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: | \(60\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.92818 | −1.74237 | −0.871187 | − | 0.490951i | \(-0.836650\pi\) | ||||
−0.871187 | + | 0.490951i | \(0.836650\pi\) | |||||||
\(3\) | 1.20886 | 0.232645 | 0.116323 | − | 0.993211i | \(-0.462889\pi\) | ||||
0.116323 | + | 0.993211i | \(0.462889\pi\) | |||||||
\(4\) | 16.2870 | 2.03587 | ||||||||
\(5\) | −11.7477 | −1.05074 | −0.525372 | − | 0.850873i | \(-0.676074\pi\) | ||||
−0.525372 | + | 0.850873i | \(0.676074\pi\) | |||||||
\(6\) | −5.95749 | −0.405356 | ||||||||
\(7\) | −36.0345 | −1.94568 | −0.972841 | − | 0.231475i | \(-0.925645\pi\) | ||||
−0.972841 | + | 0.231475i | \(0.925645\pi\) | |||||||
\(8\) | −40.8396 | −1.80487 | ||||||||
\(9\) | −25.5387 | −0.945876 | ||||||||
\(10\) | 57.8946 | 1.83079 | ||||||||
\(11\) | 4.39201 | 0.120385 | 0.0601927 | − | 0.998187i | \(-0.480828\pi\) | ||||
0.0601927 | + | 0.998187i | \(0.480828\pi\) | |||||||
\(12\) | 19.6887 | 0.473636 | ||||||||
\(13\) | −77.3553 | −1.65035 | −0.825173 | − | 0.564880i | \(-0.808922\pi\) | ||||
−0.825173 | + | 0.564880i | \(0.808922\pi\) | |||||||
\(14\) | 177.585 | 3.39011 | ||||||||
\(15\) | −14.2013 | −0.244451 | ||||||||
\(16\) | 70.9695 | 1.10890 | ||||||||
\(17\) | 51.7769 | 0.738690 | 0.369345 | − | 0.929292i | \(-0.379582\pi\) | ||||
0.369345 | + | 0.929292i | \(0.379582\pi\) | |||||||
\(18\) | 125.859 | 1.64807 | ||||||||
\(19\) | −48.2283 | −0.582334 | −0.291167 | − | 0.956672i | \(-0.594043\pi\) | ||||
−0.291167 | + | 0.956672i | \(0.594043\pi\) | |||||||
\(20\) | −191.334 | −2.13918 | ||||||||
\(21\) | −43.5607 | −0.452654 | ||||||||
\(22\) | −21.6446 | −0.209757 | ||||||||
\(23\) | 49.8143 | 0.451608 | 0.225804 | − | 0.974173i | \(-0.427499\pi\) | ||||
0.225804 | + | 0.974173i | \(0.427499\pi\) | |||||||
\(24\) | −49.3695 | −0.419896 | ||||||||
\(25\) | 13.0077 | 0.104062 | ||||||||
\(26\) | 381.221 | 2.87552 | ||||||||
\(27\) | −63.5119 | −0.452699 | ||||||||
\(28\) | −586.893 | −3.96116 | ||||||||
\(29\) | −101.263 | −0.648414 | −0.324207 | − | 0.945986i | \(-0.605098\pi\) | ||||
−0.324207 | + | 0.945986i | \(0.605098\pi\) | |||||||
\(30\) | 69.9866 | 0.425925 | ||||||||
\(31\) | 189.182 | 1.09607 | 0.548034 | − | 0.836456i | \(-0.315376\pi\) | ||||
0.548034 | + | 0.836456i | \(0.315376\pi\) | |||||||
\(32\) | −23.0331 | −0.127241 | ||||||||
\(33\) | 5.30933 | 0.0280071 | ||||||||
\(34\) | −255.166 | −1.28708 | ||||||||
\(35\) | 423.322 | 2.04441 | ||||||||
\(36\) | −415.947 | −1.92568 | ||||||||
\(37\) | −64.1616 | −0.285084 | −0.142542 | − | 0.989789i | \(-0.545528\pi\) | ||||
−0.142542 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(38\) | 237.678 | 1.01464 | ||||||||
\(39\) | −93.5118 | −0.383945 | ||||||||
\(40\) | 479.771 | 1.89646 | ||||||||
\(41\) | 123.447 | 0.470222 | 0.235111 | − | 0.971968i | \(-0.424455\pi\) | ||||
0.235111 | + | 0.971968i | \(0.424455\pi\) | |||||||
\(42\) | 214.675 | 0.788693 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 71.5325 | 0.245089 | ||||||||
\(45\) | 300.020 | 0.993873 | ||||||||
\(46\) | −245.494 | −0.786871 | ||||||||
\(47\) | 442.017 | 1.37180 | 0.685902 | − | 0.727694i | \(-0.259408\pi\) | ||||
0.685902 | + | 0.727694i | \(0.259408\pi\) | |||||||
\(48\) | 85.7922 | 0.257980 | ||||||||
\(49\) | 955.487 | 2.78568 | ||||||||
\(50\) | −64.1043 | −0.181314 | ||||||||
\(51\) | 62.5910 | 0.171853 | ||||||||
\(52\) | −1259.88 | −3.35989 | ||||||||
\(53\) | 396.700 | 1.02813 | 0.514066 | − | 0.857751i | \(-0.328139\pi\) | ||||
0.514066 | + | 0.857751i | \(0.328139\pi\) | |||||||
\(54\) | 312.998 | 0.788772 | ||||||||
\(55\) | −51.5958 | −0.126494 | ||||||||
\(56\) | 1471.64 | 3.51171 | ||||||||
\(57\) | −58.3014 | −0.135477 | ||||||||
\(58\) | 499.041 | 1.12978 | ||||||||
\(59\) | −408.711 | −0.901858 | −0.450929 | − | 0.892560i | \(-0.648907\pi\) | ||||
−0.450929 | + | 0.892560i | \(0.648907\pi\) | |||||||
\(60\) | −231.296 | −0.497670 | ||||||||
\(61\) | 60.4412 | 0.126864 | 0.0634320 | − | 0.997986i | \(-0.479795\pi\) | ||||
0.0634320 | + | 0.997986i | \(0.479795\pi\) | |||||||
\(62\) | −932.323 | −1.90976 | ||||||||
\(63\) | 920.273 | 1.84037 | ||||||||
\(64\) | −454.244 | −0.887196 | ||||||||
\(65\) | 908.744 | 1.73409 | ||||||||
\(66\) | −26.1653 | −0.0487989 | ||||||||
\(67\) | 586.165 | 1.06883 | 0.534414 | − | 0.845223i | \(-0.320532\pi\) | ||||
0.534414 | + | 0.845223i | \(0.320532\pi\) | |||||||
\(68\) | 843.288 | 1.50388 | ||||||||
\(69\) | 60.2185 | 0.105065 | ||||||||
\(70\) | −2086.21 | −3.56213 | ||||||||
\(71\) | 138.373 | 0.231293 | 0.115647 | − | 0.993290i | \(-0.463106\pi\) | ||||
0.115647 | + | 0.993290i | \(0.463106\pi\) | |||||||
\(72\) | 1042.99 | 1.70719 | ||||||||
\(73\) | 572.504 | 0.917897 | 0.458948 | − | 0.888463i | \(-0.348226\pi\) | ||||
0.458948 | + | 0.888463i | \(0.348226\pi\) | |||||||
\(74\) | 316.200 | 0.496723 | ||||||||
\(75\) | 15.7245 | 0.0242094 | ||||||||
\(76\) | −785.493 | −1.18556 | ||||||||
\(77\) | −158.264 | −0.234232 | ||||||||
\(78\) | 460.843 | 0.668977 | ||||||||
\(79\) | −1043.69 | −1.48638 | −0.743190 | − | 0.669080i | \(-0.766688\pi\) | ||||
−0.743190 | + | 0.669080i | \(0.766688\pi\) | |||||||
\(80\) | −833.726 | −1.16517 | ||||||||
\(81\) | 612.767 | 0.840558 | ||||||||
\(82\) | −608.367 | −0.819304 | ||||||||
\(83\) | −521.618 | −0.689819 | −0.344909 | − | 0.938636i | \(-0.612090\pi\) | ||||
−0.344909 | + | 0.938636i | \(0.612090\pi\) | |||||||
\(84\) | −709.472 | −0.921545 | ||||||||
\(85\) | −608.257 | −0.776174 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −122.413 | −0.150851 | ||||||||
\(88\) | −179.368 | −0.217281 | ||||||||
\(89\) | −101.737 | −0.121169 | −0.0605846 | − | 0.998163i | \(-0.519297\pi\) | ||||
−0.0605846 | + | 0.998163i | \(0.519297\pi\) | |||||||
\(90\) | −1478.55 | −1.73170 | ||||||||
\(91\) | 2787.46 | 3.21105 | ||||||||
\(92\) | 811.323 | 0.919416 | ||||||||
\(93\) | 228.695 | 0.254995 | ||||||||
\(94\) | −2178.34 | −2.39020 | ||||||||
\(95\) | 566.571 | 0.611883 | ||||||||
\(96\) | −27.8438 | −0.0296021 | ||||||||
\(97\) | 289.303 | 0.302827 | 0.151414 | − | 0.988470i | \(-0.451617\pi\) | ||||
0.151414 | + | 0.988470i | \(0.451617\pi\) | |||||||
\(98\) | −4708.81 | −4.85369 | ||||||||
\(99\) | −112.166 | −0.113870 | ||||||||
\(100\) | 211.856 | 0.211856 | ||||||||
\(101\) | −1791.73 | −1.76519 | −0.882594 | − | 0.470137i | \(-0.844205\pi\) | ||||
−0.882594 | + | 0.470137i | \(0.844205\pi\) | |||||||
\(102\) | −308.460 | −0.299432 | ||||||||
\(103\) | 618.181 | 0.591370 | 0.295685 | − | 0.955285i | \(-0.404452\pi\) | ||||
0.295685 | + | 0.955285i | \(0.404452\pi\) | |||||||
\(104\) | 3159.16 | 2.97867 | ||||||||
\(105\) | 511.737 | 0.475623 | ||||||||
\(106\) | −1955.01 | −1.79139 | ||||||||
\(107\) | −242.781 | −0.219351 | −0.109675 | − | 0.993967i | \(-0.534981\pi\) | ||||
−0.109675 | + | 0.993967i | \(0.534981\pi\) | |||||||
\(108\) | −1034.42 | −0.921637 | ||||||||
\(109\) | −664.305 | −0.583751 | −0.291876 | − | 0.956456i | \(-0.594279\pi\) | ||||
−0.291876 | + | 0.956456i | \(0.594279\pi\) | |||||||
\(110\) | 254.274 | 0.220400 | ||||||||
\(111\) | −77.5625 | −0.0663234 | ||||||||
\(112\) | −2557.35 | −2.15756 | ||||||||
\(113\) | −1281.76 | −1.06706 | −0.533532 | − | 0.845780i | \(-0.679136\pi\) | ||||
−0.533532 | + | 0.845780i | \(0.679136\pi\) | |||||||
\(114\) | 287.320 | 0.236052 | ||||||||
\(115\) | −585.202 | −0.474525 | ||||||||
\(116\) | −1649.26 | −1.32009 | ||||||||
\(117\) | 1975.55 | 1.56102 | ||||||||
\(118\) | 2014.20 | 1.57137 | ||||||||
\(119\) | −1865.76 | −1.43726 | ||||||||
\(120\) | 579.976 | 0.441203 | ||||||||
\(121\) | −1311.71 | −0.985507 | ||||||||
\(122\) | −297.865 | −0.221045 | ||||||||
\(123\) | 149.230 | 0.109395 | ||||||||
\(124\) | 3081.20 | 2.23145 | ||||||||
\(125\) | 1315.65 | 0.941401 | ||||||||
\(126\) | −4535.27 | −3.20662 | ||||||||
\(127\) | 828.066 | 0.578575 | 0.289287 | − | 0.957242i | \(-0.406582\pi\) | ||||
0.289287 | + | 0.957242i | \(0.406582\pi\) | |||||||
\(128\) | 2422.86 | 1.67307 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4478.46 | −3.02143 | ||||||||
\(131\) | 1094.85 | 0.730212 | 0.365106 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365106 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(132\) | 86.4728 | 0.0570189 | ||||||||
\(133\) | 1737.89 | 1.13304 | ||||||||
\(134\) | −2888.73 | −1.86230 | ||||||||
\(135\) | 746.117 | 0.475671 | ||||||||
\(136\) | −2114.55 | −1.33324 | ||||||||
\(137\) | −182.197 | −0.113622 | −0.0568108 | − | 0.998385i | \(-0.518093\pi\) | ||||
−0.0568108 | + | 0.998385i | \(0.518093\pi\) | |||||||
\(138\) | −296.768 | −0.183062 | ||||||||
\(139\) | −210.240 | −0.128290 | −0.0641451 | − | 0.997941i | \(-0.520432\pi\) | ||||
−0.0641451 | + | 0.997941i | \(0.520432\pi\) | |||||||
\(140\) | 6894.62 | 4.16216 | ||||||||
\(141\) | 534.337 | 0.319144 | ||||||||
\(142\) | −681.926 | −0.403000 | ||||||||
\(143\) | −339.745 | −0.198678 | ||||||||
\(144\) | −1812.46 | −1.04888 | ||||||||
\(145\) | 1189.60 | 0.681317 | ||||||||
\(146\) | −2821.40 | −1.59932 | ||||||||
\(147\) | 1155.05 | 0.648075 | ||||||||
\(148\) | −1045.00 | −0.580394 | ||||||||
\(149\) | −1439.06 | −0.791224 | −0.395612 | − | 0.918418i | \(-0.629468\pi\) | ||||
−0.395612 | + | 0.918418i | \(0.629468\pi\) | |||||||
\(150\) | −77.4931 | −0.0421819 | ||||||||
\(151\) | 1023.21 | 0.551439 | 0.275720 | − | 0.961238i | \(-0.411084\pi\) | ||||
0.275720 | + | 0.961238i | \(0.411084\pi\) | |||||||
\(152\) | 1969.63 | 1.05104 | ||||||||
\(153\) | −1322.31 | −0.698709 | ||||||||
\(154\) | 779.953 | 0.408120 | ||||||||
\(155\) | −2222.45 | −1.15169 | ||||||||
\(156\) | −1523.02 | −0.781663 | ||||||||
\(157\) | −51.6584 | −0.0262598 | −0.0131299 | − | 0.999914i | \(-0.504179\pi\) | ||||
−0.0131299 | + | 0.999914i | \(0.504179\pi\) | |||||||
\(158\) | 5143.48 | 2.58983 | ||||||||
\(159\) | 479.556 | 0.239190 | ||||||||
\(160\) | 270.585 | 0.133698 | ||||||||
\(161\) | −1795.03 | −0.878686 | ||||||||
\(162\) | −3019.82 | −1.46457 | ||||||||
\(163\) | 2910.24 | 1.39845 | 0.699225 | − | 0.714901i | \(-0.253528\pi\) | ||||
0.699225 | + | 0.714901i | \(0.253528\pi\) | |||||||
\(164\) | 2010.57 | 0.957312 | ||||||||
\(165\) | −62.3722 | −0.0294283 | ||||||||
\(166\) | 2570.63 | 1.20192 | ||||||||
\(167\) | −3365.95 | −1.55967 | −0.779836 | − | 0.625984i | \(-0.784698\pi\) | ||||
−0.779836 | + | 0.625984i | \(0.784698\pi\) | |||||||
\(168\) | 1779.01 | 0.816984 | ||||||||
\(169\) | 3786.84 | 1.72364 | ||||||||
\(170\) | 2997.60 | 1.35239 | ||||||||
\(171\) | 1231.69 | 0.550816 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2181.52 | −0.958715 | −0.479358 | − | 0.877620i | \(-0.659130\pi\) | ||||
−0.479358 | + | 0.877620i | \(0.659130\pi\) | |||||||
\(174\) | 603.271 | 0.262838 | ||||||||
\(175\) | −468.726 | −0.202471 | ||||||||
\(176\) | 311.698 | 0.133495 | ||||||||
\(177\) | −494.074 | −0.209813 | ||||||||
\(178\) | 501.377 | 0.211122 | ||||||||
\(179\) | 386.165 | 0.161248 | 0.0806238 | − | 0.996745i | \(-0.474309\pi\) | ||||
0.0806238 | + | 0.996745i | \(0.474309\pi\) | |||||||
\(180\) | 4886.41 | 2.02340 | ||||||||
\(181\) | −1249.25 | −0.513017 | −0.256509 | − | 0.966542i | \(-0.582572\pi\) | ||||
−0.256509 | + | 0.966542i | \(0.582572\pi\) | |||||||
\(182\) | −13737.1 | −5.59485 | ||||||||
\(183\) | 73.0650 | 0.0295143 | ||||||||
\(184\) | −2034.40 | −0.815097 | ||||||||
\(185\) | 753.749 | 0.299550 | ||||||||
\(186\) | −1127.05 | −0.444297 | ||||||||
\(187\) | 227.404 | 0.0889276 | ||||||||
\(188\) | 7199.12 | 2.79282 | ||||||||
\(189\) | 2288.62 | 0.880809 | ||||||||
\(190\) | −2792.16 | −1.06613 | ||||||||
\(191\) | 2266.57 | 0.858655 | 0.429327 | − | 0.903149i | \(-0.358751\pi\) | ||||
0.429327 | + | 0.903149i | \(0.358751\pi\) | |||||||
\(192\) | −549.118 | −0.206402 | ||||||||
\(193\) | 3168.70 | 1.18180 | 0.590901 | − | 0.806744i | \(-0.298772\pi\) | ||||
0.590901 | + | 0.806744i | \(0.298772\pi\) | |||||||
\(194\) | −1425.74 | −0.527639 | ||||||||
\(195\) | 1098.55 | 0.403428 | ||||||||
\(196\) | 15562.0 | 5.67128 | ||||||||
\(197\) | 4300.78 | 1.55542 | 0.777710 | − | 0.628623i | \(-0.216381\pi\) | ||||
0.777710 | + | 0.628623i | \(0.216381\pi\) | |||||||
\(198\) | 552.774 | 0.198404 | ||||||||
\(199\) | −345.668 | −0.123134 | −0.0615672 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615672 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(200\) | −531.230 | −0.187818 | ||||||||
\(201\) | 708.592 | 0.248658 | ||||||||
\(202\) | 8829.97 | 3.07562 | ||||||||
\(203\) | 3648.96 | 1.26161 | ||||||||
\(204\) | 1019.42 | 0.349870 | ||||||||
\(205\) | −1450.21 | −0.494083 | ||||||||
\(206\) | −3046.51 | −1.03039 | ||||||||
\(207\) | −1272.19 | −0.427166 | ||||||||
\(208\) | −5489.86 | −1.83006 | ||||||||
\(209\) | −211.819 | −0.0701045 | ||||||||
\(210\) | −2521.93 | −0.828714 | ||||||||
\(211\) | 1209.20 | 0.394524 | 0.197262 | − | 0.980351i | \(-0.436795\pi\) | ||||
0.197262 | + | 0.980351i | \(0.436795\pi\) | |||||||
\(212\) | 6461.05 | 2.09314 | ||||||||
\(213\) | 167.274 | 0.0538094 | ||||||||
\(214\) | 1196.47 | 0.382191 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2593.81 | 0.817065 | ||||||||
\(217\) | −6817.09 | −2.13260 | ||||||||
\(218\) | 3273.82 | 1.01711 | ||||||||
\(219\) | 692.077 | 0.213545 | ||||||||
\(220\) | −840.340 | −0.257526 | ||||||||
\(221\) | −4005.21 | −1.21909 | ||||||||
\(222\) | 382.242 | 0.115560 | ||||||||
\(223\) | −113.234 | −0.0340031 | −0.0170016 | − | 0.999855i | \(-0.505412\pi\) | ||||
−0.0170016 | + | 0.999855i | \(0.505412\pi\) | |||||||
\(224\) | 829.987 | 0.247571 | ||||||||
\(225\) | −332.199 | −0.0984293 | ||||||||
\(226\) | 6316.76 | 1.85923 | ||||||||
\(227\) | 4807.72 | 1.40572 | 0.702862 | − | 0.711326i | \(-0.251905\pi\) | ||||
0.702862 | + | 0.711326i | \(0.251905\pi\) | |||||||
\(228\) | −949.552 | −0.275814 | ||||||||
\(229\) | 3584.27 | 1.03430 | 0.517151 | − | 0.855894i | \(-0.326992\pi\) | ||||
0.517151 | + | 0.855894i | \(0.326992\pi\) | |||||||
\(230\) | 2883.98 | 0.826800 | ||||||||
\(231\) | −191.319 | −0.0544930 | ||||||||
\(232\) | 4135.54 | 1.17031 | ||||||||
\(233\) | 3418.57 | 0.961194 | 0.480597 | − | 0.876942i | \(-0.340420\pi\) | ||||
0.480597 | + | 0.876942i | \(0.340420\pi\) | |||||||
\(234\) | −9735.87 | −2.71989 | ||||||||
\(235\) | −5192.67 | −1.44141 | ||||||||
\(236\) | −6656.66 | −1.83607 | ||||||||
\(237\) | −1261.67 | −0.345800 | ||||||||
\(238\) | 9194.78 | 2.50424 | ||||||||
\(239\) | −2254.44 | −0.610156 | −0.305078 | − | 0.952327i | \(-0.598683\pi\) | ||||
−0.305078 | + | 0.952327i | \(0.598683\pi\) | |||||||
\(240\) | −1007.86 | −0.271071 | ||||||||
\(241\) | −6812.13 | −1.82078 | −0.910390 | − | 0.413752i | \(-0.864218\pi\) | ||||
−0.910390 | + | 0.413752i | \(0.864218\pi\) | |||||||
\(242\) | 6464.34 | 1.71712 | ||||||||
\(243\) | 2455.57 | 0.648251 | ||||||||
\(244\) | 984.404 | 0.258279 | ||||||||
\(245\) | −11224.7 | −2.92703 | ||||||||
\(246\) | −735.431 | −0.190607 | ||||||||
\(247\) | 3730.72 | 0.961052 | ||||||||
\(248\) | −7726.13 | −1.97826 | ||||||||
\(249\) | −630.563 | −0.160483 | ||||||||
\(250\) | −6483.75 | −1.64027 | ||||||||
\(251\) | 5005.14 | 1.25865 | 0.629326 | − | 0.777141i | \(-0.283331\pi\) | ||||
0.629326 | + | 0.777141i | \(0.283331\pi\) | |||||||
\(252\) | 14988.5 | 3.74676 | ||||||||
\(253\) | 218.785 | 0.0543671 | ||||||||
\(254\) | −4080.86 | −1.00809 | ||||||||
\(255\) | −735.299 | −0.180573 | ||||||||
\(256\) | −8306.35 | −2.02792 | ||||||||
\(257\) | 5169.88 | 1.25482 | 0.627409 | − | 0.778690i | \(-0.284115\pi\) | ||||
0.627409 | + | 0.778690i | \(0.284115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2312.03 | 0.554682 | ||||||||
\(260\) | 14800.7 | 3.53038 | ||||||||
\(261\) | 2586.11 | 0.613320 | ||||||||
\(262\) | −5395.63 | −1.27230 | ||||||||
\(263\) | −2888.77 | −0.677298 | −0.338649 | − | 0.940913i | \(-0.609970\pi\) | ||||
−0.338649 | + | 0.940913i | \(0.609970\pi\) | |||||||
\(264\) | −216.831 | −0.0505494 | ||||||||
\(265\) | −4660.30 | −1.08030 | ||||||||
\(266\) | −8564.61 | −1.97417 | ||||||||
\(267\) | −122.986 | −0.0281895 | ||||||||
\(268\) | 9546.85 | 2.17600 | ||||||||
\(269\) | −3530.65 | −0.800250 | −0.400125 | − | 0.916460i | \(-0.631033\pi\) | ||||
−0.400125 | + | 0.916460i | \(0.631033\pi\) | |||||||
\(270\) | −3677.00 | −0.828797 | ||||||||
\(271\) | 2873.34 | 0.644069 | 0.322034 | − | 0.946728i | \(-0.395633\pi\) | ||||
0.322034 | + | 0.946728i | \(0.395633\pi\) | |||||||
\(272\) | 3674.58 | 0.819132 | ||||||||
\(273\) | 3369.65 | 0.747036 | ||||||||
\(274\) | 897.900 | 0.197971 | ||||||||
\(275\) | 57.1299 | 0.0125275 | ||||||||
\(276\) | 980.777 | 0.213898 | ||||||||
\(277\) | −450.892 | −0.0978032 | −0.0489016 | − | 0.998804i | \(-0.515572\pi\) | ||||
−0.0489016 | + | 0.998804i | \(0.515572\pi\) | |||||||
\(278\) | 1036.10 | 0.223529 | ||||||||
\(279\) | −4831.46 | −1.03674 | ||||||||
\(280\) | −17288.3 | −3.68991 | ||||||||
\(281\) | −7939.94 | −1.68561 | −0.842806 | − | 0.538217i | \(-0.819098\pi\) | ||||
−0.842806 | + | 0.538217i | \(0.819098\pi\) | |||||||
\(282\) | −2633.31 | −0.556069 | ||||||||
\(283\) | −65.3796 | −0.0137329 | −0.00686645 | − | 0.999976i | \(-0.502186\pi\) | ||||
−0.00686645 | + | 0.999976i | \(0.502186\pi\) | |||||||
\(284\) | 2253.67 | 0.470884 | ||||||||
\(285\) | 684.905 | 0.142352 | ||||||||
\(286\) | 1674.32 | 0.346171 | ||||||||
\(287\) | −4448.34 | −0.914903 | ||||||||
\(288\) | 588.235 | 0.120354 | ||||||||
\(289\) | −2232.16 | −0.454337 | ||||||||
\(290\) | −5862.57 | −1.18711 | ||||||||
\(291\) | 349.727 | 0.0704514 | ||||||||
\(292\) | 9324.34 | 1.86872 | ||||||||
\(293\) | −4525.53 | −0.902336 | −0.451168 | − | 0.892439i | \(-0.648993\pi\) | ||||
−0.451168 | + | 0.892439i | \(0.648993\pi\) | |||||||
\(294\) | −5692.30 | −1.12919 | ||||||||
\(295\) | 4801.40 | 0.947621 | ||||||||
\(296\) | 2620.34 | 0.514540 | ||||||||
\(297\) | −278.945 | −0.0544984 | ||||||||
\(298\) | 7091.95 | 1.37861 | ||||||||
\(299\) | −3853.40 | −0.745310 | ||||||||
\(300\) | 256.104 | 0.0492873 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5042.54 | −0.960814 | ||||||||
\(303\) | −2165.95 | −0.410663 | ||||||||
\(304\) | −3422.74 | −0.645749 | ||||||||
\(305\) | −710.043 | −0.133301 | ||||||||
\(306\) | 6516.59 | 1.21741 | ||||||||
\(307\) | 812.297 | 0.151010 | 0.0755052 | − | 0.997145i | \(-0.475943\pi\) | ||||
0.0755052 | + | 0.997145i | \(0.475943\pi\) | |||||||
\(308\) | −2577.64 | −0.476866 | ||||||||
\(309\) | 747.295 | 0.137580 | ||||||||
\(310\) | 10952.6 | 2.00667 | ||||||||
\(311\) | −316.376 | −0.0576850 | −0.0288425 | − | 0.999584i | \(-0.509182\pi\) | ||||
−0.0288425 | + | 0.999584i | \(0.509182\pi\) | |||||||
\(312\) | 3818.99 | 0.692973 | ||||||||
\(313\) | −4792.06 | −0.865377 | −0.432689 | − | 0.901543i | \(-0.642435\pi\) | ||||
−0.432689 | + | 0.901543i | \(0.642435\pi\) | |||||||
\(314\) | 254.582 | 0.0457544 | ||||||||
\(315\) | −10811.1 | −1.93376 | ||||||||
\(316\) | −16998.5 | −3.02608 | ||||||||
\(317\) | 4766.60 | 0.844538 | 0.422269 | − | 0.906470i | \(-0.361234\pi\) | ||||
0.422269 | + | 0.906470i | \(0.361234\pi\) | |||||||
\(318\) | −2363.34 | −0.416759 | ||||||||
\(319\) | −444.747 | −0.0780597 | ||||||||
\(320\) | 5336.31 | 0.932215 | ||||||||
\(321\) | −293.489 | −0.0510310 | ||||||||
\(322\) | 8846.25 | 1.53100 | ||||||||
\(323\) | −2497.11 | −0.430164 | ||||||||
\(324\) | 9980.11 | 1.71127 | ||||||||
\(325\) | −1006.21 | −0.171738 | ||||||||
\(326\) | −14342.2 | −2.43663 | ||||||||
\(327\) | −803.053 | −0.135807 | ||||||||
\(328\) | −5041.52 | −0.848693 | ||||||||
\(329\) | −15927.9 | −2.66910 | ||||||||
\(330\) | 307.382 | 0.0512751 | ||||||||
\(331\) | 6872.71 | 1.14126 | 0.570632 | − | 0.821206i | \(-0.306698\pi\) | ||||
0.570632 | + | 0.821206i | \(0.306698\pi\) | |||||||
\(332\) | −8495.57 | −1.40438 | ||||||||
\(333\) | 1638.60 | 0.269654 | ||||||||
\(334\) | 16588.0 | 2.71753 | ||||||||
\(335\) | −6886.08 | −1.12306 | ||||||||
\(336\) | −3091.48 | −0.501947 | ||||||||
\(337\) | 7556.73 | 1.22149 | 0.610744 | − | 0.791828i | \(-0.290871\pi\) | ||||
0.610744 | + | 0.791828i | \(0.290871\pi\) | |||||||
\(338\) | −18662.2 | −3.00323 | ||||||||
\(339\) | −1549.47 | −0.248248 | ||||||||
\(340\) | −9906.67 | −1.58019 | ||||||||
\(341\) | 830.889 | 0.131951 | ||||||||
\(342\) | −6069.98 | −0.959727 | ||||||||
\(343\) | −22070.7 | −3.47436 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −707.427 | −0.110396 | ||||||||
\(346\) | 10750.9 | 1.67044 | ||||||||
\(347\) | 8236.05 | 1.27416 | 0.637081 | − | 0.770797i | \(-0.280141\pi\) | ||||
0.637081 | + | 0.770797i | \(0.280141\pi\) | |||||||
\(348\) | −1993.73 | −0.307112 | ||||||||
\(349\) | 7553.43 | 1.15853 | 0.579264 | − | 0.815140i | \(-0.303340\pi\) | ||||
0.579264 | + | 0.815140i | \(0.303340\pi\) | |||||||
\(350\) | 2309.97 | 0.352780 | ||||||||
\(351\) | 4912.98 | 0.747110 | ||||||||
\(352\) | −101.162 | −0.0153180 | ||||||||
\(353\) | −752.070 | −0.113396 | −0.0566978 | − | 0.998391i | \(-0.518057\pi\) | ||||
−0.0566978 | + | 0.998391i | \(0.518057\pi\) | |||||||
\(354\) | 2434.89 | 0.365573 | ||||||||
\(355\) | −1625.56 | −0.243030 | ||||||||
\(356\) | −1656.98 | −0.246685 | ||||||||
\(357\) | −2255.44 | −0.334371 | ||||||||
\(358\) | −1903.09 | −0.280954 | ||||||||
\(359\) | 2146.31 | 0.315538 | 0.157769 | − | 0.987476i | \(-0.449570\pi\) | ||||
0.157769 | + | 0.987476i | \(0.449570\pi\) | |||||||
\(360\) | −12252.7 | −1.79382 | ||||||||
\(361\) | −4533.03 | −0.660887 | ||||||||
\(362\) | 6156.54 | 0.893868 | ||||||||
\(363\) | −1585.68 | −0.229274 | ||||||||
\(364\) | 45399.3 | 6.53728 | ||||||||
\(365\) | −6725.58 | −0.964474 | ||||||||
\(366\) | −360.078 | −0.0514250 | ||||||||
\(367\) | −3278.23 | −0.466273 | −0.233137 | − | 0.972444i | \(-0.574899\pi\) | ||||
−0.233137 | + | 0.972444i | \(0.574899\pi\) | |||||||
\(368\) | 3535.29 | 0.500788 | ||||||||
\(369\) | −3152.66 | −0.444772 | ||||||||
\(370\) | −3714.61 | −0.521928 | ||||||||
\(371\) | −14294.9 | −2.00042 | ||||||||
\(372\) | 3724.74 | 0.519137 | ||||||||
\(373\) | 2443.41 | 0.339183 | 0.169591 | − | 0.985514i | \(-0.445755\pi\) | ||||
0.169591 | + | 0.985514i | \(0.445755\pi\) | |||||||
\(374\) | −1120.69 | −0.154945 | ||||||||
\(375\) | 1590.44 | 0.219013 | ||||||||
\(376\) | −18051.8 | −2.47594 | ||||||||
\(377\) | 7833.21 | 1.07011 | ||||||||
\(378\) | −11278.7 | −1.53470 | ||||||||
\(379\) | 10011.0 | 1.35680 | 0.678401 | − | 0.734692i | \(-0.262673\pi\) | ||||
0.678401 | + | 0.734692i | \(0.262673\pi\) | |||||||
\(380\) | 9227.71 | 1.24572 | ||||||||
\(381\) | 1001.02 | 0.134603 | ||||||||
\(382\) | −11170.1 | −1.49610 | ||||||||
\(383\) | −12291.6 | −1.63987 | −0.819936 | − | 0.572455i | \(-0.805991\pi\) | ||||
−0.819936 | + | 0.572455i | \(0.805991\pi\) | |||||||
\(384\) | 2928.91 | 0.389232 | ||||||||
\(385\) | 1859.23 | 0.246118 | ||||||||
\(386\) | −15615.9 | −2.05914 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4711.87 | 0.616518 | ||||||||
\(389\) | −6820.52 | −0.888982 | −0.444491 | − | 0.895783i | \(-0.646615\pi\) | ||||
−0.444491 | + | 0.895783i | \(0.646615\pi\) | |||||||
\(390\) | −5413.83 | −0.702923 | ||||||||
\(391\) | 2579.23 | 0.333599 | ||||||||
\(392\) | −39021.8 | −5.02780 | ||||||||
\(393\) | 1323.53 | 0.169880 | ||||||||
\(394\) | −21195.0 | −2.71012 | ||||||||
\(395\) | 12260.9 | 1.56180 | ||||||||
\(396\) | −1826.84 | −0.231824 | ||||||||
\(397\) | 151.591 | 0.0191640 | 0.00958202 | − | 0.999954i | \(-0.496950\pi\) | ||||
0.00958202 | + | 0.999954i | \(0.496950\pi\) | |||||||
\(398\) | 1703.51 | 0.214546 | ||||||||
\(399\) | 2100.86 | 0.263596 | ||||||||
\(400\) | 923.149 | 0.115394 | ||||||||
\(401\) | −8900.01 | −1.10834 | −0.554171 | − | 0.832403i | \(-0.686965\pi\) | ||||
−0.554171 | + | 0.832403i | \(0.686965\pi\) | |||||||
\(402\) | −3492.07 | −0.433255 | ||||||||
\(403\) | −14634.2 | −1.80889 | ||||||||
\(404\) | −29181.9 | −3.59369 | ||||||||
\(405\) | −7198.58 | −0.883210 | ||||||||
\(406\) | −17982.7 | −2.19819 | ||||||||
\(407\) | −281.798 | −0.0343199 | ||||||||
\(408\) | −2556.20 | −0.310173 | ||||||||
\(409\) | 9621.19 | 1.16317 | 0.581586 | − | 0.813485i | \(-0.302432\pi\) | ||||
0.581586 | + | 0.813485i | \(0.302432\pi\) | |||||||
\(410\) | 7146.90 | 0.860878 | ||||||||
\(411\) | −220.251 | −0.0264335 | ||||||||
\(412\) | 10068.3 | 1.20395 | ||||||||
\(413\) | 14727.7 | 1.75473 | ||||||||
\(414\) | 6269.58 | 0.744283 | ||||||||
\(415\) | 6127.79 | 0.724823 | ||||||||
\(416\) | 1781.73 | 0.209992 | ||||||||
\(417\) | −254.151 | −0.0298461 | ||||||||
\(418\) | 1043.88 | 0.122148 | ||||||||
\(419\) | −4299.21 | −0.501265 | −0.250632 | − | 0.968082i | \(-0.580639\pi\) | ||||
−0.250632 | + | 0.968082i | \(0.580639\pi\) | |||||||
\(420\) | 8334.64 | 0.968307 | ||||||||
\(421\) | −2833.15 | −0.327979 | −0.163990 | − | 0.986462i | \(-0.552436\pi\) | ||||
−0.163990 | + | 0.986462i | \(0.552436\pi\) | |||||||
\(422\) | −5959.14 | −0.687409 | ||||||||
\(423\) | −11288.5 | −1.29756 | ||||||||
\(424\) | −16201.1 | −1.85565 | ||||||||
\(425\) | 673.498 | 0.0768692 | ||||||||
\(426\) | −824.354 | −0.0937561 | ||||||||
\(427\) | −2177.97 | −0.246837 | ||||||||
\(428\) | −3954.17 | −0.446570 | ||||||||
\(429\) | −410.705 | −0.0462214 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5988.00 | −0.669215 | −0.334608 | − | 0.942358i | \(-0.608604\pi\) | ||||
−0.334608 | + | 0.942358i | \(0.608604\pi\) | |||||||
\(432\) | −4507.41 | −0.501997 | ||||||||
\(433\) | 5090.17 | 0.564937 | 0.282469 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282469 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(434\) | 33595.8 | 3.71579 | ||||||||
\(435\) | 1438.06 | 0.158505 | ||||||||
\(436\) | −10819.5 | −1.18844 | ||||||||
\(437\) | −2402.46 | −0.262987 | ||||||||
\(438\) | −3410.68 | −0.372075 | ||||||||
\(439\) | −6863.79 | −0.746220 | −0.373110 | − | 0.927787i | \(-0.621709\pi\) | ||||
−0.373110 | + | 0.927787i | \(0.621709\pi\) | |||||||
\(440\) | 2107.16 | 0.228306 | ||||||||
\(441\) | −24401.9 | −2.63491 | ||||||||
\(442\) | 19738.4 | 2.12412 | ||||||||
\(443\) | −12487.5 | −1.33928 | −0.669640 | − | 0.742686i | \(-0.733552\pi\) | ||||
−0.669640 | + | 0.742686i | \(0.733552\pi\) | |||||||
\(444\) | −1263.26 | −0.135026 | ||||||||
\(445\) | 1195.17 | 0.127318 | ||||||||
\(446\) | 558.036 | 0.0592462 | ||||||||
\(447\) | −1739.62 | −0.184075 | ||||||||
\(448\) | 16368.5 | 1.72620 | ||||||||
\(449\) | −6436.15 | −0.676483 | −0.338241 | − | 0.941059i | \(-0.609832\pi\) | ||||
−0.338241 | + | 0.941059i | \(0.609832\pi\) | |||||||
\(450\) | 1637.14 | 0.171501 | ||||||||
\(451\) | 542.178 | 0.0566080 | ||||||||
\(452\) | −20876.0 | −2.17240 | ||||||||
\(453\) | 1236.91 | 0.128290 | ||||||||
\(454\) | −23693.3 | −2.44930 | ||||||||
\(455\) | −32746.2 | −3.37399 | ||||||||
\(456\) | 2381.01 | 0.244520 | ||||||||
\(457\) | 1479.45 | 0.151435 | 0.0757176 | − | 0.997129i | \(-0.475875\pi\) | ||||
0.0757176 | + | 0.997129i | \(0.475875\pi\) | |||||||
\(458\) | −17663.9 | −1.80214 | ||||||||
\(459\) | −3288.45 | −0.334404 | ||||||||
\(460\) | −9531.16 | −0.966071 | ||||||||
\(461\) | 9925.64 | 1.00278 | 0.501392 | − | 0.865220i | \(-0.332821\pi\) | ||||
0.501392 | + | 0.865220i | \(0.332821\pi\) | |||||||
\(462\) | 942.855 | 0.0949472 | ||||||||
\(463\) | −5956.67 | −0.597905 | −0.298953 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298953 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(464\) | −7186.56 | −0.719025 | ||||||||
\(465\) | −2686.63 | −0.267934 | ||||||||
\(466\) | −16847.4 | −1.67476 | ||||||||
\(467\) | 10264.0 | 1.01705 | 0.508526 | − | 0.861047i | \(-0.330191\pi\) | ||||
0.508526 | + | 0.861047i | \(0.330191\pi\) | |||||||
\(468\) | 32175.7 | 3.17804 | ||||||||
\(469\) | −21122.2 | −2.07960 | ||||||||
\(470\) | 25590.4 | 2.51148 | ||||||||
\(471\) | −62.4478 | −0.00610922 | ||||||||
\(472\) | 16691.6 | 1.62774 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6217.76 | 0.602513 | ||||||||
\(475\) | −627.339 | −0.0605985 | ||||||||
\(476\) | −30387.5 | −2.92607 | ||||||||
\(477\) | −10131.2 | −0.972485 | ||||||||
\(478\) | 11110.3 | 1.06312 | ||||||||
\(479\) | 10147.3 | 0.967941 | 0.483971 | − | 0.875084i | \(-0.339194\pi\) | ||||
0.483971 | + | 0.875084i | \(0.339194\pi\) | |||||||
\(480\) | 327.100 | 0.0311042 | ||||||||
\(481\) | 4963.24 | 0.470487 | ||||||||
\(482\) | 33571.4 | 3.17248 | ||||||||
\(483\) | −2169.95 | −0.204422 | ||||||||
\(484\) | −21363.8 | −2.00637 | ||||||||
\(485\) | −3398.64 | −0.318194 | ||||||||
\(486\) | −12101.5 | −1.12950 | ||||||||
\(487\) | −8735.65 | −0.812834 | −0.406417 | − | 0.913688i | \(-0.633222\pi\) | ||||
−0.406417 | + | 0.913688i | \(0.633222\pi\) | |||||||
\(488\) | −2468.40 | −0.228974 | ||||||||
\(489\) | 3518.07 | 0.325343 | ||||||||
\(490\) | 55317.6 | 5.09999 | ||||||||
\(491\) | −7578.86 | −0.696597 | −0.348299 | − | 0.937384i | \(-0.613240\pi\) | ||||
−0.348299 | + | 0.937384i | \(0.613240\pi\) | |||||||
\(492\) | 2430.50 | 0.222714 | ||||||||
\(493\) | −5243.07 | −0.478977 | ||||||||
\(494\) | −18385.6 | −1.67451 | ||||||||
\(495\) | 1317.69 | 0.119648 | ||||||||
\(496\) | 13426.1 | 1.21543 | ||||||||
\(497\) | −4986.20 | −0.450024 | ||||||||
\(498\) | 3107.53 | 0.279622 | ||||||||
\(499\) | 15869.8 | 1.42371 | 0.711854 | − | 0.702328i | \(-0.247856\pi\) | ||||
0.711854 | + | 0.702328i | \(0.247856\pi\) | |||||||
\(500\) | 21427.9 | 1.91657 | ||||||||
\(501\) | −4068.97 | −0.362851 | ||||||||
\(502\) | −24666.2 | −2.19304 | ||||||||
\(503\) | 6653.57 | 0.589797 | 0.294899 | − | 0.955529i | \(-0.404714\pi\) | ||||
0.294899 | + | 0.955529i | \(0.404714\pi\) | |||||||
\(504\) | −37583.6 | −3.32164 | ||||||||
\(505\) | 21048.7 | 1.85476 | ||||||||
\(506\) | −1078.21 | −0.0947279 | ||||||||
\(507\) | 4577.76 | 0.400997 | ||||||||
\(508\) | 13486.7 | 1.17790 | ||||||||
\(509\) | 10218.1 | 0.889800 | 0.444900 | − | 0.895580i | \(-0.353239\pi\) | ||||
0.444900 | + | 0.895580i | \(0.353239\pi\) | |||||||
\(510\) | 3623.68 | 0.314626 | ||||||||
\(511\) | −20629.9 | −1.78594 | ||||||||
\(512\) | 21552.3 | 1.86032 | ||||||||
\(513\) | 3063.08 | 0.263622 | ||||||||
\(514\) | −25478.1 | −2.18636 | ||||||||
\(515\) | −7262.18 | −0.621378 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1941.34 | 0.165145 | ||||||||
\(518\) | −11394.1 | −0.966465 | ||||||||
\(519\) | −2637.15 | −0.223041 | ||||||||
\(520\) | −37112.8 | −3.12981 | ||||||||
\(521\) | −12801.7 | −1.07650 | −0.538248 | − | 0.842787i | \(-0.680914\pi\) | ||||
−0.538248 | + | 0.842787i | \(0.680914\pi\) | |||||||
\(522\) | −12744.8 | −1.06863 | ||||||||
\(523\) | −3708.23 | −0.310038 | −0.155019 | − | 0.987912i | \(-0.549544\pi\) | ||||
−0.155019 | + | 0.987912i | \(0.549544\pi\) | |||||||
\(524\) | 17831.8 | 1.48662 | ||||||||
\(525\) | −566.625 | −0.0471039 | ||||||||
\(526\) | 14236.4 | 1.18011 | ||||||||
\(527\) | 9795.25 | 0.809655 | ||||||||
\(528\) | 376.800 | 0.0310570 | ||||||||
\(529\) | −9685.54 | −0.796050 | ||||||||
\(530\) | 22966.8 | 1.88229 | ||||||||
\(531\) | 10437.9 | 0.853046 | ||||||||
\(532\) | 28304.9 | 2.30671 | ||||||||
\(533\) | −9549.25 | −0.776030 | ||||||||
\(534\) | 606.095 | 0.0491166 | ||||||||
\(535\) | 2852.11 | 0.230481 | ||||||||
\(536\) | −23938.8 | −1.92910 | ||||||||
\(537\) | 466.820 | 0.0375135 | ||||||||
\(538\) | 17399.7 | 1.39434 | ||||||||
\(539\) | 4196.51 | 0.335355 | ||||||||
\(540\) | 12152.0 | 0.968404 | ||||||||
\(541\) | 18444.5 | 1.46579 | 0.732893 | − | 0.680344i | \(-0.238170\pi\) | ||||
0.732893 | + | 0.680344i | \(0.238170\pi\) | |||||||
\(542\) | −14160.3 | −1.12221 | ||||||||
\(543\) | −1510.17 | −0.119351 | ||||||||
\(544\) | −1192.58 | −0.0939918 | ||||||||
\(545\) | 7804.04 | 0.613373 | ||||||||
\(546\) | −16606.3 | −1.30162 | ||||||||
\(547\) | −2665.35 | −0.208340 | −0.104170 | − | 0.994559i | \(-0.533219\pi\) | ||||
−0.104170 | + | 0.994559i | \(0.533219\pi\) | |||||||
\(548\) | −2967.44 | −0.231319 | ||||||||
\(549\) | −1543.59 | −0.119998 | ||||||||
\(550\) | −281.546 | −0.0218276 | ||||||||
\(551\) | 4883.73 | 0.377594 | ||||||||
\(552\) | −2459.30 | −0.189629 | ||||||||
\(553\) | 37608.8 | 2.89202 | ||||||||
\(554\) | 2222.08 | 0.170410 | ||||||||
\(555\) | 911.178 | 0.0696889 | ||||||||
\(556\) | −3424.17 | −0.261182 | ||||||||
\(557\) | 6223.14 | 0.473398 | 0.236699 | − | 0.971583i | \(-0.423934\pi\) | ||||
0.236699 | + | 0.971583i | \(0.423934\pi\) | |||||||
\(558\) | 23810.3 | 1.80640 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 30042.9 | 2.26704 | ||||||||
\(561\) | 274.900 | 0.0206886 | ||||||||
\(562\) | 39129.5 | 2.93697 | ||||||||
\(563\) | 16282.3 | 1.21886 | 0.609431 | − | 0.792839i | \(-0.291398\pi\) | ||||
0.609431 | + | 0.792839i | \(0.291398\pi\) | |||||||
\(564\) | 8702.73 | 0.649736 | ||||||||
\(565\) | 15057.7 | 1.12121 | ||||||||
\(566\) | 322.202 | 0.0239279 | ||||||||
\(567\) | −22080.8 | −1.63546 | ||||||||
\(568\) | −5651.10 | −0.417456 | ||||||||
\(569\) | 8186.09 | 0.603126 | 0.301563 | − | 0.953446i | \(-0.402492\pi\) | ||||
0.301563 | + | 0.953446i | \(0.402492\pi\) | |||||||
\(570\) | −3375.34 | −0.248030 | ||||||||
\(571\) | 22181.2 | 1.62567 | 0.812834 | − | 0.582496i | \(-0.197924\pi\) | ||||
0.812834 | + | 0.582496i | \(0.197924\pi\) | |||||||
\(572\) | −5533.41 | −0.404482 | ||||||||
\(573\) | 2739.97 | 0.199762 | ||||||||
\(574\) | 21922.2 | 1.59410 | ||||||||
\(575\) | 647.969 | 0.0469951 | ||||||||
\(576\) | 11600.8 | 0.839178 | ||||||||
\(577\) | −8781.20 | −0.633563 | −0.316782 | − | 0.948499i | \(-0.602602\pi\) | ||||
−0.316782 | + | 0.948499i | \(0.602602\pi\) | |||||||
\(578\) | 11000.5 | 0.791625 | ||||||||
\(579\) | 3830.52 | 0.274941 | ||||||||
\(580\) | 19375.0 | 1.38707 | ||||||||
\(581\) | 18796.2 | 1.34217 | ||||||||
\(582\) | −1723.52 | −0.122753 | ||||||||
\(583\) | 1742.31 | 0.123772 | ||||||||
\(584\) | −23380.8 | −1.65669 | ||||||||
\(585\) | −23208.1 | −1.64023 | ||||||||
\(586\) | 22302.7 | 1.57221 | ||||||||
\(587\) | 15965.9 | 1.12263 | 0.561313 | − | 0.827604i | \(-0.310296\pi\) | ||||
0.561313 | + | 0.827604i | \(0.310296\pi\) | |||||||
\(588\) | 18812.3 | 1.31940 | ||||||||
\(589\) | −9123.94 | −0.638277 | ||||||||
\(590\) | −23662.2 | −1.65111 | ||||||||
\(591\) | 5199.04 | 0.361861 | ||||||||
\(592\) | −4553.51 | −0.316129 | ||||||||
\(593\) | 4928.88 | 0.341324 | 0.170662 | − | 0.985330i | \(-0.445409\pi\) | ||||
0.170662 | + | 0.985330i | \(0.445409\pi\) | |||||||
\(594\) | 1374.69 | 0.0949567 | ||||||||
\(595\) | 21918.3 | 1.51019 | ||||||||
\(596\) | −23437.9 | −1.61083 | ||||||||
\(597\) | −417.865 | −0.0286467 | ||||||||
\(598\) | 18990.2 | 1.29861 | ||||||||
\(599\) | −12943.4 | −0.882891 | −0.441446 | − | 0.897288i | \(-0.645534\pi\) | ||||
−0.441446 | + | 0.897288i | \(0.645534\pi\) | |||||||
\(600\) | −642.183 | −0.0436950 | ||||||||
\(601\) | 4989.56 | 0.338650 | 0.169325 | − | 0.985560i | \(-0.445841\pi\) | ||||
0.169325 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14969.9 | −1.01098 | ||||||||
\(604\) | 16664.9 | 1.12266 | ||||||||
\(605\) | 15409.5 | 1.03552 | ||||||||
\(606\) | 10674.2 | 0.715528 | ||||||||
\(607\) | 16584.3 | 1.10896 | 0.554478 | − | 0.832198i | \(-0.312918\pi\) | ||||
0.554478 | + | 0.832198i | \(0.312918\pi\) | |||||||
\(608\) | 1110.85 | 0.0740968 | ||||||||
\(609\) | 4411.08 | 0.293507 | ||||||||
\(610\) | 3499.22 | 0.232261 | ||||||||
\(611\) | −34192.4 | −2.26395 | ||||||||
\(612\) | −21536.4 | −1.42248 | ||||||||
\(613\) | 2154.47 | 0.141955 | 0.0709773 | − | 0.997478i | \(-0.477388\pi\) | ||||
0.0709773 | + | 0.997478i | \(0.477388\pi\) | |||||||
\(614\) | −4003.14 | −0.263117 | ||||||||
\(615\) | −1753.10 | −0.114946 | ||||||||
\(616\) | 6463.44 | 0.422759 | ||||||||
\(617\) | −4703.27 | −0.306883 | −0.153441 | − | 0.988158i | \(-0.549036\pi\) | ||||
−0.153441 | + | 0.988158i | \(0.549036\pi\) | |||||||
\(618\) | −3682.80 | −0.239715 | ||||||||
\(619\) | −12587.5 | −0.817340 | −0.408670 | − | 0.912682i | \(-0.634007\pi\) | ||||
−0.408670 | + | 0.912682i | \(0.634007\pi\) | |||||||
\(620\) | −36196.9 | −2.34468 | ||||||||
\(621\) | −3163.80 | −0.204443 | ||||||||
\(622\) | 1559.16 | 0.100509 | ||||||||
\(623\) | 3666.03 | 0.235757 | ||||||||
\(624\) | −6636.48 | −0.425756 | ||||||||
\(625\) | −17081.8 | −1.09323 | ||||||||
\(626\) | 23616.1 | 1.50781 | ||||||||
\(627\) | −256.060 | −0.0163095 | ||||||||
\(628\) | −841.358 | −0.0534615 | ||||||||
\(629\) | −3322.09 | −0.210589 | ||||||||
\(630\) | 53278.9 | 3.36934 | ||||||||
\(631\) | 19165.7 | 1.20915 | 0.604576 | − | 0.796547i | \(-0.293342\pi\) | ||||
0.604576 | + | 0.796547i | \(0.293342\pi\) | |||||||
\(632\) | 42623.8 | 2.68273 | ||||||||
\(633\) | 1461.75 | 0.0917842 | ||||||||
\(634\) | −23490.6 | −1.47150 | ||||||||
\(635\) | −9727.84 | −0.607933 | ||||||||
\(636\) | 7810.51 | 0.486960 | ||||||||
\(637\) | −73912.0 | −4.59733 | ||||||||
\(638\) | 2191.79 | 0.136009 | ||||||||
\(639\) | −3533.86 | −0.218775 | ||||||||
\(640\) | −28463.0 | −1.75797 | ||||||||
\(641\) | 15441.3 | 0.951475 | 0.475738 | − | 0.879587i | \(-0.342181\pi\) | ||||
0.475738 | + | 0.879587i | \(0.342181\pi\) | |||||||
\(642\) | 1446.36 | 0.0889151 | ||||||||
\(643\) | −12967.4 | −0.795307 | −0.397654 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397654 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(644\) | −29235.7 | −1.78889 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12306.2 | 0.749507 | ||||||||
\(647\) | −1957.15 | −0.118924 | −0.0594618 | − | 0.998231i | \(-0.518938\pi\) | ||||
−0.0594618 | + | 0.998231i | \(0.518938\pi\) | |||||||
\(648\) | −25025.2 | −1.51710 | ||||||||
\(649\) | −1795.06 | −0.108571 | ||||||||
\(650\) | 4958.80 | 0.299231 | ||||||||
\(651\) | −8240.91 | −0.496139 | ||||||||
\(652\) | 47398.9 | 2.84706 | ||||||||
\(653\) | 22721.6 | 1.36166 | 0.680830 | − | 0.732442i | \(-0.261619\pi\) | ||||
0.680830 | + | 0.732442i | \(0.261619\pi\) | |||||||
\(654\) | 3957.59 | 0.236627 | ||||||||
\(655\) | −12862.0 | −0.767265 | ||||||||
\(656\) | 8760.94 | 0.521429 | ||||||||
\(657\) | −14621.0 | −0.868217 | ||||||||
\(658\) | 78495.5 | 4.65056 | ||||||||
\(659\) | −14970.8 | −0.884946 | −0.442473 | − | 0.896782i | \(-0.645899\pi\) | ||||
−0.442473 | + | 0.896782i | \(0.645899\pi\) | |||||||
\(660\) | −1015.85 | −0.0599122 | ||||||||
\(661\) | −13729.4 | −0.807886 | −0.403943 | − | 0.914784i | \(-0.632361\pi\) | ||||
−0.403943 | + | 0.914784i | \(0.632361\pi\) | |||||||
\(662\) | −33869.9 | −1.98851 | ||||||||
\(663\) | −4841.75 | −0.283617 | ||||||||
\(664\) | 21302.7 | 1.24504 | ||||||||
\(665\) | −20416.1 | −1.19053 | ||||||||
\(666\) | −8075.32 | −0.469838 | ||||||||
\(667\) | −5044.33 | −0.292829 | ||||||||
\(668\) | −54821.1 | −3.17529 | ||||||||
\(669\) | −136.884 | −0.00791067 | ||||||||
\(670\) | 33935.8 | 1.95680 | ||||||||
\(671\) | 265.458 | 0.0152726 | ||||||||
\(672\) | 1003.34 | 0.0575962 | ||||||||
\(673\) | −33165.2 | −1.89959 | −0.949795 | − | 0.312874i | \(-0.898708\pi\) | ||||
−0.949795 | + | 0.312874i | \(0.898708\pi\) | |||||||
\(674\) | −37240.9 | −2.12829 | ||||||||
\(675\) | −826.144 | −0.0471086 | ||||||||
\(676\) | 61676.1 | 3.50911 | ||||||||
\(677\) | −24360.0 | −1.38291 | −0.691455 | − | 0.722419i | \(-0.743030\pi\) | ||||
−0.691455 | + | 0.722419i | \(0.743030\pi\) | |||||||
\(678\) | 7636.09 | 0.432540 | ||||||||
\(679\) | −10424.9 | −0.589206 | ||||||||
\(680\) | 24841.0 | 1.40090 | ||||||||
\(681\) | 5811.86 | 0.327035 | ||||||||
\(682\) | −4094.77 | −0.229907 | ||||||||
\(683\) | −21088.4 | −1.18144 | −0.590720 | − | 0.806876i | \(-0.701156\pi\) | ||||
−0.590720 | + | 0.806876i | \(0.701156\pi\) | |||||||
\(684\) | 20060.4 | 1.12139 | ||||||||
\(685\) | 2140.39 | 0.119387 | ||||||||
\(686\) | 108768. | 6.05364 | ||||||||
\(687\) | 4332.89 | 0.240626 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30686.9 | −1.69677 | ||||||||
\(690\) | 3486.33 | 0.192351 | ||||||||
\(691\) | −2625.67 | −0.144551 | −0.0722757 | − | 0.997385i | \(-0.523026\pi\) | ||||
−0.0722757 | + | 0.997385i | \(0.523026\pi\) | |||||||
\(692\) | −35530.3 | −1.95182 | ||||||||
\(693\) | 4041.85 | 0.221554 | ||||||||
\(694\) | −40588.8 | −2.22007 | ||||||||
\(695\) | 2469.83 | 0.134800 | ||||||||
\(696\) | 4999.29 | 0.272267 | ||||||||
\(697\) | 6391.68 | 0.347349 | ||||||||
\(698\) | −37224.7 | −2.01859 | ||||||||
\(699\) | 4132.58 | 0.223617 | ||||||||
\(700\) | −7634.12 | −0.412204 | ||||||||
\(701\) | −32287.1 | −1.73961 | −0.869805 | − | 0.493396i | \(-0.835755\pi\) | ||||
−0.869805 | + | 0.493396i | \(0.835755\pi\) | |||||||
\(702\) | −24212.1 | −1.30175 | ||||||||
\(703\) | 3094.41 | 0.166014 | ||||||||
\(704\) | −1995.04 | −0.106806 | ||||||||
\(705\) | −6277.22 | −0.335338 | ||||||||
\(706\) | 3706.34 | 0.197578 | ||||||||
\(707\) | 64564.2 | 3.43449 | ||||||||
\(708\) | −8046.97 | −0.427152 | ||||||||
\(709\) | 24228.5 | 1.28338 | 0.641692 | − | 0.766962i | \(-0.278233\pi\) | ||||
0.641692 | + | 0.766962i | \(0.278233\pi\) | |||||||
\(710\) | 8011.05 | 0.423450 | ||||||||
\(711\) | 26654.4 | 1.40593 | ||||||||
\(712\) | 4154.89 | 0.218695 | ||||||||
\(713\) | 9423.97 | 0.494994 | ||||||||
\(714\) | 11115.2 | 0.582600 | ||||||||
\(715\) | 3991.21 | 0.208759 | ||||||||
\(716\) | 6289.45 | 0.328279 | ||||||||
\(717\) | −2725.30 | −0.141950 | ||||||||
\(718\) | −10577.4 | −0.549786 | ||||||||
\(719\) | 26115.0 | 1.35455 | 0.677277 | − | 0.735729i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735729i | \(0.263160\pi\) | |||||||
\(720\) | 21292.2 | 1.10210 | ||||||||
\(721\) | −22275.8 | −1.15062 | ||||||||
\(722\) | 22339.6 | 1.15151 | ||||||||
\(723\) | −8234.92 | −0.423596 | ||||||||
\(724\) | −20346.5 | −1.04444 | ||||||||
\(725\) | −1317.19 | −0.0674750 | ||||||||
\(726\) | 7814.50 | 0.399481 | ||||||||
\(727\) | 11600.5 | 0.591799 | 0.295899 | − | 0.955219i | \(-0.404381\pi\) | ||||
0.295899 | + | 0.955219i | \(0.404381\pi\) | |||||||
\(728\) | −113839. | −5.79554 | ||||||||
\(729\) | −13576.3 | −0.689745 | ||||||||
\(730\) | 33144.9 | 1.68048 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1190.01 | 0.0600873 | ||||||||
\(733\) | −1893.82 | −0.0954296 | −0.0477148 | − | 0.998861i | \(-0.515194\pi\) | ||||
−0.0477148 | + | 0.998861i | \(0.515194\pi\) | |||||||
\(734\) | 16155.7 | 0.812422 | ||||||||
\(735\) | −13569.2 | −0.680961 | ||||||||
\(736\) | −1147.38 | −0.0574632 | ||||||||
\(737\) | 2574.44 | 0.128671 | ||||||||
\(738\) | 15536.9 | 0.774960 | ||||||||
\(739\) | −32380.7 | −1.61183 | −0.805916 | − | 0.592030i | \(-0.798327\pi\) | ||||
−0.805916 | + | 0.592030i | \(0.798327\pi\) | |||||||
\(740\) | 12276.3 | 0.609845 | ||||||||
\(741\) | 4509.92 | 0.223584 | ||||||||
\(742\) | 70447.9 | 3.48548 | ||||||||
\(743\) | −14950.3 | −0.738187 | −0.369093 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369093 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(744\) | −9339.82 | −0.460234 | ||||||||
\(745\) | 16905.6 | 0.831374 | ||||||||
\(746\) | −12041.6 | −0.590984 | ||||||||
\(747\) | 13321.4 | 0.652483 | ||||||||
\(748\) | 3703.73 | 0.181045 | ||||||||
\(749\) | 8748.50 | 0.426787 | ||||||||
\(750\) | −7837.96 | −0.381602 | ||||||||
\(751\) | −38699.6 | −1.88039 | −0.940193 | − | 0.340643i | \(-0.889355\pi\) | ||||
−0.940193 | + | 0.340643i | \(0.889355\pi\) | |||||||
\(752\) | 31369.7 | 1.52119 | ||||||||
\(753\) | 6050.52 | 0.292820 | ||||||||
\(754\) | −38603.5 | −1.86453 | ||||||||
\(755\) | −12020.3 | −0.579421 | ||||||||
\(756\) | 37274.7 | 1.79321 | ||||||||
\(757\) | 555.655 | 0.0266785 | 0.0133392 | − | 0.999911i | \(-0.495754\pi\) | ||||
0.0133392 | + | 0.999911i | \(0.495754\pi\) | |||||||
\(758\) | −49335.8 | −2.36406 | ||||||||
\(759\) | 264.480 | 0.0126483 | ||||||||
\(760\) | −23138.5 | −1.10437 | ||||||||
\(761\) | −30618.8 | −1.45852 | −0.729259 | − | 0.684238i | \(-0.760135\pi\) | ||||
−0.729259 | + | 0.684238i | \(0.760135\pi\) | |||||||
\(762\) | −4933.19 | −0.234528 | ||||||||
\(763\) | 23937.9 | 1.13579 | ||||||||
\(764\) | 36915.5 | 1.74811 | ||||||||
\(765\) | 15534.1 | 0.734164 | ||||||||
\(766\) | 60575.2 | 2.85727 | ||||||||
\(767\) | 31615.9 | 1.48838 | ||||||||
\(768\) | −10041.2 | −0.471786 | ||||||||
\(769\) | 10000.6 | 0.468962 | 0.234481 | − | 0.972121i | \(-0.424661\pi\) | ||||
0.234481 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(770\) | −9162.63 | −0.428829 | ||||||||
\(771\) | 6249.67 | 0.291928 | ||||||||
\(772\) | 51608.5 | 2.40600 | ||||||||
\(773\) | 14348.4 | 0.667626 | 0.333813 | − | 0.942639i | \(-0.391665\pi\) | ||||
0.333813 | + | 0.942639i | \(0.391665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2460.82 | 0.114059 | ||||||||
\(776\) | −11815.0 | −0.546566 | ||||||||
\(777\) | 2794.93 | 0.129044 | ||||||||
\(778\) | 33612.7 | 1.54894 | ||||||||
\(779\) | −5953.63 | −0.273826 | ||||||||
\(780\) | 17892.0 | 0.821327 | ||||||||
\(781\) | 607.735 | 0.0278444 | ||||||||
\(782\) | −12710.9 | −0.581254 | ||||||||
\(783\) | 6431.39 | 0.293537 | ||||||||
\(784\) | 67810.4 | 3.08903 | ||||||||
\(785\) | 606.866 | 0.0275923 | ||||||||
\(786\) | −6522.57 | −0.295995 | ||||||||
\(787\) | 42907.3 | 1.94343 | 0.971716 | − | 0.236151i | \(-0.0758860\pi\) | ||||
0.971716 | + | 0.236151i | \(0.0758860\pi\) | |||||||
\(788\) | 70046.6 | 3.16663 | ||||||||
\(789\) | −3492.13 | −0.157570 | ||||||||
\(790\) | −60423.9 | −2.72125 | ||||||||
\(791\) | 46187.8 | 2.07617 | ||||||||
\(792\) | 4580.82 | 0.205521 | ||||||||
\(793\) | −4675.45 | −0.209369 | ||||||||
\(794\) | −747.067 | −0.0333909 | ||||||||
\(795\) | −5633.66 | −0.251328 | ||||||||
\(796\) | −5629.88 | −0.250686 | ||||||||
\(797\) | −23001.4 | −1.02227 | −0.511136 | − | 0.859500i | \(-0.670775\pi\) | ||||
−0.511136 | + | 0.859500i | \(0.670775\pi\) | |||||||
\(798\) | −10353.4 | −0.459283 | ||||||||
\(799\) | 22886.3 | 1.01334 | ||||||||
\(800\) | −299.608 | −0.0132409 | ||||||||
\(801\) | 2598.22 | 0.114611 | ||||||||
\(802\) | 43860.8 | 1.93115 | ||||||||
\(803\) | 2514.44 | 0.110501 | ||||||||
\(804\) | 11540.8 | 0.506235 | ||||||||
\(805\) | 21087.5 | 0.923274 | ||||||||
\(806\) | 72120.1 | 3.15177 | ||||||||
\(807\) | −4268.06 | −0.186175 | ||||||||
\(808\) | 73173.7 | 3.18594 | ||||||||
\(809\) | 28862.5 | 1.25433 | 0.627164 | − | 0.778888i | \(-0.284216\pi\) | ||||
0.627164 | + | 0.778888i | \(0.284216\pi\) | |||||||
\(810\) | 35475.9 | 1.53888 | ||||||||
\(811\) | −14854.2 | −0.643159 | −0.321580 | − | 0.946883i | \(-0.604214\pi\) | ||||
−0.321580 | + | 0.946883i | \(0.604214\pi\) | |||||||
\(812\) | 59430.4 | 2.56847 | ||||||||
\(813\) | 3473.46 | 0.149840 | ||||||||
\(814\) | 1388.75 | 0.0597982 | ||||||||
\(815\) | −34188.5 | −1.46941 | ||||||||
\(816\) | 4442.05 | 0.190567 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −47415.0 | −2.02668 | ||||||||
\(819\) | −71188.0 | −3.03725 | ||||||||
\(820\) | −23619.5 | −1.00589 | ||||||||
\(821\) | 1806.78 | 0.0768052 | 0.0384026 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384026 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(822\) | 1085.44 | 0.0460571 | ||||||||
\(823\) | 22648.5 | 0.959269 | 0.479634 | − | 0.877468i | \(-0.340769\pi\) | ||||
0.479634 | + | 0.877468i | \(0.340769\pi\) | |||||||
\(824\) | −25246.3 | −1.06735 | ||||||||
\(825\) | 69.0621 | 0.00291447 | ||||||||
\(826\) | −72580.8 | −3.05739 | ||||||||
\(827\) | 17580.0 | 0.739198 | 0.369599 | − | 0.929191i | \(-0.379495\pi\) | ||||
0.369599 | + | 0.929191i | \(0.379495\pi\) | |||||||
\(828\) | −20720.1 | −0.869654 | ||||||||
\(829\) | −778.570 | −0.0326186 | −0.0163093 | − | 0.999867i | \(-0.505192\pi\) | ||||
−0.0163093 | + | 0.999867i | \(0.505192\pi\) | |||||||
\(830\) | −30198.9 | −1.26291 | ||||||||
\(831\) | −545.066 | −0.0227535 | ||||||||
\(832\) | 35138.2 | 1.46418 | ||||||||
\(833\) | 49472.1 | 2.05775 | ||||||||
\(834\) | 1252.50 | 0.0520031 | ||||||||
\(835\) | 39542.1 | 1.63881 | ||||||||
\(836\) | −3449.89 | −0.142724 | ||||||||
\(837\) | −12015.3 | −0.496189 | ||||||||
\(838\) | 21187.3 | 0.873391 | ||||||||
\(839\) | −9935.89 | −0.408850 | −0.204425 | − | 0.978882i | \(-0.565532\pi\) | ||||
−0.204425 | + | 0.978882i | \(0.565532\pi\) | |||||||
\(840\) | −20899.2 | −0.858440 | ||||||||
\(841\) | −14134.9 | −0.579559 | ||||||||
\(842\) | 13962.3 | 0.571463 | ||||||||
\(843\) | −9598.29 | −0.392150 | ||||||||
\(844\) | 19694.1 | 0.803200 | ||||||||
\(845\) | −44486.5 | −1.81110 | ||||||||
\(846\) | 55631.9 | 2.26083 | ||||||||
\(847\) | 47266.9 | 1.91748 | ||||||||
\(848\) | 28153.6 | 1.14009 | ||||||||
\(849\) | −79.0348 | −0.00319490 | ||||||||
\(850\) | −3319.12 | −0.133935 | ||||||||
\(851\) | −3196.16 | −0.128746 | ||||||||
\(852\) | 2724.38 | 0.109549 | ||||||||
\(853\) | −25751.3 | −1.03365 | −0.516827 | − | 0.856090i | \(-0.672887\pi\) | ||||
−0.516827 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(854\) | 10733.4 | 0.430082 | ||||||||
\(855\) | −14469.4 | −0.578766 | ||||||||
\(856\) | 9915.09 | 0.395901 | ||||||||
\(857\) | −16458.1 | −0.656007 | −0.328004 | − | 0.944676i | \(-0.606376\pi\) | ||||
−0.328004 | + | 0.944676i | \(0.606376\pi\) | |||||||
\(858\) | 2024.03 | 0.0805351 | ||||||||
\(859\) | 14331.0 | 0.569231 | 0.284615 | − | 0.958642i | \(-0.408134\pi\) | ||||
0.284615 | + | 0.958642i | \(0.408134\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5377.43 | −0.212848 | ||||||||
\(862\) | 29509.9 | 1.16602 | ||||||||
\(863\) | −13078.3 | −0.515864 | −0.257932 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257932 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(864\) | 1462.88 | 0.0576020 | ||||||||
\(865\) | 25627.7 | 1.00736 | ||||||||
\(866\) | −25085.3 | −0.984333 | ||||||||
\(867\) | −2698.37 | −0.105699 | ||||||||
\(868\) | −111030. | −4.34170 | ||||||||
\(869\) | −4583.88 | −0.178939 | ||||||||
\(870\) | −7087.03 | −0.276176 | ||||||||
\(871\) | −45343.0 | −1.76394 | ||||||||
\(872\) | 27130.0 | 1.05360 | ||||||||
\(873\) | −7388.41 | −0.286437 | ||||||||
\(874\) | 11839.8 | 0.458222 | ||||||||
\(875\) | −47408.8 | −1.83167 | ||||||||
\(876\) | 11271.8 | 0.434749 | ||||||||
\(877\) | 3287.88 | 0.126595 | 0.0632974 | − | 0.997995i | \(-0.479838\pi\) | ||||
0.0632974 | + | 0.997995i | \(0.479838\pi\) | |||||||
\(878\) | 33826.0 | 1.30020 | ||||||||
\(879\) | −5470.74 | −0.209924 | ||||||||
\(880\) | −3661.73 | −0.140269 | ||||||||
\(881\) | 34036.1 | 1.30160 | 0.650798 | − | 0.759251i | \(-0.274435\pi\) | ||||
0.650798 | + | 0.759251i | \(0.274435\pi\) | |||||||
\(882\) | 120257. | 4.59099 | ||||||||
\(883\) | 26799.0 | 1.02136 | 0.510678 | − | 0.859772i | \(-0.329395\pi\) | ||||
0.510678 | + | 0.859772i | \(0.329395\pi\) | |||||||
\(884\) | −65232.8 | −2.48192 | ||||||||
\(885\) | 5804.22 | 0.220460 | ||||||||
\(886\) | 61540.9 | 2.33353 | ||||||||
\(887\) | −44323.8 | −1.67784 | −0.838921 | − | 0.544253i | \(-0.816813\pi\) | ||||
−0.838921 | + | 0.544253i | \(0.816813\pi\) | |||||||
\(888\) | 3167.62 | 0.119705 | ||||||||
\(889\) | −29839.0 | −1.12572 | ||||||||
\(890\) | −5890.01 | −0.221835 | ||||||||
\(891\) | 2691.28 | 0.101191 | ||||||||
\(892\) | −1844.23 | −0.0692259 | ||||||||
\(893\) | −21317.8 | −0.798848 | ||||||||
\(894\) | 8573.18 | 0.320727 | ||||||||
\(895\) | −4536.54 | −0.169430 | ||||||||
\(896\) | −87306.7 | −3.25526 | ||||||||
\(897\) | −4658.22 | −0.173393 | ||||||||
\(898\) | 31718.5 | 1.17869 | ||||||||
\(899\) | −19157.1 | −0.710706 | ||||||||
\(900\) | −5410.51 | −0.200389 | ||||||||
\(901\) | 20539.9 | 0.759471 | ||||||||
\(902\) | −2671.95 | −0.0986323 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 52346.8 | 1.92592 | ||||||||
\(905\) | 14675.8 | 0.539049 | ||||||||
\(906\) | −6095.73 | −0.223529 | ||||||||
\(907\) | −4653.88 | −0.170374 | −0.0851872 | − | 0.996365i | \(-0.527149\pi\) | ||||
−0.0851872 | + | 0.996365i | \(0.527149\pi\) | |||||||
\(908\) | 78303.1 | 2.86187 | ||||||||
\(909\) | 45758.4 | 1.66965 | ||||||||
\(910\) | 161379. | 5.87875 | ||||||||
\(911\) | 25937.6 | 0.943305 | 0.471653 | − | 0.881784i | \(-0.343658\pi\) | ||||
0.471653 | + | 0.881784i | \(0.343658\pi\) | |||||||
\(912\) | −4137.62 | −0.150230 | ||||||||
\(913\) | −2290.95 | −0.0830442 | ||||||||
\(914\) | −7291.01 | −0.263857 | ||||||||
\(915\) | −858.343 | −0.0310120 | ||||||||
\(916\) | 58376.9 | 2.10571 | ||||||||
\(917\) | −39452.5 | −1.42076 | ||||||||
\(918\) | 16206.1 | 0.582658 | ||||||||
\(919\) | −34390.1 | −1.23441 | −0.617206 | − | 0.786802i | \(-0.711736\pi\) | ||||
−0.617206 | + | 0.786802i | \(0.711736\pi\) | |||||||
\(920\) | 23899.4 | 0.856457 | ||||||||
\(921\) | 981.954 | 0.0351319 | ||||||||
\(922\) | −48915.4 | −1.74723 | ||||||||
\(923\) | −10703.9 | −0.381714 | ||||||||
\(924\) | −3116.01 | −0.110941 | ||||||||
\(925\) | −834.594 | −0.0296663 | ||||||||
\(926\) | 29355.6 | 1.04178 | ||||||||
\(927\) | −15787.5 | −0.559363 | ||||||||
\(928\) | 2332.40 | 0.0825050 | ||||||||
\(929\) | −4086.19 | −0.144310 | −0.0721548 | − | 0.997393i | \(-0.522988\pi\) | ||||
−0.0721548 | + | 0.997393i | \(0.522988\pi\) | |||||||
\(930\) | 13240.2 | 0.466842 | ||||||||
\(931\) | −46081.6 | −1.62219 | ||||||||
\(932\) | 55678.2 | 1.95687 | ||||||||
\(933\) | −382.455 | −0.0134202 | ||||||||
\(934\) | −50583.0 | −1.77209 | ||||||||
\(935\) | −2671.47 | −0.0934401 | ||||||||
\(936\) | −80680.8 | −2.81745 | ||||||||
\(937\) | −42025.6 | −1.46523 | −0.732613 | − | 0.680646i | \(-0.761699\pi\) | ||||
−0.732613 | + | 0.680646i | \(0.761699\pi\) | |||||||
\(938\) | 104094. | 3.62344 | ||||||||
\(939\) | −5792.93 | −0.201326 | ||||||||
\(940\) | −84572.8 | −2.93453 | ||||||||
\(941\) | −7204.96 | −0.249602 | −0.124801 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124801 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(942\) | 307.754 | 0.0106446 | ||||||||
\(943\) | 6149.40 | 0.212356 | ||||||||
\(944\) | −29006.0 | −1.00007 | ||||||||
\(945\) | −26886.0 | −0.925504 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38797.3 | 1.33130 | 0.665651 | − | 0.746263i | \(-0.268154\pi\) | ||||
0.665651 | + | 0.746263i | \(0.268154\pi\) | |||||||
\(948\) | −20548.8 | −0.704003 | ||||||||
\(949\) | −44286.2 | −1.51485 | ||||||||
\(950\) | 3091.64 | 0.105585 | ||||||||
\(951\) | 5762.15 | 0.196478 | ||||||||
\(952\) | 76196.8 | 2.59407 | ||||||||
\(953\) | −43711.5 | −1.48579 | −0.742893 | − | 0.669410i | \(-0.766547\pi\) | ||||
−0.742893 | + | 0.669410i | \(0.766547\pi\) | |||||||
\(954\) | 49928.4 | 1.69443 | ||||||||
\(955\) | −26626.9 | −0.902226 | ||||||||
\(956\) | −36717.9 | −1.24220 | ||||||||
\(957\) | −537.637 | −0.0181602 | ||||||||
\(958\) | −50007.9 | −1.68652 | ||||||||
\(959\) | 6565.39 | 0.221071 | ||||||||
\(960\) | 6450.86 | 0.216876 | ||||||||
\(961\) | 5998.85 | 0.201365 | ||||||||
\(962\) | −24459.7 | −0.819764 | ||||||||
\(963\) | 6200.30 | 0.207479 | ||||||||
\(964\) | −110949. | −3.70687 | ||||||||
\(965\) | −37224.8 | −1.24177 | ||||||||
\(966\) | 10693.9 | 0.356180 | ||||||||
\(967\) | −9219.24 | −0.306588 | −0.153294 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153294 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(968\) | 53569.8 | 1.77872 | ||||||||
\(969\) | −3018.66 | −0.100076 | ||||||||
\(970\) | 16749.1 | 0.554413 | ||||||||
\(971\) | −3770.19 | −0.124605 | −0.0623023 | − | 0.998057i | \(-0.519844\pi\) | ||||
−0.0623023 | + | 0.998057i | \(0.519844\pi\) | |||||||
\(972\) | 39993.8 | 1.31976 | ||||||||
\(973\) | 7575.90 | 0.249612 | ||||||||
\(974\) | 43050.9 | 1.41626 | ||||||||
\(975\) | −1216.37 | −0.0399540 | ||||||||
\(976\) | 4289.48 | 0.140679 | ||||||||
\(977\) | 40226.1 | 1.31724 | 0.658622 | − | 0.752474i | \(-0.271140\pi\) | ||||
0.658622 | + | 0.752474i | \(0.271140\pi\) | |||||||
\(978\) | −17337.7 | −0.566870 | ||||||||
\(979\) | −446.828 | −0.0145870 | ||||||||
\(980\) | −182817. | −5.95906 | ||||||||
\(981\) | 16965.5 | 0.552157 | ||||||||
\(982\) | 37350.0 | 1.21373 | ||||||||
\(983\) | −8280.68 | −0.268680 | −0.134340 | − | 0.990935i | \(-0.542891\pi\) | ||||
−0.134340 | + | 0.990935i | \(0.542891\pi\) | |||||||
\(984\) | −6094.49 | −0.197444 | ||||||||
\(985\) | −50524.1 | −1.63435 | ||||||||
\(986\) | 25838.8 | 0.834558 | ||||||||
\(987\) | −19254.6 | −0.620953 | ||||||||
\(988\) | 60762.1 | 1.95658 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6493.81 | −0.208471 | ||||||||
\(991\) | 14631.2 | 0.468997 | 0.234498 | − | 0.972117i | \(-0.424655\pi\) | ||||
0.234498 | + | 0.972117i | \(0.424655\pi\) | |||||||
\(992\) | −4357.45 | −0.139465 | ||||||||
\(993\) | 8308.15 | 0.265510 | ||||||||
\(994\) | 24572.9 | 0.784110 | ||||||||
\(995\) | 4060.79 | 0.129383 | ||||||||
\(996\) | −10270.0 | −0.326723 | ||||||||
\(997\) | 7486.54 | 0.237814 | 0.118907 | − | 0.992905i | \(-0.462061\pi\) | ||||
0.118907 | + | 0.992905i | \(0.462061\pi\) | |||||||
\(998\) | −78209.3 | −2.48063 | ||||||||
\(999\) | 4075.03 | 0.129057 |
(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.k.1.6 | 60 | ||
43.30 | odd | 42 | 43.4.g.a.40.1 | yes | 120 | ||
43.33 | odd | 42 | 43.4.g.a.14.1 | ✓ | 120 | ||
43.42 | odd | 2 | 1849.4.a.l.1.55 | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.g.a.14.1 | ✓ | 120 | 43.33 | odd | 42 | ||
43.4.g.a.40.1 | yes | 120 | 43.30 | odd | 42 | ||
1849.4.a.k.1.6 | 60 | 1.1 | even | 1 | trivial | ||
1849.4.a.l.1.55 | 60 | 43.42 | odd | 2 |