Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,4,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.165");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.5643743611\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.165 |
Dual form | 196.4.e.a.177.1 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.00000 | + | 8.66025i | −0.962250 | + | 1.66667i | −0.245423 | + | 0.969416i | \(0.578927\pi\) |
−0.716827 | + | 0.697251i | \(0.754406\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | − | 6.92820i | −0.357771 | − | 0.619677i | 0.629817 | − | 0.776743i | \(-0.283130\pi\) |
−0.987588 | + | 0.157066i | \(0.949796\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −36.5000 | − | 63.2199i | −1.35185 | − | 2.34148i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.0000 | − | 34.6410i | 0.548202 | − | 0.949514i | −0.450195 | − | 0.892930i | \(-0.648646\pi\) |
0.998398 | − | 0.0565844i | \(-0.0180210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0000 | 0.256015 | 0.128008 | − | 0.991773i | \(-0.459142\pi\) | ||||
0.128008 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 80.0000 | 1.37706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −29.0000 | + | 50.2295i | −0.413737 | + | 0.716614i | −0.995295 | − | 0.0968912i | \(-0.969110\pi\) |
0.581558 | + | 0.813505i | \(0.302443\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.0000 | + | 22.5167i | 0.156969 | + | 0.271878i | 0.933774 | − | 0.357863i | \(-0.116495\pi\) |
−0.776805 | + | 0.629741i | \(0.783161\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 32.0000 | + | 55.4256i | 0.290107 | + | 0.502480i | 0.973835 | − | 0.227257i | \(-0.0729758\pi\) |
−0.683728 | + | 0.729737i | \(0.739642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.5000 | − | 52.8275i | 0.244000 | − | 0.422620i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 460.000 | 3.27878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −62.0000 | −0.397004 | −0.198502 | − | 0.980101i | \(-0.563608\pi\) | ||||
−0.198502 | + | 0.980101i | \(0.563608\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 126.000 | − | 218.238i | 0.730009 | − | 1.26441i | −0.226870 | − | 0.973925i | \(-0.572849\pi\) |
0.956879 | − | 0.290487i | \(-0.0938173\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 200.000 | + | 346.410i | 1.05502 | + | 1.82734i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.0000 | − | 22.5167i | −0.0577618 | − | 0.100046i | 0.835699 | − | 0.549188i | \(-0.185063\pi\) |
−0.893460 | + | 0.449142i | \(0.851730\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −60.0000 | + | 103.923i | −0.246351 | + | 0.426692i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.0228547 | −0.0114273 | − | 0.999935i | \(-0.503638\pi\) | ||||
−0.0114273 | + | 0.999935i | \(0.503638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 416.000 | 1.47534 | 0.737668 | − | 0.675164i | \(-0.235927\pi\) | ||||
0.737668 | + | 0.675164i | \(0.235927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −292.000 | + | 505.759i | −0.967306 | + | 1.67542i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −198.000 | − | 342.946i | −0.614495 | − | 1.06434i | −0.990473 | − | 0.137708i | \(-0.956026\pi\) |
0.375978 | − | 0.926629i | \(-0.377307\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −290.000 | − | 502.295i | −0.796238 | − | 1.37912i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 225.000 | − | 389.711i | 0.583134 | − | 1.01002i | −0.411971 | − | 0.911197i | \(-0.635159\pi\) |
0.995105 | − | 0.0988214i | \(-0.0315073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −320.000 | −0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −260.000 | −0.604173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 137.000 | − | 237.291i | 0.302303 | − | 0.523604i | −0.674354 | − | 0.738408i | \(-0.735578\pi\) |
0.976657 | + | 0.214804i | \(0.0689112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −288.000 | − | 498.831i | −0.604502 | − | 1.04703i | −0.992130 | − | 0.125212i | \(-0.960039\pi\) |
0.387628 | − | 0.921816i | \(-0.373295\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −48.0000 | − | 83.1384i | −0.0915949 | − | 0.158647i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 238.000 | − | 412.228i | 0.433975 | − | 0.751667i | −0.563236 | − | 0.826296i | \(-0.690444\pi\) |
0.997211 | + | 0.0746290i | \(0.0237773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −640.000 | −1.11662 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −448.000 | −0.748843 | −0.374421 | − | 0.927259i | \(-0.622159\pi\) | ||||
−0.374421 | + | 0.927259i | \(0.622159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −79.0000 | + | 136.832i | −0.126661 | + | 0.219383i | −0.922381 | − | 0.386281i | \(-0.873759\pi\) |
0.795720 | + | 0.605665i | \(0.207093\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 305.000 | + | 528.275i | 0.469578 | + | 0.813333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 468.000 | + | 810.600i | 0.666508 | + | 1.15443i | 0.978874 | + | 0.204464i | \(0.0655450\pi\) |
−0.312366 | + | 0.949962i | \(0.601122\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1314.50 | + | 2276.78i | −1.80316 | + | 3.12316i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −530.000 | −0.700904 | −0.350452 | − | 0.936581i | \(-0.613972\pi\) | ||||
−0.350452 | + | 0.936581i | \(0.613972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 464.000 | 0.592093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 310.000 | − | 536.936i | 0.382017 | − | 0.661673i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −195.000 | − | 337.750i | −0.232247 | − | 0.402263i | 0.726222 | − | 0.687460i | \(-0.241274\pi\) |
−0.958469 | + | 0.285197i | \(0.907941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1260.00 | + | 2182.38i | 1.40490 | + | 2.43336i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 104.000 | − | 180.133i | 0.112318 | − | 0.194540i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −214.000 | −0.224004 | −0.112002 | − | 0.993708i | \(-0.535726\pi\) | ||||
−0.112002 | + | 0.993708i | \(0.535726\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2920.00 | −2.96435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 716.000 | − | 1240.15i | 0.705393 | − | 1.22178i | −0.261157 | − | 0.965296i | \(-0.584104\pi\) |
0.966550 | − | 0.256480i | \(-0.0825627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 382.000 | + | 661.643i | 0.365433 | + | 0.632948i | 0.988846 | − | 0.148945i | \(-0.0475877\pi\) |
−0.623413 | + | 0.781893i | \(0.714254\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −162.000 | − | 280.592i | −0.146366 | − | 0.253513i | 0.783516 | − | 0.621372i | \(-0.213424\pi\) |
−0.929882 | + | 0.367859i | \(0.880091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 667.000 | − | 1155.28i | 0.586119 | − | 1.01519i | −0.408615 | − | 0.912707i | \(-0.633988\pi\) |
0.994735 | − | 0.102482i | \(-0.0326784\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 260.000 | 0.222325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1798.00 | 1.49683 | 0.748414 | − | 0.663232i | \(-0.230816\pi\) | ||||
0.748414 | + | 0.663232i | \(0.230816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 256.000 | − | 443.405i | 0.207584 | − | 0.359545i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −438.000 | − | 758.638i | −0.346095 | − | 0.599454i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −134.500 | − | 232.961i | −0.101052 | − | 0.175027i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.0000 | − | 51.9615i | 0.0219919 | − | 0.0380912i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1488.00 | −1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −384.000 | −0.268303 | −0.134152 | − | 0.990961i | \(-0.542831\pi\) | ||||
−0.134152 | + | 0.990961i | \(0.542831\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2080.00 | + | 3602.67i | −1.41964 | + | 2.45889i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −907.000 | − | 1570.97i | −0.604923 | − | 1.04776i | −0.992064 | − | 0.125737i | \(-0.959870\pi\) |
0.387140 | − | 0.922021i | \(-0.373463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1840.00 | − | 3186.97i | −1.17305 | − | 2.03179i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −833.000 | + | 1442.80i | −0.519474 | + | 0.899756i | 0.480269 | + | 0.877121i | \(0.340539\pi\) |
−0.999744 | + | 0.0226350i | \(0.992794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1126.00 | −0.687094 | −0.343547 | − | 0.939135i | \(-0.611628\pi\) | ||||
−0.343547 | + | 0.939135i | \(0.611628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3960.00 | 2.36519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 240.000 | − | 415.692i | 0.140348 | − | 0.243090i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 248.000 | + | 429.549i | 0.142036 | + | 0.246014i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1347.00 | − | 2333.07i | −0.740608 | − | 1.28277i | −0.952219 | − | 0.305416i | \(-0.901204\pi\) |
0.211611 | − | 0.977354i | \(-0.432129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1324.00 | − | 2293.24i | 0.713547 | − | 1.23590i | −0.249970 | − | 0.968253i | \(-0.580421\pi\) |
0.963517 | − | 0.267646i | \(-0.0862458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4234.00 | 2.23725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2016.00 | −1.04470 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −278.000 | + | 481.510i | −0.141317 | + | 0.244769i | −0.927993 | − | 0.372598i | \(-0.878467\pi\) |
0.786676 | + | 0.617367i | \(0.211800\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2250.00 | + | 3897.11i | 1.12224 | + | 1.94378i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 164.000 | + | 284.056i | 0.0788066 | + | 0.136497i | 0.902735 | − | 0.430196i | \(-0.141556\pi\) |
−0.823929 | + | 0.566693i | \(0.808222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1600.00 | − | 2771.28i | 0.754908 | − | 1.30754i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4268.00 | 1.97765 | 0.988826 | − | 0.149077i | \(-0.0476302\pi\) | ||||
0.988826 | + | 0.149077i | \(0.0476302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 949.000 | − | 1643.72i | 0.424397 | − | 0.735077i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1738.00 | − | 3010.30i | −0.763802 | − | 1.32294i | −0.940878 | − | 0.338746i | \(-0.889997\pi\) |
0.177076 | − | 0.984197i | \(-0.443336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1370.00 | + | 2372.91i | 0.581783 | + | 1.00768i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1134.00 | + | 1964.15i | −0.473515 | + | 0.820152i | −0.999540 | − | 0.0303171i | \(-0.990348\pi\) |
0.526026 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 276.000 | 0.113342 | 0.0566710 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566710 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5760.00 | 2.32673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −104.000 | + | 180.133i | −0.0413310 | + | 0.0715874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1160.00 | + | 2009.18i | 0.453624 | + | 0.785699i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1500.00 | + | 2598.08i | 0.568252 | + | 0.984242i | 0.996739 | + | 0.0806937i | \(0.0257136\pi\) |
−0.428487 | + | 0.903548i | \(0.640953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1639.00 | + | 2838.83i | −0.611284 | + | 1.05877i | 0.379740 | + | 0.925093i | \(0.376013\pi\) |
−0.991024 | + | 0.133682i | \(0.957320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 960.000 | 0.352549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2362.00 | −0.854241 | −0.427121 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427121 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −518.000 | + | 897.202i | −0.184523 | + | 0.319603i | −0.943416 | − | 0.331613i | \(-0.892407\pi\) |
0.758893 | + | 0.651216i | \(0.225741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2380.00 | + | 4122.28i | 0.835185 | + | 1.44658i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | + | 41.5692i | 0.00817674 | + | 0.0141625i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2336.00 | − | 4046.07i | 0.784363 | − | 1.35856i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1040.00 | 0.344202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3524.00 | 1.14977 | 0.574887 | − | 0.818233i | \(-0.305046\pi\) | ||||
0.574887 | + | 0.818233i | \(0.305046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2240.00 | − | 3879.79i | 0.720574 | − | 1.24807i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1664.00 | − | 2882.13i | −0.527832 | − | 0.914232i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −790.000 | − | 1368.32i | −0.243759 | − | 0.422203i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −348.000 | + | 602.754i | −0.105923 | + | 0.183464i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1336.00 | 0.401189 | 0.200595 | − | 0.979674i | \(-0.435713\pi\) | ||||
0.200595 | + | 0.979674i | \(0.435713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4453.00 | −1.31941 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 645.000 | − | 1117.17i | 0.188591 | − | 0.326649i | −0.756190 | − | 0.654352i | \(-0.772941\pi\) |
0.944781 | + | 0.327703i | \(0.106275\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2762.00 | + | 4783.92i | 0.797022 | + | 1.38048i | 0.921547 | + | 0.388267i | \(0.126926\pi\) |
−0.124525 | + | 0.992216i | \(0.539741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3157.00 | − | 5468.08i | −0.887648 | − | 1.53745i | −0.842648 | − | 0.538464i | \(-0.819005\pi\) |
−0.0449994 | − | 0.998987i | \(-0.514329\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1584.00 | + | 2743.57i | −0.439697 | + | 0.761577i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9360.00 | −2.56539 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3960.00 | −1.07176 | −0.535881 | − | 0.844294i | \(-0.680020\pi\) | ||||
−0.535881 | + | 0.844294i | \(0.680020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3509.00 | + | 6077.77i | −0.937903 | + | 1.62450i | −0.168529 | + | 0.985697i | \(0.553902\pi\) |
−0.769374 | + | 0.638798i | \(0.779432\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6935.00 | − | 12011.8i | −1.83078 | − | 3.17101i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 156.000 | + | 270.200i | 0.0401864 | + | 0.0696049i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2650.00 | − | 4589.93i | 0.674445 | − | 1.16817i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2394.00 | 0.602024 | 0.301012 | − | 0.953620i | \(-0.402676\pi\) | ||||
0.301012 | + | 0.953620i | \(0.402676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2560.00 | 0.636149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2320.00 | + | 4018.36i | −0.569741 | + | 0.986821i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1383.00 | − | 2395.43i | −0.335678 | − | 0.581411i | 0.647937 | − | 0.761694i | \(-0.275632\pi\) |
−0.983615 | + | 0.180283i | \(0.942299\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2263.00 | + | 3919.63i | 0.536690 | + | 0.929575i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3984.00 | + | 6900.49i | −0.934084 | + | 1.61788i | −0.157823 | + | 0.987467i | \(0.550448\pi\) |
−0.776260 | + | 0.630413i | \(0.782886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3600.00 | −0.834514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3900.00 | 0.893918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1450.00 | + | 2511.47i | −0.328654 | + | 0.569246i | −0.982245 | − | 0.187602i | \(-0.939928\pi\) |
0.653591 | + | 0.756848i | \(0.273262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1320.00 | + | 2286.31i | 0.295883 | + | 0.512484i | 0.975190 | − | 0.221370i | \(-0.0710528\pi\) |
−0.679307 | + | 0.733854i | \(0.737719\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1220.00 | − | 2113.10i | −0.267523 | − | 0.463363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 761.000 | − | 1318.09i | 0.165069 | − | 0.285908i | −0.771611 | − | 0.636095i | \(-0.780549\pi\) |
0.936680 | + | 0.350187i | \(0.113882\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18396.0 | −3.94745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4534.00 | −0.962547 | −0.481274 | − | 0.876570i | \(-0.659826\pi\) | ||||
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2417.00 | − | 4186.37i | 0.507688 | − | 0.879342i | −0.492272 | − | 0.870441i | \(-0.663834\pi\) |
0.999960 | − | 0.00890034i | \(-0.00283310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1040.00 | + | 1801.33i | 0.216155 | + | 0.374392i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 774.500 | + | 1341.47i | 0.157643 | + | 0.273046i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1070.00 | − | 1853.29i | 0.215548 | − | 0.373340i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4656.00 | 0.928350 | 0.464175 | − | 0.885744i | \(-0.346351\pi\) | ||||
0.464175 | + | 0.885744i | \(0.346351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2192.00 | −0.432621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9200.00 | − | 15934.9i | 1.79743 | − | 3.11325i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 384.000 | + | 665.108i | 0.0742719 | + | 0.128643i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7160.00 | + | 12401.5i | 1.35753 | + | 2.35131i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2304.00 | + | 3990.65i | −0.432546 | + | 0.749192i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7238.00 | 1.34558 | 0.672792 | − | 0.739831i | \(-0.265095\pi\) | ||||
0.672792 | + | 0.739831i | \(0.265095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7640.00 | −1.40655 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 548.000 | − | 949.164i | 0.0999171 | − | 0.173062i | −0.811733 | − | 0.584029i | \(-0.801476\pi\) |
0.911650 | + | 0.410967i | \(0.134809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1909.00 | − | 3306.48i | −0.344738 | − | 0.597104i | 0.640568 | − | 0.767901i | \(-0.278699\pi\) |
−0.985306 | + | 0.170797i | \(0.945366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −999.000 | − | 1730.32i | −0.177001 | − | 0.306575i | 0.763851 | − | 0.645393i | \(-0.223306\pi\) |
−0.940852 | + | 0.338818i | \(0.889973\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1240.00 | + | 2147.74i | −0.217638 | + | 0.376961i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3240.00 | 0.563362 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1508.00 | −0.259775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 366.000 | − | 633.931i | 0.0624678 | − | 0.108197i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6670.00 | + | 11552.8i | 1.12799 | + | 1.95373i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3968.00 | + | 6872.78i | 0.658915 | + | 1.14127i | 0.980897 | + | 0.194529i | \(0.0623178\pi\) |
−0.321981 | + | 0.946746i | \(0.604349\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −949.000 | + | 1643.72i | −0.156171 | + | 0.270496i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3808.00 | −0.621055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2766.00 | 0.447103 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8990.00 | + | 15571.1i | −1.44032 | + | 2.49471i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5040.00 | − | 8729.54i | −0.800385 | − | 1.38631i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2560.00 | + | 4434.05i | 0.399495 | + | 0.691946i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4176.00 | + | 7233.04i | −0.646050 | + | 1.11899i | 0.338008 | + | 0.941143i | \(0.390247\pi\) |
−0.984058 | + | 0.177848i | \(0.943086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5924.00 | 0.908609 | 0.454304 | − | 0.890847i | \(-0.349888\pi\) | ||||
0.454304 | + | 0.890847i | \(0.349888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5520.00 | 0.839418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1113.00 | − | 1927.77i | 0.167816 | − | 0.290666i | −0.769836 | − | 0.638242i | \(-0.779662\pi\) |
0.937652 | + | 0.347576i | \(0.112995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1792.00 | + | 3103.84i | 0.267914 | + | 0.464041i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1940.00 | − | 3360.18i | −0.285207 | − | 0.493993i | 0.687452 | − | 0.726229i | \(-0.258729\pi\) |
−0.972659 | + | 0.232237i | \(0.925396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3091.50 | − | 5354.64i | 0.450722 | − | 0.780673i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2690.00 | 0.388949 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1264.00 | 0.181262 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1292.00 | + | 2237.81i | −0.183765 | + | 0.318291i | −0.943160 | − | 0.332340i | \(-0.892162\pi\) |
0.759394 | + | 0.650630i | \(0.225495\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 219.000 | + | 379.319i | 0.0308962 | + | 0.0535137i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5267.00 | − | 9122.71i | −0.731139 | − | 1.26637i | −0.956397 | − | 0.292071i | \(-0.905656\pi\) |
0.225257 | − | 0.974299i | \(-0.427678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7440.00 | − | 12886.5i | 1.02453 | − | 1.77454i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −744.000 | −0.101639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4472.00 | −0.606098 | −0.303049 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1920.00 | − | 3325.54i | 0.258175 | − | 0.447172i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1234.00 | + | 2137.35i | 0.164633 | + | 0.285153i | 0.936525 | − | 0.350601i | \(-0.114023\pi\) |
−0.771892 | + | 0.635754i | \(0.780689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15184.0 | − | 26299.5i | −1.99443 | − | 3.45446i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 523.000 | − | 905.863i | 0.0681675 | − | 0.118070i | −0.829927 | − | 0.557872i | \(-0.811618\pi\) |
0.898095 | + | 0.439802i | \(0.144951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3712.00 | −0.480112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18140.0 | 2.32835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3744.00 | − | 6484.80i | 0.476914 | − | 0.826040i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1062.00 | + | 1839.44i | 0.134258 | + | 0.232541i | 0.925314 | − | 0.379203i | \(-0.123802\pi\) |
−0.791056 | + | 0.611744i | \(0.790468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5799.00 | − | 10044.2i | −0.722165 | − | 1.25083i | −0.960130 | − | 0.279553i | \(-0.909814\pi\) |
0.237965 | − | 0.971274i | \(-0.423520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1512.00 | − | 2618.86i | 0.186894 | − | 0.323709i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21032.0 | 2.58047 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1040.00 | −0.126661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1385.00 | + | 2398.89i | −0.167442 | + | 0.290018i | −0.937520 | − | 0.347932i | \(-0.886884\pi\) |
0.770078 | + | 0.637950i | \(0.220217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8330.00 | − | 14428.0i | −0.999729 | − | 1.73158i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2120.00 | + | 3671.95i | 0.250763 | + | 0.434335i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5630.00 | − | 9751.45i | 0.661157 | − | 1.14516i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9438.00 | −1.10042 | −0.550211 | − | 0.835026i | \(-0.685453\pi\) | ||||
−0.550211 | + | 0.835026i | \(0.685453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5550.00 | 0.642495 | 0.321248 | − | 0.946995i | \(-0.395898\pi\) | ||||
0.321248 | + | 0.946995i | \(0.395898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14454.0 | + | 25035.1i | −1.66141 | + | 2.87765i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1769.00 | + | 3064.00i | 0.201904 | + | 0.349708i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2400.00 | + | 4156.92i | 0.270100 | + | 0.467828i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1500.00 | − | 2598.08i | 0.167639 | − | 0.290359i | −0.769950 | − | 0.638104i | \(-0.779719\pi\) |
0.937589 | + | 0.347744i | \(0.113052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12926.0 | −1.43460 | −0.717302 | − | 0.696762i | \(-0.754623\pi\) | ||||
−0.717302 | + | 0.696762i | \(0.754623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4960.00 | −0.546698 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −832.000 | + | 1441.07i | −0.0910754 | + | 0.157747i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −204.000 | − | 353.338i | −0.0221786 | − | 0.0384144i | 0.854723 | − | 0.519084i | \(-0.173727\pi\) |
−0.876902 | + | 0.480670i | \(0.840394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7226.00 | + | 12515.8i | 0.774983 | + | 1.34231i | 0.934804 | + | 0.355164i | \(0.115575\pi\) |
−0.159821 | + | 0.987146i | \(0.551092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1560.00 | + | 2702.00i | −0.166182 | + | 0.287836i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26940.0 | 2.85060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10258.0 | 1.07818 | 0.539092 | − | 0.842247i | \(-0.318767\pi\) | ||||
0.539092 | + | 0.842247i | \(0.318767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −120.000 | + | 207.846i | −0.0125290 | + | 0.0217009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13240.0 | + | 22932.4i | 1.37322 | + | 2.37849i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2749.00 | + | 4761.41i | 0.281385 | + | 0.487373i | 0.971726 | − | 0.236111i | \(-0.0758730\pi\) |
−0.690341 | + | 0.723484i | \(0.742540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13340.0 | + | 23105.6i | −1.35655 | + | 2.34962i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16316.0 | 1.64840 | 0.824199 | − | 0.566300i | \(-0.191625\pi\) | ||||
0.824199 | + | 0.566300i | \(0.191625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8944.00 | 0.897760 | 0.448880 | − | 0.893592i | \(-0.351823\pi\) | ||||
0.448880 | + | 0.893592i | \(0.351823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10080.0 | − | 17459.1i | 1.00527 | − | 1.74117i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4711.00 | − | 8159.69i | −0.466807 | − | 0.808534i | 0.532474 | − | 0.846447i | \(-0.321263\pi\) |
−0.999281 | + | 0.0379124i | \(0.987929\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2780.00 | − | 4815.10i | −0.271965 | − | 0.471058i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8320.00 | − | 14410.7i | 0.808782 | − | 1.40085i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1586.00 | 0.153201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32850.0 | −3.15325 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6910.00 | − | 11968.5i | 0.659136 | − | 1.14166i | −0.321704 | − | 0.946840i | \(-0.604256\pi\) |
0.980840 | − | 0.194816i | \(-0.0624110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −156.000 | − | 270.200i | −0.0147879 | − | 0.0256134i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 856.000 | + | 1482.64i | 0.0801422 | + | 0.138810i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6632.00 | − | 11487.0i | 0.617094 | − | 1.06884i | −0.372920 | − | 0.927864i | \(-0.621643\pi\) |
0.990013 | − | 0.140974i | \(-0.0450234\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3280.00 | −0.303327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5940.00 | −0.545964 | −0.272982 | − | 0.962019i | \(-0.588010\pi\) | ||||
−0.272982 | + | 0.962019i | \(0.588010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1798.00 | − | 3114.23i | 0.164255 | − | 0.284498i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11680.0 | + | 20230.4i | 1.06056 | + | 1.83694i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4126.00 | + | 7146.44i | 0.370151 | + | 0.641120i | 0.989588 | − | 0.143926i | \(-0.0459728\pi\) |
−0.619438 | + | 0.785046i | \(0.712639\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21340.0 | + | 36962.0i | −1.90300 | + | 3.29609i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4704.00 | −0.416980 | −0.208490 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208490 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11456.0 | −1.00948 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10265.0 | − | 17779.5i | 0.899181 | − | 1.55743i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5394.00 | − | 9342.68i | −0.469715 | − | 0.813570i | 0.529686 | − | 0.848194i | \(-0.322310\pi\) |
−0.999400 | + | 0.0346241i | \(0.988977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5980.00 | + | 10357.7i | 0.514666 | + | 0.891427i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3056.00 | − | 5293.15i | 0.261482 | − | 0.452901i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15840.0 | −1.34747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34760.0 | 2.93987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7293.00 | + | 12631.8i | −0.613267 | + | 1.06221i | 0.377419 | + | 0.926043i | \(0.376812\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0000 | + | 22.5167i | 0.00108690 | + | 0.00188257i | 0.866568 | − | 0.499058i | \(-0.166321\pi\) |
−0.865481 | + | 0.500941i | \(0.832987\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7308.00 | + | 12657.8i | 0.604064 | + | 1.04627i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4035.50 | − | 6989.69i | 0.331676 | − | 0.574479i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20002.0 | −1.63468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −72.0000 | −0.00585116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1296.00 | + | 2244.74i | −0.104731 | + | 0.181399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11340.0 | − | 19641.5i | −0.911280 | − | 1.57838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5607.00 | − | 9711.61i | −0.445589 | − | 0.771783i | 0.552504 | − | 0.833510i | \(-0.313672\pi\) |
−0.998093 | + | 0.0617272i | \(0.980339\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1380.00 | + | 2390.23i | −0.109063 | + | 0.188903i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10672.0 | −0.838786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5424.00 | −0.423973 | −0.211987 | − | 0.977273i | \(-0.567993\pi\) | ||||
−0.211987 | + | 0.977273i | \(0.567993\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21024.0 | + | 36414.6i | −1.63439 | + | 2.83085i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −806.000 | − | 1396.03i | −0.0623172 | − | 0.107936i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1040.00 | − | 1801.33i | −0.0795415 | − | 0.137770i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8809.00 | − | 15257.6i | 0.670106 | − | 1.16066i | −0.307767 | − | 0.951462i | \(-0.599582\pi\) |
0.977874 | − | 0.209197i | \(-0.0670849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4992.00 | 0.377709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23200.0 | −1.74600 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1781.00 | + | 3084.78i | −0.133322 | + | 0.230920i | −0.924955 | − | 0.380076i | \(-0.875898\pi\) |
0.791633 | + | 0.610997i | \(0.209231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7192.00 | − | 12456.9i | −0.535522 | − | 0.927551i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1419.00 | − | 2457.78i | −0.104548 | − | 0.181082i | 0.809006 | − | 0.587801i | \(-0.200006\pi\) |
−0.913553 | + | 0.406719i | \(0.866673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 180.000 | − | 311.769i | 0.0131922 | − | 0.0228496i | −0.859354 | − | 0.511381i | \(-0.829134\pi\) |
0.872546 | + | 0.488532i | \(0.162467\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30000.0 | −2.18720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3904.00 | 0.283144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11009.0 | − | 19068.1i | 0.794299 | − | 1.37577i | −0.128984 | − | 0.991647i | \(-0.541172\pi\) |
0.923283 | − | 0.384120i | \(-0.125495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16390.0 | − | 28388.3i | −1.17642 | − | 2.03761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9000.00 | − | 15588.5i | −0.639351 | − | 1.10739i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3504.00 | + | 6069.11i | −0.247645 | + | 0.428934i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1454.00 | −0.102237 | −0.0511184 | − | 0.998693i | \(-0.516279\pi\) | ||||
−0.0511184 | + | 0.998693i | \(0.516279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6552.00 | 0.458354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11810.0 | − | 20455.5i | 0.821994 | − | 1.42374i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6909.00 | + | 11966.7i | 0.478446 | + | 0.828693i | 0.999695 | − | 0.0247118i | \(-0.00786682\pi\) |
−0.521248 | + | 0.853405i | \(0.674533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5180.00 | − | 8972.02i | −0.355114 | − | 0.615076i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3348.00 | + | 5798.91i | −0.228373 | + | 0.395554i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) |
0.728953 | + | 0.684564i | \(0.240007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10010.0 | −0.679395 | −0.339698 | − | 0.940535i | \(-0.610325\pi\) | ||||
−0.339698 | + | 0.940535i | \(0.610325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34748.0 | −2.34668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1076.00 | + | 1863.69i | −0.0723068 | + | 0.125239i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1440.00 | + | 2494.15i | 0.0962896 | + | 0.166779i | 0.910146 | − | 0.414287i | \(-0.135969\pi\) |
−0.813856 | + | 0.581066i | \(0.802636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2376.00 | − | 4115.35i | −0.157320 | − | 0.272487i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3261.00 | + | 5648.22i | −0.214862 | + | 0.372152i | −0.953230 | − | 0.302246i | \(-0.902264\pi\) |
0.738368 | + | 0.674398i | \(0.235597\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −480.000 | −0.0314723 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6614.00 | 0.431555 | 0.215778 | − | 0.976443i | \(-0.430771\pi\) | ||||
0.215778 | + | 0.976443i | \(0.430771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2633.00 | − | 4560.49i | 0.170968 | − | 0.296125i | −0.767791 | − | 0.640701i | \(-0.778644\pi\) |
0.938759 | + | 0.344576i | \(0.111977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14720.0 | + | 25495.8i | 0.951197 | + | 1.64752i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2139.50 | + | 3705.72i | 0.136928 | + | 0.237166i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5200.00 | + | 9006.66i | −0.331209 | + | 0.573671i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1508.00 | 0.0955928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3344.00 | 0.210971 | 0.105485 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105485 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17620.0 | + | 30518.7i | −1.10637 | + | 1.91629i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1536.00 | + | 2660.43i | 0.0959910 | + | 0.166261i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16352.0 | + | 28322.5i | 1.01232 | + | 1.75340i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2441.00 | − | 4227.94i | 0.150411 | − | 0.260520i | −0.780967 | − | 0.624572i | \(-0.785274\pi\) |
0.931379 | + | 0.364052i | \(0.118607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15898.0 | 0.975048 | 0.487524 | − | 0.873110i | \(-0.337900\pi\) | ||||
0.487524 | + | 0.873110i | \(0.337900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33280.0 | 2.03163 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3066.00 | − | 5310.47i | 0.186301 | − | 0.322683i | −0.757713 | − | 0.652588i | \(-0.773683\pi\) |
0.944014 | + | 0.329905i | \(0.107017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5480.00 | − | 9491.64i | −0.331447 | − | 0.574082i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12099.0 | + | 20956.1i | 0.725070 | + | 1.25586i | 0.958945 | + | 0.283591i | \(0.0915258\pi\) |
−0.233876 | + | 0.972266i | \(0.575141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7256.00 | + | 12567.8i | −0.432848 | + | 0.749715i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11534.0 | 0.684907 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17456.0 | 1.03185 | 0.515925 | − | 0.856634i | \(-0.327448\pi\) | ||||
0.515925 | + | 0.856634i | \(0.327448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −328.000 | + | 568.113i | −0.0193006 | + | 0.0334297i | −0.875514 | − | 0.483192i | \(-0.839477\pi\) |
0.856214 | + | 0.516622i | \(0.172811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3480.00 | − | 6027.54i | −0.203849 | − | 0.353077i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1984.00 | − | 3436.39i | −0.115174 | − | 0.199487i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6680.00 | + | 11570.1i | −0.386044 | + | 0.668649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23040.0 | −1.32556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18214.0 | −1.04324 | −0.521618 | − | 0.853179i | \(-0.674671\pi\) | ||||
−0.521618 | + | 0.853179i | \(0.674671\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14030.0 | − | 24300.7i | 0.800022 | − | 1.38568i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15126.0 | + | 26199.0i | 0.858699 | + | 1.48731i | 0.873170 | + | 0.487415i | \(0.162060\pi\) |
−0.0144709 | + | 0.999895i | \(0.504606\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6450.00 | + | 11171.7i | 0.362944 | + | 0.628637i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5418.00 | − | 9384.25i | 0.303534 | − | 0.525737i | −0.673400 | − | 0.739279i | \(-0.735167\pi\) |
0.976934 | + | 0.213542i | \(0.0684999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13328.0 | 0.743411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −55240.0 | −3.06774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2700.00 | − | 4676.54i | 0.149291 | − | 0.258580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4789.00 | + | 8294.79i | 0.263650 | + | 0.456655i | 0.967209 | − | 0.253982i | \(-0.0817403\pi\) |
−0.703559 | + | 0.710637i | \(0.748407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4504.00 | + | 7801.16i | 0.245822 | + | 0.425777i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 174.000 | − | 301.377i | 0.00945584 | − | 0.0163780i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 63140.0 | 3.41656 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12442.0 | 0.670368 | 0.335184 | − | 0.942153i | \(-0.391202\pi\) | ||||
0.335184 | + | 0.942153i | \(0.391202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 338.000 | − | 585.433i | 0.0181336 | − | 0.0314083i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15840.0 | − | 27435.7i | −0.846197 | − | 1.46566i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12587.0 | + | 21801.3i | 0.666734 | + | 1.15482i | 0.978812 | + | 0.204761i | \(0.0656418\pi\) |
−0.312078 | + | 0.950057i | \(0.601025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34164.0 | − | 59173.8i | 1.80204 | − | 3.12122i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16128.0 | 0.847123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3840.00 | −0.200850 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19800.0 | − | 34294.6i | 1.03130 | − | 1.78627i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17094.0 | + | 29607.7i | 0.886646 | + | 1.53572i | 0.843815 | + | 0.536634i | \(0.180304\pi\) |
0.0428311 | + | 0.999082i | \(0.486362\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35090.0 | − | 60777.7i | −1.80499 | − | 3.12634i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1891.00 | + | 3275.31i | −0.0968689 | + | 0.167782i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5204.00 | 0.265482 | 0.132741 | − | 0.991151i | \(-0.457622\pi\) | ||||
0.132741 | + | 0.991151i | \(0.457622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 67717.0 | 3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12064.0 | + | 20895.5i | −0.610401 | + | 1.05725i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16440.0 | − | 28474.9i | −0.828411 | − | 1.43485i | −0.899284 | − | 0.437365i | \(-0.855912\pi\) |
0.0708733 | − | 0.997485i | \(-0.477421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9520.00 | − | 16489.1i | −0.475812 | − | 0.824131i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1956.00 | − | 3387.89i | 0.0973648 | − | 0.168641i | −0.813228 | − | 0.581945i | \(-0.802292\pi\) |
0.910593 | + | 0.413304i | \(0.135625\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3120.00 | −0.154678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16008.0 | −0.790413 | −0.395206 | − | 0.918592i | \(-0.629327\pi\) | ||||
−0.395206 | + | 0.918592i | \(0.629327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10776.0 | + | 18664.6i | −0.529936 | + | 0.917876i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19345.0 | + | 33506.5i | 0.947519 | + | 1.64115i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4980.00 | − | 8625.61i | −0.241974 | − | 0.419112i | 0.719302 | − | 0.694697i | \(-0.244462\pi\) |
−0.961277 | + | 0.275585i | \(0.911128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11970.0 | + | 20732.6i | −0.579298 | + | 1.00337i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21184.0 | −1.02115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12378.0 | 0.594301 | 0.297151 | − | 0.954831i | \(-0.403964\pi\) | ||||
0.297151 | + | 0.954831i | \(0.403964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12800.0 | + | 22170.3i | −0.612135 | + | 1.06025i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17335.0 | + | 30025.1i | 0.825747 | + | 1.43024i | 0.901347 | + | 0.433097i | \(0.142579\pi\) |
−0.0756005 | + | 0.997138i | \(0.524087\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16936.0 | − | 29334.0i | −0.800421 | − | 1.38637i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1644.00 | − | 2847.49i | 0.0773943 | − | 0.134051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10898.0 | 0.511043 | 0.255521 | − | 0.966803i | \(-0.417753\pi\) | ||||
0.255521 | + | 0.966803i | \(0.417753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27660.0 | 1.29202 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12904.0 | + | 22350.4i | −0.600420 | + | 1.03996i | 0.392337 | + | 0.919821i | \(0.371667\pi\) |
−0.992757 | + | 0.120136i | \(0.961667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7686.00 | − | 13312.5i | −0.356244 | − | 0.617033i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −78.0000 | − | 135.100i | −0.00358747 | − | 0.00621368i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8960.00 | + | 15519.2i | −0.410517 | + | 0.711037i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28520.0 | −1.30169 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4448.00 | 0.202237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10527.0 | + | 18233.3i | −0.476807 | + | 0.825854i | −0.999647 | − | 0.0265772i | \(-0.991539\pi\) |
0.522840 | + | 0.852431i | \(0.324873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39840.0 | − | 69004.9i | −1.79764 | − | 3.11361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3456.00 | − | 5985.97i | −0.154762 | − | 0.268055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18000.0 | − | 31176.9i | 0.803012 | − | 1.39086i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24276.0 | 1.07892 | 0.539461 | − | 0.842011i | \(-0.318628\pi\) | ||||
0.539461 | + | 0.842011i | \(0.318628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22968.0 | 1.01696 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14235.0 | + | 24655.7i | −0.627926 | + | 1.08760i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3160.00 | + | 5473.28i | 0.138872 | + | 0.240533i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14500.0 | − | 25114.7i | −0.632496 | − | 1.09551i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10763.0 | + | 18642.1i | −0.467747 | + | 0.810161i | −0.999321 | − | 0.0368510i | \(-0.988267\pi\) |
0.531574 | + | 0.847012i | \(0.321601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12806.0 | 0.554475 | 0.277238 | − | 0.960801i | \(-0.410581\pi\) | ||||
0.277238 | + | 0.960801i | \(0.410581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26400.0 | −1.13885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1312.00 | − | 2272.45i | 0.0563894 | − | 0.0976693i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5408.00 | + | 9366.93i | 0.231581 | + | 0.401111i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6607.00 | − | 11443.7i | −0.280860 | − | 0.486463i | 0.690737 | − | 0.723106i | \(-0.257286\pi\) |
−0.971597 | + | 0.236643i | \(0.923953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16124.0 | + | 27927.6i | −0.682925 | + | 1.18286i | 0.291159 | + | 0.956675i | \(0.405959\pi\) |
−0.974084 | + | 0.226186i | \(0.927374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24400.0 | 1.02970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14316.0 | −0.601954 | −0.300977 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300977 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12584.0 | − | 21796.1i | 0.527214 | − | 0.913161i | −0.472283 | − | 0.881447i | \(-0.656570\pi\) |
0.999497 | − | 0.0317144i | \(-0.0100967\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7610.00 | + | 13180.9i | 0.317675 | + | 0.550229i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17072.0 | − | 29569.6i | −0.707546 | − | 1.22551i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 57960.0 | − | 100390.i | 2.39354 | − | 4.14573i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9356.00 | −0.384988 | −0.192494 | − | 0.981298i | \(-0.561658\pi\) | ||||
−0.192494 | + | 0.981298i | \(0.561658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20545.0 | −0.842388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22670.0 | − | 39265.6i | 0.926211 | − | 1.60425i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8212.00 | + | 14223.6i | 0.334321 | + | 0.579061i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24170.0 | + | 41863.7i | 0.977046 | + | 1.69229i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 832.000 | − | 1441.07i | 0.0335142 | − | 0.0580483i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2372.00 | −0.0952119 | −0.0476059 | − | 0.998866i | \(-0.515159\pi\) | ||||
−0.0476059 | + | 0.998866i | \(0.515159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15184.0 | −0.607347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5847.00 | − | 10127.3i | 0.233057 | − | 0.403666i | −0.725649 | − | 0.688065i | \(-0.758461\pi\) |
0.958706 | + | 0.284398i | \(0.0917938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10253.0 | − | 17758.7i | −0.407250 | − | 0.705378i | 0.587330 | − | 0.809347i | \(-0.300179\pi\) |
−0.994580 | + | 0.103969i | \(0.966846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14068.0 | + | 24366.5i | 0.554902 | + | 0.961118i | 0.997911 | + | 0.0646012i | \(0.0205775\pi\) |
−0.443009 | + | 0.896517i | \(0.646089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13904.0 | + | 24082.4i | −0.546532 | + | 0.946621i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15490.0 | −0.606768 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37440.0 | 1.46152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2856.00 | − | 4946.74i | 0.111104 | − | 0.192438i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7811.00 | + | 13529.0i | 0.302821 | + | 0.524500i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18535.0 | + | 32103.6i | 0.713663 | + | 1.23610i | 0.963473 | + | 0.267806i | \(0.0862985\pi\) |
−0.249810 | + | 0.968295i | \(0.580368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23280.0 | + | 40322.1i | −0.893305 | + | 1.54725i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6198.00 | 0.237021 | 0.118511 | − | 0.992953i | \(-0.462188\pi\) | ||||
0.118511 | + | 0.992953i | \(0.462188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31876.0 | −1.21485 | −0.607425 | − | 0.794377i | \(-0.707798\pi\) | ||||
−0.607425 | + | 0.794377i | \(0.707798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10960.0 | − | 18983.3i | 0.416290 | − | 0.721035i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −66.0000 | − | 114.315i | −0.00249838 | − | 0.00432732i | 0.864774 | − | 0.502162i | \(-0.167462\pi\) |
−0.867272 | + | 0.497835i | \(0.834129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52580.0 | + | 91071.2i | 1.97699 | + | 3.42424i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5148.00 | − | 8916.60i | 0.192913 | − | 0.334135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18144.0 | 0.677639 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7680.00 | −0.285873 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7812.00 | + | 13530.8i | −0.289816 | + | 0.501976i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13050.0 | + | 22603.3i | 0.482529 | + | 0.835765i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1104.00 | − | 1912.18i | −0.0405505 | − | 0.0702355i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19122.0 | + | 33120.3i | −0.700039 | + | 1.21250i | 0.268413 | + | 0.963304i | \(0.413501\pi\) |
−0.968452 | + | 0.249200i | \(0.919832\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −104536. | −3.81435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7008.00 | −0.254869 | −0.127434 | − | 0.991847i | \(-0.540674\pi\) | ||||
−0.127434 | + | 0.991847i | \(0.540674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10600.0 | + | 18359.7i | −0.384237 | + | 0.665519i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23040.0 | − | 39906.5i | −0.832436 | − | 1.44182i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18332.0 | − | 31752.0i | −0.658016 | − | 1.13972i | −0.981128 | − | 0.193357i | \(-0.938062\pi\) |
0.323112 | − | 0.946361i | \(-0.395271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36190.0 | + | 62682.9i | −1.29479 | + | 2.24264i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5376.00 | −0.191715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1586.00 | −0.0563755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27886.0 | − | 48300.0i | 0.988022 | − | 1.71130i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22755.0 | + | 39412.8i | 0.803625 | + | 1.39192i | 0.917216 | + | 0.398391i | \(0.130431\pi\) |
−0.113591 | + | 0.993528i | \(0.536235\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5480.00 | + | 9491.64i | 0.192291 | + | 0.333057i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9280.00 | − | 16073.4i | 0.324587 | − | 0.562200i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3838.00 | 0.133812 | 0.0669061 | − | 0.997759i | \(-0.478687\pi\) | ||||
0.0669061 | + | 0.997759i | \(0.478687\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38180.0 | 1.32690 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8416.00 | + | 14576.9i | −0.291556 | + | 0.504989i | −0.974178 | − | 0.225782i | \(-0.927506\pi\) |
0.682622 | + | 0.730771i | \(0.260839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −192.000 | − | 332.554i | −0.00663031 | − | 0.0114840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20464.0 | + | 35444.7i | 0.702208 | + | 1.21626i | 0.967690 | + | 0.252144i | \(0.0811355\pi\) |
−0.265482 | + | 0.964116i | \(0.585531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −948.000 | + | 1641.98i | −0.0324272 | + | 0.0561655i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19980.0 | 0.681279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24070.0 | −0.818157 | −0.409079 | − | 0.912499i | \(-0.634150\pi\) | ||||
−0.409079 | + | 0.912499i | \(0.634150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12000.0 | − | 20784.6i | 0.406608 | − | 0.704266i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12400.0 | − | 21477.4i | −0.418845 | − | 0.725462i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16856.5 | − | 29196.3i | −0.565825 | − | 0.980038i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11826.0 | + | 20483.2i | −0.395730 | + | 0.685424i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26224.0 | 0.874798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17152.0 | −0.570394 | −0.285197 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285197 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7540.00 | − | 13059.7i | 0.249969 | − | 0.432959i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16455.0 | − | 28500.9i | −0.543837 | − | 0.941954i | −0.998679 | − | 0.0513817i | \(-0.983638\pi\) |
0.454842 | − | 0.890572i | \(-0.349696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3660.00 | + | 6339.31i | 0.120219 | + | 0.208226i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3411.00 | − | 5908.03i | 0.111697 | − | 0.193464i | −0.804758 | − | 0.593603i | \(-0.797705\pi\) |
0.916454 | + | 0.400139i | \(0.131038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15600.0 | −0.509273 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −97382.0 | −3.16939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24210.0 | + | 41933.0i | −0.785533 | + | 1.36058i | 0.143147 | + | 0.989701i | \(0.454278\pi\) |
−0.928680 | + | 0.370882i | \(0.879055\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9448.00 | + | 16364.4i | 0.305623 | + | 0.529354i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13312.0 | + | 23057.1i | 0.428005 | + | 0.741326i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24608.0 | − | 42622.3i | 0.788798 | − | 1.36624i | −0.137906 | − | 0.990445i | \(-0.544037\pi\) |
0.926704 | − | 0.375793i | \(-0.122630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −79360.0 | −2.53617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8288.00 | 0.264068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17632.0 | − | 30539.5i | 0.560091 | − | 0.970107i | −0.437397 | − | 0.899269i | \(-0.644099\pi\) |
0.997488 | − | 0.0708379i | \(-0.0225673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5980.00 | − | 10357.7i | −0.189388 | − | 0.328030i |
(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 | 196.4.e.a.165.1 | 2 | ||
3.2 | odd | 2 | 1764.4.k.m.361.1 | 2 | |||
7.2 | even | 3 | inner | 196.4.e.a.177.1 | 2 | ||
7.3 | odd | 6 | 28.4.a.a.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 196.4.a.d.1.1 | 1 | |||
7.5 | odd | 6 | 196.4.e.f.177.1 | 2 | |||
7.6 | odd | 2 | 196.4.e.f.165.1 | 2 | |||
21.2 | odd | 6 | 1764.4.k.m.1549.1 | 2 | |||
21.5 | even | 6 | 1764.4.k.d.1549.1 | 2 | |||
21.11 | odd | 6 | 1764.4.a.c.1.1 | 1 | |||
21.17 | even | 6 | 252.4.a.d.1.1 | 1 | |||
21.20 | even | 2 | 1764.4.k.d.361.1 | 2 | |||
28.3 | even | 6 | 112.4.a.g.1.1 | 1 | |||
28.11 | odd | 6 | 784.4.a.a.1.1 | 1 | |||
35.3 | even | 12 | 700.4.e.a.449.1 | 2 | |||
35.17 | even | 12 | 700.4.e.a.449.2 | 2 | |||
35.24 | odd | 6 | 700.4.a.n.1.1 | 1 | |||
56.3 | even | 6 | 448.4.a.a.1.1 | 1 | |||
56.45 | odd | 6 | 448.4.a.p.1.1 | 1 | |||
84.59 | odd | 6 | 1008.4.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.a.a.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
112.4.a.g.1.1 | 1 | 28.3 | even | 6 | |||
196.4.a.d.1.1 | 1 | 7.4 | even | 3 | |||
196.4.e.a.165.1 | 2 | 1.1 | even | 1 | trivial | ||
196.4.e.a.177.1 | 2 | 7.2 | even | 3 | inner | ||
196.4.e.f.165.1 | 2 | 7.6 | odd | 2 | |||
196.4.e.f.177.1 | 2 | 7.5 | odd | 6 | |||
252.4.a.d.1.1 | 1 | 21.17 | even | 6 | |||
448.4.a.a.1.1 | 1 | 56.3 | even | 6 | |||
448.4.a.p.1.1 | 1 | 56.45 | odd | 6 | |||
700.4.a.n.1.1 | 1 | 35.24 | odd | 6 | |||
700.4.e.a.449.1 | 2 | 35.3 | even | 12 | |||
700.4.e.a.449.2 | 2 | 35.17 | even | 12 | |||
784.4.a.a.1.1 | 1 | 28.11 | odd | 6 | |||
1008.4.a.o.1.1 | 1 | 84.59 | odd | 6 | |||
1764.4.a.c.1.1 | 1 | 21.11 | odd | 6 | |||
1764.4.k.d.361.1 | 2 | 21.20 | even | 2 | |||
1764.4.k.d.1549.1 | 2 | 21.5 | even | 6 | |||
1764.4.k.m.361.1 | 2 | 3.2 | odd | 2 | |||
1764.4.k.m.1549.1 | 2 | 21.2 | odd | 6 |