808i | ||||||||
\(543\) | − 11637.3i | − 0.919710i | ||||||||
\(544\) | −2314.98 | −0.182452 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3457.19 | −0.270978 | ||||||||
\(547\) | 13695.1i | 1.07049i | 0.844696 | + | 0.535247i | \(0.179781\pi\) | ||||
−0.844696 | + | 0.535247i | \(0.820219\pi\) | |||||||
\(548\) | − 535.847i | − 0.0417705i | ||||||||
\(549\) | 6380.38 | 0.496007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14452.5 | −1.11742 | ||||||||
\(552\) | 12543.3i | 0.967171i | ||||||||
\(553\) | 6232.71i | 0.479280i | ||||||||
\(554\) | 21515.2 | 1.64999 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2589.75 | 0.197536 | ||||||||
\(557\) | − 7850.44i | − 0.597188i | −0.954380 | − | 0.298594i | \(-0.903482\pi\) | ||||
0.954380 | − | 0.298594i | \(-0.0965177\pi\) | |||||||
\(558\) | − 3751.54i | − 0.284615i | ||||||||
\(559\) | 4277.38 | 0.323638 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1359.13 | −0.102286 | ||||||||
\(562\) | 6387.33i | 0.479419i | ||||||||
\(563\) | − 4948.81i | − 0.370457i | −0.982695 | − | 0.185229i | \(-0.940697\pi\) | ||||
0.982695 | − | 0.185229i | \(-0.0593026\pi\) | |||||||
\(564\) | −14988.4 | −1.11902 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18265.7 | 1.35648 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | 12351.3i | 0.912408i | ||||||||
\(569\) | 8115.76 | 0.597945 | 0.298972 | − | 0.954262i | \(-0.403356\pi\) | ||||
0.298972 | + | 0.954262i | \(0.403356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5656.42 | 0.414560 | 0.207280 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207280 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(572\) | 12148.0i | 0.887996i | ||||||||
\(573\) | 4724.71i | 0.344463i | ||||||||
\(574\) | 11116.3 | 0.808336 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6909.82 | −0.499842 | ||||||||
\(577\) | 9536.77i | 0.688078i | 0.938955 | + | 0.344039i | \(0.111795\pi\) | ||||
−0.938955 | + | 0.344039i | \(0.888205\pi\) | |||||||
\(578\) | − 21503.8i | − 1.54747i | ||||||||
\(579\) | 14327.0 | 1.02834 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7400.05 | −0.528409 | ||||||||
\(582\) | − 7828.58i | − 0.557569i | ||||||||
\(583\) | 16644.5i | 1.18241i | ||||||||
\(584\) | −1186.54 | −0.0840743 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18965.7 | −1.33697 | ||||||||
\(587\) | 13089.6i | 0.920383i | 0.887820 | + | 0.460191i | \(0.152219\pi\) | ||||
−0.887820 | + | 0.460191i | \(0.847781\pi\) | |||||||
\(588\) | 2073.39i | 0.145417i | ||||||||
\(589\) | −5975.92 | −0.418053 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8410.73 | −0.585400 | ||||||||
\(592\) | − 3583.72i | − 0.248801i | ||||||||
\(593\) | 4281.96i | 0.296524i | 0.988948 | + | 0.148262i | \(0.0473679\pi\) | ||||
−0.988948 | + | 0.148262i | \(0.952632\pi\) | |||||||
\(594\) | −3122.38 | −0.215678 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19511.5 | −1.34098 | ||||||||
\(597\) | − 12308.7i | − 0.843825i | ||||||||
\(598\) | 23982.2i | 1.63997i | ||||||||
\(599\) | −3699.92 | −0.252378 | −0.126189 | − | 0.992006i | \(-0.540275\pi\) | ||||
−0.126189 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17286.1 | −1.17323 | −0.586616 | − | 0.809865i | \(-0.699540\pi\) | ||||
−0.586616 | + | 0.809865i | \(0.699540\pi\) | |||||||
\(602\) | − 4020.28i | − 0.272183i | ||||||||
\(603\) | − 8171.61i | − 0.551863i | ||||||||
\(604\) | −10793.7 | −0.727135 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 26659.9 | 1.78710 | ||||||||
\(607\) | − 14456.7i | − 0.966689i | −0.875430 | − | 0.483344i | \(-0.839422\pi\) | ||||
0.875430 | − | 0.483344i | \(-0.160578\pi\) | |||||||
\(608\) | 8471.63i | 0.565082i | ||||||||
\(609\) | −4502.79 | −0.299610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12403.2 | −0.821243 | ||||||||
\(612\) | 2338.12i | 0.154433i | ||||||||
\(613\) | 17981.9i | 1.18480i | 0.805644 | + | 0.592400i | \(0.201819\pi\) | ||||
−0.805644 | + | 0.592400i | \(0.798181\pi\) | |||||||
\(614\) | 21722.9 | 1.42779 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4941.78 | 0.323231 | ||||||||
\(617\) | − 19614.7i | − 1.27983i | −0.768445 | − | 0.639916i | \(-0.778969\pi\) | ||||
0.768445 | − | 0.639916i | \(-0.221031\pi\) | |||||||
\(618\) | 9347.17i | 0.608412i | ||||||||
\(619\) | 10462.9 | 0.679385 | 0.339692 | − | 0.940537i | \(-0.389677\pi\) | ||||
0.339692 | + | 0.940537i | \(0.389677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3933.22 | −0.254162 | ||||||||
\(622\) | − 31387.1i | − 2.02332i | ||||||||
\(623\) | 10316.1i | 0.663411i | ||||||||
\(624\) | 2322.03 | 0.148967 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13337.3 | 0.851544 | ||||||||
\(627\) | 4973.72i | 0.316796i | ||||||||
\(628\) | − 33382.4i | − 2.12118i | ||||||||
\(629\) | 2986.14 | 0.189293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24481.9 | 1.54454 | 0.772272 | − | 0.635292i | \(-0.219120\pi\) | ||||
0.772272 | + | 0.635292i | \(0.219120\pi\) | |||||||
\(632\) | − 25555.5i | − 1.60846i | ||||||||
\(633\) | − 2470.54i | − 0.155126i | ||||||||
\(634\) | −18856.2 | −1.18119 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28633.5 | 1.78521 | ||||||||
\(637\) | 1715.77i | 0.106721i | ||||||||
\(638\) | 24796.2i | 1.53870i | ||||||||
\(639\) | −3873.01 | −0.239771 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1109.39 | −0.0683595 | −0.0341797 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341797 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(642\) | − 22772.5i | − 1.39993i | ||||||||
\(643\) | 30112.5i | 1.84684i | 0.383787 | + | 0.923422i | \(0.374620\pi\) | ||||
−0.383787 | + | 0.923422i | \(0.625380\pi\) | |||||||
\(644\) | 14382.9 | 0.880071 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5836.90 | 0.355495 | ||||||||
\(647\) | 4260.27i | 0.258869i | 0.991588 | + | 0.129435i | \(0.0413162\pi\) | ||||
−0.991588 | + | 0.129435i | \(0.958684\pi\) | |||||||
\(648\) | 2324.83i | 0.140938i | ||||||||
\(649\) | −12330.9 | −0.745808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1861.85 | −0.112091 | ||||||||
\(652\) | 44256.2i | 2.65829i | ||||||||
\(653\) | − 10576.8i | − 0.633844i | −0.948452 | − | 0.316922i | \(-0.897351\pi\) | ||||
0.948452 | − | 0.316922i | \(-0.102649\pi\) | |||||||
\(654\) | −3063.63 | −0.183176 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7466.27 | −0.444373 | ||||||||
\(657\) | − 372.066i | − 0.0220939i | ||||||||
\(658\) | 11657.7i | 0.690674i | ||||||||
\(659\) | −3394.70 | −0.200666 | −0.100333 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100333 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33174.4 | −1.95210 | −0.976048 | − | 0.217554i | \(-0.930192\pi\) | ||||
−0.976048 | + | 0.217554i | \(0.930192\pi\) | |||||||
\(662\) | − 52128.7i | − 3.06048i | ||||||||
\(663\) | 1934.83i | 0.113337i | ||||||||
\(664\) | 30341.9 | 1.77333 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6860.17 | 0.399138 | ||||||||
\(667\) | 31235.4i | 1.81326i | ||||||||
\(668\) | 2065.89i | 0.119658i | ||||||||
\(669\) | −2451.58 | −0.141680 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17437.5 | −1.00323 | ||||||||
\(672\) | 2639.40i | 0.151514i | ||||||||
\(673\) | 753.881i | 0.0431797i | 0.999767 | + | 0.0215899i | \(0.00687280\pi\) | ||||
−0.999767 | + | 0.0215899i | \(0.993127\pi\) | |||||||
\(674\) | −56976.9 | −3.25619 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13694.3 | −0.779149 | ||||||||
\(677\) | − 15668.8i | − 0.889511i | −0.895652 | − | 0.444756i | \(-0.853291\pi\) | ||||
0.895652 | − | 0.444756i | \(-0.146709\pi\) | |||||||
\(678\) | − 23388.3i | − 1.32481i | ||||||||
\(679\) | −3885.24 | −0.219590 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10967.5 | 0.617147 | ||||||||
\(682\) | 10252.9i | 0.575665i | ||||||||
\(683\) | − 11557.4i | − 0.647485i | −0.946145 | − | 0.323742i | \(-0.895059\pi\) | ||||
0.946145 | − | 0.323742i | \(-0.104941\pi\) | |||||||
\(684\) | 8556.30 | 0.478302 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1612.64 | 0.0897532 | ||||||||
\(687\) | − 2818.18i | − 0.156507i | ||||||||
\(688\) | 2700.22i | 0.149630i | ||||||||
\(689\) | 23694.7 | 1.31016 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18503.1 | −1.01866 | −0.509328 | − | 0.860572i | \(-0.670106\pi\) | ||||
−0.509328 | + | 0.860572i | \(0.670106\pi\) | |||||||
\(692\) | 20086.8i | 1.10344i | ||||||||
\(693\) | 1549.60i | 0.0849416i | ||||||||
\(694\) | 29907.7 | 1.63585 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 18462.5 | 1.00549 | ||||||||
\(697\) | − 6221.28i | − 0.338088i | ||||||||
\(698\) | − 14646.2i | − 0.794223i | ||||||||
\(699\) | 22.9410 | 0.00124136 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22580.4 | 1.21662 | 0.608311 | − | 0.793699i | \(-0.291847\pi\) | ||||
0.608311 | + | 0.793699i | \(0.291847\pi\) | |||||||
\(702\) | 4444.96i | 0.238980i | ||||||||
\(703\) | − 10927.7i | − 0.586269i | ||||||||
\(704\) | 18884.4 | 1.01099 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −56077.4 | −2.98938 | ||||||||
\(707\) | − 13231.0i | − 0.703823i | ||||||||
\(708\) | 21212.8i | 1.12603i | ||||||||
\(709\) | 27426.6 | 1.45279 | 0.726394 | − | 0.687278i | \(-0.241195\pi\) | ||||
0.726394 | + | 0.687278i | \(0.241195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8013.49 | 0.422685 | ||||||||
\(712\) | − 42298.2i | − 2.22639i | ||||||||
\(713\) | 12915.5i | 0.678383i | ||||||||
\(714\) | 1818.53 | 0.0953178 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17556.1 | 0.916342 | ||||||||
\(717\) | 2667.35i | 0.138931i | ||||||||
\(718\) | − 28886.1i | − 1.50142i | ||||||||
\(719\) | −19383.0 | −1.00538 | −0.502688 | − | 0.864468i | \(-0.667656\pi\) | ||||
−0.502688 | + | 0.864468i | \(0.667656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4638.90 | 0.239614 | ||||||||
\(722\) | 10888.0i | 0.561230i | ||||||||
\(723\) | 6420.69i | 0.330274i | ||||||||
\(724\) | 54713.3 | 2.80857 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10239.9 | −0.523469 | ||||||||
\(727\) | 12317.3i | 0.628368i | 0.949362 | + | 0.314184i | \(0.101731\pi\) | ||||
−0.949362 | + | 0.314184i | \(0.898269\pi\) | |||||||
\(728\) | − 7035.02i | − 0.358153i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2249.96 | −0.113841 | ||||||||
\(732\) | 29997.8i | 1.51468i | ||||||||
\(733\) | 1234.02i | 0.0621822i | 0.999517 | + | 0.0310911i | \(0.00989821\pi\) | ||||
−0.999517 | + | 0.0310911i | \(0.990102\pi\) | |||||||
\(734\) | 9063.05 | 0.455754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18309.3 | 0.916970 | ||||||||
\(737\) | 22332.9i | 1.11620i | ||||||||
\(738\) | − 14292.4i | − 0.712885i | ||||||||
\(739\) | 15257.3 | 0.759473 | 0.379736 | − | 0.925095i | \(-0.376015\pi\) | ||||
0.379736 | + | 0.925095i | \(0.376015\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7080.49 | 0.351023 | ||||||||
\(742\) | − 22270.5i | − 1.10186i | ||||||||
\(743\) | − 35565.1i | − 1.75606i | −0.478602 | − | 0.878032i | \(-0.658856\pi\) | ||||
0.478602 | − | 0.878032i | \(-0.341144\pi\) | |||||||
\(744\) | 7633.99 | 0.376177 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 49140.8 | 2.41176 | ||||||||
\(747\) | 9514.35i | 0.466013i | ||||||||
\(748\) | − 6390.04i | − 0.312357i | ||||||||
\(749\) | −11301.7 | −0.551343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14266.7 | 0.693209 | 0.346605 | − | 0.938011i | \(-0.387335\pi\) | ||||
0.346605 | + | 0.938011i | \(0.387335\pi\) | |||||||
\(752\) | − 7829.89i | − 0.379690i | ||||||||
\(753\) | − 20249.4i | − 0.979986i | ||||||||
\(754\) | 35299.4 | 1.70494 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2665.79 | 0.128246 | ||||||||
\(757\) | 15927.9i | 0.764744i | 0.924009 | + | 0.382372i | \(0.124893\pi\) | ||||
−0.924009 | + | 0.382372i | \(0.875107\pi\) | |||||||
\(758\) | 33223.3i | 1.59198i | ||||||||
\(759\) | 10749.4 | 0.514071 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2566.48 | −0.122253 | −0.0611266 | − | 0.998130i | \(-0.519469\pi\) | ||||
−0.0611266 | + | 0.998130i | \(0.519469\pi\) | |||||||
\(762\) | 15639.4i | 0.743514i | ||||||||
\(763\) | 1520.44i | 0.0721413i | ||||||||
\(764\) | −22213.5 | −1.05191 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33701.0 | 1.58964 | ||||||||
\(767\) | 17554.0i | 0.826386i | ||||||||
\(768\) | − 18304.9i | − 0.860052i | ||||||||
\(769\) | −14433.1 | −0.676816 | −0.338408 | − | 0.940999i | \(-0.609888\pi\) | ||||
−0.338408 | + | 0.940999i | \(0.609888\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9205.91 | 0.430017 | ||||||||
\(772\) | 67359.4i | 3.14031i | ||||||||
\(773\) | − 29443.2i | − 1.36999i | −0.728550 | − | 0.684993i | \(-0.759805\pi\) | ||||
0.728550 | − | 0.684993i | \(-0.240195\pi\) | |||||||
\(774\) | −5168.93 | −0.240043 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15930.4 | 0.736941 | ||||||||
\(777\) | − 3404.62i | − 0.157195i | ||||||||
\(778\) | − 34857.7i | − 1.60631i | ||||||||
\(779\) | −22766.7 | −1.04711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10584.9 | 0.484964 | ||||||||
\(782\) | − 12615.0i | − 0.576869i | ||||||||
\(783\) | 5789.31i | 0.264231i | ||||||||
\(784\) | −1083.13 | −0.0493408 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2616.24 | 0.118726 | ||||||||
\(787\) | − 26390.6i | − 1.19533i | −0.801747 | − | 0.597664i | \(-0.796096\pi\) | ||||
0.801747 | − | 0.597664i | \(-0.203904\pi\) | |||||||
\(788\) | − 39543.6i | − 1.78767i | ||||||||
\(789\) | 14022.4 | 0.632711 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11607.4 | −0.521758 | ||||||||
\(792\) | − 6353.72i | − 0.285063i | ||||||||
\(793\) | 24823.7i | 1.11162i | ||||||||
\(794\) | 42013.2 | 1.87783 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 57870.3 | 2.57683 | ||||||||
\(797\) | 3738.33i | 0.166146i | 0.996543 | + | 0.0830730i | \(0.0264735\pi\) | ||||
−0.996543 | + | 0.0830730i | \(0.973527\pi\) | |||||||
\(798\) | − 6654.90i | − 0.295214i | ||||||||
\(799\) | 6524.26 | 0.288876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13263.5 | 0.585073 | ||||||||
\(802\) | − 8382.48i | − 0.369072i | ||||||||
\(803\) | 1016.85i | 0.0446873i | ||||||||
\(804\) | 38419.3 | 1.68525 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14595.8 | 0.637861 | ||||||||
\(807\) | − 7252.14i | − 0.316341i | ||||||||
\(808\) | 54250.1i | 2.36202i | ||||||||
\(809\) | −43204.1 | −1.87760 | −0.938798 | − | 0.344468i | \(-0.888059\pi\) | ||||
−0.938798 | + | 0.344468i | \(0.888059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30192.4 | −1.30727 | −0.653637 | − | 0.756809i | \(-0.726758\pi\) | ||||
−0.653637 | + | 0.756809i | \(0.726758\pi\) | |||||||
\(812\) | − 21170.2i | − 0.914935i | ||||||||
\(813\) | 23172.9i | 0.999642i | ||||||||
\(814\) | −18748.7 | −0.807301 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1221.42 | −0.0523999 | ||||||||
\(817\) | 8233.71i | 0.352584i | ||||||||
\(818\) | − 41185.3i | − 1.76041i | ||||||||
\(819\) | 2205.98 | 0.0941188 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40274.7 | −1.71206 | −0.856028 | − | 0.516929i | \(-0.827075\pi\) | ||||
−0.856028 | + | 0.516929i | \(0.827075\pi\) | |||||||
\(822\) | 535.847i | 0.0227370i | ||||||||
\(823\) | 25184.2i | 1.06667i | 0.845905 | + | 0.533334i | \(0.179061\pi\) | ||||
−0.845905 | + | 0.533334i | \(0.820939\pi\) | |||||||
\(824\) | −19020.5 | −0.804140 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16498.9 | 0.694999 | ||||||||
\(827\) | 38941.7i | 1.63741i | 0.574218 | + | 0.818703i | \(0.305306\pi\) | ||||
−0.574218 | + | 0.818703i | \(0.694694\pi\) | |||||||
\(828\) | − 18492.3i | − 0.776150i | ||||||||
\(829\) | 8327.05 | 0.348867 | 0.174433 | − | 0.984669i | \(-0.444191\pi\) | ||||
0.174433 | + | 0.984669i | \(0.444191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13728.5 | −0.573089 | ||||||||
\(832\) | − 26883.5i | − 1.12021i | ||||||||
\(833\) | − 902.519i | − 0.0375395i | ||||||||
\(834\) | −2589.75 | −0.107525 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23384.2 | −0.967418 | ||||||||
\(837\) | 2393.80i | 0.0988553i | ||||||||
\(838\) | − 15104.9i | − 0.622660i | ||||||||
\(839\) | −8784.41 | −0.361468 | −0.180734 | − | 0.983532i | \(-0.557847\pi\) | ||||
−0.180734 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21586.4 | 0.885087 | ||||||||
\(842\) | − 74086.4i | − 3.03229i | ||||||||
\(843\) | − 4075.67i | − 0.166517i | ||||||||
\(844\) | 11615.4 | 0.473718 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14988.4 | 0.609117 | ||||||||
\(847\) | 5081.96i | 0.206161i | ||||||||
\(848\) | 14958.0i | 0.605732i | ||||||||
\(849\) | −11655.1 | −0.471145 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23617.6 | −0.951350 | ||||||||
\(852\) | − 18209.2i | − 0.732203i | ||||||||
\(853\) | − 9076.15i | − 0.364316i | −0.983269 | − | 0.182158i | \(-0.941692\pi\) | ||||
0.983269 | − | 0.182158i | \(-0.0583082\pi\) | |||||||
\(854\) | 23331.6 | 0.934884 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46339.6 | 1.85030 | ||||||||
\(857\) | − 36396.7i | − 1.45074i | −0.688357 | − | 0.725372i | \(-0.741668\pi\) | ||||
0.688357 | − | 0.725372i | \(-0.258332\pi\) | |||||||
\(858\) | − 12148.0i | − 0.483364i | ||||||||
\(859\) | −8915.27 | −0.354115 | −0.177058 | − | 0.984200i | \(-0.556658\pi\) | ||||
−0.177058 | + | 0.984200i | \(0.556658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7093.14 | −0.280759 | ||||||||
\(862\) | 1908.44i | 0.0754081i | ||||||||
\(863\) | − 6148.26i | − 0.242514i | −0.992621 | − | 0.121257i | \(-0.961308\pi\) | ||||
0.992621 | − | 0.121257i | \(-0.0386925\pi\) | |||||||
\(864\) | 3393.52 | 0.133623 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36884.9 | −1.44735 | ||||||||
\(867\) | 13721.2i | 0.537483i | ||||||||
\(868\) | − 8753.59i | − 0.342300i | ||||||||
\(869\) | −21900.8 | −0.854928 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31792.6 | 1.23680 | ||||||||
\(872\) | − 6234.16i | − 0.242105i | ||||||||
\(873\) | 4995.31i | 0.193660i | ||||||||
\(874\) | −46164.4 | −1.78665 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1749.29 | 0.0674692 | ||||||||
\(877\) | 14287.0i | 0.550101i | 0.961430 | + | 0.275050i | \(0.0886945\pi\) | ||||
−0.961430 | + | 0.275050i | \(0.911306\pi\) | |||||||
\(878\) | 1988.90i | 0.0764488i | ||||||||
\(879\) | 12101.7 | 0.464370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13315.9 | −0.509221 | −0.254610 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254610 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(882\) | − 2073.39i | − 0.0791549i | ||||||||
\(883\) | − 5271.78i | − 0.200917i | −0.994941 | − | 0.100458i | \(-0.967969\pi\) | ||||
0.994941 | − | 0.100458i | \(-0.0320309\pi\) | |||||||
\(884\) | −9096.73 | −0.346104 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −75501.1 | −2.86288 | ||||||||
\(887\) | − 2606.07i | − 0.0986507i | −0.998783 | − | 0.0493253i | \(-0.984293\pi\) | ||||
0.998783 | − | 0.0493253i | \(-0.0157071\pi\) | |||||||
\(888\) | 13959.7i | 0.527542i | ||||||||
\(889\) | 7761.69 | 0.292822 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1992.35 | 0.0749115 | ||||||||
\(892\) | − 11526.3i | − 0.432654i | ||||||||
\(893\) | − 23875.4i | − 0.894694i | ||||||||
\(894\) | 19511.5 | 0.729937 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18229.2 | −0.679682 | ||||||||
\(897\) | − 15302.7i | − 0.569612i | ||||||||
\(898\) | 10281.1i | 0.382056i | ||||||||
\(899\) | 19010.2 | 0.705258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12463.8 | −0.460854 | ||||||||
\(902\) | 39060.8i | 1.44189i | ||||||||
\(903\) | 2565.28i | 0.0945373i | ||||||||
\(904\) | 47592.8 | 1.75101 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10793.7 | 0.395802 | ||||||||
\(907\) | − 18610.6i | − 0.681317i | −0.940187 | − | 0.340659i | \(-0.889350\pi\) | ||||
0.940187 | − | 0.340659i | \(-0.110650\pi\) | |||||||
\(908\) | 51564.6i | 1.88462i | ||||||||
\(909\) | −17011.3 | −0.620714 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41091.7 | 1.49443 | 0.747216 | − | 0.664581i | \(-0.231390\pi\) | ||||
0.747216 | + | 0.664581i | \(0.231390\pi\) | |||||||
\(912\) | 4469.77i | 0.162291i | ||||||||
\(913\) | − 26002.6i | − 0.942563i | ||||||||
\(914\) | 27265.4 | 0.986716 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13249.8 | 0.477934 | ||||||||
\(917\) | − 1298.41i | − 0.0467583i | ||||||||
\(918\) | − 2338.12i | − 0.0840624i | ||||||||
\(919\) | −38891.3 | −1.39598 | −0.697990 | − | 0.716107i | \(-0.745922\pi\) | ||||
−0.697990 | + | 0.716107i | \(0.745922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13861.1 | −0.495915 | ||||||||
\(922\) | − 46420.2i | − 1.65810i | ||||||||
\(923\) | − 15068.4i | − 0.537360i | ||||||||
\(924\) | −7285.56 | −0.259391 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29064.3 | −1.03144 | ||||||||
\(927\) | − 5964.30i | − 0.211320i | ||||||||
\(928\) | − 26949.4i | − 0.953295i | ||||||||
\(929\) | −18699.4 | −0.660396 | −0.330198 | − | 0.943912i | \(-0.607115\pi\) | ||||
−0.330198 | + | 0.943912i | \(0.607115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3302.75 | −0.116266 | ||||||||
\(932\) | 107.859i | 0.00379080i | ||||||||
\(933\) | 20027.7i | 0.702761i | ||||||||
\(934\) | −28893.4 | −1.01223 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9045.03 | −0.315861 | ||||||||
\(937\) | − 21509.6i | − 0.749933i | −0.927038 | − | 0.374967i | \(-0.877654\pi\) | ||||
0.927038 | − | 0.374967i | \(-0.122346\pi\) | |||||||
\(938\) | − 29881.7i | − 1.04016i | ||||||||
\(939\) | −8510.35 | −0.295767 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11241.7 | −0.389448 | −0.194724 | − | 0.980858i | \(-0.562381\pi\) | ||||
−0.194724 | + | 0.980858i | \(0.562381\pi\) | |||||||
\(942\) | 33382.4i | 1.15463i | ||||||||
\(943\) | 49204.5i | 1.69917i | ||||||||
\(944\) | −11081.5 | −0.382068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14126.6 | 0.485513 | ||||||||
\(947\) | 36556.3i | 1.25441i | 0.778856 | + | 0.627203i | \(0.215800\pi\) | ||||
−0.778856 | + | 0.627203i | \(0.784200\pi\) | |||||||
\(948\) | 37675.9i | 1.29078i | ||||||||
\(949\) | 1447.57 | 0.0495153 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12031.9 | 0.410263 | ||||||||
\(952\) | 3700.53i | 0.125982i | ||||||||
\(953\) | − 36633.4i | − 1.24520i | −0.782542 | − | 0.622598i | \(-0.786077\pi\) | ||||
0.782542 | − | 0.622598i | \(-0.213923\pi\) | |||||||
\(954\) | −28633.5 | −0.971745 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12540.7 | −0.424263 | ||||||||
\(957\) | − 15822.1i | − 0.534436i | ||||||||
\(958\) | 51150.3i | 1.72504i | ||||||||
\(959\) | 265.935 | 0.00895462 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21930.5 | −0.736146 | ||||||||
\(962\) | 26690.3i | 0.894523i | ||||||||
\(963\) | 14530.8i | 0.486239i | ||||||||
\(964\) | −30187.3 | −1.00858 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14382.9 | −0.479050 | ||||||||
\(967\) | 35515.8i | 1.18109i | 0.807006 | + | 0.590544i | \(0.201087\pi\) | ||||
−0.807006 | + | 0.590544i | \(0.798913\pi\) | |||||||
\(968\) | − 20837.2i | − 0.691871i | ||||||||
\(969\) | −3724.44 | −0.123474 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39661.0 | −1.31080 | −0.655398 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(972\) | − 3427.44i | − 0.113102i | ||||||||
\(973\) | 1285.26i | 0.0423471i | ||||||||
\(974\) | −38023.9 | −1.25089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15670.7 | −0.513942 | ||||||||
\(977\) | − 50325.3i | − 1.64795i | −0.566624 | − | 0.823977i | \(-0.691751\pi\) | ||||
0.566624 | − | 0.823977i | \(-0.308249\pi\) | |||||||
\(978\) | − 44256.2i | − 1.44699i | ||||||||
\(979\) | −36249.0 | −1.18337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1954.86 | 0.0636226 | ||||||||
\(982\) | 32722.4i | 1.06335i | ||||||||
\(983\) | 51189.0i | 1.66091i | 0.557084 | + | 0.830456i | \(0.311920\pi\) | ||||
−0.557084 | + | 0.830456i | \(0.688080\pi\) | |||||||
\(984\) | 29083.5 | 0.942223 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18568.0 | −0.599721 | ||||||||
\(987\) | − 7438.59i | − 0.239892i | ||||||||
\(988\) | 33289.3i | 1.07194i | ||||||||
\(989\) | 17795.1 | 0.572145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55137.3 | −1.76740 | −0.883700 | − | 0.468054i | \(-0.844955\pi\) | ||||
−0.883700 | + | 0.468054i | \(0.844955\pi\) | |||||||
\(992\) | − 11143.2i | − 0.356651i | ||||||||
\(993\) | 33262.6i | 1.06300i | ||||||||
\(994\) | −14162.7 | −0.451925 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −44732.3 | −1.42309 | ||||||||
\(997\) | − 41606.5i | − 1.32166i | −0.750537 | − | 0.660828i | \(-0.770205\pi\) | ||||
0.750537 | − | 0.660828i | \(-0.229795\pi\) | |||||||
\(998\) | 87599.6i | 2.77848i | ||||||||
\(999\) | −4377.37 | −0.138633 |
(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 | 525.4.d.j.274.1 | 4 | ||
5.2 | odd | 4 | 105.4.a.g.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.i.1.1 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.j.274.4 | 4 | ||
15.2 | even | 4 | 315.4.a.g.1.1 | 2 | |||
15.8 | even | 4 | 1575.4.a.y.1.2 | 2 | |||
20.7 | even | 4 | 1680.4.a.y.1.2 | 2 | |||
35.27 | even | 4 | 735.4.a.q.1.2 | 2 | |||
105.62 | odd | 4 | 2205.4.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.g.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.g.1.1 | 2 | 15.2 | even | 4 | |||
525.4.a.i.1.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.j.274.1 | 4 | 1.1 | even | 1 | trivial | ||
525.4.d.j.274.4 | 4 | 5.4 | even | 2 | inner | ||
735.4.a.q.1.2 | 2 | 35.27 | even | 4 | |||
1575.4.a.y.1.2 | 2 | 15.8 | even | 4 | |||
1680.4.a.y.1.2 | 2 | 20.7 | even | 4 | |||
2205.4.a.v.1.1 | 2 | 105.62 | odd | 4 |