Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 4x^{6} + 22x^{5} + 3x^{4} - 28x^{3} + 7x^{2} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.394661\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.394661 | −0.227857 | −0.113929 | − | 0.993489i | \(-0.536344\pi\) | ||||
−0.113929 | + | 0.993489i | \(0.536344\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.507765 | 0.227079 | 0.113540 | − | 0.993533i | \(-0.463781\pi\) | ||||
0.113540 | + | 0.993533i | \(0.463781\pi\) | |||||||
\(6\) | 0.394661 | 0.161120 | ||||||||
\(7\) | 1.24955 | 0.472285 | 0.236142 | − | 0.971718i | \(-0.424117\pi\) | ||||
0.236142 | + | 0.971718i | \(0.424117\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.84424 | −0.948081 | ||||||||
\(10\) | −0.507765 | −0.160569 | ||||||||
\(11\) | −2.69825 | −0.813552 | −0.406776 | − | 0.913528i | \(-0.633347\pi\) | ||||
−0.406776 | + | 0.913528i | \(0.633347\pi\) | |||||||
\(12\) | −0.394661 | −0.113929 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.24955 | −0.333956 | ||||||||
\(15\) | −0.200395 | −0.0517417 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.56219 | 1.10649 | 0.553247 | − | 0.833017i | \(-0.313389\pi\) | ||||
0.553247 | + | 0.833017i | \(0.313389\pi\) | |||||||
\(18\) | 2.84424 | 0.670395 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.507765 | 0.113540 | ||||||||
\(21\) | −0.493147 | −0.107614 | ||||||||
\(22\) | 2.69825 | 0.575268 | ||||||||
\(23\) | 2.24994 | 0.469145 | 0.234572 | − | 0.972099i | \(-0.424631\pi\) | ||||
0.234572 | + | 0.972099i | \(0.424631\pi\) | |||||||
\(24\) | 0.394661 | 0.0805598 | ||||||||
\(25\) | −4.74218 | −0.948435 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.30649 | 0.443885 | ||||||||
\(28\) | 1.24955 | 0.236142 | ||||||||
\(29\) | −9.14046 | −1.69734 | −0.848671 | − | 0.528922i | \(-0.822597\pi\) | ||||
−0.848671 | + | 0.528922i | \(0.822597\pi\) | |||||||
\(30\) | 0.200395 | 0.0365869 | ||||||||
\(31\) | −1.74898 | −0.314126 | −0.157063 | − | 0.987589i | \(-0.550203\pi\) | ||||
−0.157063 | + | 0.987589i | \(0.550203\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.06489 | 0.185374 | ||||||||
\(34\) | −4.56219 | −0.782409 | ||||||||
\(35\) | 0.634476 | 0.107246 | ||||||||
\(36\) | −2.84424 | −0.474041 | ||||||||
\(37\) | 8.71511 | 1.43275 | 0.716377 | − | 0.697713i | \(-0.245799\pi\) | ||||
0.716377 | + | 0.697713i | \(0.245799\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.507765 | −0.0802846 | ||||||||
\(41\) | 9.55485 | 1.49222 | 0.746109 | − | 0.665824i | \(-0.231920\pi\) | ||||
0.746109 | + | 0.665824i | \(0.231920\pi\) | |||||||
\(42\) | 0.493147 | 0.0760943 | ||||||||
\(43\) | 3.72738 | 0.568421 | 0.284210 | − | 0.958762i | \(-0.408269\pi\) | ||||
0.284210 | + | 0.958762i | \(0.408269\pi\) | |||||||
\(44\) | −2.69825 | −0.406776 | ||||||||
\(45\) | −1.44421 | −0.215289 | ||||||||
\(46\) | −2.24994 | −0.331736 | ||||||||
\(47\) | −8.96128 | −1.30714 | −0.653568 | − | 0.756867i | \(-0.726729\pi\) | ||||
−0.653568 | + | 0.756867i | \(0.726729\pi\) | |||||||
\(48\) | −0.394661 | −0.0569644 | ||||||||
\(49\) | −5.43863 | −0.776947 | ||||||||
\(50\) | 4.74218 | 0.670645 | ||||||||
\(51\) | −1.80052 | −0.252123 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.80547 | 0.797443 | 0.398721 | − | 0.917072i | \(-0.369454\pi\) | ||||
0.398721 | + | 0.917072i | \(0.369454\pi\) | |||||||
\(54\) | −2.30649 | −0.313874 | ||||||||
\(55\) | −1.37007 | −0.184741 | ||||||||
\(56\) | −1.24955 | −0.166978 | ||||||||
\(57\) | −0.394661 | −0.0522741 | ||||||||
\(58\) | 9.14046 | 1.20020 | ||||||||
\(59\) | 8.65749 | 1.12711 | 0.563555 | − | 0.826079i | \(-0.309433\pi\) | ||||
0.563555 | + | 0.826079i | \(0.309433\pi\) | |||||||
\(60\) | −0.200395 | −0.0258708 | ||||||||
\(61\) | −0.618453 | −0.0791848 | −0.0395924 | − | 0.999216i | \(-0.512606\pi\) | ||||
−0.0395924 | + | 0.999216i | \(0.512606\pi\) | |||||||
\(62\) | 1.74898 | 0.222120 | ||||||||
\(63\) | −3.55402 | −0.447764 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.06489 | −0.131079 | ||||||||
\(67\) | −12.2636 | −1.49824 | −0.749118 | − | 0.662436i | \(-0.769523\pi\) | ||||
−0.749118 | + | 0.662436i | \(0.769523\pi\) | |||||||
\(68\) | 4.56219 | 0.553247 | ||||||||
\(69\) | −0.887963 | −0.106898 | ||||||||
\(70\) | −0.634476 | −0.0758344 | ||||||||
\(71\) | 0.995275 | 0.118117 | 0.0590587 | − | 0.998255i | \(-0.481190\pi\) | ||||
0.0590587 | + | 0.998255i | \(0.481190\pi\) | |||||||
\(72\) | 2.84424 | 0.335197 | ||||||||
\(73\) | −0.150857 | −0.0176564 | −0.00882821 | − | 0.999961i | \(-0.502810\pi\) | ||||
−0.00882821 | + | 0.999961i | \(0.502810\pi\) | |||||||
\(74\) | −8.71511 | −1.01311 | ||||||||
\(75\) | 1.87155 | 0.216108 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −3.37159 | −0.384228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.80849 | −0.653506 | −0.326753 | − | 0.945110i | \(-0.605955\pi\) | ||||
−0.326753 | + | 0.945110i | \(0.605955\pi\) | |||||||
\(80\) | 0.507765 | 0.0567698 | ||||||||
\(81\) | 7.62245 | 0.846939 | ||||||||
\(82\) | −9.55485 | −1.05516 | ||||||||
\(83\) | 8.15004 | 0.894583 | 0.447291 | − | 0.894388i | \(-0.352389\pi\) | ||||
0.447291 | + | 0.894388i | \(0.352389\pi\) | |||||||
\(84\) | −0.493147 | −0.0538068 | ||||||||
\(85\) | 2.31652 | 0.251262 | ||||||||
\(86\) | −3.72738 | −0.401934 | ||||||||
\(87\) | 3.60738 | 0.386752 | ||||||||
\(88\) | 2.69825 | 0.287634 | ||||||||
\(89\) | −2.44741 | −0.259424 | −0.129712 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129712 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(90\) | 1.44421 | 0.152233 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.24994 | 0.234572 | ||||||||
\(93\) | 0.690253 | 0.0715759 | ||||||||
\(94\) | 8.96128 | 0.924285 | ||||||||
\(95\) | 0.507765 | 0.0520955 | ||||||||
\(96\) | 0.394661 | 0.0402799 | ||||||||
\(97\) | 5.19401 | 0.527372 | 0.263686 | − | 0.964609i | \(-0.415062\pi\) | ||||
0.263686 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(98\) | 5.43863 | 0.549385 | ||||||||
\(99\) | 7.67447 | 0.771313 | ||||||||
\(100\) | −4.74218 | −0.474218 | ||||||||
\(101\) | −16.9227 | −1.68387 | −0.841936 | − | 0.539577i | \(-0.818584\pi\) | ||||
−0.841936 | + | 0.539577i | \(0.818584\pi\) | |||||||
\(102\) | 1.80052 | 0.178278 | ||||||||
\(103\) | 4.09263 | 0.403259 | 0.201629 | − | 0.979462i | \(-0.435376\pi\) | ||||
0.201629 | + | 0.979462i | \(0.435376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.250403 | −0.0244368 | ||||||||
\(106\) | −5.80547 | −0.563877 | ||||||||
\(107\) | 17.5881 | 1.70031 | 0.850154 | − | 0.526534i | \(-0.176509\pi\) | ||||
0.850154 | + | 0.526534i | \(0.176509\pi\) | |||||||
\(108\) | 2.30649 | 0.221942 | ||||||||
\(109\) | −19.6811 | −1.88510 | −0.942552 | − | 0.334059i | \(-0.891581\pi\) | ||||
−0.942552 | + | 0.334059i | \(0.891581\pi\) | |||||||
\(110\) | 1.37007 | 0.130631 | ||||||||
\(111\) | −3.43951 | −0.326464 | ||||||||
\(112\) | 1.24955 | 0.118071 | ||||||||
\(113\) | −10.0150 | −0.942128 | −0.471064 | − | 0.882099i | \(-0.656130\pi\) | ||||
−0.471064 | + | 0.882099i | \(0.656130\pi\) | |||||||
\(114\) | 0.394661 | 0.0369634 | ||||||||
\(115\) | 1.14244 | 0.106533 | ||||||||
\(116\) | −9.14046 | −0.848671 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.65749 | −0.796987 | ||||||||
\(119\) | 5.70067 | 0.522580 | ||||||||
\(120\) | 0.200395 | 0.0182934 | ||||||||
\(121\) | −3.71947 | −0.338133 | ||||||||
\(122\) | 0.618453 | 0.0559921 | ||||||||
\(123\) | −3.77092 | −0.340013 | ||||||||
\(124\) | −1.74898 | −0.157063 | ||||||||
\(125\) | −4.94673 | −0.442449 | ||||||||
\(126\) | 3.55402 | 0.316617 | ||||||||
\(127\) | −22.1440 | −1.96497 | −0.982483 | − | 0.186352i | \(-0.940333\pi\) | ||||
−0.982483 | + | 0.186352i | \(0.940333\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.47105 | −0.129519 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4396 | −1.69845 | −0.849223 | − | 0.528034i | \(-0.822929\pi\) | ||||
−0.849223 | + | 0.528034i | \(0.822929\pi\) | |||||||
\(132\) | 1.06489 | 0.0926869 | ||||||||
\(133\) | 1.24955 | 0.108350 | ||||||||
\(134\) | 12.2636 | 1.05941 | ||||||||
\(135\) | 1.17116 | 0.100797 | ||||||||
\(136\) | −4.56219 | −0.391205 | ||||||||
\(137\) | 5.54764 | 0.473966 | 0.236983 | − | 0.971514i | \(-0.423841\pi\) | ||||
0.236983 | + | 0.971514i | \(0.423841\pi\) | |||||||
\(138\) | 0.887963 | 0.0755884 | ||||||||
\(139\) | 11.9267 | 1.01161 | 0.505806 | − | 0.862647i | \(-0.331195\pi\) | ||||
0.505806 | + | 0.862647i | \(0.331195\pi\) | |||||||
\(140\) | 0.634476 | 0.0536230 | ||||||||
\(141\) | 3.53666 | 0.297841 | ||||||||
\(142\) | −0.995275 | −0.0835216 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.84424 | −0.237020 | ||||||||
\(145\) | −4.64120 | −0.385431 | ||||||||
\(146\) | 0.150857 | 0.0124850 | ||||||||
\(147\) | 2.14641 | 0.177033 | ||||||||
\(148\) | 8.71511 | 0.716377 | ||||||||
\(149\) | 15.2350 | 1.24810 | 0.624052 | − | 0.781383i | \(-0.285485\pi\) | ||||
0.624052 | + | 0.781383i | \(0.285485\pi\) | |||||||
\(150\) | −1.87155 | −0.152811 | ||||||||
\(151\) | −16.5771 | −1.34902 | −0.674512 | − | 0.738264i | \(-0.735646\pi\) | ||||
−0.674512 | + | 0.738264i | \(0.735646\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −12.9760 | −1.04905 | ||||||||
\(154\) | 3.37159 | 0.271690 | ||||||||
\(155\) | −0.888069 | −0.0713314 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.699811 | 0.0558510 | 0.0279255 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279255 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(158\) | 5.80849 | 0.462099 | ||||||||
\(159\) | −2.29119 | −0.181703 | ||||||||
\(160\) | −0.507765 | −0.0401423 | ||||||||
\(161\) | 2.81141 | 0.221570 | ||||||||
\(162\) | −7.62245 | −0.598876 | ||||||||
\(163\) | 23.5897 | 1.84769 | 0.923844 | − | 0.382770i | \(-0.125030\pi\) | ||||
0.923844 | + | 0.382770i | \(0.125030\pi\) | |||||||
\(164\) | 9.55485 | 0.746109 | ||||||||
\(165\) | 0.540714 | 0.0420945 | ||||||||
\(166\) | −8.15004 | −0.632565 | ||||||||
\(167\) | 9.79491 | 0.757953 | 0.378976 | − | 0.925406i | \(-0.376276\pi\) | ||||
0.378976 | + | 0.925406i | \(0.376276\pi\) | |||||||
\(168\) | 0.493147 | 0.0380471 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.31652 | −0.177669 | ||||||||
\(171\) | −2.84424 | −0.217505 | ||||||||
\(172\) | 3.72738 | 0.284210 | ||||||||
\(173\) | −7.53389 | −0.572791 | −0.286396 | − | 0.958111i | \(-0.592457\pi\) | ||||
−0.286396 | + | 0.958111i | \(0.592457\pi\) | |||||||
\(174\) | −3.60738 | −0.273475 | ||||||||
\(175\) | −5.92557 | −0.447931 | ||||||||
\(176\) | −2.69825 | −0.203388 | ||||||||
\(177\) | −3.41677 | −0.256820 | ||||||||
\(178\) | 2.44741 | 0.183441 | ||||||||
\(179\) | −5.33482 | −0.398743 | −0.199372 | − | 0.979924i | \(-0.563890\pi\) | ||||
−0.199372 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(180\) | −1.44421 | −0.107645 | ||||||||
\(181\) | −24.1292 | −1.79351 | −0.896755 | − | 0.442527i | \(-0.854082\pi\) | ||||
−0.896755 | + | 0.442527i | \(0.854082\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.244079 | 0.0180428 | ||||||||
\(184\) | −2.24994 | −0.165868 | ||||||||
\(185\) | 4.42522 | 0.325349 | ||||||||
\(186\) | −0.690253 | −0.0506118 | ||||||||
\(187\) | −12.3099 | −0.900190 | ||||||||
\(188\) | −8.96128 | −0.653568 | ||||||||
\(189\) | 2.88207 | 0.209640 | ||||||||
\(190\) | −0.507765 | −0.0368371 | ||||||||
\(191\) | −20.7322 | −1.50013 | −0.750064 | − | 0.661365i | \(-0.769978\pi\) | ||||
−0.750064 | + | 0.661365i | \(0.769978\pi\) | |||||||
\(192\) | −0.394661 | −0.0284822 | ||||||||
\(193\) | 9.89665 | 0.712376 | 0.356188 | − | 0.934414i | \(-0.384076\pi\) | ||||
0.356188 | + | 0.934414i | \(0.384076\pi\) | |||||||
\(194\) | −5.19401 | −0.372908 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.43863 | −0.388474 | ||||||||
\(197\) | −5.46053 | −0.389046 | −0.194523 | − | 0.980898i | \(-0.562316\pi\) | ||||
−0.194523 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(198\) | −7.67447 | −0.545401 | ||||||||
\(199\) | −15.8738 | −1.12526 | −0.562632 | − | 0.826708i | \(-0.690211\pi\) | ||||
−0.562632 | + | 0.826708i | \(0.690211\pi\) | |||||||
\(200\) | 4.74218 | 0.335322 | ||||||||
\(201\) | 4.83996 | 0.341384 | ||||||||
\(202\) | 16.9227 | 1.19068 | ||||||||
\(203\) | −11.4214 | −0.801628 | ||||||||
\(204\) | −1.80052 | −0.126061 | ||||||||
\(205\) | 4.85162 | 0.338852 | ||||||||
\(206\) | −4.09263 | −0.285147 | ||||||||
\(207\) | −6.39938 | −0.444787 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.69825 | −0.186642 | ||||||||
\(210\) | 0.250403 | 0.0172794 | ||||||||
\(211\) | −19.8984 | −1.36986 | −0.684931 | − | 0.728608i | \(-0.740167\pi\) | ||||
−0.684931 | + | 0.728608i | \(0.740167\pi\) | |||||||
\(212\) | 5.80547 | 0.398721 | ||||||||
\(213\) | −0.392796 | −0.0269139 | ||||||||
\(214\) | −17.5881 | −1.20230 | ||||||||
\(215\) | 1.89263 | 0.129076 | ||||||||
\(216\) | −2.30649 | −0.156937 | ||||||||
\(217\) | −2.18543 | −0.148357 | ||||||||
\(218\) | 19.6811 | 1.33297 | ||||||||
\(219\) | 0.0595371 | 0.00402315 | ||||||||
\(220\) | −1.37007 | −0.0923703 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.43951 | 0.230845 | ||||||||
\(223\) | −10.3506 | −0.693126 | −0.346563 | − | 0.938027i | \(-0.612651\pi\) | ||||
−0.346563 | + | 0.938027i | \(0.612651\pi\) | |||||||
\(224\) | −1.24955 | −0.0834889 | ||||||||
\(225\) | 13.4879 | 0.899193 | ||||||||
\(226\) | 10.0150 | 0.666185 | ||||||||
\(227\) | 6.04541 | 0.401248 | 0.200624 | − | 0.979668i | \(-0.435703\pi\) | ||||
0.200624 | + | 0.979668i | \(0.435703\pi\) | |||||||
\(228\) | −0.394661 | −0.0261370 | ||||||||
\(229\) | 11.3666 | 0.751125 | 0.375563 | − | 0.926797i | \(-0.377449\pi\) | ||||
0.375563 | + | 0.926797i | \(0.377449\pi\) | |||||||
\(230\) | −1.14244 | −0.0753302 | ||||||||
\(231\) | 1.33063 | 0.0875492 | ||||||||
\(232\) | 9.14046 | 0.600101 | ||||||||
\(233\) | −19.6434 | −1.28688 | −0.643441 | − | 0.765496i | \(-0.722494\pi\) | ||||
−0.643441 | + | 0.765496i | \(0.722494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.55022 | −0.296824 | ||||||||
\(236\) | 8.65749 | 0.563555 | ||||||||
\(237\) | 2.29238 | 0.148906 | ||||||||
\(238\) | −5.70067 | −0.369520 | ||||||||
\(239\) | 8.02294 | 0.518961 | 0.259481 | − | 0.965748i | \(-0.416449\pi\) | ||||
0.259481 | + | 0.965748i | \(0.416449\pi\) | |||||||
\(240\) | −0.200395 | −0.0129354 | ||||||||
\(241\) | −13.5781 | −0.874640 | −0.437320 | − | 0.899306i | \(-0.644072\pi\) | ||||
−0.437320 | + | 0.899306i | \(0.644072\pi\) | |||||||
\(242\) | 3.71947 | 0.239096 | ||||||||
\(243\) | −9.92776 | −0.636866 | ||||||||
\(244\) | −0.618453 | −0.0395924 | ||||||||
\(245\) | −2.76154 | −0.176429 | ||||||||
\(246\) | 3.77092 | 0.240425 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.74898 | 0.111060 | ||||||||
\(249\) | −3.21650 | −0.203837 | ||||||||
\(250\) | 4.94673 | 0.312859 | ||||||||
\(251\) | −21.7978 | −1.37587 | −0.687933 | − | 0.725774i | \(-0.741482\pi\) | ||||
−0.687933 | + | 0.725774i | \(0.741482\pi\) | |||||||
\(252\) | −3.55402 | −0.223882 | ||||||||
\(253\) | −6.07089 | −0.381674 | ||||||||
\(254\) | 22.1440 | 1.38944 | ||||||||
\(255\) | −0.914239 | −0.0572518 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.9326 | 1.36812 | 0.684059 | − | 0.729427i | \(-0.260213\pi\) | ||||
0.684059 | + | 0.729427i | \(0.260213\pi\) | |||||||
\(258\) | 1.47105 | 0.0915836 | ||||||||
\(259\) | 10.8899 | 0.676668 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.9977 | 1.60922 | ||||||||
\(262\) | 19.4396 | 1.20098 | ||||||||
\(263\) | 8.68002 | 0.535233 | 0.267616 | − | 0.963526i | \(-0.413764\pi\) | ||||
0.267616 | + | 0.963526i | \(0.413764\pi\) | |||||||
\(264\) | −1.06489 | −0.0655395 | ||||||||
\(265\) | 2.94781 | 0.181083 | ||||||||
\(266\) | −1.24955 | −0.0766147 | ||||||||
\(267\) | 0.965894 | 0.0591118 | ||||||||
\(268\) | −12.2636 | −0.749118 | ||||||||
\(269\) | 10.2644 | 0.625832 | 0.312916 | − | 0.949781i | \(-0.398694\pi\) | ||||
0.312916 | + | 0.949781i | \(0.398694\pi\) | |||||||
\(270\) | −1.17116 | −0.0712742 | ||||||||
\(271\) | 19.1893 | 1.16566 | 0.582832 | − | 0.812593i | \(-0.301945\pi\) | ||||
0.582832 | + | 0.812593i | \(0.301945\pi\) | |||||||
\(272\) | 4.56219 | 0.276623 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.54764 | −0.335145 | ||||||||
\(275\) | 12.7956 | 0.771601 | ||||||||
\(276\) | −0.887963 | −0.0534491 | ||||||||
\(277\) | 3.03422 | 0.182309 | 0.0911543 | − | 0.995837i | \(-0.470944\pi\) | ||||
0.0911543 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(278\) | −11.9267 | −0.715318 | ||||||||
\(279\) | 4.97452 | 0.297817 | ||||||||
\(280\) | −0.634476 | −0.0379172 | ||||||||
\(281\) | 6.21368 | 0.370677 | 0.185339 | − | 0.982675i | \(-0.440662\pi\) | ||||
0.185339 | + | 0.982675i | \(0.440662\pi\) | |||||||
\(282\) | −3.53666 | −0.210605 | ||||||||
\(283\) | −12.5355 | −0.745157 | −0.372578 | − | 0.928001i | \(-0.621526\pi\) | ||||
−0.372578 | + | 0.928001i | \(0.621526\pi\) | |||||||
\(284\) | 0.995275 | 0.0590587 | ||||||||
\(285\) | −0.200395 | −0.0118704 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.9392 | 0.704751 | ||||||||
\(288\) | 2.84424 | 0.167599 | ||||||||
\(289\) | 3.81359 | 0.224329 | ||||||||
\(290\) | 4.64120 | 0.272541 | ||||||||
\(291\) | −2.04987 | −0.120166 | ||||||||
\(292\) | −0.150857 | −0.00882821 | ||||||||
\(293\) | 14.9894 | 0.875689 | 0.437845 | − | 0.899051i | \(-0.355742\pi\) | ||||
0.437845 | + | 0.899051i | \(0.355742\pi\) | |||||||
\(294\) | −2.14641 | −0.125181 | ||||||||
\(295\) | 4.39597 | 0.255943 | ||||||||
\(296\) | −8.71511 | −0.506555 | ||||||||
\(297\) | −6.22348 | −0.361123 | ||||||||
\(298\) | −15.2350 | −0.882542 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.87155 | 0.108054 | ||||||||
\(301\) | 4.65754 | 0.268456 | ||||||||
\(302\) | 16.5771 | 0.953904 | ||||||||
\(303\) | 6.67873 | 0.383683 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −0.314029 | −0.0179812 | ||||||||
\(306\) | 12.9760 | 0.741787 | ||||||||
\(307\) | −29.9417 | −1.70886 | −0.854431 | − | 0.519564i | \(-0.826094\pi\) | ||||
−0.854431 | + | 0.519564i | \(0.826094\pi\) | |||||||
\(308\) | −3.37159 | −0.192114 | ||||||||
\(309\) | −1.61520 | −0.0918855 | ||||||||
\(310\) | 0.888069 | 0.0504389 | ||||||||
\(311\) | −4.40422 | −0.249740 | −0.124870 | − | 0.992173i | \(-0.539851\pi\) | ||||
−0.124870 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8316 | 0.612238 | 0.306119 | − | 0.951993i | \(-0.400969\pi\) | ||||
0.306119 | + | 0.951993i | \(0.400969\pi\) | |||||||
\(314\) | −0.699811 | −0.0394926 | ||||||||
\(315\) | −1.80460 | −0.101678 | ||||||||
\(316\) | −5.80849 | −0.326753 | ||||||||
\(317\) | −27.7571 | −1.55900 | −0.779498 | − | 0.626405i | \(-0.784526\pi\) | ||||
−0.779498 | + | 0.626405i | \(0.784526\pi\) | |||||||
\(318\) | 2.29119 | 0.128484 | ||||||||
\(319\) | 24.6632 | 1.38088 | ||||||||
\(320\) | 0.507765 | 0.0283849 | ||||||||
\(321\) | −6.94134 | −0.387428 | ||||||||
\(322\) | −2.81141 | −0.156674 | ||||||||
\(323\) | 4.56219 | 0.253847 | ||||||||
\(324\) | 7.62245 | 0.423469 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.5897 | −1.30651 | ||||||||
\(327\) | 7.76734 | 0.429535 | ||||||||
\(328\) | −9.55485 | −0.527579 | ||||||||
\(329\) | −11.1975 | −0.617341 | ||||||||
\(330\) | −0.540714 | −0.0297653 | ||||||||
\(331\) | 15.6936 | 0.862600 | 0.431300 | − | 0.902209i | \(-0.358055\pi\) | ||||
0.431300 | + | 0.902209i | \(0.358055\pi\) | |||||||
\(332\) | 8.15004 | 0.447291 | ||||||||
\(333\) | −24.7879 | −1.35837 | ||||||||
\(334\) | −9.79491 | −0.535953 | ||||||||
\(335\) | −6.22702 | −0.340218 | ||||||||
\(336\) | −0.493147 | −0.0269034 | ||||||||
\(337\) | 20.3658 | 1.10940 | 0.554698 | − | 0.832052i | \(-0.312834\pi\) | ||||
0.554698 | + | 0.832052i | \(0.312834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.95251 | 0.214671 | ||||||||
\(340\) | 2.31652 | 0.125631 | ||||||||
\(341\) | 4.71917 | 0.255558 | ||||||||
\(342\) | 2.84424 | 0.153799 | ||||||||
\(343\) | −15.5427 | −0.839225 | ||||||||
\(344\) | −3.72738 | −0.200967 | ||||||||
\(345\) | −0.450876 | −0.0242743 | ||||||||
\(346\) | 7.53389 | 0.405025 | ||||||||
\(347\) | 20.8429 | 1.11890 | 0.559451 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(348\) | 3.60738 | 0.193376 | ||||||||
\(349\) | −1.36583 | −0.0731113 | −0.0365556 | − | 0.999332i | \(-0.511639\pi\) | ||||
−0.0365556 | + | 0.999332i | \(0.511639\pi\) | |||||||
\(350\) | 5.92557 | 0.316735 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.69825 | 0.143817 | ||||||||
\(353\) | 1.42712 | 0.0759581 | 0.0379791 | − | 0.999279i | \(-0.487908\pi\) | ||||
0.0379791 | + | 0.999279i | \(0.487908\pi\) | |||||||
\(354\) | 3.41677 | 0.181599 | ||||||||
\(355\) | 0.505365 | 0.0268220 | ||||||||
\(356\) | −2.44741 | −0.129712 | ||||||||
\(357\) | −2.24983 | −0.119074 | ||||||||
\(358\) | 5.33482 | 0.281954 | ||||||||
\(359\) | 27.3665 | 1.44435 | 0.722173 | − | 0.691712i | \(-0.243143\pi\) | ||||
0.722173 | + | 0.691712i | \(0.243143\pi\) | |||||||
\(360\) | 1.44421 | 0.0761163 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 24.1292 | 1.26820 | ||||||||
\(363\) | 1.46793 | 0.0770462 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0765996 | −0.00400941 | ||||||||
\(366\) | −0.244079 | −0.0127582 | ||||||||
\(367\) | 24.9590 | 1.30285 | 0.651424 | − | 0.758714i | \(-0.274172\pi\) | ||||
0.651424 | + | 0.758714i | \(0.274172\pi\) | |||||||
\(368\) | 2.24994 | 0.117286 | ||||||||
\(369\) | −27.1763 | −1.41474 | ||||||||
\(370\) | −4.42522 | −0.230056 | ||||||||
\(371\) | 7.25421 | 0.376620 | ||||||||
\(372\) | 0.690253 | 0.0357879 | ||||||||
\(373\) | −17.5861 | −0.910573 | −0.455286 | − | 0.890345i | \(-0.650463\pi\) | ||||
−0.455286 | + | 0.890345i | \(0.650463\pi\) | |||||||
\(374\) | 12.3099 | 0.636531 | ||||||||
\(375\) | 1.95228 | 0.100815 | ||||||||
\(376\) | 8.96128 | 0.462143 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.88207 | −0.148238 | ||||||||
\(379\) | −14.2698 | −0.732992 | −0.366496 | − | 0.930420i | \(-0.619443\pi\) | ||||
−0.366496 | + | 0.930420i | \(0.619443\pi\) | |||||||
\(380\) | 0.507765 | 0.0260478 | ||||||||
\(381\) | 8.73938 | 0.447732 | ||||||||
\(382\) | 20.7322 | 1.06075 | ||||||||
\(383\) | −12.8820 | −0.658241 | −0.329121 | − | 0.944288i | \(-0.606752\pi\) | ||||
−0.329121 | + | 0.944288i | \(0.606752\pi\) | |||||||
\(384\) | 0.394661 | 0.0201399 | ||||||||
\(385\) | −1.71197 | −0.0872502 | ||||||||
\(386\) | −9.89665 | −0.503726 | ||||||||
\(387\) | −10.6016 | −0.538909 | ||||||||
\(388\) | 5.19401 | 0.263686 | ||||||||
\(389\) | 4.94578 | 0.250761 | 0.125380 | − | 0.992109i | \(-0.459985\pi\) | ||||
0.125380 | + | 0.992109i | \(0.459985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2647 | 0.519106 | ||||||||
\(392\) | 5.43863 | 0.274692 | ||||||||
\(393\) | 7.67205 | 0.387003 | ||||||||
\(394\) | 5.46053 | 0.275097 | ||||||||
\(395\) | −2.94934 | −0.148398 | ||||||||
\(396\) | 7.67447 | 0.385657 | ||||||||
\(397\) | −22.0346 | −1.10589 | −0.552943 | − | 0.833219i | \(-0.686495\pi\) | ||||
−0.552943 | + | 0.833219i | \(0.686495\pi\) | |||||||
\(398\) | 15.8738 | 0.795681 | ||||||||
\(399\) | −0.493147 | −0.0246882 | ||||||||
\(400\) | −4.74218 | −0.237109 | ||||||||
\(401\) | 2.94800 | 0.147216 | 0.0736082 | − | 0.997287i | \(-0.476549\pi\) | ||||
0.0736082 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(402\) | −4.83996 | −0.241395 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −16.9227 | −0.841936 | ||||||||
\(405\) | 3.87041 | 0.192322 | ||||||||
\(406\) | 11.4214 | 0.566837 | ||||||||
\(407\) | −23.5155 | −1.16562 | ||||||||
\(408\) | 1.80052 | 0.0891389 | ||||||||
\(409\) | −18.3674 | −0.908211 | −0.454105 | − | 0.890948i | \(-0.650041\pi\) | ||||
−0.454105 | + | 0.890948i | \(0.650041\pi\) | |||||||
\(410\) | −4.85162 | −0.239604 | ||||||||
\(411\) | −2.18943 | −0.107997 | ||||||||
\(412\) | 4.09263 | 0.201629 | ||||||||
\(413\) | 10.8179 | 0.532316 | ||||||||
\(414\) | 6.39938 | 0.314512 | ||||||||
\(415\) | 4.13830 | 0.203141 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.70701 | −0.230503 | ||||||||
\(418\) | 2.69825 | 0.131976 | ||||||||
\(419\) | −7.18949 | −0.351229 | −0.175615 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175615 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(420\) | −0.250403 | −0.0122184 | ||||||||
\(421\) | −13.4228 | −0.654189 | −0.327095 | − | 0.944992i | \(-0.606070\pi\) | ||||
−0.327095 | + | 0.944992i | \(0.606070\pi\) | |||||||
\(422\) | 19.8984 | 0.968638 | ||||||||
\(423\) | 25.4881 | 1.23927 | ||||||||
\(424\) | −5.80547 | −0.281939 | ||||||||
\(425\) | −21.6347 | −1.04944 | ||||||||
\(426\) | 0.392796 | 0.0190310 | ||||||||
\(427\) | −0.772787 | −0.0373978 | ||||||||
\(428\) | 17.5881 | 0.850154 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.89263 | −0.0912709 | ||||||||
\(431\) | −19.5840 | −0.943328 | −0.471664 | − | 0.881778i | \(-0.656347\pi\) | ||||
−0.471664 | + | 0.881778i | \(0.656347\pi\) | |||||||
\(432\) | 2.30649 | 0.110971 | ||||||||
\(433\) | −33.5004 | −1.60993 | −0.804964 | − | 0.593324i | \(-0.797815\pi\) | ||||
−0.804964 | + | 0.593324i | \(0.797815\pi\) | |||||||
\(434\) | 2.18543 | 0.104904 | ||||||||
\(435\) | 1.83170 | 0.0878233 | ||||||||
\(436\) | −19.6811 | −0.942552 | ||||||||
\(437\) | 2.24994 | 0.107629 | ||||||||
\(438\) | −0.0595371 | −0.00284479 | ||||||||
\(439\) | −4.74365 | −0.226402 | −0.113201 | − | 0.993572i | \(-0.536110\pi\) | ||||
−0.113201 | + | 0.993572i | \(0.536110\pi\) | |||||||
\(440\) | 1.37007 | 0.0653157 | ||||||||
\(441\) | 15.4688 | 0.736609 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.0710 | 1.47623 | 0.738114 | − | 0.674676i | \(-0.235717\pi\) | ||||
0.738114 | + | 0.674676i | \(0.235717\pi\) | |||||||
\(444\) | −3.43951 | −0.163232 | ||||||||
\(445\) | −1.24271 | −0.0589099 | ||||||||
\(446\) | 10.3506 | 0.490114 | ||||||||
\(447\) | −6.01267 | −0.284390 | ||||||||
\(448\) | 1.24955 | 0.0590356 | ||||||||
\(449\) | −15.7887 | −0.745117 | −0.372558 | − | 0.928009i | \(-0.621519\pi\) | ||||
−0.372558 | + | 0.928009i | \(0.621519\pi\) | |||||||
\(450\) | −13.4879 | −0.635826 | ||||||||
\(451\) | −25.7813 | −1.21400 | ||||||||
\(452\) | −10.0150 | −0.471064 | ||||||||
\(453\) | 6.54232 | 0.307385 | ||||||||
\(454\) | −6.04541 | −0.283725 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.394661 | 0.0184817 | ||||||||
\(457\) | −1.77056 | −0.0828232 | −0.0414116 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414116 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(458\) | −11.3666 | −0.531126 | ||||||||
\(459\) | 10.5227 | 0.491156 | ||||||||
\(460\) | 1.14244 | 0.0532665 | ||||||||
\(461\) | −11.8636 | −0.552545 | −0.276272 | − | 0.961079i | \(-0.589099\pi\) | ||||
−0.276272 | + | 0.961079i | \(0.589099\pi\) | |||||||
\(462\) | −1.33063 | −0.0619066 | ||||||||
\(463\) | 4.13269 | 0.192063 | 0.0960313 | − | 0.995378i | \(-0.469385\pi\) | ||||
0.0960313 | + | 0.995378i | \(0.469385\pi\) | |||||||
\(464\) | −9.14046 | −0.424335 | ||||||||
\(465\) | 0.350486 | 0.0162534 | ||||||||
\(466\) | 19.6434 | 0.909962 | ||||||||
\(467\) | −18.5126 | −0.856662 | −0.428331 | − | 0.903622i | \(-0.640898\pi\) | ||||
−0.428331 | + | 0.903622i | \(0.640898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.3239 | −0.707594 | ||||||||
\(470\) | 4.55022 | 0.209886 | ||||||||
\(471\) | −0.276188 | −0.0127261 | ||||||||
\(472\) | −8.65749 | −0.398493 | ||||||||
\(473\) | −10.0574 | −0.462440 | ||||||||
\(474\) | −2.29238 | −0.105293 | ||||||||
\(475\) | −4.74218 | −0.217586 | ||||||||
\(476\) | 5.70067 | 0.261290 | ||||||||
\(477\) | −16.5122 | −0.756040 | ||||||||
\(478\) | −8.02294 | −0.366961 | ||||||||
\(479\) | −18.4074 | −0.841055 | −0.420527 | − | 0.907280i | \(-0.638155\pi\) | ||||
−0.420527 | + | 0.907280i | \(0.638155\pi\) | |||||||
\(480\) | 0.200395 | 0.00914672 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 13.5781 | 0.618464 | ||||||||
\(483\) | −1.10955 | −0.0504863 | ||||||||
\(484\) | −3.71947 | −0.169067 | ||||||||
\(485\) | 2.63733 | 0.119755 | ||||||||
\(486\) | 9.92776 | 0.450332 | ||||||||
\(487\) | −1.99282 | −0.0903034 | −0.0451517 | − | 0.998980i | \(-0.514377\pi\) | ||||
−0.0451517 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(488\) | 0.618453 | 0.0279961 | ||||||||
\(489\) | −9.30992 | −0.421009 | ||||||||
\(490\) | 2.76154 | 0.124754 | ||||||||
\(491\) | −34.5469 | −1.55908 | −0.779540 | − | 0.626353i | \(-0.784547\pi\) | ||||
−0.779540 | + | 0.626353i | \(0.784547\pi\) | |||||||
\(492\) | −3.77092 | −0.170006 | ||||||||
\(493\) | −41.7005 | −1.87810 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.89682 | 0.175149 | ||||||||
\(496\) | −1.74898 | −0.0785314 | ||||||||
\(497\) | 1.24364 | 0.0557850 | ||||||||
\(498\) | 3.21650 | 0.144135 | ||||||||
\(499\) | −24.5129 | −1.09735 | −0.548675 | − | 0.836036i | \(-0.684867\pi\) | ||||
−0.548675 | + | 0.836036i | \(0.684867\pi\) | |||||||
\(500\) | −4.94673 | −0.221225 | ||||||||
\(501\) | −3.86566 | −0.172705 | ||||||||
\(502\) | 21.7978 | 0.972884 | ||||||||
\(503\) | 31.8996 | 1.42233 | 0.711165 | − | 0.703025i | \(-0.248168\pi\) | ||||
0.711165 | + | 0.703025i | \(0.248168\pi\) | |||||||
\(504\) | 3.55402 | 0.158308 | ||||||||
\(505\) | −8.59275 | −0.382372 | ||||||||
\(506\) | 6.07089 | 0.269884 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.1440 | −0.982483 | ||||||||
\(509\) | −40.5559 | −1.79761 | −0.898804 | − | 0.438351i | \(-0.855563\pi\) | ||||
−0.898804 | + | 0.438351i | \(0.855563\pi\) | |||||||
\(510\) | 0.914239 | 0.0404832 | ||||||||
\(511\) | −0.188502 | −0.00833885 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.30649 | 0.101834 | ||||||||
\(514\) | −21.9326 | −0.967405 | ||||||||
\(515\) | 2.07809 | 0.0915717 | ||||||||
\(516\) | −1.47105 | −0.0647594 | ||||||||
\(517\) | 24.1797 | 1.06342 | ||||||||
\(518\) | −10.8899 | −0.478477 | ||||||||
\(519\) | 2.97333 | 0.130515 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.5725 | −1.47084 | −0.735419 | − | 0.677613i | \(-0.763015\pi\) | ||||
−0.735419 | + | 0.677613i | \(0.763015\pi\) | |||||||
\(522\) | −25.9977 | −1.13789 | ||||||||
\(523\) | −37.0407 | −1.61968 | −0.809838 | − | 0.586653i | \(-0.800445\pi\) | ||||
−0.809838 | + | 0.586653i | \(0.800445\pi\) | |||||||
\(524\) | −19.4396 | −0.849223 | ||||||||
\(525\) | 2.33859 | 0.102064 | ||||||||
\(526\) | −8.68002 | −0.378467 | ||||||||
\(527\) | −7.97917 | −0.347578 | ||||||||
\(528\) | 1.06489 | 0.0463435 | ||||||||
\(529\) | −17.9378 | −0.779903 | ||||||||
\(530\) | −2.94781 | −0.128045 | ||||||||
\(531\) | −24.6240 | −1.06859 | ||||||||
\(532\) | 1.24955 | 0.0541748 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.965894 | −0.0417983 | ||||||||
\(535\) | 8.93063 | 0.386105 | ||||||||
\(536\) | 12.2636 | 0.529707 | ||||||||
\(537\) | 2.10544 | 0.0908566 | ||||||||
\(538\) | −10.2644 | −0.442530 | ||||||||
\(539\) | 14.6748 | 0.632087 | ||||||||
\(540\) | 1.17116 | 0.0503985 | ||||||||
\(541\) | −38.3168 | −1.64737 | −0.823684 | − | 0.567050i | \(-0.808085\pi\) | ||||
−0.823684 | + | 0.567050i | \(0.808085\pi\) | |||||||
\(542\) | −19.1893 | −0.824249 | ||||||||
\(543\) | 9.52285 | 0.408665 | ||||||||
\(544\) | −4.56219 | −0.195602 | ||||||||
\(545\) | −9.99335 | −0.428068 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.6170 | 1.39460 | 0.697302 | − | 0.716778i | \(-0.254384\pi\) | ||||
0.697302 | + | 0.716778i | \(0.254384\pi\) | |||||||
\(548\) | 5.54764 | 0.236983 | ||||||||
\(549\) | 1.75903 | 0.0750736 | ||||||||
\(550\) | −12.7956 | −0.545604 | ||||||||
\(551\) | −9.14046 | −0.389397 | ||||||||
\(552\) | 0.887963 | 0.0377942 | ||||||||
\(553\) | −7.25798 | −0.308641 | ||||||||
\(554\) | −3.03422 | −0.128912 | ||||||||
\(555\) | −1.74646 | −0.0741331 | ||||||||
\(556\) | 11.9267 | 0.505806 | ||||||||
\(557\) | 14.1172 | 0.598164 | 0.299082 | − | 0.954227i | \(-0.403320\pi\) | ||||
0.299082 | + | 0.954227i | \(0.403320\pi\) | |||||||
\(558\) | −4.97452 | −0.210588 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.634476 | 0.0268115 | ||||||||
\(561\) | 4.85824 | 0.205115 | ||||||||
\(562\) | −6.21368 | −0.262108 | ||||||||
\(563\) | 7.41776 | 0.312621 | 0.156311 | − | 0.987708i | \(-0.450040\pi\) | ||||
0.156311 | + | 0.987708i | \(0.450040\pi\) | |||||||
\(564\) | 3.53666 | 0.148920 | ||||||||
\(565\) | −5.08524 | −0.213938 | ||||||||
\(566\) | 12.5355 | 0.526905 | ||||||||
\(567\) | 9.52461 | 0.399996 | ||||||||
\(568\) | −0.995275 | −0.0417608 | ||||||||
\(569\) | −8.69486 | −0.364508 | −0.182254 | − | 0.983252i | \(-0.558339\pi\) | ||||
−0.182254 | + | 0.983252i | \(0.558339\pi\) | |||||||
\(570\) | 0.200395 | 0.00839361 | ||||||||
\(571\) | 24.1793 | 1.01187 | 0.505936 | − | 0.862571i | \(-0.331147\pi\) | ||||
0.505936 | + | 0.862571i | \(0.331147\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.18218 | 0.341815 | ||||||||
\(574\) | −11.9392 | −0.498334 | ||||||||
\(575\) | −10.6696 | −0.444953 | ||||||||
\(576\) | −2.84424 | −0.118510 | ||||||||
\(577\) | −18.3652 | −0.764554 | −0.382277 | − | 0.924048i | \(-0.624860\pi\) | ||||
−0.382277 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(578\) | −3.81359 | −0.158624 | ||||||||
\(579\) | −3.90582 | −0.162320 | ||||||||
\(580\) | −4.64120 | −0.192715 | ||||||||
\(581\) | 10.1839 | 0.422498 | ||||||||
\(582\) | 2.04987 | 0.0849699 | ||||||||
\(583\) | −15.6646 | −0.648761 | ||||||||
\(584\) | 0.150857 | 0.00624249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.9894 | −0.619206 | ||||||||
\(587\) | −19.5310 | −0.806130 | −0.403065 | − | 0.915171i | \(-0.632055\pi\) | ||||
−0.403065 | + | 0.915171i | \(0.632055\pi\) | |||||||
\(588\) | 2.14641 | 0.0885166 | ||||||||
\(589\) | −1.74898 | −0.0720654 | ||||||||
\(590\) | −4.39597 | −0.180979 | ||||||||
\(591\) | 2.15505 | 0.0886471 | ||||||||
\(592\) | 8.71511 | 0.358189 | ||||||||
\(593\) | −13.0686 | −0.536663 | −0.268331 | − | 0.963327i | \(-0.586472\pi\) | ||||
−0.268331 | + | 0.963327i | \(0.586472\pi\) | |||||||
\(594\) | 6.22348 | 0.255353 | ||||||||
\(595\) | 2.89460 | 0.118667 | ||||||||
\(596\) | 15.2350 | 0.624052 | ||||||||
\(597\) | 6.26476 | 0.256400 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29989 | 0.0531120 | 0.0265560 | − | 0.999647i | \(-0.491546\pi\) | ||||
0.0265560 | + | 0.999647i | \(0.491546\pi\) | |||||||
\(600\) | −1.87155 | −0.0764057 | ||||||||
\(601\) | −6.84573 | −0.279243 | −0.139622 | − | 0.990205i | \(-0.544589\pi\) | ||||
−0.139622 | + | 0.990205i | \(0.544589\pi\) | |||||||
\(602\) | −4.65754 | −0.189827 | ||||||||
\(603\) | 34.8806 | 1.42045 | ||||||||
\(604\) | −16.5771 | −0.674512 | ||||||||
\(605\) | −1.88861 | −0.0767831 | ||||||||
\(606\) | −6.67873 | −0.271305 | ||||||||
\(607\) | −18.2932 | −0.742499 | −0.371249 | − | 0.928533i | \(-0.621070\pi\) | ||||
−0.371249 | + | 0.928533i | \(0.621070\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 4.50759 | 0.182657 | ||||||||
\(610\) | 0.314029 | 0.0127146 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.9760 | −0.524523 | ||||||||
\(613\) | −1.71604 | −0.0693101 | −0.0346550 | − | 0.999399i | \(-0.511033\pi\) | ||||
−0.0346550 | + | 0.999399i | \(0.511033\pi\) | |||||||
\(614\) | 29.9417 | 1.20835 | ||||||||
\(615\) | −1.91474 | −0.0772098 | ||||||||
\(616\) | 3.37159 | 0.135845 | ||||||||
\(617\) | −22.6741 | −0.912823 | −0.456412 | − | 0.889769i | \(-0.650866\pi\) | ||||
−0.456412 | + | 0.889769i | \(0.650866\pi\) | |||||||
\(618\) | 1.61520 | 0.0649729 | ||||||||
\(619\) | 2.65268 | 0.106620 | 0.0533101 | − | 0.998578i | \(-0.483023\pi\) | ||||
0.0533101 | + | 0.998578i | \(0.483023\pi\) | |||||||
\(620\) | −0.888069 | −0.0356657 | ||||||||
\(621\) | 5.18947 | 0.208246 | ||||||||
\(622\) | 4.40422 | 0.176593 | ||||||||
\(623\) | −3.05815 | −0.122522 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.1991 | 0.847964 | ||||||||
\(626\) | −10.8316 | −0.432917 | ||||||||
\(627\) | 1.06489 | 0.0425277 | ||||||||
\(628\) | 0.699811 | 0.0279255 | ||||||||
\(629\) | 39.7600 | 1.58533 | ||||||||
\(630\) | 1.80460 | 0.0718971 | ||||||||
\(631\) | 12.5657 | 0.500234 | 0.250117 | − | 0.968216i | \(-0.419531\pi\) | ||||
0.250117 | + | 0.968216i | \(0.419531\pi\) | |||||||
\(632\) | 5.80849 | 0.231049 | ||||||||
\(633\) | 7.85311 | 0.312133 | ||||||||
\(634\) | 27.7571 | 1.10238 | ||||||||
\(635\) | −11.2440 | −0.446203 | ||||||||
\(636\) | −2.29119 | −0.0908516 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.6632 | −0.976426 | ||||||||
\(639\) | −2.83080 | −0.111985 | ||||||||
\(640\) | −0.507765 | −0.0200712 | ||||||||
\(641\) | 28.6389 | 1.13117 | 0.565583 | − | 0.824691i | \(-0.308651\pi\) | ||||
0.565583 | + | 0.824691i | \(0.308651\pi\) | |||||||
\(642\) | 6.94134 | 0.273953 | ||||||||
\(643\) | 30.2543 | 1.19311 | 0.596556 | − | 0.802571i | \(-0.296535\pi\) | ||||
0.596556 | + | 0.802571i | \(0.296535\pi\) | |||||||
\(644\) | 2.81141 | 0.110785 | ||||||||
\(645\) | −0.746948 | −0.0294110 | ||||||||
\(646\) | −4.56219 | −0.179497 | ||||||||
\(647\) | −2.12073 | −0.0833745 | −0.0416873 | − | 0.999131i | \(-0.513273\pi\) | ||||
−0.0416873 | + | 0.999131i | \(0.513273\pi\) | |||||||
\(648\) | −7.62245 | −0.299438 | ||||||||
\(649\) | −23.3600 | −0.916962 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.862504 | 0.0338042 | ||||||||
\(652\) | 23.5897 | 0.923844 | ||||||||
\(653\) | −30.6229 | −1.19837 | −0.599183 | − | 0.800612i | \(-0.704508\pi\) | ||||
−0.599183 | + | 0.800612i | \(0.704508\pi\) | |||||||
\(654\) | −7.76734 | −0.303727 | ||||||||
\(655\) | −9.87074 | −0.385682 | ||||||||
\(656\) | 9.55485 | 0.373054 | ||||||||
\(657\) | 0.429073 | 0.0167397 | ||||||||
\(658\) | 11.1975 | 0.436526 | ||||||||
\(659\) | 10.1419 | 0.395074 | 0.197537 | − | 0.980295i | \(-0.436706\pi\) | ||||
0.197537 | + | 0.980295i | \(0.436706\pi\) | |||||||
\(660\) | 0.540714 | 0.0210473 | ||||||||
\(661\) | −15.0540 | −0.585535 | −0.292767 | − | 0.956184i | \(-0.594576\pi\) | ||||
−0.292767 | + | 0.956184i | \(0.594576\pi\) | |||||||
\(662\) | −15.6936 | −0.609950 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.15004 | −0.316283 | ||||||||
\(665\) | 0.634476 | 0.0246039 | ||||||||
\(666\) | 24.7879 | 0.960511 | ||||||||
\(667\) | −20.5655 | −0.796299 | ||||||||
\(668\) | 9.79491 | 0.378976 | ||||||||
\(669\) | 4.08497 | 0.157934 | ||||||||
\(670\) | 6.22702 | 0.240571 | ||||||||
\(671\) | 1.66874 | 0.0644210 | ||||||||
\(672\) | 0.493147 | 0.0190236 | ||||||||
\(673\) | −30.7053 | −1.18360 | −0.591800 | − | 0.806085i | \(-0.701583\pi\) | ||||
−0.591800 | + | 0.806085i | \(0.701583\pi\) | |||||||
\(674\) | −20.3658 | −0.784462 | ||||||||
\(675\) | −10.9378 | −0.420996 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.75471 | 0.0674389 | 0.0337194 | − | 0.999431i | \(-0.489265\pi\) | ||||
0.0337194 | + | 0.999431i | \(0.489265\pi\) | |||||||
\(678\) | −3.95251 | −0.151795 | ||||||||
\(679\) | 6.49016 | 0.249070 | ||||||||
\(680\) | −2.31652 | −0.0888344 | ||||||||
\(681\) | −2.38588 | −0.0914273 | ||||||||
\(682\) | −4.71917 | −0.180707 | ||||||||
\(683\) | −1.88736 | −0.0722178 | −0.0361089 | − | 0.999348i | \(-0.511496\pi\) | ||||
−0.0361089 | + | 0.999348i | \(0.511496\pi\) | |||||||
\(684\) | −2.84424 | −0.108752 | ||||||||
\(685\) | 2.81689 | 0.107628 | ||||||||
\(686\) | 15.5427 | 0.593422 | ||||||||
\(687\) | −4.48595 | −0.171149 | ||||||||
\(688\) | 3.72738 | 0.142105 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.450876 | 0.0171646 | ||||||||
\(691\) | 16.5400 | 0.629211 | 0.314605 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314605 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(692\) | −7.53389 | −0.286396 | ||||||||
\(693\) | 9.58961 | 0.364279 | ||||||||
\(694\) | −20.8429 | −0.791184 | ||||||||
\(695\) | 6.05597 | 0.229716 | ||||||||
\(696\) | −3.60738 | −0.136737 | ||||||||
\(697\) | 43.5911 | 1.65113 | ||||||||
\(698\) | 1.36583 | 0.0516975 | ||||||||
\(699\) | 7.75247 | 0.293225 | ||||||||
\(700\) | −5.92557 | −0.223966 | ||||||||
\(701\) | −5.08097 | −0.191906 | −0.0959529 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959529 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.71511 | 0.328697 | ||||||||
\(704\) | −2.69825 | −0.101694 | ||||||||
\(705\) | 1.79579 | 0.0676335 | ||||||||
\(706\) | −1.42712 | −0.0537105 | ||||||||
\(707\) | −21.1457 | −0.795267 | ||||||||
\(708\) | −3.41677 | −0.128410 | ||||||||
\(709\) | −4.19444 | −0.157525 | −0.0787627 | − | 0.996893i | \(-0.525097\pi\) | ||||
−0.0787627 | + | 0.996893i | \(0.525097\pi\) | |||||||
\(710\) | −0.505365 | −0.0189660 | ||||||||
\(711\) | 16.5208 | 0.619577 | ||||||||
\(712\) | 2.44741 | 0.0917204 | ||||||||
\(713\) | −3.93510 | −0.147370 | ||||||||
\(714\) | 2.24983 | 0.0841978 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.33482 | −0.199372 | ||||||||
\(717\) | −3.16634 | −0.118249 | ||||||||
\(718\) | −27.3665 | −1.02131 | ||||||||
\(719\) | 25.3410 | 0.945059 | 0.472529 | − | 0.881315i | \(-0.343341\pi\) | ||||
0.472529 | + | 0.881315i | \(0.343341\pi\) | |||||||
\(720\) | −1.44421 | −0.0538224 | ||||||||
\(721\) | 5.11394 | 0.190453 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 5.35873 | 0.199293 | ||||||||
\(724\) | −24.1292 | −0.896755 | ||||||||
\(725\) | 43.3457 | 1.60982 | ||||||||
\(726\) | −1.46793 | −0.0544799 | ||||||||
\(727\) | 15.9473 | 0.591454 | 0.295727 | − | 0.955272i | \(-0.404438\pi\) | ||||
0.295727 | + | 0.955272i | \(0.404438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.9492 | −0.701824 | ||||||||
\(730\) | 0.0765996 | 0.00283508 | ||||||||
\(731\) | 17.0050 | 0.628954 | ||||||||
\(732\) | 0.244079 | 0.00902142 | ||||||||
\(733\) | 13.2154 | 0.488123 | 0.244062 | − | 0.969760i | \(-0.421520\pi\) | ||||
0.244062 | + | 0.969760i | \(0.421520\pi\) | |||||||
\(734\) | −24.9590 | −0.921253 | ||||||||
\(735\) | 1.08987 | 0.0402006 | ||||||||
\(736\) | −2.24994 | −0.0829339 | ||||||||
\(737\) | 33.0902 | 1.21889 | ||||||||
\(738\) | 27.1763 | 1.00037 | ||||||||
\(739\) | −18.2589 | −0.671665 | −0.335832 | − | 0.941922i | \(-0.609018\pi\) | ||||
−0.335832 | + | 0.941922i | \(0.609018\pi\) | |||||||
\(740\) | 4.42522 | 0.162674 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.25421 | −0.266311 | ||||||||
\(743\) | 17.4411 | 0.639852 | 0.319926 | − | 0.947443i | \(-0.396342\pi\) | ||||
0.319926 | + | 0.947443i | \(0.396342\pi\) | |||||||
\(744\) | −0.690253 | −0.0253059 | ||||||||
\(745\) | 7.73581 | 0.283418 | ||||||||
\(746\) | 17.5861 | 0.643872 | ||||||||
\(747\) | −23.1807 | −0.848137 | ||||||||
\(748\) | −12.3099 | −0.450095 | ||||||||
\(749\) | 21.9772 | 0.803029 | ||||||||
\(750\) | −1.95228 | −0.0712872 | ||||||||
\(751\) | −10.8938 | −0.397519 | −0.198759 | − | 0.980048i | \(-0.563691\pi\) | ||||
−0.198759 | + | 0.980048i | \(0.563691\pi\) | |||||||
\(752\) | −8.96128 | −0.326784 | ||||||||
\(753\) | 8.60274 | 0.313501 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.41726 | −0.306335 | ||||||||
\(756\) | 2.88207 | 0.104820 | ||||||||
\(757\) | −18.7457 | −0.681325 | −0.340662 | − | 0.940186i | \(-0.610651\pi\) | ||||
−0.340662 | + | 0.940186i | \(0.610651\pi\) | |||||||
\(758\) | 14.2698 | 0.518303 | ||||||||
\(759\) | 2.39594 | 0.0869672 | ||||||||
\(760\) | −0.507765 | −0.0184186 | ||||||||
\(761\) | 32.0451 | 1.16164 | 0.580818 | − | 0.814034i | \(-0.302733\pi\) | ||||
0.580818 | + | 0.814034i | \(0.302733\pi\) | |||||||
\(762\) | −8.73938 | −0.316594 | ||||||||
\(763\) | −24.5924 | −0.890306 | ||||||||
\(764\) | −20.7322 | −0.750064 | ||||||||
\(765\) | −6.58874 | −0.238216 | ||||||||
\(766\) | 12.8820 | 0.465447 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.394661 | −0.0142411 | ||||||||
\(769\) | 16.7370 | 0.603551 | 0.301776 | − | 0.953379i | \(-0.402421\pi\) | ||||
0.301776 | + | 0.953379i | \(0.402421\pi\) | |||||||
\(770\) | 1.71197 | 0.0616952 | ||||||||
\(771\) | −8.65593 | −0.311736 | ||||||||
\(772\) | 9.89665 | 0.356188 | ||||||||
\(773\) | −24.8714 | −0.894562 | −0.447281 | − | 0.894393i | \(-0.647608\pi\) | ||||
−0.447281 | + | 0.894393i | \(0.647608\pi\) | |||||||
\(774\) | 10.6016 | 0.381066 | ||||||||
\(775\) | 8.29396 | 0.297928 | ||||||||
\(776\) | −5.19401 | −0.186454 | ||||||||
\(777\) | −4.29783 | −0.154184 | ||||||||
\(778\) | −4.94578 | −0.177315 | ||||||||
\(779\) | 9.55485 | 0.342338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.68550 | −0.0960946 | ||||||||
\(782\) | −10.2647 | −0.367063 | ||||||||
\(783\) | −21.0824 | −0.753424 | ||||||||
\(784\) | −5.43863 | −0.194237 | ||||||||
\(785\) | 0.355339 | 0.0126826 | ||||||||
\(786\) | −7.67205 | −0.273653 | ||||||||
\(787\) | −27.9235 | −0.995367 | −0.497683 | − | 0.867359i | \(-0.665816\pi\) | ||||
−0.497683 | + | 0.867359i | \(0.665816\pi\) | |||||||
\(788\) | −5.46053 | −0.194523 | ||||||||
\(789\) | −3.42566 | −0.121957 | ||||||||
\(790\) | 2.94934 | 0.104933 | ||||||||
\(791\) | −12.5142 | −0.444952 | ||||||||
\(792\) | −7.67447 | −0.272700 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 22.0346 | 0.781980 | ||||||||
\(795\) | −1.16339 | −0.0412610 | ||||||||
\(796\) | −15.8738 | −0.562632 | ||||||||
\(797\) | −33.6046 | −1.19034 | −0.595168 | − | 0.803602i | \(-0.702914\pi\) | ||||
−0.595168 | + | 0.803602i | \(0.702914\pi\) | |||||||
\(798\) | 0.493147 | 0.0174572 | ||||||||
\(799\) | −40.8831 | −1.44634 | ||||||||
\(800\) | 4.74218 | 0.167661 | ||||||||
\(801\) | 6.96101 | 0.245955 | ||||||||
\(802\) | −2.94800 | −0.104098 | ||||||||
\(803\) | 0.407048 | 0.0143644 | ||||||||
\(804\) | 4.83996 | 0.170692 | ||||||||
\(805\) | 1.42753 | 0.0503139 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.05096 | −0.142601 | ||||||||
\(808\) | 16.9227 | 0.595339 | ||||||||
\(809\) | −16.0538 | −0.564420 | −0.282210 | − | 0.959353i | \(-0.591068\pi\) | ||||
−0.282210 | + | 0.959353i | \(0.591068\pi\) | |||||||
\(810\) | −3.87041 | −0.135992 | ||||||||
\(811\) | 4.73984 | 0.166438 | 0.0832191 | − | 0.996531i | \(-0.473480\pi\) | ||||
0.0832191 | + | 0.996531i | \(0.473480\pi\) | |||||||
\(812\) | −11.4214 | −0.400814 | ||||||||
\(813\) | −7.57324 | −0.265605 | ||||||||
\(814\) | 23.5155 | 0.824218 | ||||||||
\(815\) | 11.9780 | 0.419571 | ||||||||
\(816\) | −1.80052 | −0.0630307 | ||||||||
\(817\) | 3.72738 | 0.130405 | ||||||||
\(818\) | 18.3674 | 0.642202 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.85162 | 0.169426 | ||||||||
\(821\) | 1.82332 | 0.0636344 | 0.0318172 | − | 0.999494i | \(-0.489871\pi\) | ||||
0.0318172 | + | 0.999494i | \(0.489871\pi\) | |||||||
\(822\) | 2.18943 | 0.0763652 | ||||||||
\(823\) | −12.2522 | −0.427086 | −0.213543 | − | 0.976934i | \(-0.568500\pi\) | ||||
−0.213543 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(824\) | −4.09263 | −0.142574 | ||||||||
\(825\) | −5.04990 | −0.175815 | ||||||||
\(826\) | −10.8179 | −0.376404 | ||||||||
\(827\) | 32.2781 | 1.12242 | 0.561209 | − | 0.827674i | \(-0.310336\pi\) | ||||
0.561209 | + | 0.827674i | \(0.310336\pi\) | |||||||
\(828\) | −6.39938 | −0.222394 | ||||||||
\(829\) | −21.8654 | −0.759415 | −0.379708 | − | 0.925107i | \(-0.623975\pi\) | ||||
−0.379708 | + | 0.925107i | \(0.623975\pi\) | |||||||
\(830\) | −4.13830 | −0.143642 | ||||||||
\(831\) | −1.19749 | −0.0415404 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.8121 | −0.859687 | ||||||||
\(834\) | 4.70701 | 0.162990 | ||||||||
\(835\) | 4.97351 | 0.172115 | ||||||||
\(836\) | −2.69825 | −0.0933208 | ||||||||
\(837\) | −4.03401 | −0.139436 | ||||||||
\(838\) | 7.18949 | 0.248357 | ||||||||
\(839\) | −24.0252 | −0.829442 | −0.414721 | − | 0.909949i | \(-0.636121\pi\) | ||||
−0.414721 | + | 0.909949i | \(0.636121\pi\) | |||||||
\(840\) | 0.250403 | 0.00863971 | ||||||||
\(841\) | 54.5481 | 1.88097 | ||||||||
\(842\) | 13.4228 | 0.462582 | ||||||||
\(843\) | −2.45230 | −0.0844616 | ||||||||
\(844\) | −19.8984 | −0.684931 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.4881 | −0.876297 | ||||||||
\(847\) | −4.64765 | −0.159695 | ||||||||
\(848\) | 5.80547 | 0.199361 | ||||||||
\(849\) | 4.94726 | 0.169790 | ||||||||
\(850\) | 21.6347 | 0.742064 | ||||||||
\(851\) | 19.6085 | 0.672170 | ||||||||
\(852\) | −0.392796 | −0.0134570 | ||||||||
\(853\) | −46.1729 | −1.58093 | −0.790465 | − | 0.612508i | \(-0.790161\pi\) | ||||
−0.790465 | + | 0.612508i | \(0.790161\pi\) | |||||||
\(854\) | 0.772787 | 0.0264442 | ||||||||
\(855\) | −1.44421 | −0.0493908 | ||||||||
\(856\) | −17.5881 | −0.601150 | ||||||||
\(857\) | 28.7012 | 0.980413 | 0.490207 | − | 0.871606i | \(-0.336921\pi\) | ||||
0.490207 | + | 0.871606i | \(0.336921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4439 | 1.00461 | 0.502307 | − | 0.864689i | \(-0.332485\pi\) | ||||
0.502307 | + | 0.864689i | \(0.332485\pi\) | |||||||
\(860\) | 1.89263 | 0.0645382 | ||||||||
\(861\) | −4.71195 | −0.160583 | ||||||||
\(862\) | 19.5840 | 0.667034 | ||||||||
\(863\) | −55.2739 | −1.88155 | −0.940773 | − | 0.339038i | \(-0.889898\pi\) | ||||
−0.940773 | + | 0.339038i | \(0.889898\pi\) | |||||||
\(864\) | −2.30649 | −0.0784685 | ||||||||
\(865\) | −3.82544 | −0.130069 | ||||||||
\(866\) | 33.5004 | 1.13839 | ||||||||
\(867\) | −1.50507 | −0.0511149 | ||||||||
\(868\) | −2.18543 | −0.0741784 | ||||||||
\(869\) | 15.6727 | 0.531661 | ||||||||
\(870\) | −1.83170 | −0.0621004 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.6811 | 0.666485 | ||||||||
\(873\) | −14.7730 | −0.499991 | ||||||||
\(874\) | −2.24994 | −0.0761053 | ||||||||
\(875\) | −6.18118 | −0.208962 | ||||||||
\(876\) | 0.0595371 | 0.00201157 | ||||||||
\(877\) | 7.70433 | 0.260157 | 0.130078 | − | 0.991504i | \(-0.458477\pi\) | ||||
0.130078 | + | 0.991504i | \(0.458477\pi\) | |||||||
\(878\) | 4.74365 | 0.160090 | ||||||||
\(879\) | −5.91572 | −0.199532 | ||||||||
\(880\) | −1.37007 | −0.0461852 | ||||||||
\(881\) | 40.9945 | 1.38114 | 0.690569 | − | 0.723266i | \(-0.257360\pi\) | ||||
0.690569 | + | 0.723266i | \(0.257360\pi\) | |||||||
\(882\) | −15.4688 | −0.520861 | ||||||||
\(883\) | −50.0831 | −1.68543 | −0.842715 | − | 0.538360i | \(-0.819044\pi\) | ||||
−0.842715 | + | 0.538360i | \(0.819044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.73491 | −0.0583185 | ||||||||
\(886\) | −31.0710 | −1.04385 | ||||||||
\(887\) | 36.7002 | 1.23227 | 0.616136 | − | 0.787639i | \(-0.288697\pi\) | ||||
0.616136 | + | 0.787639i | \(0.288697\pi\) | |||||||
\(888\) | 3.43951 | 0.115422 | ||||||||
\(889\) | −27.6700 | −0.928023 | ||||||||
\(890\) | 1.24271 | 0.0416556 | ||||||||
\(891\) | −20.5672 | −0.689028 | ||||||||
\(892\) | −10.3506 | −0.346563 | ||||||||
\(893\) | −8.96128 | −0.299878 | ||||||||
\(894\) | 6.01267 | 0.201094 | ||||||||
\(895\) | −2.70883 | −0.0905463 | ||||||||
\(896\) | −1.24955 | −0.0417445 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.7887 | 0.526877 | ||||||||
\(899\) | 15.9865 | 0.533179 | ||||||||
\(900\) | 13.4879 | 0.449597 | ||||||||
\(901\) | 26.4857 | 0.882366 | ||||||||
\(902\) | 25.7813 | 0.858425 | ||||||||
\(903\) | −1.83815 | −0.0611697 | ||||||||
\(904\) | 10.0150 | 0.333093 | ||||||||
\(905\) | −12.2520 | −0.407269 | ||||||||
\(906\) | −6.54232 | −0.217354 | ||||||||
\(907\) | 23.3382 | 0.774931 | 0.387466 | − | 0.921884i | \(-0.373351\pi\) | ||||
0.387466 | + | 0.921884i | \(0.373351\pi\) | |||||||
\(908\) | 6.04541 | 0.200624 | ||||||||
\(909\) | 48.1323 | 1.59645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.7035 | 1.81241 | 0.906204 | − | 0.422841i | \(-0.138967\pi\) | ||||
0.906204 | + | 0.422841i | \(0.138967\pi\) | |||||||
\(912\) | −0.394661 | −0.0130685 | ||||||||
\(913\) | −21.9908 | −0.727789 | ||||||||
\(914\) | 1.77056 | 0.0585648 | ||||||||
\(915\) | 0.123935 | 0.00409716 | ||||||||
\(916\) | 11.3666 | 0.375563 | ||||||||
\(917\) | −24.2907 | −0.802150 | ||||||||
\(918\) | −10.5227 | −0.347300 | ||||||||
\(919\) | 38.4249 | 1.26752 | 0.633760 | − | 0.773530i | \(-0.281511\pi\) | ||||
0.633760 | + | 0.773530i | \(0.281511\pi\) | |||||||
\(920\) | −1.14244 | −0.0376651 | ||||||||
\(921\) | 11.8168 | 0.389377 | ||||||||
\(922\) | 11.8636 | 0.390708 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.33063 | 0.0437746 | ||||||||
\(925\) | −41.3286 | −1.35887 | ||||||||
\(926\) | −4.13269 | −0.135809 | ||||||||
\(927\) | −11.6404 | −0.382322 | ||||||||
\(928\) | 9.14046 | 0.300050 | ||||||||
\(929\) | 13.2117 | 0.433462 | 0.216731 | − | 0.976231i | \(-0.430461\pi\) | ||||
0.216731 | + | 0.976231i | \(0.430461\pi\) | |||||||
\(930\) | −0.350486 | −0.0114929 | ||||||||
\(931\) | −5.43863 | −0.178244 | ||||||||
\(932\) | −19.6434 | −0.643441 | ||||||||
\(933\) | 1.73817 | 0.0569052 | ||||||||
\(934\) | 18.5126 | 0.605751 | ||||||||
\(935\) | −6.25054 | −0.204414 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.6152 | −1.39218 | −0.696089 | − | 0.717955i | \(-0.745078\pi\) | ||||
−0.696089 | + | 0.717955i | \(0.745078\pi\) | |||||||
\(938\) | 15.3239 | 0.500344 | ||||||||
\(939\) | −4.27480 | −0.139503 | ||||||||
\(940\) | −4.55022 | −0.148412 | ||||||||
\(941\) | 53.3461 | 1.73903 | 0.869517 | − | 0.493902i | \(-0.164430\pi\) | ||||
0.869517 | + | 0.493902i | \(0.164430\pi\) | |||||||
\(942\) | 0.276188 | 0.00899869 | ||||||||
\(943\) | 21.4978 | 0.700066 | ||||||||
\(944\) | 8.65749 | 0.281777 | ||||||||
\(945\) | 1.46341 | 0.0476049 | ||||||||
\(946\) | 10.0574 | 0.326994 | ||||||||
\(947\) | −1.29330 | −0.0420265 | −0.0210133 | − | 0.999779i | \(-0.506689\pi\) | ||||
−0.0210133 | + | 0.999779i | \(0.506689\pi\) | |||||||
\(948\) | 2.29238 | 0.0744531 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.74218 | 0.153856 | ||||||||
\(951\) | 10.9546 | 0.355229 | ||||||||
\(952\) | −5.70067 | −0.184760 | ||||||||
\(953\) | 6.22671 | 0.201703 | 0.100851 | − | 0.994901i | \(-0.467843\pi\) | ||||
0.100851 | + | 0.994901i | \(0.467843\pi\) | |||||||
\(954\) | 16.5122 | 0.534601 | ||||||||
\(955\) | −10.5271 | −0.340648 | ||||||||
\(956\) | 8.02294 | 0.259481 | ||||||||
\(957\) | −9.73360 | −0.314643 | ||||||||
\(958\) | 18.4074 | 0.594715 | ||||||||
\(959\) | 6.93203 | 0.223847 | ||||||||
\(960\) | −0.200395 | −0.00646771 | ||||||||
\(961\) | −27.9411 | −0.901325 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.0249 | −1.61203 | ||||||||
\(964\) | −13.5781 | −0.437320 | ||||||||
\(965\) | 5.02517 | 0.161766 | ||||||||
\(966\) | 1.10955 | 0.0356992 | ||||||||
\(967\) | 34.4051 | 1.10639 | 0.553197 | − | 0.833050i | \(-0.313408\pi\) | ||||
0.553197 | + | 0.833050i | \(0.313408\pi\) | |||||||
\(968\) | 3.71947 | 0.119548 | ||||||||
\(969\) | −1.80052 | −0.0578409 | ||||||||
\(970\) | −2.63733 | −0.0846797 | ||||||||
\(971\) | −23.2656 | −0.746629 | −0.373315 | − | 0.927705i | \(-0.621779\pi\) | ||||
−0.373315 | + | 0.927705i | \(0.621779\pi\) | |||||||
\(972\) | −9.92776 | −0.318433 | ||||||||
\(973\) | 14.9030 | 0.477769 | ||||||||
\(974\) | 1.99282 | 0.0638542 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.618453 | −0.0197962 | ||||||||
\(977\) | 9.97729 | 0.319202 | 0.159601 | − | 0.987182i | \(-0.448979\pi\) | ||||
0.159601 | + | 0.987182i | \(0.448979\pi\) | |||||||
\(978\) | 9.30992 | 0.297699 | ||||||||
\(979\) | 6.60370 | 0.211055 | ||||||||
\(980\) | −2.76154 | −0.0882143 | ||||||||
\(981\) | 55.9777 | 1.78723 | ||||||||
\(982\) | 34.5469 | 1.10244 | ||||||||
\(983\) | 7.96318 | 0.253986 | 0.126993 | − | 0.991904i | \(-0.459467\pi\) | ||||
0.126993 | + | 0.991904i | \(0.459467\pi\) | |||||||
\(984\) | 3.77092 | 0.120213 | ||||||||
\(985\) | −2.77266 | −0.0883443 | ||||||||
\(986\) | 41.7005 | 1.32802 | ||||||||
\(987\) | 4.41923 | 0.140666 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.38639 | 0.266672 | ||||||||
\(990\) | −3.89682 | −0.123849 | ||||||||
\(991\) | −44.6566 | −1.41856 | −0.709281 | − | 0.704926i | \(-0.750980\pi\) | ||||
−0.709281 | + | 0.704926i | \(0.750980\pi\) | |||||||
\(992\) | 1.74898 | 0.0555301 | ||||||||
\(993\) | −6.19365 | −0.196550 | ||||||||
\(994\) | −1.24364 | −0.0394460 | ||||||||
\(995\) | −8.06015 | −0.255524 | ||||||||
\(996\) | −3.21650 | −0.101919 | ||||||||
\(997\) | −26.0993 | −0.826572 | −0.413286 | − | 0.910601i | \(-0.635619\pi\) | ||||
−0.413286 | + | 0.910601i | \(0.635619\pi\) | |||||||
\(998\) | 24.5129 | 0.775943 | ||||||||
\(999\) | 20.1013 | 0.635978 |
(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 | 6422.2.a.bg.1.5 | 8 | ||
13.2 | odd | 12 | 494.2.m.a.381.2 | yes | 16 | ||
13.7 | odd | 12 | 494.2.m.a.153.2 | ✓ | 16 | ||
13.12 | even | 2 | 6422.2.a.bh.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.a.153.2 | ✓ | 16 | 13.7 | odd | 12 | ||
494.2.m.a.381.2 | yes | 16 | 13.2 | odd | 12 | ||
6422.2.a.bg.1.5 | 8 | 1.1 | even | 1 | trivial | ||
6422.2.a.bh.1.5 | 8 | 13.12 | even | 2 |