Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3720,2,Mod(1,3720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3720.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: | \(29.7043495519\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3720.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.23607 | −0.467190 | −0.233595 | − | 0.972334i | \(-0.575049\pi\) | ||||
−0.233595 | + | 0.972334i | \(0.575049\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.47214 | 1.48481 | 0.742405 | − | 0.669951i | \(-0.233685\pi\) | ||||
0.742405 | + | 0.669951i | \(0.233685\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.23607 | 0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.23607 | −1.34370 | −0.671852 | − | 0.740685i | \(-0.734501\pi\) | ||||
−0.671852 | + | 0.740685i | \(0.734501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23607 | 0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76393 | 0.783186 | 0.391593 | − | 0.920139i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920139i | \(0.371924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.23607 | 0.518186 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.94427 | 1.30466 | 0.652328 | − | 0.757937i | \(-0.273792\pi\) | ||||
0.652328 | + | 0.757937i | \(0.273792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.47214 | −0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.47214 | −0.857255 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.76393 | 0.880589 | 0.440294 | − | 0.897853i | \(-0.354874\pi\) | ||||
0.440294 | + | 0.897853i | \(0.354874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.23607 | −0.155730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70820 | 0.453029 | 0.226515 | − | 0.974008i | \(-0.427267\pi\) | ||||
0.226515 | + | 0.974008i | \(0.427267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.23607 | −1.09612 | −0.548060 | − | 0.836439i | \(-0.684633\pi\) | ||||
−0.548060 | + | 0.836439i | \(0.684633\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1803 | 1.42560 | 0.712800 | − | 0.701367i | \(-0.247427\pi\) | ||||
0.712800 | + | 0.701367i | \(0.247427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.94427 | −0.542704 | −0.271352 | − | 0.962480i | \(-0.587471\pi\) | ||||
−0.271352 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.23607 | 0.775788 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.23607 | −0.767022 | −0.383511 | − | 0.923536i | \(-0.625285\pi\) | ||||
−0.383511 | + | 0.923536i | \(0.625285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.47214 | −0.664027 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9443 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6525 | −1.64082 | −0.820409 | − | 0.571778i | \(-0.806254\pi\) | ||||
−0.820409 | + | 0.571778i | \(0.806254\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.23607 | −0.120628 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9443 | 1.25137 | 0.625685 | − | 0.780076i | \(-0.284820\pi\) | ||||
0.625685 | + | 0.780076i | \(0.284820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.52786 | −0.337908 | −0.168954 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168954 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.76393 | −0.452172 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.94427 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.23607 | −0.299175 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.52786 | −0.506738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | 0.541002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4164 | −1.01304 | −0.506521 | − | 0.862228i | \(-0.669069\pi\) | ||||
−0.506521 | + | 0.862228i | \(0.669069\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.47214 | −0.569840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.23607 | −0.806959 | −0.403480 | − | 0.914989i | \(-0.632199\pi\) | ||||
−0.403480 | + | 0.914989i | \(0.632199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0000 | −1.19610 | −0.598050 | − | 0.801459i | \(-0.704058\pi\) | ||||
−0.598050 | + | 0.801459i | \(0.704058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.94427 | −0.753244 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.23607 | 0.600923 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.47214 | 0.451334 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9443 | −1.55198 | −0.775988 | − | 0.630748i | \(-0.782748\pi\) | ||||
−0.775988 | + | 0.630748i | \(0.782748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8885 | 1.13023 | 0.565117 | − | 0.825011i | \(-0.308831\pi\) | ||||
0.565117 | + | 0.825011i | \(0.308831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.47214 | 0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.41641 | −0.432276 | −0.216138 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216138 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.47214 | −0.671884 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.94427 | 0.389663 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.76393 | 0.529792 | 0.264896 | − | 0.964277i | \(-0.414662\pi\) | ||||
0.264896 | + | 0.964277i | \(0.414662\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.47214 | 0.494937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.0000 | −1.67263 | −0.836315 | − | 0.548250i | \(-0.815294\pi\) | ||||
−0.836315 | + | 0.548250i | \(0.815294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23607 | −0.0934380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.76393 | −0.508408 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.4164 | 1.59187 | 0.795935 | − | 0.605383i | \(-0.206980\pi\) | ||||
0.795935 | + | 0.605383i | \(0.206980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4721 | 0.921967 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.76393 | −0.350251 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.23607 | 0.0899107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7639 | −1.06828 | −0.534140 | − | 0.845396i | \(-0.679365\pi\) | ||||
−0.534140 | + | 0.845396i | \(0.679365\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.41641 | 0.677808 | 0.338904 | − | 0.940821i | \(-0.389944\pi\) | ||||
0.338904 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.23607 | −0.231740 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.94427 | 0.209771 | 0.104885 | − | 0.994484i | \(-0.466552\pi\) | ||||
0.104885 | + | 0.994484i | \(0.466552\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.8885 | 0.984533 | 0.492266 | − | 0.870445i | \(-0.336169\pi\) | ||||
0.492266 | + | 0.870445i | \(0.336169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.94427 | 0.627765 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3607 | 1.67706 | 0.838529 | − | 0.544857i | \(-0.183416\pi\) | ||||
0.838529 | + | 0.544857i | \(0.183416\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.23607 | 0.632845 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.47214 | −0.441396 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.23607 | 0.0839098 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.1803 | −0.823071 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.4164 | −1.02322 | −0.511611 | − | 0.859217i | \(-0.670951\pi\) | ||||
−0.511611 | + | 0.859217i | \(0.670951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9443 | 1.25187 | 0.625936 | − | 0.779874i | \(-0.284717\pi\) | ||||
0.625936 | + | 0.779874i | \(0.284717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.4164 | −1.92713 | −0.963566 | − | 0.267469i | \(-0.913813\pi\) | ||||
−0.963566 | + | 0.267469i | \(0.913813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.94427 | −0.583460 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.94427 | 0.580993 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.41641 | −0.479728 | −0.239864 | − | 0.970807i | \(-0.577103\pi\) | ||||
−0.239864 | + | 0.970807i | \(0.577103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05573 | −0.0680054 | −0.0340027 | − | 0.999422i | \(-0.510825\pi\) | ||||
−0.0340027 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.47214 | 0.349602 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.9443 | −1.33265 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.94427 | 0.313331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.47214 | 0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.4164 | −1.33592 | −0.667959 | − | 0.744198i | \(-0.732832\pi\) | ||||
−0.667959 | + | 0.744198i | \(0.732832\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.88854 | −0.365896 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.23607 | −0.447901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.0000 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47214 | −0.520439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.23607 | 0.442840 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.0689 | −1.83333 | −0.916666 | − | 0.399654i | \(-0.869130\pi\) | ||||
−0.916666 | + | 0.399654i | \(0.869130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.8885 | −1.57262 | −0.786309 | − | 0.617834i | \(-0.788010\pi\) | ||||
−0.786309 | + | 0.617834i | \(0.788010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.81966 | −0.229501 | −0.114751 | − | 0.993394i | \(-0.536607\pi\) | ||||
−0.114751 | + | 0.993394i | \(0.536607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4721 | −0.982645 | −0.491323 | − | 0.870978i | \(-0.663486\pi\) | ||||
−0.491323 | + | 0.870978i | \(0.663486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.1803 | −0.842934 | −0.421467 | − | 0.906844i | \(-0.638485\pi\) | ||||
−0.421467 | + | 0.906844i | \(0.638485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.47214 | 0.383376 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.41641 | 0.437777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.47214 | 0.496645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4164 | 0.783795 | 0.391897 | − | 0.920009i | \(-0.371819\pi\) | ||||
0.391897 | + | 0.920009i | \(0.371819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.76393 | −0.393811 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9443 | 0.748587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.9443 | 0.628732 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4721 | 0.714152 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.76393 | −0.386038 | −0.193019 | − | 0.981195i | \(-0.561828\pi\) | ||||
−0.193019 | + | 0.981195i | \(0.561828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.6525 | 0.947326 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7639 | −0.837186 | −0.418593 | − | 0.908174i | \(-0.637477\pi\) | ||||
−0.418593 | + | 0.908174i | \(0.637477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6525 | −0.602114 | −0.301057 | − | 0.953606i | \(-0.597339\pi\) | ||||
−0.301057 | + | 0.953606i | \(0.597339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.23607 | 0.0696445 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.4721 | −1.59915 | −0.799577 | − | 0.600563i | \(-0.794943\pi\) | ||||
−0.799577 | + | 0.600563i | \(0.794943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.9443 | −0.722479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.9443 | 1.61050 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.23607 | −0.179505 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.52786 | 0.195091 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.0557 | −0.609522 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9443 | −1.59092 | −0.795461 | − | 0.606005i | \(-0.792771\pi\) | ||||
−0.795461 | + | 0.606005i | \(0.792771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.76393 | 0.261062 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.70820 | −0.202601 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.1803 | −1.75297 | −0.876487 | − | 0.481425i | \(-0.840119\pi\) | ||||
−0.876487 | + | 0.481425i | \(0.840119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.94427 | −0.159911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4164 | 0.832408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.8885 | −0.745576 | −0.372788 | − | 0.927917i | \(-0.621598\pi\) | ||||
−0.372788 | + | 0.927917i | \(0.621598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4721 | 1.09585 | 0.547924 | − | 0.836528i | \(-0.315418\pi\) | ||||
0.547924 | + | 0.836528i | \(0.315418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.23607 | 0.172729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4721 | −0.876723 | −0.438362 | − | 0.898799i | \(-0.644441\pi\) | ||||
−0.438362 | + | 0.898799i | \(0.644441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.23607 | 0.490200 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.52786 | 0.292566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1246 | 1.43158 | 0.715791 | − | 0.698314i | \(-0.246066\pi\) | ||||
0.715791 | + | 0.698314i | \(0.246066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1803 | −0.637548 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.05573 | 0.368306 | 0.184153 | − | 0.982898i | \(-0.441046\pi\) | ||||
0.184153 | + | 0.982898i | \(0.441046\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4721 | −0.543686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.3607 | 1.57202 | 0.786008 | − | 0.618216i | \(-0.212144\pi\) | ||||
0.786008 | + | 0.618216i | \(0.212144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.4164 | 1.20601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.4164 | −0.997354 | −0.498677 | − | 0.866788i | \(-0.666181\pi\) | ||||
−0.498677 | + | 0.866788i | \(0.666181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4164 | 0.584880 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.47214 | 0.328997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.2918 | −0.521815 | −0.260907 | − | 0.965364i | \(-0.584022\pi\) | ||||
−0.260907 | + | 0.965364i | \(0.584022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8885 | −0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.23607 | 0.465898 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.94427 | 0.450035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.9443 | 1.95456 | 0.977278 | − | 0.211959i | \(-0.0679844\pi\) | ||||
0.977278 | + | 0.211959i | \(0.0679844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.76393 | −0.237899 | −0.118950 | − | 0.992900i | \(-0.537953\pi\) | ||||
−0.118950 | + | 0.992900i | \(0.537953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.23607 | 0.161200 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5836 | 0.523325 | 0.261662 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261662 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.0000 | 0.690569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.36068 | −0.411402 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.94427 | 0.242705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6525 | −1.20435 | −0.602176 | − | 0.798363i | \(-0.705700\pi\) | ||||
−0.602176 | + | 0.798363i | \(0.705700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3607 | −1.67464 | −0.837319 | − | 0.546715i | \(-0.815878\pi\) | ||||
−0.837319 | + | 0.546715i | \(0.815878\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.94427 | 0.434885 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.4164 | 0.746052 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.1246 | 1.69189 | 0.845947 | − | 0.533268i | \(-0.179036\pi\) | ||||
0.845947 | + | 0.533268i | \(0.179036\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.2361 | 1.11665 | 0.558327 | − | 0.829621i | \(-0.311443\pi\) | ||||
0.558327 | + | 0.829621i | \(0.311443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.23607 | −0.346943 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.8885 | −1.23842 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8328 | 1.47157 | 0.735785 | − | 0.677215i | \(-0.236813\pi\) | ||||
0.735785 | + | 0.677215i | \(0.236813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.47214 | −0.260578 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.5279 | 1.02282 | 0.511410 | − | 0.859337i | \(-0.329123\pi\) | ||||
0.511410 | + | 0.859337i | \(0.329123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.23607 | 0.343023 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.9443 | 0.896033 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.7082 | −1.21325 | −0.606623 | − | 0.794990i | \(-0.707476\pi\) | ||||
−0.606623 | + | 0.794990i | \(0.707476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.8885 | −0.652541 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2361 | 0.712713 | 0.356357 | − | 0.934350i | \(-0.384019\pi\) | ||||
0.356357 | + | 0.934350i | \(0.384019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.0689 | 1.95934 | 0.979672 | − | 0.200608i | \(-0.0642917\pi\) | ||||
0.979672 | + | 0.200608i | \(0.0642917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4164 | −0.530565 | −0.265283 | − | 0.964171i | \(-0.585465\pi\) | ||||
−0.265283 | + | 0.964171i | \(0.585465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.94427 | 0.228794 | 0.114397 | − | 0.993435i | \(-0.463506\pi\) | ||||
0.114397 | + | 0.993435i | \(0.463506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.58359 | −0.211651 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.41641 | 0.249575 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.47214 | 0.296962 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.47214 | 0.387912 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.2918 | −0.561626 | −0.280813 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280813 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.4164 | −0.702928 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.94427 | −0.224972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.47214 | 0.384700 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.52786 | 0.431749 | 0.215874 | − | 0.976421i | \(-0.430740\pi\) | ||||
0.215874 | + | 0.976421i | \(0.430740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.76393 | −0.305876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.583592 | 0.0263371 | 0.0131686 | − | 0.999913i | \(-0.495808\pi\) | ||||
0.0131686 | + | 0.999913i | \(0.495808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.3607 | −1.45745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.4164 | 0.512096 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.9443 | 1.47479 | 0.737394 | − | 0.675463i | \(-0.236056\pi\) | ||||
0.737394 | + | 0.675463i | \(0.236056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.8328 | −0.839714 | −0.419857 | − | 0.907590i | \(-0.637920\pi\) | ||||
−0.419857 | + | 0.907590i | \(0.637920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9443 | 0.487014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.52786 | 0.112266 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.1246 | 1.64552 | 0.822760 | − | 0.568389i | \(-0.192433\pi\) | ||||
0.822760 | + | 0.568389i | \(0.192433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0557 | −0.666026 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.47214 | −0.285752 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6525 | 0.733796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0000 | 0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.9443 | −1.18045 | −0.590225 | − | 0.807239i | \(-0.700961\pi\) | ||||
−0.590225 | + | 0.807239i | \(0.700961\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.3607 | 1.76485 | 0.882425 | − | 0.470454i | \(-0.155910\pi\) | ||||
0.882425 | + | 0.470454i | \(0.155910\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.23607 | 0.0539464 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.47214 | −0.194809 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.76393 | 0.293530 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4164 | 0.841018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9443 | −0.559630 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.3050 | −1.68985 | −0.844926 | − | 0.534883i | \(-0.820356\pi\) | ||||
−0.844926 | + | 0.534883i | \(0.820356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.4164 | −0.919066 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.52786 | 0.151117 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6525 | 0.712008 | 0.356004 | − | 0.934484i | \(-0.384139\pi\) | ||||
0.356004 | + | 0.934484i | \(0.384139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4721 | −0.532298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.8328 | −1.99515 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0557 | 0.470137 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.76393 | 0.202218 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4164 | −0.737957 | −0.368978 | − | 0.929438i | \(-0.620292\pi\) | ||||
−0.368978 | + | 0.929438i | \(0.620292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.9443 | −0.885848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.0000 | 1.34864 | 0.674320 | − | 0.738440i | \(-0.264437\pi\) | ||||
0.674320 | + | 0.738440i | \(0.264437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.94427 | −0.123866 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.23607 | −0.0519100 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.65248 | −0.278886 | −0.139443 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139443 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9443 | −1.04389 | −0.521943 | − | 0.852981i | \(-0.674793\pi\) | ||||
−0.521943 | + | 0.852981i | \(0.674793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.7639 | 0.616772 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.05573 | −0.376995 | −0.188497 | − | 0.982074i | \(-0.560362\pi\) | ||||
−0.188497 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.41641 | −0.391333 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.11146 | 0.253546 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.23607 | 0.133795 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.9443 | −1.02956 | −0.514780 | − | 0.857322i | \(-0.672126\pi\) | ||||
−0.514780 | + | 0.857322i | \(0.672126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.47214 | −0.266680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.94427 | −0.121111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.83282 | −0.362720 | −0.181360 | − | 0.983417i | \(-0.558050\pi\) | ||||
−0.181360 | + | 0.983417i | \(0.558050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52786 | 0.226620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8885 | −0.568420 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.1246 | 0.781410 | 0.390705 | − | 0.920516i | \(-0.372231\pi\) | ||||
0.390705 | + | 0.920516i | \(0.372231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.4721 | 1.48773 | 0.743865 | − | 0.668330i | \(-0.232991\pi\) | ||||
0.743865 | + | 0.668330i | \(0.232991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.70820 | 0.151010 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.59675 | −0.227165 | −0.113582 | − | 0.993529i | \(-0.536233\pi\) | ||||
−0.113582 | + | 0.993529i | \(0.536233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.94427 | −0.362440 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.9443 | −1.17096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.70820 | −0.230552 | −0.115276 | − | 0.993333i | \(-0.536775\pi\) | ||||
−0.115276 | + | 0.993333i | \(0.536775\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.8328 | 1.48283 | 0.741417 | − | 0.671045i | \(-0.234154\pi\) | ||||
0.741417 | + | 0.671045i | \(0.234154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.7771 | 1.75955 | 0.879775 | − | 0.475391i | \(-0.157693\pi\) | ||||
0.879775 | + | 0.475391i | \(0.157693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.94427 | 0.358345 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.3050 | 0.849484 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.05573 | −0.121647 | −0.0608233 | − | 0.998149i | \(-0.519373\pi\) | ||||
−0.0608233 | + | 0.998149i | \(0.519373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.3607 | −0.968250 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.4164 | 0.453046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7082 | 0.701625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.23607 | −0.365373 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.180340 | 0.00712300 | 0.00356150 | − | 0.999994i | \(-0.498866\pi\) | ||||
0.00356150 | + | 0.999994i | \(0.498866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4164 | −1.08120 | −0.540599 | − | 0.841281i | \(-0.681802\pi\) | ||||
−0.540599 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.47214 | 0.254840 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.0557 | −0.749158 | −0.374579 | − | 0.927195i | \(-0.622213\pi\) | ||||
−0.374579 | + | 0.927195i | \(0.622213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.23607 | −0.0484453 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4164 | 1.15115 | 0.575576 | − | 0.817748i | \(-0.304778\pi\) | ||||
0.575576 | + | 0.817748i | \(0.304778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.23607 | 0.360883 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.1803 | 0.475200 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2361 | 0.983058 | 0.491529 | − | 0.870861i | \(-0.336438\pi\) | ||||
0.491529 | + | 0.870861i | \(0.336438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.94427 | −0.270101 | −0.135050 | − | 0.990839i | \(-0.543120\pi\) | ||||
−0.135050 | + | 0.990839i | \(0.543120\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.4721 | 0.562051 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9443 | 1.12073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | 0.154649 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7639 | 0.492013 | 0.246007 | − | 0.969268i | \(-0.420881\pi\) | ||||
0.246007 | + | 0.969268i | \(0.420881\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.4164 | −1.28430 | −0.642148 | − | 0.766580i | \(-0.721957\pi\) | ||||
−0.642148 | + | 0.766580i | \(0.721957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4721 | 0.401884 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4164 | 0.590758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.41641 | −0.283781 | −0.141890 | − | 0.989882i | \(-0.545318\pi\) | ||||
−0.141890 | + | 0.989882i | \(0.545318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.0000 | 0.534913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.9443 | −0.722769 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.4164 | −1.04448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00000 | −0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.8328 | −1.01637 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.4164 | 1.11263 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.5279 | −1.34187 | −0.670934 | − | 0.741517i | \(-0.734107\pi\) | ||||
−0.670934 | + | 0.741517i | \(0.734107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.8328 | 1.16288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.94427 | 0.336861 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.5279 | 0.508768 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | 0.525781 | 0.262891 | − | 0.964826i | \(-0.415324\pi\) | ||||
0.262891 | + | 0.964826i | \(0.415324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.94427 | −0.335436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.41641 | 0.276971 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5836 | 0.766573 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.05573 | 0.0392630 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.23607 | −0.268741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.40325 | −0.0891317 | −0.0445658 | − | 0.999006i | \(-0.514190\pi\) | ||||
−0.0445658 | + | 0.999006i | \(0.514190\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.9443 | 1.07054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7771 | −0.952098 | −0.476049 | − | 0.879419i | \(-0.657932\pi\) | ||||
−0.476049 | + | 0.879419i | \(0.657932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.47214 | −0.201843 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9443 | 0.770447 | 0.385224 | − | 0.922823i | \(-0.374124\pi\) | ||||
0.385224 | + | 0.922823i | \(0.374124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.9443 | 0.769407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.9443 | 0.694064 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.94427 | −0.180901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.0000 | −0.584627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.88854 | 0.0689139 | 0.0344570 | − | 0.999406i | \(-0.489030\pi\) | ||||
0.0344570 | + | 0.999406i | \(0.489030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.00000 | 0.291536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.8885 | −0.505456 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.1246 | −0.477022 | −0.238511 | − | 0.971140i | \(-0.576659\pi\) | ||||
−0.238511 | + | 0.971140i | \(0.576659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.1803 | 1.45654 | 0.728268 | − | 0.685292i | \(-0.240326\pi\) | ||||
0.728268 | + | 0.685292i | \(0.240326\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.36068 | 0.157867 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.47214 | −0.161690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.8885 | −0.790350 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.47214 | 0.305513 | 0.152757 | − | 0.988264i | \(-0.451185\pi\) | ||||
0.152757 | + | 0.988264i | \(0.451185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.4164 | 0.771293 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3050 | 0.838221 | 0.419110 | − | 0.907935i | \(-0.362342\pi\) | ||||
0.419110 | + | 0.907935i | \(0.362342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.88854 | 0.211250 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.8328 | −1.39133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.23607 | 0.258596 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.41641 | 0.193320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.63932 | −0.129399 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.3607 | 1.43325 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.47214 | 0.300476 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.8328 | 1.02131 | 0.510655 | − | 0.859785i | \(-0.329403\pi\) | ||||
0.510655 | + | 0.859785i | \(0.329403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.0000 | 1.41510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.23607 | −0.255674 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.94427 | −0.174263 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.0689 | 1.05847 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.70820 | −0.0600573 | −0.0300286 | − | 0.999549i | \(-0.509560\pi\) | ||||
−0.0300286 | + | 0.999549i | \(0.509560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.3607 | −1.13634 | −0.568169 | − | 0.822912i | \(-0.692348\pi\) | ||||
−0.568169 | + | 0.822912i | \(0.692348\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.8885 | 0.907951 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.76393 | −0.236930 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.8885 | 1.46549 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.18034 | −0.145895 | −0.0729474 | − | 0.997336i | \(-0.523241\pi\) | ||||
−0.0729474 | + | 0.997336i | \(0.523241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.36068 | −0.291435 | −0.145717 | − | 0.989326i | \(-0.546549\pi\) | ||||
−0.145717 | + | 0.989326i | \(0.546549\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0000 | 0.556375 | 0.278187 | − | 0.960527i | \(-0.410266\pi\) | ||||
0.278187 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.3050 | 1.08727 | 0.543633 | − | 0.839323i | \(-0.317048\pi\) | ||||
0.543633 | + | 0.839323i | \(0.317048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.81966 | 0.132503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.4721 | −0.847909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23607 | 0.0426738 | 0.0213369 | − | 0.999772i | \(-0.493208\pi\) | ||||
0.0213369 | + | 0.999772i | \(0.493208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3607 | 0.805541 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.4721 | 0.567330 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.52786 | 0.0869612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.5967 | 0.467190 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.1803 | 0.486668 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.0557 | −0.653222 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7771 | 1.29346 | 0.646731 | − | 0.762718i | \(-0.276135\pi\) | ||||
0.646731 | + | 0.762718i | \(0.276135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.47214 | −0.221342 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.00000 | −0.0683187 | −0.0341593 | − | 0.999416i | \(-0.510875\pi\) | ||||
−0.0341593 | + | 0.999416i | \(0.510875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.8885 | 1.83865 | 0.919327 | − | 0.393495i | \(-0.128734\pi\) | ||||
0.919327 | + | 0.393495i | \(0.128734\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.41641 | −0.252751 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0000 | 1.08929 | 0.544646 | − | 0.838666i | \(-0.316664\pi\) | ||||
0.544646 | + | 0.838666i | \(0.316664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0000 | 0.748022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.00000 | −0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.47214 | −0.286738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.23607 | 0.0417867 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.9443 | 0.504632 | 0.252316 | − | 0.967645i | \(-0.418808\pi\) | ||||
0.252316 | + | 0.967645i | \(0.418808\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.4164 | −0.452524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0689 | −0.473993 | −0.236996 | − | 0.971511i | \(-0.576163\pi\) | ||||
−0.236996 | + | 0.971511i | \(0.576163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.8328 | −1.17222 | −0.586109 | − | 0.810232i | \(-0.699341\pi\) | ||||
−0.586109 | + | 0.810232i | \(0.699341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.76393 | 0.227367 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.4164 | −0.651939 | −0.325970 | − | 0.945380i | \(-0.605691\pi\) | ||||
−0.325970 | + | 0.945380i | \(0.605691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1115 | 0.473283 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.8885 | 1.93717 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.9443 | −0.432197 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.23607 | 0.241336 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8885 | 1.26225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.4164 | −0.711905 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.5410 | −1.67819 | −0.839094 | − | 0.543987i | \(-0.816914\pi\) | ||||
−0.839094 | + | 0.543987i | \(0.816914\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.9443 | −0.362999 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.88854 | −0.327622 | −0.163811 | − | 0.986492i | \(-0.552379\pi\) | ||||
−0.163811 | + | 0.986492i | \(0.552379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.4721 | −0.412316 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.4164 | 0.377003 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.3050 | −1.09863 | −0.549314 | − | 0.835616i | \(-0.685111\pi\) | ||||
−0.549314 | + | 0.835616i | \(0.685111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.76393 | 0.222879 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.8885 | 0.983793 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.76393 | 0.156637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.6525 | −0.546939 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.5967 | 0.774184 | 0.387092 | − | 0.922041i | \(-0.373480\pi\) | ||||
0.387092 | + | 0.922041i | \(0.373480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.4164 | −1.16073 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7639 | 0.483349 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58359 | 0.0844023 | 0.0422011 | − | 0.999109i | \(-0.486563\pi\) | ||||
0.0422011 | + | 0.999109i | \(0.486563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6525 | 0.347630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.4853 | 1.09159 | 0.545795 | − | 0.837919i | \(-0.316228\pi\) | ||||
0.545795 | + | 0.837919i | \(0.316228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.23607 | −0.0402093 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.94427 | −0.160667 | −0.0803336 | − | 0.996768i | \(-0.525599\pi\) | ||||
−0.0803336 | + | 0.996768i | \(0.525599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.4164 | −1.27951 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.4721 | 0.923272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.9443 | −0.872811 | −0.436405 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436405 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7639 | 0.477750 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3050 | 0.558806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.9443 | 0.417123 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.41641 | −0.303125 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0000 | −1.41494 | −0.707472 | − | 0.706741i | \(-0.750165\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.9443 | −0.929824 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7082 | −0.632466 | −0.316233 | − | 0.948681i | \(-0.602418\pi\) | ||||
−0.316233 | + | 0.948681i | \(0.602418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.94427 | −0.158506 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.23607 | 0.103637 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.94427 | 0.0941956 | 0.0470978 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470978 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.52786 | −0.112636 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.7771 | −0.375631 | −0.187815 | − | 0.982204i | \(-0.560141\pi\) | ||||
−0.187815 | + | 0.982204i | \(0.560141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.94427 | −0.0938123 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.0557 | 0.351908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.8885 | −0.823208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.9443 | 0.918519 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.8885 | −0.440296 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5279 | −0.365091 | −0.182546 | − | 0.983197i | \(-0.558434\pi\) | ||||
−0.182546 | + | 0.983197i | \(0.558434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.76393 | −0.150724 |
(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 | 3720.2.a.i.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 7440.2.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3720.2.a.i.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
7440.2.a.bi.1.2 | 2 | 4.3 | odd | 2 |