Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.09192\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.09192 | 1.38275 | 0.691375 | − | 0.722496i | \(-0.257005\pi\) | ||||
0.691375 | + | 0.722496i | \(0.257005\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.21340 | −1.59251 | −0.796257 | − | 0.604958i | \(-0.793190\pi\) | ||||
−0.796257 | + | 0.604958i | \(0.793190\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.09192 | 0.977751 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.518474 | −0.143799 | −0.0718995 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0718995 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(14\) | −4.21340 | −1.12608 | ||||||||
\(15\) | 3.09192 | 0.798331 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.01037 | −0.730121 | −0.365061 | − | 0.930984i | \(-0.618952\pi\) | ||||
−0.365061 | + | 0.930984i | \(0.618952\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 8.39142 | 1.92512 | 0.962562 | − | 0.271061i | \(-0.0873745\pi\) | ||||
0.962562 | + | 0.271061i | \(0.0873745\pi\) | |||||||
\(20\) | 3.09192 | 0.691375 | ||||||||
\(21\) | −4.21340 | −0.919439 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.337593 | −0.0703930 | −0.0351965 | − | 0.999380i | \(-0.511206\pi\) | ||||
−0.0351965 | + | 0.999380i | \(0.511206\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.55998 | 0.911996 | ||||||||
\(26\) | −0.518474 | −0.101681 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.21340 | −0.796257 | ||||||||
\(29\) | 5.57973 | 1.03613 | 0.518065 | − | 0.855341i | \(-0.326652\pi\) | ||||
0.518065 | + | 0.855341i | \(0.326652\pi\) | |||||||
\(30\) | 3.09192 | 0.564505 | ||||||||
\(31\) | 4.75433 | 0.853903 | 0.426951 | − | 0.904275i | \(-0.359588\pi\) | ||||
0.426951 | + | 0.904275i | \(0.359588\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −3.01037 | −0.516274 | ||||||||
\(35\) | −13.0275 | −2.20205 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.867362 | 0.142593 | 0.0712967 | − | 0.997455i | \(-0.477286\pi\) | ||||
0.0712967 | + | 0.997455i | \(0.477286\pi\) | |||||||
\(38\) | 8.39142 | 1.36127 | ||||||||
\(39\) | −0.518474 | −0.0830223 | ||||||||
\(40\) | 3.09192 | 0.488876 | ||||||||
\(41\) | 8.17976 | 1.27746 | 0.638732 | − | 0.769429i | \(-0.279459\pi\) | ||||
0.638732 | + | 0.769429i | \(0.279459\pi\) | |||||||
\(42\) | −4.21340 | −0.650141 | ||||||||
\(43\) | −9.01482 | −1.37475 | −0.687374 | − | 0.726304i | \(-0.741236\pi\) | ||||
−0.687374 | + | 0.726304i | \(0.741236\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 3.09192 | 0.460916 | ||||||||
\(46\) | −0.337593 | −0.0497753 | ||||||||
\(47\) | 2.07039 | 0.301998 | 0.150999 | − | 0.988534i | \(-0.451751\pi\) | ||||
0.150999 | + | 0.988534i | \(0.451751\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 10.7527 | 1.53610 | ||||||||
\(50\) | 4.55998 | 0.644878 | ||||||||
\(51\) | −3.01037 | −0.421536 | ||||||||
\(52\) | −0.518474 | −0.0718995 | ||||||||
\(53\) | 4.08394 | 0.560972 | 0.280486 | − | 0.959858i | \(-0.409504\pi\) | ||||
0.280486 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.09192 | 0.416915 | ||||||||
\(56\) | −4.21340 | −0.563039 | ||||||||
\(57\) | 8.39142 | 1.11147 | ||||||||
\(58\) | 5.57973 | 0.732655 | ||||||||
\(59\) | −2.99101 | −0.389397 | −0.194698 | − | 0.980863i | \(-0.562373\pi\) | ||||
−0.194698 | + | 0.980863i | \(0.562373\pi\) | |||||||
\(60\) | 3.09192 | 0.399165 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 4.75433 | 0.603800 | ||||||||
\(63\) | −4.21340 | −0.530838 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.60308 | −0.198838 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −1.16994 | −0.142930 | −0.0714652 | − | 0.997443i | \(-0.522767\pi\) | ||||
−0.0714652 | + | 0.997443i | \(0.522767\pi\) | |||||||
\(68\) | −3.01037 | −0.365061 | ||||||||
\(69\) | −0.337593 | −0.0406414 | ||||||||
\(70\) | −13.0275 | −1.55708 | ||||||||
\(71\) | 15.3353 | 1.81997 | 0.909983 | − | 0.414645i | \(-0.136094\pi\) | ||||
0.909983 | + | 0.414645i | \(0.136094\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 8.24649 | 0.965179 | 0.482590 | − | 0.875847i | \(-0.339696\pi\) | ||||
0.482590 | + | 0.875847i | \(0.339696\pi\) | |||||||
\(74\) | 0.867362 | 0.100829 | ||||||||
\(75\) | 4.55998 | 0.526541 | ||||||||
\(76\) | 8.39142 | 0.962562 | ||||||||
\(77\) | −4.21340 | −0.480161 | ||||||||
\(78\) | −0.518474 | −0.0587057 | ||||||||
\(79\) | −15.3981 | −1.73243 | −0.866213 | − | 0.499675i | \(-0.833453\pi\) | ||||
−0.866213 | + | 0.499675i | \(0.833453\pi\) | |||||||
\(80\) | 3.09192 | 0.345687 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.17976 | 0.903304 | ||||||||
\(83\) | −8.21682 | −0.901913 | −0.450957 | − | 0.892546i | \(-0.648917\pi\) | ||||
−0.450957 | + | 0.892546i | \(0.648917\pi\) | |||||||
\(84\) | −4.21340 | −0.459719 | ||||||||
\(85\) | −9.30782 | −1.00957 | ||||||||
\(86\) | −9.01482 | −0.972093 | ||||||||
\(87\) | 5.57973 | 0.598210 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 8.31023 | 0.880882 | 0.440441 | − | 0.897782i | \(-0.354822\pi\) | ||||
0.440441 | + | 0.897782i | \(0.354822\pi\) | |||||||
\(90\) | 3.09192 | 0.325917 | ||||||||
\(91\) | 2.18454 | 0.229002 | ||||||||
\(92\) | −0.337593 | −0.0351965 | ||||||||
\(93\) | 4.75433 | 0.493001 | ||||||||
\(94\) | 2.07039 | 0.213545 | ||||||||
\(95\) | 25.9456 | 2.66196 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.53172 | −0.460126 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(98\) | 10.7527 | 1.08619 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 4.55998 | 0.455998 | ||||||||
\(101\) | −1.63654 | −0.162842 | −0.0814208 | − | 0.996680i | \(-0.525946\pi\) | ||||
−0.0814208 | + | 0.996680i | \(0.525946\pi\) | |||||||
\(102\) | −3.01037 | −0.298071 | ||||||||
\(103\) | 7.63116 | 0.751920 | 0.375960 | − | 0.926636i | \(-0.377313\pi\) | ||||
0.375960 | + | 0.926636i | \(0.377313\pi\) | |||||||
\(104\) | −0.518474 | −0.0508406 | ||||||||
\(105\) | −13.0275 | −1.27135 | ||||||||
\(106\) | 4.08394 | 0.396667 | ||||||||
\(107\) | −8.45294 | −0.817176 | −0.408588 | − | 0.912719i | \(-0.633979\pi\) | ||||
−0.408588 | + | 0.912719i | \(0.633979\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −2.43637 | −0.233362 | −0.116681 | − | 0.993169i | \(-0.537225\pi\) | ||||
−0.116681 | + | 0.993169i | \(0.537225\pi\) | |||||||
\(110\) | 3.09192 | 0.294803 | ||||||||
\(111\) | 0.867362 | 0.0823264 | ||||||||
\(112\) | −4.21340 | −0.398129 | ||||||||
\(113\) | 15.3057 | 1.43984 | 0.719919 | − | 0.694059i | \(-0.244179\pi\) | ||||
0.719919 | + | 0.694059i | \(0.244179\pi\) | |||||||
\(114\) | 8.39142 | 0.785929 | ||||||||
\(115\) | −1.04381 | −0.0973358 | ||||||||
\(116\) | 5.57973 | 0.518065 | ||||||||
\(117\) | −0.518474 | −0.0479330 | ||||||||
\(118\) | −2.99101 | −0.275345 | ||||||||
\(119\) | 12.6839 | 1.16273 | ||||||||
\(120\) | 3.09192 | 0.282253 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 8.17976 | 0.737544 | ||||||||
\(124\) | 4.75433 | 0.426951 | ||||||||
\(125\) | −1.36051 | −0.121688 | ||||||||
\(126\) | −4.21340 | −0.375359 | ||||||||
\(127\) | 15.9129 | 1.41204 | 0.706019 | − | 0.708192i | \(-0.250489\pi\) | ||||
0.706019 | + | 0.708192i | \(0.250489\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.01482 | −0.793711 | ||||||||
\(130\) | −1.60308 | −0.140600 | ||||||||
\(131\) | −0.798822 | −0.0697934 | −0.0348967 | − | 0.999391i | \(-0.511110\pi\) | ||||
−0.0348967 | + | 0.999391i | \(0.511110\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −35.3564 | −3.06579 | ||||||||
\(134\) | −1.16994 | −0.101067 | ||||||||
\(135\) | 3.09192 | 0.266110 | ||||||||
\(136\) | −3.01037 | −0.258137 | ||||||||
\(137\) | −2.23605 | −0.191038 | −0.0955191 | − | 0.995428i | \(-0.530451\pi\) | ||||
−0.0955191 | + | 0.995428i | \(0.530451\pi\) | |||||||
\(138\) | −0.337593 | −0.0287378 | ||||||||
\(139\) | −14.7025 | −1.24705 | −0.623526 | − | 0.781803i | \(-0.714301\pi\) | ||||
−0.623526 | + | 0.781803i | \(0.714301\pi\) | |||||||
\(140\) | −13.0275 | −1.10102 | ||||||||
\(141\) | 2.07039 | 0.174359 | ||||||||
\(142\) | 15.3353 | 1.28691 | ||||||||
\(143\) | −0.518474 | −0.0433570 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 17.2521 | 1.43271 | ||||||||
\(146\) | 8.24649 | 0.682485 | ||||||||
\(147\) | 10.7527 | 0.886870 | ||||||||
\(148\) | 0.867362 | 0.0712967 | ||||||||
\(149\) | 2.72711 | 0.223413 | 0.111707 | − | 0.993741i | \(-0.464368\pi\) | ||||
0.111707 | + | 0.993741i | \(0.464368\pi\) | |||||||
\(150\) | 4.55998 | 0.372321 | ||||||||
\(151\) | −10.1402 | −0.825195 | −0.412597 | − | 0.910914i | \(-0.635378\pi\) | ||||
−0.412597 | + | 0.910914i | \(0.635378\pi\) | |||||||
\(152\) | 8.39142 | 0.680634 | ||||||||
\(153\) | −3.01037 | −0.243374 | ||||||||
\(154\) | −4.21340 | −0.339525 | ||||||||
\(155\) | 14.7000 | 1.18073 | ||||||||
\(156\) | −0.518474 | −0.0415112 | ||||||||
\(157\) | −21.1790 | −1.69027 | −0.845135 | − | 0.534552i | \(-0.820480\pi\) | ||||
−0.845135 | + | 0.534552i | \(0.820480\pi\) | |||||||
\(158\) | −15.3981 | −1.22501 | ||||||||
\(159\) | 4.08394 | 0.323877 | ||||||||
\(160\) | 3.09192 | 0.244438 | ||||||||
\(161\) | 1.42241 | 0.112102 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.185111 | 0.0144990 | 0.00724951 | − | 0.999974i | \(-0.497692\pi\) | ||||
0.00724951 | + | 0.999974i | \(0.497692\pi\) | |||||||
\(164\) | 8.17976 | 0.638732 | ||||||||
\(165\) | 3.09192 | 0.240706 | ||||||||
\(166\) | −8.21682 | −0.637749 | ||||||||
\(167\) | −17.7975 | −1.37721 | −0.688606 | − | 0.725136i | \(-0.741777\pi\) | ||||
−0.688606 | + | 0.725136i | \(0.741777\pi\) | |||||||
\(168\) | −4.21340 | −0.325071 | ||||||||
\(169\) | −12.7312 | −0.979322 | ||||||||
\(170\) | −9.30782 | −0.713877 | ||||||||
\(171\) | 8.39142 | 0.641708 | ||||||||
\(172\) | −9.01482 | −0.687374 | ||||||||
\(173\) | −4.92214 | −0.374223 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(174\) | 5.57973 | 0.422999 | ||||||||
\(175\) | −19.2130 | −1.45237 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −2.99101 | −0.224818 | ||||||||
\(178\) | 8.31023 | 0.622878 | ||||||||
\(179\) | −5.64476 | −0.421909 | −0.210955 | − | 0.977496i | \(-0.567657\pi\) | ||||
−0.210955 | + | 0.977496i | \(0.567657\pi\) | |||||||
\(180\) | 3.09192 | 0.230458 | ||||||||
\(181\) | −4.40261 | −0.327243 | −0.163622 | − | 0.986523i | \(-0.552318\pi\) | ||||
−0.163622 | + | 0.986523i | \(0.552318\pi\) | |||||||
\(182\) | 2.18454 | 0.161929 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −0.337593 | −0.0248877 | ||||||||
\(185\) | 2.68182 | 0.197171 | ||||||||
\(186\) | 4.75433 | 0.348604 | ||||||||
\(187\) | −3.01037 | −0.220140 | ||||||||
\(188\) | 2.07039 | 0.150999 | ||||||||
\(189\) | −4.21340 | −0.306480 | ||||||||
\(190\) | 25.9456 | 1.88229 | ||||||||
\(191\) | 27.0598 | 1.95798 | 0.978988 | − | 0.203920i | \(-0.0653681\pi\) | ||||
0.978988 | + | 0.203920i | \(0.0653681\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −10.7214 | −0.771743 | −0.385871 | − | 0.922553i | \(-0.626099\pi\) | ||||
−0.385871 | + | 0.922553i | \(0.626099\pi\) | |||||||
\(194\) | −4.53172 | −0.325358 | ||||||||
\(195\) | −1.60308 | −0.114799 | ||||||||
\(196\) | 10.7527 | 0.768052 | ||||||||
\(197\) | 11.7458 | 0.836852 | 0.418426 | − | 0.908251i | \(-0.362582\pi\) | ||||
0.418426 | + | 0.908251i | \(0.362582\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −0.770322 | −0.0546067 | −0.0273034 | − | 0.999627i | \(-0.508692\pi\) | ||||
−0.0273034 | + | 0.999627i | \(0.508692\pi\) | |||||||
\(200\) | 4.55998 | 0.322439 | ||||||||
\(201\) | −1.16994 | −0.0825209 | ||||||||
\(202\) | −1.63654 | −0.115146 | ||||||||
\(203\) | −23.5096 | −1.65005 | ||||||||
\(204\) | −3.01037 | −0.210768 | ||||||||
\(205\) | 25.2912 | 1.76641 | ||||||||
\(206\) | 7.63116 | 0.531688 | ||||||||
\(207\) | −0.337593 | −0.0234643 | ||||||||
\(208\) | −0.518474 | −0.0359497 | ||||||||
\(209\) | 8.39142 | 0.580447 | ||||||||
\(210\) | −13.0275 | −0.898983 | ||||||||
\(211\) | −3.55095 | −0.244458 | −0.122229 | − | 0.992502i | \(-0.539004\pi\) | ||||
−0.122229 | + | 0.992502i | \(0.539004\pi\) | |||||||
\(212\) | 4.08394 | 0.280486 | ||||||||
\(213\) | 15.3353 | 1.05076 | ||||||||
\(214\) | −8.45294 | −0.577831 | ||||||||
\(215\) | −27.8731 | −1.90093 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −20.0319 | −1.35985 | ||||||||
\(218\) | −2.43637 | −0.165012 | ||||||||
\(219\) | 8.24649 | 0.557246 | ||||||||
\(220\) | 3.09192 | 0.208457 | ||||||||
\(221\) | 1.56080 | 0.104991 | ||||||||
\(222\) | 0.867362 | 0.0582135 | ||||||||
\(223\) | −25.4930 | −1.70714 | −0.853569 | − | 0.520980i | \(-0.825566\pi\) | ||||
−0.853569 | + | 0.520980i | \(0.825566\pi\) | |||||||
\(224\) | −4.21340 | −0.281519 | ||||||||
\(225\) | 4.55998 | 0.303999 | ||||||||
\(226\) | 15.3057 | 1.01812 | ||||||||
\(227\) | 0.170623 | 0.0113247 | 0.00566233 | − | 0.999984i | \(-0.498198\pi\) | ||||
0.00566233 | + | 0.999984i | \(0.498198\pi\) | |||||||
\(228\) | 8.39142 | 0.555736 | ||||||||
\(229\) | 11.6894 | 0.772460 | 0.386230 | − | 0.922402i | \(-0.373777\pi\) | ||||
0.386230 | + | 0.922402i | \(0.373777\pi\) | |||||||
\(230\) | −1.04381 | −0.0688268 | ||||||||
\(231\) | −4.21340 | −0.277221 | ||||||||
\(232\) | 5.57973 | 0.366327 | ||||||||
\(233\) | −3.78322 | −0.247847 | −0.123924 | − | 0.992292i | \(-0.539548\pi\) | ||||
−0.123924 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(234\) | −0.518474 | −0.0338937 | ||||||||
\(235\) | 6.40149 | 0.417587 | ||||||||
\(236\) | −2.99101 | −0.194698 | ||||||||
\(237\) | −15.3981 | −1.00022 | ||||||||
\(238\) | 12.6839 | 0.822174 | ||||||||
\(239\) | −1.37684 | −0.0890604 | −0.0445302 | − | 0.999008i | \(-0.514179\pi\) | ||||
−0.0445302 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(240\) | 3.09192 | 0.199583 | ||||||||
\(241\) | 5.21306 | 0.335803 | 0.167901 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167901 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 33.2466 | 2.12405 | ||||||||
\(246\) | 8.17976 | 0.521523 | ||||||||
\(247\) | −4.35074 | −0.276831 | ||||||||
\(248\) | 4.75433 | 0.301900 | ||||||||
\(249\) | −8.21682 | −0.520720 | ||||||||
\(250\) | −1.36051 | −0.0860464 | ||||||||
\(251\) | 8.63092 | 0.544779 | 0.272389 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272389 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(252\) | −4.21340 | −0.265419 | ||||||||
\(253\) | −0.337593 | −0.0212243 | ||||||||
\(254\) | 15.9129 | 0.998462 | ||||||||
\(255\) | −9.30782 | −0.582878 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.3616 | −1.76915 | −0.884573 | − | 0.466401i | \(-0.845550\pi\) | ||||
−0.884573 | + | 0.466401i | \(0.845550\pi\) | |||||||
\(258\) | −9.01482 | −0.561238 | ||||||||
\(259\) | −3.65454 | −0.227082 | ||||||||
\(260\) | −1.60308 | −0.0994189 | ||||||||
\(261\) | 5.57973 | 0.345377 | ||||||||
\(262\) | −0.798822 | −0.0493514 | ||||||||
\(263\) | −29.9754 | −1.84836 | −0.924182 | − | 0.381953i | \(-0.875252\pi\) | ||||
−0.924182 | + | 0.381953i | \(0.875252\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 12.6272 | 0.775684 | ||||||||
\(266\) | −35.3564 | −2.16784 | ||||||||
\(267\) | 8.31023 | 0.508578 | ||||||||
\(268\) | −1.16994 | −0.0714652 | ||||||||
\(269\) | −13.1706 | −0.803027 | −0.401514 | − | 0.915853i | \(-0.631516\pi\) | ||||
−0.401514 | + | 0.915853i | \(0.631516\pi\) | |||||||
\(270\) | 3.09192 | 0.188168 | ||||||||
\(271\) | −7.45328 | −0.452754 | −0.226377 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226377 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(272\) | −3.01037 | −0.182530 | ||||||||
\(273\) | 2.18454 | 0.132214 | ||||||||
\(274\) | −2.23605 | −0.135084 | ||||||||
\(275\) | 4.55998 | 0.274977 | ||||||||
\(276\) | −0.337593 | −0.0203207 | ||||||||
\(277\) | 18.2143 | 1.09439 | 0.547194 | − | 0.837006i | \(-0.315696\pi\) | ||||
0.547194 | + | 0.837006i | \(0.315696\pi\) | |||||||
\(278\) | −14.7025 | −0.881799 | ||||||||
\(279\) | 4.75433 | 0.284634 | ||||||||
\(280\) | −13.0275 | −0.778542 | ||||||||
\(281\) | −0.772012 | −0.0460544 | −0.0230272 | − | 0.999735i | \(-0.507330\pi\) | ||||
−0.0230272 | + | 0.999735i | \(0.507330\pi\) | |||||||
\(282\) | 2.07039 | 0.123290 | ||||||||
\(283\) | 18.9952 | 1.12915 | 0.564574 | − | 0.825383i | \(-0.309041\pi\) | ||||
0.564574 | + | 0.825383i | \(0.309041\pi\) | |||||||
\(284\) | 15.3353 | 0.909983 | ||||||||
\(285\) | 25.9456 | 1.53689 | ||||||||
\(286\) | −0.518474 | −0.0306580 | ||||||||
\(287\) | −34.4646 | −2.03438 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −7.93769 | −0.466923 | ||||||||
\(290\) | 17.2521 | 1.01308 | ||||||||
\(291\) | −4.53172 | −0.265654 | ||||||||
\(292\) | 8.24649 | 0.482590 | ||||||||
\(293\) | 23.3929 | 1.36663 | 0.683314 | − | 0.730125i | \(-0.260538\pi\) | ||||
0.683314 | + | 0.730125i | \(0.260538\pi\) | |||||||
\(294\) | 10.7527 | 0.627112 | ||||||||
\(295\) | −9.24798 | −0.538438 | ||||||||
\(296\) | 0.867362 | 0.0504144 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 2.72711 | 0.157977 | ||||||||
\(299\) | 0.175033 | 0.0101224 | ||||||||
\(300\) | 4.55998 | 0.263270 | ||||||||
\(301\) | 37.9830 | 2.18931 | ||||||||
\(302\) | −10.1402 | −0.583501 | ||||||||
\(303\) | −1.63654 | −0.0940167 | ||||||||
\(304\) | 8.39142 | 0.481281 | ||||||||
\(305\) | −3.09192 | −0.177043 | ||||||||
\(306\) | −3.01037 | −0.172091 | ||||||||
\(307\) | −17.5170 | −0.999750 | −0.499875 | − | 0.866098i | \(-0.666621\pi\) | ||||
−0.499875 | + | 0.866098i | \(0.666621\pi\) | |||||||
\(308\) | −4.21340 | −0.240081 | ||||||||
\(309\) | 7.63116 | 0.434121 | ||||||||
\(310\) | 14.7000 | 0.834904 | ||||||||
\(311\) | −19.9778 | −1.13284 | −0.566418 | − | 0.824118i | \(-0.691671\pi\) | ||||
−0.566418 | + | 0.824118i | \(0.691671\pi\) | |||||||
\(312\) | −0.518474 | −0.0293528 | ||||||||
\(313\) | 7.60209 | 0.429696 | 0.214848 | − | 0.976648i | \(-0.431074\pi\) | ||||
0.214848 | + | 0.976648i | \(0.431074\pi\) | |||||||
\(314\) | −21.1790 | −1.19520 | ||||||||
\(315\) | −13.0275 | −0.734016 | ||||||||
\(316\) | −15.3981 | −0.866213 | ||||||||
\(317\) | −1.61257 | −0.0905709 | −0.0452855 | − | 0.998974i | \(-0.514420\pi\) | ||||
−0.0452855 | + | 0.998974i | \(0.514420\pi\) | |||||||
\(318\) | 4.08394 | 0.229016 | ||||||||
\(319\) | 5.57973 | 0.312405 | ||||||||
\(320\) | 3.09192 | 0.172844 | ||||||||
\(321\) | −8.45294 | −0.471797 | ||||||||
\(322\) | 1.42241 | 0.0792680 | ||||||||
\(323\) | −25.2613 | −1.40557 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.36423 | −0.131144 | ||||||||
\(326\) | 0.185111 | 0.0102524 | ||||||||
\(327\) | −2.43637 | −0.134731 | ||||||||
\(328\) | 8.17976 | 0.451652 | ||||||||
\(329\) | −8.72339 | −0.480936 | ||||||||
\(330\) | 3.09192 | 0.170205 | ||||||||
\(331\) | −18.9630 | −1.04230 | −0.521149 | − | 0.853465i | \(-0.674497\pi\) | ||||
−0.521149 | + | 0.853465i | \(0.674497\pi\) | |||||||
\(332\) | −8.21682 | −0.450957 | ||||||||
\(333\) | 0.867362 | 0.0475312 | ||||||||
\(334\) | −17.7975 | −0.973836 | ||||||||
\(335\) | −3.61735 | −0.197637 | ||||||||
\(336\) | −4.21340 | −0.229860 | ||||||||
\(337\) | −15.7924 | −0.860268 | −0.430134 | − | 0.902765i | \(-0.641534\pi\) | ||||
−0.430134 | + | 0.902765i | \(0.641534\pi\) | |||||||
\(338\) | −12.7312 | −0.692485 | ||||||||
\(339\) | 15.3057 | 0.831290 | ||||||||
\(340\) | −9.30782 | −0.504787 | ||||||||
\(341\) | 4.75433 | 0.257461 | ||||||||
\(342\) | 8.39142 | 0.453756 | ||||||||
\(343\) | −15.8117 | −0.853752 | ||||||||
\(344\) | −9.01482 | −0.486047 | ||||||||
\(345\) | −1.04381 | −0.0561969 | ||||||||
\(346\) | −4.92214 | −0.264616 | ||||||||
\(347\) | −18.7955 | −1.00900 | −0.504498 | − | 0.863413i | \(-0.668323\pi\) | ||||
−0.504498 | + | 0.863413i | \(0.668323\pi\) | |||||||
\(348\) | 5.57973 | 0.299105 | ||||||||
\(349\) | −6.73963 | −0.360764 | −0.180382 | − | 0.983597i | \(-0.557733\pi\) | ||||
−0.180382 | + | 0.983597i | \(0.557733\pi\) | |||||||
\(350\) | −19.2130 | −1.02698 | ||||||||
\(351\) | −0.518474 | −0.0276741 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −8.54806 | −0.454967 | −0.227484 | − | 0.973782i | \(-0.573050\pi\) | ||||
−0.227484 | + | 0.973782i | \(0.573050\pi\) | |||||||
\(354\) | −2.99101 | −0.158971 | ||||||||
\(355\) | 47.4156 | 2.51656 | ||||||||
\(356\) | 8.31023 | 0.440441 | ||||||||
\(357\) | 12.6839 | 0.671302 | ||||||||
\(358\) | −5.64476 | −0.298335 | ||||||||
\(359\) | 13.9622 | 0.736896 | 0.368448 | − | 0.929648i | \(-0.379889\pi\) | ||||
0.368448 | + | 0.929648i | \(0.379889\pi\) | |||||||
\(360\) | 3.09192 | 0.162959 | ||||||||
\(361\) | 51.4160 | 2.70610 | ||||||||
\(362\) | −4.40261 | −0.231396 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 2.18454 | 0.114501 | ||||||||
\(365\) | 25.4975 | 1.33460 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 20.4701 | 1.06853 | 0.534264 | − | 0.845318i | \(-0.320589\pi\) | ||||
0.534264 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(368\) | −0.337593 | −0.0175982 | ||||||||
\(369\) | 8.17976 | 0.425821 | ||||||||
\(370\) | 2.68182 | 0.139421 | ||||||||
\(371\) | −17.2073 | −0.893356 | ||||||||
\(372\) | 4.75433 | 0.246500 | ||||||||
\(373\) | −12.4446 | −0.644355 | −0.322178 | − | 0.946679i | \(-0.604415\pi\) | ||||
−0.322178 | + | 0.946679i | \(0.604415\pi\) | |||||||
\(374\) | −3.01037 | −0.155662 | ||||||||
\(375\) | −1.36051 | −0.0702566 | ||||||||
\(376\) | 2.07039 | 0.106772 | ||||||||
\(377\) | −2.89295 | −0.148994 | ||||||||
\(378\) | −4.21340 | −0.216714 | ||||||||
\(379\) | −16.3449 | −0.839579 | −0.419789 | − | 0.907622i | \(-0.637896\pi\) | ||||
−0.419789 | + | 0.907622i | \(0.637896\pi\) | |||||||
\(380\) | 25.9456 | 1.33098 | ||||||||
\(381\) | 15.9129 | 0.815241 | ||||||||
\(382\) | 27.0598 | 1.38450 | ||||||||
\(383\) | 5.46817 | 0.279411 | 0.139705 | − | 0.990193i | \(-0.455384\pi\) | ||||
0.139705 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −13.0275 | −0.663943 | ||||||||
\(386\) | −10.7214 | −0.545705 | ||||||||
\(387\) | −9.01482 | −0.458249 | ||||||||
\(388\) | −4.53172 | −0.230063 | ||||||||
\(389\) | 11.8690 | 0.601781 | 0.300890 | − | 0.953659i | \(-0.402716\pi\) | ||||
0.300890 | + | 0.953659i | \(0.402716\pi\) | |||||||
\(390\) | −1.60308 | −0.0811752 | ||||||||
\(391\) | 1.01628 | 0.0513954 | ||||||||
\(392\) | 10.7527 | 0.543094 | ||||||||
\(393\) | −0.798822 | −0.0402953 | ||||||||
\(394\) | 11.7458 | 0.591744 | ||||||||
\(395\) | −47.6098 | −2.39551 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −6.85274 | −0.343929 | −0.171965 | − | 0.985103i | \(-0.555011\pi\) | ||||
−0.171965 | + | 0.985103i | \(0.555011\pi\) | |||||||
\(398\) | −0.770322 | −0.0386128 | ||||||||
\(399\) | −35.3564 | −1.77003 | ||||||||
\(400\) | 4.55998 | 0.227999 | ||||||||
\(401\) | −32.3814 | −1.61705 | −0.808526 | − | 0.588461i | \(-0.799734\pi\) | ||||
−0.808526 | + | 0.588461i | \(0.799734\pi\) | |||||||
\(402\) | −1.16994 | −0.0583511 | ||||||||
\(403\) | −2.46500 | −0.122790 | ||||||||
\(404\) | −1.63654 | −0.0814208 | ||||||||
\(405\) | 3.09192 | 0.153639 | ||||||||
\(406\) | −23.5096 | −1.16676 | ||||||||
\(407\) | 0.867362 | 0.0429936 | ||||||||
\(408\) | −3.01037 | −0.149035 | ||||||||
\(409\) | 1.99757 | 0.0987732 | 0.0493866 | − | 0.998780i | \(-0.484273\pi\) | ||||
0.0493866 | + | 0.998780i | \(0.484273\pi\) | |||||||
\(410\) | 25.2912 | 1.24904 | ||||||||
\(411\) | −2.23605 | −0.110296 | ||||||||
\(412\) | 7.63116 | 0.375960 | ||||||||
\(413\) | 12.6023 | 0.620120 | ||||||||
\(414\) | −0.337593 | −0.0165918 | ||||||||
\(415\) | −25.4058 | −1.24712 | ||||||||
\(416\) | −0.518474 | −0.0254203 | ||||||||
\(417\) | −14.7025 | −0.719986 | ||||||||
\(418\) | 8.39142 | 0.410438 | ||||||||
\(419\) | −33.6785 | −1.64530 | −0.822651 | − | 0.568546i | \(-0.807506\pi\) | ||||
−0.822651 | + | 0.568546i | \(0.807506\pi\) | |||||||
\(420\) | −13.0275 | −0.635677 | ||||||||
\(421\) | 24.8542 | 1.21132 | 0.605660 | − | 0.795723i | \(-0.292909\pi\) | ||||
0.605660 | + | 0.795723i | \(0.292909\pi\) | |||||||
\(422\) | −3.55095 | −0.172858 | ||||||||
\(423\) | 2.07039 | 0.100666 | ||||||||
\(424\) | 4.08394 | 0.198334 | ||||||||
\(425\) | −13.7272 | −0.665867 | ||||||||
\(426\) | 15.3353 | 0.742998 | ||||||||
\(427\) | 4.21340 | 0.203901 | ||||||||
\(428\) | −8.45294 | −0.408588 | ||||||||
\(429\) | −0.518474 | −0.0250322 | ||||||||
\(430\) | −27.8731 | −1.34416 | ||||||||
\(431\) | 23.2622 | 1.12050 | 0.560250 | − | 0.828324i | \(-0.310705\pi\) | ||||
0.560250 | + | 0.828324i | \(0.310705\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 37.3989 | 1.79728 | 0.898638 | − | 0.438692i | \(-0.144558\pi\) | ||||
0.898638 | + | 0.438692i | \(0.144558\pi\) | |||||||
\(434\) | −20.0319 | −0.961561 | ||||||||
\(435\) | 17.2521 | 0.827175 | ||||||||
\(436\) | −2.43637 | −0.116681 | ||||||||
\(437\) | −2.83288 | −0.135515 | ||||||||
\(438\) | 8.24649 | 0.394033 | ||||||||
\(439\) | −10.1292 | −0.483438 | −0.241719 | − | 0.970346i | \(-0.577711\pi\) | ||||
−0.241719 | + | 0.970346i | \(0.577711\pi\) | |||||||
\(440\) | 3.09192 | 0.147402 | ||||||||
\(441\) | 10.7527 | 0.512034 | ||||||||
\(442\) | 1.56080 | 0.0742396 | ||||||||
\(443\) | −24.2824 | −1.15369 | −0.576845 | − | 0.816853i | \(-0.695716\pi\) | ||||
−0.576845 | + | 0.816853i | \(0.695716\pi\) | |||||||
\(444\) | 0.867362 | 0.0411632 | ||||||||
\(445\) | 25.6946 | 1.21804 | ||||||||
\(446\) | −25.4930 | −1.20713 | ||||||||
\(447\) | 2.72711 | 0.128988 | ||||||||
\(448\) | −4.21340 | −0.199064 | ||||||||
\(449\) | 30.9258 | 1.45948 | 0.729740 | − | 0.683724i | \(-0.239641\pi\) | ||||
0.729740 | + | 0.683724i | \(0.239641\pi\) | |||||||
\(450\) | 4.55998 | 0.214959 | ||||||||
\(451\) | 8.17976 | 0.385170 | ||||||||
\(452\) | 15.3057 | 0.719919 | ||||||||
\(453\) | −10.1402 | −0.476426 | ||||||||
\(454\) | 0.170623 | 0.00800774 | ||||||||
\(455\) | 6.75442 | 0.316652 | ||||||||
\(456\) | 8.39142 | 0.392964 | ||||||||
\(457\) | 22.6296 | 1.05857 | 0.529284 | − | 0.848445i | \(-0.322461\pi\) | ||||
0.529284 | + | 0.848445i | \(0.322461\pi\) | |||||||
\(458\) | 11.6894 | 0.546212 | ||||||||
\(459\) | −3.01037 | −0.140512 | ||||||||
\(460\) | −1.04381 | −0.0486679 | ||||||||
\(461\) | 21.0195 | 0.978975 | 0.489488 | − | 0.872010i | \(-0.337184\pi\) | ||||
0.489488 | + | 0.872010i | \(0.337184\pi\) | |||||||
\(462\) | −4.21340 | −0.196025 | ||||||||
\(463\) | −8.76779 | −0.407474 | −0.203737 | − | 0.979026i | \(-0.565309\pi\) | ||||
−0.203737 | + | 0.979026i | \(0.565309\pi\) | |||||||
\(464\) | 5.57973 | 0.259033 | ||||||||
\(465\) | 14.7000 | 0.681697 | ||||||||
\(466\) | −3.78322 | −0.175254 | ||||||||
\(467\) | −16.6077 | −0.768514 | −0.384257 | − | 0.923226i | \(-0.625542\pi\) | ||||
−0.384257 | + | 0.923226i | \(0.625542\pi\) | |||||||
\(468\) | −0.518474 | −0.0239665 | ||||||||
\(469\) | 4.92940 | 0.227619 | ||||||||
\(470\) | 6.40149 | 0.295279 | ||||||||
\(471\) | −21.1790 | −0.975878 | ||||||||
\(472\) | −2.99101 | −0.137673 | ||||||||
\(473\) | −9.01482 | −0.414502 | ||||||||
\(474\) | −15.3981 | −0.707260 | ||||||||
\(475\) | 38.2647 | 1.75570 | ||||||||
\(476\) | 12.6839 | 0.581364 | ||||||||
\(477\) | 4.08394 | 0.186991 | ||||||||
\(478\) | −1.37684 | −0.0629752 | ||||||||
\(479\) | 8.73112 | 0.398935 | 0.199467 | − | 0.979904i | \(-0.436079\pi\) | ||||
0.199467 | + | 0.979904i | \(0.436079\pi\) | |||||||
\(480\) | 3.09192 | 0.141126 | ||||||||
\(481\) | −0.449705 | −0.0205048 | ||||||||
\(482\) | 5.21306 | 0.237448 | ||||||||
\(483\) | 1.42241 | 0.0647220 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −14.0117 | −0.636239 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.8409 | 0.944393 | 0.472196 | − | 0.881493i | \(-0.343461\pi\) | ||||
0.472196 | + | 0.881493i | \(0.343461\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 0.185111 | 0.00837101 | ||||||||
\(490\) | 33.2466 | 1.50193 | ||||||||
\(491\) | −12.7316 | −0.574567 | −0.287284 | − | 0.957846i | \(-0.592752\pi\) | ||||
−0.287284 | + | 0.957846i | \(0.592752\pi\) | |||||||
\(492\) | 8.17976 | 0.368772 | ||||||||
\(493\) | −16.7970 | −0.756501 | ||||||||
\(494\) | −4.35074 | −0.195749 | ||||||||
\(495\) | 3.09192 | 0.138972 | ||||||||
\(496\) | 4.75433 | 0.213476 | ||||||||
\(497\) | −64.6138 | −2.89832 | ||||||||
\(498\) | −8.21682 | −0.368205 | ||||||||
\(499\) | −14.9212 | −0.667964 | −0.333982 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333982 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(500\) | −1.36051 | −0.0608440 | ||||||||
\(501\) | −17.7975 | −0.795134 | ||||||||
\(502\) | 8.63092 | 0.385217 | ||||||||
\(503\) | 8.87163 | 0.395567 | 0.197783 | − | 0.980246i | \(-0.436626\pi\) | ||||
0.197783 | + | 0.980246i | \(0.436626\pi\) | |||||||
\(504\) | −4.21340 | −0.187680 | ||||||||
\(505\) | −5.06005 | −0.225169 | ||||||||
\(506\) | −0.337593 | −0.0150078 | ||||||||
\(507\) | −12.7312 | −0.565412 | ||||||||
\(508\) | 15.9129 | 0.706019 | ||||||||
\(509\) | −4.80090 | −0.212796 | −0.106398 | − | 0.994324i | \(-0.533932\pi\) | ||||
−0.106398 | + | 0.994324i | \(0.533932\pi\) | |||||||
\(510\) | −9.30782 | −0.412157 | ||||||||
\(511\) | −34.7458 | −1.53706 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.39142 | 0.370490 | ||||||||
\(514\) | −28.3616 | −1.25098 | ||||||||
\(515\) | 23.5949 | 1.03972 | ||||||||
\(516\) | −9.01482 | −0.396855 | ||||||||
\(517\) | 2.07039 | 0.0910558 | ||||||||
\(518\) | −3.65454 | −0.160571 | ||||||||
\(519\) | −4.92214 | −0.216058 | ||||||||
\(520\) | −1.60308 | −0.0702998 | ||||||||
\(521\) | 36.6061 | 1.60374 | 0.801870 | − | 0.597498i | \(-0.203839\pi\) | ||||
0.801870 | + | 0.597498i | \(0.203839\pi\) | |||||||
\(522\) | 5.57973 | 0.244218 | ||||||||
\(523\) | 40.8389 | 1.78576 | 0.892880 | − | 0.450296i | \(-0.148681\pi\) | ||||
0.892880 | + | 0.450296i | \(0.148681\pi\) | |||||||
\(524\) | −0.798822 | −0.0348967 | ||||||||
\(525\) | −19.2130 | −0.838524 | ||||||||
\(526\) | −29.9754 | −1.30699 | ||||||||
\(527\) | −14.3123 | −0.623453 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −22.8860 | −0.995045 | ||||||||
\(530\) | 12.6272 | 0.548491 | ||||||||
\(531\) | −2.99101 | −0.129799 | ||||||||
\(532\) | −35.3564 | −1.53289 | ||||||||
\(533\) | −4.24100 | −0.183698 | ||||||||
\(534\) | 8.31023 | 0.359619 | ||||||||
\(535\) | −26.1358 | −1.12995 | ||||||||
\(536\) | −1.16994 | −0.0505335 | ||||||||
\(537\) | −5.64476 | −0.243589 | ||||||||
\(538\) | −13.1706 | −0.567826 | ||||||||
\(539\) | 10.7527 | 0.463153 | ||||||||
\(540\) | 3.09192 | 0.133055 | ||||||||
\(541\) | 32.2117 | 1.38489 | 0.692444 | − | 0.721472i | \(-0.256534\pi\) | ||||
0.692444 | + | 0.721472i | \(0.256534\pi\) | |||||||
\(542\) | −7.45328 | −0.320146 | ||||||||
\(543\) | −4.40261 | −0.188934 | ||||||||
\(544\) | −3.01037 | −0.129068 | ||||||||
\(545\) | −7.53305 | −0.322681 | ||||||||
\(546\) | 2.18454 | 0.0934896 | ||||||||
\(547\) | −17.2349 | −0.736910 | −0.368455 | − | 0.929646i | \(-0.620113\pi\) | ||||
−0.368455 | + | 0.929646i | \(0.620113\pi\) | |||||||
\(548\) | −2.23605 | −0.0955191 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 4.55998 | 0.194438 | ||||||||
\(551\) | 46.8219 | 1.99468 | ||||||||
\(552\) | −0.337593 | −0.0143689 | ||||||||
\(553\) | 64.8785 | 2.75891 | ||||||||
\(554\) | 18.2143 | 0.773850 | ||||||||
\(555\) | 2.68182 | 0.113837 | ||||||||
\(556\) | −14.7025 | −0.623526 | ||||||||
\(557\) | −19.3746 | −0.820927 | −0.410463 | − | 0.911877i | \(-0.634633\pi\) | ||||
−0.410463 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(558\) | 4.75433 | 0.201267 | ||||||||
\(559\) | 4.67395 | 0.197687 | ||||||||
\(560\) | −13.0275 | −0.550512 | ||||||||
\(561\) | −3.01037 | −0.127098 | ||||||||
\(562\) | −0.772012 | −0.0325654 | ||||||||
\(563\) | −27.7582 | −1.16987 | −0.584933 | − | 0.811081i | \(-0.698879\pi\) | ||||
−0.584933 | + | 0.811081i | \(0.698879\pi\) | |||||||
\(564\) | 2.07039 | 0.0871793 | ||||||||
\(565\) | 47.3240 | 1.99093 | ||||||||
\(566\) | 18.9952 | 0.798428 | ||||||||
\(567\) | −4.21340 | −0.176946 | ||||||||
\(568\) | 15.3353 | 0.643455 | ||||||||
\(569\) | −22.9603 | −0.962546 | −0.481273 | − | 0.876571i | \(-0.659825\pi\) | ||||
−0.481273 | + | 0.876571i | \(0.659825\pi\) | |||||||
\(570\) | 25.9456 | 1.08674 | ||||||||
\(571\) | −5.52471 | −0.231202 | −0.115601 | − | 0.993296i | \(-0.536879\pi\) | ||||
−0.115601 | + | 0.993296i | \(0.536879\pi\) | |||||||
\(572\) | −0.518474 | −0.0216785 | ||||||||
\(573\) | 27.0598 | 1.13044 | ||||||||
\(574\) | −34.4646 | −1.43852 | ||||||||
\(575\) | −1.53942 | −0.0641981 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 38.0739 | 1.58504 | 0.792519 | − | 0.609847i | \(-0.208769\pi\) | ||||
0.792519 | + | 0.609847i | \(0.208769\pi\) | |||||||
\(578\) | −7.93769 | −0.330164 | ||||||||
\(579\) | −10.7214 | −0.445566 | ||||||||
\(580\) | 17.2521 | 0.716354 | ||||||||
\(581\) | 34.6207 | 1.43631 | ||||||||
\(582\) | −4.53172 | −0.187846 | ||||||||
\(583\) | 4.08394 | 0.169139 | ||||||||
\(584\) | 8.24649 | 0.341242 | ||||||||
\(585\) | −1.60308 | −0.0662793 | ||||||||
\(586\) | 23.3929 | 0.966352 | ||||||||
\(587\) | −30.4377 | −1.25630 | −0.628149 | − | 0.778093i | \(-0.716187\pi\) | ||||
−0.628149 | + | 0.778093i | \(0.716187\pi\) | |||||||
\(588\) | 10.7527 | 0.443435 | ||||||||
\(589\) | 39.8956 | 1.64387 | ||||||||
\(590\) | −9.24798 | −0.380733 | ||||||||
\(591\) | 11.7458 | 0.483157 | ||||||||
\(592\) | 0.867362 | 0.0356484 | ||||||||
\(593\) | −26.0646 | −1.07034 | −0.535172 | − | 0.844743i | \(-0.679753\pi\) | ||||
−0.535172 | + | 0.844743i | \(0.679753\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 39.2175 | 1.60776 | ||||||||
\(596\) | 2.72711 | 0.111707 | ||||||||
\(597\) | −0.770322 | −0.0315272 | ||||||||
\(598\) | 0.175033 | 0.00715764 | ||||||||
\(599\) | 14.3108 | 0.584725 | 0.292362 | − | 0.956308i | \(-0.405559\pi\) | ||||
0.292362 | + | 0.956308i | \(0.405559\pi\) | |||||||
\(600\) | 4.55998 | 0.186160 | ||||||||
\(601\) | 12.7673 | 0.520790 | 0.260395 | − | 0.965502i | \(-0.416147\pi\) | ||||
0.260395 | + | 0.965502i | \(0.416147\pi\) | |||||||
\(602\) | 37.9830 | 1.54807 | ||||||||
\(603\) | −1.16994 | −0.0476434 | ||||||||
\(604\) | −10.1402 | −0.412597 | ||||||||
\(605\) | 3.09192 | 0.125704 | ||||||||
\(606\) | −1.63654 | −0.0664798 | ||||||||
\(607\) | −19.3392 | −0.784956 | −0.392478 | − | 0.919761i | \(-0.628382\pi\) | ||||
−0.392478 | + | 0.919761i | \(0.628382\pi\) | |||||||
\(608\) | 8.39142 | 0.340317 | ||||||||
\(609\) | −23.5096 | −0.952659 | ||||||||
\(610\) | −3.09192 | −0.125188 | ||||||||
\(611\) | −1.07345 | −0.0434270 | ||||||||
\(612\) | −3.01037 | −0.121687 | ||||||||
\(613\) | −18.5922 | −0.750931 | −0.375466 | − | 0.926836i | \(-0.622517\pi\) | ||||
−0.375466 | + | 0.926836i | \(0.622517\pi\) | |||||||
\(614\) | −17.5170 | −0.706930 | ||||||||
\(615\) | 25.2912 | 1.01984 | ||||||||
\(616\) | −4.21340 | −0.169763 | ||||||||
\(617\) | 39.8237 | 1.60324 | 0.801621 | − | 0.597832i | \(-0.203971\pi\) | ||||
0.801621 | + | 0.597832i | \(0.203971\pi\) | |||||||
\(618\) | 7.63116 | 0.306970 | ||||||||
\(619\) | −12.4565 | −0.500670 | −0.250335 | − | 0.968159i | \(-0.580541\pi\) | ||||
−0.250335 | + | 0.968159i | \(0.580541\pi\) | |||||||
\(620\) | 14.7000 | 0.590367 | ||||||||
\(621\) | −0.337593 | −0.0135471 | ||||||||
\(622\) | −19.9778 | −0.801035 | ||||||||
\(623\) | −35.0143 | −1.40282 | ||||||||
\(624\) | −0.518474 | −0.0207556 | ||||||||
\(625\) | −27.0065 | −1.08026 | ||||||||
\(626\) | 7.60209 | 0.303841 | ||||||||
\(627\) | 8.39142 | 0.335121 | ||||||||
\(628\) | −21.1790 | −0.845135 | ||||||||
\(629\) | −2.61108 | −0.104111 | ||||||||
\(630\) | −13.0275 | −0.519028 | ||||||||
\(631\) | 41.6083 | 1.65640 | 0.828200 | − | 0.560433i | \(-0.189365\pi\) | ||||
0.828200 | + | 0.560433i | \(0.189365\pi\) | |||||||
\(632\) | −15.3981 | −0.612505 | ||||||||
\(633\) | −3.55095 | −0.141138 | ||||||||
\(634\) | −1.61257 | −0.0640433 | ||||||||
\(635\) | 49.2013 | 1.95250 | ||||||||
\(636\) | 4.08394 | 0.161939 | ||||||||
\(637\) | −5.57501 | −0.220890 | ||||||||
\(638\) | 5.57973 | 0.220904 | ||||||||
\(639\) | 15.3353 | 0.606656 | ||||||||
\(640\) | 3.09192 | 0.122219 | ||||||||
\(641\) | −28.3780 | −1.12087 | −0.560433 | − | 0.828200i | \(-0.689365\pi\) | ||||
−0.560433 | + | 0.828200i | \(0.689365\pi\) | |||||||
\(642\) | −8.45294 | −0.333611 | ||||||||
\(643\) | 38.6590 | 1.52456 | 0.762282 | − | 0.647246i | \(-0.224079\pi\) | ||||
0.762282 | + | 0.647246i | \(0.224079\pi\) | |||||||
\(644\) | 1.42241 | 0.0560509 | ||||||||
\(645\) | −27.8731 | −1.09750 | ||||||||
\(646\) | −25.2613 | −0.993891 | ||||||||
\(647\) | 11.4466 | 0.450013 | 0.225006 | − | 0.974357i | \(-0.427760\pi\) | ||||
0.225006 | + | 0.974357i | \(0.427760\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.99101 | −0.117408 | ||||||||
\(650\) | −2.36423 | −0.0927328 | ||||||||
\(651\) | −20.0319 | −0.785111 | ||||||||
\(652\) | 0.185111 | 0.00724951 | ||||||||
\(653\) | −1.95068 | −0.0763359 | −0.0381679 | − | 0.999271i | \(-0.512152\pi\) | ||||
−0.0381679 | + | 0.999271i | \(0.512152\pi\) | |||||||
\(654\) | −2.43637 | −0.0952695 | ||||||||
\(655\) | −2.46990 | −0.0965068 | ||||||||
\(656\) | 8.17976 | 0.319366 | ||||||||
\(657\) | 8.24649 | 0.321726 | ||||||||
\(658\) | −8.72339 | −0.340073 | ||||||||
\(659\) | 32.5826 | 1.26924 | 0.634620 | − | 0.772825i | \(-0.281157\pi\) | ||||
0.634620 | + | 0.772825i | \(0.281157\pi\) | |||||||
\(660\) | 3.09192 | 0.120353 | ||||||||
\(661\) | 16.5972 | 0.645557 | 0.322779 | − | 0.946475i | \(-0.395383\pi\) | ||||
0.322779 | + | 0.946475i | \(0.395383\pi\) | |||||||
\(662\) | −18.9630 | −0.737017 | ||||||||
\(663\) | 1.56080 | 0.0606164 | ||||||||
\(664\) | −8.21682 | −0.318875 | ||||||||
\(665\) | −109.319 | −4.23922 | ||||||||
\(666\) | 0.867362 | 0.0336096 | ||||||||
\(667\) | −1.88368 | −0.0729363 | ||||||||
\(668\) | −17.7975 | −0.688606 | ||||||||
\(669\) | −25.4930 | −0.985616 | ||||||||
\(670\) | −3.61735 | −0.139750 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −4.21340 | −0.162535 | ||||||||
\(673\) | 8.92671 | 0.344099 | 0.172050 | − | 0.985088i | \(-0.444961\pi\) | ||||
0.172050 | + | 0.985088i | \(0.444961\pi\) | |||||||
\(674\) | −15.7924 | −0.608301 | ||||||||
\(675\) | 4.55998 | 0.175514 | ||||||||
\(676\) | −12.7312 | −0.489661 | ||||||||
\(677\) | −36.3408 | −1.39669 | −0.698345 | − | 0.715761i | \(-0.746080\pi\) | ||||
−0.698345 | + | 0.715761i | \(0.746080\pi\) | |||||||
\(678\) | 15.3057 | 0.587811 | ||||||||
\(679\) | 19.0939 | 0.732758 | ||||||||
\(680\) | −9.30782 | −0.356939 | ||||||||
\(681\) | 0.170623 | 0.00653830 | ||||||||
\(682\) | 4.75433 | 0.182053 | ||||||||
\(683\) | 47.8386 | 1.83049 | 0.915247 | − | 0.402894i | \(-0.131996\pi\) | ||||
0.915247 | + | 0.402894i | \(0.131996\pi\) | |||||||
\(684\) | 8.39142 | 0.320854 | ||||||||
\(685\) | −6.91368 | −0.264158 | ||||||||
\(686\) | −15.8117 | −0.603694 | ||||||||
\(687\) | 11.6894 | 0.445980 | ||||||||
\(688\) | −9.01482 | −0.343687 | ||||||||
\(689\) | −2.11742 | −0.0806672 | ||||||||
\(690\) | −1.04381 | −0.0397372 | ||||||||
\(691\) | −14.9486 | −0.568670 | −0.284335 | − | 0.958725i | \(-0.591773\pi\) | ||||
−0.284335 | + | 0.958725i | \(0.591773\pi\) | |||||||
\(692\) | −4.92214 | −0.187112 | ||||||||
\(693\) | −4.21340 | −0.160054 | ||||||||
\(694\) | −18.7955 | −0.713468 | ||||||||
\(695\) | −45.4591 | −1.72436 | ||||||||
\(696\) | 5.57973 | 0.211499 | ||||||||
\(697\) | −24.6241 | −0.932704 | ||||||||
\(698\) | −6.73963 | −0.255099 | ||||||||
\(699\) | −3.78322 | −0.143095 | ||||||||
\(700\) | −19.2130 | −0.726183 | ||||||||
\(701\) | −7.00137 | −0.264438 | −0.132219 | − | 0.991221i | \(-0.542210\pi\) | ||||
−0.132219 | + | 0.991221i | \(0.542210\pi\) | |||||||
\(702\) | −0.518474 | −0.0195686 | ||||||||
\(703\) | 7.27840 | 0.274510 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 6.40149 | 0.241094 | ||||||||
\(706\) | −8.54806 | −0.321710 | ||||||||
\(707\) | 6.89539 | 0.259328 | ||||||||
\(708\) | −2.99101 | −0.112409 | ||||||||
\(709\) | −2.70293 | −0.101511 | −0.0507554 | − | 0.998711i | \(-0.516163\pi\) | ||||
−0.0507554 | + | 0.998711i | \(0.516163\pi\) | |||||||
\(710\) | 47.4156 | 1.77948 | ||||||||
\(711\) | −15.3981 | −0.577475 | ||||||||
\(712\) | 8.31023 | 0.311439 | ||||||||
\(713\) | −1.60503 | −0.0601087 | ||||||||
\(714\) | 12.6839 | 0.474682 | ||||||||
\(715\) | −1.60308 | −0.0599519 | ||||||||
\(716\) | −5.64476 | −0.210955 | ||||||||
\(717\) | −1.37684 | −0.0514190 | ||||||||
\(718\) | 13.9622 | 0.521064 | ||||||||
\(719\) | −25.4169 | −0.947889 | −0.473944 | − | 0.880555i | \(-0.657170\pi\) | ||||
−0.473944 | + | 0.880555i | \(0.657170\pi\) | |||||||
\(720\) | 3.09192 | 0.115229 | ||||||||
\(721\) | −32.1531 | −1.19744 | ||||||||
\(722\) | 51.4160 | 1.91350 | ||||||||
\(723\) | 5.21306 | 0.193876 | ||||||||
\(724\) | −4.40261 | −0.163622 | ||||||||
\(725\) | 25.4435 | 0.944946 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −12.0829 | −0.448128 | −0.224064 | − | 0.974574i | \(-0.571933\pi\) | ||||
−0.224064 | + | 0.974574i | \(0.571933\pi\) | |||||||
\(728\) | 2.18454 | 0.0809644 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 25.4975 | 0.943705 | ||||||||
\(731\) | 27.1379 | 1.00373 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 48.9537 | 1.80815 | 0.904074 | − | 0.427376i | \(-0.140562\pi\) | ||||
0.904074 | + | 0.427376i | \(0.140562\pi\) | |||||||
\(734\) | 20.4701 | 0.755564 | ||||||||
\(735\) | 33.2466 | 1.22632 | ||||||||
\(736\) | −0.337593 | −0.0124438 | ||||||||
\(737\) | −1.16994 | −0.0430951 | ||||||||
\(738\) | 8.17976 | 0.301101 | ||||||||
\(739\) | −21.3134 | −0.784028 | −0.392014 | − | 0.919959i | \(-0.628222\pi\) | ||||
−0.392014 | + | 0.919959i | \(0.628222\pi\) | |||||||
\(740\) | 2.68182 | 0.0985855 | ||||||||
\(741\) | −4.35074 | −0.159828 | ||||||||
\(742\) | −17.2073 | −0.631698 | ||||||||
\(743\) | −22.9101 | −0.840490 | −0.420245 | − | 0.907411i | \(-0.638056\pi\) | ||||
−0.420245 | + | 0.907411i | \(0.638056\pi\) | |||||||
\(744\) | 4.75433 | 0.174302 | ||||||||
\(745\) | 8.43200 | 0.308925 | ||||||||
\(746\) | −12.4446 | −0.455628 | ||||||||
\(747\) | −8.21682 | −0.300638 | ||||||||
\(748\) | −3.01037 | −0.110070 | ||||||||
\(749\) | 35.6156 | 1.30137 | ||||||||
\(750\) | −1.36051 | −0.0496789 | ||||||||
\(751\) | −15.5280 | −0.566624 | −0.283312 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283312 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(752\) | 2.07039 | 0.0754995 | ||||||||
\(753\) | 8.63092 | 0.314528 | ||||||||
\(754\) | −2.89295 | −0.105355 | ||||||||
\(755\) | −31.3526 | −1.14104 | ||||||||
\(756\) | −4.21340 | −0.153240 | ||||||||
\(757\) | −27.9683 | −1.01652 | −0.508262 | − | 0.861202i | \(-0.669712\pi\) | ||||
−0.508262 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(758\) | −16.3449 | −0.593672 | ||||||||
\(759\) | −0.337593 | −0.0122538 | ||||||||
\(760\) | 25.9456 | 0.941147 | ||||||||
\(761\) | 7.42468 | 0.269144 | 0.134572 | − | 0.990904i | \(-0.457034\pi\) | ||||
0.134572 | + | 0.990904i | \(0.457034\pi\) | |||||||
\(762\) | 15.9129 | 0.576462 | ||||||||
\(763\) | 10.2654 | 0.371632 | ||||||||
\(764\) | 27.0598 | 0.978988 | ||||||||
\(765\) | −9.30782 | −0.336525 | ||||||||
\(766\) | 5.46817 | 0.197573 | ||||||||
\(767\) | 1.55076 | 0.0559948 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −3.42766 | −0.123605 | −0.0618023 | − | 0.998088i | \(-0.519685\pi\) | ||||
−0.0618023 | + | 0.998088i | \(0.519685\pi\) | |||||||
\(770\) | −13.0275 | −0.469478 | ||||||||
\(771\) | −28.3616 | −1.02142 | ||||||||
\(772\) | −10.7214 | −0.385871 | ||||||||
\(773\) | 43.7871 | 1.57491 | 0.787456 | − | 0.616371i | \(-0.211398\pi\) | ||||
0.787456 | + | 0.616371i | \(0.211398\pi\) | |||||||
\(774\) | −9.01482 | −0.324031 | ||||||||
\(775\) | 21.6796 | 0.778755 | ||||||||
\(776\) | −4.53172 | −0.162679 | ||||||||
\(777\) | −3.65454 | −0.131106 | ||||||||
\(778\) | 11.8690 | 0.425523 | ||||||||
\(779\) | 68.6398 | 2.45928 | ||||||||
\(780\) | −1.60308 | −0.0573995 | ||||||||
\(781\) | 15.3353 | 0.548741 | ||||||||
\(782\) | 1.01628 | 0.0363420 | ||||||||
\(783\) | 5.57973 | 0.199403 | ||||||||
\(784\) | 10.7527 | 0.384026 | ||||||||
\(785\) | −65.4839 | −2.33722 | ||||||||
\(786\) | −0.798822 | −0.0284931 | ||||||||
\(787\) | −32.0797 | −1.14352 | −0.571759 | − | 0.820422i | \(-0.693739\pi\) | ||||
−0.571759 | + | 0.820422i | \(0.693739\pi\) | |||||||
\(788\) | 11.7458 | 0.418426 | ||||||||
\(789\) | −29.9754 | −1.06715 | ||||||||
\(790\) | −47.6098 | −1.69388 | ||||||||
\(791\) | −64.4889 | −2.29296 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 0.518474 | 0.0184116 | ||||||||
\(794\) | −6.85274 | −0.243195 | ||||||||
\(795\) | 12.6272 | 0.447841 | ||||||||
\(796\) | −0.770322 | −0.0273034 | ||||||||
\(797\) | −13.5820 | −0.481098 | −0.240549 | − | 0.970637i | \(-0.577327\pi\) | ||||
−0.240549 | + | 0.970637i | \(0.577327\pi\) | |||||||
\(798\) | −35.3564 | −1.25160 | ||||||||
\(799\) | −6.23264 | −0.220495 | ||||||||
\(800\) | 4.55998 | 0.161220 | ||||||||
\(801\) | 8.31023 | 0.293627 | ||||||||
\(802\) | −32.3814 | −1.14343 | ||||||||
\(803\) | 8.24649 | 0.291012 | ||||||||
\(804\) | −1.16994 | −0.0412604 | ||||||||
\(805\) | 4.39799 | 0.155009 | ||||||||
\(806\) | −2.46500 | −0.0868258 | ||||||||
\(807\) | −13.1706 | −0.463628 | ||||||||
\(808\) | −1.63654 | −0.0575732 | ||||||||
\(809\) | −6.04913 | −0.212676 | −0.106338 | − | 0.994330i | \(-0.533913\pi\) | ||||
−0.106338 | + | 0.994330i | \(0.533913\pi\) | |||||||
\(810\) | 3.09192 | 0.108639 | ||||||||
\(811\) | −33.4456 | −1.17444 | −0.587218 | − | 0.809429i | \(-0.699777\pi\) | ||||
−0.587218 | + | 0.809429i | \(0.699777\pi\) | |||||||
\(812\) | −23.5096 | −0.825027 | ||||||||
\(813\) | −7.45328 | −0.261398 | ||||||||
\(814\) | 0.867362 | 0.0304010 | ||||||||
\(815\) | 0.572349 | 0.0200485 | ||||||||
\(816\) | −3.01037 | −0.105384 | ||||||||
\(817\) | −75.6472 | −2.64656 | ||||||||
\(818\) | 1.99757 | 0.0698432 | ||||||||
\(819\) | 2.18454 | 0.0763340 | ||||||||
\(820\) | 25.2912 | 0.883206 | ||||||||
\(821\) | −55.1716 | −1.92550 | −0.962750 | − | 0.270392i | \(-0.912847\pi\) | ||||
−0.962750 | + | 0.270392i | \(0.912847\pi\) | |||||||
\(822\) | −2.23605 | −0.0779910 | ||||||||
\(823\) | −26.8584 | −0.936225 | −0.468113 | − | 0.883669i | \(-0.655066\pi\) | ||||
−0.468113 | + | 0.883669i | \(0.655066\pi\) | |||||||
\(824\) | 7.63116 | 0.265844 | ||||||||
\(825\) | 4.55998 | 0.158758 | ||||||||
\(826\) | 12.6023 | 0.438491 | ||||||||
\(827\) | 22.2204 | 0.772678 | 0.386339 | − | 0.922357i | \(-0.373740\pi\) | ||||
0.386339 | + | 0.922357i | \(0.373740\pi\) | |||||||
\(828\) | −0.337593 | −0.0117322 | ||||||||
\(829\) | 49.8459 | 1.73122 | 0.865610 | − | 0.500719i | \(-0.166931\pi\) | ||||
0.865610 | + | 0.500719i | \(0.166931\pi\) | |||||||
\(830\) | −25.4058 | −0.881847 | ||||||||
\(831\) | 18.2143 | 0.631846 | ||||||||
\(832\) | −0.518474 | −0.0179749 | ||||||||
\(833\) | −32.3696 | −1.12154 | ||||||||
\(834\) | −14.7025 | −0.509107 | ||||||||
\(835\) | −55.0285 | −1.90434 | ||||||||
\(836\) | 8.39142 | 0.290223 | ||||||||
\(837\) | 4.75433 | 0.164334 | ||||||||
\(838\) | −33.6785 | −1.16340 | ||||||||
\(839\) | −47.6798 | −1.64609 | −0.823045 | − | 0.567977i | \(-0.807726\pi\) | ||||
−0.823045 | + | 0.567977i | \(0.807726\pi\) | |||||||
\(840\) | −13.0275 | −0.449491 | ||||||||
\(841\) | 2.13343 | 0.0735665 | ||||||||
\(842\) | 24.8542 | 0.856533 | ||||||||
\(843\) | −0.772012 | −0.0265895 | ||||||||
\(844\) | −3.55095 | −0.122229 | ||||||||
\(845\) | −39.3638 | −1.35416 | ||||||||
\(846\) | 2.07039 | 0.0711816 | ||||||||
\(847\) | −4.21340 | −0.144774 | ||||||||
\(848\) | 4.08394 | 0.140243 | ||||||||
\(849\) | 18.9952 | 0.651913 | ||||||||
\(850\) | −13.7272 | −0.470839 | ||||||||
\(851\) | −0.292815 | −0.0100376 | ||||||||
\(852\) | 15.3353 | 0.525379 | ||||||||
\(853\) | −49.5406 | −1.69624 | −0.848118 | − | 0.529807i | \(-0.822264\pi\) | ||||
−0.848118 | + | 0.529807i | \(0.822264\pi\) | |||||||
\(854\) | 4.21340 | 0.144180 | ||||||||
\(855\) | 25.9456 | 0.887321 | ||||||||
\(856\) | −8.45294 | −0.288916 | ||||||||
\(857\) | −52.9842 | −1.80991 | −0.904953 | − | 0.425511i | \(-0.860094\pi\) | ||||
−0.904953 | + | 0.425511i | \(0.860094\pi\) | |||||||
\(858\) | −0.518474 | −0.0177004 | ||||||||
\(859\) | −21.6621 | −0.739102 | −0.369551 | − | 0.929211i | \(-0.620488\pi\) | ||||
−0.369551 | + | 0.929211i | \(0.620488\pi\) | |||||||
\(860\) | −27.8731 | −0.950465 | ||||||||
\(861\) | −34.4646 | −1.17455 | ||||||||
\(862\) | 23.2622 | 0.792313 | ||||||||
\(863\) | 9.97990 | 0.339720 | 0.169860 | − | 0.985468i | \(-0.445669\pi\) | ||||
0.169860 | + | 0.985468i | \(0.445669\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −15.2189 | −0.517457 | ||||||||
\(866\) | 37.3989 | 1.27087 | ||||||||
\(867\) | −7.93769 | −0.269578 | ||||||||
\(868\) | −20.0319 | −0.679926 | ||||||||
\(869\) | −15.3981 | −0.522346 | ||||||||
\(870\) | 17.2521 | 0.584901 | ||||||||
\(871\) | 0.606581 | 0.0205532 | ||||||||
\(872\) | −2.43637 | −0.0825058 | ||||||||
\(873\) | −4.53172 | −0.153375 | ||||||||
\(874\) | −2.83288 | −0.0958237 | ||||||||
\(875\) | 5.73239 | 0.193790 | ||||||||
\(876\) | 8.24649 | 0.278623 | ||||||||
\(877\) | −36.9177 | −1.24662 | −0.623311 | − | 0.781974i | \(-0.714213\pi\) | ||||
−0.623311 | + | 0.781974i | \(0.714213\pi\) | |||||||
\(878\) | −10.1292 | −0.341843 | ||||||||
\(879\) | 23.3929 | 0.789023 | ||||||||
\(880\) | 3.09192 | 0.104229 | ||||||||
\(881\) | −15.2974 | −0.515382 | −0.257691 | − | 0.966227i | \(-0.582962\pi\) | ||||
−0.257691 | + | 0.966227i | \(0.582962\pi\) | |||||||
\(882\) | 10.7527 | 0.362063 | ||||||||
\(883\) | −27.4386 | −0.923383 | −0.461691 | − | 0.887041i | \(-0.652757\pi\) | ||||
−0.461691 | + | 0.887041i | \(0.652757\pi\) | |||||||
\(884\) | 1.56080 | 0.0524953 | ||||||||
\(885\) | −9.24798 | −0.310867 | ||||||||
\(886\) | −24.2824 | −0.815782 | ||||||||
\(887\) | −41.9719 | −1.40928 | −0.704640 | − | 0.709565i | \(-0.748891\pi\) | ||||
−0.704640 | + | 0.709565i | \(0.748891\pi\) | |||||||
\(888\) | 0.867362 | 0.0291068 | ||||||||
\(889\) | −67.0473 | −2.24869 | ||||||||
\(890\) | 25.6946 | 0.861284 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −25.4930 | −0.853569 | ||||||||
\(893\) | 17.3735 | 0.581383 | ||||||||
\(894\) | 2.72711 | 0.0912081 | ||||||||
\(895\) | −17.4531 | −0.583394 | ||||||||
\(896\) | −4.21340 | −0.140760 | ||||||||
\(897\) | 0.175033 | 0.00584419 | ||||||||
\(898\) | 30.9258 | 1.03201 | ||||||||
\(899\) | 26.5279 | 0.884755 | ||||||||
\(900\) | 4.55998 | 0.151999 | ||||||||
\(901\) | −12.2942 | −0.409578 | ||||||||
\(902\) | 8.17976 | 0.272356 | ||||||||
\(903\) | 37.9830 | 1.26400 | ||||||||
\(904\) | 15.3057 | 0.509059 | ||||||||
\(905\) | −13.6125 | −0.452495 | ||||||||
\(906\) | −10.1402 | −0.336884 | ||||||||
\(907\) | −44.2849 | −1.47045 | −0.735227 | − | 0.677821i | \(-0.762925\pi\) | ||||
−0.735227 | + | 0.677821i | \(0.762925\pi\) | |||||||
\(908\) | 0.170623 | 0.00566233 | ||||||||
\(909\) | −1.63654 | −0.0542806 | ||||||||
\(910\) | 6.75442 | 0.223907 | ||||||||
\(911\) | 30.5798 | 1.01315 | 0.506576 | − | 0.862195i | \(-0.330911\pi\) | ||||
0.506576 | + | 0.862195i | \(0.330911\pi\) | |||||||
\(912\) | 8.39142 | 0.277868 | ||||||||
\(913\) | −8.21682 | −0.271937 | ||||||||
\(914\) | 22.6296 | 0.748520 | ||||||||
\(915\) | −3.09192 | −0.102216 | ||||||||
\(916\) | 11.6894 | 0.386230 | ||||||||
\(917\) | 3.36576 | 0.111147 | ||||||||
\(918\) | −3.01037 | −0.0993569 | ||||||||
\(919\) | −8.45262 | −0.278826 | −0.139413 | − | 0.990234i | \(-0.544522\pi\) | ||||
−0.139413 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(920\) | −1.04381 | −0.0344134 | ||||||||
\(921\) | −17.5170 | −0.577206 | ||||||||
\(922\) | 21.0195 | 0.692240 | ||||||||
\(923\) | −7.95097 | −0.261709 | ||||||||
\(924\) | −4.21340 | −0.138611 | ||||||||
\(925\) | 3.95515 | 0.130045 | ||||||||
\(926\) | −8.76779 | −0.288127 | ||||||||
\(927\) | 7.63116 | 0.250640 | ||||||||
\(928\) | 5.57973 | 0.183164 | ||||||||
\(929\) | −44.0589 | −1.44553 | −0.722763 | − | 0.691096i | \(-0.757128\pi\) | ||||
−0.722763 | + | 0.691096i | \(0.757128\pi\) | |||||||
\(930\) | 14.7000 | 0.482032 | ||||||||
\(931\) | 90.2306 | 2.95719 | ||||||||
\(932\) | −3.78322 | −0.123924 | ||||||||
\(933\) | −19.9778 | −0.654043 | ||||||||
\(934\) | −16.6077 | −0.543421 | ||||||||
\(935\) | −9.30782 | −0.304398 | ||||||||
\(936\) | −0.518474 | −0.0169469 | ||||||||
\(937\) | 14.8733 | 0.485888 | 0.242944 | − | 0.970040i | \(-0.421887\pi\) | ||||
0.242944 | + | 0.970040i | \(0.421887\pi\) | |||||||
\(938\) | 4.92940 | 0.160951 | ||||||||
\(939\) | 7.60209 | 0.248085 | ||||||||
\(940\) | 6.40149 | 0.208794 | ||||||||
\(941\) | 10.2978 | 0.335700 | 0.167850 | − | 0.985813i | \(-0.446318\pi\) | ||||
0.167850 | + | 0.985813i | \(0.446318\pi\) | |||||||
\(942\) | −21.1790 | −0.690050 | ||||||||
\(943\) | −2.76143 | −0.0899245 | ||||||||
\(944\) | −2.99101 | −0.0973492 | ||||||||
\(945\) | −13.0275 | −0.423784 | ||||||||
\(946\) | −9.01482 | −0.293097 | ||||||||
\(947\) | −1.47097 | −0.0478001 | −0.0239000 | − | 0.999714i | \(-0.507608\pi\) | ||||
−0.0239000 | + | 0.999714i | \(0.507608\pi\) | |||||||
\(948\) | −15.3981 | −0.500108 | ||||||||
\(949\) | −4.27560 | −0.138792 | ||||||||
\(950\) | 38.2647 | 1.24147 | ||||||||
\(951\) | −1.61257 | −0.0522912 | ||||||||
\(952\) | 12.6839 | 0.411087 | ||||||||
\(953\) | −33.7619 | −1.09366 | −0.546828 | − | 0.837245i | \(-0.684165\pi\) | ||||
−0.546828 | + | 0.837245i | \(0.684165\pi\) | |||||||
\(954\) | 4.08394 | 0.132222 | ||||||||
\(955\) | 83.6666 | 2.70739 | ||||||||
\(956\) | −1.37684 | −0.0445302 | ||||||||
\(957\) | 5.57973 | 0.180367 | ||||||||
\(958\) | 8.73112 | 0.282090 | ||||||||
\(959\) | 9.42135 | 0.304231 | ||||||||
\(960\) | 3.09192 | 0.0997913 | ||||||||
\(961\) | −8.39636 | −0.270850 | ||||||||
\(962\) | −0.449705 | −0.0144991 | ||||||||
\(963\) | −8.45294 | −0.272392 | ||||||||
\(964\) | 5.21306 | 0.167901 | ||||||||
\(965\) | −33.1497 | −1.06713 | ||||||||
\(966\) | 1.42241 | 0.0457654 | ||||||||
\(967\) | 46.1024 | 1.48255 | 0.741276 | − | 0.671200i | \(-0.234221\pi\) | ||||
0.741276 | + | 0.671200i | \(0.234221\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −25.2613 | −0.811509 | ||||||||
\(970\) | −14.0117 | −0.449889 | ||||||||
\(971\) | −45.4790 | −1.45949 | −0.729745 | − | 0.683719i | \(-0.760361\pi\) | ||||
−0.729745 | + | 0.683719i | \(0.760361\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 61.9476 | 1.98595 | ||||||||
\(974\) | 20.8409 | 0.667786 | ||||||||
\(975\) | −2.36423 | −0.0757160 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 36.5909 | 1.17065 | 0.585324 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585324 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(978\) | 0.185111 | 0.00591920 | ||||||||
\(979\) | 8.31023 | 0.265596 | ||||||||
\(980\) | 33.2466 | 1.06202 | ||||||||
\(981\) | −2.43637 | −0.0777872 | ||||||||
\(982\) | −12.7316 | −0.406280 | ||||||||
\(983\) | 14.1244 | 0.450498 | 0.225249 | − | 0.974301i | \(-0.427681\pi\) | ||||
0.225249 | + | 0.974301i | \(0.427681\pi\) | |||||||
\(984\) | 8.17976 | 0.260761 | ||||||||
\(985\) | 36.3170 | 1.15716 | ||||||||
\(986\) | −16.7970 | −0.534927 | ||||||||
\(987\) | −8.72339 | −0.277669 | ||||||||
\(988\) | −4.35074 | −0.138415 | ||||||||
\(989\) | 3.04334 | 0.0967725 | ||||||||
\(990\) | 3.09192 | 0.0982677 | ||||||||
\(991\) | −47.5467 | −1.51037 | −0.755185 | − | 0.655512i | \(-0.772453\pi\) | ||||
−0.755185 | + | 0.655512i | \(0.772453\pi\) | |||||||
\(992\) | 4.75433 | 0.150950 | ||||||||
\(993\) | −18.9630 | −0.601771 | ||||||||
\(994\) | −64.6138 | −2.04942 | ||||||||
\(995\) | −2.38178 | −0.0755074 | ||||||||
\(996\) | −8.21682 | −0.260360 | ||||||||
\(997\) | −13.1638 | −0.416900 | −0.208450 | − | 0.978033i | \(-0.566842\pi\) | ||||
−0.208450 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(998\) | −14.9212 | −0.472322 | ||||||||
\(999\) | 0.867362 | 0.0274421 |
(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 | 4026.2.a.bc.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bc.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |