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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.179767\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.179767 | −0.0635573 | −0.0317786 | − | 0.999495i | \(-0.510117\pi\) | ||||
−0.0317786 | + | 0.999495i | \(0.510117\pi\) | |||||||
\(3\) | 6.02248 | 1.15903 | 0.579513 | − | 0.814963i | \(-0.303243\pi\) | ||||
0.579513 | + | 0.814963i | \(0.303243\pi\) | |||||||
\(4\) | −7.96768 | −0.995960 | ||||||||
\(5\) | 10.9703 | 0.981217 | 0.490609 | − | 0.871380i | \(-0.336774\pi\) | ||||
0.490609 | + | 0.871380i | \(0.336774\pi\) | |||||||
\(6\) | −1.08264 | −0.0736646 | ||||||||
\(7\) | −8.78367 | −0.474273 | −0.237137 | − | 0.971476i | \(-0.576209\pi\) | ||||
−0.237137 | + | 0.971476i | \(0.576209\pi\) | |||||||
\(8\) | 2.87047 | 0.126858 | ||||||||
\(9\) | 9.27026 | 0.343343 | ||||||||
\(10\) | −1.97211 | −0.0623635 | ||||||||
\(11\) | 46.3162 | 1.26953 | 0.634766 | − | 0.772705i | \(-0.281097\pi\) | ||||
0.634766 | + | 0.772705i | \(0.281097\pi\) | |||||||
\(12\) | −47.9852 | −1.15434 | ||||||||
\(13\) | 11.3698 | 0.242571 | 0.121285 | − | 0.992618i | \(-0.461298\pi\) | ||||
0.121285 | + | 0.992618i | \(0.461298\pi\) | |||||||
\(14\) | 1.57901 | 0.0301435 | ||||||||
\(15\) | 66.0687 | 1.13726 | ||||||||
\(16\) | 63.2255 | 0.987898 | ||||||||
\(17\) | −50.4617 | −0.719927 | −0.359963 | − | 0.932966i | \(-0.617211\pi\) | ||||
−0.359963 | + | 0.932966i | \(0.617211\pi\) | |||||||
\(18\) | −1.66649 | −0.0218219 | ||||||||
\(19\) | −108.773 | −1.31338 | −0.656688 | − | 0.754162i | \(-0.728043\pi\) | ||||
−0.656688 | + | 0.754162i | \(0.728043\pi\) | |||||||
\(20\) | −87.4082 | −0.977254 | ||||||||
\(21\) | −52.8995 | −0.549696 | ||||||||
\(22\) | −8.32612 | −0.0806880 | ||||||||
\(23\) | 54.6579 | 0.495520 | 0.247760 | − | 0.968821i | \(-0.420306\pi\) | ||||
0.247760 | + | 0.968821i | \(0.420306\pi\) | |||||||
\(24\) | 17.2873 | 0.147032 | ||||||||
\(25\) | −4.65154 | −0.0372123 | ||||||||
\(26\) | −2.04392 | −0.0154171 | ||||||||
\(27\) | −106.777 | −0.761083 | ||||||||
\(28\) | 69.9855 | 0.472358 | ||||||||
\(29\) | −146.430 | −0.937636 | −0.468818 | − | 0.883295i | \(-0.655320\pi\) | ||||
−0.468818 | + | 0.883295i | \(0.655320\pi\) | |||||||
\(30\) | −11.8770 | −0.0722810 | ||||||||
\(31\) | −218.022 | −1.26316 | −0.631579 | − | 0.775311i | \(-0.717593\pi\) | ||||
−0.631579 | + | 0.775311i | \(0.717593\pi\) | |||||||
\(32\) | −34.3296 | −0.189646 | ||||||||
\(33\) | 278.938 | 1.47142 | ||||||||
\(34\) | 9.07135 | 0.0457566 | ||||||||
\(35\) | −96.3599 | −0.465365 | ||||||||
\(36\) | −73.8625 | −0.341956 | ||||||||
\(37\) | 99.5281 | 0.442225 | 0.221113 | − | 0.975248i | \(-0.429031\pi\) | ||||
0.221113 | + | 0.975248i | \(0.429031\pi\) | |||||||
\(38\) | 19.5538 | 0.0834747 | ||||||||
\(39\) | 68.4745 | 0.281146 | ||||||||
\(40\) | 31.4900 | 0.124475 | ||||||||
\(41\) | −343.185 | −1.30723 | −0.653616 | − | 0.756826i | \(-0.726749\pi\) | ||||
−0.653616 | + | 0.756826i | \(0.726749\pi\) | |||||||
\(42\) | 9.50959 | 0.0349372 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −369.032 | −1.26440 | ||||||||
\(45\) | 101.698 | 0.336894 | ||||||||
\(46\) | −9.82570 | −0.0314939 | ||||||||
\(47\) | 136.751 | 0.424408 | 0.212204 | − | 0.977225i | \(-0.431936\pi\) | ||||
0.212204 | + | 0.977225i | \(0.431936\pi\) | |||||||
\(48\) | 380.774 | 1.14500 | ||||||||
\(49\) | −265.847 | −0.775065 | ||||||||
\(50\) | 0.836195 | 0.00236512 | ||||||||
\(51\) | −303.904 | −0.834414 | ||||||||
\(52\) | −90.5911 | −0.241591 | ||||||||
\(53\) | 472.691 | 1.22508 | 0.612539 | − | 0.790440i | \(-0.290148\pi\) | ||||
0.612539 | + | 0.790440i | \(0.290148\pi\) | |||||||
\(54\) | 19.1950 | 0.0483724 | ||||||||
\(55\) | 508.104 | 1.24569 | ||||||||
\(56\) | −25.2132 | −0.0601653 | ||||||||
\(57\) | −655.081 | −1.52224 | ||||||||
\(58\) | 26.3234 | 0.0595936 | ||||||||
\(59\) | −626.211 | −1.38179 | −0.690896 | − | 0.722955i | \(-0.742784\pi\) | ||||
−0.690896 | + | 0.722955i | \(0.742784\pi\) | |||||||
\(60\) | −526.414 | −1.13266 | ||||||||
\(61\) | 59.9402 | 0.125812 | 0.0629062 | − | 0.998019i | \(-0.479963\pi\) | ||||
0.0629062 | + | 0.998019i | \(0.479963\pi\) | |||||||
\(62\) | 39.1932 | 0.0802830 | ||||||||
\(63\) | −81.4269 | −0.162838 | ||||||||
\(64\) | −499.632 | −0.975844 | ||||||||
\(65\) | 124.731 | 0.238015 | ||||||||
\(66\) | −50.1439 | −0.0935195 | ||||||||
\(67\) | 1065.79 | 1.94339 | 0.971693 | − | 0.236248i | \(-0.0759179\pi\) | ||||
0.971693 | + | 0.236248i | \(0.0759179\pi\) | |||||||
\(68\) | 402.063 | 0.717018 | ||||||||
\(69\) | 329.176 | 0.574321 | ||||||||
\(70\) | 17.3223 | 0.0295774 | ||||||||
\(71\) | 1106.95 | 1.85029 | 0.925144 | − | 0.379616i | \(-0.123944\pi\) | ||||
0.925144 | + | 0.379616i | \(0.123944\pi\) | |||||||
\(72\) | 26.6100 | 0.0435557 | ||||||||
\(73\) | −739.936 | −1.18634 | −0.593171 | − | 0.805077i | \(-0.702124\pi\) | ||||
−0.593171 | + | 0.805077i | \(0.702124\pi\) | |||||||
\(74\) | −17.8919 | −0.0281066 | ||||||||
\(75\) | −28.0138 | −0.0431301 | ||||||||
\(76\) | 866.666 | 1.30807 | ||||||||
\(77\) | −406.826 | −0.602105 | ||||||||
\(78\) | −12.3095 | −0.0178689 | ||||||||
\(79\) | 129.283 | 0.184120 | 0.0920599 | − | 0.995753i | \(-0.470655\pi\) | ||||
0.0920599 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(80\) | 693.605 | 0.969342 | ||||||||
\(81\) | −893.359 | −1.22546 | ||||||||
\(82\) | 61.6934 | 0.0830841 | ||||||||
\(83\) | 211.790 | 0.280085 | 0.140042 | − | 0.990146i | \(-0.455276\pi\) | ||||
0.140042 | + | 0.990146i | \(0.455276\pi\) | |||||||
\(84\) | 421.486 | 0.547475 | ||||||||
\(85\) | −553.582 | −0.706405 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −881.874 | −1.08675 | ||||||||
\(88\) | 132.949 | 0.161050 | ||||||||
\(89\) | −102.968 | −0.122636 | −0.0613179 | − | 0.998118i | \(-0.519530\pi\) | ||||
−0.0613179 | + | 0.998118i | \(0.519530\pi\) | |||||||
\(90\) | −18.2820 | −0.0214121 | ||||||||
\(91\) | −99.8687 | −0.115045 | ||||||||
\(92\) | −435.497 | −0.493518 | ||||||||
\(93\) | −1313.03 | −1.46403 | ||||||||
\(94\) | −24.5833 | −0.0269742 | ||||||||
\(95\) | −1193.27 | −1.28871 | ||||||||
\(96\) | −206.749 | −0.219805 | ||||||||
\(97\) | 828.788 | 0.867532 | 0.433766 | − | 0.901025i | \(-0.357184\pi\) | ||||
0.433766 | + | 0.901025i | \(0.357184\pi\) | |||||||
\(98\) | 47.7906 | 0.0492610 | ||||||||
\(99\) | 429.363 | 0.435885 | ||||||||
\(100\) | 37.0620 | 0.0370620 | ||||||||
\(101\) | 1066.33 | 1.05053 | 0.525267 | − | 0.850938i | \(-0.323966\pi\) | ||||
0.525267 | + | 0.850938i | \(0.323966\pi\) | |||||||
\(102\) | 54.6320 | 0.0530331 | ||||||||
\(103\) | −1766.45 | −1.68984 | −0.844920 | − | 0.534893i | \(-0.820352\pi\) | ||||
−0.844920 | + | 0.534893i | \(0.820352\pi\) | |||||||
\(104\) | 32.6367 | 0.0307720 | ||||||||
\(105\) | −580.325 | −0.539371 | ||||||||
\(106\) | −84.9744 | −0.0778626 | ||||||||
\(107\) | −1842.93 | −1.66508 | −0.832538 | − | 0.553968i | \(-0.813113\pi\) | ||||
−0.832538 | + | 0.553968i | \(0.813113\pi\) | |||||||
\(108\) | 850.765 | 0.758009 | ||||||||
\(109\) | −621.315 | −0.545974 | −0.272987 | − | 0.962018i | \(-0.588012\pi\) | ||||
−0.272987 | + | 0.962018i | \(0.588012\pi\) | |||||||
\(110\) | −91.3404 | −0.0791724 | ||||||||
\(111\) | 599.406 | 0.512551 | ||||||||
\(112\) | −555.351 | −0.468534 | ||||||||
\(113\) | −800.425 | −0.666351 | −0.333175 | − | 0.942865i | \(-0.608120\pi\) | ||||
−0.333175 | + | 0.942865i | \(0.608120\pi\) | |||||||
\(114\) | 117.762 | 0.0967494 | ||||||||
\(115\) | 599.616 | 0.486213 | ||||||||
\(116\) | 1166.71 | 0.933849 | ||||||||
\(117\) | 105.401 | 0.0832849 | ||||||||
\(118\) | 112.572 | 0.0878229 | ||||||||
\(119\) | 443.239 | 0.341442 | ||||||||
\(120\) | 189.648 | 0.144270 | ||||||||
\(121\) | 814.186 | 0.611710 | ||||||||
\(122\) | −10.7753 | −0.00799630 | ||||||||
\(123\) | −2066.83 | −1.51512 | ||||||||
\(124\) | 1737.13 | 1.25806 | ||||||||
\(125\) | −1422.32 | −1.01773 | ||||||||
\(126\) | 14.6379 | 0.0103496 | ||||||||
\(127\) | −1398.51 | −0.977144 | −0.488572 | − | 0.872523i | \(-0.662482\pi\) | ||||
−0.488572 | + | 0.872523i | \(0.662482\pi\) | |||||||
\(128\) | 364.454 | 0.251668 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.4225 | −0.0151276 | ||||||||
\(131\) | −684.081 | −0.456248 | −0.228124 | − | 0.973632i | \(-0.573259\pi\) | ||||
−0.228124 | + | 0.973632i | \(0.573259\pi\) | |||||||
\(132\) | −2222.49 | −1.46548 | ||||||||
\(133\) | 955.423 | 0.622900 | ||||||||
\(134\) | −191.594 | −0.123516 | ||||||||
\(135\) | −1171.38 | −0.746788 | ||||||||
\(136\) | −144.848 | −0.0913283 | ||||||||
\(137\) | 379.077 | 0.236400 | 0.118200 | − | 0.992990i | \(-0.462288\pi\) | ||||
0.118200 | + | 0.992990i | \(0.462288\pi\) | |||||||
\(138\) | −59.1751 | −0.0365023 | ||||||||
\(139\) | −142.612 | −0.0870231 | −0.0435116 | − | 0.999053i | \(-0.513855\pi\) | ||||
−0.0435116 | + | 0.999053i | \(0.513855\pi\) | |||||||
\(140\) | 767.765 | 0.463486 | ||||||||
\(141\) | 823.580 | 0.491900 | ||||||||
\(142\) | −198.993 | −0.117599 | ||||||||
\(143\) | 526.606 | 0.307951 | ||||||||
\(144\) | 586.116 | 0.339188 | ||||||||
\(145\) | −1606.39 | −0.920025 | ||||||||
\(146\) | 133.016 | 0.0754007 | ||||||||
\(147\) | −1601.06 | −0.898321 | ||||||||
\(148\) | −793.009 | −0.440439 | ||||||||
\(149\) | −2368.91 | −1.30247 | −0.651236 | − | 0.758875i | \(-0.725749\pi\) | ||||
−0.651236 | + | 0.758875i | \(0.725749\pi\) | |||||||
\(150\) | 5.03596 | 0.00274123 | ||||||||
\(151\) | −310.386 | −0.167277 | −0.0836387 | − | 0.996496i | \(-0.526654\pi\) | ||||
−0.0836387 | + | 0.996496i | \(0.526654\pi\) | |||||||
\(152\) | −312.228 | −0.166612 | ||||||||
\(153\) | −467.793 | −0.247182 | ||||||||
\(154\) | 73.1339 | 0.0382682 | ||||||||
\(155\) | −2391.78 | −1.23943 | ||||||||
\(156\) | −545.583 | −0.280010 | ||||||||
\(157\) | −2789.22 | −1.41786 | −0.708931 | − | 0.705278i | \(-0.750822\pi\) | ||||
−0.708931 | + | 0.705278i | \(0.750822\pi\) | |||||||
\(158\) | −23.2408 | −0.0117022 | ||||||||
\(159\) | 2846.77 | 1.41990 | ||||||||
\(160\) | −376.607 | −0.186084 | ||||||||
\(161\) | −480.097 | −0.235012 | ||||||||
\(162\) | 160.597 | 0.0778868 | ||||||||
\(163\) | 902.183 | 0.433524 | 0.216762 | − | 0.976224i | \(-0.430450\pi\) | ||||
0.216762 | + | 0.976224i | \(0.430450\pi\) | |||||||
\(164\) | 2734.39 | 1.30195 | ||||||||
\(165\) | 3060.05 | 1.44378 | ||||||||
\(166\) | −38.0730 | −0.0178014 | ||||||||
\(167\) | −465.543 | −0.215717 | −0.107859 | − | 0.994166i | \(-0.534399\pi\) | ||||
−0.107859 | + | 0.994166i | \(0.534399\pi\) | |||||||
\(168\) | −151.846 | −0.0697332 | ||||||||
\(169\) | −2067.73 | −0.941159 | ||||||||
\(170\) | 99.5159 | 0.0448972 | ||||||||
\(171\) | −1008.35 | −0.450939 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1590.49 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(174\) | 158.532 | 0.0690706 | ||||||||
\(175\) | 40.8576 | 0.0176488 | ||||||||
\(176\) | 2928.36 | 1.25417 | ||||||||
\(177\) | −3771.34 | −1.60153 | ||||||||
\(178\) | 18.5103 | 0.00779440 | ||||||||
\(179\) | 167.955 | 0.0701317 | 0.0350658 | − | 0.999385i | \(-0.488836\pi\) | ||||
0.0350658 | + | 0.999385i | \(0.488836\pi\) | |||||||
\(180\) | −810.297 | −0.335533 | ||||||||
\(181\) | 1728.02 | 0.709630 | 0.354815 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354815 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(182\) | 17.9531 | 0.00731194 | ||||||||
\(183\) | 360.989 | 0.145820 | ||||||||
\(184\) | 156.894 | 0.0628606 | ||||||||
\(185\) | 1091.86 | 0.433919 | ||||||||
\(186\) | 236.040 | 0.0930501 | ||||||||
\(187\) | −2337.19 | −0.913969 | ||||||||
\(188\) | −1089.59 | −0.422694 | ||||||||
\(189\) | 937.894 | 0.360961 | ||||||||
\(190\) | 214.511 | 0.0819068 | ||||||||
\(191\) | 5178.15 | 1.96166 | 0.980832 | − | 0.194854i | \(-0.0624234\pi\) | ||||
0.980832 | + | 0.194854i | \(0.0624234\pi\) | |||||||
\(192\) | −3009.03 | −1.13103 | ||||||||
\(193\) | −5142.11 | −1.91781 | −0.958905 | − | 0.283729i | \(-0.908428\pi\) | ||||
−0.958905 | + | 0.283729i | \(0.908428\pi\) | |||||||
\(194\) | −148.989 | −0.0551380 | ||||||||
\(195\) | 751.189 | 0.275865 | ||||||||
\(196\) | 2118.19 | 0.771934 | ||||||||
\(197\) | 1749.19 | 0.632614 | 0.316307 | − | 0.948657i | \(-0.397557\pi\) | ||||
0.316307 | + | 0.948657i | \(0.397557\pi\) | |||||||
\(198\) | −77.1853 | −0.0277036 | ||||||||
\(199\) | 1298.98 | 0.462724 | 0.231362 | − | 0.972868i | \(-0.425682\pi\) | ||||
0.231362 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(200\) | −13.3521 | −0.00472068 | ||||||||
\(201\) | 6418.69 | 2.25244 | ||||||||
\(202\) | −191.691 | −0.0667691 | ||||||||
\(203\) | 1286.20 | 0.444696 | ||||||||
\(204\) | 2421.41 | 0.831044 | ||||||||
\(205\) | −3764.86 | −1.28268 | ||||||||
\(206\) | 317.550 | 0.107402 | ||||||||
\(207\) | 506.693 | 0.170133 | ||||||||
\(208\) | 718.862 | 0.239635 | ||||||||
\(209\) | −5037.93 | −1.66737 | ||||||||
\(210\) | 104.323 | 0.0342810 | ||||||||
\(211\) | −3800.59 | −1.24001 | −0.620007 | − | 0.784596i | \(-0.712870\pi\) | ||||
−0.620007 | + | 0.784596i | \(0.712870\pi\) | |||||||
\(212\) | −3766.25 | −1.22013 | ||||||||
\(213\) | 6666.57 | 2.14453 | ||||||||
\(214\) | 331.299 | 0.105828 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −306.500 | −0.0965494 | ||||||||
\(217\) | 1915.03 | 0.599083 | ||||||||
\(218\) | 111.692 | 0.0347006 | ||||||||
\(219\) | −4456.25 | −1.37500 | ||||||||
\(220\) | −4048.41 | −1.24065 | ||||||||
\(221\) | −573.740 | −0.174633 | ||||||||
\(222\) | −107.754 | −0.0325763 | ||||||||
\(223\) | −6061.77 | −1.82030 | −0.910148 | − | 0.414283i | \(-0.864032\pi\) | ||||
−0.910148 | + | 0.414283i | \(0.864032\pi\) | |||||||
\(224\) | 301.540 | 0.0899440 | ||||||||
\(225\) | −43.1210 | −0.0127766 | ||||||||
\(226\) | 143.890 | 0.0423514 | ||||||||
\(227\) | −4088.42 | −1.19541 | −0.597705 | − | 0.801716i | \(-0.703921\pi\) | ||||
−0.597705 | + | 0.801716i | \(0.703921\pi\) | |||||||
\(228\) | 5219.48 | 1.51609 | ||||||||
\(229\) | −2877.79 | −0.830437 | −0.415218 | − | 0.909722i | \(-0.636295\pi\) | ||||
−0.415218 | + | 0.909722i | \(0.636295\pi\) | |||||||
\(230\) | −107.791 | −0.0309024 | ||||||||
\(231\) | −2450.10 | −0.697856 | ||||||||
\(232\) | −420.324 | −0.118947 | ||||||||
\(233\) | 1902.91 | 0.535038 | 0.267519 | − | 0.963553i | \(-0.413796\pi\) | ||||
0.267519 | + | 0.963553i | \(0.413796\pi\) | |||||||
\(234\) | −18.9477 | −0.00529337 | ||||||||
\(235\) | 1500.20 | 0.416436 | ||||||||
\(236\) | 4989.45 | 1.37621 | ||||||||
\(237\) | 778.603 | 0.213400 | ||||||||
\(238\) | −79.6797 | −0.0217011 | ||||||||
\(239\) | −1734.10 | −0.469330 | −0.234665 | − | 0.972076i | \(-0.575399\pi\) | ||||
−0.234665 | + | 0.972076i | \(0.575399\pi\) | |||||||
\(240\) | 4177.22 | 1.12349 | ||||||||
\(241\) | −4551.08 | −1.21643 | −0.608217 | − | 0.793771i | \(-0.708115\pi\) | ||||
−0.608217 | + | 0.793771i | \(0.708115\pi\) | |||||||
\(242\) | −146.364 | −0.0388786 | ||||||||
\(243\) | −2497.26 | −0.659256 | ||||||||
\(244\) | −477.585 | −0.125304 | ||||||||
\(245\) | −2916.44 | −0.760507 | ||||||||
\(246\) | 371.547 | 0.0962967 | ||||||||
\(247\) | −1236.73 | −0.318587 | ||||||||
\(248\) | −625.825 | −0.160242 | ||||||||
\(249\) | 1275.50 | 0.324626 | ||||||||
\(250\) | 255.687 | 0.0646842 | ||||||||
\(251\) | 2331.55 | 0.586318 | 0.293159 | − | 0.956064i | \(-0.405293\pi\) | ||||
0.293159 | + | 0.956064i | \(0.405293\pi\) | |||||||
\(252\) | 648.784 | 0.162181 | ||||||||
\(253\) | 2531.54 | 0.629078 | ||||||||
\(254\) | 251.405 | 0.0621047 | ||||||||
\(255\) | −3333.94 | −0.818742 | ||||||||
\(256\) | 3931.54 | 0.959849 | ||||||||
\(257\) | 4135.09 | 1.00366 | 0.501829 | − | 0.864967i | \(-0.332661\pi\) | ||||
0.501829 | + | 0.864967i | \(0.332661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −874.222 | −0.209736 | ||||||||
\(260\) | −993.815 | −0.237053 | ||||||||
\(261\) | −1357.45 | −0.321931 | ||||||||
\(262\) | 122.975 | 0.0289979 | ||||||||
\(263\) | −3680.89 | −0.863016 | −0.431508 | − | 0.902109i | \(-0.642018\pi\) | ||||
−0.431508 | + | 0.902109i | \(0.642018\pi\) | |||||||
\(264\) | 800.682 | 0.186661 | ||||||||
\(265\) | 5185.58 | 1.20207 | ||||||||
\(266\) | −171.754 | −0.0395898 | ||||||||
\(267\) | −620.123 | −0.142138 | ||||||||
\(268\) | −8491.87 | −1.93554 | ||||||||
\(269\) | −1522.77 | −0.345148 | −0.172574 | − | 0.984997i | \(-0.555208\pi\) | ||||
−0.172574 | + | 0.984997i | \(0.555208\pi\) | |||||||
\(270\) | 210.576 | 0.0474638 | ||||||||
\(271\) | 6268.22 | 1.40505 | 0.702523 | − | 0.711661i | \(-0.252057\pi\) | ||||
0.702523 | + | 0.711661i | \(0.252057\pi\) | |||||||
\(272\) | −3190.46 | −0.711214 | ||||||||
\(273\) | −601.457 | −0.133340 | ||||||||
\(274\) | −68.1457 | −0.0150249 | ||||||||
\(275\) | −215.442 | −0.0472422 | ||||||||
\(276\) | −2622.77 | −0.572001 | ||||||||
\(277\) | 5011.99 | 1.08715 | 0.543576 | − | 0.839360i | \(-0.317070\pi\) | ||||
0.543576 | + | 0.839360i | \(0.317070\pi\) | |||||||
\(278\) | 25.6370 | 0.00553095 | ||||||||
\(279\) | −2021.12 | −0.433697 | ||||||||
\(280\) | −276.598 | −0.0590352 | ||||||||
\(281\) | 7611.02 | 1.61578 | 0.807892 | − | 0.589330i | \(-0.200608\pi\) | ||||
0.807892 | + | 0.589330i | \(0.200608\pi\) | |||||||
\(282\) | −148.053 | −0.0312638 | ||||||||
\(283\) | −133.300 | −0.0279995 | −0.0139998 | − | 0.999902i | \(-0.504456\pi\) | ||||
−0.0139998 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(284\) | −8819.80 | −1.84281 | ||||||||
\(285\) | −7186.47 | −1.49365 | ||||||||
\(286\) | −94.6665 | −0.0195725 | ||||||||
\(287\) | 3014.42 | 0.619985 | ||||||||
\(288\) | −318.244 | −0.0651136 | ||||||||
\(289\) | −2366.62 | −0.481706 | ||||||||
\(290\) | 288.777 | 0.0584743 | ||||||||
\(291\) | 4991.36 | 1.00549 | ||||||||
\(292\) | 5895.57 | 1.18155 | ||||||||
\(293\) | −926.124 | −0.184658 | −0.0923289 | − | 0.995729i | \(-0.529431\pi\) | ||||
−0.0923289 | + | 0.995729i | \(0.529431\pi\) | |||||||
\(294\) | 287.818 | 0.0570948 | ||||||||
\(295\) | −6869.75 | −1.35584 | ||||||||
\(296\) | 285.692 | 0.0560997 | ||||||||
\(297\) | −4945.50 | −0.966219 | ||||||||
\(298\) | 425.851 | 0.0827816 | ||||||||
\(299\) | 621.450 | 0.120199 | ||||||||
\(300\) | 223.205 | 0.0429559 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 55.7973 | 0.0106317 | ||||||||
\(303\) | 6421.95 | 1.21760 | ||||||||
\(304\) | −6877.20 | −1.29748 | ||||||||
\(305\) | 657.565 | 0.123449 | ||||||||
\(306\) | 84.0938 | 0.0157102 | ||||||||
\(307\) | −4658.81 | −0.866099 | −0.433049 | − | 0.901370i | \(-0.642562\pi\) | ||||
−0.433049 | + | 0.901370i | \(0.642562\pi\) | |||||||
\(308\) | 3241.46 | 0.599673 | ||||||||
\(309\) | −10638.4 | −1.95857 | ||||||||
\(310\) | 429.963 | 0.0787750 | ||||||||
\(311\) | 8026.62 | 1.46350 | 0.731749 | − | 0.681575i | \(-0.238705\pi\) | ||||
0.731749 | + | 0.681575i | \(0.238705\pi\) | |||||||
\(312\) | 196.554 | 0.0356656 | ||||||||
\(313\) | −2987.24 | −0.539454 | −0.269727 | − | 0.962937i | \(-0.586933\pi\) | ||||
−0.269727 | + | 0.962937i | \(0.586933\pi\) | |||||||
\(314\) | 501.411 | 0.0901154 | ||||||||
\(315\) | −893.281 | −0.159780 | ||||||||
\(316\) | −1030.08 | −0.183376 | ||||||||
\(317\) | −2897.23 | −0.513327 | −0.256663 | − | 0.966501i | \(-0.582623\pi\) | ||||
−0.256663 | + | 0.966501i | \(0.582623\pi\) | |||||||
\(318\) | −511.756 | −0.0902449 | ||||||||
\(319\) | −6782.10 | −1.19036 | ||||||||
\(320\) | −5481.14 | −0.957515 | ||||||||
\(321\) | −11099.0 | −1.92987 | ||||||||
\(322\) | 86.3057 | 0.0149367 | ||||||||
\(323\) | 5488.85 | 0.945535 | ||||||||
\(324\) | 7118.00 | 1.22051 | ||||||||
\(325\) | −52.8872 | −0.00902662 | ||||||||
\(326\) | −162.183 | −0.0275536 | ||||||||
\(327\) | −3741.86 | −0.632798 | ||||||||
\(328\) | −985.101 | −0.165833 | ||||||||
\(329\) | −1201.17 | −0.201285 | ||||||||
\(330\) | −550.096 | −0.0917630 | ||||||||
\(331\) | −1748.09 | −0.290283 | −0.145142 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145142 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(332\) | −1687.48 | −0.278953 | ||||||||
\(333\) | 922.652 | 0.151835 | ||||||||
\(334\) | 83.6893 | 0.0137104 | ||||||||
\(335\) | 11692.1 | 1.90688 | ||||||||
\(336\) | −3344.59 | −0.543043 | ||||||||
\(337\) | −11113.9 | −1.79648 | −0.898239 | − | 0.439508i | \(-0.855153\pi\) | ||||
−0.898239 | + | 0.439508i | \(0.855153\pi\) | |||||||
\(338\) | 371.709 | 0.0598175 | ||||||||
\(339\) | −4820.54 | −0.772318 | ||||||||
\(340\) | 4410.77 | 0.703551 | ||||||||
\(341\) | −10097.9 | −1.60362 | ||||||||
\(342\) | 181.268 | 0.0286604 | ||||||||
\(343\) | 5347.91 | 0.841866 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3611.18 | 0.563534 | ||||||||
\(346\) | −285.918 | −0.0444249 | ||||||||
\(347\) | 3843.41 | 0.594596 | 0.297298 | − | 0.954785i | \(-0.403914\pi\) | ||||
0.297298 | + | 0.954785i | \(0.403914\pi\) | |||||||
\(348\) | 7026.50 | 1.08236 | ||||||||
\(349\) | 8760.22 | 1.34362 | 0.671811 | − | 0.740723i | \(-0.265517\pi\) | ||||
0.671811 | + | 0.740723i | \(0.265517\pi\) | |||||||
\(350\) | −7.34486 | −0.00112171 | ||||||||
\(351\) | −1214.03 | −0.184616 | ||||||||
\(352\) | −1590.01 | −0.240761 | ||||||||
\(353\) | 5665.74 | 0.854269 | 0.427134 | − | 0.904188i | \(-0.359523\pi\) | ||||
0.427134 | + | 0.904188i | \(0.359523\pi\) | |||||||
\(354\) | 677.963 | 0.101789 | ||||||||
\(355\) | 12143.6 | 1.81554 | ||||||||
\(356\) | 820.416 | 0.122140 | ||||||||
\(357\) | 2669.39 | 0.395740 | ||||||||
\(358\) | −30.1929 | −0.00445738 | ||||||||
\(359\) | 11124.2 | 1.63541 | 0.817706 | − | 0.575636i | \(-0.195246\pi\) | ||||
0.817706 | + | 0.575636i | \(0.195246\pi\) | |||||||
\(360\) | 291.920 | 0.0427377 | ||||||||
\(361\) | 4972.49 | 0.724959 | ||||||||
\(362\) | −310.642 | −0.0451021 | ||||||||
\(363\) | 4903.42 | 0.708988 | ||||||||
\(364\) | 795.722 | 0.114580 | ||||||||
\(365\) | −8117.35 | −1.16406 | ||||||||
\(366\) | −64.8939 | −0.00926792 | ||||||||
\(367\) | 227.952 | 0.0324224 | 0.0162112 | − | 0.999869i | \(-0.494840\pi\) | ||||
0.0162112 | + | 0.999869i | \(0.494840\pi\) | |||||||
\(368\) | 3455.77 | 0.489523 | ||||||||
\(369\) | −3181.42 | −0.448829 | ||||||||
\(370\) | −196.280 | −0.0275787 | ||||||||
\(371\) | −4151.96 | −0.581022 | ||||||||
\(372\) | 10461.8 | 1.45812 | ||||||||
\(373\) | 1568.45 | 0.217725 | 0.108862 | − | 0.994057i | \(-0.465279\pi\) | ||||
0.108862 | + | 0.994057i | \(0.465279\pi\) | |||||||
\(374\) | 420.150 | 0.0580894 | ||||||||
\(375\) | −8565.91 | −1.17958 | ||||||||
\(376\) | 392.539 | 0.0538395 | ||||||||
\(377\) | −1664.89 | −0.227443 | ||||||||
\(378\) | −168.602 | −0.0229417 | ||||||||
\(379\) | 7004.15 | 0.949286 | 0.474643 | − | 0.880179i | \(-0.342577\pi\) | ||||
0.474643 | + | 0.880179i | \(0.342577\pi\) | |||||||
\(380\) | 9507.63 | 1.28350 | ||||||||
\(381\) | −8422.47 | −1.13254 | ||||||||
\(382\) | −930.862 | −0.124678 | ||||||||
\(383\) | 4031.43 | 0.537850 | 0.268925 | − | 0.963161i | \(-0.413332\pi\) | ||||
0.268925 | + | 0.963161i | \(0.413332\pi\) | |||||||
\(384\) | 2194.92 | 0.291690 | ||||||||
\(385\) | −4463.02 | −0.590796 | ||||||||
\(386\) | 924.383 | 0.121891 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6603.52 | −0.864028 | ||||||||
\(389\) | 9948.60 | 1.29669 | 0.648347 | − | 0.761345i | \(-0.275461\pi\) | ||||
0.648347 | + | 0.761345i | \(0.275461\pi\) | |||||||
\(390\) | −135.039 | −0.0175333 | ||||||||
\(391\) | −2758.13 | −0.356738 | ||||||||
\(392\) | −763.105 | −0.0983230 | ||||||||
\(393\) | −4119.87 | −0.528804 | ||||||||
\(394\) | −314.448 | −0.0402072 | ||||||||
\(395\) | 1418.28 | 0.180661 | ||||||||
\(396\) | −3421.03 | −0.434124 | ||||||||
\(397\) | 2056.77 | 0.260016 | 0.130008 | − | 0.991513i | \(-0.458500\pi\) | ||||
0.130008 | + | 0.991513i | \(0.458500\pi\) | |||||||
\(398\) | −233.513 | −0.0294095 | ||||||||
\(399\) | 5754.01 | 0.721957 | ||||||||
\(400\) | −294.096 | −0.0367620 | ||||||||
\(401\) | −8372.29 | −1.04262 | −0.521312 | − | 0.853366i | \(-0.674557\pi\) | ||||
−0.521312 | + | 0.853366i | \(0.674557\pi\) | |||||||
\(402\) | −1153.87 | −0.143159 | ||||||||
\(403\) | −2478.87 | −0.306405 | ||||||||
\(404\) | −8496.19 | −1.04629 | ||||||||
\(405\) | −9800.46 | −1.20244 | ||||||||
\(406\) | −231.216 | −0.0282637 | ||||||||
\(407\) | 4609.76 | 0.561419 | ||||||||
\(408\) | −872.347 | −0.105852 | ||||||||
\(409\) | −11934.3 | −1.44282 | −0.721409 | − | 0.692509i | \(-0.756505\pi\) | ||||
−0.721409 | + | 0.692509i | \(0.756505\pi\) | |||||||
\(410\) | 676.798 | 0.0815236 | ||||||||
\(411\) | 2282.99 | 0.273994 | ||||||||
\(412\) | 14074.5 | 1.68301 | ||||||||
\(413\) | 5500.43 | 0.655347 | ||||||||
\(414\) | −91.0868 | −0.0108132 | ||||||||
\(415\) | 2323.41 | 0.274824 | ||||||||
\(416\) | −390.321 | −0.0460026 | ||||||||
\(417\) | −858.879 | −0.100862 | ||||||||
\(418\) | 905.655 | 0.105974 | ||||||||
\(419\) | −10251.3 | −1.19525 | −0.597625 | − | 0.801776i | \(-0.703889\pi\) | ||||
−0.597625 | + | 0.801776i | \(0.703889\pi\) | |||||||
\(420\) | 4623.85 | 0.537192 | ||||||||
\(421\) | −5728.06 | −0.663108 | −0.331554 | − | 0.943436i | \(-0.607573\pi\) | ||||
−0.331554 | + | 0.943436i | \(0.607573\pi\) | |||||||
\(422\) | 683.220 | 0.0788120 | ||||||||
\(423\) | 1267.72 | 0.145717 | ||||||||
\(424\) | 1356.84 | 0.155411 | ||||||||
\(425\) | 234.725 | 0.0267902 | ||||||||
\(426\) | −1198.43 | −0.136301 | ||||||||
\(427\) | −526.495 | −0.0596695 | ||||||||
\(428\) | 14683.9 | 1.65835 | ||||||||
\(429\) | 3171.47 | 0.356924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7647.18 | −0.854644 | −0.427322 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427322 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(432\) | −6751.02 | −0.751872 | ||||||||
\(433\) | −10141.0 | −1.12551 | −0.562756 | − | 0.826623i | \(-0.690259\pi\) | ||||
−0.562756 | + | 0.826623i | \(0.690259\pi\) | |||||||
\(434\) | −344.260 | −0.0380761 | ||||||||
\(435\) | −9674.47 | −1.06633 | ||||||||
\(436\) | 4950.44 | 0.543768 | ||||||||
\(437\) | −5945.29 | −0.650805 | ||||||||
\(438\) | 801.087 | 0.0873914 | ||||||||
\(439\) | −15713.4 | −1.70833 | −0.854166 | − | 0.520000i | \(-0.825932\pi\) | ||||
−0.854166 | + | 0.520000i | \(0.825932\pi\) | |||||||
\(440\) | 1458.50 | 0.158025 | ||||||||
\(441\) | −2464.47 | −0.266113 | ||||||||
\(442\) | 103.140 | 0.0110992 | ||||||||
\(443\) | 1587.42 | 0.170250 | 0.0851248 | − | 0.996370i | \(-0.472871\pi\) | ||||
0.0851248 | + | 0.996370i | \(0.472871\pi\) | |||||||
\(444\) | −4775.88 | −0.510480 | ||||||||
\(445\) | −1129.59 | −0.120332 | ||||||||
\(446\) | 1089.71 | 0.115693 | ||||||||
\(447\) | −14266.7 | −1.50960 | ||||||||
\(448\) | 4388.60 | 0.462817 | ||||||||
\(449\) | −7805.84 | −0.820446 | −0.410223 | − | 0.911985i | \(-0.634549\pi\) | ||||
−0.410223 | + | 0.911985i | \(0.634549\pi\) | |||||||
\(450\) | 7.75174 | 0.000812046 0 | ||||||||
\(451\) | −15895.0 | −1.65957 | ||||||||
\(452\) | 6377.53 | 0.663659 | ||||||||
\(453\) | −1869.30 | −0.193879 | ||||||||
\(454\) | 734.964 | 0.0759770 | ||||||||
\(455\) | −1095.59 | −0.112884 | ||||||||
\(456\) | −1880.39 | −0.193108 | ||||||||
\(457\) | −3366.22 | −0.344563 | −0.172281 | − | 0.985048i | \(-0.555114\pi\) | ||||
−0.172281 | + | 0.985048i | \(0.555114\pi\) | |||||||
\(458\) | 517.333 | 0.0527803 | ||||||||
\(459\) | 5388.15 | 0.547924 | ||||||||
\(460\) | −4777.55 | −0.484249 | ||||||||
\(461\) | 13238.1 | 1.33744 | 0.668721 | − | 0.743514i | \(-0.266842\pi\) | ||||
0.668721 | + | 0.743514i | \(0.266842\pi\) | |||||||
\(462\) | 440.447 | 0.0443538 | ||||||||
\(463\) | 7100.96 | 0.712764 | 0.356382 | − | 0.934340i | \(-0.384010\pi\) | ||||
0.356382 | + | 0.934340i | \(0.384010\pi\) | |||||||
\(464\) | −9258.13 | −0.926289 | ||||||||
\(465\) | −14404.4 | −1.43654 | ||||||||
\(466\) | −342.081 | −0.0340056 | ||||||||
\(467\) | 3809.73 | 0.377502 | 0.188751 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188751 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(468\) | −839.803 | −0.0829485 | ||||||||
\(469\) | −9361.53 | −0.921696 | ||||||||
\(470\) | −269.688 | −0.0264676 | ||||||||
\(471\) | −16798.0 | −1.64334 | ||||||||
\(472\) | −1797.52 | −0.175291 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −139.967 | −0.0135631 | ||||||||
\(475\) | 505.961 | 0.0488738 | ||||||||
\(476\) | −3531.58 | −0.340063 | ||||||||
\(477\) | 4381.97 | 0.420622 | ||||||||
\(478\) | 311.735 | 0.0298294 | ||||||||
\(479\) | −8042.01 | −0.767117 | −0.383558 | − | 0.923517i | \(-0.625302\pi\) | ||||
−0.383558 | + | 0.923517i | \(0.625302\pi\) | |||||||
\(480\) | −2268.11 | −0.215676 | ||||||||
\(481\) | 1131.62 | 0.107271 | ||||||||
\(482\) | 818.134 | 0.0773133 | ||||||||
\(483\) | −2891.37 | −0.272385 | ||||||||
\(484\) | −6487.17 | −0.609239 | ||||||||
\(485\) | 9092.09 | 0.851238 | ||||||||
\(486\) | 448.925 | 0.0419005 | ||||||||
\(487\) | −1053.58 | −0.0980334 | −0.0490167 | − | 0.998798i | \(-0.515609\pi\) | ||||
−0.0490167 | + | 0.998798i | \(0.515609\pi\) | |||||||
\(488\) | 172.056 | 0.0159603 | ||||||||
\(489\) | 5433.38 | 0.502466 | ||||||||
\(490\) | 524.279 | 0.0483358 | ||||||||
\(491\) | 13496.0 | 1.24046 | 0.620230 | − | 0.784420i | \(-0.287039\pi\) | ||||
0.620230 | + | 0.784420i | \(0.287039\pi\) | |||||||
\(492\) | 16467.8 | 1.50900 | ||||||||
\(493\) | 7389.13 | 0.675029 | ||||||||
\(494\) | 222.323 | 0.0202485 | ||||||||
\(495\) | 4710.26 | 0.427698 | ||||||||
\(496\) | −13784.5 | −1.24787 | ||||||||
\(497\) | −9723.06 | −0.877543 | ||||||||
\(498\) | −229.294 | −0.0206323 | ||||||||
\(499\) | 6049.65 | 0.542724 | 0.271362 | − | 0.962477i | \(-0.412526\pi\) | ||||
0.271362 | + | 0.962477i | \(0.412526\pi\) | |||||||
\(500\) | 11332.6 | 1.01362 | ||||||||
\(501\) | −2803.72 | −0.250022 | ||||||||
\(502\) | −419.136 | −0.0372648 | ||||||||
\(503\) | 6920.90 | 0.613494 | 0.306747 | − | 0.951791i | \(-0.400759\pi\) | ||||
0.306747 | + | 0.951791i | \(0.400759\pi\) | |||||||
\(504\) | −233.733 | −0.0206573 | ||||||||
\(505\) | 11698.0 | 1.03080 | ||||||||
\(506\) | −455.089 | −0.0399825 | ||||||||
\(507\) | −12452.8 | −1.09083 | ||||||||
\(508\) | 11142.9 | 0.973197 | ||||||||
\(509\) | 10827.3 | 0.942853 | 0.471426 | − | 0.881905i | \(-0.343739\pi\) | ||||
0.471426 | + | 0.881905i | \(0.343739\pi\) | |||||||
\(510\) | 599.332 | 0.0520370 | ||||||||
\(511\) | 6499.35 | 0.562650 | ||||||||
\(512\) | −3622.40 | −0.312673 | ||||||||
\(513\) | 11614.4 | 0.999589 | ||||||||
\(514\) | −743.354 | −0.0637898 | ||||||||
\(515\) | −19378.6 | −1.65810 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6333.78 | 0.538799 | ||||||||
\(518\) | 157.156 | 0.0133302 | ||||||||
\(519\) | 9578.68 | 0.810130 | ||||||||
\(520\) | 358.035 | 0.0301940 | ||||||||
\(521\) | 7024.80 | 0.590714 | 0.295357 | − | 0.955387i | \(-0.404561\pi\) | ||||
0.295357 | + | 0.955387i | \(0.404561\pi\) | |||||||
\(522\) | 244.025 | 0.0204611 | ||||||||
\(523\) | −16744.9 | −1.40001 | −0.700003 | − | 0.714140i | \(-0.746818\pi\) | ||||
−0.700003 | + | 0.714140i | \(0.746818\pi\) | |||||||
\(524\) | 5450.54 | 0.454405 | ||||||||
\(525\) | 246.064 | 0.0204555 | ||||||||
\(526\) | 661.702 | 0.0548509 | ||||||||
\(527\) | 11001.8 | 0.909382 | ||||||||
\(528\) | 17636.0 | 1.45361 | ||||||||
\(529\) | −9179.51 | −0.754460 | ||||||||
\(530\) | −932.198 | −0.0764002 | ||||||||
\(531\) | −5805.13 | −0.474428 | ||||||||
\(532\) | −7612.51 | −0.620384 | ||||||||
\(533\) | −3901.95 | −0.317096 | ||||||||
\(534\) | 111.478 | 0.00903392 | ||||||||
\(535\) | −20217.6 | −1.63380 | ||||||||
\(536\) | 3059.31 | 0.246534 | ||||||||
\(537\) | 1011.51 | 0.0812845 | ||||||||
\(538\) | 273.744 | 0.0219367 | ||||||||
\(539\) | −12313.0 | −0.983969 | ||||||||
\(540\) | 9333.19 | 0.743771 | ||||||||
\(541\) | 9818.86 | 0.780306 | 0.390153 | − | 0.920750i | \(-0.372422\pi\) | ||||
0.390153 | + | 0.920750i | \(0.372422\pi\) | |||||||
\(542\) | −1126.82 | −0.0893009 | ||||||||
\(543\) | 10407.0 | 0.822480 | ||||||||
\(544\) | 1732.33 | 0.136531 | ||||||||
\(545\) | −6816.04 | −0.535719 | ||||||||
\(546\) | 108.122 | 0.00847473 | ||||||||
\(547\) | 7182.55 | 0.561433 | 0.280717 | − | 0.959791i | \(-0.409428\pi\) | ||||
0.280717 | + | 0.959791i | \(0.409428\pi\) | |||||||
\(548\) | −3020.37 | −0.235445 | ||||||||
\(549\) | 555.661 | 0.0431968 | ||||||||
\(550\) | 38.7293 | 0.00300259 | ||||||||
\(551\) | 15927.6 | 1.23147 | ||||||||
\(552\) | 944.889 | 0.0728571 | ||||||||
\(553\) | −1135.58 | −0.0873231 | ||||||||
\(554\) | −900.992 | −0.0690965 | ||||||||
\(555\) | 6575.69 | 0.502924 | ||||||||
\(556\) | 1136.29 | 0.0866716 | ||||||||
\(557\) | −13961.8 | −1.06208 | −0.531041 | − | 0.847346i | \(-0.678199\pi\) | ||||
−0.531041 | + | 0.847346i | \(0.678199\pi\) | |||||||
\(558\) | 363.331 | 0.0275646 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6092.40 | −0.459733 | ||||||||
\(561\) | −14075.7 | −1.05932 | ||||||||
\(562\) | −1368.21 | −0.102695 | ||||||||
\(563\) | 15626.3 | 1.16975 | 0.584876 | − | 0.811123i | \(-0.301143\pi\) | ||||
0.584876 | + | 0.811123i | \(0.301143\pi\) | |||||||
\(564\) | −6562.02 | −0.489913 | ||||||||
\(565\) | −8780.94 | −0.653835 | ||||||||
\(566\) | 23.9630 | 0.00177957 | ||||||||
\(567\) | 7846.97 | 0.581202 | ||||||||
\(568\) | 3177.45 | 0.234724 | ||||||||
\(569\) | 385.443 | 0.0283983 | 0.0141991 | − | 0.999899i | \(-0.495480\pi\) | ||||
0.0141991 | + | 0.999899i | \(0.495480\pi\) | |||||||
\(570\) | 1291.89 | 0.0949322 | ||||||||
\(571\) | −21838.8 | −1.60057 | −0.800284 | − | 0.599622i | \(-0.795318\pi\) | ||||
−0.800284 | + | 0.599622i | \(0.795318\pi\) | |||||||
\(572\) | −4195.83 | −0.306707 | ||||||||
\(573\) | 31185.3 | 2.27362 | ||||||||
\(574\) | −541.894 | −0.0394046 | ||||||||
\(575\) | −254.244 | −0.0184395 | ||||||||
\(576\) | −4631.72 | −0.335049 | ||||||||
\(577\) | −3620.99 | −0.261254 | −0.130627 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130627 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(578\) | 425.441 | 0.0306159 | ||||||||
\(579\) | −30968.3 | −2.22279 | ||||||||
\(580\) | 12799.2 | 0.916309 | ||||||||
\(581\) | −1860.30 | −0.132837 | ||||||||
\(582\) | −897.282 | −0.0639064 | ||||||||
\(583\) | 21893.2 | 1.55527 | ||||||||
\(584\) | −2123.96 | −0.150497 | ||||||||
\(585\) | 1156.29 | 0.0817206 | ||||||||
\(586\) | 166.487 | 0.0117364 | ||||||||
\(587\) | −5240.21 | −0.368461 | −0.184230 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184230 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(588\) | 12756.7 | 0.894692 | ||||||||
\(589\) | 23714.8 | 1.65900 | ||||||||
\(590\) | 1234.95 | 0.0861734 | ||||||||
\(591\) | 10534.5 | 0.733216 | ||||||||
\(592\) | 6292.71 | 0.436873 | ||||||||
\(593\) | 19636.0 | 1.35979 | 0.679893 | − | 0.733311i | \(-0.262026\pi\) | ||||
0.679893 | + | 0.733311i | \(0.262026\pi\) | |||||||
\(594\) | 889.038 | 0.0614103 | ||||||||
\(595\) | 4862.48 | 0.335029 | ||||||||
\(596\) | 18874.7 | 1.29721 | ||||||||
\(597\) | 7823.06 | 0.536309 | ||||||||
\(598\) | −111.716 | −0.00763950 | ||||||||
\(599\) | 6122.04 | 0.417595 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(600\) | −80.4127 | −0.00547139 | ||||||||
\(601\) | −7342.47 | −0.498345 | −0.249173 | − | 0.968459i | \(-0.580159\pi\) | ||||
−0.249173 | + | 0.968459i | \(0.580159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9880.14 | 0.667248 | ||||||||
\(604\) | 2473.06 | 0.166602 | ||||||||
\(605\) | 8931.90 | 0.600220 | ||||||||
\(606\) | −1154.46 | −0.0773871 | ||||||||
\(607\) | 7350.03 | 0.491480 | 0.245740 | − | 0.969336i | \(-0.420969\pi\) | ||||
0.245740 | + | 0.969336i | \(0.420969\pi\) | |||||||
\(608\) | 3734.12 | 0.249077 | ||||||||
\(609\) | 7746.09 | 0.515415 | ||||||||
\(610\) | −118.209 | −0.00784611 | ||||||||
\(611\) | 1554.83 | 0.102949 | ||||||||
\(612\) | 3727.23 | 0.246183 | ||||||||
\(613\) | −5836.04 | −0.384528 | −0.192264 | − | 0.981343i | \(-0.561583\pi\) | ||||
−0.192264 | + | 0.981343i | \(0.561583\pi\) | |||||||
\(614\) | 837.501 | 0.0550469 | ||||||||
\(615\) | −22673.8 | −1.48666 | ||||||||
\(616\) | −1167.78 | −0.0763817 | ||||||||
\(617\) | 27825.0 | 1.81555 | 0.907774 | − | 0.419460i | \(-0.137781\pi\) | ||||
0.907774 | + | 0.419460i | \(0.137781\pi\) | |||||||
\(618\) | 1912.44 | 0.124481 | ||||||||
\(619\) | 21192.7 | 1.37610 | 0.688050 | − | 0.725664i | \(-0.258467\pi\) | ||||
0.688050 | + | 0.725664i | \(0.258467\pi\) | |||||||
\(620\) | 19056.9 | 1.23443 | ||||||||
\(621\) | −5836.21 | −0.377132 | ||||||||
\(622\) | −1442.92 | −0.0930159 | ||||||||
\(623\) | 904.436 | 0.0581629 | ||||||||
\(624\) | 4329.33 | 0.277743 | ||||||||
\(625\) | −15021.9 | −0.961403 | ||||||||
\(626\) | 537.009 | 0.0342862 | ||||||||
\(627\) | −30340.8 | −1.93253 | ||||||||
\(628\) | 22223.7 | 1.41213 | ||||||||
\(629\) | −5022.36 | −0.318370 | ||||||||
\(630\) | 160.583 | 0.0101552 | ||||||||
\(631\) | −24191.0 | −1.52619 | −0.763097 | − | 0.646283i | \(-0.776322\pi\) | ||||
−0.763097 | + | 0.646283i | \(0.776322\pi\) | |||||||
\(632\) | 371.102 | 0.0233570 | ||||||||
\(633\) | −22888.9 | −1.43721 | ||||||||
\(634\) | 520.827 | 0.0326257 | ||||||||
\(635\) | −15342.1 | −0.958791 | ||||||||
\(636\) | −22682.2 | −1.41416 | ||||||||
\(637\) | −3022.63 | −0.188008 | ||||||||
\(638\) | 1219.20 | 0.0756560 | ||||||||
\(639\) | 10261.7 | 0.635283 | ||||||||
\(640\) | 3998.19 | 0.246941 | ||||||||
\(641\) | 4043.14 | 0.249134 | 0.124567 | − | 0.992211i | \(-0.460246\pi\) | ||||
0.124567 | + | 0.992211i | \(0.460246\pi\) | |||||||
\(642\) | 1995.24 | 0.122657 | ||||||||
\(643\) | −17665.3 | −1.08344 | −0.541721 | − | 0.840558i | \(-0.682227\pi\) | ||||
−0.541721 | + | 0.840558i | \(0.682227\pi\) | |||||||
\(644\) | 3825.26 | 0.234063 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −986.715 | −0.0600956 | ||||||||
\(647\) | −20855.7 | −1.26727 | −0.633634 | − | 0.773633i | \(-0.718437\pi\) | ||||
−0.633634 | + | 0.773633i | \(0.718437\pi\) | |||||||
\(648\) | −2564.36 | −0.155459 | ||||||||
\(649\) | −29003.7 | −1.75423 | ||||||||
\(650\) | 9.50738 | 0.000573708 0 | ||||||||
\(651\) | 11533.3 | 0.694353 | ||||||||
\(652\) | −7188.31 | −0.431773 | ||||||||
\(653\) | 13837.3 | 0.829244 | 0.414622 | − | 0.909994i | \(-0.363914\pi\) | ||||
0.414622 | + | 0.909994i | \(0.363914\pi\) | |||||||
\(654\) | 672.663 | 0.0402190 | ||||||||
\(655\) | −7504.61 | −0.447678 | ||||||||
\(656\) | −21698.0 | −1.29141 | ||||||||
\(657\) | −6859.40 | −0.407322 | ||||||||
\(658\) | 215.932 | 0.0127932 | ||||||||
\(659\) | 25875.9 | 1.52956 | 0.764782 | − | 0.644289i | \(-0.222847\pi\) | ||||
0.764782 | + | 0.644289i | \(0.222847\pi\) | |||||||
\(660\) | −24381.5 | −1.43795 | ||||||||
\(661\) | 15103.3 | 0.888728 | 0.444364 | − | 0.895846i | \(-0.353430\pi\) | ||||
0.444364 | + | 0.895846i | \(0.353430\pi\) | |||||||
\(662\) | 314.249 | 0.0184496 | ||||||||
\(663\) | −3455.34 | −0.202404 | ||||||||
\(664\) | 607.937 | 0.0355309 | ||||||||
\(665\) | 10481.3 | 0.611200 | ||||||||
\(666\) | −165.862 | −0.00965021 | ||||||||
\(667\) | −8003.58 | −0.464618 | ||||||||
\(668\) | 3709.30 | 0.214846 | ||||||||
\(669\) | −36506.9 | −2.10977 | ||||||||
\(670\) | −2101.85 | −0.121196 | ||||||||
\(671\) | 2776.20 | 0.159723 | ||||||||
\(672\) | 1816.02 | 0.104248 | ||||||||
\(673\) | −13737.3 | −0.786827 | −0.393413 | − | 0.919362i | \(-0.628706\pi\) | ||||
−0.393413 | + | 0.919362i | \(0.628706\pi\) | |||||||
\(674\) | 1997.92 | 0.114179 | ||||||||
\(675\) | 496.678 | 0.0283217 | ||||||||
\(676\) | 16475.0 | 0.937358 | ||||||||
\(677\) | −29510.0 | −1.67528 | −0.837638 | − | 0.546225i | \(-0.816064\pi\) | ||||
−0.837638 | + | 0.546225i | \(0.816064\pi\) | |||||||
\(678\) | 866.575 | 0.0490865 | ||||||||
\(679\) | −7279.80 | −0.411448 | ||||||||
\(680\) | −1589.04 | −0.0896130 | ||||||||
\(681\) | −24622.4 | −1.38551 | ||||||||
\(682\) | 1815.28 | 0.101922 | ||||||||
\(683\) | −12530.8 | −0.702015 | −0.351008 | − | 0.936373i | \(-0.614161\pi\) | ||||
−0.351008 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(684\) | 8034.22 | 0.449117 | ||||||||
\(685\) | 4158.61 | 0.231960 | ||||||||
\(686\) | −961.379 | −0.0535067 | ||||||||
\(687\) | −17331.5 | −0.962498 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5374.41 | 0.297168 | ||||||||
\(690\) | −649.171 | −0.0358167 | ||||||||
\(691\) | 16655.9 | 0.916961 | 0.458480 | − | 0.888705i | \(-0.348394\pi\) | ||||
0.458480 | + | 0.888705i | \(0.348394\pi\) | |||||||
\(692\) | −12672.5 | −0.696151 | ||||||||
\(693\) | −3771.38 | −0.206729 | ||||||||
\(694\) | −690.919 | −0.0377909 | ||||||||
\(695\) | −1564.51 | −0.0853886 | ||||||||
\(696\) | −2531.39 | −0.137862 | ||||||||
\(697\) | 17317.7 | 0.941111 | ||||||||
\(698\) | −1574.80 | −0.0853969 | ||||||||
\(699\) | 11460.2 | 0.620124 | ||||||||
\(700\) | −325.540 | −0.0175775 | ||||||||
\(701\) | 13256.3 | 0.714242 | 0.357121 | − | 0.934058i | \(-0.383758\pi\) | ||||
0.357121 | + | 0.934058i | \(0.383758\pi\) | |||||||
\(702\) | 218.244 | 0.0117337 | ||||||||
\(703\) | −10825.9 | −0.580808 | ||||||||
\(704\) | −23141.0 | −1.23886 | ||||||||
\(705\) | 9034.95 | 0.482661 | ||||||||
\(706\) | −1018.51 | −0.0542950 | ||||||||
\(707\) | −9366.29 | −0.498240 | ||||||||
\(708\) | 30048.8 | 1.59506 | ||||||||
\(709\) | 21810.7 | 1.15531 | 0.577656 | − | 0.816280i | \(-0.303967\pi\) | ||||
0.577656 | + | 0.816280i | \(0.303967\pi\) | |||||||
\(710\) | −2183.02 | −0.115390 | ||||||||
\(711\) | 1198.49 | 0.0632162 | ||||||||
\(712\) | −295.566 | −0.0155573 | ||||||||
\(713\) | −11916.6 | −0.625921 | ||||||||
\(714\) | −479.870 | −0.0251522 | ||||||||
\(715\) | 5777.05 | 0.302167 | ||||||||
\(716\) | −1338.22 | −0.0698484 | ||||||||
\(717\) | −10443.6 | −0.543966 | ||||||||
\(718\) | −1999.77 | −0.103942 | ||||||||
\(719\) | −6338.79 | −0.328786 | −0.164393 | − | 0.986395i | \(-0.552566\pi\) | ||||
−0.164393 | + | 0.986395i | \(0.552566\pi\) | |||||||
\(720\) | 6429.90 | 0.332817 | ||||||||
\(721\) | 15515.9 | 0.801446 | ||||||||
\(722\) | −893.891 | −0.0460764 | ||||||||
\(723\) | −27408.8 | −1.40988 | ||||||||
\(724\) | −13768.3 | −0.706763 | ||||||||
\(725\) | 681.128 | 0.0348916 | ||||||||
\(726\) | −881.473 | −0.0450614 | ||||||||
\(727\) | −10574.8 | −0.539476 | −0.269738 | − | 0.962934i | \(-0.586937\pi\) | ||||
−0.269738 | + | 0.962934i | \(0.586937\pi\) | |||||||
\(728\) | −286.670 | −0.0145943 | ||||||||
\(729\) | 9081.01 | 0.461363 | ||||||||
\(730\) | 1459.23 | 0.0739844 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2876.24 | −0.145231 | ||||||||
\(733\) | −892.660 | −0.0449811 | −0.0224906 | − | 0.999747i | \(-0.507160\pi\) | ||||
−0.0224906 | + | 0.999747i | \(0.507160\pi\) | |||||||
\(734\) | −40.9783 | −0.00206068 | ||||||||
\(735\) | −17564.2 | −0.881448 | ||||||||
\(736\) | −1876.38 | −0.0939734 | ||||||||
\(737\) | 49363.2 | 2.46719 | ||||||||
\(738\) | 571.914 | 0.0285264 | ||||||||
\(739\) | 26234.1 | 1.30587 | 0.652933 | − | 0.757415i | \(-0.273538\pi\) | ||||
0.652933 | + | 0.757415i | \(0.273538\pi\) | |||||||
\(740\) | −8699.58 | −0.432166 | ||||||||
\(741\) | −7448.15 | −0.369251 | ||||||||
\(742\) | 746.386 | 0.0369282 | ||||||||
\(743\) | −20825.8 | −1.02829 | −0.514147 | − | 0.857702i | \(-0.671892\pi\) | ||||
−0.514147 | + | 0.857702i | \(0.671892\pi\) | |||||||
\(744\) | −3769.02 | −0.185724 | ||||||||
\(745\) | −25987.7 | −1.27801 | ||||||||
\(746\) | −281.956 | −0.0138380 | ||||||||
\(747\) | 1963.35 | 0.0961651 | ||||||||
\(748\) | 18622.0 | 0.910277 | ||||||||
\(749\) | 16187.7 | 0.789702 | ||||||||
\(750\) | 1539.87 | 0.0749707 | ||||||||
\(751\) | −2115.01 | −0.102767 | −0.0513833 | − | 0.998679i | \(-0.516363\pi\) | ||||
−0.0513833 | + | 0.998679i | \(0.516363\pi\) | |||||||
\(752\) | 8646.14 | 0.419272 | ||||||||
\(753\) | 14041.7 | 0.679559 | ||||||||
\(754\) | 299.292 | 0.0144557 | ||||||||
\(755\) | −3405.05 | −0.164136 | ||||||||
\(756\) | −7472.84 | −0.359503 | ||||||||
\(757\) | −5066.96 | −0.243279 | −0.121639 | − | 0.992574i | \(-0.538815\pi\) | ||||
−0.121639 | + | 0.992574i | \(0.538815\pi\) | |||||||
\(758\) | −1259.12 | −0.0603340 | ||||||||
\(759\) | 15246.2 | 0.729119 | ||||||||
\(760\) | −3425.25 | −0.163483 | ||||||||
\(761\) | −17080.0 | −0.813601 | −0.406801 | − | 0.913517i | \(-0.633356\pi\) | ||||
−0.406801 | + | 0.913517i | \(0.633356\pi\) | |||||||
\(762\) | 1514.08 | 0.0719810 | ||||||||
\(763\) | 5457.42 | 0.258941 | ||||||||
\(764\) | −41257.9 | −1.95374 | ||||||||
\(765\) | −5131.85 | −0.242539 | ||||||||
\(766\) | −724.719 | −0.0341843 | ||||||||
\(767\) | −7119.90 | −0.335182 | ||||||||
\(768\) | 23677.6 | 1.11249 | ||||||||
\(769\) | −5044.34 | −0.236545 | −0.118273 | − | 0.992981i | \(-0.537736\pi\) | ||||
−0.118273 | + | 0.992981i | \(0.537736\pi\) | |||||||
\(770\) | 802.304 | 0.0375494 | ||||||||
\(771\) | 24903.5 | 1.16327 | ||||||||
\(772\) | 40970.7 | 1.91006 | ||||||||
\(773\) | 27638.0 | 1.28599 | 0.642994 | − | 0.765871i | \(-0.277692\pi\) | ||||
0.642994 | + | 0.765871i | \(0.277692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1014.14 | 0.0470051 | ||||||||
\(776\) | 2379.01 | 0.110053 | ||||||||
\(777\) | −5264.98 | −0.243089 | ||||||||
\(778\) | −1788.43 | −0.0824143 | ||||||||
\(779\) | 37329.2 | 1.71689 | ||||||||
\(780\) | −5985.23 | −0.274751 | ||||||||
\(781\) | 51269.5 | 2.34900 | ||||||||
\(782\) | 495.821 | 0.0226733 | ||||||||
\(783\) | 15635.4 | 0.713619 | ||||||||
\(784\) | −16808.3 | −0.765685 | ||||||||
\(785\) | −30598.7 | −1.39123 | ||||||||
\(786\) | 740.617 | 0.0336093 | ||||||||
\(787\) | −35998.4 | −1.63050 | −0.815251 | − | 0.579107i | \(-0.803401\pi\) | ||||
−0.815251 | + | 0.579107i | \(0.803401\pi\) | |||||||
\(788\) | −13937.0 | −0.630058 | ||||||||
\(789\) | −22168.1 | −1.00026 | ||||||||
\(790\) | −254.960 | −0.0114824 | ||||||||
\(791\) | 7030.66 | 0.316032 | ||||||||
\(792\) | 1232.47 | 0.0552954 | ||||||||
\(793\) | 681.509 | 0.0305184 | ||||||||
\(794\) | −369.739 | −0.0165259 | ||||||||
\(795\) | 31230.1 | 1.39323 | ||||||||
\(796\) | −10349.8 | −0.460854 | ||||||||
\(797\) | 20078.9 | 0.892384 | 0.446192 | − | 0.894937i | \(-0.352780\pi\) | ||||
0.446192 | + | 0.894937i | \(0.352780\pi\) | |||||||
\(798\) | −1034.38 | −0.0458857 | ||||||||
\(799\) | −6900.68 | −0.305543 | ||||||||
\(800\) | 159.686 | 0.00705717 | ||||||||
\(801\) | −954.540 | −0.0421061 | ||||||||
\(802\) | 1505.06 | 0.0662664 | ||||||||
\(803\) | −34271.0 | −1.50610 | ||||||||
\(804\) | −51142.1 | −2.24334 | ||||||||
\(805\) | −5266.83 | −0.230598 | ||||||||
\(806\) | 445.620 | 0.0194743 | ||||||||
\(807\) | −9170.85 | −0.400036 | ||||||||
\(808\) | 3060.87 | 0.133268 | ||||||||
\(809\) | 12677.6 | 0.550952 | 0.275476 | − | 0.961308i | \(-0.411165\pi\) | ||||
0.275476 | + | 0.961308i | \(0.411165\pi\) | |||||||
\(810\) | 1761.80 | 0.0764239 | ||||||||
\(811\) | 8763.58 | 0.379446 | 0.189723 | − | 0.981838i | \(-0.439241\pi\) | ||||
0.189723 | + | 0.981838i | \(0.439241\pi\) | |||||||
\(812\) | −10248.0 | −0.442900 | ||||||||
\(813\) | 37750.2 | 1.62849 | ||||||||
\(814\) | −828.684 | −0.0356822 | ||||||||
\(815\) | 9897.26 | 0.425381 | ||||||||
\(816\) | −19214.5 | −0.824316 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2145.39 | 0.0917017 | ||||||||
\(819\) | −925.809 | −0.0394998 | ||||||||
\(820\) | 29997.2 | 1.27750 | ||||||||
\(821\) | 9411.97 | 0.400097 | 0.200049 | − | 0.979786i | \(-0.435890\pi\) | ||||
0.200049 | + | 0.979786i | \(0.435890\pi\) | |||||||
\(822\) | −410.406 | −0.0174143 | ||||||||
\(823\) | −7299.97 | −0.309187 | −0.154593 | − | 0.987978i | \(-0.549407\pi\) | ||||
−0.154593 | + | 0.987978i | \(0.549407\pi\) | |||||||
\(824\) | −5070.53 | −0.214369 | ||||||||
\(825\) | −1297.49 | −0.0547550 | ||||||||
\(826\) | −988.796 | −0.0416521 | ||||||||
\(827\) | 22811.7 | 0.959179 | 0.479589 | − | 0.877493i | \(-0.340786\pi\) | ||||
0.479589 | + | 0.877493i | \(0.340786\pi\) | |||||||
\(828\) | −4037.17 | −0.169446 | ||||||||
\(829\) | 6005.69 | 0.251612 | 0.125806 | − | 0.992055i | \(-0.459848\pi\) | ||||
0.125806 | + | 0.992055i | \(0.459848\pi\) | |||||||
\(830\) | −417.674 | −0.0174671 | ||||||||
\(831\) | 30184.6 | 1.26004 | ||||||||
\(832\) | −5680.73 | −0.236711 | ||||||||
\(833\) | 13415.1 | 0.557990 | ||||||||
\(834\) | 154.398 | 0.00641052 | ||||||||
\(835\) | −5107.17 | −0.211666 | ||||||||
\(836\) | 40140.6 | 1.66064 | ||||||||
\(837\) | 23279.7 | 0.961369 | ||||||||
\(838\) | 1842.85 | 0.0759669 | ||||||||
\(839\) | −10725.8 | −0.441353 | −0.220676 | − | 0.975347i | \(-0.570826\pi\) | ||||
−0.220676 | + | 0.975347i | \(0.570826\pi\) | |||||||
\(840\) | −1665.80 | −0.0684234 | ||||||||
\(841\) | −2947.12 | −0.120838 | ||||||||
\(842\) | 1029.72 | 0.0421454 | ||||||||
\(843\) | 45837.2 | 1.87274 | ||||||||
\(844\) | 30281.9 | 1.23501 | ||||||||
\(845\) | −22683.7 | −0.923482 | ||||||||
\(846\) | −227.894 | −0.00926141 | ||||||||
\(847\) | −7151.54 | −0.290118 | ||||||||
\(848\) | 29886.1 | 1.21025 | ||||||||
\(849\) | −802.797 | −0.0324522 | ||||||||
\(850\) | −42.1958 | −0.00170271 | ||||||||
\(851\) | 5440.00 | 0.219131 | ||||||||
\(852\) | −53117.1 | −2.13587 | ||||||||
\(853\) | −23341.2 | −0.936914 | −0.468457 | − | 0.883486i | \(-0.655190\pi\) | ||||
−0.468457 | + | 0.883486i | \(0.655190\pi\) | |||||||
\(854\) | 94.6465 | 0.00379243 | ||||||||
\(855\) | −11062.0 | −0.442469 | ||||||||
\(856\) | −5290.08 | −0.211228 | ||||||||
\(857\) | 10896.2 | 0.434315 | 0.217158 | − | 0.976137i | \(-0.430321\pi\) | ||||
0.217158 | + | 0.976137i | \(0.430321\pi\) | |||||||
\(858\) | −570.127 | −0.0226851 | ||||||||
\(859\) | 31094.1 | 1.23506 | 0.617531 | − | 0.786546i | \(-0.288133\pi\) | ||||
0.617531 | + | 0.786546i | \(0.288133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18154.3 | 0.718580 | ||||||||
\(862\) | 1374.71 | 0.0543189 | ||||||||
\(863\) | 13092.4 | 0.516420 | 0.258210 | − | 0.966089i | \(-0.416867\pi\) | ||||
0.258210 | + | 0.966089i | \(0.416867\pi\) | |||||||
\(864\) | 3665.61 | 0.144336 | ||||||||
\(865\) | 17448.2 | 0.685846 | ||||||||
\(866\) | 1823.02 | 0.0715345 | ||||||||
\(867\) | −14252.9 | −0.558310 | ||||||||
\(868\) | −15258.4 | −0.596663 | ||||||||
\(869\) | 5987.88 | 0.233746 | ||||||||
\(870\) | 1739.15 | 0.0677733 | ||||||||
\(871\) | 12117.8 | 0.471408 | ||||||||
\(872\) | −1783.46 | −0.0692611 | ||||||||
\(873\) | 7683.08 | 0.297861 | ||||||||
\(874\) | 1068.77 | 0.0413634 | ||||||||
\(875\) | 12493.2 | 0.482683 | ||||||||
\(876\) | 35506.0 | 1.36945 | ||||||||
\(877\) | 44742.9 | 1.72276 | 0.861380 | − | 0.507961i | \(-0.169601\pi\) | ||||
0.861380 | + | 0.507961i | \(0.169601\pi\) | |||||||
\(878\) | 2824.75 | 0.108577 | ||||||||
\(879\) | −5577.56 | −0.214023 | ||||||||
\(880\) | 32125.1 | 1.23061 | ||||||||
\(881\) | 43123.8 | 1.64912 | 0.824562 | − | 0.565772i | \(-0.191422\pi\) | ||||
0.824562 | + | 0.565772i | \(0.191422\pi\) | |||||||
\(882\) | 443.031 | 0.0169134 | ||||||||
\(883\) | 28032.8 | 1.06838 | 0.534190 | − | 0.845364i | \(-0.320617\pi\) | ||||
0.534190 | + | 0.845364i | \(0.320617\pi\) | |||||||
\(884\) | 4571.38 | 0.173928 | ||||||||
\(885\) | −41372.9 | −1.57145 | ||||||||
\(886\) | −285.366 | −0.0108206 | ||||||||
\(887\) | −20827.9 | −0.788426 | −0.394213 | − | 0.919019i | \(-0.628983\pi\) | ||||
−0.394213 | + | 0.919019i | \(0.628983\pi\) | |||||||
\(888\) | 1720.57 | 0.0650211 | ||||||||
\(889\) | 12284.0 | 0.463434 | ||||||||
\(890\) | 203.064 | 0.00764800 | ||||||||
\(891\) | −41377.0 | −1.55576 | ||||||||
\(892\) | 48298.3 | 1.81294 | ||||||||
\(893\) | −14874.8 | −0.557408 | ||||||||
\(894\) | 2564.68 | 0.0959461 | ||||||||
\(895\) | 1842.53 | 0.0688144 | ||||||||
\(896\) | −3201.24 | −0.119359 | ||||||||
\(897\) | 3742.67 | 0.139313 | ||||||||
\(898\) | 1403.23 | 0.0521453 | ||||||||
\(899\) | 31925.1 | 1.18438 | ||||||||
\(900\) | 343.575 | 0.0127250 | ||||||||
\(901\) | −23852.8 | −0.881966 | ||||||||
\(902\) | 2857.40 | 0.105478 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2297.59 | −0.0845318 | ||||||||
\(905\) | 18957.0 | 0.696301 | ||||||||
\(906\) | 336.038 | 0.0123224 | ||||||||
\(907\) | 16190.9 | 0.592736 | 0.296368 | − | 0.955074i | \(-0.404225\pi\) | ||||
0.296368 | + | 0.955074i | \(0.404225\pi\) | |||||||
\(908\) | 32575.2 | 1.19058 | ||||||||
\(909\) | 9885.16 | 0.360693 | ||||||||
\(910\) | 196.952 | 0.00717460 | ||||||||
\(911\) | 3349.72 | 0.121824 | 0.0609118 | − | 0.998143i | \(-0.480599\pi\) | ||||
0.0609118 | + | 0.998143i | \(0.480599\pi\) | |||||||
\(912\) | −41417.8 | −1.50382 | ||||||||
\(913\) | 9809.32 | 0.355576 | ||||||||
\(914\) | 605.136 | 0.0218995 | ||||||||
\(915\) | 3960.17 | 0.143081 | ||||||||
\(916\) | 22929.4 | 0.827082 | ||||||||
\(917\) | 6008.74 | 0.216386 | ||||||||
\(918\) | −968.612 | −0.0348246 | ||||||||
\(919\) | 44655.3 | 1.60287 | 0.801437 | − | 0.598079i | \(-0.204069\pi\) | ||||
0.801437 | + | 0.598079i | \(0.204069\pi\) | |||||||
\(920\) | 1721.18 | 0.0616799 | ||||||||
\(921\) | −28057.6 | −1.00383 | ||||||||
\(922\) | −2379.78 | −0.0850041 | ||||||||
\(923\) | 12585.8 | 0.448826 | ||||||||
\(924\) | 19521.6 | 0.695037 | ||||||||
\(925\) | −462.959 | −0.0164562 | ||||||||
\(926\) | −1276.52 | −0.0453013 | ||||||||
\(927\) | −16375.4 | −0.580194 | ||||||||
\(928\) | 5026.90 | 0.177819 | ||||||||
\(929\) | −13304.5 | −0.469867 | −0.234933 | − | 0.972011i | \(-0.575487\pi\) | ||||
−0.234933 | + | 0.972011i | \(0.575487\pi\) | |||||||
\(930\) | 2589.44 | 0.0913024 | ||||||||
\(931\) | 28916.9 | 1.01795 | ||||||||
\(932\) | −15161.8 | −0.532877 | ||||||||
\(933\) | 48340.1 | 1.69623 | ||||||||
\(934\) | −684.864 | −0.0239930 | ||||||||
\(935\) | −25639.8 | −0.896803 | ||||||||
\(936\) | 302.550 | 0.0105653 | ||||||||
\(937\) | 22887.4 | 0.797972 | 0.398986 | − | 0.916957i | \(-0.369362\pi\) | ||||
0.398986 | + | 0.916957i | \(0.369362\pi\) | |||||||
\(938\) | 1682.90 | 0.0585805 | ||||||||
\(939\) | −17990.6 | −0.625241 | ||||||||
\(940\) | −11953.2 | −0.414754 | ||||||||
\(941\) | 29622.2 | 1.02620 | 0.513102 | − | 0.858328i | \(-0.328496\pi\) | ||||
0.513102 | + | 0.858328i | \(0.328496\pi\) | |||||||
\(942\) | 3019.74 | 0.104446 | ||||||||
\(943\) | −18757.8 | −0.647760 | ||||||||
\(944\) | −39592.4 | −1.36507 | ||||||||
\(945\) | 10289.0 | 0.354182 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2789.42 | 0.0957170 | 0.0478585 | − | 0.998854i | \(-0.484760\pi\) | ||||
0.0478585 | + | 0.998854i | \(0.484760\pi\) | |||||||
\(948\) | −6203.67 | −0.212538 | ||||||||
\(949\) | −8412.93 | −0.287772 | ||||||||
\(950\) | −90.9551 | −0.00310629 | ||||||||
\(951\) | −17448.5 | −0.594960 | ||||||||
\(952\) | 1272.30 | 0.0433146 | ||||||||
\(953\) | 44625.1 | 1.51684 | 0.758421 | − | 0.651765i | \(-0.225971\pi\) | ||||
0.758421 | + | 0.651765i | \(0.225971\pi\) | |||||||
\(954\) | −787.734 | −0.0267336 | ||||||||
\(955\) | 56806.1 | 1.92482 | ||||||||
\(956\) | 13816.8 | 0.467434 | ||||||||
\(957\) | −40845.0 | −1.37966 | ||||||||
\(958\) | 1445.69 | 0.0487559 | ||||||||
\(959\) | −3329.69 | −0.112118 | ||||||||
\(960\) | −33010.0 | −1.10979 | ||||||||
\(961\) | 17742.6 | 0.595570 | ||||||||
\(962\) | −203.428 | −0.00681784 | ||||||||
\(963\) | −17084.5 | −0.571692 | ||||||||
\(964\) | 36261.5 | 1.21152 | ||||||||
\(965\) | −56410.7 | −1.88179 | ||||||||
\(966\) | 519.774 | 0.0173121 | ||||||||
\(967\) | −3384.54 | −0.112554 | −0.0562769 | − | 0.998415i | \(-0.517923\pi\) | ||||
−0.0562769 | + | 0.998415i | \(0.517923\pi\) | |||||||
\(968\) | 2337.09 | 0.0776002 | ||||||||
\(969\) | 33056.5 | 1.09590 | ||||||||
\(970\) | −1634.46 | −0.0541024 | ||||||||
\(971\) | 32899.0 | 1.08731 | 0.543656 | − | 0.839308i | \(-0.317039\pi\) | ||||
0.543656 | + | 0.839308i | \(0.317039\pi\) | |||||||
\(972\) | 19897.4 | 0.656593 | ||||||||
\(973\) | 1252.66 | 0.0412728 | ||||||||
\(974\) | 189.399 | 0.00623074 | ||||||||
\(975\) | −318.512 | −0.0104621 | ||||||||
\(976\) | 3789.75 | 0.124290 | ||||||||
\(977\) | 13662.3 | 0.447384 | 0.223692 | − | 0.974660i | \(-0.428189\pi\) | ||||
0.223692 | + | 0.974660i | \(0.428189\pi\) | |||||||
\(978\) | −976.743 | −0.0319354 | ||||||||
\(979\) | −4769.08 | −0.155690 | ||||||||
\(980\) | 23237.2 | 0.757435 | ||||||||
\(981\) | −5759.75 | −0.187456 | ||||||||
\(982\) | −2426.14 | −0.0788403 | ||||||||
\(983\) | 1388.86 | 0.0450638 | 0.0225319 | − | 0.999746i | \(-0.492827\pi\) | ||||
0.0225319 | + | 0.999746i | \(0.492827\pi\) | |||||||
\(984\) | −5932.75 | −0.192204 | ||||||||
\(985\) | 19189.3 | 0.620732 | ||||||||
\(986\) | −1328.32 | −0.0429030 | ||||||||
\(987\) | −7234.05 | −0.233295 | ||||||||
\(988\) | 9853.83 | 0.317300 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −846.750 | −0.0271833 | ||||||||
\(991\) | 2331.34 | 0.0747299 | 0.0373650 | − | 0.999302i | \(-0.488104\pi\) | ||||
0.0373650 | + | 0.999302i | \(0.488104\pi\) | |||||||
\(992\) | 7484.61 | 0.239553 | ||||||||
\(993\) | −10527.8 | −0.336446 | ||||||||
\(994\) | 1747.89 | 0.0557742 | ||||||||
\(995\) | 14250.2 | 0.454032 | ||||||||
\(996\) | −10162.8 | −0.323314 | ||||||||
\(997\) | 41298.8 | 1.31188 | 0.655941 | − | 0.754812i | \(-0.272272\pi\) | ||||
0.655941 | + | 0.754812i | \(0.272272\pi\) | |||||||
\(998\) | −1087.53 | −0.0344941 | ||||||||
\(999\) | −10627.3 | −0.336570 |
(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.f.1.5 | 10 | ||
43.7 | odd | 6 | 43.4.c.a.6.6 | ✓ | 20 | ||
43.37 | odd | 6 | 43.4.c.a.36.6 | yes | 20 | ||
43.42 | odd | 2 | 1849.4.a.d.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.c.a.6.6 | ✓ | 20 | 43.7 | odd | 6 | ||
43.4.c.a.36.6 | yes | 20 | 43.37 | odd | 6 | ||
1849.4.a.d.1.6 | 10 | 43.42 | odd | 2 | |||
1849.4.a.f.1.5 | 10 | 1.1 | even | 1 | trivial |