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 | 1.7 | ||
Root | \(-4.83218\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.03025 | 1.42491 | 0.712454 | − | 0.701719i | \(-0.247584\pi\) | ||||
0.712454 | + | 0.701719i | \(0.247584\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.24289 | 1.03036 | ||||||||
\(5\) | 8.08864 | 0.723470 | 0.361735 | − | 0.932281i | \(-0.382184\pi\) | ||||
0.361735 | + | 0.932281i | \(0.382184\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.95078 | −0.321312 | −0.160656 | − | 0.987010i | \(-0.551361\pi\) | ||||
−0.160656 | + | 0.987010i | \(0.551361\pi\) | |||||||
\(8\) | 0.978887 | 0.0432611 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 32.5992 | 1.03088 | ||||||||
\(11\) | 17.2359 | 0.472437 | 0.236219 | − | 0.971700i | \(-0.424092\pi\) | ||||
0.236219 | + | 0.971700i | \(0.424092\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −23.9831 | −0.457840 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −61.9979 | −0.968718 | ||||||||
\(17\) | −92.9299 | −1.32581 | −0.662907 | − | 0.748702i | \(-0.730677\pi\) | ||||
−0.662907 | + | 0.748702i | \(0.730677\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.3832 | −0.161596 | −0.0807979 | − | 0.996731i | \(-0.525747\pi\) | ||||
−0.0807979 | + | 0.996731i | \(0.525747\pi\) | |||||||
\(20\) | 66.6738 | 0.745435 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 69.4648 | 0.673179 | ||||||||
\(23\) | −219.710 | −1.99186 | −0.995930 | − | 0.0901293i | \(-0.971272\pi\) | ||||
−0.995930 | + | 0.0901293i | \(0.971272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −59.5738 | −0.476591 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −49.0516 | −0.331067 | ||||||||
\(29\) | 199.485 | 1.27736 | 0.638681 | − | 0.769471i | \(-0.279480\pi\) | ||||
0.638681 | + | 0.769471i | \(0.279480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −307.777 | −1.78317 | −0.891586 | − | 0.452851i | \(-0.850407\pi\) | ||||
−0.891586 | + | 0.452851i | \(0.850407\pi\) | |||||||
\(32\) | −257.698 | −1.42359 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −374.531 | −1.88916 | ||||||||
\(35\) | −48.1337 | −0.232460 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 333.777 | 1.48304 | 0.741521 | − | 0.670930i | \(-0.234105\pi\) | ||||
0.741521 | + | 0.670930i | \(0.234105\pi\) | |||||||
\(38\) | −53.9376 | −0.230259 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.91787 | 0.0312981 | ||||||||
\(41\) | −200.689 | −0.764446 | −0.382223 | − | 0.924070i | \(-0.624841\pi\) | ||||
−0.382223 | + | 0.924070i | \(0.624841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 116.806 | 0.414248 | 0.207124 | − | 0.978315i | \(-0.433590\pi\) | ||||
0.207124 | + | 0.978315i | \(0.433590\pi\) | |||||||
\(44\) | 142.073 | 0.486781 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −885.487 | −2.83822 | ||||||||
\(47\) | 338.610 | 1.05088 | 0.525440 | − | 0.850831i | \(-0.323901\pi\) | ||||
0.525440 | + | 0.850831i | \(0.323901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.588 | −0.896759 | ||||||||
\(50\) | −240.097 | −0.679097 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.6215 | 0.0689951 | 0.0344975 | − | 0.999405i | \(-0.489017\pi\) | ||||
0.0344975 | + | 0.999405i | \(0.489017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 139.415 | 0.341794 | ||||||||
\(56\) | −5.82514 | −0.0139003 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 803.976 | 1.82012 | ||||||||
\(59\) | −280.058 | −0.617973 | −0.308987 | − | 0.951066i | \(-0.599990\pi\) | ||||
−0.308987 | + | 0.951066i | \(0.599990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −207.084 | −0.434663 | −0.217332 | − | 0.976098i | \(-0.569735\pi\) | ||||
−0.217332 | + | 0.976098i | \(0.569735\pi\) | |||||||
\(62\) | −1240.42 | −2.54086 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −542.603 | −1.05977 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 285.981 | 0.521465 | 0.260732 | − | 0.965411i | \(-0.416036\pi\) | ||||
0.260732 | + | 0.965411i | \(0.416036\pi\) | |||||||
\(68\) | −766.011 | −1.36607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −193.991 | −0.331233 | ||||||||
\(71\) | −317.673 | −0.530998 | −0.265499 | − | 0.964111i | \(-0.585537\pi\) | ||||
−0.265499 | + | 0.964111i | \(0.585537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.0668 | 0.101115 | 0.0505576 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505576 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(74\) | 1345.20 | 2.11320 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −110.316 | −0.166502 | ||||||||
\(77\) | −102.567 | −0.151800 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −623.835 | −0.888443 | −0.444221 | − | 0.895917i | \(-0.646520\pi\) | ||||
−0.444221 | + | 0.895917i | \(0.646520\pi\) | |||||||
\(80\) | −501.479 | −0.700838 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −808.824 | −1.08926 | ||||||||
\(83\) | 659.874 | 0.872658 | 0.436329 | − | 0.899787i | \(-0.356278\pi\) | ||||
0.436329 | + | 0.899787i | \(0.356278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −751.677 | −0.959186 | ||||||||
\(86\) | 470.755 | 0.590265 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.8720 | 0.0204382 | ||||||||
\(89\) | 1273.19 | 1.51638 | 0.758191 | − | 0.652032i | \(-0.226083\pi\) | ||||
0.758191 | + | 0.652032i | \(0.226083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1811.05 | −2.05233 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1364.68 | 1.49741 | ||||||||
\(95\) | −108.252 | −0.116910 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −603.746 | −0.631970 | −0.315985 | − | 0.948764i | \(-0.602335\pi\) | ||||
−0.315985 | + | 0.948764i | \(0.602335\pi\) | |||||||
\(98\) | −1239.66 | −1.27780 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −491.060 | −0.491060 | ||||||||
\(101\) | 740.588 | 0.729616 | 0.364808 | − | 0.931083i | \(-0.381135\pi\) | ||||
0.364808 | + | 0.931083i | \(0.381135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1888.57 | −1.80666 | −0.903332 | − | 0.428942i | \(-0.858887\pi\) | ||||
−0.903332 | + | 0.428942i | \(0.858887\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 107.291 | 0.0983116 | ||||||||
\(107\) | 919.463 | 0.830728 | 0.415364 | − | 0.909655i | \(-0.363654\pi\) | ||||
0.415364 | + | 0.909655i | \(0.363654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1570.40 | −1.37998 | −0.689988 | − | 0.723821i | \(-0.742384\pi\) | ||||
−0.689988 | + | 0.723821i | \(0.742384\pi\) | |||||||
\(110\) | 561.876 | 0.487025 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 368.936 | 0.311260 | ||||||||
\(113\) | 1324.66 | 1.10277 | 0.551386 | − | 0.834250i | \(-0.314099\pi\) | ||||
0.551386 | + | 0.834250i | \(0.314099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1777.16 | −1.44105 | ||||||||
\(116\) | 1644.34 | 1.31614 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1128.70 | −0.880555 | ||||||||
\(119\) | 553.006 | 0.426000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1033.92 | −0.776803 | ||||||||
\(122\) | −834.601 | −0.619354 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2536.97 | −1.83731 | ||||||||
\(125\) | −1492.95 | −1.06827 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2350.39 | −1.64223 | −0.821115 | − | 0.570763i | \(-0.806648\pi\) | ||||
−0.821115 | + | 0.570763i | \(0.806648\pi\) | |||||||
\(128\) | −125.240 | −0.0864824 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2308.69 | −1.53978 | −0.769890 | − | 0.638177i | \(-0.779689\pi\) | ||||
−0.769890 | + | 0.638177i | \(0.779689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 79.6405 | 0.0519226 | ||||||||
\(134\) | 1152.57 | 0.743039 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −90.9680 | −0.0573562 | ||||||||
\(137\) | −374.912 | −0.233802 | −0.116901 | − | 0.993144i | \(-0.537296\pi\) | ||||
−0.116901 | + | 0.993144i | \(0.537296\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 487.711 | 0.297605 | 0.148802 | − | 0.988867i | \(-0.452458\pi\) | ||||
0.148802 | + | 0.988867i | \(0.452458\pi\) | |||||||
\(140\) | −396.761 | −0.239517 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1280.30 | −0.756623 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1613.57 | 0.924134 | ||||||||
\(146\) | 254.175 | 0.144080 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2751.28 | 1.52807 | ||||||||
\(149\) | 1055.91 | 0.580558 | 0.290279 | − | 0.956942i | \(-0.406252\pi\) | ||||
0.290279 | + | 0.956942i | \(0.406252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 888.560 | 0.478874 | 0.239437 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239437 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(152\) | −13.1007 | −0.00699081 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −413.370 | −0.216301 | ||||||||
\(155\) | −2489.50 | −1.29007 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3648.56 | −1.85469 | −0.927346 | − | 0.374206i | \(-0.877915\pi\) | ||||
−0.927346 | + | 0.374206i | \(0.877915\pi\) | |||||||
\(158\) | −2514.21 | −1.26595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2084.43 | −1.02993 | ||||||||
\(161\) | 1307.45 | 0.640008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1386.49 | −0.666249 | −0.333125 | − | 0.942883i | \(-0.608103\pi\) | ||||
−0.333125 | + | 0.942883i | \(0.608103\pi\) | |||||||
\(164\) | −1654.25 | −0.787655 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2659.46 | 1.24346 | ||||||||
\(167\) | −3376.19 | −1.56442 | −0.782209 | − | 0.623017i | \(-0.785907\pi\) | ||||
−0.782209 | + | 0.623017i | \(0.785907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3029.44 | −1.36675 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 962.815 | 0.426825 | ||||||||
\(173\) | −341.817 | −0.150219 | −0.0751095 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751095 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 354.511 | 0.153134 | ||||||||
\(176\) | −1068.59 | −0.457658 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5131.28 | 2.16070 | ||||||||
\(179\) | 2885.55 | 1.20489 | 0.602446 | − | 0.798159i | \(-0.294193\pi\) | ||||
0.602446 | + | 0.798159i | \(0.294193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3795.62 | 1.55871 | 0.779354 | − | 0.626584i | \(-0.215547\pi\) | ||||
0.779354 | + | 0.626584i | \(0.215547\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −215.072 | −0.0861701 | ||||||||
\(185\) | 2699.80 | 1.07294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1601.73 | −0.626363 | ||||||||
\(188\) | 2791.12 | 1.08278 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −436.282 | −0.166586 | ||||||||
\(191\) | 2805.90 | 1.06297 | 0.531486 | − | 0.847067i | \(-0.321634\pi\) | ||||
0.531486 | + | 0.847067i | \(0.321634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2485.64 | 0.927048 | 0.463524 | − | 0.886084i | \(-0.346585\pi\) | ||||
0.463524 | + | 0.886084i | \(0.346585\pi\) | |||||||
\(194\) | −2433.24 | −0.900499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2535.41 | −0.923985 | ||||||||
\(197\) | 2750.70 | 0.994818 | 0.497409 | − | 0.867516i | \(-0.334285\pi\) | ||||
0.497409 | + | 0.867516i | \(0.334285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3998.53 | 1.42436 | 0.712182 | − | 0.701994i | \(-0.247707\pi\) | ||||
0.712182 | + | 0.701994i | \(0.247707\pi\) | |||||||
\(200\) | −58.3161 | −0.0206178 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2984.75 | 1.03964 | ||||||||
\(203\) | −1187.09 | −0.410432 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1623.30 | −0.553054 | ||||||||
\(206\) | −7611.41 | −2.57433 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −230.671 | −0.0763438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1375.80 | −0.448882 | −0.224441 | − | 0.974488i | \(-0.572056\pi\) | ||||
−0.224441 | + | 0.974488i | \(0.572056\pi\) | |||||||
\(212\) | 219.438 | 0.0710898 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3705.66 | 1.18371 | ||||||||
\(215\) | 944.799 | 0.299696 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1831.51 | 0.572955 | ||||||||
\(218\) | −6329.12 | −1.96634 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1149.18 | 0.352171 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1694.37 | −0.508805 | −0.254403 | − | 0.967098i | \(-0.581879\pi\) | ||||
−0.254403 | + | 0.967098i | \(0.581879\pi\) | |||||||
\(224\) | 1533.50 | 0.457418 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5338.70 | 1.57135 | ||||||||
\(227\) | −405.400 | −0.118534 | −0.0592672 | − | 0.998242i | \(-0.518876\pi\) | ||||
−0.0592672 | + | 0.998242i | \(0.518876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2359.54 | −0.680884 | −0.340442 | − | 0.940265i | \(-0.610577\pi\) | ||||
−0.340442 | + | 0.940265i | \(0.610577\pi\) | |||||||
\(230\) | −7162.39 | −2.05337 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 195.274 | 0.0552601 | ||||||||
\(233\) | −938.507 | −0.263878 | −0.131939 | − | 0.991258i | \(-0.542120\pi\) | ||||
−0.131939 | + | 0.991258i | \(0.542120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2738.90 | 0.760280 | ||||||||
\(236\) | −2308.49 | −0.636736 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2228.75 | 0.607010 | ||||||||
\(239\) | 4664.25 | 1.26237 | 0.631183 | − | 0.775634i | \(-0.282570\pi\) | ||||
0.631183 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3774.94 | 1.00898 | 0.504492 | − | 0.863416i | \(-0.331680\pi\) | ||||
0.504492 | + | 0.863416i | \(0.331680\pi\) | |||||||
\(242\) | −4166.97 | −1.10687 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1706.97 | −0.447860 | ||||||||
\(245\) | −2487.97 | −0.648778 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −301.279 | −0.0771421 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6016.96 | −1.52219 | ||||||||
\(251\) | 960.695 | 0.241588 | 0.120794 | − | 0.992678i | \(-0.461456\pi\) | ||||
0.120794 | + | 0.992678i | \(0.461456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3786.90 | −0.941029 | ||||||||
\(254\) | −9472.64 | −2.34003 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3836.08 | 0.936542 | ||||||||
\(257\) | 16.7302 | 0.00406070 | 0.00203035 | − | 0.999998i | \(-0.499354\pi\) | ||||
0.00203035 | + | 0.999998i | \(0.499354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1986.23 | −0.476519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9304.58 | −2.19404 | ||||||||
\(263\) | 400.736 | 0.0939560 | 0.0469780 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469780 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 215.332 | 0.0499159 | ||||||||
\(266\) | 320.971 | 0.0739849 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2357.31 | 0.537297 | ||||||||
\(269\) | −2236.97 | −0.507027 | −0.253514 | − | 0.967332i | \(-0.581586\pi\) | ||||
−0.253514 | + | 0.967332i | \(0.581586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4018.89 | 0.900850 | 0.450425 | − | 0.892814i | \(-0.351273\pi\) | ||||
0.450425 | + | 0.892814i | \(0.351273\pi\) | |||||||
\(272\) | 5761.46 | 1.28434 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1510.99 | −0.333147 | ||||||||
\(275\) | −1026.81 | −0.225159 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6792.95 | 1.47346 | 0.736731 | − | 0.676186i | \(-0.236368\pi\) | ||||
0.736731 | + | 0.676186i | \(0.236368\pi\) | |||||||
\(278\) | 1965.59 | 0.424059 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −47.1175 | −0.0100565 | ||||||||
\(281\) | −7286.80 | −1.54695 | −0.773477 | − | 0.633824i | \(-0.781484\pi\) | ||||
−0.773477 | + | 0.633824i | \(0.781484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2429.77 | −0.510369 | −0.255185 | − | 0.966892i | \(-0.582136\pi\) | ||||
−0.255185 | + | 0.966892i | \(0.582136\pi\) | |||||||
\(284\) | −2618.54 | −0.547120 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1194.25 | 0.245626 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3722.97 | 0.757780 | ||||||||
\(290\) | 6503.07 | 1.31681 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 519.853 | 0.104185 | ||||||||
\(293\) | 4211.25 | 0.839672 | 0.419836 | − | 0.907600i | \(-0.362088\pi\) | ||||
0.419836 | + | 0.907600i | \(0.362088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2265.29 | −0.447085 | ||||||||
\(296\) | 326.730 | 0.0641580 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4255.56 | 0.827242 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −695.084 | −0.133103 | ||||||||
\(302\) | 3581.12 | 0.682351 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 829.731 | 0.156541 | ||||||||
\(305\) | −1675.03 | −0.314466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8212.27 | −1.52671 | −0.763353 | − | 0.645982i | \(-0.776448\pi\) | ||||
−0.763353 | + | 0.645982i | \(0.776448\pi\) | |||||||
\(308\) | −845.447 | −0.156408 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10033.3 | −1.83823 | ||||||||
\(311\) | 4238.55 | 0.772818 | 0.386409 | − | 0.922328i | \(-0.373715\pi\) | ||||
0.386409 | + | 0.922328i | \(0.373715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3807.82 | 0.687638 | 0.343819 | − | 0.939036i | \(-0.388279\pi\) | ||||
0.343819 | + | 0.939036i | \(0.388279\pi\) | |||||||
\(314\) | −14704.6 | −2.64276 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5142.20 | −0.915416 | ||||||||
\(317\) | −10497.7 | −1.85996 | −0.929981 | − | 0.367608i | \(-0.880177\pi\) | ||||
−0.929981 | + | 0.367608i | \(0.880177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3438.31 | 0.603474 | ||||||||
\(320\) | −4388.92 | −0.766713 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5269.34 | 0.911953 | ||||||||
\(323\) | 1243.70 | 0.214246 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5587.91 | −0.949343 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −196.452 | −0.0330708 | ||||||||
\(329\) | −2014.99 | −0.337660 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11905.2 | −1.97695 | −0.988474 | − | 0.151389i | \(-0.951625\pi\) | ||||
−0.988474 | + | 0.151389i | \(0.951625\pi\) | |||||||
\(332\) | 5439.27 | 0.899152 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13606.9 | −2.22915 | ||||||||
\(335\) | 2313.20 | 0.377264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8981.18 | 1.45174 | 0.725869 | − | 0.687833i | \(-0.241438\pi\) | ||||
0.725869 | + | 0.687833i | \(0.241438\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6195.99 | −0.988308 | ||||||||
\(341\) | −5304.80 | −0.842437 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3871.51 | 0.609451 | ||||||||
\(344\) | 114.339 | 0.0179208 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1377.61 | −0.214048 | ||||||||
\(347\) | 5712.87 | 0.883813 | 0.441906 | − | 0.897061i | \(-0.354302\pi\) | ||||
0.441906 | + | 0.897061i | \(0.354302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9507.28 | −1.45820 | −0.729102 | − | 0.684406i | \(-0.760062\pi\) | ||||
−0.729102 | + | 0.684406i | \(0.760062\pi\) | |||||||
\(350\) | 1428.77 | 0.218202 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4441.65 | −0.672559 | ||||||||
\(353\) | −3972.96 | −0.599035 | −0.299518 | − | 0.954091i | \(-0.596826\pi\) | ||||
−0.299518 | + | 0.954091i | \(0.596826\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2569.55 | −0.384162 | ||||||||
\(356\) | 10494.8 | 1.56242 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11629.5 | 1.71686 | ||||||||
\(359\) | −109.866 | −0.0161519 | −0.00807594 | − | 0.999967i | \(-0.502571\pi\) | ||||
−0.00807594 | + | 0.999967i | \(0.502571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6679.89 | −0.973887 | ||||||||
\(362\) | 15297.3 | 2.22101 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 510.125 | 0.0731539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7020.02 | 0.998480 | 0.499240 | − | 0.866464i | \(-0.333613\pi\) | ||||
0.499240 | + | 0.866464i | \(0.333613\pi\) | |||||||
\(368\) | 13621.6 | 1.92955 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10880.9 | 1.52884 | ||||||||
\(371\) | −158.418 | −0.0221689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2227.18 | 0.309166 | 0.154583 | − | 0.987980i | \(-0.450597\pi\) | ||||
0.154583 | + | 0.987980i | \(0.450597\pi\) | |||||||
\(374\) | −6455.36 | −0.892510 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 331.461 | 0.0454622 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11004.6 | 1.49147 | 0.745734 | − | 0.666244i | \(-0.232099\pi\) | ||||
0.745734 | + | 0.666244i | \(0.232099\pi\) | |||||||
\(380\) | −892.309 | −0.120459 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11308.5 | 1.51464 | ||||||||
\(383\) | −4436.85 | −0.591938 | −0.295969 | − | 0.955198i | \(-0.595643\pi\) | ||||
−0.295969 | + | 0.955198i | \(0.595643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −829.627 | −0.109823 | ||||||||
\(386\) | 10017.7 | 1.32096 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4976.61 | −0.651157 | ||||||||
\(389\) | 2561.58 | 0.333874 | 0.166937 | − | 0.985968i | \(-0.446612\pi\) | ||||
0.166937 | + | 0.985968i | \(0.446612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20417.7 | 2.64083 | ||||||||
\(392\) | −301.094 | −0.0387948 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11086.0 | 1.41752 | ||||||||
\(395\) | −5045.98 | −0.642762 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2206.90 | −0.278996 | −0.139498 | − | 0.990222i | \(-0.544549\pi\) | ||||
−0.139498 | + | 0.990222i | \(0.544549\pi\) | |||||||
\(398\) | 16115.1 | 2.02959 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3693.45 | 0.461682 | ||||||||
\(401\) | −8071.02 | −1.00511 | −0.502553 | − | 0.864546i | \(-0.667606\pi\) | ||||
−0.502553 | + | 0.864546i | \(0.667606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6104.58 | 0.751768 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4784.28 | −0.584827 | ||||||||
\(407\) | 5752.93 | 0.700644 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6298.36 | −0.761452 | −0.380726 | − | 0.924688i | \(-0.624326\pi\) | ||||
−0.380726 | + | 0.924688i | \(0.624326\pi\) | |||||||
\(410\) | −6542.29 | −0.788051 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15567.3 | −1.86152 | ||||||||
\(413\) | 1666.56 | 0.198562 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5337.49 | 0.631342 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −929.662 | −0.108783 | ||||||||
\(419\) | 1432.01 | 0.166965 | 0.0834824 | − | 0.996509i | \(-0.473396\pi\) | ||||
0.0834824 | + | 0.996509i | \(0.473396\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9641.43 | −1.11614 | −0.558069 | − | 0.829794i | \(-0.688458\pi\) | ||||
−0.558069 | + | 0.829794i | \(0.688458\pi\) | |||||||
\(422\) | −5544.82 | −0.639615 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.0594 | 0.00298480 | ||||||||
\(425\) | 5536.19 | 0.631870 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1232.31 | 0.139662 | ||||||||
\(428\) | 7579.03 | 0.855949 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3807.77 | 0.427040 | ||||||||
\(431\) | 3370.61 | 0.376698 | 0.188349 | − | 0.982102i | \(-0.439686\pi\) | ||||
0.188349 | + | 0.982102i | \(0.439686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6248.91 | 0.693541 | 0.346770 | − | 0.937950i | \(-0.387278\pi\) | ||||
0.346770 | + | 0.937950i | \(0.387278\pi\) | |||||||
\(434\) | 7381.45 | 0.816407 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12944.7 | −1.42187 | ||||||||
\(437\) | 2940.43 | 0.321876 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2866.16 | 0.311604 | 0.155802 | − | 0.987788i | \(-0.450204\pi\) | ||||
0.155802 | + | 0.987788i | \(0.450204\pi\) | |||||||
\(440\) | 136.471 | 0.0147864 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10776.3 | −1.15575 | −0.577877 | − | 0.816124i | \(-0.696119\pi\) | ||||
−0.577877 | + | 0.816124i | \(0.696119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10298.4 | 1.09706 | ||||||||
\(446\) | −6828.74 | −0.725000 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3228.91 | 0.340517 | ||||||||
\(449\) | 13834.9 | 1.45414 | 0.727069 | − | 0.686564i | \(-0.240882\pi\) | ||||
0.727069 | + | 0.686564i | \(0.240882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3459.04 | −0.361153 | ||||||||
\(452\) | 10919.0 | 1.13625 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1633.86 | −0.168901 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17233.0 | −1.76395 | −0.881976 | − | 0.471295i | \(-0.843787\pi\) | ||||
−0.881976 | + | 0.471295i | \(0.843787\pi\) | |||||||
\(458\) | −9509.51 | −0.970197 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14648.9 | −1.48480 | ||||||||
\(461\) | 11485.0 | 1.16033 | 0.580164 | − | 0.814500i | \(-0.302988\pi\) | ||||
0.580164 | + | 0.814500i | \(0.302988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1613.61 | −0.161967 | −0.0809837 | − | 0.996715i | \(-0.525806\pi\) | ||||
−0.0809837 | + | 0.996715i | \(0.525806\pi\) | |||||||
\(464\) | −12367.7 | −1.23740 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3782.41 | −0.376002 | ||||||||
\(467\) | 8149.20 | 0.807495 | 0.403747 | − | 0.914871i | \(-0.367707\pi\) | ||||
0.403747 | + | 0.914871i | \(0.367707\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1701.81 | −0.167553 | ||||||||
\(470\) | 11038.4 | 1.08333 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −274.145 | −0.0267342 | ||||||||
\(473\) | 2013.24 | 0.195706 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 797.289 | 0.0770150 | ||||||||
\(476\) | 4558.36 | 0.438933 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18798.1 | 1.79875 | ||||||||
\(479\) | 1827.62 | 0.174334 | 0.0871670 | − | 0.996194i | \(-0.472219\pi\) | ||||
0.0871670 | + | 0.996194i | \(0.472219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15213.9 | 1.43771 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8522.52 | −0.800387 | ||||||||
\(485\) | −4883.49 | −0.457212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7838.95 | 0.729398 | 0.364699 | − | 0.931125i | \(-0.381172\pi\) | ||||
0.364699 | + | 0.931125i | \(0.381172\pi\) | |||||||
\(488\) | −202.712 | −0.0188040 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10027.1 | −0.924449 | ||||||||
\(491\) | −17196.1 | −1.58055 | −0.790273 | − | 0.612755i | \(-0.790061\pi\) | ||||
−0.790273 | + | 0.612755i | \(0.790061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18538.2 | −1.69354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19081.5 | 1.72739 | ||||||||
\(497\) | 1890.40 | 0.170616 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5355.28 | −0.480431 | −0.240216 | − | 0.970720i | \(-0.577218\pi\) | ||||
−0.240216 | + | 0.970720i | \(0.577218\pi\) | |||||||
\(500\) | −12306.2 | −1.10070 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3871.84 | 0.344240 | ||||||||
\(503\) | −2979.80 | −0.264141 | −0.132071 | − | 0.991240i | \(-0.542163\pi\) | ||||
−0.132071 | + | 0.991240i | \(0.542163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5990.35 | 0.527856 | ||||||||
\(506\) | −15262.1 | −1.34088 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19374.0 | −1.69209 | ||||||||
\(509\) | 15353.7 | 1.33701 | 0.668507 | − | 0.743706i | \(-0.266934\pi\) | ||||
0.668507 | + | 0.743706i | \(0.266934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −375.297 | −0.0324895 | ||||||||
\(512\) | 16462.3 | 1.42097 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 67.4267 | 0.00578611 | ||||||||
\(515\) | −15276.0 | −1.30707 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5836.24 | 0.496475 | ||||||||
\(518\) | −8005.00 | −0.678995 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −433.801 | −0.0364783 | −0.0182391 | − | 0.999834i | \(-0.505806\pi\) | ||||
−0.0182391 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18900.3 | 1.58021 | 0.790106 | − | 0.612970i | \(-0.210026\pi\) | ||||
0.790106 | + | 0.612970i | \(0.210026\pi\) | |||||||
\(524\) | −19030.3 | −1.58653 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1615.06 | 0.133879 | ||||||||
\(527\) | 28601.7 | 2.36415 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36105.7 | 2.96751 | ||||||||
\(530\) | 867.839 | 0.0711255 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 656.468 | 0.0534990 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7437.21 | 0.601007 | ||||||||
\(536\) | 279.943 | 0.0225592 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9015.53 | −0.722467 | ||||||||
\(539\) | −5301.55 | −0.423662 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13247.5 | −1.05278 | −0.526391 | − | 0.850243i | \(-0.676455\pi\) | ||||
−0.526391 | + | 0.850243i | \(0.676455\pi\) | |||||||
\(542\) | 16197.1 | 1.28363 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23947.9 | 1.88742 | ||||||||
\(545\) | −12702.4 | −0.998372 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5543.52 | −0.433316 | −0.216658 | − | 0.976248i | \(-0.569516\pi\) | ||||
−0.216658 | + | 0.976248i | \(0.569516\pi\) | |||||||
\(548\) | −3090.36 | −0.240901 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4138.28 | −0.320831 | ||||||||
\(551\) | −2669.76 | −0.206416 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3712.31 | 0.285467 | ||||||||
\(554\) | 27377.3 | 2.09955 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4020.14 | 0.306640 | ||||||||
\(557\) | 6733.19 | 0.512198 | 0.256099 | − | 0.966651i | \(-0.417563\pi\) | ||||
0.256099 | + | 0.966651i | \(0.417563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2984.19 | 0.225188 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29367.6 | −2.20427 | ||||||||
\(563\) | −24282.4 | −1.81773 | −0.908863 | − | 0.417096i | \(-0.863048\pi\) | ||||
−0.908863 | + | 0.417096i | \(0.863048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10714.7 | 0.797823 | ||||||||
\(566\) | −9792.55 | −0.727229 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −310.966 | −0.0229716 | ||||||||
\(569\) | 19876.2 | 1.46441 | 0.732207 | − | 0.681082i | \(-0.238490\pi\) | ||||
0.732207 | + | 0.681082i | \(0.238490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 225.014 | 0.0164913 | 0.00824567 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824567 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4813.14 | 0.349994 | ||||||||
\(575\) | 13089.0 | 0.949302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12258.1 | 0.884424 | 0.442212 | − | 0.896910i | \(-0.354194\pi\) | ||||
0.442212 | + | 0.896910i | \(0.354194\pi\) | |||||||
\(578\) | 15004.5 | 1.07977 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13300.4 | 0.952191 | ||||||||
\(581\) | −3926.77 | −0.280395 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 458.844 | 0.0325958 | ||||||||
\(584\) | 61.7353 | 0.00437436 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16972.4 | 1.19645 | ||||||||
\(587\) | 10282.3 | 0.722992 | 0.361496 | − | 0.932374i | \(-0.382266\pi\) | ||||
0.361496 | + | 0.932374i | \(0.382266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4119.04 | 0.288153 | ||||||||
\(590\) | −9129.67 | −0.637055 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20693.5 | −1.43665 | ||||||||
\(593\) | 12355.1 | 0.855586 | 0.427793 | − | 0.903877i | \(-0.359291\pi\) | ||||
0.427793 | + | 0.903877i | \(0.359291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4473.07 | 0.308198 | ||||||||
\(596\) | 8703.71 | 0.598184 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13035.2 | −0.889157 | −0.444578 | − | 0.895740i | \(-0.646646\pi\) | ||||
−0.444578 | + | 0.895740i | \(0.646646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5153.36 | −0.349767 | −0.174884 | − | 0.984589i | \(-0.555955\pi\) | ||||
−0.174884 | + | 0.984589i | \(0.555955\pi\) | |||||||
\(602\) | −2801.36 | −0.189659 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7324.30 | 0.493413 | ||||||||
\(605\) | −8363.05 | −0.561994 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1406.55 | −0.0940530 | −0.0470265 | − | 0.998894i | \(-0.514975\pi\) | ||||
−0.0470265 | + | 0.998894i | \(0.514975\pi\) | |||||||
\(608\) | 3448.83 | 0.230047 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6750.79 | −0.448085 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15984.3 | 1.05318 | 0.526590 | − | 0.850120i | \(-0.323470\pi\) | ||||
0.526590 | + | 0.850120i | \(0.323470\pi\) | |||||||
\(614\) | −33097.5 | −2.17541 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −100.401 | −0.00656703 | ||||||||
\(617\) | −10324.4 | −0.673652 | −0.336826 | − | 0.941567i | \(-0.609353\pi\) | ||||
−0.336826 | + | 0.941567i | \(0.609353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7423.00 | 0.481996 | 0.240998 | − | 0.970526i | \(-0.422525\pi\) | ||||
0.240998 | + | 0.970526i | \(0.422525\pi\) | |||||||
\(620\) | −20520.6 | −1.32924 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17082.4 | 1.10119 | ||||||||
\(623\) | −7576.48 | −0.487232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4629.23 | −0.296271 | ||||||||
\(626\) | 15346.4 | 0.979820 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30074.6 | −1.91100 | ||||||||
\(629\) | −31017.8 | −1.96624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1190.30 | −0.0750954 | −0.0375477 | − | 0.999295i | \(-0.511955\pi\) | ||||
−0.0375477 | + | 0.999295i | \(0.511955\pi\) | |||||||
\(632\) | −610.665 | −0.0384350 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42308.2 | −2.65027 | ||||||||
\(635\) | −19011.5 | −1.18810 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13857.2 | 0.859894 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1013.02 | −0.0625674 | ||||||||
\(641\) | −705.064 | −0.0434451 | −0.0217226 | − | 0.999764i | \(-0.506915\pi\) | ||||
−0.0217226 | + | 0.999764i | \(0.506915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14641.4 | −0.897976 | −0.448988 | − | 0.893538i | \(-0.648215\pi\) | ||||
−0.448988 | + | 0.893538i | \(0.648215\pi\) | |||||||
\(644\) | 10777.1 | 0.659439 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5012.42 | 0.305280 | ||||||||
\(647\) | −1520.83 | −0.0924111 | −0.0462056 | − | 0.998932i | \(-0.514713\pi\) | ||||
−0.0462056 | + | 0.998932i | \(0.514713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4827.04 | −0.291954 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11428.7 | −0.686477 | ||||||||
\(653\) | 22054.4 | 1.32168 | 0.660838 | − | 0.750529i | \(-0.270201\pi\) | ||||
0.660838 | + | 0.750529i | \(0.270201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18674.2 | −1.11398 | ||||||||
\(656\) | 12442.3 | 0.740532 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8120.92 | −0.481134 | ||||||||
\(659\) | 12652.3 | 0.747895 | 0.373947 | − | 0.927450i | \(-0.378004\pi\) | ||||
0.373947 | + | 0.927450i | \(0.378004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10893.2 | 0.640994 | 0.320497 | − | 0.947250i | \(-0.396150\pi\) | ||||
0.320497 | + | 0.947250i | \(0.396150\pi\) | |||||||
\(662\) | −47981.0 | −2.81697 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 645.942 | 0.0377522 | ||||||||
\(665\) | 644.184 | 0.0375645 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43829.0 | −2.54433 | ||||||||
\(668\) | −27829.6 | −1.61191 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9322.76 | 0.537567 | ||||||||
\(671\) | −3569.28 | −0.205351 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9019.75 | −0.516621 | −0.258310 | − | 0.966062i | \(-0.583166\pi\) | ||||
−0.258310 | + | 0.966062i | \(0.583166\pi\) | |||||||
\(674\) | 36196.4 | 2.06859 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24923.6 | 1.41491 | 0.707454 | − | 0.706760i | \(-0.249844\pi\) | ||||
0.707454 | + | 0.706760i | \(0.249844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3592.76 | 0.203060 | ||||||||
\(680\) | −735.807 | −0.0414955 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21379.7 | −1.20039 | ||||||||
\(683\) | −24634.2 | −1.38009 | −0.690044 | − | 0.723767i | \(-0.742409\pi\) | ||||
−0.690044 | + | 0.723767i | \(0.742409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3032.53 | −0.169149 | ||||||||
\(686\) | 15603.1 | 0.868411 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7241.70 | −0.401290 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10340.2 | 0.569264 | 0.284632 | − | 0.958637i | \(-0.408129\pi\) | ||||
0.284632 | + | 0.958637i | \(0.408129\pi\) | |||||||
\(692\) | −2817.56 | −0.154780 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23024.3 | 1.25935 | ||||||||
\(695\) | 3944.92 | 0.215308 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18650.0 | 1.01351 | ||||||||
\(698\) | −38316.7 | −2.07780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2922.19 | 0.157784 | ||||||||
\(701\) | 20833.9 | 1.12252 | 0.561258 | − | 0.827641i | \(-0.310317\pi\) | ||||
0.561258 | + | 0.827641i | \(0.310317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4467.00 | −0.239653 | ||||||||
\(704\) | −9352.23 | −0.500676 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16012.0 | −0.853569 | ||||||||
\(707\) | −4407.07 | −0.234434 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9189.56 | −0.486772 | −0.243386 | − | 0.969930i | \(-0.578258\pi\) | ||||
−0.243386 | + | 0.969930i | \(0.578258\pi\) | |||||||
\(710\) | −10355.9 | −0.547395 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1246.31 | 0.0656004 | ||||||||
\(713\) | 67621.8 | 3.55183 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23785.2 | 1.24147 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −442.788 | −0.0230149 | ||||||||
\(719\) | −7503.22 | −0.389183 | −0.194592 | − | 0.980884i | \(-0.562338\pi\) | ||||
−0.194592 | + | 0.980884i | \(0.562338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11238.5 | 0.580503 | ||||||||
\(722\) | −26921.6 | −1.38770 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31286.8 | 1.60603 | ||||||||
\(725\) | −11884.1 | −0.608779 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20727.2 | −1.05740 | −0.528700 | − | 0.848809i | \(-0.677320\pi\) | ||||
−0.528700 | + | 0.848809i | \(0.677320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2055.93 | 0.104237 | ||||||||
\(731\) | −10854.7 | −0.549216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17361.3 | −0.874836 | −0.437418 | − | 0.899258i | \(-0.644107\pi\) | ||||
−0.437418 | + | 0.899258i | \(0.644107\pi\) | |||||||
\(734\) | 28292.4 | 1.42274 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 56618.9 | 2.83560 | ||||||||
\(737\) | 4929.13 | 0.246359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18093.8 | −0.900663 | −0.450331 | − | 0.892861i | \(-0.648694\pi\) | ||||
−0.450331 | + | 0.892861i | \(0.648694\pi\) | |||||||
\(740\) | 22254.1 | 1.10551 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −638.466 | −0.0315887 | ||||||||
\(743\) | −14875.3 | −0.734482 | −0.367241 | − | 0.930126i | \(-0.619698\pi\) | ||||
−0.367241 | + | 0.930126i | \(0.619698\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8540.85 | 0.420017 | ||||||||
\(746\) | 8976.07 | 0.440533 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13202.9 | −0.645380 | ||||||||
\(749\) | −5471.52 | −0.266923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17750.9 | −0.862502 | −0.431251 | − | 0.902232i | \(-0.641928\pi\) | ||||
−0.431251 | + | 0.902232i | \(0.641928\pi\) | |||||||
\(752\) | −20993.1 | −1.01801 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7187.25 | 0.346451 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10220.3 | −0.490702 | −0.245351 | − | 0.969434i | \(-0.578903\pi\) | ||||
−0.245351 | + | 0.969434i | \(0.578903\pi\) | |||||||
\(758\) | 44351.1 | 2.12520 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −105.967 | −0.00505765 | ||||||||
\(761\) | −14112.0 | −0.672221 | −0.336110 | − | 0.941823i | \(-0.609112\pi\) | ||||
−0.336110 | + | 0.941823i | \(0.609112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9345.13 | 0.443403 | ||||||||
\(764\) | 23128.7 | 1.09525 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17881.6 | −0.843457 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22736.7 | 1.06620 | 0.533100 | − | 0.846052i | \(-0.321027\pi\) | ||||
0.533100 | + | 0.846052i | \(0.321027\pi\) | |||||||
\(770\) | −3343.60 | −0.156487 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20488.8 | 0.955194 | ||||||||
\(773\) | −343.173 | −0.0159678 | −0.00798388 | − | 0.999968i | \(-0.502541\pi\) | ||||
−0.00798388 | + | 0.999968i | \(0.502541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18335.4 | 0.849844 | ||||||||
\(776\) | −590.999 | −0.0273397 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10323.8 | 0.475740 | ||||||||
\(779\) | 2685.86 | 0.123531 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5475.37 | −0.250863 | ||||||||
\(782\) | 82288.3 | 3.76294 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19069.8 | 0.868706 | ||||||||
\(785\) | −29511.9 | −1.34181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19086.4 | 0.864496 | 0.432248 | − | 0.901755i | \(-0.357721\pi\) | ||||
0.432248 | + | 0.901755i | \(0.357721\pi\) | |||||||
\(788\) | 22673.7 | 1.02502 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20336.6 | −0.915876 | ||||||||
\(791\) | −7882.74 | −0.354334 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8894.36 | −0.397543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32959.5 | 1.46761 | ||||||||
\(797\) | −12031.1 | −0.534709 | −0.267354 | − | 0.963598i | \(-0.586149\pi\) | ||||
−0.267354 | + | 0.963598i | \(0.586149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31467.0 | −1.39327 | ||||||||
\(800\) | 15352.1 | 0.678471 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32528.2 | −1.43218 | ||||||||
\(803\) | 1087.01 | 0.0477706 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10575.5 | 0.463027 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 724.952 | 0.0315640 | ||||||||
\(809\) | −10175.4 | −0.442210 | −0.221105 | − | 0.975250i | \(-0.570966\pi\) | ||||
−0.221105 | + | 0.975250i | \(0.570966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26754.1 | −1.15840 | −0.579201 | − | 0.815185i | \(-0.696635\pi\) | ||||
−0.579201 | + | 0.815185i | \(0.696635\pi\) | |||||||
\(812\) | −9785.08 | −0.422893 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23185.7 | 0.998353 | ||||||||
\(815\) | −11214.9 | −0.482011 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1563.23 | −0.0669408 | ||||||||
\(818\) | −25383.9 | −1.08500 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13380.7 | −0.569845 | ||||||||
\(821\) | −15777.5 | −0.670693 | −0.335347 | − | 0.942095i | \(-0.608853\pi\) | ||||
−0.335347 | + | 0.942095i | \(0.608853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13863.9 | −0.587197 | −0.293599 | − | 0.955929i | \(-0.594853\pi\) | ||||
−0.293599 | + | 0.955929i | \(0.594853\pi\) | |||||||
\(824\) | −1848.70 | −0.0781583 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6716.66 | 0.282933 | ||||||||
\(827\) | −26835.0 | −1.12835 | −0.564175 | − | 0.825655i | \(-0.690806\pi\) | ||||
−0.564175 | + | 0.825655i | \(0.690806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 625.251 | 0.0261953 | 0.0130976 | − | 0.999914i | \(-0.495831\pi\) | ||||
0.0130976 | + | 0.999914i | \(0.495831\pi\) | |||||||
\(830\) | 21511.4 | 0.899604 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28584.2 | 1.18893 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27308.8 | −1.13181 | ||||||||
\(836\) | −1901.40 | −0.0786617 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5771.35 | 0.237909 | ||||||||
\(839\) | −27307.4 | −1.12367 | −0.561833 | − | 0.827251i | \(-0.689904\pi\) | ||||
−0.561833 | + | 0.827251i | \(0.689904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15405.4 | 0.631656 | ||||||||
\(842\) | −38857.3 | −1.59039 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11340.6 | −0.462510 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6152.66 | 0.249596 | ||||||||
\(848\) | −1650.48 | −0.0668368 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22312.2 | 0.900356 | ||||||||
\(851\) | −73334.2 | −2.95401 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44801.9 | −1.79834 | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(854\) | 4966.53 | 0.199006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 900.051 | 0.0359382 | ||||||||
\(857\) | 25167.1 | 1.00314 | 0.501571 | − | 0.865116i | \(-0.332756\pi\) | ||||
0.501571 | + | 0.865116i | \(0.332756\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4059.10 | 0.161228 | 0.0806138 | − | 0.996745i | \(-0.474312\pi\) | ||||
0.0806138 | + | 0.996745i | \(0.474312\pi\) | |||||||
\(860\) | 7787.87 | 0.308795 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13584.4 | 0.536759 | ||||||||
\(863\) | 818.924 | 0.0323019 | 0.0161509 | − | 0.999870i | \(-0.494859\pi\) | ||||
0.0161509 | + | 0.999870i | \(0.494859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2764.84 | −0.108679 | ||||||||
\(866\) | 25184.6 | 0.988231 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15096.9 | 0.590350 | ||||||||
\(869\) | −10752.3 | −0.419733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1537.25 | −0.0596993 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11850.7 | 0.458644 | ||||||||
\(875\) | 8884.23 | 0.343248 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −190.251 | −0.00732533 | −0.00366267 | − | 0.999993i | \(-0.501166\pi\) | ||||
−0.00366267 | + | 0.999993i | \(0.501166\pi\) | |||||||
\(878\) | 11551.3 | 0.444007 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8643.43 | −0.331102 | ||||||||
\(881\) | 19803.4 | 0.757315 | 0.378657 | − | 0.925537i | \(-0.376386\pi\) | ||||
0.378657 | + | 0.925537i | \(0.376386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19652.1 | 0.748974 | 0.374487 | − | 0.927232i | \(-0.377819\pi\) | ||||
0.374487 | + | 0.927232i | \(0.377819\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43431.2 | −1.64684 | ||||||||
\(887\) | 26295.0 | 0.995379 | 0.497689 | − | 0.867355i | \(-0.334182\pi\) | ||||
0.497689 | + | 0.867355i | \(0.334182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13986.6 | 0.527668 | ||||||||
\(890\) | 41505.1 | 1.56321 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13966.5 | −0.524253 | ||||||||
\(893\) | −4531.69 | −0.169818 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23340.2 | 0.871704 | ||||||||
\(896\) | 745.275 | 0.0277878 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 55758.0 | 2.07201 | ||||||||
\(899\) | −61397.0 | −2.27776 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2473.93 | −0.0914746 | ||||||||
\(902\) | −13940.8 | −0.514609 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1296.69 | 0.0477072 | ||||||||
\(905\) | 30701.4 | 1.12768 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42417.3 | 1.55286 | 0.776429 | − | 0.630204i | \(-0.217029\pi\) | ||||
0.776429 | + | 0.630204i | \(0.217029\pi\) | |||||||
\(908\) | −3341.66 | −0.122133 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 872.245 | 0.0317220 | 0.0158610 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158610 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11373.5 | 0.412276 | ||||||||
\(914\) | −69453.2 | −2.51347 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19449.4 | −0.701557 | ||||||||
\(917\) | 13738.5 | 0.494749 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17181.4 | −0.616716 | −0.308358 | − | 0.951270i | \(-0.599779\pi\) | ||||
−0.308358 | + | 0.951270i | \(0.599779\pi\) | |||||||
\(920\) | −1739.64 | −0.0623415 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46287.5 | 1.65336 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19884.4 | −0.706804 | ||||||||
\(926\) | −6503.25 | −0.230788 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −51407.0 | −1.81845 | ||||||||
\(929\) | −56042.9 | −1.97923 | −0.989617 | − | 0.143728i | \(-0.954091\pi\) | ||||
−0.989617 | + | 0.143728i | \(0.954091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4116.52 | 0.144912 | ||||||||
\(932\) | −7736.00 | −0.271890 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32843.3 | 1.15060 | ||||||||
\(935\) | −12955.8 | −0.453155 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36672.5 | −1.27859 | −0.639295 | − | 0.768961i | \(-0.720774\pi\) | ||||
−0.639295 | + | 0.768961i | \(0.720774\pi\) | |||||||
\(938\) | −6858.71 | −0.238747 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22576.4 | 0.783363 | ||||||||
\(941\) | 21069.0 | 0.729895 | 0.364947 | − | 0.931028i | \(-0.381087\pi\) | ||||
0.364947 | + | 0.931028i | \(0.381087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44093.4 | 1.52267 | ||||||||
\(944\) | 17363.0 | 0.598642 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8113.87 | 0.278863 | ||||||||
\(947\) | 1838.70 | 0.0630938 | 0.0315469 | − | 0.999502i | \(-0.489957\pi\) | ||||
0.0315469 | + | 0.999502i | \(0.489957\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3213.27 | 0.109739 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 541.330 | 0.0184292 | ||||||||
\(953\) | −13599.8 | −0.462266 | −0.231133 | − | 0.972922i | \(-0.574243\pi\) | ||||
−0.231133 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22695.9 | 0.769029 | ||||||||
\(956\) | 38446.9 | 1.30069 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7365.75 | 0.248410 | ||||||||
\(959\) | 2231.02 | 0.0751235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64935.6 | 2.17971 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31116.4 | 1.03962 | ||||||||
\(965\) | 20105.5 | 0.670692 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2081.30 | 0.0692141 | 0.0346070 | − | 0.999401i | \(-0.488982\pi\) | ||||
0.0346070 | + | 0.999401i | \(0.488982\pi\) | |||||||
\(968\) | −1012.10 | −0.0336054 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19681.6 | −0.651484 | ||||||||
\(971\) | −1636.62 | −0.0540904 | −0.0270452 | − | 0.999634i | \(-0.508610\pi\) | ||||
−0.0270452 | + | 0.999634i | \(0.508610\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2902.26 | −0.0956240 | ||||||||
\(974\) | 31592.9 | 1.03932 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12838.8 | 0.421066 | ||||||||
\(977\) | 29387.1 | 0.962311 | 0.481156 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481156 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21944.6 | 0.716396 | ||||||||
\(980\) | −20508.1 | −0.668476 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −69304.4 | −2.25213 | ||||||||
\(983\) | −24084.4 | −0.781457 | −0.390728 | − | 0.920506i | \(-0.627777\pi\) | ||||
−0.390728 | + | 0.920506i | \(0.627777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22249.4 | 0.719722 | ||||||||
\(986\) | −74713.4 | −2.41314 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25663.4 | −0.825125 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1413.43 | 0.0453068 | 0.0226534 | − | 0.999743i | \(-0.492789\pi\) | ||||
0.0226534 | + | 0.999743i | \(0.492789\pi\) | |||||||
\(992\) | 79313.5 | 2.53851 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7618.79 | 0.243112 | ||||||||
\(995\) | 32342.7 | 1.03049 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33357.4 | −1.05962 | −0.529809 | − | 0.848117i | \(-0.677737\pi\) | ||||
−0.529809 | + | 0.848117i | \(0.677737\pi\) | |||||||
\(998\) | −21583.1 | −0.684570 | ||||||||
\(999\) | 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.1.7 | 9 | ||
3.2 | odd | 2 | 507.4.a.o.1.3 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.bf.1.3 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.15 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.4 | 18 | |||
39.38 | odd | 2 | 507.4.a.p.1.7 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.3 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.p.1.7 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.k.337.4 | 18 | 39.8 | even | 4 | |||
507.4.b.k.337.15 | 18 | 39.5 | even | 4 | |||
1521.4.a.bf.1.3 | 9 | 13.12 | even | 2 | |||
1521.4.a.bi.1.7 | 9 | 1.1 | even | 1 | trivial |