Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
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: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.06791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82093 | −0.997349 | −0.498674 | − | 0.866789i | \(-0.666180\pi\) | ||||
−0.498674 | + | 0.866789i | \(0.666180\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0423641 | −0.00529552 | ||||||||
\(5\) | −3.41089 | −0.305079 | −0.152539 | − | 0.988297i | \(-0.548745\pi\) | ||||
−0.152539 | + | 0.988297i | \(0.548745\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.3442 | −0.720518 | −0.360259 | − | 0.932852i | \(-0.617312\pi\) | ||||
−0.360259 | + | 0.932852i | \(0.617312\pi\) | |||||||
\(8\) | 22.6869 | 1.00263 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.62187 | 0.304270 | ||||||||
\(11\) | 35.4529 | 0.971769 | 0.485885 | − | 0.874023i | \(-0.338498\pi\) | ||||
0.485885 | + | 0.874023i | \(0.338498\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 37.6430 | 0.718607 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −63.6593 | −0.994676 | ||||||||
\(17\) | −69.6526 | −0.993720 | −0.496860 | − | 0.867831i | \(-0.665514\pi\) | ||||
−0.496860 | + | 0.867831i | \(0.665514\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.4014 | −0.149740 | −0.0748701 | − | 0.997193i | \(-0.523854\pi\) | ||||
−0.0748701 | + | 0.997193i | \(0.523854\pi\) | |||||||
\(20\) | 0.144499 | 0.00161555 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −100.010 | −0.969193 | ||||||||
\(23\) | 126.251 | 1.14457 | 0.572287 | − | 0.820053i | \(-0.306056\pi\) | ||||
0.572287 | + | 0.820053i | \(0.306056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −113.366 | −0.906927 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.565314 | 0.00381551 | ||||||||
\(29\) | 179.060 | 1.14657 | 0.573286 | − | 0.819356i | \(-0.305669\pi\) | ||||
0.573286 | + | 0.819356i | \(0.305669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −255.935 | −1.48281 | −0.741407 | − | 0.671055i | \(-0.765841\pi\) | ||||
−0.741407 | + | 0.671055i | \(0.765841\pi\) | |||||||
\(32\) | −1.91716 | −0.0105909 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 196.485 | 0.991085 | ||||||||
\(35\) | 45.5155 | 0.219815 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −207.235 | −0.920790 | −0.460395 | − | 0.887714i | \(-0.652292\pi\) | ||||
−0.460395 | + | 0.887714i | \(0.652292\pi\) | |||||||
\(38\) | 34.9833 | 0.149343 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −77.3825 | −0.305881 | ||||||||
\(41\) | −117.701 | −0.448337 | −0.224169 | − | 0.974550i | \(-0.571967\pi\) | ||||
−0.224169 | + | 0.974550i | \(0.571967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 553.224 | 1.96200 | 0.980998 | − | 0.194016i | \(-0.0621515\pi\) | ||||
0.980998 | + | 0.194016i | \(0.0621515\pi\) | |||||||
\(44\) | −1.50193 | −0.00514602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −356.146 | −1.14154 | ||||||||
\(47\) | 62.9185 | 0.195268 | 0.0976341 | − | 0.995222i | \(-0.468873\pi\) | ||||
0.0976341 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −164.933 | −0.480854 | ||||||||
\(50\) | 319.797 | 0.904522 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 147.031 | 0.381061 | 0.190531 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190531 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −120.926 | −0.296466 | ||||||||
\(56\) | −302.738 | −0.722413 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −505.115 | −1.14353 | ||||||||
\(59\) | 274.087 | 0.604798 | 0.302399 | − | 0.953181i | \(-0.402213\pi\) | ||||
0.302399 | + | 0.953181i | \(0.402213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 603.039 | 1.26576 | 0.632879 | − | 0.774251i | \(-0.281873\pi\) | ||||
0.632879 | + | 0.774251i | \(0.281873\pi\) | |||||||
\(62\) | 721.974 | 1.47888 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 514.683 | 1.00524 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 741.019 | 1.35119 | 0.675596 | − | 0.737272i | \(-0.263887\pi\) | ||||
0.675596 | + | 0.737272i | \(0.263887\pi\) | |||||||
\(68\) | 2.95077 | 0.00526226 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −128.396 | −0.219232 | ||||||||
\(71\) | 572.574 | 0.957071 | 0.478536 | − | 0.878068i | \(-0.341168\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26.7155 | −0.0428330 | −0.0214165 | − | 0.999771i | \(-0.506818\pi\) | ||||
−0.0214165 | + | 0.999771i | \(0.506818\pi\) | |||||||
\(74\) | 584.595 | 0.918349 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.525372 | 0.000792952 0 | ||||||||
\(77\) | −473.090 | −0.700177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −207.798 | −0.295938 | −0.147969 | − | 0.988992i | \(-0.547274\pi\) | ||||
−0.147969 | + | 0.988992i | \(0.547274\pi\) | |||||||
\(80\) | 217.135 | 0.303455 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 332.026 | 0.447149 | ||||||||
\(83\) | −1031.37 | −1.36395 | −0.681976 | − | 0.731374i | \(-0.738879\pi\) | ||||
−0.681976 | + | 0.731374i | \(0.738879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 237.577 | 0.303163 | ||||||||
\(86\) | −1560.60 | −1.95679 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 804.318 | 0.974325 | ||||||||
\(89\) | 1229.66 | 1.46453 | 0.732266 | − | 0.681019i | \(-0.238463\pi\) | ||||
0.732266 | + | 0.681019i | \(0.238463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.34852 | −0.00606111 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −177.488 | −0.194750 | ||||||||
\(95\) | 42.2996 | 0.0456826 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1795.12 | −1.87903 | −0.939517 | − | 0.342502i | \(-0.888726\pi\) | ||||
−0.939517 | + | 0.342502i | \(0.888726\pi\) | |||||||
\(98\) | 465.264 | 0.479579 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.80265 | 0.00480265 | ||||||||
\(101\) | 769.697 | 0.758295 | 0.379147 | − | 0.925336i | \(-0.376217\pi\) | ||||
0.379147 | + | 0.925336i | \(0.376217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1543.66 | 1.47671 | 0.738357 | − | 0.674410i | \(-0.235602\pi\) | ||||
0.738357 | + | 0.674410i | \(0.235602\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −414.764 | −0.380051 | ||||||||
\(107\) | −2027.64 | −1.83196 | −0.915978 | − | 0.401228i | \(-0.868583\pi\) | ||||
−0.915978 | + | 0.401228i | \(0.868583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1644.97 | −1.44550 | −0.722751 | − | 0.691108i | \(-0.757123\pi\) | ||||
−0.722751 | + | 0.691108i | \(0.757123\pi\) | |||||||
\(110\) | 341.123 | 0.295680 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 849.481 | 0.716682 | ||||||||
\(113\) | 654.514 | 0.544880 | 0.272440 | − | 0.962173i | \(-0.412169\pi\) | ||||
0.272440 | + | 0.962173i | \(0.412169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −430.629 | −0.349186 | ||||||||
\(116\) | −7.58571 | −0.00607169 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −773.179 | −0.603194 | ||||||||
\(119\) | 929.456 | 0.715993 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −74.0896 | −0.0556646 | ||||||||
\(122\) | −1701.13 | −1.26240 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.8425 | 0.00785227 | ||||||||
\(125\) | 813.039 | 0.581763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1325.54 | 0.926161 | 0.463080 | − | 0.886316i | \(-0.346744\pi\) | ||||
0.463080 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(128\) | −1436.55 | −0.991983 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −930.114 | −0.620339 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 165.486 | 0.107891 | ||||||||
\(134\) | −2090.36 | −1.34761 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1580.20 | −0.996333 | ||||||||
\(137\) | −2751.03 | −1.71559 | −0.857797 | − | 0.513989i | \(-0.828167\pi\) | ||||
−0.857797 | + | 0.513989i | \(0.828167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2436.65 | 1.48686 | 0.743432 | − | 0.668812i | \(-0.233197\pi\) | ||||
0.743432 | + | 0.668812i | \(0.233197\pi\) | |||||||
\(140\) | −1.92822 | −0.00116403 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1615.19 | −0.954534 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −610.753 | −0.349795 | ||||||||
\(146\) | 75.3624 | 0.0427194 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.77933 | 0.00487606 | ||||||||
\(149\) | −1517.58 | −0.834397 | −0.417198 | − | 0.908815i | \(-0.636988\pi\) | ||||
−0.417198 | + | 0.908815i | \(0.636988\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −583.642 | −0.314544 | −0.157272 | − | 0.987555i | \(-0.550270\pi\) | ||||
−0.157272 | + | 0.987555i | \(0.550270\pi\) | |||||||
\(152\) | −281.349 | −0.150134 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1334.55 | 0.698321 | ||||||||
\(155\) | 872.965 | 0.452376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26.0932 | 0.0132641 | 0.00663206 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663206 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(158\) | 586.184 | 0.295154 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.53922 | 0.00323107 | ||||||||
\(161\) | −1684.72 | −0.824686 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.0905 | −0.00821246 | −0.00410623 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410623 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(164\) | 4.98631 | 0.00237418 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2909.43 | 1.36034 | ||||||||
\(167\) | 3919.48 | 1.81616 | 0.908079 | − | 0.418799i | \(-0.137549\pi\) | ||||
0.908079 | + | 0.418799i | \(0.137549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −670.188 | −0.302359 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.4368 | −0.0103898 | ||||||||
\(173\) | 1976.35 | 0.868551 | 0.434276 | − | 0.900780i | \(-0.357004\pi\) | ||||
0.434276 | + | 0.900780i | \(0.357004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1512.77 | 0.653457 | ||||||||
\(176\) | −2256.91 | −0.966596 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3468.77 | −1.46065 | ||||||||
\(179\) | 2784.34 | 1.16263 | 0.581316 | − | 0.813678i | \(-0.302538\pi\) | ||||
0.581316 | + | 0.813678i | \(0.302538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1886.53 | −0.774723 | −0.387361 | − | 0.921928i | \(-0.626613\pi\) | ||||
−0.387361 | + | 0.921928i | \(0.626613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2864.25 | 1.14758 | ||||||||
\(185\) | 706.855 | 0.280914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2469.39 | −0.965666 | ||||||||
\(188\) | −2.66549 | −0.00103405 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −119.324 | −0.0455615 | ||||||||
\(191\) | −2447.94 | −0.927364 | −0.463682 | − | 0.886002i | \(-0.653472\pi\) | ||||
−0.463682 | + | 0.886002i | \(0.653472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1925.66 | 0.718196 | 0.359098 | − | 0.933300i | \(-0.383084\pi\) | ||||
0.359098 | + | 0.933300i | \(0.383084\pi\) | |||||||
\(194\) | 5063.89 | 1.87405 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.98724 | 0.00254637 | ||||||||
\(197\) | −1819.95 | −0.658203 | −0.329102 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329102 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1273.97 | −0.453816 | −0.226908 | − | 0.973916i | \(-0.572862\pi\) | ||||
−0.226908 | + | 0.973916i | \(0.572862\pi\) | |||||||
\(200\) | −2571.92 | −0.909312 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2171.26 | −0.756284 | ||||||||
\(203\) | −2389.40 | −0.826125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 401.465 | 0.136778 | ||||||||
\(206\) | −4354.56 | −1.47280 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −439.664 | −0.145513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1319.44 | −0.430492 | −0.215246 | − | 0.976560i | \(-0.569055\pi\) | ||||
−0.215246 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(212\) | −6.22884 | −0.00201792 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5719.83 | 1.82710 | ||||||||
\(215\) | −1886.98 | −0.598564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3415.24 | 1.06839 | ||||||||
\(218\) | 4640.35 | 1.44167 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.12292 | 0.00156994 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1203.45 | −0.361384 | −0.180692 | − | 0.983540i | \(-0.557834\pi\) | ||||
−0.180692 | + | 0.983540i | \(0.557834\pi\) | |||||||
\(224\) | 25.5829 | 0.00763095 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1846.34 | −0.543436 | ||||||||
\(227\) | −4361.23 | −1.27518 | −0.637589 | − | 0.770377i | \(-0.720068\pi\) | ||||
−0.637589 | + | 0.770377i | \(0.720068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5384.29 | −1.55373 | −0.776864 | − | 0.629669i | \(-0.783191\pi\) | ||||
−0.776864 | + | 0.629669i | \(0.783191\pi\) | |||||||
\(230\) | 1214.77 | 0.348260 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4062.32 | 1.14959 | ||||||||
\(233\) | 4913.60 | 1.38155 | 0.690774 | − | 0.723070i | \(-0.257270\pi\) | ||||
0.690774 | + | 0.723070i | \(0.257270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −214.608 | −0.0595722 | ||||||||
\(236\) | −11.6114 | −0.00320272 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2621.93 | −0.714094 | ||||||||
\(239\) | 963.718 | 0.260827 | 0.130414 | − | 0.991460i | \(-0.458369\pi\) | ||||
0.130414 | + | 0.991460i | \(0.458369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1544.48 | −0.412817 | −0.206409 | − | 0.978466i | \(-0.566178\pi\) | ||||
−0.206409 | + | 0.978466i | \(0.566178\pi\) | |||||||
\(242\) | 209.001 | 0.0555170 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25.5472 | −0.00670284 | ||||||||
\(245\) | 562.568 | 0.146698 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5806.38 | −1.48671 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2293.52 | −0.580221 | ||||||||
\(251\) | −3768.17 | −0.947588 | −0.473794 | − | 0.880636i | \(-0.657116\pi\) | ||||
−0.473794 | + | 0.880636i | \(0.657116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4475.98 | 1.11226 | ||||||||
\(254\) | −3739.25 | −0.923705 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −65.0695 | −0.0158861 | ||||||||
\(257\) | −1282.68 | −0.311327 | −0.155664 | − | 0.987810i | \(-0.549752\pi\) | ||||
−0.155664 | + | 0.987810i | \(0.549752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2765.38 | 0.663445 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2623.78 | 0.618694 | ||||||||
\(263\) | −5029.74 | −1.17927 | −0.589633 | − | 0.807671i | \(-0.700728\pi\) | ||||
−0.589633 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −501.506 | −0.116254 | ||||||||
\(266\) | −466.824 | −0.107604 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −31.3926 | −0.00715526 | ||||||||
\(269\) | −5628.46 | −1.27574 | −0.637868 | − | 0.770146i | \(-0.720184\pi\) | ||||
−0.637868 | + | 0.770146i | \(0.720184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3368.39 | −0.755037 | −0.377518 | − | 0.926002i | \(-0.623222\pi\) | ||||
−0.377518 | + | 0.926002i | \(0.623222\pi\) | |||||||
\(272\) | 4434.03 | 0.988429 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7760.45 | 1.71104 | ||||||||
\(275\) | −4019.15 | −0.881324 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6507.75 | −1.41160 | −0.705799 | − | 0.708412i | \(-0.749412\pi\) | ||||
−0.705799 | + | 0.708412i | \(0.749412\pi\) | |||||||
\(278\) | −6873.62 | −1.48292 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1032.61 | 0.220393 | ||||||||
\(281\) | −3625.51 | −0.769680 | −0.384840 | − | 0.922983i | \(-0.625743\pi\) | ||||
−0.384840 | + | 0.922983i | \(0.625743\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4635.41 | −0.973662 | −0.486831 | − | 0.873496i | \(-0.661847\pi\) | ||||
−0.486831 | + | 0.873496i | \(0.661847\pi\) | |||||||
\(284\) | −24.2566 | −0.00506819 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1570.62 | 0.323035 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −61.5178 | −0.0125214 | ||||||||
\(290\) | 1722.89 | 0.348867 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.13178 | 0.000226823 0 | ||||||||
\(293\) | −2907.07 | −0.579634 | −0.289817 | − | 0.957082i | \(-0.593594\pi\) | ||||
−0.289817 | + | 0.957082i | \(0.593594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −934.879 | −0.184511 | ||||||||
\(296\) | −4701.53 | −0.923212 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4280.99 | 0.832185 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7382.32 | −1.41365 | ||||||||
\(302\) | 1646.41 | 0.313710 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 789.461 | 0.148943 | ||||||||
\(305\) | −2056.90 | −0.386156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −933.950 | −0.173627 | −0.0868133 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868133 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(308\) | 20.0421 | 0.00370780 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2462.57 | −0.451176 | ||||||||
\(311\) | 3633.55 | 0.662508 | 0.331254 | − | 0.943542i | \(-0.392528\pi\) | ||||
0.331254 | + | 0.943542i | \(0.392528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7507.26 | −1.35570 | −0.677852 | − | 0.735198i | \(-0.737089\pi\) | ||||
−0.677852 | + | 0.735198i | \(0.737089\pi\) | |||||||
\(314\) | −73.6071 | −0.0132289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.80319 | 0.00156715 | ||||||||
\(317\) | 1214.60 | 0.215202 | 0.107601 | − | 0.994194i | \(-0.465683\pi\) | ||||
0.107601 | + | 0.994194i | \(0.465683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6348.19 | 1.11420 | ||||||||
\(320\) | −1755.52 | −0.306677 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4752.47 | 0.822500 | ||||||||
\(323\) | 863.786 | 0.148800 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 48.2111 | 0.00819069 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2670.28 | −0.449517 | ||||||||
\(329\) | −839.595 | −0.140694 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2443.20 | −0.405712 | −0.202856 | − | 0.979209i | \(-0.565022\pi\) | ||||
−0.202856 | + | 0.979209i | \(0.565022\pi\) | |||||||
\(332\) | 43.6933 | 0.00722283 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11056.6 | −1.81134 | ||||||||
\(335\) | −2527.53 | −0.412220 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1890.96 | 0.305660 | 0.152830 | − | 0.988253i | \(-0.451161\pi\) | ||||
0.152830 | + | 0.988253i | \(0.451161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.0647 | −0.00160540 | ||||||||
\(341\) | −9073.64 | −1.44095 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6777.95 | 1.06698 | ||||||||
\(344\) | 12551.0 | 1.96716 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5575.15 | −0.866248 | ||||||||
\(347\) | 2791.57 | 0.431872 | 0.215936 | − | 0.976408i | \(-0.430720\pi\) | ||||
0.215936 | + | 0.976408i | \(0.430720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6917.33 | 1.06096 | 0.530482 | − | 0.847696i | \(-0.322011\pi\) | ||||
0.530482 | + | 0.847696i | \(0.322011\pi\) | |||||||
\(350\) | −4267.43 | −0.651724 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −67.9690 | −0.0102919 | ||||||||
\(353\) | 7638.37 | 1.15170 | 0.575849 | − | 0.817556i | \(-0.304672\pi\) | ||||
0.575849 | + | 0.817556i | \(0.304672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1952.99 | −0.291982 | ||||||||
\(356\) | −52.0933 | −0.00775545 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7854.42 | −1.15955 | ||||||||
\(359\) | −5490.97 | −0.807249 | −0.403625 | − | 0.914925i | \(-0.632250\pi\) | ||||
−0.403625 | + | 0.914925i | \(0.632250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6705.21 | −0.977578 | ||||||||
\(362\) | 5321.77 | 0.772669 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 91.1234 | 0.0130674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6737.43 | 0.958287 | 0.479143 | − | 0.877737i | \(-0.340947\pi\) | ||||
0.479143 | + | 0.877737i | \(0.340947\pi\) | |||||||
\(368\) | −8037.07 | −1.13848 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1993.99 | −0.280169 | ||||||||
\(371\) | −1962.01 | −0.274561 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3930.42 | −0.545602 | −0.272801 | − | 0.962070i | \(-0.587950\pi\) | ||||
−0.272801 | + | 0.962070i | \(0.587950\pi\) | |||||||
\(374\) | 6965.97 | 0.963106 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1427.43 | 0.195782 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11897.7 | −1.61252 | −0.806258 | − | 0.591563i | \(-0.798511\pi\) | ||||
−0.806258 | + | 0.591563i | \(0.798511\pi\) | |||||||
\(380\) | −1.79199 | −0.000241913 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6905.46 | 0.924906 | ||||||||
\(383\) | 4748.31 | 0.633492 | 0.316746 | − | 0.948510i | \(-0.397410\pi\) | ||||
0.316746 | + | 0.948510i | \(0.397410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1613.66 | 0.213609 | ||||||||
\(386\) | −5432.14 | −0.716292 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 76.0485 | 0.00995046 | ||||||||
\(389\) | −11299.5 | −1.47277 | −0.736386 | − | 0.676561i | \(-0.763469\pi\) | ||||
−0.736386 | + | 0.676561i | \(0.763469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8793.73 | −1.13739 | ||||||||
\(392\) | −3741.82 | −0.482119 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5133.95 | 0.656458 | ||||||||
\(395\) | 708.776 | 0.0902845 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13853.0 | −1.75129 | −0.875646 | − | 0.482953i | \(-0.839564\pi\) | ||||
−0.875646 | + | 0.482953i | \(0.839564\pi\) | |||||||
\(398\) | 3593.78 | 0.452613 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7216.79 | 0.902099 | ||||||||
\(401\) | 5434.64 | 0.676790 | 0.338395 | − | 0.941004i | \(-0.390116\pi\) | ||||
0.338395 | + | 0.941004i | \(0.390116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −32.6076 | −0.00401556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6740.34 | 0.823935 | ||||||||
\(407\) | −7347.09 | −0.894795 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3472.43 | 0.419806 | 0.209903 | − | 0.977722i | \(-0.432685\pi\) | ||||
0.209903 | + | 0.977722i | \(0.432685\pi\) | |||||||
\(410\) | −1132.50 | −0.136416 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −65.3959 | −0.00781996 | ||||||||
\(413\) | −3657.46 | −0.435767 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3517.90 | 0.416113 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1240.26 | 0.145127 | ||||||||
\(419\) | 4261.65 | 0.496886 | 0.248443 | − | 0.968647i | \(-0.420081\pi\) | ||||
0.248443 | + | 0.968647i | \(0.420081\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6235.06 | −0.721801 | −0.360900 | − | 0.932604i | \(-0.617531\pi\) | ||||
−0.360900 | + | 0.932604i | \(0.617531\pi\) | |||||||
\(422\) | 3722.04 | 0.429351 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3335.68 | 0.382064 | ||||||||
\(425\) | 7896.22 | 0.901231 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8047.06 | −0.912001 | ||||||||
\(428\) | 85.8992 | 0.00970115 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5323.05 | 0.596977 | ||||||||
\(431\) | 2520.58 | 0.281698 | 0.140849 | − | 0.990031i | \(-0.455017\pi\) | ||||
0.140849 | + | 0.990031i | \(0.455017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1283.89 | −0.142494 | −0.0712468 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712468 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(434\) | −9634.15 | −1.06556 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 69.6878 | 0.00765468 | ||||||||
\(437\) | −1565.69 | −0.171389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16942.0 | −1.84190 | −0.920951 | − | 0.389677i | \(-0.872586\pi\) | ||||
−0.920951 | + | 0.389677i | \(0.872586\pi\) | |||||||
\(440\) | −2743.44 | −0.297246 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2163.00 | 0.231980 | 0.115990 | − | 0.993250i | \(-0.462996\pi\) | ||||
0.115990 | + | 0.993250i | \(0.462996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4194.22 | −0.446798 | ||||||||
\(446\) | 3394.83 | 0.360426 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6868.01 | −0.724293 | ||||||||
\(449\) | −1673.35 | −0.175880 | −0.0879400 | − | 0.996126i | \(-0.528028\pi\) | ||||
−0.0879400 | + | 0.996126i | \(0.528028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4172.85 | −0.435680 | ||||||||
\(452\) | −27.7279 | −0.00288542 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12302.7 | 1.27180 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4652.38 | 0.476212 | 0.238106 | − | 0.971239i | \(-0.423473\pi\) | ||||
0.238106 | + | 0.971239i | \(0.423473\pi\) | |||||||
\(458\) | 15188.7 | 1.54961 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.2432 | 0.00184912 | ||||||||
\(461\) | 3460.07 | 0.349570 | 0.174785 | − | 0.984607i | \(-0.444077\pi\) | ||||
0.174785 | + | 0.984607i | \(0.444077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2105.64 | 0.211355 | 0.105677 | − | 0.994400i | \(-0.466299\pi\) | ||||
0.105677 | + | 0.994400i | \(0.466299\pi\) | |||||||
\(464\) | −11398.8 | −1.14047 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13860.9 | −1.37789 | ||||||||
\(467\) | 1415.88 | 0.140298 | 0.0701489 | − | 0.997537i | \(-0.477653\pi\) | ||||
0.0701489 | + | 0.997537i | \(0.477653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9888.28 | −0.973557 | ||||||||
\(470\) | 605.393 | 0.0594143 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6218.19 | 0.606388 | ||||||||
\(473\) | 19613.4 | 1.90661 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1405.89 | 0.135803 | ||||||||
\(476\) | −39.3756 | −0.00379155 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2718.58 | −0.260136 | ||||||||
\(479\) | −985.594 | −0.0940145 | −0.0470073 | − | 0.998895i | \(-0.514968\pi\) | ||||
−0.0470073 | + | 0.998895i | \(0.514968\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4356.88 | 0.411723 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.13874 | 0.000294773 0 | ||||||||
\(485\) | 6122.93 | 0.573254 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14724.7 | −1.37011 | −0.685053 | − | 0.728494i | \(-0.740221\pi\) | ||||
−0.685053 | + | 0.728494i | \(0.740221\pi\) | |||||||
\(488\) | 13681.1 | 1.26909 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1586.96 | −0.146310 | ||||||||
\(491\) | 16301.2 | 1.49830 | 0.749149 | − | 0.662401i | \(-0.230463\pi\) | ||||
0.749149 | + | 0.662401i | \(0.230463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12472.0 | −1.13937 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16292.6 | 1.47492 | ||||||||
\(497\) | −7640.53 | −0.689587 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3230.42 | −0.289806 | −0.144903 | − | 0.989446i | \(-0.546287\pi\) | ||||
−0.144903 | + | 0.989446i | \(0.546287\pi\) | |||||||
\(500\) | −34.4437 | −0.00308074 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10629.7 | 0.945076 | ||||||||
\(503\) | 3577.57 | 0.317129 | 0.158565 | − | 0.987349i | \(-0.449313\pi\) | ||||
0.158565 | + | 0.987349i | \(0.449313\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2625.35 | −0.231340 | ||||||||
\(506\) | −12626.4 | −1.10931 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −56.1552 | −0.00490450 | ||||||||
\(509\) | −13864.7 | −1.20735 | −0.603674 | − | 0.797231i | \(-0.706297\pi\) | ||||
−0.603674 | + | 0.797231i | \(0.706297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 356.496 | 0.0308619 | ||||||||
\(512\) | 11675.9 | 1.00783 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3618.34 | 0.310502 | ||||||||
\(515\) | −5265.25 | −0.450514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2230.64 | 0.189756 | ||||||||
\(518\) | −7800.94 | −0.661686 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9554.66 | 0.803449 | 0.401725 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401725 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19809.1 | −1.65620 | −0.828098 | − | 0.560583i | \(-0.810577\pi\) | ||||
−0.828098 | + | 0.560583i | \(0.810577\pi\) | |||||||
\(524\) | 39.4035 | 0.00328502 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14188.5 | 1.17614 | ||||||||
\(527\) | 17826.5 | 1.47350 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3772.38 | 0.310050 | ||||||||
\(530\) | 1414.71 | 0.115946 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.01066 | −0.000571336 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6916.05 | 0.558891 | ||||||||
\(536\) | 16811.4 | 1.35475 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15877.5 | 1.27235 | ||||||||
\(539\) | −5847.36 | −0.467279 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1011.14 | 0.0803551 | 0.0401775 | − | 0.999193i | \(-0.487208\pi\) | ||||
0.0401775 | + | 0.999193i | \(0.487208\pi\) | |||||||
\(542\) | 9501.98 | 0.753035 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 133.535 | 0.0105244 | ||||||||
\(545\) | 5610.81 | 0.440992 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15745.2 | 1.23074 | 0.615372 | − | 0.788237i | \(-0.289006\pi\) | ||||
0.615372 | + | 0.788237i | \(0.289006\pi\) | |||||||
\(548\) | 116.545 | 0.00908495 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11337.7 | 0.878987 | ||||||||
\(551\) | −2220.58 | −0.171688 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2772.89 | 0.213229 | ||||||||
\(554\) | 18357.9 | 1.40785 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −103.227 | −0.00787371 | ||||||||
\(557\) | 8510.94 | 0.647433 | 0.323716 | − | 0.946154i | \(-0.395068\pi\) | ||||
0.323716 | + | 0.946154i | \(0.395068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2897.48 | −0.218645 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10227.3 | 0.767639 | ||||||||
\(563\) | −16764.1 | −1.25493 | −0.627463 | − | 0.778646i | \(-0.715907\pi\) | ||||
−0.627463 | + | 0.778646i | \(0.715907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2232.47 | −0.166232 | ||||||||
\(566\) | 13076.1 | 0.971080 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12990.0 | 0.959589 | ||||||||
\(569\) | −20755.4 | −1.52919 | −0.764597 | − | 0.644508i | \(-0.777062\pi\) | ||||
−0.764597 | + | 0.644508i | \(0.777062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23408.6 | −1.71562 | −0.857810 | − | 0.513968i | \(-0.828175\pi\) | ||||
−0.857810 | + | 0.513968i | \(0.828175\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4430.62 | −0.322179 | ||||||||
\(575\) | −14312.6 | −1.03805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10387.2 | −0.749436 | −0.374718 | − | 0.927139i | \(-0.622261\pi\) | ||||
−0.374718 | + | 0.927139i | \(0.622261\pi\) | |||||||
\(578\) | 173.537 | 0.0124882 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.8740 | 0.00185234 | ||||||||
\(581\) | 13762.8 | 0.982752 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5212.68 | 0.370304 | ||||||||
\(584\) | −606.092 | −0.0429457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8200.63 | 0.578097 | ||||||||
\(587\) | −2898.42 | −0.203800 | −0.101900 | − | 0.994795i | \(-0.532492\pi\) | ||||
−0.101900 | + | 0.994795i | \(0.532492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3173.94 | 0.222037 | ||||||||
\(590\) | 2637.23 | 0.184022 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13192.4 | 0.915888 | ||||||||
\(593\) | 8805.33 | 0.609766 | 0.304883 | − | 0.952390i | \(-0.401383\pi\) | ||||
0.304883 | + | 0.952390i | \(0.401383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3170.27 | −0.218434 | ||||||||
\(596\) | 64.2910 | 0.00441856 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20236.8 | 1.38039 | 0.690194 | − | 0.723624i | \(-0.257525\pi\) | ||||
0.690194 | + | 0.723624i | \(0.257525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9884.92 | −0.670906 | −0.335453 | − | 0.942057i | \(-0.608889\pi\) | ||||
−0.335453 | + | 0.942057i | \(0.608889\pi\) | |||||||
\(602\) | 20825.0 | 1.40991 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.7255 | 0.00166567 | ||||||||
\(605\) | 252.711 | 0.0169821 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22919.3 | 1.53256 | 0.766281 | − | 0.642505i | \(-0.222105\pi\) | ||||
0.766281 | + | 0.642505i | \(0.222105\pi\) | |||||||
\(608\) | 23.7754 | 0.00158589 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5802.36 | 0.385132 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −916.052 | −0.0603572 | −0.0301786 | − | 0.999545i | \(-0.509608\pi\) | ||||
−0.0301786 | + | 0.999545i | \(0.509608\pi\) | |||||||
\(614\) | 2634.61 | 0.173166 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10733.0 | −0.702019 | ||||||||
\(617\) | −30179.4 | −1.96917 | −0.984584 | − | 0.174915i | \(-0.944035\pi\) | ||||
−0.984584 | + | 0.174915i | \(0.944035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5571.12 | −0.361748 | −0.180874 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180874 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(620\) | −36.9824 | −0.00239556 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10250.0 | −0.660751 | ||||||||
\(623\) | −16408.8 | −1.05522 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11397.5 | 0.729443 | ||||||||
\(626\) | 21177.5 | 1.35211 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.10542 | −7.02403e−5 0 | ||||||||
\(629\) | 14434.5 | 0.915007 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11360.1 | 0.716703 | 0.358352 | − | 0.933587i | \(-0.383339\pi\) | ||||
0.358352 | + | 0.933587i | \(0.383339\pi\) | |||||||
\(632\) | −4714.30 | −0.296717 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3426.31 | −0.214631 | ||||||||
\(635\) | −4521.26 | −0.282552 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −17907.8 | −1.11125 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4899.89 | 0.302633 | ||||||||
\(641\) | 24709.8 | 1.52259 | 0.761293 | − | 0.648408i | \(-0.224565\pi\) | ||||
0.761293 | + | 0.648408i | \(0.224565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15226.6 | −0.933869 | −0.466934 | − | 0.884292i | \(-0.654642\pi\) | ||||
−0.466934 | + | 0.884292i | \(0.654642\pi\) | |||||||
\(644\) | 71.3717 | 0.00436714 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2436.68 | −0.148405 | ||||||||
\(647\) | −16706.6 | −1.01515 | −0.507576 | − | 0.861607i | \(-0.669458\pi\) | ||||
−0.507576 | + | 0.861607i | \(0.669458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9717.18 | 0.587724 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.724024 | 4.34892e−5 0 | ||||||||
\(653\) | 28205.8 | 1.69032 | 0.845158 | − | 0.534516i | \(-0.179506\pi\) | ||||
0.845158 | + | 0.534516i | \(0.179506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3172.51 | 0.189252 | ||||||||
\(656\) | 7492.77 | 0.445951 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2368.44 | 0.140321 | ||||||||
\(659\) | 11424.2 | 0.675299 | 0.337649 | − | 0.941272i | \(-0.390368\pi\) | ||||
0.337649 | + | 0.941272i | \(0.390368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26518.2 | 1.56042 | 0.780211 | − | 0.625516i | \(-0.215112\pi\) | ||||
0.780211 | + | 0.625516i | \(0.215112\pi\) | |||||||
\(662\) | 6892.10 | 0.404636 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23398.7 | −1.36754 | ||||||||
\(665\) | −564.453 | −0.0329151 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22606.5 | 1.31234 | ||||||||
\(668\) | −166.045 | −0.00961749 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7129.98 | 0.411127 | ||||||||
\(671\) | 21379.5 | 1.23002 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22816.8 | 1.30687 | 0.653434 | − | 0.756984i | \(-0.273328\pi\) | ||||
0.653434 | + | 0.756984i | \(0.273328\pi\) | |||||||
\(674\) | −5334.27 | −0.304849 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17737.6 | −1.00696 | −0.503478 | − | 0.864008i | \(-0.667947\pi\) | ||||
−0.503478 | + | 0.864008i | \(0.667947\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23954.3 | 1.35388 | ||||||||
\(680\) | 5389.89 | 0.303960 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 25596.1 | 1.43713 | ||||||||
\(683\) | −18878.4 | −1.05763 | −0.528816 | − | 0.848737i | \(-0.677364\pi\) | ||||
−0.528816 | + | 0.848737i | \(0.677364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9383.45 | 0.523391 | ||||||||
\(686\) | −19120.1 | −1.06415 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −35217.8 | −1.95155 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11692.8 | −0.643726 | −0.321863 | − | 0.946786i | \(-0.604309\pi\) | ||||
−0.321863 | + | 0.946786i | \(0.604309\pi\) | |||||||
\(692\) | −83.7265 | −0.00459943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7874.82 | −0.430726 | ||||||||
\(695\) | −8311.14 | −0.453611 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8198.19 | 0.445522 | ||||||||
\(698\) | −19513.3 | −1.05815 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −64.0873 | −0.00346039 | ||||||||
\(701\) | −20658.1 | −1.11304 | −0.556522 | − | 0.830833i | \(-0.687865\pi\) | ||||
−0.556522 | + | 0.830833i | \(0.687865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2569.99 | 0.137879 | ||||||||
\(704\) | 18247.0 | 0.976861 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21547.3 | −1.14864 | ||||||||
\(707\) | −10271.0 | −0.546365 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20695.8 | 1.09626 | 0.548128 | − | 0.836394i | \(-0.315341\pi\) | ||||
0.548128 | + | 0.836394i | \(0.315341\pi\) | |||||||
\(710\) | 5509.23 | 0.291208 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27897.1 | 1.46838 | ||||||||
\(713\) | −32312.1 | −1.69719 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −117.956 | −0.00615674 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15489.6 | 0.805109 | ||||||||
\(719\) | 26299.2 | 1.36411 | 0.682053 | − | 0.731302i | \(-0.261087\pi\) | ||||
0.682053 | + | 0.731302i | \(0.261087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20598.9 | −1.06400 | ||||||||
\(722\) | 18914.9 | 0.974986 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 79.9213 | 0.00410256 | ||||||||
\(725\) | −20299.3 | −1.03986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16915.6 | −0.862952 | −0.431476 | − | 0.902125i | \(-0.642007\pi\) | ||||
−0.431476 | + | 0.902125i | \(0.642007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −257.053 | −0.0130328 | ||||||||
\(731\) | −38533.5 | −1.94967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13203.1 | 0.665302 | 0.332651 | − | 0.943050i | \(-0.392057\pi\) | ||||
0.332651 | + | 0.943050i | \(0.392057\pi\) | |||||||
\(734\) | −19005.8 | −0.955746 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −242.044 | −0.0121221 | ||||||||
\(737\) | 26271.3 | 1.31305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16813.9 | 0.836954 | 0.418477 | − | 0.908227i | \(-0.362564\pi\) | ||||
0.418477 | + | 0.908227i | \(0.362564\pi\) | |||||||
\(740\) | −29.9453 | −0.00148758 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5534.68 | 0.273834 | ||||||||
\(743\) | −32682.1 | −1.61371 | −0.806857 | − | 0.590747i | \(-0.798833\pi\) | ||||
−0.806857 | + | 0.590747i | \(0.798833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5176.30 | 0.254557 | ||||||||
\(746\) | 11087.4 | 0.544156 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 104.613 | 0.00511370 | ||||||||
\(749\) | 27057.2 | 1.31996 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2157.76 | 0.104844 | 0.0524219 | − | 0.998625i | \(-0.483306\pi\) | ||||
0.0524219 | + | 0.998625i | \(0.483306\pi\) | |||||||
\(752\) | −4005.35 | −0.194229 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1990.74 | 0.0959606 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13769.6 | 0.661117 | 0.330558 | − | 0.943786i | \(-0.392763\pi\) | ||||
0.330558 | + | 0.943786i | \(0.392763\pi\) | |||||||
\(758\) | 33562.6 | 1.60824 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 959.648 | 0.0458028 | ||||||||
\(761\) | 16905.2 | 0.805272 | 0.402636 | − | 0.915360i | \(-0.368094\pi\) | ||||
0.402636 | + | 0.915360i | \(0.368094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21950.8 | 1.04151 | ||||||||
\(764\) | 103.705 | 0.00491087 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13394.7 | −0.631813 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1153.35 | 0.0540845 | 0.0270422 | − | 0.999634i | \(-0.491391\pi\) | ||||
0.0270422 | + | 0.999634i | \(0.491391\pi\) | |||||||
\(770\) | −4552.01 | −0.213043 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −81.5787 | −0.00380322 | ||||||||
\(773\) | 20713.9 | 0.963811 | 0.481905 | − | 0.876223i | \(-0.339945\pi\) | ||||
0.481905 | + | 0.876223i | \(0.339945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29014.3 | 1.34480 | ||||||||
\(776\) | −40725.7 | −1.88398 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31875.1 | 1.46887 | ||||||||
\(779\) | 1459.65 | 0.0671341 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20299.4 | 0.930053 | ||||||||
\(782\) | 24806.5 | 1.13437 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10499.5 | 0.478294 | ||||||||
\(785\) | −89.0010 | −0.00404660 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10870.2 | 0.492353 | 0.246177 | − | 0.969225i | \(-0.420826\pi\) | ||||
0.246177 | + | 0.969225i | \(0.420826\pi\) | |||||||
\(788\) | 77.1006 | 0.00348553 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1999.41 | −0.0900451 | ||||||||
\(791\) | −8733.95 | −0.392596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 39078.4 | 1.74665 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 53.9706 | 0.00240319 | ||||||||
\(797\) | −12026.6 | −0.534511 | −0.267255 | − | 0.963626i | \(-0.586117\pi\) | ||||
−0.267255 | + | 0.963626i | \(0.586117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4382.43 | −0.194042 | ||||||||
\(800\) | 217.341 | 0.00960519 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15330.7 | −0.674996 | ||||||||
\(803\) | −947.142 | −0.0416238 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5746.39 | 0.251594 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17462.1 | 0.760289 | ||||||||
\(809\) | 32384.0 | 1.40737 | 0.703685 | − | 0.710512i | \(-0.251537\pi\) | ||||
0.703685 | + | 0.710512i | \(0.251537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42506.8 | 1.84046 | 0.920231 | − | 0.391375i | \(-0.128000\pi\) | ||||
0.920231 | + | 0.391375i | \(0.128000\pi\) | |||||||
\(812\) | 101.225 | 0.00437476 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20725.6 | 0.892423 | ||||||||
\(815\) | 58.2937 | 0.00250545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6860.72 | −0.293790 | ||||||||
\(818\) | −9795.47 | −0.418693 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.0077 | −0.000724312 0 | ||||||||
\(821\) | 20052.6 | 0.852427 | 0.426213 | − | 0.904623i | \(-0.359847\pi\) | ||||
0.426213 | + | 0.904623i | \(0.359847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31625.5 | −1.33948 | −0.669742 | − | 0.742594i | \(-0.733595\pi\) | ||||
−0.669742 | + | 0.742594i | \(0.733595\pi\) | |||||||
\(824\) | 35020.9 | 1.48060 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10317.4 | 0.434612 | ||||||||
\(827\) | −5440.97 | −0.228780 | −0.114390 | − | 0.993436i | \(-0.536491\pi\) | ||||
−0.114390 | + | 0.993436i | \(0.536491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24845.8 | −1.04093 | −0.520465 | − | 0.853883i | \(-0.674241\pi\) | ||||
−0.520465 | + | 0.853883i | \(0.674241\pi\) | |||||||
\(830\) | −9923.75 | −0.415010 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11488.0 | 0.477834 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13368.9 | −0.554071 | ||||||||
\(836\) | 18.6260 | 0.000770566 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12021.8 | −0.495568 | ||||||||
\(839\) | −45887.8 | −1.88823 | −0.944113 | − | 0.329621i | \(-0.893079\pi\) | ||||
−0.944113 | + | 0.329621i | \(0.893079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7673.40 | 0.314625 | ||||||||
\(842\) | 17588.7 | 0.719887 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 55.8969 | 0.00227968 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 988.665 | 0.0401073 | ||||||||
\(848\) | −9359.88 | −0.379033 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22274.7 | −0.898842 | ||||||||
\(851\) | −26163.7 | −1.05391 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33655.3 | −1.35092 | −0.675460 | − | 0.737397i | \(-0.736055\pi\) | ||||
−0.675460 | + | 0.737397i | \(0.736055\pi\) | |||||||
\(854\) | 22700.2 | 0.909583 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46000.9 | −1.83677 | ||||||||
\(857\) | −41365.6 | −1.64880 | −0.824399 | − | 0.566009i | \(-0.808487\pi\) | ||||
−0.824399 | + | 0.566009i | \(0.808487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14866.0 | 0.590480 | 0.295240 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295240 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(860\) | 79.9404 | 0.00316970 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7110.37 | −0.280952 | ||||||||
\(863\) | −15469.1 | −0.610167 | −0.305083 | − | 0.952326i | \(-0.598684\pi\) | ||||
−0.305083 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6741.12 | −0.264977 | ||||||||
\(866\) | 3621.76 | 0.142116 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −144.684 | −0.00565770 | ||||||||
\(869\) | −7367.05 | −0.287584 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −37319.4 | −1.44930 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4416.69 | 0.170934 | ||||||||
\(875\) | −10849.3 | −0.419171 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38100.7 | 1.46701 | 0.733505 | − | 0.679684i | \(-0.237883\pi\) | ||||
0.733505 | + | 0.679684i | \(0.237883\pi\) | |||||||
\(878\) | 47792.0 | 1.83702 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7698.06 | 0.294888 | ||||||||
\(881\) | −3879.84 | −0.148371 | −0.0741857 | − | 0.997244i | \(-0.523636\pi\) | ||||
−0.0741857 | + | 0.997244i | \(0.523636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13046.5 | 0.497225 | 0.248613 | − | 0.968603i | \(-0.420025\pi\) | ||||
0.248613 | + | 0.968603i | \(0.420025\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6101.66 | −0.231365 | ||||||||
\(887\) | 32833.2 | 1.24288 | 0.621438 | − | 0.783463i | \(-0.286549\pi\) | ||||
0.621438 | + | 0.783463i | \(0.286549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17688.2 | −0.667315 | ||||||||
\(890\) | 11831.6 | 0.445613 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 50.9829 | 0.00191372 | ||||||||
\(893\) | −780.274 | −0.0292395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9497.06 | −0.354695 | ||||||||
\(896\) | 19169.5 | 0.714741 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4720.39 | 0.175414 | ||||||||
\(899\) | −45827.6 | −1.70015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10241.1 | −0.378668 | ||||||||
\(902\) | 11771.3 | 0.434525 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14848.9 | 0.546314 | ||||||||
\(905\) | 6434.74 | 0.236352 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21346.3 | 0.781468 | 0.390734 | − | 0.920504i | \(-0.372221\pi\) | ||||
0.390734 | + | 0.920504i | \(0.372221\pi\) | |||||||
\(908\) | 184.760 | 0.00675272 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7792.71 | −0.283407 | −0.141704 | − | 0.989909i | \(-0.545258\pi\) | ||||
−0.141704 | + | 0.989909i | \(0.545258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36565.2 | −1.32545 | ||||||||
\(914\) | −13124.0 | −0.474950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 228.101 | 0.00822779 | ||||||||
\(917\) | 12411.6 | 0.446965 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31352.0 | −1.12536 | −0.562681 | − | 0.826674i | \(-0.690230\pi\) | ||||
−0.562681 | + | 0.826674i | \(0.690230\pi\) | |||||||
\(920\) | −9769.64 | −0.350104 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9760.61 | −0.348643 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23493.4 | 0.835089 | ||||||||
\(926\) | −5939.85 | −0.210794 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −343.286 | −0.0121432 | ||||||||
\(929\) | 12675.3 | 0.447646 | 0.223823 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223823 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2045.39 | 0.0720032 | ||||||||
\(932\) | −208.161 | −0.00731601 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3994.09 | −0.139926 | ||||||||
\(935\) | 8422.80 | 0.294604 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12308.5 | −0.429138 | −0.214569 | − | 0.976709i | \(-0.568835\pi\) | ||||
−0.214569 | + | 0.976709i | \(0.568835\pi\) | |||||||
\(938\) | 27894.1 | 0.970976 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.09167 | 0.000315466 0 | ||||||||
\(941\) | 20465.2 | 0.708978 | 0.354489 | − | 0.935060i | \(-0.384655\pi\) | ||||
0.354489 | + | 0.935060i | \(0.384655\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14859.9 | −0.513155 | ||||||||
\(944\) | −17448.2 | −0.601578 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55328.0 | −1.90155 | ||||||||
\(947\) | 11170.8 | 0.383318 | 0.191659 | − | 0.981462i | \(-0.438613\pi\) | ||||
0.191659 | + | 0.981462i | \(0.438613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3965.91 | −0.135443 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21086.5 | 0.717876 | ||||||||
\(953\) | −14109.4 | −0.479587 | −0.239794 | − | 0.970824i | \(-0.577080\pi\) | ||||
−0.239794 | + | 0.970824i | \(0.577080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8349.64 | 0.282919 | ||||||||
\(956\) | −40.8271 | −0.00138122 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2780.29 | 0.0937653 | ||||||||
\(959\) | 36710.2 | 1.23612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35711.6 | 1.19874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 65.4307 | 0.00218608 | ||||||||
\(965\) | −6568.19 | −0.219106 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40785.8 | 1.35634 | 0.678171 | − | 0.734904i | \(-0.262773\pi\) | ||||
0.678171 | + | 0.734904i | \(0.262773\pi\) | |||||||
\(968\) | −1680.87 | −0.0558110 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17272.4 | −0.571734 | ||||||||
\(971\) | −4230.29 | −0.139811 | −0.0699055 | − | 0.997554i | \(-0.522270\pi\) | ||||
−0.0699055 | + | 0.997554i | \(0.522270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32515.1 | −1.07131 | ||||||||
\(974\) | 41537.4 | 1.36647 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38389.0 | −1.25902 | ||||||||
\(977\) | −59925.0 | −1.96230 | −0.981151 | − | 0.193242i | \(-0.938100\pi\) | ||||
−0.981151 | + | 0.193242i | \(0.938100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43594.9 | 1.42319 | ||||||||
\(980\) | −23.8327 | −0.000776844 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −45984.6 | −1.49433 | ||||||||
\(983\) | −23333.3 | −0.757087 | −0.378543 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378543 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6207.64 | 0.200804 | ||||||||
\(986\) | 35182.5 | 1.13635 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69845.2 | 2.24565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32523.5 | −1.04253 | −0.521263 | − | 0.853396i | \(-0.674539\pi\) | ||||
−0.521263 | + | 0.853396i | \(0.674539\pi\) | |||||||
\(992\) | 490.668 | 0.0157044 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21553.4 | 0.687759 | ||||||||
\(995\) | 4345.37 | 0.138450 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7114.35 | −0.225992 | −0.112996 | − | 0.993595i | \(-0.536045\pi\) | ||||
−0.112996 | + | 0.993595i | \(0.536045\pi\) | |||||||
\(998\) | 9112.77 | 0.289038 | ||||||||
\(999\) | 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 | 1521.4.a.bi.1.3 | 9 | ||
3.2 | odd | 2 | 507.4.a.o.1.7 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.bf.1.7 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.6 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.13 | 18 | |||
39.38 | odd | 2 | 507.4.a.p.1.3 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.7 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.p.1.3 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.k.337.6 | 18 | 39.5 | even | 4 | |||
507.4.b.k.337.13 | 18 | 39.8 | even | 4 | |||
1521.4.a.bf.1.7 | 9 | 13.12 | even | 2 | |||
1521.4.a.bi.1.3 | 9 | 1.1 | even | 1 | trivial |