Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1573,4,Mod(1,1573)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1573, 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("1573.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1573 = 11^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1573.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: | \(92.8100044390\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 1573.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74116 | 0.969147 | 0.484573 | − | 0.874751i | \(-0.338975\pi\) | ||||
0.484573 | + | 0.874751i | \(0.338975\pi\) | |||||||
\(3\) | 6.45484 | 1.24223 | 0.621117 | − | 0.783718i | \(-0.286679\pi\) | ||||
0.621117 | + | 0.783718i | \(0.286679\pi\) | |||||||
\(4\) | −0.486036 | −0.0607545 | ||||||||
\(5\) | 6.42298 | 0.574489 | 0.287244 | − | 0.957857i | \(-0.407261\pi\) | ||||
0.287244 | + | 0.957857i | \(0.407261\pi\) | |||||||
\(6\) | 17.6937 | 1.20391 | ||||||||
\(7\) | −11.8479 | −0.639725 | −0.319862 | − | 0.947464i | \(-0.603637\pi\) | ||||
−0.319862 | + | 0.947464i | \(0.603637\pi\) | |||||||
\(8\) | −23.2616 | −1.02803 | ||||||||
\(9\) | 14.6649 | 0.543145 | ||||||||
\(10\) | 17.6064 | 0.556764 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.13728 | −0.0754713 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −32.4769 | −0.619987 | ||||||||
\(15\) | 41.4593 | 0.713649 | ||||||||
\(16\) | −59.8755 | −0.935554 | ||||||||
\(17\) | −28.8944 | −0.412231 | −0.206115 | − | 0.978528i | \(-0.566082\pi\) | ||||
−0.206115 | + | 0.978528i | \(0.566082\pi\) | |||||||
\(18\) | 40.1989 | 0.526388 | ||||||||
\(19\) | 126.470 | 1.52707 | 0.763534 | − | 0.645767i | \(-0.223462\pi\) | ||||
0.763534 | + | 0.645767i | \(0.223462\pi\) | |||||||
\(20\) | −3.12180 | −0.0349028 | ||||||||
\(21\) | −76.4760 | −0.794688 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.23121 | −0.0746228 | −0.0373114 | − | 0.999304i | \(-0.511879\pi\) | ||||
−0.0373114 | + | 0.999304i | \(0.511879\pi\) | |||||||
\(24\) | −150.150 | −1.27705 | ||||||||
\(25\) | −83.7453 | −0.669963 | ||||||||
\(26\) | −35.6351 | −0.268793 | ||||||||
\(27\) | −79.6209 | −0.567520 | ||||||||
\(28\) | 5.75849 | 0.0388661 | ||||||||
\(29\) | −174.077 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(30\) | 113.647 | 0.691631 | ||||||||
\(31\) | −247.562 | −1.43430 | −0.717152 | − | 0.696916i | \(-0.754555\pi\) | ||||
−0.717152 | + | 0.696916i | \(0.754555\pi\) | |||||||
\(32\) | 21.9644 | 0.121337 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −79.2042 | −0.399512 | ||||||||
\(35\) | −76.0986 | −0.367515 | ||||||||
\(36\) | −7.12768 | −0.0329985 | ||||||||
\(37\) | −238.942 | −1.06167 | −0.530835 | − | 0.847475i | \(-0.678122\pi\) | ||||
−0.530835 | + | 0.847475i | \(0.678122\pi\) | |||||||
\(38\) | 346.676 | 1.47995 | ||||||||
\(39\) | −83.9129 | −0.344534 | ||||||||
\(40\) | −149.409 | −0.590590 | ||||||||
\(41\) | 178.576 | 0.680217 | 0.340109 | − | 0.940386i | \(-0.389536\pi\) | ||||
0.340109 | + | 0.940386i | \(0.389536\pi\) | |||||||
\(42\) | −209.633 | −0.770169 | ||||||||
\(43\) | 336.857 | 1.19466 | 0.597328 | − | 0.801997i | \(-0.296229\pi\) | ||||
0.597328 | + | 0.801997i | \(0.296229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 94.1925 | 0.312031 | ||||||||
\(46\) | −22.5631 | −0.0723205 | ||||||||
\(47\) | 257.326 | 0.798615 | 0.399307 | − | 0.916817i | \(-0.369251\pi\) | ||||
0.399307 | + | 0.916817i | \(0.369251\pi\) | |||||||
\(48\) | −386.487 | −1.16218 | ||||||||
\(49\) | −202.628 | −0.590752 | ||||||||
\(50\) | −229.559 | −0.649292 | ||||||||
\(51\) | −186.509 | −0.512087 | ||||||||
\(52\) | 6.31846 | 0.0168503 | ||||||||
\(53\) | −688.666 | −1.78482 | −0.892411 | − | 0.451224i | \(-0.850988\pi\) | ||||
−0.892411 | + | 0.451224i | \(0.850988\pi\) | |||||||
\(54\) | −218.254 | −0.550011 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 275.600 | 0.657654 | ||||||||
\(57\) | 816.346 | 1.89698 | ||||||||
\(58\) | −477.172 | −1.08027 | ||||||||
\(59\) | 399.431 | 0.881382 | 0.440691 | − | 0.897659i | \(-0.354733\pi\) | ||||
0.440691 | + | 0.897659i | \(0.354733\pi\) | |||||||
\(60\) | −20.1507 | −0.0433574 | ||||||||
\(61\) | −26.9793 | −0.0566286 | −0.0283143 | − | 0.999599i | \(-0.509014\pi\) | ||||
−0.0283143 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(62\) | −678.607 | −1.39005 | ||||||||
\(63\) | −173.748 | −0.347463 | ||||||||
\(64\) | 539.212 | 1.05315 | ||||||||
\(65\) | −83.4987 | −0.159334 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −767.765 | −1.39996 | −0.699981 | − | 0.714161i | \(-0.746808\pi\) | ||||
−0.699981 | + | 0.714161i | \(0.746808\pi\) | |||||||
\(68\) | 14.0437 | 0.0250449 | ||||||||
\(69\) | −53.1311 | −0.0926990 | ||||||||
\(70\) | −208.599 | −0.356176 | ||||||||
\(71\) | −335.419 | −0.560661 | −0.280330 | − | 0.959904i | \(-0.590444\pi\) | ||||
−0.280330 | + | 0.959904i | \(0.590444\pi\) | |||||||
\(72\) | −341.129 | −0.558368 | ||||||||
\(73\) | −791.129 | −1.26842 | −0.634210 | − | 0.773161i | \(-0.718674\pi\) | ||||
−0.634210 | + | 0.773161i | \(0.718674\pi\) | |||||||
\(74\) | −654.978 | −1.02891 | ||||||||
\(75\) | −540.563 | −0.832251 | ||||||||
\(76\) | −61.4691 | −0.0927762 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −230.019 | −0.333904 | ||||||||
\(79\) | 708.443 | 1.00894 | 0.504469 | − | 0.863430i | \(-0.331688\pi\) | ||||
0.504469 | + | 0.863430i | \(0.331688\pi\) | |||||||
\(80\) | −384.579 | −0.537465 | ||||||||
\(81\) | −909.893 | −1.24814 | ||||||||
\(82\) | 489.506 | 0.659230 | ||||||||
\(83\) | −821.370 | −1.08623 | −0.543115 | − | 0.839658i | \(-0.682755\pi\) | ||||
−0.543115 | + | 0.839658i | \(0.682755\pi\) | |||||||
\(84\) | 37.1701 | 0.0482808 | ||||||||
\(85\) | −185.588 | −0.236822 | ||||||||
\(86\) | 923.379 | 1.15780 | ||||||||
\(87\) | −1123.64 | −1.38467 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 44.1841 | 0.0526237 | 0.0263118 | − | 0.999654i | \(-0.491624\pi\) | ||||
0.0263118 | + | 0.999654i | \(0.491624\pi\) | |||||||
\(90\) | 258.197 | 0.302404 | ||||||||
\(91\) | 154.022 | 0.177428 | ||||||||
\(92\) | 4.00066 | 0.00453367 | ||||||||
\(93\) | −1597.97 | −1.78174 | ||||||||
\(94\) | 705.373 | 0.773975 | ||||||||
\(95\) | 812.317 | 0.877284 | ||||||||
\(96\) | 141.777 | 0.150729 | ||||||||
\(97\) | −886.256 | −0.927687 | −0.463844 | − | 0.885917i | \(-0.653530\pi\) | ||||
−0.463844 | + | 0.885917i | \(0.653530\pi\) | |||||||
\(98\) | −555.436 | −0.572526 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 40.7032 | 0.0407032 | ||||||||
\(101\) | 153.088 | 0.150820 | 0.0754099 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754099 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(102\) | −511.250 | −0.496288 | ||||||||
\(103\) | 477.777 | 0.457056 | 0.228528 | − | 0.973537i | \(-0.426609\pi\) | ||||
0.228528 | + | 0.973537i | \(0.426609\pi\) | |||||||
\(104\) | 302.401 | 0.285123 | ||||||||
\(105\) | −491.204 | −0.456539 | ||||||||
\(106\) | −1887.74 | −1.72975 | ||||||||
\(107\) | −779.559 | −0.704326 | −0.352163 | − | 0.935939i | \(-0.614554\pi\) | ||||
−0.352163 | + | 0.935939i | \(0.614554\pi\) | |||||||
\(108\) | 38.6986 | 0.0344794 | ||||||||
\(109\) | −1344.92 | −1.18184 | −0.590918 | − | 0.806731i | \(-0.701234\pi\) | ||||
−0.590918 | + | 0.806731i | \(0.701234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1542.33 | −1.31884 | ||||||||
\(112\) | 709.397 | 0.598497 | ||||||||
\(113\) | 265.242 | 0.220813 | 0.110406 | − | 0.993887i | \(-0.464785\pi\) | ||||
0.110406 | + | 0.993887i | \(0.464785\pi\) | |||||||
\(114\) | 2237.74 | 1.83845 | ||||||||
\(115\) | −52.8689 | −0.0428700 | ||||||||
\(116\) | 84.6074 | 0.0677207 | ||||||||
\(117\) | −190.644 | −0.150641 | ||||||||
\(118\) | 1094.91 | 0.854189 | ||||||||
\(119\) | 342.337 | 0.263714 | ||||||||
\(120\) | −964.409 | −0.733651 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −73.9546 | −0.0548814 | ||||||||
\(123\) | 1152.68 | 0.844989 | ||||||||
\(124\) | 120.324 | 0.0871404 | ||||||||
\(125\) | −1340.77 | −0.959375 | ||||||||
\(126\) | −476.271 | −0.336743 | ||||||||
\(127\) | 2710.62 | 1.89392 | 0.946962 | − | 0.321344i | \(-0.104135\pi\) | ||||
0.946962 | + | 0.321344i | \(0.104135\pi\) | |||||||
\(128\) | 1302.35 | 0.899318 | ||||||||
\(129\) | 2174.36 | 1.48404 | ||||||||
\(130\) | −228.883 | −0.154419 | ||||||||
\(131\) | 146.682 | 0.0978293 | 0.0489147 | − | 0.998803i | \(-0.484424\pi\) | ||||
0.0489147 | + | 0.998803i | \(0.484424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1498.40 | −0.976903 | ||||||||
\(134\) | −2104.57 | −1.35677 | ||||||||
\(135\) | −511.403 | −0.326034 | ||||||||
\(136\) | 672.130 | 0.423784 | ||||||||
\(137\) | 1020.60 | 0.636462 | 0.318231 | − | 0.948013i | \(-0.396911\pi\) | ||||
0.318231 | + | 0.948013i | \(0.396911\pi\) | |||||||
\(138\) | −145.641 | −0.0898390 | ||||||||
\(139\) | −402.255 | −0.245459 | −0.122730 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122730 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(140\) | 36.9866 | 0.0223282 | ||||||||
\(141\) | 1661.00 | 0.992066 | ||||||||
\(142\) | −919.437 | −0.543363 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −878.069 | −0.508142 | ||||||||
\(145\) | −1118.09 | −0.640361 | ||||||||
\(146\) | −2168.61 | −1.22928 | ||||||||
\(147\) | −1307.93 | −0.733853 | ||||||||
\(148\) | 116.134 | 0.0645012 | ||||||||
\(149\) | −2209.84 | −1.21501 | −0.607507 | − | 0.794315i | \(-0.707830\pi\) | ||||
−0.607507 | + | 0.794315i | \(0.707830\pi\) | |||||||
\(150\) | −1481.77 | −0.806573 | ||||||||
\(151\) | 1940.88 | 1.04600 | 0.523001 | − | 0.852332i | \(-0.324812\pi\) | ||||
0.523001 | + | 0.852332i | \(0.324812\pi\) | |||||||
\(152\) | −2941.90 | −1.56987 | ||||||||
\(153\) | −423.734 | −0.223901 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1590.09 | −0.823992 | ||||||||
\(156\) | 40.7847 | 0.0209320 | ||||||||
\(157\) | 3068.67 | 1.55991 | 0.779957 | − | 0.625833i | \(-0.215241\pi\) | ||||
0.779957 | + | 0.625833i | \(0.215241\pi\) | |||||||
\(158\) | 1941.96 | 0.977809 | ||||||||
\(159\) | −4445.23 | −2.21717 | ||||||||
\(160\) | 141.077 | 0.0697069 | ||||||||
\(161\) | 97.5222 | 0.0477381 | ||||||||
\(162\) | −2494.16 | −1.20963 | ||||||||
\(163\) | −1440.08 | −0.691998 | −0.345999 | − | 0.938235i | \(-0.612460\pi\) | ||||
−0.345999 | + | 0.938235i | \(0.612460\pi\) | |||||||
\(164\) | −86.7944 | −0.0413262 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2251.51 | −1.05272 | ||||||||
\(167\) | 2279.71 | 1.05634 | 0.528172 | − | 0.849137i | \(-0.322877\pi\) | ||||
0.528172 | + | 0.849137i | \(0.322877\pi\) | |||||||
\(168\) | 1778.95 | 0.816960 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −508.727 | −0.229515 | ||||||||
\(171\) | 1854.68 | 0.829420 | ||||||||
\(172\) | −163.724 | −0.0725807 | ||||||||
\(173\) | 1028.14 | 0.451840 | 0.225920 | − | 0.974146i | \(-0.427461\pi\) | ||||
0.225920 | + | 0.974146i | \(0.427461\pi\) | |||||||
\(174\) | −3080.07 | −1.34195 | ||||||||
\(175\) | 992.204 | 0.428592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2578.27 | 1.09488 | ||||||||
\(178\) | 121.116 | 0.0510001 | ||||||||
\(179\) | −560.960 | −0.234235 | −0.117118 | − | 0.993118i | \(-0.537365\pi\) | ||||
−0.117118 | + | 0.993118i | \(0.537365\pi\) | |||||||
\(180\) | −45.7809 | −0.0189573 | ||||||||
\(181\) | 2102.75 | 0.863516 | 0.431758 | − | 0.901990i | \(-0.357894\pi\) | ||||
0.431758 | + | 0.901990i | \(0.357894\pi\) | |||||||
\(182\) | 422.200 | 0.171953 | ||||||||
\(183\) | −174.147 | −0.0703460 | ||||||||
\(184\) | 191.471 | 0.0767143 | ||||||||
\(185\) | −1534.72 | −0.609917 | ||||||||
\(186\) | −4380.30 | −1.72677 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −125.070 | −0.0485194 | ||||||||
\(189\) | 943.338 | 0.363057 | ||||||||
\(190\) | 2226.69 | 0.850217 | ||||||||
\(191\) | 3786.37 | 1.43441 | 0.717204 | − | 0.696863i | \(-0.245421\pi\) | ||||
0.717204 | + | 0.696863i | \(0.245421\pi\) | |||||||
\(192\) | 3480.52 | 1.30826 | ||||||||
\(193\) | −1599.14 | −0.596417 | −0.298209 | − | 0.954501i | \(-0.596389\pi\) | ||||
−0.298209 | + | 0.954501i | \(0.596389\pi\) | |||||||
\(194\) | −2429.37 | −0.899065 | ||||||||
\(195\) | −538.971 | −0.197931 | ||||||||
\(196\) | 98.4845 | 0.0358908 | ||||||||
\(197\) | −3796.39 | −1.37300 | −0.686502 | − | 0.727128i | \(-0.740855\pi\) | ||||
−0.686502 | + | 0.727128i | \(0.740855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1968.49 | 0.701220 | 0.350610 | − | 0.936522i | \(-0.385974\pi\) | ||||
0.350610 | + | 0.936522i | \(0.385974\pi\) | |||||||
\(200\) | 1948.05 | 0.688740 | ||||||||
\(201\) | −4955.80 | −1.73908 | ||||||||
\(202\) | 419.638 | 0.146166 | ||||||||
\(203\) | 2062.44 | 0.713077 | ||||||||
\(204\) | 90.6499 | 0.0311116 | ||||||||
\(205\) | 1146.99 | 0.390777 | ||||||||
\(206\) | 1309.66 | 0.442954 | ||||||||
\(207\) | −120.710 | −0.0405310 | ||||||||
\(208\) | 778.381 | 0.259476 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1346.47 | −0.442453 | ||||||||
\(211\) | 935.411 | 0.305196 | 0.152598 | − | 0.988288i | \(-0.451236\pi\) | ||||
0.152598 | + | 0.988288i | \(0.451236\pi\) | |||||||
\(212\) | 334.716 | 0.108436 | ||||||||
\(213\) | −2165.07 | −0.696472 | ||||||||
\(214\) | −2136.90 | −0.682595 | ||||||||
\(215\) | 2163.62 | 0.686316 | ||||||||
\(216\) | 1852.11 | 0.583426 | ||||||||
\(217\) | 2933.08 | 0.917560 | ||||||||
\(218\) | −3686.65 | −1.14537 | ||||||||
\(219\) | −5106.61 | −1.57567 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 375.627 | 0.114332 | ||||||||
\(222\) | −4227.77 | −1.27815 | ||||||||
\(223\) | 3825.18 | 1.14867 | 0.574333 | − | 0.818622i | \(-0.305261\pi\) | ||||
0.574333 | + | 0.818622i | \(0.305261\pi\) | |||||||
\(224\) | −260.231 | −0.0776224 | ||||||||
\(225\) | −1228.12 | −0.363887 | ||||||||
\(226\) | 727.070 | 0.214000 | ||||||||
\(227\) | 4391.43 | 1.28401 | 0.642004 | − | 0.766702i | \(-0.278103\pi\) | ||||
0.642004 | + | 0.766702i | \(0.278103\pi\) | |||||||
\(228\) | −396.773 | −0.115250 | ||||||||
\(229\) | −4398.63 | −1.26930 | −0.634650 | − | 0.772800i | \(-0.718856\pi\) | ||||
−0.634650 | + | 0.772800i | \(0.718856\pi\) | |||||||
\(230\) | −144.922 | −0.0415473 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4049.30 | 1.14590 | ||||||||
\(233\) | −6718.90 | −1.88914 | −0.944570 | − | 0.328310i | \(-0.893521\pi\) | ||||
−0.944570 | + | 0.328310i | \(0.893521\pi\) | |||||||
\(234\) | −522.586 | −0.145994 | ||||||||
\(235\) | 1652.80 | 0.458795 | ||||||||
\(236\) | −194.138 | −0.0535479 | ||||||||
\(237\) | 4572.89 | 1.25334 | ||||||||
\(238\) | 938.401 | 0.255578 | ||||||||
\(239\) | 2793.52 | 0.756057 | 0.378029 | − | 0.925794i | \(-0.376602\pi\) | ||||
0.378029 | + | 0.925794i | \(0.376602\pi\) | |||||||
\(240\) | −2482.39 | −0.667658 | ||||||||
\(241\) | 1560.19 | 0.417014 | 0.208507 | − | 0.978021i | \(-0.433140\pi\) | ||||
0.208507 | + | 0.978021i | \(0.433140\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3723.45 | −0.982960 | ||||||||
\(244\) | 13.1129 | 0.00344044 | ||||||||
\(245\) | −1301.48 | −0.339381 | ||||||||
\(246\) | 3159.68 | 0.818918 | ||||||||
\(247\) | −1644.12 | −0.423533 | ||||||||
\(248\) | 5758.69 | 1.47450 | ||||||||
\(249\) | −5301.81 | −1.34935 | ||||||||
\(250\) | −3675.26 | −0.929775 | ||||||||
\(251\) | −3479.53 | −0.875005 | −0.437502 | − | 0.899217i | \(-0.644137\pi\) | ||||
−0.437502 | + | 0.899217i | \(0.644137\pi\) | |||||||
\(252\) | 84.4478 | 0.0211100 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 7430.24 | 1.83549 | ||||||||
\(255\) | −1197.94 | −0.294188 | ||||||||
\(256\) | −743.739 | −0.181577 | ||||||||
\(257\) | 3947.32 | 0.958083 | 0.479041 | − | 0.877792i | \(-0.340984\pi\) | ||||
0.479041 | + | 0.877792i | \(0.340984\pi\) | |||||||
\(258\) | 5960.26 | 1.43825 | ||||||||
\(259\) | 2830.95 | 0.679176 | ||||||||
\(260\) | 40.5834 | 0.00968028 | ||||||||
\(261\) | −2552.82 | −0.605424 | ||||||||
\(262\) | 402.078 | 0.0948110 | ||||||||
\(263\) | 4529.13 | 1.06189 | 0.530947 | − | 0.847405i | \(-0.321836\pi\) | ||||
0.530947 | + | 0.847405i | \(0.321836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4423.29 | −1.02536 | ||||||||
\(266\) | −4107.37 | −0.946763 | ||||||||
\(267\) | 285.201 | 0.0653709 | ||||||||
\(268\) | 373.161 | 0.0850540 | ||||||||
\(269\) | −1892.61 | −0.428975 | −0.214488 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214488 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(270\) | −1401.84 | −0.315975 | ||||||||
\(271\) | −2314.70 | −0.518848 | −0.259424 | − | 0.965763i | \(-0.583533\pi\) | ||||
−0.259424 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(272\) | 1730.07 | 0.385664 | ||||||||
\(273\) | 994.189 | 0.220407 | ||||||||
\(274\) | 2797.62 | 0.616825 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 25.8236 | 0.00563188 | ||||||||
\(277\) | 1677.72 | 0.363915 | 0.181958 | − | 0.983306i | \(-0.441757\pi\) | ||||
0.181958 | + | 0.983306i | \(0.441757\pi\) | |||||||
\(278\) | −1102.65 | −0.237886 | ||||||||
\(279\) | −3630.48 | −0.779036 | ||||||||
\(280\) | 1770.17 | 0.377815 | ||||||||
\(281\) | 1018.89 | 0.216306 | 0.108153 | − | 0.994134i | \(-0.465506\pi\) | ||||
0.108153 | + | 0.994134i | \(0.465506\pi\) | |||||||
\(282\) | 4553.07 | 0.961458 | ||||||||
\(283\) | −729.505 | −0.153232 | −0.0766159 | − | 0.997061i | \(-0.524412\pi\) | ||||
−0.0766159 | + | 0.997061i | \(0.524412\pi\) | |||||||
\(284\) | 163.026 | 0.0340626 | ||||||||
\(285\) | 5243.37 | 1.08979 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2115.75 | −0.435152 | ||||||||
\(288\) | 322.106 | 0.0659037 | ||||||||
\(289\) | −4078.11 | −0.830066 | ||||||||
\(290\) | −3064.86 | −0.620604 | ||||||||
\(291\) | −5720.64 | −1.15240 | ||||||||
\(292\) | 384.517 | 0.0770622 | ||||||||
\(293\) | −1800.83 | −0.359064 | −0.179532 | − | 0.983752i | \(-0.557458\pi\) | ||||
−0.179532 | + | 0.983752i | \(0.557458\pi\) | |||||||
\(294\) | −3585.25 | −0.711211 | ||||||||
\(295\) | 2565.54 | 0.506344 | ||||||||
\(296\) | 5558.16 | 1.09142 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6057.52 | −1.17753 | ||||||||
\(299\) | 107.006 | 0.0206967 | ||||||||
\(300\) | 262.733 | 0.0505629 | ||||||||
\(301\) | −3991.03 | −0.764251 | ||||||||
\(302\) | 5320.25 | 1.01373 | ||||||||
\(303\) | 988.156 | 0.187353 | ||||||||
\(304\) | −7572.48 | −1.42866 | ||||||||
\(305\) | −173.287 | −0.0325325 | ||||||||
\(306\) | −1161.52 | −0.216993 | ||||||||
\(307\) | −9880.21 | −1.83679 | −0.918393 | − | 0.395669i | \(-0.870513\pi\) | ||||
−0.918393 | + | 0.395669i | \(0.870513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3083.97 | 0.567770 | ||||||||
\(310\) | −4358.68 | −0.798569 | ||||||||
\(311\) | −1135.46 | −0.207029 | −0.103515 | − | 0.994628i | \(-0.533009\pi\) | ||||
−0.103515 | + | 0.994628i | \(0.533009\pi\) | |||||||
\(312\) | 1951.95 | 0.354190 | ||||||||
\(313\) | −2421.26 | −0.437246 | −0.218623 | − | 0.975809i | \(-0.570156\pi\) | ||||
−0.218623 | + | 0.975809i | \(0.570156\pi\) | |||||||
\(314\) | 8411.72 | 1.51179 | ||||||||
\(315\) | −1115.98 | −0.199614 | ||||||||
\(316\) | −344.329 | −0.0612975 | ||||||||
\(317\) | 5840.36 | 1.03479 | 0.517393 | − | 0.855748i | \(-0.326902\pi\) | ||||
0.517393 | + | 0.855748i | \(0.326902\pi\) | |||||||
\(318\) | −12185.1 | −2.14876 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3463.35 | 0.605022 | ||||||||
\(321\) | −5031.93 | −0.874937 | ||||||||
\(322\) | 267.324 | 0.0462652 | ||||||||
\(323\) | −3654.29 | −0.629505 | ||||||||
\(324\) | 442.240 | 0.0758300 | ||||||||
\(325\) | 1088.69 | 0.185814 | ||||||||
\(326\) | −3947.49 | −0.670648 | ||||||||
\(327\) | −8681.26 | −1.46812 | ||||||||
\(328\) | −4153.96 | −0.699281 | ||||||||
\(329\) | −3048.77 | −0.510893 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11721.9 | −1.94651 | −0.973255 | − | 0.229727i | \(-0.926217\pi\) | ||||
−0.973255 | + | 0.229727i | \(0.926217\pi\) | |||||||
\(332\) | 399.215 | 0.0659933 | ||||||||
\(333\) | −3504.06 | −0.576641 | ||||||||
\(334\) | 6249.06 | 1.02375 | ||||||||
\(335\) | −4931.34 | −0.804263 | ||||||||
\(336\) | 4579.04 | 0.743474 | ||||||||
\(337\) | 5816.16 | 0.940138 | 0.470069 | − | 0.882630i | \(-0.344229\pi\) | ||||
0.470069 | + | 0.882630i | \(0.344229\pi\) | |||||||
\(338\) | 463.256 | 0.0745498 | ||||||||
\(339\) | 1712.09 | 0.274301 | ||||||||
\(340\) | 90.2025 | 0.0143880 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5083.97 | 0.803830 | ||||||||
\(343\) | 6464.53 | 1.01764 | ||||||||
\(344\) | −7835.83 | −1.22814 | ||||||||
\(345\) | −341.260 | −0.0532545 | ||||||||
\(346\) | 2818.31 | 0.437900 | ||||||||
\(347\) | −318.503 | −0.0492742 | −0.0246371 | − | 0.999696i | \(-0.507843\pi\) | ||||
−0.0246371 | + | 0.999696i | \(0.507843\pi\) | |||||||
\(348\) | 546.127 | 0.0841250 | ||||||||
\(349\) | 8472.72 | 1.29952 | 0.649762 | − | 0.760137i | \(-0.274868\pi\) | ||||
0.649762 | + | 0.760137i | \(0.274868\pi\) | |||||||
\(350\) | 2719.79 | 0.415368 | ||||||||
\(351\) | 1035.07 | 0.157402 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6551.05 | −0.987754 | −0.493877 | − | 0.869532i | \(-0.664421\pi\) | ||||
−0.493877 | + | 0.869532i | \(0.664421\pi\) | |||||||
\(354\) | 7067.44 | 1.06110 | ||||||||
\(355\) | −2154.39 | −0.322093 | ||||||||
\(356\) | −21.4751 | −0.00319712 | ||||||||
\(357\) | 2209.73 | 0.327595 | ||||||||
\(358\) | −1537.68 | −0.227009 | ||||||||
\(359\) | 8284.19 | 1.21789 | 0.608945 | − | 0.793212i | \(-0.291593\pi\) | ||||
0.608945 | + | 0.793212i | \(0.291593\pi\) | |||||||
\(360\) | −2191.07 | −0.320776 | ||||||||
\(361\) | 9135.77 | 1.33194 | ||||||||
\(362\) | 5763.98 | 0.836873 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −74.8603 | −0.0107795 | ||||||||
\(365\) | −5081.40 | −0.728693 | ||||||||
\(366\) | −477.365 | −0.0681756 | ||||||||
\(367\) | −10965.3 | −1.55963 | −0.779814 | − | 0.626011i | \(-0.784686\pi\) | ||||
−0.779814 | + | 0.626011i | \(0.784686\pi\) | |||||||
\(368\) | 492.847 | 0.0698137 | ||||||||
\(369\) | 2618.81 | 0.369457 | ||||||||
\(370\) | −4206.91 | −0.591099 | ||||||||
\(371\) | 8159.22 | 1.14179 | ||||||||
\(372\) | 776.672 | 0.108249 | ||||||||
\(373\) | 149.528 | 0.0207567 | 0.0103784 | − | 0.999946i | \(-0.496696\pi\) | ||||
0.0103784 | + | 0.999946i | \(0.496696\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8654.43 | −1.19177 | ||||||||
\(376\) | −5985.82 | −0.820997 | ||||||||
\(377\) | 2262.99 | 0.309152 | ||||||||
\(378\) | 2585.84 | 0.351855 | ||||||||
\(379\) | 12796.0 | 1.73426 | 0.867129 | − | 0.498083i | \(-0.165963\pi\) | ||||
0.867129 | + | 0.498083i | \(0.165963\pi\) | |||||||
\(380\) | −394.815 | −0.0532989 | ||||||||
\(381\) | 17496.6 | 2.35270 | ||||||||
\(382\) | 10379.0 | 1.39015 | ||||||||
\(383\) | 5275.81 | 0.703868 | 0.351934 | − | 0.936025i | \(-0.385524\pi\) | ||||
0.351934 | + | 0.936025i | \(0.385524\pi\) | |||||||
\(384\) | 8406.47 | 1.11716 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4383.50 | −0.578016 | ||||||||
\(387\) | 4939.98 | 0.648872 | ||||||||
\(388\) | 430.752 | 0.0563611 | ||||||||
\(389\) | −3870.70 | −0.504505 | −0.252252 | − | 0.967661i | \(-0.581171\pi\) | ||||
−0.252252 | + | 0.967661i | \(0.581171\pi\) | |||||||
\(390\) | −1477.41 | −0.191824 | ||||||||
\(391\) | 237.836 | 0.0307618 | ||||||||
\(392\) | 4713.45 | 0.607309 | ||||||||
\(393\) | 946.807 | 0.121527 | ||||||||
\(394\) | −10406.5 | −1.33064 | ||||||||
\(395\) | 4550.32 | 0.579624 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13053.5 | −1.65021 | −0.825107 | − | 0.564977i | \(-0.808885\pi\) | ||||
−0.825107 | + | 0.564977i | \(0.808885\pi\) | |||||||
\(398\) | 5395.96 | 0.679585 | ||||||||
\(399\) | −9671.96 | −1.21354 | ||||||||
\(400\) | 5014.29 | 0.626787 | ||||||||
\(401\) | 7487.14 | 0.932394 | 0.466197 | − | 0.884681i | \(-0.345624\pi\) | ||||
0.466197 | + | 0.884681i | \(0.345624\pi\) | |||||||
\(402\) | −13584.6 | −1.68542 | ||||||||
\(403\) | 3218.31 | 0.397805 | ||||||||
\(404\) | −74.4061 | −0.00916297 | ||||||||
\(405\) | −5844.22 | −0.717041 | ||||||||
\(406\) | 5653.47 | 0.691076 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4338.49 | 0.526439 | ||||||||
\(409\) | 12866.2 | 1.55548 | 0.777741 | − | 0.628585i | \(-0.216365\pi\) | ||||
0.777741 | + | 0.628585i | \(0.216365\pi\) | |||||||
\(410\) | 3144.09 | 0.378720 | ||||||||
\(411\) | 6587.78 | 0.790635 | ||||||||
\(412\) | −232.217 | −0.0277682 | ||||||||
\(413\) | −4732.41 | −0.563842 | ||||||||
\(414\) | −330.886 | −0.0392805 | ||||||||
\(415\) | −5275.64 | −0.624027 | ||||||||
\(416\) | −285.537 | −0.0336529 | ||||||||
\(417\) | −2596.49 | −0.304918 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5102.25 | −0.594896 | −0.297448 | − | 0.954738i | \(-0.596135\pi\) | ||||
−0.297448 | + | 0.954738i | \(0.596135\pi\) | |||||||
\(420\) | 238.743 | 0.0277368 | ||||||||
\(421\) | −11685.5 | −1.35277 | −0.676385 | − | 0.736549i | \(-0.736454\pi\) | ||||
−0.676385 | + | 0.736549i | \(0.736454\pi\) | |||||||
\(422\) | 2564.11 | 0.295780 | ||||||||
\(423\) | 3773.67 | 0.433764 | ||||||||
\(424\) | 16019.5 | 1.83484 | ||||||||
\(425\) | 2419.77 | 0.276179 | ||||||||
\(426\) | −5934.82 | −0.674983 | ||||||||
\(427\) | 319.647 | 0.0362267 | ||||||||
\(428\) | 378.894 | 0.0427909 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5930.84 | 0.665141 | ||||||||
\(431\) | 9740.02 | 1.08854 | 0.544269 | − | 0.838911i | \(-0.316807\pi\) | ||||
0.544269 | + | 0.838911i | \(0.316807\pi\) | |||||||
\(432\) | 4767.34 | 0.530946 | ||||||||
\(433\) | 2235.01 | 0.248054 | 0.124027 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124027 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(434\) | 8040.05 | 0.889251 | ||||||||
\(435\) | −7217.09 | −0.795478 | ||||||||
\(436\) | 653.680 | 0.0718019 | ||||||||
\(437\) | −1041.00 | −0.113954 | ||||||||
\(438\) | −13998.0 | −1.52706 | ||||||||
\(439\) | 5942.10 | 0.646016 | 0.323008 | − | 0.946396i | \(-0.395306\pi\) | ||||
0.323008 | + | 0.946396i | \(0.395306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2971.53 | −0.320864 | ||||||||
\(442\) | 1029.66 | 0.110805 | ||||||||
\(443\) | 3674.40 | 0.394077 | 0.197039 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197039 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(444\) | 749.627 | 0.0801255 | ||||||||
\(445\) | 283.794 | 0.0302317 | ||||||||
\(446\) | 10485.4 | 1.11323 | ||||||||
\(447\) | −14264.1 | −1.50933 | ||||||||
\(448\) | −6388.51 | −0.673725 | ||||||||
\(449\) | −7109.28 | −0.747233 | −0.373616 | − | 0.927583i | \(-0.621882\pi\) | ||||
−0.373616 | + | 0.927583i | \(0.621882\pi\) | |||||||
\(450\) | −3366.47 | −0.352660 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −128.917 | −0.0134154 | ||||||||
\(453\) | 12528.0 | 1.29938 | ||||||||
\(454\) | 12037.6 | 1.24439 | ||||||||
\(455\) | 989.282 | 0.101930 | ||||||||
\(456\) | −18989.5 | −1.95014 | ||||||||
\(457\) | −1236.47 | −0.126564 | −0.0632818 | − | 0.997996i | \(-0.520157\pi\) | ||||
−0.0632818 | + | 0.997996i | \(0.520157\pi\) | |||||||
\(458\) | −12057.4 | −1.23014 | ||||||||
\(459\) | 2300.60 | 0.233949 | ||||||||
\(460\) | 25.6962 | 0.00260454 | ||||||||
\(461\) | 16234.6 | 1.64018 | 0.820090 | − | 0.572235i | \(-0.193923\pi\) | ||||
0.820090 | + | 0.572235i | \(0.193923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12760.1 | 1.28080 | 0.640400 | − | 0.768041i | \(-0.278768\pi\) | ||||
0.640400 | + | 0.768041i | \(0.278768\pi\) | |||||||
\(464\) | 10422.9 | 1.04283 | ||||||||
\(465\) | −10263.7 | −1.02359 | ||||||||
\(466\) | −18417.6 | −1.83085 | ||||||||
\(467\) | 4165.54 | 0.412758 | 0.206379 | − | 0.978472i | \(-0.433832\pi\) | ||||
0.206379 | + | 0.978472i | \(0.433832\pi\) | |||||||
\(468\) | 92.6598 | 0.00915214 | ||||||||
\(469\) | 9096.38 | 0.895590 | ||||||||
\(470\) | 4530.59 | 0.444640 | ||||||||
\(471\) | 19807.8 | 1.93778 | ||||||||
\(472\) | −9291.41 | −0.906085 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12535.0 | 1.21467 | ||||||||
\(475\) | −10591.3 | −1.02308 | ||||||||
\(476\) | −166.388 | −0.0160218 | ||||||||
\(477\) | −10099.2 | −0.969418 | ||||||||
\(478\) | 7657.48 | 0.732730 | ||||||||
\(479\) | −4314.66 | −0.411570 | −0.205785 | − | 0.978597i | \(-0.565975\pi\) | ||||
−0.205785 | + | 0.978597i | \(0.565975\pi\) | |||||||
\(480\) | 910.628 | 0.0865922 | ||||||||
\(481\) | 3106.24 | 0.294454 | ||||||||
\(482\) | 4276.72 | 0.404148 | ||||||||
\(483\) | 629.490 | 0.0593018 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5692.40 | −0.532946 | ||||||||
\(486\) | −10206.6 | −0.952632 | ||||||||
\(487\) | −10237.5 | −0.952575 | −0.476287 | − | 0.879290i | \(-0.658018\pi\) | ||||
−0.476287 | + | 0.879290i | \(0.658018\pi\) | |||||||
\(488\) | 627.581 | 0.0582157 | ||||||||
\(489\) | −9295.48 | −0.859624 | ||||||||
\(490\) | −3567.55 | −0.328910 | ||||||||
\(491\) | −14700.6 | −1.35118 | −0.675590 | − | 0.737278i | \(-0.736111\pi\) | ||||
−0.675590 | + | 0.737278i | \(0.736111\pi\) | |||||||
\(492\) | −560.243 | −0.0513368 | ||||||||
\(493\) | 5029.84 | 0.459498 | ||||||||
\(494\) | −4506.79 | −0.410465 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14822.9 | 1.34187 | ||||||||
\(497\) | 3974.00 | 0.358668 | ||||||||
\(498\) | −14533.1 | −1.30772 | ||||||||
\(499\) | −9368.46 | −0.840461 | −0.420231 | − | 0.907417i | \(-0.638051\pi\) | ||||
−0.420231 | + | 0.907417i | \(0.638051\pi\) | |||||||
\(500\) | 651.661 | 0.0582863 | ||||||||
\(501\) | 14715.2 | 1.31223 | ||||||||
\(502\) | −9537.96 | −0.848008 | ||||||||
\(503\) | 2328.19 | 0.206379 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(504\) | 4041.66 | 0.357202 | ||||||||
\(505\) | 983.279 | 0.0866443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1090.87 | 0.0955565 | ||||||||
\(508\) | −1317.46 | −0.115064 | ||||||||
\(509\) | 12803.9 | 1.11498 | 0.557490 | − | 0.830184i | \(-0.311764\pi\) | ||||
0.557490 | + | 0.830184i | \(0.311764\pi\) | |||||||
\(510\) | −3283.75 | −0.285112 | ||||||||
\(511\) | 9373.19 | 0.811439 | ||||||||
\(512\) | −12457.5 | −1.07529 | ||||||||
\(513\) | −10069.7 | −0.866643 | ||||||||
\(514\) | 10820.2 | 0.928523 | ||||||||
\(515\) | 3068.75 | 0.262573 | ||||||||
\(516\) | −1056.81 | −0.0901622 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7760.09 | 0.658221 | ||||||||
\(519\) | 6636.51 | 0.561292 | ||||||||
\(520\) | 1942.31 | 0.163800 | ||||||||
\(521\) | −6553.55 | −0.551087 | −0.275544 | − | 0.961289i | \(-0.588858\pi\) | ||||
−0.275544 | + | 0.961289i | \(0.588858\pi\) | |||||||
\(522\) | −6997.69 | −0.586744 | ||||||||
\(523\) | −17975.9 | −1.50293 | −0.751465 | − | 0.659772i | \(-0.770653\pi\) | ||||
−0.751465 | + | 0.659772i | \(0.770653\pi\) | |||||||
\(524\) | −71.2926 | −0.00594357 | ||||||||
\(525\) | 6404.51 | 0.532411 | ||||||||
\(526\) | 12415.1 | 1.02913 | ||||||||
\(527\) | 7153.16 | 0.591265 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12099.2 | −0.994431 | ||||||||
\(530\) | −12124.9 | −0.993724 | ||||||||
\(531\) | 5857.63 | 0.478719 | ||||||||
\(532\) | 728.278 | 0.0593512 | ||||||||
\(533\) | −2321.49 | −0.188658 | ||||||||
\(534\) | 781.783 | 0.0633540 | ||||||||
\(535\) | −5007.09 | −0.404627 | ||||||||
\(536\) | 17859.4 | 1.43920 | ||||||||
\(537\) | −3620.91 | −0.290975 | ||||||||
\(538\) | −5187.95 | −0.415740 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 248.560 | 0.0198080 | ||||||||
\(541\) | −10913.5 | −0.867294 | −0.433647 | − | 0.901083i | \(-0.642773\pi\) | ||||
−0.433647 | + | 0.901083i | \(0.642773\pi\) | |||||||
\(542\) | −6344.96 | −0.502840 | ||||||||
\(543\) | 13572.9 | 1.07269 | ||||||||
\(544\) | −634.648 | −0.0500189 | ||||||||
\(545\) | −8638.41 | −0.678952 | ||||||||
\(546\) | 2725.23 | 0.213606 | ||||||||
\(547\) | −17756.0 | −1.38792 | −0.693960 | − | 0.720013i | \(-0.744136\pi\) | ||||
−0.693960 | + | 0.720013i | \(0.744136\pi\) | |||||||
\(548\) | −496.046 | −0.0386679 | ||||||||
\(549\) | −395.649 | −0.0307576 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22015.5 | −1.70217 | ||||||||
\(552\) | 1235.91 | 0.0952971 | ||||||||
\(553\) | −8393.54 | −0.645443 | ||||||||
\(554\) | 4598.90 | 0.352687 | ||||||||
\(555\) | −9906.35 | −0.757660 | ||||||||
\(556\) | 195.510 | 0.0149127 | ||||||||
\(557\) | −5104.86 | −0.388330 | −0.194165 | − | 0.980969i | \(-0.562200\pi\) | ||||
−0.194165 | + | 0.980969i | \(0.562200\pi\) | |||||||
\(558\) | −9951.73 | −0.755000 | ||||||||
\(559\) | −4379.14 | −0.331338 | ||||||||
\(560\) | 4556.44 | 0.343830 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2792.95 | 0.209633 | ||||||||
\(563\) | −10312.2 | −0.771951 | −0.385976 | − | 0.922509i | \(-0.626135\pi\) | ||||
−0.385976 | + | 0.922509i | \(0.626135\pi\) | |||||||
\(564\) | −807.305 | −0.0602725 | ||||||||
\(565\) | 1703.64 | 0.126854 | ||||||||
\(566\) | −1999.69 | −0.148504 | ||||||||
\(567\) | 10780.3 | 0.798465 | ||||||||
\(568\) | 7802.38 | 0.576374 | ||||||||
\(569\) | −25108.1 | −1.84989 | −0.924944 | − | 0.380103i | \(-0.875889\pi\) | ||||
−0.924944 | + | 0.380103i | \(0.875889\pi\) | |||||||
\(570\) | 14372.9 | 1.05617 | ||||||||
\(571\) | −6657.00 | −0.487893 | −0.243947 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243947 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24440.4 | 1.78187 | ||||||||
\(574\) | −5799.60 | −0.421726 | ||||||||
\(575\) | 689.325 | 0.0499945 | ||||||||
\(576\) | 7907.50 | 0.572012 | ||||||||
\(577\) | 16007.7 | 1.15495 | 0.577477 | − | 0.816407i | \(-0.304037\pi\) | ||||
0.577477 | + | 0.816407i | \(0.304037\pi\) | |||||||
\(578\) | −11178.8 | −0.804456 | ||||||||
\(579\) | −10322.2 | −0.740890 | ||||||||
\(580\) | 543.432 | 0.0389048 | ||||||||
\(581\) | 9731.48 | 0.694888 | ||||||||
\(582\) | −15681.2 | −1.11685 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 18402.9 | 1.30397 | ||||||||
\(585\) | −1224.50 | −0.0865418 | ||||||||
\(586\) | −4936.38 | −0.347986 | ||||||||
\(587\) | −8868.71 | −0.623596 | −0.311798 | − | 0.950148i | \(-0.600931\pi\) | ||||
−0.311798 | + | 0.950148i | \(0.600931\pi\) | |||||||
\(588\) | 635.701 | 0.0445848 | ||||||||
\(589\) | −31309.3 | −2.19028 | ||||||||
\(590\) | 7032.56 | 0.490722 | ||||||||
\(591\) | −24505.1 | −1.70559 | ||||||||
\(592\) | 14306.7 | 0.993250 | ||||||||
\(593\) | 14032.9 | 0.971776 | 0.485888 | − | 0.874021i | \(-0.338496\pi\) | ||||
0.485888 | + | 0.874021i | \(0.338496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2198.82 | 0.151501 | ||||||||
\(596\) | 1074.06 | 0.0738175 | ||||||||
\(597\) | 12706.3 | 0.871080 | ||||||||
\(598\) | 293.320 | 0.0200581 | ||||||||
\(599\) | −700.332 | −0.0477710 | −0.0238855 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238855 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(600\) | 12574.3 | 0.855576 | ||||||||
\(601\) | −7170.01 | −0.486641 | −0.243320 | − | 0.969946i | \(-0.578237\pi\) | ||||
−0.243320 | + | 0.969946i | \(0.578237\pi\) | |||||||
\(602\) | −10940.1 | −0.740671 | ||||||||
\(603\) | −11259.2 | −0.760383 | ||||||||
\(604\) | −943.335 | −0.0635493 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2708.70 | 0.181573 | ||||||||
\(607\) | −3601.91 | −0.240852 | −0.120426 | − | 0.992722i | \(-0.538426\pi\) | ||||
−0.120426 | + | 0.992722i | \(0.538426\pi\) | |||||||
\(608\) | 2777.84 | 0.185290 | ||||||||
\(609\) | 13312.7 | 0.885808 | ||||||||
\(610\) | −475.009 | −0.0315288 | ||||||||
\(611\) | −3345.24 | −0.221496 | ||||||||
\(612\) | 205.950 | 0.0136030 | ||||||||
\(613\) | 22733.0 | 1.49784 | 0.748920 | − | 0.662660i | \(-0.230573\pi\) | ||||
0.748920 | + | 0.662660i | \(0.230573\pi\) | |||||||
\(614\) | −27083.2 | −1.78012 | ||||||||
\(615\) | 7403.64 | 0.485437 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3377.01 | 0.220346 | 0.110173 | − | 0.993912i | \(-0.464860\pi\) | ||||
0.110173 | + | 0.993912i | \(0.464860\pi\) | |||||||
\(618\) | 8453.67 | 0.550253 | ||||||||
\(619\) | 21458.3 | 1.39335 | 0.696675 | − | 0.717387i | \(-0.254662\pi\) | ||||
0.696675 | + | 0.717387i | \(0.254662\pi\) | |||||||
\(620\) | 772.838 | 0.0500612 | ||||||||
\(621\) | 655.376 | 0.0423500 | ||||||||
\(622\) | −3112.48 | −0.200642 | ||||||||
\(623\) | −523.487 | −0.0336647 | ||||||||
\(624\) | 5024.32 | 0.322330 | ||||||||
\(625\) | 1856.45 | 0.118813 | ||||||||
\(626\) | −6637.08 | −0.423755 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1491.48 | −0.0947718 | ||||||||
\(629\) | 6904.08 | 0.437653 | ||||||||
\(630\) | −3059.08 | −0.193455 | ||||||||
\(631\) | −522.005 | −0.0329330 | −0.0164665 | − | 0.999864i | \(-0.505242\pi\) | ||||
−0.0164665 | + | 0.999864i | \(0.505242\pi\) | |||||||
\(632\) | −16479.5 | −1.03722 | ||||||||
\(633\) | 6037.93 | 0.379125 | ||||||||
\(634\) | 16009.4 | 1.00286 | ||||||||
\(635\) | 17410.2 | 1.08804 | ||||||||
\(636\) | 2160.54 | 0.134703 | ||||||||
\(637\) | 2634.16 | 0.163845 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4918.89 | −0.304520 | ||||||||
\(640\) | 8364.97 | 0.516648 | ||||||||
\(641\) | 29005.3 | 1.78727 | 0.893637 | − | 0.448791i | \(-0.148145\pi\) | ||||
0.893637 | + | 0.448791i | \(0.148145\pi\) | |||||||
\(642\) | −13793.3 | −0.847943 | ||||||||
\(643\) | −12739.8 | −0.781351 | −0.390675 | − | 0.920529i | \(-0.627759\pi\) | ||||
−0.390675 | + | 0.920529i | \(0.627759\pi\) | |||||||
\(644\) | −47.3993 | −0.00290030 | ||||||||
\(645\) | 13965.8 | 0.852565 | ||||||||
\(646\) | −10017.0 | −0.610083 | ||||||||
\(647\) | −7919.69 | −0.481229 | −0.240614 | − | 0.970621i | \(-0.577349\pi\) | ||||
−0.240614 | + | 0.970621i | \(0.577349\pi\) | |||||||
\(648\) | 21165.6 | 1.28312 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2984.27 | 0.180081 | ||||||||
\(651\) | 18932.6 | 1.13982 | ||||||||
\(652\) | 699.930 | 0.0420420 | ||||||||
\(653\) | −24265.4 | −1.45418 | −0.727090 | − | 0.686542i | \(-0.759128\pi\) | ||||
−0.727090 | + | 0.686542i | \(0.759128\pi\) | |||||||
\(654\) | −23796.7 | −1.42282 | ||||||||
\(655\) | 942.134 | 0.0562018 | ||||||||
\(656\) | −10692.3 | −0.636380 | ||||||||
\(657\) | −11601.8 | −0.688936 | ||||||||
\(658\) | −8357.16 | −0.495131 | ||||||||
\(659\) | −18366.0 | −1.08564 | −0.542820 | − | 0.839849i | \(-0.682644\pi\) | ||||
−0.542820 | + | 0.839849i | \(0.682644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5671.15 | 0.333710 | 0.166855 | − | 0.985981i | \(-0.446639\pi\) | ||||
0.166855 | + | 0.985981i | \(0.446639\pi\) | |||||||
\(662\) | −32131.7 | −1.88645 | ||||||||
\(663\) | 2424.61 | 0.142027 | ||||||||
\(664\) | 19106.4 | 1.11667 | ||||||||
\(665\) | −9624.22 | −0.561220 | ||||||||
\(666\) | −9605.20 | −0.558850 | ||||||||
\(667\) | 1432.86 | 0.0831792 | ||||||||
\(668\) | −1108.02 | −0.0641777 | ||||||||
\(669\) | 24690.9 | 1.42691 | ||||||||
\(670\) | −13517.6 | −0.779448 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1679.75 | −0.0964252 | ||||||||
\(673\) | −25014.1 | −1.43272 | −0.716361 | − | 0.697729i | \(-0.754194\pi\) | ||||
−0.716361 | + | 0.697729i | \(0.754194\pi\) | |||||||
\(674\) | 15943.0 | 0.911132 | ||||||||
\(675\) | 6667.88 | 0.380218 | ||||||||
\(676\) | −82.1400 | −0.00467342 | ||||||||
\(677\) | −19365.2 | −1.09936 | −0.549678 | − | 0.835376i | \(-0.685250\pi\) | ||||
−0.549678 | + | 0.835376i | \(0.685250\pi\) | |||||||
\(678\) | 4693.12 | 0.265838 | ||||||||
\(679\) | 10500.2 | 0.593464 | ||||||||
\(680\) | 4317.08 | 0.243459 | ||||||||
\(681\) | 28346.0 | 1.59504 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12269.1 | 0.687357 | 0.343679 | − | 0.939087i | \(-0.388327\pi\) | ||||
0.343679 | + | 0.939087i | \(0.388327\pi\) | |||||||
\(684\) | −901.440 | −0.0503910 | ||||||||
\(685\) | 6555.26 | 0.365640 | ||||||||
\(686\) | 17720.3 | 0.986246 | ||||||||
\(687\) | −28392.4 | −1.57677 | ||||||||
\(688\) | −20169.5 | −1.11767 | ||||||||
\(689\) | 8952.66 | 0.495021 | ||||||||
\(690\) | −935.448 | −0.0516115 | ||||||||
\(691\) | −7851.67 | −0.432260 | −0.216130 | − | 0.976365i | \(-0.569344\pi\) | ||||
−0.216130 | + | 0.976365i | \(0.569344\pi\) | |||||||
\(692\) | −499.715 | −0.0274513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −873.069 | −0.0477540 | ||||||||
\(695\) | −2583.67 | −0.141013 | ||||||||
\(696\) | 26137.6 | 1.42348 | ||||||||
\(697\) | −5159.85 | −0.280406 | ||||||||
\(698\) | 23225.1 | 1.25943 | ||||||||
\(699\) | −43369.4 | −2.34675 | ||||||||
\(700\) | −482.246 | −0.0260389 | ||||||||
\(701\) | −2411.31 | −0.129920 | −0.0649600 | − | 0.997888i | \(-0.520692\pi\) | ||||
−0.0649600 | + | 0.997888i | \(0.520692\pi\) | |||||||
\(702\) | 2837.30 | 0.152545 | ||||||||
\(703\) | −30219.1 | −1.62124 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10668.6 | 0.569931 | ||||||||
\(706\) | −17957.5 | −0.957279 | ||||||||
\(707\) | −1813.76 | −0.0964831 | ||||||||
\(708\) | −1253.13 | −0.0665190 | ||||||||
\(709\) | 14927.1 | 0.790688 | 0.395344 | − | 0.918533i | \(-0.370625\pi\) | ||||
0.395344 | + | 0.918533i | \(0.370625\pi\) | |||||||
\(710\) | −5905.53 | −0.312156 | ||||||||
\(711\) | 10389.3 | 0.548000 | ||||||||
\(712\) | −1027.79 | −0.0540985 | ||||||||
\(713\) | 2037.73 | 0.107032 | ||||||||
\(714\) | 6057.23 | 0.317487 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 272.647 | 0.0142309 | ||||||||
\(717\) | 18031.7 | 0.939200 | ||||||||
\(718\) | 22708.3 | 1.18031 | ||||||||
\(719\) | 26655.2 | 1.38257 | 0.691287 | − | 0.722581i | \(-0.257044\pi\) | ||||
0.691287 | + | 0.722581i | \(0.257044\pi\) | |||||||
\(720\) | −5639.82 | −0.291922 | ||||||||
\(721\) | −5660.64 | −0.292390 | ||||||||
\(722\) | 25042.6 | 1.29084 | ||||||||
\(723\) | 10070.7 | 0.518029 | ||||||||
\(724\) | −1022.01 | −0.0524624 | ||||||||
\(725\) | 14578.1 | 0.746782 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7253.73 | 0.370049 | 0.185025 | − | 0.982734i | \(-0.440764\pi\) | ||||
0.185025 | + | 0.982734i | \(0.440764\pi\) | |||||||
\(728\) | −3582.80 | −0.182400 | ||||||||
\(729\) | 532.868 | 0.0270725 | ||||||||
\(730\) | −13928.9 | −0.706210 | ||||||||
\(731\) | −9733.28 | −0.492474 | ||||||||
\(732\) | 84.6416 | 0.00427383 | ||||||||
\(733\) | −11539.7 | −0.581485 | −0.290742 | − | 0.956801i | \(-0.593902\pi\) | ||||
−0.290742 | + | 0.956801i | \(0.593902\pi\) | |||||||
\(734\) | −30057.6 | −1.51151 | ||||||||
\(735\) | −8400.81 | −0.421590 | ||||||||
\(736\) | −180.793 | −0.00905453 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 7178.57 | 0.358058 | ||||||||
\(739\) | 18477.5 | 0.919765 | 0.459882 | − | 0.887980i | \(-0.347892\pi\) | ||||
0.459882 | + | 0.887980i | \(0.347892\pi\) | |||||||
\(740\) | 745.927 | 0.0370552 | ||||||||
\(741\) | −10612.5 | −0.526127 | ||||||||
\(742\) | 22365.7 | 1.10657 | ||||||||
\(743\) | 35737.3 | 1.76457 | 0.882284 | − | 0.470718i | \(-0.156005\pi\) | ||||
0.882284 | + | 0.470718i | \(0.156005\pi\) | |||||||
\(744\) | 37171.4 | 1.83168 | ||||||||
\(745\) | −14193.7 | −0.698011 | ||||||||
\(746\) | 409.879 | 0.0201163 | ||||||||
\(747\) | −12045.3 | −0.589981 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9236.11 | 0.450574 | ||||||||
\(750\) | −23723.2 | −1.15500 | ||||||||
\(751\) | −10462.9 | −0.508386 | −0.254193 | − | 0.967153i | \(-0.581810\pi\) | ||||
−0.254193 | + | 0.967153i | \(0.581810\pi\) | |||||||
\(752\) | −15407.5 | −0.747148 | ||||||||
\(753\) | −22459.8 | −1.08696 | ||||||||
\(754\) | 6203.23 | 0.299613 | ||||||||
\(755\) | 12466.2 | 0.600916 | ||||||||
\(756\) | −458.496 | −0.0220573 | ||||||||
\(757\) | 22149.3 | 1.06345 | 0.531723 | − | 0.846918i | \(-0.321545\pi\) | ||||
0.531723 | + | 0.846918i | \(0.321545\pi\) | |||||||
\(758\) | 35075.8 | 1.68075 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18895.8 | −0.901871 | ||||||||
\(761\) | 20621.6 | 0.982301 | 0.491151 | − | 0.871075i | \(-0.336577\pi\) | ||||
0.491151 | + | 0.871075i | \(0.336577\pi\) | |||||||
\(762\) | 47961.0 | 2.28011 | ||||||||
\(763\) | 15934.5 | 0.756050 | ||||||||
\(764\) | −1840.31 | −0.0871467 | ||||||||
\(765\) | −2721.64 | −0.128629 | ||||||||
\(766\) | 14461.8 | 0.682151 | ||||||||
\(767\) | −5192.61 | −0.244451 | ||||||||
\(768\) | −4800.72 | −0.225561 | ||||||||
\(769\) | −11029.1 | −0.517191 | −0.258595 | − | 0.965986i | \(-0.583260\pi\) | ||||
−0.258595 | + | 0.965986i | \(0.583260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25479.3 | 1.19016 | ||||||||
\(772\) | 777.239 | 0.0362350 | ||||||||
\(773\) | 4034.81 | 0.187739 | 0.0938693 | − | 0.995585i | \(-0.470076\pi\) | ||||
0.0938693 | + | 0.995585i | \(0.470076\pi\) | |||||||
\(774\) | 13541.3 | 0.628852 | ||||||||
\(775\) | 20732.2 | 0.960931 | ||||||||
\(776\) | 20615.7 | 0.953687 | ||||||||
\(777\) | 18273.3 | 0.843696 | ||||||||
\(778\) | −10610.2 | −0.488939 | ||||||||
\(779\) | 22584.6 | 1.03874 | ||||||||
\(780\) | 261.959 | 0.0120252 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 651.946 | 0.0298127 | ||||||||
\(783\) | 13860.1 | 0.632593 | ||||||||
\(784\) | 12132.5 | 0.552681 | ||||||||
\(785\) | 19710.0 | 0.896153 | ||||||||
\(786\) | 2595.35 | 0.117777 | ||||||||
\(787\) | −14830.3 | −0.671719 | −0.335859 | − | 0.941912i | \(-0.609027\pi\) | ||||
−0.335859 | + | 0.941912i | \(0.609027\pi\) | |||||||
\(788\) | 1845.18 | 0.0834162 | ||||||||
\(789\) | 29234.8 | 1.31912 | ||||||||
\(790\) | 12473.2 | 0.561740 | ||||||||
\(791\) | −3142.55 | −0.141259 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 350.731 | 0.0157059 | ||||||||
\(794\) | −35781.7 | −1.59930 | ||||||||
\(795\) | −28551.6 | −1.27374 | ||||||||
\(796\) | −956.758 | −0.0426023 | ||||||||
\(797\) | −14863.5 | −0.660594 | −0.330297 | − | 0.943877i | \(-0.607149\pi\) | ||||
−0.330297 | + | 0.943877i | \(0.607149\pi\) | |||||||
\(798\) | −26512.4 | −1.17610 | ||||||||
\(799\) | −7435.29 | −0.329214 | ||||||||
\(800\) | −1839.41 | −0.0812914 | ||||||||
\(801\) | 647.957 | 0.0285823 | ||||||||
\(802\) | 20523.5 | 0.903627 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2408.70 | 0.105657 | ||||||||
\(805\) | 626.383 | 0.0274250 | ||||||||
\(806\) | 8821.90 | 0.385531 | ||||||||
\(807\) | −12216.5 | −0.532888 | ||||||||
\(808\) | −3561.06 | −0.155047 | ||||||||
\(809\) | 38102.8 | 1.65590 | 0.827951 | − | 0.560801i | \(-0.189507\pi\) | ||||
0.827951 | + | 0.560801i | \(0.189507\pi\) | |||||||
\(810\) | −16020.0 | −0.694918 | ||||||||
\(811\) | 5682.59 | 0.246045 | 0.123023 | − | 0.992404i | \(-0.460741\pi\) | ||||
0.123023 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(812\) | −1002.42 | −0.0433226 | ||||||||
\(813\) | −14941.0 | −0.644531 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9249.60 | −0.397545 | ||||||||
\(816\) | 11167.3 | 0.479085 | ||||||||
\(817\) | 42602.4 | 1.82432 | ||||||||
\(818\) | 35268.3 | 1.50749 | ||||||||
\(819\) | 2258.72 | 0.0963690 | ||||||||
\(820\) | −557.478 | −0.0237414 | ||||||||
\(821\) | −8095.12 | −0.344119 | −0.172059 | − | 0.985087i | \(-0.555042\pi\) | ||||
−0.172059 | + | 0.985087i | \(0.555042\pi\) | |||||||
\(822\) | 18058.2 | 0.766242 | ||||||||
\(823\) | 31491.5 | 1.33381 | 0.666904 | − | 0.745144i | \(-0.267619\pi\) | ||||
0.666904 | + | 0.745144i | \(0.267619\pi\) | |||||||
\(824\) | −11113.9 | −0.469866 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12972.3 | −0.546446 | ||||||||
\(827\) | 19957.4 | 0.839162 | 0.419581 | − | 0.907718i | \(-0.362177\pi\) | ||||
0.419581 | + | 0.907718i | \(0.362177\pi\) | |||||||
\(828\) | 58.6694 | 0.00246244 | ||||||||
\(829\) | −30724.7 | −1.28723 | −0.643614 | − | 0.765350i | \(-0.722566\pi\) | ||||
−0.643614 | + | 0.765350i | \(0.722566\pi\) | |||||||
\(830\) | −14461.4 | −0.604773 | ||||||||
\(831\) | 10829.4 | 0.452068 | ||||||||
\(832\) | −7009.75 | −0.292091 | ||||||||
\(833\) | 5854.82 | 0.243526 | ||||||||
\(834\) | −7117.39 | −0.295510 | ||||||||
\(835\) | 14642.6 | 0.606858 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19711.1 | 0.813997 | ||||||||
\(838\) | −13986.1 | −0.576541 | ||||||||
\(839\) | −5845.86 | −0.240550 | −0.120275 | − | 0.992741i | \(-0.538378\pi\) | ||||
−0.120275 | + | 0.992741i | \(0.538378\pi\) | |||||||
\(840\) | 11426.2 | 0.469334 | ||||||||
\(841\) | 5913.64 | 0.242472 | ||||||||
\(842\) | −32031.8 | −1.31103 | ||||||||
\(843\) | 6576.79 | 0.268703 | ||||||||
\(844\) | −454.643 | −0.0185420 | ||||||||
\(845\) | 1085.48 | 0.0441914 | ||||||||
\(846\) | 10344.2 | 0.420381 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 41234.2 | 1.66980 | ||||||||
\(849\) | −4708.84 | −0.190350 | ||||||||
\(850\) | 6632.99 | 0.267658 | ||||||||
\(851\) | 1966.78 | 0.0792248 | ||||||||
\(852\) | 1052.30 | 0.0423138 | ||||||||
\(853\) | 7389.71 | 0.296622 | 0.148311 | − | 0.988941i | \(-0.452616\pi\) | ||||
0.148311 | + | 0.988941i | \(0.452616\pi\) | |||||||
\(854\) | 876.204 | 0.0351090 | ||||||||
\(855\) | 11912.6 | 0.476493 | ||||||||
\(856\) | 18133.8 | 0.724066 | ||||||||
\(857\) | 1153.62 | 0.0459824 | 0.0229912 | − | 0.999736i | \(-0.492681\pi\) | ||||
0.0229912 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27141.2 | −1.07805 | −0.539025 | − | 0.842290i | \(-0.681207\pi\) | ||||
−0.539025 | + | 0.842290i | \(0.681207\pi\) | |||||||
\(860\) | −1051.60 | −0.0416968 | ||||||||
\(861\) | −13656.8 | −0.540560 | ||||||||
\(862\) | 26699.0 | 1.05495 | ||||||||
\(863\) | −27066.2 | −1.06761 | −0.533803 | − | 0.845609i | \(-0.679238\pi\) | ||||
−0.533803 | + | 0.845609i | \(0.679238\pi\) | |||||||
\(864\) | −1748.82 | −0.0688613 | ||||||||
\(865\) | 6603.75 | 0.259577 | ||||||||
\(866\) | 6126.51 | 0.240401 | ||||||||
\(867\) | −26323.6 | −1.03114 | ||||||||
\(868\) | −1425.58 | −0.0557459 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −19783.2 | −0.770935 | ||||||||
\(871\) | 9980.95 | 0.388280 | ||||||||
\(872\) | 31285.0 | 1.21496 | ||||||||
\(873\) | −12996.9 | −0.503869 | ||||||||
\(874\) | −2853.56 | −0.110438 | ||||||||
\(875\) | 15885.2 | 0.613736 | ||||||||
\(876\) | 2481.99 | 0.0957292 | ||||||||
\(877\) | −28364.5 | −1.09213 | −0.546066 | − | 0.837742i | \(-0.683875\pi\) | ||||
−0.546066 | + | 0.837742i | \(0.683875\pi\) | |||||||
\(878\) | 16288.2 | 0.626084 | ||||||||
\(879\) | −11624.1 | −0.446042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47799.4 | 1.82792 | 0.913962 | − | 0.405799i | \(-0.133007\pi\) | ||||
0.913962 | + | 0.405799i | \(0.133007\pi\) | |||||||
\(882\) | −8145.43 | −0.310965 | ||||||||
\(883\) | −43112.7 | −1.64310 | −0.821551 | − | 0.570135i | \(-0.806891\pi\) | ||||
−0.821551 | + | 0.570135i | \(0.806891\pi\) | |||||||
\(884\) | −182.568 | −0.00694620 | ||||||||
\(885\) | 16560.1 | 0.628998 | ||||||||
\(886\) | 10072.1 | 0.381919 | ||||||||
\(887\) | −16423.9 | −0.621713 | −0.310856 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310856 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(888\) | 35877.0 | 1.35580 | ||||||||
\(889\) | −32115.0 | −1.21159 | ||||||||
\(890\) | 777.924 | 0.0292990 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1859.17 | −0.0697866 | ||||||||
\(893\) | 32544.2 | 1.21954 | ||||||||
\(894\) | −39100.3 | −1.46276 | ||||||||
\(895\) | −3603.04 | −0.134566 | ||||||||
\(896\) | −15430.1 | −0.575316 | ||||||||
\(897\) | 690.704 | 0.0257101 | ||||||||
\(898\) | −19487.7 | −0.724178 | ||||||||
\(899\) | 43094.7 | 1.59877 | ||||||||
\(900\) | 596.910 | 0.0221078 | ||||||||
\(901\) | 19898.6 | 0.735759 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25761.5 | −0.949378 | ||||||||
\(904\) | −6169.94 | −0.227001 | ||||||||
\(905\) | 13505.9 | 0.496080 | ||||||||
\(906\) | 34341.4 | 1.25929 | ||||||||
\(907\) | 27518.0 | 1.00741 | 0.503705 | − | 0.863876i | \(-0.331970\pi\) | ||||
0.503705 | + | 0.863876i | \(0.331970\pi\) | |||||||
\(908\) | −2134.39 | −0.0780092 | ||||||||
\(909\) | 2245.02 | 0.0819171 | ||||||||
\(910\) | 2711.78 | 0.0987853 | ||||||||
\(911\) | 30022.2 | 1.09186 | 0.545928 | − | 0.837832i | \(-0.316177\pi\) | ||||
0.545928 | + | 0.837832i | \(0.316177\pi\) | |||||||
\(912\) | −48879.1 | −1.77472 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3389.36 | −0.122659 | ||||||||
\(915\) | −1118.54 | −0.0404130 | ||||||||
\(916\) | 2137.89 | 0.0771157 | ||||||||
\(917\) | −1737.87 | −0.0625838 | ||||||||
\(918\) | 6306.31 | 0.226731 | ||||||||
\(919\) | 5023.55 | 0.180317 | 0.0901587 | − | 0.995927i | \(-0.471263\pi\) | ||||
0.0901587 | + | 0.995927i | \(0.471263\pi\) | |||||||
\(920\) | 1229.81 | 0.0440715 | ||||||||
\(921\) | −63775.1 | −2.28172 | ||||||||
\(922\) | 44501.8 | 1.58957 | ||||||||
\(923\) | 4360.45 | 0.155499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20010.3 | 0.711279 | ||||||||
\(926\) | 34977.4 | 1.24128 | ||||||||
\(927\) | 7006.56 | 0.248248 | ||||||||
\(928\) | −3823.48 | −0.135250 | ||||||||
\(929\) | −27305.8 | −0.964344 | −0.482172 | − | 0.876077i | \(-0.660152\pi\) | ||||
−0.482172 | + | 0.876077i | \(0.660152\pi\) | |||||||
\(930\) | −28134.6 | −0.992010 | ||||||||
\(931\) | −25626.5 | −0.902119 | ||||||||
\(932\) | 3265.62 | 0.114774 | ||||||||
\(933\) | −7329.22 | −0.257179 | ||||||||
\(934\) | 11418.4 | 0.400023 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4434.68 | 0.154863 | ||||||||
\(937\) | −21720.8 | −0.757296 | −0.378648 | − | 0.925541i | \(-0.623611\pi\) | ||||
−0.378648 | + | 0.925541i | \(0.623611\pi\) | |||||||
\(938\) | 24934.6 | 0.867959 | ||||||||
\(939\) | −15628.9 | −0.543162 | ||||||||
\(940\) | −803.320 | −0.0278739 | ||||||||
\(941\) | 43011.0 | 1.49003 | 0.745015 | − | 0.667048i | \(-0.232442\pi\) | ||||
0.745015 | + | 0.667048i | \(0.232442\pi\) | |||||||
\(942\) | 54296.3 | 1.87799 | ||||||||
\(943\) | −1469.90 | −0.0507597 | ||||||||
\(944\) | −23916.2 | −0.824581 | ||||||||
\(945\) | 6059.04 | 0.208572 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27400.4 | 0.940226 | 0.470113 | − | 0.882606i | \(-0.344213\pi\) | ||||
0.470113 | + | 0.882606i | \(0.344213\pi\) | |||||||
\(948\) | −2222.59 | −0.0761458 | ||||||||
\(949\) | 10284.7 | 0.351796 | ||||||||
\(950\) | −29032.5 | −0.991514 | ||||||||
\(951\) | 37698.6 | 1.28545 | ||||||||
\(952\) | −7963.31 | −0.271105 | ||||||||
\(953\) | −56931.4 | −1.93514 | −0.967570 | − | 0.252603i | \(-0.918713\pi\) | ||||
−0.967570 | + | 0.252603i | \(0.918713\pi\) | |||||||
\(954\) | −27683.6 | −0.939508 | ||||||||
\(955\) | 24319.8 | 0.824052 | ||||||||
\(956\) | −1357.75 | −0.0459338 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11827.2 | −0.398871 | ||||||||
\(959\) | −12091.9 | −0.407161 | ||||||||
\(960\) | 22355.3 | 0.751578 | ||||||||
\(961\) | 31496.0 | 1.05723 | ||||||||
\(962\) | 8514.71 | 0.285369 | ||||||||
\(963\) | −11432.2 | −0.382551 | ||||||||
\(964\) | −758.306 | −0.0253355 | ||||||||
\(965\) | −10271.2 | −0.342635 | ||||||||
\(966\) | 1725.53 | 0.0574722 | ||||||||
\(967\) | −56583.6 | −1.88170 | −0.940852 | − | 0.338818i | \(-0.889973\pi\) | ||||
−0.940852 | + | 0.338818i | \(0.889973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23587.8 | −0.781992 | ||||||||
\(970\) | −15603.8 | −0.516503 | ||||||||
\(971\) | −17988.7 | −0.594526 | −0.297263 | − | 0.954796i | \(-0.596074\pi\) | ||||
−0.297263 | + | 0.954796i | \(0.596074\pi\) | |||||||
\(972\) | 1809.73 | 0.0597192 | ||||||||
\(973\) | 4765.86 | 0.157026 | ||||||||
\(974\) | −28062.5 | −0.923185 | ||||||||
\(975\) | 7027.31 | 0.230825 | ||||||||
\(976\) | 1615.40 | 0.0529791 | ||||||||
\(977\) | −15197.5 | −0.497658 | −0.248829 | − | 0.968547i | \(-0.580046\pi\) | ||||
−0.248829 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(978\) | −25480.4 | −0.833102 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 632.564 | 0.0206189 | ||||||||
\(981\) | −19723.2 | −0.641909 | ||||||||
\(982\) | −40296.7 | −1.30949 | ||||||||
\(983\) | −51622.4 | −1.67497 | −0.837487 | − | 0.546457i | \(-0.815976\pi\) | ||||
−0.837487 | + | 0.546457i | \(0.815976\pi\) | |||||||
\(984\) | −26813.2 | −0.868671 | ||||||||
\(985\) | −24384.2 | −0.788776 | ||||||||
\(986\) | 13787.6 | 0.445321 | ||||||||
\(987\) | −19679.3 | −0.634649 | ||||||||
\(988\) | 799.099 | 0.0257315 | ||||||||
\(989\) | −2772.74 | −0.0891486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12481.7 | 0.400095 | 0.200048 | − | 0.979786i | \(-0.435890\pi\) | ||||
0.200048 | + | 0.979786i | \(0.435890\pi\) | |||||||
\(992\) | −5437.55 | −0.174035 | ||||||||
\(993\) | −75663.1 | −2.41802 | ||||||||
\(994\) | 10893.4 | 0.347602 | ||||||||
\(995\) | 12643.6 | 0.402843 | ||||||||
\(996\) | 2576.87 | 0.0819791 | ||||||||
\(997\) | −32585.6 | −1.03510 | −0.517551 | − | 0.855652i | \(-0.673156\pi\) | ||||
−0.517551 | + | 0.855652i | \(0.673156\pi\) | |||||||
\(998\) | −25680.5 | −0.814530 | ||||||||
\(999\) | 19024.8 | 0.602519 |
(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 | 1573.4.a.p.1.25 | 34 | ||
11.7 | odd | 10 | 143.4.h.a.27.5 | ✓ | 68 | ||
11.8 | odd | 10 | 143.4.h.a.53.5 | yes | 68 | ||
11.10 | odd | 2 | 1573.4.a.o.1.10 | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.h.a.27.5 | ✓ | 68 | 11.7 | odd | 10 | ||
143.4.h.a.53.5 | yes | 68 | 11.8 | odd | 10 | ||
1573.4.a.o.1.10 | 34 | 11.10 | odd | 2 | |||
1573.4.a.p.1.25 | 34 | 1.1 | even | 1 | trivial |