Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,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, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.24698\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.554958 | −0.392415 | −0.196207 | − | 0.980562i | \(-0.562863\pi\) | ||||
−0.196207 | + | 0.980562i | \(0.562863\pi\) | |||||||
\(3\) | −0.198062 | −0.114351 | −0.0571757 | − | 0.998364i | \(-0.518210\pi\) | ||||
−0.0571757 | + | 0.998364i | \(0.518210\pi\) | |||||||
\(4\) | −1.69202 | −0.846011 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0.109916 | 0.0448731 | ||||||||
\(7\) | −2.55496 | −0.965683 | −0.482842 | − | 0.875708i | \(-0.660395\pi\) | ||||
−0.482842 | + | 0.875708i | \(0.660395\pi\) | |||||||
\(8\) | 2.04892 | 0.724402 | ||||||||
\(9\) | −2.96077 | −0.986924 | ||||||||
\(10\) | 1.10992 | 0.350986 | ||||||||
\(11\) | 4.74094 | 1.42945 | 0.714723 | − | 0.699407i | \(-0.246553\pi\) | ||||
0.714723 | + | 0.699407i | \(0.246553\pi\) | |||||||
\(12\) | 0.335126 | 0.0967424 | ||||||||
\(13\) | 0.643104 | 0.178365 | 0.0891825 | − | 0.996015i | \(-0.471575\pi\) | ||||
0.0891825 | + | 0.996015i | \(0.471575\pi\) | |||||||
\(14\) | 1.41789 | 0.378948 | ||||||||
\(15\) | 0.396125 | 0.102279 | ||||||||
\(16\) | 2.24698 | 0.561745 | ||||||||
\(17\) | 1.10992 | 0.269194 | 0.134597 | − | 0.990900i | \(-0.457026\pi\) | ||||
0.134597 | + | 0.990900i | \(0.457026\pi\) | |||||||
\(18\) | 1.64310 | 0.387283 | ||||||||
\(19\) | 5.35690 | 1.22896 | 0.614478 | − | 0.788934i | \(-0.289367\pi\) | ||||
0.614478 | + | 0.788934i | \(0.289367\pi\) | |||||||
\(20\) | 3.38404 | 0.756695 | ||||||||
\(21\) | 0.506041 | 0.110427 | ||||||||
\(22\) | −2.63102 | −0.560936 | ||||||||
\(23\) | 5.24698 | 1.09407 | 0.547035 | − | 0.837109i | \(-0.315756\pi\) | ||||
0.547035 | + | 0.837109i | \(0.315756\pi\) | |||||||
\(24\) | −0.405813 | −0.0828363 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.356896 | −0.0699930 | ||||||||
\(27\) | 1.18060 | 0.227207 | ||||||||
\(28\) | 4.32304 | 0.816979 | ||||||||
\(29\) | −0.911854 | −0.169327 | −0.0846635 | − | 0.996410i | \(-0.526982\pi\) | ||||
−0.0846635 | + | 0.996410i | \(0.526982\pi\) | |||||||
\(30\) | −0.219833 | −0.0401357 | ||||||||
\(31\) | 5.96077 | 1.07059 | 0.535293 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535293 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(32\) | −5.34481 | −0.944839 | ||||||||
\(33\) | −0.939001 | −0.163459 | ||||||||
\(34\) | −0.615957 | −0.105636 | ||||||||
\(35\) | 5.10992 | 0.863733 | ||||||||
\(36\) | 5.00969 | 0.834948 | ||||||||
\(37\) | −11.3937 | −1.87312 | −0.936559 | − | 0.350510i | \(-0.886008\pi\) | ||||
−0.936559 | + | 0.350510i | \(0.886008\pi\) | |||||||
\(38\) | −2.97285 | −0.482260 | ||||||||
\(39\) | −0.127375 | −0.0203963 | ||||||||
\(40\) | −4.09783 | −0.647925 | ||||||||
\(41\) | −7.76271 | −1.21233 | −0.606166 | − | 0.795338i | \(-0.707293\pi\) | ||||
−0.606166 | + | 0.795338i | \(0.707293\pi\) | |||||||
\(42\) | −0.280831 | −0.0433332 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −8.02177 | −1.20933 | ||||||||
\(45\) | 5.92154 | 0.882731 | ||||||||
\(46\) | −2.91185 | −0.429329 | ||||||||
\(47\) | −1.00000 | −0.145865 | −0.0729325 | − | 0.997337i | \(-0.523236\pi\) | ||||
−0.0729325 | + | 0.997337i | \(0.523236\pi\) | |||||||
\(48\) | −0.445042 | −0.0642363 | ||||||||
\(49\) | −0.472189 | −0.0674556 | ||||||||
\(50\) | 0.554958 | 0.0784829 | ||||||||
\(51\) | −0.219833 | −0.0307827 | ||||||||
\(52\) | −1.08815 | −0.150899 | ||||||||
\(53\) | 7.74094 | 1.06330 | 0.531650 | − | 0.846964i | \(-0.321572\pi\) | ||||
0.531650 | + | 0.846964i | \(0.321572\pi\) | |||||||
\(54\) | −0.655186 | −0.0891595 | ||||||||
\(55\) | −9.48188 | −1.27854 | ||||||||
\(56\) | −5.23490 | −0.699543 | ||||||||
\(57\) | −1.06100 | −0.140533 | ||||||||
\(58\) | 0.506041 | 0.0664464 | ||||||||
\(59\) | −8.33513 | −1.08514 | −0.542570 | − | 0.840010i | \(-0.682549\pi\) | ||||
−0.542570 | + | 0.840010i | \(0.682549\pi\) | |||||||
\(60\) | −0.670251 | −0.0865291 | ||||||||
\(61\) | −7.89977 | −1.01146 | −0.505731 | − | 0.862691i | \(-0.668777\pi\) | ||||
−0.505731 | + | 0.862691i | \(0.668777\pi\) | |||||||
\(62\) | −3.30798 | −0.420114 | ||||||||
\(63\) | 7.56465 | 0.953056 | ||||||||
\(64\) | −1.52781 | −0.190976 | ||||||||
\(65\) | −1.28621 | −0.159535 | ||||||||
\(66\) | 0.521106 | 0.0641437 | ||||||||
\(67\) | 0.466812 | 0.0570302 | 0.0285151 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285151 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(68\) | −1.87800 | −0.227741 | ||||||||
\(69\) | −1.03923 | −0.125108 | ||||||||
\(70\) | −2.83579 | −0.338942 | ||||||||
\(71\) | 9.48188 | 1.12529 | 0.562646 | − | 0.826698i | \(-0.309783\pi\) | ||||
0.562646 | + | 0.826698i | \(0.309783\pi\) | |||||||
\(72\) | −6.06638 | −0.714929 | ||||||||
\(73\) | −12.6799 | −1.48407 | −0.742037 | − | 0.670359i | \(-0.766140\pi\) | ||||
−0.742037 | + | 0.670359i | \(0.766140\pi\) | |||||||
\(74\) | 6.32304 | 0.735039 | ||||||||
\(75\) | 0.198062 | 0.0228703 | ||||||||
\(76\) | −9.06398 | −1.03971 | ||||||||
\(77\) | −12.1129 | −1.38039 | ||||||||
\(78\) | 0.0706876 | 0.00800380 | ||||||||
\(79\) | −5.09783 | −0.573551 | −0.286776 | − | 0.957998i | \(-0.592583\pi\) | ||||
−0.286776 | + | 0.957998i | \(0.592583\pi\) | |||||||
\(80\) | −4.49396 | −0.502440 | ||||||||
\(81\) | 8.64848 | 0.960942 | ||||||||
\(82\) | 4.30798 | 0.475737 | ||||||||
\(83\) | 14.9215 | 1.63785 | 0.818926 | − | 0.573899i | \(-0.194570\pi\) | ||||
0.818926 | + | 0.573899i | \(0.194570\pi\) | |||||||
\(84\) | −0.856232 | −0.0934226 | ||||||||
\(85\) | −2.21983 | −0.240775 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.180604 | 0.0193628 | ||||||||
\(88\) | 9.71379 | 1.03549 | ||||||||
\(89\) | −17.0151 | −1.80359 | −0.901797 | − | 0.432161i | \(-0.857751\pi\) | ||||
−0.901797 | + | 0.432161i | \(0.857751\pi\) | |||||||
\(90\) | −3.28621 | −0.346397 | ||||||||
\(91\) | −1.64310 | −0.172244 | ||||||||
\(92\) | −8.87800 | −0.925596 | ||||||||
\(93\) | −1.18060 | −0.122423 | ||||||||
\(94\) | 0.554958 | 0.0572396 | ||||||||
\(95\) | −10.7138 | −1.09921 | ||||||||
\(96\) | 1.05861 | 0.108044 | ||||||||
\(97\) | 16.5550 | 1.68090 | 0.840451 | − | 0.541888i | \(-0.182290\pi\) | ||||
0.840451 | + | 0.541888i | \(0.182290\pi\) | |||||||
\(98\) | 0.262045 | 0.0264706 | ||||||||
\(99\) | −14.0368 | −1.41076 | ||||||||
\(100\) | 1.69202 | 0.169202 | ||||||||
\(101\) | −3.79225 | −0.377343 | −0.188671 | − | 0.982040i | \(-0.560418\pi\) | ||||
−0.188671 | + | 0.982040i | \(0.560418\pi\) | |||||||
\(102\) | 0.121998 | 0.0120796 | ||||||||
\(103\) | −5.92154 | −0.583467 | −0.291733 | − | 0.956500i | \(-0.594232\pi\) | ||||
−0.291733 | + | 0.956500i | \(0.594232\pi\) | |||||||
\(104\) | 1.31767 | 0.129208 | ||||||||
\(105\) | −1.01208 | −0.0987690 | ||||||||
\(106\) | −4.29590 | −0.417254 | ||||||||
\(107\) | 1.96615 | 0.190075 | 0.0950374 | − | 0.995474i | \(-0.469703\pi\) | ||||
0.0950374 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(108\) | −1.99761 | −0.192220 | ||||||||
\(109\) | −8.32304 | −0.797203 | −0.398602 | − | 0.917124i | \(-0.630504\pi\) | ||||
−0.398602 | + | 0.917124i | \(0.630504\pi\) | |||||||
\(110\) | 5.26205 | 0.501716 | ||||||||
\(111\) | 2.25667 | 0.214193 | ||||||||
\(112\) | −5.74094 | −0.542468 | ||||||||
\(113\) | −1.82908 | −0.172066 | −0.0860329 | − | 0.996292i | \(-0.527419\pi\) | ||||
−0.0860329 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(114\) | 0.588810 | 0.0551471 | ||||||||
\(115\) | −10.4940 | −0.978567 | ||||||||
\(116\) | 1.54288 | 0.143252 | ||||||||
\(117\) | −1.90408 | −0.176033 | ||||||||
\(118\) | 4.62565 | 0.425825 | ||||||||
\(119\) | −2.83579 | −0.259956 | ||||||||
\(120\) | 0.811626 | 0.0740910 | ||||||||
\(121\) | 11.4765 | 1.04332 | ||||||||
\(122\) | 4.38404 | 0.396913 | ||||||||
\(123\) | 1.53750 | 0.138632 | ||||||||
\(124\) | −10.0858 | −0.905727 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −4.19806 | −0.373993 | ||||||||
\(127\) | 2.96615 | 0.263203 | 0.131602 | − | 0.991303i | \(-0.457988\pi\) | ||||
0.131602 | + | 0.991303i | \(0.457988\pi\) | |||||||
\(128\) | 11.5375 | 1.01978 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.713792 | 0.0626037 | ||||||||
\(131\) | −7.10992 | −0.621196 | −0.310598 | − | 0.950541i | \(-0.600529\pi\) | ||||
−0.310598 | + | 0.950541i | \(0.600529\pi\) | |||||||
\(132\) | 1.58881 | 0.138288 | ||||||||
\(133\) | −13.6866 | −1.18678 | ||||||||
\(134\) | −0.259061 | −0.0223795 | ||||||||
\(135\) | −2.36121 | −0.203220 | ||||||||
\(136\) | 2.27413 | 0.195005 | ||||||||
\(137\) | 8.32304 | 0.711086 | 0.355543 | − | 0.934660i | \(-0.384296\pi\) | ||||
0.355543 | + | 0.934660i | \(0.384296\pi\) | |||||||
\(138\) | 0.576728 | 0.0490944 | ||||||||
\(139\) | 6.03923 | 0.512241 | 0.256120 | − | 0.966645i | \(-0.417556\pi\) | ||||
0.256120 | + | 0.966645i | \(0.417556\pi\) | |||||||
\(140\) | −8.64609 | −0.730728 | ||||||||
\(141\) | 0.198062 | 0.0166799 | ||||||||
\(142\) | −5.26205 | −0.441581 | ||||||||
\(143\) | 3.04892 | 0.254963 | ||||||||
\(144\) | −6.65279 | −0.554399 | ||||||||
\(145\) | 1.82371 | 0.151451 | ||||||||
\(146\) | 7.03684 | 0.582373 | ||||||||
\(147\) | 0.0935228 | 0.00771363 | ||||||||
\(148\) | 19.2784 | 1.58468 | ||||||||
\(149\) | 2.22521 | 0.182296 | 0.0911481 | − | 0.995837i | \(-0.470946\pi\) | ||||
0.0911481 | + | 0.995837i | \(0.470946\pi\) | |||||||
\(150\) | −0.109916 | −0.00897463 | ||||||||
\(151\) | 0.493959 | 0.0401978 | 0.0200989 | − | 0.999798i | \(-0.493602\pi\) | ||||
0.0200989 | + | 0.999798i | \(0.493602\pi\) | |||||||
\(152\) | 10.9758 | 0.890258 | ||||||||
\(153\) | −3.28621 | −0.265674 | ||||||||
\(154\) | 6.72215 | 0.541686 | ||||||||
\(155\) | −11.9215 | −0.957561 | ||||||||
\(156\) | 0.215521 | 0.0172555 | ||||||||
\(157\) | −7.71140 | −0.615437 | −0.307718 | − | 0.951478i | \(-0.599565\pi\) | ||||
−0.307718 | + | 0.951478i | \(0.599565\pi\) | |||||||
\(158\) | 2.82908 | 0.225070 | ||||||||
\(159\) | −1.53319 | −0.121590 | ||||||||
\(160\) | 10.6896 | 0.845089 | ||||||||
\(161\) | −13.4058 | −1.05653 | ||||||||
\(162\) | −4.79954 | −0.377088 | ||||||||
\(163\) | 0.975837 | 0.0764334 | 0.0382167 | − | 0.999269i | \(-0.487832\pi\) | ||||
0.0382167 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(164\) | 13.1347 | 1.02565 | ||||||||
\(165\) | 1.87800 | 0.146202 | ||||||||
\(166\) | −8.28083 | −0.642717 | ||||||||
\(167\) | −5.64848 | −0.437093 | −0.218546 | − | 0.975827i | \(-0.570131\pi\) | ||||
−0.218546 | + | 0.975827i | \(0.570131\pi\) | |||||||
\(168\) | 1.03684 | 0.0799936 | ||||||||
\(169\) | −12.5864 | −0.968186 | ||||||||
\(170\) | 1.23191 | 0.0944835 | ||||||||
\(171\) | −15.8605 | −1.21289 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.65279 | −0.657860 | −0.328930 | − | 0.944354i | \(-0.606688\pi\) | ||||
−0.328930 | + | 0.944354i | \(0.606688\pi\) | |||||||
\(174\) | −0.100228 | −0.00759823 | ||||||||
\(175\) | 2.55496 | 0.193137 | ||||||||
\(176\) | 10.6528 | 0.802984 | ||||||||
\(177\) | 1.65087 | 0.124087 | ||||||||
\(178\) | 9.44265 | 0.707756 | ||||||||
\(179\) | −1.99462 | −0.149085 | −0.0745426 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745426 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(180\) | −10.0194 | −0.746800 | ||||||||
\(181\) | −8.85623 | −0.658279 | −0.329139 | − | 0.944281i | \(-0.606759\pi\) | ||||
−0.329139 | + | 0.944281i | \(0.606759\pi\) | |||||||
\(182\) | 0.911854 | 0.0675911 | ||||||||
\(183\) | 1.56465 | 0.115662 | ||||||||
\(184\) | 10.7506 | 0.792547 | ||||||||
\(185\) | 22.7875 | 1.67537 | ||||||||
\(186\) | 0.655186 | 0.0480405 | ||||||||
\(187\) | 5.26205 | 0.384799 | ||||||||
\(188\) | 1.69202 | 0.123403 | ||||||||
\(189\) | −3.01639 | −0.219410 | ||||||||
\(190\) | 5.94571 | 0.431347 | ||||||||
\(191\) | −7.54527 | −0.545957 | −0.272978 | − | 0.962020i | \(-0.588009\pi\) | ||||
−0.272978 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(192\) | 0.302602 | 0.0218384 | ||||||||
\(193\) | −8.04221 | −0.578891 | −0.289446 | − | 0.957194i | \(-0.593471\pi\) | ||||
−0.289446 | + | 0.957194i | \(0.593471\pi\) | |||||||
\(194\) | −9.18731 | −0.659610 | ||||||||
\(195\) | 0.254749 | 0.0182430 | ||||||||
\(196\) | 0.798954 | 0.0570681 | ||||||||
\(197\) | −19.3913 | −1.38158 | −0.690788 | − | 0.723058i | \(-0.742736\pi\) | ||||
−0.690788 | + | 0.723058i | \(0.742736\pi\) | |||||||
\(198\) | 7.78986 | 0.553601 | ||||||||
\(199\) | 22.6625 | 1.60650 | 0.803250 | − | 0.595642i | \(-0.203102\pi\) | ||||
0.803250 | + | 0.595642i | \(0.203102\pi\) | |||||||
\(200\) | −2.04892 | −0.144880 | ||||||||
\(201\) | −0.0924579 | −0.00652148 | ||||||||
\(202\) | 2.10454 | 0.148075 | ||||||||
\(203\) | 2.32975 | 0.163516 | ||||||||
\(204\) | 0.371961 | 0.0260425 | ||||||||
\(205\) | 15.5254 | 1.08434 | ||||||||
\(206\) | 3.28621 | 0.228961 | ||||||||
\(207\) | −15.5351 | −1.07976 | ||||||||
\(208\) | 1.44504 | 0.100196 | ||||||||
\(209\) | 25.3967 | 1.75673 | ||||||||
\(210\) | 0.561663 | 0.0387584 | ||||||||
\(211\) | −16.4916 | −1.13533 | −0.567663 | − | 0.823261i | \(-0.692152\pi\) | ||||
−0.567663 | + | 0.823261i | \(0.692152\pi\) | |||||||
\(212\) | −13.0978 | −0.899563 | ||||||||
\(213\) | −1.87800 | −0.128679 | ||||||||
\(214\) | −1.09113 | −0.0745881 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.41896 | 0.164589 | ||||||||
\(217\) | −15.2295 | −1.03385 | ||||||||
\(218\) | 4.61894 | 0.312834 | ||||||||
\(219\) | 2.51142 | 0.169706 | ||||||||
\(220\) | 16.0435 | 1.08166 | ||||||||
\(221\) | 0.713792 | 0.0480148 | ||||||||
\(222\) | −1.25236 | −0.0840527 | ||||||||
\(223\) | −1.50604 | −0.100852 | −0.0504260 | − | 0.998728i | \(-0.516058\pi\) | ||||
−0.0504260 | + | 0.998728i | \(0.516058\pi\) | |||||||
\(224\) | 13.6558 | 0.912415 | ||||||||
\(225\) | 2.96077 | 0.197385 | ||||||||
\(226\) | 1.01507 | 0.0675212 | ||||||||
\(227\) | −18.3599 | −1.21859 | −0.609294 | − | 0.792944i | \(-0.708547\pi\) | ||||
−0.609294 | + | 0.792944i | \(0.708547\pi\) | |||||||
\(228\) | 1.79523 | 0.118892 | ||||||||
\(229\) | 6.18359 | 0.408623 | 0.204311 | − | 0.978906i | \(-0.434504\pi\) | ||||
0.204311 | + | 0.978906i | \(0.434504\pi\) | |||||||
\(230\) | 5.82371 | 0.384004 | ||||||||
\(231\) | 2.39911 | 0.157850 | ||||||||
\(232\) | −1.86831 | −0.122661 | ||||||||
\(233\) | 4.42088 | 0.289621 | 0.144811 | − | 0.989459i | \(-0.453743\pi\) | ||||
0.144811 | + | 0.989459i | \(0.453743\pi\) | |||||||
\(234\) | 1.05669 | 0.0690778 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 14.1032 | 0.918041 | ||||||||
\(237\) | 1.00969 | 0.0655863 | ||||||||
\(238\) | 1.57374 | 0.102011 | ||||||||
\(239\) | −10.4494 | −0.675913 | −0.337956 | − | 0.941162i | \(-0.609736\pi\) | ||||
−0.337956 | + | 0.941162i | \(0.609736\pi\) | |||||||
\(240\) | 0.890084 | 0.0574547 | ||||||||
\(241\) | 24.3002 | 1.56531 | 0.782657 | − | 0.622453i | \(-0.213864\pi\) | ||||
0.782657 | + | 0.622453i | \(0.213864\pi\) | |||||||
\(242\) | −6.36898 | −0.409413 | ||||||||
\(243\) | −5.25475 | −0.337092 | ||||||||
\(244\) | 13.3666 | 0.855708 | ||||||||
\(245\) | 0.944378 | 0.0603341 | ||||||||
\(246\) | −0.853248 | −0.0544011 | ||||||||
\(247\) | 3.44504 | 0.219203 | ||||||||
\(248\) | 12.2131 | 0.775534 | ||||||||
\(249\) | −2.95539 | −0.187291 | ||||||||
\(250\) | −6.65950 | −0.421184 | ||||||||
\(251\) | −21.9269 | −1.38401 | −0.692007 | − | 0.721890i | \(-0.743273\pi\) | ||||
−0.692007 | + | 0.721890i | \(0.743273\pi\) | |||||||
\(252\) | −12.7995 | −0.806296 | ||||||||
\(253\) | 24.8756 | 1.56392 | ||||||||
\(254\) | −1.64609 | −0.103285 | ||||||||
\(255\) | 0.439665 | 0.0275329 | ||||||||
\(256\) | −3.34721 | −0.209200 | ||||||||
\(257\) | −2.89546 | −0.180614 | −0.0903069 | − | 0.995914i | \(-0.528785\pi\) | ||||
−0.0903069 | + | 0.995914i | \(0.528785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.1105 | 1.80884 | ||||||||
\(260\) | 2.17629 | 0.134968 | ||||||||
\(261\) | 2.69979 | 0.167113 | ||||||||
\(262\) | 3.94571 | 0.243767 | ||||||||
\(263\) | −17.3744 | −1.07135 | −0.535674 | − | 0.844425i | \(-0.679943\pi\) | ||||
−0.535674 | + | 0.844425i | \(0.679943\pi\) | |||||||
\(264\) | −1.92394 | −0.118410 | ||||||||
\(265\) | −15.4819 | −0.951044 | ||||||||
\(266\) | 7.59551 | 0.465711 | ||||||||
\(267\) | 3.37004 | 0.206243 | ||||||||
\(268\) | −0.789856 | −0.0482481 | ||||||||
\(269\) | −14.0707 | −0.857905 | −0.428952 | − | 0.903327i | \(-0.641117\pi\) | ||||
−0.428952 | + | 0.903327i | \(0.641117\pi\) | |||||||
\(270\) | 1.31037 | 0.0797467 | ||||||||
\(271\) | −2.14377 | −0.130225 | −0.0651123 | − | 0.997878i | \(-0.520741\pi\) | ||||
−0.0651123 | + | 0.997878i | \(0.520741\pi\) | |||||||
\(272\) | 2.49396 | 0.151218 | ||||||||
\(273\) | 0.325437 | 0.0196963 | ||||||||
\(274\) | −4.61894 | −0.279040 | ||||||||
\(275\) | −4.74094 | −0.285889 | ||||||||
\(276\) | 1.75840 | 0.105843 | ||||||||
\(277\) | −23.2597 | −1.39754 | −0.698769 | − | 0.715348i | \(-0.746268\pi\) | ||||
−0.698769 | + | 0.715348i | \(0.746268\pi\) | |||||||
\(278\) | −3.35152 | −0.201011 | ||||||||
\(279\) | −17.6485 | −1.05659 | ||||||||
\(280\) | 10.4698 | 0.625690 | ||||||||
\(281\) | −17.7342 | −1.05794 | −0.528968 | − | 0.848642i | \(-0.677421\pi\) | ||||
−0.528968 | + | 0.848642i | \(0.677421\pi\) | |||||||
\(282\) | −0.109916 | −0.00654542 | ||||||||
\(283\) | 3.90946 | 0.232393 | 0.116197 | − | 0.993226i | \(-0.462930\pi\) | ||||
0.116197 | + | 0.993226i | \(0.462930\pi\) | |||||||
\(284\) | −16.0435 | −0.952009 | ||||||||
\(285\) | 2.12200 | 0.125696 | ||||||||
\(286\) | −1.69202 | −0.100051 | ||||||||
\(287\) | 19.8334 | 1.17073 | ||||||||
\(288\) | 15.8248 | 0.932484 | ||||||||
\(289\) | −15.7681 | −0.927534 | ||||||||
\(290\) | −1.01208 | −0.0594315 | ||||||||
\(291\) | −3.27891 | −0.192213 | ||||||||
\(292\) | 21.4547 | 1.25554 | ||||||||
\(293\) | −28.0320 | −1.63765 | −0.818825 | − | 0.574043i | \(-0.805374\pi\) | ||||
−0.818825 | + | 0.574043i | \(0.805374\pi\) | |||||||
\(294\) | −0.0519012 | −0.00302694 | ||||||||
\(295\) | 16.6703 | 0.970580 | ||||||||
\(296\) | −23.3448 | −1.35689 | ||||||||
\(297\) | 5.59717 | 0.324781 | ||||||||
\(298\) | −1.23490 | −0.0715357 | ||||||||
\(299\) | 3.37435 | 0.195144 | ||||||||
\(300\) | −0.335126 | −0.0193485 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.274127 | −0.0157742 | ||||||||
\(303\) | 0.751101 | 0.0431496 | ||||||||
\(304\) | 12.0368 | 0.690360 | ||||||||
\(305\) | 15.7995 | 0.904679 | ||||||||
\(306\) | 1.82371 | 0.104254 | ||||||||
\(307\) | −0.633415 | −0.0361509 | −0.0180755 | − | 0.999837i | \(-0.505754\pi\) | ||||
−0.0180755 | + | 0.999837i | \(0.505754\pi\) | |||||||
\(308\) | 20.4953 | 1.16783 | ||||||||
\(309\) | 1.17283 | 0.0667202 | ||||||||
\(310\) | 6.61596 | 0.375761 | ||||||||
\(311\) | −25.3666 | −1.43841 | −0.719204 | − | 0.694799i | \(-0.755493\pi\) | ||||
−0.719204 | + | 0.694799i | \(0.755493\pi\) | |||||||
\(312\) | −0.260980 | −0.0147751 | ||||||||
\(313\) | 14.9463 | 0.844815 | 0.422407 | − | 0.906406i | \(-0.361185\pi\) | ||||
0.422407 | + | 0.906406i | \(0.361185\pi\) | |||||||
\(314\) | 4.27950 | 0.241506 | ||||||||
\(315\) | −15.1293 | −0.852439 | ||||||||
\(316\) | 8.62565 | 0.485230 | ||||||||
\(317\) | −4.84548 | −0.272149 | −0.136075 | − | 0.990699i | \(-0.543449\pi\) | ||||
−0.136075 | + | 0.990699i | \(0.543449\pi\) | |||||||
\(318\) | 0.850855 | 0.0477136 | ||||||||
\(319\) | −4.32304 | −0.242044 | ||||||||
\(320\) | 3.05562 | 0.170814 | ||||||||
\(321\) | −0.389420 | −0.0217353 | ||||||||
\(322\) | 7.43967 | 0.414596 | ||||||||
\(323\) | 5.94571 | 0.330828 | ||||||||
\(324\) | −14.6334 | −0.812968 | ||||||||
\(325\) | −0.643104 | −0.0356730 | ||||||||
\(326\) | −0.541549 | −0.0299936 | ||||||||
\(327\) | 1.64848 | 0.0911612 | ||||||||
\(328\) | −15.9051 | −0.878215 | ||||||||
\(329\) | 2.55496 | 0.140859 | ||||||||
\(330\) | −1.04221 | −0.0573719 | ||||||||
\(331\) | 12.3472 | 0.678664 | 0.339332 | − | 0.940667i | \(-0.389799\pi\) | ||||
0.339332 | + | 0.940667i | \(0.389799\pi\) | |||||||
\(332\) | −25.2476 | −1.38564 | ||||||||
\(333\) | 33.7342 | 1.84862 | ||||||||
\(334\) | 3.13467 | 0.171522 | ||||||||
\(335\) | −0.933624 | −0.0510093 | ||||||||
\(336\) | 1.13706 | 0.0620319 | ||||||||
\(337\) | 6.20344 | 0.337923 | 0.168961 | − | 0.985623i | \(-0.445959\pi\) | ||||
0.168961 | + | 0.985623i | \(0.445959\pi\) | |||||||
\(338\) | 6.98493 | 0.379930 | ||||||||
\(339\) | 0.362273 | 0.0196760 | ||||||||
\(340\) | 3.75600 | 0.203698 | ||||||||
\(341\) | 28.2597 | 1.53035 | ||||||||
\(342\) | 8.80194 | 0.475954 | ||||||||
\(343\) | 19.0911 | 1.03082 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.07846 | 0.111900 | ||||||||
\(346\) | 4.80194 | 0.258154 | ||||||||
\(347\) | 18.0901 | 0.971126 | 0.485563 | − | 0.874202i | \(-0.338615\pi\) | ||||
0.485563 | + | 0.874202i | \(0.338615\pi\) | |||||||
\(348\) | −0.305586 | −0.0163811 | ||||||||
\(349\) | 7.25667 | 0.388441 | 0.194220 | − | 0.980958i | \(-0.437782\pi\) | ||||
0.194220 | + | 0.980958i | \(0.437782\pi\) | |||||||
\(350\) | −1.41789 | −0.0757897 | ||||||||
\(351\) | 0.759251 | 0.0405258 | ||||||||
\(352\) | −25.3394 | −1.35060 | ||||||||
\(353\) | 10.4397 | 0.555647 | 0.277824 | − | 0.960632i | \(-0.410387\pi\) | ||||
0.277824 | + | 0.960632i | \(0.410387\pi\) | |||||||
\(354\) | −0.916166 | −0.0486937 | ||||||||
\(355\) | −18.9638 | −1.00649 | ||||||||
\(356\) | 28.7899 | 1.52586 | ||||||||
\(357\) | 0.561663 | 0.0297264 | ||||||||
\(358\) | 1.10693 | 0.0585032 | ||||||||
\(359\) | −28.1347 | −1.48489 | −0.742446 | − | 0.669906i | \(-0.766334\pi\) | ||||
−0.742446 | + | 0.669906i | \(0.766334\pi\) | |||||||
\(360\) | 12.1328 | 0.639452 | ||||||||
\(361\) | 9.69633 | 0.510333 | ||||||||
\(362\) | 4.91484 | 0.258318 | ||||||||
\(363\) | −2.27306 | −0.119305 | ||||||||
\(364\) | 2.78017 | 0.145720 | ||||||||
\(365\) | 25.3599 | 1.32740 | ||||||||
\(366\) | −0.868313 | −0.0453875 | ||||||||
\(367\) | 16.4480 | 0.858580 | 0.429290 | − | 0.903167i | \(-0.358764\pi\) | ||||
0.429290 | + | 0.903167i | \(0.358764\pi\) | |||||||
\(368\) | 11.7899 | 0.614589 | ||||||||
\(369\) | 22.9836 | 1.19648 | ||||||||
\(370\) | −12.6461 | −0.657439 | ||||||||
\(371\) | −19.7778 | −1.02681 | ||||||||
\(372\) | 1.99761 | 0.103571 | ||||||||
\(373\) | −10.8062 | −0.559526 | −0.279763 | − | 0.960069i | \(-0.590256\pi\) | ||||
−0.279763 | + | 0.960069i | \(0.590256\pi\) | |||||||
\(374\) | −2.92021 | −0.151001 | ||||||||
\(375\) | −2.37675 | −0.122735 | ||||||||
\(376\) | −2.04892 | −0.105665 | ||||||||
\(377\) | −0.586417 | −0.0302020 | ||||||||
\(378\) | 1.67397 | 0.0860998 | ||||||||
\(379\) | −9.71917 | −0.499240 | −0.249620 | − | 0.968344i | \(-0.580306\pi\) | ||||
−0.249620 | + | 0.968344i | \(0.580306\pi\) | |||||||
\(380\) | 18.1280 | 0.929945 | ||||||||
\(381\) | −0.587482 | −0.0300976 | ||||||||
\(382\) | 4.18731 | 0.214241 | ||||||||
\(383\) | −23.6407 | −1.20798 | −0.603992 | − | 0.796990i | \(-0.706424\pi\) | ||||
−0.603992 | + | 0.796990i | \(0.706424\pi\) | |||||||
\(384\) | −2.28514 | −0.116613 | ||||||||
\(385\) | 24.2258 | 1.23466 | ||||||||
\(386\) | 4.46309 | 0.227165 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.0113 | −1.42206 | ||||||||
\(389\) | −7.89307 | −0.400194 | −0.200097 | − | 0.979776i | \(-0.564126\pi\) | ||||
−0.200097 | + | 0.979776i | \(0.564126\pi\) | |||||||
\(390\) | −0.141375 | −0.00715881 | ||||||||
\(391\) | 5.82371 | 0.294518 | ||||||||
\(392\) | −0.967476 | −0.0488649 | ||||||||
\(393\) | 1.40821 | 0.0710346 | ||||||||
\(394\) | 10.7614 | 0.542151 | ||||||||
\(395\) | 10.1957 | 0.513000 | ||||||||
\(396\) | 23.7506 | 1.19351 | ||||||||
\(397\) | −25.5894 | −1.28430 | −0.642148 | − | 0.766581i | \(-0.721956\pi\) | ||||
−0.642148 | + | 0.766581i | \(0.721956\pi\) | |||||||
\(398\) | −12.5767 | −0.630414 | ||||||||
\(399\) | 2.71081 | 0.135710 | ||||||||
\(400\) | −2.24698 | −0.112349 | ||||||||
\(401\) | −8.70948 | −0.434931 | −0.217465 | − | 0.976068i | \(-0.569779\pi\) | ||||
−0.217465 | + | 0.976068i | \(0.569779\pi\) | |||||||
\(402\) | 0.0513102 | 0.00255912 | ||||||||
\(403\) | 3.83340 | 0.190955 | ||||||||
\(404\) | 6.41657 | 0.319236 | ||||||||
\(405\) | −17.2970 | −0.859493 | ||||||||
\(406\) | −1.29291 | −0.0641662 | ||||||||
\(407\) | −54.0170 | −2.67752 | ||||||||
\(408\) | −0.450419 | −0.0222990 | ||||||||
\(409\) | 13.2567 | 0.655500 | 0.327750 | − | 0.944764i | \(-0.393710\pi\) | ||||
0.327750 | + | 0.944764i | \(0.393710\pi\) | |||||||
\(410\) | −8.61596 | −0.425512 | ||||||||
\(411\) | −1.64848 | −0.0813136 | ||||||||
\(412\) | 10.0194 | 0.493619 | ||||||||
\(413\) | 21.2959 | 1.04790 | ||||||||
\(414\) | 8.62133 | 0.423715 | ||||||||
\(415\) | −29.8431 | −1.46494 | ||||||||
\(416\) | −3.43727 | −0.168526 | ||||||||
\(417\) | −1.19614 | −0.0585754 | ||||||||
\(418\) | −14.0941 | −0.689366 | ||||||||
\(419\) | 1.14138 | 0.0557598 | 0.0278799 | − | 0.999611i | \(-0.491124\pi\) | ||||
0.0278799 | + | 0.999611i | \(0.491124\pi\) | |||||||
\(420\) | 1.71246 | 0.0835597 | ||||||||
\(421\) | 3.33214 | 0.162399 | 0.0811993 | − | 0.996698i | \(-0.474125\pi\) | ||||
0.0811993 | + | 0.996698i | \(0.474125\pi\) | |||||||
\(422\) | 9.15213 | 0.445519 | ||||||||
\(423\) | 2.96077 | 0.143958 | ||||||||
\(424\) | 15.8605 | 0.770256 | ||||||||
\(425\) | −1.10992 | −0.0538388 | ||||||||
\(426\) | 1.04221 | 0.0504954 | ||||||||
\(427\) | 20.1836 | 0.976752 | ||||||||
\(428\) | −3.32676 | −0.160805 | ||||||||
\(429\) | −0.603875 | −0.0291554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3515 | 0.980298 | 0.490149 | − | 0.871639i | \(-0.336942\pi\) | ||||
0.490149 | + | 0.871639i | \(0.336942\pi\) | |||||||
\(432\) | 2.65279 | 0.127633 | ||||||||
\(433\) | 9.96316 | 0.478799 | 0.239400 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239400 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(434\) | 8.45175 | 0.405697 | ||||||||
\(435\) | −0.361208 | −0.0173186 | ||||||||
\(436\) | 14.0828 | 0.674442 | ||||||||
\(437\) | 28.1075 | 1.34457 | ||||||||
\(438\) | −1.39373 | −0.0665951 | ||||||||
\(439\) | 8.18731 | 0.390759 | 0.195379 | − | 0.980728i | \(-0.437406\pi\) | ||||
0.195379 | + | 0.980728i | \(0.437406\pi\) | |||||||
\(440\) | −19.4276 | −0.926174 | ||||||||
\(441\) | 1.39804 | 0.0665735 | ||||||||
\(442\) | −0.396125 | −0.0188417 | ||||||||
\(443\) | 30.4077 | 1.44471 | 0.722357 | − | 0.691520i | \(-0.243059\pi\) | ||||
0.722357 | + | 0.691520i | \(0.243059\pi\) | |||||||
\(444\) | −3.81833 | −0.181210 | ||||||||
\(445\) | 34.0301 | 1.61318 | ||||||||
\(446\) | 0.835790 | 0.0395758 | ||||||||
\(447\) | −0.440730 | −0.0208458 | ||||||||
\(448\) | 3.90349 | 0.184423 | ||||||||
\(449\) | −22.2000 | −1.04768 | −0.523841 | − | 0.851816i | \(-0.675501\pi\) | ||||
−0.523841 | + | 0.851816i | \(0.675501\pi\) | |||||||
\(450\) | −1.64310 | −0.0774567 | ||||||||
\(451\) | −36.8025 | −1.73296 | ||||||||
\(452\) | 3.09485 | 0.145570 | ||||||||
\(453\) | −0.0978347 | −0.00459667 | ||||||||
\(454\) | 10.1890 | 0.478192 | ||||||||
\(455\) | 3.28621 | 0.154060 | ||||||||
\(456\) | −2.17390 | −0.101802 | ||||||||
\(457\) | 11.2185 | 0.524780 | 0.262390 | − | 0.964962i | \(-0.415489\pi\) | ||||
0.262390 | + | 0.964962i | \(0.415489\pi\) | |||||||
\(458\) | −3.43163 | −0.160350 | ||||||||
\(459\) | 1.31037 | 0.0611629 | ||||||||
\(460\) | 17.7560 | 0.827878 | ||||||||
\(461\) | −34.5459 | −1.60896 | −0.804481 | − | 0.593979i | \(-0.797556\pi\) | ||||
−0.804481 | + | 0.593979i | \(0.797556\pi\) | |||||||
\(462\) | −1.33140 | −0.0619426 | ||||||||
\(463\) | 10.1806 | 0.473133 | 0.236566 | − | 0.971615i | \(-0.423978\pi\) | ||||
0.236566 | + | 0.971615i | \(0.423978\pi\) | |||||||
\(464\) | −2.04892 | −0.0951186 | ||||||||
\(465\) | 2.36121 | 0.109498 | ||||||||
\(466\) | −2.45340 | −0.113652 | ||||||||
\(467\) | 14.9782 | 0.693110 | 0.346555 | − | 0.938030i | \(-0.387351\pi\) | ||||
0.346555 | + | 0.938030i | \(0.387351\pi\) | |||||||
\(468\) | 3.22175 | 0.148926 | ||||||||
\(469\) | −1.19269 | −0.0550731 | ||||||||
\(470\) | −1.10992 | −0.0511966 | ||||||||
\(471\) | 1.52734 | 0.0703760 | ||||||||
\(472\) | −17.0780 | −0.786078 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.560335 | −0.0257370 | ||||||||
\(475\) | −5.35690 | −0.245791 | ||||||||
\(476\) | 4.79822 | 0.219926 | ||||||||
\(477\) | −22.9191 | −1.04940 | ||||||||
\(478\) | 5.79895 | 0.265238 | ||||||||
\(479\) | 29.0573 | 1.32766 | 0.663830 | − | 0.747883i | \(-0.268930\pi\) | ||||
0.663830 | + | 0.747883i | \(0.268930\pi\) | |||||||
\(480\) | −2.11721 | −0.0966371 | ||||||||
\(481\) | −7.32736 | −0.334099 | ||||||||
\(482\) | −13.4856 | −0.614252 | ||||||||
\(483\) | 2.65519 | 0.120815 | ||||||||
\(484\) | −19.4185 | −0.882658 | ||||||||
\(485\) | −33.1099 | −1.50344 | ||||||||
\(486\) | 2.91617 | 0.132280 | ||||||||
\(487\) | −23.8810 | −1.08215 | −0.541075 | − | 0.840974i | \(-0.681983\pi\) | ||||
−0.541075 | + | 0.840974i | \(0.681983\pi\) | |||||||
\(488\) | −16.1860 | −0.732705 | ||||||||
\(489\) | −0.193276 | −0.00874026 | ||||||||
\(490\) | −0.524090 | −0.0236760 | ||||||||
\(491\) | −0.675628 | −0.0304907 | −0.0152453 | − | 0.999884i | \(-0.504853\pi\) | ||||
−0.0152453 | + | 0.999884i | \(0.504853\pi\) | |||||||
\(492\) | −2.60148 | −0.117284 | ||||||||
\(493\) | −1.01208 | −0.0455819 | ||||||||
\(494\) | −1.91185 | −0.0860184 | ||||||||
\(495\) | 28.0737 | 1.26182 | ||||||||
\(496\) | 13.3937 | 0.601396 | ||||||||
\(497\) | −24.2258 | −1.08668 | ||||||||
\(498\) | 1.64012 | 0.0734955 | ||||||||
\(499\) | 32.1943 | 1.44122 | 0.720608 | − | 0.693342i | \(-0.243863\pi\) | ||||
0.720608 | + | 0.693342i | \(0.243863\pi\) | |||||||
\(500\) | −20.3043 | −0.908034 | ||||||||
\(501\) | 1.11875 | 0.0499821 | ||||||||
\(502\) | 12.1685 | 0.543108 | ||||||||
\(503\) | −23.1491 | −1.03217 | −0.516085 | − | 0.856538i | \(-0.672611\pi\) | ||||
−0.516085 | + | 0.856538i | \(0.672611\pi\) | |||||||
\(504\) | 15.4993 | 0.690395 | ||||||||
\(505\) | 7.58450 | 0.337506 | ||||||||
\(506\) | −13.8049 | −0.613704 | ||||||||
\(507\) | 2.49289 | 0.110713 | ||||||||
\(508\) | −5.01879 | −0.222673 | ||||||||
\(509\) | −29.2010 | −1.29431 | −0.647157 | − | 0.762357i | \(-0.724042\pi\) | ||||
−0.647157 | + | 0.762357i | \(0.724042\pi\) | |||||||
\(510\) | −0.243996 | −0.0108043 | ||||||||
\(511\) | 32.3967 | 1.43315 | ||||||||
\(512\) | −21.2174 | −0.937687 | ||||||||
\(513\) | 6.32437 | 0.279228 | ||||||||
\(514\) | 1.60686 | 0.0708755 | ||||||||
\(515\) | 11.8431 | 0.521869 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.74094 | −0.208506 | ||||||||
\(518\) | −16.1551 | −0.709815 | ||||||||
\(519\) | 1.71379 | 0.0752271 | ||||||||
\(520\) | −2.63533 | −0.115567 | ||||||||
\(521\) | 0.948690 | 0.0415629 | 0.0207814 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207814 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(522\) | −1.49827 | −0.0655775 | ||||||||
\(523\) | −36.8853 | −1.61288 | −0.806441 | − | 0.591315i | \(-0.798609\pi\) | ||||
−0.806441 | + | 0.591315i | \(0.798609\pi\) | |||||||
\(524\) | 12.0301 | 0.525539 | ||||||||
\(525\) | −0.506041 | −0.0220854 | ||||||||
\(526\) | 9.64204 | 0.420413 | ||||||||
\(527\) | 6.61596 | 0.288196 | ||||||||
\(528\) | −2.10992 | −0.0918223 | ||||||||
\(529\) | 4.53079 | 0.196991 | ||||||||
\(530\) | 8.59179 | 0.373204 | ||||||||
\(531\) | 24.6784 | 1.07095 | ||||||||
\(532\) | 23.1581 | 1.00403 | ||||||||
\(533\) | −4.99223 | −0.216237 | ||||||||
\(534\) | −1.87023 | −0.0809329 | ||||||||
\(535\) | −3.93230 | −0.170008 | ||||||||
\(536\) | 0.956459 | 0.0413128 | ||||||||
\(537\) | 0.395060 | 0.0170481 | ||||||||
\(538\) | 7.80864 | 0.336654 | ||||||||
\(539\) | −2.23862 | −0.0964241 | ||||||||
\(540\) | 3.99521 | 0.171927 | ||||||||
\(541\) | −17.5157 | −0.753060 | −0.376530 | − | 0.926404i | \(-0.622883\pi\) | ||||
−0.376530 | + | 0.926404i | \(0.622883\pi\) | |||||||
\(542\) | 1.18970 | 0.0511021 | ||||||||
\(543\) | 1.75409 | 0.0752750 | ||||||||
\(544\) | −5.93230 | −0.254345 | ||||||||
\(545\) | 16.6461 | 0.713040 | ||||||||
\(546\) | −0.180604 | −0.00772913 | ||||||||
\(547\) | 16.1032 | 0.688524 | 0.344262 | − | 0.938874i | \(-0.388129\pi\) | ||||
0.344262 | + | 0.938874i | \(0.388129\pi\) | |||||||
\(548\) | −14.0828 | −0.601586 | ||||||||
\(549\) | 23.3894 | 0.998236 | ||||||||
\(550\) | 2.63102 | 0.112187 | ||||||||
\(551\) | −4.88471 | −0.208096 | ||||||||
\(552\) | −2.12929 | −0.0906288 | ||||||||
\(553\) | 13.0248 | 0.553869 | ||||||||
\(554\) | 12.9081 | 0.548414 | ||||||||
\(555\) | −4.51334 | −0.191580 | ||||||||
\(556\) | −10.2185 | −0.433361 | ||||||||
\(557\) | 5.46788 | 0.231681 | 0.115841 | − | 0.993268i | \(-0.463044\pi\) | ||||
0.115841 | + | 0.993268i | \(0.463044\pi\) | |||||||
\(558\) | 9.79417 | 0.414620 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 11.4819 | 0.485198 | ||||||||
\(561\) | −1.04221 | −0.0440022 | ||||||||
\(562\) | 9.84176 | 0.415149 | ||||||||
\(563\) | 34.9874 | 1.47454 | 0.737272 | − | 0.675595i | \(-0.236113\pi\) | ||||
0.737272 | + | 0.675595i | \(0.236113\pi\) | |||||||
\(564\) | −0.335126 | −0.0141113 | ||||||||
\(565\) | 3.65817 | 0.153900 | ||||||||
\(566\) | −2.16959 | −0.0911946 | ||||||||
\(567\) | −22.0965 | −0.927966 | ||||||||
\(568\) | 19.4276 | 0.815163 | ||||||||
\(569\) | −6.32245 | −0.265051 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(570\) | −1.17762 | −0.0493251 | ||||||||
\(571\) | 19.6606 | 0.822769 | 0.411384 | − | 0.911462i | \(-0.365045\pi\) | ||||
0.411384 | + | 0.911462i | \(0.365045\pi\) | |||||||
\(572\) | −5.15883 | −0.215702 | ||||||||
\(573\) | 1.49443 | 0.0624308 | ||||||||
\(574\) | −11.0067 | −0.459411 | ||||||||
\(575\) | −5.24698 | −0.218814 | ||||||||
\(576\) | 4.52350 | 0.188479 | ||||||||
\(577\) | 15.1377 | 0.630189 | 0.315094 | − | 0.949060i | \(-0.397964\pi\) | ||||
0.315094 | + | 0.949060i | \(0.397964\pi\) | |||||||
\(578\) | 8.75063 | 0.363978 | ||||||||
\(579\) | 1.59286 | 0.0661970 | ||||||||
\(580\) | −3.08575 | −0.128129 | ||||||||
\(581\) | −38.1239 | −1.58165 | ||||||||
\(582\) | 1.81966 | 0.0754273 | ||||||||
\(583\) | 36.6993 | 1.51993 | ||||||||
\(584\) | −25.9801 | −1.07507 | ||||||||
\(585\) | 3.80817 | 0.157448 | ||||||||
\(586\) | 15.5566 | 0.642638 | ||||||||
\(587\) | −6.02416 | −0.248644 | −0.124322 | − | 0.992242i | \(-0.539676\pi\) | ||||
−0.124322 | + | 0.992242i | \(0.539676\pi\) | |||||||
\(588\) | −0.158243 | −0.00652582 | ||||||||
\(589\) | 31.9312 | 1.31570 | ||||||||
\(590\) | −9.25129 | −0.380870 | ||||||||
\(591\) | 3.84069 | 0.157985 | ||||||||
\(592\) | −25.6015 | −1.05221 | ||||||||
\(593\) | 40.7894 | 1.67502 | 0.837510 | − | 0.546423i | \(-0.184011\pi\) | ||||
0.837510 | + | 0.546423i | \(0.184011\pi\) | |||||||
\(594\) | −3.10620 | −0.127449 | ||||||||
\(595\) | 5.67158 | 0.232512 | ||||||||
\(596\) | −3.76510 | −0.154225 | ||||||||
\(597\) | −4.48858 | −0.183705 | ||||||||
\(598\) | −1.87263 | −0.0765773 | ||||||||
\(599\) | −22.9293 | −0.936866 | −0.468433 | − | 0.883499i | \(-0.655181\pi\) | ||||
−0.468433 | + | 0.883499i | \(0.655181\pi\) | |||||||
\(600\) | 0.405813 | 0.0165673 | ||||||||
\(601\) | −11.6974 | −0.477147 | −0.238573 | − | 0.971124i | \(-0.576680\pi\) | ||||
−0.238573 | + | 0.971124i | \(0.576680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.38212 | −0.0562844 | ||||||||
\(604\) | −0.835790 | −0.0340078 | ||||||||
\(605\) | −22.9530 | −0.933172 | ||||||||
\(606\) | −0.416830 | −0.0169326 | ||||||||
\(607\) | −15.8659 | −0.643978 | −0.321989 | − | 0.946743i | \(-0.604351\pi\) | ||||
−0.321989 | + | 0.946743i | \(0.604351\pi\) | |||||||
\(608\) | −28.6316 | −1.16117 | ||||||||
\(609\) | −0.461435 | −0.0186983 | ||||||||
\(610\) | −8.76809 | −0.355009 | ||||||||
\(611\) | −0.643104 | −0.0260172 | ||||||||
\(612\) | 5.56033 | 0.224763 | ||||||||
\(613\) | 32.6461 | 1.31856 | 0.659282 | − | 0.751896i | \(-0.270861\pi\) | ||||
0.659282 | + | 0.751896i | \(0.270861\pi\) | |||||||
\(614\) | 0.351519 | 0.0141862 | ||||||||
\(615\) | −3.07500 | −0.123996 | ||||||||
\(616\) | −24.8183 | −0.999959 | ||||||||
\(617\) | 36.0575 | 1.45162 | 0.725811 | − | 0.687894i | \(-0.241465\pi\) | ||||
0.725811 | + | 0.687894i | \(0.241465\pi\) | |||||||
\(618\) | −0.650874 | −0.0261820 | ||||||||
\(619\) | 9.03577 | 0.363178 | 0.181589 | − | 0.983374i | \(-0.441876\pi\) | ||||
0.181589 | + | 0.983374i | \(0.441876\pi\) | |||||||
\(620\) | 20.1715 | 0.810107 | ||||||||
\(621\) | 6.19460 | 0.248581 | ||||||||
\(622\) | 14.0774 | 0.564452 | ||||||||
\(623\) | 43.4728 | 1.74170 | ||||||||
\(624\) | −0.286208 | −0.0114575 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −8.29457 | −0.331518 | ||||||||
\(627\) | −5.03013 | −0.200884 | ||||||||
\(628\) | 13.0479 | 0.520666 | ||||||||
\(629\) | −12.6461 | −0.504233 | ||||||||
\(630\) | 8.39612 | 0.334510 | ||||||||
\(631\) | 17.0224 | 0.677650 | 0.338825 | − | 0.940850i | \(-0.389971\pi\) | ||||
0.338825 | + | 0.940850i | \(0.389971\pi\) | |||||||
\(632\) | −10.4450 | −0.415481 | ||||||||
\(633\) | 3.26636 | 0.129826 | ||||||||
\(634\) | 2.68904 | 0.106795 | ||||||||
\(635\) | −5.93230 | −0.235416 | ||||||||
\(636\) | 2.59419 | 0.102866 | ||||||||
\(637\) | −0.303667 | −0.0120317 | ||||||||
\(638\) | 2.39911 | 0.0949816 | ||||||||
\(639\) | −28.0737 | −1.11058 | ||||||||
\(640\) | −23.0750 | −0.912119 | ||||||||
\(641\) | −5.35152 | −0.211372 | −0.105686 | − | 0.994400i | \(-0.533704\pi\) | ||||
−0.105686 | + | 0.994400i | \(0.533704\pi\) | |||||||
\(642\) | 0.216112 | 0.00852925 | ||||||||
\(643\) | −18.5241 | −0.730519 | −0.365259 | − | 0.930906i | \(-0.619020\pi\) | ||||
−0.365259 | + | 0.930906i | \(0.619020\pi\) | |||||||
\(644\) | 22.6829 | 0.893832 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.29962 | −0.129822 | ||||||||
\(647\) | 21.3357 | 0.838794 | 0.419397 | − | 0.907803i | \(-0.362242\pi\) | ||||
0.419397 | + | 0.907803i | \(0.362242\pi\) | |||||||
\(648\) | 17.7200 | 0.696108 | ||||||||
\(649\) | −39.5163 | −1.55115 | ||||||||
\(650\) | 0.356896 | 0.0139986 | ||||||||
\(651\) | 3.01639 | 0.118222 | ||||||||
\(652\) | −1.65114 | −0.0646635 | ||||||||
\(653\) | 34.6698 | 1.35673 | 0.678367 | − | 0.734724i | \(-0.262688\pi\) | ||||
0.678367 | + | 0.734724i | \(0.262688\pi\) | |||||||
\(654\) | −0.914838 | −0.0357730 | ||||||||
\(655\) | 14.2198 | 0.555615 | ||||||||
\(656\) | −17.4426 | −0.681021 | ||||||||
\(657\) | 37.5424 | 1.46467 | ||||||||
\(658\) | −1.41789 | −0.0552753 | ||||||||
\(659\) | 46.9124 | 1.82745 | 0.913725 | − | 0.406334i | \(-0.133193\pi\) | ||||
0.913725 | + | 0.406334i | \(0.133193\pi\) | |||||||
\(660\) | −3.17762 | −0.123689 | ||||||||
\(661\) | 14.1062 | 0.548667 | 0.274334 | − | 0.961635i | \(-0.411543\pi\) | ||||
0.274334 | + | 0.961635i | \(0.411543\pi\) | |||||||
\(662\) | −6.85218 | −0.266318 | ||||||||
\(663\) | −0.141375 | −0.00549056 | ||||||||
\(664\) | 30.5730 | 1.18646 | ||||||||
\(665\) | 27.3733 | 1.06149 | ||||||||
\(666\) | −18.7211 | −0.725427 | ||||||||
\(667\) | −4.78448 | −0.185256 | ||||||||
\(668\) | 9.55735 | 0.369785 | ||||||||
\(669\) | 0.298290 | 0.0115326 | ||||||||
\(670\) | 0.518122 | 0.0200168 | ||||||||
\(671\) | −37.4523 | −1.44583 | ||||||||
\(672\) | −2.70469 | −0.104336 | ||||||||
\(673\) | 24.3207 | 0.937492 | 0.468746 | − | 0.883333i | \(-0.344706\pi\) | ||||
0.468746 | + | 0.883333i | \(0.344706\pi\) | |||||||
\(674\) | −3.44265 | −0.132606 | ||||||||
\(675\) | −1.18060 | −0.0454415 | ||||||||
\(676\) | 21.2965 | 0.819096 | ||||||||
\(677\) | −34.6571 | −1.33198 | −0.665990 | − | 0.745960i | \(-0.731991\pi\) | ||||
−0.665990 | + | 0.745960i | \(0.731991\pi\) | |||||||
\(678\) | −0.201046 | −0.00772113 | ||||||||
\(679\) | −42.2972 | −1.62322 | ||||||||
\(680\) | −4.54825 | −0.174418 | ||||||||
\(681\) | 3.63640 | 0.139347 | ||||||||
\(682\) | −15.6829 | −0.600530 | ||||||||
\(683\) | −29.2790 | −1.12033 | −0.560165 | − | 0.828381i | \(-0.689262\pi\) | ||||
−0.560165 | + | 0.828381i | \(0.689262\pi\) | |||||||
\(684\) | 26.8364 | 1.02611 | ||||||||
\(685\) | −16.6461 | −0.636014 | ||||||||
\(686\) | −10.5948 | −0.404510 | ||||||||
\(687\) | −1.22474 | −0.0467266 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.97823 | 0.189655 | ||||||||
\(690\) | −1.15346 | −0.0439113 | ||||||||
\(691\) | 4.59956 | 0.174976 | 0.0874878 | − | 0.996166i | \(-0.472116\pi\) | ||||
0.0874878 | + | 0.996166i | \(0.472116\pi\) | |||||||
\(692\) | 14.6407 | 0.556556 | ||||||||
\(693\) | 35.8635 | 1.36234 | ||||||||
\(694\) | −10.0392 | −0.381084 | ||||||||
\(695\) | −12.0785 | −0.458162 | ||||||||
\(696\) | 0.370042 | 0.0140264 | ||||||||
\(697\) | −8.61596 | −0.326353 | ||||||||
\(698\) | −4.02715 | −0.152430 | ||||||||
\(699\) | −0.875609 | −0.0331186 | ||||||||
\(700\) | −4.32304 | −0.163396 | ||||||||
\(701\) | 3.77373 | 0.142532 | 0.0712658 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712658 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(702\) | −0.421353 | −0.0159029 | ||||||||
\(703\) | −61.0350 | −2.30198 | ||||||||
\(704\) | −7.24326 | −0.272991 | ||||||||
\(705\) | −0.396125 | −0.0149189 | ||||||||
\(706\) | −5.79358 | −0.218044 | ||||||||
\(707\) | 9.68904 | 0.364394 | ||||||||
\(708\) | −2.79331 | −0.104979 | ||||||||
\(709\) | 4.86353 | 0.182654 | 0.0913268 | − | 0.995821i | \(-0.470889\pi\) | ||||
0.0913268 | + | 0.995821i | \(0.470889\pi\) | |||||||
\(710\) | 10.5241 | 0.394962 | ||||||||
\(711\) | 15.0935 | 0.566051 | ||||||||
\(712\) | −34.8625 | −1.30653 | ||||||||
\(713\) | 31.2760 | 1.17130 | ||||||||
\(714\) | −0.311699 | −0.0116651 | ||||||||
\(715\) | −6.09783 | −0.228046 | ||||||||
\(716\) | 3.37495 | 0.126128 | ||||||||
\(717\) | 2.06962 | 0.0772915 | ||||||||
\(718\) | 15.6136 | 0.582693 | ||||||||
\(719\) | −12.2911 | −0.458381 | −0.229191 | − | 0.973382i | \(-0.573608\pi\) | ||||
−0.229191 | + | 0.973382i | \(0.573608\pi\) | |||||||
\(720\) | 13.3056 | 0.495870 | ||||||||
\(721\) | 15.1293 | 0.563444 | ||||||||
\(722\) | −5.38106 | −0.200262 | ||||||||
\(723\) | −4.81295 | −0.178996 | ||||||||
\(724\) | 14.9849 | 0.556911 | ||||||||
\(725\) | 0.911854 | 0.0338654 | ||||||||
\(726\) | 1.26145 | 0.0468170 | ||||||||
\(727\) | 43.2127 | 1.60267 | 0.801334 | − | 0.598217i | \(-0.204124\pi\) | ||||
0.801334 | + | 0.598217i | \(0.204124\pi\) | |||||||
\(728\) | −3.36658 | −0.124774 | ||||||||
\(729\) | −24.9047 | −0.922395 | ||||||||
\(730\) | −14.0737 | −0.520890 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.64742 | −0.0978513 | ||||||||
\(733\) | −26.7590 | −0.988366 | −0.494183 | − | 0.869358i | \(-0.664533\pi\) | ||||
−0.494183 | + | 0.869358i | \(0.664533\pi\) | |||||||
\(734\) | −9.12797 | −0.336919 | ||||||||
\(735\) | −0.187046 | −0.00689928 | ||||||||
\(736\) | −28.0441 | −1.03372 | ||||||||
\(737\) | 2.21313 | 0.0815216 | ||||||||
\(738\) | −12.7549 | −0.469516 | ||||||||
\(739\) | 10.9535 | 0.402930 | 0.201465 | − | 0.979496i | \(-0.435430\pi\) | ||||
0.201465 | + | 0.979496i | \(0.435430\pi\) | |||||||
\(740\) | −38.5569 | −1.41738 | ||||||||
\(741\) | −0.682333 | −0.0250661 | ||||||||
\(742\) | 10.9758 | 0.402936 | ||||||||
\(743\) | −39.1661 | −1.43687 | −0.718433 | − | 0.695596i | \(-0.755140\pi\) | ||||
−0.718433 | + | 0.695596i | \(0.755140\pi\) | |||||||
\(744\) | −2.41896 | −0.0886834 | ||||||||
\(745\) | −4.45042 | −0.163051 | ||||||||
\(746\) | 5.99702 | 0.219566 | ||||||||
\(747\) | −44.1793 | −1.61644 | ||||||||
\(748\) | −8.90349 | −0.325544 | ||||||||
\(749\) | −5.02343 | −0.183552 | ||||||||
\(750\) | 1.31900 | 0.0481629 | ||||||||
\(751\) | 11.4131 | 0.416470 | 0.208235 | − | 0.978079i | \(-0.433228\pi\) | ||||
0.208235 | + | 0.978079i | \(0.433228\pi\) | |||||||
\(752\) | −2.24698 | −0.0819389 | ||||||||
\(753\) | 4.34290 | 0.158264 | ||||||||
\(754\) | 0.325437 | 0.0118517 | ||||||||
\(755\) | −0.987918 | −0.0359540 | ||||||||
\(756\) | 5.10380 | 0.185624 | ||||||||
\(757\) | −27.9995 | −1.01766 | −0.508830 | − | 0.860867i | \(-0.669922\pi\) | ||||
−0.508830 | + | 0.860867i | \(0.669922\pi\) | |||||||
\(758\) | 5.39373 | 0.195909 | ||||||||
\(759\) | −4.92692 | −0.178836 | ||||||||
\(760\) | −21.9517 | −0.796271 | ||||||||
\(761\) | −31.0659 | −1.12614 | −0.563069 | − | 0.826410i | \(-0.690379\pi\) | ||||
−0.563069 | + | 0.826410i | \(0.690379\pi\) | |||||||
\(762\) | 0.326028 | 0.0118107 | ||||||||
\(763\) | 21.2650 | 0.769846 | ||||||||
\(764\) | 12.7668 | 0.461885 | ||||||||
\(765\) | 6.57242 | 0.237626 | ||||||||
\(766\) | 13.1196 | 0.474031 | ||||||||
\(767\) | −5.36035 | −0.193551 | ||||||||
\(768\) | 0.662955 | 0.0239223 | ||||||||
\(769\) | −10.6267 | −0.383209 | −0.191604 | − | 0.981472i | \(-0.561369\pi\) | ||||
−0.191604 | + | 0.981472i | \(0.561369\pi\) | |||||||
\(770\) | −13.4443 | −0.484499 | ||||||||
\(771\) | 0.573481 | 0.0206534 | ||||||||
\(772\) | 13.6076 | 0.489748 | ||||||||
\(773\) | −26.4359 | −0.950835 | −0.475417 | − | 0.879760i | \(-0.657703\pi\) | ||||
−0.475417 | + | 0.879760i | \(0.657703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.96077 | −0.214117 | ||||||||
\(776\) | 33.9197 | 1.21765 | ||||||||
\(777\) | −5.76569 | −0.206843 | ||||||||
\(778\) | 4.38032 | 0.157042 | ||||||||
\(779\) | −41.5840 | −1.48990 | ||||||||
\(780\) | −0.431041 | −0.0154338 | ||||||||
\(781\) | 44.9530 | 1.60854 | ||||||||
\(782\) | −3.23191 | −0.115573 | ||||||||
\(783\) | −1.07654 | −0.0384723 | ||||||||
\(784\) | −1.06100 | −0.0378928 | ||||||||
\(785\) | 15.4228 | 0.550463 | ||||||||
\(786\) | −0.781495 | −0.0278750 | ||||||||
\(787\) | −16.6517 | −0.593570 | −0.296785 | − | 0.954944i | \(-0.595914\pi\) | ||||
−0.296785 | + | 0.954944i | \(0.595914\pi\) | |||||||
\(788\) | 32.8106 | 1.16883 | ||||||||
\(789\) | 3.44120 | 0.122510 | ||||||||
\(790\) | −5.65817 | −0.201309 | ||||||||
\(791\) | 4.67324 | 0.166161 | ||||||||
\(792\) | −28.7603 | −1.02195 | ||||||||
\(793\) | −5.08038 | −0.180409 | ||||||||
\(794\) | 14.2010 | 0.503976 | ||||||||
\(795\) | 3.06638 | 0.108753 | ||||||||
\(796\) | −38.3454 | −1.35912 | ||||||||
\(797\) | −7.39612 | −0.261984 | −0.130992 | − | 0.991383i | \(-0.541816\pi\) | ||||
−0.130992 | + | 0.991383i | \(0.541816\pi\) | |||||||
\(798\) | −1.50438 | −0.0532546 | ||||||||
\(799\) | −1.10992 | −0.0392660 | ||||||||
\(800\) | 5.34481 | 0.188968 | ||||||||
\(801\) | 50.3777 | 1.78001 | ||||||||
\(802\) | 4.83340 | 0.170673 | ||||||||
\(803\) | −60.1148 | −2.12141 | ||||||||
\(804\) | 0.156441 | 0.00551724 | ||||||||
\(805\) | 26.8116 | 0.944986 | ||||||||
\(806\) | −2.12737 | −0.0749336 | ||||||||
\(807\) | 2.78687 | 0.0981025 | ||||||||
\(808\) | −7.77000 | −0.273348 | ||||||||
\(809\) | 25.5687 | 0.898947 | 0.449474 | − | 0.893294i | \(-0.351612\pi\) | ||||
0.449474 | + | 0.893294i | \(0.351612\pi\) | |||||||
\(810\) | 9.59909 | 0.337278 | ||||||||
\(811\) | −23.1166 | −0.811734 | −0.405867 | − | 0.913932i | \(-0.633030\pi\) | ||||
−0.405867 | + | 0.913932i | \(0.633030\pi\) | |||||||
\(812\) | −3.94198 | −0.138337 | ||||||||
\(813\) | 0.424600 | 0.0148914 | ||||||||
\(814\) | 29.9772 | 1.05070 | ||||||||
\(815\) | −1.95167 | −0.0683641 | ||||||||
\(816\) | −0.493959 | −0.0172920 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7.35690 | −0.257228 | ||||||||
\(819\) | 4.86486 | 0.169992 | ||||||||
\(820\) | −26.2693 | −0.917365 | ||||||||
\(821\) | −15.8619 | −0.553583 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(822\) | 0.914838 | 0.0319086 | ||||||||
\(823\) | −17.6209 | −0.614225 | −0.307112 | − | 0.951673i | \(-0.599363\pi\) | ||||
−0.307112 | + | 0.951673i | \(0.599363\pi\) | |||||||
\(824\) | −12.1328 | −0.422664 | ||||||||
\(825\) | 0.939001 | 0.0326918 | ||||||||
\(826\) | −11.8183 | −0.411212 | ||||||||
\(827\) | 28.6552 | 0.996438 | 0.498219 | − | 0.867051i | \(-0.333987\pi\) | ||||
0.498219 | + | 0.867051i | \(0.333987\pi\) | |||||||
\(828\) | 26.2857 | 0.913492 | ||||||||
\(829\) | −13.9011 | −0.482805 | −0.241403 | − | 0.970425i | \(-0.577607\pi\) | ||||
−0.241403 | + | 0.970425i | \(0.577607\pi\) | |||||||
\(830\) | 16.5617 | 0.574864 | ||||||||
\(831\) | 4.60686 | 0.159810 | ||||||||
\(832\) | −0.982542 | −0.0340635 | ||||||||
\(833\) | −0.524090 | −0.0181586 | ||||||||
\(834\) | 0.663809 | 0.0229858 | ||||||||
\(835\) | 11.2970 | 0.390947 | ||||||||
\(836\) | −42.9718 | −1.48621 | ||||||||
\(837\) | 7.03731 | 0.243245 | ||||||||
\(838\) | −0.633415 | −0.0218810 | ||||||||
\(839\) | −25.2131 | −0.870454 | −0.435227 | − | 0.900321i | \(-0.643332\pi\) | ||||
−0.435227 | + | 0.900321i | \(0.643332\pi\) | |||||||
\(840\) | −2.07367 | −0.0715485 | ||||||||
\(841\) | −28.1685 | −0.971328 | ||||||||
\(842\) | −1.84920 | −0.0637276 | ||||||||
\(843\) | 3.51248 | 0.120976 | ||||||||
\(844\) | 27.9041 | 0.960498 | ||||||||
\(845\) | 25.1728 | 0.865972 | ||||||||
\(846\) | −1.64310 | −0.0564911 | ||||||||
\(847\) | −29.3220 | −1.00752 | ||||||||
\(848\) | 17.3937 | 0.597303 | ||||||||
\(849\) | −0.774317 | −0.0265745 | ||||||||
\(850\) | 0.615957 | 0.0211272 | ||||||||
\(851\) | −59.7827 | −2.04932 | ||||||||
\(852\) | 3.17762 | 0.108863 | ||||||||
\(853\) | 21.9135 | 0.750304 | 0.375152 | − | 0.926963i | \(-0.377590\pi\) | ||||
0.375152 | + | 0.926963i | \(0.377590\pi\) | |||||||
\(854\) | −11.2010 | −0.383292 | ||||||||
\(855\) | 31.7211 | 1.08484 | ||||||||
\(856\) | 4.02848 | 0.137690 | ||||||||
\(857\) | 13.8804 | 0.474145 | 0.237073 | − | 0.971492i | \(-0.423812\pi\) | ||||
0.237073 | + | 0.971492i | \(0.423812\pi\) | |||||||
\(858\) | 0.335126 | 0.0114410 | ||||||||
\(859\) | −31.4959 | −1.07463 | −0.537313 | − | 0.843383i | \(-0.680561\pi\) | ||||
−0.537313 | + | 0.843383i | \(0.680561\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.92825 | −0.133874 | ||||||||
\(862\) | −11.2942 | −0.384683 | ||||||||
\(863\) | −48.7958 | −1.66103 | −0.830515 | − | 0.556997i | \(-0.811954\pi\) | ||||
−0.830515 | + | 0.556997i | \(0.811954\pi\) | |||||||
\(864\) | −6.31011 | −0.214674 | ||||||||
\(865\) | 17.3056 | 0.588408 | ||||||||
\(866\) | −5.52914 | −0.187888 | ||||||||
\(867\) | 3.12306 | 0.106065 | ||||||||
\(868\) | 25.7687 | 0.874646 | ||||||||
\(869\) | −24.1685 | −0.819861 | ||||||||
\(870\) | 0.200455 | 0.00679607 | ||||||||
\(871\) | 0.300209 | 0.0101722 | ||||||||
\(872\) | −17.0532 | −0.577495 | ||||||||
\(873\) | −49.0154 | −1.65892 | ||||||||
\(874\) | −15.5985 | −0.527627 | ||||||||
\(875\) | −30.6595 | −1.03648 | ||||||||
\(876\) | −4.24937 | −0.143573 | ||||||||
\(877\) | 0.398517 | 0.0134570 | 0.00672849 | − | 0.999977i | \(-0.497858\pi\) | ||||
0.00672849 | + | 0.999977i | \(0.497858\pi\) | |||||||
\(878\) | −4.54361 | −0.153340 | ||||||||
\(879\) | 5.55209 | 0.187267 | ||||||||
\(880\) | −21.3056 | −0.718211 | ||||||||
\(881\) | 20.7651 | 0.699594 | 0.349797 | − | 0.936826i | \(-0.386251\pi\) | ||||
0.349797 | + | 0.936826i | \(0.386251\pi\) | |||||||
\(882\) | −0.775856 | −0.0261244 | ||||||||
\(883\) | 21.3840 | 0.719630 | 0.359815 | − | 0.933024i | \(-0.382840\pi\) | ||||
0.359815 | + | 0.933024i | \(0.382840\pi\) | |||||||
\(884\) | −1.20775 | −0.0406211 | ||||||||
\(885\) | −3.30175 | −0.110987 | ||||||||
\(886\) | −16.8750 | −0.566927 | ||||||||
\(887\) | −39.8659 | −1.33857 | −0.669283 | − | 0.743007i | \(-0.733399\pi\) | ||||
−0.669283 | + | 0.743007i | \(0.733399\pi\) | |||||||
\(888\) | 4.62373 | 0.155162 | ||||||||
\(889\) | −7.57838 | −0.254171 | ||||||||
\(890\) | −18.8853 | −0.633037 | ||||||||
\(891\) | 41.0019 | 1.37362 | ||||||||
\(892\) | 2.54825 | 0.0853218 | ||||||||
\(893\) | −5.35690 | −0.179262 | ||||||||
\(894\) | 0.244587 | 0.00818020 | ||||||||
\(895\) | 3.98925 | 0.133346 | ||||||||
\(896\) | −29.4778 | −0.984785 | ||||||||
\(897\) | −0.668332 | −0.0223150 | ||||||||
\(898\) | 12.3201 | 0.411126 | ||||||||
\(899\) | −5.43535 | −0.181279 | ||||||||
\(900\) | −5.00969 | −0.166990 | ||||||||
\(901\) | 8.59179 | 0.286234 | ||||||||
\(902\) | 20.4239 | 0.680040 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.74764 | −0.124645 | ||||||||
\(905\) | 17.7125 | 0.588782 | ||||||||
\(906\) | 0.0542942 | 0.00180380 | ||||||||
\(907\) | 3.90217 | 0.129569 | 0.0647846 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647846 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(908\) | 31.0653 | 1.03094 | ||||||||
\(909\) | 11.2280 | 0.372409 | ||||||||
\(910\) | −1.82371 | −0.0604553 | ||||||||
\(911\) | −47.1667 | −1.56270 | −0.781352 | − | 0.624091i | \(-0.785469\pi\) | ||||
−0.781352 | + | 0.624091i | \(0.785469\pi\) | |||||||
\(912\) | −2.38404 | −0.0789436 | ||||||||
\(913\) | 70.7421 | 2.34122 | ||||||||
\(914\) | −6.22580 | −0.205931 | ||||||||
\(915\) | −3.12929 | −0.103451 | ||||||||
\(916\) | −10.4628 | −0.345699 | ||||||||
\(917\) | 18.1655 | 0.599879 | ||||||||
\(918\) | −0.727201 | −0.0240012 | ||||||||
\(919\) | −5.53511 | −0.182586 | −0.0912932 | − | 0.995824i | \(-0.529100\pi\) | ||||
−0.0912932 | + | 0.995824i | \(0.529100\pi\) | |||||||
\(920\) | −21.5013 | −0.708875 | ||||||||
\(921\) | 0.125456 | 0.00413391 | ||||||||
\(922\) | 19.1715 | 0.631380 | ||||||||
\(923\) | 6.09783 | 0.200713 | ||||||||
\(924\) | −4.05934 | −0.133543 | ||||||||
\(925\) | 11.3937 | 0.374624 | ||||||||
\(926\) | −5.64981 | −0.185664 | ||||||||
\(927\) | 17.5323 | 0.575837 | ||||||||
\(928\) | 4.87369 | 0.159987 | ||||||||
\(929\) | −33.9541 | −1.11400 | −0.556998 | − | 0.830514i | \(-0.688047\pi\) | ||||
−0.556998 | + | 0.830514i | \(0.688047\pi\) | |||||||
\(930\) | −1.31037 | −0.0429688 | ||||||||
\(931\) | −2.52947 | −0.0828999 | ||||||||
\(932\) | −7.48022 | −0.245023 | ||||||||
\(933\) | 5.02416 | 0.164484 | ||||||||
\(934\) | −8.31229 | −0.271986 | ||||||||
\(935\) | −10.5241 | −0.344175 | ||||||||
\(936\) | −3.90131 | −0.127518 | ||||||||
\(937\) | 9.20775 | 0.300804 | 0.150402 | − | 0.988625i | \(-0.451943\pi\) | ||||
0.150402 | + | 0.988625i | \(0.451943\pi\) | |||||||
\(938\) | 0.661890 | 0.0216115 | ||||||||
\(939\) | −2.96030 | −0.0966057 | ||||||||
\(940\) | −3.38404 | −0.110375 | ||||||||
\(941\) | −39.0307 | −1.27237 | −0.636183 | − | 0.771539i | \(-0.719487\pi\) | ||||
−0.636183 | + | 0.771539i | \(0.719487\pi\) | |||||||
\(942\) | −0.847608 | −0.0276166 | ||||||||
\(943\) | −40.7308 | −1.32638 | ||||||||
\(944\) | −18.7289 | −0.609572 | ||||||||
\(945\) | 6.03279 | 0.196247 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.4166 | 0.598458 | 0.299229 | − | 0.954181i | \(-0.403271\pi\) | ||||
0.299229 | + | 0.954181i | \(0.403271\pi\) | |||||||
\(948\) | −1.70841 | −0.0554867 | ||||||||
\(949\) | −8.15452 | −0.264707 | ||||||||
\(950\) | 2.97285 | 0.0964521 | ||||||||
\(951\) | 0.959706 | 0.0311206 | ||||||||
\(952\) | −5.81030 | −0.188313 | ||||||||
\(953\) | 9.60819 | 0.311240 | 0.155620 | − | 0.987817i | \(-0.450263\pi\) | ||||
0.155620 | + | 0.987817i | \(0.450263\pi\) | |||||||
\(954\) | 12.7192 | 0.411798 | ||||||||
\(955\) | 15.0905 | 0.488318 | ||||||||
\(956\) | 17.6805 | 0.571829 | ||||||||
\(957\) | 0.856232 | 0.0276780 | ||||||||
\(958\) | −16.1256 | −0.520994 | ||||||||
\(959\) | −21.2650 | −0.686684 | ||||||||
\(960\) | −0.605203 | −0.0195329 | ||||||||
\(961\) | 4.53079 | 0.146155 | ||||||||
\(962\) | 4.06638 | 0.131105 | ||||||||
\(963\) | −5.82132 | −0.187589 | ||||||||
\(964\) | −41.1165 | −1.32427 | ||||||||
\(965\) | 16.0844 | 0.517776 | ||||||||
\(966\) | −1.47352 | −0.0474096 | ||||||||
\(967\) | −58.7235 | −1.88842 | −0.944210 | − | 0.329344i | \(-0.893172\pi\) | ||||
−0.944210 | + | 0.329344i | \(0.893172\pi\) | |||||||
\(968\) | 23.5144 | 0.755781 | ||||||||
\(969\) | −1.17762 | −0.0378306 | ||||||||
\(970\) | 18.3746 | 0.589973 | ||||||||
\(971\) | −46.0887 | −1.47906 | −0.739529 | − | 0.673125i | \(-0.764952\pi\) | ||||
−0.739529 | + | 0.673125i | \(0.764952\pi\) | |||||||
\(972\) | 8.89115 | 0.285184 | ||||||||
\(973\) | −15.4300 | −0.494662 | ||||||||
\(974\) | 13.2529 | 0.424652 | ||||||||
\(975\) | 0.127375 | 0.00407925 | ||||||||
\(976\) | −17.7506 | −0.568184 | ||||||||
\(977\) | 11.7963 | 0.377397 | 0.188699 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188699 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(978\) | 0.107260 | 0.00342981 | ||||||||
\(979\) | −80.6674 | −2.57814 | ||||||||
\(980\) | −1.59791 | −0.0510433 | ||||||||
\(981\) | 24.6426 | 0.786779 | ||||||||
\(982\) | 0.374945 | 0.0119650 | ||||||||
\(983\) | −1.78581 | −0.0569584 | −0.0284792 | − | 0.999594i | \(-0.509066\pi\) | ||||
−0.0284792 | + | 0.999594i | \(0.509066\pi\) | |||||||
\(984\) | 3.15021 | 0.100425 | ||||||||
\(985\) | 38.7827 | 1.23572 | ||||||||
\(986\) | 0.561663 | 0.0178870 | ||||||||
\(987\) | −0.506041 | −0.0161075 | ||||||||
\(988\) | −5.82908 | −0.185448 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −15.5797 | −0.495156 | ||||||||
\(991\) | 48.0334 | 1.52583 | 0.762915 | − | 0.646498i | \(-0.223767\pi\) | ||||
0.762915 | + | 0.646498i | \(0.223767\pi\) | |||||||
\(992\) | −31.8592 | −1.01153 | ||||||||
\(993\) | −2.44552 | −0.0776061 | ||||||||
\(994\) | 13.4443 | 0.426427 | ||||||||
\(995\) | −45.3250 | −1.43690 | ||||||||
\(996\) | 5.00059 | 0.158450 | ||||||||
\(997\) | 9.12690 | 0.289052 | 0.144526 | − | 0.989501i | \(-0.453834\pi\) | ||||
0.144526 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(998\) | −17.8665 | −0.565555 | ||||||||
\(999\) | −13.4515 | −0.425586 |
(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 | 1849.2.a.i.1.2 | 3 | ||
43.16 | even | 7 | 43.2.e.b.41.1 | yes | 6 | ||
43.35 | even | 7 | 43.2.e.b.21.1 | ✓ | 6 | ||
43.42 | odd | 2 | 1849.2.a.l.1.2 | 3 | |||
129.35 | odd | 14 | 387.2.u.a.64.1 | 6 | |||
129.59 | odd | 14 | 387.2.u.a.127.1 | 6 | |||
172.35 | odd | 14 | 688.2.u.c.193.1 | 6 | |||
172.59 | odd | 14 | 688.2.u.c.385.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.e.b.21.1 | ✓ | 6 | 43.35 | even | 7 | ||
43.2.e.b.41.1 | yes | 6 | 43.16 | even | 7 | ||
387.2.u.a.64.1 | 6 | 129.35 | odd | 14 | |||
387.2.u.a.127.1 | 6 | 129.59 | odd | 14 | |||
688.2.u.c.193.1 | 6 | 172.35 | odd | 14 | |||
688.2.u.c.385.1 | 6 | 172.59 | odd | 14 | |||
1849.2.a.i.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1849.2.a.l.1.2 | 3 | 43.42 | odd | 2 |