Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 17 x^{10} + 49 x^{9} + 106 x^{8} - 277 x^{7} - 317 x^{6} + 644 x^{5} + 537 x^{4} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.69680\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.69680 | −1.55700 | −0.778501 | − | 0.627644i | \(-0.784019\pi\) | ||||
−0.778501 | + | 0.627644i | \(0.784019\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00937 | −0.451406 | −0.225703 | − | 0.974196i | \(-0.572468\pi\) | ||||
−0.225703 | + | 0.974196i | \(0.572468\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.288703 | 0.109120 | 0.0545598 | − | 0.998511i | \(-0.482624\pi\) | ||||
0.0545598 | + | 0.998511i | \(0.482624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.27276 | 1.42425 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.03273 | 0.311380 | 0.155690 | − | 0.987806i | \(-0.450240\pi\) | ||||
0.155690 | + | 0.987806i | \(0.450240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.06167 | 1.12651 | 0.563253 | − | 0.826285i | \(-0.309550\pi\) | ||||
0.563253 | + | 0.826285i | \(0.309550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.72209 | 0.702840 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.28109 | −0.310710 | −0.155355 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155355 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.18702 | −1.41940 | −0.709699 | − | 0.704505i | \(-0.751169\pi\) | ||||
−0.709699 | + | 0.704505i | \(0.751169\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.778576 | −0.169899 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.48944 | −0.936113 | −0.468057 | − | 0.883698i | \(-0.655046\pi\) | ||||
−0.468057 | + | 0.883698i | \(0.655046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.98116 | −0.796233 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.43238 | −0.660561 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.25699 | 0.790504 | 0.395252 | − | 0.918573i | \(-0.370657\pi\) | ||||
0.395252 | + | 0.918573i | \(0.370657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.81811 | −0.326542 | −0.163271 | − | 0.986581i | \(-0.552204\pi\) | ||||
−0.163271 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.78507 | −0.484819 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.291410 | −0.0492572 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.80644 | −0.296978 | −0.148489 | − | 0.988914i | \(-0.547441\pi\) | ||||
−0.148489 | + | 0.988914i | \(0.547441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9535 | −1.75397 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.25628 | 1.44559 | 0.722794 | − | 0.691063i | \(-0.242857\pi\) | ||||
0.722794 | + | 0.691063i | \(0.242857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.92555 | 0.751139 | 0.375569 | − | 0.926794i | \(-0.377447\pi\) | ||||
0.375569 | + | 0.926794i | \(0.377447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.31281 | −0.642916 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.94149 | −0.866656 | −0.433328 | − | 0.901236i | \(-0.642661\pi\) | ||||
−0.433328 | + | 0.901236i | \(0.642661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91665 | −0.988093 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.45485 | 0.483776 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.90488 | 1.08582 | 0.542909 | − | 0.839791i | \(-0.317323\pi\) | ||||
0.542909 | + | 0.839791i | \(0.317323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04241 | −0.140559 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.6852 | 2.21001 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2791 | 1.72879 | 0.864395 | − | 0.502814i | \(-0.167702\pi\) | ||||
0.864395 | + | 0.502814i | \(0.167702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7786 | 1.38006 | 0.690030 | − | 0.723780i | \(-0.257597\pi\) | ||||
0.690030 | + | 0.723780i | \(0.257597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.23356 | 0.155414 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.09975 | −0.508511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8430 | 1.93554 | 0.967768 | − | 0.251845i | \(-0.0810373\pi\) | ||||
0.967768 | + | 0.251845i | \(0.0810373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.1071 | 1.45753 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4700 | −1.47992 | −0.739961 | − | 0.672650i | \(-0.765156\pi\) | ||||
−0.739961 | + | 0.672650i | \(0.765156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.47640 | 0.875047 | 0.437523 | − | 0.899207i | \(-0.355856\pi\) | ||||
0.437523 | + | 0.899207i | \(0.355856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.7364 | 1.23974 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.298153 | 0.0339776 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06251 | 0.119542 | 0.0597710 | − | 0.998212i | \(-0.480963\pi\) | ||||
0.0597710 | + | 0.998212i | \(0.480963\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.56182 | −0.395758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7001 | −1.61355 | −0.806773 | − | 0.590862i | \(-0.798788\pi\) | ||||
−0.806773 | + | 0.590862i | \(0.798788\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.29310 | 0.140256 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.4803 | −1.23082 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.36960 | −0.569176 | −0.284588 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284588 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.17262 | 0.122924 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.90308 | 0.508426 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.24501 | 0.640725 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0437136 | 0.00443844 | 0.00221922 | − | 0.999998i | \(-0.499294\pi\) | ||||
0.00221922 | + | 0.999998i | \(0.499294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.41260 | 0.443483 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.61118 | 0.359326 | 0.179663 | − | 0.983728i | \(-0.442499\pi\) | ||||
0.179663 | + | 0.983728i | \(0.442499\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.97316 | −0.391487 | −0.195744 | − | 0.980655i | \(-0.562712\pi\) | ||||
−0.195744 | + | 0.980655i | \(0.562712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.785875 | 0.0766936 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.88695 | −0.472440 | −0.236220 | − | 0.971700i | \(-0.575909\pi\) | ||||
−0.236220 | + | 0.971700i | \(0.575909\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.4454 | −1.86253 | −0.931267 | − | 0.364338i | \(-0.881295\pi\) | ||||
−0.931267 | + | 0.364338i | \(0.881295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.87163 | 0.462394 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.13361 | 0.765145 | 0.382573 | − | 0.923925i | \(-0.375038\pi\) | ||||
0.382573 | + | 0.923925i | \(0.375038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.53153 | 0.422567 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3545 | 1.60443 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.369855 | −0.0339046 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.93347 | −0.903043 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −24.9624 | −2.25078 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.06536 | 0.810830 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.44714 | 0.572091 | 0.286046 | − | 0.958216i | \(-0.407659\pi\) | ||||
0.286046 | + | 0.958216i | \(0.407659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.2832 | −1.16952 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4394 | −1.08684 | −0.543418 | − | 0.839462i | \(-0.682870\pi\) | ||||
−0.543418 | + | 0.839462i | \(0.682870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78621 | −0.154884 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.46455 | 0.298181 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0326 | −0.942575 | −0.471287 | − | 0.881980i | \(-0.656211\pi\) | ||||
−0.471287 | + | 0.881980i | \(0.656211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9303 | 0.927092 | 0.463546 | − | 0.886073i | \(-0.346577\pi\) | ||||
0.463546 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0230 | 1.34938 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.19461 | 0.350771 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.29690 | −0.356838 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.6529 | 1.53846 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.74492 | −0.634488 | −0.317244 | − | 0.948344i | \(-0.602757\pi\) | ||||
−0.317244 | + | 0.948344i | \(0.602757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.26685 | −0.428610 | −0.214305 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214305 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.47379 | −0.442530 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.83515 | 0.147403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3756 | −1.14730 | −0.573650 | − | 0.819101i | \(-0.694473\pi\) | ||||
−0.573650 | + | 0.819101i | \(0.694473\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.3179 | −1.69062 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.29612 | −0.102148 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2193 | −0.957090 | −0.478545 | − | 0.878063i | \(-0.658836\pi\) | ||||
−0.478545 | + | 0.878063i | \(0.658836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.81118 | 0.218850 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6457 | 0.901172 | 0.450586 | − | 0.892733i | \(-0.351215\pi\) | ||||
0.450586 | + | 0.892733i | \(0.351215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.49720 | 0.269016 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.4356 | −2.02158 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.12380 | −0.0854412 | −0.0427206 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427206 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.14938 | −0.0868846 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.8111 | −2.69173 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.30904 | −0.247330 | −0.123665 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123665 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0124 | −1.63617 | −0.818083 | − | 0.575100i | \(-0.804963\pi\) | ||||
−0.818083 | + | 0.575100i | \(0.804963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.0678 | −2.14876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.82338 | 0.134057 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.32302 | −0.0967489 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.990938 | −0.0720802 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.7291 | 1.49991 | 0.749954 | − | 0.661490i | \(-0.230076\pi\) | ||||
0.749954 | + | 0.661490i | \(0.230076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4310 | −1.18273 | −0.591363 | − | 0.806405i | \(-0.701410\pi\) | ||||
−0.591363 | + | 0.806405i | \(0.701410\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.0562 | 0.791753 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1156 | −1.07695 | −0.538473 | − | 0.842643i | \(-0.680998\pi\) | ||||
−0.538473 | + | 0.842643i | \(0.680998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.62670 | −0.186202 | −0.0931010 | − | 0.995657i | \(-0.529678\pi\) | ||||
−0.0931010 | + | 0.995657i | \(0.529678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −42.7256 | −3.01363 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.22901 | 0.0862595 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.34305 | −0.652547 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.1823 | −1.33326 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.38952 | −0.441972 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.81977 | −0.676021 | −0.338011 | − | 0.941142i | \(-0.609754\pi\) | ||||
−0.338011 | + | 0.941142i | \(0.609754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 33.6293 | 2.30424 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.97172 | −0.339069 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.524894 | −0.0356321 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.1624 | −1.36245 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.20338 | −0.350017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.163679 | −0.0109607 | −0.00548036 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00548036 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.0105 | −1.13404 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.9242 | 1.58790 | 0.793952 | − | 0.607981i | \(-0.208020\pi\) | ||||
0.793952 | + | 0.607981i | \(0.208020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.56103 | −0.565729 | −0.282864 | − | 0.959160i | \(-0.591285\pi\) | ||||
−0.282864 | + | 0.959160i | \(0.591285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.804059 | −0.0529032 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8195 | −1.03637 | −0.518184 | − | 0.855269i | \(-0.673392\pi\) | ||||
−0.518184 | + | 0.855269i | \(0.673392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.99719 | 0.391214 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.86539 | −0.186127 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.67926 | 0.302676 | 0.151338 | − | 0.988482i | \(-0.451642\pi\) | ||||
0.151338 | + | 0.988482i | \(0.451642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6813 | 0.688046 | 0.344023 | − | 0.938961i | \(-0.388210\pi\) | ||||
0.344023 | + | 0.938961i | \(0.388210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.9027 | 1.27676 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.98149 | 0.446031 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.1296 | −1.59896 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 39.6433 | 2.51229 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.63638 | −0.291487 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.48724 | −0.218379 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.8086 | 0.861354 | 0.430677 | − | 0.902506i | \(-0.358275\pi\) | ||||
0.430677 | + | 0.902506i | \(0.358275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.521526 | −0.0324061 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.1891 | 1.12588 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8052 | 0.851265 | 0.425632 | − | 0.904896i | \(-0.360052\pi\) | ||||
0.425632 | + | 0.904896i | \(0.360052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.97898 | −0.490145 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4808 | 0.886208 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.984309 | 0.0600144 | 0.0300072 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300072 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.6461 | −1.55789 | −0.778946 | − | 0.627091i | \(-0.784245\pi\) | ||||
−0.778946 | + | 0.627091i | \(0.784245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.16232 | −0.191393 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.11147 | −0.247931 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.67136 | −0.160506 | −0.0802532 | − | 0.996775i | \(-0.525573\pi\) | ||||
−0.0802532 | + | 0.996775i | \(0.525573\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.76833 | −0.465078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.20183 | −0.429625 | −0.214813 | − | 0.976655i | \(-0.568914\pi\) | ||||
−0.214813 | + | 0.976655i | \(0.568914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.7017 | −0.992813 | −0.496407 | − | 0.868090i | \(-0.665347\pi\) | ||||
−0.496407 | + | 0.868090i | \(0.665347\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.8416 | −0.997609 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.67232 | 0.157742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3588 | −0.903459 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.117887 | −0.00691066 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.01774 | 0.351560 | 0.175780 | − | 0.984429i | \(-0.443755\pi\) | ||||
0.175780 | + | 0.984429i | \(0.443755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4036 | −0.780386 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.54472 | −0.205685 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.2347 | −1.05454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.42202 | 0.0819640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.73865 | −0.559471 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8797 | −0.622968 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6706 | 0.723148 | 0.361574 | − | 0.932343i | \(-0.382239\pi\) | ||||
0.361574 | + | 0.932343i | \(0.382239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.7148 | 0.609546 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.93352 | 0.279754 | 0.139877 | − | 0.990169i | \(-0.455329\pi\) | ||||
0.139877 | + | 0.990169i | \(0.455329\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9191 | 0.786755 | 0.393378 | − | 0.919377i | \(-0.371306\pi\) | ||||
0.393378 | + | 0.919377i | \(0.371306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.24512 | −0.0701547 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.7839 | 1.56050 | 0.780251 | − | 0.625467i | \(-0.215092\pi\) | ||||
0.780251 | + | 0.625467i | \(0.215092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.39632 | 0.246147 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1792 | 0.735589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.92613 | 0.441022 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.1702 | −0.896961 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 52.4405 | 2.89997 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.71533 | −0.0945691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4171 | −0.627539 | −0.313769 | − | 0.949499i | \(-0.601592\pi\) | ||||
−0.313769 | + | 0.949499i | \(0.601592\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.71850 | −0.422971 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.9916 | −0.873712 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4903 | −1.27960 | −0.639799 | − | 0.768542i | \(-0.720982\pi\) | ||||
−0.639799 | + | 0.768542i | \(0.720982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.9347 | −1.19133 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.87761 | −0.101679 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.01778 | −0.216940 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.2206 | −0.657937 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.6516 | −1.00127 | −0.500636 | − | 0.865658i | \(-0.666900\pi\) | ||||
−0.500636 | + | 0.865658i | \(0.666900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.588035 | 0.0314768 | 0.0157384 | − | 0.999876i | \(-0.494990\pi\) | ||||
0.0157384 | + | 0.999876i | \(0.494990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.9412 | −0.744126 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2475 | 1.02444 | 0.512219 | − | 0.858855i | \(-0.328824\pi\) | ||||
0.512219 | + | 0.858855i | \(0.328824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.5869 | 0.668046 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.997428 | 0.0527895 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.6652 | −0.932334 | −0.466167 | − | 0.884697i | \(-0.654365\pi\) | ||||
−0.466167 | + | 0.884697i | \(0.654365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.2792 | 1.01469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.7886 | 1.40604 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.54649 | −0.395001 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.4976 | −1.43536 | −0.717681 | − | 0.696372i | \(-0.754796\pi\) | ||||
−0.717681 | + | 0.696372i | \(0.754796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.5498 | 2.05888 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.28216 | 0.118484 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.11956 | −0.368637 | −0.184318 | − | 0.982867i | \(-0.559008\pi\) | ||||
−0.184318 | + | 0.982867i | \(0.559008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.4475 | −1.26246 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.2905 | 0.890507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7739 | 0.964348 | 0.482174 | − | 0.876075i | \(-0.339847\pi\) | ||||
0.482174 | + | 0.876075i | \(0.339847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3867 | −0.890747 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.78814 | −0.397955 | −0.198978 | − | 0.980004i | \(-0.563762\pi\) | ||||
−0.198978 | + | 0.980004i | \(0.563762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.300947 | −0.0153377 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.0457 | 1.06981 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.8918 | −1.71838 | −0.859192 | − | 0.511654i | \(-0.829033\pi\) | ||||
−0.859192 | + | 0.511654i | \(0.829033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.75138 | 0.290860 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.5466 | 1.69220 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.07247 | −0.0539620 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8246 | −1.29610 | −0.648050 | − | 0.761598i | \(-0.724415\pi\) | ||||
−0.648050 | + | 0.761598i | \(0.724415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.81706 | 0.241155 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.7073 | −0.784386 | −0.392193 | − | 0.919883i | \(-0.628283\pi\) | ||||
−0.392193 | + | 0.919883i | \(0.628283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.38457 | −0.367851 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.59521 | 0.178647 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.86557 | −0.0924728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.21682 | 0.257955 | 0.128978 | − | 0.991648i | \(-0.458830\pi\) | ||||
0.128978 | + | 0.991648i | \(0.458830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.7527 | 1.46759 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.83372 | 0.188645 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8379 | 0.728364 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.4768 | −1.44348 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2603 | −1.33175 | −0.665877 | − | 0.746062i | \(-0.731942\pi\) | ||||
−0.665877 | + | 0.746062i | \(0.731942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2693 | 1.23155 | 0.615774 | − | 0.787923i | \(-0.288843\pi\) | ||||
0.615774 | + | 0.787923i | \(0.288843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.3866 | −1.23434 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.10023 | 0.247398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.11182 | 0.150592 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.3121 | −0.546151 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4441 | 1.17743 | 0.588715 | − | 0.808341i | \(-0.299634\pi\) | ||||
0.588715 | + | 0.808341i | \(0.299634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.7732 | −1.33470 | −0.667348 | − | 0.744746i | \(-0.732571\pi\) | ||||
−0.667348 | + | 0.744746i | \(0.732571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.5879 | 0.555597 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.7762 | 1.32872 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.91559 | 0.377791 | 0.188895 | − | 0.981997i | \(-0.439509\pi\) | ||||
0.188895 | + | 0.981997i | \(0.439509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.5532 | −1.40729 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5041 | 0.879158 | 0.439579 | − | 0.898204i | \(-0.355128\pi\) | ||||
0.439579 | + | 0.898204i | \(0.355128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.41993 | 0.256929 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.8865 | 0.987899 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.6933 | −1.92044 | −0.960218 | − | 0.279251i | \(-0.909914\pi\) | ||||
−0.960218 | + | 0.279251i | \(0.909914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.55924 | 0.450127 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.2037 | 0.667346 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.18361 | −0.0554886 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0572 | −0.844678 | −0.422339 | − | 0.906438i | \(-0.638791\pi\) | ||||
−0.422339 | + | 0.906438i | \(0.638791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.39719 | 0.205243 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.776649 | 0.0361722 | 0.0180861 | − | 0.999836i | \(-0.494243\pi\) | ||||
0.0180861 | + | 0.999836i | \(0.494243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.07384 | −0.189328 | −0.0946638 | − | 0.995509i | \(-0.530178\pi\) | ||||
−0.0946638 | + | 0.995509i | \(0.530178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.94905 | −0.229507 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.95790 | −0.136875 | −0.0684376 | − | 0.997655i | \(-0.521801\pi\) | ||||
−0.0684376 | + | 0.997655i | \(0.521801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.57394 | 0.211205 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.7682 | 1.78635 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.08676 | 0.233889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.6315 | 1.13017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.7756 | 1.54648 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.8615 | −1.31872 | −0.659358 | − | 0.751829i | \(-0.729172\pi\) | ||||
−0.659358 | + | 0.751829i | \(0.729172\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.33719 | −0.334547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.49537 | 0.159045 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0441234 | −0.00200354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6500 | −0.709169 | −0.354584 | − | 0.935024i | \(-0.615378\pi\) | ||||
−0.354584 | + | 0.935024i | \(0.615378\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.9531 | 1.49019 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9880 | −0.856916 | −0.428458 | − | 0.903562i | \(-0.640943\pi\) | ||||
−0.428458 | + | 0.903562i | \(0.640943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.45360 | −0.245618 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.45397 | −0.200191 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.60014 | −0.161489 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3484 | −1.04522 | −0.522609 | − | 0.852572i | \(-0.675041\pi\) | ||||
−0.522609 | + | 0.852572i | \(0.675041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.4062 | −1.40313 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6239 | −0.696635 | −0.348317 | − | 0.937377i | \(-0.613247\pi\) | ||||
−0.348317 | + | 0.937377i | \(0.613247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.64503 | −0.162202 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.43127 | −0.418858 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.7297 | −0.564233 | −0.282117 | − | 0.959380i | \(-0.591036\pi\) | ||||
−0.282117 | + | 0.959380i | \(0.591036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.15846 | 0.0954847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.2362 | 0.937600 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.01041 | 0.176720 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.13596 | −0.269859 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.03068 | 0.133032 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8996 | −0.565140 | −0.282570 | − | 0.959247i | \(-0.591187\pi\) | ||||
−0.282570 | + | 0.959247i | \(0.591187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.5603 | 1.77358 | 0.886789 | − | 0.462175i | \(-0.152931\pi\) | ||||
0.886789 | + | 0.462175i | \(0.152931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.09964 | 0.135279 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.32916 | 0.101460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.84492 | −0.123692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 56.7383 | 2.46223 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.5960 | 1.62846 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.93276 | 0.213262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.92384 | 0.385092 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.14303 | −0.307672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.39339 | −0.231880 | −0.115940 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115940 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 59.3630 | 2.54751 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.6277 | 0.840759 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.6382 | −1.60929 | −0.804647 | − | 0.593754i | \(-0.797645\pi\) | ||||
−0.804647 | + | 0.593754i | \(0.797645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 46.0544 | 1.96555 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.3381 | −1.12204 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.306751 | 0.0130444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.91730 | −0.208728 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.6932 | −0.453084 | −0.226542 | − | 0.974001i | \(-0.572742\pi\) | ||||
−0.226542 | + | 0.974001i | \(0.572742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0060 | 0.846162 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.56793 | 0.150638 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.46712 | −0.0618319 | −0.0309159 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309159 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.20985 | −0.345391 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.02831 | −0.0431849 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.6472 | −1.57825 | −0.789127 | − | 0.614230i | \(-0.789467\pi\) | ||||
−0.789127 | + | 0.614230i | \(0.789467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5441 | 1.15269 | 0.576343 | − | 0.817208i | \(-0.304479\pi\) | ||||
0.576343 | + | 0.817208i | \(0.304479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.9025 | −2.33536 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.8732 | 0.745364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.9119 | −0.745681 | −0.372840 | − | 0.927896i | \(-0.621616\pi\) | ||||
−0.372840 | + | 0.927896i | \(0.621616\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 44.3111 | 1.84151 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.24397 | −0.176069 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.16360 | 0.338102 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.5172 | −0.724249 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.3934 | −0.552807 | −0.276403 | − | 0.961042i | \(-0.589143\pi\) | ||||
−0.276403 | + | 0.961042i | \(0.589143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2487 | 0.463493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.7640 | 1.67680 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.27519 | −0.257691 | −0.128846 | − | 0.991665i | \(-0.541127\pi\) | ||||
−0.128846 | + | 0.991665i | \(0.541127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.373322 | 0.0153047 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.08370 | 0.289917 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8224 | 0.769063 | 0.384531 | − | 0.923112i | \(-0.374363\pi\) | ||||
0.384531 | + | 0.923112i | \(0.374363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2664 | −1.03064 | −0.515319 | − | 0.856999i | \(-0.672326\pi\) | ||||
−0.515319 | + | 0.856999i | \(0.672326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 67.6934 | 2.75669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0266 | 0.407639 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.6865 | 1.69200 | 0.846002 | − | 0.533180i | \(-0.179003\pi\) | ||||
0.846002 | + | 0.533180i | \(0.179003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.31439 | −0.134306 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.1324 | −0.976293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.97877 | −0.362649 | −0.181324 | − | 0.983423i | \(-0.558038\pi\) | ||||
−0.181324 | + | 0.983423i | \(0.558038\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25.1964 | 1.01602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1638 | 1.57667 | 0.788337 | − | 0.615243i | \(-0.210942\pi\) | ||||
0.788337 | + | 0.615243i | \(0.210942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.8011 | −1.03703 | −0.518517 | − | 0.855068i | \(-0.673516\pi\) | ||||
−0.518517 | + | 0.855068i | \(0.673516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.4095 | 0.618360 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.55022 | −0.0621083 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.7555 | 0.430219 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.2313 | 0.688151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.31422 | 0.0922740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.1780 | −0.524609 | −0.262305 | − | 0.964985i | \(-0.584483\pi\) | ||||
−0.262305 | + | 0.964985i | \(0.584483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.4820 | 1.05257 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.50758 | −0.258245 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.0932 | −1.11309 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −53.2815 | −2.10778 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.405055 | 0.0159987 | 0.00799935 | − | 0.999968i | \(-0.497454\pi\) | ||||
0.00799935 | + | 0.999968i | \(0.497454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.47002 | 0.255153 | 0.127576 | − | 0.991829i | \(-0.459280\pi\) | ||||
0.127576 | + | 0.991829i | \(0.459280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.4078 | 0.527930 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.19928 | 0.361661 | 0.180831 | − | 0.983514i | \(-0.442121\pi\) | ||||
0.180831 | + | 0.983514i | \(0.442121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.7137 | 0.538310 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.41554 | 0.0554792 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.1285 | −0.865956 | −0.432978 | − | 0.901405i | \(-0.642537\pi\) | ||||
−0.432978 | + | 0.901405i | \(0.642537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.5560 | 0.490604 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.9448 | 1.24629 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6686 | 0.883043 | 0.441522 | − | 0.897251i | \(-0.354439\pi\) | ||||
0.441522 | + | 0.897251i | \(0.354439\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4738 | 1.02971 | 0.514855 | − | 0.857277i | \(-0.327846\pi\) | ||||
0.514855 | + | 0.857277i | \(0.327846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.0325 | 0.544977 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.80296 | 0.0699156 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1115 | −0.740001 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.441409 | 0.0170659 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1314 | 0.429723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.2170 | −0.933497 | −0.466749 | − | 0.884390i | \(-0.654575\pi\) | ||||
−0.466749 | + | 0.884390i | \(0.654575\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.6649 | 0.525960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.2605 | 1.04771 | 0.523854 | − | 0.851808i | \(-0.324494\pi\) | ||||
0.523854 | + | 0.851808i | \(0.324494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0126203 | 0.000484321 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −64.5188 | −2.47237 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0331 | 0.690018 | 0.345009 | − | 0.938599i | \(-0.387876\pi\) | ||||
0.345009 | + | 0.938599i | \(0.387876\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.1360 | 0.425484 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.0874 | 0.880841 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.1070 | 1.22318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6322 | −1.46964 | −0.734820 | − | 0.678262i | \(-0.762733\pi\) | ||||
−0.734820 | + | 0.678262i | \(0.762733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.27393 | 0.0483927 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0327 | −0.418495 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.8581 | −0.449159 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.6620 | 1.61363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9562 | 1.32028 | 0.660138 | − | 0.751144i | \(-0.270498\pi\) | ||||
0.660138 | + | 0.751144i | \(0.270498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1765 | 0.421530 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.1733 | −0.609120 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.04256 | 0.0392095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8712 | 0.934056 | 0.467028 | − | 0.884242i | \(-0.345325\pi\) | ||||
0.467028 | + | 0.884242i | \(0.345325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.53986 | 0.170258 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.16229 | 0.305680 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.23393 | −0.158340 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.6191 | −0.471267 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.5465 | −1.06460 | −0.532302 | − | 0.846554i | \(-0.678673\pi\) | ||||
−0.532302 | + | 0.846554i | \(0.678673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.14706 | −0.0427189 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.8055 | −1.07129 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.9478 | −0.629425 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.20507 | −0.155957 | −0.0779787 | − | 0.996955i | \(-0.524847\pi\) | ||||
−0.0779787 | + | 0.996955i | \(0.524847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.9881 | −1.59215 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.31008 | −0.233387 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4058 | 0.753704 | 0.376852 | − | 0.926274i | \(-0.377007\pi\) | ||||
0.376852 | + | 0.926274i | \(0.377007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.8277 | −0.694471 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.3616 | 0.602686 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0671 | −1.10604 | −0.553018 | − | 0.833169i | \(-0.686524\pi\) | ||||
−0.553018 | + | 0.833169i | \(0.686524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 67.7697 | 2.48958 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1188 | 1.25170 | 0.625849 | − | 0.779944i | \(-0.284752\pi\) | ||||
0.625849 | + | 0.779944i | \(0.284752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.81752 | 0.286412 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.8100 | −2.29810 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.41088 | −0.0515524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3085 | −1.28843 | −0.644214 | − | 0.764846i | \(-0.722815\pi\) | ||||
−0.644214 | + | 0.764846i | \(0.722815\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.69680 | 0.0982770 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.31622 | 0.193477 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.6466 | −1.65906 | −0.829528 | − | 0.558466i | \(-0.811390\pi\) | ||||
−0.829528 | + | 0.558466i | \(0.811390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.5034 | 0.453845 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1422 | 0.440156 | 0.220078 | − | 0.975482i | \(-0.429369\pi\) | ||||
0.220078 | + | 0.975482i | \(0.429369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.61396 | −0.203239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.52511 | 0.199761 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.9353 | 1.94749 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.24418 | −0.333354 | −0.166677 | − | 0.986012i | \(-0.553304\pi\) | ||||
−0.166677 | + | 0.986012i | \(0.553304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.2390 | −1.34113 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.6524 | 1.06652 | 0.533261 | − | 0.845951i | \(-0.320967\pi\) | ||||
0.533261 | + | 0.845951i | \(0.320967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.23819 | 0.260003 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.40645 | 0.0504563 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.2688 | −2.05187 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8782 | −0.460818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.6116 | −0.522176 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.5104 | 0.517898 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3362 | −0.475383 | −0.237692 | − | 0.971341i | \(-0.576391\pi\) | ||||
−0.237692 | + | 0.971341i | \(0.576391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.2299 | −1.32542 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.34820 | 0.0834923 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.7792 | 1.55465 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.5177 | 0.763156 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.88865 | −0.279430 | −0.139715 | − | 0.990192i | \(-0.544619\pi\) | ||||
−0.139715 | + | 0.990192i | \(0.544619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.61160 | 0.269279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.9430 | −0.810650 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.72110 | 0.272472 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.30827 | 0.0461103 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.65449 | −0.0934424 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.9335 | 1.79073 | 0.895364 | − | 0.445336i | \(-0.146916\pi\) | ||||
0.895364 | + | 0.445336i | \(0.146916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9831 | 1.29865 | 0.649327 | − | 0.760510i | \(-0.275051\pi\) | ||||
0.649327 | + | 0.760510i | \(0.275051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69.1626 | 2.42564 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.3339 | 0.432036 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4744 | −1.06617 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.01032 | 0.175075 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5449 | 0.647222 | 0.323611 | − | 0.946190i | \(-0.395103\pi\) | ||||
0.323611 | + | 0.946190i | \(0.395103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.8020 | 1.38741 | 0.693705 | − | 0.720260i | \(-0.255977\pi\) | ||||
0.693705 | + | 0.720260i | \(0.255977\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.0878 | 0.386028 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.0765 | 0.663356 | 0.331678 | − | 0.943393i | \(-0.392385\pi\) | ||||
0.331678 | + | 0.943393i | \(0.392385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8074 | −0.687940 | −0.343970 | − | 0.938981i | \(-0.611772\pi\) | ||||
−0.343970 | + | 0.938981i | \(0.611772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.20414 | 0.249909 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.86086 | 0.307011 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.7549 | −0.406794 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.24043 | 0.215701 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.9883 | 1.34603 | 0.673014 | − | 0.739630i | \(-0.265000\pi\) | ||||
0.673014 | + | 0.739630i | \(0.265000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8780 | −0.375104 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.4219 | 0.668927 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.52999 | −0.121435 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.86783 | −0.0985396 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 45.0412 | 1.54581 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.10992 | 0.278005 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.35100 | 0.0804967 | 0.0402483 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402483 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.6834 | 0.912554 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.3305 | 0.421202 | 0.210601 | − | 0.977572i | \(-0.432458\pi\) | ||||
0.210601 | + | 0.977572i | \(0.432458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.32101 | −0.0450722 | −0.0225361 | − | 0.999746i | \(-0.507174\pi\) | ||||
−0.0225361 | + | 0.999746i | \(0.507174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.20672 | −0.245604 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.0590 | −1.84019 | −0.920095 | − | 0.391695i | \(-0.871889\pi\) | ||||
−0.920095 | + | 0.391695i | \(0.871889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.13434 | 0.0385686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.4197 | 1.40669 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.09729 | 0.0372230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.3493 | 2.18039 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.186778 | 0.00632146 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.61720 | 0.0884774 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6983 | 0.428792 | 0.214396 | − | 0.976747i | \(-0.431222\pi\) | ||||
0.214396 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2287 | −0.547379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.68845 | 0.292721 | 0.146361 | − | 0.989231i | \(-0.453244\pi\) | ||||
0.146361 | + | 0.989231i | \(0.453244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.20965 | 0.242624 | 0.121312 | − | 0.992614i | \(-0.461290\pi\) | ||||
0.121312 | + | 0.992614i | \(0.461290\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.1468 | 1.21506 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.47682 | −0.116740 | −0.0583700 | − | 0.998295i | \(-0.518590\pi\) | ||||
−0.0583700 | + | 0.998295i | \(0.518590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.86131 | 0.0624264 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.67840 | −0.123231 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.7601 | 1.23013 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.34006 | 0.111646 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.1753 | 1.64192 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.73968 | −0.258133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.1269 | −0.337375 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.83491 | −0.127618 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.2187 | 0.738575 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.4021 | −1.73998 | −0.869991 | − | 0.493067i | \(-0.835876\pi\) | ||||
−0.869991 | + | 0.493067i | \(0.835876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.4297 | 0.511771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.4971 | −1.30860 | −0.654299 | − | 0.756236i | \(-0.727036\pi\) | ||||
−0.654299 | + | 0.756236i | \(0.727036\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.1812 | −0.502426 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.3403 | 0.969961 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.59130 | −0.118595 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.18486 | −0.302981 | −0.151490 | − | 0.988459i | \(-0.548407\pi\) | ||||
−0.151490 | + | 0.988459i | \(0.548407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.1701 | −1.12594 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.6493 | −1.66714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.19175 | 0.236463 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9763 | −0.557576 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.1618 | −1.25205 | −0.626024 | − | 0.779804i | \(-0.715319\pi\) | ||||
−0.626024 | + | 0.779804i | \(0.715319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.7934 | 1.40250 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.3047 | −0.435578 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.33542 | 0.0436730 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.9986 | −0.555319 | −0.277660 | − | 0.960679i | \(-0.589559\pi\) | ||||
−0.277660 | + | 0.960679i | \(0.589559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.5372 | −1.22498 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.04432 | 0.131841 | 0.0659205 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659205 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.5555 | −1.35323 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00023 | 0.0325374 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.0183 | −0.812985 | −0.406492 | − | 0.913654i | \(-0.633248\pi\) | ||||
−0.406492 | + | 0.913654i | \(0.633248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.3667 | 0.985745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.9278 | −2.42970 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1448 | −0.522980 | −0.261490 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261490 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.9235 | −0.677067 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.8560 | −0.383251 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.18514 | −0.102853 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6945 | −0.893370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.8808 | −0.672873 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5850 | 0.533890 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6494 | 0.438935 | 0.219468 | − | 0.975620i | \(-0.429568\pi\) | ||||
0.219468 | + | 0.975620i | \(0.429568\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.3752 | −0.686671 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.65596 | 0.0852337 | 0.0426169 | − | 0.999091i | \(-0.486431\pi\) | ||||
0.0426169 | + | 0.999091i | \(0.486431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.15560 | 0.101164 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.6079 | 1.39657 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9401 | 0.381998 | 0.190999 | − | 0.981590i | \(-0.438827\pi\) | ||||
0.190999 | + | 0.981590i | \(0.438827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.54534 | −0.177230 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −83.0856 | −2.65272 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.33228 | 0.201968 | 0.100984 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100984 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.2573 | 0.486140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.62591 | 0.147244 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.1130 | −0.703151 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.7733 | 1.04108 | 0.520539 | − | 0.853838i | \(-0.325731\pi\) | ||||
0.520539 | + | 0.853838i | \(0.325731\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7896 | 0.977078 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.65133 | 0.0840527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.5223 | 1.79008 | 0.895039 | − | 0.445987i | \(-0.147147\pi\) | ||||
0.895039 | + | 0.445987i | \(0.147147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.20040 | 0.196172 |
(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 | 4016.2.a.i.1.2 | 12 | ||
4.3 | odd | 2 | 2008.2.a.b.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.b.1.11 | ✓ | 12 | 4.3 | odd | 2 | ||
4016.2.a.i.1.2 | 12 | 1.1 | even | 1 | trivial |