Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 17x^{6} - 2x^{5} + 71x^{4} - 18x^{3} - 81x^{2} + 36x + 9 \) |
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 | 1.5 | ||
Root | \(0.854224\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.854224 | 0.382021 | 0.191010 | − | 0.981588i | \(-0.438824\pi\) | ||||
0.191010 | + | 0.981588i | \(0.438824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.727081 | 0.274811 | 0.137405 | − | 0.990515i | \(-0.456124\pi\) | ||||
0.137405 | + | 0.990515i | \(0.456124\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.854224 | −0.270129 | ||||||||
\(11\) | −4.77784 | −1.44057 | −0.720286 | − | 0.693677i | \(-0.755989\pi\) | ||||
−0.720286 | + | 0.693677i | \(0.755989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.670363 | 0.185925 | 0.0929626 | − | 0.995670i | \(-0.470366\pi\) | ||||
0.0929626 | + | 0.995670i | \(0.470366\pi\) | |||||||
\(14\) | −0.727081 | −0.194321 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.231641 | 0.0561811 | 0.0280906 | − | 0.999605i | \(-0.491057\pi\) | ||||
0.0280906 | + | 0.999605i | \(0.491057\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.18376 | −1.18924 | −0.594618 | − | 0.804008i | \(-0.702697\pi\) | ||||
−0.594618 | + | 0.804008i | \(0.702697\pi\) | |||||||
\(20\) | 0.854224 | 0.191010 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.77784 | 1.01864 | ||||||||
\(23\) | 7.77399 | 1.62099 | 0.810494 | − | 0.585747i | \(-0.199199\pi\) | ||||
0.810494 | + | 0.585747i | \(0.199199\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.27030 | −0.854060 | ||||||||
\(26\) | −0.670363 | −0.131469 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.727081 | 0.137405 | ||||||||
\(29\) | 7.62010 | 1.41502 | 0.707509 | − | 0.706704i | \(-0.249819\pi\) | ||||
0.707509 | + | 0.706704i | \(0.249819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13797 | −0.563595 | −0.281798 | − | 0.959474i | \(-0.590931\pi\) | ||||
−0.281798 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.231641 | −0.0397261 | ||||||||
\(35\) | 0.621090 | 0.104983 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.35811 | −0.387671 | −0.193836 | − | 0.981034i | \(-0.562093\pi\) | ||||
−0.193836 | + | 0.981034i | \(0.562093\pi\) | |||||||
\(38\) | 5.18376 | 0.840917 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.854224 | −0.135065 | ||||||||
\(41\) | −0.350412 | −0.0547252 | −0.0273626 | − | 0.999626i | \(-0.508711\pi\) | ||||
−0.0273626 | + | 0.999626i | \(0.508711\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.96304 | −0.451860 | −0.225930 | − | 0.974144i | \(-0.572542\pi\) | ||||
−0.225930 | + | 0.974144i | \(0.572542\pi\) | |||||||
\(44\) | −4.77784 | −0.720286 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.77399 | −1.14621 | ||||||||
\(47\) | 12.9412 | 1.88767 | 0.943834 | − | 0.330421i | \(-0.107191\pi\) | ||||
0.943834 | + | 0.330421i | \(0.107191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47135 | −0.924479 | ||||||||
\(50\) | 4.27030 | 0.603912 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.670363 | 0.0929626 | ||||||||
\(53\) | −7.38511 | −1.01442 | −0.507212 | − | 0.861822i | \(-0.669324\pi\) | ||||
−0.507212 | + | 0.861822i | \(0.669324\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.08134 | −0.550328 | ||||||||
\(56\) | −0.727081 | −0.0971603 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.62010 | −1.00057 | ||||||||
\(59\) | −1.60351 | −0.208759 | −0.104379 | − | 0.994538i | \(-0.533286\pi\) | ||||
−0.104379 | + | 0.994538i | \(0.533286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0488 | 1.41465 | 0.707326 | − | 0.706887i | \(-0.249901\pi\) | ||||
0.707326 | + | 0.706887i | \(0.249901\pi\) | |||||||
\(62\) | 3.13797 | 0.398522 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.572640 | 0.0710273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.83357 | 1.20136 | 0.600681 | − | 0.799489i | \(-0.294896\pi\) | ||||
0.600681 | + | 0.799489i | \(0.294896\pi\) | |||||||
\(68\) | 0.231641 | 0.0280906 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.621090 | −0.0742345 | ||||||||
\(71\) | 10.3649 | 1.23008 | 0.615042 | − | 0.788495i | \(-0.289139\pi\) | ||||
0.615042 | + | 0.788495i | \(0.289139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.70538 | −0.550723 | −0.275361 | − | 0.961341i | \(-0.588797\pi\) | ||||
−0.275361 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(74\) | 2.35811 | 0.274125 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.18376 | −0.594618 | ||||||||
\(77\) | −3.47387 | −0.395885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.56476 | −0.851102 | −0.425551 | − | 0.904934i | \(-0.639920\pi\) | ||||
−0.425551 | + | 0.904934i | \(0.639920\pi\) | |||||||
\(80\) | 0.854224 | 0.0955052 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.350412 | 0.0386966 | ||||||||
\(83\) | −0.603787 | −0.0662742 | −0.0331371 | − | 0.999451i | \(-0.510550\pi\) | ||||
−0.0331371 | + | 0.999451i | \(0.510550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.197873 | 0.0214624 | ||||||||
\(86\) | 2.96304 | 0.319513 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.77784 | 0.509319 | ||||||||
\(89\) | 4.00132 | 0.424139 | 0.212070 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212070 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.487408 | 0.0510943 | ||||||||
\(92\) | 7.77399 | 0.810494 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.9412 | −1.33478 | ||||||||
\(95\) | −4.42810 | −0.454313 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.56015 | −0.463013 | −0.231507 | − | 0.972833i | \(-0.574366\pi\) | ||||
−0.231507 | + | 0.972833i | \(0.574366\pi\) | |||||||
\(98\) | 6.47135 | 0.653705 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.27030 | −0.427030 | ||||||||
\(101\) | 1.17615 | 0.117031 | 0.0585156 | − | 0.998286i | \(-0.481363\pi\) | ||||
0.0585156 | + | 0.998286i | \(0.481363\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6760 | −1.05194 | −0.525970 | − | 0.850503i | \(-0.676298\pi\) | ||||
−0.525970 | + | 0.850503i | \(0.676298\pi\) | |||||||
\(104\) | −0.670363 | −0.0657345 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.38511 | 0.717305 | ||||||||
\(107\) | −4.79486 | −0.463536 | −0.231768 | − | 0.972771i | \(-0.574451\pi\) | ||||
−0.231768 | + | 0.972771i | \(0.574451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.76535 | 0.169090 | 0.0845448 | − | 0.996420i | \(-0.473056\pi\) | ||||
0.0845448 | + | 0.996420i | \(0.473056\pi\) | |||||||
\(110\) | 4.08134 | 0.389141 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.727081 | 0.0687027 | ||||||||
\(113\) | −14.2839 | −1.34371 | −0.671857 | − | 0.740681i | \(-0.734503\pi\) | ||||
−0.671857 | + | 0.740681i | \(0.734503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.64073 | 0.619251 | ||||||||
\(116\) | 7.62010 | 0.707509 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.60351 | 0.147615 | ||||||||
\(119\) | 0.168422 | 0.0154392 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8277 | 1.07525 | ||||||||
\(122\) | −11.0488 | −1.00031 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.13797 | −0.281798 | ||||||||
\(125\) | −7.91892 | −0.708289 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1662 | −1.07958 | −0.539789 | − | 0.841800i | \(-0.681496\pi\) | ||||
−0.539789 | + | 0.841800i | \(0.681496\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.572640 | −0.0502239 | ||||||||
\(131\) | −18.7356 | −1.63694 | −0.818470 | − | 0.574549i | \(-0.805178\pi\) | ||||
−0.818470 | + | 0.574549i | \(0.805178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.76902 | −0.326815 | ||||||||
\(134\) | −9.83357 | −0.849491 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.231641 | −0.0198630 | ||||||||
\(137\) | 6.33265 | 0.541035 | 0.270517 | − | 0.962715i | \(-0.412805\pi\) | ||||
0.270517 | + | 0.962715i | \(0.412805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6958 | 1.50094 | 0.750470 | − | 0.660904i | \(-0.229827\pi\) | ||||
0.750470 | + | 0.660904i | \(0.229827\pi\) | |||||||
\(140\) | 0.621090 | 0.0524917 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3649 | −0.869800 | ||||||||
\(143\) | −3.20288 | −0.267839 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.50928 | 0.540566 | ||||||||
\(146\) | 4.70538 | 0.389420 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.35811 | −0.193836 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.78677 | −0.796436 | −0.398218 | − | 0.917291i | \(-0.630371\pi\) | ||||
−0.398218 | + | 0.917291i | \(0.630371\pi\) | |||||||
\(152\) | 5.18376 | 0.420459 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.47387 | 0.279933 | ||||||||
\(155\) | −2.68053 | −0.215305 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.3607 | −1.70477 | −0.852384 | − | 0.522916i | \(-0.824844\pi\) | ||||
−0.852384 | + | 0.522916i | \(0.824844\pi\) | |||||||
\(158\) | 7.56476 | 0.601820 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.854224 | −0.0675324 | ||||||||
\(161\) | 5.65232 | 0.445465 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.23469 | 0.410013 | 0.205006 | − | 0.978761i | \(-0.434278\pi\) | ||||
0.205006 | + | 0.978761i | \(0.434278\pi\) | |||||||
\(164\) | −0.350412 | −0.0273626 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.603787 | 0.0468630 | ||||||||
\(167\) | −24.8724 | −1.92469 | −0.962343 | − | 0.271839i | \(-0.912368\pi\) | ||||
−0.962343 | + | 0.271839i | \(0.912368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5506 | −0.965432 | ||||||||
\(170\) | −0.197873 | −0.0151762 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.96304 | −0.225930 | ||||||||
\(173\) | −13.4677 | −1.02393 | −0.511965 | − | 0.859006i | \(-0.671082\pi\) | ||||
−0.511965 | + | 0.859006i | \(0.671082\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.10485 | −0.234705 | ||||||||
\(176\) | −4.77784 | −0.360143 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.00132 | −0.299912 | ||||||||
\(179\) | 0.661451 | 0.0494392 | 0.0247196 | − | 0.999694i | \(-0.492131\pi\) | ||||
0.0247196 | + | 0.999694i | \(0.492131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.6399 | −1.23683 | −0.618415 | − | 0.785851i | \(-0.712225\pi\) | ||||
−0.618415 | + | 0.785851i | \(0.712225\pi\) | |||||||
\(182\) | −0.487408 | −0.0361291 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.77399 | −0.573106 | ||||||||
\(185\) | −2.01436 | −0.148098 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.10674 | −0.0809329 | ||||||||
\(188\) | 12.9412 | 0.943834 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.42810 | 0.321248 | ||||||||
\(191\) | 9.87624 | 0.714620 | 0.357310 | − | 0.933986i | \(-0.383694\pi\) | ||||
0.357310 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6732 | −0.984220 | −0.492110 | − | 0.870533i | \(-0.663774\pi\) | ||||
−0.492110 | + | 0.870533i | \(0.663774\pi\) | |||||||
\(194\) | 4.56015 | 0.327400 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47135 | −0.462240 | ||||||||
\(197\) | −17.4921 | −1.24626 | −0.623131 | − | 0.782118i | \(-0.714140\pi\) | ||||
−0.623131 | + | 0.782118i | \(0.714140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.45845 | −0.528715 | −0.264358 | − | 0.964425i | \(-0.585160\pi\) | ||||
−0.264358 | + | 0.964425i | \(0.585160\pi\) | |||||||
\(200\) | 4.27030 | 0.301956 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.17615 | −0.0827535 | ||||||||
\(203\) | 5.54043 | 0.388862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.299331 | −0.0209062 | ||||||||
\(206\) | 10.6760 | 0.743834 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.670363 | 0.0464813 | ||||||||
\(209\) | 24.7672 | 1.71318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2465 | 1.11845 | 0.559227 | − | 0.829014i | \(-0.311098\pi\) | ||||
0.559227 | + | 0.829014i | \(0.311098\pi\) | |||||||
\(212\) | −7.38511 | −0.507212 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.79486 | 0.327770 | ||||||||
\(215\) | −2.53110 | −0.172620 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.28155 | −0.154882 | ||||||||
\(218\) | −1.76535 | −0.119564 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.08134 | −0.275164 | ||||||||
\(221\) | 0.155283 | 0.0104455 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.84038 | −0.458065 | −0.229033 | − | 0.973419i | \(-0.573556\pi\) | ||||
−0.229033 | + | 0.973419i | \(0.573556\pi\) | |||||||
\(224\) | −0.727081 | −0.0485801 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.2839 | 0.950149 | ||||||||
\(227\) | −5.73148 | −0.380412 | −0.190206 | − | 0.981744i | \(-0.560916\pi\) | ||||
−0.190206 | + | 0.981744i | \(0.560916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.17916 | −0.144003 | −0.0720016 | − | 0.997405i | \(-0.522939\pi\) | ||||
−0.0720016 | + | 0.997405i | \(0.522939\pi\) | |||||||
\(230\) | −6.64073 | −0.437877 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.62010 | −0.500284 | ||||||||
\(233\) | 0.993187 | 0.0650659 | 0.0325329 | − | 0.999471i | \(-0.489643\pi\) | ||||
0.0325329 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0547 | 0.721128 | ||||||||
\(236\) | −1.60351 | −0.104379 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.168422 | −0.0109171 | ||||||||
\(239\) | 12.0854 | 0.781739 | 0.390869 | − | 0.920446i | \(-0.372174\pi\) | ||||
0.390869 | + | 0.920446i | \(0.372174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.47303 | 0.223718 | 0.111859 | − | 0.993724i | \(-0.464320\pi\) | ||||
0.111859 | + | 0.993724i | \(0.464320\pi\) | |||||||
\(242\) | −11.8277 | −0.760314 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0488 | 0.707326 | ||||||||
\(245\) | −5.52799 | −0.353170 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.47500 | −0.221109 | ||||||||
\(248\) | 3.13797 | 0.199261 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.91892 | 0.500836 | ||||||||
\(251\) | 26.4004 | 1.66638 | 0.833189 | − | 0.552988i | \(-0.186512\pi\) | ||||
0.833189 | + | 0.552988i | \(0.186512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.1428 | −2.33515 | ||||||||
\(254\) | 12.1662 | 0.763377 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.12809 | −0.382260 | −0.191130 | − | 0.981565i | \(-0.561215\pi\) | ||||
−0.191130 | + | 0.981565i | \(0.561215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.71454 | −0.106536 | ||||||||
\(260\) | 0.572640 | 0.0355137 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.7356 | 1.15749 | ||||||||
\(263\) | 5.97299 | 0.368310 | 0.184155 | − | 0.982897i | \(-0.441045\pi\) | ||||
0.184155 | + | 0.982897i | \(0.441045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.30854 | −0.387531 | ||||||||
\(266\) | 3.76902 | 0.231093 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.83357 | 0.600681 | ||||||||
\(269\) | −24.5254 | −1.49534 | −0.747669 | − | 0.664072i | \(-0.768827\pi\) | ||||
−0.747669 | + | 0.664072i | \(0.768827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.1399 | 1.70938 | 0.854688 | − | 0.519142i | \(-0.173748\pi\) | ||||
0.854688 | + | 0.519142i | \(0.173748\pi\) | |||||||
\(272\) | 0.231641 | 0.0140453 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.33265 | −0.382569 | ||||||||
\(275\) | 20.4028 | 1.23033 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.98202 | −0.539677 | −0.269839 | − | 0.962906i | \(-0.586970\pi\) | ||||
−0.269839 | + | 0.962906i | \(0.586970\pi\) | |||||||
\(278\) | −17.6958 | −1.06133 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.621090 | −0.0371172 | ||||||||
\(281\) | −11.1755 | −0.666674 | −0.333337 | − | 0.942808i | \(-0.608175\pi\) | ||||
−0.333337 | + | 0.942808i | \(0.608175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9249 | 0.887192 | 0.443596 | − | 0.896227i | \(-0.353702\pi\) | ||||
0.443596 | + | 0.896227i | \(0.353702\pi\) | |||||||
\(284\) | 10.3649 | 0.615042 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.20288 | 0.189391 | ||||||||
\(287\) | −0.254778 | −0.0150391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9463 | −0.996844 | ||||||||
\(290\) | −6.50928 | −0.382238 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.70538 | −0.275361 | ||||||||
\(293\) | 26.6015 | 1.55408 | 0.777039 | − | 0.629453i | \(-0.216721\pi\) | ||||
0.777039 | + | 0.629453i | \(0.216721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.36976 | −0.0797503 | ||||||||
\(296\) | 2.35811 | 0.137062 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 5.21139 | 0.301383 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.15437 | −0.124176 | ||||||||
\(302\) | 9.78677 | 0.563166 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.18376 | −0.297309 | ||||||||
\(305\) | 9.43814 | 0.540426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.45072 | 0.0827969 | 0.0413985 | − | 0.999143i | \(-0.486819\pi\) | ||||
0.0413985 | + | 0.999143i | \(0.486819\pi\) | |||||||
\(308\) | −3.47387 | −0.197942 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.68053 | 0.152244 | ||||||||
\(311\) | −3.25940 | −0.184823 | −0.0924117 | − | 0.995721i | \(-0.529458\pi\) | ||||
−0.0924117 | + | 0.995721i | \(0.529458\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.77542 | 0.100353 | 0.0501763 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501763 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(314\) | 21.3607 | 1.20545 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.56476 | −0.425551 | ||||||||
\(317\) | 1.58023 | 0.0887547 | 0.0443773 | − | 0.999015i | \(-0.485870\pi\) | ||||
0.0443773 | + | 0.999015i | \(0.485870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.4076 | −2.03843 | ||||||||
\(320\) | 0.854224 | 0.0477526 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.65232 | −0.314991 | ||||||||
\(323\) | −1.20077 | −0.0668127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.86265 | −0.158791 | ||||||||
\(326\) | −5.23469 | −0.289923 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.350412 | 0.0193483 | ||||||||
\(329\) | 9.40930 | 0.518751 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1065 | −0.610469 | −0.305235 | − | 0.952277i | \(-0.598735\pi\) | ||||
−0.305235 | + | 0.952277i | \(0.598735\pi\) | |||||||
\(332\) | −0.603787 | −0.0331371 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.8724 | 1.36096 | ||||||||
\(335\) | 8.40007 | 0.458945 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1798 | −0.772423 | −0.386212 | − | 0.922410i | \(-0.626217\pi\) | ||||
−0.386212 | + | 0.922410i | \(0.626217\pi\) | |||||||
\(338\) | 12.5506 | 0.682663 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.197873 | 0.0107312 | ||||||||
\(341\) | 14.9927 | 0.811899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.79476 | −0.528868 | ||||||||
\(344\) | 2.96304 | 0.159757 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4677 | 0.724027 | ||||||||
\(347\) | 16.8746 | 0.905877 | 0.452938 | − | 0.891542i | \(-0.350376\pi\) | ||||
0.452938 | + | 0.891542i | \(0.350376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.49710 | −0.401310 | −0.200655 | − | 0.979662i | \(-0.564307\pi\) | ||||
−0.200655 | + | 0.979662i | \(0.564307\pi\) | |||||||
\(350\) | 3.10485 | 0.165961 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.77784 | 0.254659 | ||||||||
\(353\) | −2.81437 | −0.149794 | −0.0748968 | − | 0.997191i | \(-0.523863\pi\) | ||||
−0.0748968 | + | 0.997191i | \(0.523863\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.85392 | 0.469917 | ||||||||
\(356\) | 4.00132 | 0.212070 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.661451 | −0.0349588 | ||||||||
\(359\) | −2.13488 | −0.112674 | −0.0563372 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563372 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.87140 | 0.414284 | ||||||||
\(362\) | 16.6399 | 0.874571 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.487408 | 0.0255471 | ||||||||
\(365\) | −4.01945 | −0.210387 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7363 | −0.925828 | −0.462914 | − | 0.886403i | \(-0.653196\pi\) | ||||
−0.462914 | + | 0.886403i | \(0.653196\pi\) | |||||||
\(368\) | 7.77399 | 0.405247 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.01436 | 0.104721 | ||||||||
\(371\) | −5.36957 | −0.278774 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.3027 | −1.72435 | −0.862175 | − | 0.506610i | \(-0.830898\pi\) | ||||
−0.862175 | + | 0.506610i | \(0.830898\pi\) | |||||||
\(374\) | 1.10674 | 0.0572282 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.9412 | −0.667391 | ||||||||
\(377\) | 5.10824 | 0.263088 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1957 | −0.523718 | −0.261859 | − | 0.965106i | \(-0.584336\pi\) | ||||
−0.261859 | + | 0.965106i | \(0.584336\pi\) | |||||||
\(380\) | −4.42810 | −0.227157 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.87624 | −0.505312 | ||||||||
\(383\) | −25.9640 | −1.32670 | −0.663348 | − | 0.748311i | \(-0.730865\pi\) | ||||
−0.663348 | + | 0.748311i | \(0.730865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.96747 | −0.151236 | ||||||||
\(386\) | 13.6732 | 0.695949 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.56015 | −0.231507 | ||||||||
\(389\) | −4.83469 | −0.245129 | −0.122564 | − | 0.992461i | \(-0.539112\pi\) | ||||
−0.122564 | + | 0.992461i | \(0.539112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.80077 | 0.0910689 | ||||||||
\(392\) | 6.47135 | 0.326853 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.4921 | 0.881240 | ||||||||
\(395\) | −6.46200 | −0.325139 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9337 | 1.00044 | 0.500221 | − | 0.865898i | \(-0.333252\pi\) | ||||
0.500221 | + | 0.865898i | \(0.333252\pi\) | |||||||
\(398\) | 7.45845 | 0.373858 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.27030 | −0.213515 | ||||||||
\(401\) | −4.33155 | −0.216307 | −0.108154 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108154 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.10358 | −0.104787 | ||||||||
\(404\) | 1.17615 | 0.0585156 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.54043 | −0.274967 | ||||||||
\(407\) | 11.2667 | 0.558468 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.5272 | −1.46002 | −0.730012 | − | 0.683434i | \(-0.760486\pi\) | ||||
−0.730012 | + | 0.683434i | \(0.760486\pi\) | |||||||
\(410\) | 0.299331 | 0.0147829 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.6760 | −0.525970 | ||||||||
\(413\) | −1.16588 | −0.0573692 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.515769 | −0.0253181 | ||||||||
\(416\) | −0.670363 | −0.0328673 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −24.7672 | −1.21140 | ||||||||
\(419\) | 22.5113 | 1.09975 | 0.549874 | − | 0.835248i | \(-0.314676\pi\) | ||||
0.549874 | + | 0.835248i | \(0.314676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0732 | 0.783360 | 0.391680 | − | 0.920101i | \(-0.371894\pi\) | ||||
0.391680 | + | 0.920101i | \(0.371894\pi\) | |||||||
\(422\) | −16.2465 | −0.790867 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.38511 | 0.358653 | ||||||||
\(425\) | −0.989175 | −0.0479821 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.03336 | 0.388762 | ||||||||
\(428\) | −4.79486 | −0.231768 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.53110 | 0.122061 | ||||||||
\(431\) | −35.7406 | −1.72157 | −0.860783 | − | 0.508973i | \(-0.830025\pi\) | ||||
−0.860783 | + | 0.508973i | \(0.830025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.3282 | 1.40943 | 0.704713 | − | 0.709493i | \(-0.251076\pi\) | ||||
0.704713 | + | 0.709493i | \(0.251076\pi\) | |||||||
\(434\) | 2.28155 | 0.109518 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.76535 | 0.0845448 | ||||||||
\(437\) | −40.2985 | −1.92774 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.48140 | −0.404795 | −0.202398 | − | 0.979303i | \(-0.564873\pi\) | ||||
−0.202398 | + | 0.979303i | \(0.564873\pi\) | |||||||
\(440\) | 4.08134 | 0.194570 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.155283 | −0.00738608 | ||||||||
\(443\) | 29.2319 | 1.38885 | 0.694425 | − | 0.719565i | \(-0.255659\pi\) | ||||
0.694425 | + | 0.719565i | \(0.255659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.41802 | 0.162030 | ||||||||
\(446\) | 6.84038 | 0.323901 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.727081 | 0.0343513 | ||||||||
\(449\) | 23.7240 | 1.11961 | 0.559803 | − | 0.828626i | \(-0.310877\pi\) | ||||
0.559803 | + | 0.828626i | \(0.310877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67421 | 0.0788356 | ||||||||
\(452\) | −14.2839 | −0.671857 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.73148 | 0.268992 | ||||||||
\(455\) | 0.416356 | 0.0195191 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6691 | 0.920083 | 0.460042 | − | 0.887897i | \(-0.347835\pi\) | ||||
0.460042 | + | 0.887897i | \(0.347835\pi\) | |||||||
\(458\) | 2.17916 | 0.101826 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.64073 | 0.309626 | ||||||||
\(461\) | 2.86113 | 0.133256 | 0.0666280 | − | 0.997778i | \(-0.478776\pi\) | ||||
0.0666280 | + | 0.997778i | \(0.478776\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0230 | −0.930548 | −0.465274 | − | 0.885167i | \(-0.654044\pi\) | ||||
−0.465274 | + | 0.885167i | \(0.654044\pi\) | |||||||
\(464\) | 7.62010 | 0.353754 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.993187 | −0.0460085 | ||||||||
\(467\) | 28.7449 | 1.33015 | 0.665077 | − | 0.746775i | \(-0.268399\pi\) | ||||
0.665077 | + | 0.746775i | \(0.268399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.14980 | 0.330147 | ||||||||
\(470\) | −11.0547 | −0.509914 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.60351 | 0.0738074 | ||||||||
\(473\) | 14.1569 | 0.650936 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.1362 | 1.01568 | ||||||||
\(476\) | 0.168422 | 0.00771959 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0854 | −0.552773 | ||||||||
\(479\) | 19.5108 | 0.891471 | 0.445736 | − | 0.895165i | \(-0.352942\pi\) | ||||
0.445736 | + | 0.895165i | \(0.352942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.58079 | −0.0720779 | ||||||||
\(482\) | −3.47303 | −0.158192 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.8277 | 0.537623 | ||||||||
\(485\) | −3.89539 | −0.176881 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.99490 | 0.135712 | 0.0678559 | − | 0.997695i | \(-0.478384\pi\) | ||||
0.0678559 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(488\) | −11.0488 | −0.500155 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.52799 | 0.249729 | ||||||||
\(491\) | −43.3760 | −1.95753 | −0.978765 | − | 0.204985i | \(-0.934285\pi\) | ||||
−0.978765 | + | 0.204985i | \(0.934285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.76513 | 0.0794973 | ||||||||
\(494\) | 3.47500 | 0.156348 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.13797 | −0.140899 | ||||||||
\(497\) | 7.53610 | 0.338040 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.987622 | −0.0442120 | −0.0221060 | − | 0.999756i | \(-0.507037\pi\) | ||||
−0.0221060 | + | 0.999756i | \(0.507037\pi\) | |||||||
\(500\) | −7.91892 | −0.354145 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.4004 | −1.17831 | ||||||||
\(503\) | 2.91509 | 0.129977 | 0.0649887 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649887 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00469 | 0.0447083 | ||||||||
\(506\) | 37.1428 | 1.65120 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.1662 | −0.539789 | ||||||||
\(509\) | 4.42528 | 0.196147 | 0.0980735 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980735 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.42119 | −0.151345 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.12809 | 0.270299 | ||||||||
\(515\) | −9.11972 | −0.401863 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −61.8309 | −2.71932 | ||||||||
\(518\) | 1.71454 | 0.0753325 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.572640 | −0.0251119 | ||||||||
\(521\) | −32.7467 | −1.43466 | −0.717329 | − | 0.696734i | \(-0.754636\pi\) | ||||
−0.717329 | + | 0.696734i | \(0.754636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.4770 | 1.33267 | 0.666333 | − | 0.745655i | \(-0.267863\pi\) | ||||
0.666333 | + | 0.745655i | \(0.267863\pi\) | |||||||
\(524\) | −18.7356 | −0.818470 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.97299 | −0.260435 | ||||||||
\(527\) | −0.726880 | −0.0316634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.4349 | 1.62760 | ||||||||
\(530\) | 6.30854 | 0.274026 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.76902 | −0.163408 | ||||||||
\(533\) | −0.234904 | −0.0101748 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.09588 | −0.177080 | ||||||||
\(536\) | −9.83357 | −0.424745 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.5254 | 1.05736 | ||||||||
\(539\) | 30.9191 | 1.33178 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.2314 | −1.12778 | −0.563888 | − | 0.825851i | \(-0.690695\pi\) | ||||
−0.563888 | + | 0.825851i | \(0.690695\pi\) | |||||||
\(542\) | −28.1399 | −1.20871 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.231641 | −0.00993151 | ||||||||
\(545\) | 1.50800 | 0.0645957 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.202324 | 0.00865075 | 0.00432537 | − | 0.999991i | \(-0.498623\pi\) | ||||
0.00432537 | + | 0.999991i | \(0.498623\pi\) | |||||||
\(548\) | 6.33265 | 0.270517 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.4028 | −0.869978 | ||||||||
\(551\) | −39.5008 | −1.68279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.50020 | −0.233892 | ||||||||
\(554\) | 8.98202 | 0.381609 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6958 | 0.750470 | ||||||||
\(557\) | −28.3170 | −1.19983 | −0.599915 | − | 0.800064i | \(-0.704799\pi\) | ||||
−0.599915 | + | 0.800064i | \(0.704799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.98631 | −0.0840122 | ||||||||
\(560\) | 0.621090 | 0.0262459 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1755 | 0.471410 | ||||||||
\(563\) | −39.4649 | −1.66325 | −0.831623 | − | 0.555341i | \(-0.812588\pi\) | ||||
−0.831623 | + | 0.555341i | \(0.812588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2016 | −0.513327 | ||||||||
\(566\) | −14.9249 | −0.627340 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3649 | −0.434900 | ||||||||
\(569\) | −9.91014 | −0.415455 | −0.207727 | − | 0.978187i | \(-0.566607\pi\) | ||||
−0.207727 | + | 0.978187i | \(0.566607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50941 | 0.105016 | 0.0525078 | − | 0.998621i | \(-0.483279\pi\) | ||||
0.0525078 | + | 0.998621i | \(0.483279\pi\) | |||||||
\(572\) | −3.20288 | −0.133919 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.254778 | 0.0106342 | ||||||||
\(575\) | −33.1973 | −1.38442 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.25345 | −0.301965 | −0.150983 | − | 0.988536i | \(-0.548244\pi\) | ||||
−0.150983 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(578\) | 16.9463 | 0.704875 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.50928 | 0.270283 | ||||||||
\(581\) | −0.439002 | −0.0182129 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.2848 | 1.46135 | ||||||||
\(584\) | 4.70538 | 0.194710 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.6015 | −1.09890 | ||||||||
\(587\) | 17.7989 | 0.734639 | 0.367320 | − | 0.930095i | \(-0.380276\pi\) | ||||
0.367320 | + | 0.930095i | \(0.380276\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2665 | 0.670248 | ||||||||
\(590\) | 1.36976 | 0.0563919 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.35811 | −0.0969178 | ||||||||
\(593\) | −36.9970 | −1.51928 | −0.759642 | − | 0.650342i | \(-0.774626\pi\) | ||||
−0.759642 | + | 0.650342i | \(0.774626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.143870 | 0.00589809 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.21139 | −0.213110 | ||||||||
\(599\) | −14.7297 | −0.601839 | −0.300920 | − | 0.953650i | \(-0.597294\pi\) | ||||
−0.300920 | + | 0.953650i | \(0.597294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.3930 | −0.872639 | −0.436320 | − | 0.899792i | \(-0.643718\pi\) | ||||
−0.436320 | + | 0.899792i | \(0.643718\pi\) | |||||||
\(602\) | 2.15437 | 0.0878056 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.78677 | −0.398218 | ||||||||
\(605\) | 10.1035 | 0.410766 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4540 | 1.19550 | 0.597750 | − | 0.801682i | \(-0.296061\pi\) | ||||
0.597750 | + | 0.801682i | \(0.296061\pi\) | |||||||
\(608\) | 5.18376 | 0.210229 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.43814 | −0.382139 | ||||||||
\(611\) | 8.67530 | 0.350965 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.7334 | 1.48365 | 0.741825 | − | 0.670594i | \(-0.233961\pi\) | ||||
0.741825 | + | 0.670594i | \(0.233961\pi\) | |||||||
\(614\) | −1.45072 | −0.0585463 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.47387 | 0.139966 | ||||||||
\(617\) | 6.07036 | 0.244384 | 0.122192 | − | 0.992507i | \(-0.461008\pi\) | ||||
0.122192 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.7969 | −1.80054 | −0.900270 | − | 0.435333i | \(-0.856631\pi\) | ||||
−0.900270 | + | 0.435333i | \(0.856631\pi\) | |||||||
\(620\) | −2.68053 | −0.107653 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.25940 | 0.130690 | ||||||||
\(623\) | 2.90928 | 0.116558 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5870 | 0.583479 | ||||||||
\(626\) | −1.77542 | −0.0709600 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.3607 | −0.852384 | ||||||||
\(629\) | −0.546234 | −0.0217798 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.2177 | −1.48161 | −0.740807 | − | 0.671718i | \(-0.765557\pi\) | ||||
−0.740807 | + | 0.671718i | \(0.765557\pi\) | |||||||
\(632\) | 7.56476 | 0.300910 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.58023 | −0.0627590 | ||||||||
\(635\) | −10.3927 | −0.412421 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.33816 | −0.171884 | ||||||||
\(638\) | 36.4076 | 1.44139 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.854224 | −0.0337662 | ||||||||
\(641\) | −5.94517 | −0.234820 | −0.117410 | − | 0.993084i | \(-0.537459\pi\) | ||||
−0.117410 | + | 0.993084i | \(0.537459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.9686 | −1.14241 | −0.571205 | − | 0.820808i | \(-0.693524\pi\) | ||||
−0.571205 | + | 0.820808i | \(0.693524\pi\) | |||||||
\(644\) | 5.65232 | 0.222733 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.20077 | 0.0472437 | ||||||||
\(647\) | −9.56665 | −0.376104 | −0.188052 | − | 0.982159i | \(-0.560217\pi\) | ||||
−0.188052 | + | 0.982159i | \(0.560217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.66130 | 0.300732 | ||||||||
\(650\) | 2.86265 | 0.112282 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.23469 | 0.205006 | ||||||||
\(653\) | 31.2008 | 1.22098 | 0.610491 | − | 0.792023i | \(-0.290972\pi\) | ||||
0.610491 | + | 0.792023i | \(0.290972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0044 | −0.625345 | ||||||||
\(656\) | −0.350412 | −0.0136813 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.40930 | −0.366813 | ||||||||
\(659\) | 11.7460 | 0.457558 | 0.228779 | − | 0.973478i | \(-0.426527\pi\) | ||||
0.228779 | + | 0.973478i | \(0.426527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.54839 | −0.371389 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(662\) | 11.1065 | 0.431667 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.603787 | 0.0234315 | ||||||||
\(665\) | −3.21958 | −0.124850 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.2386 | 2.29373 | ||||||||
\(668\) | −24.8724 | −0.962343 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.40007 | −0.324523 | ||||||||
\(671\) | −52.7893 | −2.03791 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.2722 | −0.550151 | −0.275075 | − | 0.961423i | \(-0.588703\pi\) | ||||
−0.275075 | + | 0.961423i | \(0.588703\pi\) | |||||||
\(674\) | 14.1798 | 0.546186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.5506 | −0.482716 | ||||||||
\(677\) | 14.0794 | 0.541114 | 0.270557 | − | 0.962704i | \(-0.412792\pi\) | ||||
0.270557 | + | 0.962704i | \(0.412792\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.31560 | −0.127241 | ||||||||
\(680\) | −0.197873 | −0.00758809 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.9927 | −0.574099 | ||||||||
\(683\) | −3.93615 | −0.150613 | −0.0753063 | − | 0.997160i | \(-0.523993\pi\) | ||||
−0.0753063 | + | 0.997160i | \(0.523993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.40950 | 0.206687 | ||||||||
\(686\) | 9.79476 | 0.373966 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.96304 | −0.112965 | ||||||||
\(689\) | −4.95071 | −0.188607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7349 | −0.522500 | −0.261250 | − | 0.965271i | \(-0.584135\pi\) | ||||
−0.261250 | + | 0.965271i | \(0.584135\pi\) | |||||||
\(692\) | −13.4677 | −0.511965 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.8746 | −0.640551 | ||||||||
\(695\) | 15.1162 | 0.573391 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0811698 | −0.00307452 | ||||||||
\(698\) | 7.49710 | 0.283769 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.10485 | −0.117352 | ||||||||
\(701\) | −2.86040 | −0.108036 | −0.0540179 | − | 0.998540i | \(-0.517203\pi\) | ||||
−0.0540179 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2239 | 0.461033 | ||||||||
\(704\) | −4.77784 | −0.180071 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.81437 | 0.105920 | ||||||||
\(707\) | 0.855155 | 0.0321614 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.8083 | 1.98326 | 0.991630 | − | 0.129116i | \(-0.0412139\pi\) | ||||
0.991630 | + | 0.129116i | \(0.0412139\pi\) | |||||||
\(710\) | −8.85392 | −0.332282 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00132 | −0.149956 | ||||||||
\(713\) | −24.3945 | −0.913581 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.73598 | −0.102320 | ||||||||
\(716\) | 0.661451 | 0.0247196 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.13488 | 0.0796729 | ||||||||
\(719\) | 18.0840 | 0.674419 | 0.337209 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337209 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.76233 | −0.289084 | ||||||||
\(722\) | −7.87140 | −0.292943 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.6399 | −0.618415 | ||||||||
\(725\) | −32.5401 | −1.20851 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0928 | −0.671026 | −0.335513 | − | 0.942036i | \(-0.608910\pi\) | ||||
−0.335513 | + | 0.942036i | \(0.608910\pi\) | |||||||
\(728\) | −0.487408 | −0.0180646 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.01945 | 0.148766 | ||||||||
\(731\) | −0.686361 | −0.0253860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8322 | 0.510904 | 0.255452 | − | 0.966822i | \(-0.417776\pi\) | ||||
0.255452 | + | 0.966822i | \(0.417776\pi\) | |||||||
\(734\) | 17.7363 | 0.654659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.77399 | −0.286553 | ||||||||
\(737\) | −46.9832 | −1.73065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.1027 | 0.371634 | 0.185817 | − | 0.982584i | \(-0.440507\pi\) | ||||
0.185817 | + | 0.982584i | \(0.440507\pi\) | |||||||
\(740\) | −2.01436 | −0.0740492 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.36957 | 0.197123 | ||||||||
\(743\) | −30.1747 | −1.10700 | −0.553501 | − | 0.832848i | \(-0.686709\pi\) | ||||
−0.553501 | + | 0.832848i | \(0.686709\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.854224 | −0.0312964 | ||||||||
\(746\) | 33.3027 | 1.21930 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.10674 | −0.0404665 | ||||||||
\(749\) | −3.48625 | −0.127385 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.83745 | −0.140031 | −0.0700153 | − | 0.997546i | \(-0.522305\pi\) | ||||
−0.0700153 | + | 0.997546i | \(0.522305\pi\) | |||||||
\(752\) | 12.9412 | 0.471917 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.10824 | −0.186031 | ||||||||
\(755\) | −8.36010 | −0.304255 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3476 | 0.739546 | 0.369773 | − | 0.929122i | \(-0.379435\pi\) | ||||
0.369773 | + | 0.929122i | \(0.379435\pi\) | |||||||
\(758\) | 10.1957 | 0.370325 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.42810 | 0.160624 | ||||||||
\(761\) | −39.0730 | −1.41640 | −0.708198 | − | 0.706014i | \(-0.750491\pi\) | ||||
−0.708198 | + | 0.706014i | \(0.750491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.28355 | 0.0464677 | ||||||||
\(764\) | 9.87624 | 0.357310 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.9640 | 0.938116 | ||||||||
\(767\) | −1.07493 | −0.0388136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.30369 | −0.191256 | −0.0956280 | − | 0.995417i | \(-0.530486\pi\) | ||||
−0.0956280 | + | 0.995417i | \(0.530486\pi\) | |||||||
\(770\) | 2.96747 | 0.106940 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.6732 | −0.492110 | ||||||||
\(773\) | −11.4090 | −0.410352 | −0.205176 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205176 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4001 | 0.481344 | ||||||||
\(776\) | 4.56015 | 0.163700 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.83469 | 0.173332 | ||||||||
\(779\) | 1.81645 | 0.0650812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.5216 | −1.77202 | ||||||||
\(782\) | −1.80077 | −0.0643955 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.47135 | −0.231120 | ||||||||
\(785\) | −18.2468 | −0.651257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.89189 | −0.103085 | −0.0515424 | − | 0.998671i | \(-0.516414\pi\) | ||||
−0.0515424 | + | 0.998671i | \(0.516414\pi\) | |||||||
\(788\) | −17.4921 | −0.623131 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.46200 | 0.229908 | ||||||||
\(791\) | −10.3855 | −0.369267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.40670 | 0.263020 | ||||||||
\(794\) | −19.9337 | −0.707419 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.45845 | −0.264358 | ||||||||
\(797\) | 21.9507 | 0.777534 | 0.388767 | − | 0.921336i | \(-0.372901\pi\) | ||||
0.388767 | + | 0.921336i | \(0.372901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.99771 | 0.106051 | ||||||||
\(800\) | 4.27030 | 0.150978 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.33155 | 0.152952 | ||||||||
\(803\) | 22.4815 | 0.793355 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.82835 | 0.170177 | ||||||||
\(806\) | 2.10358 | 0.0740953 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.17615 | −0.0413768 | ||||||||
\(809\) | −25.0091 | −0.879274 | −0.439637 | − | 0.898176i | \(-0.644893\pi\) | ||||
−0.439637 | + | 0.898176i | \(0.644893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.7179 | 1.99163 | 0.995817 | − | 0.0913711i | \(-0.0291249\pi\) | ||||
0.995817 | + | 0.0913711i | \(0.0291249\pi\) | |||||||
\(812\) | 5.54043 | 0.194431 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.2667 | −0.394896 | ||||||||
\(815\) | 4.47160 | 0.156633 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.3597 | 0.537368 | ||||||||
\(818\) | 29.5272 | 1.03239 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.299331 | −0.0104531 | ||||||||
\(821\) | 17.3257 | 0.604672 | 0.302336 | − | 0.953201i | \(-0.402234\pi\) | ||||
0.302336 | + | 0.953201i | \(0.402234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2353 | −0.809930 | −0.404965 | − | 0.914332i | \(-0.632716\pi\) | ||||
−0.404965 | + | 0.914332i | \(0.632716\pi\) | |||||||
\(824\) | 10.6760 | 0.371917 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.16588 | 0.0405662 | ||||||||
\(827\) | −37.1661 | −1.29239 | −0.646197 | − | 0.763171i | \(-0.723641\pi\) | ||||
−0.646197 | + | 0.763171i | \(0.723641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.51796 | 0.122184 | 0.0610919 | − | 0.998132i | \(-0.480542\pi\) | ||||
0.0610919 | + | 0.998132i | \(0.480542\pi\) | |||||||
\(830\) | 0.515769 | 0.0179026 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.670363 | 0.0232407 | ||||||||
\(833\) | −1.49903 | −0.0519383 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.2466 | −0.735270 | ||||||||
\(836\) | 24.7672 | 0.856590 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.5113 | −0.777639 | ||||||||
\(839\) | −2.89793 | −0.100048 | −0.0500238 | − | 0.998748i | \(-0.515930\pi\) | ||||
−0.0500238 | + | 0.998748i | \(0.515930\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0660 | 1.00228 | ||||||||
\(842\) | −16.0732 | −0.553919 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.2465 | 0.559227 | ||||||||
\(845\) | −10.7210 | −0.368815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.59970 | 0.295489 | ||||||||
\(848\) | −7.38511 | −0.253606 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.989175 | 0.0339284 | ||||||||
\(851\) | −18.3319 | −0.628410 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.8771 | 1.63928 | 0.819641 | − | 0.572877i | \(-0.194173\pi\) | ||||
0.819641 | + | 0.572877i | \(0.194173\pi\) | |||||||
\(854\) | −8.03336 | −0.274896 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.79486 | 0.163885 | ||||||||
\(857\) | 6.59365 | 0.225235 | 0.112617 | − | 0.993638i | \(-0.464077\pi\) | ||||
0.112617 | + | 0.993638i | \(0.464077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.5642 | −0.735761 | −0.367880 | − | 0.929873i | \(-0.619916\pi\) | ||||
−0.367880 | + | 0.929873i | \(0.619916\pi\) | |||||||
\(860\) | −2.53110 | −0.0863099 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.7406 | 1.21733 | ||||||||
\(863\) | 24.6863 | 0.840331 | 0.420166 | − | 0.907447i | \(-0.361972\pi\) | ||||
0.420166 | + | 0.907447i | \(0.361972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5044 | −0.391162 | ||||||||
\(866\) | −29.3282 | −0.996614 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.28155 | −0.0774410 | ||||||||
\(869\) | 36.1432 | 1.22607 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.59206 | 0.223363 | ||||||||
\(872\) | −1.76535 | −0.0597822 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 40.2985 | 1.36312 | ||||||||
\(875\) | −5.75769 | −0.194646 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.5780 | −1.70790 | −0.853949 | − | 0.520357i | \(-0.825799\pi\) | ||||
−0.853949 | + | 0.520357i | \(0.825799\pi\) | |||||||
\(878\) | 8.48140 | 0.286233 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.08134 | −0.137582 | ||||||||
\(881\) | −19.5105 | −0.657324 | −0.328662 | − | 0.944448i | \(-0.606598\pi\) | ||||
−0.328662 | + | 0.944448i | \(0.606598\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.5096 | −0.824813 | −0.412406 | − | 0.911000i | \(-0.635312\pi\) | ||||
−0.412406 | + | 0.911000i | \(0.635312\pi\) | |||||||
\(884\) | 0.155283 | 0.00522275 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.2319 | −0.982065 | ||||||||
\(887\) | −47.6436 | −1.59972 | −0.799858 | − | 0.600190i | \(-0.795092\pi\) | ||||
−0.799858 | + | 0.600190i | \(0.795092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.84583 | −0.296680 | ||||||||
\(890\) | −3.41802 | −0.114572 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.84038 | −0.229033 | ||||||||
\(893\) | −67.0841 | −2.24488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.565027 | 0.0188868 | ||||||||
\(896\) | −0.727081 | −0.0242901 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.7240 | −0.791681 | ||||||||
\(899\) | −23.9116 | −0.797497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.71069 | −0.0569914 | ||||||||
\(902\) | −1.67421 | −0.0557452 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.2839 | 0.475075 | ||||||||
\(905\) | −14.2142 | −0.472495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3679 | 1.10796 | 0.553981 | − | 0.832529i | \(-0.313108\pi\) | ||||
0.553981 | + | 0.832529i | \(0.313108\pi\) | |||||||
\(908\) | −5.73148 | −0.190206 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.416356 | −0.0138021 | ||||||||
\(911\) | 19.1967 | 0.636014 | 0.318007 | − | 0.948088i | \(-0.396986\pi\) | ||||
0.318007 | + | 0.948088i | \(0.396986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.88479 | 0.0954728 | ||||||||
\(914\) | −19.6691 | −0.650597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.17916 | −0.0720016 | ||||||||
\(917\) | −13.6223 | −0.449849 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.6307 | −1.47223 | −0.736115 | − | 0.676856i | \(-0.763342\pi\) | ||||
−0.736115 | + | 0.676856i | \(0.763342\pi\) | |||||||
\(920\) | −6.64073 | −0.218938 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.86113 | −0.0942262 | ||||||||
\(923\) | 6.94822 | 0.228704 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0698 | 0.331094 | ||||||||
\(926\) | 20.0230 | 0.657997 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.62010 | −0.250142 | ||||||||
\(929\) | −28.9324 | −0.949240 | −0.474620 | − | 0.880191i | \(-0.657415\pi\) | ||||
−0.474620 | + | 0.880191i | \(0.657415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.5460 | 1.09942 | ||||||||
\(932\) | 0.993187 | 0.0325329 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.7449 | −0.940561 | ||||||||
\(935\) | −0.945405 | −0.0309181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.8230 | −1.17029 | −0.585144 | − | 0.810929i | \(-0.698962\pi\) | ||||
−0.585144 | + | 0.810929i | \(0.698962\pi\) | |||||||
\(938\) | −7.14980 | −0.233449 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.0547 | 0.360564 | ||||||||
\(941\) | 35.5526 | 1.15898 | 0.579491 | − | 0.814979i | \(-0.303252\pi\) | ||||
0.579491 | + | 0.814979i | \(0.303252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.72410 | −0.0887089 | ||||||||
\(944\) | −1.60351 | −0.0521897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.1569 | −0.460281 | ||||||||
\(947\) | 1.71004 | 0.0555688 | 0.0277844 | − | 0.999614i | \(-0.491155\pi\) | ||||
0.0277844 | + | 0.999614i | \(0.491155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.15431 | −0.102393 | ||||||||
\(950\) | −22.1362 | −0.718194 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.168422 | −0.00545857 | ||||||||
\(953\) | 57.4750 | 1.86180 | 0.930899 | − | 0.365277i | \(-0.119026\pi\) | ||||
0.930899 | + | 0.365277i | \(0.119026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.43652 | 0.272999 | ||||||||
\(956\) | 12.0854 | 0.390869 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.5108 | −0.630365 | ||||||||
\(959\) | 4.60435 | 0.148682 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.1532 | −0.682360 | ||||||||
\(962\) | 1.58079 | 0.0509667 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.47303 | 0.111859 | ||||||||
\(965\) | −11.6800 | −0.375993 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.8876 | −0.478753 | −0.239376 | − | 0.970927i | \(-0.576943\pi\) | ||||
−0.239376 | + | 0.970927i | \(0.576943\pi\) | |||||||
\(968\) | −11.8277 | −0.380157 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.89539 | 0.125074 | ||||||||
\(971\) | 31.8123 | 1.02090 | 0.510452 | − | 0.859906i | \(-0.329478\pi\) | ||||
0.510452 | + | 0.859906i | \(0.329478\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.8663 | 0.412475 | ||||||||
\(974\) | −2.99490 | −0.0959627 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.0488 | 0.353663 | ||||||||
\(977\) | −15.8528 | −0.507175 | −0.253588 | − | 0.967312i | \(-0.581611\pi\) | ||||
−0.253588 | + | 0.967312i | \(0.581611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.1176 | −0.611003 | ||||||||
\(980\) | −5.52799 | −0.176585 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43.3760 | 1.38418 | ||||||||
\(983\) | 39.9556 | 1.27439 | 0.637193 | − | 0.770704i | \(-0.280095\pi\) | ||||
0.637193 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.9422 | −0.476098 | ||||||||
\(986\) | −1.76513 | −0.0562131 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.47500 | −0.110555 | ||||||||
\(989\) | −23.0346 | −0.732459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.5807 | −0.653768 | −0.326884 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326884 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(992\) | 3.13797 | 0.0996305 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.53610 | −0.239030 | ||||||||
\(995\) | −6.37119 | −0.201980 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.70445 | 0.212332 | 0.106166 | − | 0.994348i | \(-0.466143\pi\) | ||||
0.106166 | + | 0.994348i | \(0.466143\pi\) | |||||||
\(998\) | 0.987622 | 0.0312626 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.e.1.5 | ✓ | 8 | |
3.2 | odd | 2 | 8046.2.a.f.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.e.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8046.2.a.f.1.4 | yes | 8 | 3.2 | odd | 2 |