Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.87939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.41147 | −1.52566 | −0.762829 | − | 0.646601i | \(-0.776190\pi\) | ||||
−0.762829 | + | 0.646601i | \(0.776190\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.87939 | −1.08831 | −0.544153 | − | 0.838986i | \(-0.683149\pi\) | ||||
−0.544153 | + | 0.838986i | \(0.683149\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.41147 | −1.07880 | ||||||||
\(11\) | −0.347296 | −0.104714 | −0.0523569 | − | 0.998628i | \(-0.516673\pi\) | ||||
−0.0523569 | + | 0.998628i | \(0.516673\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.65270 | 0.458378 | 0.229189 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229189 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(14\) | −2.87939 | −0.769548 | ||||||||
\(15\) | −3.41147 | −0.880839 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.94356 | 1.68406 | 0.842031 | − | 0.539430i | \(-0.181360\pi\) | ||||
0.842031 | + | 0.539430i | \(0.181360\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.41147 | −0.762829 | ||||||||
\(21\) | −2.87939 | −0.628333 | ||||||||
\(22\) | −0.347296 | −0.0740438 | ||||||||
\(23\) | 6.80066 | 1.41804 | 0.709018 | − | 0.705191i | \(-0.249139\pi\) | ||||
0.709018 | + | 0.705191i | \(0.249139\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 6.63816 | 1.32763 | ||||||||
\(26\) | 1.65270 | 0.324122 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.87939 | −0.544153 | ||||||||
\(29\) | −6.35504 | −1.18010 | −0.590050 | − | 0.807366i | \(-0.700892\pi\) | ||||
−0.590050 | + | 0.807366i | \(0.700892\pi\) | |||||||
\(30\) | −3.41147 | −0.622847 | ||||||||
\(31\) | −1.59627 | −0.286698 | −0.143349 | − | 0.989672i | \(-0.545787\pi\) | ||||
−0.143349 | + | 0.989672i | \(0.545787\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.347296 | −0.0604565 | ||||||||
\(34\) | 6.94356 | 1.19081 | ||||||||
\(35\) | 9.82295 | 1.66038 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 11.2121 | 1.84326 | 0.921632 | − | 0.388066i | \(-0.126857\pi\) | ||||
0.921632 | + | 0.388066i | \(0.126857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.65270 | 0.264644 | ||||||||
\(40\) | −3.41147 | −0.539401 | ||||||||
\(41\) | 3.49020 | 0.545078 | 0.272539 | − | 0.962145i | \(-0.412137\pi\) | ||||
0.272539 | + | 0.962145i | \(0.412137\pi\) | |||||||
\(42\) | −2.87939 | −0.444299 | ||||||||
\(43\) | 2.28312 | 0.348172 | 0.174086 | − | 0.984730i | \(-0.444303\pi\) | ||||
0.174086 | + | 0.984730i | \(0.444303\pi\) | |||||||
\(44\) | −0.347296 | −0.0523569 | ||||||||
\(45\) | −3.41147 | −0.508553 | ||||||||
\(46\) | 6.80066 | 1.00270 | ||||||||
\(47\) | 5.59627 | 0.816299 | 0.408150 | − | 0.912915i | \(-0.366174\pi\) | ||||
0.408150 | + | 0.912915i | \(0.366174\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.29086 | 0.184408 | ||||||||
\(50\) | 6.63816 | 0.938777 | ||||||||
\(51\) | 6.94356 | 0.972293 | ||||||||
\(52\) | 1.65270 | 0.229189 | ||||||||
\(53\) | −1.98040 | −0.272029 | −0.136014 | − | 0.990707i | \(-0.543429\pi\) | ||||
−0.136014 | + | 0.990707i | \(0.543429\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.18479 | 0.159757 | ||||||||
\(56\) | −2.87939 | −0.384774 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.35504 | −0.834457 | ||||||||
\(59\) | −0.445622 | −0.0580151 | −0.0290075 | − | 0.999579i | \(-0.509235\pi\) | ||||
−0.0290075 | + | 0.999579i | \(0.509235\pi\) | |||||||
\(60\) | −3.41147 | −0.440419 | ||||||||
\(61\) | −12.5321 | −1.60457 | −0.802285 | − | 0.596941i | \(-0.796382\pi\) | ||||
−0.802285 | + | 0.596941i | \(0.796382\pi\) | |||||||
\(62\) | −1.59627 | −0.202726 | ||||||||
\(63\) | −2.87939 | −0.362768 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.63816 | −0.699327 | ||||||||
\(66\) | −0.347296 | −0.0427492 | ||||||||
\(67\) | 1.07873 | 0.131787 | 0.0658937 | − | 0.997827i | \(-0.479010\pi\) | ||||
0.0658937 | + | 0.997827i | \(0.479010\pi\) | |||||||
\(68\) | 6.94356 | 0.842031 | ||||||||
\(69\) | 6.80066 | 0.818703 | ||||||||
\(70\) | 9.82295 | 1.17407 | ||||||||
\(71\) | 16.6236 | 1.97286 | 0.986430 | − | 0.164185i | \(-0.0524993\pi\) | ||||
0.986430 | + | 0.164185i | \(0.0524993\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 12.4192 | 1.45356 | 0.726780 | − | 0.686871i | \(-0.241016\pi\) | ||||
0.726780 | + | 0.686871i | \(0.241016\pi\) | |||||||
\(74\) | 11.2121 | 1.30338 | ||||||||
\(75\) | 6.63816 | 0.766508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 1.65270 | 0.187132 | ||||||||
\(79\) | 10.9240 | 1.22904 | 0.614521 | − | 0.788901i | \(-0.289349\pi\) | ||||
0.614521 | + | 0.788901i | \(0.289349\pi\) | |||||||
\(80\) | −3.41147 | −0.381414 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.49020 | 0.385428 | ||||||||
\(83\) | 11.7169 | 1.28609 | 0.643047 | − | 0.765826i | \(-0.277670\pi\) | ||||
0.643047 | + | 0.765826i | \(0.277670\pi\) | |||||||
\(84\) | −2.87939 | −0.314167 | ||||||||
\(85\) | −23.6878 | −2.56930 | ||||||||
\(86\) | 2.28312 | 0.246195 | ||||||||
\(87\) | −6.35504 | −0.681331 | ||||||||
\(88\) | −0.347296 | −0.0370219 | ||||||||
\(89\) | −1.79292 | −0.190049 | −0.0950245 | − | 0.995475i | \(-0.530293\pi\) | ||||
−0.0950245 | + | 0.995475i | \(0.530293\pi\) | |||||||
\(90\) | −3.41147 | −0.359601 | ||||||||
\(91\) | −4.75877 | −0.498855 | ||||||||
\(92\) | 6.80066 | 0.709018 | ||||||||
\(93\) | −1.59627 | −0.165525 | ||||||||
\(94\) | 5.59627 | 0.577211 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −3.65270 | −0.370876 | −0.185438 | − | 0.982656i | \(-0.559370\pi\) | ||||
−0.185438 | + | 0.982656i | \(0.559370\pi\) | |||||||
\(98\) | 1.29086 | 0.130396 | ||||||||
\(99\) | −0.347296 | −0.0349046 | ||||||||
\(100\) | 6.63816 | 0.663816 | ||||||||
\(101\) | −9.90673 | −0.985756 | −0.492878 | − | 0.870098i | \(-0.664055\pi\) | ||||
−0.492878 | + | 0.870098i | \(0.664055\pi\) | |||||||
\(102\) | 6.94356 | 0.687515 | ||||||||
\(103\) | −7.84524 | −0.773014 | −0.386507 | − | 0.922286i | \(-0.626319\pi\) | ||||
−0.386507 | + | 0.922286i | \(0.626319\pi\) | |||||||
\(104\) | 1.65270 | 0.162061 | ||||||||
\(105\) | 9.82295 | 0.958622 | ||||||||
\(106\) | −1.98040 | −0.192353 | ||||||||
\(107\) | 0.0273411 | 0.00264317 | 0.00132158 | − | 0.999999i | \(-0.499579\pi\) | ||||
0.00132158 | + | 0.999999i | \(0.499579\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.7733 | 1.03190 | 0.515948 | − | 0.856620i | \(-0.327440\pi\) | ||||
0.515948 | + | 0.856620i | \(0.327440\pi\) | |||||||
\(110\) | 1.18479 | 0.112966 | ||||||||
\(111\) | 11.2121 | 1.06421 | ||||||||
\(112\) | −2.87939 | −0.272076 | ||||||||
\(113\) | 11.6604 | 1.09692 | 0.548461 | − | 0.836176i | \(-0.315214\pi\) | ||||
0.548461 | + | 0.836176i | \(0.315214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.2003 | −2.16344 | ||||||||
\(116\) | −6.35504 | −0.590050 | ||||||||
\(117\) | 1.65270 | 0.152793 | ||||||||
\(118\) | −0.445622 | −0.0410229 | ||||||||
\(119\) | −19.9932 | −1.83277 | ||||||||
\(120\) | −3.41147 | −0.311424 | ||||||||
\(121\) | −10.8794 | −0.989035 | ||||||||
\(122\) | −12.5321 | −1.13460 | ||||||||
\(123\) | 3.49020 | 0.314701 | ||||||||
\(124\) | −1.59627 | −0.143349 | ||||||||
\(125\) | −5.58853 | −0.499853 | ||||||||
\(126\) | −2.87939 | −0.256516 | ||||||||
\(127\) | −16.2121 | −1.43859 | −0.719297 | − | 0.694703i | \(-0.755536\pi\) | ||||
−0.719297 | + | 0.694703i | \(0.755536\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.28312 | 0.201017 | ||||||||
\(130\) | −5.63816 | −0.494499 | ||||||||
\(131\) | −2.80066 | −0.244695 | −0.122347 | − | 0.992487i | \(-0.539042\pi\) | ||||
−0.122347 | + | 0.992487i | \(0.539042\pi\) | |||||||
\(132\) | −0.347296 | −0.0302283 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.07873 | 0.0931877 | ||||||||
\(135\) | −3.41147 | −0.293613 | ||||||||
\(136\) | 6.94356 | 0.595406 | ||||||||
\(137\) | 16.0351 | 1.36997 | 0.684985 | − | 0.728557i | \(-0.259809\pi\) | ||||
0.684985 | + | 0.728557i | \(0.259809\pi\) | |||||||
\(138\) | 6.80066 | 0.578911 | ||||||||
\(139\) | −2.07873 | −0.176315 | −0.0881576 | − | 0.996107i | \(-0.528098\pi\) | ||||
−0.0881576 | + | 0.996107i | \(0.528098\pi\) | |||||||
\(140\) | 9.82295 | 0.830191 | ||||||||
\(141\) | 5.59627 | 0.471291 | ||||||||
\(142\) | 16.6236 | 1.39502 | ||||||||
\(143\) | −0.573978 | −0.0479984 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 21.6800 | 1.80043 | ||||||||
\(146\) | 12.4192 | 1.02782 | ||||||||
\(147\) | 1.29086 | 0.106468 | ||||||||
\(148\) | 11.2121 | 0.921632 | ||||||||
\(149\) | −1.66725 | −0.136587 | −0.0682933 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682933 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(150\) | 6.63816 | 0.542003 | ||||||||
\(151\) | −20.0523 | −1.63183 | −0.815917 | − | 0.578169i | \(-0.803768\pi\) | ||||
−0.815917 | + | 0.578169i | \(0.803768\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.94356 | 0.561354 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 5.44562 | 0.437403 | ||||||||
\(156\) | 1.65270 | 0.132322 | ||||||||
\(157\) | −4.09833 | −0.327082 | −0.163541 | − | 0.986537i | \(-0.552292\pi\) | ||||
−0.163541 | + | 0.986537i | \(0.552292\pi\) | |||||||
\(158\) | 10.9240 | 0.869064 | ||||||||
\(159\) | −1.98040 | −0.157056 | ||||||||
\(160\) | −3.41147 | −0.269701 | ||||||||
\(161\) | −19.5817 | −1.54326 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.13516 | −0.637195 | −0.318598 | − | 0.947890i | \(-0.603212\pi\) | ||||
−0.318598 | + | 0.947890i | \(0.603212\pi\) | |||||||
\(164\) | 3.49020 | 0.272539 | ||||||||
\(165\) | 1.18479 | 0.0922360 | ||||||||
\(166\) | 11.7169 | 0.909406 | ||||||||
\(167\) | 13.3969 | 1.03669 | 0.518343 | − | 0.855173i | \(-0.326549\pi\) | ||||
0.518343 | + | 0.855173i | \(0.326549\pi\) | |||||||
\(168\) | −2.87939 | −0.222149 | ||||||||
\(169\) | −10.2686 | −0.789890 | ||||||||
\(170\) | −23.6878 | −1.81677 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.28312 | 0.174086 | ||||||||
\(173\) | 1.02229 | 0.0777232 | 0.0388616 | − | 0.999245i | \(-0.487627\pi\) | ||||
0.0388616 | + | 0.999245i | \(0.487627\pi\) | |||||||
\(174\) | −6.35504 | −0.481774 | ||||||||
\(175\) | −19.1138 | −1.44487 | ||||||||
\(176\) | −0.347296 | −0.0261784 | ||||||||
\(177\) | −0.445622 | −0.0334950 | ||||||||
\(178\) | −1.79292 | −0.134385 | ||||||||
\(179\) | −2.03508 | −0.152109 | −0.0760546 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760546 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(180\) | −3.41147 | −0.254276 | ||||||||
\(181\) | −22.3037 | −1.65782 | −0.828909 | − | 0.559384i | \(-0.811038\pi\) | ||||
−0.828909 | + | 0.559384i | \(0.811038\pi\) | |||||||
\(182\) | −4.75877 | −0.352744 | ||||||||
\(183\) | −12.5321 | −0.926399 | ||||||||
\(184\) | 6.80066 | 0.501351 | ||||||||
\(185\) | −38.2499 | −2.81219 | ||||||||
\(186\) | −1.59627 | −0.117044 | ||||||||
\(187\) | −2.41147 | −0.176344 | ||||||||
\(188\) | 5.59627 | 0.408150 | ||||||||
\(189\) | −2.87939 | −0.209444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.7861 | 0.780456 | 0.390228 | − | 0.920718i | \(-0.372396\pi\) | ||||
0.390228 | + | 0.920718i | \(0.372396\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 2.86484 | 0.206216 | 0.103108 | − | 0.994670i | \(-0.467121\pi\) | ||||
0.103108 | + | 0.994670i | \(0.467121\pi\) | |||||||
\(194\) | −3.65270 | −0.262249 | ||||||||
\(195\) | −5.63816 | −0.403757 | ||||||||
\(196\) | 1.29086 | 0.0922042 | ||||||||
\(197\) | −8.33544 | −0.593875 | −0.296938 | − | 0.954897i | \(-0.595965\pi\) | ||||
−0.296938 | + | 0.954897i | \(0.595965\pi\) | |||||||
\(198\) | −0.347296 | −0.0246813 | ||||||||
\(199\) | −3.03415 | −0.215085 | −0.107543 | − | 0.994200i | \(-0.534298\pi\) | ||||
−0.107543 | + | 0.994200i | \(0.534298\pi\) | |||||||
\(200\) | 6.63816 | 0.469388 | ||||||||
\(201\) | 1.07873 | 0.0760874 | ||||||||
\(202\) | −9.90673 | −0.697035 | ||||||||
\(203\) | 18.2986 | 1.28431 | ||||||||
\(204\) | 6.94356 | 0.486147 | ||||||||
\(205\) | −11.9067 | −0.831602 | ||||||||
\(206\) | −7.84524 | −0.546604 | ||||||||
\(207\) | 6.80066 | 0.472679 | ||||||||
\(208\) | 1.65270 | 0.114594 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.82295 | 0.677848 | ||||||||
\(211\) | 16.6382 | 1.14542 | 0.572709 | − | 0.819759i | \(-0.305893\pi\) | ||||
0.572709 | + | 0.819759i | \(0.305893\pi\) | |||||||
\(212\) | −1.98040 | −0.136014 | ||||||||
\(213\) | 16.6236 | 1.13903 | ||||||||
\(214\) | 0.0273411 | 0.00186900 | ||||||||
\(215\) | −7.78880 | −0.531192 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.59627 | 0.312015 | ||||||||
\(218\) | 10.7733 | 0.729661 | ||||||||
\(219\) | 12.4192 | 0.839213 | ||||||||
\(220\) | 1.18479 | 0.0798787 | ||||||||
\(221\) | 11.4757 | 0.771936 | ||||||||
\(222\) | 11.2121 | 0.752509 | ||||||||
\(223\) | 8.17024 | 0.547120 | 0.273560 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273560 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(224\) | −2.87939 | −0.192387 | ||||||||
\(225\) | 6.63816 | 0.442544 | ||||||||
\(226\) | 11.6604 | 0.775641 | ||||||||
\(227\) | −1.80066 | −0.119514 | −0.0597570 | − | 0.998213i | \(-0.519033\pi\) | ||||
−0.0597570 | + | 0.998213i | \(0.519033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7392 | −1.23832 | −0.619160 | − | 0.785265i | \(-0.712527\pi\) | ||||
−0.619160 | + | 0.785265i | \(0.712527\pi\) | |||||||
\(230\) | −23.2003 | −1.52978 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −6.35504 | −0.417229 | ||||||||
\(233\) | −4.09833 | −0.268490 | −0.134245 | − | 0.990948i | \(-0.542861\pi\) | ||||
−0.134245 | + | 0.990948i | \(0.542861\pi\) | |||||||
\(234\) | 1.65270 | 0.108041 | ||||||||
\(235\) | −19.0915 | −1.24539 | ||||||||
\(236\) | −0.445622 | −0.0290075 | ||||||||
\(237\) | 10.9240 | 0.709588 | ||||||||
\(238\) | −19.9932 | −1.29597 | ||||||||
\(239\) | −28.2276 | −1.82589 | −0.912946 | − | 0.408080i | \(-0.866199\pi\) | ||||
−0.912946 | + | 0.408080i | \(0.866199\pi\) | |||||||
\(240\) | −3.41147 | −0.220210 | ||||||||
\(241\) | −6.56212 | −0.422703 | −0.211352 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211352 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(242\) | −10.8794 | −0.699353 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.5321 | −0.802285 | ||||||||
\(245\) | −4.40373 | −0.281344 | ||||||||
\(246\) | 3.49020 | 0.222527 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.59627 | −0.101363 | ||||||||
\(249\) | 11.7169 | 0.742527 | ||||||||
\(250\) | −5.58853 | −0.353449 | ||||||||
\(251\) | 8.89393 | 0.561380 | 0.280690 | − | 0.959798i | \(-0.409437\pi\) | ||||
0.280690 | + | 0.959798i | \(0.409437\pi\) | |||||||
\(252\) | −2.87939 | −0.181384 | ||||||||
\(253\) | −2.36184 | −0.148488 | ||||||||
\(254\) | −16.2121 | −1.01724 | ||||||||
\(255\) | −23.6878 | −1.48339 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.4662 | 0.839996 | 0.419998 | − | 0.907525i | \(-0.362031\pi\) | ||||
0.419998 | + | 0.907525i | \(0.362031\pi\) | |||||||
\(258\) | 2.28312 | 0.142141 | ||||||||
\(259\) | −32.2841 | −2.00603 | ||||||||
\(260\) | −5.63816 | −0.349664 | ||||||||
\(261\) | −6.35504 | −0.393367 | ||||||||
\(262\) | −2.80066 | −0.173025 | ||||||||
\(263\) | −16.7520 | −1.03297 | −0.516485 | − | 0.856296i | \(-0.672760\pi\) | ||||
−0.516485 | + | 0.856296i | \(0.672760\pi\) | |||||||
\(264\) | −0.347296 | −0.0213746 | ||||||||
\(265\) | 6.75608 | 0.415023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.79292 | −0.109725 | ||||||||
\(268\) | 1.07873 | 0.0658937 | ||||||||
\(269\) | −3.58946 | −0.218853 | −0.109427 | − | 0.993995i | \(-0.534901\pi\) | ||||
−0.109427 | + | 0.993995i | \(0.534901\pi\) | |||||||
\(270\) | −3.41147 | −0.207616 | ||||||||
\(271\) | 23.9590 | 1.45541 | 0.727704 | − | 0.685891i | \(-0.240587\pi\) | ||||
0.727704 | + | 0.685891i | \(0.240587\pi\) | |||||||
\(272\) | 6.94356 | 0.421015 | ||||||||
\(273\) | −4.75877 | −0.288014 | ||||||||
\(274\) | 16.0351 | 0.968715 | ||||||||
\(275\) | −2.30541 | −0.139021 | ||||||||
\(276\) | 6.80066 | 0.409352 | ||||||||
\(277\) | −18.7219 | −1.12489 | −0.562446 | − | 0.826834i | \(-0.690140\pi\) | ||||
−0.562446 | + | 0.826834i | \(0.690140\pi\) | |||||||
\(278\) | −2.07873 | −0.124674 | ||||||||
\(279\) | −1.59627 | −0.0955660 | ||||||||
\(280\) | 9.82295 | 0.587033 | ||||||||
\(281\) | 10.6382 | 0.634619 | 0.317310 | − | 0.948322i | \(-0.397221\pi\) | ||||
0.317310 | + | 0.948322i | \(0.397221\pi\) | |||||||
\(282\) | 5.59627 | 0.333253 | ||||||||
\(283\) | −14.0128 | −0.832974 | −0.416487 | − | 0.909142i | \(-0.636739\pi\) | ||||
−0.416487 | + | 0.909142i | \(0.636739\pi\) | |||||||
\(284\) | 16.6236 | 0.986430 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.573978 | −0.0339400 | ||||||||
\(287\) | −10.0496 | −0.593211 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 31.2131 | 1.83606 | ||||||||
\(290\) | 21.6800 | 1.27310 | ||||||||
\(291\) | −3.65270 | −0.214125 | ||||||||
\(292\) | 12.4192 | 0.726780 | ||||||||
\(293\) | 11.5202 | 0.673019 | 0.336509 | − | 0.941680i | \(-0.390754\pi\) | ||||
0.336509 | + | 0.941680i | \(0.390754\pi\) | |||||||
\(294\) | 1.29086 | 0.0752844 | ||||||||
\(295\) | 1.52023 | 0.0885112 | ||||||||
\(296\) | 11.2121 | 0.651692 | ||||||||
\(297\) | −0.347296 | −0.0201522 | ||||||||
\(298\) | −1.66725 | −0.0965813 | ||||||||
\(299\) | 11.2395 | 0.649996 | ||||||||
\(300\) | 6.63816 | 0.383254 | ||||||||
\(301\) | −6.57398 | −0.378918 | ||||||||
\(302\) | −20.0523 | −1.15388 | ||||||||
\(303\) | −9.90673 | −0.569127 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.7529 | 2.44802 | ||||||||
\(306\) | 6.94356 | 0.396937 | ||||||||
\(307\) | −4.29767 | −0.245281 | −0.122640 | − | 0.992451i | \(-0.539136\pi\) | ||||
−0.122640 | + | 0.992451i | \(0.539136\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −7.84524 | −0.446300 | ||||||||
\(310\) | 5.44562 | 0.309291 | ||||||||
\(311\) | −22.9932 | −1.30382 | −0.651912 | − | 0.758294i | \(-0.726033\pi\) | ||||
−0.651912 | + | 0.758294i | \(0.726033\pi\) | |||||||
\(312\) | 1.65270 | 0.0935659 | ||||||||
\(313\) | −9.20977 | −0.520567 | −0.260283 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260283 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(314\) | −4.09833 | −0.231282 | ||||||||
\(315\) | 9.82295 | 0.553460 | ||||||||
\(316\) | 10.9240 | 0.614521 | ||||||||
\(317\) | −3.35504 | −0.188438 | −0.0942188 | − | 0.995552i | \(-0.530035\pi\) | ||||
−0.0942188 | + | 0.995552i | \(0.530035\pi\) | |||||||
\(318\) | −1.98040 | −0.111055 | ||||||||
\(319\) | 2.20708 | 0.123573 | ||||||||
\(320\) | −3.41147 | −0.190707 | ||||||||
\(321\) | 0.0273411 | 0.00152603 | ||||||||
\(322\) | −19.5817 | −1.09125 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 10.9709 | 0.608556 | ||||||||
\(326\) | −8.13516 | −0.450565 | ||||||||
\(327\) | 10.7733 | 0.595766 | ||||||||
\(328\) | 3.49020 | 0.192714 | ||||||||
\(329\) | −16.1138 | −0.888383 | ||||||||
\(330\) | 1.18479 | 0.0652207 | ||||||||
\(331\) | 22.0743 | 1.21331 | 0.606656 | − | 0.794964i | \(-0.292510\pi\) | ||||
0.606656 | + | 0.794964i | \(0.292510\pi\) | |||||||
\(332\) | 11.7169 | 0.643047 | ||||||||
\(333\) | 11.2121 | 0.614421 | ||||||||
\(334\) | 13.3969 | 0.733047 | ||||||||
\(335\) | −3.68004 | −0.201062 | ||||||||
\(336\) | −2.87939 | −0.157083 | ||||||||
\(337\) | 13.1165 | 0.714501 | 0.357251 | − | 0.934009i | \(-0.383714\pi\) | ||||
0.357251 | + | 0.934009i | \(0.383714\pi\) | |||||||
\(338\) | −10.2686 | −0.558537 | ||||||||
\(339\) | 11.6604 | 0.633308 | ||||||||
\(340\) | −23.6878 | −1.28465 | ||||||||
\(341\) | 0.554378 | 0.0300212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4388 | 0.887613 | ||||||||
\(344\) | 2.28312 | 0.123098 | ||||||||
\(345\) | −23.2003 | −1.24906 | ||||||||
\(346\) | 1.02229 | 0.0549586 | ||||||||
\(347\) | 8.75877 | 0.470195 | 0.235098 | − | 0.971972i | \(-0.424459\pi\) | ||||
0.235098 | + | 0.971972i | \(0.424459\pi\) | |||||||
\(348\) | −6.35504 | −0.340666 | ||||||||
\(349\) | 3.26352 | 0.174692 | 0.0873461 | − | 0.996178i | \(-0.472161\pi\) | ||||
0.0873461 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(350\) | −19.1138 | −1.02168 | ||||||||
\(351\) | 1.65270 | 0.0882148 | ||||||||
\(352\) | −0.347296 | −0.0185110 | ||||||||
\(353\) | 29.0838 | 1.54797 | 0.773987 | − | 0.633202i | \(-0.218260\pi\) | ||||
0.773987 | + | 0.633202i | \(0.218260\pi\) | |||||||
\(354\) | −0.445622 | −0.0236846 | ||||||||
\(355\) | −56.7110 | −3.00991 | ||||||||
\(356\) | −1.79292 | −0.0950245 | ||||||||
\(357\) | −19.9932 | −1.05815 | ||||||||
\(358\) | −2.03508 | −0.107557 | ||||||||
\(359\) | 6.61081 | 0.348905 | 0.174453 | − | 0.984666i | \(-0.444184\pi\) | ||||
0.174453 | + | 0.984666i | \(0.444184\pi\) | |||||||
\(360\) | −3.41147 | −0.179800 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −22.3037 | −1.17225 | ||||||||
\(363\) | −10.8794 | −0.571020 | ||||||||
\(364\) | −4.75877 | −0.249427 | ||||||||
\(365\) | −42.3678 | −2.21763 | ||||||||
\(366\) | −12.5321 | −0.655063 | ||||||||
\(367\) | −5.79561 | −0.302528 | −0.151264 | − | 0.988493i | \(-0.548334\pi\) | ||||
−0.151264 | + | 0.988493i | \(0.548334\pi\) | |||||||
\(368\) | 6.80066 | 0.354509 | ||||||||
\(369\) | 3.49020 | 0.181693 | ||||||||
\(370\) | −38.2499 | −1.98852 | ||||||||
\(371\) | 5.70233 | 0.296050 | ||||||||
\(372\) | −1.59627 | −0.0827626 | ||||||||
\(373\) | 25.8898 | 1.34052 | 0.670262 | − | 0.742125i | \(-0.266182\pi\) | ||||
0.670262 | + | 0.742125i | \(0.266182\pi\) | |||||||
\(374\) | −2.41147 | −0.124694 | ||||||||
\(375\) | −5.58853 | −0.288590 | ||||||||
\(376\) | 5.59627 | 0.288605 | ||||||||
\(377\) | −10.5030 | −0.540932 | ||||||||
\(378\) | −2.87939 | −0.148100 | ||||||||
\(379\) | 19.1557 | 0.983962 | 0.491981 | − | 0.870606i | \(-0.336273\pi\) | ||||
0.491981 | + | 0.870606i | \(0.336273\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.2121 | −0.830573 | ||||||||
\(382\) | 10.7861 | 0.551865 | ||||||||
\(383\) | 9.69459 | 0.495371 | 0.247685 | − | 0.968841i | \(-0.420330\pi\) | ||||
0.247685 | + | 0.968841i | \(0.420330\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.41147 | −0.173865 | ||||||||
\(386\) | 2.86484 | 0.145816 | ||||||||
\(387\) | 2.28312 | 0.116057 | ||||||||
\(388\) | −3.65270 | −0.185438 | ||||||||
\(389\) | −0.817896 | −0.0414690 | −0.0207345 | − | 0.999785i | \(-0.506600\pi\) | ||||
−0.0207345 | + | 0.999785i | \(0.506600\pi\) | |||||||
\(390\) | −5.63816 | −0.285499 | ||||||||
\(391\) | 47.2208 | 2.38806 | ||||||||
\(392\) | 1.29086 | 0.0651982 | ||||||||
\(393\) | −2.80066 | −0.141275 | ||||||||
\(394\) | −8.33544 | −0.419933 | ||||||||
\(395\) | −37.2668 | −1.87510 | ||||||||
\(396\) | −0.347296 | −0.0174523 | ||||||||
\(397\) | −3.69728 | −0.185561 | −0.0927806 | − | 0.995687i | \(-0.529576\pi\) | ||||
−0.0927806 | + | 0.995687i | \(0.529576\pi\) | |||||||
\(398\) | −3.03415 | −0.152088 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.63816 | 0.331908 | ||||||||
\(401\) | 21.7401 | 1.08565 | 0.542824 | − | 0.839846i | \(-0.317355\pi\) | ||||
0.542824 | + | 0.839846i | \(0.317355\pi\) | |||||||
\(402\) | 1.07873 | 0.0538019 | ||||||||
\(403\) | −2.63816 | −0.131416 | ||||||||
\(404\) | −9.90673 | −0.492878 | ||||||||
\(405\) | −3.41147 | −0.169518 | ||||||||
\(406\) | 18.2986 | 0.908144 | ||||||||
\(407\) | −3.89393 | −0.193015 | ||||||||
\(408\) | 6.94356 | 0.343758 | ||||||||
\(409\) | 4.05468 | 0.200491 | 0.100246 | − | 0.994963i | \(-0.468037\pi\) | ||||
0.100246 | + | 0.994963i | \(0.468037\pi\) | |||||||
\(410\) | −11.9067 | −0.588031 | ||||||||
\(411\) | 16.0351 | 0.790952 | ||||||||
\(412\) | −7.84524 | −0.386507 | ||||||||
\(413\) | 1.28312 | 0.0631381 | ||||||||
\(414\) | 6.80066 | 0.334234 | ||||||||
\(415\) | −39.9718 | −1.96214 | ||||||||
\(416\) | 1.65270 | 0.0810305 | ||||||||
\(417\) | −2.07873 | −0.101796 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4989 | 1.14800 | 0.573998 | − | 0.818857i | \(-0.305392\pi\) | ||||
0.573998 | + | 0.818857i | \(0.305392\pi\) | |||||||
\(420\) | 9.82295 | 0.479311 | ||||||||
\(421\) | 23.0729 | 1.12450 | 0.562251 | − | 0.826967i | \(-0.309935\pi\) | ||||
0.562251 | + | 0.826967i | \(0.309935\pi\) | |||||||
\(422\) | 16.6382 | 0.809933 | ||||||||
\(423\) | 5.59627 | 0.272100 | ||||||||
\(424\) | −1.98040 | −0.0961767 | ||||||||
\(425\) | 46.0925 | 2.23581 | ||||||||
\(426\) | 16.6236 | 0.805416 | ||||||||
\(427\) | 36.0847 | 1.74626 | ||||||||
\(428\) | 0.0273411 | 0.00132158 | ||||||||
\(429\) | −0.573978 | −0.0277119 | ||||||||
\(430\) | −7.78880 | −0.375609 | ||||||||
\(431\) | 3.51485 | 0.169304 | 0.0846522 | − | 0.996411i | \(-0.473022\pi\) | ||||
0.0846522 | + | 0.996411i | \(0.473022\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 34.1147 | 1.63945 | 0.819725 | − | 0.572757i | \(-0.194126\pi\) | ||||
0.819725 | + | 0.572757i | \(0.194126\pi\) | |||||||
\(434\) | 4.59627 | 0.220628 | ||||||||
\(435\) | 21.6800 | 1.03948 | ||||||||
\(436\) | 10.7733 | 0.515948 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.4192 | 0.593413 | ||||||||
\(439\) | −9.70140 | −0.463023 | −0.231511 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231511 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(440\) | 1.18479 | 0.0564828 | ||||||||
\(441\) | 1.29086 | 0.0614695 | ||||||||
\(442\) | 11.4757 | 0.545841 | ||||||||
\(443\) | 15.1821 | 0.721324 | 0.360662 | − | 0.932697i | \(-0.382551\pi\) | ||||
0.360662 | + | 0.932697i | \(0.382551\pi\) | |||||||
\(444\) | 11.2121 | 0.532104 | ||||||||
\(445\) | 6.11650 | 0.289950 | ||||||||
\(446\) | 8.17024 | 0.386872 | ||||||||
\(447\) | −1.66725 | −0.0788583 | ||||||||
\(448\) | −2.87939 | −0.136038 | ||||||||
\(449\) | −34.8384 | −1.64413 | −0.822064 | − | 0.569396i | \(-0.807177\pi\) | ||||
−0.822064 | + | 0.569396i | \(0.807177\pi\) | |||||||
\(450\) | 6.63816 | 0.312926 | ||||||||
\(451\) | −1.21213 | −0.0570771 | ||||||||
\(452\) | 11.6604 | 0.548461 | ||||||||
\(453\) | −20.0523 | −0.942140 | ||||||||
\(454\) | −1.80066 | −0.0845091 | ||||||||
\(455\) | 16.2344 | 0.761081 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.8749 | −1.49105 | −0.745523 | − | 0.666479i | \(-0.767800\pi\) | ||||
−0.745523 | + | 0.666479i | \(0.767800\pi\) | |||||||
\(458\) | −18.7392 | −0.875624 | ||||||||
\(459\) | 6.94356 | 0.324098 | ||||||||
\(460\) | −23.2003 | −1.08172 | ||||||||
\(461\) | −10.6895 | −0.497862 | −0.248931 | − | 0.968521i | \(-0.580079\pi\) | ||||
−0.248931 | + | 0.968521i | \(0.580079\pi\) | |||||||
\(462\) | 1.00000 | 0.0465242 | ||||||||
\(463\) | 15.3182 | 0.711897 | 0.355949 | − | 0.934506i | \(-0.384158\pi\) | ||||
0.355949 | + | 0.934506i | \(0.384158\pi\) | |||||||
\(464\) | −6.35504 | −0.295025 | ||||||||
\(465\) | 5.44562 | 0.252535 | ||||||||
\(466\) | −4.09833 | −0.189851 | ||||||||
\(467\) | 28.5125 | 1.31940 | 0.659700 | − | 0.751529i | \(-0.270683\pi\) | ||||
0.659700 | + | 0.751529i | \(0.270683\pi\) | |||||||
\(468\) | 1.65270 | 0.0763963 | ||||||||
\(469\) | −3.10607 | −0.143425 | ||||||||
\(470\) | −19.0915 | −0.880626 | ||||||||
\(471\) | −4.09833 | −0.188841 | ||||||||
\(472\) | −0.445622 | −0.0205114 | ||||||||
\(473\) | −0.792919 | −0.0364584 | ||||||||
\(474\) | 10.9240 | 0.501754 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.9932 | −0.916386 | ||||||||
\(477\) | −1.98040 | −0.0906763 | ||||||||
\(478\) | −28.2276 | −1.29110 | ||||||||
\(479\) | 8.05138 | 0.367877 | 0.183939 | − | 0.982938i | \(-0.441115\pi\) | ||||
0.183939 | + | 0.982938i | \(0.441115\pi\) | |||||||
\(480\) | −3.41147 | −0.155712 | ||||||||
\(481\) | 18.5303 | 0.844911 | ||||||||
\(482\) | −6.56212 | −0.298896 | ||||||||
\(483\) | −19.5817 | −0.890999 | ||||||||
\(484\) | −10.8794 | −0.494518 | ||||||||
\(485\) | 12.4611 | 0.565830 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.11556 | −0.277123 | −0.138561 | − | 0.990354i | \(-0.544248\pi\) | ||||
−0.138561 | + | 0.990354i | \(0.544248\pi\) | |||||||
\(488\) | −12.5321 | −0.567301 | ||||||||
\(489\) | −8.13516 | −0.367885 | ||||||||
\(490\) | −4.40373 | −0.198940 | ||||||||
\(491\) | −22.6851 | −1.02376 | −0.511882 | − | 0.859056i | \(-0.671052\pi\) | ||||
−0.511882 | + | 0.859056i | \(0.671052\pi\) | |||||||
\(492\) | 3.49020 | 0.157350 | ||||||||
\(493\) | −44.1266 | −1.98736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.18479 | 0.0532525 | ||||||||
\(496\) | −1.59627 | −0.0716745 | ||||||||
\(497\) | −47.8658 | −2.14707 | ||||||||
\(498\) | 11.7169 | 0.525046 | ||||||||
\(499\) | 24.8557 | 1.11269 | 0.556346 | − | 0.830951i | \(-0.312203\pi\) | ||||
0.556346 | + | 0.830951i | \(0.312203\pi\) | |||||||
\(500\) | −5.58853 | −0.249926 | ||||||||
\(501\) | 13.3969 | 0.598531 | ||||||||
\(502\) | 8.89393 | 0.396956 | ||||||||
\(503\) | 25.0232 | 1.11573 | 0.557865 | − | 0.829932i | \(-0.311621\pi\) | ||||
0.557865 | + | 0.829932i | \(0.311621\pi\) | |||||||
\(504\) | −2.87939 | −0.128258 | ||||||||
\(505\) | 33.7965 | 1.50393 | ||||||||
\(506\) | −2.36184 | −0.104997 | ||||||||
\(507\) | −10.2686 | −0.456043 | ||||||||
\(508\) | −16.2121 | −0.719297 | ||||||||
\(509\) | −0.899310 | −0.0398612 | −0.0199306 | − | 0.999801i | \(-0.506345\pi\) | ||||
−0.0199306 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(510\) | −23.6878 | −1.04891 | ||||||||
\(511\) | −35.7597 | −1.58192 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.4662 | 0.593967 | ||||||||
\(515\) | 26.7638 | 1.17935 | ||||||||
\(516\) | 2.28312 | 0.100509 | ||||||||
\(517\) | −1.94356 | −0.0854778 | ||||||||
\(518\) | −32.2841 | −1.41848 | ||||||||
\(519\) | 1.02229 | 0.0448735 | ||||||||
\(520\) | −5.63816 | −0.247249 | ||||||||
\(521\) | 6.63547 | 0.290705 | 0.145353 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145353 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(522\) | −6.35504 | −0.278152 | ||||||||
\(523\) | −37.9522 | −1.65954 | −0.829768 | − | 0.558109i | \(-0.811527\pi\) | ||||
−0.829768 | + | 0.558109i | \(0.811527\pi\) | |||||||
\(524\) | −2.80066 | −0.122347 | ||||||||
\(525\) | −19.1138 | −0.834195 | ||||||||
\(526\) | −16.7520 | −0.730420 | ||||||||
\(527\) | −11.0838 | −0.482817 | ||||||||
\(528\) | −0.347296 | −0.0151141 | ||||||||
\(529\) | 23.2490 | 1.01082 | ||||||||
\(530\) | 6.75608 | 0.293465 | ||||||||
\(531\) | −0.445622 | −0.0193384 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.76827 | 0.249851 | ||||||||
\(534\) | −1.79292 | −0.0775872 | ||||||||
\(535\) | −0.0932736 | −0.00403257 | ||||||||
\(536\) | 1.07873 | 0.0465939 | ||||||||
\(537\) | −2.03508 | −0.0878203 | ||||||||
\(538\) | −3.58946 | −0.154753 | ||||||||
\(539\) | −0.448311 | −0.0193101 | ||||||||
\(540\) | −3.41147 | −0.146806 | ||||||||
\(541\) | 15.1307 | 0.650520 | 0.325260 | − | 0.945625i | \(-0.394548\pi\) | ||||
0.325260 | + | 0.945625i | \(0.394548\pi\) | |||||||
\(542\) | 23.9590 | 1.02913 | ||||||||
\(543\) | −22.3037 | −0.957141 | ||||||||
\(544\) | 6.94356 | 0.297703 | ||||||||
\(545\) | −36.7529 | −1.57432 | ||||||||
\(546\) | −4.75877 | −0.203657 | ||||||||
\(547\) | −32.5868 | −1.39331 | −0.696655 | − | 0.717406i | \(-0.745329\pi\) | ||||
−0.696655 | + | 0.717406i | \(0.745329\pi\) | |||||||
\(548\) | 16.0351 | 0.684985 | ||||||||
\(549\) | −12.5321 | −0.534857 | ||||||||
\(550\) | −2.30541 | −0.0983029 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.80066 | 0.289455 | ||||||||
\(553\) | −31.4543 | −1.33757 | ||||||||
\(554\) | −18.7219 | −0.795419 | ||||||||
\(555\) | −38.2499 | −1.62362 | ||||||||
\(556\) | −2.07873 | −0.0881576 | ||||||||
\(557\) | −19.9436 | −0.845036 | −0.422518 | − | 0.906355i | \(-0.638854\pi\) | ||||
−0.422518 | + | 0.906355i | \(0.638854\pi\) | |||||||
\(558\) | −1.59627 | −0.0675754 | ||||||||
\(559\) | 3.77332 | 0.159594 | ||||||||
\(560\) | 9.82295 | 0.415095 | ||||||||
\(561\) | −2.41147 | −0.101813 | ||||||||
\(562\) | 10.6382 | 0.448744 | ||||||||
\(563\) | −3.96822 | −0.167240 | −0.0836202 | − | 0.996498i | \(-0.526648\pi\) | ||||
−0.0836202 | + | 0.996498i | \(0.526648\pi\) | |||||||
\(564\) | 5.59627 | 0.235645 | ||||||||
\(565\) | −39.7793 | −1.67353 | ||||||||
\(566\) | −14.0128 | −0.589002 | ||||||||
\(567\) | −2.87939 | −0.120923 | ||||||||
\(568\) | 16.6236 | 0.697511 | ||||||||
\(569\) | −14.8135 | −0.621012 | −0.310506 | − | 0.950571i | \(-0.600499\pi\) | ||||
−0.310506 | + | 0.950571i | \(0.600499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.0615 | 0.881396 | 0.440698 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440698 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(572\) | −0.573978 | −0.0239992 | ||||||||
\(573\) | 10.7861 | 0.450596 | ||||||||
\(574\) | −10.0496 | −0.419463 | ||||||||
\(575\) | 45.1438 | 1.88263 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −44.2422 | −1.84183 | −0.920913 | − | 0.389769i | \(-0.872555\pi\) | ||||
−0.920913 | + | 0.389769i | \(0.872555\pi\) | |||||||
\(578\) | 31.2131 | 1.29829 | ||||||||
\(579\) | 2.86484 | 0.119059 | ||||||||
\(580\) | 21.6800 | 0.900215 | ||||||||
\(581\) | −33.7374 | −1.39966 | ||||||||
\(582\) | −3.65270 | −0.151409 | ||||||||
\(583\) | 0.687786 | 0.0284852 | ||||||||
\(584\) | 12.4192 | 0.513911 | ||||||||
\(585\) | −5.63816 | −0.233109 | ||||||||
\(586\) | 11.5202 | 0.475896 | ||||||||
\(587\) | 10.0024 | 0.412842 | 0.206421 | − | 0.978463i | \(-0.433818\pi\) | ||||
0.206421 | + | 0.978463i | \(0.433818\pi\) | |||||||
\(588\) | 1.29086 | 0.0532341 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.52023 | 0.0625869 | ||||||||
\(591\) | −8.33544 | −0.342874 | ||||||||
\(592\) | 11.2121 | 0.460816 | ||||||||
\(593\) | −11.4911 | −0.471884 | −0.235942 | − | 0.971767i | \(-0.575818\pi\) | ||||
−0.235942 | + | 0.971767i | \(0.575818\pi\) | |||||||
\(594\) | −0.347296 | −0.0142497 | ||||||||
\(595\) | 68.2063 | 2.79618 | ||||||||
\(596\) | −1.66725 | −0.0682933 | ||||||||
\(597\) | −3.03415 | −0.124179 | ||||||||
\(598\) | 11.2395 | 0.459616 | ||||||||
\(599\) | −6.41653 | −0.262172 | −0.131086 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131086 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(600\) | 6.63816 | 0.271002 | ||||||||
\(601\) | −31.5158 | −1.28556 | −0.642778 | − | 0.766053i | \(-0.722218\pi\) | ||||
−0.642778 | + | 0.766053i | \(0.722218\pi\) | |||||||
\(602\) | −6.57398 | −0.267935 | ||||||||
\(603\) | 1.07873 | 0.0439291 | ||||||||
\(604\) | −20.0523 | −0.815917 | ||||||||
\(605\) | 37.1147 | 1.50893 | ||||||||
\(606\) | −9.90673 | −0.402433 | ||||||||
\(607\) | −0.748341 | −0.0303742 | −0.0151871 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151871 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.2986 | 0.741497 | ||||||||
\(610\) | 42.7529 | 1.73101 | ||||||||
\(611\) | 9.24897 | 0.374173 | ||||||||
\(612\) | 6.94356 | 0.280677 | ||||||||
\(613\) | −30.6878 | −1.23947 | −0.619734 | − | 0.784812i | \(-0.712760\pi\) | ||||
−0.619734 | + | 0.784812i | \(0.712760\pi\) | |||||||
\(614\) | −4.29767 | −0.173440 | ||||||||
\(615\) | −11.9067 | −0.480126 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −27.2918 | −1.09873 | −0.549363 | − | 0.835584i | \(-0.685130\pi\) | ||||
−0.549363 | + | 0.835584i | \(0.685130\pi\) | |||||||
\(618\) | −7.84524 | −0.315582 | ||||||||
\(619\) | −13.2371 | −0.532044 | −0.266022 | − | 0.963967i | \(-0.585709\pi\) | ||||
−0.266022 | + | 0.963967i | \(0.585709\pi\) | |||||||
\(620\) | 5.44562 | 0.218701 | ||||||||
\(621\) | 6.80066 | 0.272901 | ||||||||
\(622\) | −22.9932 | −0.921943 | ||||||||
\(623\) | 5.16250 | 0.206831 | ||||||||
\(624\) | 1.65270 | 0.0661611 | ||||||||
\(625\) | −14.1257 | −0.565027 | ||||||||
\(626\) | −9.20977 | −0.368096 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.09833 | −0.163541 | ||||||||
\(629\) | 77.8522 | 3.10417 | ||||||||
\(630\) | 9.82295 | 0.391356 | ||||||||
\(631\) | −12.2395 | −0.487246 | −0.243623 | − | 0.969870i | \(-0.578336\pi\) | ||||
−0.243623 | + | 0.969870i | \(0.578336\pi\) | |||||||
\(632\) | 10.9240 | 0.434532 | ||||||||
\(633\) | 16.6382 | 0.661307 | ||||||||
\(634\) | −3.35504 | −0.133246 | ||||||||
\(635\) | 55.3073 | 2.19480 | ||||||||
\(636\) | −1.98040 | −0.0785280 | ||||||||
\(637\) | 2.13341 | 0.0845287 | ||||||||
\(638\) | 2.20708 | 0.0873792 | ||||||||
\(639\) | 16.6236 | 0.657620 | ||||||||
\(640\) | −3.41147 | −0.134850 | ||||||||
\(641\) | −8.95367 | −0.353649 | −0.176824 | − | 0.984242i | \(-0.556582\pi\) | ||||
−0.176824 | + | 0.984242i | \(0.556582\pi\) | |||||||
\(642\) | 0.0273411 | 0.00107907 | ||||||||
\(643\) | −31.3696 | −1.23710 | −0.618548 | − | 0.785747i | \(-0.712279\pi\) | ||||
−0.618548 | + | 0.785747i | \(0.712279\pi\) | |||||||
\(644\) | −19.5817 | −0.771628 | ||||||||
\(645\) | −7.78880 | −0.306684 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.54933 | −0.218166 | −0.109083 | − | 0.994033i | \(-0.534792\pi\) | ||||
−0.109083 | + | 0.994033i | \(0.534792\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0.154763 | 0.00607498 | ||||||||
\(650\) | 10.9709 | 0.430314 | ||||||||
\(651\) | 4.59627 | 0.180142 | ||||||||
\(652\) | −8.13516 | −0.318598 | ||||||||
\(653\) | 38.9103 | 1.52268 | 0.761340 | − | 0.648353i | \(-0.224542\pi\) | ||||
0.761340 | + | 0.648353i | \(0.224542\pi\) | |||||||
\(654\) | 10.7733 | 0.421270 | ||||||||
\(655\) | 9.55438 | 0.373320 | ||||||||
\(656\) | 3.49020 | 0.136269 | ||||||||
\(657\) | 12.4192 | 0.484520 | ||||||||
\(658\) | −16.1138 | −0.628182 | ||||||||
\(659\) | 39.5158 | 1.53932 | 0.769658 | − | 0.638456i | \(-0.220427\pi\) | ||||
0.769658 | + | 0.638456i | \(0.220427\pi\) | |||||||
\(660\) | 1.18479 | 0.0461180 | ||||||||
\(661\) | 0.0915189 | 0.00355967 | 0.00177984 | − | 0.999998i | \(-0.499433\pi\) | ||||
0.00177984 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(662\) | 22.0743 | 0.857941 | ||||||||
\(663\) | 11.4757 | 0.445677 | ||||||||
\(664\) | 11.7169 | 0.454703 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.2121 | 0.434461 | ||||||||
\(667\) | −43.2184 | −1.67342 | ||||||||
\(668\) | 13.3969 | 0.518343 | ||||||||
\(669\) | 8.17024 | 0.315880 | ||||||||
\(670\) | −3.68004 | −0.142173 | ||||||||
\(671\) | 4.35235 | 0.168021 | ||||||||
\(672\) | −2.87939 | −0.111075 | ||||||||
\(673\) | 39.8563 | 1.53635 | 0.768173 | − | 0.640242i | \(-0.221166\pi\) | ||||
0.768173 | + | 0.640242i | \(0.221166\pi\) | |||||||
\(674\) | 13.1165 | 0.505229 | ||||||||
\(675\) | 6.63816 | 0.255503 | ||||||||
\(676\) | −10.2686 | −0.394945 | ||||||||
\(677\) | −29.3824 | −1.12926 | −0.564628 | − | 0.825345i | \(-0.690980\pi\) | ||||
−0.564628 | + | 0.825345i | \(0.690980\pi\) | |||||||
\(678\) | 11.6604 | 0.447817 | ||||||||
\(679\) | 10.5175 | 0.403626 | ||||||||
\(680\) | −23.6878 | −0.908385 | ||||||||
\(681\) | −1.80066 | −0.0690014 | ||||||||
\(682\) | 0.554378 | 0.0212282 | ||||||||
\(683\) | 21.0933 | 0.807112 | 0.403556 | − | 0.914955i | \(-0.367774\pi\) | ||||
0.403556 | + | 0.914955i | \(0.367774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.7033 | −2.09010 | ||||||||
\(686\) | 16.4388 | 0.627637 | ||||||||
\(687\) | −18.7392 | −0.714944 | ||||||||
\(688\) | 2.28312 | 0.0870431 | ||||||||
\(689\) | −3.27301 | −0.124692 | ||||||||
\(690\) | −23.2003 | −0.883219 | ||||||||
\(691\) | −16.1634 | −0.614886 | −0.307443 | − | 0.951566i | \(-0.599473\pi\) | ||||
−0.307443 | + | 0.951566i | \(0.599473\pi\) | |||||||
\(692\) | 1.02229 | 0.0388616 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 8.75877 | 0.332478 | ||||||||
\(695\) | 7.09152 | 0.268997 | ||||||||
\(696\) | −6.35504 | −0.240887 | ||||||||
\(697\) | 24.2344 | 0.917944 | ||||||||
\(698\) | 3.26352 | 0.123526 | ||||||||
\(699\) | −4.09833 | −0.155013 | ||||||||
\(700\) | −19.1138 | −0.722434 | ||||||||
\(701\) | −20.0729 | −0.758141 | −0.379071 | − | 0.925368i | \(-0.623756\pi\) | ||||
−0.379071 | + | 0.925368i | \(0.623756\pi\) | |||||||
\(702\) | 1.65270 | 0.0623773 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.347296 | −0.0130892 | ||||||||
\(705\) | −19.0915 | −0.719028 | ||||||||
\(706\) | 29.0838 | 1.09458 | ||||||||
\(707\) | 28.5253 | 1.07280 | ||||||||
\(708\) | −0.445622 | −0.0167475 | ||||||||
\(709\) | −38.9009 | −1.46095 | −0.730476 | − | 0.682938i | \(-0.760702\pi\) | ||||
−0.730476 | + | 0.682938i | \(0.760702\pi\) | |||||||
\(710\) | −56.7110 | −2.12833 | ||||||||
\(711\) | 10.9240 | 0.409681 | ||||||||
\(712\) | −1.79292 | −0.0671925 | ||||||||
\(713\) | −10.8557 | −0.406548 | ||||||||
\(714\) | −19.9932 | −0.748226 | ||||||||
\(715\) | 1.95811 | 0.0732292 | ||||||||
\(716\) | −2.03508 | −0.0760546 | ||||||||
\(717\) | −28.2276 | −1.05418 | ||||||||
\(718\) | 6.61081 | 0.246713 | ||||||||
\(719\) | 3.06181 | 0.114186 | 0.0570932 | − | 0.998369i | \(-0.481817\pi\) | ||||
0.0570932 | + | 0.998369i | \(0.481817\pi\) | |||||||
\(720\) | −3.41147 | −0.127138 | ||||||||
\(721\) | 22.5895 | 0.841275 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.56212 | −0.244048 | ||||||||
\(724\) | −22.3037 | −0.828909 | ||||||||
\(725\) | −42.1857 | −1.56674 | ||||||||
\(726\) | −10.8794 | −0.403772 | ||||||||
\(727\) | −17.4766 | −0.648171 | −0.324085 | − | 0.946028i | \(-0.605056\pi\) | ||||
−0.324085 | + | 0.946028i | \(0.605056\pi\) | |||||||
\(728\) | −4.75877 | −0.176372 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −42.3678 | −1.56810 | ||||||||
\(731\) | 15.8530 | 0.586344 | ||||||||
\(732\) | −12.5321 | −0.463199 | ||||||||
\(733\) | −41.4175 | −1.52979 | −0.764894 | − | 0.644156i | \(-0.777209\pi\) | ||||
−0.764894 | + | 0.644156i | \(0.777209\pi\) | |||||||
\(734\) | −5.79561 | −0.213920 | ||||||||
\(735\) | −4.40373 | −0.162434 | ||||||||
\(736\) | 6.80066 | 0.250676 | ||||||||
\(737\) | −0.374638 | −0.0137999 | ||||||||
\(738\) | 3.49020 | 0.128476 | ||||||||
\(739\) | 26.4534 | 0.973103 | 0.486551 | − | 0.873652i | \(-0.338255\pi\) | ||||
0.486551 | + | 0.873652i | \(0.338255\pi\) | |||||||
\(740\) | −38.2499 | −1.40609 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.70233 | 0.209339 | ||||||||
\(743\) | 15.0760 | 0.553086 | 0.276543 | − | 0.961002i | \(-0.410811\pi\) | ||||
0.276543 | + | 0.961002i | \(0.410811\pi\) | |||||||
\(744\) | −1.59627 | −0.0585220 | ||||||||
\(745\) | 5.68779 | 0.208384 | ||||||||
\(746\) | 25.8898 | 0.947893 | ||||||||
\(747\) | 11.7169 | 0.428698 | ||||||||
\(748\) | −2.41147 | −0.0881722 | ||||||||
\(749\) | −0.0787257 | −0.00287657 | ||||||||
\(750\) | −5.58853 | −0.204064 | ||||||||
\(751\) | 5.30541 | 0.193597 | 0.0967985 | − | 0.995304i | \(-0.469140\pi\) | ||||
0.0967985 | + | 0.995304i | \(0.469140\pi\) | |||||||
\(752\) | 5.59627 | 0.204075 | ||||||||
\(753\) | 8.89393 | 0.324113 | ||||||||
\(754\) | −10.5030 | −0.382496 | ||||||||
\(755\) | 68.4080 | 2.48962 | ||||||||
\(756\) | −2.87939 | −0.104722 | ||||||||
\(757\) | 8.13846 | 0.295797 | 0.147899 | − | 0.989003i | \(-0.452749\pi\) | ||||
0.147899 | + | 0.989003i | \(0.452749\pi\) | |||||||
\(758\) | 19.1557 | 0.695766 | ||||||||
\(759\) | −2.36184 | −0.0857295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.2113 | −1.67516 | −0.837579 | − | 0.546316i | \(-0.816030\pi\) | ||||
−0.837579 | + | 0.546316i | \(0.816030\pi\) | |||||||
\(762\) | −16.2121 | −0.587304 | ||||||||
\(763\) | −31.0205 | −1.12302 | ||||||||
\(764\) | 10.7861 | 0.390228 | ||||||||
\(765\) | −23.6878 | −0.856434 | ||||||||
\(766\) | 9.69459 | 0.350280 | ||||||||
\(767\) | −0.736482 | −0.0265928 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −26.8435 | −0.968001 | −0.484000 | − | 0.875068i | \(-0.660817\pi\) | ||||
−0.484000 | + | 0.875068i | \(0.660817\pi\) | |||||||
\(770\) | −3.41147 | −0.122941 | ||||||||
\(771\) | 13.4662 | 0.484972 | ||||||||
\(772\) | 2.86484 | 0.103108 | ||||||||
\(773\) | 21.0256 | 0.756238 | 0.378119 | − | 0.925757i | \(-0.376571\pi\) | ||||
0.378119 | + | 0.925757i | \(0.376571\pi\) | |||||||
\(774\) | 2.28312 | 0.0820650 | ||||||||
\(775\) | −10.5963 | −0.380629 | ||||||||
\(776\) | −3.65270 | −0.131124 | ||||||||
\(777\) | −32.2841 | −1.15818 | ||||||||
\(778\) | −0.817896 | −0.0293230 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −5.63816 | −0.201878 | ||||||||
\(781\) | −5.77332 | −0.206586 | ||||||||
\(782\) | 47.2208 | 1.68861 | ||||||||
\(783\) | −6.35504 | −0.227110 | ||||||||
\(784\) | 1.29086 | 0.0461021 | ||||||||
\(785\) | 13.9813 | 0.499015 | ||||||||
\(786\) | −2.80066 | −0.0998962 | ||||||||
\(787\) | −45.5313 | −1.62301 | −0.811507 | − | 0.584342i | \(-0.801353\pi\) | ||||
−0.811507 | + | 0.584342i | \(0.801353\pi\) | |||||||
\(788\) | −8.33544 | −0.296938 | ||||||||
\(789\) | −16.7520 | −0.596386 | ||||||||
\(790\) | −37.2668 | −1.32589 | ||||||||
\(791\) | −33.5749 | −1.19379 | ||||||||
\(792\) | −0.347296 | −0.0123406 | ||||||||
\(793\) | −20.7118 | −0.735499 | ||||||||
\(794\) | −3.69728 | −0.131212 | ||||||||
\(795\) | 6.75608 | 0.239614 | ||||||||
\(796\) | −3.03415 | −0.107543 | ||||||||
\(797\) | −36.1780 | −1.28149 | −0.640745 | − | 0.767754i | \(-0.721374\pi\) | ||||
−0.640745 | + | 0.767754i | \(0.721374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.8580 | 1.37470 | ||||||||
\(800\) | 6.63816 | 0.234694 | ||||||||
\(801\) | −1.79292 | −0.0633497 | ||||||||
\(802\) | 21.7401 | 0.767670 | ||||||||
\(803\) | −4.31315 | −0.152208 | ||||||||
\(804\) | 1.07873 | 0.0380437 | ||||||||
\(805\) | 66.8025 | 2.35448 | ||||||||
\(806\) | −2.63816 | −0.0929251 | ||||||||
\(807\) | −3.58946 | −0.126355 | ||||||||
\(808\) | −9.90673 | −0.348517 | ||||||||
\(809\) | 2.37876 | 0.0836326 | 0.0418163 | − | 0.999125i | \(-0.486686\pi\) | ||||
0.0418163 | + | 0.999125i | \(0.486686\pi\) | |||||||
\(810\) | −3.41147 | −0.119867 | ||||||||
\(811\) | 37.0610 | 1.30139 | 0.650694 | − | 0.759340i | \(-0.274478\pi\) | ||||
0.650694 | + | 0.759340i | \(0.274478\pi\) | |||||||
\(812\) | 18.2986 | 0.642155 | ||||||||
\(813\) | 23.9590 | 0.840280 | ||||||||
\(814\) | −3.89393 | −0.136482 | ||||||||
\(815\) | 27.7529 | 0.972142 | ||||||||
\(816\) | 6.94356 | 0.243073 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.05468 | 0.141769 | ||||||||
\(819\) | −4.75877 | −0.166285 | ||||||||
\(820\) | −11.9067 | −0.415801 | ||||||||
\(821\) | −25.9605 | −0.906027 | −0.453013 | − | 0.891504i | \(-0.649651\pi\) | ||||
−0.453013 | + | 0.891504i | \(0.649651\pi\) | |||||||
\(822\) | 16.0351 | 0.559288 | ||||||||
\(823\) | −45.0110 | −1.56899 | −0.784493 | − | 0.620138i | \(-0.787077\pi\) | ||||
−0.784493 | + | 0.620138i | \(0.787077\pi\) | |||||||
\(824\) | −7.84524 | −0.273302 | ||||||||
\(825\) | −2.30541 | −0.0802640 | ||||||||
\(826\) | 1.28312 | 0.0446454 | ||||||||
\(827\) | 16.8429 | 0.585684 | 0.292842 | − | 0.956161i | \(-0.405399\pi\) | ||||
0.292842 | + | 0.956161i | \(0.405399\pi\) | |||||||
\(828\) | 6.80066 | 0.236339 | ||||||||
\(829\) | 13.0000 | 0.451509 | 0.225754 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225754 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(830\) | −39.9718 | −1.38744 | ||||||||
\(831\) | −18.7219 | −0.649457 | ||||||||
\(832\) | 1.65270 | 0.0572972 | ||||||||
\(833\) | 8.96316 | 0.310555 | ||||||||
\(834\) | −2.07873 | −0.0719804 | ||||||||
\(835\) | −45.7033 | −1.58163 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.59627 | −0.0551750 | ||||||||
\(838\) | 23.4989 | 0.811755 | ||||||||
\(839\) | −1.34049 | −0.0462788 | −0.0231394 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231394 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(840\) | 9.82295 | 0.338924 | ||||||||
\(841\) | 11.3865 | 0.392638 | ||||||||
\(842\) | 23.0729 | 0.795143 | ||||||||
\(843\) | 10.6382 | 0.366398 | ||||||||
\(844\) | 16.6382 | 0.572709 | ||||||||
\(845\) | 35.0310 | 1.20510 | ||||||||
\(846\) | 5.59627 | 0.192404 | ||||||||
\(847\) | 31.3259 | 1.07637 | ||||||||
\(848\) | −1.98040 | −0.0680072 | ||||||||
\(849\) | −14.0128 | −0.480918 | ||||||||
\(850\) | 46.0925 | 1.58096 | ||||||||
\(851\) | 76.2499 | 2.61381 | ||||||||
\(852\) | 16.6236 | 0.569515 | ||||||||
\(853\) | −7.94532 | −0.272042 | −0.136021 | − | 0.990706i | \(-0.543432\pi\) | ||||
−0.136021 | + | 0.990706i | \(0.543432\pi\) | |||||||
\(854\) | 36.0847 | 1.23479 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0273411 | 0.000934501 0 | ||||||||
\(857\) | −47.8759 | −1.63541 | −0.817704 | − | 0.575638i | \(-0.804754\pi\) | ||||
−0.817704 | + | 0.575638i | \(0.804754\pi\) | |||||||
\(858\) | −0.573978 | −0.0195953 | ||||||||
\(859\) | 1.63722 | 0.0558613 | 0.0279306 | − | 0.999610i | \(-0.491108\pi\) | ||||
0.0279306 | + | 0.999610i | \(0.491108\pi\) | |||||||
\(860\) | −7.78880 | −0.265596 | ||||||||
\(861\) | −10.0496 | −0.342490 | ||||||||
\(862\) | 3.51485 | 0.119716 | ||||||||
\(863\) | −34.9231 | −1.18880 | −0.594399 | − | 0.804170i | \(-0.702610\pi\) | ||||
−0.594399 | + | 0.804170i | \(0.702610\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.48751 | −0.118579 | ||||||||
\(866\) | 34.1147 | 1.15927 | ||||||||
\(867\) | 31.2131 | 1.06005 | ||||||||
\(868\) | 4.59627 | 0.156007 | ||||||||
\(869\) | −3.79385 | −0.128698 | ||||||||
\(870\) | 21.6800 | 0.735022 | ||||||||
\(871\) | 1.78281 | 0.0604083 | ||||||||
\(872\) | 10.7733 | 0.364831 | ||||||||
\(873\) | −3.65270 | −0.123625 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0915 | 0.543993 | ||||||||
\(876\) | 12.4192 | 0.419606 | ||||||||
\(877\) | 6.37195 | 0.215165 | 0.107583 | − | 0.994196i | \(-0.465689\pi\) | ||||
0.107583 | + | 0.994196i | \(0.465689\pi\) | |||||||
\(878\) | −9.70140 | −0.327406 | ||||||||
\(879\) | 11.5202 | 0.388568 | ||||||||
\(880\) | 1.18479 | 0.0399393 | ||||||||
\(881\) | 5.27395 | 0.177684 | 0.0888419 | − | 0.996046i | \(-0.471683\pi\) | ||||
0.0888419 | + | 0.996046i | \(0.471683\pi\) | |||||||
\(882\) | 1.29086 | 0.0434655 | ||||||||
\(883\) | −3.25133 | −0.109416 | −0.0547081 | − | 0.998502i | \(-0.517423\pi\) | ||||
−0.0547081 | + | 0.998502i | \(0.517423\pi\) | |||||||
\(884\) | 11.4757 | 0.385968 | ||||||||
\(885\) | 1.52023 | 0.0511019 | ||||||||
\(886\) | 15.1821 | 0.510053 | ||||||||
\(887\) | 22.3705 | 0.751129 | 0.375564 | − | 0.926796i | \(-0.377449\pi\) | ||||
0.375564 | + | 0.926796i | \(0.377449\pi\) | |||||||
\(888\) | 11.2121 | 0.376255 | ||||||||
\(889\) | 46.6810 | 1.56563 | ||||||||
\(890\) | 6.11650 | 0.205025 | ||||||||
\(891\) | −0.347296 | −0.0116349 | ||||||||
\(892\) | 8.17024 | 0.273560 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.66725 | −0.0557612 | ||||||||
\(895\) | 6.94263 | 0.232067 | ||||||||
\(896\) | −2.87939 | −0.0961935 | ||||||||
\(897\) | 11.2395 | 0.375275 | ||||||||
\(898\) | −34.8384 | −1.16257 | ||||||||
\(899\) | 10.1443 | 0.338332 | ||||||||
\(900\) | 6.63816 | 0.221272 | ||||||||
\(901\) | −13.7510 | −0.458113 | ||||||||
\(902\) | −1.21213 | −0.0403596 | ||||||||
\(903\) | −6.57398 | −0.218768 | ||||||||
\(904\) | 11.6604 | 0.387821 | ||||||||
\(905\) | 76.0883 | 2.52926 | ||||||||
\(906\) | −20.0523 | −0.666194 | ||||||||
\(907\) | −3.15745 | −0.104841 | −0.0524207 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524207 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(908\) | −1.80066 | −0.0597570 | ||||||||
\(909\) | −9.90673 | −0.328585 | ||||||||
\(910\) | 16.2344 | 0.538166 | ||||||||
\(911\) | 44.3387 | 1.46901 | 0.734504 | − | 0.678604i | \(-0.237415\pi\) | ||||
0.734504 | + | 0.678604i | \(0.237415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.06923 | −0.134672 | ||||||||
\(914\) | −31.8749 | −1.05433 | ||||||||
\(915\) | 42.7529 | 1.41337 | ||||||||
\(916\) | −18.7392 | −0.619160 | ||||||||
\(917\) | 8.06418 | 0.266303 | ||||||||
\(918\) | 6.94356 | 0.229172 | ||||||||
\(919\) | 14.2044 | 0.468560 | 0.234280 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234280 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(920\) | −23.2003 | −0.764890 | ||||||||
\(921\) | −4.29767 | −0.141613 | ||||||||
\(922\) | −10.6895 | −0.352041 | ||||||||
\(923\) | 27.4739 | 0.904314 | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | 74.4279 | 2.44717 | ||||||||
\(926\) | 15.3182 | 0.503387 | ||||||||
\(927\) | −7.84524 | −0.257671 | ||||||||
\(928\) | −6.35504 | −0.208614 | ||||||||
\(929\) | −15.4266 | −0.506131 | −0.253066 | − | 0.967449i | \(-0.581439\pi\) | ||||
−0.253066 | + | 0.967449i | \(0.581439\pi\) | |||||||
\(930\) | 5.44562 | 0.178569 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.09833 | −0.134245 | ||||||||
\(933\) | −22.9932 | −0.752763 | ||||||||
\(934\) | 28.5125 | 0.932957 | ||||||||
\(935\) | 8.22668 | 0.269041 | ||||||||
\(936\) | 1.65270 | 0.0540203 | ||||||||
\(937\) | −9.69696 | −0.316786 | −0.158393 | − | 0.987376i | \(-0.550631\pi\) | ||||
−0.158393 | + | 0.987376i | \(0.550631\pi\) | |||||||
\(938\) | −3.10607 | −0.101417 | ||||||||
\(939\) | −9.20977 | −0.300549 | ||||||||
\(940\) | −19.0915 | −0.622697 | ||||||||
\(941\) | 17.9855 | 0.586309 | 0.293154 | − | 0.956065i | \(-0.405295\pi\) | ||||
0.293154 | + | 0.956065i | \(0.405295\pi\) | |||||||
\(942\) | −4.09833 | −0.133531 | ||||||||
\(943\) | 23.7357 | 0.772939 | ||||||||
\(944\) | −0.445622 | −0.0145038 | ||||||||
\(945\) | 9.82295 | 0.319541 | ||||||||
\(946\) | −0.792919 | −0.0257800 | ||||||||
\(947\) | 2.19396 | 0.0712942 | 0.0356471 | − | 0.999364i | \(-0.488651\pi\) | ||||
0.0356471 | + | 0.999364i | \(0.488651\pi\) | |||||||
\(948\) | 10.9240 | 0.354794 | ||||||||
\(949\) | 20.5253 | 0.666279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.35504 | −0.108795 | ||||||||
\(952\) | −19.9932 | −0.647983 | ||||||||
\(953\) | 11.3108 | 0.366392 | 0.183196 | − | 0.983076i | \(-0.441356\pi\) | ||||
0.183196 | + | 0.983076i | \(0.441356\pi\) | |||||||
\(954\) | −1.98040 | −0.0641178 | ||||||||
\(955\) | −36.7965 | −1.19071 | ||||||||
\(956\) | −28.2276 | −0.912946 | ||||||||
\(957\) | 2.20708 | 0.0713448 | ||||||||
\(958\) | 8.05138 | 0.260128 | ||||||||
\(959\) | −46.1712 | −1.49095 | ||||||||
\(960\) | −3.41147 | −0.110105 | ||||||||
\(961\) | −28.4519 | −0.917804 | ||||||||
\(962\) | 18.5303 | 0.597442 | ||||||||
\(963\) | 0.0273411 | 0.000881056 0 | ||||||||
\(964\) | −6.56212 | −0.211352 | ||||||||
\(965\) | −9.77332 | −0.314614 | ||||||||
\(966\) | −19.5817 | −0.630031 | ||||||||
\(967\) | 46.7844 | 1.50448 | 0.752242 | − | 0.658887i | \(-0.228973\pi\) | ||||
0.752242 | + | 0.658887i | \(0.228973\pi\) | |||||||
\(968\) | −10.8794 | −0.349677 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.4611 | 0.400102 | ||||||||
\(971\) | −60.3715 | −1.93741 | −0.968706 | − | 0.248211i | \(-0.920157\pi\) | ||||
−0.968706 | + | 0.248211i | \(0.920157\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 5.98545 | 0.191885 | ||||||||
\(974\) | −6.11556 | −0.195955 | ||||||||
\(975\) | 10.9709 | 0.351350 | ||||||||
\(976\) | −12.5321 | −0.401142 | ||||||||
\(977\) | −22.7956 | −0.729296 | −0.364648 | − | 0.931145i | \(-0.618811\pi\) | ||||
−0.364648 | + | 0.931145i | \(0.618811\pi\) | |||||||
\(978\) | −8.13516 | −0.260134 | ||||||||
\(979\) | 0.622674 | 0.0199008 | ||||||||
\(980\) | −4.40373 | −0.140672 | ||||||||
\(981\) | 10.7733 | 0.343966 | ||||||||
\(982\) | −22.6851 | −0.723911 | ||||||||
\(983\) | 30.7929 | 0.982142 | 0.491071 | − | 0.871120i | \(-0.336606\pi\) | ||||
0.491071 | + | 0.871120i | \(0.336606\pi\) | |||||||
\(984\) | 3.49020 | 0.111264 | ||||||||
\(985\) | 28.4361 | 0.906050 | ||||||||
\(986\) | −44.1266 | −1.40528 | ||||||||
\(987\) | −16.1138 | −0.512908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.5267 | 0.493721 | ||||||||
\(990\) | 1.18479 | 0.0376552 | ||||||||
\(991\) | 38.1789 | 1.21279 | 0.606397 | − | 0.795162i | \(-0.292614\pi\) | ||||
0.606397 | + | 0.795162i | \(0.292614\pi\) | |||||||
\(992\) | −1.59627 | −0.0506815 | ||||||||
\(993\) | 22.0743 | 0.700506 | ||||||||
\(994\) | −47.8658 | −1.51821 | ||||||||
\(995\) | 10.3509 | 0.328146 | ||||||||
\(996\) | 11.7169 | 0.371264 | ||||||||
\(997\) | 30.9489 | 0.980163 | 0.490081 | − | 0.871677i | \(-0.336967\pi\) | ||||
0.490081 | + | 0.871677i | \(0.336967\pi\) | |||||||
\(998\) | 24.8557 | 0.786792 | ||||||||
\(999\) | 11.2121 | 0.354736 |
(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 | 2166.2.a.u.1.1 | 3 | ||
3.2 | odd | 2 | 6498.2.a.bn.1.3 | 3 | |||
19.3 | odd | 18 | 114.2.i.d.85.1 | yes | 6 | ||
19.13 | odd | 18 | 114.2.i.d.55.1 | ✓ | 6 | ||
19.18 | odd | 2 | 2166.2.a.o.1.1 | 3 | |||
57.32 | even | 18 | 342.2.u.a.55.1 | 6 | |||
57.41 | even | 18 | 342.2.u.a.199.1 | 6 | |||
57.56 | even | 2 | 6498.2.a.bs.1.3 | 3 | |||
76.3 | even | 18 | 912.2.bo.f.769.1 | 6 | |||
76.51 | even | 18 | 912.2.bo.f.625.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.d.55.1 | ✓ | 6 | 19.13 | odd | 18 | ||
114.2.i.d.85.1 | yes | 6 | 19.3 | odd | 18 | ||
342.2.u.a.55.1 | 6 | 57.32 | even | 18 | |||
342.2.u.a.199.1 | 6 | 57.41 | even | 18 | |||
912.2.bo.f.625.1 | 6 | 76.51 | even | 18 | |||
912.2.bo.f.769.1 | 6 | 76.3 | even | 18 | |||
2166.2.a.o.1.1 | 3 | 19.18 | odd | 2 | |||
2166.2.a.u.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6498.2.a.bn.1.3 | 3 | 3.2 | odd | 2 | |||
6498.2.a.bs.1.3 | 3 | 57.56 | even | 2 |