Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,4,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, 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("387.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(22.8337391722\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(4.31455\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.31455 | 1.17187 | 0.585936 | − | 0.810357i | \(-0.300727\pi\) | ||||
0.585936 | + | 0.810357i | \(0.300727\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.98627 | 0.373283 | ||||||||
\(5\) | −8.51910 | −0.761971 | −0.380986 | − | 0.924581i | \(-0.624415\pi\) | ||||
−0.380986 | + | 0.924581i | \(0.624415\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.84502 | 0.531581 | 0.265791 | − | 0.964031i | \(-0.414367\pi\) | ||||
0.265791 | + | 0.964031i | \(0.414367\pi\) | |||||||
\(8\) | −16.6183 | −0.734432 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −28.2370 | −0.892933 | ||||||||
\(11\) | −0.597776 | −0.0163851 | −0.00819256 | − | 0.999966i | \(-0.502608\pi\) | ||||
−0.00819256 | + | 0.999966i | \(0.502608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.9021 | 0.744623 | 0.372311 | − | 0.928108i | \(-0.378565\pi\) | ||||
0.372311 | + | 0.928108i | \(0.378565\pi\) | |||||||
\(14\) | 32.6318 | 0.622945 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.9723 | −1.23394 | ||||||||
\(17\) | −91.3552 | −1.30335 | −0.651673 | − | 0.758500i | \(-0.725933\pi\) | ||||
−0.651673 | + | 0.758500i | \(0.725933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.0324 | −0.290179 | −0.145089 | − | 0.989419i | \(-0.546347\pi\) | ||||
−0.145089 | + | 0.989419i | \(0.546347\pi\) | |||||||
\(20\) | −25.4403 | −0.284431 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.98136 | −0.0192013 | ||||||||
\(23\) | −127.719 | −1.15788 | −0.578938 | − | 0.815371i | \(-0.696533\pi\) | ||||
−0.578938 | + | 0.815371i | \(0.696533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −52.4250 | −0.419400 | ||||||||
\(26\) | 115.685 | 0.872602 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 29.3999 | 0.198430 | ||||||||
\(29\) | −285.724 | −1.82957 | −0.914786 | − | 0.403939i | \(-0.867641\pi\) | ||||
−0.914786 | + | 0.403939i | \(0.867641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −192.699 | −1.11644 | −0.558221 | − | 0.829692i | \(-0.688516\pi\) | ||||
−0.558221 | + | 0.829692i | \(0.688516\pi\) | |||||||
\(32\) | −128.812 | −0.711591 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −302.802 | −1.52735 | ||||||||
\(35\) | −83.8707 | −0.405050 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 363.399 | 1.61466 | 0.807329 | − | 0.590101i | \(-0.200912\pi\) | ||||
0.807329 | + | 0.590101i | \(0.200912\pi\) | |||||||
\(38\) | −79.6565 | −0.340053 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 141.573 | 0.559616 | ||||||||
\(41\) | −191.586 | −0.729774 | −0.364887 | − | 0.931052i | \(-0.618892\pi\) | ||||
−0.364887 | + | 0.931052i | \(0.618892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.0000 | −0.152499 | ||||||||
\(44\) | −1.78512 | −0.00611629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −423.330 | −1.35688 | ||||||||
\(47\) | 458.267 | 1.42223 | 0.711117 | − | 0.703073i | \(-0.248189\pi\) | ||||
0.711117 | + | 0.703073i | \(0.248189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −246.076 | −0.717422 | ||||||||
\(50\) | −173.765 | −0.491483 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 104.227 | 0.277955 | ||||||||
\(53\) | 583.068 | 1.51114 | 0.755572 | − | 0.655066i | \(-0.227359\pi\) | ||||
0.755572 | + | 0.655066i | \(0.227359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.09252 | 0.0124850 | ||||||||
\(56\) | −163.607 | −0.390410 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −947.047 | −2.14402 | ||||||||
\(59\) | −416.589 | −0.919243 | −0.459621 | − | 0.888115i | \(-0.652015\pi\) | ||||
−0.459621 | + | 0.888115i | \(0.652015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −30.9376 | −0.0649369 | −0.0324685 | − | 0.999473i | \(-0.510337\pi\) | ||||
−0.0324685 | + | 0.999473i | \(0.510337\pi\) | |||||||
\(62\) | −638.710 | −1.30833 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 204.825 | 0.400049 | ||||||||
\(65\) | −297.334 | −0.567381 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.1466 | 0.0294421 | 0.0147210 | − | 0.999892i | \(-0.495314\pi\) | ||||
0.0147210 | + | 0.999892i | \(0.495314\pi\) | |||||||
\(68\) | −272.811 | −0.486517 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −277.994 | −0.474666 | ||||||||
\(71\) | 219.461 | 0.366835 | 0.183418 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183418 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1031.07 | 1.65311 | 0.826557 | − | 0.562853i | \(-0.190296\pi\) | ||||
0.826557 | + | 0.562853i | \(0.190296\pi\) | |||||||
\(74\) | 1204.50 | 1.89217 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −71.7670 | −0.108319 | ||||||||
\(77\) | −5.88512 | −0.00871002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 445.438 | 0.634375 | 0.317188 | − | 0.948363i | \(-0.397262\pi\) | ||||
0.317188 | + | 0.948363i | \(0.397262\pi\) | |||||||
\(80\) | 672.773 | 0.940229 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −635.022 | −0.855201 | ||||||||
\(83\) | −298.511 | −0.394769 | −0.197384 | − | 0.980326i | \(-0.563245\pi\) | ||||
−0.197384 | + | 0.980326i | \(0.563245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 778.264 | 0.993112 | ||||||||
\(86\) | −142.526 | −0.178709 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.93402 | 0.0120338 | ||||||||
\(89\) | −846.185 | −1.00781 | −0.503907 | − | 0.863758i | \(-0.668105\pi\) | ||||
−0.503907 | + | 0.863758i | \(0.668105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 343.612 | 0.395827 | ||||||||
\(92\) | −381.402 | −0.432216 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1518.95 | 1.66668 | ||||||||
\(95\) | 204.734 | 0.221108 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −259.068 | −0.271179 | −0.135590 | − | 0.990765i | \(-0.543293\pi\) | ||||
−0.135590 | + | 0.990765i | \(0.543293\pi\) | |||||||
\(98\) | −815.631 | −0.840726 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −156.555 | −0.156555 | ||||||||
\(101\) | 1182.01 | 1.16450 | 0.582252 | − | 0.813009i | \(-0.302172\pi\) | ||||
0.582252 | + | 0.813009i | \(0.302172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 319.565 | 0.305706 | 0.152853 | − | 0.988249i | \(-0.451154\pi\) | ||||
0.152853 | + | 0.988249i | \(0.451154\pi\) | |||||||
\(104\) | −580.013 | −0.546874 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1932.61 | 1.77087 | ||||||||
\(107\) | −1647.14 | −1.48818 | −0.744089 | − | 0.668081i | \(-0.767116\pi\) | ||||
−0.744089 | + | 0.668081i | \(0.767116\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −560.538 | −0.492567 | −0.246283 | − | 0.969198i | \(-0.579209\pi\) | ||||
−0.246283 | + | 0.969198i | \(0.579209\pi\) | |||||||
\(110\) | 16.8794 | 0.0146308 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −777.484 | −0.655941 | ||||||||
\(113\) | 65.6852 | 0.0546827 | 0.0273414 | − | 0.999626i | \(-0.491296\pi\) | ||||
0.0273414 | + | 0.999626i | \(0.491296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1088.05 | 0.882269 | ||||||||
\(116\) | −853.248 | −0.682949 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1380.81 | −1.07723 | ||||||||
\(119\) | −899.393 | −0.692834 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.64 | −0.999732 | ||||||||
\(122\) | −102.544 | −0.0760977 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −575.450 | −0.416749 | ||||||||
\(125\) | 1511.50 | 1.08154 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1906.92 | −1.33238 | −0.666189 | − | 0.745783i | \(-0.732076\pi\) | ||||
−0.666189 | + | 0.745783i | \(0.732076\pi\) | |||||||
\(128\) | 1709.40 | 1.18040 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −985.530 | −0.664898 | ||||||||
\(131\) | 1536.09 | 1.02449 | 0.512246 | − | 0.858839i | \(-0.328814\pi\) | ||||
0.512246 | + | 0.858839i | \(0.328814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −236.599 | −0.154254 | ||||||||
\(134\) | 53.5187 | 0.0345023 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1518.17 | 0.957218 | ||||||||
\(137\) | 1695.38 | 1.05727 | 0.528634 | − | 0.848850i | \(-0.322704\pi\) | ||||
0.528634 | + | 0.848850i | \(0.322704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 947.580 | 0.578221 | 0.289110 | − | 0.957296i | \(-0.406641\pi\) | ||||
0.289110 | + | 0.957296i | \(0.406641\pi\) | |||||||
\(140\) | −250.460 | −0.151198 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 727.417 | 0.429884 | ||||||||
\(143\) | −20.8636 | −0.0122007 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2434.11 | 1.39408 | ||||||||
\(146\) | 3417.53 | 1.93724 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1085.21 | 0.602725 | ||||||||
\(149\) | −3084.10 | −1.69570 | −0.847850 | − | 0.530236i | \(-0.822103\pi\) | ||||
−0.847850 | + | 0.530236i | \(0.822103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2346.83 | −1.26478 | −0.632391 | − | 0.774649i | \(-0.717926\pi\) | ||||
−0.632391 | + | 0.774649i | \(0.717926\pi\) | |||||||
\(152\) | 399.377 | 0.213117 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.5066 | −0.0102070 | ||||||||
\(155\) | 1641.62 | 0.850697 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1582.73 | 0.804556 | 0.402278 | − | 0.915517i | \(-0.368218\pi\) | ||||
0.402278 | + | 0.915517i | \(0.368218\pi\) | |||||||
\(158\) | 1476.43 | 0.743406 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1097.36 | 0.542212 | ||||||||
\(161\) | −1257.39 | −0.615505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −820.887 | −0.394459 | −0.197229 | − | 0.980357i | \(-0.563194\pi\) | ||||
−0.197229 | + | 0.980357i | \(0.563194\pi\) | |||||||
\(164\) | −572.127 | −0.272412 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −989.430 | −0.462618 | ||||||||
\(167\) | −1690.58 | −0.783358 | −0.391679 | − | 0.920102i | \(-0.628106\pi\) | ||||
−0.391679 | + | 0.920102i | \(0.628106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −978.845 | −0.445537 | ||||||||
\(170\) | 2579.60 | 1.16380 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −128.409 | −0.0569252 | ||||||||
\(173\) | −1390.24 | −0.610973 | −0.305486 | − | 0.952196i | \(-0.598819\pi\) | ||||
−0.305486 | + | 0.952196i | \(0.598819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −516.125 | −0.222945 | ||||||||
\(176\) | 47.2078 | 0.0202183 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2804.73 | −1.18103 | ||||||||
\(179\) | −693.895 | −0.289744 | −0.144872 | − | 0.989450i | \(-0.546277\pi\) | ||||
−0.144872 | + | 0.989450i | \(0.546277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2355.50 | −0.967309 | −0.483655 | − | 0.875259i | \(-0.660691\pi\) | ||||
−0.483655 | + | 0.875259i | \(0.660691\pi\) | |||||||
\(182\) | 1138.92 | 0.463859 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2122.46 | 0.850381 | ||||||||
\(185\) | −3095.83 | −1.23032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 54.6100 | 0.0213555 | ||||||||
\(188\) | 1368.51 | 0.530897 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 678.602 | 0.259110 | ||||||||
\(191\) | 2168.09 | 0.821349 | 0.410674 | − | 0.911782i | \(-0.365293\pi\) | ||||
0.410674 | + | 0.911782i | \(0.365293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1305.00 | 0.486717 | 0.243358 | − | 0.969936i | \(-0.421751\pi\) | ||||
0.243358 | + | 0.969936i | \(0.421751\pi\) | |||||||
\(194\) | −858.695 | −0.317787 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −734.847 | −0.267802 | ||||||||
\(197\) | 4800.27 | 1.73607 | 0.868033 | − | 0.496507i | \(-0.165384\pi\) | ||||
0.868033 | + | 0.496507i | \(0.165384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2113.34 | −0.752816 | −0.376408 | − | 0.926454i | \(-0.622841\pi\) | ||||
−0.376408 | + | 0.926454i | \(0.622841\pi\) | |||||||
\(200\) | 871.213 | 0.308020 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3917.85 | 1.36465 | ||||||||
\(203\) | −2812.96 | −0.972566 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1632.14 | 0.556067 | ||||||||
\(206\) | 1059.22 | 0.358248 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2756.30 | −0.918822 | ||||||||
\(209\) | 14.3660 | 0.00475462 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5564.31 | 1.81546 | 0.907732 | − | 0.419551i | \(-0.137812\pi\) | ||||
0.907732 | + | 0.419551i | \(0.137812\pi\) | |||||||
\(212\) | 1741.20 | 0.564085 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5459.53 | −1.74395 | ||||||||
\(215\) | 366.321 | 0.116200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1897.12 | −0.593480 | ||||||||
\(218\) | −1857.93 | −0.577225 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.2076 | 0.00466044 | ||||||||
\(221\) | −3188.49 | −0.970501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1709.75 | −0.513422 | −0.256711 | − | 0.966488i | \(-0.582639\pi\) | ||||
−0.256711 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(224\) | −1268.15 | −0.378268 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 217.717 | 0.0640811 | ||||||||
\(227\) | −347.506 | −0.101607 | −0.0508035 | − | 0.998709i | \(-0.516178\pi\) | ||||
−0.0508035 | + | 0.998709i | \(0.516178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 713.508 | 0.205895 | 0.102947 | − | 0.994687i | \(-0.467173\pi\) | ||||
0.102947 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(230\) | 3606.39 | 1.03391 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4748.24 | 1.34370 | ||||||||
\(233\) | 6539.93 | 1.83882 | 0.919410 | − | 0.393300i | \(-0.128667\pi\) | ||||
0.919410 | + | 0.393300i | \(0.128667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3904.02 | −1.08370 | ||||||||
\(236\) | −1244.05 | −0.343138 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2981.09 | −0.811913 | ||||||||
\(239\) | 2561.41 | 0.693238 | 0.346619 | − | 0.938006i | \(-0.387330\pi\) | ||||
0.346619 | + | 0.938006i | \(0.387330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4656.80 | −1.24469 | −0.622346 | − | 0.782742i | \(-0.713820\pi\) | ||||
−0.622346 | + | 0.782742i | \(0.713820\pi\) | |||||||
\(242\) | −4410.49 | −1.17156 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −92.3879 | −0.0242399 | ||||||||
\(245\) | 2096.34 | 0.546655 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −838.779 | −0.216074 | ||||||||
\(248\) | 3202.32 | 0.819950 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5009.95 | 1.26743 | ||||||||
\(251\) | −6104.04 | −1.53499 | −0.767497 | − | 0.641053i | \(-0.778498\pi\) | ||||
−0.767497 | + | 0.641053i | \(0.778498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 76.3471 | 0.0189720 | ||||||||
\(254\) | −6320.60 | −1.56138 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4027.29 | 0.983225 | ||||||||
\(257\) | −682.439 | −0.165640 | −0.0828199 | − | 0.996565i | \(-0.526393\pi\) | ||||
−0.0828199 | + | 0.996565i | \(0.526393\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3577.67 | 0.858322 | ||||||||
\(260\) | −887.919 | −0.211794 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5091.44 | 1.20057 | ||||||||
\(263\) | −1671.87 | −0.391984 | −0.195992 | − | 0.980605i | \(-0.562793\pi\) | ||||
−0.195992 | + | 0.980605i | \(0.562793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4967.22 | −1.15145 | ||||||||
\(266\) | −784.220 | −0.180766 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 48.2180 | 0.0109902 | ||||||||
\(269\) | 261.999 | 0.0593843 | 0.0296921 | − | 0.999559i | \(-0.490547\pi\) | ||||
0.0296921 | + | 0.999559i | \(0.490547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4620.04 | 1.03560 | 0.517800 | − | 0.855502i | \(-0.326751\pi\) | ||||
0.517800 | + | 0.855502i | \(0.326751\pi\) | |||||||
\(272\) | 7214.53 | 1.60825 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5619.41 | 1.23898 | ||||||||
\(275\) | 31.3384 | 0.00687192 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5163.93 | 1.12011 | 0.560055 | − | 0.828456i | \(-0.310780\pi\) | ||||
0.560055 | + | 0.828456i | \(0.310780\pi\) | |||||||
\(278\) | 3140.81 | 0.677601 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1393.79 | 0.297481 | ||||||||
\(281\) | 5275.67 | 1.12000 | 0.560000 | − | 0.828493i | \(-0.310801\pi\) | ||||
0.560000 | + | 0.828493i | \(0.310801\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5028.34 | −1.05620 | −0.528098 | − | 0.849183i | \(-0.677095\pi\) | ||||
−0.528098 | + | 0.849183i | \(0.677095\pi\) | |||||||
\(284\) | 655.371 | 0.136933 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −69.1537 | −0.0142977 | ||||||||
\(287\) | −1886.17 | −0.387934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3432.77 | 0.698711 | ||||||||
\(290\) | 8067.99 | 1.63368 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3079.04 | 0.617080 | ||||||||
\(293\) | −8840.69 | −1.76273 | −0.881363 | − | 0.472439i | \(-0.843374\pi\) | ||||
−0.881363 | + | 0.472439i | \(0.843374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3548.96 | 0.700436 | ||||||||
\(296\) | −6039.06 | −1.18586 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10222.4 | −1.98714 | ||||||||
\(299\) | −4457.64 | −0.862181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −423.336 | −0.0810654 | ||||||||
\(302\) | −7778.68 | −1.48216 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1897.89 | 0.358064 | ||||||||
\(305\) | 263.560 | 0.0494801 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6565.15 | 1.22050 | 0.610249 | − | 0.792209i | \(-0.291069\pi\) | ||||
0.610249 | + | 0.792209i | \(0.291069\pi\) | |||||||
\(308\) | −17.5745 | −0.00325131 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5441.23 | 0.996908 | ||||||||
\(311\) | −1250.31 | −0.227969 | −0.113985 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113985 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2968.85 | −0.536132 | −0.268066 | − | 0.963401i | \(-0.586385\pi\) | ||||
−0.268066 | + | 0.963401i | \(0.586385\pi\) | |||||||
\(314\) | 5246.03 | 0.942837 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1330.20 | 0.236802 | ||||||||
\(317\) | −1054.32 | −0.186803 | −0.0934013 | − | 0.995629i | \(-0.529774\pi\) | ||||
−0.0934013 | + | 0.995629i | \(0.529774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 170.799 | 0.0299778 | ||||||||
\(320\) | −1744.93 | −0.304826 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4167.69 | −0.721293 | ||||||||
\(323\) | 2195.48 | 0.378204 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1829.74 | −0.312295 | ||||||||
\(326\) | −2720.87 | −0.462255 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3183.83 | 0.535969 | ||||||||
\(329\) | 4511.64 | 0.756033 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2881.73 | −0.478532 | −0.239266 | − | 0.970954i | \(-0.576907\pi\) | ||||
−0.239266 | + | 0.970954i | \(0.576907\pi\) | |||||||
\(332\) | −891.432 | −0.147361 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5603.51 | −0.917995 | ||||||||
\(335\) | −137.554 | −0.0224340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6147.77 | −0.993740 | −0.496870 | − | 0.867825i | \(-0.665517\pi\) | ||||
−0.496870 | + | 0.867825i | \(0.665517\pi\) | |||||||
\(338\) | −3244.43 | −0.522112 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2324.10 | 0.370712 | ||||||||
\(341\) | 115.191 | 0.0182930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5799.46 | −0.912949 | ||||||||
\(344\) | 714.586 | 0.112000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4608.04 | −0.715982 | ||||||||
\(347\) | −1404.42 | −0.217271 | −0.108636 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108636 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4472.14 | −0.685926 | −0.342963 | − | 0.939349i | \(-0.611430\pi\) | ||||
−0.342963 | + | 0.939349i | \(0.611430\pi\) | |||||||
\(350\) | −1710.72 | −0.261263 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 77.0007 | 0.0116595 | ||||||||
\(353\) | −2146.48 | −0.323642 | −0.161821 | − | 0.986820i | \(-0.551737\pi\) | ||||
−0.161821 | + | 0.986820i | \(0.551737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1869.61 | −0.279518 | ||||||||
\(356\) | −2526.93 | −0.376200 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2299.95 | −0.339543 | ||||||||
\(359\) | −1960.49 | −0.288219 | −0.144109 | − | 0.989562i | \(-0.546032\pi\) | ||||
−0.144109 | + | 0.989562i | \(0.546032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6281.45 | −0.915796 | ||||||||
\(362\) | −7807.43 | −1.13356 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1026.12 | 0.147756 | ||||||||
\(365\) | −8783.77 | −1.25963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13485.2 | 1.91804 | 0.959021 | − | 0.283337i | \(-0.0914414\pi\) | ||||
0.959021 | + | 0.283337i | \(0.0914414\pi\) | |||||||
\(368\) | 10086.2 | 1.42875 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10261.3 | −1.44178 | ||||||||
\(371\) | 5740.32 | 0.803295 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12034.5 | −1.67057 | −0.835285 | − | 0.549817i | \(-0.814697\pi\) | ||||
−0.835285 | + | 0.549817i | \(0.814697\pi\) | |||||||
\(374\) | 181.008 | 0.0250259 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7615.60 | −1.04453 | ||||||||
\(377\) | −9972.36 | −1.36234 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10185.1 | −1.38041 | −0.690204 | − | 0.723615i | \(-0.742479\pi\) | ||||
−0.690204 | + | 0.723615i | \(0.742479\pi\) | |||||||
\(380\) | 611.390 | 0.0825359 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7186.26 | 0.962515 | ||||||||
\(383\) | −13508.3 | −1.80219 | −0.901097 | − | 0.433618i | \(-0.857237\pi\) | ||||
−0.901097 | + | 0.433618i | \(0.857237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 50.1359 | 0.00663679 | ||||||||
\(386\) | 4325.51 | 0.570369 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −773.646 | −0.101227 | ||||||||
\(389\) | 6651.52 | 0.866954 | 0.433477 | − | 0.901165i | \(-0.357286\pi\) | ||||
0.433477 | + | 0.901165i | \(0.357286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11667.7 | 1.50911 | ||||||||
\(392\) | 4089.35 | 0.526897 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15910.7 | 2.03445 | ||||||||
\(395\) | −3794.73 | −0.483376 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8308.29 | −1.05033 | −0.525165 | − | 0.851000i | \(-0.675996\pi\) | ||||
−0.525165 | + | 0.851000i | \(0.675996\pi\) | |||||||
\(398\) | −7004.77 | −0.882204 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4140.12 | 0.517515 | ||||||||
\(401\) | −2963.57 | −0.369061 | −0.184530 | − | 0.982827i | \(-0.559076\pi\) | ||||
−0.184530 | + | 0.982827i | \(0.559076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6725.59 | −0.831328 | ||||||||
\(404\) | 3529.81 | 0.434690 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9323.70 | −1.13972 | ||||||||
\(407\) | −217.231 | −0.0264564 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9951.28 | −1.20308 | −0.601540 | − | 0.798843i | \(-0.705446\pi\) | ||||
−0.601540 | + | 0.798843i | \(0.705446\pi\) | |||||||
\(410\) | 5409.82 | 0.651639 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 954.308 | 0.114115 | ||||||||
\(413\) | −4101.33 | −0.488652 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2543.04 | 0.300802 | ||||||||
\(416\) | −4495.80 | −0.529867 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 47.6168 | 0.00557180 | ||||||||
\(419\) | −5281.70 | −0.615818 | −0.307909 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307909 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1668.54 | −0.193159 | −0.0965795 | − | 0.995325i | \(-0.530790\pi\) | ||||
−0.0965795 | + | 0.995325i | \(0.530790\pi\) | |||||||
\(422\) | 18443.2 | 2.12749 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9689.60 | −1.10983 | ||||||||
\(425\) | 4789.29 | 0.546623 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −304.581 | −0.0345192 | ||||||||
\(428\) | −4918.80 | −0.555512 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1214.19 | 0.136171 | ||||||||
\(431\) | 10348.7 | 1.15657 | 0.578284 | − | 0.815835i | \(-0.303722\pi\) | ||||
0.578284 | + | 0.815835i | \(0.303722\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2968.27 | 0.329436 | 0.164718 | − | 0.986341i | \(-0.447329\pi\) | ||||
0.164718 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(434\) | −6288.12 | −0.695482 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1673.91 | −0.183867 | ||||||||
\(437\) | 3069.38 | 0.335991 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9224.53 | −1.00288 | −0.501438 | − | 0.865194i | \(-0.667196\pi\) | ||||
−0.501438 | + | 0.865194i | \(0.667196\pi\) | |||||||
\(440\) | −84.6289 | −0.00916937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10568.4 | −1.13730 | ||||||||
\(443\) | 10115.5 | 1.08488 | 0.542438 | − | 0.840096i | \(-0.317501\pi\) | ||||
0.542438 | + | 0.840096i | \(0.317501\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7208.73 | 0.767925 | ||||||||
\(446\) | −5667.05 | −0.601665 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2016.51 | 0.212659 | ||||||||
\(449\) | −14386.0 | −1.51207 | −0.756034 | − | 0.654532i | \(-0.772866\pi\) | ||||
−0.756034 | + | 0.654532i | \(0.772866\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 114.526 | 0.0119574 | ||||||||
\(452\) | 196.154 | 0.0204121 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1151.83 | −0.119070 | ||||||||
\(455\) | −2927.26 | −0.301609 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10031.8 | −1.02684 | −0.513421 | − | 0.858137i | \(-0.671622\pi\) | ||||
−0.513421 | + | 0.858137i | \(0.671622\pi\) | |||||||
\(458\) | 2364.96 | 0.241282 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3249.20 | 0.329336 | ||||||||
\(461\) | 124.788 | 0.0126072 | 0.00630362 | − | 0.999980i | \(-0.497993\pi\) | ||||
0.00630362 | + | 0.999980i | \(0.497993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15438.9 | 1.54969 | 0.774847 | − | 0.632148i | \(-0.217827\pi\) | ||||
0.774847 | + | 0.632148i | \(0.217827\pi\) | |||||||
\(464\) | 22564.3 | 2.25759 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21677.0 | 2.15486 | ||||||||
\(467\) | 12014.7 | 1.19052 | 0.595259 | − | 0.803534i | \(-0.297049\pi\) | ||||
0.595259 | + | 0.803534i | \(0.297049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 158.963 | 0.0156508 | ||||||||
\(470\) | −12940.1 | −1.26996 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6923.00 | 0.675121 | ||||||||
\(473\) | 25.7044 | 0.00249871 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1259.90 | 0.121701 | ||||||||
\(476\) | −2685.83 | −0.258623 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8489.93 | 0.812386 | ||||||||
\(479\) | −6241.39 | −0.595358 | −0.297679 | − | 0.954666i | \(-0.596212\pi\) | ||||
−0.297679 | + | 0.954666i | \(0.596212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12683.4 | 1.20231 | ||||||||
\(482\) | −15435.2 | −1.45862 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3973.65 | −0.373183 | ||||||||
\(485\) | 2207.03 | 0.206631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 924.180 | 0.0859930 | 0.0429965 | − | 0.999075i | \(-0.486310\pi\) | ||||
0.0429965 | + | 0.999075i | \(0.486310\pi\) | |||||||
\(488\) | 514.130 | 0.0476917 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6948.44 | 0.640609 | ||||||||
\(491\) | 7044.15 | 0.647451 | 0.323725 | − | 0.946151i | \(-0.395065\pi\) | ||||
0.323725 | + | 0.946151i | \(0.395065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26102.3 | 2.38457 | ||||||||
\(494\) | −2780.18 | −0.253211 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15217.9 | 1.37763 | ||||||||
\(497\) | 2160.60 | 0.195003 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3981.76 | −0.357210 | −0.178605 | − | 0.983921i | \(-0.557158\pi\) | ||||
−0.178605 | + | 0.983921i | \(0.557158\pi\) | |||||||
\(500\) | 4513.74 | 0.403722 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −20232.2 | −1.79882 | ||||||||
\(503\) | 11650.2 | 1.03272 | 0.516358 | − | 0.856373i | \(-0.327288\pi\) | ||||
0.516358 | + | 0.856373i | \(0.327288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10069.7 | −0.887318 | ||||||||
\(506\) | 253.057 | 0.0222327 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5694.58 | −0.497354 | ||||||||
\(509\) | −11408.7 | −0.993481 | −0.496740 | − | 0.867899i | \(-0.665470\pi\) | ||||
−0.496740 | + | 0.867899i | \(0.665470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10150.9 | 0.878764 | ||||||||
\(512\) | −326.513 | −0.0281836 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2261.98 | −0.194108 | ||||||||
\(515\) | −2722.41 | −0.232939 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −273.941 | −0.0233035 | ||||||||
\(518\) | 11858.4 | 1.00584 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4941.19 | 0.416703 | ||||||||
\(521\) | −15272.4 | −1.28425 | −0.642127 | − | 0.766598i | \(-0.721948\pi\) | ||||
−0.642127 | + | 0.766598i | \(0.721948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20831.4 | −1.74167 | −0.870835 | − | 0.491575i | \(-0.836421\pi\) | ||||
−0.870835 | + | 0.491575i | \(0.836421\pi\) | |||||||
\(524\) | 4587.16 | 0.382426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5541.50 | −0.459355 | ||||||||
\(527\) | 17604.0 | 1.45511 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4145.03 | 0.340678 | ||||||||
\(530\) | −16464.1 | −1.34935 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −706.548 | −0.0575803 | ||||||||
\(533\) | −6686.75 | −0.543406 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14032.1 | 1.13395 | ||||||||
\(536\) | −268.328 | −0.0216232 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 868.410 | 0.0695907 | ||||||||
\(539\) | 147.098 | 0.0117550 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1411.76 | −0.112192 | −0.0560962 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560962 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(542\) | 15313.4 | 1.21359 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11767.6 | 0.927450 | ||||||||
\(545\) | 4775.27 | 0.375322 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −328.281 | −0.0256605 | −0.0128302 | − | 0.999918i | \(-0.504084\pi\) | ||||
−0.0128302 | + | 0.999918i | \(0.504084\pi\) | |||||||
\(548\) | 5062.84 | 0.394661 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 103.873 | 0.00805301 | ||||||||
\(551\) | 6866.62 | 0.530903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4385.34 | 0.337222 | ||||||||
\(554\) | 17116.1 | 1.31262 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2829.73 | 0.215840 | ||||||||
\(557\) | 1908.49 | 0.145180 | 0.0725901 | − | 0.997362i | \(-0.476874\pi\) | ||||
0.0725901 | + | 0.997362i | \(0.476874\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1500.79 | −0.113554 | ||||||||
\(560\) | 6623.46 | 0.499808 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17486.5 | 1.31250 | ||||||||
\(563\) | −3413.23 | −0.255507 | −0.127753 | − | 0.991806i | \(-0.540777\pi\) | ||||
−0.127753 | + | 0.991806i | \(0.540777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −559.579 | −0.0416667 | ||||||||
\(566\) | −16666.7 | −1.23773 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3647.07 | −0.269415 | ||||||||
\(569\) | 15405.8 | 1.13505 | 0.567527 | − | 0.823355i | \(-0.307900\pi\) | ||||
0.567527 | + | 0.823355i | \(0.307900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18819.2 | 1.37926 | 0.689632 | − | 0.724160i | \(-0.257772\pi\) | ||||
0.689632 | + | 0.724160i | \(0.257772\pi\) | |||||||
\(572\) | −62.3044 | −0.00455433 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6251.81 | −0.454609 | ||||||||
\(575\) | 6695.64 | 0.485613 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8098.53 | 0.584309 | 0.292154 | − | 0.956371i | \(-0.405628\pi\) | ||||
0.292154 | + | 0.956371i | \(0.405628\pi\) | |||||||
\(578\) | 11378.1 | 0.818799 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7268.90 | 0.520387 | ||||||||
\(581\) | −2938.84 | −0.209852 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −348.545 | −0.0247603 | ||||||||
\(584\) | −17134.6 | −1.21410 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29303.0 | −2.06569 | ||||||||
\(587\) | 3631.44 | 0.255342 | 0.127671 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127671 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4631.00 | 0.323968 | ||||||||
\(590\) | 11763.2 | 0.820822 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28698.4 | −1.99240 | ||||||||
\(593\) | 14298.2 | 0.990147 | 0.495073 | − | 0.868851i | \(-0.335141\pi\) | ||||
0.495073 | + | 0.868851i | \(0.335141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7662.02 | 0.527920 | ||||||||
\(596\) | −9209.95 | −0.632977 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14775.1 | −1.01037 | ||||||||
\(599\) | 27823.6 | 1.89790 | 0.948949 | − | 0.315430i | \(-0.102149\pi\) | ||||
0.948949 | + | 0.315430i | \(0.102149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3557.15 | 0.241430 | 0.120715 | − | 0.992687i | \(-0.461481\pi\) | ||||
0.120715 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(602\) | −1403.17 | −0.0949982 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7008.25 | −0.472122 | ||||||||
\(605\) | 11335.9 | 0.761767 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19170.9 | 1.28192 | 0.640958 | − | 0.767576i | \(-0.278537\pi\) | ||||
0.640958 | + | 0.767576i | \(0.278537\pi\) | |||||||
\(608\) | 3095.65 | 0.206489 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 873.585 | 0.0579843 | ||||||||
\(611\) | 15994.5 | 1.05903 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4287.83 | 0.282518 | 0.141259 | − | 0.989973i | \(-0.454885\pi\) | ||||
0.141259 | + | 0.989973i | \(0.454885\pi\) | |||||||
\(614\) | 21760.6 | 1.43027 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 97.8006 | 0.00639692 | ||||||||
\(617\) | 10569.5 | 0.689649 | 0.344824 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344824 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19947.5 | 1.29525 | 0.647624 | − | 0.761960i | \(-0.275763\pi\) | ||||
0.647624 | + | 0.761960i | \(0.275763\pi\) | |||||||
\(620\) | 4902.31 | 0.317551 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4144.21 | −0.267150 | ||||||||
\(623\) | −8330.71 | −0.535735 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6323.50 | −0.404704 | ||||||||
\(626\) | −9840.42 | −0.628278 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4726.44 | 0.300328 | ||||||||
\(629\) | −33198.3 | −2.10446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8854.29 | 0.558611 | 0.279306 | − | 0.960202i | \(-0.409896\pi\) | ||||
0.279306 | + | 0.960202i | \(0.409896\pi\) | |||||||
\(632\) | −7402.41 | −0.465905 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3494.60 | −0.218909 | ||||||||
\(635\) | 16245.3 | 1.01523 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8588.55 | −0.534208 | ||||||||
\(638\) | 566.122 | 0.0351301 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14562.5 | −0.899429 | ||||||||
\(641\) | −10022.5 | −0.617571 | −0.308786 | − | 0.951132i | \(-0.599923\pi\) | ||||
−0.308786 | + | 0.951132i | \(0.599923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5806.52 | −0.356123 | −0.178061 | − | 0.984019i | \(-0.556983\pi\) | ||||
−0.178061 | + | 0.984019i | \(0.556983\pi\) | |||||||
\(644\) | −3754.91 | −0.229758 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7277.04 | 0.443206 | ||||||||
\(647\) | −8583.93 | −0.521591 | −0.260795 | − | 0.965394i | \(-0.583985\pi\) | ||||
−0.260795 | + | 0.965394i | \(0.583985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 249.027 | 0.0150619 | ||||||||
\(650\) | −6064.77 | −0.365969 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2451.39 | −0.147245 | ||||||||
\(653\) | −17048.8 | −1.02170 | −0.510849 | − | 0.859670i | \(-0.670669\pi\) | ||||
−0.510849 | + | 0.859670i | \(0.670669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13086.1 | −0.780633 | ||||||||
\(656\) | 15130.0 | 0.900499 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14954.1 | 0.885974 | ||||||||
\(659\) | 2694.69 | 0.159287 | 0.0796437 | − | 0.996823i | \(-0.474622\pi\) | ||||
0.0796437 | + | 0.996823i | \(0.474622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29666.8 | −1.74570 | −0.872848 | − | 0.487992i | \(-0.837730\pi\) | ||||
−0.872848 | + | 0.487992i | \(0.837730\pi\) | |||||||
\(662\) | −9551.64 | −0.560778 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4960.74 | 0.289931 | ||||||||
\(665\) | 2015.61 | 0.117537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36492.2 | 2.11842 | ||||||||
\(668\) | −5048.52 | −0.292415 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −455.931 | −0.0262898 | ||||||||
\(671\) | 18.4938 | 0.00106400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17932.8 | 1.02713 | 0.513564 | − | 0.858051i | \(-0.328325\pi\) | ||||
0.513564 | + | 0.858051i | \(0.328325\pi\) | |||||||
\(674\) | −20377.1 | −1.16454 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2923.09 | −0.166312 | ||||||||
\(677\) | −2440.74 | −0.138560 | −0.0692801 | − | 0.997597i | \(-0.522070\pi\) | ||||
−0.0692801 | + | 0.997597i | \(0.522070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2550.53 | −0.144154 | ||||||||
\(680\) | −12933.4 | −0.729373 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 381.806 | 0.0214371 | ||||||||
\(683\) | 12722.2 | 0.712737 | 0.356369 | − | 0.934345i | \(-0.384015\pi\) | ||||
0.356369 | + | 0.934345i | \(0.384015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14443.1 | −0.805608 | ||||||||
\(686\) | −19222.6 | −1.06986 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3395.81 | 0.188175 | ||||||||
\(689\) | 20350.3 | 1.12523 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5584.80 | −0.307461 | −0.153731 | − | 0.988113i | \(-0.549129\pi\) | ||||
−0.153731 | + | 0.988113i | \(0.549129\pi\) | |||||||
\(692\) | −4151.64 | −0.228066 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4655.02 | −0.254614 | ||||||||
\(695\) | −8072.53 | −0.440588 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17502.4 | 0.951148 | ||||||||
\(698\) | −14823.1 | −0.803817 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1541.29 | −0.0832217 | ||||||||
\(701\) | −19891.2 | −1.07173 | −0.535864 | − | 0.844304i | \(-0.680014\pi\) | ||||
−0.535864 | + | 0.844304i | \(0.680014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8733.33 | −0.468540 | ||||||||
\(704\) | −122.440 | −0.00655486 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7114.62 | −0.379266 | ||||||||
\(707\) | 11637.0 | 0.619028 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14613.5 | −0.774078 | −0.387039 | − | 0.922063i | \(-0.626502\pi\) | ||||
−0.387039 | + | 0.922063i | \(0.626502\pi\) | |||||||
\(710\) | −6196.94 | −0.327559 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14062.1 | 0.740170 | ||||||||
\(713\) | 24611.2 | 1.29270 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 177.739 | 0.00929661 | ||||||||
\(716\) | −2072.16 | −0.108157 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6498.14 | −0.337755 | ||||||||
\(719\) | 11027.7 | 0.571995 | 0.285998 | − | 0.958230i | \(-0.407675\pi\) | ||||
0.285998 | + | 0.958230i | \(0.407675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3146.13 | 0.162508 | ||||||||
\(722\) | −20820.2 | −1.07320 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7034.15 | −0.361080 | ||||||||
\(725\) | 14979.1 | 0.767322 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1650.84 | 0.0842178 | 0.0421089 | − | 0.999113i | \(-0.486592\pi\) | ||||
0.0421089 | + | 0.999113i | \(0.486592\pi\) | |||||||
\(728\) | −5710.24 | −0.290708 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29114.3 | −1.47612 | ||||||||
\(731\) | 3928.27 | 0.198758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28314.8 | −1.42678 | −0.713391 | − | 0.700767i | \(-0.752841\pi\) | ||||
−0.713391 | + | 0.700767i | \(0.752841\pi\) | |||||||
\(734\) | 44697.4 | 2.24770 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16451.7 | 0.823935 | ||||||||
\(737\) | −9.65204 | −0.000482412 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28963.4 | −1.44172 | −0.720862 | − | 0.693078i | \(-0.756254\pi\) | ||||
−0.720862 | + | 0.693078i | \(0.756254\pi\) | |||||||
\(740\) | −9244.97 | −0.459259 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19026.6 | 0.941359 | ||||||||
\(743\) | 15510.4 | 0.765844 | 0.382922 | − | 0.923781i | \(-0.374918\pi\) | ||||
0.382922 | + | 0.923781i | \(0.374918\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26273.8 | 1.29208 | ||||||||
\(746\) | −39889.0 | −1.95769 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 163.080 | 0.00797165 | ||||||||
\(749\) | −16216.1 | −0.791087 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2901.63 | −0.140988 | −0.0704941 | − | 0.997512i | \(-0.522458\pi\) | ||||
−0.0704941 | + | 0.997512i | \(0.522458\pi\) | |||||||
\(752\) | −36190.4 | −1.75496 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −33053.9 | −1.59649 | ||||||||
\(755\) | 19992.8 | 0.963727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9260.00 | 0.444598 | 0.222299 | − | 0.974979i | \(-0.428644\pi\) | ||||
0.222299 | + | 0.974979i | \(0.428644\pi\) | |||||||
\(758\) | −33759.2 | −1.61766 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3402.33 | −0.162389 | ||||||||
\(761\) | 6418.29 | 0.305733 | 0.152866 | − | 0.988247i | \(-0.451150\pi\) | ||||
0.152866 | + | 0.988247i | \(0.451150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5518.50 | −0.261839 | ||||||||
\(764\) | 6474.50 | 0.306596 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −44773.9 | −2.11194 | ||||||||
\(767\) | −14539.8 | −0.684489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5335.88 | 0.250217 | 0.125108 | − | 0.992143i | \(-0.460072\pi\) | ||||
0.125108 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(770\) | 166.178 | 0.00777746 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3897.09 | 0.181683 | ||||||||
\(773\) | −20062.9 | −0.933520 | −0.466760 | − | 0.884384i | \(-0.654579\pi\) | ||||
−0.466760 | + | 0.884384i | \(0.654579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10102.2 | 0.468236 | ||||||||
\(776\) | 4305.27 | 0.199162 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22046.8 | 1.01596 | ||||||||
\(779\) | 4604.26 | 0.211765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −131.189 | −0.00601064 | ||||||||
\(782\) | 38673.4 | 1.76849 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19433.2 | 0.885257 | ||||||||
\(785\) | −13483.4 | −0.613049 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17182.2 | 0.778248 | 0.389124 | − | 0.921185i | \(-0.372778\pi\) | ||||
0.389124 | + | 0.921185i | \(0.372778\pi\) | |||||||
\(788\) | 14334.9 | 0.648045 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12577.8 | −0.566454 | ||||||||
\(791\) | 646.672 | 0.0290683 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1079.79 | −0.0483535 | ||||||||
\(794\) | −27538.3 | −1.23085 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6310.99 | −0.281014 | ||||||||
\(797\) | 3342.90 | 0.148572 | 0.0742859 | − | 0.997237i | \(-0.476332\pi\) | ||||
0.0742859 | + | 0.997237i | \(0.476332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41865.0 | −1.85366 | ||||||||
\(800\) | 6752.95 | 0.298441 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9822.90 | −0.432492 | ||||||||
\(803\) | −616.348 | −0.0270865 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10711.8 | 0.468997 | ||||||||
\(806\) | −22292.3 | −0.974210 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19643.1 | −0.855248 | ||||||||
\(809\) | 10782.5 | 0.468596 | 0.234298 | − | 0.972165i | \(-0.424721\pi\) | ||||
0.234298 | + | 0.972165i | \(0.424721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22440.1 | −0.971612 | −0.485806 | − | 0.874067i | \(-0.661474\pi\) | ||||
−0.485806 | + | 0.874067i | \(0.661474\pi\) | |||||||
\(812\) | −8400.24 | −0.363043 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −720.024 | −0.0310035 | ||||||||
\(815\) | 6993.21 | 0.300566 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1033.39 | 0.0442519 | ||||||||
\(818\) | −32984.1 | −1.40985 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4874.01 | 0.207570 | ||||||||
\(821\) | 10938.7 | 0.464996 | 0.232498 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232498 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37928.5 | −1.60645 | −0.803223 | − | 0.595678i | \(-0.796883\pi\) | ||||
−0.803223 | + | 0.595678i | \(0.796883\pi\) | |||||||
\(824\) | −5310.63 | −0.224520 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13594.1 | −0.572637 | ||||||||
\(827\) | −36038.1 | −1.51532 | −0.757660 | − | 0.652650i | \(-0.773657\pi\) | ||||
−0.757660 | + | 0.652650i | \(0.773657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29221.5 | 1.22425 | 0.612127 | − | 0.790760i | \(-0.290314\pi\) | ||||
0.612127 | + | 0.790760i | \(0.290314\pi\) | |||||||
\(830\) | 8429.05 | 0.352502 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7148.82 | 0.297886 | ||||||||
\(833\) | 22480.3 | 0.935048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14402.2 | 0.596896 | ||||||||
\(836\) | 42.9006 | 0.00177482 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17506.5 | −0.721660 | ||||||||
\(839\) | 6285.44 | 0.258638 | 0.129319 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129319 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57249.1 | 2.34733 | ||||||||
\(842\) | −5530.48 | −0.226357 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16616.5 | 0.677682 | ||||||||
\(845\) | 8338.87 | 0.339486 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13100.2 | −0.531438 | ||||||||
\(848\) | −46046.3 | −1.86466 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15874.4 | 0.640572 | ||||||||
\(851\) | −46412.8 | −1.86958 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35129.3 | −1.41009 | −0.705044 | − | 0.709164i | \(-0.749073\pi\) | ||||
−0.705044 | + | 0.709164i | \(0.749073\pi\) | |||||||
\(854\) | −1009.55 | −0.0404521 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27372.6 | 1.09296 | ||||||||
\(857\) | −32983.7 | −1.31470 | −0.657352 | − | 0.753584i | \(-0.728324\pi\) | ||||
−0.657352 | + | 0.753584i | \(0.728324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35152.9 | −1.39628 | −0.698139 | − | 0.715962i | \(-0.745988\pi\) | ||||
−0.698139 | + | 0.715962i | \(0.745988\pi\) | |||||||
\(860\) | 1093.93 | 0.0433753 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34301.4 | 1.35535 | ||||||||
\(863\) | −24925.6 | −0.983173 | −0.491587 | − | 0.870829i | \(-0.663583\pi\) | ||||
−0.491587 | + | 0.870829i | \(0.663583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11843.6 | 0.465544 | ||||||||
\(866\) | 9838.48 | 0.386057 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5665.31 | −0.221536 | ||||||||
\(869\) | −266.272 | −0.0103943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 563.549 | 0.0219232 | ||||||||
\(872\) | 9315.17 | 0.361756 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10173.6 | 0.393739 | ||||||||
\(875\) | 14880.8 | 0.574927 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2057.63 | 0.0792261 | 0.0396131 | − | 0.999215i | \(-0.487387\pi\) | ||||
0.0396131 | + | 0.999215i | \(0.487387\pi\) | |||||||
\(878\) | −30575.2 | −1.17524 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −402.168 | −0.0154058 | ||||||||
\(881\) | −17912.5 | −0.685004 | −0.342502 | − | 0.939517i | \(-0.611274\pi\) | ||||
−0.342502 | + | 0.939517i | \(0.611274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27215.2 | −1.03722 | −0.518610 | − | 0.855011i | \(-0.673550\pi\) | ||||
−0.518610 | + | 0.855011i | \(0.673550\pi\) | |||||||
\(884\) | −9521.67 | −0.362272 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33528.2 | 1.27133 | ||||||||
\(887\) | −25313.0 | −0.958206 | −0.479103 | − | 0.877759i | \(-0.659038\pi\) | ||||
−0.479103 | + | 0.877759i | \(0.659038\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18773.7 | −0.708267 | ||||||||
\(890\) | 23893.7 | 0.899910 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5105.76 | −0.191652 | ||||||||
\(893\) | −11013.2 | −0.412703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5911.36 | 0.220777 | ||||||||
\(896\) | 16829.1 | 0.627477 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47683.3 | −1.77195 | ||||||||
\(899\) | 55058.6 | 2.04261 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53266.3 | −1.96954 | ||||||||
\(902\) | 379.601 | 0.0140126 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1091.58 | −0.0401607 | ||||||||
\(905\) | 20066.7 | 0.737062 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45998.9 | 1.68398 | 0.841989 | − | 0.539495i | \(-0.181385\pi\) | ||||
0.841989 | + | 0.539495i | \(0.181385\pi\) | |||||||
\(908\) | −1037.75 | −0.0379282 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9702.57 | −0.353447 | ||||||||
\(911\) | 46592.7 | 1.69449 | 0.847247 | − | 0.531199i | \(-0.178258\pi\) | ||||
0.847247 | + | 0.531199i | \(0.178258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 178.443 | 0.00646833 | ||||||||
\(914\) | −33250.9 | −1.20333 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2130.72 | 0.0768571 | ||||||||
\(917\) | 15122.8 | 0.544601 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33168.1 | 1.19055 | 0.595274 | − | 0.803523i | \(-0.297043\pi\) | ||||
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(920\) | −18081.5 | −0.647966 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 413.615 | 0.0147741 | ||||||||
\(923\) | 7659.66 | 0.273154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19051.2 | −0.677188 | ||||||||
\(926\) | 51173.2 | 1.81604 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36804.6 | 1.30191 | ||||||||
\(929\) | −19909.9 | −0.703148 | −0.351574 | − | 0.936160i | \(-0.614353\pi\) | ||||
−0.351574 | + | 0.936160i | \(0.614353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5913.78 | 0.208181 | ||||||||
\(932\) | 19530.0 | 0.686401 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39823.2 | 1.39514 | ||||||||
\(935\) | −465.228 | −0.0162723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26262.2 | 0.915634 | 0.457817 | − | 0.889046i | \(-0.348631\pi\) | ||||
0.457817 | + | 0.889046i | \(0.348631\pi\) | |||||||
\(938\) | 526.893 | 0.0183408 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11658.4 | −0.404528 | ||||||||
\(941\) | −42227.8 | −1.46290 | −0.731449 | − | 0.681896i | \(-0.761155\pi\) | ||||
−0.731449 | + | 0.681896i | \(0.761155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24469.1 | 0.844988 | ||||||||
\(944\) | 32899.0 | 1.13429 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 85.1986 | 0.00292817 | ||||||||
\(947\) | 35227.0 | 1.20879 | 0.604394 | − | 0.796685i | \(-0.293415\pi\) | ||||
0.604394 | + | 0.796685i | \(0.293415\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35986.4 | 1.23095 | ||||||||
\(950\) | 4175.99 | 0.142618 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14946.4 | 0.508839 | ||||||||
\(953\) | −49209.9 | −1.67268 | −0.836340 | − | 0.548211i | \(-0.815309\pi\) | ||||
−0.836340 | + | 0.548211i | \(0.815309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18470.2 | −0.625844 | ||||||||
\(956\) | 7649.06 | 0.258774 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20687.4 | −0.697683 | ||||||||
\(959\) | 16691.0 | 0.562024 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7341.79 | 0.246443 | ||||||||
\(962\) | 42039.7 | 1.40895 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13906.4 | −0.464623 | ||||||||
\(965\) | −11117.5 | −0.370864 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13452.5 | 0.447366 | 0.223683 | − | 0.974662i | \(-0.428192\pi\) | ||||
0.223683 | + | 0.974662i | \(0.428192\pi\) | |||||||
\(968\) | 22113.0 | 0.734234 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7315.30 | 0.242145 | ||||||||
\(971\) | −37322.8 | −1.23352 | −0.616758 | − | 0.787152i | \(-0.711554\pi\) | ||||
−0.616758 | + | 0.787152i | \(0.711554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9328.95 | 0.307371 | ||||||||
\(974\) | 3063.24 | 0.100773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2443.21 | 0.0801285 | ||||||||
\(977\) | 45153.4 | 1.47859 | 0.739297 | − | 0.673380i | \(-0.235158\pi\) | ||||
0.739297 | + | 0.673380i | \(0.235158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 505.829 | 0.0165132 | ||||||||
\(980\) | 6260.24 | 0.204057 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23348.2 | 0.758729 | ||||||||
\(983\) | 15802.7 | 0.512745 | 0.256372 | − | 0.966578i | \(-0.417473\pi\) | ||||
0.256372 | + | 0.966578i | \(0.417473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40894.0 | −1.32283 | ||||||||
\(986\) | 86517.6 | 2.79440 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2504.82 | −0.0806568 | ||||||||
\(989\) | 5491.90 | 0.176575 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27570.0 | 0.883744 | 0.441872 | − | 0.897078i | \(-0.354315\pi\) | ||||
0.441872 | + | 0.897078i | \(0.354315\pi\) | |||||||
\(992\) | 24821.9 | 0.794451 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7161.43 | 0.228518 | ||||||||
\(995\) | 18003.7 | 0.573624 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14969.8 | −0.475526 | −0.237763 | − | 0.971323i | \(-0.576414\pi\) | ||||
−0.237763 | + | 0.971323i | \(0.576414\pi\) | |||||||
\(998\) | −13197.7 | −0.418605 | ||||||||
\(999\) | 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 | 387.4.a.h.1.6 | 6 | ||
3.2 | odd | 2 | 43.4.a.b.1.1 | ✓ | 6 | ||
12.11 | even | 2 | 688.4.a.i.1.6 | 6 | |||
15.14 | odd | 2 | 1075.4.a.b.1.6 | 6 | |||
21.20 | even | 2 | 2107.4.a.c.1.1 | 6 | |||
129.128 | even | 2 | 1849.4.a.c.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.a.b.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
387.4.a.h.1.6 | 6 | 1.1 | even | 1 | trivial | ||
688.4.a.i.1.6 | 6 | 12.11 | even | 2 | |||
1075.4.a.b.1.6 | 6 | 15.14 | odd | 2 | |||
1849.4.a.c.1.6 | 6 | 129.128 | even | 2 | |||
2107.4.a.c.1.1 | 6 | 21.20 | even | 2 |