Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | 0.233595 | 0.116797 | − | 0.993156i | \(-0.462737\pi\) | ||||
0.116797 | + | 0.993156i | \(0.462737\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607 | 1.57873 | 0.789367 | − | 0.613922i | \(-0.210409\pi\) | ||||
0.789367 | + | 0.613922i | \(0.210409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.85410 | 0.514235 | 0.257118 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257118 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.854102 | 0.195944 | 0.0979722 | − | 0.995189i | \(-0.468764\pi\) | ||||
0.0979722 | + | 0.995189i | \(0.468764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.47214 | 1.80627 | ||||||||
\(23\) | −3.76393 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.381966 | 0.0721848 | ||||||||
\(29\) | 3.61803 | 0.671852 | 0.335926 | − | 0.941888i | \(-0.390951\pi\) | ||||
0.335926 | + | 0.941888i | \(0.390951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.47214 | 1.45296 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.236068 | −0.0388093 | −0.0194047 | − | 0.999812i | \(-0.506177\pi\) | ||||
−0.0194047 | + | 0.999812i | \(0.506177\pi\) | |||||||
\(38\) | 1.38197 | 0.224184 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.763932 | 0.119306 | 0.0596531 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596531 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.85410 | −0.740244 | −0.370122 | − | 0.928983i | \(-0.620684\pi\) | ||||
−0.370122 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(44\) | 3.23607 | 0.487856 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.09017 | −0.897947 | ||||||||
\(47\) | −0.618034 | −0.0901495 | −0.0450748 | − | 0.998984i | \(-0.514353\pi\) | ||||
−0.0450748 | + | 0.998984i | \(0.514353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.14590 | 0.158907 | ||||||||
\(53\) | 3.47214 | 0.476935 | 0.238467 | − | 0.971151i | \(-0.423355\pi\) | ||||
0.238467 | + | 0.971151i | \(0.423355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.38197 | −0.184673 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.85410 | 0.768681 | ||||||||
\(59\) | 10.8541 | 1.41308 | 0.706542 | − | 0.707671i | \(-0.250254\pi\) | ||||
0.706542 | + | 0.707671i | \(0.250254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.70820 | 1.11497 | 0.557486 | − | 0.830187i | \(-0.311766\pi\) | ||||
0.557486 | + | 0.830187i | \(0.311766\pi\) | |||||||
\(62\) | −4.85410 | −0.616472 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76393 | 0.582007 | 0.291003 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291003 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.61803 | 0.785416 | 0.392708 | − | 0.919663i | \(-0.371538\pi\) | ||||
0.392708 | + | 0.919663i | \(0.371538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.00000 | −1.05337 | −0.526685 | − | 0.850060i | \(-0.676565\pi\) | ||||
−0.526685 | + | 0.850060i | \(0.676565\pi\) | |||||||
\(74\) | −0.381966 | −0.0444026 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.527864 | 0.0605502 | ||||||||
\(77\) | 3.23607 | 0.368784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.09017 | −0.910215 | −0.455108 | − | 0.890436i | \(-0.650399\pi\) | ||||
−0.455108 | + | 0.890436i | \(0.650399\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.23607 | 0.136501 | ||||||||
\(83\) | 6.23607 | 0.684497 | 0.342249 | − | 0.939609i | \(-0.388811\pi\) | ||||
0.342249 | + | 0.939609i | \(0.388811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.85410 | −0.846930 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.7082 | −1.24810 | ||||||||
\(89\) | 8.94427 | 0.948091 | 0.474045 | − | 0.880500i | \(-0.342793\pi\) | ||||
0.474045 | + | 0.880500i | \(0.342793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.14590 | 0.120123 | ||||||||
\(92\) | −2.32624 | −0.242527 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.00000 | −0.103142 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.85410 | −0.391325 | −0.195662 | − | 0.980671i | \(-0.562686\pi\) | ||||
−0.195662 | + | 0.980671i | \(0.562686\pi\) | |||||||
\(98\) | −10.7082 | −1.08169 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.47214 | −0.146483 | −0.0732415 | − | 0.997314i | \(-0.523334\pi\) | ||||
−0.0732415 | + | 0.997314i | \(0.523334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.56231 | 0.843669 | 0.421835 | − | 0.906673i | \(-0.361386\pi\) | ||||
0.421835 | + | 0.906673i | \(0.361386\pi\) | |||||||
\(104\) | −4.14590 | −0.406539 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.61803 | 0.545672 | ||||||||
\(107\) | 16.4164 | 1.58703 | 0.793517 | − | 0.608548i | \(-0.208248\pi\) | ||||
0.793517 | + | 0.608548i | \(0.208248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | −16.8541 | −1.58550 | −0.792750 | − | 0.609547i | \(-0.791352\pi\) | ||||
−0.792750 | + | 0.609547i | \(0.791352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.23607 | 0.207614 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.5623 | 1.61674 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 14.0902 | 1.27566 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.85410 | −0.166503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8885 | 1.76482 | 0.882411 | − | 0.470479i | \(-0.155919\pi\) | ||||
0.882411 | + | 0.470479i | \(0.155919\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.79837 | −0.593977 | −0.296988 | − | 0.954881i | \(-0.595982\pi\) | ||||
−0.296988 | + | 0.954881i | \(0.595982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.527864 | 0.0457716 | ||||||||
\(134\) | 7.70820 | 0.665887 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.7082 | −1.00397 | ||||||||
\(137\) | 11.9443 | 1.02047 | 0.510234 | − | 0.860036i | \(-0.329559\pi\) | ||||
0.510234 | + | 0.860036i | \(0.329559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.7082 | 0.898613 | ||||||||
\(143\) | 9.70820 | 0.811841 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.5623 | −1.20519 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.145898 | −0.0119927 | ||||||||
\(149\) | 3.94427 | 0.323127 | 0.161564 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161564 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5623 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298128\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298128\pi\) | |||||||
\(152\) | −1.90983 | −0.154908 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.23607 | 0.421934 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1803 | 1.05191 | 0.525953 | − | 0.850514i | \(-0.323709\pi\) | ||||
0.525953 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(158\) | −13.0902 | −1.04140 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32624 | −0.183333 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 0.472136 | 0.0368676 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.0902 | 0.783149 | ||||||||
\(167\) | −14.5623 | −1.12687 | −0.563433 | − | 0.826162i | \(-0.690520\pi\) | ||||
−0.563433 | + | 0.826162i | \(0.690520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.00000 | −0.228748 | ||||||||
\(173\) | −18.8885 | −1.43607 | −0.718035 | − | 0.696007i | \(-0.754958\pi\) | ||||
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −25.4164 | −1.91583 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.4721 | 1.08473 | ||||||||
\(179\) | 0.527864 | 0.0394544 | 0.0197272 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197272 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.291796 | 0.0216890 | 0.0108445 | − | 0.999941i | \(-0.496548\pi\) | ||||
0.0108445 | + | 0.999941i | \(0.496548\pi\) | |||||||
\(182\) | 1.85410 | 0.137435 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.41641 | 0.620466 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4164 | 2.00489 | ||||||||
\(188\) | −0.381966 | −0.0278577 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.81966 | 0.131666 | 0.0658330 | − | 0.997831i | \(-0.479030\pi\) | ||||
0.0658330 | + | 0.997831i | \(0.479030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.70820 | 0.554849 | 0.277424 | − | 0.960747i | \(-0.410519\pi\) | ||||
0.277424 | + | 0.960747i | \(0.410519\pi\) | |||||||
\(194\) | −6.23607 | −0.447724 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.09017 | −0.292155 | ||||||||
\(197\) | −3.70820 | −0.264199 | −0.132099 | − | 0.991236i | \(-0.542172\pi\) | ||||
−0.132099 | + | 0.991236i | \(0.542172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5623 | −1.24496 | −0.622479 | − | 0.782636i | \(-0.713875\pi\) | ||||
−0.622479 | + | 0.782636i | \(0.713875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.38197 | −0.167595 | ||||||||
\(203\) | 2.23607 | 0.156941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.8541 | 0.965261 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.00000 | −0.624038 | ||||||||
\(209\) | 4.47214 | 0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.18034 | −0.632001 | −0.316000 | − | 0.948759i | \(-0.602340\pi\) | ||||
−0.316000 | + | 0.948759i | \(0.602340\pi\) | |||||||
\(212\) | 2.14590 | 0.147381 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.5623 | 1.81576 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.85410 | −0.125865 | ||||||||
\(218\) | 16.1803 | 1.09587 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70820 | 0.653044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.180340 | −0.0120765 | −0.00603823 | − | 0.999982i | \(-0.501922\pi\) | ||||
−0.00603823 | + | 0.999982i | \(0.501922\pi\) | |||||||
\(224\) | −2.09017 | −0.139655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.2705 | −1.81401 | ||||||||
\(227\) | −14.7639 | −0.979917 | −0.489958 | − | 0.871746i | \(-0.662988\pi\) | ||||
−0.489958 | + | 0.871746i | \(0.662988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.7082 | 1.43452 | 0.717259 | − | 0.696806i | \(-0.245396\pi\) | ||||
0.717259 | + | 0.696806i | \(0.245396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.09017 | −0.531146 | ||||||||
\(233\) | 2.94427 | 0.192886 | 0.0964428 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964428 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.70820 | 0.436667 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.23607 | 0.339404 | ||||||||
\(239\) | 20.5279 | 1.32784 | 0.663919 | − | 0.747805i | \(-0.268892\pi\) | ||||
0.663919 | + | 0.747805i | \(0.268892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.52786 | 0.162834 | 0.0814170 | − | 0.996680i | \(-0.474055\pi\) | ||||
0.0814170 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(242\) | 26.5623 | 1.70749 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.38197 | 0.344545 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.58359 | 0.100762 | ||||||||
\(248\) | 6.70820 | 0.425971 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1803 | 1.84185 | 0.920923 | − | 0.389744i | \(-0.127436\pi\) | ||||
0.920923 | + | 0.389744i | \(0.127436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.7082 | −1.23904 | ||||||||
\(254\) | 32.1803 | 2.01917 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −22.8541 | −1.42560 | −0.712800 | − | 0.701367i | \(-0.752573\pi\) | ||||
−0.712800 | + | 0.701367i | \(0.752573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.145898 | −0.00906566 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.0000 | −0.679582 | ||||||||
\(263\) | 10.9098 | 0.672729 | 0.336364 | − | 0.941732i | \(-0.390803\pi\) | ||||
0.336364 | + | 0.941732i | \(0.390803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.854102 | 0.0523684 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.94427 | 0.179850 | ||||||||
\(269\) | 12.7639 | 0.778231 | 0.389115 | − | 0.921189i | \(-0.372781\pi\) | ||||
0.389115 | + | 0.921189i | \(0.372781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −25.4164 | −1.54110 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.3262 | 1.16754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.7082 | −1.48457 | −0.742286 | − | 0.670083i | \(-0.766258\pi\) | ||||
−0.742286 | + | 0.670083i | \(0.766258\pi\) | |||||||
\(278\) | 8.09017 | 0.485216 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0902 | −0.601929 | −0.300965 | − | 0.953635i | \(-0.597309\pi\) | ||||
−0.300965 | + | 0.953635i | \(0.597309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.8541 | −1.77464 | −0.887321 | − | 0.461152i | \(-0.847436\pi\) | ||||
−0.887321 | + | 0.461152i | \(0.847436\pi\) | |||||||
\(284\) | 4.09017 | 0.242707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.7082 | 0.928846 | ||||||||
\(287\) | 0.472136 | 0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.56231 | −0.325509 | ||||||||
\(293\) | 19.5279 | 1.14083 | 0.570415 | − | 0.821357i | \(-0.306782\pi\) | ||||
0.570415 | + | 0.821357i | \(0.306782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.527864 | 0.0306815 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.38197 | 0.369697 | ||||||||
\(299\) | −6.97871 | −0.403589 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 23.5623 | 1.35586 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.14590 | −0.237784 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.23607 | 0.527130 | 0.263565 | − | 0.964642i | \(-0.415102\pi\) | ||||
0.263565 | + | 0.964642i | \(0.415102\pi\) | |||||||
\(308\) | 2.00000 | 0.113961 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.50658 | −0.482364 | −0.241182 | − | 0.970480i | \(-0.577535\pi\) | ||||
−0.241182 | + | 0.970480i | \(0.577535\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7639 | −0.947553 | −0.473777 | − | 0.880645i | \(-0.657110\pi\) | ||||
−0.473777 | + | 0.880645i | \(0.657110\pi\) | |||||||
\(314\) | 21.3262 | 1.20351 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00000 | −0.281272 | ||||||||
\(317\) | −7.65248 | −0.429806 | −0.214903 | − | 0.976635i | \(-0.568944\pi\) | ||||
−0.214903 | + | 0.976635i | \(0.568944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9443 | 1.06068 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.76393 | −0.209756 | ||||||||
\(323\) | 4.47214 | 0.248836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.7984 | 0.985761 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.70820 | −0.0943198 | ||||||||
\(329\) | −0.381966 | −0.0210585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.1246 | −1.27104 | −0.635522 | − | 0.772083i | \(-0.719215\pi\) | ||||
−0.635522 | + | 0.772083i | \(0.719215\pi\) | |||||||
\(332\) | 3.85410 | 0.211521 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.5623 | −1.28927 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.85410 | 0.427840 | 0.213920 | − | 0.976851i | \(-0.431377\pi\) | ||||
0.213920 | + | 0.976851i | \(0.431377\pi\) | |||||||
\(338\) | −15.4721 | −0.841573 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7082 | −0.850647 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.41641 | −0.454443 | ||||||||
\(344\) | 10.8541 | 0.585214 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.5623 | −1.64304 | ||||||||
\(347\) | 19.9098 | 1.06882 | 0.534408 | − | 0.845227i | \(-0.320535\pi\) | ||||
0.534408 | + | 0.845227i | \(0.320535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7082 | 1.16201 | 0.581007 | − | 0.813899i | \(-0.302659\pi\) | ||||
0.581007 | + | 0.813899i | \(0.302659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.7082 | −0.943850 | ||||||||
\(353\) | −12.9098 | −0.687121 | −0.343560 | − | 0.939131i | \(-0.611633\pi\) | ||||
−0.343560 | + | 0.939131i | \(0.611633\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.52786 | 0.292976 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.854102 | 0.0451407 | ||||||||
\(359\) | −13.7426 | −0.725309 | −0.362655 | − | 0.931924i | \(-0.618130\pi\) | ||||
−0.362655 | + | 0.931924i | \(0.618130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2705 | −0.961606 | ||||||||
\(362\) | 0.472136 | 0.0248149 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.708204 | 0.0371200 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.5623 | −1.33434 | −0.667171 | − | 0.744905i | \(-0.732495\pi\) | ||||
−0.667171 | + | 0.744905i | \(0.732495\pi\) | |||||||
\(368\) | 18.2705 | 0.952416 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.14590 | 0.111409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2705 | −1.46379 | −0.731896 | − | 0.681417i | \(-0.761364\pi\) | ||||
−0.731896 | + | 0.681417i | \(0.761364\pi\) | |||||||
\(374\) | 44.3607 | 2.29384 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.38197 | 0.0712695 | ||||||||
\(377\) | 6.70820 | 0.345490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5967 | 0.749785 | 0.374892 | − | 0.927068i | \(-0.377680\pi\) | ||||
0.374892 | + | 0.927068i | \(0.377680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.94427 | 0.150642 | ||||||||
\(383\) | −33.3607 | −1.70465 | −0.852326 | − | 0.523012i | \(-0.824808\pi\) | ||||
−0.852326 | + | 0.523012i | \(0.824808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4721 | 0.634815 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.38197 | −0.120926 | ||||||||
\(389\) | −15.0000 | −0.760530 | −0.380265 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380265 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7082 | −0.996687 | ||||||||
\(392\) | 14.7984 | 0.747431 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.0344 | 1.45720 | 0.728598 | − | 0.684941i | \(-0.240172\pi\) | ||||
0.728598 | + | 0.684941i | \(0.240172\pi\) | |||||||
\(398\) | −28.4164 | −1.42439 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.5967 | −1.32818 | −0.664089 | − | 0.747653i | \(-0.731180\pi\) | ||||
−0.664089 | + | 0.747653i | \(0.731180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.56231 | −0.277078 | ||||||||
\(404\) | −0.909830 | −0.0452657 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.61803 | 0.179560 | ||||||||
\(407\) | −1.23607 | −0.0612696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.58359 | 0.0783036 | 0.0391518 | − | 0.999233i | \(-0.487534\pi\) | ||||
0.0391518 | + | 0.999233i | \(0.487534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.29180 | 0.260708 | ||||||||
\(413\) | 6.70820 | 0.330089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.27051 | −0.307437 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.23607 | 0.353928 | ||||||||
\(419\) | 9.47214 | 0.462744 | 0.231372 | − | 0.972865i | \(-0.425679\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | −14.8541 | −0.723086 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.76393 | −0.377050 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.38197 | 0.260452 | ||||||||
\(428\) | 10.1459 | 0.490420 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.8328 | 1.43700 | 0.718498 | − | 0.695529i | \(-0.244830\pi\) | ||||
0.718498 | + | 0.695529i | \(0.244830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8541 | 1.29053 | 0.645263 | − | 0.763961i | \(-0.276748\pi\) | ||||
0.645263 | + | 0.763961i | \(0.276748\pi\) | |||||||
\(434\) | −3.00000 | −0.144005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.18034 | 0.295985 | ||||||||
\(437\) | −3.21478 | −0.153784 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.9787 | −1.95581 | −0.977904 | − | 0.209056i | \(-0.932961\pi\) | ||||
−0.977904 | + | 0.209056i | \(0.932961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.7082 | 0.747163 | ||||||||
\(443\) | −29.9443 | −1.42270 | −0.711348 | − | 0.702840i | \(-0.751915\pi\) | ||||
−0.711348 | + | 0.702840i | \(0.751915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.291796 | −0.0138169 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.61803 | 0.123690 | ||||||||
\(449\) | −4.67376 | −0.220568 | −0.110284 | − | 0.993900i | \(-0.535176\pi\) | ||||
−0.110284 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −10.4164 | −0.489947 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.8885 | −1.12114 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4164 | −1.00182 | −0.500909 | − | 0.865500i | \(-0.667001\pi\) | ||||
−0.500909 | + | 0.865500i | \(0.667001\pi\) | |||||||
\(458\) | 35.1246 | 1.64127 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.819660 | −0.0381754 | −0.0190877 | − | 0.999818i | \(-0.506076\pi\) | ||||
−0.0190877 | + | 0.999818i | \(0.506076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1246 | −1.12117 | −0.560583 | − | 0.828098i | \(-0.689423\pi\) | ||||
−0.560583 | + | 0.828098i | \(0.689423\pi\) | |||||||
\(464\) | −17.5623 | −0.815310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.76393 | 0.220685 | ||||||||
\(467\) | −27.4508 | −1.27027 | −0.635137 | − | 0.772400i | \(-0.719056\pi\) | ||||
−0.635137 | + | 0.772400i | \(0.719056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.94427 | 0.135954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.2705 | −1.11714 | ||||||||
\(473\) | −25.4164 | −1.16865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 33.2148 | 1.51921 | ||||||||
\(479\) | 10.8541 | 0.495937 | 0.247968 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247968 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.437694 | −0.0199571 | ||||||||
\(482\) | 4.09017 | 0.186302 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.1459 | 0.461177 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.4164 | −1.65018 | −0.825092 | − | 0.564998i | \(-0.808877\pi\) | ||||
−0.825092 | + | 0.564998i | \(0.808877\pi\) | |||||||
\(488\) | −19.4721 | −0.881462 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.2492 | 1.95181 | 0.975905 | − | 0.218196i | \(-0.0700171\pi\) | ||||
0.975905 | + | 0.218196i | \(0.0700171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.9443 | 0.853207 | ||||||||
\(494\) | 2.56231 | 0.115284 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.5623 | 0.653867 | ||||||||
\(497\) | 4.09017 | 0.183469 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.56231 | 0.338535 | 0.169268 | − | 0.985570i | \(-0.445860\pi\) | ||||
0.169268 | + | 0.985570i | \(0.445860\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 47.2148 | 2.10730 | ||||||||
\(503\) | 37.4164 | 1.66832 | 0.834158 | − | 0.551526i | \(-0.185954\pi\) | ||||
0.834158 | + | 0.551526i | \(0.185954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −31.8885 | −1.41762 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.2918 | 0.545360 | ||||||||
\(509\) | 20.3262 | 0.900945 | 0.450472 | − | 0.892790i | \(-0.351256\pi\) | ||||
0.450472 | + | 0.892790i | \(0.351256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.56231 | −0.246062 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −36.9787 | −1.63106 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.23607 | −0.142322 | ||||||||
\(518\) | −0.236068 | −0.0103722 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3607 | −1.28631 | −0.643157 | − | 0.765734i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765734i | \(0.722376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1459 | −0.574830 | −0.287415 | − | 0.957806i | \(-0.592796\pi\) | ||||
−0.287415 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(524\) | −4.20163 | −0.183549 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.6525 | 0.769685 | ||||||||
\(527\) | −15.7082 | −0.684260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.326238 | 0.0141442 | ||||||||
\(533\) | 1.41641 | 0.0613514 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.6525 | −0.460117 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.6525 | 0.890391 | ||||||||
\(539\) | −34.6525 | −1.49259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1246 | 1.16618 | 0.583089 | − | 0.812408i | \(-0.301844\pi\) | ||||
0.583089 | + | 0.812408i | \(0.301844\pi\) | |||||||
\(542\) | −12.9443 | −0.556004 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.7082 | −0.759233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2918 | −0.910371 | −0.455186 | − | 0.890397i | \(-0.650427\pi\) | ||||
−0.455186 | + | 0.890397i | \(0.650427\pi\) | |||||||
\(548\) | 7.38197 | 0.315342 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.09017 | 0.131646 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | −0.212622 | ||||||||
\(554\) | −39.9787 | −1.69853 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.09017 | 0.131052 | ||||||||
\(557\) | −4.76393 | −0.201854 | −0.100927 | − | 0.994894i | \(-0.532181\pi\) | ||||
−0.100927 | + | 0.994894i | \(0.532181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.00000 | −0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.3262 | −0.688681 | ||||||||
\(563\) | −7.38197 | −0.311113 | −0.155556 | − | 0.987827i | \(-0.549717\pi\) | ||||
−0.155556 | + | 0.987827i | \(0.549717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −48.3050 | −2.03041 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7984 | −0.620926 | ||||||||
\(569\) | −20.5279 | −0.860573 | −0.430286 | − | 0.902692i | \(-0.641587\pi\) | ||||
−0.430286 | + | 0.902692i | \(0.641587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.12461 | −0.340004 | −0.170002 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170002 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(572\) | 6.00000 | 0.250873 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.763932 | 0.0318859 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.7771 | −1.40616 | −0.703079 | − | 0.711111i | \(-0.748192\pi\) | ||||
−0.703079 | + | 0.711111i | \(0.748192\pi\) | |||||||
\(578\) | 16.8541 | 0.701038 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.85410 | 0.159895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.1803 | 0.752953 | ||||||||
\(584\) | 20.1246 | 0.832762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.5967 | 1.30525 | ||||||||
\(587\) | −5.29180 | −0.218416 | −0.109208 | − | 0.994019i | \(-0.534831\pi\) | ||||
−0.109208 | + | 0.994019i | \(0.534831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.56231 | −0.105578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.14590 | 0.0470961 | ||||||||
\(593\) | 10.9098 | 0.448013 | 0.224007 | − | 0.974588i | \(-0.428086\pi\) | ||||
0.224007 | + | 0.974588i | \(0.428086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.43769 | 0.0998518 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.2918 | −0.461756 | ||||||||
\(599\) | 9.47214 | 0.387021 | 0.193510 | − | 0.981098i | \(-0.438013\pi\) | ||||
0.193510 | + | 0.981098i | \(0.438013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.72949 | 0.111338 | 0.0556691 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556691 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(602\) | −4.85410 | −0.197838 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.00000 | 0.366205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.5623 | −1.44343 | −0.721715 | − | 0.692191i | \(-0.756646\pi\) | ||||
−0.721715 | + | 0.692191i | \(0.756646\pi\) | |||||||
\(608\) | −2.88854 | −0.117146 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.14590 | −0.0463581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9787 | −0.604985 | −0.302492 | − | 0.953152i | \(-0.597819\pi\) | ||||
−0.302492 | + | 0.953152i | \(0.597819\pi\) | |||||||
\(614\) | 14.9443 | 0.603102 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.23607 | −0.291549 | ||||||||
\(617\) | −14.2361 | −0.573123 | −0.286561 | − | 0.958062i | \(-0.592512\pi\) | ||||
−0.286561 | + | 0.958062i | \(0.592512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5279 | 1.22702 | 0.613509 | − | 0.789688i | \(-0.289757\pi\) | ||||
0.613509 | + | 0.789688i | \(0.289757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.7639 | −0.551883 | ||||||||
\(623\) | 5.52786 | 0.221469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.1246 | −1.08412 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.14590 | 0.325057 | ||||||||
\(629\) | −1.23607 | −0.0492853 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.2361 | −0.407491 | −0.203746 | − | 0.979024i | \(-0.565312\pi\) | ||||
−0.203746 | + | 0.979024i | \(0.565312\pi\) | |||||||
\(632\) | 18.0902 | 0.719588 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3820 | −0.491751 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.2705 | −0.486175 | ||||||||
\(638\) | 30.6525 | 1.21354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.09017 | 0.0430591 | 0.0215296 | − | 0.999768i | \(-0.493146\pi\) | ||||
0.0215296 | + | 0.999768i | \(0.493146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.8328 | −1.21593 | −0.607964 | − | 0.793965i | \(-0.708013\pi\) | ||||
−0.607964 | + | 0.793965i | \(0.708013\pi\) | |||||||
\(644\) | −1.43769 | −0.0566531 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.23607 | 0.284699 | ||||||||
\(647\) | 36.5410 | 1.43658 | 0.718288 | − | 0.695746i | \(-0.244926\pi\) | ||||
0.718288 | + | 0.695746i | \(0.244926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.8328 | 2.23088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.79837 | 0.266245 | ||||||||
\(653\) | −19.0902 | −0.747056 | −0.373528 | − | 0.927619i | \(-0.621852\pi\) | ||||
−0.373528 | + | 0.927619i | \(0.621852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.70820 | −0.144781 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.618034 | −0.0240935 | ||||||||
\(659\) | −15.5279 | −0.604880 | −0.302440 | − | 0.953168i | \(-0.597801\pi\) | ||||
−0.302440 | + | 0.953168i | \(0.597801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.6869 | 0.765732 | 0.382866 | − | 0.923804i | \(-0.374937\pi\) | ||||
0.382866 | + | 0.923804i | \(0.374937\pi\) | |||||||
\(662\) | −37.4164 | −1.45423 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.9443 | −0.541143 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6180 | −0.527292 | ||||||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.5967 | 1.76024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1803 | 0.469518 | 0.234759 | − | 0.972054i | \(-0.424570\pi\) | ||||
0.234759 | + | 0.972054i | \(0.424570\pi\) | |||||||
\(674\) | 12.7082 | 0.489502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | −10.6180 | −0.408084 | −0.204042 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204042 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.38197 | −0.0914115 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −25.4164 | −0.973245 | ||||||||
\(683\) | 13.4721 | 0.515497 | 0.257748 | − | 0.966212i | \(-0.417019\pi\) | ||||
0.257748 | + | 0.966212i | \(0.417019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.6180 | −0.519939 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.5623 | 0.898304 | ||||||||
\(689\) | 6.43769 | 0.245257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2705 | 1.37980 | 0.689898 | − | 0.723907i | \(-0.257656\pi\) | ||||
0.689898 | + | 0.723907i | \(0.257656\pi\) | |||||||
\(692\) | −11.6738 | −0.443770 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.2148 | 1.22286 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 35.1246 | 1.32949 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0132 | 1.54905 | 0.774523 | − | 0.632546i | \(-0.217990\pi\) | ||||
0.774523 | + | 0.632546i | \(0.217990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.201626 | −0.00760447 | ||||||||
\(704\) | 22.1803 | 0.835953 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.8885 | −0.786151 | ||||||||
\(707\) | −0.909830 | −0.0342177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.5410 | −1.25966 | −0.629830 | − | 0.776733i | \(-0.716875\pi\) | ||||
−0.629830 | + | 0.776733i | \(0.716875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.0000 | −0.749532 | ||||||||
\(713\) | 11.2918 | 0.422881 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.326238 | 0.0121921 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.2361 | −0.829843 | ||||||||
\(719\) | 23.2918 | 0.868637 | 0.434319 | − | 0.900759i | \(-0.356989\pi\) | ||||
0.434319 | + | 0.900759i | \(0.356989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.29180 | 0.197077 | ||||||||
\(722\) | −29.5623 | −1.10020 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.180340 | 0.00670228 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.5623 | 0.910966 | 0.455483 | − | 0.890245i | \(-0.349467\pi\) | ||||
0.455483 | + | 0.890245i | \(0.349467\pi\) | |||||||
\(728\) | −2.56231 | −0.0949654 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.4164 | −0.940060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.9787 | −0.737931 | −0.368965 | − | 0.929443i | \(-0.620288\pi\) | ||||
−0.368965 | + | 0.929443i | \(0.620288\pi\) | |||||||
\(734\) | −41.3607 | −1.52665 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.7295 | 0.469215 | ||||||||
\(737\) | 24.9443 | 0.918834 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9787 | 0.587786 | 0.293893 | − | 0.955838i | \(-0.405049\pi\) | ||||
0.293893 | + | 0.955838i | \(0.405049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.47214 | 0.127466 | ||||||||
\(743\) | −28.3607 | −1.04045 | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.7426 | −1.67476 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.9443 | 0.619544 | ||||||||
\(749\) | 10.1459 | 0.370723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.11146 | −0.186520 | −0.0932598 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932598 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.8541 | 0.395283 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.4164 | 1.10550 | 0.552752 | − | 0.833346i | \(-0.313578\pi\) | ||||
0.552752 | + | 0.833346i | \(0.313578\pi\) | |||||||
\(758\) | 23.6180 | 0.857846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4508 | 0.668843 | 0.334421 | − | 0.942424i | \(-0.391459\pi\) | ||||
0.334421 | + | 0.942424i | \(0.391459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.18034 | 0.223743 | ||||||||
\(764\) | 1.12461 | 0.0406870 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −53.9787 | −1.95033 | ||||||||
\(767\) | 20.1246 | 0.726658 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4164 | 0.483808 | 0.241904 | − | 0.970300i | \(-0.422228\pi\) | ||||
0.241904 | + | 0.970300i | \(0.422228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.76393 | 0.171458 | ||||||||
\(773\) | 36.1591 | 1.30055 | 0.650275 | − | 0.759699i | \(-0.274654\pi\) | ||||
0.650275 | + | 0.759699i | \(0.274654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.61803 | 0.309369 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.2705 | −0.870140 | ||||||||
\(779\) | 0.652476 | 0.0233774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.6525 | 1.23996 | ||||||||
\(782\) | −31.8885 | −1.14033 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 32.1246 | 1.14731 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8197 | −0.421325 | −0.210663 | − | 0.977559i | \(-0.567562\pi\) | ||||
−0.210663 | + | 0.977559i | \(0.567562\pi\) | |||||||
\(788\) | −2.29180 | −0.0816419 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4164 | −0.370365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1459 | 0.573358 | ||||||||
\(794\) | 46.9787 | 1.66721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.8541 | −0.384713 | ||||||||
\(797\) | −9.76393 | −0.345856 | −0.172928 | − | 0.984934i | \(-0.555323\pi\) | ||||
−0.172928 | + | 0.984934i | \(0.555323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.23607 | −0.114484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −43.0344 | −1.51960 | ||||||||
\(803\) | −47.1246 | −1.66299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.00000 | −0.317011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.29180 | 0.115805 | ||||||||
\(809\) | −30.9787 | −1.08915 | −0.544577 | − | 0.838711i | \(-0.683310\pi\) | ||||
−0.544577 | + | 0.838711i | \(0.683310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.7082 | −0.516475 | −0.258237 | − | 0.966081i | \(-0.583142\pi\) | ||||
−0.258237 | + | 0.966081i | \(0.583142\pi\) | |||||||
\(812\) | 1.38197 | 0.0484975 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.14590 | −0.145047 | ||||||||
\(818\) | 2.56231 | 0.0895889 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6869 | 1.41998 | 0.709992 | − | 0.704210i | \(-0.248699\pi\) | ||||
0.709992 | + | 0.704210i | \(0.248699\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.7082 | 1.66300 | 0.831502 | − | 0.555522i | \(-0.187482\pi\) | ||||
0.831502 | + | 0.555522i | \(0.187482\pi\) | |||||||
\(824\) | −19.1459 | −0.666979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8541 | 0.377663 | ||||||||
\(827\) | 0.965558 | 0.0335757 | 0.0167879 | − | 0.999859i | \(-0.494656\pi\) | ||||
0.0167879 | + | 0.999859i | \(0.494656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.8541 | −1.24526 | −0.622632 | − | 0.782515i | \(-0.713937\pi\) | ||||
−0.622632 | + | 0.782515i | \(0.713937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.85410 | 0.272292 | ||||||||
\(833\) | −34.6525 | −1.20064 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.76393 | 0.0955926 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.3262 | 0.529436 | ||||||||
\(839\) | −10.8541 | −0.374725 | −0.187363 | − | 0.982291i | \(-0.559994\pi\) | ||||
−0.187363 | + | 0.982291i | \(0.559994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 51.7771 | 1.78436 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.67376 | −0.195299 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1459 | 0.348617 | ||||||||
\(848\) | −16.8541 | −0.578772 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.888544 | 0.0304589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3050 | −0.524032 | −0.262016 | − | 0.965064i | \(-0.584387\pi\) | ||||
−0.262016 | + | 0.965064i | \(0.584387\pi\) | |||||||
\(854\) | 8.70820 | 0.297989 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | −19.6869 | −0.672492 | −0.336246 | − | 0.941774i | \(-0.609157\pi\) | ||||
−0.336246 | + | 0.941774i | \(0.609157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.58359 | −0.0540315 | −0.0270157 | − | 0.999635i | \(-0.508600\pi\) | ||||
−0.0270157 | + | 0.999635i | \(0.508600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 48.2705 | 1.64410 | ||||||||
\(863\) | 21.4377 | 0.729748 | 0.364874 | − | 0.931057i | \(-0.381112\pi\) | ||||
0.364874 | + | 0.931057i | \(0.381112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43.4508 | 1.47652 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.14590 | −0.0388943 | ||||||||
\(869\) | −42.3607 | −1.43699 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.83282 | 0.299289 | ||||||||
\(872\) | −22.3607 | −0.757228 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.20163 | −0.175948 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.5410 | −1.23390 | −0.616951 | − | 0.787001i | \(-0.711632\pi\) | ||||
−0.616951 | + | 0.787001i | \(0.711632\pi\) | |||||||
\(878\) | −66.3050 | −2.23768 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3607 | 1.35979 | 0.679893 | − | 0.733311i | \(-0.262026\pi\) | ||||
0.679893 | + | 0.733311i | \(0.262026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.5836 | −0.692693 | −0.346347 | − | 0.938107i | \(-0.612578\pi\) | ||||
−0.346347 | + | 0.938107i | \(0.612578\pi\) | |||||||
\(884\) | 6.00000 | 0.201802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.4508 | −1.62774 | ||||||||
\(887\) | −29.8885 | −1.00356 | −0.501780 | − | 0.864996i | \(-0.667321\pi\) | ||||
−0.501780 | + | 0.864996i | \(0.667321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.2918 | 0.412254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.111456 | −0.00373183 | ||||||||
\(893\) | −0.527864 | −0.0176643 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.41641 | 0.281172 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.56231 | −0.252357 | ||||||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1803 | 0.605675 | ||||||||
\(902\) | 6.47214 | 0.215499 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.6869 | 1.25345 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.2492 | −1.10402 | −0.552011 | − | 0.833837i | \(-0.686139\pi\) | ||||
−0.552011 | + | 0.833837i | \(0.686139\pi\) | |||||||
\(908\) | −9.12461 | −0.302811 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2361 | 1.33308 | 0.666540 | − | 0.745469i | \(-0.267774\pi\) | ||||
0.666540 | + | 0.745469i | \(0.267774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.6525 | 1.08064 | ||||||||
\(914\) | −34.6525 | −1.14620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.4164 | 0.443291 | ||||||||
\(917\) | −4.20163 | −0.138750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.2148 | −1.75539 | −0.877697 | − | 0.479216i | \(-0.840921\pi\) | ||||
−0.877697 | + | 0.479216i | \(0.840921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.32624 | −0.0436773 | ||||||||
\(923\) | 12.2705 | 0.403889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39.0344 | −1.28275 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.2361 | −0.401669 | ||||||||
\(929\) | −41.6312 | −1.36588 | −0.682938 | − | 0.730477i | \(-0.739298\pi\) | ||||
−0.682938 | + | 0.730477i | \(0.739298\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65248 | −0.185252 | ||||||||
\(932\) | 1.81966 | 0.0596049 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −44.4164 | −1.45335 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7295 | 0.579197 | 0.289599 | − | 0.957148i | \(-0.406478\pi\) | ||||
0.289599 | + | 0.957148i | \(0.406478\pi\) | |||||||
\(938\) | 4.76393 | 0.155548 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.4164 | 1.51313 | 0.756566 | − | 0.653918i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653918i | \(0.226876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.87539 | −0.0936355 | ||||||||
\(944\) | −52.6869 | −1.71481 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.1246 | −1.33708 | ||||||||
\(947\) | −2.65248 | −0.0861939 | −0.0430969 | − | 0.999071i | \(-0.513722\pi\) | ||||
−0.0430969 | + | 0.999071i | \(0.513722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.6869 | −0.541680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.23607 | −0.234522 | ||||||||
\(953\) | 7.74265 | 0.250809 | 0.125404 | − | 0.992106i | \(-0.459977\pi\) | ||||
0.125404 | + | 0.992106i | \(0.459977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.6869 | 0.410324 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.5623 | 0.567412 | ||||||||
\(959\) | 7.38197 | 0.238376 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | −0.708204 | −0.0228334 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.56231 | 0.0503185 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.11146 | 0.132216 | 0.0661078 | − | 0.997812i | \(-0.478942\pi\) | ||||
0.0661078 | + | 0.997812i | \(0.478942\pi\) | |||||||
\(968\) | −36.7082 | −1.17985 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.61803 | −0.180291 | −0.0901456 | − | 0.995929i | \(-0.528733\pi\) | ||||
−0.0901456 | + | 0.995929i | \(0.528733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.09017 | 0.0990663 | ||||||||
\(974\) | −58.9230 | −1.88801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.2705 | −1.35305 | ||||||||
\(977\) | 2.34752 | 0.0751040 | 0.0375520 | − | 0.999295i | \(-0.488044\pi\) | ||||
0.0375520 | + | 0.999295i | \(0.488044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.8328 | 1.49678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 69.9787 | 2.23311 | ||||||||
\(983\) | −9.61803 | −0.306768 | −0.153384 | − | 0.988167i | \(-0.549017\pi\) | ||||
−0.153384 | + | 0.988167i | \(0.549017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 30.6525 | 0.976174 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.978714 | 0.0311370 | ||||||||
\(989\) | 18.2705 | 0.580968 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3607 | −0.487948 | −0.243974 | − | 0.969782i | \(-0.578451\pi\) | ||||
−0.243974 | + | 0.969782i | \(0.578451\pi\) | |||||||
\(992\) | 10.1459 | 0.322133 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.61803 | 0.209911 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8885 | 0.788228 | 0.394114 | − | 0.919062i | \(-0.371051\pi\) | ||||
0.394114 | + | 0.919062i | \(0.371051\pi\) | |||||||
\(998\) | 12.2361 | 0.387326 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 625.2.a.b.1.1 | 2 | |||
5.4 | even | 2 | 5625.2.a.d.1.1 | 2 | |||
12.11 | even | 2 | 10000.2.a.c.1.1 | 2 | |||
15.2 | even | 4 | 625.2.b.a.624.1 | 4 | |||
15.8 | even | 4 | 625.2.b.a.624.4 | 4 | |||
15.14 | odd | 2 | 625.2.a.c.1.2 | 2 | |||
25.11 | even | 5 | 225.2.h.b.46.1 | 4 | |||
25.16 | even | 5 | 225.2.h.b.181.1 | 4 | |||
60.59 | even | 2 | 10000.2.a.l.1.2 | 2 | |||
75.2 | even | 20 | 125.2.e.a.24.1 | 8 | |||
75.8 | even | 20 | 625.2.e.c.374.1 | 8 | |||
75.11 | odd | 10 | 25.2.d.a.21.1 | yes | 4 | ||
75.14 | odd | 10 | 125.2.d.a.101.1 | 4 | |||
75.17 | even | 20 | 625.2.e.c.374.2 | 8 | |||
75.23 | even | 20 | 125.2.e.a.24.2 | 8 | |||
75.29 | odd | 10 | 625.2.d.b.376.1 | 4 | |||
75.38 | even | 20 | 125.2.e.a.99.1 | 8 | |||
75.41 | odd | 10 | 25.2.d.a.6.1 | ✓ | 4 | ||
75.44 | odd | 10 | 625.2.d.b.251.1 | 4 | |||
75.47 | even | 20 | 625.2.e.c.249.1 | 8 | |||
75.53 | even | 20 | 625.2.e.c.249.2 | 8 | |||
75.56 | odd | 10 | 625.2.d.h.251.1 | 4 | |||
75.59 | odd | 10 | 125.2.d.a.26.1 | 4 | |||
75.62 | even | 20 | 125.2.e.a.99.2 | 8 | |||
75.71 | odd | 10 | 625.2.d.h.376.1 | 4 | |||
300.11 | even | 10 | 400.2.u.b.321.1 | 4 | |||
300.191 | even | 10 | 400.2.u.b.81.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.6.1 | ✓ | 4 | 75.41 | odd | 10 | ||
25.2.d.a.21.1 | yes | 4 | 75.11 | odd | 10 | ||
125.2.d.a.26.1 | 4 | 75.59 | odd | 10 | |||
125.2.d.a.101.1 | 4 | 75.14 | odd | 10 | |||
125.2.e.a.24.1 | 8 | 75.2 | even | 20 | |||
125.2.e.a.24.2 | 8 | 75.23 | even | 20 | |||
125.2.e.a.99.1 | 8 | 75.38 | even | 20 | |||
125.2.e.a.99.2 | 8 | 75.62 | even | 20 | |||
225.2.h.b.46.1 | 4 | 25.11 | even | 5 | |||
225.2.h.b.181.1 | 4 | 25.16 | even | 5 | |||
400.2.u.b.81.1 | 4 | 300.191 | even | 10 | |||
400.2.u.b.321.1 | 4 | 300.11 | even | 10 | |||
625.2.a.b.1.1 | 2 | 3.2 | odd | 2 | |||
625.2.a.c.1.2 | 2 | 15.14 | odd | 2 | |||
625.2.b.a.624.1 | 4 | 15.2 | even | 4 | |||
625.2.b.a.624.4 | 4 | 15.8 | even | 4 | |||
625.2.d.b.251.1 | 4 | 75.44 | odd | 10 | |||
625.2.d.b.376.1 | 4 | 75.29 | odd | 10 | |||
625.2.d.h.251.1 | 4 | 75.56 | odd | 10 | |||
625.2.d.h.376.1 | 4 | 75.71 | odd | 10 | |||
625.2.e.c.249.1 | 8 | 75.47 | even | 20 | |||
625.2.e.c.249.2 | 8 | 75.53 | even | 20 | |||
625.2.e.c.374.1 | 8 | 75.8 | even | 20 | |||
625.2.e.c.374.2 | 8 | 75.17 | even | 20 | |||
5625.2.a.d.1.1 | 2 | 5.4 | even | 2 | |||
5625.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
10000.2.a.c.1.1 | 2 | 12.11 | even | 2 | |||
10000.2.a.l.1.2 | 2 | 60.59 | even | 2 |