Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(1,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, 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("4900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.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: | \(39.1266969904\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.1 |
$q$-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 | ||||||||
\(3\) | −0.874032 | −0.504623 | −0.252311 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.47214 | 1.04689 | 0.523444 | − | 0.852060i | \(-0.324647\pi\) | ||||
0.523444 | + | 0.852060i | \(0.324647\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28825 | 0.634645 | 0.317323 | − | 0.948318i | \(-0.397216\pi\) | ||||
0.317323 | + | 0.948318i | \(0.397216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.74806 | −0.423968 | −0.211984 | − | 0.977273i | \(-0.567992\pi\) | ||||
−0.211984 | + | 0.977273i | \(0.567992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.333851 | 0.0765906 | 0.0382953 | − | 0.999266i | \(-0.487807\pi\) | ||||
0.0382953 | + | 0.999266i | \(0.487807\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.47214 | −1.14102 | −0.570510 | − | 0.821291i | \(-0.693254\pi\) | ||||
−0.570510 | + | 0.821291i | \(0.693254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57649 | 0.880746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.23607 | −0.786618 | −0.393309 | − | 0.919406i | \(-0.628670\pi\) | ||||
−0.393309 | + | 0.919406i | \(0.628670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.20788 | 0.216942 | 0.108471 | − | 0.994100i | \(-0.465405\pi\) | ||||
0.108471 | + | 0.994100i | \(0.465405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.03476 | −0.528284 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.95440 | −0.305225 | −0.152613 | − | 0.988286i | \(-0.548769\pi\) | ||||
−0.152613 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.23607 | −1.25599 | −0.627994 | − | 0.778218i | \(-0.716124\pi\) | ||||
−0.627994 | + | 0.778218i | \(0.716124\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.73877 | −1.12882 | −0.564408 | − | 0.825496i | \(-0.690895\pi\) | ||||
−0.564408 | + | 0.825496i | \(0.690895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.52786 | 0.213944 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.70820 | 0.234640 | 0.117320 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117320 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.291796 | −0.0386493 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.11667 | 0.666134 | 0.333067 | − | 0.942903i | \(-0.391916\pi\) | ||||
0.333067 | + | 0.942903i | \(0.391916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6035 | 1.86979 | 0.934894 | − | 0.354928i | \(-0.115495\pi\) | ||||
0.934894 | + | 0.354928i | \(0.115495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.94427 | −0.481870 | −0.240935 | − | 0.970541i | \(-0.577454\pi\) | ||||
−0.240935 | + | 0.970541i | \(0.577454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.78282 | 0.575784 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.29180 | 0.390664 | 0.195332 | − | 0.980737i | \(-0.437422\pi\) | ||||
0.195332 | + | 0.980737i | \(0.437422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6035 | 1.70921 | 0.854606 | − | 0.519278i | \(-0.173799\pi\) | ||||
0.854606 | + | 0.519278i | \(0.173799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.52786 | −0.284407 | −0.142203 | − | 0.989837i | \(-0.545419\pi\) | ||||
−0.142203 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.02546 | 0.990673 | 0.495337 | − | 0.868701i | \(-0.335045\pi\) | ||||
0.495337 | + | 0.868701i | \(0.335045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.70246 | 0.396945 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3500 | −1.62710 | −0.813549 | − | 0.581496i | \(-0.802468\pi\) | ||||
−0.813549 | + | 0.581496i | \(0.802468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.05573 | −0.109474 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1089 | −1.22948 | −0.614738 | − | 0.788732i | \(-0.710738\pi\) | ||||
−0.614738 | + | 0.788732i | \(0.710738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.76393 | −0.780305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.53089 | −0.649847 | −0.324924 | − | 0.945740i | \(-0.605339\pi\) | ||||
−0.324924 | + | 0.945740i | \(0.605339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3848 | −1.81151 | −0.905753 | − | 0.423806i | \(-0.860694\pi\) | ||||
−0.905753 | + | 0.423806i | \(0.860694\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.52786 | −0.341051 | −0.170526 | − | 0.985353i | \(-0.554547\pi\) | ||||
−0.170526 | + | 0.985353i | \(0.554547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4164 | 0.997711 | 0.498855 | − | 0.866685i | \(-0.333754\pi\) | ||||
0.498855 | + | 0.866685i | \(0.333754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.206331 | −0.0195841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.2361 | −1.71550 | −0.857752 | − | 0.514063i | \(-0.828140\pi\) | ||||
−0.857752 | + | 0.514063i | \(0.828140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.11667 | −0.473037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.05573 | 0.0959753 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.70820 | 0.154024 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1803 | −0.992095 | −0.496047 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496047 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.19859 | 0.633800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8098 | 1.29394 | 0.646971 | − | 0.762515i | \(-0.276036\pi\) | ||||
0.646971 | + | 0.762515i | \(0.276036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7751 | 0.998749 | 0.499375 | − | 0.866386i | \(-0.333563\pi\) | ||||
0.499375 | + | 0.866386i | \(0.333563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.76393 | 0.569626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.94510 | 0.664403 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.70820 | −0.549557 | −0.274779 | − | 0.961507i | \(-0.588605\pi\) | ||||
−0.274779 | + | 0.961507i | \(0.588605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.76393 | 0.306304 | 0.153152 | − | 0.988203i | \(-0.451058\pi\) | ||||
0.153152 | + | 0.988203i | \(0.451058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.90879 | 0.316007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1877 | 0.972688 | 0.486344 | − | 0.873768i | \(-0.338330\pi\) | ||||
0.486344 | + | 0.873768i | \(0.338330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.49302 | −0.118405 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.1803 | −1.58065 | −0.790323 | − | 0.612690i | \(-0.790087\pi\) | ||||
−0.790323 | + | 0.612690i | \(0.790087\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.9265 | 1.54196 | 0.770980 | − | 0.636860i | \(-0.219767\pi\) | ||||
0.770980 | + | 0.636860i | \(0.219767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.76393 | −0.597226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.746512 | −0.0570872 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.3848 | −1.39777 | −0.698884 | − | 0.715235i | \(-0.746320\pi\) | ||||
−0.698884 | + | 0.715235i | \(0.746320\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.47214 | −0.336146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7082 | −0.875112 | −0.437556 | − | 0.899191i | \(-0.644156\pi\) | ||||
−0.437556 | + | 0.899191i | \(0.644156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.8369 | −1.84611 | −0.923054 | − | 0.384670i | \(-0.874315\pi\) | ||||
−0.923054 | + | 0.384670i | \(0.874315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7639 | −0.943537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.06952 | −0.443847 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1803 | 0.736624 | 0.368312 | − | 0.929702i | \(-0.379936\pi\) | ||||
0.368312 | + | 0.929702i | \(0.379936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6525 | −1.12669 | −0.563345 | − | 0.826222i | \(-0.690486\pi\) | ||||
−0.563345 | + | 0.826222i | \(0.690486\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5279 | −0.750079 | −0.375040 | − | 0.927009i | \(-0.622371\pi\) | ||||
−0.375040 | + | 0.927009i | \(0.622371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.461370 | −0.0327057 | −0.0163528 | − | 0.999866i | \(-0.505205\pi\) | ||||
−0.0163528 | + | 0.999866i | \(0.505205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.44742 | 0.243162 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.2361 | 0.850466 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.15917 | 0.0801818 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4721 | 1.27167 | 0.635837 | − | 0.771823i | \(-0.280655\pi\) | ||||
0.635837 | + | 0.771823i | \(0.280655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.87714 | −0.197138 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7639 | −0.862507 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0162 | 1.00556 | 0.502778 | − | 0.864415i | \(-0.332311\pi\) | ||||
0.502778 | + | 0.864415i | \(0.332311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.0525 | −1.26456 | −0.632279 | − | 0.774741i | \(-0.717880\pi\) | ||||
−0.632279 | + | 0.774741i | \(0.717880\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.7202 | −1.30315 | −0.651573 | − | 0.758586i | \(-0.725891\pi\) | ||||
−0.651573 | + | 0.758586i | \(0.725891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.4721 | −1.27566 | −0.637831 | − | 0.770176i | \(-0.720168\pi\) | ||||
−0.637831 | + | 0.770176i | \(0.720168\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.20943 | 0.143518 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6525 | −1.46527 | −0.732633 | − | 0.680623i | \(-0.761709\pi\) | ||||
−0.732633 | + | 0.680623i | \(0.761709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.41421 | 0.0910975 | 0.0455488 | − | 0.998962i | \(-0.485496\pi\) | ||||
0.0455488 | + | 0.998962i | \(0.485496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0965 | −1.03259 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.763932 | 0.0486078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.88854 | −0.499916 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.57649 | 0.288866 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0000 | −1.19452 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.20788 | −0.0753456 | −0.0376728 | − | 0.999290i | \(-0.511994\pi\) | ||||
−0.0376728 | + | 0.999290i | \(0.511994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.47214 | 0.586310 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.70820 | −0.166995 | −0.0834975 | − | 0.996508i | \(-0.526609\pi\) | ||||
−0.0834975 | + | 0.996508i | \(0.526609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4164 | 0.821071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.54328 | −0.155067 | −0.0775334 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775334 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.62365 | −0.220121 | −0.110060 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110060 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.05573 | −0.183601 | −0.0918005 | − | 0.995777i | \(-0.529262\pi\) | ||||
−0.0918005 | + | 0.995777i | \(0.529262\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.70091 | −0.161699 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1246 | 0.961914 | 0.480957 | − | 0.876744i | \(-0.340289\pi\) | ||||
0.480957 | + | 0.876744i | \(0.340289\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.08191 | −0.123757 | −0.0618785 | − | 0.998084i | \(-0.519709\pi\) | ||||
−0.0618785 | + | 0.998084i | \(0.519709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9443 | −0.820251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5836 | 0.620421 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.2619 | 1.24213 | 0.621067 | − | 0.783757i | \(-0.286699\pi\) | ||||
0.621067 | + | 0.783757i | \(0.286699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.8902 | 0.922043 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.5216 | −0.724142 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.70820 | 0.327928 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3941 | 0.707367 | 0.353684 | − | 0.935365i | \(-0.384929\pi\) | ||||
0.353684 | + | 0.935365i | \(0.384929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0689 | 0.914127 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.8639 | −1.97695 | −0.988474 | − | 0.151389i | \(-0.951625\pi\) | ||||
−0.988474 | + | 0.151389i | \(0.951625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2241 | −0.917038 | −0.458519 | − | 0.888685i | \(-0.651620\pi\) | ||||
−0.458519 | + | 0.888685i | \(0.651620\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.4164 | −1.48369 | −0.741847 | − | 0.670570i | \(-0.766050\pi\) | ||||
−0.741847 | + | 0.670570i | \(0.766050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.7082 | −0.823501 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.08347 | 0.172102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.583592 | −0.0324719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.10427 | −0.503468 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3607 | 1.50388 | 0.751939 | − | 0.659232i | \(-0.229119\pi\) | ||||
0.751939 | + | 0.659232i | \(0.229119\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.527864 | −0.0289268 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1246 | −1.25968 | −0.629839 | − | 0.776726i | \(-0.716879\pi\) | ||||
−0.629839 | + | 0.776726i | \(0.716879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.9389 | 0.865683 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.19393 | 0.227114 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.3607 | 1.03934 | 0.519668 | − | 0.854368i | \(-0.326056\pi\) | ||||
0.519668 | + | 0.854368i | \(0.326056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9690 | 0.854802 | 0.427401 | − | 0.904062i | \(-0.359429\pi\) | ||||
0.427401 | + | 0.904062i | \(0.359429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.4721 | 0.558961 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3609 | 0.551453 | 0.275727 | − | 0.961236i | \(-0.411082\pi\) | ||||
0.275727 | + | 0.961236i | \(0.411082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.0689 | 1.53420 | 0.767099 | − | 0.641529i | \(-0.221700\pi\) | ||||
0.767099 | + | 0.641529i | \(0.221700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8885 | −0.994134 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.922740 | −0.0484313 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0270 | 0.523406 | 0.261703 | − | 0.965148i | \(-0.415716\pi\) | ||||
0.261703 | + | 0.965148i | \(0.415716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.37016 | 0.227501 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1246 | 0.524233 | 0.262116 | − | 0.965036i | \(-0.415580\pi\) | ||||
0.262116 | + | 0.965036i | \(0.415580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.69316 | −0.499223 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.1246 | −1.54740 | −0.773699 | − | 0.633554i | \(-0.781596\pi\) | ||||
−0.773699 | + | 0.633554i | \(0.781596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.77198 | 0.500633 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.8384 | −1.32028 | −0.660140 | − | 0.751142i | \(-0.729503\pi\) | ||||
−0.660140 | + | 0.751142i | \(0.729503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.4164 | 0.936159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.1803 | 0.972482 | 0.486241 | − | 0.873825i | \(-0.338368\pi\) | ||||
0.486241 | + | 0.873825i | \(0.338368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.56564 | 0.483755 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.9443 | −0.652952 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.91034 | −0.246443 | −0.123221 | − | 0.992379i | \(-0.539323\pi\) | ||||
−0.123221 | + | 0.992379i | \(0.539323\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7082 | −0.634617 | −0.317309 | − | 0.948322i | \(-0.602779\pi\) | ||||
−0.317309 | + | 0.948322i | \(0.602779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.76393 | 0.137681 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.819660 | 0.0406290 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.89949 | −0.489499 | −0.244749 | − | 0.969586i | \(-0.578706\pi\) | ||||
−0.244749 | + | 0.969586i | \(0.578706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.74032 | 0.431128 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2918 | −0.503991 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.9343 | −0.631880 | −0.315940 | − | 0.948779i | \(-0.602320\pi\) | ||||
−0.315940 | + | 0.948779i | \(0.602320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5967 | −0.906350 | −0.453175 | − | 0.891422i | \(-0.649709\pi\) | ||||
−0.453175 | + | 0.891422i | \(0.649709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.3044 | 0.841369 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.94427 | −0.335273 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6525 | −0.802122 | −0.401061 | − | 0.916051i | \(-0.631358\pi\) | ||||
−0.401061 | + | 0.916051i | \(0.631358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.5579 | −0.795722 | −0.397861 | − | 0.917446i | \(-0.630247\pi\) | ||||
−0.397861 | + | 0.917446i | \(0.630247\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.82688 | −0.0873913 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0286 | −0.526365 | −0.263182 | − | 0.964746i | \(-0.584772\pi\) | ||||
−0.263182 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.12461 | 0.0534319 | 0.0267160 | − | 0.999643i | \(-0.491495\pi\) | ||||
0.0267160 | + | 0.999643i | \(0.491495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.86319 | 0.277319 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2361 | 0.671842 | 0.335921 | − | 0.941890i | \(-0.390953\pi\) | ||||
0.335921 | + | 0.941890i | \(0.390953\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.78593 | −0.319537 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.28980 | −0.154568 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.65248 | −0.264412 | −0.132206 | − | 0.991222i | \(-0.542206\pi\) | ||||
−0.132206 | + | 0.991222i | \(0.542206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0903 | −1.12200 | −0.560999 | − | 0.827816i | \(-0.689583\pi\) | ||||
−0.560999 | + | 0.827816i | \(0.689583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4164 | 0.623513 | 0.311757 | − | 0.950162i | \(-0.399083\pi\) | ||||
0.311757 | + | 0.950162i | \(0.399083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3879 | 0.943439 | 0.471719 | − | 0.881749i | \(-0.343634\pi\) | ||||
0.471719 | + | 0.881749i | \(0.343634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6525 | −0.490840 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.5967 | −1.31488 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.81966 | −0.174890 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.5725 | 1.39689 | 0.698447 | − | 0.715662i | \(-0.253875\pi\) | ||||
0.698447 | + | 0.715662i | \(0.253875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.540182 | 0.0246302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.5279 | 1.02083 | 0.510417 | − | 0.859927i | \(-0.329491\pi\) | ||||
0.510417 | + | 0.859927i | \(0.329491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.6383 | 0.797630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.23607 | 0.281430 | 0.140715 | − | 0.990050i | \(-0.455060\pi\) | ||||
0.140715 | + | 0.990050i | \(0.455060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.40492 | 0.333501 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.05573 | −0.405390 | −0.202695 | − | 0.979242i | \(-0.564970\pi\) | ||||
−0.202695 | + | 0.979242i | \(0.564970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.4164 | −0.778108 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.65841 | −0.296884 | −0.148442 | − | 0.988921i | \(-0.547426\pi\) | ||||
−0.148442 | + | 0.988921i | \(0.547426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.78593 | 0.301374 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.8539 | −0.525414 | −0.262707 | − | 0.964876i | \(-0.584615\pi\) | ||||
−0.262707 | + | 0.964876i | \(0.584615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.52786 | 0.0674568 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.8701 | −1.18174 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0689 | 0.705346 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.41732 | 0.149715 | 0.0748577 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748577 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.2333 | 0.447473 | 0.223736 | − | 0.974650i | \(-0.428175\pi\) | ||||
0.223736 | + | 0.974650i | \(0.428175\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.11146 | −0.0919765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.94427 | 0.301925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.4412 | −0.496507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.47214 | −0.193710 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.2333 | 0.441601 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.70820 | 0.116435 | 0.0582174 | − | 0.998304i | \(-0.481458\pi\) | ||||
0.0582174 | + | 0.998304i | \(0.481458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.7082 | 0.931588 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7082 | 0.714391 | 0.357196 | − | 0.934030i | \(-0.383733\pi\) | ||||
0.357196 | + | 0.934030i | \(0.383733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.6544 | −1.39366 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | −0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.6525 | −1.93436 | −0.967179 | − | 0.254097i | \(-0.918222\pi\) | ||||
−0.967179 | + | 0.254097i | \(0.918222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.8461 | −0.797107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.30495 | 0.223975 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.0308 | −1.22350 | −0.611751 | − | 0.791051i | \(-0.709534\pi\) | ||||
−0.611751 | + | 0.791051i | \(0.709534\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.05573 | 0.253869 | 0.126935 | − | 0.991911i | \(-0.459486\pi\) | ||||
0.126935 | + | 0.991911i | \(0.459486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.6525 | 1.49201 | 0.746005 | − | 0.665941i | \(-0.231970\pi\) | ||||
0.746005 | + | 0.665941i | \(0.231970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.89794 | −0.371717 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2209 | 0.592026 | 0.296013 | − | 0.955184i | \(-0.404343\pi\) | ||||
0.296013 | + | 0.955184i | \(0.404343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.6808 | 0.568553 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.93112 | 0.245642 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0857 | 0.870299 | 0.435150 | − | 0.900358i | \(-0.356695\pi\) | ||||
0.435150 | + | 0.900358i | \(0.356695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.403252 | 0.0166157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.20169 | 0.378507 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.0277 | 1.60268 | 0.801338 | − | 0.598212i | \(-0.204122\pi\) | ||||
0.801338 | + | 0.598212i | \(0.204122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.403252 | 0.0165040 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.4721 | 0.713892 | 0.356946 | − | 0.934125i | \(-0.383818\pi\) | ||||
0.356946 | + | 0.934125i | \(0.383818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.14988 | −0.291650 | −0.145825 | − | 0.989310i | \(-0.546584\pi\) | ||||
−0.145825 | + | 0.989310i | \(0.546584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.81966 | 0.359164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4226 | −0.950696 | −0.475348 | − | 0.879798i | \(-0.657678\pi\) | ||||
−0.475348 | + | 0.879798i | \(0.657678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.7082 | −0.716397 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.88854 | 0.359005 | 0.179502 | − | 0.983758i | \(-0.442551\pi\) | ||||
0.179502 | + | 0.983758i | \(0.442551\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3607 | −1.18202 | −0.591008 | − | 0.806666i | \(-0.701270\pi\) | ||||
−0.591008 | + | 0.806666i | \(0.701270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.5865 | −1.10879 | −0.554397 | − | 0.832252i | \(-0.687051\pi\) | ||||
−0.554397 | + | 0.832252i | \(0.687051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.0432 | −1.00495 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.01316 | −0.0404615 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.412662 | −0.0164539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.1452 | −0.641716 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.36068 | −0.291184 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.36068 | 0.211734 | 0.105867 | − | 0.994380i | \(-0.466238\pi\) | ||||
0.105867 | + | 0.994380i | \(0.466238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.8933 | 0.705643 | 0.352821 | − | 0.935691i | \(-0.385222\pi\) | ||||
0.352821 | + | 0.935691i | \(0.385222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.0957 | −1.73358 | −0.866790 | − | 0.498674i | \(-0.833821\pi\) | ||||
−0.866790 | + | 0.498674i | \(0.833821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.7658 | 0.697368 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.3050 | −1.06853 | −0.534263 | − | 0.845319i | \(-0.679411\pi\) | ||||
−0.534263 | + | 0.845319i | \(0.679411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.6544 | −1.27397 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.52786 | 0.293244 | 0.146622 | − | 0.989193i | \(-0.453160\pi\) | ||||
0.146622 | + | 0.989193i | \(0.453160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.4729 | 0.485139 | 0.242569 | − | 0.970134i | \(-0.422010\pi\) | ||||
0.242569 | + | 0.970134i | \(0.422010\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49613 | 0.135778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.1803 | 0.897546 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.1246 | −0.507427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 50.7054 | 1.95746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.7082 | 0.836790 | 0.418395 | − | 0.908265i | \(-0.362593\pi\) | ||||
0.418395 | + | 0.908265i | \(0.362593\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.1034 | 1.42600 | 0.713000 | − | 0.701164i | \(-0.247336\pi\) | ||||
0.713000 | + | 0.701164i | \(0.247336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.6525 | 0.638124 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.527864 | −0.0201982 | −0.0100991 | − | 0.999949i | \(-0.503215\pi\) | ||||
−0.0100991 | + | 0.999949i | \(0.503215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.2361 | 0.657597 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.90879 | 0.148913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.5632 | −1.39093 | −0.695465 | − | 0.718560i | \(-0.744802\pi\) | ||||
−0.695465 | + | 0.718560i | \(0.744802\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.41641 | 0.129406 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.0193 | 0.643728 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.2492 | −1.74681 | −0.873405 | − | 0.486995i | \(-0.838093\pi\) | ||||
−0.873405 | + | 0.486995i | \(0.838093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0788114 | 0.00297243 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8885 | 0.746930 | 0.373465 | − | 0.927644i | \(-0.378170\pi\) | ||||
0.373465 | + | 0.927644i | \(0.378170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.65248 | 0.211984 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.60970 | −0.247535 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.7990 | 0.739407 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.4056 | 1.35770 | 0.678850 | − | 0.734277i | \(-0.262479\pi\) | ||||
0.678850 | + | 0.734277i | \(0.262479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.23607 | −0.0459699 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9473 | 1.40739 | 0.703694 | − | 0.710503i | \(-0.251532\pi\) | ||||
0.703694 | + | 0.710503i | \(0.251532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94427 | 0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3972 | 0.532499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.7804 | 1.17384 | 0.586918 | − | 0.809646i | \(-0.300341\pi\) | ||||
0.586918 | + | 0.809646i | \(0.300341\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.6950 | −0.504464 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.9443 | −1.32223 | −0.661116 | − | 0.750284i | \(-0.729917\pi\) | ||||
−0.661116 | + | 0.750284i | \(0.729917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.667701 | −0.0245286 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.8197 | 0.873859 | 0.436929 | − | 0.899496i | \(-0.356066\pi\) | ||||
0.436929 | + | 0.899496i | \(0.356066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.1815 | −0.738404 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9443 | −0.472343 | −0.236172 | − | 0.971711i | \(-0.575893\pi\) | ||||
−0.236172 | + | 0.971711i | \(0.575893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.7214 | 1.44370 | 0.721849 | − | 0.692051i | \(-0.243293\pi\) | ||||
0.721849 | + | 0.692051i | \(0.243293\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.6066 | 0.602782 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.6150 | 1.39979 | 0.699897 | − | 0.714244i | \(-0.253229\pi\) | ||||
0.699897 | + | 0.714244i | \(0.253229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.7082 | 0.422759 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0996 | −0.652689 | −0.326345 | − | 0.945251i | \(-0.605817\pi\) | ||||
−0.326345 | + | 0.945251i | \(0.605817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.05573 | 0.0380211 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.7549 | −0.818438 | −0.409219 | − | 0.912436i | \(-0.634199\pi\) | ||||
−0.409219 | + | 0.912436i | \(0.634199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.652476 | −0.0233774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4296 | 0.408982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.3863 | −0.692811 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.2449 | −1.22070 | −0.610349 | − | 0.792133i | \(-0.708971\pi\) | ||||
−0.610349 | + | 0.792133i | \(0.708971\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.36706 | 0.0842695 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.4164 | 1.18665 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2256 | −0.610162 | −0.305081 | − | 0.952326i | \(-0.598684\pi\) | ||||
−0.305081 | + | 0.952326i | \(0.598684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5279 | 0.478581 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.3237 | 1.21277 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.7054 | 1.78935 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.22291 | 0.0782502 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.1246 | 1.83260 | 0.916302 | − | 0.400488i | \(-0.131159\pi\) | ||||
0.916302 | + | 0.400488i | \(0.131159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.4682 | 0.753852 | 0.376926 | − | 0.926243i | \(-0.376981\pi\) | ||||
0.376926 | + | 0.926243i | \(0.376981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.16718 | 0.111078 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.74962 | −0.0961969 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4721 | −0.993684 | −0.496842 | − | 0.867841i | \(-0.665507\pi\) | ||||
−0.496842 | + | 0.867841i | \(0.665507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.9443 | 1.18322 | 0.591611 | − | 0.806223i | \(-0.298492\pi\) | ||||
0.591611 | + | 0.806223i | \(0.298492\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3475 | 0.568459 | 0.284230 | − | 0.958756i | \(-0.408262\pi\) | ||||
0.284230 | + | 0.958756i | \(0.408262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.922740 | 0.0320481 | 0.0160240 | − | 0.999872i | \(-0.494899\pi\) | ||||
0.0160240 | + | 0.999872i | \(0.494899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.67080 | 0.0926492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.52786 | 0.191071 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.7162 | −1.57830 | −0.789149 | − | 0.614201i | \(-0.789478\pi\) | ||||
−0.789149 | + | 0.614201i | \(0.789478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0557 | −0.381232 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.0934 | −0.485403 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.81966 | 0.0624506 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.29180 | −0.0442822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.3677 | −1.07401 | −0.537005 | − | 0.843579i | \(-0.680445\pi\) | ||||
−0.537005 | + | 0.843579i | \(0.680445\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.3948 | −1.41402 | −0.707009 | − | 0.707205i | \(-0.749956\pi\) | ||||
−0.707009 | + | 0.707205i | \(0.749956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.8360 | 1.80274 | 0.901370 | − | 0.433049i | \(-0.142562\pi\) | ||||
0.901370 | + | 0.433049i | \(0.142562\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 50.1246 | 1.70626 | 0.853131 | − | 0.521697i | \(-0.174701\pi\) | ||||
0.853131 | + | 0.521697i | \(0.174701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.1877 | 0.413917 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.77709 | −0.297742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.02546 | −0.305816 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.0764 | 0.916397 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.4296 | 1.97303 | 0.986513 | − | 0.163682i | \(-0.0523372\pi\) | ||||
0.986513 | + | 0.163682i | \(0.0523372\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.5836 | −0.626809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.60970 | −0.222686 | −0.111343 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111343 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9443 | 0.805789 | 0.402894 | − | 0.915246i | \(-0.368004\pi\) | ||||
0.402894 | + | 0.915246i | \(0.368004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.03165 | 0.0346396 | 0.0173198 | − | 0.999850i | \(-0.494487\pi\) | ||||
0.0173198 | + | 0.999850i | \(0.494487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.40325 | 0.315021 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.58359 | −0.0864566 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9443 | 0.365419 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.11667 | −0.170651 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.98605 | −0.0994797 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.7771 | 1.45359 | 0.726797 | − | 0.686852i | \(-0.241008\pi\) | ||||
0.726797 | + | 0.686852i | \(0.241008\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.6035 | 0.484368 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.8885 | −1.42096 | −0.710480 | − | 0.703717i | \(-0.751522\pi\) | ||||
−0.710480 | + | 0.703717i | \(0.751522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.3376 | 1.03712 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.29180 | 0.174560 | 0.0872801 | − | 0.996184i | \(-0.472182\pi\) | ||||
0.0872801 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8328 | −0.356953 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.53244 | 0.247933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.1096 | 1.35022 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.78593 | −0.222639 | −0.111319 | − | 0.993785i | \(-0.535508\pi\) | ||||
−0.111319 | + | 0.993785i | \(0.535508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.4721 | 0.997613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.4798 | −1.09374 | −0.546868 | − | 0.837219i | \(-0.684180\pi\) | ||||
−0.546868 | + | 0.837219i | \(0.684180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1803 | 0.462758 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.9991 | −0.912746 | −0.456373 | − | 0.889789i | \(-0.650852\pi\) | ||||
−0.456373 | + | 0.889789i | \(0.650852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6947 | 0.348268 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −55.7771 | −1.81251 | −0.906256 | − | 0.422730i | \(-0.861072\pi\) | ||||
−0.906256 | + | 0.422730i | \(0.861072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.4164 | 1.08474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.0888 | 0.748705 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.9017 | 1.81083 | 0.905417 | − | 0.424524i | \(-0.139558\pi\) | ||||
0.905417 | + | 0.424524i | \(0.139558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.8554 | 0.415557 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5410 | −0.952936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.88854 | 0.254205 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.4164 | 1.01028 | 0.505142 | − | 0.863036i | \(-0.331440\pi\) | ||||
0.505142 | + | 0.863036i | \(0.331440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.510078 | 0.0163861 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.0957 | −1.41510 | −0.707549 | − | 0.706665i | \(-0.750199\pi\) | ||||
−0.707549 | + | 0.706665i | \(0.750199\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.5967 | −1.36279 | −0.681395 | − | 0.731916i | \(-0.738627\pi\) | ||||
−0.681395 | + | 0.731916i | \(0.738627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.2974 | −1.70339 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.2918 | −0.743650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.36551 | −0.0435529 | −0.0217764 | − | 0.999763i | \(-0.506932\pi\) | ||||
−0.0217764 | + | 0.999763i | \(0.506932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.0689 | 1.43311 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.6525 | 1.13254 | 0.566269 | − | 0.824220i | \(-0.308386\pi\) | ||||
0.566269 | + | 0.824220i | \(0.308386\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.9141 | −0.758891 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.8809 | 0.692975 | 0.346488 | − | 0.938055i | \(-0.387374\pi\) | ||||
0.346488 | + | 0.938055i | \(0.387374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.08036 | 0.0341812 |
(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 | 4900.2.a.bg.1.2 | ✓ | 4 | |
5.2 | odd | 4 | 4900.2.e.u.2549.5 | 8 | |||
5.3 | odd | 4 | 4900.2.e.u.2549.3 | 8 | |||
5.4 | even | 2 | 4900.2.a.bi.1.3 | yes | 4 | ||
7.6 | odd | 2 | inner | 4900.2.a.bg.1.3 | yes | 4 | |
35.13 | even | 4 | 4900.2.e.u.2549.6 | 8 | |||
35.27 | even | 4 | 4900.2.e.u.2549.4 | 8 | |||
35.34 | odd | 2 | 4900.2.a.bi.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4900.2.a.bg.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4900.2.a.bg.1.3 | yes | 4 | 7.6 | odd | 2 | inner | |
4900.2.a.bi.1.2 | yes | 4 | 35.34 | odd | 2 | ||
4900.2.a.bi.1.3 | yes | 4 | 5.4 | even | 2 | ||
4900.2.e.u.2549.3 | 8 | 5.3 | odd | 4 | |||
4900.2.e.u.2549.4 | 8 | 35.27 | even | 4 | |||
4900.2.e.u.2549.5 | 8 | 5.2 | odd | 4 | |||
4900.2.e.u.2549.6 | 8 | 35.13 | even | 4 |