Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618313 | −0.218607 | −0.109303 | − | 0.994008i | \(-0.534862\pi\) | ||||
−0.109303 | + | 0.994008i | \(0.534862\pi\) | |||||||
\(3\) | −9.18025 | −1.76674 | −0.883370 | − | 0.468676i | \(-0.844731\pi\) | ||||
−0.883370 | + | 0.468676i | \(0.844731\pi\) | |||||||
\(4\) | −7.61769 | −0.952211 | ||||||||
\(5\) | 19.4242 | 1.73736 | 0.868678 | − | 0.495377i | \(-0.164970\pi\) | ||||
0.868678 | + | 0.495377i | \(0.164970\pi\) | |||||||
\(6\) | 5.67627 | 0.386221 | ||||||||
\(7\) | 15.1594 | 0.818531 | 0.409265 | − | 0.912415i | \(-0.365785\pi\) | ||||
0.409265 | + | 0.912415i | \(0.365785\pi\) | |||||||
\(8\) | 9.65662 | 0.426766 | ||||||||
\(9\) | 57.2770 | 2.12137 | ||||||||
\(10\) | −12.0103 | −0.379798 | ||||||||
\(11\) | −7.19433 | −0.197198 | −0.0985988 | − | 0.995127i | \(-0.531436\pi\) | ||||
−0.0985988 | + | 0.995127i | \(0.531436\pi\) | |||||||
\(12\) | 69.9323 | 1.68231 | ||||||||
\(13\) | 36.4617 | 0.777897 | 0.388948 | − | 0.921260i | \(-0.372838\pi\) | ||||
0.388948 | + | 0.921260i | \(0.372838\pi\) | |||||||
\(14\) | −9.37325 | −0.178936 | ||||||||
\(15\) | −178.319 | −3.06946 | ||||||||
\(16\) | 54.9707 | 0.858917 | ||||||||
\(17\) | 102.264 | 1.45899 | 0.729493 | − | 0.683989i | \(-0.239756\pi\) | ||||
0.729493 | + | 0.683989i | \(0.239756\pi\) | |||||||
\(18\) | −35.4151 | −0.463745 | ||||||||
\(19\) | −51.6991 | −0.624241 | −0.312121 | − | 0.950043i | \(-0.601039\pi\) | ||||
−0.312121 | + | 0.950043i | \(0.601039\pi\) | |||||||
\(20\) | −147.968 | −1.65433 | ||||||||
\(21\) | −139.167 | −1.44613 | ||||||||
\(22\) | 4.44835 | 0.0431087 | ||||||||
\(23\) | −102.545 | −0.929655 | −0.464827 | − | 0.885401i | \(-0.653884\pi\) | ||||
−0.464827 | + | 0.885401i | \(0.653884\pi\) | |||||||
\(24\) | −88.6502 | −0.753985 | ||||||||
\(25\) | 252.301 | 2.01841 | ||||||||
\(26\) | −22.5447 | −0.170053 | ||||||||
\(27\) | −277.950 | −1.98117 | ||||||||
\(28\) | −115.480 | −0.779414 | ||||||||
\(29\) | −96.3830 | −0.617168 | −0.308584 | − | 0.951197i | \(-0.599855\pi\) | ||||
−0.308584 | + | 0.951197i | \(0.599855\pi\) | |||||||
\(30\) | 110.257 | 0.671003 | ||||||||
\(31\) | −157.016 | −0.909709 | −0.454854 | − | 0.890566i | \(-0.650309\pi\) | ||||
−0.454854 | + | 0.890566i | \(0.650309\pi\) | |||||||
\(32\) | −111.242 | −0.614531 | ||||||||
\(33\) | 66.0458 | 0.348397 | ||||||||
\(34\) | −63.2314 | −0.318944 | ||||||||
\(35\) | 294.460 | 1.42208 | ||||||||
\(36\) | −436.318 | −2.01999 | ||||||||
\(37\) | −233.730 | −1.03851 | −0.519257 | − | 0.854618i | \(-0.673791\pi\) | ||||
−0.519257 | + | 0.854618i | \(0.673791\pi\) | |||||||
\(38\) | 31.9662 | 0.136463 | ||||||||
\(39\) | −334.728 | −1.37434 | ||||||||
\(40\) | 187.572 | 0.741445 | ||||||||
\(41\) | −39.6529 | −0.151043 | −0.0755213 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755213 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(42\) | 86.0488 | 0.316134 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 54.8042 | 0.187774 | ||||||||
\(45\) | 1112.56 | 3.68557 | ||||||||
\(46\) | 63.4047 | 0.203229 | ||||||||
\(47\) | −455.256 | −1.41289 | −0.706446 | − | 0.707767i | \(-0.749703\pi\) | ||||
−0.706446 | + | 0.707767i | \(0.749703\pi\) | |||||||
\(48\) | −504.645 | −1.51748 | ||||||||
\(49\) | −113.193 | −0.330008 | ||||||||
\(50\) | −156.001 | −0.441237 | ||||||||
\(51\) | −938.812 | −2.57765 | ||||||||
\(52\) | −277.754 | −0.740722 | ||||||||
\(53\) | −602.876 | −1.56248 | −0.781240 | − | 0.624231i | \(-0.785413\pi\) | ||||
−0.781240 | + | 0.624231i | \(0.785413\pi\) | |||||||
\(54\) | 171.860 | 0.433096 | ||||||||
\(55\) | −139.744 | −0.342602 | ||||||||
\(56\) | 146.388 | 0.349321 | ||||||||
\(57\) | 474.610 | 1.10287 | ||||||||
\(58\) | 59.5949 | 0.134917 | ||||||||
\(59\) | −124.432 | −0.274571 | −0.137285 | − | 0.990532i | \(-0.543838\pi\) | ||||
−0.137285 | + | 0.990532i | \(0.543838\pi\) | |||||||
\(60\) | 1358.38 | 2.92277 | ||||||||
\(61\) | 838.549 | 1.76008 | 0.880042 | − | 0.474896i | \(-0.157514\pi\) | ||||
0.880042 | + | 0.474896i | \(0.157514\pi\) | |||||||
\(62\) | 97.0852 | 0.198868 | ||||||||
\(63\) | 868.284 | 1.73641 | ||||||||
\(64\) | −370.983 | −0.724577 | ||||||||
\(65\) | 708.241 | 1.35148 | ||||||||
\(66\) | −40.8370 | −0.0761618 | ||||||||
\(67\) | −166.437 | −0.303486 | −0.151743 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151743 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(68\) | −779.018 | −1.38926 | ||||||||
\(69\) | 941.386 | 1.64246 | ||||||||
\(70\) | −182.068 | −0.310876 | ||||||||
\(71\) | 215.480 | 0.360180 | 0.180090 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180090 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(72\) | 553.102 | 0.905329 | ||||||||
\(73\) | −108.227 | −0.173521 | −0.0867606 | − | 0.996229i | \(-0.527652\pi\) | ||||
−0.0867606 | + | 0.996229i | \(0.527652\pi\) | |||||||
\(74\) | 144.518 | 0.227026 | ||||||||
\(75\) | −2316.18 | −3.56600 | ||||||||
\(76\) | 393.827 | 0.594409 | ||||||||
\(77\) | −109.062 | −0.161412 | ||||||||
\(78\) | 206.966 | 0.300440 | ||||||||
\(79\) | −494.914 | −0.704837 | −0.352419 | − | 0.935843i | \(-0.614641\pi\) | ||||
−0.352419 | + | 0.935843i | \(0.614641\pi\) | |||||||
\(80\) | 1067.76 | 1.49225 | ||||||||
\(81\) | 1005.17 | 1.37884 | ||||||||
\(82\) | 24.5179 | 0.0330189 | ||||||||
\(83\) | 712.724 | 0.942549 | 0.471275 | − | 0.881987i | \(-0.343794\pi\) | ||||
0.471275 | + | 0.881987i | \(0.343794\pi\) | |||||||
\(84\) | 1060.13 | 1.37702 | ||||||||
\(85\) | 1986.41 | 2.53478 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 884.820 | 1.09038 | ||||||||
\(88\) | −69.4729 | −0.0841573 | ||||||||
\(89\) | −431.700 | −0.514158 | −0.257079 | − | 0.966390i | \(-0.582760\pi\) | ||||
−0.257079 | + | 0.966390i | \(0.582760\pi\) | |||||||
\(90\) | −687.911 | −0.805691 | ||||||||
\(91\) | 552.738 | 0.636732 | ||||||||
\(92\) | 781.154 | 0.885227 | ||||||||
\(93\) | 1441.45 | 1.60722 | ||||||||
\(94\) | 281.491 | 0.308868 | ||||||||
\(95\) | −1004.21 | −1.08453 | ||||||||
\(96\) | 1021.23 | 1.08572 | ||||||||
\(97\) | 1299.31 | 1.36005 | 0.680025 | − | 0.733189i | \(-0.261969\pi\) | ||||
0.680025 | + | 0.733189i | \(0.261969\pi\) | |||||||
\(98\) | 69.9885 | 0.0721419 | ||||||||
\(99\) | −412.070 | −0.418329 | ||||||||
\(100\) | −1921.95 | −1.92195 | ||||||||
\(101\) | −1475.52 | −1.45366 | −0.726831 | − | 0.686817i | \(-0.759007\pi\) | ||||
−0.726831 | + | 0.686817i | \(0.759007\pi\) | |||||||
\(102\) | 580.480 | 0.563491 | ||||||||
\(103\) | −291.930 | −0.279269 | −0.139635 | − | 0.990203i | \(-0.544593\pi\) | ||||
−0.139635 | + | 0.990203i | \(0.544593\pi\) | |||||||
\(104\) | 352.097 | 0.331980 | ||||||||
\(105\) | −2703.21 | −2.51244 | ||||||||
\(106\) | 372.766 | 0.341568 | ||||||||
\(107\) | −1552.74 | −1.40289 | −0.701444 | − | 0.712725i | \(-0.747461\pi\) | ||||
−0.701444 | + | 0.712725i | \(0.747461\pi\) | |||||||
\(108\) | 2117.34 | 1.88649 | ||||||||
\(109\) | 1809.11 | 1.58973 | 0.794867 | − | 0.606784i | \(-0.207541\pi\) | ||||
0.794867 | + | 0.606784i | \(0.207541\pi\) | |||||||
\(110\) | 86.4058 | 0.0748952 | ||||||||
\(111\) | 2145.70 | 1.83478 | ||||||||
\(112\) | 833.323 | 0.703050 | ||||||||
\(113\) | −677.063 | −0.563652 | −0.281826 | − | 0.959466i | \(-0.590940\pi\) | ||||
−0.281826 | + | 0.959466i | \(0.590940\pi\) | |||||||
\(114\) | −293.458 | −0.241095 | ||||||||
\(115\) | −1991.85 | −1.61514 | ||||||||
\(116\) | 734.216 | 0.587675 | ||||||||
\(117\) | 2088.42 | 1.65021 | ||||||||
\(118\) | 76.9380 | 0.0600230 | ||||||||
\(119\) | 1550.27 | 1.19422 | ||||||||
\(120\) | −1721.96 | −1.30994 | ||||||||
\(121\) | −1279.24 | −0.961113 | ||||||||
\(122\) | −518.485 | −0.384766 | ||||||||
\(123\) | 364.024 | 0.266853 | ||||||||
\(124\) | 1196.10 | 0.866235 | ||||||||
\(125\) | 2472.72 | 1.76934 | ||||||||
\(126\) | −536.871 | −0.379590 | ||||||||
\(127\) | −10.4671 | −0.00731340 | −0.00365670 | − | 0.999993i | \(-0.501164\pi\) | ||||
−0.00365670 | + | 0.999993i | \(0.501164\pi\) | |||||||
\(128\) | 1119.32 | 0.772928 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −437.914 | −0.295443 | ||||||||
\(131\) | −26.6364 | −0.0177652 | −0.00888258 | − | 0.999961i | \(-0.502827\pi\) | ||||
−0.00888258 | + | 0.999961i | \(0.502827\pi\) | |||||||
\(132\) | −503.116 | −0.331747 | ||||||||
\(133\) | −783.727 | −0.510960 | ||||||||
\(134\) | 102.910 | 0.0663439 | ||||||||
\(135\) | −5398.97 | −3.44199 | ||||||||
\(136\) | 987.528 | 0.622646 | ||||||||
\(137\) | 748.264 | 0.466632 | 0.233316 | − | 0.972401i | \(-0.425042\pi\) | ||||
0.233316 | + | 0.972401i | \(0.425042\pi\) | |||||||
\(138\) | −582.071 | −0.359052 | ||||||||
\(139\) | −1029.41 | −0.628152 | −0.314076 | − | 0.949398i | \(-0.601695\pi\) | ||||
−0.314076 | + | 0.949398i | \(0.601695\pi\) | |||||||
\(140\) | −2243.10 | −1.35412 | ||||||||
\(141\) | 4179.37 | 2.49621 | ||||||||
\(142\) | −133.234 | −0.0787378 | ||||||||
\(143\) | −262.318 | −0.153399 | ||||||||
\(144\) | 3148.56 | 1.82208 | ||||||||
\(145\) | −1872.17 | −1.07224 | ||||||||
\(146\) | 66.9183 | 0.0379329 | ||||||||
\(147\) | 1039.14 | 0.583038 | ||||||||
\(148\) | 1780.48 | 0.988885 | ||||||||
\(149\) | −1048.80 | −0.576649 | −0.288324 | − | 0.957533i | \(-0.593098\pi\) | ||||
−0.288324 | + | 0.957533i | \(0.593098\pi\) | |||||||
\(150\) | 1432.13 | 0.779551 | ||||||||
\(151\) | −2902.66 | −1.56434 | −0.782168 | − | 0.623068i | \(-0.785886\pi\) | ||||
−0.782168 | + | 0.623068i | \(0.785886\pi\) | |||||||
\(152\) | −499.238 | −0.266405 | ||||||||
\(153\) | 5857.39 | 3.09505 | ||||||||
\(154\) | 67.4343 | 0.0352858 | ||||||||
\(155\) | −3049.92 | −1.58049 | ||||||||
\(156\) | 2549.85 | 1.30866 | ||||||||
\(157\) | −524.942 | −0.266847 | −0.133423 | − | 0.991059i | \(-0.542597\pi\) | ||||
−0.133423 | + | 0.991059i | \(0.542597\pi\) | |||||||
\(158\) | 306.011 | 0.154082 | ||||||||
\(159\) | 5534.56 | 2.76050 | ||||||||
\(160\) | −2160.79 | −1.06766 | ||||||||
\(161\) | −1554.52 | −0.760951 | ||||||||
\(162\) | −621.512 | −0.301423 | ||||||||
\(163\) | −40.9398 | −0.0196727 | −0.00983635 | − | 0.999952i | \(-0.503131\pi\) | ||||
−0.00983635 | + | 0.999952i | \(0.503131\pi\) | |||||||
\(164\) | 302.064 | 0.143824 | ||||||||
\(165\) | 1282.89 | 0.605289 | ||||||||
\(166\) | −440.686 | −0.206047 | ||||||||
\(167\) | −1168.95 | −0.541652 | −0.270826 | − | 0.962628i | \(-0.587297\pi\) | ||||
−0.270826 | + | 0.962628i | \(0.587297\pi\) | |||||||
\(168\) | −1343.88 | −0.617160 | ||||||||
\(169\) | −867.544 | −0.394877 | ||||||||
\(170\) | −1228.22 | −0.554119 | ||||||||
\(171\) | −2961.17 | −1.32425 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2210.67 | −0.971528 | −0.485764 | − | 0.874090i | \(-0.661459\pi\) | ||||
−0.485764 | + | 0.874090i | \(0.661459\pi\) | |||||||
\(174\) | −547.096 | −0.238363 | ||||||||
\(175\) | 3824.73 | 1.65213 | ||||||||
\(176\) | −395.478 | −0.169376 | ||||||||
\(177\) | 1142.32 | 0.485095 | ||||||||
\(178\) | 266.925 | 0.112398 | ||||||||
\(179\) | −2397.80 | −1.00123 | −0.500615 | − | 0.865670i | \(-0.666893\pi\) | ||||
−0.500615 | + | 0.865670i | \(0.666893\pi\) | |||||||
\(180\) | −8475.15 | −3.50945 | ||||||||
\(181\) | 68.3076 | 0.0280512 | 0.0140256 | − | 0.999902i | \(-0.495535\pi\) | ||||
0.0140256 | + | 0.999902i | \(0.495535\pi\) | |||||||
\(182\) | −341.765 | −0.139194 | ||||||||
\(183\) | −7698.08 | −3.10961 | ||||||||
\(184\) | −990.235 | −0.396745 | ||||||||
\(185\) | −4540.03 | −1.80427 | ||||||||
\(186\) | −891.267 | −0.351349 | ||||||||
\(187\) | −735.724 | −0.287708 | ||||||||
\(188\) | 3468.00 | 1.34537 | ||||||||
\(189\) | −4213.56 | −1.62165 | ||||||||
\(190\) | 620.919 | 0.237085 | ||||||||
\(191\) | 585.643 | 0.221862 | 0.110931 | − | 0.993828i | \(-0.464617\pi\) | ||||
0.110931 | + | 0.993828i | \(0.464617\pi\) | |||||||
\(192\) | 3405.72 | 1.28014 | ||||||||
\(193\) | −4104.42 | −1.53079 | −0.765395 | − | 0.643561i | \(-0.777456\pi\) | ||||
−0.765395 | + | 0.643561i | \(0.777456\pi\) | |||||||
\(194\) | −803.380 | −0.297316 | ||||||||
\(195\) | −6501.83 | −2.38772 | ||||||||
\(196\) | 862.267 | 0.314237 | ||||||||
\(197\) | 787.155 | 0.284683 | 0.142341 | − | 0.989818i | \(-0.454537\pi\) | ||||
0.142341 | + | 0.989818i | \(0.454537\pi\) | |||||||
\(198\) | 254.788 | 0.0914495 | ||||||||
\(199\) | 4673.04 | 1.66464 | 0.832319 | − | 0.554297i | \(-0.187013\pi\) | ||||
0.832319 | + | 0.554297i | \(0.187013\pi\) | |||||||
\(200\) | 2436.37 | 0.861388 | ||||||||
\(201\) | 1527.93 | 0.536180 | ||||||||
\(202\) | 912.333 | 0.317780 | ||||||||
\(203\) | −1461.11 | −0.505171 | ||||||||
\(204\) | 7151.58 | 2.45446 | ||||||||
\(205\) | −770.227 | −0.262415 | ||||||||
\(206\) | 180.504 | 0.0610501 | ||||||||
\(207\) | −5873.45 | −1.97214 | ||||||||
\(208\) | 2004.33 | 0.668149 | ||||||||
\(209\) | 371.940 | 0.123099 | ||||||||
\(210\) | 1671.43 | 0.549237 | ||||||||
\(211\) | 1152.23 | 0.375939 | 0.187969 | − | 0.982175i | \(-0.439809\pi\) | ||||
0.187969 | + | 0.982175i | \(0.439809\pi\) | |||||||
\(212\) | 4592.53 | 1.48781 | ||||||||
\(213\) | −1978.16 | −0.636345 | ||||||||
\(214\) | 960.079 | 0.306680 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2684.06 | −0.845496 | ||||||||
\(217\) | −2380.27 | −0.744624 | ||||||||
\(218\) | −1118.59 | −0.347526 | ||||||||
\(219\) | 993.554 | 0.306567 | ||||||||
\(220\) | 1064.53 | 0.326230 | ||||||||
\(221\) | 3728.73 | 1.13494 | ||||||||
\(222\) | −1326.72 | −0.401096 | ||||||||
\(223\) | 2655.51 | 0.797426 | 0.398713 | − | 0.917076i | \(-0.369457\pi\) | ||||
0.398713 | + | 0.917076i | \(0.369457\pi\) | |||||||
\(224\) | −1686.36 | −0.503013 | ||||||||
\(225\) | 14451.0 | 4.28179 | ||||||||
\(226\) | 418.636 | 0.123218 | ||||||||
\(227\) | 3747.98 | 1.09587 | 0.547934 | − | 0.836521i | \(-0.315414\pi\) | ||||
0.547934 | + | 0.836521i | \(0.315414\pi\) | |||||||
\(228\) | −3615.43 | −1.05017 | ||||||||
\(229\) | 1183.25 | 0.341446 | 0.170723 | − | 0.985319i | \(-0.445390\pi\) | ||||
0.170723 | + | 0.985319i | \(0.445390\pi\) | |||||||
\(230\) | 1231.59 | 0.353080 | ||||||||
\(231\) | 1001.21 | 0.285173 | ||||||||
\(232\) | −930.734 | −0.263387 | ||||||||
\(233\) | −2800.12 | −0.787304 | −0.393652 | − | 0.919259i | \(-0.628789\pi\) | ||||
−0.393652 | + | 0.919259i | \(0.628789\pi\) | |||||||
\(234\) | −1291.29 | −0.360746 | ||||||||
\(235\) | −8843.00 | −2.45470 | ||||||||
\(236\) | 947.885 | 0.261449 | ||||||||
\(237\) | 4543.43 | 1.24526 | ||||||||
\(238\) | −958.549 | −0.261065 | ||||||||
\(239\) | −2888.20 | −0.781682 | −0.390841 | − | 0.920458i | \(-0.627816\pi\) | ||||
−0.390841 | + | 0.920458i | \(0.627816\pi\) | |||||||
\(240\) | −9802.34 | −2.63641 | ||||||||
\(241\) | 48.4148 | 0.0129405 | 0.00647027 | − | 0.999979i | \(-0.497940\pi\) | ||||
0.00647027 | + | 0.999979i | \(0.497940\pi\) | |||||||
\(242\) | 790.971 | 0.210106 | ||||||||
\(243\) | −1723.09 | −0.454882 | ||||||||
\(244\) | −6387.80 | −1.67597 | ||||||||
\(245\) | −2198.68 | −0.573341 | ||||||||
\(246\) | −225.080 | −0.0583358 | ||||||||
\(247\) | −1885.04 | −0.485595 | ||||||||
\(248\) | −1516.25 | −0.388233 | ||||||||
\(249\) | −6542.98 | −1.66524 | ||||||||
\(250\) | −1528.92 | −0.386788 | ||||||||
\(251\) | −4735.73 | −1.19090 | −0.595452 | − | 0.803391i | \(-0.703027\pi\) | ||||
−0.595452 | + | 0.803391i | \(0.703027\pi\) | |||||||
\(252\) | −6614.32 | −1.65342 | ||||||||
\(253\) | 737.741 | 0.183326 | ||||||||
\(254\) | 6.47192 | 0.00159876 | ||||||||
\(255\) | −18235.7 | −4.47829 | ||||||||
\(256\) | 2275.78 | 0.555609 | ||||||||
\(257\) | 642.806 | 0.156020 | 0.0780100 | − | 0.996953i | \(-0.475143\pi\) | ||||
0.0780100 | + | 0.996953i | \(0.475143\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3543.21 | −0.850055 | ||||||||
\(260\) | −5395.16 | −1.28690 | ||||||||
\(261\) | −5520.53 | −1.30924 | ||||||||
\(262\) | 16.4696 | 0.00388358 | ||||||||
\(263\) | 5427.16 | 1.27245 | 0.636223 | − | 0.771505i | \(-0.280496\pi\) | ||||
0.636223 | + | 0.771505i | \(0.280496\pi\) | |||||||
\(264\) | 637.779 | 0.148684 | ||||||||
\(265\) | −11710.4 | −2.71458 | ||||||||
\(266\) | 484.588 | 0.111699 | ||||||||
\(267\) | 3963.11 | 0.908383 | ||||||||
\(268\) | 1267.87 | 0.288982 | ||||||||
\(269\) | 4408.39 | 0.999199 | 0.499599 | − | 0.866257i | \(-0.333481\pi\) | ||||
0.499599 | + | 0.866257i | \(0.333481\pi\) | |||||||
\(270\) | 3338.25 | 0.752443 | ||||||||
\(271\) | 5005.29 | 1.12196 | 0.560978 | − | 0.827831i | \(-0.310425\pi\) | ||||
0.560978 | + | 0.827831i | \(0.310425\pi\) | |||||||
\(272\) | 5621.54 | 1.25315 | ||||||||
\(273\) | −5074.27 | −1.12494 | ||||||||
\(274\) | −462.661 | −0.102009 | ||||||||
\(275\) | −1815.14 | −0.398025 | ||||||||
\(276\) | −7171.19 | −1.56397 | ||||||||
\(277\) | −8864.55 | −1.92281 | −0.961407 | − | 0.275132i | \(-0.911279\pi\) | ||||
−0.961407 | + | 0.275132i | \(0.911279\pi\) | |||||||
\(278\) | 636.495 | 0.137318 | ||||||||
\(279\) | −8993.42 | −1.92983 | ||||||||
\(280\) | 2843.48 | 0.606895 | ||||||||
\(281\) | 3796.45 | 0.805968 | 0.402984 | − | 0.915207i | \(-0.367973\pi\) | ||||
0.402984 | + | 0.915207i | \(0.367973\pi\) | |||||||
\(282\) | −2584.16 | −0.545689 | ||||||||
\(283\) | −4707.79 | −0.988867 | −0.494433 | − | 0.869216i | \(-0.664624\pi\) | ||||
−0.494433 | + | 0.869216i | \(0.664624\pi\) | |||||||
\(284\) | −1641.46 | −0.342968 | ||||||||
\(285\) | 9218.94 | 1.91608 | ||||||||
\(286\) | 162.194 | 0.0335341 | ||||||||
\(287\) | −601.114 | −0.123633 | ||||||||
\(288\) | −6371.61 | −1.30365 | ||||||||
\(289\) | 5545.00 | 1.12864 | ||||||||
\(290\) | 1157.58 | 0.234399 | ||||||||
\(291\) | −11928.0 | −2.40286 | ||||||||
\(292\) | 824.442 | 0.165229 | ||||||||
\(293\) | −6455.57 | −1.28716 | −0.643581 | − | 0.765378i | \(-0.722552\pi\) | ||||
−0.643581 | + | 0.765378i | \(0.722552\pi\) | |||||||
\(294\) | −642.512 | −0.127456 | ||||||||
\(295\) | −2417.00 | −0.477027 | ||||||||
\(296\) | −2257.04 | −0.443203 | ||||||||
\(297\) | 1999.67 | 0.390682 | ||||||||
\(298\) | 648.484 | 0.126059 | ||||||||
\(299\) | −3738.96 | −0.723175 | ||||||||
\(300\) | 17644.0 | 3.39558 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1794.75 | 0.341974 | ||||||||
\(303\) | 13545.6 | 2.56824 | ||||||||
\(304\) | −2841.93 | −0.536171 | ||||||||
\(305\) | 16288.2 | 3.05789 | ||||||||
\(306\) | −3621.70 | −0.676598 | ||||||||
\(307\) | 373.270 | 0.0693930 | 0.0346965 | − | 0.999398i | \(-0.488954\pi\) | ||||
0.0346965 | + | 0.999398i | \(0.488954\pi\) | |||||||
\(308\) | 830.799 | 0.153699 | ||||||||
\(309\) | 2679.99 | 0.493396 | ||||||||
\(310\) | 1885.81 | 0.345505 | ||||||||
\(311\) | 2560.85 | 0.466921 | 0.233461 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233461 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(312\) | −3232.34 | −0.586522 | ||||||||
\(313\) | −9039.94 | −1.63249 | −0.816243 | − | 0.577709i | \(-0.803947\pi\) | ||||
−0.816243 | + | 0.577709i | \(0.803947\pi\) | |||||||
\(314\) | 324.578 | 0.0583344 | ||||||||
\(315\) | 16865.8 | 3.01676 | ||||||||
\(316\) | 3770.10 | 0.671154 | ||||||||
\(317\) | 2482.03 | 0.439762 | 0.219881 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219881 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(318\) | −3422.09 | −0.603463 | ||||||||
\(319\) | 693.412 | 0.121704 | ||||||||
\(320\) | −7206.07 | −1.25885 | ||||||||
\(321\) | 14254.5 | 2.47854 | ||||||||
\(322\) | 961.177 | 0.166349 | ||||||||
\(323\) | −5286.97 | −0.910758 | ||||||||
\(324\) | −7657.10 | −1.31295 | ||||||||
\(325\) | 9199.32 | 1.57011 | ||||||||
\(326\) | 25.3136 | 0.00430058 | ||||||||
\(327\) | −16608.0 | −2.80864 | ||||||||
\(328\) | −382.913 | −0.0644599 | ||||||||
\(329\) | −6901.41 | −1.15650 | ||||||||
\(330\) | −793.227 | −0.132320 | ||||||||
\(331\) | 4063.14 | 0.674715 | 0.337357 | − | 0.941377i | \(-0.390467\pi\) | ||||
0.337357 | + | 0.941377i | \(0.390467\pi\) | |||||||
\(332\) | −5429.31 | −0.897506 | ||||||||
\(333\) | −13387.4 | −2.20307 | ||||||||
\(334\) | 722.775 | 0.118409 | ||||||||
\(335\) | −3232.91 | −0.527263 | ||||||||
\(336\) | −7650.11 | −1.24211 | ||||||||
\(337\) | −985.260 | −0.159260 | −0.0796299 | − | 0.996824i | \(-0.525374\pi\) | ||||
−0.0796299 | + | 0.996824i | \(0.525374\pi\) | |||||||
\(338\) | 536.413 | 0.0863226 | ||||||||
\(339\) | 6215.60 | 0.995827 | ||||||||
\(340\) | −15131.8 | −2.41364 | ||||||||
\(341\) | 1129.63 | 0.179392 | ||||||||
\(342\) | 1830.93 | 0.289489 | ||||||||
\(343\) | −6915.61 | −1.08865 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18285.7 | 2.85353 | ||||||||
\(346\) | 1366.89 | 0.212383 | ||||||||
\(347\) | −1072.53 | −0.165927 | −0.0829633 | − | 0.996553i | \(-0.526438\pi\) | ||||
−0.0829633 | + | 0.996553i | \(0.526438\pi\) | |||||||
\(348\) | −6740.29 | −1.03827 | ||||||||
\(349\) | 293.309 | 0.0449870 | 0.0224935 | − | 0.999747i | \(-0.492839\pi\) | ||||
0.0224935 | + | 0.999747i | \(0.492839\pi\) | |||||||
\(350\) | −2364.88 | −0.361166 | ||||||||
\(351\) | −10134.5 | −1.54114 | ||||||||
\(352\) | 800.312 | 0.121184 | ||||||||
\(353\) | −1149.23 | −0.173279 | −0.0866396 | − | 0.996240i | \(-0.527613\pi\) | ||||
−0.0866396 | + | 0.996240i | \(0.527613\pi\) | |||||||
\(354\) | −706.310 | −0.106045 | ||||||||
\(355\) | 4185.54 | 0.625762 | ||||||||
\(356\) | 3288.55 | 0.489587 | ||||||||
\(357\) | −14231.8 | −2.10988 | ||||||||
\(358\) | 1482.59 | 0.218875 | ||||||||
\(359\) | 8685.57 | 1.27690 | 0.638450 | − | 0.769663i | \(-0.279576\pi\) | ||||
0.638450 | + | 0.769663i | \(0.279576\pi\) | |||||||
\(360\) | 10743.6 | 1.57288 | ||||||||
\(361\) | −4186.21 | −0.610323 | ||||||||
\(362\) | −42.2354 | −0.00613217 | ||||||||
\(363\) | 11743.8 | 1.69804 | ||||||||
\(364\) | −4210.58 | −0.606304 | ||||||||
\(365\) | −2102.23 | −0.301468 | ||||||||
\(366\) | 4759.82 | 0.679781 | ||||||||
\(367\) | −12096.1 | −1.72047 | −0.860234 | − | 0.509899i | \(-0.829683\pi\) | ||||
−0.860234 | + | 0.509899i | \(0.829683\pi\) | |||||||
\(368\) | −5636.96 | −0.798496 | ||||||||
\(369\) | −2271.20 | −0.320417 | ||||||||
\(370\) | 2807.16 | 0.394425 | ||||||||
\(371\) | −9139.24 | −1.27894 | ||||||||
\(372\) | −10980.5 | −1.53041 | ||||||||
\(373\) | 6887.99 | 0.956157 | 0.478079 | − | 0.878317i | \(-0.341333\pi\) | ||||
0.478079 | + | 0.878317i | \(0.341333\pi\) | |||||||
\(374\) | 454.908 | 0.0628949 | ||||||||
\(375\) | −22700.2 | −3.12595 | ||||||||
\(376\) | −4396.23 | −0.602975 | ||||||||
\(377\) | −3514.29 | −0.480093 | ||||||||
\(378\) | 2605.30 | 0.354503 | ||||||||
\(379\) | −2089.36 | −0.283175 | −0.141588 | − | 0.989926i | \(-0.545221\pi\) | ||||
−0.141588 | + | 0.989926i | \(0.545221\pi\) | |||||||
\(380\) | 7649.80 | 1.03270 | ||||||||
\(381\) | 96.0903 | 0.0129209 | ||||||||
\(382\) | −362.110 | −0.0485005 | ||||||||
\(383\) | 3454.11 | 0.460827 | 0.230413 | − | 0.973093i | \(-0.425992\pi\) | ||||
0.230413 | + | 0.973093i | \(0.425992\pi\) | |||||||
\(384\) | −10275.6 | −1.36556 | ||||||||
\(385\) | −2118.44 | −0.280431 | ||||||||
\(386\) | 2537.81 | 0.334641 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9897.74 | −1.29506 | ||||||||
\(389\) | 15107.6 | 1.96911 | 0.984555 | − | 0.175073i | \(-0.0560162\pi\) | ||||
0.984555 | + | 0.175073i | \(0.0560162\pi\) | |||||||
\(390\) | 4020.16 | 0.521971 | ||||||||
\(391\) | −10486.7 | −1.35635 | ||||||||
\(392\) | −1093.06 | −0.140836 | ||||||||
\(393\) | 244.529 | 0.0313864 | ||||||||
\(394\) | −486.708 | −0.0622335 | ||||||||
\(395\) | −9613.32 | −1.22455 | ||||||||
\(396\) | 3139.02 | 0.398338 | ||||||||
\(397\) | 1850.76 | 0.233972 | 0.116986 | − | 0.993134i | \(-0.462677\pi\) | ||||
0.116986 | + | 0.993134i | \(0.462677\pi\) | |||||||
\(398\) | −2889.40 | −0.363901 | ||||||||
\(399\) | 7194.81 | 0.902734 | ||||||||
\(400\) | 13869.2 | 1.73364 | ||||||||
\(401\) | −4757.23 | −0.592430 | −0.296215 | − | 0.955121i | \(-0.595725\pi\) | ||||
−0.296215 | + | 0.955121i | \(0.595725\pi\) | |||||||
\(402\) | −944.741 | −0.117212 | ||||||||
\(403\) | −5725.09 | −0.707660 | ||||||||
\(404\) | 11240.1 | 1.38419 | ||||||||
\(405\) | 19524.7 | 2.39553 | ||||||||
\(406\) | 903.422 | 0.110434 | ||||||||
\(407\) | 1681.53 | 0.204792 | ||||||||
\(408\) | −9065.75 | −1.10005 | ||||||||
\(409\) | 1964.94 | 0.237555 | 0.118778 | − | 0.992921i | \(-0.462102\pi\) | ||||
0.118778 | + | 0.992921i | \(0.462102\pi\) | |||||||
\(410\) | 476.241 | 0.0573656 | ||||||||
\(411\) | −6869.25 | −0.824417 | ||||||||
\(412\) | 2223.83 | 0.265923 | ||||||||
\(413\) | −1886.32 | −0.224745 | ||||||||
\(414\) | 3631.63 | 0.431123 | ||||||||
\(415\) | 13844.1 | 1.63754 | ||||||||
\(416\) | −4056.07 | −0.478042 | ||||||||
\(417\) | 9450.21 | 1.10978 | ||||||||
\(418\) | −229.976 | −0.0269102 | ||||||||
\(419\) | 12920.8 | 1.50650 | 0.753249 | − | 0.657735i | \(-0.228485\pi\) | ||||
0.753249 | + | 0.657735i | \(0.228485\pi\) | |||||||
\(420\) | 20592.2 | 2.39238 | ||||||||
\(421\) | 1779.75 | 0.206033 | 0.103016 | − | 0.994680i | \(-0.467151\pi\) | ||||
0.103016 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(422\) | −712.441 | −0.0821827 | ||||||||
\(423\) | −26075.7 | −2.99727 | ||||||||
\(424\) | −5821.75 | −0.666814 | ||||||||
\(425\) | 25801.4 | 2.94483 | ||||||||
\(426\) | 1223.12 | 0.139109 | ||||||||
\(427\) | 12711.9 | 1.44068 | ||||||||
\(428\) | 11828.3 | 1.33585 | ||||||||
\(429\) | 2408.14 | 0.271017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10329.4 | −1.15441 | −0.577205 | − | 0.816599i | \(-0.695857\pi\) | ||||
−0.577205 | + | 0.816599i | \(0.695857\pi\) | |||||||
\(432\) | −15279.1 | −1.70166 | ||||||||
\(433\) | −35.7668 | −0.00396961 | −0.00198481 | − | 0.999998i | \(-0.500632\pi\) | ||||
−0.00198481 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(434\) | 1471.75 | 0.162780 | ||||||||
\(435\) | 17187.0 | 1.89437 | ||||||||
\(436\) | −13781.2 | −1.51376 | ||||||||
\(437\) | 5301.47 | 0.580329 | ||||||||
\(438\) | −614.327 | −0.0670175 | ||||||||
\(439\) | 5776.48 | 0.628010 | 0.314005 | − | 0.949421i | \(-0.398329\pi\) | ||||
0.314005 | + | 0.949421i | \(0.398329\pi\) | |||||||
\(440\) | −1349.46 | −0.146211 | ||||||||
\(441\) | −6483.33 | −0.700068 | ||||||||
\(442\) | −2305.52 | −0.248105 | ||||||||
\(443\) | −12268.5 | −1.31578 | −0.657892 | − | 0.753112i | \(-0.728552\pi\) | ||||
−0.657892 | + | 0.753112i | \(0.728552\pi\) | |||||||
\(444\) | −16345.3 | −1.74710 | ||||||||
\(445\) | −8385.43 | −0.893276 | ||||||||
\(446\) | −1641.93 | −0.174323 | ||||||||
\(447\) | 9628.20 | 1.01879 | ||||||||
\(448\) | −5623.88 | −0.593088 | ||||||||
\(449\) | 11796.6 | 1.23990 | 0.619952 | − | 0.784640i | \(-0.287152\pi\) | ||||
0.619952 | + | 0.784640i | \(0.287152\pi\) | |||||||
\(450\) | −8935.26 | −0.936027 | ||||||||
\(451\) | 285.276 | 0.0297852 | ||||||||
\(452\) | 5157.65 | 0.536716 | ||||||||
\(453\) | 26647.1 | 2.76377 | ||||||||
\(454\) | −2317.42 | −0.239564 | ||||||||
\(455\) | 10736.5 | 1.10623 | ||||||||
\(456\) | 4583.13 | 0.470668 | ||||||||
\(457\) | 8101.46 | 0.829256 | 0.414628 | − | 0.909991i | \(-0.363912\pi\) | ||||
0.414628 | + | 0.909991i | \(0.363912\pi\) | |||||||
\(458\) | −731.616 | −0.0746423 | ||||||||
\(459\) | −28424.4 | −2.89050 | ||||||||
\(460\) | 15173.3 | 1.53796 | ||||||||
\(461\) | 11117.9 | 1.12324 | 0.561618 | − | 0.827396i | \(-0.310179\pi\) | ||||
0.561618 | + | 0.827396i | \(0.310179\pi\) | |||||||
\(462\) | −619.064 | −0.0623408 | ||||||||
\(463\) | −16742.2 | −1.68051 | −0.840255 | − | 0.542191i | \(-0.817595\pi\) | ||||
−0.840255 | + | 0.542191i | \(0.817595\pi\) | |||||||
\(464\) | −5298.24 | −0.530096 | ||||||||
\(465\) | 27999.1 | 2.79231 | ||||||||
\(466\) | 1731.35 | 0.172110 | ||||||||
\(467\) | 16116.5 | 1.59697 | 0.798485 | − | 0.602015i | \(-0.205635\pi\) | ||||
0.798485 | + | 0.602015i | \(0.205635\pi\) | |||||||
\(468\) | −15908.9 | −1.57135 | ||||||||
\(469\) | −2523.09 | −0.248412 | ||||||||
\(470\) | 5467.74 | 0.536613 | ||||||||
\(471\) | 4819.10 | 0.471448 | ||||||||
\(472\) | −1201.59 | −0.117178 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2809.26 | −0.272223 | ||||||||
\(475\) | −13043.7 | −1.25997 | ||||||||
\(476\) | −11809.4 | −1.13715 | ||||||||
\(477\) | −34530.9 | −3.31460 | ||||||||
\(478\) | 1785.81 | 0.170881 | ||||||||
\(479\) | 2987.24 | 0.284949 | 0.142474 | − | 0.989798i | \(-0.454494\pi\) | ||||
0.142474 | + | 0.989798i | \(0.454494\pi\) | |||||||
\(480\) | 19836.6 | 1.88628 | ||||||||
\(481\) | −8522.21 | −0.807857 | ||||||||
\(482\) | −29.9355 | −0.00282889 | ||||||||
\(483\) | 14270.8 | 1.34440 | ||||||||
\(484\) | 9744.86 | 0.915183 | ||||||||
\(485\) | 25238.1 | 2.36289 | ||||||||
\(486\) | 1065.41 | 0.0994402 | ||||||||
\(487\) | −19072.7 | −1.77468 | −0.887338 | − | 0.461119i | \(-0.847448\pi\) | ||||
−0.887338 | + | 0.461119i | \(0.847448\pi\) | |||||||
\(488\) | 8097.54 | 0.751144 | ||||||||
\(489\) | 375.837 | 0.0347566 | ||||||||
\(490\) | 1359.47 | 0.125336 | ||||||||
\(491\) | −8855.63 | −0.813949 | −0.406975 | − | 0.913439i | \(-0.633416\pi\) | ||||
−0.406975 | + | 0.913439i | \(0.633416\pi\) | |||||||
\(492\) | −2773.02 | −0.254100 | ||||||||
\(493\) | −9856.55 | −0.900439 | ||||||||
\(494\) | 1165.54 | 0.106154 | ||||||||
\(495\) | −8004.14 | −0.726786 | ||||||||
\(496\) | −8631.30 | −0.781365 | ||||||||
\(497\) | 3266.55 | 0.294819 | ||||||||
\(498\) | 4045.61 | 0.364032 | ||||||||
\(499\) | 12489.5 | 1.12046 | 0.560229 | − | 0.828338i | \(-0.310713\pi\) | ||||
0.560229 | + | 0.828338i | \(0.310713\pi\) | |||||||
\(500\) | −18836.4 | −1.68478 | ||||||||
\(501\) | 10731.2 | 0.956958 | ||||||||
\(502\) | 2928.17 | 0.260339 | ||||||||
\(503\) | 1022.04 | 0.0905977 | 0.0452989 | − | 0.998973i | \(-0.485576\pi\) | ||||
0.0452989 | + | 0.998973i | \(0.485576\pi\) | |||||||
\(504\) | 8384.69 | 0.741039 | ||||||||
\(505\) | −28660.9 | −2.52553 | ||||||||
\(506\) | −456.155 | −0.0400762 | ||||||||
\(507\) | 7964.27 | 0.697644 | ||||||||
\(508\) | 79.7349 | 0.00696390 | ||||||||
\(509\) | 3665.05 | 0.319156 | 0.159578 | − | 0.987185i | \(-0.448987\pi\) | ||||
0.159578 | + | 0.987185i | \(0.448987\pi\) | |||||||
\(510\) | 11275.4 | 0.978984 | ||||||||
\(511\) | −1640.66 | −0.142032 | ||||||||
\(512\) | −10361.7 | −0.894388 | ||||||||
\(513\) | 14369.8 | 1.23673 | ||||||||
\(514\) | −397.455 | −0.0341070 | ||||||||
\(515\) | −5670.52 | −0.485190 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3275.27 | 0.278619 | ||||||||
\(518\) | 2190.81 | 0.185828 | ||||||||
\(519\) | 20294.5 | 1.71644 | ||||||||
\(520\) | 6839.21 | 0.576768 | ||||||||
\(521\) | −5845.70 | −0.491564 | −0.245782 | − | 0.969325i | \(-0.579045\pi\) | ||||
−0.245782 | + | 0.969325i | \(0.579045\pi\) | |||||||
\(522\) | 3413.41 | 0.286209 | ||||||||
\(523\) | 16090.3 | 1.34528 | 0.672639 | − | 0.739971i | \(-0.265161\pi\) | ||||
0.672639 | + | 0.739971i | \(0.265161\pi\) | |||||||
\(524\) | 202.908 | 0.0169162 | ||||||||
\(525\) | −35112.0 | −2.91888 | ||||||||
\(526\) | −3355.69 | −0.278165 | ||||||||
\(527\) | −16057.2 | −1.32725 | ||||||||
\(528\) | 3630.58 | 0.299244 | ||||||||
\(529\) | −1651.58 | −0.135743 | ||||||||
\(530\) | 7240.70 | 0.593426 | ||||||||
\(531\) | −7127.09 | −0.582466 | ||||||||
\(532\) | 5970.19 | 0.486542 | ||||||||
\(533\) | −1445.81 | −0.117496 | ||||||||
\(534\) | −2450.44 | −0.198579 | ||||||||
\(535\) | −30160.8 | −2.43732 | ||||||||
\(536\) | −1607.22 | −0.129517 | ||||||||
\(537\) | 22012.4 | 1.76891 | ||||||||
\(538\) | −2725.77 | −0.218431 | ||||||||
\(539\) | 814.346 | 0.0650767 | ||||||||
\(540\) | 41127.7 | 3.27751 | ||||||||
\(541\) | 2502.60 | 0.198882 | 0.0994410 | − | 0.995043i | \(-0.468295\pi\) | ||||
0.0994410 | + | 0.995043i | \(0.468295\pi\) | |||||||
\(542\) | −3094.84 | −0.245267 | ||||||||
\(543\) | −627.080 | −0.0495591 | ||||||||
\(544\) | −11376.1 | −0.896592 | ||||||||
\(545\) | 35140.5 | 2.76193 | ||||||||
\(546\) | 3137.49 | 0.245919 | ||||||||
\(547\) | 25182.5 | 1.96842 | 0.984210 | − | 0.177004i | \(-0.0566405\pi\) | ||||
0.984210 | + | 0.177004i | \(0.0566405\pi\) | |||||||
\(548\) | −5700.04 | −0.444332 | ||||||||
\(549\) | 48029.5 | 3.73379 | ||||||||
\(550\) | 1122.32 | 0.0870109 | ||||||||
\(551\) | 4982.91 | 0.385262 | ||||||||
\(552\) | 9090.61 | 0.700945 | ||||||||
\(553\) | −7502.59 | −0.576931 | ||||||||
\(554\) | 5481.07 | 0.420340 | ||||||||
\(555\) | 41678.6 | 3.18767 | ||||||||
\(556\) | 7841.70 | 0.598133 | ||||||||
\(557\) | 3635.57 | 0.276560 | 0.138280 | − | 0.990393i | \(-0.455843\pi\) | ||||
0.138280 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(558\) | 5560.75 | 0.421873 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 16186.7 | 1.22145 | ||||||||
\(561\) | 6754.13 | 0.508306 | ||||||||
\(562\) | −2347.39 | −0.176190 | ||||||||
\(563\) | 12158.4 | 0.910153 | 0.455077 | − | 0.890452i | \(-0.349612\pi\) | ||||
0.455077 | + | 0.890452i | \(0.349612\pi\) | |||||||
\(564\) | −31837.1 | −2.37692 | ||||||||
\(565\) | −13151.4 | −0.979264 | ||||||||
\(566\) | 2910.89 | 0.216173 | ||||||||
\(567\) | 15237.8 | 1.12862 | ||||||||
\(568\) | 2080.81 | 0.153713 | ||||||||
\(569\) | −16684.3 | −1.22925 | −0.614625 | − | 0.788819i | \(-0.710693\pi\) | ||||
−0.614625 | + | 0.788819i | \(0.710693\pi\) | |||||||
\(570\) | −5700.19 | −0.418868 | ||||||||
\(571\) | −20545.1 | −1.50576 | −0.752879 | − | 0.658159i | \(-0.771335\pi\) | ||||
−0.752879 | + | 0.658159i | \(0.771335\pi\) | |||||||
\(572\) | 1998.26 | 0.146069 | ||||||||
\(573\) | −5376.35 | −0.391972 | ||||||||
\(574\) | 371.677 | 0.0270270 | ||||||||
\(575\) | −25872.1 | −1.87642 | ||||||||
\(576\) | −21248.8 | −1.53709 | ||||||||
\(577\) | 25550.0 | 1.84344 | 0.921718 | − | 0.387861i | \(-0.126786\pi\) | ||||
0.921718 | + | 0.387861i | \(0.126786\pi\) | |||||||
\(578\) | −3428.54 | −0.246728 | ||||||||
\(579\) | 37679.6 | 2.70451 | ||||||||
\(580\) | 14261.6 | 1.02100 | ||||||||
\(581\) | 10804.5 | 0.771505 | ||||||||
\(582\) | 7375.23 | 0.525280 | ||||||||
\(583\) | 4337.30 | 0.308117 | ||||||||
\(584\) | −1045.11 | −0.0740530 | ||||||||
\(585\) | 40565.9 | 2.86700 | ||||||||
\(586\) | 3991.56 | 0.281382 | ||||||||
\(587\) | 21850.9 | 1.53643 | 0.768214 | − | 0.640193i | \(-0.221146\pi\) | ||||
0.768214 | + | 0.640193i | \(0.221146\pi\) | |||||||
\(588\) | −7915.82 | −0.555175 | ||||||||
\(589\) | 8117.60 | 0.567878 | ||||||||
\(590\) | 1494.46 | 0.104281 | ||||||||
\(591\) | −7226.28 | −0.502960 | ||||||||
\(592\) | −12848.3 | −0.891998 | ||||||||
\(593\) | −15140.1 | −1.04845 | −0.524224 | − | 0.851580i | \(-0.675645\pi\) | ||||
−0.524224 | + | 0.851580i | \(0.675645\pi\) | |||||||
\(594\) | −1236.42 | −0.0854056 | ||||||||
\(595\) | 30112.7 | 2.07479 | ||||||||
\(596\) | 7989.40 | 0.549091 | ||||||||
\(597\) | −42899.7 | −2.94098 | ||||||||
\(598\) | 2311.84 | 0.158091 | ||||||||
\(599\) | −7836.05 | −0.534511 | −0.267256 | − | 0.963626i | \(-0.586117\pi\) | ||||
−0.267256 | + | 0.963626i | \(0.586117\pi\) | |||||||
\(600\) | −22366.5 | −1.52185 | ||||||||
\(601\) | −11113.3 | −0.754279 | −0.377140 | − | 0.926156i | \(-0.623092\pi\) | ||||
−0.377140 | + | 0.926156i | \(0.623092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9533.02 | −0.643805 | ||||||||
\(604\) | 22111.5 | 1.48958 | ||||||||
\(605\) | −24848.3 | −1.66980 | ||||||||
\(606\) | −8375.45 | −0.561434 | ||||||||
\(607\) | 17388.4 | 1.16272 | 0.581361 | − | 0.813646i | \(-0.302520\pi\) | ||||
0.581361 | + | 0.813646i | \(0.302520\pi\) | |||||||
\(608\) | 5751.11 | 0.383616 | ||||||||
\(609\) | 13413.3 | 0.892506 | ||||||||
\(610\) | −10071.2 | −0.668476 | ||||||||
\(611\) | −16599.4 | −1.09908 | ||||||||
\(612\) | −44619.8 | −2.94714 | ||||||||
\(613\) | 16616.6 | 1.09484 | 0.547421 | − | 0.836857i | \(-0.315610\pi\) | ||||
0.547421 | + | 0.836857i | \(0.315610\pi\) | |||||||
\(614\) | −230.798 | −0.0151698 | ||||||||
\(615\) | 7070.88 | 0.463619 | ||||||||
\(616\) | −1053.17 | −0.0688853 | ||||||||
\(617\) | 4402.51 | 0.287258 | 0.143629 | − | 0.989632i | \(-0.454123\pi\) | ||||
0.143629 | + | 0.989632i | \(0.454123\pi\) | |||||||
\(618\) | −1657.07 | −0.107860 | ||||||||
\(619\) | −16295.5 | −1.05811 | −0.529055 | − | 0.848587i | \(-0.677454\pi\) | ||||
−0.529055 | + | 0.848587i | \(0.677454\pi\) | |||||||
\(620\) | 23233.4 | 1.50496 | ||||||||
\(621\) | 28502.3 | 1.84180 | ||||||||
\(622\) | −1583.41 | −0.102072 | ||||||||
\(623\) | −6544.30 | −0.420854 | ||||||||
\(624\) | −18400.2 | −1.18045 | ||||||||
\(625\) | 16493.1 | 1.05556 | ||||||||
\(626\) | 5589.51 | 0.356872 | ||||||||
\(627\) | −3414.51 | −0.217484 | ||||||||
\(628\) | 3998.84 | 0.254094 | ||||||||
\(629\) | −23902.3 | −1.51518 | ||||||||
\(630\) | −10428.3 | −0.659483 | ||||||||
\(631\) | 10777.3 | 0.679935 | 0.339967 | − | 0.940437i | \(-0.389584\pi\) | ||||
0.339967 | + | 0.940437i | \(0.389584\pi\) | |||||||
\(632\) | −4779.19 | −0.300801 | ||||||||
\(633\) | −10577.8 | −0.664186 | ||||||||
\(634\) | −1534.67 | −0.0961350 | ||||||||
\(635\) | −203.315 | −0.0127060 | ||||||||
\(636\) | −42160.5 | −2.62858 | ||||||||
\(637\) | −4127.20 | −0.256712 | ||||||||
\(638\) | −428.745 | −0.0266053 | ||||||||
\(639\) | 12342.1 | 0.764076 | ||||||||
\(640\) | 21741.9 | 1.34285 | ||||||||
\(641\) | −18764.1 | −1.15622 | −0.578109 | − | 0.815959i | \(-0.696209\pi\) | ||||
−0.578109 | + | 0.815959i | \(0.696209\pi\) | |||||||
\(642\) | −8813.76 | −0.541825 | ||||||||
\(643\) | −7517.75 | −0.461075 | −0.230537 | − | 0.973063i | \(-0.574048\pi\) | ||||
−0.230537 | + | 0.973063i | \(0.574048\pi\) | |||||||
\(644\) | 11841.8 | 0.724586 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3269.00 | 0.199098 | ||||||||
\(647\) | −20711.1 | −1.25848 | −0.629241 | − | 0.777210i | \(-0.716634\pi\) | ||||
−0.629241 | + | 0.777210i | \(0.716634\pi\) | |||||||
\(648\) | 9706.58 | 0.588442 | ||||||||
\(649\) | 895.206 | 0.0541447 | ||||||||
\(650\) | −5688.06 | −0.343237 | ||||||||
\(651\) | 21851.5 | 1.31556 | ||||||||
\(652\) | 311.867 | 0.0187326 | ||||||||
\(653\) | −6658.64 | −0.399039 | −0.199520 | − | 0.979894i | \(-0.563938\pi\) | ||||
−0.199520 | + | 0.979894i | \(0.563938\pi\) | |||||||
\(654\) | 10269.0 | 0.613988 | ||||||||
\(655\) | −517.392 | −0.0308644 | ||||||||
\(656\) | −2179.75 | −0.129733 | ||||||||
\(657\) | −6198.93 | −0.368103 | ||||||||
\(658\) | 4267.23 | 0.252818 | ||||||||
\(659\) | −11926.7 | −0.705004 | −0.352502 | − | 0.935811i | \(-0.614669\pi\) | ||||
−0.352502 | + | 0.935811i | \(0.614669\pi\) | |||||||
\(660\) | −9772.65 | −0.576363 | ||||||||
\(661\) | −31886.9 | −1.87634 | −0.938168 | − | 0.346180i | \(-0.887479\pi\) | ||||
−0.938168 | + | 0.346180i | \(0.887479\pi\) | |||||||
\(662\) | −2512.29 | −0.147497 | ||||||||
\(663\) | −34230.7 | −2.00514 | ||||||||
\(664\) | 6882.50 | 0.402248 | ||||||||
\(665\) | −15223.3 | −0.887720 | ||||||||
\(666\) | 8277.58 | 0.481606 | ||||||||
\(667\) | 9883.57 | 0.573753 | ||||||||
\(668\) | 8904.67 | 0.515767 | ||||||||
\(669\) | −24378.2 | −1.40884 | ||||||||
\(670\) | 1998.95 | 0.115263 | ||||||||
\(671\) | −6032.80 | −0.347084 | ||||||||
\(672\) | 15481.2 | 0.888692 | ||||||||
\(673\) | −21903.5 | −1.25456 | −0.627279 | − | 0.778794i | \(-0.715832\pi\) | ||||
−0.627279 | + | 0.778794i | \(0.715832\pi\) | |||||||
\(674\) | 609.199 | 0.0348152 | ||||||||
\(675\) | −70127.1 | −3.99880 | ||||||||
\(676\) | 6608.68 | 0.376006 | ||||||||
\(677\) | 12230.4 | 0.694317 | 0.347159 | − | 0.937806i | \(-0.387147\pi\) | ||||
0.347159 | + | 0.937806i | \(0.387147\pi\) | |||||||
\(678\) | −3843.19 | −0.217694 | ||||||||
\(679\) | 19696.8 | 1.11324 | ||||||||
\(680\) | 19182.0 | 1.08176 | ||||||||
\(681\) | −34407.4 | −1.93611 | ||||||||
\(682\) | −698.464 | −0.0392164 | ||||||||
\(683\) | −17621.4 | −0.987207 | −0.493604 | − | 0.869687i | \(-0.664321\pi\) | ||||
−0.493604 | + | 0.869687i | \(0.664321\pi\) | |||||||
\(684\) | 22557.2 | 1.26096 | ||||||||
\(685\) | 14534.5 | 0.810705 | ||||||||
\(686\) | 4276.01 | 0.237986 | ||||||||
\(687\) | −10862.5 | −0.603246 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21981.9 | −1.21545 | ||||||||
\(690\) | −11306.3 | −0.623801 | ||||||||
\(691\) | 25629.9 | 1.41101 | 0.705504 | − | 0.708706i | \(-0.250721\pi\) | ||||
0.705504 | + | 0.708706i | \(0.250721\pi\) | |||||||
\(692\) | 16840.2 | 0.925100 | ||||||||
\(693\) | −6246.73 | −0.342415 | ||||||||
\(694\) | 663.160 | 0.0362726 | ||||||||
\(695\) | −19995.4 | −1.09132 | ||||||||
\(696\) | 8544.37 | 0.465336 | ||||||||
\(697\) | −4055.08 | −0.220369 | ||||||||
\(698\) | −181.357 | −0.00983445 | ||||||||
\(699\) | 25705.8 | 1.39096 | ||||||||
\(700\) | −29135.6 | −1.57317 | ||||||||
\(701\) | 6140.99 | 0.330873 | 0.165437 | − | 0.986220i | \(-0.447097\pi\) | ||||
0.165437 | + | 0.986220i | \(0.447097\pi\) | |||||||
\(702\) | 6266.32 | 0.336904 | ||||||||
\(703\) | 12083.6 | 0.648283 | ||||||||
\(704\) | 2668.98 | 0.142885 | ||||||||
\(705\) | 81181.0 | 4.33681 | ||||||||
\(706\) | 710.587 | 0.0378800 | ||||||||
\(707\) | −22368.0 | −1.18987 | ||||||||
\(708\) | −8701.82 | −0.461913 | ||||||||
\(709\) | −36700.3 | −1.94402 | −0.972009 | − | 0.234943i | \(-0.924510\pi\) | ||||
−0.972009 | + | 0.234943i | \(0.924510\pi\) | |||||||
\(710\) | −2587.97 | −0.136796 | ||||||||
\(711\) | −28347.2 | −1.49522 | ||||||||
\(712\) | −4168.76 | −0.219425 | ||||||||
\(713\) | 16101.2 | 0.845715 | ||||||||
\(714\) | 8799.72 | 0.461234 | ||||||||
\(715\) | −5095.32 | −0.266509 | ||||||||
\(716\) | 18265.7 | 0.953382 | ||||||||
\(717\) | 26514.4 | 1.38103 | ||||||||
\(718\) | −5370.40 | −0.279139 | ||||||||
\(719\) | 19467.1 | 1.00973 | 0.504867 | − | 0.863197i | \(-0.331542\pi\) | ||||
0.504867 | + | 0.863197i | \(0.331542\pi\) | |||||||
\(720\) | 61158.3 | 3.16560 | ||||||||
\(721\) | −4425.49 | −0.228590 | ||||||||
\(722\) | 2588.38 | 0.133421 | ||||||||
\(723\) | −444.460 | −0.0228626 | ||||||||
\(724\) | −520.346 | −0.0267106 | ||||||||
\(725\) | −24317.5 | −1.24570 | ||||||||
\(726\) | −7261.31 | −0.371202 | ||||||||
\(727\) | −11021.6 | −0.562269 | −0.281135 | − | 0.959668i | \(-0.590711\pi\) | ||||
−0.281135 | + | 0.959668i | \(0.590711\pi\) | |||||||
\(728\) | 5337.57 | 0.271736 | ||||||||
\(729\) | −11321.3 | −0.575181 | ||||||||
\(730\) | 1299.84 | 0.0659029 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 58641.6 | 2.96101 | ||||||||
\(733\) | −29262.9 | −1.47455 | −0.737277 | − | 0.675590i | \(-0.763889\pi\) | ||||
−0.737277 | + | 0.675590i | \(0.763889\pi\) | |||||||
\(734\) | 7479.18 | 0.376106 | ||||||||
\(735\) | 20184.4 | 1.01294 | ||||||||
\(736\) | 11407.3 | 0.571302 | ||||||||
\(737\) | 1197.40 | 0.0598466 | ||||||||
\(738\) | 1404.31 | 0.0700453 | ||||||||
\(739\) | 14025.7 | 0.698167 | 0.349083 | − | 0.937092i | \(-0.386493\pi\) | ||||
0.349083 | + | 0.937092i | \(0.386493\pi\) | |||||||
\(740\) | 34584.5 | 1.71804 | ||||||||
\(741\) | 17305.1 | 0.857920 | ||||||||
\(742\) | 5650.91 | 0.279584 | ||||||||
\(743\) | −2161.22 | −0.106712 | −0.0533562 | − | 0.998576i | \(-0.516992\pi\) | ||||
−0.0533562 | + | 0.998576i | \(0.516992\pi\) | |||||||
\(744\) | 13919.5 | 0.685907 | ||||||||
\(745\) | −20372.0 | −1.00184 | ||||||||
\(746\) | −4258.93 | −0.209022 | ||||||||
\(747\) | 40822.7 | 1.99950 | ||||||||
\(748\) | 5604.52 | 0.273959 | ||||||||
\(749\) | −23538.6 | −1.14831 | ||||||||
\(750\) | 14035.8 | 0.683354 | ||||||||
\(751\) | −29152.5 | −1.41650 | −0.708250 | − | 0.705962i | \(-0.750515\pi\) | ||||
−0.708250 | + | 0.705962i | \(0.750515\pi\) | |||||||
\(752\) | −25025.8 | −1.21356 | ||||||||
\(753\) | 43475.2 | 2.10402 | ||||||||
\(754\) | 2172.93 | 0.104952 | ||||||||
\(755\) | −56381.9 | −2.71781 | ||||||||
\(756\) | 32097.6 | 1.54415 | ||||||||
\(757\) | −26927.3 | −1.29285 | −0.646427 | − | 0.762976i | \(-0.723737\pi\) | ||||
−0.646427 | + | 0.762976i | \(0.723737\pi\) | |||||||
\(758\) | 1291.88 | 0.0619040 | ||||||||
\(759\) | −6772.65 | −0.323889 | ||||||||
\(760\) | −9697.32 | −0.462840 | ||||||||
\(761\) | 1001.36 | 0.0476996 | 0.0238498 | − | 0.999716i | \(-0.492408\pi\) | ||||
0.0238498 | + | 0.999716i | \(0.492408\pi\) | |||||||
\(762\) | −59.4139 | −0.00282459 | ||||||||
\(763\) | 27425.0 | 1.30125 | ||||||||
\(764\) | −4461.24 | −0.211259 | ||||||||
\(765\) | 113775. | 5.37720 | ||||||||
\(766\) | −2135.72 | −0.100740 | ||||||||
\(767\) | −4537.01 | −0.213588 | ||||||||
\(768\) | −20892.2 | −0.981617 | ||||||||
\(769\) | 34146.0 | 1.60122 | 0.800609 | − | 0.599187i | \(-0.204510\pi\) | ||||
0.800609 | + | 0.599187i | \(0.204510\pi\) | |||||||
\(770\) | 1309.86 | 0.0613040 | ||||||||
\(771\) | −5901.12 | −0.275647 | ||||||||
\(772\) | 31266.2 | 1.45764 | ||||||||
\(773\) | −12617.5 | −0.587090 | −0.293545 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293545 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39615.4 | −1.83616 | ||||||||
\(776\) | 12546.9 | 0.580424 | ||||||||
\(777\) | 32527.6 | 1.50183 | ||||||||
\(778\) | −9341.20 | −0.430461 | ||||||||
\(779\) | 2050.02 | 0.0942870 | ||||||||
\(780\) | 49528.9 | 2.27361 | ||||||||
\(781\) | −1550.24 | −0.0710267 | ||||||||
\(782\) | 6484.04 | 0.296508 | ||||||||
\(783\) | 26789.7 | 1.22271 | ||||||||
\(784\) | −6222.28 | −0.283449 | ||||||||
\(785\) | −10196.6 | −0.463608 | ||||||||
\(786\) | −151.195 | −0.00686128 | ||||||||
\(787\) | −3944.55 | −0.178663 | −0.0893317 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893317 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(788\) | −5996.30 | −0.271078 | ||||||||
\(789\) | −49822.7 | −2.24808 | ||||||||
\(790\) | 5944.04 | 0.267695 | ||||||||
\(791\) | −10263.9 | −0.461366 | ||||||||
\(792\) | −3979.20 | −0.178529 | ||||||||
\(793\) | 30574.9 | 1.36916 | ||||||||
\(794\) | −1144.35 | −0.0511479 | ||||||||
\(795\) | 107505. | 4.79596 | ||||||||
\(796\) | −35597.7 | −1.58509 | ||||||||
\(797\) | −15295.0 | −0.679768 | −0.339884 | − | 0.940467i | \(-0.610388\pi\) | ||||
−0.339884 | + | 0.940467i | \(0.610388\pi\) | |||||||
\(798\) | −4448.64 | −0.197344 | ||||||||
\(799\) | −46556.5 | −2.06139 | ||||||||
\(800\) | −28066.5 | −1.24037 | ||||||||
\(801\) | −24726.4 | −1.09072 | ||||||||
\(802\) | 2941.45 | 0.129509 | ||||||||
\(803\) | 778.624 | 0.0342180 | ||||||||
\(804\) | −11639.3 | −0.510557 | ||||||||
\(805\) | −30195.3 | −1.32204 | ||||||||
\(806\) | 3539.89 | 0.154699 | ||||||||
\(807\) | −40470.1 | −1.76532 | ||||||||
\(808\) | −14248.5 | −0.620374 | ||||||||
\(809\) | −10980.7 | −0.477208 | −0.238604 | − | 0.971117i | \(-0.576690\pi\) | ||||
−0.238604 | + | 0.971117i | \(0.576690\pi\) | |||||||
\(810\) | −12072.4 | −0.523680 | ||||||||
\(811\) | −40654.8 | −1.76028 | −0.880138 | − | 0.474719i | \(-0.842550\pi\) | ||||
−0.880138 | + | 0.474719i | \(0.842550\pi\) | |||||||
\(812\) | 11130.3 | 0.481030 | ||||||||
\(813\) | −45949.8 | −1.98220 | ||||||||
\(814\) | −1039.71 | −0.0447690 | ||||||||
\(815\) | −795.224 | −0.0341785 | ||||||||
\(816\) | −51607.2 | −2.21399 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1214.95 | −0.0519312 | ||||||||
\(819\) | 31659.1 | 1.35074 | ||||||||
\(820\) | 5867.35 | 0.249874 | ||||||||
\(821\) | 21851.2 | 0.928880 | 0.464440 | − | 0.885604i | \(-0.346256\pi\) | ||||
0.464440 | + | 0.885604i | \(0.346256\pi\) | |||||||
\(822\) | 4247.35 | 0.180223 | ||||||||
\(823\) | −8135.35 | −0.344569 | −0.172285 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172285 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(824\) | −2819.06 | −0.119183 | ||||||||
\(825\) | 16663.4 | 0.703206 | ||||||||
\(826\) | 1166.33 | 0.0491307 | ||||||||
\(827\) | −39430.9 | −1.65798 | −0.828988 | − | 0.559266i | \(-0.811083\pi\) | ||||
−0.828988 | + | 0.559266i | \(0.811083\pi\) | |||||||
\(828\) | 44742.1 | 1.87789 | ||||||||
\(829\) | 7493.89 | 0.313961 | 0.156980 | − | 0.987602i | \(-0.449824\pi\) | ||||
0.156980 | + | 0.987602i | \(0.449824\pi\) | |||||||
\(830\) | −8559.99 | −0.357978 | ||||||||
\(831\) | 81378.8 | 3.39711 | ||||||||
\(832\) | −13526.7 | −0.563646 | ||||||||
\(833\) | −11575.6 | −0.481476 | ||||||||
\(834\) | −5843.18 | −0.242605 | ||||||||
\(835\) | −22705.9 | −0.941042 | ||||||||
\(836\) | −2833.33 | −0.117216 | ||||||||
\(837\) | 43642.7 | 1.80229 | ||||||||
\(838\) | −7989.10 | −0.329330 | ||||||||
\(839\) | −31112.0 | −1.28022 | −0.640110 | − | 0.768283i | \(-0.721111\pi\) | ||||
−0.640110 | + | 0.768283i | \(0.721111\pi\) | |||||||
\(840\) | −26103.9 | −1.07223 | ||||||||
\(841\) | −15099.3 | −0.619103 | ||||||||
\(842\) | −1100.44 | −0.0450401 | ||||||||
\(843\) | −34852.3 | −1.42394 | ||||||||
\(844\) | −8777.36 | −0.357973 | ||||||||
\(845\) | −16851.4 | −0.686041 | ||||||||
\(846\) | 16122.9 | 0.655222 | ||||||||
\(847\) | −19392.5 | −0.786700 | ||||||||
\(848\) | −33140.5 | −1.34204 | ||||||||
\(849\) | 43218.7 | 1.74707 | ||||||||
\(850\) | −15953.3 | −0.643758 | ||||||||
\(851\) | 23967.8 | 0.965459 | ||||||||
\(852\) | 15069.0 | 0.605935 | ||||||||
\(853\) | 34197.2 | 1.37267 | 0.686336 | − | 0.727284i | \(-0.259218\pi\) | ||||
0.686336 | + | 0.727284i | \(0.259218\pi\) | |||||||
\(854\) | −7859.92 | −0.314943 | ||||||||
\(855\) | −57518.4 | −2.30069 | ||||||||
\(856\) | −14994.2 | −0.598705 | ||||||||
\(857\) | 48162.3 | 1.91971 | 0.959856 | − | 0.280493i | \(-0.0904981\pi\) | ||||
0.959856 | + | 0.280493i | \(0.0904981\pi\) | |||||||
\(858\) | −1488.99 | −0.0592461 | ||||||||
\(859\) | 16199.5 | 0.643447 | 0.321723 | − | 0.946834i | \(-0.395738\pi\) | ||||
0.321723 | + | 0.946834i | \(0.395738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5518.38 | 0.218427 | ||||||||
\(862\) | 6386.81 | 0.252362 | ||||||||
\(863\) | −33115.5 | −1.30622 | −0.653108 | − | 0.757264i | \(-0.726535\pi\) | ||||
−0.653108 | + | 0.757264i | \(0.726535\pi\) | |||||||
\(864\) | 30919.7 | 1.21749 | ||||||||
\(865\) | −42940.6 | −1.68789 | ||||||||
\(866\) | 22.1151 | 0.000867784 0 | ||||||||
\(867\) | −50904.5 | −1.99401 | ||||||||
\(868\) | 18132.2 | 0.709040 | ||||||||
\(869\) | 3560.57 | 0.138992 | ||||||||
\(870\) | −10626.9 | −0.414122 | ||||||||
\(871\) | −6068.58 | −0.236080 | ||||||||
\(872\) | 17469.8 | 0.678444 | ||||||||
\(873\) | 74420.5 | 2.88517 | ||||||||
\(874\) | −3277.96 | −0.126864 | ||||||||
\(875\) | 37485.0 | 1.44825 | ||||||||
\(876\) | −7568.58 | −0.291916 | ||||||||
\(877\) | −1323.92 | −0.0509756 | −0.0254878 | − | 0.999675i | \(-0.508114\pi\) | ||||
−0.0254878 | + | 0.999675i | \(0.508114\pi\) | |||||||
\(878\) | −3571.67 | −0.137287 | ||||||||
\(879\) | 59263.8 | 2.27408 | ||||||||
\(880\) | −7681.85 | −0.294267 | ||||||||
\(881\) | −27090.2 | −1.03597 | −0.517987 | − | 0.855388i | \(-0.673318\pi\) | ||||
−0.517987 | + | 0.855388i | \(0.673318\pi\) | |||||||
\(882\) | 4008.73 | 0.153040 | ||||||||
\(883\) | 42910.9 | 1.63541 | 0.817705 | − | 0.575637i | \(-0.195246\pi\) | ||||
0.817705 | + | 0.575637i | \(0.195246\pi\) | |||||||
\(884\) | −28404.3 | −1.08070 | ||||||||
\(885\) | 22188.6 | 0.842783 | ||||||||
\(886\) | 7585.75 | 0.287639 | ||||||||
\(887\) | 42010.3 | 1.59027 | 0.795133 | − | 0.606435i | \(-0.207401\pi\) | ||||
0.795133 | + | 0.606435i | \(0.207401\pi\) | |||||||
\(888\) | 20720.2 | 0.783024 | ||||||||
\(889\) | −158.674 | −0.00598624 | ||||||||
\(890\) | 5184.82 | 0.195276 | ||||||||
\(891\) | −7231.56 | −0.271904 | ||||||||
\(892\) | −20228.8 | −0.759318 | ||||||||
\(893\) | 23536.3 | 0.881985 | ||||||||
\(894\) | −5953.24 | −0.222714 | ||||||||
\(895\) | −46575.4 | −1.73949 | ||||||||
\(896\) | 16968.2 | 0.632666 | ||||||||
\(897\) | 34324.5 | 1.27766 | ||||||||
\(898\) | −7294.00 | −0.271051 | ||||||||
\(899\) | 15133.7 | 0.561443 | ||||||||
\(900\) | −110083. | −4.07716 | ||||||||
\(901\) | −61652.8 | −2.27964 | ||||||||
\(902\) | −176.390 | −0.00651125 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6538.13 | −0.240548 | ||||||||
\(905\) | 1326.82 | 0.0487349 | ||||||||
\(906\) | −16476.2 | −0.604179 | ||||||||
\(907\) | 11550.7 | 0.422861 | 0.211431 | − | 0.977393i | \(-0.432188\pi\) | ||||
0.211431 | + | 0.977393i | \(0.432188\pi\) | |||||||
\(908\) | −28550.9 | −1.04350 | ||||||||
\(909\) | −84513.4 | −3.08375 | ||||||||
\(910\) | −6638.52 | −0.241829 | ||||||||
\(911\) | 5375.85 | 0.195510 | 0.0977552 | − | 0.995210i | \(-0.468834\pi\) | ||||
0.0977552 | + | 0.995210i | \(0.468834\pi\) | |||||||
\(912\) | 26089.7 | 0.947275 | ||||||||
\(913\) | −5127.57 | −0.185868 | ||||||||
\(914\) | −5009.23 | −0.181281 | ||||||||
\(915\) | −149529. | −5.40250 | ||||||||
\(916\) | −9013.60 | −0.325129 | ||||||||
\(917\) | −403.792 | −0.0145413 | ||||||||
\(918\) | 17575.2 | 0.631881 | ||||||||
\(919\) | 1541.87 | 0.0553447 | 0.0276723 | − | 0.999617i | \(-0.491190\pi\) | ||||
0.0276723 | + | 0.999617i | \(0.491190\pi\) | |||||||
\(920\) | −19234.6 | −0.689288 | ||||||||
\(921\) | −3426.72 | −0.122599 | ||||||||
\(922\) | −6874.34 | −0.245547 | ||||||||
\(923\) | 7856.78 | 0.280183 | ||||||||
\(924\) | −7626.94 | −0.271545 | ||||||||
\(925\) | −58970.3 | −2.09614 | ||||||||
\(926\) | 10351.9 | 0.367371 | ||||||||
\(927\) | −16720.9 | −0.592433 | ||||||||
\(928\) | 10721.8 | 0.379269 | ||||||||
\(929\) | 20669.5 | 0.729973 | 0.364987 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364987 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(930\) | −17312.2 | −0.610418 | ||||||||
\(931\) | 5851.96 | 0.206004 | ||||||||
\(932\) | 21330.4 | 0.749680 | ||||||||
\(933\) | −23509.3 | −0.824929 | ||||||||
\(934\) | −9965.07 | −0.349108 | ||||||||
\(935\) | −14290.9 | −0.499852 | ||||||||
\(936\) | 20167.0 | 0.704252 | ||||||||
\(937\) | −31002.3 | −1.08090 | −0.540449 | − | 0.841377i | \(-0.681745\pi\) | ||||
−0.540449 | + | 0.841377i | \(0.681745\pi\) | |||||||
\(938\) | 1560.06 | 0.0543045 | ||||||||
\(939\) | 82988.9 | 2.88418 | ||||||||
\(940\) | 67363.2 | 2.33739 | ||||||||
\(941\) | −31759.6 | −1.10025 | −0.550124 | − | 0.835083i | \(-0.685420\pi\) | ||||
−0.550124 | + | 0.835083i | \(0.685420\pi\) | |||||||
\(942\) | −2979.71 | −0.103062 | ||||||||
\(943\) | 4066.20 | 0.140417 | ||||||||
\(944\) | −6840.12 | −0.235834 | ||||||||
\(945\) | −81845.1 | −2.81738 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31056.3 | 1.06567 | 0.532837 | − | 0.846218i | \(-0.321126\pi\) | ||||
0.532837 | + | 0.846218i | \(0.321126\pi\) | |||||||
\(948\) | −34610.4 | −1.18575 | ||||||||
\(949\) | −3946.15 | −0.134982 | ||||||||
\(950\) | 8065.10 | 0.275438 | ||||||||
\(951\) | −22785.7 | −0.776946 | ||||||||
\(952\) | 14970.3 | 0.509654 | ||||||||
\(953\) | −22084.7 | −0.750676 | −0.375338 | − | 0.926888i | \(-0.622473\pi\) | ||||
−0.375338 | + | 0.926888i | \(0.622473\pi\) | |||||||
\(954\) | 21350.9 | 0.724593 | ||||||||
\(955\) | 11375.7 | 0.385453 | ||||||||
\(956\) | 22001.4 | 0.744327 | ||||||||
\(957\) | −6365.69 | −0.215019 | ||||||||
\(958\) | −1847.05 | −0.0622917 | ||||||||
\(959\) | 11343.2 | 0.381952 | ||||||||
\(960\) | 66153.5 | 2.22406 | ||||||||
\(961\) | −5136.86 | −0.172430 | ||||||||
\(962\) | 5269.39 | 0.176603 | ||||||||
\(963\) | −88936.2 | −2.97604 | ||||||||
\(964\) | −368.809 | −0.0123221 | ||||||||
\(965\) | −79725.2 | −2.65953 | ||||||||
\(966\) | −8823.85 | −0.293895 | ||||||||
\(967\) | 45620.1 | 1.51711 | 0.758554 | − | 0.651610i | \(-0.225906\pi\) | ||||
0.758554 | + | 0.651610i | \(0.225906\pi\) | |||||||
\(968\) | −12353.1 | −0.410171 | ||||||||
\(969\) | 48535.7 | 1.60907 | ||||||||
\(970\) | −15605.0 | −0.516544 | ||||||||
\(971\) | −39645.2 | −1.31027 | −0.655137 | − | 0.755510i | \(-0.727389\pi\) | ||||
−0.655137 | + | 0.755510i | \(0.727389\pi\) | |||||||
\(972\) | 13126.0 | 0.433144 | ||||||||
\(973\) | −15605.2 | −0.514162 | ||||||||
\(974\) | 11792.9 | 0.387956 | ||||||||
\(975\) | −84452.0 | −2.77398 | ||||||||
\(976\) | 46095.6 | 1.51177 | ||||||||
\(977\) | −58085.8 | −1.90208 | −0.951038 | − | 0.309074i | \(-0.899981\pi\) | ||||
−0.951038 | + | 0.309074i | \(0.899981\pi\) | |||||||
\(978\) | −232.385 | −0.00759801 | ||||||||
\(979\) | 3105.79 | 0.101391 | ||||||||
\(980\) | 16748.9 | 0.545942 | ||||||||
\(981\) | 103620. | 3.37241 | ||||||||
\(982\) | 5475.55 | 0.177935 | ||||||||
\(983\) | 8705.96 | 0.282479 | 0.141240 | − | 0.989975i | \(-0.454891\pi\) | ||||
0.141240 | + | 0.989975i | \(0.454891\pi\) | |||||||
\(984\) | 3515.24 | 0.113884 | ||||||||
\(985\) | 15289.9 | 0.494595 | ||||||||
\(986\) | 6094.43 | 0.196842 | ||||||||
\(987\) | 63356.7 | 2.04323 | ||||||||
\(988\) | 14359.6 | 0.462389 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 4949.06 | 0.158880 | ||||||||
\(991\) | 234.516 | 0.00751732 | 0.00375866 | − | 0.999993i | \(-0.498804\pi\) | ||||
0.00375866 | + | 0.999993i | \(0.498804\pi\) | |||||||
\(992\) | 17466.8 | 0.559044 | ||||||||
\(993\) | −37300.7 | −1.19205 | ||||||||
\(994\) | −2019.75 | −0.0644493 | ||||||||
\(995\) | 90770.2 | 2.89207 | ||||||||
\(996\) | 49842.4 | 1.58566 | ||||||||
\(997\) | 36443.3 | 1.15764 | 0.578822 | − | 0.815454i | \(-0.303512\pi\) | ||||
0.578822 | + | 0.815454i | \(0.303512\pi\) | |||||||
\(998\) | −7722.44 | −0.244939 | ||||||||
\(999\) | 64965.4 | 2.05747 |
(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 | 1849.4.a.j.1.23 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.28 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.28 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.23 | yes | 50 | 1.1 | even | 1 | trivial |