Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.507824\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.507824 | 0.359086 | 0.179543 | − | 0.983750i | \(-0.442538\pi\) | ||||
0.179543 | + | 0.983750i | \(0.442538\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.74212 | −0.871058 | ||||||||
\(5\) | 3.36946 | 1.50687 | 0.753435 | − | 0.657523i | \(-0.228396\pi\) | ||||
0.753435 | + | 0.657523i | \(0.228396\pi\) | |||||||
\(6\) | 0.507824 | 0.207318 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.90033 | −0.671870 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.71109 | 0.541095 | ||||||||
\(11\) | 3.52145 | 1.06176 | 0.530878 | − | 0.847448i | \(-0.321862\pi\) | ||||
0.530878 | + | 0.847448i | \(0.321862\pi\) | |||||||
\(12\) | −1.74212 | −0.502905 | ||||||||
\(13\) | −0.582156 | −0.161461 | −0.0807305 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807305 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.36946 | 0.869991 | ||||||||
\(16\) | 2.51920 | 0.629799 | ||||||||
\(17\) | 4.36722 | 1.05921 | 0.529604 | − | 0.848245i | \(-0.322341\pi\) | ||||
0.529604 | + | 0.848245i | \(0.322341\pi\) | |||||||
\(18\) | 0.507824 | 0.119695 | ||||||||
\(19\) | 1.57451 | 0.361217 | 0.180609 | − | 0.983555i | \(-0.442193\pi\) | ||||
0.180609 | + | 0.983555i | \(0.442193\pi\) | |||||||
\(20\) | −5.86999 | −1.31257 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.78827 | 0.381261 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.90033 | −0.387904 | ||||||||
\(25\) | 6.35327 | 1.27065 | ||||||||
\(26\) | −0.295633 | −0.0579783 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.29806 | 1.16952 | 0.584760 | − | 0.811206i | \(-0.301189\pi\) | ||||
0.584760 | + | 0.811206i | \(0.301189\pi\) | |||||||
\(30\) | 1.71109 | 0.312401 | ||||||||
\(31\) | −3.71809 | −0.667788 | −0.333894 | − | 0.942611i | \(-0.608363\pi\) | ||||
−0.333894 | + | 0.942611i | \(0.608363\pi\) | |||||||
\(32\) | 5.07998 | 0.898021 | ||||||||
\(33\) | 3.52145 | 0.613005 | ||||||||
\(34\) | 2.21778 | 0.380346 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.74212 | −0.290353 | ||||||||
\(37\) | −5.02204 | −0.825619 | −0.412809 | − | 0.910817i | \(-0.635452\pi\) | ||||
−0.412809 | + | 0.910817i | \(0.635452\pi\) | |||||||
\(38\) | 0.799574 | 0.129708 | ||||||||
\(39\) | −0.582156 | −0.0932196 | ||||||||
\(40\) | −6.40311 | −1.01242 | ||||||||
\(41\) | −11.5320 | −1.80100 | −0.900498 | − | 0.434860i | \(-0.856798\pi\) | ||||
−0.900498 | + | 0.434860i | \(0.856798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16853 | 0.483196 | 0.241598 | − | 0.970376i | \(-0.422328\pi\) | ||||
0.241598 | + | 0.970376i | \(0.422328\pi\) | |||||||
\(44\) | −6.13477 | −0.924851 | ||||||||
\(45\) | 3.36946 | 0.502290 | ||||||||
\(46\) | −0.507824 | −0.0748745 | ||||||||
\(47\) | −12.5184 | −1.82600 | −0.912999 | − | 0.407962i | \(-0.866239\pi\) | ||||
−0.912999 | + | 0.407962i | \(0.866239\pi\) | |||||||
\(48\) | 2.51920 | 0.363615 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.22634 | 0.456274 | ||||||||
\(51\) | 4.36722 | 0.611534 | ||||||||
\(52\) | 1.01418 | 0.140642 | ||||||||
\(53\) | −5.42622 | −0.745348 | −0.372674 | − | 0.927962i | \(-0.621559\pi\) | ||||
−0.372674 | + | 0.927962i | \(0.621559\pi\) | |||||||
\(54\) | 0.507824 | 0.0691061 | ||||||||
\(55\) | 11.8654 | 1.59993 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.57451 | 0.208549 | ||||||||
\(58\) | 3.19830 | 0.419958 | ||||||||
\(59\) | 12.8936 | 1.67860 | 0.839302 | − | 0.543666i | \(-0.182964\pi\) | ||||
0.839302 | + | 0.543666i | \(0.182964\pi\) | |||||||
\(60\) | −5.86999 | −0.757812 | ||||||||
\(61\) | 11.9423 | 1.52906 | 0.764528 | − | 0.644591i | \(-0.222972\pi\) | ||||
0.764528 | + | 0.644591i | \(0.222972\pi\) | |||||||
\(62\) | −1.88813 | −0.239793 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.45866 | −0.307332 | ||||||||
\(65\) | −1.96155 | −0.243301 | ||||||||
\(66\) | 1.78827 | 0.220121 | ||||||||
\(67\) | 9.68141 | 1.18277 | 0.591386 | − | 0.806389i | \(-0.298581\pi\) | ||||
0.591386 | + | 0.806389i | \(0.298581\pi\) | |||||||
\(68\) | −7.60821 | −0.922630 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.15303 | 0.967587 | 0.483793 | − | 0.875182i | \(-0.339259\pi\) | ||||
0.483793 | + | 0.875182i | \(0.339259\pi\) | |||||||
\(72\) | −1.90033 | −0.223957 | ||||||||
\(73\) | 3.05034 | 0.357015 | 0.178508 | − | 0.983939i | \(-0.442873\pi\) | ||||
0.178508 | + | 0.983939i | \(0.442873\pi\) | |||||||
\(74\) | −2.55031 | −0.296468 | ||||||||
\(75\) | 6.35327 | 0.733613 | ||||||||
\(76\) | −2.74298 | −0.314641 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.295633 | −0.0334738 | ||||||||
\(79\) | −5.16206 | −0.580777 | −0.290388 | − | 0.956909i | \(-0.593785\pi\) | ||||
−0.290388 | + | 0.956909i | \(0.593785\pi\) | |||||||
\(80\) | 8.48833 | 0.949024 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.85622 | −0.646712 | ||||||||
\(83\) | −0.437777 | −0.0480523 | −0.0240262 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240262 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7152 | 1.59609 | ||||||||
\(86\) | 1.60905 | 0.173509 | ||||||||
\(87\) | 6.29806 | 0.675223 | ||||||||
\(88\) | −6.69193 | −0.713362 | ||||||||
\(89\) | 8.36773 | 0.886977 | 0.443489 | − | 0.896280i | \(-0.353741\pi\) | ||||
0.443489 | + | 0.896280i | \(0.353741\pi\) | |||||||
\(90\) | 1.71109 | 0.180365 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.74212 | 0.181628 | ||||||||
\(93\) | −3.71809 | −0.385548 | ||||||||
\(94\) | −6.35714 | −0.655689 | ||||||||
\(95\) | 5.30525 | 0.544307 | ||||||||
\(96\) | 5.07998 | 0.518473 | ||||||||
\(97\) | 6.27355 | 0.636983 | 0.318491 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318491 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.52145 | 0.353919 | ||||||||
\(100\) | −11.0681 | −1.10681 | ||||||||
\(101\) | −1.47545 | −0.146813 | −0.0734065 | − | 0.997302i | \(-0.523387\pi\) | ||||
−0.0734065 | + | 0.997302i | \(0.523387\pi\) | |||||||
\(102\) | 2.21778 | 0.219593 | ||||||||
\(103\) | 10.4958 | 1.03419 | 0.517093 | − | 0.855929i | \(-0.327014\pi\) | ||||
0.517093 | + | 0.855929i | \(0.327014\pi\) | |||||||
\(104\) | 1.10629 | 0.108481 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.75556 | −0.267644 | ||||||||
\(107\) | −11.2699 | −1.08951 | −0.544753 | − | 0.838596i | \(-0.683377\pi\) | ||||
−0.544753 | + | 0.838596i | \(0.683377\pi\) | |||||||
\(108\) | −1.74212 | −0.167635 | ||||||||
\(109\) | −14.8940 | −1.42659 | −0.713294 | − | 0.700865i | \(-0.752798\pi\) | ||||
−0.713294 | + | 0.700865i | \(0.752798\pi\) | |||||||
\(110\) | 6.02552 | 0.574511 | ||||||||
\(111\) | −5.02204 | −0.476671 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2097 | 1.05452 | 0.527258 | − | 0.849705i | \(-0.323220\pi\) | ||||
0.527258 | + | 0.849705i | \(0.323220\pi\) | |||||||
\(114\) | 0.799574 | 0.0748869 | ||||||||
\(115\) | −3.36946 | −0.314204 | ||||||||
\(116\) | −10.9719 | −1.01872 | ||||||||
\(117\) | −0.582156 | −0.0538204 | ||||||||
\(118\) | 6.54767 | 0.602762 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.40311 | −0.584521 | ||||||||
\(121\) | 1.40059 | 0.127327 | ||||||||
\(122\) | 6.06458 | 0.549062 | ||||||||
\(123\) | −11.5320 | −1.03981 | ||||||||
\(124\) | 6.47733 | 0.581682 | ||||||||
\(125\) | 4.55980 | 0.407841 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.83306 | 0.606336 | 0.303168 | − | 0.952937i | \(-0.401956\pi\) | ||||
0.303168 | + | 0.952937i | \(0.401956\pi\) | |||||||
\(128\) | −11.4085 | −1.00838 | ||||||||
\(129\) | 3.16853 | 0.278973 | ||||||||
\(130\) | −0.996123 | −0.0873658 | ||||||||
\(131\) | 5.14200 | 0.449259 | 0.224629 | − | 0.974444i | \(-0.427883\pi\) | ||||
0.224629 | + | 0.974444i | \(0.427883\pi\) | |||||||
\(132\) | −6.13477 | −0.533963 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.91645 | 0.424716 | ||||||||
\(135\) | 3.36946 | 0.289997 | ||||||||
\(136\) | −8.29919 | −0.711649 | ||||||||
\(137\) | −11.9922 | −1.02456 | −0.512280 | − | 0.858818i | \(-0.671199\pi\) | ||||
−0.512280 | + | 0.858818i | \(0.671199\pi\) | |||||||
\(138\) | −0.507824 | −0.0432288 | ||||||||
\(139\) | 18.8938 | 1.60255 | 0.801275 | − | 0.598296i | \(-0.204155\pi\) | ||||
0.801275 | + | 0.598296i | \(0.204155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.5184 | −1.05424 | ||||||||
\(142\) | 4.14030 | 0.347446 | ||||||||
\(143\) | −2.05003 | −0.171432 | ||||||||
\(144\) | 2.51920 | 0.209933 | ||||||||
\(145\) | 21.2211 | 1.76231 | ||||||||
\(146\) | 1.54903 | 0.128199 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.74898 | 0.719162 | ||||||||
\(149\) | −9.67711 | −0.792780 | −0.396390 | − | 0.918082i | \(-0.629737\pi\) | ||||
−0.396390 | + | 0.918082i | \(0.629737\pi\) | |||||||
\(150\) | 3.22634 | 0.263430 | ||||||||
\(151\) | −2.72866 | −0.222055 | −0.111028 | − | 0.993817i | \(-0.535414\pi\) | ||||
−0.111028 | + | 0.993817i | \(0.535414\pi\) | |||||||
\(152\) | −2.99210 | −0.242691 | ||||||||
\(153\) | 4.36722 | 0.353069 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5280 | −1.00627 | ||||||||
\(156\) | 1.01418 | 0.0811996 | ||||||||
\(157\) | −7.52810 | −0.600808 | −0.300404 | − | 0.953812i | \(-0.597122\pi\) | ||||
−0.300404 | + | 0.953812i | \(0.597122\pi\) | |||||||
\(158\) | −2.62141 | −0.208549 | ||||||||
\(159\) | −5.42622 | −0.430327 | ||||||||
\(160\) | 17.1168 | 1.35320 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.507824 | 0.0398984 | ||||||||
\(163\) | 11.1525 | 0.873530 | 0.436765 | − | 0.899576i | \(-0.356124\pi\) | ||||
0.436765 | + | 0.899576i | \(0.356124\pi\) | |||||||
\(164\) | 20.0901 | 1.56877 | ||||||||
\(165\) | 11.8654 | 0.923719 | ||||||||
\(166\) | −0.222314 | −0.0172549 | ||||||||
\(167\) | 6.62408 | 0.512587 | 0.256293 | − | 0.966599i | \(-0.417499\pi\) | ||||
0.256293 | + | 0.966599i | \(0.417499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6611 | −0.973930 | ||||||||
\(170\) | 7.47272 | 0.573132 | ||||||||
\(171\) | 1.57451 | 0.120406 | ||||||||
\(172\) | −5.51994 | −0.420892 | ||||||||
\(173\) | −18.7223 | −1.42343 | −0.711714 | − | 0.702470i | \(-0.752081\pi\) | ||||
−0.711714 | + | 0.702470i | \(0.752081\pi\) | |||||||
\(174\) | 3.19830 | 0.242463 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.87121 | 0.668693 | ||||||||
\(177\) | 12.8936 | 0.969142 | ||||||||
\(178\) | 4.24933 | 0.318501 | ||||||||
\(179\) | 15.9914 | 1.19526 | 0.597628 | − | 0.801774i | \(-0.296110\pi\) | ||||
0.597628 | + | 0.801774i | \(0.296110\pi\) | |||||||
\(180\) | −5.86999 | −0.437523 | ||||||||
\(181\) | 16.6859 | 1.24026 | 0.620128 | − | 0.784501i | \(-0.287081\pi\) | ||||
0.620128 | + | 0.784501i | \(0.287081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9423 | 0.882800 | ||||||||
\(184\) | 1.90033 | 0.140095 | ||||||||
\(185\) | −16.9216 | −1.24410 | ||||||||
\(186\) | −1.88813 | −0.138445 | ||||||||
\(187\) | 15.3789 | 1.12462 | ||||||||
\(188\) | 21.8085 | 1.59055 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69413 | 0.195453 | ||||||||
\(191\) | −16.4938 | −1.19345 | −0.596726 | − | 0.802445i | \(-0.703532\pi\) | ||||
−0.596726 | + | 0.802445i | \(0.703532\pi\) | |||||||
\(192\) | −2.45866 | −0.177438 | ||||||||
\(193\) | −2.49327 | −0.179469 | −0.0897347 | − | 0.995966i | \(-0.528602\pi\) | ||||
−0.0897347 | + | 0.995966i | \(0.528602\pi\) | |||||||
\(194\) | 3.18586 | 0.228731 | ||||||||
\(195\) | −1.96155 | −0.140470 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1473 | −0.722963 | −0.361481 | − | 0.932379i | \(-0.617729\pi\) | ||||
−0.361481 | + | 0.932379i | \(0.617729\pi\) | |||||||
\(198\) | 1.78827 | 0.127087 | ||||||||
\(199\) | 10.6987 | 0.758413 | 0.379207 | − | 0.925312i | \(-0.376197\pi\) | ||||
0.379207 | + | 0.925312i | \(0.376197\pi\) | |||||||
\(200\) | −12.0733 | −0.853714 | ||||||||
\(201\) | 9.68141 | 0.682874 | ||||||||
\(202\) | −0.749270 | −0.0527184 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.60821 | −0.532681 | ||||||||
\(205\) | −38.8566 | −2.71387 | ||||||||
\(206\) | 5.33003 | 0.371361 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −1.46656 | −0.101688 | ||||||||
\(209\) | 5.54456 | 0.383525 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.45788 | 0.306893 | 0.153447 | − | 0.988157i | \(-0.450963\pi\) | ||||
0.153447 | + | 0.988157i | \(0.450963\pi\) | |||||||
\(212\) | 9.45309 | 0.649241 | ||||||||
\(213\) | 8.15303 | 0.558637 | ||||||||
\(214\) | −5.72314 | −0.391226 | ||||||||
\(215\) | 10.6762 | 0.728113 | ||||||||
\(216\) | −1.90033 | −0.129301 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.56354 | −0.512267 | ||||||||
\(219\) | 3.05034 | 0.206123 | ||||||||
\(220\) | −20.6709 | −1.39363 | ||||||||
\(221\) | −2.54241 | −0.171021 | ||||||||
\(222\) | −2.55031 | −0.171166 | ||||||||
\(223\) | −10.5752 | −0.708166 | −0.354083 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354083 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.35327 | 0.423552 | ||||||||
\(226\) | 5.69253 | 0.378661 | ||||||||
\(227\) | −20.8124 | −1.38137 | −0.690684 | − | 0.723157i | \(-0.742690\pi\) | ||||
−0.690684 | + | 0.723157i | \(0.742690\pi\) | |||||||
\(228\) | −2.74298 | −0.181658 | ||||||||
\(229\) | −10.0157 | −0.661857 | −0.330928 | − | 0.943656i | \(-0.607362\pi\) | ||||
−0.330928 | + | 0.943656i | \(0.607362\pi\) | |||||||
\(230\) | −1.71109 | −0.112826 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.9684 | −0.785765 | ||||||||
\(233\) | 9.84802 | 0.645165 | 0.322583 | − | 0.946541i | \(-0.395449\pi\) | ||||
0.322583 | + | 0.946541i | \(0.395449\pi\) | |||||||
\(234\) | −0.295633 | −0.0193261 | ||||||||
\(235\) | −42.1803 | −2.75154 | ||||||||
\(236\) | −22.4621 | −1.46216 | ||||||||
\(237\) | −5.16206 | −0.335312 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00670 | −0.194487 | −0.0972435 | − | 0.995261i | \(-0.531003\pi\) | ||||
−0.0972435 | + | 0.995261i | \(0.531003\pi\) | |||||||
\(240\) | 8.48833 | 0.547919 | ||||||||
\(241\) | 22.5330 | 1.45148 | 0.725738 | − | 0.687971i | \(-0.241498\pi\) | ||||
0.725738 | + | 0.687971i | \(0.241498\pi\) | |||||||
\(242\) | 0.711254 | 0.0457211 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −20.8049 | −1.33189 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.85622 | −0.373379 | ||||||||
\(247\) | −0.916611 | −0.0583226 | ||||||||
\(248\) | 7.06561 | 0.448667 | ||||||||
\(249\) | −0.437777 | −0.0277430 | ||||||||
\(250\) | 2.31557 | 0.146450 | ||||||||
\(251\) | −0.240327 | −0.0151693 | −0.00758464 | − | 0.999971i | \(-0.502414\pi\) | ||||
−0.00758464 | + | 0.999971i | \(0.502414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.52145 | −0.221392 | ||||||||
\(254\) | 3.46999 | 0.217727 | ||||||||
\(255\) | 14.7152 | 0.921501 | ||||||||
\(256\) | −0.876200 | −0.0547625 | ||||||||
\(257\) | 0.158016 | 0.00985675 | 0.00492837 | − | 0.999988i | \(-0.498431\pi\) | ||||
0.00492837 | + | 0.999988i | \(0.498431\pi\) | |||||||
\(258\) | 1.60905 | 0.100175 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.41725 | 0.211929 | ||||||||
\(261\) | 6.29806 | 0.389840 | ||||||||
\(262\) | 2.61123 | 0.161322 | ||||||||
\(263\) | 18.4642 | 1.13855 | 0.569275 | − | 0.822147i | \(-0.307224\pi\) | ||||
0.569275 | + | 0.822147i | \(0.307224\pi\) | |||||||
\(264\) | −6.69193 | −0.411860 | ||||||||
\(265\) | −18.2834 | −1.12314 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.36773 | 0.512096 | ||||||||
\(268\) | −16.8661 | −1.03026 | ||||||||
\(269\) | 0.958502 | 0.0584409 | 0.0292205 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292205 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(270\) | 1.71109 | 0.104134 | ||||||||
\(271\) | −23.5098 | −1.42812 | −0.714059 | − | 0.700086i | \(-0.753145\pi\) | ||||
−0.714059 | + | 0.700086i | \(0.753145\pi\) | |||||||
\(272\) | 11.0019 | 0.667087 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.08991 | −0.367905 | ||||||||
\(275\) | 22.3727 | 1.34913 | ||||||||
\(276\) | 1.74212 | 0.104863 | ||||||||
\(277\) | 31.2642 | 1.87848 | 0.939240 | − | 0.343260i | \(-0.111531\pi\) | ||||
0.939240 | + | 0.343260i | \(0.111531\pi\) | |||||||
\(278\) | 9.59471 | 0.575452 | ||||||||
\(279\) | −3.71809 | −0.222596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.61573 | −0.215696 | −0.107848 | − | 0.994167i | \(-0.534396\pi\) | ||||
−0.107848 | + | 0.994167i | \(0.534396\pi\) | |||||||
\(282\) | −6.35714 | −0.378562 | ||||||||
\(283\) | −5.48645 | −0.326135 | −0.163068 | − | 0.986615i | \(-0.552139\pi\) | ||||
−0.163068 | + | 0.986615i | \(0.552139\pi\) | |||||||
\(284\) | −14.2035 | −0.842824 | ||||||||
\(285\) | 5.30525 | 0.314256 | ||||||||
\(286\) | −1.04105 | −0.0615589 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.07998 | 0.299340 | ||||||||
\(289\) | 2.07264 | 0.121920 | ||||||||
\(290\) | 10.7766 | 0.632821 | ||||||||
\(291\) | 6.27355 | 0.367762 | ||||||||
\(292\) | −5.31404 | −0.310981 | ||||||||
\(293\) | −18.5359 | −1.08288 | −0.541438 | − | 0.840740i | \(-0.682120\pi\) | ||||
−0.541438 | + | 0.840740i | \(0.682120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.4445 | 2.52944 | ||||||||
\(296\) | 9.54356 | 0.554708 | ||||||||
\(297\) | 3.52145 | 0.204335 | ||||||||
\(298\) | −4.91427 | −0.284676 | ||||||||
\(299\) | 0.582156 | 0.0336670 | ||||||||
\(300\) | −11.0681 | −0.639019 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.38568 | −0.0797369 | ||||||||
\(303\) | −1.47545 | −0.0847625 | ||||||||
\(304\) | 3.96650 | 0.227494 | ||||||||
\(305\) | 40.2391 | 2.30409 | ||||||||
\(306\) | 2.21778 | 0.126782 | ||||||||
\(307\) | 4.00645 | 0.228660 | 0.114330 | − | 0.993443i | \(-0.463528\pi\) | ||||
0.114330 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4958 | 0.597087 | ||||||||
\(310\) | −6.36199 | −0.361337 | ||||||||
\(311\) | 27.7513 | 1.57363 | 0.786817 | − | 0.617187i | \(-0.211728\pi\) | ||||
0.786817 | + | 0.617187i | \(0.211728\pi\) | |||||||
\(312\) | 1.10629 | 0.0626314 | ||||||||
\(313\) | −28.6113 | −1.61721 | −0.808604 | − | 0.588353i | \(-0.799777\pi\) | ||||
−0.808604 | + | 0.588353i | \(0.799777\pi\) | |||||||
\(314\) | −3.82295 | −0.215742 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.99290 | 0.505890 | ||||||||
\(317\) | 1.93708 | 0.108797 | 0.0543986 | − | 0.998519i | \(-0.482676\pi\) | ||||
0.0543986 | + | 0.998519i | \(0.482676\pi\) | |||||||
\(318\) | −2.75556 | −0.154524 | ||||||||
\(319\) | 22.1783 | 1.24174 | ||||||||
\(320\) | −8.28435 | −0.463109 | ||||||||
\(321\) | −11.2699 | −0.629027 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.87624 | 0.382604 | ||||||||
\(324\) | −1.74212 | −0.0967842 | ||||||||
\(325\) | −3.69860 | −0.205161 | ||||||||
\(326\) | 5.66349 | 0.313672 | ||||||||
\(327\) | −14.8940 | −0.823641 | ||||||||
\(328\) | 21.9147 | 1.21003 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.02552 | 0.331694 | ||||||||
\(331\) | −29.4869 | −1.62074 | −0.810372 | − | 0.585916i | \(-0.800735\pi\) | ||||
−0.810372 | + | 0.585916i | \(0.800735\pi\) | |||||||
\(332\) | 0.762659 | 0.0418563 | ||||||||
\(333\) | −5.02204 | −0.275206 | ||||||||
\(334\) | 3.36386 | 0.184062 | ||||||||
\(335\) | 32.6211 | 1.78228 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5959 | −0.958510 | −0.479255 | − | 0.877676i | \(-0.659093\pi\) | ||||
−0.479255 | + | 0.877676i | \(0.659093\pi\) | |||||||
\(338\) | −6.42960 | −0.349724 | ||||||||
\(339\) | 11.2097 | 0.608825 | ||||||||
\(340\) | −25.6356 | −1.39028 | ||||||||
\(341\) | −13.0930 | −0.709028 | ||||||||
\(342\) | 0.799574 | 0.0432360 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.02127 | −0.324645 | ||||||||
\(345\) | −3.36946 | −0.181406 | ||||||||
\(346\) | −9.50761 | −0.511132 | ||||||||
\(347\) | −5.99228 | −0.321683 | −0.160841 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160841 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(348\) | −10.9719 | −0.588158 | ||||||||
\(349\) | 31.6524 | 1.69431 | 0.847156 | − | 0.531344i | \(-0.178313\pi\) | ||||
0.847156 | + | 0.531344i | \(0.178313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.582156 | −0.0310732 | ||||||||
\(352\) | 17.8889 | 0.953480 | ||||||||
\(353\) | 31.1107 | 1.65585 | 0.827927 | − | 0.560836i | \(-0.189520\pi\) | ||||
0.827927 | + | 0.560836i | \(0.189520\pi\) | |||||||
\(354\) | 6.54767 | 0.348005 | ||||||||
\(355\) | 27.4713 | 1.45803 | ||||||||
\(356\) | −14.5775 | −0.772608 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.12082 | 0.429199 | ||||||||
\(359\) | 24.8310 | 1.31053 | 0.655266 | − | 0.755398i | \(-0.272557\pi\) | ||||
0.655266 | + | 0.755398i | \(0.272557\pi\) | |||||||
\(360\) | −6.40311 | −0.337473 | ||||||||
\(361\) | −16.5209 | −0.869522 | ||||||||
\(362\) | 8.47351 | 0.445358 | ||||||||
\(363\) | 1.40059 | 0.0735120 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2780 | 0.537975 | ||||||||
\(366\) | 6.06458 | 0.317001 | ||||||||
\(367\) | −25.5768 | −1.33510 | −0.667548 | − | 0.744567i | \(-0.732656\pi\) | ||||
−0.667548 | + | 0.744567i | \(0.732656\pi\) | |||||||
\(368\) | −2.51920 | −0.131322 | ||||||||
\(369\) | −11.5320 | −0.600332 | ||||||||
\(370\) | −8.59318 | −0.446738 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.47733 | 0.335834 | ||||||||
\(373\) | −16.3483 | −0.846485 | −0.423242 | − | 0.906016i | \(-0.639108\pi\) | ||||
−0.423242 | + | 0.906016i | \(0.639108\pi\) | |||||||
\(374\) | 7.80979 | 0.403835 | ||||||||
\(375\) | 4.55980 | 0.235467 | ||||||||
\(376\) | 23.7892 | 1.22683 | ||||||||
\(377\) | −3.66645 | −0.188832 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5632 | −0.542597 | −0.271299 | − | 0.962495i | \(-0.587453\pi\) | ||||
−0.271299 | + | 0.962495i | \(0.587453\pi\) | |||||||
\(380\) | −9.24236 | −0.474123 | ||||||||
\(381\) | 6.83306 | 0.350068 | ||||||||
\(382\) | −8.37596 | −0.428552 | ||||||||
\(383\) | −29.1796 | −1.49101 | −0.745505 | − | 0.666500i | \(-0.767792\pi\) | ||||
−0.745505 | + | 0.666500i | \(0.767792\pi\) | |||||||
\(384\) | −11.4085 | −0.582188 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.26614 | −0.0644448 | ||||||||
\(387\) | 3.16853 | 0.161065 | ||||||||
\(388\) | −10.9293 | −0.554849 | ||||||||
\(389\) | −10.8298 | −0.549091 | −0.274545 | − | 0.961574i | \(-0.588527\pi\) | ||||
−0.274545 | + | 0.961574i | \(0.588527\pi\) | |||||||
\(390\) | −0.996123 | −0.0504406 | ||||||||
\(391\) | −4.36722 | −0.220860 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.14200 | 0.259380 | ||||||||
\(394\) | −5.15302 | −0.259605 | ||||||||
\(395\) | −17.3934 | −0.875155 | ||||||||
\(396\) | −6.13477 | −0.308284 | ||||||||
\(397\) | −16.8982 | −0.848099 | −0.424049 | − | 0.905639i | \(-0.639392\pi\) | ||||
−0.424049 | + | 0.905639i | \(0.639392\pi\) | |||||||
\(398\) | 5.43307 | 0.272335 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0051 | 0.800257 | ||||||||
\(401\) | 9.40385 | 0.469606 | 0.234803 | − | 0.972043i | \(-0.424556\pi\) | ||||
0.234803 | + | 0.972043i | \(0.424556\pi\) | |||||||
\(402\) | 4.91645 | 0.245210 | ||||||||
\(403\) | 2.16451 | 0.107822 | ||||||||
\(404\) | 2.57041 | 0.127883 | ||||||||
\(405\) | 3.36946 | 0.167430 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6849 | −0.876606 | ||||||||
\(408\) | −8.29919 | −0.410871 | ||||||||
\(409\) | 28.7565 | 1.42192 | 0.710959 | − | 0.703233i | \(-0.248261\pi\) | ||||
0.710959 | + | 0.703233i | \(0.248261\pi\) | |||||||
\(410\) | −19.7323 | −0.974510 | ||||||||
\(411\) | −11.9922 | −0.591530 | ||||||||
\(412\) | −18.2850 | −0.900835 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.507824 | −0.0249582 | ||||||||
\(415\) | −1.47507 | −0.0724085 | ||||||||
\(416\) | −2.95734 | −0.144995 | ||||||||
\(417\) | 18.8938 | 0.925232 | ||||||||
\(418\) | 2.81566 | 0.137718 | ||||||||
\(419\) | 3.08384 | 0.150655 | 0.0753277 | − | 0.997159i | \(-0.476000\pi\) | ||||
0.0753277 | + | 0.997159i | \(0.476000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.4121 | −1.48220 | −0.741098 | − | 0.671397i | \(-0.765695\pi\) | ||||
−0.741098 | + | 0.671397i | \(0.765695\pi\) | |||||||
\(422\) | 2.26382 | 0.110201 | ||||||||
\(423\) | −12.5184 | −0.608666 | ||||||||
\(424\) | 10.3116 | 0.500777 | ||||||||
\(425\) | 27.7462 | 1.34589 | ||||||||
\(426\) | 4.14030 | 0.200598 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.6335 | 0.949023 | ||||||||
\(429\) | −2.05003 | −0.0989765 | ||||||||
\(430\) | 5.42165 | 0.261455 | ||||||||
\(431\) | −22.4322 | −1.08052 | −0.540260 | − | 0.841498i | \(-0.681674\pi\) | ||||
−0.540260 | + | 0.841498i | \(0.681674\pi\) | |||||||
\(432\) | 2.51920 | 0.121205 | ||||||||
\(433\) | −16.9261 | −0.813419 | −0.406709 | − | 0.913558i | \(-0.633324\pi\) | ||||
−0.406709 | + | 0.913558i | \(0.633324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.2211 | 1.01747 | ||||||||
\(436\) | 25.9471 | 1.24264 | ||||||||
\(437\) | −1.57451 | −0.0753190 | ||||||||
\(438\) | 1.54903 | 0.0740157 | ||||||||
\(439\) | −17.8468 | −0.851782 | −0.425891 | − | 0.904775i | \(-0.640039\pi\) | ||||
−0.425891 | + | 0.904775i | \(0.640039\pi\) | |||||||
\(440\) | −22.5482 | −1.07494 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.29109 | −0.0614111 | ||||||||
\(443\) | 9.99727 | 0.474985 | 0.237492 | − | 0.971389i | \(-0.423675\pi\) | ||||
0.237492 | + | 0.971389i | \(0.423675\pi\) | |||||||
\(444\) | 8.74898 | 0.415208 | ||||||||
\(445\) | 28.1947 | 1.33656 | ||||||||
\(446\) | −5.37033 | −0.254292 | ||||||||
\(447\) | −9.67711 | −0.457712 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2739 | −0.579239 | −0.289620 | − | 0.957142i | \(-0.593529\pi\) | ||||
−0.289620 | + | 0.957142i | \(0.593529\pi\) | |||||||
\(450\) | 3.22634 | 0.152091 | ||||||||
\(451\) | −40.6093 | −1.91222 | ||||||||
\(452\) | −19.5285 | −0.918544 | ||||||||
\(453\) | −2.72866 | −0.128204 | ||||||||
\(454\) | −10.5690 | −0.496029 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.99210 | −0.140118 | ||||||||
\(457\) | −7.46202 | −0.349059 | −0.174529 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174529 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(458\) | −5.08622 | −0.237663 | ||||||||
\(459\) | 4.36722 | 0.203845 | ||||||||
\(460\) | 5.86999 | 0.273690 | ||||||||
\(461\) | −26.5396 | −1.23607 | −0.618035 | − | 0.786150i | \(-0.712071\pi\) | ||||
−0.618035 | + | 0.786150i | \(0.712071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9728 | 0.742321 | 0.371161 | − | 0.928569i | \(-0.378960\pi\) | ||||
0.371161 | + | 0.928569i | \(0.378960\pi\) | |||||||
\(464\) | 15.8660 | 0.736562 | ||||||||
\(465\) | −12.5280 | −0.580970 | ||||||||
\(466\) | 5.00106 | 0.231670 | ||||||||
\(467\) | −14.7648 | −0.683232 | −0.341616 | − | 0.939840i | \(-0.610974\pi\) | ||||
−0.341616 | + | 0.939840i | \(0.610974\pi\) | |||||||
\(468\) | 1.01418 | 0.0468806 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21.4202 | −0.988038 | ||||||||
\(471\) | −7.52810 | −0.346877 | ||||||||
\(472\) | −24.5022 | −1.12780 | ||||||||
\(473\) | 11.1578 | 0.513037 | ||||||||
\(474\) | −2.62141 | −0.120406 | ||||||||
\(475\) | 10.0033 | 0.458983 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.42622 | −0.248449 | ||||||||
\(478\) | −1.52687 | −0.0698375 | ||||||||
\(479\) | −1.85487 | −0.0847514 | −0.0423757 | − | 0.999102i | \(-0.513493\pi\) | ||||
−0.0423757 | + | 0.999102i | \(0.513493\pi\) | |||||||
\(480\) | 17.1168 | 0.781271 | ||||||||
\(481\) | 2.92361 | 0.133305 | ||||||||
\(482\) | 11.4428 | 0.521204 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.43999 | −0.110909 | ||||||||
\(485\) | 21.1385 | 0.959850 | ||||||||
\(486\) | 0.507824 | 0.0230354 | ||||||||
\(487\) | −23.3766 | −1.05930 | −0.529648 | − | 0.848218i | \(-0.677676\pi\) | ||||
−0.529648 | + | 0.848218i | \(0.677676\pi\) | |||||||
\(488\) | −22.6944 | −1.02733 | ||||||||
\(489\) | 11.1525 | 0.504333 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4930 | −1.55665 | −0.778325 | − | 0.627862i | \(-0.783930\pi\) | ||||
−0.778325 | + | 0.627862i | \(0.783930\pi\) | |||||||
\(492\) | 20.0901 | 0.905730 | ||||||||
\(493\) | 27.5050 | 1.23876 | ||||||||
\(494\) | −0.465477 | −0.0209428 | ||||||||
\(495\) | 11.8654 | 0.533309 | ||||||||
\(496\) | −9.36659 | −0.420572 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.222314 | −0.00996212 | ||||||||
\(499\) | −33.3579 | −1.49331 | −0.746653 | − | 0.665214i | \(-0.768340\pi\) | ||||
−0.746653 | + | 0.665214i | \(0.768340\pi\) | |||||||
\(500\) | −7.94370 | −0.355253 | ||||||||
\(501\) | 6.62408 | 0.295942 | ||||||||
\(502\) | −0.122044 | −0.00544707 | ||||||||
\(503\) | 39.1129 | 1.74396 | 0.871979 | − | 0.489544i | \(-0.162837\pi\) | ||||
0.871979 | + | 0.489544i | \(0.162837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.97148 | −0.221228 | ||||||||
\(506\) | −1.78827 | −0.0794985 | ||||||||
\(507\) | −12.6611 | −0.562299 | ||||||||
\(508\) | −11.9040 | −0.528154 | ||||||||
\(509\) | 28.3813 | 1.25798 | 0.628990 | − | 0.777413i | \(-0.283469\pi\) | ||||
0.628990 | + | 0.777413i | \(0.283469\pi\) | |||||||
\(510\) | 7.47272 | 0.330898 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3721 | 0.988716 | ||||||||
\(513\) | 1.57451 | 0.0695163 | ||||||||
\(514\) | 0.0802441 | 0.00353942 | ||||||||
\(515\) | 35.3653 | 1.55838 | ||||||||
\(516\) | −5.51994 | −0.243002 | ||||||||
\(517\) | −44.0829 | −1.93876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.7223 | −0.821816 | ||||||||
\(520\) | 3.72761 | 0.163466 | ||||||||
\(521\) | 0.701087 | 0.0307152 | 0.0153576 | − | 0.999882i | \(-0.495111\pi\) | ||||
0.0153576 | + | 0.999882i | \(0.495111\pi\) | |||||||
\(522\) | 3.19830 | 0.139986 | ||||||||
\(523\) | 14.0416 | 0.613997 | 0.306999 | − | 0.951710i | \(-0.400675\pi\) | ||||
0.306999 | + | 0.951710i | \(0.400675\pi\) | |||||||
\(524\) | −8.95796 | −0.391330 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.37654 | 0.408837 | ||||||||
\(527\) | −16.2377 | −0.707326 | ||||||||
\(528\) | 8.87121 | 0.386070 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −9.28476 | −0.403304 | ||||||||
\(531\) | 12.8936 | 0.559534 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.71343 | 0.290791 | ||||||||
\(534\) | 4.24933 | 0.183886 | ||||||||
\(535\) | −37.9736 | −1.64174 | ||||||||
\(536\) | −18.3979 | −0.794669 | ||||||||
\(537\) | 15.9914 | 0.690081 | ||||||||
\(538\) | 0.486750 | 0.0209853 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.86999 | −0.252604 | ||||||||
\(541\) | −7.90191 | −0.339730 | −0.169865 | − | 0.985467i | \(-0.554333\pi\) | ||||
−0.169865 | + | 0.985467i | \(0.554333\pi\) | |||||||
\(542\) | −11.9388 | −0.512816 | ||||||||
\(543\) | 16.6859 | 0.716062 | ||||||||
\(544\) | 22.1854 | 0.951191 | ||||||||
\(545\) | −50.1848 | −2.14968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.7535 | −1.35768 | −0.678841 | − | 0.734285i | \(-0.737518\pi\) | ||||
−0.678841 | + | 0.734285i | \(0.737518\pi\) | |||||||
\(548\) | 20.8918 | 0.892451 | ||||||||
\(549\) | 11.9423 | 0.509685 | ||||||||
\(550\) | 11.3614 | 0.484452 | ||||||||
\(551\) | 9.91636 | 0.422451 | ||||||||
\(552\) | 1.90033 | 0.0808836 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.8767 | 0.674535 | ||||||||
\(555\) | −16.9216 | −0.718281 | ||||||||
\(556\) | −32.9151 | −1.39591 | ||||||||
\(557\) | −40.5194 | −1.71686 | −0.858430 | − | 0.512930i | \(-0.828560\pi\) | ||||
−0.858430 | + | 0.512930i | \(0.828560\pi\) | |||||||
\(558\) | −1.88813 | −0.0799310 | ||||||||
\(559\) | −1.84458 | −0.0780174 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.3789 | 0.649300 | ||||||||
\(562\) | −1.83615 | −0.0774535 | ||||||||
\(563\) | 11.6983 | 0.493026 | 0.246513 | − | 0.969139i | \(-0.420715\pi\) | ||||
0.246513 | + | 0.969139i | \(0.420715\pi\) | |||||||
\(564\) | 21.8085 | 0.918304 | ||||||||
\(565\) | 37.7705 | 1.58902 | ||||||||
\(566\) | −2.78615 | −0.117111 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.4935 | −0.650092 | ||||||||
\(569\) | 2.88940 | 0.121130 | 0.0605649 | − | 0.998164i | \(-0.480710\pi\) | ||||
0.0605649 | + | 0.998164i | \(0.480710\pi\) | |||||||
\(570\) | 2.69413 | 0.112845 | ||||||||
\(571\) | 7.00219 | 0.293033 | 0.146516 | − | 0.989208i | \(-0.453194\pi\) | ||||
0.146516 | + | 0.989208i | \(0.453194\pi\) | |||||||
\(572\) | 3.57139 | 0.149327 | ||||||||
\(573\) | −16.4938 | −0.689040 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.35327 | −0.264950 | ||||||||
\(576\) | −2.45866 | −0.102444 | ||||||||
\(577\) | −21.0327 | −0.875602 | −0.437801 | − | 0.899072i | \(-0.644243\pi\) | ||||
−0.437801 | + | 0.899072i | \(0.644243\pi\) | |||||||
\(578\) | 1.05254 | 0.0437797 | ||||||||
\(579\) | −2.49327 | −0.103617 | ||||||||
\(580\) | −36.9695 | −1.53508 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.18586 | 0.132058 | ||||||||
\(583\) | −19.1081 | −0.791378 | ||||||||
\(584\) | −5.79666 | −0.239868 | ||||||||
\(585\) | −1.96155 | −0.0811002 | ||||||||
\(586\) | −9.41295 | −0.388845 | ||||||||
\(587\) | 24.1793 | 0.997986 | 0.498993 | − | 0.866606i | \(-0.333703\pi\) | ||||
0.498993 | + | 0.866606i | \(0.333703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.85417 | −0.241217 | ||||||||
\(590\) | 22.0621 | 0.908284 | ||||||||
\(591\) | −10.1473 | −0.417403 | ||||||||
\(592\) | −12.6515 | −0.519974 | ||||||||
\(593\) | 24.3877 | 1.00148 | 0.500742 | − | 0.865597i | \(-0.333061\pi\) | ||||
0.500742 | + | 0.865597i | \(0.333061\pi\) | |||||||
\(594\) | 1.78827 | 0.0733738 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.8586 | 0.690557 | ||||||||
\(597\) | 10.6987 | 0.437870 | ||||||||
\(598\) | 0.295633 | 0.0120893 | ||||||||
\(599\) | 31.2133 | 1.27534 | 0.637670 | − | 0.770310i | \(-0.279898\pi\) | ||||
0.637670 | + | 0.770310i | \(0.279898\pi\) | |||||||
\(600\) | −12.0733 | −0.492892 | ||||||||
\(601\) | 8.22360 | 0.335448 | 0.167724 | − | 0.985834i | \(-0.446358\pi\) | ||||
0.167724 | + | 0.985834i | \(0.446358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.68141 | 0.394257 | ||||||||
\(604\) | 4.75364 | 0.193423 | ||||||||
\(605\) | 4.71924 | 0.191864 | ||||||||
\(606\) | −0.749270 | −0.0304370 | ||||||||
\(607\) | −15.0851 | −0.612286 | −0.306143 | − | 0.951986i | \(-0.599039\pi\) | ||||
−0.306143 | + | 0.951986i | \(0.599039\pi\) | |||||||
\(608\) | 7.99848 | 0.324381 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.4344 | 0.827364 | ||||||||
\(611\) | 7.28767 | 0.294827 | ||||||||
\(612\) | −7.60821 | −0.307543 | ||||||||
\(613\) | −25.1438 | −1.01555 | −0.507773 | − | 0.861491i | \(-0.669531\pi\) | ||||
−0.507773 | + | 0.861491i | \(0.669531\pi\) | |||||||
\(614\) | 2.03457 | 0.0821085 | ||||||||
\(615\) | −38.8566 | −1.56685 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3212 | −1.01939 | −0.509696 | − | 0.860354i | \(-0.670242\pi\) | ||||
−0.509696 | + | 0.860354i | \(0.670242\pi\) | |||||||
\(618\) | 5.33003 | 0.214405 | ||||||||
\(619\) | 2.77129 | 0.111388 | 0.0556938 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556938 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(620\) | 21.8251 | 0.876518 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 14.0928 | 0.565069 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.46656 | −0.0587096 | ||||||||
\(625\) | −16.4023 | −0.656092 | ||||||||
\(626\) | −14.5295 | −0.580716 | ||||||||
\(627\) | 5.54456 | 0.221428 | ||||||||
\(628\) | 13.1148 | 0.523338 | ||||||||
\(629\) | −21.9324 | −0.874502 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0907 | −1.35713 | −0.678564 | − | 0.734541i | \(-0.737397\pi\) | ||||
−0.678564 | + | 0.734541i | \(0.737397\pi\) | |||||||
\(632\) | 9.80964 | 0.390206 | ||||||||
\(633\) | 4.45788 | 0.177185 | ||||||||
\(634\) | 0.983695 | 0.0390675 | ||||||||
\(635\) | 23.0237 | 0.913669 | ||||||||
\(636\) | 9.45309 | 0.374839 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.2627 | 0.445893 | ||||||||
\(639\) | 8.15303 | 0.322529 | ||||||||
\(640\) | −38.4406 | −1.51950 | ||||||||
\(641\) | 41.0169 | 1.62007 | 0.810034 | − | 0.586383i | \(-0.199449\pi\) | ||||
0.810034 | + | 0.586383i | \(0.199449\pi\) | |||||||
\(642\) | −5.72314 | −0.225874 | ||||||||
\(643\) | 12.5304 | 0.494153 | 0.247076 | − | 0.968996i | \(-0.420530\pi\) | ||||
0.247076 | + | 0.968996i | \(0.420530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6762 | 0.420377 | ||||||||
\(646\) | 3.49192 | 0.137388 | ||||||||
\(647\) | −23.4635 | −0.922444 | −0.461222 | − | 0.887285i | \(-0.652589\pi\) | ||||
−0.461222 | + | 0.887285i | \(0.652589\pi\) | |||||||
\(648\) | −1.90033 | −0.0746522 | ||||||||
\(649\) | 45.4041 | 1.78227 | ||||||||
\(650\) | −1.87823 | −0.0736704 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.4289 | −0.760895 | ||||||||
\(653\) | −42.1303 | −1.64868 | −0.824342 | − | 0.566092i | \(-0.808455\pi\) | ||||
−0.824342 | + | 0.566092i | \(0.808455\pi\) | |||||||
\(654\) | −7.56354 | −0.295758 | ||||||||
\(655\) | 17.3258 | 0.676974 | ||||||||
\(656\) | −29.0514 | −1.13427 | ||||||||
\(657\) | 3.05034 | 0.119005 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6112 | 0.608126 | 0.304063 | − | 0.952652i | \(-0.401657\pi\) | ||||
0.304063 | + | 0.952652i | \(0.401657\pi\) | |||||||
\(660\) | −20.6709 | −0.804612 | ||||||||
\(661\) | −10.1039 | −0.392997 | −0.196498 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196498 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(662\) | −14.9741 | −0.581986 | ||||||||
\(663\) | −2.54241 | −0.0987389 | ||||||||
\(664\) | 0.831924 | 0.0322849 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.55031 | −0.0988226 | ||||||||
\(667\) | −6.29806 | −0.243862 | ||||||||
\(668\) | −11.5399 | −0.446492 | ||||||||
\(669\) | −10.5752 | −0.408860 | ||||||||
\(670\) | 16.5658 | 0.639992 | ||||||||
\(671\) | 42.0542 | 1.62348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.5723 | −1.44830 | −0.724152 | − | 0.689640i | \(-0.757769\pi\) | ||||
−0.724152 | + | 0.689640i | \(0.757769\pi\) | |||||||
\(674\) | −8.93561 | −0.344187 | ||||||||
\(675\) | 6.35327 | 0.244538 | ||||||||
\(676\) | 22.0571 | 0.848349 | ||||||||
\(677\) | −37.6674 | −1.44768 | −0.723838 | − | 0.689970i | \(-0.757624\pi\) | ||||
−0.723838 | + | 0.689970i | \(0.757624\pi\) | |||||||
\(678\) | 5.69253 | 0.218620 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −27.9638 | −1.07236 | ||||||||
\(681\) | −20.8124 | −0.797533 | ||||||||
\(682\) | −6.64896 | −0.254602 | ||||||||
\(683\) | 32.1942 | 1.23188 | 0.615938 | − | 0.787795i | \(-0.288777\pi\) | ||||
0.615938 | + | 0.787795i | \(0.288777\pi\) | |||||||
\(684\) | −2.74298 | −0.104880 | ||||||||
\(685\) | −40.4072 | −1.54388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0157 | −0.382123 | ||||||||
\(688\) | 7.98214 | 0.304316 | ||||||||
\(689\) | 3.15890 | 0.120345 | ||||||||
\(690\) | −1.71109 | −0.0651402 | ||||||||
\(691\) | −1.85398 | −0.0705286 | −0.0352643 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352643 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(692\) | 32.6163 | 1.23989 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.04302 | −0.115512 | ||||||||
\(695\) | 63.6619 | 2.41483 | ||||||||
\(696\) | −11.9684 | −0.453662 | ||||||||
\(697\) | −50.3628 | −1.90763 | ||||||||
\(698\) | 16.0738 | 0.608403 | ||||||||
\(699\) | 9.84802 | 0.372486 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.2504 | 1.21808 | 0.609040 | − | 0.793139i | \(-0.291555\pi\) | ||||
0.609040 | + | 0.793139i | \(0.291555\pi\) | |||||||
\(702\) | −0.295633 | −0.0111579 | ||||||||
\(703\) | −7.90726 | −0.298228 | ||||||||
\(704\) | −8.65803 | −0.326312 | ||||||||
\(705\) | −42.1803 | −1.58860 | ||||||||
\(706\) | 15.7987 | 0.594593 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.4621 | −0.844179 | ||||||||
\(709\) | −39.2019 | −1.47226 | −0.736130 | − | 0.676841i | \(-0.763349\pi\) | ||||
−0.736130 | + | 0.676841i | \(0.763349\pi\) | |||||||
\(710\) | 13.9506 | 0.523556 | ||||||||
\(711\) | −5.16206 | −0.193592 | ||||||||
\(712\) | −15.9015 | −0.595933 | ||||||||
\(713\) | 3.71809 | 0.139243 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.90750 | −0.258326 | ||||||||
\(716\) | −27.8589 | −1.04114 | ||||||||
\(717\) | −3.00670 | −0.112287 | ||||||||
\(718\) | 12.6098 | 0.470593 | ||||||||
\(719\) | 44.4526 | 1.65780 | 0.828901 | − | 0.559396i | \(-0.188967\pi\) | ||||
0.828901 | + | 0.559396i | \(0.188967\pi\) | |||||||
\(720\) | 8.48833 | 0.316341 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.38971 | −0.312233 | ||||||||
\(723\) | 22.5330 | 0.838010 | ||||||||
\(724\) | −29.0688 | −1.08033 | ||||||||
\(725\) | 40.0133 | 1.48606 | ||||||||
\(726\) | 0.711254 | 0.0263971 | ||||||||
\(727\) | 19.5784 | 0.726123 | 0.363062 | − | 0.931765i | \(-0.381731\pi\) | ||||
0.363062 | + | 0.931765i | \(0.381731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.21941 | 0.193179 | ||||||||
\(731\) | 13.8377 | 0.511805 | ||||||||
\(732\) | −20.8049 | −0.768970 | ||||||||
\(733\) | −3.23986 | −0.119667 | −0.0598335 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598335 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(734\) | −12.9885 | −0.479414 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.07998 | −0.187250 | ||||||||
\(737\) | 34.0926 | 1.25582 | ||||||||
\(738\) | −5.85622 | −0.215571 | ||||||||
\(739\) | −23.6779 | −0.871004 | −0.435502 | − | 0.900188i | \(-0.643429\pi\) | ||||
−0.435502 | + | 0.900188i | \(0.643429\pi\) | |||||||
\(740\) | 29.4794 | 1.08368 | ||||||||
\(741\) | −0.916611 | −0.0336725 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.0714 | −1.80026 | −0.900128 | − | 0.435625i | \(-0.856527\pi\) | ||||
−0.900128 | + | 0.435625i | \(0.856527\pi\) | |||||||
\(744\) | 7.06561 | 0.259038 | ||||||||
\(745\) | −32.6067 | −1.19462 | ||||||||
\(746\) | −8.30207 | −0.303961 | ||||||||
\(747\) | −0.437777 | −0.0160174 | ||||||||
\(748\) | −26.7919 | −0.979609 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.31557 | 0.0845528 | ||||||||
\(751\) | 23.8607 | 0.870690 | 0.435345 | − | 0.900264i | \(-0.356626\pi\) | ||||
0.435345 | + | 0.900264i | \(0.356626\pi\) | |||||||
\(752\) | −31.5363 | −1.15001 | ||||||||
\(753\) | −0.240327 | −0.00875799 | ||||||||
\(754\) | −1.86191 | −0.0678068 | ||||||||
\(755\) | −9.19413 | −0.334608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4095 | −0.560068 | −0.280034 | − | 0.959990i | \(-0.590346\pi\) | ||||
−0.280034 | + | 0.959990i | \(0.590346\pi\) | |||||||
\(758\) | −5.36426 | −0.194839 | ||||||||
\(759\) | −3.52145 | −0.127820 | ||||||||
\(760\) | −10.0818 | −0.365704 | ||||||||
\(761\) | −39.3607 | −1.42683 | −0.713413 | − | 0.700744i | \(-0.752851\pi\) | ||||
−0.713413 | + | 0.700744i | \(0.752851\pi\) | |||||||
\(762\) | 3.46999 | 0.125705 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 28.7342 | 1.03957 | ||||||||
\(765\) | 14.7152 | 0.532029 | ||||||||
\(766\) | −14.8181 | −0.535400 | ||||||||
\(767\) | −7.50609 | −0.271029 | ||||||||
\(768\) | −0.876200 | −0.0316171 | ||||||||
\(769\) | 18.1247 | 0.653592 | 0.326796 | − | 0.945095i | \(-0.394031\pi\) | ||||
0.326796 | + | 0.945095i | \(0.394031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.158016 | 0.00569079 | ||||||||
\(772\) | 4.34356 | 0.156328 | ||||||||
\(773\) | 26.5742 | 0.955807 | 0.477903 | − | 0.878412i | \(-0.341397\pi\) | ||||
0.477903 | + | 0.878412i | \(0.341397\pi\) | |||||||
\(774\) | 1.60905 | 0.0578363 | ||||||||
\(775\) | −23.6220 | −0.848528 | ||||||||
\(776\) | −11.9219 | −0.427969 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.49961 | −0.197171 | ||||||||
\(779\) | −18.1573 | −0.650551 | ||||||||
\(780\) | 3.41725 | 0.122357 | ||||||||
\(781\) | 28.7105 | 1.02734 | ||||||||
\(782\) | −2.21778 | −0.0793076 | ||||||||
\(783\) | 6.29806 | 0.225074 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.3657 | −0.905339 | ||||||||
\(786\) | 2.61123 | 0.0931395 | ||||||||
\(787\) | 38.1617 | 1.36032 | 0.680160 | − | 0.733064i | \(-0.261910\pi\) | ||||
0.680160 | + | 0.733064i | \(0.261910\pi\) | |||||||
\(788\) | 17.6777 | 0.629742 | ||||||||
\(789\) | 18.4642 | 0.657342 | ||||||||
\(790\) | −8.83276 | −0.314255 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.69193 | −0.237787 | ||||||||
\(793\) | −6.95228 | −0.246883 | ||||||||
\(794\) | −8.58133 | −0.304540 | ||||||||
\(795\) | −18.2834 | −0.648446 | ||||||||
\(796\) | −18.6384 | −0.660621 | ||||||||
\(797\) | −21.2237 | −0.751780 | −0.375890 | − | 0.926664i | \(-0.622663\pi\) | ||||
−0.375890 | + | 0.926664i | \(0.622663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.6707 | −1.93411 | ||||||||
\(800\) | 32.2745 | 1.14108 | ||||||||
\(801\) | 8.36773 | 0.295659 | ||||||||
\(802\) | 4.77550 | 0.168629 | ||||||||
\(803\) | 10.7416 | 0.379063 | ||||||||
\(804\) | −16.8661 | −0.594822 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.09919 | 0.0387172 | ||||||||
\(807\) | 0.958502 | 0.0337409 | ||||||||
\(808\) | 2.80385 | 0.0986392 | ||||||||
\(809\) | 48.7399 | 1.71360 | 0.856801 | − | 0.515647i | \(-0.172448\pi\) | ||||
0.856801 | + | 0.515647i | \(0.172448\pi\) | |||||||
\(810\) | 1.71109 | 0.0601217 | ||||||||
\(811\) | 20.6607 | 0.725496 | 0.362748 | − | 0.931887i | \(-0.381839\pi\) | ||||
0.362748 | + | 0.931887i | \(0.381839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.5098 | −0.824524 | ||||||||
\(814\) | −8.98079 | −0.314777 | ||||||||
\(815\) | 37.5779 | 1.31629 | ||||||||
\(816\) | 11.0019 | 0.385143 | ||||||||
\(817\) | 4.98888 | 0.174539 | ||||||||
\(818\) | 14.6032 | 0.510590 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 67.6927 | 2.36393 | ||||||||
\(821\) | −16.5527 | −0.577694 | −0.288847 | − | 0.957375i | \(-0.593272\pi\) | ||||
−0.288847 | + | 0.957375i | \(0.593272\pi\) | |||||||
\(822\) | −6.08991 | −0.212410 | ||||||||
\(823\) | −56.3756 | −1.96513 | −0.982565 | − | 0.185921i | \(-0.940473\pi\) | ||||
−0.982565 | + | 0.185921i | \(0.940473\pi\) | |||||||
\(824\) | −19.9456 | −0.694838 | ||||||||
\(825\) | 22.3727 | 0.778918 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.5907 | −1.02897 | −0.514485 | − | 0.857499i | \(-0.672017\pi\) | ||||
−0.514485 | + | 0.857499i | \(0.672017\pi\) | |||||||
\(828\) | 1.74212 | 0.0605427 | ||||||||
\(829\) | 23.1935 | 0.805544 | 0.402772 | − | 0.915300i | \(-0.368047\pi\) | ||||
0.402772 | + | 0.915300i | \(0.368047\pi\) | |||||||
\(830\) | −0.749078 | −0.0260009 | ||||||||
\(831\) | 31.2642 | 1.08454 | ||||||||
\(832\) | 1.43132 | 0.0496222 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.59471 | 0.332238 | ||||||||
\(835\) | 22.3196 | 0.772401 | ||||||||
\(836\) | −9.65925 | −0.334072 | ||||||||
\(837\) | −3.71809 | −0.128516 | ||||||||
\(838\) | 1.56605 | 0.0540982 | ||||||||
\(839\) | −38.4657 | −1.32798 | −0.663992 | − | 0.747739i | \(-0.731139\pi\) | ||||
−0.663992 | + | 0.747739i | \(0.731139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6655 | 0.367776 | ||||||||
\(842\) | −15.4440 | −0.532235 | ||||||||
\(843\) | −3.61573 | −0.124532 | ||||||||
\(844\) | −7.76615 | −0.267322 | ||||||||
\(845\) | −42.6611 | −1.46759 | ||||||||
\(846\) | −6.35714 | −0.218563 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −13.6697 | −0.469419 | ||||||||
\(849\) | −5.48645 | −0.188294 | ||||||||
\(850\) | 14.0902 | 0.483288 | ||||||||
\(851\) | 5.02204 | 0.172153 | ||||||||
\(852\) | −14.2035 | −0.486605 | ||||||||
\(853\) | 20.7509 | 0.710499 | 0.355249 | − | 0.934772i | \(-0.384396\pi\) | ||||
0.355249 | + | 0.934772i | \(0.384396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.30525 | 0.181436 | ||||||||
\(856\) | 21.4167 | 0.732006 | ||||||||
\(857\) | −16.1412 | −0.551372 | −0.275686 | − | 0.961248i | \(-0.588905\pi\) | ||||
−0.275686 | + | 0.961248i | \(0.588905\pi\) | |||||||
\(858\) | −1.04105 | −0.0355410 | ||||||||
\(859\) | 42.5954 | 1.45334 | 0.726668 | − | 0.686989i | \(-0.241068\pi\) | ||||
0.726668 | + | 0.686989i | \(0.241068\pi\) | |||||||
\(860\) | −18.5992 | −0.634229 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.3916 | −0.387999 | ||||||||
\(863\) | −34.7858 | −1.18412 | −0.592061 | − | 0.805893i | \(-0.701686\pi\) | ||||
−0.592061 | + | 0.805893i | \(0.701686\pi\) | |||||||
\(864\) | 5.07998 | 0.172824 | ||||||||
\(865\) | −63.0839 | −2.14492 | ||||||||
\(866\) | −8.59550 | −0.292087 | ||||||||
\(867\) | 2.07264 | 0.0703905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.1779 | −0.616643 | ||||||||
\(870\) | 10.7766 | 0.365359 | ||||||||
\(871\) | −5.63609 | −0.190972 | ||||||||
\(872\) | 28.3036 | 0.958482 | ||||||||
\(873\) | 6.27355 | 0.212328 | ||||||||
\(874\) | −0.799574 | −0.0270460 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.31404 | −0.179545 | ||||||||
\(877\) | −10.9171 | −0.368643 | −0.184322 | − | 0.982866i | \(-0.559009\pi\) | ||||
−0.184322 | + | 0.982866i | \(0.559009\pi\) | |||||||
\(878\) | −9.06303 | −0.305863 | ||||||||
\(879\) | −18.5359 | −0.625199 | ||||||||
\(880\) | 29.8912 | 1.00763 | ||||||||
\(881\) | −40.9354 | −1.37915 | −0.689575 | − | 0.724214i | \(-0.742203\pi\) | ||||
−0.689575 | + | 0.724214i | \(0.742203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8540 | 0.634486 | 0.317243 | − | 0.948344i | \(-0.397243\pi\) | ||||
0.317243 | + | 0.948344i | \(0.397243\pi\) | |||||||
\(884\) | 4.42916 | 0.148969 | ||||||||
\(885\) | 43.4445 | 1.46037 | ||||||||
\(886\) | 5.07685 | 0.170560 | ||||||||
\(887\) | 0.248770 | 0.00835289 | 0.00417645 | − | 0.999991i | \(-0.498671\pi\) | ||||
0.00417645 | + | 0.999991i | \(0.498671\pi\) | |||||||
\(888\) | 9.54356 | 0.320261 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.3180 | 0.479939 | ||||||||
\(891\) | 3.52145 | 0.117973 | ||||||||
\(892\) | 18.4232 | 0.616854 | ||||||||
\(893\) | −19.7104 | −0.659582 | ||||||||
\(894\) | −4.91427 | −0.164358 | ||||||||
\(895\) | 53.8825 | 1.80109 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.582156 | 0.0194376 | ||||||||
\(898\) | −6.23296 | −0.207996 | ||||||||
\(899\) | −23.4167 | −0.780991 | ||||||||
\(900\) | −11.0681 | −0.368938 | ||||||||
\(901\) | −23.6975 | −0.789478 | ||||||||
\(902\) | −20.6224 | −0.686650 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.3021 | −0.708497 | ||||||||
\(905\) | 56.2226 | 1.86890 | ||||||||
\(906\) | −1.38568 | −0.0460361 | ||||||||
\(907\) | 53.4014 | 1.77316 | 0.886582 | − | 0.462572i | \(-0.153073\pi\) | ||||
0.886582 | + | 0.462572i | \(0.153073\pi\) | |||||||
\(908\) | 36.2576 | 1.20325 | ||||||||
\(909\) | −1.47545 | −0.0489377 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0659 | −0.830471 | −0.415235 | − | 0.909714i | \(-0.636301\pi\) | ||||
−0.415235 | + | 0.909714i | \(0.636301\pi\) | |||||||
\(912\) | 3.96650 | 0.131344 | ||||||||
\(913\) | −1.54161 | −0.0510198 | ||||||||
\(914\) | −3.78939 | −0.125342 | ||||||||
\(915\) | 40.2391 | 1.33026 | ||||||||
\(916\) | 17.4485 | 0.576516 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.21778 | 0.0731976 | ||||||||
\(919\) | −7.51211 | −0.247802 | −0.123901 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123901 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(920\) | 6.40311 | 0.211104 | ||||||||
\(921\) | 4.00645 | 0.132017 | ||||||||
\(922\) | −13.4774 | −0.443855 | ||||||||
\(923\) | −4.74634 | −0.156228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.9064 | −1.04908 | ||||||||
\(926\) | 8.11139 | 0.266557 | ||||||||
\(927\) | 10.4958 | 0.344729 | ||||||||
\(928\) | 31.9940 | 1.05025 | ||||||||
\(929\) | −41.5253 | −1.36240 | −0.681201 | − | 0.732096i | \(-0.738542\pi\) | ||||
−0.681201 | + | 0.732096i | \(0.738542\pi\) | |||||||
\(930\) | −6.36199 | −0.208618 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.1564 | −0.561976 | ||||||||
\(933\) | 27.7513 | 0.908538 | ||||||||
\(934\) | −7.49790 | −0.245339 | ||||||||
\(935\) | 51.8188 | 1.69466 | ||||||||
\(936\) | 1.10629 | 0.0361603 | ||||||||
\(937\) | 0.268875 | 0.00878377 | 0.00439188 | − | 0.999990i | \(-0.498602\pi\) | ||||
0.00439188 | + | 0.999990i | \(0.498602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.6113 | −0.933696 | ||||||||
\(940\) | 73.4829 | 2.39675 | ||||||||
\(941\) | −43.1875 | −1.40787 | −0.703937 | − | 0.710263i | \(-0.748576\pi\) | ||||
−0.703937 | + | 0.710263i | \(0.748576\pi\) | |||||||
\(942\) | −3.82295 | −0.124558 | ||||||||
\(943\) | 11.5320 | 0.375534 | ||||||||
\(944\) | 32.4815 | 1.05718 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.66620 | 0.184224 | ||||||||
\(947\) | −3.35228 | −0.108934 | −0.0544672 | − | 0.998516i | \(-0.517346\pi\) | ||||
−0.0544672 | + | 0.998516i | \(0.517346\pi\) | |||||||
\(948\) | 8.99290 | 0.292076 | ||||||||
\(949\) | −1.77577 | −0.0576440 | ||||||||
\(950\) | 5.07991 | 0.164814 | ||||||||
\(951\) | 1.93708 | 0.0628141 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.5918 | 1.73601 | 0.868004 | − | 0.496558i | \(-0.165403\pi\) | ||||
0.868004 | + | 0.496558i | \(0.165403\pi\) | |||||||
\(954\) | −2.75556 | −0.0892146 | ||||||||
\(955\) | −55.5754 | −1.79838 | ||||||||
\(956\) | 5.23801 | 0.169409 | ||||||||
\(957\) | 22.1783 | 0.716922 | ||||||||
\(958\) | −0.941949 | −0.0304330 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.28435 | −0.267376 | ||||||||
\(961\) | −17.1758 | −0.554059 | ||||||||
\(962\) | 1.48468 | 0.0478680 | ||||||||
\(963\) | −11.2699 | −0.363169 | ||||||||
\(964\) | −39.2550 | −1.26432 | ||||||||
\(965\) | −8.40097 | −0.270437 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.7474 | 0.506401 | 0.253201 | − | 0.967414i | \(-0.418517\pi\) | ||||
0.253201 | + | 0.967414i | \(0.418517\pi\) | |||||||
\(968\) | −2.66159 | −0.0855469 | ||||||||
\(969\) | 6.87624 | 0.220897 | ||||||||
\(970\) | 10.7346 | 0.344668 | ||||||||
\(971\) | 30.6603 | 0.983935 | 0.491967 | − | 0.870614i | \(-0.336278\pi\) | ||||
0.491967 | + | 0.870614i | \(0.336278\pi\) | |||||||
\(972\) | −1.74212 | −0.0558784 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.8712 | −0.380378 | ||||||||
\(975\) | −3.69860 | −0.118450 | ||||||||
\(976\) | 30.0850 | 0.962997 | ||||||||
\(977\) | −14.8183 | −0.474081 | −0.237040 | − | 0.971500i | \(-0.576177\pi\) | ||||
−0.237040 | + | 0.971500i | \(0.576177\pi\) | |||||||
\(978\) | 5.66349 | 0.181099 | ||||||||
\(979\) | 29.4665 | 0.941754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.8940 | −0.475529 | ||||||||
\(982\) | −17.5164 | −0.558970 | ||||||||
\(983\) | 27.7690 | 0.885692 | 0.442846 | − | 0.896598i | \(-0.353969\pi\) | ||||
0.442846 | + | 0.896598i | \(0.353969\pi\) | |||||||
\(984\) | 21.9147 | 0.698614 | ||||||||
\(985\) | −34.1908 | −1.08941 | ||||||||
\(986\) | 13.9677 | 0.444822 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.59684 | 0.0508023 | ||||||||
\(989\) | −3.16853 | −0.100753 | ||||||||
\(990\) | 6.02552 | 0.191504 | ||||||||
\(991\) | 38.5662 | 1.22510 | 0.612548 | − | 0.790433i | \(-0.290145\pi\) | ||||
0.612548 | + | 0.790433i | \(0.290145\pi\) | |||||||
\(992\) | −18.8878 | −0.599688 | ||||||||
\(993\) | −29.4869 | −0.935737 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0490 | 1.14283 | ||||||||
\(996\) | 0.762659 | 0.0241658 | ||||||||
\(997\) | 45.2497 | 1.43307 | 0.716536 | − | 0.697550i | \(-0.245727\pi\) | ||||
0.716536 | + | 0.697550i | \(0.245727\pi\) | |||||||
\(998\) | −16.9399 | −0.536225 | ||||||||
\(999\) | −5.02204 | −0.158890 |
(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 | 3381.2.a.bl.1.5 | yes | 10 | |
7.6 | odd | 2 | 3381.2.a.bk.1.5 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3381.2.a.bk.1.5 | ✓ | 10 | 7.6 | odd | 2 | ||
3381.2.a.bl.1.5 | yes | 10 | 1.1 | even | 1 | trivial |