Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 15 x^{10} + 100 x^{9} + 36 x^{8} - 641 x^{7} + 129 x^{6} + 1804 x^{5} - 433 x^{4} - 2399 x^{3} + 148 x^{2} + 1224 x + 224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.94180\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.94180 | 1.12110 | 0.560549 | − | 0.828122i | \(-0.310590\pi\) | ||||
0.560549 | + | 0.828122i | \(0.310590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.68233 | −1.64679 | −0.823395 | − | 0.567469i | \(-0.807923\pi\) | ||||
−0.823395 | + | 0.567469i | \(0.807923\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51484 | −0.950519 | −0.475260 | − | 0.879846i | \(-0.657646\pi\) | ||||
−0.475260 | + | 0.879846i | \(0.657646\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.770577 | 0.256859 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.53131 | 0.763218 | 0.381609 | − | 0.924324i | \(-0.375370\pi\) | ||||
0.381609 | + | 0.924324i | \(0.375370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.40241 | 0.388959 | 0.194480 | − | 0.980907i | \(-0.437698\pi\) | ||||
0.194480 | + | 0.980907i | \(0.437698\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.15035 | −1.84621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.24242 | 1.51401 | 0.757005 | − | 0.653409i | \(-0.226662\pi\) | ||||
0.757005 | + | 0.653409i | \(0.226662\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.03220 | 1.38388 | 0.691940 | − | 0.721955i | \(-0.256756\pi\) | ||||
0.691940 | + | 0.721955i | \(0.256756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.88330 | −1.06562 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.990062 | −0.206442 | −0.103221 | − | 0.994658i | \(-0.532915\pi\) | ||||
−0.103221 | + | 0.994658i | \(0.532915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.55959 | 1.71192 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.32909 | −0.833133 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.81567 | 0.522857 | 0.261428 | − | 0.965223i | \(-0.415806\pi\) | ||||
0.261428 | + | 0.965223i | \(0.415806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.19863 | 1.47252 | 0.736259 | − | 0.676700i | \(-0.236591\pi\) | ||||
0.736259 | + | 0.676700i | \(0.236591\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.91529 | 0.855642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.26047 | 1.56531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.90678 | −0.971069 | −0.485534 | − | 0.874218i | \(-0.661375\pi\) | ||||
−0.485534 | + | 0.874218i | \(0.661375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.72320 | 0.436061 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.9031 | 1.85896 | 0.929479 | − | 0.368876i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368876i | \(0.120257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.71591 | −1.17666 | −0.588332 | − | 0.808619i | \(-0.700215\pi\) | ||||
−0.588332 | + | 0.808619i | \(0.700215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.83752 | −0.422993 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.4013 | −1.66305 | −0.831525 | − | 0.555487i | \(-0.812532\pi\) | ||||
−0.831525 | + | 0.555487i | \(0.812532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.675594 | −0.0965134 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.1215 | 1.69735 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3529 | 1.83416 | 0.917078 | − | 0.398707i | \(-0.130541\pi\) | ||||
0.917078 | + | 0.398707i | \(0.130541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.32112 | −1.25686 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.7133 | 1.55146 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.7570 | 1.66082 | 0.830409 | − | 0.557155i | \(-0.188107\pi\) | ||||
0.830409 | + | 0.557155i | \(0.188107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0171 | 1.28256 | 0.641281 | − | 0.767306i | \(-0.278403\pi\) | ||||
0.641281 | + | 0.767306i | \(0.278403\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.93788 | −0.244149 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.16415 | −0.640534 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.22542 | 0.638387 | 0.319194 | − | 0.947690i | \(-0.396588\pi\) | ||||
0.319194 | + | 0.947690i | \(0.396588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.92250 | −0.231442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5563 | 1.60883 | 0.804417 | − | 0.594066i | \(-0.202478\pi\) | ||||
0.804417 | + | 0.594066i | \(0.202478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.1689 | −1.77538 | −0.887691 | − | 0.460439i | \(-0.847692\pi\) | ||||
−0.887691 | + | 0.460439i | \(0.847692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.6210 | 1.91923 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.36583 | −0.725453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.02509 | 0.902893 | 0.451447 | − | 0.892298i | \(-0.350908\pi\) | ||||
0.451447 | + | 0.892298i | \(0.350908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7179 | −1.19088 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.79046 | −0.964879 | −0.482439 | − | 0.875929i | \(-0.660249\pi\) | ||||
−0.482439 | + | 0.875929i | \(0.660249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.9867 | −2.49326 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.46746 | 0.586173 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.44999 | −0.895697 | −0.447849 | − | 0.894109i | \(-0.647810\pi\) | ||||
−0.447849 | + | 0.894109i | \(0.647810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.52684 | −0.369713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.9201 | 1.65083 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22.2126 | −2.27896 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.29010 | 0.334059 | 0.167029 | − | 0.985952i | \(-0.446583\pi\) | ||||
0.167029 | + | 0.985952i | \(0.446583\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95057 | 0.196039 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.48311 | −0.247078 | −0.123539 | − | 0.992340i | \(-0.539424\pi\) | ||||
−0.123539 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.24951 | 0.812848 | 0.406424 | − | 0.913684i | \(-0.366776\pi\) | ||||
0.406424 | + | 0.913684i | \(0.366776\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.9820 | 1.75486 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.81289 | −0.175259 | −0.0876295 | − | 0.996153i | \(-0.527929\pi\) | ||||
−0.0876295 | + | 0.996153i | \(0.527929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5606 | −1.10730 | −0.553652 | − | 0.832748i | \(-0.686766\pi\) | ||||
−0.553652 | + | 0.832748i | \(0.686766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4698 | −1.08866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.22979 | −0.586049 | −0.293025 | − | 0.956105i | \(-0.594662\pi\) | ||||
−0.293025 | + | 0.956105i | \(0.594662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.64574 | 0.339967 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.08067 | 0.0999077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.6987 | −1.43910 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.59248 | −0.417498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.1135 | 2.08407 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.1076 | −1.17238 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.82117 | 0.516545 | 0.258273 | − | 0.966072i | \(-0.416847\pi\) | ||||
0.258273 | + | 0.966072i | \(0.416847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.9827 | −1.31916 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5722 | 1.01107 | 0.505534 | − | 0.862806i | \(-0.331295\pi\) | ||||
0.505534 | + | 0.862806i | \(0.331295\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1700 | −1.31540 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.9411 | 1.37200 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.12029 | 0.693763 | 0.346882 | − | 0.937909i | \(-0.387241\pi\) | ||||
0.346882 | + | 0.937909i | \(0.387241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.0550 | −1.61623 | −0.808113 | − | 0.589027i | \(-0.799511\pi\) | ||||
−0.808113 | + | 0.589027i | \(0.799511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.1390 | −1.86444 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.54994 | 0.296861 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3682 | −0.861035 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.31187 | −0.108201 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1870 | −0.998396 | −0.499198 | − | 0.866488i | \(-0.666372\pi\) | ||||
−0.499198 | + | 0.866488i | \(0.666372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.39930 | 0.276631 | 0.138315 | − | 0.990388i | \(-0.455831\pi\) | ||||
0.138315 | + | 0.990388i | \(0.455831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.81027 | 0.388887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.1901 | −2.42493 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.74134 | −0.218783 | −0.109391 | − | 0.993999i | \(-0.534890\pi\) | ||||
−0.109391 | + | 0.993999i | \(0.534890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.9286 | 2.05627 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.48985 | 0.196227 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.654254 | 0.0512451 | 0.0256225 | − | 0.999672i | \(-0.491843\pi\) | ||||
0.0256225 | + | 0.999672i | \(0.491843\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.0997 | −1.40906 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0332 | −0.848711 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.64827 | 0.355462 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.27460 | 0.629106 | 0.314553 | − | 0.949240i | \(-0.398145\pi\) | ||||
0.314553 | + | 0.949240i | \(0.398145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5260 | −1.62721 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.7715 | 1.86194 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7422 | 0.802913 | 0.401457 | − | 0.915878i | \(-0.368504\pi\) | ||||
0.401457 | + | 0.915878i | \(0.368504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.32871 | 0.470409 | 0.235205 | − | 0.971946i | \(-0.424424\pi\) | ||||
0.235205 | + | 0.971946i | \(0.424424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.4512 | 1.43788 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.7507 | 1.59915 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8015 | 1.15552 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.8870 | 0.791909 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.08743 | 0.657543 | 0.328772 | − | 0.944409i | \(-0.393365\pi\) | ||||
0.328772 | + | 0.944409i | \(0.393365\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7682 | −0.847093 | −0.423547 | − | 0.905874i | \(-0.639215\pi\) | ||||
−0.423547 | + | 0.905874i | \(0.639215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.0277 | −0.718101 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.53903 | −0.252145 | −0.126073 | − | 0.992021i | \(-0.540237\pi\) | ||||
−0.126073 | + | 0.992021i | \(0.540237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3303 | 1.79562 | 0.897808 | − | 0.440386i | \(-0.145159\pi\) | ||||
0.897808 | + | 0.440386i | \(0.145159\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.1467 | 0.715694 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.08095 | −0.496985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −43.8313 | −3.06131 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.762919 | −0.0530266 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.2693 | 1.05620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.18822 | −0.632543 | −0.316272 | − | 0.948669i | \(-0.602431\pi\) | ||||
−0.316272 | + | 0.948669i | \(0.602431\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.3235 | 1.80366 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.4125 | 1.93772 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.6182 | −1.39966 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.4549 | −1.99038 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.75445 | 0.588888 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.936602 | −0.0627195 | −0.0313598 | − | 0.999508i | \(-0.509984\pi\) | ||||
−0.0313598 | + | 0.999508i | \(0.509984\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.59582 | 0.439722 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.57719 | −0.436544 | −0.218272 | − | 0.975888i | \(-0.570042\pi\) | ||||
−0.218272 | + | 0.975888i | \(0.570042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.15337 | −0.406626 | −0.203313 | − | 0.979114i | \(-0.565171\pi\) | ||||
−0.203313 | + | 0.979114i | \(0.565171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.3611 | −0.813304 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.88639 | 0.189094 | 0.0945469 | − | 0.995520i | \(-0.469860\pi\) | ||||
0.0945469 | + | 0.995520i | \(0.469860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.9834 | 2.73870 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5831 | 1.01223 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7704 | 0.826049 | 0.413025 | − | 0.910720i | \(-0.364472\pi\) | ||||
0.413025 | + | 0.910720i | \(0.364472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8333 | 0.697832 | 0.348916 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348916 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.82481 | −0.501962 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.48776 | 0.158937 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.45963 | 0.538273 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.0693 | −1.08172 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.22678 | 0.266792 | 0.133396 | − | 0.991063i | \(-0.457412\pi\) | ||||
0.133396 | + | 0.991063i | \(0.457412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.50615 | −0.157560 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −44.6355 | −2.79518 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.7786 | 1.85754 | 0.928768 | − | 0.370662i | \(-0.120869\pi\) | ||||
0.928768 | + | 0.370662i | \(0.120869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.8546 | 0.923019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.16969 | 0.134300 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.393566 | 0.0242683 | 0.0121342 | − | 0.999926i | \(-0.496137\pi\) | ||||
0.0121342 | + | 0.999926i | \(0.496137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −49.1697 | −3.02047 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.4082 | −1.00416 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.97029 | −0.303044 | −0.151522 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151522 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.6033 | −1.37306 | −0.686528 | − | 0.727104i | \(-0.740866\pi\) | ||||
−0.686528 | + | 0.727104i | \(0.740866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.84841 | −0.414485 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.6670 | 1.30657 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.3056 | −1.15996 | −0.579981 | − | 0.814630i | \(-0.696940\pi\) | ||||
−0.579981 | + | 0.814630i | \(0.696940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.31768 | 0.378229 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.7704 | 1.77595 | 0.887977 | − | 0.459888i | \(-0.152111\pi\) | ||||
0.887977 | + | 0.459888i | \(0.152111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.5284 | 1.93361 | 0.966807 | − | 0.255507i | \(-0.0822425\pi\) | ||||
0.966807 | + | 0.255507i | \(0.0822425\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −43.1323 | −2.55494 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.9344 | −1.76697 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.9678 | 1.29223 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.38870 | 0.374512 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.8005 | −0.864657 | −0.432328 | − | 0.901716i | \(-0.642308\pi\) | ||||
−0.432328 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.9755 | −2.73502 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.9583 | −0.635862 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.38848 | −0.0802976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.4042 | 1.11844 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.82169 | −0.276999 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.8864 | −2.11211 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7387 | −0.955330 | −0.477665 | − | 0.878542i | \(-0.658517\pi\) | ||||
−0.477665 | + | 0.878542i | \(0.658517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0189 | 0.911282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.8231 | 0.953951 | 0.476975 | − | 0.878917i | \(-0.341733\pi\) | ||||
0.476975 | + | 0.878917i | \(0.341733\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.0431 | −1.41552 | −0.707759 | − | 0.706454i | \(-0.750294\pi\) | ||||
−0.707759 | + | 0.706454i | \(0.750294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.13591 | 0.402063 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.3304 | −1.02954 | −0.514768 | − | 0.857330i | \(-0.672122\pi\) | ||||
−0.514768 | + | 0.857330i | \(0.672122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.12733 | 0.399054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.52027 | −0.196482 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.6555 | 2.09521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0041 | 0.665866 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.4483 | −1.24140 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.6724 | 1.58076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.09542 | −0.335035 | −0.167517 | − | 0.985869i | \(-0.553575\pi\) | ||||
−0.167517 | + | 0.985869i | \(0.553575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.55163 | −0.249428 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.2418 | −1.05129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8720 | 0.973550 | 0.486775 | − | 0.873527i | \(-0.338173\pi\) | ||||
0.486775 | + | 0.873527i | \(0.338173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0970 | −0.657018 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7533 | 1.12385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3029 | 1.04226 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.07929 | 0.381136 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.7608 | −0.792401 | −0.396201 | − | 0.918164i | \(-0.629671\pi\) | ||||
−0.396201 | + | 0.918164i | \(0.629671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.8320 | −1.06158 | −0.530792 | − | 0.847502i | \(-0.678106\pi\) | ||||
−0.530792 | + | 0.847502i | \(0.678106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.07117 | −0.324055 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8103 | 0.841498 | 0.420749 | − | 0.907177i | \(-0.361767\pi\) | ||||
0.420749 | + | 0.907177i | \(0.361767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −49.9187 | −2.64941 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.4836 | −1.61337 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.298461 | −0.0157522 | −0.00787608 | − | 0.999969i | \(-0.502507\pi\) | ||||
−0.00787608 | + | 0.999969i | \(0.502507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3874 | 0.915125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.91767 | −0.468056 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 55.8569 | 2.92368 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.71709 | −0.298430 | −0.149215 | − | 0.988805i | \(-0.547675\pi\) | ||||
−0.149215 | + | 0.988805i | \(0.547675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.17228 | 0.477490 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.5803 | −1.74340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.6296 | 1.48238 | 0.741192 | − | 0.671293i | \(-0.234261\pi\) | ||||
0.741192 | + | 0.671293i | \(0.234261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.4523 | −1.31435 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.94873 | 0.203370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5972 | −1.10937 | −0.554686 | − | 0.832060i | \(-0.687162\pi\) | ||||
−0.554686 | + | 0.832060i | \(0.687162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3035 | 0.579098 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00419 | 0.408995 | 0.204497 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204497 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.4411 | 1.19467 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.94570 | −0.302237 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.5102 | −0.786401 | −0.393200 | − | 0.919453i | \(-0.628632\pi\) | ||||
−0.393200 | + | 0.919453i | \(0.628632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.18039 | −0.312556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.4709 | 1.13351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.5511 | −1.48688 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.55297 | −0.429261 | −0.214631 | − | 0.976695i | \(-0.568855\pi\) | ||||
−0.214631 | + | 0.976695i | \(0.568855\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.4570 | −1.47470 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8505 | −1.29091 | −0.645457 | − | 0.763796i | \(-0.723333\pi\) | ||||
−0.645457 | + | 0.763796i | \(0.723333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4979 | 0.572749 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 39.4671 | 1.96113 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.9519 | −0.741137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7146 | −0.579252 | −0.289626 | − | 0.957140i | \(-0.593531\pi\) | ||||
−0.289626 | + | 0.957140i | \(0.593531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.7680 | 0.777776 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.0817 | −1.57864 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.3694 | 1.58895 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.0010 | −1.81195 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.43634 | 0.119023 | 0.0595116 | − | 0.998228i | \(-0.481046\pi\) | ||||
0.0595116 | + | 0.998228i | \(0.481046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3748 | −1.28543 | −0.642714 | − | 0.766106i | \(-0.722192\pi\) | ||||
−0.642714 | + | 0.766106i | \(0.722192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.78558 | −0.427170 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 53.4326 | 2.59186 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.1915 | −1.21910 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.89326 | 0.332810 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3288 | −0.642024 | −0.321012 | − | 0.947075i | \(-0.604023\pi\) | ||||
−0.321012 | + | 0.947075i | \(0.604023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2184 | 1.16386 | 0.581930 | − | 0.813239i | \(-0.302298\pi\) | ||||
0.581930 | + | 0.813239i | \(0.302298\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.1330 | −0.965304 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.97225 | −0.285691 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.2041 | −1.63247 | −0.816237 | − | 0.577717i | \(-0.803944\pi\) | ||||
−0.816237 | + | 0.577717i | \(0.803944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.520597 | −0.0247903 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.02481 | −0.286248 | −0.143124 | − | 0.989705i | \(-0.545715\pi\) | ||||
−0.143124 | + | 0.989705i | \(0.545715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.1157 | 1.47503 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.6646 | −1.11930 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4523 | −1.62590 | −0.812952 | − | 0.582330i | \(-0.802141\pi\) | ||||
−0.812952 | + | 0.582330i | \(0.802141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.1305 | 1.41879 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.60075 | 0.310130 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.9870 | 0.608840 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1048 | −0.613017 | −0.306509 | − | 0.951868i | \(-0.599161\pi\) | ||||
−0.306509 | + | 0.951868i | \(0.599161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0240 | −1.26137 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4582 | −1.37201 | −0.686003 | − | 0.727599i | \(-0.740636\pi\) | ||||
−0.686003 | + | 0.727599i | \(0.740636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.5619 | 1.28091 | 0.640456 | − | 0.767995i | \(-0.278745\pi\) | ||||
0.640456 | + | 0.767995i | \(0.278745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −58.6230 | −2.71858 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.81919 | −0.315555 | −0.157777 | − | 0.987475i | \(-0.550433\pi\) | ||||
−0.157777 | + | 0.987475i | \(0.550433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1411 | −0.606799 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.32312 | −0.245276 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.5313 | −0.898052 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 51.6331 | 2.36909 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.2894 | 0.471120 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3817 | 0.657118 | 0.328559 | − | 0.944483i | \(-0.393437\pi\) | ||||
0.328559 | + | 0.944483i | \(0.393437\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.28375 | −0.377706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.83478 | 0.219990 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.1152 | −0.550125 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7508 | 0.804367 | 0.402184 | − | 0.915559i | \(-0.368251\pi\) | ||||
0.402184 | + | 0.915559i | \(0.368251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.27043 | 0.0574507 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.7017 | 1.11477 | 0.557387 | − | 0.830253i | \(-0.311804\pi\) | ||||
0.557387 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.5766 | 0.791610 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.18264 | −0.322836 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.0918 | −1.52923 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4029 | 0.555230 | 0.277615 | − | 0.960692i | \(-0.410456\pi\) | ||||
0.277615 | + | 0.960692i | \(0.410456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.94180 | 0.0867531 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.58294 | 0.159755 | 0.0798777 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798777 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.14363 | 0.406886 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.4243 | −0.951487 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8392 | 0.702062 | 0.351031 | − | 0.936364i | \(-0.385831\pi\) | ||||
0.351031 | + | 0.936364i | \(0.385831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.1472 | 1.68753 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.1139 | −1.15296 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.3775 | −1.33859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.8602 | −1.26927 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0676 | 0.705289 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.4884 | 1.55478 | 0.777388 | − | 0.629021i | \(-0.216544\pi\) | ||||
0.777388 | + | 0.629021i | \(0.216544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6911 | −1.03594 | −0.517970 | − | 0.855399i | \(-0.673312\pi\) | ||||
−0.517970 | + | 0.855399i | \(0.673312\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −41.7991 | −1.82426 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.1793 | 2.22941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0198 | −0.957382 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.83024 | 0.426596 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.6931 | 0.723059 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.67568 | 0.288615 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.8593 | 0.900144 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.71014 | −0.0736607 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1705 | 1.16815 | 0.584076 | − | 0.811699i | \(-0.301457\pi\) | ||||
0.584076 | + | 0.811699i | \(0.301457\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.2891 | 0.527375 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.5700 | 1.82350 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1554 | −0.690756 | −0.345378 | − | 0.938464i | \(-0.612249\pi\) | ||||
−0.345378 | + | 0.938464i | \(0.612249\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.71897 | 0.329438 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9847 | 0.723571 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.1818 | −0.858217 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.2355 | 1.79280 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.22505 | 0.263764 | 0.131882 | − | 0.991265i | \(-0.457898\pi\) | ||||
0.131882 | + | 0.991265i | \(0.457898\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.8209 | −0.457675 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.6833 | 1.29545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.13126 | 0.342692 | 0.171346 | − | 0.985211i | \(-0.445188\pi\) | ||||
0.171346 | + | 0.985211i | \(0.445188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.9402 | 0.965100 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9539 | 1.13196 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.2871 | 1.89854 | 0.949268 | − | 0.314469i | \(-0.101826\pi\) | ||||
0.949268 | + | 0.314469i | \(0.101826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.7671 | 0.743528 | 0.371764 | − | 0.928327i | \(-0.378753\pi\) | ||||
0.371764 | + | 0.928327i | \(0.378753\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.6460 | 0.737170 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.47453 | −0.353412 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.3505 | 1.05535 | 0.527677 | − | 0.849445i | \(-0.323063\pi\) | ||||
0.527677 | + | 0.849445i | \(0.323063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.8515 | −0.949674 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.1066 | 0.917136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8002 | 1.39986 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.97938 | −0.164527 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.23794 | −0.257467 | −0.128734 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128734 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.4557 | 2.03779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.87207 | −0.282679 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.77480 | 0.360338 | 0.180169 | − | 0.983636i | \(-0.442336\pi\) | ||||
0.180169 | + | 0.983636i | \(0.442336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57.8078 | 2.36989 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 49.1863 | 2.01306 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.6324 | 1.37418 | 0.687092 | − | 0.726570i | \(-0.258887\pi\) | ||||
0.687092 | + | 0.726570i | \(0.258887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0193 | −0.490278 | −0.245139 | − | 0.969488i | \(-0.578834\pi\) | ||||
−0.245139 | + | 0.969488i | \(0.578834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.02659 | 0.163975 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.9111 | 0.687532 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2311 | −0.455855 | −0.227928 | − | 0.973678i | \(-0.573195\pi\) | ||||
−0.227928 | + | 0.973678i | \(0.573195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.7498 | −0.557169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.9893 | −0.646859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.5509 | −1.67823 | −0.839113 | − | 0.543957i | \(-0.816925\pi\) | ||||
−0.839113 | + | 0.543957i | \(0.816925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −85.1116 | −3.43203 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.87722 | −0.276866 | −0.138433 | − | 0.990372i | \(-0.544207\pi\) | ||||
−0.138433 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.08552 | −0.244598 | −0.122299 | − | 0.992493i | \(-0.539027\pi\) | ||||
−0.122299 | + | 0.992493i | \(0.539027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.28607 | 0.171994 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.2503 | 0.851377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.46862 | 0.218745 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.6500 | 1.18411 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.8726 | −1.47021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.91686 | −0.275356 | −0.137678 | − | 0.990477i | \(-0.543964\pi\) | ||||
−0.137678 | + | 0.990477i | \(0.543964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.8417 | −0.709143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.4355 | −0.850642 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.947461 | −0.0375398 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.4462 | 0.413243 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.1119 | −1.38684 | −0.693419 | − | 0.720534i | \(-0.743897\pi\) | ||||
−0.693419 | + | 0.720534i | \(0.743897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.58940 | −0.220425 | −0.110212 | − | 0.993908i | \(-0.535153\pi\) | ||||
−0.110212 | + | 0.993908i | \(0.535153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 55.1714 | 2.17237 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.7389 | −1.01190 | −0.505949 | − | 0.862563i | \(-0.668858\pi\) | ||||
−0.505949 | + | 0.862563i | \(0.668858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.2918 | 1.26757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.0364 | −1.56915 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.21923 | −0.165111 | −0.0825557 | − | 0.996586i | \(-0.526308\pi\) | ||||
−0.0825557 | + | 0.996586i | \(0.526308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.6128 | −1.66502 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.6888 | −0.456023 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.00339238 | 0.000132148 0 | 6.60741e−5 | − | 1.00000i | \(-0.499979\pi\) | ||||
6.60741e−5 | 1.00000i | \(0.499979\pi\) | ||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.251775 | 0.00979290 | 0.00489645 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489645 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.9994 | 0.660201 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.8610 | 2.16620 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.78769 | −0.107940 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.81869 | −0.0703147 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.3564 | 0.978874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.29797 | −0.127127 | −0.0635637 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635637 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −37.0552 | −1.42626 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.5673 | −1.17480 | −0.587398 | − | 0.809298i | \(-0.699848\pi\) | ||||
−0.587398 | + | 0.809298i | \(0.699848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.27406 | −0.317529 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.7716 | −0.489408 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.05889 | −0.155309 | −0.0776546 | − | 0.996980i | \(-0.524743\pi\) | ||||
−0.0776546 | + | 0.996980i | \(0.524743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.9016 | −1.14248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.9486 | −0.455867 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.7262 | 0.713412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1912 | −1.22461 | −0.612305 | − | 0.790622i | \(-0.709758\pi\) | ||||
−0.612305 | + | 0.790622i | \(0.709758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.90536 | −0.186339 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 70.1670 | 2.66159 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 74.3044 | 2.81448 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.60479 | 0.211993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4257 | 0.771469 | 0.385735 | − | 0.922610i | \(-0.373948\pi\) | ||||
0.385735 | + | 0.922610i | \(0.373948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.6309 | −1.34384 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 81.5233 | 3.07034 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.24461 | 0.234853 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.7428 | −1.15457 | −0.577285 | − | 0.816542i | \(-0.695888\pi\) | ||||
−0.577285 | + | 0.816542i | \(0.695888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.18395 | 0.231916 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.11715 | −0.303990 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0721 | −0.488867 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.7976 | 0.926082 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.99493 | 0.260867 | 0.130433 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130433 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.7462 | −0.772628 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.0360 | 0.782338 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.1010 | 0.895088 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.8854 | 0.811685 | 0.405842 | − | 0.913943i | \(-0.366978\pi\) | ||||
0.405842 | + | 0.913943i | \(0.366978\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.9596 | 0.628134 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.1659 | −1.78148 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.1139 | 1.00147 | 0.500737 | − | 0.865599i | \(-0.333062\pi\) | ||||
0.500737 | + | 0.865599i | \(0.333062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.83073 | 0.178184 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2272 | 0.487228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.59944 | 0.279550 | 0.139775 | − | 0.990183i | \(-0.455362\pi\) | ||||
0.139775 | + | 0.990183i | \(0.455362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4269 | 0.603457 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.3660 | 1.92112 | 0.960562 | − | 0.278066i | \(-0.0896935\pi\) | ||||
0.960562 | + | 0.278066i | \(0.0896935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.8765 | 1.64415 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.77373 | −0.247838 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.55913 | 0.166587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8593 | −0.505734 | −0.252867 | − | 0.967501i | \(-0.581374\pi\) | ||||
−0.252867 | + | 0.967501i | \(0.581374\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.20754 | 0.299100 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.5174 | −0.455553 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.489528 | −0.0177922 | −0.00889610 | − | 0.999960i | \(-0.502832\pi\) | ||||
−0.00889610 | + | 0.999960i | \(0.502832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.86644 | −0.176641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.0553 | −0.582005 | −0.291002 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291002 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.0730 | 1.05251 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.7130 | −0.640415 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.8906 | 0.645990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9309 | −0.430239 | −0.215120 | − | 0.976588i | \(-0.569014\pi\) | ||||
−0.215120 | + | 0.976588i | \(0.569014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.8239 | 2.08248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.5255 | −1.60147 | −0.800736 | − | 0.599017i | \(-0.795558\pi\) | ||||
−0.800736 | + | 0.599017i | \(0.795558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 70.1769 | 2.52083 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.8446 | 1.03479 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 71.8020 | 2.57257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.3151 | 1.22789 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.1893 | −0.435609 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0945 | 0.360289 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.8006 | −0.884045 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.764225 | 0.0272071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.6669 | 0.557051 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.0482 | 0.498865 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −95.4776 | −3.38624 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.5955 | −1.86303 | −0.931515 | − | 0.363704i | \(-0.881512\pi\) | ||||
−0.931515 | + | 0.363704i | \(0.881512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −71.1717 | −2.51787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.51137 | −0.230068 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.3971 | −1.35500 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.16844 | −0.323145 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.65130 | −0.339742 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8948 | 0.734621 | 0.367310 | − | 0.930098i | \(-0.380279\pi\) | ||||
0.367310 | + | 0.930098i | \(0.380279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0344 | −0.808846 | −0.404423 | − | 0.914572i | \(-0.632528\pi\) | ||||
−0.404423 | + | 0.914572i | \(0.632528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.8911 | −1.53933 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.40918 | −0.0843899 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.5438 | −1.62836 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.71770 | −0.0949642 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.0016 | −0.488658 | −0.244329 | − | 0.969692i | \(-0.578568\pi\) | ||||
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.5218 | 0.750202 | 0.375101 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375101 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.0728 | 1.46479 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0650 | 1.60184 | 0.800918 | − | 0.598774i | \(-0.204345\pi\) | ||||
0.800918 | + | 0.598774i | \(0.204345\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.4817 | −0.989210 | −0.494605 | − | 0.869118i | \(-0.664687\pi\) | ||||
−0.494605 | + | 0.869118i | \(0.664687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.4876 | −1.30043 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.21734 | −0.146122 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.68233 | −0.127432 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.4926 | −1.22680 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.5227 | −1.01924 | −0.509619 | − | 0.860400i | \(-0.670213\pi\) | ||||
−0.509619 | + | 0.860400i | \(0.670213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0720 | −0.726621 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57.8081 | 1.99102 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.6281 | 1.39765 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5493 | 0.396840 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 63.1636 | 2.16777 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.84808 | 0.200470 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.35509 | 0.183355 | 0.0916773 | − | 0.995789i | \(-0.470777\pi\) | ||||
0.0916773 | + | 0.995789i | \(0.470777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.1165 | −0.585372 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.2566 | −0.452835 | −0.226418 | − | 0.974030i | \(-0.572701\pi\) | ||||
−0.226418 | + | 0.974030i | \(0.572701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.80254 | 0.0956215 | 0.0478107 | − | 0.998856i | \(-0.484776\pi\) | ||||
0.0478107 | + | 0.998856i | \(0.484776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −58.1266 | −1.98095 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.3178 | −1.13415 | −0.567075 | − | 0.823666i | \(-0.691925\pi\) | ||||
−0.567075 | + | 0.823666i | \(0.691925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.4699 | −1.03601 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.6571 | 1.44871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.3140 | 0.689104 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.32820 | 0.248307 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.53527 | 0.0858060 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.9635 | 1.11437 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.6528 | 1.77796 | 0.888979 | − | 0.457947i | \(-0.151415\pi\) | ||||
0.888979 | + | 0.457947i | \(0.151415\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.7396 | −0.969364 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.06476 | −0.170636 | −0.0853181 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853181 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.48451 | 0.0836105 | 0.0418052 | − | 0.999126i | \(-0.486689\pi\) | ||||
0.0418052 | + | 0.999126i | \(0.486689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −91.2168 | −3.06622 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.7059 | 0.728811 | 0.364406 | − | 0.931240i | \(-0.381272\pi\) | ||||
0.364406 | + | 0.931240i | \(0.381272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6393 | −0.490986 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.1304 | −0.908903 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −68.7749 | −2.30146 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.5566 | −1.32223 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.69614 | −0.0900215 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.0846 | 0.769915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.3542 | 2.77693 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.6791 | 1.25388 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3044 | −0.774666 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.87267 | 0.228203 | 0.114102 | − | 0.993469i | \(-0.463601\pi\) | ||||
0.114102 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.91342 | −0.0634643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4501 | 1.24078 | 0.620389 | − | 0.784294i | \(-0.286975\pi\) | ||||
0.620389 | + | 0.784294i | \(0.286975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.2514 | −0.736413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −71.6260 | −2.36788 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.1022 | −0.961040 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.1748 | 0.929402 | 0.464701 | − | 0.885468i | \(-0.346162\pi\) | ||||
0.464701 | + | 0.885468i | \(0.346162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.5032 | −1.07102 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.0115 | 0.625771 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.5596 | −1.66239 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.35688 | 0.208787 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4167 | −0.833896 | −0.416948 | − | 0.908930i | \(-0.636900\pi\) | ||||
−0.416948 | + | 0.908930i | \(0.636900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.07531 | −0.133563 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.6671 | 1.06947 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −58.1864 | −1.90290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3436 | −0.501254 | −0.250627 | − | 0.968084i | \(-0.580637\pi\) | ||||
−0.250627 | + | 0.968084i | \(0.580637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.6286 | −1.58693 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.7781 | −0.970739 | −0.485369 | − | 0.874309i | \(-0.661315\pi\) | ||||
−0.485369 | + | 0.874309i | \(0.661315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.7848 | −0.383767 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −40.0894 | −1.30411 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.4473 | 0.826926 | 0.413463 | − | 0.910521i | \(-0.364319\pi\) | ||||
0.413463 | + | 0.910521i | \(0.364319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.2730 | −0.690552 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.5938 | −1.15421 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.0702 | 1.23322 | 0.616608 | − | 0.787271i | \(-0.288506\pi\) | ||||
0.616608 | + | 0.787271i | \(0.288506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.4630 | −1.08284 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.8398 | 0.447378 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.4212 | −0.659435 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.2175 | 1.16831 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.39697 | −0.0450168 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.3344 | 1.39499 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.0135 | −0.933010 | −0.466505 | − | 0.884519i | \(-0.654487\pi\) | ||||
−0.466505 | + | 0.884519i | \(0.654487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 73.1194 | 2.34893 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.12130 | −0.260625 | −0.130312 | − | 0.991473i | \(-0.541598\pi\) | ||||
−0.130312 | + | 0.991473i | \(0.541598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.9203 | 1.53625 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.3095 | 0.746501 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.9592 | −0.638551 | −0.319275 | − | 0.947662i | \(-0.603440\pi\) | ||||
−0.319275 | + | 0.947662i | \(0.603440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.3895 | −0.683612 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.90834 | −0.284421 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.7024 | −1.64905 | −0.824525 | − | 0.565826i | \(-0.808557\pi\) | ||||
−0.824525 | + | 0.565826i | \(0.808557\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0319 | 0.415230 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 55.6760 | 1.77219 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.63923 | 0.242913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.944892 | 0.0300155 | 0.0150077 | − | 0.999887i | \(-0.495223\pi\) | ||||
0.0150077 | + | 0.999887i | \(0.495223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.8361 | −0.375607 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −93.2746 | −2.95700 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.18542 | 0.0375428 | 0.0187714 | − | 0.999824i | \(-0.494025\pi\) | ||||
0.0187714 | + | 0.999824i | \(0.494025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.5710 | 0.809030 |
(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 | 1336.2.a.e.1.9 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.n.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.e.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.n.1.4 | 12 | 4.3 | odd | 2 |