Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 25x^{2} + 24x + 78 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.36176\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36176 | −0.835009 | −0.417505 | − | 0.908675i | \(-0.637095\pi\) | ||||
−0.417505 | + | 0.908675i | \(0.637095\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −2.42208 | −0.302760 | ||||||||
\(5\) | −6.42208 | −0.574408 | −0.287204 | − | 0.957869i | \(-0.592726\pi\) | ||||
−0.287204 | + | 0.957869i | \(0.592726\pi\) | |||||||
\(6\) | 7.08529 | 0.482093 | ||||||||
\(7\) | 29.4938 | 1.59252 | 0.796259 | − | 0.604956i | \(-0.206809\pi\) | ||||
0.796259 | + | 0.604956i | \(0.206809\pi\) | |||||||
\(8\) | 24.6145 | 1.08782 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 15.1674 | 0.479636 | ||||||||
\(11\) | 0.624715 | 0.0171235 | 0.00856176 | − | 0.999963i | \(-0.497275\pi\) | ||||
0.00856176 | + | 0.999963i | \(0.497275\pi\) | |||||||
\(12\) | 7.26623 | 0.174798 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −69.6575 | −1.32977 | ||||||||
\(15\) | 19.2662 | 0.331635 | ||||||||
\(16\) | −38.7569 | −0.605577 | ||||||||
\(17\) | 87.7291 | 1.25161 | 0.625807 | − | 0.779978i | \(-0.284770\pi\) | ||||
0.625807 | + | 0.779978i | \(0.284770\pi\) | |||||||
\(18\) | −21.2559 | −0.278336 | ||||||||
\(19\) | −82.8018 | −0.999792 | −0.499896 | − | 0.866085i | \(-0.666628\pi\) | ||||
−0.499896 | + | 0.866085i | \(0.666628\pi\) | |||||||
\(20\) | 15.5548 | 0.173908 | ||||||||
\(21\) | −88.4815 | −0.919441 | ||||||||
\(22\) | −1.47543 | −0.0142983 | ||||||||
\(23\) | −74.7977 | −0.678104 | −0.339052 | − | 0.940768i | \(-0.610106\pi\) | ||||
−0.339052 | + | 0.940768i | \(0.610106\pi\) | |||||||
\(24\) | −73.8434 | −0.628051 | ||||||||
\(25\) | −83.7569 | −0.670055 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −71.4364 | −0.482150 | ||||||||
\(29\) | 226.329 | 1.44925 | 0.724625 | − | 0.689143i | \(-0.242013\pi\) | ||||
0.724625 | + | 0.689143i | \(0.242013\pi\) | |||||||
\(30\) | −45.5023 | −0.276918 | ||||||||
\(31\) | −173.660 | −1.00614 | −0.503070 | − | 0.864246i | \(-0.667796\pi\) | ||||
−0.503070 | + | 0.864246i | \(0.667796\pi\) | |||||||
\(32\) | −105.381 | −0.582154 | ||||||||
\(33\) | −1.87415 | −0.00988627 | ||||||||
\(34\) | −207.195 | −1.04511 | ||||||||
\(35\) | −189.412 | −0.914755 | ||||||||
\(36\) | −21.7987 | −0.100920 | ||||||||
\(37\) | −112.020 | −0.497730 | −0.248865 | − | 0.968538i | \(-0.580058\pi\) | ||||
−0.248865 | + | 0.968538i | \(0.580058\pi\) | |||||||
\(38\) | 195.558 | 0.834835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −158.076 | −0.624850 | ||||||||
\(41\) | 267.011 | 1.01708 | 0.508538 | − | 0.861040i | \(-0.330186\pi\) | ||||
0.508538 | + | 0.861040i | \(0.330186\pi\) | |||||||
\(42\) | 208.972 | 0.767741 | ||||||||
\(43\) | 383.450 | 1.35990 | 0.679948 | − | 0.733260i | \(-0.262002\pi\) | ||||
0.679948 | + | 0.733260i | \(0.262002\pi\) | |||||||
\(44\) | −1.51311 | −0.00518431 | ||||||||
\(45\) | −57.7987 | −0.191469 | ||||||||
\(46\) | 176.654 | 0.566223 | ||||||||
\(47\) | −337.380 | −1.04706 | −0.523530 | − | 0.852007i | \(-0.675385\pi\) | ||||
−0.523530 | + | 0.852007i | \(0.675385\pi\) | |||||||
\(48\) | 116.271 | 0.349630 | ||||||||
\(49\) | 526.887 | 1.53611 | ||||||||
\(50\) | 197.814 | 0.559502 | ||||||||
\(51\) | −263.187 | −0.722619 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −146.354 | −0.379308 | −0.189654 | − | 0.981851i | \(-0.560737\pi\) | ||||
−0.189654 | + | 0.981851i | \(0.560737\pi\) | |||||||
\(54\) | 63.7676 | 0.160698 | ||||||||
\(55\) | −4.01197 | −0.00983589 | ||||||||
\(56\) | 725.975 | 1.73237 | ||||||||
\(57\) | 248.406 | 0.577230 | ||||||||
\(58\) | −534.536 | −1.21014 | ||||||||
\(59\) | 529.173 | 1.16767 | 0.583834 | − | 0.811873i | \(-0.301552\pi\) | ||||
0.583834 | + | 0.811873i | \(0.301552\pi\) | |||||||
\(60\) | −46.6643 | −0.100406 | ||||||||
\(61\) | 203.272 | 0.426660 | 0.213330 | − | 0.976980i | \(-0.431569\pi\) | ||||
0.213330 | + | 0.976980i | \(0.431569\pi\) | |||||||
\(62\) | 410.144 | 0.840135 | ||||||||
\(63\) | 265.445 | 0.530839 | ||||||||
\(64\) | 558.941 | 1.09168 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.42629 | 0.00825513 | ||||||||
\(67\) | −121.497 | −0.221540 | −0.110770 | − | 0.993846i | \(-0.535332\pi\) | ||||
−0.110770 | + | 0.993846i | \(0.535332\pi\) | |||||||
\(68\) | −212.487 | −0.378938 | ||||||||
\(69\) | 224.393 | 0.391504 | ||||||||
\(70\) | 447.346 | 0.763829 | ||||||||
\(71\) | 661.314 | 1.10540 | 0.552701 | − | 0.833380i | \(-0.313597\pi\) | ||||
0.552701 | + | 0.833380i | \(0.313597\pi\) | |||||||
\(72\) | 221.530 | 0.362605 | ||||||||
\(73\) | −167.341 | −0.268299 | −0.134150 | − | 0.990961i | \(-0.542830\pi\) | ||||
−0.134150 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(74\) | 264.565 | 0.415609 | ||||||||
\(75\) | 251.271 | 0.386857 | ||||||||
\(76\) | 200.552 | 0.302697 | ||||||||
\(77\) | 18.4253 | 0.0272695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −101.399 | −0.144408 | −0.0722042 | − | 0.997390i | \(-0.523003\pi\) | ||||
−0.0722042 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(80\) | 248.900 | 0.347848 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −630.617 | −0.849268 | ||||||||
\(83\) | 506.985 | 0.670468 | 0.335234 | − | 0.942135i | \(-0.391185\pi\) | ||||
0.335234 | + | 0.942135i | \(0.391185\pi\) | |||||||
\(84\) | 214.309 | 0.278370 | ||||||||
\(85\) | −563.403 | −0.718937 | ||||||||
\(86\) | −905.617 | −1.13553 | ||||||||
\(87\) | −678.988 | −0.836725 | ||||||||
\(88\) | 15.3770 | 0.0186272 | ||||||||
\(89\) | −1402.33 | −1.67019 | −0.835095 | − | 0.550106i | \(-0.814587\pi\) | ||||
−0.835095 | + | 0.550106i | \(0.814587\pi\) | |||||||
\(90\) | 136.507 | 0.159879 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 181.166 | 0.205303 | ||||||||
\(93\) | 520.981 | 0.580895 | ||||||||
\(94\) | 796.810 | 0.874306 | ||||||||
\(95\) | 531.760 | 0.574289 | ||||||||
\(96\) | 316.143 | 0.336107 | ||||||||
\(97\) | −1902.89 | −1.99185 | −0.995924 | − | 0.0901969i | \(-0.971250\pi\) | ||||
−0.995924 | + | 0.0901969i | \(0.971250\pi\) | |||||||
\(98\) | −1244.38 | −1.28267 | ||||||||
\(99\) | 5.62244 | 0.00570784 | ||||||||
\(100\) | 202.866 | 0.202866 | ||||||||
\(101\) | 1833.09 | 1.80594 | 0.902968 | − | 0.429708i | \(-0.141383\pi\) | ||||
0.902968 | + | 0.429708i | \(0.141383\pi\) | |||||||
\(102\) | 621.586 | 0.603394 | ||||||||
\(103\) | 1446.99 | 1.38423 | 0.692115 | − | 0.721787i | \(-0.256679\pi\) | ||||
0.692115 | + | 0.721787i | \(0.256679\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 568.235 | 0.528134 | ||||||||
\(106\) | 345.654 | 0.316725 | ||||||||
\(107\) | −369.286 | −0.333647 | −0.166823 | − | 0.985987i | \(-0.553351\pi\) | ||||
−0.166823 | + | 0.985987i | \(0.553351\pi\) | |||||||
\(108\) | 65.3961 | 0.0582661 | ||||||||
\(109\) | 815.694 | 0.716782 | 0.358391 | − | 0.933572i | \(-0.383325\pi\) | ||||
0.358391 | + | 0.933572i | \(0.383325\pi\) | |||||||
\(110\) | 9.47532 | 0.00821306 | ||||||||
\(111\) | 336.061 | 0.287365 | ||||||||
\(112\) | −1143.09 | −0.964392 | ||||||||
\(113\) | 1790.56 | 1.49064 | 0.745319 | − | 0.666708i | \(-0.232297\pi\) | ||||
0.745319 | + | 0.666708i | \(0.232297\pi\) | |||||||
\(114\) | −586.675 | −0.481992 | ||||||||
\(115\) | 480.357 | 0.389509 | ||||||||
\(116\) | −548.187 | −0.438775 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1249.78 | −0.975014 | ||||||||
\(119\) | 2587.47 | 1.99322 | ||||||||
\(120\) | 474.228 | 0.360758 | ||||||||
\(121\) | −1330.61 | −0.999707 | ||||||||
\(122\) | −480.079 | −0.356265 | ||||||||
\(123\) | −801.033 | −0.587209 | ||||||||
\(124\) | 420.619 | 0.304618 | ||||||||
\(125\) | 1340.65 | 0.959293 | ||||||||
\(126\) | −626.917 | −0.443256 | ||||||||
\(127\) | −45.2900 | −0.0316444 | −0.0158222 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158222 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(128\) | −477.036 | −0.329410 | ||||||||
\(129\) | −1150.35 | −0.785137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1051.82 | 0.701511 | 0.350756 | − | 0.936467i | \(-0.385925\pi\) | ||||
0.350756 | + | 0.936467i | \(0.385925\pi\) | |||||||
\(132\) | 4.53933 | 0.00299316 | ||||||||
\(133\) | −2442.14 | −1.59219 | ||||||||
\(134\) | 286.946 | 0.184988 | ||||||||
\(135\) | 173.396 | 0.110545 | ||||||||
\(136\) | 2159.41 | 1.36153 | ||||||||
\(137\) | 1542.94 | 0.962208 | 0.481104 | − | 0.876664i | \(-0.340236\pi\) | ||||
0.481104 | + | 0.876664i | \(0.340236\pi\) | |||||||
\(138\) | −529.963 | −0.326909 | ||||||||
\(139\) | 37.8644 | 0.0231052 | 0.0115526 | − | 0.999933i | \(-0.496323\pi\) | ||||
0.0115526 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(140\) | 458.770 | 0.276951 | ||||||||
\(141\) | 1012.14 | 0.604521 | ||||||||
\(142\) | −1561.87 | −0.923020 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −348.812 | −0.201859 | ||||||||
\(145\) | −1453.50 | −0.832461 | ||||||||
\(146\) | 395.221 | 0.224032 | ||||||||
\(147\) | −1580.66 | −0.886875 | ||||||||
\(148\) | 271.322 | 0.150693 | ||||||||
\(149\) | 1822.40 | 1.00199 | 0.500995 | − | 0.865450i | \(-0.332967\pi\) | ||||
0.500995 | + | 0.865450i | \(0.332967\pi\) | |||||||
\(150\) | −593.442 | −0.323029 | ||||||||
\(151\) | 3239.36 | 1.74580 | 0.872900 | − | 0.487899i | \(-0.162237\pi\) | ||||
0.872900 | + | 0.487899i | \(0.162237\pi\) | |||||||
\(152\) | −2038.12 | −1.08759 | ||||||||
\(153\) | 789.562 | 0.417205 | ||||||||
\(154\) | −43.5161 | −0.0227703 | ||||||||
\(155\) | 1115.26 | 0.577934 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 830.565 | 0.422206 | 0.211103 | − | 0.977464i | \(-0.432295\pi\) | ||||
0.211103 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(158\) | 239.480 | 0.120582 | ||||||||
\(159\) | 439.063 | 0.218993 | ||||||||
\(160\) | 676.766 | 0.334394 | ||||||||
\(161\) | −2206.07 | −1.07989 | ||||||||
\(162\) | −191.303 | −0.0927788 | ||||||||
\(163\) | 2079.90 | 0.999451 | 0.499725 | − | 0.866184i | \(-0.333434\pi\) | ||||
0.499725 | + | 0.866184i | \(0.333434\pi\) | |||||||
\(164\) | −646.721 | −0.307930 | ||||||||
\(165\) | 12.0359 | 0.00567875 | ||||||||
\(166\) | −1197.38 | −0.559847 | ||||||||
\(167\) | −85.9790 | −0.0398398 | −0.0199199 | − | 0.999802i | \(-0.506341\pi\) | ||||
−0.0199199 | + | 0.999802i | \(0.506341\pi\) | |||||||
\(168\) | −2177.93 | −1.00018 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1330.62 | 0.600319 | ||||||||
\(171\) | −745.217 | −0.333264 | ||||||||
\(172\) | −928.745 | −0.411722 | ||||||||
\(173\) | 2706.47 | 1.18942 | 0.594708 | − | 0.803942i | \(-0.297268\pi\) | ||||
0.594708 | + | 0.803942i | \(0.297268\pi\) | |||||||
\(174\) | 1603.61 | 0.698673 | ||||||||
\(175\) | −2470.31 | −1.06708 | ||||||||
\(176\) | −24.2120 | −0.0103696 | ||||||||
\(177\) | −1587.52 | −0.674154 | ||||||||
\(178\) | 3311.97 | 1.39462 | ||||||||
\(179\) | −4402.10 | −1.83815 | −0.919074 | − | 0.394085i | \(-0.871062\pi\) | ||||
−0.919074 | + | 0.394085i | \(0.871062\pi\) | |||||||
\(180\) | 139.993 | 0.0579692 | ||||||||
\(181\) | −1673.98 | −0.687435 | −0.343718 | − | 0.939073i | \(-0.611686\pi\) | ||||
−0.343718 | + | 0.939073i | \(0.611686\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −609.815 | −0.246332 | ||||||||
\(184\) | −1841.11 | −0.737653 | ||||||||
\(185\) | 719.403 | 0.285900 | ||||||||
\(186\) | −1230.43 | −0.485052 | ||||||||
\(187\) | 54.8057 | 0.0214320 | ||||||||
\(188\) | 817.159 | 0.317008 | ||||||||
\(189\) | −796.334 | −0.306480 | ||||||||
\(190\) | −1255.89 | −0.479536 | ||||||||
\(191\) | −290.117 | −0.109907 | −0.0549533 | − | 0.998489i | \(-0.517501\pi\) | ||||
−0.0549533 | + | 0.998489i | \(0.517501\pi\) | |||||||
\(192\) | −1676.82 | −0.630282 | ||||||||
\(193\) | −1039.50 | −0.387693 | −0.193847 | − | 0.981032i | \(-0.562096\pi\) | ||||
−0.193847 | + | 0.981032i | \(0.562096\pi\) | |||||||
\(194\) | 4494.18 | 1.66321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1276.16 | −0.465073 | ||||||||
\(197\) | −1418.70 | −0.513089 | −0.256544 | − | 0.966532i | \(-0.582584\pi\) | ||||
−0.256544 | + | 0.966532i | \(0.582584\pi\) | |||||||
\(198\) | −13.2789 | −0.00476610 | ||||||||
\(199\) | −2388.39 | −0.850795 | −0.425398 | − | 0.905007i | \(-0.639866\pi\) | ||||
−0.425398 | + | 0.905007i | \(0.639866\pi\) | |||||||
\(200\) | −2061.63 | −0.728897 | ||||||||
\(201\) | 364.490 | 0.127906 | ||||||||
\(202\) | −4329.33 | −1.50797 | ||||||||
\(203\) | 6675.32 | 2.30796 | ||||||||
\(204\) | 637.460 | 0.218780 | ||||||||
\(205\) | −1714.77 | −0.584217 | ||||||||
\(206\) | −3417.44 | −1.15584 | ||||||||
\(207\) | −673.179 | −0.226035 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −51.7276 | −0.0171200 | ||||||||
\(210\) | −1342.04 | −0.440997 | ||||||||
\(211\) | 4341.45 | 1.41648 | 0.708241 | − | 0.705971i | \(-0.249489\pi\) | ||||
0.708241 | + | 0.705971i | \(0.249489\pi\) | |||||||
\(212\) | 354.481 | 0.114839 | ||||||||
\(213\) | −1983.94 | −0.638204 | ||||||||
\(214\) | 872.165 | 0.278598 | ||||||||
\(215\) | −2462.54 | −0.781136 | ||||||||
\(216\) | −664.591 | −0.209350 | ||||||||
\(217\) | −5121.91 | −1.60229 | ||||||||
\(218\) | −1926.47 | −0.598520 | ||||||||
\(219\) | 502.024 | 0.154903 | ||||||||
\(220\) | 9.71730 | 0.00297791 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −793.696 | −0.239952 | ||||||||
\(223\) | −4615.37 | −1.38596 | −0.692978 | − | 0.720959i | \(-0.743702\pi\) | ||||
−0.692978 | + | 0.720959i | \(0.743702\pi\) | |||||||
\(224\) | −3108.09 | −0.927091 | ||||||||
\(225\) | −753.812 | −0.223352 | ||||||||
\(226\) | −4228.89 | −1.24470 | ||||||||
\(227\) | 2163.44 | 0.632565 | 0.316283 | − | 0.948665i | \(-0.397565\pi\) | ||||
0.316283 | + | 0.948665i | \(0.397565\pi\) | |||||||
\(228\) | −601.657 | −0.174762 | ||||||||
\(229\) | −1859.48 | −0.536584 | −0.268292 | − | 0.963338i | \(-0.586459\pi\) | ||||
−0.268292 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(230\) | −1134.49 | −0.325243 | ||||||||
\(231\) | −55.2758 | −0.0157441 | ||||||||
\(232\) | 5570.97 | 1.57652 | ||||||||
\(233\) | 2866.87 | 0.806073 | 0.403037 | − | 0.915184i | \(-0.367955\pi\) | ||||
0.403037 | + | 0.915184i | \(0.367955\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2166.68 | 0.601440 | ||||||||
\(236\) | −1281.70 | −0.353523 | ||||||||
\(237\) | 304.197 | 0.0833743 | ||||||||
\(238\) | −6110.99 | −1.66435 | ||||||||
\(239\) | −1893.55 | −0.512485 | −0.256242 | − | 0.966613i | \(-0.582484\pi\) | ||||
−0.256242 | + | 0.966613i | \(0.582484\pi\) | |||||||
\(240\) | −746.700 | −0.200830 | ||||||||
\(241\) | 1813.58 | 0.484741 | 0.242371 | − | 0.970184i | \(-0.422075\pi\) | ||||
0.242371 | + | 0.970184i | \(0.422075\pi\) | |||||||
\(242\) | 3142.58 | 0.834764 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −492.340 | −0.129176 | ||||||||
\(245\) | −3383.71 | −0.882356 | ||||||||
\(246\) | 1891.85 | 0.490325 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4274.56 | −1.09449 | ||||||||
\(249\) | −1520.96 | −0.387095 | ||||||||
\(250\) | −3166.30 | −0.801019 | ||||||||
\(251\) | 4162.32 | 1.04671 | 0.523353 | − | 0.852116i | \(-0.324681\pi\) | ||||
0.523353 | + | 0.852116i | \(0.324681\pi\) | |||||||
\(252\) | −642.927 | −0.160717 | ||||||||
\(253\) | −46.7273 | −0.0116115 | ||||||||
\(254\) | 106.964 | 0.0264234 | ||||||||
\(255\) | 1690.21 | 0.415078 | ||||||||
\(256\) | −3344.88 | −0.816621 | ||||||||
\(257\) | 5985.30 | 1.45274 | 0.726368 | − | 0.687306i | \(-0.241207\pi\) | ||||
0.726368 | + | 0.687306i | \(0.241207\pi\) | |||||||
\(258\) | 2716.85 | 0.655596 | ||||||||
\(259\) | −3303.91 | −0.792645 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2036.96 | 0.483084 | ||||||||
\(262\) | −2484.15 | −0.585768 | ||||||||
\(263\) | 574.618 | 0.134724 | 0.0673621 | − | 0.997729i | \(-0.478542\pi\) | ||||
0.0673621 | + | 0.997729i | \(0.478542\pi\) | |||||||
\(264\) | −46.1311 | −0.0107544 | ||||||||
\(265\) | 939.899 | 0.217877 | ||||||||
\(266\) | 5767.77 | 1.32949 | ||||||||
\(267\) | 4206.99 | 0.964284 | ||||||||
\(268\) | 294.275 | 0.0670734 | ||||||||
\(269\) | 6348.61 | 1.43896 | 0.719482 | − | 0.694511i | \(-0.244379\pi\) | ||||
0.719482 | + | 0.694511i | \(0.244379\pi\) | |||||||
\(270\) | −409.520 | −0.0923060 | ||||||||
\(271\) | 3278.38 | 0.734861 | 0.367431 | − | 0.930051i | \(-0.380238\pi\) | ||||
0.367431 | + | 0.930051i | \(0.380238\pi\) | |||||||
\(272\) | −3400.11 | −0.757948 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3644.06 | −0.803452 | ||||||||
\(275\) | −52.3242 | −0.0114737 | ||||||||
\(276\) | −543.498 | −0.118532 | ||||||||
\(277\) | 3952.17 | 0.857267 | 0.428633 | − | 0.903478i | \(-0.358995\pi\) | ||||
0.428633 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(278\) | −89.4267 | −0.0192930 | ||||||||
\(279\) | −1562.94 | −0.335380 | ||||||||
\(280\) | −4662.27 | −0.995085 | ||||||||
\(281\) | 411.389 | 0.0873360 | 0.0436680 | − | 0.999046i | \(-0.486096\pi\) | ||||
0.0436680 | + | 0.999046i | \(0.486096\pi\) | |||||||
\(282\) | −2390.43 | −0.504781 | ||||||||
\(283\) | −5872.78 | −1.23357 | −0.616785 | − | 0.787131i | \(-0.711565\pi\) | ||||
−0.616785 | + | 0.787131i | \(0.711565\pi\) | |||||||
\(284\) | −1601.75 | −0.334671 | ||||||||
\(285\) | −1595.28 | −0.331566 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7875.18 | 1.61971 | ||||||||
\(288\) | −948.430 | −0.194051 | ||||||||
\(289\) | 2783.39 | 0.566537 | ||||||||
\(290\) | 3432.83 | 0.695113 | ||||||||
\(291\) | 5708.67 | 1.14999 | ||||||||
\(292\) | 405.314 | 0.0812301 | ||||||||
\(293\) | 500.957 | 0.0998847 | 0.0499423 | − | 0.998752i | \(-0.484096\pi\) | ||||
0.0499423 | + | 0.998752i | \(0.484096\pi\) | |||||||
\(294\) | 3733.14 | 0.740549 | ||||||||
\(295\) | −3398.39 | −0.670718 | ||||||||
\(296\) | −2757.32 | −0.541439 | ||||||||
\(297\) | −16.8673 | −0.00329542 | ||||||||
\(298\) | −4304.07 | −0.836671 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −608.597 | −0.117125 | ||||||||
\(301\) | 11309.4 | 2.16566 | ||||||||
\(302\) | −7650.61 | −1.45776 | ||||||||
\(303\) | −5499.28 | −1.04266 | ||||||||
\(304\) | 3209.14 | 0.605451 | ||||||||
\(305\) | −1305.43 | −0.245077 | ||||||||
\(306\) | −1864.76 | −0.348370 | ||||||||
\(307\) | 5975.57 | 1.11089 | 0.555446 | − | 0.831553i | \(-0.312548\pi\) | ||||
0.555446 | + | 0.831553i | \(0.312548\pi\) | |||||||
\(308\) | −44.6274 | −0.00825611 | ||||||||
\(309\) | −4340.96 | −0.799185 | ||||||||
\(310\) | −2633.98 | −0.482581 | ||||||||
\(311\) | 44.4925 | 0.00811234 | 0.00405617 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405617 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9957.78 | 1.79823 | 0.899117 | − | 0.437709i | \(-0.144210\pi\) | ||||
0.899117 | + | 0.437709i | \(0.144210\pi\) | |||||||
\(314\) | −1961.60 | −0.352546 | ||||||||
\(315\) | −1704.71 | −0.304918 | ||||||||
\(316\) | 245.596 | 0.0437211 | ||||||||
\(317\) | −7752.29 | −1.37354 | −0.686770 | − | 0.726875i | \(-0.740972\pi\) | ||||
−0.686770 | + | 0.726875i | \(0.740972\pi\) | |||||||
\(318\) | −1036.96 | −0.182862 | ||||||||
\(319\) | 141.391 | 0.0248163 | ||||||||
\(320\) | −3589.56 | −0.627070 | ||||||||
\(321\) | 1107.86 | 0.192631 | ||||||||
\(322\) | 5210.22 | 0.901721 | ||||||||
\(323\) | −7264.13 | −1.25135 | ||||||||
\(324\) | −196.188 | −0.0336400 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4912.23 | −0.834550 | ||||||||
\(327\) | −2447.08 | −0.413834 | ||||||||
\(328\) | 6572.34 | 1.10639 | ||||||||
\(329\) | −9950.62 | −1.66746 | ||||||||
\(330\) | −28.4260 | −0.00474181 | ||||||||
\(331\) | 1338.85 | 0.222326 | 0.111163 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111163 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(332\) | −1227.96 | −0.202991 | ||||||||
\(333\) | −1008.18 | −0.165910 | ||||||||
\(334\) | 203.062 | 0.0332666 | ||||||||
\(335\) | 780.261 | 0.127254 | ||||||||
\(336\) | 3429.27 | 0.556792 | ||||||||
\(337\) | 3788.95 | 0.612454 | 0.306227 | − | 0.951958i | \(-0.400933\pi\) | ||||
0.306227 | + | 0.951958i | \(0.400933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5371.69 | −0.860621 | ||||||||
\(340\) | 1364.61 | 0.217665 | ||||||||
\(341\) | −108.488 | −0.0172286 | ||||||||
\(342\) | 1760.02 | 0.278278 | ||||||||
\(343\) | 5423.53 | 0.853770 | ||||||||
\(344\) | 9438.42 | 1.47932 | ||||||||
\(345\) | −1441.07 | −0.224883 | ||||||||
\(346\) | −6392.03 | −0.993173 | ||||||||
\(347\) | 7795.15 | 1.20595 | 0.602977 | − | 0.797759i | \(-0.293981\pi\) | ||||
0.602977 | + | 0.797759i | \(0.293981\pi\) | |||||||
\(348\) | 1644.56 | 0.253327 | ||||||||
\(349\) | −134.533 | −0.0206344 | −0.0103172 | − | 0.999947i | \(-0.503284\pi\) | ||||
−0.0103172 | + | 0.999947i | \(0.503284\pi\) | |||||||
\(350\) | 5834.29 | 0.891018 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −65.8332 | −0.00996853 | ||||||||
\(353\) | 2973.71 | 0.448370 | 0.224185 | − | 0.974547i | \(-0.428028\pi\) | ||||
0.224185 | + | 0.974547i | \(0.428028\pi\) | |||||||
\(354\) | 3749.34 | 0.562925 | ||||||||
\(355\) | −4247.01 | −0.634952 | ||||||||
\(356\) | 3396.56 | 0.505666 | ||||||||
\(357\) | −7762.40 | −1.15078 | ||||||||
\(358\) | 10396.7 | 1.53487 | ||||||||
\(359\) | −8671.60 | −1.27485 | −0.637423 | − | 0.770514i | \(-0.719999\pi\) | ||||
−0.637423 | + | 0.770514i | \(0.719999\pi\) | |||||||
\(360\) | −1422.68 | −0.208283 | ||||||||
\(361\) | −2.85364 | −0.000416043 0 | ||||||||
\(362\) | 3953.54 | 0.574015 | ||||||||
\(363\) | 3991.83 | 0.577181 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1074.68 | 0.154113 | ||||||||
\(366\) | 1440.24 | 0.205690 | ||||||||
\(367\) | 4514.32 | 0.642086 | 0.321043 | − | 0.947065i | \(-0.395967\pi\) | ||||
0.321043 | + | 0.947065i | \(0.395967\pi\) | |||||||
\(368\) | 2898.93 | 0.410644 | ||||||||
\(369\) | 2403.10 | 0.339025 | ||||||||
\(370\) | −1699.06 | −0.238729 | ||||||||
\(371\) | −4316.55 | −0.604054 | ||||||||
\(372\) | −1261.86 | −0.175871 | ||||||||
\(373\) | 6570.60 | 0.912099 | 0.456049 | − | 0.889955i | \(-0.349264\pi\) | ||||
0.456049 | + | 0.889955i | \(0.349264\pi\) | |||||||
\(374\) | −129.438 | −0.0178959 | ||||||||
\(375\) | −4021.96 | −0.553848 | ||||||||
\(376\) | −8304.42 | −1.13901 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1880.75 | 0.255914 | ||||||||
\(379\) | 5490.38 | 0.744121 | 0.372060 | − | 0.928209i | \(-0.378651\pi\) | ||||
0.372060 | + | 0.928209i | \(0.378651\pi\) | |||||||
\(380\) | −1287.96 | −0.173871 | ||||||||
\(381\) | 135.870 | 0.0182699 | ||||||||
\(382\) | 685.188 | 0.0917730 | ||||||||
\(383\) | −10187.3 | −1.35912 | −0.679562 | − | 0.733618i | \(-0.737830\pi\) | ||||
−0.679562 | + | 0.733618i | \(0.737830\pi\) | |||||||
\(384\) | 1431.11 | 0.190185 | ||||||||
\(385\) | −118.328 | −0.0156638 | ||||||||
\(386\) | 2455.05 | 0.323728 | ||||||||
\(387\) | 3451.05 | 0.453299 | ||||||||
\(388\) | 4608.95 | 0.603051 | ||||||||
\(389\) | 4883.97 | 0.636573 | 0.318287 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318287 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6561.94 | −0.848725 | ||||||||
\(392\) | 12969.0 | 1.67101 | ||||||||
\(393\) | −3155.46 | −0.405018 | ||||||||
\(394\) | 3350.64 | 0.428434 | ||||||||
\(395\) | 651.192 | 0.0829494 | ||||||||
\(396\) | −13.6180 | −0.00172810 | ||||||||
\(397\) | 2115.04 | 0.267382 | 0.133691 | − | 0.991023i | \(-0.457317\pi\) | ||||
0.133691 | + | 0.991023i | \(0.457317\pi\) | |||||||
\(398\) | 5640.80 | 0.710422 | ||||||||
\(399\) | 7326.43 | 0.919249 | ||||||||
\(400\) | 3246.16 | 0.405770 | ||||||||
\(401\) | 674.254 | 0.0839667 | 0.0419834 | − | 0.999118i | \(-0.486632\pi\) | ||||
0.0419834 | + | 0.999118i | \(0.486632\pi\) | |||||||
\(402\) | −860.839 | −0.106803 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4439.89 | −0.546765 | ||||||||
\(405\) | −520.188 | −0.0638231 | ||||||||
\(406\) | −15765.5 | −1.92717 | ||||||||
\(407\) | −69.9808 | −0.00852290 | ||||||||
\(408\) | −6478.22 | −0.786077 | ||||||||
\(409\) | −4673.33 | −0.564991 | −0.282496 | − | 0.959269i | \(-0.591162\pi\) | ||||
−0.282496 | + | 0.959269i | \(0.591162\pi\) | |||||||
\(410\) | 4049.87 | 0.487826 | ||||||||
\(411\) | −4628.83 | −0.555531 | ||||||||
\(412\) | −3504.71 | −0.419089 | ||||||||
\(413\) | 15607.3 | 1.85953 | ||||||||
\(414\) | 1589.89 | 0.188741 | ||||||||
\(415\) | −3255.90 | −0.385122 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −113.593 | −0.0133398 | ||||||||
\(418\) | 122.168 | 0.0142953 | ||||||||
\(419\) | −256.853 | −0.0299477 | −0.0149739 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149739 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(420\) | −1376.31 | −0.159898 | ||||||||
\(421\) | 8746.82 | 1.01257 | 0.506287 | − | 0.862365i | \(-0.331018\pi\) | ||||
0.506287 | + | 0.862365i | \(0.331018\pi\) | |||||||
\(422\) | −10253.5 | −1.18278 | ||||||||
\(423\) | −3036.42 | −0.349020 | ||||||||
\(424\) | −3602.43 | −0.412617 | ||||||||
\(425\) | −7347.92 | −0.838650 | ||||||||
\(426\) | 4685.60 | 0.532906 | ||||||||
\(427\) | 5995.26 | 0.679464 | ||||||||
\(428\) | 894.439 | 0.101015 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5815.95 | 0.652255 | ||||||||
\(431\) | −8762.72 | −0.979316 | −0.489658 | − | 0.871914i | \(-0.662878\pi\) | ||||
−0.489658 | + | 0.871914i | \(0.662878\pi\) | |||||||
\(432\) | 1046.44 | 0.116543 | ||||||||
\(433\) | 6425.50 | 0.713140 | 0.356570 | − | 0.934269i | \(-0.383946\pi\) | ||||
0.356570 | + | 0.934269i | \(0.383946\pi\) | |||||||
\(434\) | 12096.7 | 1.33793 | ||||||||
\(435\) | 4360.51 | 0.480622 | ||||||||
\(436\) | −1975.67 | −0.217013 | ||||||||
\(437\) | 6193.39 | 0.677963 | ||||||||
\(438\) | −1185.66 | −0.129345 | ||||||||
\(439\) | 6820.28 | 0.741490 | 0.370745 | − | 0.928735i | \(-0.379102\pi\) | ||||
0.370745 | + | 0.928735i | \(0.379102\pi\) | |||||||
\(440\) | −98.7525 | −0.0106996 | ||||||||
\(441\) | 4741.98 | 0.512038 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5062.48 | 0.542948 | 0.271474 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271474 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(444\) | −813.966 | −0.0870025 | ||||||||
\(445\) | 9005.88 | 0.959370 | ||||||||
\(446\) | 10900.4 | 1.15729 | ||||||||
\(447\) | −5467.19 | −0.578500 | ||||||||
\(448\) | 16485.3 | 1.73852 | ||||||||
\(449\) | 6590.82 | 0.692740 | 0.346370 | − | 0.938098i | \(-0.387414\pi\) | ||||
0.346370 | + | 0.938098i | \(0.387414\pi\) | |||||||
\(450\) | 1780.33 | 0.186501 | ||||||||
\(451\) | 166.806 | 0.0174159 | ||||||||
\(452\) | −4336.89 | −0.451305 | ||||||||
\(453\) | −9718.09 | −1.00794 | ||||||||
\(454\) | −5109.52 | −0.528198 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6114.37 | 0.627920 | ||||||||
\(457\) | 2254.75 | 0.230793 | 0.115397 | − | 0.993319i | \(-0.463186\pi\) | ||||
0.115397 | + | 0.993319i | \(0.463186\pi\) | |||||||
\(458\) | 4391.65 | 0.448053 | ||||||||
\(459\) | −2368.69 | −0.240873 | ||||||||
\(460\) | −1163.46 | −0.117928 | ||||||||
\(461\) | −7358.79 | −0.743456 | −0.371728 | − | 0.928342i | \(-0.621235\pi\) | ||||
−0.371728 | + | 0.928342i | \(0.621235\pi\) | |||||||
\(462\) | 130.548 | 0.0131464 | ||||||||
\(463\) | −11598.3 | −1.16419 | −0.582096 | − | 0.813120i | \(-0.697767\pi\) | ||||
−0.582096 | + | 0.813120i | \(0.697767\pi\) | |||||||
\(464\) | −8771.82 | −0.877633 | ||||||||
\(465\) | −3345.78 | −0.333671 | ||||||||
\(466\) | −6770.87 | −0.673079 | ||||||||
\(467\) | −302.150 | −0.0299397 | −0.0149698 | − | 0.999888i | \(-0.504765\pi\) | ||||
−0.0149698 | + | 0.999888i | \(0.504765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3583.41 | −0.352807 | ||||||||
\(470\) | −5117.18 | −0.502208 | ||||||||
\(471\) | −2491.69 | −0.243760 | ||||||||
\(472\) | 13025.3 | 1.27021 | ||||||||
\(473\) | 239.547 | 0.0232862 | ||||||||
\(474\) | −718.441 | −0.0696183 | ||||||||
\(475\) | 6935.23 | 0.669916 | ||||||||
\(476\) | −6267.05 | −0.603466 | ||||||||
\(477\) | −1317.19 | −0.126436 | ||||||||
\(478\) | 4472.12 | 0.427929 | ||||||||
\(479\) | 3146.15 | 0.300107 | 0.150053 | − | 0.988678i | \(-0.452055\pi\) | ||||
0.150053 | + | 0.988678i | \(0.452055\pi\) | |||||||
\(480\) | −2030.30 | −0.193062 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4283.24 | −0.404764 | ||||||||
\(483\) | 6618.22 | 0.623477 | ||||||||
\(484\) | 3222.84 | 0.302671 | ||||||||
\(485\) | 12220.5 | 1.14413 | ||||||||
\(486\) | 573.908 | 0.0535659 | ||||||||
\(487\) | −3068.16 | −0.285486 | −0.142743 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142743 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(488\) | 5003.43 | 0.464128 | ||||||||
\(489\) | −6239.70 | −0.577033 | ||||||||
\(490\) | 7991.51 | 0.736775 | ||||||||
\(491\) | −100.558 | −0.00924262 | −0.00462131 | − | 0.999989i | \(-0.501471\pi\) | ||||
−0.00462131 | + | 0.999989i | \(0.501471\pi\) | |||||||
\(492\) | 1940.16 | 0.177783 | ||||||||
\(493\) | 19855.7 | 1.81390 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −36.1077 | −0.00327863 | ||||||||
\(496\) | 6730.54 | 0.609295 | ||||||||
\(497\) | 19504.7 | 1.76037 | ||||||||
\(498\) | 3592.14 | 0.323228 | ||||||||
\(499\) | −3616.55 | −0.324447 | −0.162223 | − | 0.986754i | \(-0.551867\pi\) | ||||
−0.162223 | + | 0.986754i | \(0.551867\pi\) | |||||||
\(500\) | −3247.17 | −0.290435 | ||||||||
\(501\) | 257.937 | 0.0230015 | ||||||||
\(502\) | −9830.40 | −0.874009 | ||||||||
\(503\) | −5372.64 | −0.476251 | −0.238125 | − | 0.971234i | \(-0.576533\pi\) | ||||
−0.238125 | + | 0.971234i | \(0.576533\pi\) | |||||||
\(504\) | 6533.78 | 0.577456 | ||||||||
\(505\) | −11772.3 | −1.03734 | ||||||||
\(506\) | 110.359 | 0.00969574 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 109.696 | 0.00958065 | ||||||||
\(509\) | 11314.7 | 0.985298 | 0.492649 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492649 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(510\) | −3991.87 | −0.346594 | ||||||||
\(511\) | −4935.54 | −0.427271 | ||||||||
\(512\) | 11716.1 | 1.01130 | ||||||||
\(513\) | 2235.65 | 0.192410 | ||||||||
\(514\) | −14135.9 | −1.21305 | ||||||||
\(515\) | −9292.65 | −0.795113 | ||||||||
\(516\) | 2786.24 | 0.237708 | ||||||||
\(517\) | −210.766 | −0.0179294 | ||||||||
\(518\) | 7803.05 | 0.661865 | ||||||||
\(519\) | −8119.40 | −0.686709 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18470.9 | −1.55321 | −0.776606 | − | 0.629986i | \(-0.783061\pi\) | ||||
−0.776606 | + | 0.629986i | \(0.783061\pi\) | |||||||
\(522\) | −4810.82 | −0.403379 | ||||||||
\(523\) | 10891.0 | 0.910576 | 0.455288 | − | 0.890344i | \(-0.349536\pi\) | ||||
0.455288 | + | 0.890344i | \(0.349536\pi\) | |||||||
\(524\) | −2547.59 | −0.212389 | ||||||||
\(525\) | 7410.94 | 0.616076 | ||||||||
\(526\) | −1357.11 | −0.112496 | ||||||||
\(527\) | −15235.1 | −1.25930 | ||||||||
\(528\) | 72.6361 | 0.00598690 | ||||||||
\(529\) | −6572.30 | −0.540174 | ||||||||
\(530\) | −2219.82 | −0.181930 | ||||||||
\(531\) | 4762.56 | 0.389223 | ||||||||
\(532\) | 5915.06 | 0.482050 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9935.92 | −0.805186 | ||||||||
\(535\) | 2371.58 | 0.191649 | ||||||||
\(536\) | −2990.58 | −0.240995 | ||||||||
\(537\) | 13206.3 | 1.06126 | ||||||||
\(538\) | −14993.9 | −1.20155 | ||||||||
\(539\) | 329.154 | 0.0263037 | ||||||||
\(540\) | −419.979 | −0.0334685 | ||||||||
\(541\) | 13416.3 | 1.06620 | 0.533099 | − | 0.846053i | \(-0.321027\pi\) | ||||
0.533099 | + | 0.846053i | \(0.321027\pi\) | |||||||
\(542\) | −7742.75 | −0.613616 | ||||||||
\(543\) | 5021.93 | 0.396891 | ||||||||
\(544\) | −9244.99 | −0.728632 | ||||||||
\(545\) | −5238.45 | −0.411726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17849.0 | −1.39519 | −0.697593 | − | 0.716495i | \(-0.745745\pi\) | ||||
−0.697593 | + | 0.716495i | \(0.745745\pi\) | |||||||
\(548\) | −3737.13 | −0.291318 | ||||||||
\(549\) | 1829.45 | 0.142220 | ||||||||
\(550\) | 123.577 | 0.00958065 | ||||||||
\(551\) | −18740.5 | −1.44895 | ||||||||
\(552\) | 5523.32 | 0.425884 | ||||||||
\(553\) | −2990.64 | −0.229973 | ||||||||
\(554\) | −9334.09 | −0.715826 | ||||||||
\(555\) | −2158.21 | −0.165065 | ||||||||
\(556\) | −91.7105 | −0.00699531 | ||||||||
\(557\) | 20131.4 | 1.53141 | 0.765703 | − | 0.643195i | \(-0.222391\pi\) | ||||
0.765703 | + | 0.643195i | \(0.222391\pi\) | |||||||
\(558\) | 3691.30 | 0.280045 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7341.02 | 0.553955 | ||||||||
\(561\) | −164.417 | −0.0123738 | ||||||||
\(562\) | −971.603 | −0.0729263 | ||||||||
\(563\) | −22345.8 | −1.67276 | −0.836380 | − | 0.548150i | \(-0.815332\pi\) | ||||
−0.836380 | + | 0.548150i | \(0.815332\pi\) | |||||||
\(564\) | −2451.48 | −0.183025 | ||||||||
\(565\) | −11499.1 | −0.856235 | ||||||||
\(566\) | 13870.1 | 1.03004 | ||||||||
\(567\) | 2389.00 | 0.176946 | ||||||||
\(568\) | 16277.9 | 1.20247 | ||||||||
\(569\) | −8455.72 | −0.622992 | −0.311496 | − | 0.950248i | \(-0.600830\pi\) | ||||
−0.311496 | + | 0.950248i | \(0.600830\pi\) | |||||||
\(570\) | 3767.67 | 0.276860 | ||||||||
\(571\) | 12813.0 | 0.939069 | 0.469534 | − | 0.882914i | \(-0.344422\pi\) | ||||
0.469534 | + | 0.882914i | \(0.344422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 870.352 | 0.0634546 | ||||||||
\(574\) | −18599.3 | −1.35247 | ||||||||
\(575\) | 6264.83 | 0.454367 | ||||||||
\(576\) | 5030.47 | 0.363894 | ||||||||
\(577\) | −1971.59 | −0.142251 | −0.0711253 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711253 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(578\) | −6573.72 | −0.473063 | ||||||||
\(579\) | 3118.50 | 0.223835 | ||||||||
\(580\) | 3520.50 | 0.252036 | ||||||||
\(581\) | 14952.9 | 1.06773 | ||||||||
\(582\) | −13482.5 | −0.960255 | ||||||||
\(583\) | −91.4298 | −0.00649508 | ||||||||
\(584\) | −4119.02 | −0.291860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1183.14 | −0.0834046 | ||||||||
\(587\) | −8585.69 | −0.603696 | −0.301848 | − | 0.953356i | \(-0.597603\pi\) | ||||
−0.301848 | + | 0.953356i | \(0.597603\pi\) | |||||||
\(588\) | 3828.48 | 0.268510 | ||||||||
\(589\) | 14379.4 | 1.00593 | ||||||||
\(590\) | 8026.19 | 0.560056 | ||||||||
\(591\) | 4256.11 | 0.296232 | ||||||||
\(592\) | 4341.56 | 0.301414 | ||||||||
\(593\) | 1746.73 | 0.120961 | 0.0604803 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604803 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(594\) | 39.8366 | 0.00275171 | ||||||||
\(595\) | −16616.9 | −1.14492 | ||||||||
\(596\) | −4413.99 | −0.303362 | ||||||||
\(597\) | 7165.16 | 0.491207 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27531.1 | 1.87794 | 0.938972 | − | 0.343994i | \(-0.111780\pi\) | ||||
0.938972 | + | 0.343994i | \(0.111780\pi\) | |||||||
\(600\) | 6184.90 | 0.420829 | ||||||||
\(601\) | −17539.1 | −1.19041 | −0.595203 | − | 0.803575i | \(-0.702928\pi\) | ||||
−0.595203 | + | 0.803575i | \(0.702928\pi\) | |||||||
\(602\) | −26710.1 | −1.80835 | ||||||||
\(603\) | −1093.47 | −0.0738467 | ||||||||
\(604\) | −7845.99 | −0.528558 | ||||||||
\(605\) | 8545.28 | 0.574240 | ||||||||
\(606\) | 12988.0 | 0.870629 | ||||||||
\(607\) | −22691.1 | −1.51730 | −0.758651 | − | 0.651497i | \(-0.774141\pi\) | ||||
−0.758651 | + | 0.651497i | \(0.774141\pi\) | |||||||
\(608\) | 8725.75 | 0.582033 | ||||||||
\(609\) | −20026.0 | −1.33250 | ||||||||
\(610\) | 3083.11 | 0.204642 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1912.38 | −0.126313 | ||||||||
\(613\) | −7215.30 | −0.475405 | −0.237702 | − | 0.971338i | \(-0.576394\pi\) | ||||
−0.237702 | + | 0.971338i | \(0.576394\pi\) | |||||||
\(614\) | −14112.9 | −0.927605 | ||||||||
\(615\) | 5144.30 | 0.337298 | ||||||||
\(616\) | 453.528 | 0.0296642 | ||||||||
\(617\) | 16870.4 | 1.10077 | 0.550387 | − | 0.834909i | \(-0.314480\pi\) | ||||
0.550387 | + | 0.834909i | \(0.314480\pi\) | |||||||
\(618\) | 10252.3 | 0.667327 | ||||||||
\(619\) | −2244.53 | −0.145743 | −0.0728717 | − | 0.997341i | \(-0.523216\pi\) | ||||
−0.0728717 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(620\) | −2701.25 | −0.174975 | ||||||||
\(621\) | 2019.54 | 0.130501 | ||||||||
\(622\) | −105.081 | −0.00677388 | ||||||||
\(623\) | −41360.1 | −2.65981 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1859.84 | 0.119030 | ||||||||
\(626\) | −23517.9 | −1.50154 | ||||||||
\(627\) | 155.183 | 0.00988421 | ||||||||
\(628\) | −2011.69 | −0.127827 | ||||||||
\(629\) | −9827.44 | −0.622966 | ||||||||
\(630\) | 4026.11 | 0.254610 | ||||||||
\(631\) | 3669.22 | 0.231488 | 0.115744 | − | 0.993279i | \(-0.463075\pi\) | ||||
0.115744 | + | 0.993279i | \(0.463075\pi\) | |||||||
\(632\) | −2495.88 | −0.157090 | ||||||||
\(633\) | −13024.3 | −0.817806 | ||||||||
\(634\) | 18309.1 | 1.14692 | ||||||||
\(635\) | 290.856 | 0.0181768 | ||||||||
\(636\) | −1063.44 | −0.0663024 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −333.933 | −0.0207218 | ||||||||
\(639\) | 5951.82 | 0.368467 | ||||||||
\(640\) | 3063.56 | 0.189215 | ||||||||
\(641\) | 14678.6 | 0.904477 | 0.452239 | − | 0.891897i | \(-0.350626\pi\) | ||||
0.452239 | + | 0.891897i | \(0.350626\pi\) | |||||||
\(642\) | −2616.50 | −0.160849 | ||||||||
\(643\) | −5519.72 | −0.338533 | −0.169266 | − | 0.985570i | \(-0.554140\pi\) | ||||
−0.169266 | + | 0.985570i | \(0.554140\pi\) | |||||||
\(644\) | 5343.28 | 0.326948 | ||||||||
\(645\) | 7387.63 | 0.450989 | ||||||||
\(646\) | 17156.2 | 1.04489 | ||||||||
\(647\) | −11326.9 | −0.688261 | −0.344131 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344131 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(648\) | 1993.77 | 0.120868 | ||||||||
\(649\) | 330.582 | 0.0199946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15365.7 | 0.925085 | ||||||||
\(652\) | −5037.68 | −0.302593 | ||||||||
\(653\) | 3902.89 | 0.233893 | 0.116946 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116946 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(654\) | 5779.42 | 0.345556 | ||||||||
\(655\) | −6754.87 | −0.402954 | ||||||||
\(656\) | −10348.5 | −0.615918 | ||||||||
\(657\) | −1506.07 | −0.0894330 | ||||||||
\(658\) | 23501.0 | 1.39235 | ||||||||
\(659\) | 8022.47 | 0.474220 | 0.237110 | − | 0.971483i | \(-0.423800\pi\) | ||||
0.237110 | + | 0.971483i | \(0.423800\pi\) | |||||||
\(660\) | −29.1519 | −0.00171930 | ||||||||
\(661\) | 5168.76 | 0.304147 | 0.152074 | − | 0.988369i | \(-0.451405\pi\) | ||||
0.152074 | + | 0.988369i | \(0.451405\pi\) | |||||||
\(662\) | −3162.05 | −0.185645 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12479.2 | 0.729346 | ||||||||
\(665\) | 15683.6 | 0.914565 | ||||||||
\(666\) | 2381.09 | 0.138536 | ||||||||
\(667\) | −16928.9 | −0.982743 | ||||||||
\(668\) | 208.248 | 0.0120619 | ||||||||
\(669\) | 13846.1 | 0.800182 | ||||||||
\(670\) | −1842.79 | −0.106259 | ||||||||
\(671\) | 126.987 | 0.00730593 | ||||||||
\(672\) | 9324.28 | 0.535256 | ||||||||
\(673\) | −6654.10 | −0.381124 | −0.190562 | − | 0.981675i | \(-0.561031\pi\) | ||||
−0.190562 | + | 0.981675i | \(0.561031\pi\) | |||||||
\(674\) | −8948.59 | −0.511405 | ||||||||
\(675\) | 2261.44 | 0.128952 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20649.4 | −1.17226 | −0.586130 | − | 0.810217i | \(-0.699349\pi\) | ||||
−0.586130 | + | 0.810217i | \(0.699349\pi\) | |||||||
\(678\) | 12686.7 | 0.718626 | ||||||||
\(679\) | −56123.6 | −3.17205 | ||||||||
\(680\) | −13867.9 | −0.782071 | ||||||||
\(681\) | −6490.31 | −0.365212 | ||||||||
\(682\) | 256.223 | 0.0143861 | ||||||||
\(683\) | −28475.6 | −1.59530 | −0.797649 | − | 0.603122i | \(-0.793923\pi\) | ||||
−0.797649 | + | 0.603122i | \(0.793923\pi\) | |||||||
\(684\) | 1804.97 | 0.100899 | ||||||||
\(685\) | −9908.90 | −0.552700 | ||||||||
\(686\) | −12809.1 | −0.712905 | ||||||||
\(687\) | 5578.43 | 0.309797 | ||||||||
\(688\) | −14861.3 | −0.823522 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3403.47 | 0.187779 | ||||||||
\(691\) | −10610.8 | −0.584160 | −0.292080 | − | 0.956394i | \(-0.594347\pi\) | ||||
−0.292080 | + | 0.956394i | \(0.594347\pi\) | |||||||
\(692\) | −6555.27 | −0.360107 | ||||||||
\(693\) | 165.827 | 0.00908984 | ||||||||
\(694\) | −18410.3 | −1.00698 | ||||||||
\(695\) | −243.168 | −0.0132718 | ||||||||
\(696\) | −16712.9 | −0.910203 | ||||||||
\(697\) | 23424.6 | 1.27299 | ||||||||
\(698\) | 317.736 | 0.0172299 | ||||||||
\(699\) | −8600.62 | −0.465387 | ||||||||
\(700\) | 5983.29 | 0.323067 | ||||||||
\(701\) | −13518.9 | −0.728390 | −0.364195 | − | 0.931323i | \(-0.618656\pi\) | ||||
−0.364195 | + | 0.931323i | \(0.618656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9275.49 | 0.497627 | ||||||||
\(704\) | 349.179 | 0.0186934 | ||||||||
\(705\) | −6500.03 | −0.347242 | ||||||||
\(706\) | −7023.19 | −0.374393 | ||||||||
\(707\) | 54064.9 | 2.87599 | ||||||||
\(708\) | 3845.09 | 0.204107 | ||||||||
\(709\) | −14845.4 | −0.786361 | −0.393180 | − | 0.919461i | \(-0.628625\pi\) | ||||
−0.393180 | + | 0.919461i | \(0.628625\pi\) | |||||||
\(710\) | 10030.4 | 0.530190 | ||||||||
\(711\) | −912.590 | −0.0481362 | ||||||||
\(712\) | −34517.7 | −1.81686 | ||||||||
\(713\) | 12989.4 | 0.682267 | ||||||||
\(714\) | 18333.0 | 0.960915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10662.2 | 0.556517 | ||||||||
\(717\) | 5680.66 | 0.295883 | ||||||||
\(718\) | 20480.3 | 1.06451 | ||||||||
\(719\) | −35900.1 | −1.86210 | −0.931049 | − | 0.364893i | \(-0.881106\pi\) | ||||
−0.931049 | + | 0.364893i | \(0.881106\pi\) | |||||||
\(720\) | 2240.10 | 0.115949 | ||||||||
\(721\) | 42677.2 | 2.20441 | ||||||||
\(722\) | 6.73962 | 0.000347400 0 | ||||||||
\(723\) | −5440.73 | −0.279866 | ||||||||
\(724\) | 4054.50 | 0.208128 | ||||||||
\(725\) | −18956.6 | −0.971078 | ||||||||
\(726\) | −9427.75 | −0.481951 | ||||||||
\(727\) | 12951.4 | 0.660715 | 0.330357 | − | 0.943856i | \(-0.392831\pi\) | ||||
0.330357 | + | 0.943856i | \(0.392831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2538.14 | −0.128686 | ||||||||
\(731\) | 33639.7 | 1.70206 | ||||||||
\(732\) | 1477.02 | 0.0745795 | ||||||||
\(733\) | 1105.36 | 0.0556989 | 0.0278494 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278494 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(734\) | −10661.8 | −0.536148 | ||||||||
\(735\) | 10151.1 | 0.509428 | ||||||||
\(736\) | 7882.27 | 0.394761 | ||||||||
\(737\) | −75.9009 | −0.00379355 | ||||||||
\(738\) | −5675.55 | −0.283089 | ||||||||
\(739\) | −13638.1 | −0.678869 | −0.339434 | − | 0.940630i | \(-0.610236\pi\) | ||||
−0.339434 | + | 0.940630i | \(0.610236\pi\) | |||||||
\(740\) | −1742.45 | −0.0865591 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10194.7 | 0.504391 | ||||||||
\(743\) | −10154.9 | −0.501408 | −0.250704 | − | 0.968064i | \(-0.580662\pi\) | ||||
−0.250704 | + | 0.968064i | \(0.580662\pi\) | |||||||
\(744\) | 12823.7 | 0.631907 | ||||||||
\(745\) | −11703.6 | −0.575552 | ||||||||
\(746\) | −15518.2 | −0.761611 | ||||||||
\(747\) | 4562.87 | 0.223489 | ||||||||
\(748\) | −132.744 | −0.00648876 | ||||||||
\(749\) | −10891.7 | −0.531338 | ||||||||
\(750\) | 9498.91 | 0.462468 | ||||||||
\(751\) | 26579.5 | 1.29148 | 0.645738 | − | 0.763559i | \(-0.276550\pi\) | ||||
0.645738 | + | 0.763559i | \(0.276550\pi\) | |||||||
\(752\) | 13075.8 | 0.634076 | ||||||||
\(753\) | −12487.0 | −0.604316 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20803.5 | −1.00280 | ||||||||
\(756\) | 1928.78 | 0.0927898 | ||||||||
\(757\) | −13677.7 | −0.656705 | −0.328352 | − | 0.944555i | \(-0.606493\pi\) | ||||
−0.328352 | + | 0.944555i | \(0.606493\pi\) | |||||||
\(758\) | −12967.0 | −0.621348 | ||||||||
\(759\) | 140.182 | 0.00670392 | ||||||||
\(760\) | 13089.0 | 0.624720 | ||||||||
\(761\) | −17996.7 | −0.857268 | −0.428634 | − | 0.903478i | \(-0.641005\pi\) | ||||
−0.428634 | + | 0.903478i | \(0.641005\pi\) | |||||||
\(762\) | −320.893 | −0.0152555 | ||||||||
\(763\) | 24057.9 | 1.14149 | ||||||||
\(764\) | 702.687 | 0.0332753 | ||||||||
\(765\) | −5070.63 | −0.239646 | ||||||||
\(766\) | 24059.9 | 1.13488 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10034.6 | 0.471476 | ||||||||
\(769\) | −2995.04 | −0.140447 | −0.0702236 | − | 0.997531i | \(-0.522371\pi\) | ||||
−0.0702236 | + | 0.997531i | \(0.522371\pi\) | |||||||
\(770\) | 279.464 | 0.0130794 | ||||||||
\(771\) | −17955.9 | −0.838737 | ||||||||
\(772\) | 2517.75 | 0.117378 | ||||||||
\(773\) | 26055.4 | 1.21235 | 0.606177 | − | 0.795330i | \(-0.292702\pi\) | ||||
0.606177 | + | 0.795330i | \(0.292702\pi\) | |||||||
\(774\) | −8150.56 | −0.378509 | ||||||||
\(775\) | 14545.3 | 0.674169 | ||||||||
\(776\) | −46838.6 | −2.16676 | ||||||||
\(777\) | 9911.73 | 0.457634 | ||||||||
\(778\) | −11534.8 | −0.531545 | ||||||||
\(779\) | −22109.0 | −1.01686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 413.133 | 0.0189284 | ||||||||
\(782\) | 15497.7 | 0.708693 | ||||||||
\(783\) | −6110.89 | −0.278908 | ||||||||
\(784\) | −20420.5 | −0.930235 | ||||||||
\(785\) | −5333.95 | −0.242518 | ||||||||
\(786\) | 7452.45 | 0.338193 | ||||||||
\(787\) | 22992.0 | 1.04139 | 0.520697 | − | 0.853741i | \(-0.325672\pi\) | ||||
0.520697 | + | 0.853741i | \(0.325672\pi\) | |||||||
\(788\) | 3436.21 | 0.155343 | ||||||||
\(789\) | −1723.85 | −0.0777830 | ||||||||
\(790\) | −1537.96 | −0.0692635 | ||||||||
\(791\) | 52810.6 | 2.37387 | ||||||||
\(792\) | 138.393 | 0.00620908 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4995.22 | −0.223267 | ||||||||
\(795\) | −2819.70 | −0.125792 | ||||||||
\(796\) | 5784.86 | 0.257587 | ||||||||
\(797\) | −25826.3 | −1.14782 | −0.573910 | − | 0.818918i | \(-0.694574\pi\) | ||||
−0.573910 | + | 0.818918i | \(0.694574\pi\) | |||||||
\(798\) | −17303.3 | −0.767582 | ||||||||
\(799\) | −29598.0 | −1.31052 | ||||||||
\(800\) | 8826.40 | 0.390075 | ||||||||
\(801\) | −12621.0 | −0.556730 | ||||||||
\(802\) | −1592.43 | −0.0701130 | ||||||||
\(803\) | −104.541 | −0.00459423 | ||||||||
\(804\) | −882.824 | −0.0387249 | ||||||||
\(805\) | 14167.6 | 0.620299 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19045.8 | −0.830787 | ||||||||
\(808\) | 45120.6 | 1.96453 | ||||||||
\(809\) | −28495.8 | −1.23839 | −0.619195 | − | 0.785237i | \(-0.712541\pi\) | ||||
−0.619195 | + | 0.785237i | \(0.712541\pi\) | |||||||
\(810\) | 1228.56 | 0.0532929 | ||||||||
\(811\) | −6992.41 | −0.302758 | −0.151379 | − | 0.988476i | \(-0.548371\pi\) | ||||
−0.151379 | + | 0.988476i | \(0.548371\pi\) | |||||||
\(812\) | −16168.1 | −0.698757 | ||||||||
\(813\) | −9835.14 | −0.424272 | ||||||||
\(814\) | 165.278 | 0.00711670 | ||||||||
\(815\) | −13357.3 | −0.574093 | ||||||||
\(816\) | 10200.3 | 0.437602 | ||||||||
\(817\) | −31750.4 | −1.35961 | ||||||||
\(818\) | 11037.3 | 0.471773 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4153.29 | 0.176877 | ||||||||
\(821\) | −31512.7 | −1.33959 | −0.669793 | − | 0.742547i | \(-0.733617\pi\) | ||||
−0.669793 | + | 0.742547i | \(0.733617\pi\) | |||||||
\(822\) | 10932.2 | 0.463873 | ||||||||
\(823\) | 39159.6 | 1.65859 | 0.829293 | − | 0.558814i | \(-0.188743\pi\) | ||||
0.829293 | + | 0.558814i | \(0.188743\pi\) | |||||||
\(824\) | 35616.8 | 1.50579 | ||||||||
\(825\) | 156.973 | 0.00662435 | ||||||||
\(826\) | −36860.8 | −1.55273 | ||||||||
\(827\) | 36557.6 | 1.53716 | 0.768581 | − | 0.639752i | \(-0.220963\pi\) | ||||
0.768581 | + | 0.639752i | \(0.220963\pi\) | |||||||
\(828\) | 1630.49 | 0.0684342 | ||||||||
\(829\) | 14675.2 | 0.614825 | 0.307413 | − | 0.951576i | \(-0.400537\pi\) | ||||
0.307413 | + | 0.951576i | \(0.400537\pi\) | |||||||
\(830\) | 7689.66 | 0.321581 | ||||||||
\(831\) | −11856.5 | −0.494943 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46223.3 | 1.92262 | ||||||||
\(834\) | 268.280 | 0.0111388 | ||||||||
\(835\) | 552.164 | 0.0228843 | ||||||||
\(836\) | 125.288 | 0.00518323 | ||||||||
\(837\) | 4688.83 | 0.193632 | ||||||||
\(838\) | 606.626 | 0.0250066 | ||||||||
\(839\) | 8515.56 | 0.350405 | 0.175202 | − | 0.984532i | \(-0.443942\pi\) | ||||
0.175202 | + | 0.984532i | \(0.443942\pi\) | |||||||
\(840\) | 13986.8 | 0.574513 | ||||||||
\(841\) | 26835.9 | 1.10033 | ||||||||
\(842\) | −20657.9 | −0.845509 | ||||||||
\(843\) | −1234.17 | −0.0504234 | ||||||||
\(844\) | −10515.3 | −0.428854 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7171.29 | 0.291435 | ||||||||
\(847\) | −39244.8 | −1.59205 | ||||||||
\(848\) | 5672.24 | 0.229700 | ||||||||
\(849\) | 17618.3 | 0.712202 | ||||||||
\(850\) | 17354.0 | 0.700281 | ||||||||
\(851\) | 8378.86 | 0.337513 | ||||||||
\(852\) | 4805.26 | 0.193222 | ||||||||
\(853\) | −9645.93 | −0.387187 | −0.193593 | − | 0.981082i | \(-0.562014\pi\) | ||||
−0.193593 | + | 0.981082i | \(0.562014\pi\) | |||||||
\(854\) | −14159.4 | −0.567359 | ||||||||
\(855\) | 4785.84 | 0.191430 | ||||||||
\(856\) | −9089.77 | −0.362946 | ||||||||
\(857\) | 36139.6 | 1.44050 | 0.720248 | − | 0.693717i | \(-0.244028\pi\) | ||||
0.720248 | + | 0.693717i | \(0.244028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7108.04 | −0.282332 | −0.141166 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141166 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(860\) | 5964.47 | 0.236496 | ||||||||
\(861\) | −23625.5 | −0.935141 | ||||||||
\(862\) | 20695.5 | 0.817738 | ||||||||
\(863\) | −16225.8 | −0.640016 | −0.320008 | − | 0.947415i | \(-0.603686\pi\) | ||||
−0.320008 | + | 0.947415i | \(0.603686\pi\) | |||||||
\(864\) | 2845.29 | 0.112036 | ||||||||
\(865\) | −17381.1 | −0.683210 | ||||||||
\(866\) | −15175.5 | −0.595478 | ||||||||
\(867\) | −8350.18 | −0.327090 | ||||||||
\(868\) | 12405.7 | 0.485110 | ||||||||
\(869\) | −63.3455 | −0.00247278 | ||||||||
\(870\) | −10298.5 | −0.401324 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 20077.9 | 0.779727 | ||||||||
\(873\) | −17126.0 | −0.663949 | ||||||||
\(874\) | −14627.3 | −0.566106 | ||||||||
\(875\) | 39541.0 | 1.52769 | ||||||||
\(876\) | −1215.94 | −0.0468982 | ||||||||
\(877\) | 30983.0 | 1.19295 | 0.596477 | − | 0.802630i | \(-0.296567\pi\) | ||||
0.596477 | + | 0.802630i | \(0.296567\pi\) | |||||||
\(878\) | −16107.9 | −0.619151 | ||||||||
\(879\) | −1502.87 | −0.0576684 | ||||||||
\(880\) | 155.492 | 0.00595639 | ||||||||
\(881\) | −7670.76 | −0.293342 | −0.146671 | − | 0.989185i | \(-0.546856\pi\) | ||||
−0.146671 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(882\) | −11199.4 | −0.427556 | ||||||||
\(883\) | −34340.6 | −1.30878 | −0.654390 | − | 0.756157i | \(-0.727075\pi\) | ||||
−0.654390 | + | 0.756157i | \(0.727075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10195.2 | 0.387239 | ||||||||
\(886\) | −11956.4 | −0.453366 | ||||||||
\(887\) | −19208.3 | −0.727118 | −0.363559 | − | 0.931571i | \(-0.618438\pi\) | ||||
−0.363559 | + | 0.931571i | \(0.618438\pi\) | |||||||
\(888\) | 8271.96 | 0.312600 | ||||||||
\(889\) | −1335.78 | −0.0503943 | ||||||||
\(890\) | −21269.8 | −0.801083 | ||||||||
\(891\) | 50.6019 | 0.00190261 | ||||||||
\(892\) | 11178.8 | 0.419611 | ||||||||
\(893\) | 27935.7 | 1.04684 | ||||||||
\(894\) | 12912.2 | 0.483052 | ||||||||
\(895\) | 28270.6 | 1.05585 | ||||||||
\(896\) | −14069.6 | −0.524591 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15566.0 | −0.578444 | ||||||||
\(899\) | −39304.4 | −1.45815 | ||||||||
\(900\) | 1825.79 | 0.0676219 | ||||||||
\(901\) | −12839.5 | −0.474747 | ||||||||
\(902\) | −393.956 | −0.0145425 | ||||||||
\(903\) | −33928.2 | −1.25034 | ||||||||
\(904\) | 44073.8 | 1.62154 | ||||||||
\(905\) | 10750.4 | 0.394868 | ||||||||
\(906\) | 22951.8 | 0.841637 | ||||||||
\(907\) | −46481.0 | −1.70163 | −0.850813 | − | 0.525468i | \(-0.823890\pi\) | ||||
−0.850813 | + | 0.525468i | \(0.823890\pi\) | |||||||
\(908\) | −5240.01 | −0.191515 | ||||||||
\(909\) | 16497.8 | 0.601979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34109.3 | −1.24050 | −0.620248 | − | 0.784406i | \(-0.712968\pi\) | ||||
−0.620248 | + | 0.784406i | \(0.712968\pi\) | |||||||
\(912\) | −9627.43 | −0.349557 | ||||||||
\(913\) | 316.721 | 0.0114808 | ||||||||
\(914\) | −5325.18 | −0.192715 | ||||||||
\(915\) | 3916.28 | 0.141495 | ||||||||
\(916\) | 4503.80 | 0.162456 | ||||||||
\(917\) | 31022.2 | 1.11717 | ||||||||
\(918\) | 5594.27 | 0.201131 | ||||||||
\(919\) | −37533.6 | −1.34725 | −0.673623 | − | 0.739075i | \(-0.735263\pi\) | ||||
−0.673623 | + | 0.739075i | \(0.735263\pi\) | |||||||
\(920\) | 11823.7 | 0.423714 | ||||||||
\(921\) | −17926.7 | −0.641373 | ||||||||
\(922\) | 17379.7 | 0.620793 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 133.882 | 0.00476667 | ||||||||
\(925\) | 9382.48 | 0.333507 | ||||||||
\(926\) | 27392.5 | 0.972111 | ||||||||
\(927\) | 13022.9 | 0.461410 | ||||||||
\(928\) | −23850.8 | −0.843687 | ||||||||
\(929\) | −4966.75 | −0.175408 | −0.0877038 | − | 0.996147i | \(-0.527953\pi\) | ||||
−0.0877038 | + | 0.996147i | \(0.527953\pi\) | |||||||
\(930\) | 7901.94 | 0.278618 | ||||||||
\(931\) | −43627.2 | −1.53579 | ||||||||
\(932\) | −6943.79 | −0.244047 | ||||||||
\(933\) | −133.477 | −0.00468366 | ||||||||
\(934\) | 713.606 | 0.0249999 | ||||||||
\(935\) | −351.966 | −0.0123107 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5096.90 | −0.177704 | −0.0888519 | − | 0.996045i | \(-0.528320\pi\) | ||||
−0.0888519 | + | 0.996045i | \(0.528320\pi\) | |||||||
\(938\) | 8463.15 | 0.294597 | ||||||||
\(939\) | −29873.3 | −1.03821 | ||||||||
\(940\) | −5247.86 | −0.182092 | ||||||||
\(941\) | −54774.8 | −1.89756 | −0.948781 | − | 0.315933i | \(-0.897682\pi\) | ||||
−0.948781 | + | 0.315933i | \(0.897682\pi\) | |||||||
\(942\) | 5884.79 | 0.203542 | ||||||||
\(943\) | −19971.8 | −0.689684 | ||||||||
\(944\) | −20509.1 | −0.707113 | ||||||||
\(945\) | 5114.12 | 0.176045 | ||||||||
\(946\) | −565.753 | −0.0194442 | ||||||||
\(947\) | 13768.5 | 0.472456 | 0.236228 | − | 0.971698i | \(-0.424089\pi\) | ||||
0.236228 | + | 0.971698i | \(0.424089\pi\) | |||||||
\(948\) | −736.788 | −0.0252424 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −16379.4 | −0.559386 | ||||||||
\(951\) | 23256.9 | 0.793013 | ||||||||
\(952\) | 63689.2 | 2.16825 | ||||||||
\(953\) | 35866.6 | 1.21913 | 0.609566 | − | 0.792735i | \(-0.291344\pi\) | ||||
0.609566 | + | 0.792735i | \(0.291344\pi\) | |||||||
\(954\) | 3110.89 | 0.105575 | ||||||||
\(955\) | 1863.16 | 0.0631312 | ||||||||
\(956\) | 4586.33 | 0.155160 | ||||||||
\(957\) | −424.174 | −0.0143277 | ||||||||
\(958\) | −7430.46 | −0.250592 | ||||||||
\(959\) | 45507.3 | 1.53233 | ||||||||
\(960\) | 10768.7 | 0.362039 | ||||||||
\(961\) | 366.899 | 0.0123158 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3323.57 | −0.111216 | ||||||||
\(964\) | −4392.62 | −0.146760 | ||||||||
\(965\) | 6675.75 | 0.222694 | ||||||||
\(966\) | −15630.7 | −0.520609 | ||||||||
\(967\) | 24476.5 | 0.813972 | 0.406986 | − | 0.913434i | \(-0.366580\pi\) | ||||
0.406986 | + | 0.913434i | \(0.366580\pi\) | |||||||
\(968\) | −32752.3 | −1.08750 | ||||||||
\(969\) | 21792.4 | 0.722469 | ||||||||
\(970\) | −28861.9 | −0.955362 | ||||||||
\(971\) | −8976.07 | −0.296659 | −0.148329 | − | 0.988938i | \(-0.547390\pi\) | ||||
−0.148329 | + | 0.988938i | \(0.547390\pi\) | |||||||
\(972\) | 588.565 | 0.0194220 | ||||||||
\(973\) | 1116.77 | 0.0367954 | ||||||||
\(974\) | 7246.26 | 0.238383 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7878.18 | −0.258376 | ||||||||
\(977\) | 42002.8 | 1.37542 | 0.687711 | − | 0.725984i | \(-0.258615\pi\) | ||||
0.687711 | + | 0.725984i | \(0.258615\pi\) | |||||||
\(978\) | 14736.7 | 0.481828 | ||||||||
\(979\) | −876.058 | −0.0285995 | ||||||||
\(980\) | 8195.60 | 0.267142 | ||||||||
\(981\) | 7341.24 | 0.238927 | ||||||||
\(982\) | 237.495 | 0.00771767 | ||||||||
\(983\) | −43240.7 | −1.40301 | −0.701507 | − | 0.712662i | \(-0.747489\pi\) | ||||
−0.701507 | + | 0.712662i | \(0.747489\pi\) | |||||||
\(984\) | −19717.0 | −0.638776 | ||||||||
\(985\) | 9111.03 | 0.294722 | ||||||||
\(986\) | −46894.3 | −1.51462 | ||||||||
\(987\) | 29851.9 | 0.962710 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28681.2 | −0.922152 | ||||||||
\(990\) | 85.2779 | 0.00273769 | ||||||||
\(991\) | 37916.5 | 1.21540 | 0.607698 | − | 0.794168i | \(-0.292093\pi\) | ||||
0.607698 | + | 0.794168i | \(0.292093\pi\) | |||||||
\(992\) | 18300.5 | 0.585728 | ||||||||
\(993\) | −4016.56 | −0.128360 | ||||||||
\(994\) | −46065.4 | −1.46993 | ||||||||
\(995\) | 15338.4 | 0.488704 | ||||||||
\(996\) | 3683.87 | 0.117197 | ||||||||
\(997\) | 6634.86 | 0.210760 | 0.105380 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(998\) | 8541.43 | 0.270916 | ||||||||
\(999\) | 3024.55 | 0.0957883 |
(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 | 507.4.a.i.1.2 | 4 | ||
3.2 | odd | 2 | 1521.4.a.bb.1.3 | 4 | |||
13.4 | even | 6 | 39.4.e.c.16.2 | ✓ | 8 | ||
13.5 | odd | 4 | 507.4.b.h.337.6 | 8 | |||
13.8 | odd | 4 | 507.4.b.h.337.3 | 8 | |||
13.10 | even | 6 | 39.4.e.c.22.2 | yes | 8 | ||
13.12 | even | 2 | 507.4.a.m.1.3 | 4 | |||
39.17 | odd | 6 | 117.4.g.e.55.3 | 8 | |||
39.23 | odd | 6 | 117.4.g.e.100.3 | 8 | |||
39.38 | odd | 2 | 1521.4.a.v.1.2 | 4 | |||
52.23 | odd | 6 | 624.4.q.i.529.3 | 8 | |||
52.43 | odd | 6 | 624.4.q.i.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.2 | ✓ | 8 | 13.4 | even | 6 | ||
39.4.e.c.22.2 | yes | 8 | 13.10 | even | 6 | ||
117.4.g.e.55.3 | 8 | 39.17 | odd | 6 | |||
117.4.g.e.100.3 | 8 | 39.23 | odd | 6 | |||
507.4.a.i.1.2 | 4 | 1.1 | even | 1 | trivial | ||
507.4.a.m.1.3 | 4 | 13.12 | even | 2 | |||
507.4.b.h.337.3 | 8 | 13.8 | odd | 4 | |||
507.4.b.h.337.6 | 8 | 13.5 | odd | 4 | |||
624.4.q.i.289.3 | 8 | 52.43 | odd | 6 | |||
624.4.q.i.529.3 | 8 | 52.23 | odd | 6 | |||
1521.4.a.v.1.2 | 4 | 39.38 | odd | 2 | |||
1521.4.a.bb.1.3 | 4 | 3.2 | odd | 2 |