Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.37954\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37954 | 1.68259 | 0.841296 | − | 0.540575i | \(-0.181793\pi\) | ||||
0.841296 | + | 0.540575i | \(0.181793\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.66223 | 1.83112 | ||||||||
\(5\) | 2.05928 | 0.920936 | 0.460468 | − | 0.887676i | \(-0.347682\pi\) | ||||
0.460468 | + | 0.887676i | \(0.347682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.08987 | 1.92379 | 0.961896 | − | 0.273416i | \(-0.0881537\pi\) | ||||
0.961896 | + | 0.273416i | \(0.0881537\pi\) | |||||||
\(8\) | 3.95536 | 1.39843 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.90014 | 1.54956 | ||||||||
\(11\) | 4.57737 | 1.38013 | 0.690064 | − | 0.723748i | \(-0.257582\pi\) | ||||
0.690064 | + | 0.723748i | \(0.257582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.87097 | −0.518915 | −0.259457 | − | 0.965755i | \(-0.583544\pi\) | ||||
−0.259457 | + | 0.965755i | \(0.583544\pi\) | |||||||
\(14\) | 12.1116 | 3.23696 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.08748 | 0.521870 | ||||||||
\(17\) | 0.272178 | 0.0660129 | 0.0330065 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330065 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.546501 | 0.125376 | 0.0626879 | − | 0.998033i | \(-0.480033\pi\) | ||||
0.0626879 | + | 0.998033i | \(0.480033\pi\) | |||||||
\(20\) | 7.54155 | 1.68634 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.8920 | 2.32219 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.759381 | −0.151876 | ||||||||
\(26\) | −4.45206 | −0.873122 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.6403 | 3.52269 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.25284 | −0.763832 | −0.381916 | − | 0.924197i | \(-0.624736\pi\) | ||||
−0.381916 | + | 0.924197i | \(0.624736\pi\) | |||||||
\(32\) | −2.94346 | −0.520335 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.647660 | 0.111073 | ||||||||
\(35\) | 10.4815 | 1.77169 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.52870 | 0.251318 | 0.125659 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125659 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(38\) | 1.30042 | 0.210956 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.14517 | 1.28786 | ||||||||
\(41\) | 8.02619 | 1.25348 | 0.626740 | − | 0.779228i | \(-0.284389\pi\) | ||||
0.626740 | + | 0.779228i | \(0.284389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.67751 | −1.32331 | −0.661654 | − | 0.749809i | \(-0.730145\pi\) | ||||
−0.661654 | + | 0.749809i | \(0.730145\pi\) | |||||||
\(44\) | 16.7634 | 2.52717 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.37954 | −0.350845 | ||||||||
\(47\) | −8.58972 | −1.25294 | −0.626470 | − | 0.779446i | \(-0.715501\pi\) | ||||
−0.626470 | + | 0.779446i | \(0.715501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.9068 | 2.70097 | ||||||||
\(50\) | −1.80698 | −0.255546 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.85194 | −0.950193 | ||||||||
\(53\) | −2.34652 | −0.322319 | −0.161160 | − | 0.986928i | \(-0.551523\pi\) | ||||
−0.161160 | + | 0.986928i | \(0.551523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.42606 | 1.27101 | ||||||||
\(56\) | 20.1323 | 2.69029 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.37954 | −0.312450 | ||||||||
\(59\) | 1.14292 | 0.148795 | 0.0743975 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743975 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.40397 | −0.947981 | −0.473990 | − | 0.880530i | \(-0.657187\pi\) | ||||
−0.473990 | + | 0.880530i | \(0.657187\pi\) | |||||||
\(62\) | −10.1198 | −1.28522 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.1791 | −1.39738 | ||||||||
\(65\) | −3.85285 | −0.477887 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9170 | −1.45590 | −0.727948 | − | 0.685632i | \(-0.759526\pi\) | ||||
−0.727948 | + | 0.685632i | \(0.759526\pi\) | |||||||
\(68\) | 0.996780 | 0.120877 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.9411 | 2.98103 | ||||||||
\(71\) | 6.20236 | 0.736085 | 0.368043 | − | 0.929809i | \(-0.380028\pi\) | ||||
0.368043 | + | 0.929809i | \(0.380028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5699 | −1.23711 | −0.618556 | − | 0.785741i | \(-0.712282\pi\) | ||||
−0.618556 | + | 0.785741i | \(0.712282\pi\) | |||||||
\(74\) | 3.63762 | 0.422865 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00141 | 0.229578 | ||||||||
\(77\) | 23.2982 | 2.65508 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.3652 | −1.84123 | −0.920614 | − | 0.390474i | \(-0.872311\pi\) | ||||
−0.920614 | + | 0.390474i | \(0.872311\pi\) | |||||||
\(80\) | 4.29870 | 0.480609 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.0987 | 2.10910 | ||||||||
\(83\) | 15.9890 | 1.75502 | 0.877509 | − | 0.479561i | \(-0.159204\pi\) | ||||
0.877509 | + | 0.479561i | \(0.159204\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.560490 | 0.0607937 | ||||||||
\(86\) | −20.6485 | −2.22659 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.1051 | 1.93001 | ||||||||
\(89\) | −9.38087 | −0.994370 | −0.497185 | − | 0.867645i | \(-0.665633\pi\) | ||||
−0.497185 | + | 0.867645i | \(0.665633\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.52302 | −0.998284 | ||||||||
\(92\) | −3.66223 | −0.381814 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.4396 | −2.10819 | ||||||||
\(95\) | 1.12540 | 0.115463 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2320 | −1.34350 | −0.671751 | − | 0.740777i | \(-0.734458\pi\) | ||||
−0.671751 | + | 0.740777i | \(0.734458\pi\) | |||||||
\(98\) | 44.9896 | 4.54464 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.78103 | −0.278103 | ||||||||
\(101\) | −6.02178 | −0.599190 | −0.299595 | − | 0.954067i | \(-0.596852\pi\) | ||||
−0.299595 | + | 0.954067i | \(0.596852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3180 | 1.50933 | 0.754663 | − | 0.656113i | \(-0.227800\pi\) | ||||
0.754663 | + | 0.656113i | \(0.227800\pi\) | |||||||
\(104\) | −7.40036 | −0.725665 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.58365 | −0.542332 | ||||||||
\(107\) | −0.735546 | −0.0711079 | −0.0355540 | − | 0.999368i | \(-0.511320\pi\) | ||||
−0.0355540 | + | 0.999368i | \(0.511320\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.53593 | 0.817594 | 0.408797 | − | 0.912625i | \(-0.365948\pi\) | ||||
0.408797 | + | 0.912625i | \(0.365948\pi\) | |||||||
\(110\) | 22.4297 | 2.13859 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.6250 | 1.00397 | ||||||||
\(113\) | 0.738224 | 0.0694463 | 0.0347231 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347231 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.05928 | −0.192029 | ||||||||
\(116\) | −3.66223 | −0.340030 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.71962 | 0.250361 | ||||||||
\(119\) | 1.38535 | 0.126995 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.95228 | 0.904753 | ||||||||
\(122\) | −17.6181 | −1.59507 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.5749 | −1.39867 | ||||||||
\(125\) | −11.8602 | −1.06080 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.60130 | −0.585771 | −0.292885 | − | 0.956148i | \(-0.594615\pi\) | ||||
−0.292885 | + | 0.956148i | \(0.594615\pi\) | |||||||
\(128\) | −20.7141 | −1.83089 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.16803 | −0.804090 | ||||||||
\(131\) | 3.35350 | 0.292996 | 0.146498 | − | 0.989211i | \(-0.453200\pi\) | ||||
0.146498 | + | 0.989211i | \(0.453200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.78162 | 0.241197 | ||||||||
\(134\) | −28.3571 | −2.44968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.07656 | 0.0923144 | ||||||||
\(137\) | 9.55553 | 0.816384 | 0.408192 | − | 0.912896i | \(-0.366159\pi\) | ||||
0.408192 | + | 0.912896i | \(0.366159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.57246 | −0.557469 | −0.278734 | − | 0.960368i | \(-0.589915\pi\) | ||||
−0.278734 | + | 0.960368i | \(0.589915\pi\) | |||||||
\(140\) | 38.3855 | 3.24417 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.7588 | 1.23853 | ||||||||
\(143\) | −8.56413 | −0.716169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.05928 | −0.171014 | ||||||||
\(146\) | −25.1515 | −2.08155 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.59847 | 0.460192 | ||||||||
\(149\) | −16.8263 | −1.37846 | −0.689232 | − | 0.724540i | \(-0.742052\pi\) | ||||
−0.689232 | + | 0.724540i | \(0.742052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5683 | 1.59245 | 0.796223 | − | 0.605003i | \(-0.206828\pi\) | ||||
0.796223 | + | 0.605003i | \(0.206828\pi\) | |||||||
\(152\) | 2.16160 | 0.175329 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 55.4391 | 4.46741 | ||||||||
\(155\) | −8.75777 | −0.703441 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3661 | −0.986922 | −0.493461 | − | 0.869768i | \(-0.664268\pi\) | ||||
−0.493461 | + | 0.869768i | \(0.664268\pi\) | |||||||
\(158\) | −38.9417 | −3.09804 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.06140 | −0.479195 | ||||||||
\(161\) | −5.08987 | −0.401138 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0938 | 0.790611 | 0.395306 | − | 0.918550i | \(-0.370639\pi\) | ||||
0.395306 | + | 0.918550i | \(0.370639\pi\) | |||||||
\(164\) | 29.3938 | 2.29527 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 38.0465 | 2.95298 | ||||||||
\(167\) | −1.30505 | −0.100988 | −0.0504940 | − | 0.998724i | \(-0.516080\pi\) | ||||
−0.0504940 | + | 0.998724i | \(0.516080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.49946 | −0.730728 | ||||||||
\(170\) | 1.33371 | 0.102291 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31.7791 | −2.42313 | ||||||||
\(173\) | −2.20103 | −0.167342 | −0.0836708 | − | 0.996493i | \(-0.526664\pi\) | ||||
−0.0836708 | + | 0.996493i | \(0.526664\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.86515 | −0.292178 | ||||||||
\(176\) | 9.55516 | 0.720247 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.3222 | −1.67312 | ||||||||
\(179\) | 24.6440 | 1.84198 | 0.920991 | − | 0.389584i | \(-0.127381\pi\) | ||||
0.920991 | + | 0.389584i | \(0.127381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.45544 | 0.108182 | 0.0540908 | − | 0.998536i | \(-0.482774\pi\) | ||||
0.0540908 | + | 0.998536i | \(0.482774\pi\) | |||||||
\(182\) | −22.6604 | −1.67970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.95536 | −0.291593 | ||||||||
\(185\) | 3.14803 | 0.231447 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.24586 | 0.0911063 | ||||||||
\(188\) | −31.4575 | −2.29428 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.67793 | 0.194277 | ||||||||
\(191\) | 0.592184 | 0.0428489 | 0.0214244 | − | 0.999770i | \(-0.493180\pi\) | ||||
0.0214244 | + | 0.999770i | \(0.493180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.3728 | 1.75439 | 0.877197 | − | 0.480130i | \(-0.159410\pi\) | ||||
0.877197 | + | 0.480130i | \(0.159410\pi\) | |||||||
\(194\) | −31.4861 | −2.26057 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 69.2412 | 4.94580 | ||||||||
\(197\) | 18.2722 | 1.30184 | 0.650919 | − | 0.759147i | \(-0.274384\pi\) | ||||
0.650919 | + | 0.759147i | \(0.274384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.74033 | 0.548697 | 0.274349 | − | 0.961630i | \(-0.411538\pi\) | ||||
0.274349 | + | 0.961630i | \(0.411538\pi\) | |||||||
\(200\) | −3.00362 | −0.212388 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.3291 | −1.00819 | ||||||||
\(203\) | −5.08987 | −0.357239 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.5281 | 1.15438 | ||||||||
\(206\) | 36.4498 | 2.53958 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.90562 | −0.270806 | ||||||||
\(209\) | 2.50153 | 0.173035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6581 | 0.940262 | 0.470131 | − | 0.882597i | \(-0.344207\pi\) | ||||
0.470131 | + | 0.882597i | \(0.344207\pi\) | |||||||
\(212\) | −8.59350 | −0.590204 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.75027 | −0.119646 | ||||||||
\(215\) | −17.8694 | −1.21868 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.6464 | −1.46945 | ||||||||
\(218\) | 20.3116 | 1.37568 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 34.5204 | 2.32737 | ||||||||
\(221\) | −0.509238 | −0.0342551 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.497369 | 0.0333063 | 0.0166532 | − | 0.999861i | \(-0.494699\pi\) | ||||
0.0166532 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(224\) | −14.9818 | −1.00102 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.75664 | 0.116850 | ||||||||
\(227\) | −12.6270 | −0.838082 | −0.419041 | − | 0.907967i | \(-0.637634\pi\) | ||||
−0.419041 | + | 0.907967i | \(0.637634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.22393 | 0.345207 | 0.172603 | − | 0.984991i | \(-0.444782\pi\) | ||||
0.172603 | + | 0.984991i | \(0.444782\pi\) | |||||||
\(230\) | −4.90014 | −0.323106 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.95536 | −0.259682 | ||||||||
\(233\) | −14.1679 | −0.928173 | −0.464086 | − | 0.885790i | \(-0.653617\pi\) | ||||
−0.464086 | + | 0.885790i | \(0.653617\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.6886 | −1.15388 | ||||||||
\(236\) | 4.18563 | 0.272461 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.29651 | 0.213681 | ||||||||
\(239\) | −15.7660 | −1.01981 | −0.509907 | − | 0.860229i | \(-0.670320\pi\) | ||||
−0.509907 | + | 0.860229i | \(0.670320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7382 | 1.72236 | 0.861179 | − | 0.508302i | \(-0.169726\pi\) | ||||
0.861179 | + | 0.508302i | \(0.169726\pi\) | |||||||
\(242\) | 23.6819 | 1.52233 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −27.1150 | −1.73586 | ||||||||
\(245\) | 38.9344 | 2.48743 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.02249 | −0.0650594 | ||||||||
\(248\) | −16.8215 | −1.06817 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −28.2218 | −1.78490 | ||||||||
\(251\) | 6.69588 | 0.422640 | 0.211320 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211320 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.57737 | −0.287777 | ||||||||
\(254\) | −15.7081 | −0.985613 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −26.9321 | −1.68326 | ||||||||
\(257\) | 10.6964 | 0.667224 | 0.333612 | − | 0.942711i | \(-0.391733\pi\) | ||||
0.333612 | + | 0.942711i | \(0.391733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.78092 | 0.483483 | ||||||||
\(260\) | −14.1100 | −0.875067 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.97979 | 0.492993 | ||||||||
\(263\) | 16.9191 | 1.04328 | 0.521638 | − | 0.853167i | \(-0.325321\pi\) | ||||
0.521638 | + | 0.853167i | \(0.325321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.83213 | −0.296836 | ||||||||
\(266\) | 6.61899 | 0.405836 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −43.6429 | −2.66591 | ||||||||
\(269\) | 6.78462 | 0.413666 | 0.206833 | − | 0.978376i | \(-0.433684\pi\) | ||||
0.206833 | + | 0.978376i | \(0.433684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3901 | 1.23861 | 0.619305 | − | 0.785151i | \(-0.287415\pi\) | ||||
0.619305 | + | 0.785151i | \(0.287415\pi\) | |||||||
\(272\) | 0.568167 | 0.0344502 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.7378 | 1.37364 | ||||||||
\(275\) | −3.47596 | −0.209609 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.68828 | −0.401860 | −0.200930 | − | 0.979606i | \(-0.564396\pi\) | ||||
−0.200930 | + | 0.979606i | \(0.564396\pi\) | |||||||
\(278\) | −15.6395 | −0.937993 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 41.4579 | 2.47758 | ||||||||
\(281\) | −6.60817 | −0.394211 | −0.197105 | − | 0.980382i | \(-0.563154\pi\) | ||||
−0.197105 | + | 0.980382i | \(0.563154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0146 | 1.01141 | 0.505706 | − | 0.862706i | \(-0.331232\pi\) | ||||
0.505706 | + | 0.862706i | \(0.331232\pi\) | |||||||
\(284\) | 22.7145 | 1.34786 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.3787 | −1.20502 | ||||||||
\(287\) | 40.8523 | 2.41144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9259 | −0.995642 | ||||||||
\(290\) | −4.90014 | −0.287746 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −38.7094 | −2.26530 | ||||||||
\(293\) | 28.2553 | 1.65069 | 0.825347 | − | 0.564625i | \(-0.190979\pi\) | ||||
0.825347 | + | 0.564625i | \(0.190979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.35358 | 0.137031 | ||||||||
\(296\) | 6.04657 | 0.351450 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −40.0389 | −2.31939 | ||||||||
\(299\) | 1.87097 | 0.108201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −44.1674 | −2.54577 | ||||||||
\(302\) | 46.5637 | 2.67944 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.14081 | 0.0654299 | ||||||||
\(305\) | −15.2468 | −0.873030 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.93383 | −0.452808 | −0.226404 | − | 0.974034i | \(-0.572697\pi\) | ||||
−0.226404 | + | 0.974034i | \(0.572697\pi\) | |||||||
\(308\) | 85.3235 | 4.86176 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.8395 | −1.18360 | ||||||||
\(311\) | 8.99087 | 0.509825 | 0.254913 | − | 0.966964i | \(-0.417953\pi\) | ||||
0.254913 | + | 0.966964i | \(0.417953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2556 | 1.03187 | 0.515934 | − | 0.856628i | \(-0.327445\pi\) | ||||
0.515934 | + | 0.856628i | \(0.327445\pi\) | |||||||
\(314\) | −29.4257 | −1.66059 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −59.9331 | −3.37150 | ||||||||
\(317\) | 4.09860 | 0.230200 | 0.115100 | − | 0.993354i | \(-0.463281\pi\) | ||||
0.115100 | + | 0.993354i | \(0.463281\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.57737 | −0.256283 | ||||||||
\(320\) | −23.0208 | −1.28690 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.1116 | −0.674952 | ||||||||
\(323\) | 0.148746 | 0.00827643 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.42078 | 0.0788108 | ||||||||
\(326\) | 24.0188 | 1.33028 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 31.7464 | 1.75290 | ||||||||
\(329\) | −43.7206 | −2.41039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00388 | −0.439933 | −0.219967 | − | 0.975507i | \(-0.570595\pi\) | ||||
−0.219967 | + | 0.975507i | \(0.570595\pi\) | |||||||
\(332\) | 58.5553 | 3.21364 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.10543 | −0.169922 | ||||||||
\(335\) | −24.5404 | −1.34079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.94617 | −0.214962 | −0.107481 | − | 0.994207i | \(-0.534278\pi\) | ||||
−0.107481 | + | 0.994207i | \(0.534278\pi\) | |||||||
\(338\) | −22.6044 | −1.22952 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.05265 | 0.111320 | ||||||||
\(341\) | −19.4668 | −1.05419 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 60.6042 | 3.27232 | ||||||||
\(344\) | −34.3226 | −1.85055 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.23746 | −0.281568 | ||||||||
\(347\) | 24.9359 | 1.33863 | 0.669315 | − | 0.742979i | \(-0.266588\pi\) | ||||
0.669315 | + | 0.742979i | \(0.266588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.80474 | −0.471307 | −0.235653 | − | 0.971837i | \(-0.575723\pi\) | ||||
−0.235653 | + | 0.971837i | \(0.575723\pi\) | |||||||
\(350\) | −9.19730 | −0.491616 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.4733 | −0.718129 | ||||||||
\(353\) | 8.66021 | 0.460937 | 0.230468 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230468 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.7724 | 0.677887 | ||||||||
\(356\) | −34.3549 | −1.82081 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 58.6416 | 3.09930 | ||||||||
\(359\) | −22.8271 | −1.20477 | −0.602385 | − | 0.798205i | \(-0.705783\pi\) | ||||
−0.602385 | + | 0.798205i | \(0.705783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7013 | −0.984281 | ||||||||
\(362\) | 3.46327 | 0.182026 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −34.8755 | −1.82797 | ||||||||
\(365\) | −21.7663 | −1.13930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.3609 | 1.63702 | 0.818512 | − | 0.574489i | \(-0.194799\pi\) | ||||
0.818512 | + | 0.574489i | \(0.194799\pi\) | |||||||
\(368\) | −2.08748 | −0.108817 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.49087 | 0.389432 | ||||||||
\(371\) | −11.9435 | −0.620075 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.9416 | −1.23965 | −0.619825 | − | 0.784740i | \(-0.712796\pi\) | ||||
−0.619825 | + | 0.784740i | \(0.712796\pi\) | |||||||
\(374\) | 2.96458 | 0.153295 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.9754 | −1.75215 | ||||||||
\(377\) | 1.87097 | 0.0963600 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.9308 | 0.561478 | 0.280739 | − | 0.959784i | \(-0.409420\pi\) | ||||
0.280739 | + | 0.959784i | \(0.409420\pi\) | |||||||
\(380\) | 4.12146 | 0.211426 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.40913 | 0.0720972 | ||||||||
\(383\) | 15.2443 | 0.778946 | 0.389473 | − | 0.921038i | \(-0.372657\pi\) | ||||
0.389473 | + | 0.921038i | \(0.372657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47.9775 | 2.44516 | ||||||||
\(386\) | 57.9962 | 2.95193 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −48.4585 | −2.46011 | ||||||||
\(389\) | 28.9315 | 1.46688 | 0.733441 | − | 0.679753i | \(-0.237913\pi\) | ||||
0.733441 | + | 0.679753i | \(0.237913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.272178 | −0.0137647 | ||||||||
\(392\) | 74.7832 | 3.77712 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 43.4794 | 2.19046 | ||||||||
\(395\) | −33.7005 | −1.69565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3878 | 0.973048 | 0.486524 | − | 0.873667i | \(-0.338265\pi\) | ||||
0.486524 | + | 0.873667i | \(0.338265\pi\) | |||||||
\(398\) | 18.4185 | 0.923234 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.58519 | −0.0792596 | ||||||||
\(401\) | −5.19885 | −0.259618 | −0.129809 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129809 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.95695 | 0.396364 | ||||||||
\(404\) | −22.0532 | −1.09719 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.1116 | −0.601088 | ||||||||
\(407\) | 6.99744 | 0.346850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6121 | −1.26644 | −0.633219 | − | 0.773972i | \(-0.718267\pi\) | ||||
−0.633219 | + | 0.773972i | \(0.718267\pi\) | |||||||
\(410\) | 39.3295 | 1.94234 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 56.0980 | 2.76375 | ||||||||
\(413\) | 5.81730 | 0.286251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.9257 | 1.61626 | ||||||||
\(416\) | 5.50713 | 0.270009 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.95251 | 0.291147 | ||||||||
\(419\) | −10.3556 | −0.505907 | −0.252953 | − | 0.967478i | \(-0.581402\pi\) | ||||
−0.252953 | + | 0.967478i | \(0.581402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1491 | 0.592111 | 0.296055 | − | 0.955171i | \(-0.404329\pi\) | ||||
0.296055 | + | 0.955171i | \(0.404329\pi\) | |||||||
\(422\) | 32.5000 | 1.58208 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.28132 | −0.450741 | ||||||||
\(425\) | −0.206687 | −0.0100258 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.6853 | −1.82372 | ||||||||
\(428\) | −2.69374 | −0.130207 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −42.5210 | −2.05055 | ||||||||
\(431\) | −28.2807 | −1.36223 | −0.681116 | − | 0.732175i | \(-0.738505\pi\) | ||||
−0.681116 | + | 0.732175i | \(0.738505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.15742 | −0.199793 | −0.0998964 | − | 0.994998i | \(-0.531851\pi\) | ||||
−0.0998964 | + | 0.994998i | \(0.531851\pi\) | |||||||
\(434\) | −51.5086 | −2.47249 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.2605 | 1.49711 | ||||||||
\(437\) | −0.546501 | −0.0261427 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.6089 | 0.888153 | 0.444076 | − | 0.895989i | \(-0.353532\pi\) | ||||
0.444076 | + | 0.895989i | \(0.353532\pi\) | |||||||
\(440\) | 37.2834 | 1.77742 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.21176 | −0.0576373 | ||||||||
\(443\) | 7.39743 | 0.351462 | 0.175731 | − | 0.984438i | \(-0.443771\pi\) | ||||
0.175731 | + | 0.984438i | \(0.443771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.3178 | −0.915751 | ||||||||
\(446\) | 1.18351 | 0.0560409 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −56.9000 | −2.68827 | ||||||||
\(449\) | −23.3610 | −1.10247 | −0.551236 | − | 0.834349i | \(-0.685844\pi\) | ||||
−0.551236 | + | 0.834349i | \(0.685844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.7388 | 1.72996 | ||||||||
\(452\) | 2.70355 | 0.127164 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.0465 | −1.41015 | ||||||||
\(455\) | −19.6105 | −0.919356 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.43183 | −0.300868 | −0.150434 | − | 0.988620i | \(-0.548067\pi\) | ||||
−0.150434 | + | 0.988620i | \(0.548067\pi\) | |||||||
\(458\) | 12.4306 | 0.580842 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.54155 | −0.351626 | ||||||||
\(461\) | 28.5832 | 1.33125 | 0.665627 | − | 0.746285i | \(-0.268164\pi\) | ||||
0.665627 | + | 0.746285i | \(0.268164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8120 | 1.47843 | 0.739214 | − | 0.673470i | \(-0.235197\pi\) | ||||
0.739214 | + | 0.673470i | \(0.235197\pi\) | |||||||
\(464\) | −2.08748 | −0.0969088 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.7133 | −1.56174 | ||||||||
\(467\) | −34.9300 | −1.61637 | −0.808183 | − | 0.588931i | \(-0.799549\pi\) | ||||
−0.808183 | + | 0.588931i | \(0.799549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.6561 | −2.80084 | ||||||||
\(470\) | −42.0908 | −1.94151 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.52064 | 0.208079 | ||||||||
\(473\) | −39.7201 | −1.82633 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.415002 | −0.0190416 | ||||||||
\(476\) | 5.07349 | 0.232543 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −37.5158 | −1.71593 | ||||||||
\(479\) | 4.20878 | 0.192304 | 0.0961521 | − | 0.995367i | \(-0.469346\pi\) | ||||
0.0961521 | + | 0.995367i | \(0.469346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.86017 | −0.130412 | ||||||||
\(482\) | 63.6247 | 2.89803 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 36.4476 | 1.65671 | ||||||||
\(485\) | −27.2483 | −1.23728 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1540 | −0.505437 | −0.252719 | − | 0.967540i | \(-0.581325\pi\) | ||||
−0.252719 | + | 0.967540i | \(0.581325\pi\) | |||||||
\(488\) | −29.2853 | −1.32568 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 92.6461 | 4.18532 | ||||||||
\(491\) | −0.298683 | −0.0134794 | −0.00673969 | − | 0.999977i | \(-0.502145\pi\) | ||||
−0.00673969 | + | 0.999977i | \(0.502145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.272178 | −0.0122583 | ||||||||
\(494\) | −2.43306 | −0.109468 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.87771 | −0.398621 | ||||||||
\(497\) | 31.5692 | 1.41607 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6615 | −0.880168 | −0.440084 | − | 0.897957i | \(-0.645051\pi\) | ||||
−0.440084 | + | 0.897957i | \(0.645051\pi\) | |||||||
\(500\) | −43.4346 | −1.94246 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.9331 | 0.711131 | ||||||||
\(503\) | 0.660795 | 0.0294634 | 0.0147317 | − | 0.999891i | \(-0.495311\pi\) | ||||
0.0147317 | + | 0.999891i | \(0.495311\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4005 | −0.551816 | ||||||||
\(506\) | −10.8920 | −0.484211 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.1755 | −1.07261 | ||||||||
\(509\) | −34.5373 | −1.53084 | −0.765420 | − | 0.643531i | \(-0.777469\pi\) | ||||
−0.765420 | + | 0.643531i | \(0.777469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.7994 | −2.37995 | ||||||||
\(512\) | −22.6579 | −1.00135 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.4526 | 1.12267 | ||||||||
\(515\) | 31.5440 | 1.38999 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.3183 | −1.72922 | ||||||||
\(518\) | 18.5150 | 0.813504 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.2394 | −0.668292 | ||||||||
\(521\) | −2.47755 | −0.108543 | −0.0542717 | − | 0.998526i | \(-0.517284\pi\) | ||||
−0.0542717 | + | 0.998526i | \(0.517284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1107 | 0.923108 | 0.461554 | − | 0.887112i | \(-0.347292\pi\) | ||||
0.461554 | + | 0.887112i | \(0.347292\pi\) | |||||||
\(524\) | 12.2813 | 0.536510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.2597 | 1.75541 | ||||||||
\(527\) | −1.15753 | −0.0504228 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −11.4983 | −0.499453 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.1869 | 0.441660 | ||||||||
\(533\) | −15.0168 | −0.650449 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.51469 | −0.0654859 | ||||||||
\(536\) | −47.1361 | −2.03597 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.1443 | 0.696030 | ||||||||
\(539\) | 86.5434 | 3.72769 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.0220 | 1.16177 | 0.580884 | − | 0.813986i | \(-0.302707\pi\) | ||||
0.580884 | + | 0.813986i | \(0.302707\pi\) | |||||||
\(542\) | 48.5191 | 2.08407 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.801146 | −0.0343488 | ||||||||
\(545\) | 17.5778 | 0.752952 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.1096 | −1.71496 | −0.857481 | − | 0.514516i | \(-0.827972\pi\) | ||||
−0.857481 | + | 0.514516i | \(0.827972\pi\) | |||||||
\(548\) | 34.9946 | 1.49489 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.27121 | −0.352686 | ||||||||
\(551\) | −0.546501 | −0.0232817 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −83.2968 | −3.54214 | ||||||||
\(554\) | −15.9151 | −0.676166 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.0699 | −1.02079 | ||||||||
\(557\) | −12.7652 | −0.540880 | −0.270440 | − | 0.962737i | \(-0.587169\pi\) | ||||
−0.270440 | + | 0.962737i | \(0.587169\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2354 | 0.686684 | ||||||||
\(560\) | 21.8798 | 0.924592 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.7244 | −0.663296 | ||||||||
\(563\) | −1.70334 | −0.0717873 | −0.0358937 | − | 0.999356i | \(-0.511428\pi\) | ||||
−0.0358937 | + | 0.999356i | \(0.511428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.52021 | 0.0639556 | ||||||||
\(566\) | 40.4870 | 1.70179 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.5325 | 1.02936 | ||||||||
\(569\) | −11.6091 | −0.486678 | −0.243339 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243339 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4149 | 1.39837 | 0.699185 | − | 0.714941i | \(-0.253546\pi\) | ||||
0.699185 | + | 0.714941i | \(0.253546\pi\) | |||||||
\(572\) | −31.3638 | −1.31139 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 97.2099 | 4.05746 | ||||||||
\(575\) | 0.759381 | 0.0316684 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.6873 | 1.69384 | 0.846918 | − | 0.531723i | \(-0.178455\pi\) | ||||
0.846918 | + | 0.531723i | \(0.178455\pi\) | |||||||
\(578\) | −40.2760 | −1.67526 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.54155 | −0.313146 | ||||||||
\(581\) | 81.3818 | 3.37629 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.7409 | −0.444842 | ||||||||
\(584\) | −41.8077 | −1.73001 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 67.2349 | 2.77745 | ||||||||
\(587\) | 13.3233 | 0.549910 | 0.274955 | − | 0.961457i | \(-0.411337\pi\) | ||||
0.274955 | + | 0.961457i | \(0.411337\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32418 | −0.0957661 | ||||||||
\(590\) | 5.60045 | 0.230567 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.19114 | 0.131155 | ||||||||
\(593\) | −4.89062 | −0.200834 | −0.100417 | − | 0.994945i | \(-0.532018\pi\) | ||||
−0.100417 | + | 0.994945i | \(0.532018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.85283 | 0.116954 | ||||||||
\(596\) | −61.6218 | −2.52413 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.45206 | 0.182058 | ||||||||
\(599\) | −40.1284 | −1.63960 | −0.819800 | − | 0.572650i | \(-0.805915\pi\) | ||||
−0.819800 | + | 0.572650i | \(0.805915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.1812 | −1.51665 | −0.758326 | − | 0.651876i | \(-0.773982\pi\) | ||||
−0.758326 | + | 0.651876i | \(0.773982\pi\) | |||||||
\(602\) | −105.098 | −4.28349 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 71.6637 | 2.91595 | ||||||||
\(605\) | 20.4945 | 0.833220 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2868 | −0.458117 | −0.229058 | − | 0.973413i | \(-0.573565\pi\) | ||||
−0.229058 | + | 0.973413i | \(0.573565\pi\) | |||||||
\(608\) | −1.60860 | −0.0652374 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.2805 | −1.46895 | ||||||||
\(611\) | 16.0711 | 0.650169 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.5301 | 1.79855 | 0.899277 | − | 0.437380i | \(-0.144093\pi\) | ||||
0.899277 | + | 0.437380i | \(0.144093\pi\) | |||||||
\(614\) | −18.8789 | −0.761891 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 92.1527 | 3.71294 | ||||||||
\(617\) | −22.2432 | −0.895477 | −0.447739 | − | 0.894164i | \(-0.647771\pi\) | ||||
−0.447739 | + | 0.894164i | \(0.647771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.3967 | −0.779621 | −0.389811 | − | 0.920895i | \(-0.627460\pi\) | ||||
−0.389811 | + | 0.920895i | \(0.627460\pi\) | |||||||
\(620\) | −32.0730 | −1.28808 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.3942 | 0.857828 | ||||||||
\(623\) | −47.7474 | −1.91296 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.6264 | −0.825057 | ||||||||
\(626\) | 43.4401 | 1.73621 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −45.2875 | −1.80717 | ||||||||
\(629\) | 0.416080 | 0.0165902 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.9451 | −1.39114 | −0.695572 | − | 0.718456i | \(-0.744849\pi\) | ||||
−0.695572 | + | 0.718456i | \(0.744849\pi\) | |||||||
\(632\) | −64.7302 | −2.57483 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.75280 | 0.387333 | ||||||||
\(635\) | −13.5939 | −0.539458 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.3742 | −1.40158 | ||||||||
\(638\) | −10.8920 | −0.431220 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −42.6561 | −1.68613 | ||||||||
\(641\) | 26.1304 | 1.03209 | 0.516044 | − | 0.856562i | \(-0.327404\pi\) | ||||
0.516044 | + | 0.856562i | \(0.327404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8053 | 1.33315 | 0.666576 | − | 0.745437i | \(-0.267759\pi\) | ||||
0.666576 | + | 0.745437i | \(0.267759\pi\) | |||||||
\(644\) | −18.6403 | −0.734531 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.353947 | 0.0139259 | ||||||||
\(647\) | 41.8834 | 1.64660 | 0.823302 | − | 0.567603i | \(-0.192129\pi\) | ||||
0.823302 | + | 0.567603i | \(0.192129\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.23155 | 0.205356 | ||||||||
\(650\) | 3.38081 | 0.132606 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 36.9660 | 1.44770 | ||||||||
\(653\) | 17.5154 | 0.685432 | 0.342716 | − | 0.939439i | \(-0.388653\pi\) | ||||
0.342716 | + | 0.939439i | \(0.388653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.90578 | 0.269831 | ||||||||
\(656\) | 16.7545 | 0.654154 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −104.035 | −4.05571 | ||||||||
\(659\) | −14.8699 | −0.579247 | −0.289624 | − | 0.957141i | \(-0.593530\pi\) | ||||
−0.289624 | + | 0.957141i | \(0.593530\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7449 | −1.07915 | −0.539577 | − | 0.841936i | \(-0.681416\pi\) | ||||
−0.539577 | + | 0.841936i | \(0.681416\pi\) | |||||||
\(662\) | −19.0456 | −0.740228 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 63.2421 | 2.45427 | ||||||||
\(665\) | 5.72812 | 0.222127 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −4.77941 | −0.184921 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −58.3951 | −2.25600 | ||||||||
\(671\) | −33.8907 | −1.30833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8217 | 0.648427 | 0.324214 | − | 0.945984i | \(-0.394900\pi\) | ||||
0.324214 | + | 0.945984i | \(0.394900\pi\) | |||||||
\(674\) | −9.39010 | −0.361693 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.7892 | −1.33805 | ||||||||
\(677\) | 28.3544 | 1.08975 | 0.544874 | − | 0.838518i | \(-0.316578\pi\) | ||||
0.544874 | + | 0.838518i | \(0.316578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −67.3491 | −2.58462 | ||||||||
\(680\) | 2.21694 | 0.0850157 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −46.3221 | −1.77377 | ||||||||
\(683\) | −18.3962 | −0.703912 | −0.351956 | − | 0.936017i | \(-0.614483\pi\) | ||||
−0.351956 | + | 0.936017i | \(0.614483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.6775 | 0.751837 | ||||||||
\(686\) | 144.210 | 5.50598 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.1141 | −0.690595 | ||||||||
\(689\) | 4.39028 | 0.167256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.7956 | −1.85627 | −0.928136 | − | 0.372240i | \(-0.878590\pi\) | ||||
−0.928136 | + | 0.372240i | \(0.878590\pi\) | |||||||
\(692\) | −8.06070 | −0.306422 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 59.3361 | 2.25237 | ||||||||
\(695\) | −13.5345 | −0.513393 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.18456 | 0.0827460 | ||||||||
\(698\) | −20.9513 | −0.793017 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.1551 | −0.535012 | ||||||||
\(701\) | 11.8246 | 0.446610 | 0.223305 | − | 0.974749i | \(-0.428315\pi\) | ||||
0.223305 | + | 0.974749i | \(0.428315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.835438 | 0.0315091 | ||||||||
\(704\) | −51.1706 | −1.92857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.6074 | 0.775568 | ||||||||
\(707\) | −30.6501 | −1.15272 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.6243 | 0.699448 | 0.349724 | − | 0.936853i | \(-0.386275\pi\) | ||||
0.349724 | + | 0.936853i | \(0.386275\pi\) | |||||||
\(710\) | 30.3924 | 1.14061 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −37.1047 | −1.39056 | ||||||||
\(713\) | 4.25284 | 0.159270 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.6359 | −0.659546 | ||||||||
\(716\) | 90.2522 | 3.37288 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −54.3182 | −2.02714 | ||||||||
\(719\) | 46.0282 | 1.71656 | 0.858282 | − | 0.513178i | \(-0.171532\pi\) | ||||
0.858282 | + | 0.513178i | \(0.171532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.9666 | 2.90363 | ||||||||
\(722\) | −44.5007 | −1.65614 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.33014 | 0.198093 | ||||||||
\(725\) | 0.759381 | 0.0282027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.43522 | −0.349933 | −0.174966 | − | 0.984574i | \(-0.555982\pi\) | ||||
−0.174966 | + | 0.984574i | \(0.555982\pi\) | |||||||
\(728\) | −37.6669 | −1.39603 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −51.7939 | −1.91698 | ||||||||
\(731\) | −2.36183 | −0.0873555 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.1930 | −1.29988 | −0.649941 | − | 0.759985i | \(-0.725206\pi\) | ||||
−0.649941 | + | 0.759985i | \(0.725206\pi\) | |||||||
\(734\) | 74.6246 | 2.75444 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.94346 | 0.108497 | ||||||||
\(737\) | −54.5486 | −2.00932 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3793 | −0.749666 | −0.374833 | − | 0.927092i | \(-0.622300\pi\) | ||||
−0.374833 | + | 0.927092i | \(0.622300\pi\) | |||||||
\(740\) | 11.5288 | 0.423807 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.4201 | −1.04333 | ||||||||
\(743\) | 44.2871 | 1.62474 | 0.812368 | − | 0.583146i | \(-0.198178\pi\) | ||||
0.812368 | + | 0.583146i | \(0.198178\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.6500 | −1.26948 | ||||||||
\(746\) | −56.9701 | −2.08583 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.56263 | 0.166826 | ||||||||
\(749\) | −3.74384 | −0.136797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.1048 | −1.13503 | −0.567514 | − | 0.823363i | \(-0.692095\pi\) | ||||
−0.567514 | + | 0.823363i | \(0.692095\pi\) | |||||||
\(752\) | −17.9309 | −0.653871 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.45206 | 0.162135 | ||||||||
\(755\) | 40.2966 | 1.46654 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.6495 | −1.47743 | −0.738715 | − | 0.674018i | \(-0.764567\pi\) | ||||
−0.738715 | + | 0.674018i | \(0.764567\pi\) | |||||||
\(758\) | 26.0104 | 0.944739 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.45134 | 0.161467 | ||||||||
\(761\) | −18.6533 | −0.676180 | −0.338090 | − | 0.941114i | \(-0.609781\pi\) | ||||
−0.338090 | + | 0.941114i | \(0.609781\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.4468 | 1.57288 | ||||||||
\(764\) | 2.16871 | 0.0784613 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.2744 | 1.31065 | ||||||||
\(767\) | −2.13837 | −0.0772119 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4326 | 0.628637 | 0.314318 | − | 0.949318i | \(-0.398224\pi\) | ||||
0.314318 | + | 0.949318i | \(0.398224\pi\) | |||||||
\(770\) | 114.165 | 4.11420 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 89.2590 | 3.21250 | ||||||||
\(773\) | −46.9728 | −1.68949 | −0.844747 | − | 0.535166i | \(-0.820249\pi\) | ||||
−0.844747 | + | 0.535166i | \(0.820249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.22952 | 0.116008 | ||||||||
\(776\) | −52.3371 | −1.87879 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 68.8437 | 2.46817 | ||||||||
\(779\) | 4.38632 | 0.157156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.3905 | 1.01589 | ||||||||
\(782\) | −0.647660 | −0.0231603 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 39.4676 | 1.40956 | ||||||||
\(785\) | −25.4652 | −0.908893 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.1005 | −1.71460 | −0.857300 | − | 0.514818i | \(-0.827860\pi\) | ||||
−0.857300 | + | 0.514818i | \(0.827860\pi\) | |||||||
\(788\) | 66.9169 | 2.38382 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −80.1917 | −2.85309 | ||||||||
\(791\) | 3.75747 | 0.133600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.8526 | 0.491921 | ||||||||
\(794\) | 46.1342 | 1.63724 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.3469 | 1.00473 | ||||||||
\(797\) | 6.84219 | 0.242363 | 0.121181 | − | 0.992630i | \(-0.461332\pi\) | ||||
0.121181 | + | 0.992630i | \(0.461332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.33794 | −0.0827102 | ||||||||
\(800\) | 2.23521 | 0.0790265 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.3709 | −0.436832 | ||||||||
\(803\) | −48.3823 | −1.70737 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.4815 | −0.369423 | ||||||||
\(806\) | 18.9339 | 0.666919 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.8183 | −0.837924 | ||||||||
\(809\) | −2.15661 | −0.0758223 | −0.0379112 | − | 0.999281i | \(-0.512070\pi\) | ||||
−0.0379112 | + | 0.999281i | \(0.512070\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0010 | 1.05348 | 0.526739 | − | 0.850027i | \(-0.323414\pi\) | ||||
0.526739 | + | 0.850027i | \(0.323414\pi\) | |||||||
\(812\) | −18.6403 | −0.654146 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.6507 | 0.583608 | ||||||||
\(815\) | 20.7860 | 0.728102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.74226 | −0.165911 | ||||||||
\(818\) | −60.9452 | −2.13090 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.5299 | 2.11380 | ||||||||
\(821\) | 35.2369 | 1.22977 | 0.614887 | − | 0.788615i | \(-0.289201\pi\) | ||||
0.614887 | + | 0.788615i | \(0.289201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.9231 | −1.28706 | −0.643530 | − | 0.765421i | \(-0.722531\pi\) | ||||
−0.643530 | + | 0.765421i | \(0.722531\pi\) | |||||||
\(824\) | 60.5881 | 2.11069 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.8425 | 0.481643 | ||||||||
\(827\) | −45.8002 | −1.59263 | −0.796314 | − | 0.604884i | \(-0.793220\pi\) | ||||
−0.796314 | + | 0.604884i | \(0.793220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.3071 | 0.462176 | 0.231088 | − | 0.972933i | \(-0.425771\pi\) | ||||
0.231088 | + | 0.972933i | \(0.425771\pi\) | |||||||
\(830\) | 78.3482 | 2.71951 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.9157 | 0.725122 | ||||||||
\(833\) | 5.14603 | 0.178299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.68747 | −0.0930036 | ||||||||
\(836\) | 9.16120 | 0.316847 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.6417 | −0.851234 | ||||||||
\(839\) | −5.43546 | −0.187653 | −0.0938264 | − | 0.995589i | \(-0.529910\pi\) | ||||
−0.0938264 | + | 0.995589i | \(0.529910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 28.9093 | 0.996281 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 50.0191 | 1.72173 | ||||||||
\(845\) | −19.5620 | −0.672954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.6559 | 1.74056 | ||||||||
\(848\) | −4.89831 | −0.168209 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.491821 | −0.0168693 | ||||||||
\(851\) | −1.52870 | −0.0524033 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.95255 | 0.169572 | 0.0847861 | − | 0.996399i | \(-0.472979\pi\) | ||||
0.0847861 | + | 0.996399i | \(0.472979\pi\) | |||||||
\(854\) | −89.6738 | −3.06857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.90935 | −0.0994394 | ||||||||
\(857\) | −13.5239 | −0.461967 | −0.230983 | − | 0.972958i | \(-0.574194\pi\) | ||||
−0.230983 | + | 0.972958i | \(0.574194\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.5149 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(860\) | −65.4419 | −2.23155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −67.2951 | −2.29208 | ||||||||
\(863\) | −2.25993 | −0.0769289 | −0.0384645 | − | 0.999260i | \(-0.512247\pi\) | ||||
−0.0384645 | + | 0.999260i | \(0.512247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.53254 | −0.154111 | ||||||||
\(866\) | −9.89276 | −0.336170 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −79.2742 | −2.69074 | ||||||||
\(869\) | −74.9095 | −2.54113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.2964 | 0.755486 | ||||||||
\(872\) | 33.7626 | 1.14335 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.30042 | −0.0439874 | ||||||||
\(875\) | −60.3667 | −2.04077 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.1470 | −1.25436 | −0.627182 | − | 0.778873i | \(-0.715792\pi\) | ||||
−0.627182 | + | 0.778873i | \(0.715792\pi\) | |||||||
\(878\) | 44.2806 | 1.49440 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.6767 | 0.663302 | ||||||||
\(881\) | −3.76794 | −0.126945 | −0.0634726 | − | 0.997984i | \(-0.520218\pi\) | ||||
−0.0634726 | + | 0.997984i | \(0.520218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1564 | 1.04850 | 0.524248 | − | 0.851566i | \(-0.324347\pi\) | ||||
0.524248 | + | 0.851566i | \(0.324347\pi\) | |||||||
\(884\) | −1.86495 | −0.0627250 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.6025 | 0.591368 | ||||||||
\(887\) | 49.0264 | 1.64614 | 0.823072 | − | 0.567937i | \(-0.192258\pi\) | ||||
0.823072 | + | 0.567937i | \(0.192258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.5998 | −1.12690 | ||||||||
\(890\) | −45.9676 | −1.54084 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.82148 | 0.0609877 | ||||||||
\(893\) | −4.69429 | −0.157088 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.7489 | 1.69635 | ||||||||
\(896\) | −105.432 | −3.52225 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.5885 | −1.85501 | ||||||||
\(899\) | 4.25284 | 0.141840 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.638672 | −0.0212773 | ||||||||
\(902\) | 87.4217 | 2.91082 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.91994 | 0.0971157 | ||||||||
\(905\) | 2.99714 | 0.0996284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.47164 | 0.314501 | 0.157250 | − | 0.987559i | \(-0.449737\pi\) | ||||
0.157250 | + | 0.987559i | \(0.449737\pi\) | |||||||
\(908\) | −46.2429 | −1.53463 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −46.6641 | −1.54690 | ||||||||
\(911\) | −19.2798 | −0.638769 | −0.319385 | − | 0.947625i | \(-0.603476\pi\) | ||||
−0.319385 | + | 0.947625i | \(0.603476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.1874 | 2.42215 | ||||||||
\(914\) | −15.3048 | −0.506239 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.1312 | 0.632114 | ||||||||
\(917\) | 17.0689 | 0.563664 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8590 | −0.589115 | −0.294558 | − | 0.955634i | \(-0.595172\pi\) | ||||
−0.294558 | + | 0.955634i | \(0.595172\pi\) | |||||||
\(920\) | −8.14517 | −0.268538 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 68.0150 | 2.23996 | ||||||||
\(923\) | −11.6045 | −0.381965 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.16087 | −0.0381691 | ||||||||
\(926\) | 75.6980 | 2.48759 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.94346 | 0.0966238 | ||||||||
\(929\) | 39.6211 | 1.29993 | 0.649963 | − | 0.759966i | \(-0.274784\pi\) | ||||
0.649963 | + | 0.759966i | \(0.274784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3326 | 0.338637 | ||||||||
\(932\) | −51.8863 | −1.69959 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −83.1174 | −2.71968 | ||||||||
\(935\) | 2.56557 | 0.0839031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.4465 | −1.22332 | −0.611662 | − | 0.791119i | \(-0.709499\pi\) | ||||
−0.611662 | + | 0.791119i | \(0.709499\pi\) | |||||||
\(938\) | −144.334 | −4.71267 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −64.7798 | −2.11288 | ||||||||
\(941\) | 15.4626 | 0.504068 | 0.252034 | − | 0.967718i | \(-0.418901\pi\) | ||||
0.252034 | + | 0.967718i | \(0.418901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.02619 | −0.261369 | ||||||||
\(944\) | 2.38582 | 0.0776517 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −94.5159 | −3.07298 | ||||||||
\(947\) | 32.7987 | 1.06581 | 0.532907 | − | 0.846174i | \(-0.321100\pi\) | ||||
0.532907 | + | 0.846174i | \(0.321100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7760 | 0.641955 | ||||||||
\(950\) | −0.987516 | −0.0320392 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.47957 | 0.177594 | ||||||||
\(953\) | 16.0845 | 0.521027 | 0.260513 | − | 0.965470i | \(-0.416108\pi\) | ||||
0.260513 | + | 0.965470i | \(0.416108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.21947 | 0.0394611 | ||||||||
\(956\) | −57.7386 | −1.86740 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.0150 | 0.323570 | ||||||||
\(959\) | 48.6364 | 1.57055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9134 | −0.416560 | ||||||||
\(962\) | −6.80589 | −0.219431 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 97.9215 | 3.15384 | ||||||||
\(965\) | 50.1904 | 1.61569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.9701 | 0.802986 | 0.401493 | − | 0.915862i | \(-0.368491\pi\) | ||||
0.401493 | + | 0.915862i | \(0.368491\pi\) | |||||||
\(968\) | 39.3648 | 1.26523 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −64.8385 | −2.08184 | ||||||||
\(971\) | −1.43669 | −0.0461056 | −0.0230528 | − | 0.999734i | \(-0.507339\pi\) | ||||
−0.0230528 | + | 0.999734i | \(0.507339\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.4530 | −1.07245 | ||||||||
\(974\) | −26.5415 | −0.850445 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.4556 | −0.494723 | ||||||||
\(977\) | −45.3505 | −1.45089 | −0.725446 | − | 0.688279i | \(-0.758366\pi\) | ||||
−0.725446 | + | 0.688279i | \(0.758366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.9397 | −1.37236 | ||||||||
\(980\) | 142.587 | 4.55476 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.710729 | −0.0226803 | ||||||||
\(983\) | 60.0472 | 1.91521 | 0.957604 | − | 0.288086i | \(-0.0930190\pi\) | ||||
0.957604 | + | 0.288086i | \(0.0930190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.6274 | 1.19891 | ||||||||
\(986\) | −0.647660 | −0.0206257 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.74459 | −0.119131 | ||||||||
\(989\) | 8.67751 | 0.275929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5981 | 0.368425 | 0.184212 | − | 0.982886i | \(-0.441027\pi\) | ||||
0.184212 | + | 0.982886i | \(0.441027\pi\) | |||||||
\(992\) | 12.5181 | 0.397449 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 75.1204 | 2.38268 | ||||||||
\(995\) | 15.9395 | 0.505315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6532 | 0.717433 | 0.358717 | − | 0.933446i | \(-0.383214\pi\) | ||||
0.358717 | + | 0.933446i | \(0.383214\pi\) | |||||||
\(998\) | −46.7853 | −1.48096 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.l.1.9 | 10 | ||
3.2 | odd | 2 | 667.2.a.a.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.a.1.2 | ✓ | 10 | 3.2 | odd | 2 | ||
6003.2.a.l.1.9 | 10 | 1.1 | even | 1 | trivial |