Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (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: | \(38.2332376837\) |
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: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.217 |
Dual form | 648.4.i.b.433.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.00000 | − | 12.1244i | −0.626099 | − | 1.08444i | −0.988327 | − | 0.152346i | \(-0.951317\pi\) |
0.362228 | − | 0.932089i | \(-0.382016\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.0000 | − | 20.7846i | 0.647939 | − | 1.12226i | −0.335675 | − | 0.941978i | \(-0.608964\pi\) |
0.983614 | − | 0.180286i | \(-0.0577022\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.0000 | − | 24.2487i | 0.383742 | − | 0.664660i | −0.607852 | − | 0.794050i | \(-0.707969\pi\) |
0.991594 | + | 0.129390i | \(0.0413020\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.0000 | + | 64.0859i | 0.789381 | + | 1.36725i | 0.926347 | + | 0.376672i | \(0.122932\pi\) |
−0.136966 | + | 0.990576i | \(0.543735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 82.0000 | 1.16988 | 0.584939 | − | 0.811077i | \(-0.301118\pi\) | ||||
0.584939 | + | 0.811077i | \(0.301118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.0000 | 1.11086 | 0.555428 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555428 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.0362634 | − | 0.0628100i | 0.847324 | − | 0.531076i | \(-0.178212\pi\) |
−0.883587 | + | 0.468266i | \(0.844879\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.5000 | + | 61.4878i | −0.284000 | + | 0.491902i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 69.0000 | − | 119.512i | 0.441827 | − | 0.765267i | −0.555998 | − | 0.831183i | \(-0.687664\pi\) |
0.997825 | + | 0.0659169i | \(0.0209972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40.0000 | − | 69.2820i | −0.231749 | − | 0.401401i | 0.726574 | − | 0.687088i | \(-0.241111\pi\) |
−0.958323 | + | 0.285688i | \(0.907778\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −336.000 | −1.62270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0000 | 0.133296 | 0.0666482 | − | 0.997777i | \(-0.478769\pi\) | ||||
0.0666482 | + | 0.997777i | \(0.478769\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −141.000 | − | 244.219i | −0.537085 | − | 0.930259i | −0.999059 | − | 0.0433656i | \(-0.986192\pi\) |
0.461974 | − | 0.886894i | \(-0.347141\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.00709296 | + | 0.0122854i | −0.869550 | − | 0.493845i | \(-0.835591\pi\) |
0.862457 | + | 0.506130i | \(0.168924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.000 | + | 207.846i | −0.372421 | + | 0.645053i | −0.989937 | − | 0.141506i | \(-0.954806\pi\) |
0.617516 | + | 0.786558i | \(0.288139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −116.500 | − | 201.784i | −0.339650 | − | 0.588291i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −130.000 | −0.336922 | −0.168461 | − | 0.985708i | \(-0.553880\pi\) | ||||
−0.168461 | + | 0.985708i | \(0.553880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −392.000 | −0.961041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −298.000 | − | 516.151i | −0.657564 | − | 1.13893i | −0.981244 | − | 0.192768i | \(-0.938253\pi\) |
0.323680 | − | 0.946167i | \(-0.395080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 109.000 | − | 188.794i | 0.228787 | − | 0.396271i | −0.728662 | − | 0.684874i | \(-0.759857\pi\) |
0.957449 | + | 0.288603i | \(0.0931907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 518.000 | − | 897.202i | 0.988461 | − | 1.71207i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 218.000 | + | 377.587i | 0.397507 | + | 0.688502i | 0.993418 | − | 0.114549i | \(-0.0365423\pi\) |
−0.595911 | + | 0.803050i | \(0.703209\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 856.000 | 1.43082 | 0.715412 | − | 0.698703i | \(-0.246239\pi\) | ||||
0.715412 | + | 0.698703i | \(0.246239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −998.000 | −1.60010 | −0.800048 | − | 0.599935i | \(-0.795193\pi\) | ||||
−0.800048 | + | 0.599935i | \(0.795193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −336.000 | − | 581.969i | −0.497283 | − | 0.861319i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000 | − | 27.7128i | 0.0227866 | − | 0.0394675i | −0.854407 | − | 0.519604i | \(-0.826080\pi\) |
0.877194 | + | 0.480136i | \(0.159413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 754.000 | − | 1305.97i | 0.997136 | − | 1.72709i | 0.433066 | − | 0.901362i | \(-0.357432\pi\) |
0.564070 | − | 0.825727i | \(-0.309235\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −574.000 | − | 994.197i | −0.732459 | − | 1.26866i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −246.000 | −0.292988 | −0.146494 | − | 0.989212i | \(-0.546799\pi\) | ||||
−0.146494 | + | 0.989212i | \(0.546799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1776.00 | 2.04588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −644.000 | − | 1115.44i | −0.695505 | − | 1.20465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −433.000 | + | 749.978i | −0.453242 | + | 0.785038i | −0.998585 | − | 0.0531745i | \(-0.983066\pi\) |
0.545343 | + | 0.838213i | \(0.316399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −135.000 | + | 233.827i | −0.133000 | + | 0.230363i | −0.924832 | − | 0.380377i | \(-0.875794\pi\) |
0.791832 | + | 0.610739i | \(0.209128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 748.000 | + | 1295.57i | 0.715560 | + | 1.23939i | 0.962743 | + | 0.270417i | \(0.0871615\pi\) |
−0.247184 | + | 0.968969i | \(0.579505\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1692.00 | −1.52871 | −0.764354 | − | 0.644797i | \(-0.776942\pi\) | ||||
−0.764354 | + | 0.644797i | \(0.776942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 406.000 | 0.356768 | 0.178384 | − | 0.983961i | \(-0.442913\pi\) | ||||
0.178384 | + | 0.983961i | \(0.442913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −393.000 | − | 680.696i | −0.327171 | − | 0.566677i | 0.654778 | − | 0.755821i | \(-0.272762\pi\) |
−0.981949 | + | 0.189144i | \(0.939429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −56.0000 | + | 96.9948i | −0.0454089 | + | 0.0786506i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 984.000 | − | 1704.34i | 0.758010 | − | 1.31291i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 273.500 | + | 473.716i | 0.205485 | + | 0.355910i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1744.00 | 1.21854 | 0.609272 | − | 0.792962i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792962i | \(0.291462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −326.000 | − | 564.649i | −0.217426 | − | 0.376592i | 0.736595 | − | 0.676335i | \(-0.236433\pi\) |
−0.954020 | + | 0.299742i | \(0.903099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1104.00 | − | 1912.18i | 0.719766 | − | 1.24667i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −765.000 | + | 1325.02i | −0.477068 | + | 0.826307i | −0.999655 | − | 0.0262798i | \(-0.991634\pi\) |
0.522586 | + | 0.852586i | \(0.324967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −258.000 | − | 446.869i | −0.157434 | − | 0.272683i | 0.776509 | − | 0.630106i | \(-0.216989\pi\) |
−0.933943 | + | 0.357423i | \(0.883655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2072.00 | 1.21167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1932.00 | −1.10651 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −671.000 | − | 1162.21i | −0.368929 | − | 0.639004i | 0.620469 | − | 0.784231i | \(-0.286942\pi\) |
−0.989398 | + | 0.145227i | \(0.953609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 212.000 | − | 367.195i | 0.114254 | − | 0.197893i | −0.803227 | − | 0.595672i | \(-0.796886\pi\) |
0.917481 | + | 0.397779i | \(0.130219\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −560.000 | + | 969.948i | −0.290195 | + | 0.502633i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −131.000 | − | 226.899i | −0.0665920 | − | 0.115341i | 0.830807 | − | 0.556560i | \(-0.187879\pi\) |
−0.897399 | + | 0.441220i | \(0.854546\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.000 | −0.0939858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2292.00 | −1.10137 | −0.550685 | − | 0.834713i | \(-0.685633\pi\) | ||||
−0.550685 | + | 0.834713i | \(0.685633\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 948.000 | + | 1641.98i | 0.439272 | + | 0.760842i | 0.997633 | − | 0.0687562i | \(-0.0219031\pi\) |
−0.558361 | + | 0.829598i | \(0.688570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1639.50 | + | 2839.70i | −0.746245 | + | 1.29253i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1437.00 | − | 2488.96i | 0.631521 | − | 1.09383i | −0.355720 | − | 0.934592i | \(-0.615764\pi\) |
0.987241 | − | 0.159234i | \(-0.0509023\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 852.000 | + | 1475.71i | 0.368029 | + | 0.637446i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1188.00 | −0.496063 | −0.248032 | − | 0.968752i | \(-0.579784\pi\) | ||||
−0.248032 | + | 0.968752i | \(0.579784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3474.00 | −1.42663 | −0.713316 | − | 0.700843i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700843i | \(0.752808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −210.000 | − | 363.731i | −0.0834568 | − | 0.144551i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1148.00 | − | 1988.39i | 0.448931 | − | 0.777571i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −96.0000 | + | 166.277i | −0.0363681 | + | 0.0629915i | −0.883637 | − | 0.468173i | \(-0.844912\pi\) |
0.847268 | + | 0.531165i | \(0.178246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2401.00 | − | 4158.65i | −0.895481 | − | 1.55102i | −0.833209 | − | 0.552959i | \(-0.813499\pi\) |
−0.0622720 | − | 0.998059i | \(-0.519835\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1518.00 | 0.549000 | 0.274500 | − | 0.961587i | \(-0.411488\pi\) | ||||
0.274500 | + | 0.961587i | \(0.411488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5128.00 | 1.82670 | 0.913352 | − | 0.407170i | \(-0.133484\pi\) | ||||
0.913352 | + | 0.407170i | \(0.133484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1656.00 | − | 2868.28i | −0.572554 | − | 0.991692i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1974.00 | + | 3419.07i | −0.672537 | + | 1.16487i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1288.00 | − | 2230.88i | 0.426281 | − | 0.738341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −542.000 | − | 938.772i | −0.176838 | − | 0.306292i | 0.763958 | − | 0.645266i | \(-0.223254\pi\) |
−0.940796 | + | 0.338974i | \(0.889920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 56.0000 | 0.0177636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1920.00 | −0.600636 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3034.00 | + | 5255.04i | 0.923479 | + | 1.59951i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −344.000 | + | 595.825i | −0.103300 | + | 0.178921i | −0.913042 | − | 0.407865i | \(-0.866274\pi\) |
0.809742 | + | 0.586786i | \(0.199607\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2406.00 | + | 4167.31i | −0.703488 | + | 1.21848i | 0.263746 | + | 0.964592i | \(0.415042\pi\) |
−0.967234 | + | 0.253885i | \(0.918291\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1247.00 | − | 2159.87i | −0.359843 | − | 0.623267i | 0.628091 | − | 0.778140i | \(-0.283836\pi\) |
−0.987934 | + | 0.154873i | \(0.950503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 698.000 | 0.196255 | 0.0981277 | − | 0.995174i | \(-0.468715\pi\) | ||||
0.0981277 | + | 0.995174i | \(0.468715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3360.00 | 0.932690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3160.00 | + | 5473.28i | 0.855244 | + | 1.48133i | 0.876418 | + | 0.481551i | \(0.159926\pi\) |
−0.0211737 | + | 0.999776i | \(0.506740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3255.00 | − | 5637.83i | 0.870012 | − | 1.50691i | 0.00802978 | − | 0.999968i | \(-0.497444\pi\) |
0.861983 | − | 0.506938i | \(-0.169223\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1631.00 | + | 2824.97i | −0.425309 | + | 0.736657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3404.00 | + | 5895.90i | 0.876888 | + | 1.51881i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 628.000 | 0.157924 | 0.0789622 | − | 0.996878i | \(-0.474839\pi\) | ||||
0.0789622 | + | 0.996878i | \(0.474839\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224.000 | −0.0556631 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2431.00 | + | 4210.62i | 0.590045 | + | 1.02199i | 0.994226 | + | 0.107309i | \(0.0342234\pi\) |
−0.404181 | + | 0.914679i | \(0.632443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 360.000 | − | 623.538i | 0.0863680 | − | 0.149594i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2908.00 | + | 5036.80i | −0.681806 | + | 1.18092i | 0.292623 | + | 0.956228i | \(0.405472\pi\) |
−0.974429 | + | 0.224695i | \(0.927862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 910.000 | + | 1576.17i | 0.210947 | + | 0.365370i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3526.00 | 0.799197 | 0.399599 | − | 0.916690i | \(-0.369150\pi\) | ||||
0.399599 | + | 0.916690i | \(0.369150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −256.000 | −0.0573834 | −0.0286917 | − | 0.999588i | \(-0.509134\pi\) | ||||
−0.0286917 | + | 0.999588i | \(0.509134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 994.000 | + | 1721.66i | 0.217965 | + | 0.377527i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −71.0000 | + | 122.976i | −0.0154006 | + | 0.0266747i | −0.873623 | − | 0.486603i | \(-0.838236\pi\) |
0.858222 | + | 0.513278i | \(0.171569\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4421.00 | + | 7657.40i | −0.938558 | + | 1.62563i | −0.170394 | + | 0.985376i | \(0.554504\pi\) |
−0.768163 | + | 0.640254i | \(0.778829\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3590.00 | + | 6218.06i | 0.754075 | + | 1.30610i | 0.945833 | + | 0.324655i | \(0.105248\pi\) |
−0.191757 | + | 0.981442i | \(0.561419\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6768.00 | −1.39199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1811.00 | 0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3687.00 | − | 6386.07i | −0.735143 | − | 1.27330i | −0.954661 | − | 0.297696i | \(-0.903782\pi\) |
0.219518 | − | 0.975608i | \(-0.429552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4172.00 | + | 7226.12i | −0.823401 | + | 1.42617i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 296.000 | − | 512.687i | 0.0572512 | − | 0.0991621i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.0000 | + | 83.1384i | 0.00919161 | + | 0.0159203i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3052.00 | −0.572974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1500.00 | 0.278858 | 0.139429 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139429 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3804.00 | + | 6588.72i | 0.693585 | + | 1.20133i | 0.970655 | + | 0.240475i | \(0.0773033\pi\) |
−0.277070 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2379.00 | − | 4120.55i | 0.429614 | − | 0.744112i | −0.567225 | − | 0.823563i | \(-0.691983\pi\) |
0.996839 | + | 0.0794502i | \(0.0253165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2187.00 | + | 3788.00i | −0.387489 | + | 0.671151i | −0.992111 | − | 0.125361i | \(-0.959991\pi\) |
0.604622 | + | 0.796513i | \(0.293324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1932.00 | − | 3346.32i | −0.339095 | − | 0.587329i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7544.00 | 1.29956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5254.00 | −0.896737 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2880.00 | + | 4988.31i | 0.482613 | + | 0.835910i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3902.00 | − | 6758.46i | 0.647956 | − | 1.12229i | −0.335655 | − | 0.941985i | \(-0.608958\pi\) |
0.983610 | − | 0.180307i | \(-0.0577091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3052.00 | − | 5286.22i | 0.497757 | − | 0.862140i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2553.00 | − | 4421.93i | −0.412673 | − | 0.714770i | 0.582508 | − | 0.812825i | \(-0.302071\pi\) |
−0.995181 | + | 0.0980544i | \(0.968738\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2240.00 | −0.355727 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2640.00 | 0.415588 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2358.00 | + | 4084.18i | 0.364796 | + | 0.631845i | 0.988743 | − | 0.149622i | \(-0.0478055\pi\) |
−0.623948 | + | 0.781466i | \(0.714472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3651.00 | + | 6323.72i | −0.559982 | + | 0.969916i | 0.437516 | + | 0.899211i | \(0.355858\pi\) |
−0.997497 | + | 0.0707057i | \(0.977475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2191.00 | − | 3794.92i | 0.330355 | − | 0.572191i | −0.652227 | − | 0.758024i | \(-0.726165\pi\) |
0.982581 | + | 0.185833i | \(0.0594983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5992.00 | − | 10378.4i | −0.895838 | − | 1.55164i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7224.00 | 1.06203 | 0.531014 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531014 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6986.00 | + | 12100.1i | 1.00182 | + | 1.73520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −704.000 | + | 1219.36i | −0.100132 | + | 0.173434i | −0.911739 | − | 0.410770i | \(-0.865260\pi\) |
0.811607 | + | 0.584204i | \(0.198593\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1560.00 | + | 2702.00i | −0.218305 | + | 0.378115i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 857.000 | + | 1484.37i | 0.118965 | + | 0.206053i | 0.919358 | − | 0.393423i | \(-0.128709\pi\) |
−0.800393 | + | 0.599476i | \(0.795376\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10212.0 | 1.39508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 884.000 | 0.119810 | 0.0599051 | − | 0.998204i | \(-0.480920\pi\) | ||||
0.0599051 | + | 0.998204i | \(0.480920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5184.00 | − | 8978.95i | −0.691619 | − | 1.19792i | −0.971307 | − | 0.237828i | \(-0.923564\pi\) |
0.279688 | − | 0.960091i | \(-0.409769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4704.00 | + | 8147.57i | −0.622696 | + | 1.07854i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −199.000 | + | 344.678i | −0.0259375 | + | 0.0449251i | −0.878703 | − | 0.477369i | \(-0.841590\pi\) |
0.852765 | + | 0.522294i | \(0.174924\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −328.000 | − | 568.113i | −0.0424237 | − | 0.0734800i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −448.000 | −0.0570666 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5098.00 | −0.644487 | −0.322243 | − | 0.946657i | \(-0.604437\pi\) | ||||
−0.322243 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5001.00 | − | 8661.99i | −0.622788 | − | 1.07870i | −0.988964 | − | 0.148155i | \(-0.952667\pi\) |
0.366176 | − | 0.930546i | \(-0.380667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2960.00 | − | 5126.87i | 0.365876 | − | 0.633716i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 420.000 | − | 727.461i | 0.0511514 | − | 0.0885969i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4635.00 | + | 8028.06i | 0.560357 | + | 0.970567i | 0.997465 | + | 0.0711578i | \(0.0226694\pi\) |
−0.437108 | + | 0.899409i | \(0.643997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14304.0 | −1.70425 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21112.0 | −2.49722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3258.00 | + | 5643.02i | 0.379866 | + | 0.657947i | 0.991042 | − | 0.133548i | \(-0.0426369\pi\) |
−0.611177 | + | 0.791494i | \(0.709304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1313.00 | − | 2274.18i | 0.151999 | − | 0.263271i | −0.779963 | − | 0.625826i | \(-0.784762\pi\) |
0.931962 | + | 0.362555i | \(0.118096\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2911.00 | + | 5042.00i | −0.332245 | + | 0.575466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2616.00 | − | 4531.04i | −0.296480 | − | 0.513519i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4304.00 | −0.481012 | −0.240506 | − | 0.970648i | \(-0.577313\pi\) | ||||
−0.240506 | + | 0.970648i | \(0.577313\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11794.0 | 1.30897 | 0.654484 | − | 0.756076i | \(-0.272886\pi\) | ||||
0.654484 | + | 0.756076i | \(0.272886\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −368.000 | − | 637.395i | −0.0402834 | − | 0.0697728i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2772.00 | − | 4801.24i | 0.301368 | − | 0.521984i | −0.675078 | − | 0.737746i | \(-0.735890\pi\) |
0.976446 | + | 0.215762i | \(0.0692236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1894.00 | − | 3280.50i | 0.203130 | − | 0.351832i | −0.746405 | − | 0.665492i | \(-0.768222\pi\) |
0.949535 | + | 0.313660i | \(0.101555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1722.00 | + | 2982.59i | 0.183440 | + | 0.317727i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13342.0 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7896.00 | −0.824408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12432.0 | − | 21532.9i | −1.28093 | − | 2.21863i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2195.00 | − | 3801.85i | 0.224678 | − | 0.389153i | −0.731545 | − | 0.681793i | \(-0.761200\pi\) |
0.956223 | + | 0.292640i | \(0.0945337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2899.00 | + | 5021.22i | −0.292885 | + | 0.507291i | −0.974491 | − | 0.224428i | \(-0.927949\pi\) |
0.681606 | + | 0.731720i | \(0.261282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7328.00 | + | 12692.5i | 0.735553 | + | 1.27402i | 0.954480 | + | 0.298274i | \(0.0964109\pi\) |
−0.218927 | + | 0.975741i | \(0.570256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8412.00 | 0.833535 | 0.416768 | − | 0.909013i | \(-0.363163\pi\) | ||||
0.416768 | + | 0.909013i | \(0.363163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10464.0 | 1.03024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56.0000 | + | 96.9948i | 0.00544373 | + | 0.00942881i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3266.00 | + | 5656.88i | −0.315483 | + | 0.546432i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7424.00 | + | 12858.7i | −0.708165 | + | 1.22658i | 0.257372 | + | 0.966313i | \(0.417144\pi\) |
−0.965537 | + | 0.260266i | \(0.916190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1110.00 | + | 1922.58i | 0.105222 | + | 0.182249i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12124.0 | 1.13510 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18568.0 | 1.72771 | 0.863857 | − | 0.503738i | \(-0.168042\pi\) | ||||
0.863857 | + | 0.503738i | \(0.168042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7182.00 | + | 12439.6i | 0.660120 | + | 1.14336i | 0.980584 | + | 0.196101i | \(0.0628281\pi\) |
−0.320463 | + | 0.947261i | \(0.603839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5658.00 | − | 9799.94i | 0.516883 | − | 0.895268i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10272.0 | − | 17791.6i | 0.927087 | − | 1.60576i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10830.0 | − | 18758.1i | −0.971578 | − | 1.68282i | −0.690794 | − | 0.723051i | \(-0.742739\pi\) |
−0.280783 | − | 0.959771i | \(-0.590594\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17112.0 | −1.51687 | −0.758436 | − | 0.651748i | \(-0.774036\pi\) | ||||
−0.758436 | + | 0.651748i | \(0.774036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3780.00 | 0.333085 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5739.00 | − | 9940.24i | −0.499758 | − | 0.865606i | 0.500242 | − | 0.865886i | \(-0.333244\pi\) |
−1.00000 | 0.000279686i | \(0.999911\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11976.0 | + | 20743.0i | −1.03677 | + | 1.79573i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10472.0 | − | 18138.0i | 0.896022 | − | 1.55196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3360.00 | + | 5819.69i | 0.285827 | + | 0.495067i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13114.0 | 1.10275 | 0.551377 | − | 0.834256i | \(-0.314103\pi\) | ||||
0.551377 | + | 0.834256i | \(0.314103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4508.00 | −0.376905 | −0.188452 | − | 0.982082i | \(-0.560347\pi\) | ||||
−0.188452 | + | 0.982082i | \(0.560347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3280.00 | − | 5681.13i | −0.271118 | − | 0.469590i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6051.50 | − | 10481.5i | 0.497370 | − | 0.861470i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10434.0 | − | 18072.2i | 0.847930 | − | 1.46866i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11844.0 | + | 20514.4i | 0.957123 | + | 1.65779i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6524.00 | −0.521352 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22950.0 | 1.82384 | 0.911920 | − | 0.410368i | \(-0.134600\pi\) | ||||
0.911920 | + | 0.410368i | \(0.134600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2842.00 | − | 4922.49i | −0.223372 | − | 0.386892i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3290.00 | − | 5698.45i | 0.257167 | − | 0.445426i | −0.708315 | − | 0.705897i | \(-0.750544\pi\) |
0.965482 | + | 0.260471i | \(0.0838777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6348.00 | − | 10995.1i | 0.490806 | − | 0.850100i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −384.000 | − | 665.108i | −0.0295286 | − | 0.0511451i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7046.00 | 0.535994 | 0.267997 | − | 0.963420i | \(-0.413638\pi\) | ||||
0.267997 | + | 0.963420i | \(0.413638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −296.000 | −0.0223962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4126.00 | − | 7146.44i | −0.308864 | − | 0.534967i | 0.669251 | − | 0.743037i | \(-0.266615\pi\) |
−0.978114 | + | 0.208070i | \(0.933282\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5502.00 | + | 9529.74i | −0.409683 | + | 0.709592i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3419.00 | − | 5921.88i | 0.251901 | − | 0.436306i | −0.712148 | − | 0.702030i | \(-0.752277\pi\) |
0.964049 | + | 0.265723i | \(0.0856108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11658.0 | − | 20192.2i | −0.854417 | − | 1.47989i | −0.877185 | − | 0.480153i | \(-0.840581\pi\) |
0.0227678 | − | 0.999741i | \(-0.492752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 568.000 | 0.0411952 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10558.0 | −0.761760 | −0.380880 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18096.0 | − | 31343.2i | −1.29217 | − | 2.23810i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1820.00 | + | 3152.33i | −0.129291 | + | 0.223939i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −514.000 | + | 890.274i | −0.0361415 | + | 0.0625989i | −0.883530 | − | 0.468374i | \(-0.844840\pi\) |
0.847389 | + | 0.530973i | \(0.178173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3680.00 | − | 6373.95i | −0.257439 | − | 0.445898i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1202.00 | 0.0832382 | 0.0416191 | − | 0.999134i | \(-0.486748\pi\) | ||||
0.0416191 | + | 0.999134i | \(0.486748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27552.0 | −1.89836 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1788.00 | + | 3096.91i | 0.121963 | + | 0.211246i | 0.920542 | − | 0.390644i | \(-0.127748\pi\) |
−0.798579 | + | 0.601890i | \(0.794414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4325.00 | + | 7491.12i | −0.293545 | + | 0.508435i | −0.974645 | − | 0.223755i | \(-0.928168\pi\) |
0.681101 | + | 0.732190i | \(0.261502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3829.00 | − | 6632.02i | 0.257307 | − | 0.445670i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6328.00 | − | 10960.4i | −0.423139 | − | 0.732899i | 0.573105 | − | 0.819482i | \(-0.305739\pi\) |
−0.996245 | + | 0.0865829i | \(0.972405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17760.0 | −1.17593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3298.00 | −0.217300 | −0.108650 | − | 0.994080i | \(-0.534653\pi\) | ||||
−0.108650 | + | 0.994080i | \(0.534653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2685.00 | − | 4650.56i | −0.175193 | − | 0.303443i | 0.765035 | − | 0.643989i | \(-0.222722\pi\) |
−0.940228 | + | 0.340546i | \(0.889388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8110.00 | − | 14046.9i | 0.526605 | − | 0.912106i | −0.472915 | − | 0.881108i | \(-0.656798\pi\) |
0.999519 | − | 0.0309981i | \(-0.00986859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2952.00 | + | 5113.01i | −0.189838 | + | 0.328810i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9729.50 | + | 16852.0i | 0.622688 | + | 1.07853i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2460.00 | 0.155941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20360.0 | −1.28450 | −0.642249 | − | 0.766496i | \(-0.721999\pi\) | ||||
−0.642249 | + | 0.766496i | \(0.721999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12208.0 | − | 21144.9i | −0.762929 | − | 1.32143i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8621.00 | − | 14932.0i | 0.536227 | − | 0.928772i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7249.00 | + | 12555.6i | −0.446674 | + | 0.773663i | −0.998167 | − | 0.0605169i | \(-0.980725\pi\) |
0.551493 | + | 0.834180i | \(0.314058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10806.0 | − | 18716.5i | −0.662748 | − | 1.14791i | −0.979891 | − | 0.199536i | \(-0.936057\pi\) |
0.317142 | − | 0.948378i | \(-0.397277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12184.0 | 0.740344 | 0.370172 | − | 0.928963i | \(-0.379299\pi\) | ||||
0.370172 | + | 0.928963i | \(0.379299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16688.0 | −1.00934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14061.0 | + | 24354.4i | 0.842648 | + | 1.45951i | 0.887648 | + | 0.460523i | \(0.152338\pi\) |
−0.0449993 | + | 0.998987i | \(0.514329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4564.00 | + | 7905.08i | −0.272260 | + | 0.471568i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2850.00 | − | 4936.34i | 0.168468 | − | 0.291795i | −0.769414 | − | 0.638751i | \(-0.779451\pi\) |
0.937881 | + | 0.346956i | \(0.112785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14729.0 | + | 25511.4i | 0.866705 | + | 1.50118i | 0.865345 | + | 0.501177i | \(0.167100\pi\) |
0.00135988 | + | 0.999999i | \(0.499567\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30912.0 | −1.80258 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1104.00 | −0.0640885 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3052.00 | − | 5286.22i | −0.175590 | − | 0.304131i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9905.00 | + | 17156.0i | −0.567325 | + | 0.982636i | 0.429504 | + | 0.903065i | \(0.358688\pi\) |
−0.996829 | + | 0.0795708i | \(0.974645\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5225.00 | − | 9049.97i | 0.296622 | − | 0.513764i | −0.678739 | − | 0.734380i | \(-0.737473\pi\) |
0.975361 | + | 0.220615i | \(0.0708065\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10392.0 | + | 17999.5i | 0.587347 | + | 1.01731i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23300.0 | 1.30534 | 0.652672 | − | 0.757641i | \(-0.273648\pi\) | ||||
0.652672 | + | 0.757641i | \(0.273648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21420.0 | 1.19477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4810.00 | − | 8331.16i | −0.265960 | − | 0.460656i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7106.00 | − | 12308.0i | 0.391208 | − | 0.677593i | −0.601401 | − | 0.798947i | \(-0.705391\pi\) |
0.992609 | + | 0.121355i | \(0.0387238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3612.00 | + | 6256.17i | −0.197138 | + | 0.341453i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11562.0 | − | 20026.0i | −0.628324 | − | 1.08829i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15978.0 | −0.860885 | −0.430443 | − | 0.902618i | \(-0.641643\pi\) | ||||
−0.430443 | + | 0.902618i | \(0.641643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2760.00 | 0.148073 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3240.00 | + | 5611.84i | 0.172352 | + | 0.298522i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4433.00 | − | 7678.18i | 0.234816 | − | 0.406714i | −0.724403 | − | 0.689377i | \(-0.757884\pi\) |
0.959219 | + | 0.282663i | \(0.0912178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −320.000 | + | 554.256i | −0.0168080 | + | 0.0291123i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14504.0 | − | 25121.7i | −0.758628 | − | 1.31398i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7760.00 | 0.402502 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35904.0 | 1.85456 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4899.00 | + | 8485.32i | 0.250958 | + | 0.434671i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6540.00 | + | 11327.6i | −0.333638 | + | 0.577879i | −0.983222 | − | 0.182411i | \(-0.941610\pi\) |
0.649584 | + | 0.760290i | \(0.274943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −164.000 | + | 284.056i | −0.00829789 | + | 0.0143724i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8467.00 | − | 14665.3i | −0.426652 | − | 0.738983i | 0.569921 | − | 0.821699i | \(-0.306974\pi\) |
−0.996573 | + | 0.0827167i | \(0.973640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12208.0 | 0.610159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7060.00 | −0.351429 | −0.175715 | − | 0.984441i | \(-0.556224\pi\) | ||||
−0.175715 | + | 0.984441i | \(0.556224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6260.00 | + | 10842.6i | 0.309094 | + | 0.535367i | 0.978165 | − | 0.207832i | \(-0.0666408\pi\) |
−0.669070 | + | 0.743199i | \(0.733307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9394.00 | + | 16270.9i | −0.461973 | + | 0.800160i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20304.0 | + | 35167.6i | −0.990510 | + | 1.71561i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4896.00 | + | 8480.12i | 0.237893 | + | 0.412043i | 0.960109 | − | 0.279624i | \(-0.0902099\pi\) |
−0.722217 | + | 0.691667i | \(0.756877\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5936.00 | −0.286137 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13166.0 | 0.632135 | 0.316068 | − | 0.948737i | \(-0.397637\pi\) | ||||
0.316068 | + | 0.948737i | \(0.397637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11611.0 | + | 20110.8i | 0.553086 | + | 0.957973i | 0.998050 | + | 0.0624244i | \(0.0198832\pi\) |
−0.444964 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4872.00 | − | 8438.55i | 0.231164 | − | 0.400388i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22052.0 | − | 38195.2i | 1.03814 | − | 1.79811i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19967.0 | + | 34583.9i | 0.936318 | + | 1.62175i | 0.772267 | + | 0.635298i | \(0.219123\pi\) |
0.164051 | + | 0.986452i | \(0.447544\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17106.0 | −0.795938 | −0.397969 | − | 0.917399i | \(-0.630285\pi\) | ||||
−0.397969 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5680.00 | 0.263267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12972.0 | − | 22468.2i | −0.596624 | − | 1.03338i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11984.0 | − | 20756.9i | 0.549067 | − | 0.951012i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1834.00 | + | 3176.58i | −0.0833863 | + | 0.144429i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4978.00 | + | 8622.15i | 0.225472 | + | 0.390529i | 0.956461 | − | 0.291860i | \(-0.0942742\pi\) |
−0.730989 | + | 0.682389i | \(0.760941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18864.0 | −0.847948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16132.0 | 0.722401 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4565.00 | + | 7906.81i | 0.202887 | + | 0.351410i | 0.949457 | − | 0.313896i | \(-0.101634\pi\) |
−0.746571 | + | 0.665306i | \(0.768301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9840.00 | + | 17043.4i | −0.435687 | + | 0.754633i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13972.0 | + | 24200.2i | −0.614024 | + | 1.06352i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1344.00 | + | 2327.88i | 0.0588444 | + | 0.101922i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11482.0 | 0.498993 | 0.249497 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249497 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4612.00 | 0.199691 | 0.0998454 | − | 0.995003i | \(-0.468165\pi\) | ||||
0.0998454 | + | 0.995003i | \(0.468165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16044.0 | + | 27789.0i | 0.689567 | + | 1.19436i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −184.000 | + | 318.697i | −0.00787925 | + | 0.0136473i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17505.0 | − | 30319.5i | 0.744128 | − | 1.28887i | −0.206474 | − | 0.978452i | \(-0.566199\pi\) |
0.950601 | − | 0.310415i | \(-0.100468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6844.00 | − | 11854.2i | −0.289875 | − | 0.502078i | 0.683905 | − | 0.729571i | \(-0.260280\pi\) |
−0.973780 | + | 0.227493i | \(0.926947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11668.0 | 0.490612 | 0.245306 | − | 0.969446i | \(-0.421112\pi\) | ||||
0.245306 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29306.0 | −1.22779 | −0.613896 | − | 0.789387i | \(-0.710399\pi\) | ||||
−0.613896 | + | 0.789387i | \(0.710399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9553.00 | − | 16546.3i | −0.397349 | − | 0.688229i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13272.0 | − | 22987.8i | 0.550056 | − | 0.952724i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1332.00 | − | 2307.09i | 0.0548102 | − | 0.0949340i | −0.837318 | − | 0.546715i | \(-0.815878\pi\) |
0.892129 | + | 0.451781i | \(0.149211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2672.50 | + | 4628.91i | 0.109578 | + | 0.189795i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45906.0 | 1.86889 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13128.0 | 0.532566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −120.000 | − | 207.846i | −0.00483378 | − | 0.00837235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13015.0 | + | 22542.6i | −0.522421 | + | 0.904860i | 0.477239 | + | 0.878774i | \(0.341638\pi\) |
−0.999660 | + | 0.0260860i | \(0.991696\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22101.0 | + | 38280.1i | −0.880929 | + | 1.52581i | −0.0306184 | + | 0.999531i | \(0.509748\pi\) |
−0.850310 | + | 0.526282i | \(0.823586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16374.0 | + | 28360.6i | 0.650377 | + | 1.12649i | 0.983031 | + | 0.183437i | \(0.0587223\pi\) |
−0.332655 | + | 0.943049i | \(0.607944\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45344.0 | 1.78856 | 0.894280 | − | 0.447507i | \(-0.147688\pi\) | ||||
0.894280 | + | 0.447507i | \(0.147688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40236.0 | −1.58158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −448.000 | − | 775.959i | −0.0174883 | − | 0.0302907i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16132.0 | + | 27941.4i | −0.627568 | + | 1.08698i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9072.00 | + | 15713.2i | −0.350502 | + | 0.607088i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4389.00 | + | 7601.97i | 0.168992 | + | 0.292703i | 0.938066 | − | 0.346457i | \(-0.112615\pi\) |
−0.769074 | + | 0.639160i | \(0.779282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4142.00 | −0.158397 | −0.0791984 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791984 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22076.0 | 0.841355 | 0.420678 | − | 0.907210i | \(-0.361792\pi\) | ||||
0.420678 | + | 0.907210i | \(0.361792\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20188.0 | + | 34966.6i | 0.764201 | + | 1.32364i | 0.940668 | + | 0.339329i | \(0.110200\pi\) |
−0.176466 | + | 0.984307i | \(0.556467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20928.0 | − | 36248.4i | 0.789542 | − | 1.36753i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11040.0 | + | 19121.8i | −0.413706 | + | 0.716560i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8316.00 | + | 14403.7i | 0.310585 | + | 0.537948i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11040.0 | −0.409571 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10660.0 | −0.394158 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24318.0 | + | 42120.0i | 0.893213 | + | 1.54709i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13198.0 | − | 22859.6i | 0.483167 | − | 0.836870i | −0.516646 | − | 0.856199i | \(-0.672820\pi\) |
0.999813 | + | 0.0193293i | \(0.00615309\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12184.0 | + | 21103.3i | −0.443111 | + | 0.767490i | −0.997918 | − | 0.0644882i | \(-0.979459\pi\) |
0.554808 | + | 0.831979i | \(0.312792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21112.0 | − | 36567.1i | −0.765285 | − | 1.32551i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15648.0 | −0.563514 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5096.00 | −0.182918 | −0.0914589 | − | 0.995809i | \(-0.529153\pi\) | ||||
−0.0914589 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31672.0 | + | 54857.5i | 1.12947 | + | 1.95629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1065.00 | + | 1844.63i | −0.0378562 | + | 0.0655689i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9247.00 | − | 16016.3i | 0.326571 | − | 0.565637i | −0.655258 | − | 0.755405i | \(-0.727440\pi\) |
0.981829 | + | 0.189768i | \(0.0607735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10718.0 | − | 18564.1i | −0.377302 | − | 0.653506i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32144.0 | −1.12430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33222.0 | −1.15829 | −0.579144 | − | 0.815225i | \(-0.696613\pi\) | ||||
−0.579144 | + | 0.815225i | \(0.696613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13923.0 | − | 24115.3i | −0.482335 | − | 0.835428i | 0.517460 | − | 0.855708i | \(-0.326878\pi\) |
−0.999794 | + | 0.0202796i | \(0.993544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1128.00 | + | 1953.75i | −0.0389531 | + | 0.0674687i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20526.0 | + | 35552.1i | −0.704335 | + | 1.21994i | 0.262596 | + | 0.964906i | \(0.415421\pi\) |
−0.966931 | + | 0.255038i | \(0.917912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36926.0 | − | 63957.7i | −1.26309 | − | 2.18773i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5706.00 | 0.193951 | 0.0969756 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969756 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2688.00 | 0.0910802 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18360.0 | + | 31800.5i | 0.618222 | + | 1.07079i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11695.5 | − | 20257.2i | 0.392585 | − | 0.679977i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33614.0 | + | 58221.2i | −1.12132 | + | 1.94218i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19676.0 | + | 34079.8i | 0.654330 | + | 1.13333i | 0.982061 | + | 0.188562i | \(0.0603828\pi\) |
−0.327731 | + | 0.944771i | \(0.606284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33180.0 | −1.09660 | −0.548299 | − | 0.836282i | \(-0.684724\pi\) | ||||
−0.548299 | + | 0.836282i | \(0.684724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12384.0 | −0.408030 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2007.00 | + | 3476.23i | 0.0657212 | + | 0.113832i | 0.897014 | − | 0.442003i | \(-0.145732\pi\) |
−0.831292 | + | 0.555835i | \(0.812399\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3444.00 | + | 5965.18i | −0.112432 | + | 0.194738i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10164.0 | + | 17604.6i | −0.329788 | + | 0.571209i | −0.982470 | − | 0.186423i | \(-0.940310\pi\) |
0.652682 | + | 0.757632i | \(0.273644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10626.0 | − | 18404.8i | −0.343728 | − | 0.595355i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0000 | 0.00102886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11728.0 | 0.375936 | 0.187968 | − | 0.982175i | \(-0.439810\pi\) | ||||
0.187968 | + | 0.982175i | \(0.439810\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35896.0 | − | 62173.7i | −1.14370 | − | 1.98094i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25487.0 | + | 44144.8i | −0.809610 | + | 1.40229i | 0.103524 | + | 0.994627i | \(0.466988\pi\) |
−0.913134 | + | 0.407659i | \(0.866345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.4.i.b.217.1 | 2 | ||
3.2 | odd | 2 | 648.4.i.k.217.1 | 2 | |||
9.2 | odd | 6 | 72.4.a.b.1.1 | 1 | |||
9.4 | even | 3 | inner | 648.4.i.b.433.1 | 2 | ||
9.5 | odd | 6 | 648.4.i.k.433.1 | 2 | |||
9.7 | even | 3 | 24.4.a.a.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 48.4.a.b.1.1 | 1 | |||
36.11 | even | 6 | 144.4.a.b.1.1 | 1 | |||
45.2 | even | 12 | 1800.4.f.q.649.1 | 2 | |||
45.7 | odd | 12 | 600.4.f.b.49.1 | 2 | |||
45.29 | odd | 6 | 1800.4.a.bg.1.1 | 1 | |||
45.34 | even | 6 | 600.4.a.h.1.1 | 1 | |||
45.38 | even | 12 | 1800.4.f.q.649.2 | 2 | |||
45.43 | odd | 12 | 600.4.f.b.49.2 | 2 | |||
63.34 | odd | 6 | 1176.4.a.a.1.1 | 1 | |||
72.11 | even | 6 | 576.4.a.v.1.1 | 1 | |||
72.29 | odd | 6 | 576.4.a.u.1.1 | 1 | |||
72.43 | odd | 6 | 192.4.a.g.1.1 | 1 | |||
72.61 | even | 6 | 192.4.a.a.1.1 | 1 | |||
144.43 | odd | 12 | 768.4.d.b.385.2 | 2 | |||
144.61 | even | 12 | 768.4.d.o.385.2 | 2 | |||
144.115 | odd | 12 | 768.4.d.b.385.1 | 2 | |||
144.133 | even | 12 | 768.4.d.o.385.1 | 2 | |||
180.7 | even | 12 | 1200.4.f.p.49.2 | 2 | |||
180.43 | even | 12 | 1200.4.f.p.49.1 | 2 | |||
180.79 | odd | 6 | 1200.4.a.u.1.1 | 1 | |||
252.223 | even | 6 | 2352.4.a.w.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.a.a.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
48.4.a.b.1.1 | 1 | 36.7 | odd | 6 | |||
72.4.a.b.1.1 | 1 | 9.2 | odd | 6 | |||
144.4.a.b.1.1 | 1 | 36.11 | even | 6 | |||
192.4.a.a.1.1 | 1 | 72.61 | even | 6 | |||
192.4.a.g.1.1 | 1 | 72.43 | odd | 6 | |||
576.4.a.u.1.1 | 1 | 72.29 | odd | 6 | |||
576.4.a.v.1.1 | 1 | 72.11 | even | 6 | |||
600.4.a.h.1.1 | 1 | 45.34 | even | 6 | |||
600.4.f.b.49.1 | 2 | 45.7 | odd | 12 | |||
600.4.f.b.49.2 | 2 | 45.43 | odd | 12 | |||
648.4.i.b.217.1 | 2 | 1.1 | even | 1 | trivial | ||
648.4.i.b.433.1 | 2 | 9.4 | even | 3 | inner | ||
648.4.i.k.217.1 | 2 | 3.2 | odd | 2 | |||
648.4.i.k.433.1 | 2 | 9.5 | odd | 6 | |||
768.4.d.b.385.1 | 2 | 144.115 | odd | 12 | |||
768.4.d.b.385.2 | 2 | 144.43 | odd | 12 | |||
768.4.d.o.385.1 | 2 | 144.133 | even | 12 | |||
768.4.d.o.385.2 | 2 | 144.61 | even | 12 | |||
1176.4.a.a.1.1 | 1 | 63.34 | odd | 6 | |||
1200.4.a.u.1.1 | 1 | 180.79 | odd | 6 | |||
1200.4.f.p.49.1 | 2 | 180.43 | even | 12 | |||
1200.4.f.p.49.2 | 2 | 180.7 | even | 12 | |||
1800.4.a.bg.1.1 | 1 | 45.29 | odd | 6 | |||
1800.4.f.q.649.1 | 2 | 45.2 | even | 12 | |||
1800.4.f.q.649.2 | 2 | 45.38 | even | 12 | |||
2352.4.a.w.1.1 | 1 | 252.223 | even | 6 |