Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.57 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.15423 | 1.82229 | 0.911147 | − | 0.412081i | \(-0.135198\pi\) | ||||
0.911147 | + | 0.412081i | \(0.135198\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 18.5661 | 2.32076 | ||||||||
\(5\) | −1.27174 | −0.113747 | −0.0568737 | − | 0.998381i | \(-0.518113\pi\) | ||||
−0.0568737 | + | 0.998381i | \(0.518113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −23.0732 | −1.24584 | −0.622918 | − | 0.782287i | \(-0.714053\pi\) | ||||
−0.622918 | + | 0.782287i | \(0.714053\pi\) | |||||||
\(8\) | 54.4599 | 2.40681 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.55481 | −0.207281 | ||||||||
\(11\) | 4.21412 | 0.115510 | 0.0577548 | − | 0.998331i | \(-0.481606\pi\) | ||||
0.0577548 | + | 0.998331i | \(0.481606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.3792 | −0.349445 | −0.174723 | − | 0.984618i | \(-0.555903\pi\) | ||||
−0.174723 | + | 0.984618i | \(0.555903\pi\) | |||||||
\(14\) | −118.925 | −2.27028 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 132.170 | 2.06516 | ||||||||
\(17\) | 98.0605 | 1.39901 | 0.699505 | − | 0.714628i | \(-0.253404\pi\) | ||||
0.699505 | + | 0.714628i | \(0.253404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −60.2154 | −0.727072 | −0.363536 | − | 0.931580i | \(-0.618431\pi\) | ||||
−0.363536 | + | 0.931580i | \(0.618431\pi\) | |||||||
\(20\) | −23.6111 | −0.263980 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.7205 | 0.210493 | ||||||||
\(23\) | −168.855 | −1.53081 | −0.765406 | − | 0.643548i | \(-0.777462\pi\) | ||||
−0.765406 | + | 0.643548i | \(0.777462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123.383 | −0.987062 | ||||||||
\(26\) | −84.4224 | −0.636792 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −428.378 | −2.89128 | ||||||||
\(29\) | −72.3381 | −0.463202 | −0.231601 | − | 0.972811i | \(-0.574396\pi\) | ||||
−0.231601 | + | 0.972811i | \(0.574396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.8941 | −0.155817 | −0.0779084 | − | 0.996961i | \(-0.524824\pi\) | ||||
−0.0779084 | + | 0.996961i | \(0.524824\pi\) | |||||||
\(32\) | 245.556 | 1.35652 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 505.426 | 2.54941 | ||||||||
\(35\) | 29.3430 | 0.141711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −86.2049 | −0.383027 | −0.191514 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191514 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(38\) | −310.364 | −1.32494 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −69.2585 | −0.273768 | ||||||||
\(41\) | 137.305 | 0.523009 | 0.261505 | − | 0.965202i | \(-0.415781\pi\) | ||||
0.261505 | + | 0.965202i | \(0.415781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −406.867 | −1.44295 | −0.721473 | − | 0.692443i | \(-0.756535\pi\) | ||||
−0.721473 | + | 0.692443i | \(0.756535\pi\) | |||||||
\(44\) | 78.2396 | 0.268070 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −870.316 | −2.78959 | ||||||||
\(47\) | 382.766 | 1.18792 | 0.593959 | − | 0.804495i | \(-0.297564\pi\) | ||||
0.593959 | + | 0.804495i | \(0.297564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 189.373 | 0.552107 | ||||||||
\(50\) | −635.942 | −1.79872 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −304.098 | −0.810977 | ||||||||
\(53\) | 173.620 | 0.449972 | 0.224986 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224986 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.35925 | −0.0131389 | ||||||||
\(56\) | −1256.56 | −2.99849 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −372.847 | −0.844090 | ||||||||
\(59\) | −425.847 | −0.939670 | −0.469835 | − | 0.882754i | \(-0.655687\pi\) | ||||
−0.469835 | + | 0.882754i | \(0.655687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −508.759 | −1.06787 | −0.533933 | − | 0.845527i | \(-0.679287\pi\) | ||||
−0.533933 | + | 0.845527i | \(0.679287\pi\) | |||||||
\(62\) | −138.618 | −0.283944 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 208.290 | 0.406816 | ||||||||
\(65\) | 20.8301 | 0.0397485 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −650.419 | −1.18599 | −0.592995 | − | 0.805206i | \(-0.702055\pi\) | ||||
−0.592995 | + | 0.805206i | \(0.702055\pi\) | |||||||
\(68\) | 1820.60 | 3.24676 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 151.241 | 0.258239 | ||||||||
\(71\) | 132.426 | 0.221354 | 0.110677 | − | 0.993856i | \(-0.464698\pi\) | ||||
0.110677 | + | 0.993856i | \(0.464698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −291.054 | −0.466648 | −0.233324 | − | 0.972399i | \(-0.574960\pi\) | ||||
−0.233324 | + | 0.972399i | \(0.574960\pi\) | |||||||
\(74\) | −444.320 | −0.697988 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1117.96 | −1.68736 | ||||||||
\(77\) | −97.2333 | −0.143906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 948.306 | 1.35054 | 0.675271 | − | 0.737570i | \(-0.264027\pi\) | ||||
0.675271 | + | 0.737570i | \(0.264027\pi\) | |||||||
\(80\) | −168.085 | −0.234906 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 707.699 | 0.953077 | ||||||||
\(83\) | 585.449 | 0.774234 | 0.387117 | − | 0.922031i | \(-0.373471\pi\) | ||||
0.387117 | + | 0.922031i | \(0.373471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −124.707 | −0.159134 | ||||||||
\(86\) | −2097.09 | −2.62947 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 229.501 | 0.278010 | ||||||||
\(89\) | 587.676 | 0.699928 | 0.349964 | − | 0.936763i | \(-0.386194\pi\) | ||||
0.349964 | + | 0.936763i | \(0.386194\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 377.922 | 0.435351 | ||||||||
\(92\) | −3134.97 | −3.55264 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1972.86 | 2.16474 | ||||||||
\(95\) | 76.5781 | 0.0827026 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −479.173 | −0.501574 | −0.250787 | − | 0.968042i | \(-0.580689\pi\) | ||||
−0.250787 | + | 0.968042i | \(0.580689\pi\) | |||||||
\(98\) | 976.069 | 1.00610 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2290.73 | −2.29073 | ||||||||
\(101\) | −1714.66 | −1.68926 | −0.844630 | − | 0.535350i | \(-0.820180\pi\) | ||||
−0.844630 | + | 0.535350i | \(0.820180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41.4624 | 0.0396642 | 0.0198321 | − | 0.999803i | \(-0.493687\pi\) | ||||
0.0198321 | + | 0.999803i | \(0.493687\pi\) | |||||||
\(104\) | −892.012 | −0.841048 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 894.876 | 0.819982 | ||||||||
\(107\) | 963.414 | 0.870437 | 0.435219 | − | 0.900325i | \(-0.356671\pi\) | ||||
0.435219 | + | 0.900325i | \(0.356671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 477.755 | 0.419822 | 0.209911 | − | 0.977720i | \(-0.432683\pi\) | ||||
0.209911 | + | 0.977720i | \(0.432683\pi\) | |||||||
\(110\) | −27.6228 | −0.0239430 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3049.59 | −2.57285 | ||||||||
\(113\) | −785.408 | −0.653850 | −0.326925 | − | 0.945050i | \(-0.606012\pi\) | ||||
−0.326925 | + | 0.945050i | \(0.606012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 214.739 | 0.174126 | ||||||||
\(116\) | −1343.03 | −1.07498 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2194.91 | −1.71236 | ||||||||
\(119\) | −2262.57 | −1.74294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1313.24 | −0.986658 | ||||||||
\(122\) | −2622.26 | −1.94597 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −499.317 | −0.361613 | ||||||||
\(125\) | 315.877 | 0.226023 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −847.836 | −0.592388 | −0.296194 | − | 0.955128i | \(-0.595717\pi\) | ||||
−0.296194 | + | 0.955128i | \(0.595717\pi\) | |||||||
\(128\) | −890.874 | −0.615179 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 107.363 | 0.0724334 | ||||||||
\(131\) | 390.738 | 0.260602 | 0.130301 | − | 0.991474i | \(-0.458406\pi\) | ||||
0.130301 | + | 0.991474i | \(0.458406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1389.36 | 0.905812 | ||||||||
\(134\) | −3352.41 | −2.16122 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5340.36 | 3.36715 | ||||||||
\(137\) | −2266.41 | −1.41338 | −0.706688 | − | 0.707525i | \(-0.749812\pi\) | ||||
−0.706688 | + | 0.707525i | \(0.749812\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1891.28 | −1.15407 | −0.577036 | − | 0.816719i | \(-0.695791\pi\) | ||||
−0.577036 | + | 0.816719i | \(0.695791\pi\) | |||||||
\(140\) | 544.784 | 0.328876 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 682.556 | 0.403372 | ||||||||
\(143\) | −69.0241 | −0.0403643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 91.9949 | 0.0526880 | ||||||||
\(146\) | −1500.16 | −0.850369 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1600.49 | −0.888913 | ||||||||
\(149\) | −790.756 | −0.434773 | −0.217387 | − | 0.976086i | \(-0.569753\pi\) | ||||
−0.217387 | + | 0.976086i | \(0.569753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2688.63 | 1.44899 | 0.724495 | − | 0.689280i | \(-0.242073\pi\) | ||||
0.724495 | + | 0.689280i | \(0.242073\pi\) | |||||||
\(152\) | −3279.33 | −1.74992 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −501.162 | −0.262239 | ||||||||
\(155\) | 34.2021 | 0.0177238 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −299.027 | −0.152006 | −0.0760031 | − | 0.997108i | \(-0.524216\pi\) | ||||
−0.0760031 | + | 0.997108i | \(0.524216\pi\) | |||||||
\(158\) | 4887.79 | 2.46108 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −312.282 | −0.154300 | ||||||||
\(161\) | 3896.02 | 1.90714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 148.627 | 0.0714195 | 0.0357098 | − | 0.999362i | \(-0.488631\pi\) | ||||
0.0357098 | + | 0.999362i | \(0.488631\pi\) | |||||||
\(164\) | 2549.21 | 1.21378 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3017.54 | 1.41088 | ||||||||
\(167\) | −3277.62 | −1.51874 | −0.759372 | − | 0.650657i | \(-0.774493\pi\) | ||||
−0.759372 | + | 0.650657i | \(0.774493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1928.72 | −0.877888 | ||||||||
\(170\) | −642.768 | −0.289989 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7553.92 | −3.34873 | ||||||||
\(173\) | 3263.65 | 1.43428 | 0.717141 | − | 0.696928i | \(-0.245450\pi\) | ||||
0.717141 | + | 0.696928i | \(0.245450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2846.83 | 1.22972 | ||||||||
\(176\) | 556.981 | 0.238546 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3029.02 | 1.27547 | ||||||||
\(179\) | 4519.98 | 1.88737 | 0.943684 | − | 0.330848i | \(-0.107335\pi\) | ||||
0.943684 | + | 0.330848i | \(0.107335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3600.29 | −1.47849 | −0.739247 | − | 0.673435i | \(-0.764818\pi\) | ||||
−0.739247 | + | 0.673435i | \(0.764818\pi\) | |||||||
\(182\) | 1947.89 | 0.793338 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9195.81 | −3.68437 | ||||||||
\(185\) | 109.630 | 0.0435684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 413.239 | 0.161599 | ||||||||
\(188\) | 7106.46 | 2.75687 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 394.701 | 0.150709 | ||||||||
\(191\) | 1601.68 | 0.606773 | 0.303387 | − | 0.952868i | \(-0.401883\pi\) | ||||
0.303387 | + | 0.952868i | \(0.401883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3459.52 | −1.29027 | −0.645134 | − | 0.764069i | \(-0.723198\pi\) | ||||
−0.645134 | + | 0.764069i | \(0.723198\pi\) | |||||||
\(194\) | −2469.77 | −0.914015 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3515.90 | 1.28131 | ||||||||
\(197\) | −835.346 | −0.302111 | −0.151056 | − | 0.988525i | \(-0.548267\pi\) | ||||
−0.151056 | + | 0.988525i | \(0.548267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1250.75 | −0.445545 | −0.222772 | − | 0.974871i | \(-0.571511\pi\) | ||||
−0.222772 | + | 0.974871i | \(0.571511\pi\) | |||||||
\(200\) | −6719.41 | −2.37567 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8837.76 | −3.07833 | ||||||||
\(203\) | 1669.07 | 0.577073 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −174.615 | −0.0594910 | ||||||||
\(206\) | 213.707 | 0.0722798 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2164.85 | −0.721659 | ||||||||
\(209\) | −253.755 | −0.0839838 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 937.142 | 0.305761 | 0.152880 | − | 0.988245i | \(-0.451145\pi\) | ||||
0.152880 | + | 0.988245i | \(0.451145\pi\) | |||||||
\(212\) | 3223.44 | 1.04428 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4965.66 | 1.58619 | ||||||||
\(215\) | 517.427 | 0.164131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 620.532 | 0.194122 | ||||||||
\(218\) | 2462.46 | 0.765039 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −99.5001 | −0.0304923 | ||||||||
\(221\) | −1606.16 | −0.488877 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2589.67 | 0.777655 | 0.388827 | − | 0.921311i | \(-0.372880\pi\) | ||||
0.388827 | + | 0.921311i | \(0.372880\pi\) | |||||||
\(224\) | −5665.76 | −1.69000 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4048.17 | −1.19151 | ||||||||
\(227\) | 5121.76 | 1.49755 | 0.748773 | − | 0.662826i | \(-0.230643\pi\) | ||||
0.748773 | + | 0.662826i | \(0.230643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3590.34 | 1.03605 | 0.518027 | − | 0.855364i | \(-0.326666\pi\) | ||||
0.518027 | + | 0.855364i | \(0.326666\pi\) | |||||||
\(230\) | 1106.81 | 0.317309 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3939.52 | −1.11484 | ||||||||
\(233\) | 883.730 | 0.248477 | 0.124238 | − | 0.992252i | \(-0.460351\pi\) | ||||
0.124238 | + | 0.992252i | \(0.460351\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −486.777 | −0.135123 | ||||||||
\(236\) | −7906.30 | −2.18075 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11661.8 | −3.17614 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1447.09 | −0.386784 | −0.193392 | − | 0.981122i | \(-0.561949\pi\) | ||||
−0.193392 | + | 0.981122i | \(0.561949\pi\) | |||||||
\(242\) | −6768.74 | −1.79798 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9445.64 | −2.47826 | ||||||||
\(245\) | −240.832 | −0.0628007 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 986.284 | 0.254072 | ||||||||
\(248\) | −1464.65 | −0.375021 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1628.10 | 0.411881 | ||||||||
\(251\) | −743.264 | −0.186910 | −0.0934550 | − | 0.995624i | \(-0.529791\pi\) | ||||
−0.0934550 | + | 0.995624i | \(0.529791\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −711.575 | −0.176823 | ||||||||
\(254\) | −4369.94 | −1.07951 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6258.09 | −1.52785 | ||||||||
\(257\) | −2369.85 | −0.575204 | −0.287602 | − | 0.957750i | \(-0.592858\pi\) | ||||
−0.287602 | + | 0.957750i | \(0.592858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1989.02 | 0.477189 | ||||||||
\(260\) | 386.732 | 0.0922466 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2013.95 | 0.474894 | ||||||||
\(263\) | 6429.45 | 1.50744 | 0.753720 | − | 0.657196i | \(-0.228258\pi\) | ||||
0.753720 | + | 0.657196i | \(0.228258\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −220.799 | −0.0511832 | ||||||||
\(266\) | 7161.09 | 1.65066 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12075.7 | −2.75240 | ||||||||
\(269\) | −1740.36 | −0.394468 | −0.197234 | − | 0.980356i | \(-0.563196\pi\) | ||||
−0.197234 | + | 0.980356i | \(0.563196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 965.726 | 0.216471 | 0.108236 | − | 0.994125i | \(-0.465480\pi\) | ||||
0.108236 | + | 0.994125i | \(0.465480\pi\) | |||||||
\(272\) | 12960.7 | 2.88918 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11681.6 | −2.57559 | ||||||||
\(275\) | −519.950 | −0.114015 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1837.77 | −0.398631 | −0.199315 | − | 0.979935i | \(-0.563872\pi\) | ||||
−0.199315 | + | 0.979935i | \(0.563872\pi\) | |||||||
\(278\) | −9748.07 | −2.10306 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1598.02 | 0.341071 | ||||||||
\(281\) | 7292.56 | 1.54818 | 0.774088 | − | 0.633078i | \(-0.218209\pi\) | ||||
0.774088 | + | 0.633078i | \(0.218209\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4293.55 | 0.901855 | 0.450927 | − | 0.892561i | \(-0.351093\pi\) | ||||
0.450927 | + | 0.892561i | \(0.351093\pi\) | |||||||
\(284\) | 2458.64 | 0.513709 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −355.766 | −0.0735556 | ||||||||
\(287\) | −3168.06 | −0.651583 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4702.86 | 0.957228 | ||||||||
\(290\) | 474.163 | 0.0960131 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5403.72 | −1.08298 | ||||||||
\(293\) | 3253.10 | 0.648629 | 0.324315 | − | 0.945949i | \(-0.394866\pi\) | ||||
0.324315 | + | 0.945949i | \(0.394866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 541.564 | 0.106885 | ||||||||
\(296\) | −4694.71 | −0.921873 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4075.74 | −0.792285 | ||||||||
\(299\) | 2765.71 | 0.534934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9387.73 | 1.79767 | ||||||||
\(302\) | 13857.8 | 2.64049 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7958.68 | −1.50152 | ||||||||
\(305\) | 647.006 | 0.121467 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3914.79 | 0.727781 | 0.363890 | − | 0.931442i | \(-0.381448\pi\) | ||||
0.363890 | + | 0.931442i | \(0.381448\pi\) | |||||||
\(308\) | −1805.24 | −0.333971 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 176.286 | 0.0322979 | ||||||||
\(311\) | −3124.86 | −0.569757 | −0.284878 | − | 0.958564i | \(-0.591953\pi\) | ||||
−0.284878 | + | 0.958564i | \(0.591953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7914.98 | 1.42933 | 0.714667 | − | 0.699465i | \(-0.246578\pi\) | ||||
0.714667 | + | 0.699465i | \(0.246578\pi\) | |||||||
\(314\) | −1541.25 | −0.277000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17606.3 | 3.13428 | ||||||||
\(317\) | 3512.36 | 0.622314 | 0.311157 | − | 0.950358i | \(-0.399283\pi\) | ||||
0.311157 | + | 0.950358i | \(0.399283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −304.842 | −0.0535042 | ||||||||
\(320\) | −264.889 | −0.0462743 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20081.0 | 3.47537 | ||||||||
\(323\) | −5904.76 | −1.01718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2020.92 | 0.344924 | ||||||||
\(326\) | 766.058 | 0.130147 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7477.59 | 1.25878 | ||||||||
\(329\) | −8831.64 | −1.47995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8333.51 | 1.38384 | 0.691920 | − | 0.721974i | \(-0.256765\pi\) | ||||
0.691920 | + | 0.721974i | \(0.256765\pi\) | |||||||
\(332\) | 10869.5 | 1.79681 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16893.6 | −2.76760 | ||||||||
\(335\) | 827.161 | 0.134903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4668.20 | 0.754578 | 0.377289 | − | 0.926096i | \(-0.376856\pi\) | ||||
0.377289 | + | 0.926096i | \(0.376856\pi\) | |||||||
\(338\) | −9941.06 | −1.59977 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2315.32 | −0.369311 | ||||||||
\(341\) | −113.335 | −0.0179983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3544.68 | 0.558002 | ||||||||
\(344\) | −22157.9 | −3.47290 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16821.6 | 2.61369 | ||||||||
\(347\) | 4398.94 | 0.680541 | 0.340270 | − | 0.940328i | \(-0.389481\pi\) | ||||
0.340270 | + | 0.940328i | \(0.389481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5610.61 | 0.860541 | 0.430271 | − | 0.902700i | \(-0.358418\pi\) | ||||
0.430271 | + | 0.902700i | \(0.358418\pi\) | |||||||
\(350\) | 14673.2 | 2.24091 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1034.80 | 0.156691 | ||||||||
\(353\) | −97.4593 | −0.0146947 | −0.00734736 | − | 0.999973i | \(-0.502339\pi\) | ||||
−0.00734736 | + | 0.999973i | \(0.502339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −168.411 | −0.0251785 | ||||||||
\(356\) | 10910.8 | 1.62436 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23297.0 | 3.43934 | ||||||||
\(359\) | −8080.31 | −1.18792 | −0.593958 | − | 0.804496i | \(-0.702436\pi\) | ||||
−0.593958 | + | 0.804496i | \(0.702436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3233.10 | −0.471366 | ||||||||
\(362\) | −18556.7 | −2.69425 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7016.52 | 1.01034 | ||||||||
\(365\) | 370.143 | 0.0530800 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4871.70 | 0.692918 | 0.346459 | − | 0.938065i | \(-0.387384\pi\) | ||||
0.346459 | + | 0.938065i | \(0.387384\pi\) | |||||||
\(368\) | −22317.6 | −3.16137 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 565.057 | 0.0793944 | ||||||||
\(371\) | −4005.97 | −0.560591 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7045.04 | −0.977957 | −0.488979 | − | 0.872296i | \(-0.662630\pi\) | ||||
−0.488979 | + | 0.872296i | \(0.662630\pi\) | |||||||
\(374\) | 2129.93 | 0.294481 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20845.4 | 2.85909 | ||||||||
\(377\) | 1184.84 | 0.161864 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5969.39 | 0.809043 | 0.404521 | − | 0.914529i | \(-0.367438\pi\) | ||||
0.404521 | + | 0.914529i | \(0.367438\pi\) | |||||||
\(380\) | 1421.75 | 0.191933 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8255.44 | 1.10572 | ||||||||
\(383\) | −3617.38 | −0.482610 | −0.241305 | − | 0.970449i | \(-0.577575\pi\) | ||||
−0.241305 | + | 0.970449i | \(0.577575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 123.655 | 0.0163689 | ||||||||
\(386\) | −17831.2 | −2.35125 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8896.36 | −1.16403 | ||||||||
\(389\) | −3143.72 | −0.409750 | −0.204875 | − | 0.978788i | \(-0.565679\pi\) | ||||
−0.204875 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16558.0 | −2.14162 | ||||||||
\(392\) | 10313.2 | 1.32882 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4305.57 | −0.550536 | ||||||||
\(395\) | −1205.99 | −0.153621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3961.64 | 0.500828 | 0.250414 | − | 0.968139i | \(-0.419433\pi\) | ||||
0.250414 | + | 0.968139i | \(0.419433\pi\) | |||||||
\(398\) | −6446.65 | −0.811913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16307.5 | −2.03844 | ||||||||
\(401\) | −5164.39 | −0.643135 | −0.321568 | − | 0.946887i | \(-0.604210\pi\) | ||||
−0.321568 | + | 0.946887i | \(0.604210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 440.505 | 0.0544494 | ||||||||
\(404\) | −31834.5 | −3.92036 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8602.77 | 1.05160 | ||||||||
\(407\) | −363.278 | −0.0442433 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15261.8 | −1.84510 | −0.922550 | − | 0.385879i | \(-0.873898\pi\) | ||||
−0.922550 | + | 0.385879i | \(0.873898\pi\) | |||||||
\(410\) | −900.006 | −0.108410 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 769.793 | 0.0920510 | ||||||||
\(413\) | 9825.65 | 1.17067 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −744.537 | −0.0880671 | ||||||||
\(416\) | −4022.02 | −0.474028 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1307.91 | −0.153043 | ||||||||
\(419\) | −8757.77 | −1.02111 | −0.510555 | − | 0.859845i | \(-0.670560\pi\) | ||||
−0.510555 | + | 0.859845i | \(0.670560\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2925.07 | −0.338620 | −0.169310 | − | 0.985563i | \(-0.554154\pi\) | ||||
−0.169310 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(422\) | 4830.24 | 0.557186 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9455.32 | 1.08300 | ||||||||
\(425\) | −12099.0 | −1.38091 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11738.7 | 1.33039 | ||||||||
\(428\) | 17886.8 | 2.02007 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2666.94 | 0.299096 | ||||||||
\(431\) | 5246.34 | 0.586327 | 0.293164 | − | 0.956062i | \(-0.405292\pi\) | ||||
0.293164 | + | 0.956062i | \(0.405292\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2901.54 | −0.322030 | −0.161015 | − | 0.986952i | \(-0.551477\pi\) | ||||
−0.161015 | + | 0.986952i | \(0.551477\pi\) | |||||||
\(434\) | 3198.36 | 0.353748 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8870.02 | 0.974305 | ||||||||
\(437\) | 10167.7 | 1.11301 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4567.53 | 0.496575 | 0.248287 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248287 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(440\) | −291.864 | −0.0316229 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8278.50 | −0.890878 | ||||||||
\(443\) | 2082.15 | 0.223309 | 0.111654 | − | 0.993747i | \(-0.464385\pi\) | ||||
0.111654 | + | 0.993747i | \(0.464385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −747.369 | −0.0796150 | ||||||||
\(446\) | 13347.7 | 1.41712 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4805.91 | −0.506826 | ||||||||
\(449\) | 64.4340 | 0.00677245 | 0.00338622 | − | 0.999994i | \(-0.498922\pi\) | ||||
0.00338622 | + | 0.999994i | \(0.498922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 578.618 | 0.0604126 | ||||||||
\(452\) | −14581.9 | −1.51743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26398.7 | 2.72897 | ||||||||
\(455\) | −480.616 | −0.0495201 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8606.13 | −0.880915 | −0.440457 | − | 0.897774i | \(-0.645184\pi\) | ||||
−0.440457 | + | 0.897774i | \(0.645184\pi\) | |||||||
\(458\) | 18505.4 | 1.88800 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3986.85 | 0.404104 | ||||||||
\(461\) | −15415.3 | −1.55740 | −0.778698 | − | 0.627398i | \(-0.784120\pi\) | ||||
−0.778698 | + | 0.627398i | \(0.784120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10632.2 | 1.06722 | 0.533609 | − | 0.845732i | \(-0.320836\pi\) | ||||
0.533609 | + | 0.845732i | \(0.320836\pi\) | |||||||
\(464\) | −9560.94 | −0.956585 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4554.95 | 0.452798 | ||||||||
\(467\) | 2712.98 | 0.268826 | 0.134413 | − | 0.990925i | \(-0.457085\pi\) | ||||
0.134413 | + | 0.990925i | \(0.457085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15007.2 | 1.47755 | ||||||||
\(470\) | −2508.96 | −0.246233 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23191.6 | −2.26161 | ||||||||
\(473\) | −1714.59 | −0.166674 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7429.54 | 0.717665 | ||||||||
\(476\) | −42007.0 | −4.04493 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1231.86 | 0.117874 | ||||||||
\(479\) | −9677.65 | −0.923138 | −0.461569 | − | 0.887104i | \(-0.652713\pi\) | ||||
−0.461569 | + | 0.887104i | \(0.652713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1411.97 | 0.133847 | ||||||||
\(482\) | −7458.61 | −0.704835 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24381.7 | −2.28979 | ||||||||
\(485\) | 609.381 | 0.0570527 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1458.67 | −0.135726 | −0.0678630 | − | 0.997695i | \(-0.521618\pi\) | ||||
−0.0678630 | + | 0.997695i | \(0.521618\pi\) | |||||||
\(488\) | −27706.9 | −2.57015 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1241.30 | −0.114441 | ||||||||
\(491\) | 10497.8 | 0.964884 | 0.482442 | − | 0.875928i | \(-0.339750\pi\) | ||||
0.482442 | + | 0.875928i | \(0.339750\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7093.51 | −0.648024 | ||||||||
\(494\) | 5083.53 | 0.462994 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3554.59 | −0.321786 | ||||||||
\(497\) | −3055.50 | −0.275771 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18915.4 | 1.69694 | 0.848468 | − | 0.529247i | \(-0.177525\pi\) | ||||
0.848468 | + | 0.529247i | \(0.177525\pi\) | |||||||
\(500\) | 5864.59 | 0.524545 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3830.95 | −0.340605 | ||||||||
\(503\) | 910.675 | 0.0807257 | 0.0403628 | − | 0.999185i | \(-0.487149\pi\) | ||||
0.0403628 | + | 0.999185i | \(0.487149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2180.60 | 0.192149 | ||||||||
\(506\) | −3667.62 | −0.322224 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15741.0 | −1.37479 | ||||||||
\(509\) | −2067.73 | −0.180060 | −0.0900301 | − | 0.995939i | \(-0.528696\pi\) | ||||
−0.0900301 | + | 0.995939i | \(0.528696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6715.54 | 0.581366 | ||||||||
\(512\) | −25128.6 | −2.16902 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12214.8 | −1.04819 | ||||||||
\(515\) | −52.7292 | −0.00451170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1613.02 | 0.137216 | ||||||||
\(518\) | 10251.9 | 0.869579 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1134.40 | 0.0956670 | ||||||||
\(521\) | −9551.18 | −0.803157 | −0.401579 | − | 0.915825i | \(-0.631538\pi\) | ||||
−0.401579 | + | 0.915825i | \(0.631538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22594.0 | −1.88904 | −0.944520 | − | 0.328455i | \(-0.893472\pi\) | ||||
−0.944520 | + | 0.328455i | \(0.893472\pi\) | |||||||
\(524\) | 7254.46 | 0.604795 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33138.8 | 2.74700 | ||||||||
\(527\) | −2637.25 | −0.217989 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16345.0 | 1.34338 | ||||||||
\(530\) | −1138.05 | −0.0932709 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25795.0 | 2.10217 | ||||||||
\(533\) | −2248.95 | −0.182763 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1225.21 | −0.0990100 | ||||||||
\(536\) | −35421.7 | −2.85445 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8970.23 | −0.718837 | ||||||||
\(539\) | 798.039 | 0.0637736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10689.3 | 0.849479 | 0.424740 | − | 0.905316i | \(-0.360366\pi\) | ||||
0.424740 | + | 0.905316i | \(0.360366\pi\) | |||||||
\(542\) | 4977.57 | 0.394474 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24079.3 | 1.89778 | ||||||||
\(545\) | −607.577 | −0.0477537 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18533.4 | −1.44869 | −0.724344 | − | 0.689439i | \(-0.757857\pi\) | ||||
−0.724344 | + | 0.689439i | \(0.757857\pi\) | |||||||
\(548\) | −42078.3 | −3.28010 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2679.94 | −0.207769 | ||||||||
\(551\) | 4355.87 | 0.336781 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21880.5 | −1.68255 | ||||||||
\(554\) | −9472.27 | −0.726423 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −35113.5 | −2.67832 | ||||||||
\(557\) | −18530.5 | −1.40963 | −0.704814 | − | 0.709393i | \(-0.748969\pi\) | ||||
−0.704814 | + | 0.709393i | \(0.748969\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6664.18 | 0.504230 | ||||||||
\(560\) | 3878.27 | 0.292655 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 37587.5 | 2.82123 | ||||||||
\(563\) | 12789.8 | 0.957417 | 0.478709 | − | 0.877974i | \(-0.341105\pi\) | ||||
0.478709 | + | 0.877974i | \(0.341105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 998.832 | 0.0743737 | ||||||||
\(566\) | 22129.9 | 1.64345 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7211.93 | 0.532757 | ||||||||
\(569\) | −10151.1 | −0.747904 | −0.373952 | − | 0.927448i | \(-0.621998\pi\) | ||||
−0.373952 | + | 0.927448i | \(0.621998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3426.70 | −0.251144 | −0.125572 | − | 0.992085i | \(-0.540077\pi\) | ||||
−0.125572 | + | 0.992085i | \(0.540077\pi\) | |||||||
\(572\) | −1281.51 | −0.0936756 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16328.9 | −1.18738 | ||||||||
\(575\) | 20833.8 | 1.51101 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7548.20 | 0.544603 | 0.272301 | − | 0.962212i | \(-0.412215\pi\) | ||||
0.272301 | + | 0.962212i | \(0.412215\pi\) | |||||||
\(578\) | 24239.6 | 1.74435 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1707.98 | 0.122276 | ||||||||
\(581\) | −13508.2 | −0.964568 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 731.655 | 0.0519761 | ||||||||
\(584\) | −15850.8 | −1.12313 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16767.2 | 1.18199 | ||||||||
\(587\) | 12736.8 | 0.895577 | 0.447789 | − | 0.894139i | \(-0.352212\pi\) | ||||
0.447789 | + | 0.894139i | \(0.352212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1619.44 | 0.113290 | ||||||||
\(590\) | 2791.35 | 0.194776 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11393.7 | −0.791012 | ||||||||
\(593\) | −15108.1 | −1.04623 | −0.523117 | − | 0.852261i | \(-0.675231\pi\) | ||||
−0.523117 | + | 0.852261i | \(0.675231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2877.39 | 0.198255 | ||||||||
\(596\) | −14681.2 | −1.00900 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14255.1 | 0.974808 | ||||||||
\(599\) | −4294.17 | −0.292913 | −0.146457 | − | 0.989217i | \(-0.546787\pi\) | ||||
−0.146457 | + | 0.989217i | \(0.546787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10426.3 | −0.707648 | −0.353824 | − | 0.935312i | \(-0.615119\pi\) | ||||
−0.353824 | + | 0.935312i | \(0.615119\pi\) | |||||||
\(602\) | 48386.5 | 3.27589 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 49917.3 | 3.36276 | ||||||||
\(605\) | 1670.10 | 0.112230 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28473.2 | −1.90394 | −0.951971 | − | 0.306188i | \(-0.900946\pi\) | ||||
−0.951971 | + | 0.306188i | \(0.900946\pi\) | |||||||
\(608\) | −14786.3 | −0.986286 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3334.82 | 0.221349 | ||||||||
\(611\) | −6269.42 | −0.415112 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14942.9 | 0.984561 | 0.492281 | − | 0.870437i | \(-0.336163\pi\) | ||||
0.492281 | + | 0.870437i | \(0.336163\pi\) | |||||||
\(614\) | 20177.7 | 1.32623 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5295.31 | −0.346354 | ||||||||
\(617\) | −11955.4 | −0.780072 | −0.390036 | − | 0.920800i | \(-0.627537\pi\) | ||||
−0.390036 | + | 0.920800i | \(0.627537\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13024.9 | 0.845746 | 0.422873 | − | 0.906189i | \(-0.361022\pi\) | ||||
0.422873 | + | 0.906189i | \(0.361022\pi\) | |||||||
\(620\) | 634.999 | 0.0411325 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16106.2 | −1.03826 | ||||||||
\(623\) | −13559.6 | −0.871995 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15021.1 | 0.961352 | ||||||||
\(626\) | 40795.6 | 2.60467 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5551.76 | −0.352769 | ||||||||
\(629\) | −8453.30 | −0.535859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9384.17 | −0.592041 | −0.296021 | − | 0.955182i | \(-0.595660\pi\) | ||||
−0.296021 | + | 0.955182i | \(0.595660\pi\) | |||||||
\(632\) | 51644.6 | 3.25050 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18103.5 | 1.13404 | ||||||||
\(635\) | 1078.22 | 0.0673826 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3101.78 | −0.192931 | ||||||||
\(638\) | −1571.22 | −0.0975005 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1132.96 | 0.0699751 | ||||||||
\(641\) | 520.895 | 0.0320969 | 0.0160484 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160484 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24141.1 | −1.48061 | −0.740306 | − | 0.672270i | \(-0.765320\pi\) | ||||
−0.740306 | + | 0.672270i | \(0.765320\pi\) | |||||||
\(644\) | 72333.8 | 4.42601 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30434.5 | −1.85360 | ||||||||
\(647\) | −8801.57 | −0.534815 | −0.267408 | − | 0.963583i | \(-0.586167\pi\) | ||||
−0.267408 | + | 0.963583i | \(0.586167\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1794.57 | −0.108541 | ||||||||
\(650\) | 10416.3 | 0.628553 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2759.42 | 0.165747 | ||||||||
\(653\) | 12705.6 | 0.761422 | 0.380711 | − | 0.924694i | \(-0.375679\pi\) | ||||
0.380711 | + | 0.924694i | \(0.375679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −496.915 | −0.0296429 | ||||||||
\(656\) | 18147.6 | 1.08010 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −45520.3 | −2.69691 | ||||||||
\(659\) | 15876.5 | 0.938483 | 0.469241 | − | 0.883070i | \(-0.344527\pi\) | ||||
0.469241 | + | 0.883070i | \(0.344527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18295.7 | 1.07658 | 0.538291 | − | 0.842759i | \(-0.319070\pi\) | ||||
0.538291 | + | 0.842759i | \(0.319070\pi\) | |||||||
\(662\) | 42952.8 | 2.52176 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31883.5 | 1.86343 | ||||||||
\(665\) | −1766.90 | −0.103034 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12214.6 | 0.709075 | ||||||||
\(668\) | −60852.6 | −3.52463 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4263.38 | 0.245834 | ||||||||
\(671\) | −2143.97 | −0.123349 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20647.4 | 1.18261 | 0.591307 | − | 0.806446i | \(-0.298612\pi\) | ||||
0.591307 | + | 0.806446i | \(0.298612\pi\) | |||||||
\(674\) | 24060.9 | 1.37506 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35808.7 | −2.03737 | ||||||||
\(677\) | −32567.1 | −1.84883 | −0.924413 | − | 0.381393i | \(-0.875444\pi\) | ||||
−0.924413 | + | 0.381393i | \(0.875444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11056.1 | 0.624879 | ||||||||
\(680\) | −6791.53 | −0.383005 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −584.154 | −0.0327983 | ||||||||
\(683\) | −5557.74 | −0.311363 | −0.155682 | − | 0.987807i | \(-0.549757\pi\) | ||||
−0.155682 | + | 0.987807i | \(0.549757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2882.28 | 0.160768 | ||||||||
\(686\) | 18270.1 | 1.01684 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −53775.7 | −2.97991 | ||||||||
\(689\) | −2843.76 | −0.157241 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28353.5 | 1.56095 | 0.780477 | − | 0.625185i | \(-0.214976\pi\) | ||||
0.780477 | + | 0.625185i | \(0.214976\pi\) | |||||||
\(692\) | 60593.2 | 3.32862 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22673.1 | 1.24015 | ||||||||
\(695\) | 2405.20 | 0.131273 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13464.2 | 0.731695 | ||||||||
\(698\) | 28918.3 | 1.56816 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 52854.5 | 2.85387 | ||||||||
\(701\) | −4271.73 | −0.230159 | −0.115079 | − | 0.993356i | \(-0.536712\pi\) | ||||
−0.115079 | + | 0.993356i | \(0.536712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5190.87 | 0.278488 | ||||||||
\(704\) | 877.758 | 0.0469911 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −502.327 | −0.0267781 | ||||||||
\(707\) | 39562.8 | 2.10454 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9667.95 | 0.512112 | 0.256056 | − | 0.966662i | \(-0.417577\pi\) | ||||
0.256056 | + | 0.966662i | \(0.417577\pi\) | |||||||
\(710\) | −868.031 | −0.0458826 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32004.8 | 1.68459 | ||||||||
\(713\) | 4541.19 | 0.238526 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 87.7804 | 0.00459133 | ||||||||
\(716\) | 83918.1 | 4.38012 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41647.7 | −2.16473 | ||||||||
\(719\) | −25456.1 | −1.32038 | −0.660188 | − | 0.751100i | \(-0.729524\pi\) | ||||
−0.660188 | + | 0.751100i | \(0.729524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −956.670 | −0.0494151 | ||||||||
\(722\) | −16664.1 | −0.858968 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −66843.2 | −3.43122 | ||||||||
\(725\) | 8925.27 | 0.457209 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6884.94 | 0.351235 | 0.175618 | − | 0.984458i | \(-0.443808\pi\) | ||||
0.175618 | + | 0.984458i | \(0.443808\pi\) | |||||||
\(728\) | 20581.6 | 1.04781 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1907.80 | 0.0967274 | ||||||||
\(731\) | −39897.6 | −2.01870 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 96.5247 | 0.00486387 | 0.00243194 | − | 0.999997i | \(-0.499226\pi\) | ||||
0.00243194 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(734\) | 25109.9 | 1.26270 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41463.3 | −2.07657 | ||||||||
\(737\) | −2740.95 | −0.136993 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18330.0 | −0.912423 | −0.456212 | − | 0.889871i | \(-0.650794\pi\) | ||||
−0.456212 | + | 0.889871i | \(0.650794\pi\) | |||||||
\(740\) | 2035.39 | 0.101112 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20647.7 | −1.02156 | ||||||||
\(743\) | 17703.9 | 0.874152 | 0.437076 | − | 0.899425i | \(-0.356014\pi\) | ||||
0.437076 | + | 0.899425i | \(0.356014\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1005.63 | 0.0494544 | ||||||||
\(746\) | −36311.7 | −1.78213 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7672.22 | 0.375032 | ||||||||
\(749\) | −22229.1 | −1.08442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20342.4 | 0.988421 | 0.494210 | − | 0.869342i | \(-0.335457\pi\) | ||||
0.494210 | + | 0.869342i | \(0.335457\pi\) | |||||||
\(752\) | 50590.2 | 2.45324 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6106.95 | 0.294963 | ||||||||
\(755\) | −3419.23 | −0.164819 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26846.7 | 1.28898 | 0.644490 | − | 0.764612i | \(-0.277070\pi\) | ||||
0.644490 | + | 0.764612i | \(0.277070\pi\) | |||||||
\(758\) | 30767.6 | 1.47431 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4170.43 | 0.199049 | ||||||||
\(761\) | −1474.28 | −0.0702269 | −0.0351134 | − | 0.999383i | \(-0.511179\pi\) | ||||
−0.0351134 | + | 0.999383i | \(0.511179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11023.3 | −0.523029 | ||||||||
\(764\) | 29736.9 | 1.40817 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18644.8 | −0.879458 | ||||||||
\(767\) | 6975.05 | 0.328363 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24129.6 | 1.13152 | 0.565758 | − | 0.824571i | \(-0.308584\pi\) | ||||
0.565758 | + | 0.824571i | \(0.308584\pi\) | |||||||
\(770\) | 637.346 | 0.0298290 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −64229.7 | −2.99440 | ||||||||
\(773\) | 30272.0 | 1.40855 | 0.704273 | − | 0.709929i | \(-0.251273\pi\) | ||||
0.704273 | + | 0.709929i | \(0.251273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3318.26 | 0.153801 | ||||||||
\(776\) | −26095.7 | −1.20719 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16203.4 | −0.746686 | ||||||||
\(779\) | −8267.86 | −0.380265 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 558.061 | 0.0255685 | ||||||||
\(782\) | −85343.7 | −3.90266 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25029.4 | 1.14019 | ||||||||
\(785\) | 380.283 | 0.0172903 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30974.7 | −1.40296 | −0.701480 | − | 0.712690i | \(-0.747477\pi\) | ||||
−0.701480 | + | 0.712690i | \(0.747477\pi\) | |||||||
\(788\) | −15509.1 | −0.701128 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6215.97 | −0.279942 | ||||||||
\(791\) | 18121.9 | 0.814589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8333.08 | 0.373161 | ||||||||
\(794\) | 20419.2 | 0.912657 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23221.5 | −1.03400 | ||||||||
\(797\) | −9007.64 | −0.400335 | −0.200168 | − | 0.979762i | \(-0.564149\pi\) | ||||
−0.200168 | + | 0.979762i | \(0.564149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37534.2 | 1.66191 | ||||||||
\(800\) | −30297.3 | −1.33897 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26618.4 | −1.17198 | ||||||||
\(803\) | −1226.54 | −0.0539023 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4954.71 | −0.216932 | ||||||||
\(806\) | 2270.46 | 0.0992228 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −93380.3 | −4.06573 | ||||||||
\(809\) | 12327.4 | 0.535732 | 0.267866 | − | 0.963456i | \(-0.413682\pi\) | ||||
0.267866 | + | 0.963456i | \(0.413682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19319.9 | −0.836514 | −0.418257 | − | 0.908329i | \(-0.637359\pi\) | ||||
−0.418257 | + | 0.908329i | \(0.637359\pi\) | |||||||
\(812\) | 30988.1 | 1.33925 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1872.42 | −0.0806243 | ||||||||
\(815\) | −189.014 | −0.00812379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24499.7 | 1.04913 | ||||||||
\(818\) | −78662.6 | −3.36231 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3241.91 | −0.138064 | ||||||||
\(821\) | 811.897 | 0.0345133 | 0.0172566 | − | 0.999851i | \(-0.494507\pi\) | ||||
0.0172566 | + | 0.999851i | \(0.494507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21030.5 | 0.890737 | 0.445369 | − | 0.895347i | \(-0.353073\pi\) | ||||
0.445369 | + | 0.895347i | \(0.353073\pi\) | |||||||
\(824\) | 2258.04 | 0.0954642 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 50643.6 | 2.13331 | ||||||||
\(827\) | −33934.2 | −1.42686 | −0.713428 | − | 0.700729i | \(-0.752858\pi\) | ||||
−0.713428 | + | 0.700729i | \(0.752858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21393.4 | 0.896289 | 0.448144 | − | 0.893961i | \(-0.352085\pi\) | ||||
0.448144 | + | 0.893961i | \(0.352085\pi\) | |||||||
\(830\) | −3837.51 | −0.160484 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3411.63 | −0.142160 | ||||||||
\(833\) | 18570.0 | 0.772402 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4168.27 | 0.172753 | ||||||||
\(836\) | −4711.24 | −0.194906 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45139.6 | −1.86076 | ||||||||
\(839\) | −7747.11 | −0.318784 | −0.159392 | − | 0.987215i | \(-0.550953\pi\) | ||||
−0.159392 | + | 0.987215i | \(0.550953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19156.2 | −0.785444 | ||||||||
\(842\) | −15076.5 | −0.617066 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17399.0 | 0.709597 | ||||||||
\(845\) | 2452.82 | 0.0998575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30300.7 | 1.22921 | ||||||||
\(848\) | 22947.4 | 0.929264 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −62360.8 | −2.51642 | ||||||||
\(851\) | 14556.1 | 0.586342 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16935.0 | −0.679769 | −0.339884 | − | 0.940467i | \(-0.610388\pi\) | ||||
−0.339884 | + | 0.940467i | \(0.610388\pi\) | |||||||
\(854\) | 60503.9 | 2.42436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 52467.4 | 2.09498 | ||||||||
\(857\) | −3777.17 | −0.150555 | −0.0752776 | − | 0.997163i | \(-0.523984\pi\) | ||||
−0.0752776 | + | 0.997163i | \(0.523984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21017.0 | −0.834798 | −0.417399 | − | 0.908723i | \(-0.637058\pi\) | ||||
−0.417399 | + | 0.908723i | \(0.637058\pi\) | |||||||
\(860\) | 9606.59 | 0.380909 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27040.8 | 1.06846 | ||||||||
\(863\) | 9505.46 | 0.374936 | 0.187468 | − | 0.982271i | \(-0.439972\pi\) | ||||
0.187468 | + | 0.982271i | \(0.439972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4150.50 | −0.163146 | ||||||||
\(866\) | −14955.2 | −0.586834 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11520.8 | 0.450510 | ||||||||
\(869\) | 3996.28 | 0.156001 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10653.4 | 0.414438 | ||||||||
\(872\) | 26018.5 | 1.01043 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 52406.5 | 2.02823 | ||||||||
\(875\) | −7288.29 | −0.281588 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27293.6 | 1.05090 | 0.525450 | − | 0.850824i | \(-0.323897\pi\) | ||||
0.525450 | + | 0.850824i | \(0.323897\pi\) | |||||||
\(878\) | 23542.1 | 0.904906 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −708.332 | −0.0271340 | ||||||||
\(881\) | −28578.9 | −1.09290 | −0.546451 | − | 0.837491i | \(-0.684022\pi\) | ||||
−0.546451 | + | 0.837491i | \(0.684022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5713.16 | −0.217738 | −0.108869 | − | 0.994056i | \(-0.534723\pi\) | ||||
−0.108869 | + | 0.994056i | \(0.534723\pi\) | |||||||
\(884\) | −29820.0 | −1.13457 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10731.9 | 0.406934 | ||||||||
\(887\) | 43896.4 | 1.66166 | 0.830832 | − | 0.556523i | \(-0.187865\pi\) | ||||
0.830832 | + | 0.556523i | \(0.187865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19562.3 | 0.738018 | ||||||||
\(890\) | −3852.11 | −0.145082 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48079.9 | 1.80475 | ||||||||
\(893\) | −23048.4 | −0.863703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5748.21 | −0.214683 | ||||||||
\(896\) | 20555.3 | 0.766412 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 332.108 | 0.0123414 | ||||||||
\(899\) | 1945.47 | 0.0721746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17025.3 | 0.629515 | ||||||||
\(902\) | 2982.33 | 0.110089 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −42773.2 | −1.57369 | ||||||||
\(905\) | 4578.61 | 0.168175 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23392.1 | 0.856362 | 0.428181 | − | 0.903693i | \(-0.359155\pi\) | ||||
0.428181 | + | 0.903693i | \(0.359155\pi\) | |||||||
\(908\) | 95090.9 | 3.47544 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2477.21 | −0.0902402 | ||||||||
\(911\) | 1315.19 | 0.0478310 | 0.0239155 | − | 0.999714i | \(-0.492387\pi\) | ||||
0.0239155 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2467.15 | 0.0894314 | ||||||||
\(914\) | −44358.0 | −1.60529 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 66658.5 | 2.40443 | ||||||||
\(917\) | −9015.57 | −0.324668 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47277.7 | −1.69701 | −0.848503 | − | 0.529191i | \(-0.822496\pi\) | ||||
−0.848503 | + | 0.529191i | \(0.822496\pi\) | |||||||
\(920\) | 11694.6 | 0.419088 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −79453.7 | −2.83804 | ||||||||
\(923\) | −2169.05 | −0.0773510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10636.2 | 0.378071 | ||||||||
\(926\) | 54800.9 | 1.94478 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17763.0 | −0.628341 | ||||||||
\(929\) | 36239.8 | 1.27986 | 0.639930 | − | 0.768433i | \(-0.278963\pi\) | ||||
0.639930 | + | 0.768433i | \(0.278963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11403.2 | −0.401421 | ||||||||
\(932\) | 16407.4 | 0.576654 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13983.3 | 0.489879 | ||||||||
\(935\) | −525.531 | −0.0183815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12678.9 | 0.442051 | 0.221026 | − | 0.975268i | \(-0.429060\pi\) | ||||
0.221026 | + | 0.975268i | \(0.429060\pi\) | |||||||
\(938\) | 77350.8 | 2.69253 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9037.53 | −0.313587 | ||||||||
\(941\) | −50353.2 | −1.74438 | −0.872192 | − | 0.489163i | \(-0.837302\pi\) | ||||
−0.872192 | + | 0.489163i | \(0.837302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23184.5 | −0.800628 | ||||||||
\(944\) | −56284.2 | −1.94057 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8837.38 | −0.303729 | ||||||||
\(947\) | 33033.7 | 1.13353 | 0.566763 | − | 0.823881i | \(-0.308195\pi\) | ||||
0.566763 | + | 0.823881i | \(0.308195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4767.24 | 0.163068 | ||||||||
\(950\) | 38293.6 | 1.30780 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −123219. | −4.19492 | ||||||||
\(953\) | 12625.3 | 0.429142 | 0.214571 | − | 0.976708i | \(-0.431165\pi\) | ||||
0.214571 | + | 0.976708i | \(0.431165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2036.92 | −0.0690189 | ||||||||
\(956\) | 4437.29 | 0.150117 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −49880.8 | −1.68223 | ||||||||
\(959\) | 52293.4 | 1.76083 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29067.7 | −0.975721 | ||||||||
\(962\) | 7277.62 | 0.243909 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26866.7 | −0.897633 | ||||||||
\(965\) | 4399.59 | 0.146765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20457.9 | −0.680333 | −0.340167 | − | 0.940365i | \(-0.610484\pi\) | ||||
−0.340167 | + | 0.940365i | \(0.610484\pi\) | |||||||
\(968\) | −71519.0 | −2.37470 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3140.89 | 0.103967 | ||||||||
\(971\) | −41805.4 | −1.38167 | −0.690834 | − | 0.723014i | \(-0.742756\pi\) | ||||
−0.690834 | + | 0.723014i | \(0.742756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43637.8 | 1.43778 | ||||||||
\(974\) | −7518.31 | −0.247333 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −67242.7 | −2.20531 | ||||||||
\(977\) | −47505.6 | −1.55562 | −0.777808 | − | 0.628502i | \(-0.783669\pi\) | ||||
−0.777808 | + | 0.628502i | \(0.783669\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2476.54 | 0.0808484 | ||||||||
\(980\) | −4471.30 | −0.145745 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 54108.0 | 1.75830 | ||||||||
\(983\) | −58004.1 | −1.88204 | −0.941020 | − | 0.338352i | \(-0.890131\pi\) | ||||
−0.941020 | + | 0.338352i | \(0.890131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1062.34 | 0.0343644 | ||||||||
\(986\) | −36561.6 | −1.18089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18311.4 | 0.589639 | ||||||||
\(989\) | 68701.5 | 2.20888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46228.7 | 1.48184 | 0.740920 | − | 0.671593i | \(-0.234390\pi\) | ||||
0.740920 | + | 0.671593i | \(0.234390\pi\) | |||||||
\(992\) | −6604.00 | −0.211368 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15748.8 | −0.502535 | ||||||||
\(995\) | 1590.62 | 0.0506796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35226.8 | −1.11900 | −0.559501 | − | 0.828830i | \(-0.689007\pi\) | ||||
−0.559501 | + | 0.828830i | \(0.689007\pi\) | |||||||
\(998\) | 97494.4 | 3.09232 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.4.a.g.1.57 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.3 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.57 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.3 | yes | 59 | 3.2 | odd | 2 |