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: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.k.274.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.23607i | 1.49768i | 0.662753 | + | 0.748838i | \(0.269388\pi\) | ||||
−0.662753 | + | 0.748838i | \(0.730612\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −9.94427 | −1.24303 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −12.7082 | −0.864684 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − 8.23607i | − 0.363986i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −41.5279 | −1.13828 | −0.569142 | − | 0.822239i | \(-0.692725\pi\) | ||||
−0.569142 | + | 0.822239i | \(0.692725\pi\) | |||||||
\(12\) | − 29.8328i | − 0.717666i | ||||||||
\(13\) | 88.9706i | 1.89815i | 0.315044 | + | 0.949077i | \(0.397981\pi\) | ||||
−0.315044 | + | 0.949077i | \(0.602019\pi\) | |||||||
\(14\) | −29.6525 | −0.566068 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −44.6656 | −0.697900 | ||||||||
\(17\) | 120.387i | 1.71754i | 0.512364 | + | 0.858769i | \(0.328770\pi\) | ||||
−0.512364 | + | 0.858769i | \(0.671230\pi\) | |||||||
\(18\) | − 38.1246i | − 0.499225i | ||||||||
\(19\) | 112.138 | 1.35401 | 0.677004 | − | 0.735979i | \(-0.263278\pi\) | ||||
0.677004 | + | 0.735979i | \(0.263278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − 175.915i | − 1.70478i | ||||||||
\(23\) | − 115.279i | − 1.04510i | −0.852609 | − | 0.522549i | \(-0.824981\pi\) | ||||
0.852609 | − | 0.522549i | \(-0.175019\pi\) | |||||||
\(24\) | 24.7082 | 0.210148 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −376.885 | −2.84282 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | − 69.6099i | − 0.469823i | ||||||||
\(29\) | 144.833 | 0.927406 | 0.463703 | − | 0.885991i | \(-0.346520\pi\) | ||||
0.463703 | + | 0.885991i | \(0.346520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −258.079 | −1.49524 | −0.747618 | − | 0.664128i | \(-0.768803\pi\) | ||||
−0.747618 | + | 0.664128i | \(0.768803\pi\) | |||||||
\(32\) | − 255.095i | − 1.40922i | ||||||||
\(33\) | − 124.584i | − 0.657188i | ||||||||
\(34\) | −509.967 | −2.57231 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 89.4984 | 0.414345 | ||||||||
\(37\) | − 48.3344i | − 0.214760i | −0.994218 | − | 0.107380i | \(-0.965754\pi\) | ||||
0.994218 | − | 0.107380i | \(-0.0342461\pi\) | |||||||
\(38\) | 475.023i | 2.02787i | ||||||||
\(39\) | −266.912 | −1.09590 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 200.885 | 0.765196 | 0.382598 | − | 0.923915i | \(-0.375029\pi\) | ||||
0.382598 | + | 0.923915i | \(0.375029\pi\) | |||||||
\(42\) | − 88.9574i | − 0.326820i | ||||||||
\(43\) | − 218.217i | − 0.773901i | −0.922101 | − | 0.386950i | \(-0.873528\pi\) | ||||
0.922101 | − | 0.386950i | \(-0.126472\pi\) | |||||||
\(44\) | 412.964 | 1.41493 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 488.328 | 1.56522 | ||||||||
\(47\) | − 575.659i | − 1.78657i | −0.449496 | − | 0.893283i | \(-0.648396\pi\) | ||||
0.449496 | − | 0.893283i | \(-0.351604\pi\) | |||||||
\(48\) | − 133.997i | − 0.402933i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −361.161 | −0.991621 | ||||||||
\(52\) | − 884.748i | − 2.35947i | ||||||||
\(53\) | − 184.302i | − 0.477657i | −0.971062 | − | 0.238828i | \(-0.923237\pi\) | ||||
0.971062 | − | 0.238828i | \(-0.0767633\pi\) | |||||||
\(54\) | 114.374 | 0.288228 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 57.6525 | 0.137574 | ||||||||
\(57\) | 336.413i | 0.781737i | ||||||||
\(58\) | 613.522i | 1.38895i | ||||||||
\(59\) | 151.502 | 0.334302 | 0.167151 | − | 0.985931i | \(-0.446543\pi\) | ||||
0.167151 | + | 0.985931i | \(0.446543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −529.830 | −1.11209 | −0.556047 | − | 0.831151i | \(-0.687683\pi\) | ||||
−0.556047 | + | 0.831151i | \(0.687683\pi\) | |||||||
\(62\) | − 1093.24i | − 2.23938i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | 723.276 | 1.41265 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 527.745 | 0.984256 | ||||||||
\(67\) | − 1.28485i | − 0.00234283i | −0.999999 | − | 0.00117142i | \(-0.999627\pi\) | ||||
0.999999 | − | 0.00117142i | \(-0.000372873\pi\) | |||||||
\(68\) | − 1197.16i | − 2.13496i | ||||||||
\(69\) | 345.836 | 0.603388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.4226 | −0.102669 | −0.0513347 | − | 0.998682i | \(-0.516348\pi\) | ||||
−0.0513347 | + | 0.998682i | \(0.516348\pi\) | |||||||
\(72\) | 74.1246i | 0.121329i | ||||||||
\(73\) | 484.800i | 0.777282i | 0.921389 | + | 0.388641i | \(0.127055\pi\) | ||||
−0.921389 | + | 0.388641i | \(0.872945\pi\) | |||||||
\(74\) | 204.748 | 0.321641 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1115.13 | −1.68308 | ||||||||
\(77\) | − 290.695i | − 0.430231i | ||||||||
\(78\) | − 1130.66i | − 1.64130i | ||||||||
\(79\) | −878.257 | −1.25078 | −0.625390 | − | 0.780312i | \(-0.715060\pi\) | ||||
−0.625390 | + | 0.780312i | \(0.715060\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 850.964i | 1.14602i | ||||||||
\(83\) | 491.830i | 0.650426i | 0.945641 | + | 0.325213i | \(0.105436\pi\) | ||||
−0.945641 | + | 0.325213i | \(0.894564\pi\) | |||||||
\(84\) | 208.830 | 0.271252 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 924.381 | 1.15905 | ||||||||
\(87\) | 434.498i | 0.535438i | ||||||||
\(88\) | 342.026i | 0.414320i | ||||||||
\(89\) | 415.560 | 0.494936 | 0.247468 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247468 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −622.794 | −0.717435 | ||||||||
\(92\) | 1146.36i | 1.29909i | ||||||||
\(93\) | − 774.237i | − 0.863275i | ||||||||
\(94\) | 2438.53 | 2.67570 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 765.286 | 0.813611 | ||||||||
\(97\) | 1031.70i | 1.07993i | 0.841688 | + | 0.539964i | \(0.181562\pi\) | ||||
−0.841688 | + | 0.539964i | \(0.818438\pi\) | |||||||
\(98\) | − 207.567i | − 0.213954i | ||||||||
\(99\) | 373.751 | 0.379428 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1447.19 | 1.42576 | 0.712878 | − | 0.701288i | \(-0.247391\pi\) | ||||
0.712878 | + | 0.701288i | \(0.247391\pi\) | |||||||
\(102\) | − 1529.90i | − 1.48513i | ||||||||
\(103\) | − 163.567i | − 0.156473i | −0.996935 | − | 0.0782364i | \(-0.975071\pi\) | ||||
0.996935 | − | 0.0782364i | \(-0.0249289\pi\) | |||||||
\(104\) | 732.768 | 0.690902 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 780.715 | 0.715375 | ||||||||
\(107\) | 129.653i | 0.117141i | 0.998283 | + | 0.0585703i | \(0.0186542\pi\) | ||||
−0.998283 | + | 0.0585703i | \(0.981346\pi\) | |||||||
\(108\) | 268.495i | 0.239222i | ||||||||
\(109\) | −566.681 | −0.497965 | −0.248983 | − | 0.968508i | \(-0.580096\pi\) | ||||
−0.248983 | + | 0.968508i | \(0.580096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 145.003 | 0.123992 | ||||||||
\(112\) | − 312.659i | − 0.263782i | ||||||||
\(113\) | 809.890i | 0.674230i | 0.941463 | + | 0.337115i | \(0.109451\pi\) | ||||
−0.941463 | + | 0.337115i | \(0.890549\pi\) | |||||||
\(114\) | −1425.07 | −1.17079 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1440.26 | −1.15280 | ||||||||
\(117\) | − 800.735i | − 0.632718i | ||||||||
\(118\) | 641.771i | 0.500676i | ||||||||
\(119\) | −842.709 | −0.649168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 393.563 | 0.295690 | ||||||||
\(122\) | − 2244.39i | − 1.66556i | ||||||||
\(123\) | 602.656i | 0.441786i | ||||||||
\(124\) | 2566.41 | 1.85863 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 266.872 | 0.188689 | ||||||||
\(127\) | 2584.25i | 1.80563i | 0.430028 | + | 0.902816i | \(0.358504\pi\) | ||||
−0.430028 | + | 0.902816i | \(0.641496\pi\) | |||||||
\(128\) | 1023.08i | 0.706473i | ||||||||
\(129\) | 654.650 | 0.446812 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1421.10 | −0.947804 | −0.473902 | − | 0.880578i | \(-0.657155\pi\) | ||||
−0.473902 | + | 0.880578i | \(0.657155\pi\) | |||||||
\(132\) | 1238.89i | 0.816908i | ||||||||
\(133\) | 784.964i | 0.511767i | ||||||||
\(134\) | 5.44272 | 0.00350880 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 991.515 | 0.625160 | ||||||||
\(137\) | − 104.878i | − 0.0654037i | −0.999465 | − | 0.0327019i | \(-0.989589\pi\) | ||||
0.999465 | − | 0.0327019i | \(-0.0104112\pi\) | |||||||
\(138\) | 1464.98i | 0.903679i | ||||||||
\(139\) | 913.160 | 0.557217 | 0.278609 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278609 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1726.98 | 1.03147 | ||||||||
\(142\) | − 260.190i | − 0.153765i | ||||||||
\(143\) | − 3694.76i | − 2.16064i | ||||||||
\(144\) | 401.991 | 0.232633 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2053.65 | −1.16412 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | 480.650i | 0.266954i | ||||||||
\(149\) | −1781.45 | −0.979476 | −0.489738 | − | 0.871870i | \(-0.662908\pi\) | ||||
−0.489738 | + | 0.871870i | \(0.662908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1407.53 | 0.758564 | 0.379282 | − | 0.925281i | \(-0.376171\pi\) | ||||
0.379282 | + | 0.925281i | \(0.376171\pi\) | |||||||
\(152\) | − 923.574i | − 0.492841i | ||||||||
\(153\) | − 1083.48i | − 0.572512i | ||||||||
\(154\) | 1231.40 | 0.644346 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2654.24 | 1.36224 | ||||||||
\(157\) | 1598.94i | 0.812798i | 0.913696 | + | 0.406399i | \(0.133216\pi\) | ||||
−0.913696 | + | 0.406399i | \(0.866784\pi\) | |||||||
\(158\) | − 3720.36i | − 1.87326i | ||||||||
\(159\) | 552.906 | 0.275775 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 806.950 | 0.395010 | ||||||||
\(162\) | 343.122i | 0.166408i | ||||||||
\(163\) | − 204.892i | − 0.0984562i | −0.998788 | − | 0.0492281i | \(-0.984324\pi\) | ||||
0.998788 | − | 0.0492281i | \(-0.0156761\pi\) | |||||||
\(164\) | −1997.66 | −0.951165 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2083.42 | −0.974127 | ||||||||
\(167\) | 1165.94i | 0.540259i | 0.962824 | + | 0.270129i | \(0.0870665\pi\) | ||||
−0.962824 | + | 0.270129i | \(0.912933\pi\) | |||||||
\(168\) | 172.957i | 0.0794283i | ||||||||
\(169\) | −5718.76 | −2.60299 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1009.24 | −0.451336 | ||||||||
\(172\) | 2170.01i | 0.961985i | ||||||||
\(173\) | − 2538.00i | − 1.11538i | −0.830049 | − | 0.557690i | \(-0.811688\pi\) | ||||
0.830049 | − | 0.557690i | \(-0.188312\pi\) | |||||||
\(174\) | −1840.56 | −0.801913 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1854.87 | 0.794409 | ||||||||
\(177\) | 454.505i | 0.193009i | ||||||||
\(178\) | 1760.34i | 0.741254i | ||||||||
\(179\) | −392.255 | −0.163791 | −0.0818954 | − | 0.996641i | \(-0.526097\pi\) | ||||
−0.0818954 | + | 0.996641i | \(0.526097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2978.08 | −1.22298 | −0.611489 | − | 0.791253i | \(-0.709429\pi\) | ||||
−0.611489 | + | 0.791253i | \(0.709429\pi\) | |||||||
\(182\) | − 2638.20i | − 1.07448i | ||||||||
\(183\) | − 1589.49i | − 0.642068i | ||||||||
\(184\) | −949.443 | −0.380401 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3279.72 | 1.29291 | ||||||||
\(187\) | − 4999.41i | − 1.95504i | ||||||||
\(188\) | 5724.51i | 2.22076i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1097.37 | −0.415722 | −0.207861 | − | 0.978158i | \(-0.566650\pi\) | ||||
−0.207861 | + | 0.978158i | \(0.566650\pi\) | |||||||
\(192\) | 2169.83i | 0.815592i | ||||||||
\(193\) | 3500.31i | 1.30548i | 0.757582 | + | 0.652740i | \(0.226381\pi\) | ||||
−0.757582 | + | 0.652740i | \(0.773619\pi\) | |||||||
\(194\) | −4370.34 | −1.61738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 487.269 | 0.177576 | ||||||||
\(197\) | − 1573.96i | − 0.569237i | −0.958641 | − | 0.284618i | \(-0.908133\pi\) | ||||
0.958641 | − | 0.284618i | \(-0.0918669\pi\) | |||||||
\(198\) | 1583.23i | 0.568260i | ||||||||
\(199\) | 3396.62 | 1.20995 | 0.604976 | − | 0.796244i | \(-0.293183\pi\) | ||||
0.604976 | + | 0.796244i | \(0.293183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.85456 | 0.00135263 | ||||||||
\(202\) | 6130.42i | 2.13532i | ||||||||
\(203\) | 1013.83i | 0.350527i | ||||||||
\(204\) | 3591.48 | 1.23262 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 692.879 | 0.234346 | ||||||||
\(207\) | 1037.51i | 0.348366i | ||||||||
\(208\) | − 3973.93i | − 1.32472i | ||||||||
\(209\) | −4656.84 | −1.54125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3337.81 | 1.08903 | 0.544513 | − | 0.838753i | \(-0.316715\pi\) | ||||
0.544513 | + | 0.838753i | \(0.316715\pi\) | |||||||
\(212\) | 1832.75i | 0.593744i | ||||||||
\(213\) | − 184.268i | − 0.0592762i | ||||||||
\(214\) | −549.220 | −0.175439 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −222.374 | −0.0700492 | ||||||||
\(217\) | − 1806.55i | − 0.565146i | ||||||||
\(218\) | − 2400.50i | − 0.745791i | ||||||||
\(219\) | −1454.40 | −0.448764 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10710.9 | −3.26015 | ||||||||
\(222\) | 614.243i | 0.185700i | ||||||||
\(223\) | 127.328i | 0.0382356i | 0.999817 | + | 0.0191178i | \(0.00608575\pi\) | ||||
−0.999817 | + | 0.0191178i | \(0.993914\pi\) | |||||||
\(224\) | 1785.67 | 0.532633 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3430.75 | −1.00978 | ||||||||
\(227\) | − 3844.12i | − 1.12398i | −0.827144 | − | 0.561990i | \(-0.810036\pi\) | ||||
0.827144 | − | 0.561990i | \(-0.189964\pi\) | |||||||
\(228\) | − 3345.39i | − 0.971726i | ||||||||
\(229\) | −2536.95 | −0.732080 | −0.366040 | − | 0.930599i | \(-0.619287\pi\) | ||||
−0.366040 | + | 0.930599i | \(0.619287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 872.085 | 0.248394 | ||||||||
\(232\) | − 1192.85i | − 0.337563i | ||||||||
\(233\) | 3987.44i | 1.12114i | 0.828107 | + | 0.560570i | \(0.189418\pi\) | ||||
−0.828107 | + | 0.560570i | \(0.810582\pi\) | |||||||
\(234\) | 3391.97 | 0.947607 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1506.57 | −0.415549 | ||||||||
\(237\) | − 2634.77i | − 0.722138i | ||||||||
\(238\) | − 3569.77i | − 0.972244i | ||||||||
\(239\) | 3367.18 | 0.911317 | 0.455659 | − | 0.890155i | \(-0.349404\pi\) | ||||
0.455659 | + | 0.890155i | \(0.349404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −939.551 | −0.251128 | −0.125564 | − | 0.992086i | \(-0.540074\pi\) | ||||
−0.125564 | + | 0.992086i | \(0.540074\pi\) | |||||||
\(242\) | 1667.16i | 0.442848i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 5268.77 | 1.38237 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2552.89 | −0.661653 | ||||||||
\(247\) | 9976.96i | 2.57012i | ||||||||
\(248\) | 2125.56i | 0.544246i | ||||||||
\(249\) | −1475.49 | −0.375523 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1403.96 | −0.353056 | −0.176528 | − | 0.984296i | \(-0.556487\pi\) | ||||
−0.176528 | + | 0.984296i | \(0.556487\pi\) | |||||||
\(252\) | 626.489i | 0.156608i | ||||||||
\(253\) | 4787.28i | 1.18962i | ||||||||
\(254\) | −10947.1 | −2.70425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1452.36 | 0.354579 | ||||||||
\(257\) | 1964.86i | 0.476905i | 0.971154 | + | 0.238453i | \(0.0766402\pi\) | ||||
−0.971154 | + | 0.238453i | \(0.923360\pi\) | |||||||
\(258\) | 2773.14i | 0.669179i | ||||||||
\(259\) | 338.341 | 0.0811717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1303.50 | −0.309135 | ||||||||
\(262\) | − 6019.89i | − 1.41950i | ||||||||
\(263\) | − 393.821i | − 0.0923347i | −0.998934 | − | 0.0461673i | \(-0.985299\pi\) | ||||
0.998934 | − | 0.0461673i | \(-0.0147007\pi\) | |||||||
\(264\) | −1026.08 | −0.239208 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3325.16 | −0.766462 | ||||||||
\(267\) | 1246.68i | 0.285751i | ||||||||
\(268\) | 12.7769i | 0.00291222i | ||||||||
\(269\) | 1877.03 | 0.425444 | 0.212722 | − | 0.977113i | \(-0.431767\pi\) | ||||
0.212722 | + | 0.977113i | \(0.431767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −689.909 | −0.154646 | −0.0773228 | − | 0.997006i | \(-0.524637\pi\) | ||||
−0.0773228 | + | 0.997006i | \(0.524637\pi\) | |||||||
\(272\) | − 5377.16i | − 1.19867i | ||||||||
\(273\) | − 1868.38i | − 0.414211i | ||||||||
\(274\) | 444.269 | 0.0979536 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3439.09 | −0.750031 | ||||||||
\(277\) | − 6289.13i | − 1.36418i | −0.731270 | − | 0.682088i | \(-0.761072\pi\) | ||||
0.731270 | − | 0.682088i | \(-0.238928\pi\) | |||||||
\(278\) | 3868.21i | 0.834531i | ||||||||
\(279\) | 2322.71 | 0.498412 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1954.87 | −0.415010 | −0.207505 | − | 0.978234i | \(-0.566534\pi\) | ||||
−0.207505 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(282\) | 7315.60i | 1.54481i | ||||||||
\(283\) | 5033.96i | 1.05738i | 0.848816 | + | 0.528688i | \(0.177316\pi\) | ||||
−0.848816 | + | 0.528688i | \(0.822684\pi\) | |||||||
\(284\) | 610.803 | 0.127621 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15651.2 | 3.23594 | ||||||||
\(287\) | 1406.20i | 0.289217i | ||||||||
\(288\) | 2295.86i | 0.469738i | ||||||||
\(289\) | −9580.03 | −1.94993 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3095.09 | −0.623497 | ||||||||
\(292\) | − 4820.99i | − 0.966188i | ||||||||
\(293\) | 6369.12i | 1.26993i | 0.772543 | + | 0.634963i | \(0.218985\pi\) | ||||
−0.772543 | + | 0.634963i | \(0.781015\pi\) | |||||||
\(294\) | 622.702 | 0.123526 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −398.085 | −0.0781697 | ||||||||
\(297\) | 1121.25i | 0.219063i | ||||||||
\(298\) | − 7546.34i | − 1.46694i | ||||||||
\(299\) | 10256.4 | 1.98376 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1527.52 | 0.292507 | ||||||||
\(302\) | 5962.39i | 1.13608i | ||||||||
\(303\) | 4341.58i | 0.823160i | ||||||||
\(304\) | −5008.70 | −0.944963 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4589.71 | 0.857438 | ||||||||
\(307\) | 6619.83i | 1.23066i | 0.788268 | + | 0.615332i | \(0.210978\pi\) | ||||
−0.788268 | + | 0.615332i | \(0.789022\pi\) | |||||||
\(308\) | 2890.75i | 0.534792i | ||||||||
\(309\) | 490.700 | 0.0903396 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9909.22 | −1.80675 | −0.903377 | − | 0.428848i | \(-0.858920\pi\) | ||||
−0.903377 | + | 0.428848i | \(0.858920\pi\) | |||||||
\(312\) | 2198.30i | 0.398892i | ||||||||
\(313\) | − 422.336i | − 0.0762678i | −0.999273 | − | 0.0381339i | \(-0.987859\pi\) | ||||
0.999273 | − | 0.0381339i | \(-0.0121413\pi\) | |||||||
\(314\) | −6773.22 | −1.21731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8733.63 | 1.55476 | ||||||||
\(317\) | 4902.78i | 0.868668i | 0.900752 | + | 0.434334i | \(0.143016\pi\) | ||||
−0.900752 | + | 0.434334i | \(0.856984\pi\) | |||||||
\(318\) | 2342.15i | 0.413022i | ||||||||
\(319\) | −6014.60 | −1.05565 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −388.960 | −0.0676312 | ||||||||
\(322\) | 3418.30i | 0.591597i | ||||||||
\(323\) | 13499.9i | 2.32556i | ||||||||
\(324\) | −805.486 | −0.138115 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 867.935 | 0.147455 | ||||||||
\(327\) | − 1700.04i | − 0.287500i | ||||||||
\(328\) | − 1654.51i | − 0.278521i | ||||||||
\(329\) | 4029.62 | 0.675258 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5281.74 | −0.877071 | −0.438535 | − | 0.898714i | \(-0.644503\pi\) | ||||
−0.438535 | + | 0.898714i | \(0.644503\pi\) | |||||||
\(332\) | − 4890.89i | − 0.808501i | ||||||||
\(333\) | 435.009i | 0.0715867i | ||||||||
\(334\) | −4939.01 | −0.809133 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 937.978 | 0.152294 | ||||||||
\(337\) | − 4459.60i | − 0.720860i | −0.932786 | − | 0.360430i | \(-0.882630\pi\) | ||||
0.932786 | − | 0.360430i | \(-0.117370\pi\) | |||||||
\(338\) | − 24225.1i | − 3.89843i | ||||||||
\(339\) | −2429.67 | −0.389267 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10717.5 | 1.70200 | ||||||||
\(342\) | − 4275.21i | − 0.675956i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | −1797.25 | −0.281689 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10751.2 | 1.67048 | ||||||||
\(347\) | − 5261.97i | − 0.814056i | −0.913416 | − | 0.407028i | \(-0.866565\pi\) | ||||
0.913416 | − | 0.407028i | \(-0.133435\pi\) | |||||||
\(348\) | − 4320.77i | − 0.665568i | ||||||||
\(349\) | −960.325 | −0.147292 | −0.0736461 | − | 0.997284i | \(-0.523464\pi\) | ||||
−0.0736461 | + | 0.997284i | \(0.523464\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2402.21 | 0.365300 | ||||||||
\(352\) | 10593.6i | 1.60409i | ||||||||
\(353\) | − 8925.80i | − 1.34581i | −0.739727 | − | 0.672907i | \(-0.765045\pi\) | ||||
0.739727 | − | 0.672907i | \(-0.234955\pi\) | |||||||
\(354\) | −1925.31 | −0.289066 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4132.45 | −0.615222 | ||||||||
\(357\) | − 2528.13i | − 0.374797i | ||||||||
\(358\) | − 1661.62i | − 0.245306i | ||||||||
\(359\) | 3056.27 | 0.449314 | 0.224657 | − | 0.974438i | \(-0.427874\pi\) | ||||
0.224657 | + | 0.974438i | \(0.427874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5715.88 | 0.833340 | ||||||||
\(362\) | − 12615.4i | − 1.83162i | ||||||||
\(363\) | 1180.69i | 0.170717i | ||||||||
\(364\) | 6193.23 | 0.891796 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6733.18 | 0.961610 | ||||||||
\(367\) | 1813.52i | 0.257943i | 0.991648 | + | 0.128971i | \(0.0411675\pi\) | ||||
−0.991648 | + | 0.128971i | \(0.958832\pi\) | |||||||
\(368\) | 5148.99i | 0.729375i | ||||||||
\(369\) | −1807.97 | −0.255065 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1290.11 | 0.180537 | ||||||||
\(372\) | 7699.22i | 1.07308i | ||||||||
\(373\) | − 4517.48i | − 0.627094i | −0.949573 | − | 0.313547i | \(-0.898483\pi\) | ||||
0.949573 | − | 0.313547i | \(-0.101517\pi\) | |||||||
\(374\) | 21177.9 | 2.92802 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4741.17 | −0.650285 | ||||||||
\(377\) | 12885.9i | 1.76036i | ||||||||
\(378\) | 800.617i | 0.108940i | ||||||||
\(379\) | 4931.24 | 0.668340 | 0.334170 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334170 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7752.75 | −1.04248 | ||||||||
\(382\) | − 4648.53i | − 0.622617i | ||||||||
\(383\) | − 1482.37i | − 0.197770i | −0.995099 | − | 0.0988849i | \(-0.968472\pi\) | ||||
0.995099 | − | 0.0988849i | \(-0.0315276\pi\) | |||||||
\(384\) | −3069.25 | −0.407883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14827.5 | −1.95519 | ||||||||
\(387\) | 1963.95i | 0.257967i | ||||||||
\(388\) | − 10259.5i | − 1.34239i | ||||||||
\(389\) | 5448.98 | 0.710217 | 0.355109 | − | 0.934825i | \(-0.384444\pi\) | ||||
0.355109 | + | 0.934825i | \(0.384444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13878.0 | 1.79500 | ||||||||
\(392\) | 403.567i | 0.0519980i | ||||||||
\(393\) | − 4263.31i | − 0.547215i | ||||||||
\(394\) | 6667.38 | 0.852532 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3716.68 | −0.471642 | ||||||||
\(397\) | 13675.9i | 1.72891i | 0.502713 | + | 0.864453i | \(0.332335\pi\) | ||||
−0.502713 | + | 0.864453i | \(0.667665\pi\) | |||||||
\(398\) | 14388.3i | 1.81212i | ||||||||
\(399\) | −2354.89 | −0.295469 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14109.9 | 1.75714 | 0.878570 | − | 0.477613i | \(-0.158498\pi\) | ||||
0.878570 | + | 0.477613i | \(0.158498\pi\) | |||||||
\(402\) | 16.3282i | 0.00202581i | ||||||||
\(403\) | − 22961.4i | − 2.83819i | ||||||||
\(404\) | −14391.3 | −1.77226 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4294.65 | −0.524975 | ||||||||
\(407\) | 2007.22i | 0.244458i | ||||||||
\(408\) | 2974.55i | 0.360936i | ||||||||
\(409\) | 13995.6 | 1.69203 | 0.846015 | − | 0.533159i | \(-0.178995\pi\) | ||||
0.846015 | + | 0.533159i | \(0.178995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 314.633 | 0.0377609 | ||||||||
\(412\) | 1626.55i | 0.194501i | ||||||||
\(413\) | 1060.51i | 0.126354i | ||||||||
\(414\) | −4394.95 | −0.521740 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 22696.0 | 2.67491 | ||||||||
\(417\) | 2739.48i | 0.321709i | ||||||||
\(418\) | − 19726.7i | − 2.30829i | ||||||||
\(419\) | 9840.61 | 1.14736 | 0.573682 | − | 0.819078i | \(-0.305515\pi\) | ||||
0.573682 | + | 0.819078i | \(0.305515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12660.5 | −1.46564 | −0.732822 | − | 0.680420i | \(-0.761797\pi\) | ||||
−0.732822 | + | 0.680420i | \(0.761797\pi\) | |||||||
\(422\) | 14139.2i | 1.63101i | ||||||||
\(423\) | 5180.93i | 0.595522i | ||||||||
\(424\) | −1517.92 | −0.173860 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 780.571 | 0.0887765 | ||||||||
\(427\) | − 3708.81i | − 0.420332i | ||||||||
\(428\) | − 1289.31i | − 0.145610i | ||||||||
\(429\) | 11084.3 | 1.24744 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4578.91 | −0.511736 | −0.255868 | − | 0.966712i | \(-0.582361\pi\) | ||||
−0.255868 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(432\) | 1205.97i | 0.134311i | ||||||||
\(433\) | − 3279.88i | − 0.364020i | −0.983297 | − | 0.182010i | \(-0.941740\pi\) | ||||
0.983297 | − | 0.182010i | \(-0.0582604\pi\) | |||||||
\(434\) | 7652.68 | 0.846406 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5635.23 | 0.618988 | ||||||||
\(437\) | − 12927.1i | − 1.41507i | ||||||||
\(438\) | − 6160.94i | − 0.672103i | ||||||||
\(439\) | 427.807 | 0.0465105 | 0.0232552 | − | 0.999730i | \(-0.492597\pi\) | ||||
0.0232552 | + | 0.999730i | \(0.492597\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 45372.1i | − 4.88265i | ||||||||
\(443\) | 15441.2i | 1.65605i | 0.560688 | + | 0.828027i | \(0.310537\pi\) | ||||
−0.560688 | + | 0.828027i | \(0.689463\pi\) | |||||||
\(444\) | −1441.95 | −0.154126 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −539.371 | −0.0572645 | ||||||||
\(447\) | − 5344.35i | − 0.565501i | ||||||||
\(448\) | 5062.93i | 0.533931i | ||||||||
\(449\) | −9382.02 | −0.986113 | −0.493057 | − | 0.869997i | \(-0.664120\pi\) | ||||
−0.493057 | + | 0.869997i | \(0.664120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8342.34 | −0.871010 | ||||||||
\(452\) | − 8053.77i | − 0.838091i | ||||||||
\(453\) | 4222.59i | 0.437957i | ||||||||
\(454\) | 16284.0 | 1.68336 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2770.72 | 0.284542 | ||||||||
\(457\) | − 13570.4i | − 1.38905i | −0.719469 | − | 0.694524i | \(-0.755615\pi\) | ||||
0.719469 | − | 0.694524i | \(-0.244385\pi\) | |||||||
\(458\) | − 10746.7i | − 1.09642i | ||||||||
\(459\) | 3250.45 | 0.330540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1251.88 | 0.126477 | 0.0632386 | − | 0.997998i | \(-0.479857\pi\) | ||||
0.0632386 | + | 0.997998i | \(0.479857\pi\) | |||||||
\(462\) | 3694.21i | 0.372014i | ||||||||
\(463\) | 7934.36i | 0.796417i | 0.917295 | + | 0.398209i | \(0.130368\pi\) | ||||
−0.917295 | + | 0.398209i | \(0.869632\pi\) | |||||||
\(464\) | −6469.05 | −0.647237 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16891.1 | −1.67911 | ||||||||
\(467\) | − 7583.76i | − 0.751466i | −0.926728 | − | 0.375733i | \(-0.877391\pi\) | ||||
0.926728 | − | 0.375733i | \(-0.122609\pi\) | |||||||
\(468\) | 7962.73i | 0.786490i | ||||||||
\(469\) | 8.99396 | 0.000885507 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4796.82 | −0.469269 | ||||||||
\(472\) | − 1247.78i | − 0.121681i | ||||||||
\(473\) | 9062.07i | 0.880919i | ||||||||
\(474\) | 11161.1 | 1.08153 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8380.13 | 0.806938 | ||||||||
\(477\) | 1658.72i | 0.159219i | ||||||||
\(478\) | 14263.6i | 1.36486i | ||||||||
\(479\) | 5829.34 | 0.556053 | 0.278027 | − | 0.960573i | \(-0.410320\pi\) | ||||
0.278027 | + | 0.960573i | \(0.410320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4300.34 | 0.407648 | ||||||||
\(482\) | − 3980.00i | − 0.376108i | ||||||||
\(483\) | 2420.85i | 0.228059i | ||||||||
\(484\) | −3913.70 | −0.367553 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1029.36 | −0.0960760 | ||||||||
\(487\) | 19902.1i | 1.85185i | 0.377708 | + | 0.925925i | \(0.376712\pi\) | ||||
−0.377708 | + | 0.925925i | \(0.623288\pi\) | |||||||
\(488\) | 4363.71i | 0.404787i | ||||||||
\(489\) | 614.675 | 0.0568437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16821.6 | −1.54613 | −0.773065 | − | 0.634327i | \(-0.781277\pi\) | ||||
−0.773065 | + | 0.634327i | \(0.781277\pi\) | |||||||
\(492\) | − 5992.98i | − 0.549155i | ||||||||
\(493\) | 17436.0i | 1.59285i | ||||||||
\(494\) | −42263.1 | −3.84920 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11527.3 | 1.04353 | ||||||||
\(497\) | − 429.958i | − 0.0388054i | ||||||||
\(498\) | − 6250.27i | − 0.562412i | ||||||||
\(499\) | −6031.83 | −0.541126 | −0.270563 | − | 0.962702i | \(-0.587210\pi\) | ||||
−0.270563 | + | 0.962702i | \(0.587210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3497.82 | −0.311919 | ||||||||
\(502\) | − 5947.27i | − 0.528764i | ||||||||
\(503\) | − 17176.4i | − 1.52258i | −0.648412 | − | 0.761290i | \(-0.724566\pi\) | ||||
0.648412 | − | 0.761290i | \(-0.275434\pi\) | |||||||
\(504\) | −518.872 | −0.0458580 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20279.2 | −1.78166 | ||||||||
\(507\) | − 17156.3i | − 1.50284i | ||||||||
\(508\) | − 25698.5i | − 2.24446i | ||||||||
\(509\) | −4706.59 | −0.409854 | −0.204927 | − | 0.978777i | \(-0.565696\pi\) | ||||
−0.204927 | + | 0.978777i | \(0.565696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3393.60 | −0.293785 | ||||||||
\(512\) | 14336.9i | 1.23752i | ||||||||
\(513\) | − 3027.72i | − 0.260579i | ||||||||
\(514\) | −8323.28 | −0.714250 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6510.02 | −0.555402 | ||||||||
\(517\) | 23905.9i | 2.03362i | ||||||||
\(518\) | 1433.23i | 0.121569i | ||||||||
\(519\) | 7614.01 | 0.643965 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8557.18 | −0.719572 | −0.359786 | − | 0.933035i | \(-0.617150\pi\) | ||||
−0.359786 | + | 0.933035i | \(0.617150\pi\) | |||||||
\(522\) | − 5521.69i | − 0.462985i | ||||||||
\(523\) | 18248.5i | 1.52572i | 0.646566 | + | 0.762858i | \(0.276204\pi\) | ||||
−0.646566 | + | 0.762858i | \(0.723796\pi\) | |||||||
\(524\) | 14131.8 | 1.17815 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1668.25 | 0.138287 | ||||||||
\(527\) | − 31069.3i | − 2.56813i | ||||||||
\(528\) | 5564.60i | 0.458652i | ||||||||
\(529\) | −1122.16 | −0.0922302 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1363.51 | −0.111434 | ||||||||
\(532\) | − 7805.90i | − 0.636144i | ||||||||
\(533\) | 17872.9i | 1.45246i | ||||||||
\(534\) | −5281.03 | −0.427963 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.5821 | −0.000852758 0 | ||||||||
\(537\) | − 1176.77i | − 0.0945646i | ||||||||
\(538\) | 7951.22i | 0.637177i | ||||||||
\(539\) | 2034.87 | 0.162612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5734.17 | −0.455696 | −0.227848 | − | 0.973697i | \(-0.573169\pi\) | ||||
−0.227848 | + | 0.973697i | \(0.573169\pi\) | |||||||
\(542\) | − 2922.50i | − 0.231609i | ||||||||
\(543\) | − 8934.24i | − 0.706087i | ||||||||
\(544\) | 30710.1 | 2.42038 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7914.59 | 0.620354 | ||||||||
\(547\) | 8002.52i | 0.625527i | 0.949831 | + | 0.312763i | \(0.101255\pi\) | ||||
−0.949831 | + | 0.312763i | \(0.898745\pi\) | |||||||
\(548\) | 1042.93i | 0.0812991i | ||||||||
\(549\) | 4768.47 | 0.370698 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16241.2 | 1.25572 | ||||||||
\(552\) | − 2848.33i | − 0.219625i | ||||||||
\(553\) | − 6147.80i | − 0.472750i | ||||||||
\(554\) | 26641.2 | 2.04310 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9080.71 | −0.692640 | ||||||||
\(557\) | − 1276.82i | − 0.0971289i | −0.998820 | − | 0.0485644i | \(-0.984535\pi\) | ||||
0.998820 | − | 0.0485644i | \(-0.0154646\pi\) | |||||||
\(558\) | 9839.16i | 0.746460i | ||||||||
\(559\) | 19414.9 | 1.46898 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14998.2 | 1.12875 | ||||||||
\(562\) | − 8280.96i | − 0.621550i | ||||||||
\(563\) | 11027.7i | 0.825507i | 0.910843 | + | 0.412753i | \(0.135433\pi\) | ||||
−0.910843 | + | 0.412753i | \(0.864567\pi\) | |||||||
\(564\) | −17173.5 | −1.28216 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21324.2 | −1.58361 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 505.881i | 0.0373702i | ||||||||
\(569\) | 4519.03 | 0.332948 | 0.166474 | − | 0.986046i | \(-0.446762\pi\) | ||||
0.166474 | + | 0.986046i | \(0.446762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3598.81 | 0.263758 | 0.131879 | − | 0.991266i | \(-0.457899\pi\) | ||||
0.131879 | + | 0.991266i | \(0.457899\pi\) | |||||||
\(572\) | 36741.7i | 2.68575i | ||||||||
\(573\) | − 3292.11i | − 0.240017i | ||||||||
\(574\) | −5956.75 | −0.433153 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6509.48 | −0.470883 | ||||||||
\(577\) | 3439.23i | 0.248140i | 0.992273 | + | 0.124070i | \(0.0395948\pi\) | ||||
−0.992273 | + | 0.124070i | \(0.960405\pi\) | |||||||
\(578\) | − 40581.6i | − 2.92037i | ||||||||
\(579\) | −10500.9 | −0.753720 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3442.81 | −0.245838 | ||||||||
\(582\) | − 13111.0i | − 0.933797i | ||||||||
\(583\) | 7653.66i | 0.543709i | ||||||||
\(584\) | 3992.85 | 0.282920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26980.0 | −1.90194 | ||||||||
\(587\) | − 21285.2i | − 1.49665i | −0.663330 | − | 0.748327i | \(-0.730857\pi\) | ||||
0.663330 | − | 0.748327i | \(-0.269143\pi\) | |||||||
\(588\) | 1461.81i | 0.102524i | ||||||||
\(589\) | −28940.4 | −2.02456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4721.87 | 0.328649 | ||||||||
\(592\) | 2158.89i | 0.149881i | ||||||||
\(593\) | − 14200.8i | − 0.983404i | −0.870764 | − | 0.491702i | \(-0.836375\pi\) | ||||
0.870764 | − | 0.491702i | \(-0.163625\pi\) | |||||||
\(594\) | −4749.70 | −0.328085 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17715.2 | 1.21752 | ||||||||
\(597\) | 10189.9i | 0.698566i | ||||||||
\(598\) | 43446.8i | 2.97103i | ||||||||
\(599\) | 8885.05 | 0.606065 | 0.303033 | − | 0.952980i | \(-0.402001\pi\) | ||||
0.303033 | + | 0.952980i | \(0.402001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2052.89 | −0.139333 | −0.0696664 | − | 0.997570i | \(-0.522193\pi\) | ||||
−0.0696664 | + | 0.997570i | \(0.522193\pi\) | |||||||
\(602\) | 6470.67i | 0.438081i | ||||||||
\(603\) | 11.5637i | 0 0.000780943i | ||||||||
\(604\) | −13996.9 | −0.942920 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18391.2 | −1.23283 | ||||||||
\(607\) | − 10280.0i | − 0.687404i | −0.939079 | − | 0.343702i | \(-0.888319\pi\) | ||||
0.939079 | − | 0.343702i | \(-0.111681\pi\) | |||||||
\(608\) | − 28605.8i | − 1.90809i | ||||||||
\(609\) | −3041.49 | −0.202377 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51216.8 | 3.39118 | ||||||||
\(612\) | 10774.4i | 0.711652i | ||||||||
\(613\) | 23409.5i | 1.54242i | 0.636584 | + | 0.771208i | \(0.280347\pi\) | ||||
−0.636584 | + | 0.771208i | \(0.719653\pi\) | |||||||
\(614\) | −28042.0 | −1.84314 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2394.18 | −0.156598 | ||||||||
\(617\) | 6632.75i | 0.432779i | 0.976307 | + | 0.216389i | \(0.0694281\pi\) | ||||
−0.976307 | + | 0.216389i | \(0.930572\pi\) | |||||||
\(618\) | 2078.64i | 0.135299i | ||||||||
\(619\) | −10734.0 | −0.696990 | −0.348495 | − | 0.937311i | \(-0.613307\pi\) | ||||
−0.348495 | + | 0.937311i | \(0.613307\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3112.52 | −0.201129 | ||||||||
\(622\) | − 41976.1i | − 2.70593i | ||||||||
\(623\) | 2908.92i | 0.187068i | ||||||||
\(624\) | 11921.8 | 0.764829 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1789.04 | 0.114225 | ||||||||
\(627\) | − 13970.5i | − 0.889839i | ||||||||
\(628\) | − 15900.3i | − 1.01034i | ||||||||
\(629\) | 5818.83 | 0.368858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17071.0 | −1.07700 | −0.538499 | − | 0.842626i | \(-0.681008\pi\) | ||||
−0.538499 | + | 0.842626i | \(0.681008\pi\) | |||||||
\(632\) | 7233.38i | 0.455267i | ||||||||
\(633\) | 10013.4i | 0.628749i | ||||||||
\(634\) | −20768.5 | −1.30098 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5498.24 | −0.342798 | ||||||||
\(637\) | − 4359.56i | − 0.271165i | ||||||||
\(638\) | − 25478.2i | − 1.58102i | ||||||||
\(639\) | 552.804 | 0.0342231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19389.7 | −1.19477 | −0.597386 | − | 0.801954i | \(-0.703794\pi\) | ||||
−0.597386 | + | 0.801954i | \(0.703794\pi\) | |||||||
\(642\) | − 1647.66i | − 0.101290i | ||||||||
\(643\) | − 25409.3i | − 1.55839i | −0.626780 | − | 0.779196i | \(-0.715628\pi\) | ||||
0.626780 | − | 0.779196i | \(-0.284372\pi\) | |||||||
\(644\) | −8024.54 | −0.491011 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −57186.6 | −3.48294 | ||||||||
\(647\) | 6039.08i | 0.366956i | 0.983024 | + | 0.183478i | \(0.0587357\pi\) | ||||
−0.983024 | + | 0.183478i | \(0.941264\pi\) | |||||||
\(648\) | − 667.122i | − 0.0404429i | ||||||||
\(649\) | −6291.54 | −0.380531 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5419.66 | 0.326287 | ||||||||
\(652\) | 2037.50i | 0.122384i | ||||||||
\(653\) | − 30666.2i | − 1.83776i | −0.394532 | − | 0.918882i | \(-0.629093\pi\) | ||||
0.394532 | − | 0.918882i | \(-0.370907\pi\) | |||||||
\(654\) | 7201.50 | 0.430582 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8972.67 | −0.534031 | ||||||||
\(657\) | − 4363.20i | − 0.259094i | ||||||||
\(658\) | 17069.7i | 1.01132i | ||||||||
\(659\) | 2765.96 | 0.163500 | 0.0817500 | − | 0.996653i | \(-0.473949\pi\) | ||||
0.0817500 | + | 0.996653i | \(0.473949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27261.8 | 1.60418 | 0.802089 | − | 0.597204i | \(-0.203722\pi\) | ||||
0.802089 | + | 0.597204i | \(0.203722\pi\) | |||||||
\(662\) | − 22373.8i | − 1.31357i | ||||||||
\(663\) | − 32132.7i | − 1.88225i | ||||||||
\(664\) | 4050.74 | 0.236746 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1842.73 | −0.107214 | ||||||||
\(667\) | − 16696.1i | − 0.969230i | ||||||||
\(668\) | − 11594.4i | − 0.671560i | ||||||||
\(669\) | −381.985 | −0.0220753 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22002.7 | 1.26588 | ||||||||
\(672\) | 5357.00i | 0.307516i | ||||||||
\(673\) | − 1048.17i | − 0.0600356i | −0.999549 | − | 0.0300178i | \(-0.990444\pi\) | ||||
0.999549 | − | 0.0300178i | \(-0.00955640\pi\) | |||||||
\(674\) | 18891.2 | 1.07961 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 56869.0 | 3.23560 | ||||||||
\(677\) | 34554.7i | 1.96166i | 0.194860 | + | 0.980831i | \(0.437575\pi\) | ||||
−0.194860 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(678\) | − 10292.2i | − 0.582996i | ||||||||
\(679\) | −7221.89 | −0.408175 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11532.4 | 0.648930 | ||||||||
\(682\) | 45399.9i | 2.54905i | ||||||||
\(683\) | 14711.6i | 0.824192i | 0.911140 | + | 0.412096i | \(0.135203\pi\) | ||||
−0.911140 | + | 0.412096i | \(0.864797\pi\) | |||||||
\(684\) | 10036.2 | 0.561026 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1452.97 | 0.0808669 | ||||||||
\(687\) | − 7610.85i | − 0.422667i | ||||||||
\(688\) | 9746.79i | 0.540106i | ||||||||
\(689\) | 16397.4 | 0.906666 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24522.6 | −1.35005 | −0.675024 | − | 0.737796i | \(-0.735867\pi\) | ||||
−0.675024 | + | 0.737796i | \(0.735867\pi\) | |||||||
\(692\) | 25238.6i | 1.38646i | ||||||||
\(693\) | 2616.26i | 0.143410i | ||||||||
\(694\) | 22290.1 | 1.21919 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3578.56 | 0.194892 | ||||||||
\(697\) | 24184.0i | 1.31425i | ||||||||
\(698\) | − 4068.00i | − 0.220596i | ||||||||
\(699\) | −11962.3 | −0.647291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19912.2 | 1.07286 | 0.536429 | − | 0.843946i | \(-0.319773\pi\) | ||||
0.536429 | + | 0.843946i | \(0.319773\pi\) | |||||||
\(702\) | 10175.9i | 0.547101i | ||||||||
\(703\) | − 5420.11i | − 0.290787i | ||||||||
\(704\) | −30036.1 | −1.60799 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37810.3 | 2.01559 | ||||||||
\(707\) | 10130.4i | 0.538885i | ||||||||
\(708\) | − 4519.72i | − 0.239917i | ||||||||
\(709\) | −6208.79 | −0.328880 | −0.164440 | − | 0.986387i | \(-0.552582\pi\) | ||||
−0.164440 | + | 0.986387i | \(0.552582\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7904.31 | 0.416927 | ||||||||
\(712\) | − 3422.58i | − 0.180150i | ||||||||
\(713\) | 29751.0i | 1.56267i | ||||||||
\(714\) | 10709.3 | 0.561325 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3900.69 | 0.203597 | ||||||||
\(717\) | 10101.5i | 0.526149i | ||||||||
\(718\) | 12946.6i | 0.672927i | ||||||||
\(719\) | −13063.6 | −0.677593 | −0.338797 | − | 0.940860i | \(-0.610020\pi\) | ||||
−0.338797 | + | 0.940860i | \(0.610020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1144.97 | 0.0591411 | ||||||||
\(722\) | 24212.9i | 1.24807i | ||||||||
\(723\) | − 2818.65i | − 0.144989i | ||||||||
\(724\) | 29614.8 | 1.52020 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5001.49 | −0.255678 | ||||||||
\(727\) | 12897.0i | 0.657940i | 0.944340 | + | 0.328970i | \(0.106702\pi\) | ||||
−0.944340 | + | 0.328970i | \(0.893298\pi\) | |||||||
\(728\) | 5129.37i | 0.261136i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26270.5 | 1.32920 | ||||||||
\(732\) | 15806.3i | 0.798112i | ||||||||
\(733\) | 11699.6i | 0.589540i | 0.955568 | + | 0.294770i | \(0.0952430\pi\) | ||||
−0.955568 | + | 0.294770i | \(0.904757\pi\) | |||||||
\(734\) | −7682.19 | −0.386315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29407.0 | −1.47277 | ||||||||
\(737\) | 53.3571i | 0.00266681i | ||||||||
\(738\) | − 7658.68i | − 0.382005i | ||||||||
\(739\) | −14974.0 | −0.745368 | −0.372684 | − | 0.927958i | \(-0.621562\pi\) | ||||
−0.372684 | + | 0.927958i | \(0.621562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29930.9 | −1.48386 | ||||||||
\(742\) | 5465.01i | 0.270386i | ||||||||
\(743\) | 18500.7i | 0.913492i | 0.889597 | + | 0.456746i | \(0.150985\pi\) | ||||
−0.889597 | + | 0.456746i | \(0.849015\pi\) | |||||||
\(744\) | −6376.67 | −0.314220 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19136.3 | 0.939184 | ||||||||
\(747\) | − 4426.47i | − 0.216809i | ||||||||
\(748\) | 49715.5i | 2.43019i | ||||||||
\(749\) | −907.572 | −0.0442750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26348.4 | −1.28025 | −0.640125 | − | 0.768271i | \(-0.721117\pi\) | ||||
−0.640125 | + | 0.768271i | \(0.721117\pi\) | |||||||
\(752\) | 25712.2i | 1.24684i | ||||||||
\(753\) | − 4211.88i | − 0.203837i | ||||||||
\(754\) | −54585.4 | −2.63645 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1879.47 | −0.0904174 | ||||||||
\(757\) | 28061.7i | 1.34732i | 0.739042 | + | 0.673659i | \(0.235278\pi\) | ||||
−0.739042 | + | 0.673659i | \(0.764722\pi\) | |||||||
\(758\) | 20889.1i | 1.00096i | ||||||||
\(759\) | −14361.8 | −0.686826 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3579.22 | −0.170495 | −0.0852476 | − | 0.996360i | \(-0.527168\pi\) | ||||
−0.0852476 | + | 0.996360i | \(0.527168\pi\) | |||||||
\(762\) | − 32841.2i | − 1.56130i | ||||||||
\(763\) | − 3966.77i | − 0.188213i | ||||||||
\(764\) | 10912.5 | 0.516757 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6279.44 | 0.296195 | ||||||||
\(767\) | 13479.2i | 0.634557i | ||||||||
\(768\) | 4357.07i | 0.204716i | ||||||||
\(769\) | −4339.61 | −0.203499 | −0.101749 | − | 0.994810i | \(-0.532444\pi\) | ||||
−0.101749 | + | 0.994810i | \(0.532444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5894.58 | −0.275341 | ||||||||
\(772\) | − 34808.0i | − 1.62276i | ||||||||
\(773\) | 10005.1i | 0.465537i | 0.972532 | + | 0.232769i | \(0.0747785\pi\) | ||||
−0.972532 | + | 0.232769i | \(0.925222\pi\) | |||||||
\(774\) | −8319.43 | −0.386351 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8497.14 | 0.393079 | ||||||||
\(777\) | 1015.02i | 0.0468645i | ||||||||
\(778\) | 23082.3i | 1.06368i | ||||||||
\(779\) | 22526.8 | 1.03608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2550.75 | 0.116867 | ||||||||
\(782\) | 58788.4i | 2.68832i | ||||||||
\(783\) | − 3910.49i | − 0.178479i | ||||||||
\(784\) | 2188.62 | 0.0997001 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18059.7 | 0.819550 | ||||||||
\(787\) | − 17826.8i | − 0.807443i | −0.914882 | − | 0.403721i | \(-0.867716\pi\) | ||||
0.914882 | − | 0.403721i | \(-0.132284\pi\) | |||||||
\(788\) | 15651.8i | 0.707581i | ||||||||
\(789\) | 1181.46 | 0.0533094 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5669.23 | −0.254835 | ||||||||
\(792\) | − 3078.24i | − 0.138107i | ||||||||
\(793\) | − 47139.3i | − 2.11093i | ||||||||
\(794\) | −57932.2 | −2.58934 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33777.0 | −1.50401 | ||||||||
\(797\) | − 36723.0i | − 1.63211i | −0.577971 | − | 0.816057i | \(-0.696155\pi\) | ||||
0.577971 | − | 0.816057i | \(-0.303845\pi\) | |||||||
\(798\) | − 9975.49i | − 0.442517i | ||||||||
\(799\) | 69301.9 | 3.06849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3740.04 | −0.164979 | ||||||||
\(802\) | 59770.4i | 2.63163i | ||||||||
\(803\) | − 20132.7i | − 0.884767i | ||||||||
\(804\) | −38.3307 | −0.00168137 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 97266.2 | 4.25069 | ||||||||
\(807\) | 5631.08i | 0.245630i | ||||||||
\(808\) | − 11919.2i | − 0.518955i | ||||||||
\(809\) | −5657.55 | −0.245870 | −0.122935 | − | 0.992415i | \(-0.539231\pi\) | ||||
−0.122935 | + | 0.992415i | \(0.539231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7532.41 | 0.326139 | 0.163070 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163070 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(812\) | − 10081.8i | − 0.435716i | ||||||||
\(813\) | − 2069.73i | − 0.0892847i | ||||||||
\(814\) | −8502.73 | −0.366119 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16131.5 | 0.692053 | ||||||||
\(817\) | − 24470.3i | − 1.04787i | ||||||||
\(818\) | 59286.5i | 2.53411i | ||||||||
\(819\) | 5605.15 | 0.239145 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6489.25 | −0.275854 | −0.137927 | − | 0.990442i | \(-0.544044\pi\) | ||||
−0.137927 | + | 0.990442i | \(0.544044\pi\) | |||||||
\(822\) | 1332.81i | 0.0565535i | ||||||||
\(823\) | 7901.57i | 0.334668i | 0.985900 | + | 0.167334i | \(0.0535157\pi\) | ||||
−0.985900 | + | 0.167334i | \(0.946484\pi\) | |||||||
\(824\) | −1347.15 | −0.0569539 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4492.40 | −0.189238 | ||||||||
\(827\) | 37815.8i | 1.59007i | 0.606566 | + | 0.795033i | \(0.292547\pi\) | ||||
−0.606566 | + | 0.795033i | \(0.707453\pi\) | |||||||
\(828\) | − 10317.3i | − 0.433031i | ||||||||
\(829\) | −26073.5 | −1.09236 | −0.546182 | − | 0.837667i | \(-0.683919\pi\) | ||||
−0.546182 | + | 0.837667i | \(0.683919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18867.4 | 0.787608 | ||||||||
\(832\) | 64350.2i | 2.68142i | ||||||||
\(833\) | − 5898.96i | − 0.245362i | ||||||||
\(834\) | −11604.6 | −0.481817 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 46308.9 | 1.91582 | ||||||||
\(837\) | 6968.13i | 0.287758i | ||||||||
\(838\) | 41685.5i | 1.71838i | ||||||||
\(839\) | 15590.3 | 0.641523 | 0.320762 | − | 0.947160i | \(-0.396061\pi\) | ||||
0.320762 | + | 0.947160i | \(0.396061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3412.46 | −0.139918 | ||||||||
\(842\) | − 53630.8i | − 2.19506i | ||||||||
\(843\) | − 5864.61i | − 0.239606i | ||||||||
\(844\) | −33192.1 | −1.35370 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21946.8 | −0.891899 | ||||||||
\(847\) | 2754.94i | 0.111760i | ||||||||
\(848\) | 8231.96i | 0.333357i | ||||||||
\(849\) | −15101.9 | −0.610477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5571.92 | −0.224445 | ||||||||
\(852\) | 1832.41i | 0.0736823i | ||||||||
\(853\) | − 17476.1i | − 0.701488i | −0.936471 | − | 0.350744i | \(-0.885929\pi\) | ||||
0.936471 | − | 0.350744i | \(-0.114071\pi\) | |||||||
\(854\) | 15710.8 | 0.629521 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1067.83 | 0.0426376 | ||||||||
\(857\) | 5694.54i | 0.226980i | 0.993539 | + | 0.113490i | \(0.0362030\pi\) | ||||
−0.993539 | + | 0.113490i | \(0.963797\pi\) | |||||||
\(858\) | 46953.7i | 1.86827i | ||||||||
\(859\) | −27313.6 | −1.08490 | −0.542448 | − | 0.840089i | \(-0.682503\pi\) | ||||
−0.542448 | + | 0.840089i | \(0.682503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4218.59 | −0.166979 | ||||||||
\(862\) | − 19396.6i | − 0.766415i | ||||||||
\(863\) | − 9046.07i | − 0.356815i | −0.983957 | − | 0.178408i | \(-0.942905\pi\) | ||||
0.983957 | − | 0.178408i | \(-0.0570946\pi\) | |||||||
\(864\) | −6887.57 | −0.271204 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13893.8 | 0.545185 | ||||||||
\(867\) | − 28740.1i | − 1.12580i | ||||||||
\(868\) | 17964.8i | 0.702496i | ||||||||
\(869\) | 36472.1 | 1.42374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 114.314 | 0.00444705 | ||||||||
\(872\) | 4667.22i | 0.181252i | ||||||||
\(873\) | − 9285.28i | − 0.359976i | ||||||||
\(874\) | 54760.0 | 2.11932 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14463.0 | 0.557829 | ||||||||
\(877\) | 2104.29i | 0.0810224i | 0.999179 | + | 0.0405112i | \(0.0128986\pi\) | ||||
−0.999179 | + | 0.0405112i | \(0.987101\pi\) | |||||||
\(878\) | 1812.22i | 0.0696576i | ||||||||
\(879\) | −19107.4 | −0.733192 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22589.6 | −0.863861 | −0.431931 | − | 0.901907i | \(-0.642167\pi\) | ||||
−0.431931 | + | 0.901907i | \(0.642167\pi\) | |||||||
\(882\) | 1868.11i | 0.0713179i | ||||||||
\(883\) | − 2419.71i | − 0.0922193i | −0.998936 | − | 0.0461096i | \(-0.985318\pi\) | ||||
0.998936 | − | 0.0461096i | \(-0.0146824\pi\) | |||||||
\(884\) | 106512. | 4.05248 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −65409.8 | −2.48023 | ||||||||
\(887\) | − 13177.0i | − 0.498806i | −0.968400 | − | 0.249403i | \(-0.919766\pi\) | ||||
0.968400 | − | 0.249403i | \(-0.0802344\pi\) | |||||||
\(888\) | − 1194.26i | − 0.0451313i | ||||||||
\(889\) | −18089.8 | −0.682464 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3363.76 | −0.126476 | ||||||||
\(892\) | − 1266.19i | − 0.0475281i | ||||||||
\(893\) | − 64553.2i | − 2.41902i | ||||||||
\(894\) | 22639.0 | 0.846937 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7161.58 | −0.267022 | ||||||||
\(897\) | 30769.2i | 1.14532i | ||||||||
\(898\) | − 39742.9i | − 1.47688i | ||||||||
\(899\) | −37378.3 | −1.38669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22187.5 | 0.820393 | ||||||||
\(902\) | − 35338.7i | − 1.30449i | ||||||||
\(903\) | 4582.55i | 0.168879i | ||||||||
\(904\) | 6670.31 | 0.245411 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17887.2 | −0.655918 | ||||||||
\(907\) | − 9189.14i | − 0.336406i | −0.985752 | − | 0.168203i | \(-0.946204\pi\) | ||||
0.985752 | − | 0.168203i | \(-0.0537964\pi\) | |||||||
\(908\) | 38227.0i | 1.39714i | ||||||||
\(909\) | −13024.8 | −0.475252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17045.8 | −0.619928 | −0.309964 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309964 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(912\) | − 15026.1i | − 0.545575i | ||||||||
\(913\) | − 20424.6i | − 0.740369i | ||||||||
\(914\) | 57485.0 | 2.08034 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25228.1 | 0.910001 | ||||||||
\(917\) | − 9947.71i | − 0.358236i | ||||||||
\(918\) | 13769.1i | 0.495042i | ||||||||
\(919\) | 30825.0 | 1.10645 | 0.553223 | − | 0.833033i | \(-0.313398\pi\) | ||||
0.553223 | + | 0.833033i | \(0.313398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19859.5 | −0.710524 | ||||||||
\(922\) | 5303.06i | 0.189422i | ||||||||
\(923\) | − 5464.81i | − 0.194882i | ||||||||
\(924\) | −8672.25 | −0.308762 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33610.5 | −1.19277 | ||||||||
\(927\) | 1472.10i | 0.0521576i | ||||||||
\(928\) | − 36946.2i | − 1.30691i | ||||||||
\(929\) | 5785.88 | 0.204336 | 0.102168 | − | 0.994767i | \(-0.467422\pi\) | ||||
0.102168 | + | 0.994767i | \(0.467422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5494.75 | −0.193430 | ||||||||
\(932\) | − 39652.2i | − 1.39362i | ||||||||
\(933\) | − 29727.7i | − 1.04313i | ||||||||
\(934\) | 32125.3 | 1.12545 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6594.91 | −0.230301 | ||||||||
\(937\) | 13680.9i | 0.476986i | 0.971144 | + | 0.238493i | \(0.0766534\pi\) | ||||
−0.971144 | + | 0.238493i | \(0.923347\pi\) | |||||||
\(938\) | 38.0990i | 0.00132620i | ||||||||
\(939\) | 1267.01 | 0.0440333 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45448.8 | −1.57448 | −0.787242 | − | 0.616644i | \(-0.788492\pi\) | ||||
−0.787242 | + | 0.616644i | \(0.788492\pi\) | |||||||
\(942\) | − 20319.6i | − 0.702813i | ||||||||
\(943\) | − 23157.8i | − 0.799705i | ||||||||
\(944\) | −6766.91 | −0.233310 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38387.6 | −1.31933 | ||||||||
\(947\) | 7788.45i | 0.267255i | 0.991032 | + | 0.133628i | \(0.0426626\pi\) | ||||
−0.991032 | + | 0.133628i | \(0.957337\pi\) | |||||||
\(948\) | 26200.9i | 0.897642i | ||||||||
\(949\) | −43133.0 | −1.47540 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14708.4 | −0.501526 | ||||||||
\(952\) | 6940.61i | 0.236288i | ||||||||
\(953\) | 6149.43i | 0.209024i | 0.994524 | + | 0.104512i | \(0.0333280\pi\) | ||||
−0.994524 | + | 0.104512i | \(0.966672\pi\) | |||||||
\(954\) | −7026.44 | −0.238458 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33484.2 | −1.13280 | ||||||||
\(957\) | − 18043.8i | − 0.609481i | ||||||||
\(958\) | 24693.5i | 0.832788i | ||||||||
\(959\) | 734.144 | 0.0247203 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36813.7 | 1.23573 | ||||||||
\(962\) | 18216.5i | 0.610524i | ||||||||
\(963\) | − 1166.88i | − 0.0390469i | ||||||||
\(964\) | 9343.15 | 0.312160 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −10254.9 | −0.341559 | ||||||||
\(967\) | − 23902.9i | − 0.794896i | −0.917625 | − | 0.397448i | \(-0.869896\pi\) | ||||
0.917625 | − | 0.397448i | \(-0.130104\pi\) | |||||||
\(968\) | − 3241.42i | − 0.107627i | ||||||||
\(969\) | −40499.8 | −1.34266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8015.06 | −0.264898 | −0.132449 | − | 0.991190i | \(-0.542284\pi\) | ||||
−0.132449 | + | 0.991190i | \(0.542284\pi\) | |||||||
\(972\) | − 2416.46i | − 0.0797407i | ||||||||
\(973\) | 6392.12i | 0.210608i | ||||||||
\(974\) | −84306.7 | −2.77347 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23665.2 | 0.776131 | ||||||||
\(977\) | 34861.1i | 1.14156i | 0.821103 | + | 0.570780i | \(0.193359\pi\) | ||||
−0.821103 | + | 0.570780i | \(0.806641\pi\) | |||||||
\(978\) | 2603.80i | 0.0851334i | ||||||||
\(979\) | −17257.3 | −0.563378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5100.13 | 0.165988 | ||||||||
\(982\) | − 71257.6i | − 2.31560i | ||||||||
\(983\) | 6620.83i | 0.214824i | 0.994215 | + | 0.107412i | \(0.0342563\pi\) | ||||
−0.994215 | + | 0.107412i | \(0.965744\pi\) | |||||||
\(984\) | 4963.52 | 0.160804 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −73860.0 | −2.38558 | ||||||||
\(987\) | 12088.8i | 0.389860i | ||||||||
\(988\) | − 99213.6i | − 3.19474i | ||||||||
\(989\) | −25155.7 | −0.808802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10360.1 | 0.332089 | 0.166045 | − | 0.986118i | \(-0.446900\pi\) | ||||
0.166045 | + | 0.986118i | \(0.446900\pi\) | |||||||
\(992\) | 65834.7i | 2.10711i | ||||||||
\(993\) | − 15845.2i | − 0.506377i | ||||||||
\(994\) | 1821.33 | 0.0581179 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14672.7 | 0.466788 | ||||||||
\(997\) | 40309.3i | 1.28045i | 0.768188 | + | 0.640225i | \(0.221159\pi\) | ||||
−0.768188 | + | 0.640225i | \(0.778841\pi\) | |||||||
\(998\) | − 25551.3i | − 0.810432i | ||||||||
\(999\) | −1305.03 | −0.0413306 |
(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.k.274.4 | 4 | ||
5.2 | odd | 4 | 105.4.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.o.1.2 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.k.274.1 | 4 | ||
15.2 | even | 4 | 315.4.a.l.1.2 | 2 | |||
15.8 | even | 4 | 1575.4.a.n.1.1 | 2 | |||
20.7 | even | 4 | 1680.4.a.bd.1.1 | 2 | |||
35.27 | even | 4 | 735.4.a.m.1.1 | 2 | |||
105.62 | odd | 4 | 2205.4.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.l.1.2 | 2 | 15.2 | even | 4 | |||
525.4.a.o.1.2 | 2 | 5.3 | odd | 4 | |||
525.4.d.k.274.1 | 4 | 5.4 | even | 2 | inner | ||
525.4.d.k.274.4 | 4 | 1.1 | even | 1 | trivial | ||
735.4.a.m.1.1 | 2 | 35.27 | even | 4 | |||
1575.4.a.n.1.1 | 2 | 15.8 | even | 4 | |||
1680.4.a.bd.1.1 | 2 | 20.7 | even | 4 | |||
2205.4.a.be.1.2 | 2 | 105.62 | odd | 4 |