Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.43449.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 7x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1400) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.265362\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.26536 | 0.730557 | 0.365279 | − | 0.930898i | \(-0.380974\pi\) | ||||
0.365279 | + | 0.930898i | \(0.380974\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.39886 | −0.466286 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.43265 | 1.93952 | 0.969759 | − | 0.244065i | \(-0.0784809\pi\) | ||||
0.969759 | + | 0.244065i | \(0.0784809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.10421 | −0.306253 | −0.153127 | − | 0.988207i | \(-0.548934\pi\) | ||||
−0.153127 | + | 0.988207i | \(0.548934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.50307 | −1.09216 | −0.546078 | − | 0.837735i | \(-0.683880\pi\) | ||||
−0.546078 | + | 0.837735i | \(0.683880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.87265 | 1.34728 | 0.673639 | − | 0.739061i | \(-0.264730\pi\) | ||||
0.673639 | + | 0.739061i | \(0.264730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.77457 | −1.82963 | −0.914813 | − | 0.403879i | \(-0.867662\pi\) | ||||
−0.914813 | + | 0.403879i | \(0.867662\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56615 | −1.07121 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.87265 | 0.719132 | 0.359566 | − | 0.933120i | \(-0.382925\pi\) | ||||
0.359566 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.66422 | 1.19693 | 0.598465 | − | 0.801149i | \(-0.295778\pi\) | ||||
0.598465 | + | 0.801149i | \(0.295778\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.13964 | 1.41693 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42651 | 0.234517 | 0.117259 | − | 0.993101i | \(-0.462589\pi\) | ||||
0.117259 | + | 0.993101i | \(0.462589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.39723 | −0.223736 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8360 | 1.84848 | 0.924238 | − | 0.381817i | \(-0.124701\pi\) | ||||
0.924238 | + | 0.381817i | \(0.124701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.46645 | 0.986124 | 0.493062 | − | 0.869994i | \(-0.335878\pi\) | ||||
0.493062 | + | 0.869994i | \(0.335878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.46031 | −1.23406 | −0.617031 | − | 0.786939i | \(-0.711665\pi\) | ||||
−0.617031 | + | 0.786939i | \(0.711665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.69802 | −0.797882 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.768433 | −0.105552 | −0.0527762 | − | 0.998606i | \(-0.516807\pi\) | ||||
−0.0527762 | + | 0.998606i | \(0.516807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.43102 | 0.984263 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.79609 | 0.233831 | 0.116915 | − | 0.993142i | \(-0.462699\pi\) | ||||
0.116915 | + | 0.993142i | \(0.462699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.03994 | −0.389224 | −0.194612 | − | 0.980880i | \(-0.562345\pi\) | ||||
−0.194612 | + | 0.980880i | \(0.562345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85302 | 0.348552 | 0.174276 | − | 0.984697i | \(-0.444241\pi\) | ||||
0.174276 | + | 0.984697i | \(0.444241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.1030 | −1.33665 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.47542 | −1.12453 | −0.562263 | − | 0.826959i | \(-0.690069\pi\) | ||||
−0.562263 | + | 0.826959i | \(0.690069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3960 | 1.56789 | 0.783943 | − | 0.620832i | \(-0.213205\pi\) | ||||
0.783943 | + | 0.620832i | \(0.213205\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.30530 | −1.04693 | −0.523464 | − | 0.852048i | \(-0.675361\pi\) | ||||
−0.523464 | + | 0.852048i | \(0.675361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.84662 | −0.316291 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.20109 | −0.351365 | −0.175682 | − | 0.984447i | \(-0.556213\pi\) | ||||
−0.175682 | + | 0.984447i | \(0.556213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.90030 | 0.525367 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.92344 | 0.309884 | 0.154942 | − | 0.987924i | \(-0.450481\pi\) | ||||
0.154942 | + | 0.987924i | \(0.450481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.43265 | 0.874425 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.96338 | 0.605489 | 0.302745 | − | 0.953072i | \(-0.402097\pi\) | ||||
0.302745 | + | 0.953072i | \(0.402097\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.99837 | −0.904370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5092 | 1.04571 | 0.522853 | − | 0.852423i | \(-0.324868\pi\) | ||||
0.522853 | + | 0.852423i | \(0.324868\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.11035 | 0.897670 | 0.448835 | − | 0.893615i | \(-0.351839\pi\) | ||||
0.448835 | + | 0.893615i | \(0.351839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.39886 | −0.811948 | −0.405974 | − | 0.913885i | \(-0.633068\pi\) | ||||
−0.405974 | + | 0.913885i | \(0.633068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.84048 | 0.463634 | 0.231817 | − | 0.972759i | \(-0.425533\pi\) | ||||
0.231817 | + | 0.972759i | \(0.425533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.80505 | 0.171328 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.87879 | 0.364886 | 0.182443 | − | 0.983216i | \(-0.441600\pi\) | ||||
0.182443 | + | 0.983216i | \(0.441600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.54464 | 0.142802 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.3790 | 2.76173 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.9769 | 1.35042 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8681 | 1.05313 | 0.526563 | − | 0.850136i | \(-0.323480\pi\) | ||||
0.526563 | + | 0.850136i | \(0.323480\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.18240 | 0.720420 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9785 | 1.22131 | 0.610653 | − | 0.791898i | \(-0.290907\pi\) | ||||
0.610653 | + | 0.791898i | \(0.290907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.03831 | 0.430452 | 0.215226 | − | 0.976564i | \(-0.430951\pi\) | ||||
0.215226 | + | 0.976564i | \(0.430951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.69639 | −0.567980 | −0.283990 | − | 0.958827i | \(-0.591658\pi\) | ||||
−0.283990 | + | 0.958827i | \(0.591658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.7054 | −0.901553 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.10302 | −0.593984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.52339 | 0.616340 | 0.308170 | − | 0.951331i | \(-0.400283\pi\) | ||||
0.308170 | + | 0.951331i | \(0.400283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4034 | 1.33489 | 0.667444 | − | 0.744660i | \(-0.267389\pi\) | ||||
0.667444 | + | 0.744660i | \(0.267389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.29916 | 0.509257 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.19777 | −0.255210 | −0.127605 | − | 0.991825i | \(-0.540729\pi\) | ||||
−0.127605 | + | 0.991825i | \(0.540729\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.972346 | −0.0771121 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5076 | 1.05800 | 0.528998 | − | 0.848623i | \(-0.322568\pi\) | ||||
0.528998 | + | 0.848623i | \(0.322568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.55267 | 0.739208 | 0.369604 | − | 0.929189i | \(-0.379493\pi\) | ||||
0.369604 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7807 | −0.906209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.21500 | −0.628217 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.1137 | −1.37716 | −0.688578 | − | 0.725162i | \(-0.741765\pi\) | ||||
−0.688578 | + | 0.725162i | \(0.741765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.27270 | 0.170827 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.1937 | −1.35986 | −0.679932 | − | 0.733275i | \(-0.737991\pi\) | ||||
−0.679932 | + | 0.733275i | \(0.737991\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3542 | −1.14127 | −0.570634 | − | 0.821204i | \(-0.693303\pi\) | ||||
−0.570634 | + | 0.821204i | \(0.693303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.84662 | −0.284350 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.9667 | −2.11825 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41685 | −0.102520 | −0.0512598 | − | 0.998685i | \(-0.516324\pi\) | ||||
−0.0512598 | + | 0.998685i | \(0.516324\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.915408 | −0.0658925 | −0.0329463 | − | 0.999457i | \(-0.510489\pi\) | ||||
−0.0329463 | + | 0.999457i | \(0.510489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7167 | 1.04852 | 0.524261 | − | 0.851558i | \(-0.324342\pi\) | ||||
0.524261 | + | 0.851558i | \(0.324342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.41114 | −0.667138 | −0.333569 | − | 0.942726i | \(-0.608253\pi\) | ||||
−0.333569 | + | 0.942726i | \(0.608253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.61011 | 0.254638 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.2744 | 0.853129 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.7767 | 2.61307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.08622 | −0.212464 | −0.106232 | − | 0.994341i | \(-0.533879\pi\) | ||||
−0.106232 | + | 0.994341i | \(0.533879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.9898 | −0.821530 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.9508 | 1.14543 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.97235 | 0.334476 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.96338 | 0.265407 | 0.132704 | − | 0.991156i | \(-0.457634\pi\) | ||||
0.132704 | + | 0.991156i | \(0.457634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8930 | 1.18760 | 0.593799 | − | 0.804614i | \(-0.297628\pi\) | ||||
0.593799 | + | 0.804614i | \(0.297628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3391 | 1.74054 | 0.870268 | − | 0.492578i | \(-0.163945\pi\) | ||||
0.870268 | + | 0.492578i | \(0.163945\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.22874 | −0.408058 | −0.204029 | − | 0.978965i | \(-0.565404\pi\) | ||||
−0.204029 | + | 0.978965i | \(0.565404\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7746 | −0.764841 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.94213 | −0.513734 | −0.256867 | − | 0.966447i | \(-0.582690\pi\) | ||||
−0.256867 | + | 0.966447i | \(0.582690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.78875 | −0.308470 | −0.154235 | − | 0.988034i | \(-0.549291\pi\) | ||||
−0.154235 | + | 0.988034i | \(0.549291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.0964 | 0.840137 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.48465 | −0.412608 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.05053 | −0.256692 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.242220 | −0.0152888 | −0.00764439 | − | 0.999971i | \(-0.502433\pi\) | ||||
−0.00764439 | + | 0.999971i | \(0.502433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −56.4438 | −3.54859 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9447 | −0.994603 | −0.497301 | − | 0.867578i | \(-0.665676\pi\) | ||||
−0.497301 | + | 0.867578i | \(0.665676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.41728 | −0.335321 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.82254 | 0.605684 | 0.302842 | − | 0.953041i | \(-0.402065\pi\) | ||||
0.302842 | + | 0.953041i | \(0.402065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.69921 | 0.226388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5048 | −0.884371 | −0.442185 | − | 0.896924i | \(-0.645797\pi\) | ||||
−0.442185 | + | 0.896924i | \(0.645797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6659 | 1.55909 | 0.779545 | − | 0.626347i | \(-0.215451\pi\) | ||||
0.779545 | + | 0.626347i | \(0.215451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.35703 | −0.381957 | −0.190978 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190978 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.32230 | −0.558112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.8360 | −0.706075 | −0.353037 | − | 0.935609i | \(-0.614851\pi\) | ||||
−0.353037 | + | 0.935609i | \(0.614851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6793 | 0.872596 | 0.436298 | − | 0.899802i | \(-0.356289\pi\) | ||||
0.436298 | + | 0.899802i | \(0.356289\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.27764 | 0.192803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.54583 | 0.442345 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6800 | −0.799196 | −0.399598 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399598 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −35.8051 | −2.07762 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.68899 | 0.560329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.2980 | 0.763948 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4140 | 1.22216 | 0.611081 | − | 0.791568i | \(-0.290735\pi\) | ||||
0.611081 | + | 0.791568i | \(0.290735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.5279 | 0.655799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.0203 | 1.41877 | 0.709386 | − | 0.704820i | \(-0.248972\pi\) | ||||
0.709386 | + | 0.704820i | \(0.248972\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.20391 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48345 | 0.476478 | 0.238239 | − | 0.971207i | \(-0.423430\pi\) | ||||
0.238239 | + | 0.971207i | \(0.423430\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9114 | 1.39477 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.6276 | −0.593175 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.4449 | −1.47144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.12496 | 0.338711 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.10872 | 0.0609410 | 0.0304705 | − | 0.999536i | \(-0.490299\pi\) | ||||
0.0304705 | + | 0.999536i | \(0.490299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.99549 | −0.109352 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.00168 | −0.217986 | −0.108993 | − | 0.994043i | \(-0.534763\pi\) | ||||
−0.108993 | + | 0.994043i | \(0.534763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.90807 | 0.266570 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.8686 | 2.32147 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4005 | −1.25621 | −0.628103 | − | 0.778130i | \(-0.716169\pi\) | ||||
−0.628103 | + | 0.778130i | \(0.716169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.05059 | −0.323881 | −0.161940 | − | 0.986801i | \(-0.551775\pi\) | ||||
−0.161940 | + | 0.986801i | \(0.551775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.14621 | 0.328060 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.1217 | 1.33709 | 0.668547 | − | 0.743670i | \(-0.266917\pi\) | ||||
0.668547 | + | 0.743670i | \(0.266917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.9846 | 1.00197 | 0.500985 | − | 0.865456i | \(-0.332971\pi\) | ||||
0.500985 | + | 0.865456i | \(0.332971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.4880 | 0.815156 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 38.4405 | 2.01760 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9723 | 0.677151 | 0.338575 | − | 0.940939i | \(-0.390055\pi\) | ||||
0.338575 | + | 0.940939i | \(0.390055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.5569 | −0.861919 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.7946 | 1.74982 | 0.874910 | − | 0.484286i | \(-0.160921\pi\) | ||||
0.874910 | + | 0.484286i | \(0.160921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.27622 | −0.220237 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.9052 | −1.84433 | −0.922164 | − | 0.386799i | \(-0.873581\pi\) | ||||
−0.922164 | + | 0.386799i | \(0.873581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0175 | 0.769369 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.17695 | 0.366725 | 0.183363 | − | 0.983045i | \(-0.441302\pi\) | ||||
0.183363 | + | 0.983045i | \(0.441302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.04565 | −0.459816 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8625 | −0.905664 | −0.452832 | − | 0.891596i | \(-0.649586\pi\) | ||||
−0.452832 | + | 0.891596i | \(0.649586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.5125 | 1.99823 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.6879 | 0.892234 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.8275 | −1.79813 | −0.899065 | − | 0.437815i | \(-0.855752\pi\) | ||||
−0.899065 | + | 0.437815i | \(0.855752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.98321 | 0.0990366 | 0.0495183 | − | 0.998773i | \(-0.484231\pi\) | ||||
0.0495183 | + | 0.998773i | \(0.484231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.35871 | −0.366564 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.17626 | 0.454850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.7977 | 1.57230 | 0.786148 | − | 0.618038i | \(-0.212072\pi\) | ||||
0.786148 | + | 0.618038i | \(0.212072\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.37528 | 0.314470 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.47335 | −0.414942 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.05411 | 0.198056 | 0.0990281 | − | 0.995085i | \(-0.468427\pi\) | ||||
0.0990281 | + | 0.995085i | \(0.468427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.19163 | −0.301762 | −0.150881 | − | 0.988552i | \(-0.548211\pi\) | ||||
−0.150881 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.8348 | 0.575426 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.98789 | −0.433939 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4190 | −0.839042 | −0.419521 | − | 0.907746i | \(-0.637802\pi\) | ||||
−0.419521 | + | 0.907746i | \(0.637802\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6292 | 0.703036 | 0.351518 | − | 0.936181i | \(-0.385666\pi\) | ||||
0.351518 | + | 0.936181i | \(0.385666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −51.5300 | −2.46501 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.4868 | −1.12096 | −0.560481 | − | 0.828167i | \(-0.689384\pi\) | ||||
−0.560481 | + | 0.828167i | \(0.689384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.09524 | −0.337105 | −0.168553 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168553 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.51981 | 0.450272 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.96690 | 0.0928237 | 0.0464119 | − | 0.998922i | \(-0.485221\pi\) | ||||
0.0464119 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 76.1370 | 3.58515 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.7562 | 0.975212 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.1829 | 1.27156 | 0.635781 | − | 0.771870i | \(-0.280678\pi\) | ||||
0.635781 | + | 0.771870i | \(0.280678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.0648 | 1.16992 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9232 | 0.648467 | 0.324234 | − | 0.945977i | \(-0.394894\pi\) | ||||
0.324234 | + | 0.945977i | \(0.394894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.9834 | 1.30050 | 0.650250 | − | 0.759720i | \(-0.274664\pi\) | ||||
0.650250 | + | 0.759720i | \(0.274664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.5773 | 1.92397 | 0.961984 | − | 0.273107i | \(-0.0880512\pi\) | ||||
0.961984 | + | 0.273107i | \(0.0880512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.04634 | −0.186446 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41.5964 | 1.91261 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.07493 | 0.0492176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.0173 | 1.46291 | 0.731453 | − | 0.681891i | \(-0.238842\pi\) | ||||
0.731453 | + | 0.681891i | \(0.238842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.57517 | −0.0718217 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.4974 | −1.38197 | −0.690985 | − | 0.722869i | \(-0.742823\pi\) | ||||
−0.690985 | + | 0.722869i | \(0.742823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.0920 | 0.772926 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6253 | −0.660029 | −0.330015 | − | 0.943976i | \(-0.607054\pi\) | ||||
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.4388 | −0.785404 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.3148 | −1.58091 | −0.790453 | − | 0.612523i | \(-0.790155\pi\) | ||||
−0.790453 | + | 0.612523i | \(0.790155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0876 | 0.540034 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.4066 | 0.820711 | 0.410356 | − | 0.911926i | \(-0.365405\pi\) | ||||
0.410356 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.9069 | −0.662037 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8190 | 1.10008 | 0.550042 | − | 0.835137i | \(-0.314612\pi\) | ||||
0.550042 | + | 0.835137i | \(0.314612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.6880 | −1.44321 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −54.4222 | −2.39349 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.9204 | −1.00609 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.8663 | −1.13322 | −0.566612 | − | 0.823985i | \(-0.691746\pi\) | ||||
−0.566612 | + | 0.823985i | \(0.691746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.82369 | 0.123471 | 0.0617356 | − | 0.998093i | \(-0.480336\pi\) | ||||
0.0617356 | + | 0.998093i | \(0.480336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.0095 | −1.30723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.9931 | 2.34753 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.51247 | −0.109032 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.0695 | −0.566102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.0217 | −0.993459 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9651 | −0.772378 | −0.386189 | − | 0.922420i | \(-0.626209\pi\) | ||||
−0.386189 | + | 0.922420i | \(0.626209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.4286 | −0.833762 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.40331 | 0.102758 | 0.0513792 | − | 0.998679i | \(-0.483638\pi\) | ||||
0.0513792 | + | 0.998679i | \(0.483638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.25244 | 0.181490 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.7427 | 0.968870 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.09877 | −0.131299 | −0.0656495 | − | 0.997843i | \(-0.520912\pi\) | ||||
−0.0656495 | + | 0.997843i | \(0.520912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.14033 | −0.302004 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.6534 | −1.54751 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.4957 | 1.62240 | 0.811201 | − | 0.584768i | \(-0.198814\pi\) | ||||
0.811201 | + | 0.584768i | \(0.198814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.59474 | 0.318388 | 0.159194 | − | 0.987247i | \(-0.449110\pi\) | ||||
0.159194 | + | 0.987247i | \(0.449110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.679330 | −0.0284291 | −0.0142145 | − | 0.999899i | \(-0.504525\pi\) | ||||
−0.0142145 | + | 0.999899i | \(0.504525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.79283 | −0.0748964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6808 | 0.736059 | 0.368030 | − | 0.929814i | \(-0.380032\pi\) | ||||
0.368030 | + | 0.929814i | \(0.380032\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.15832 | −0.0481383 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.94306 | −0.204721 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0359 | −0.579324 | −0.289662 | − | 0.957129i | \(-0.593543\pi\) | ||||
−0.289662 | + | 0.957129i | \(0.593543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.1366 | 1.61260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.6220 | 0.766005 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1512 | 0.498991 | 0.249495 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249495 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.9085 | −0.487383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.8724 | −1.42485 | −0.712425 | − | 0.701749i | \(-0.752403\pi\) | ||||
−0.712425 | + | 0.701749i | \(0.752403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.8128 | −0.481855 | −0.240928 | − | 0.970543i | \(-0.577452\pi\) | ||||
−0.240928 | + | 0.970543i | \(0.577452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.99098 | −0.162525 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.3192 | −1.31180 | −0.655898 | − | 0.754849i | \(-0.727710\pi\) | ||||
−0.655898 | + | 0.754849i | \(0.727710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.34198 | 0.377936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8424 | −0.720649 | −0.360324 | − | 0.932827i | \(-0.617334\pi\) | ||||
−0.360324 | + | 0.932827i | \(0.617334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.8670 | −1.64524 | −0.822622 | − | 0.568589i | \(-0.807489\pi\) | ||||
−0.822622 | + | 0.568589i | \(0.807489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.86956 | −0.356498 | −0.178249 | − | 0.983985i | \(-0.557043\pi\) | ||||
−0.178249 | + | 0.983985i | \(0.557043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.8406 | 1.95991 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 47.8012 | 1.90900 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.42369 | −0.256129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.3216 | −1.68480 | −0.842398 | − | 0.538856i | \(-0.818857\pi\) | ||||
−0.842398 | + | 0.538856i | \(0.818857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.90519 | −0.155217 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2548 | 0.524350 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.3608 | 1.19918 | 0.599590 | − | 0.800307i | \(-0.295330\pi\) | ||||
0.599590 | + | 0.800307i | \(0.295330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.4617 | −1.59565 | −0.797827 | − | 0.602886i | \(-0.794017\pi\) | ||||
−0.797827 | + | 0.602886i | \(0.794017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.319975 | −0.0125795 | −0.00628976 | − | 0.999980i | \(-0.502002\pi\) | ||||
−0.00628976 | + | 0.999980i | \(0.502002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.5536 | 0.453519 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.50144 | −0.0978889 | −0.0489445 | − | 0.998802i | \(-0.515586\pi\) | ||||
−0.0489445 | + | 0.998802i | \(0.515586\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.7391 | −0.731084 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0291 | 0.468586 | 0.234293 | − | 0.972166i | \(-0.424722\pi\) | ||||
0.234293 | + | 0.972166i | \(0.424722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5251 | −1.03171 | −0.515853 | − | 0.856677i | \(-0.672525\pi\) | ||||
−0.515853 | + | 0.856677i | \(0.672525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.29182 | 0.244354 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.9808 | −1.31574 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.01511 | 0.193895 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5549 | −0.754907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.97566 | 0.0761561 | 0.0380781 | − | 0.999275i | \(-0.487876\pi\) | ||||
0.0380781 | + | 0.999275i | \(0.487876\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.60326 | 0.369083 | 0.184542 | − | 0.982825i | \(-0.440920\pi\) | ||||
0.184542 | + | 0.982825i | \(0.440920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.6411 | 0.867608 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0600 | 0.958894 | 0.479447 | − | 0.877571i | \(-0.340837\pi\) | ||||
0.479447 | + | 0.877571i | \(0.340837\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.3285 | 1.27156 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.848513 | 0.0323258 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6042 | −0.593611 | −0.296806 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296806 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.2984 | −2.01882 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.88161 | −0.298110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1004 | −0.381487 | −0.190743 | − | 0.981640i | \(-0.561090\pi\) | ||||
−0.190743 | + | 0.981640i | \(0.561090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.37740 | 0.315960 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.5659 | −1.71126 | −0.855632 | − | 0.517584i | \(-0.826832\pi\) | ||||
−0.855632 | + | 0.517584i | \(0.826832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.0168 | 0.488168 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −58.4757 | −2.18993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0497 | −0.375312 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.41277 | 0.313743 | 0.156872 | − | 0.987619i | \(-0.449859\pi\) | ||||
0.156872 | + | 0.987619i | \(0.449859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.05950 | −0.225355 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.22522 | −0.119617 | −0.0598084 | − | 0.998210i | \(-0.519049\pi\) | ||||
−0.0598084 | + | 0.998210i | \(0.519049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.1116 | 0.930059 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.1189 | −1.07700 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.8320 | 1.84059 | 0.920293 | − | 0.391229i | \(-0.127950\pi\) | ||||
0.920293 | + | 0.391229i | \(0.127950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.3525 | 0.676024 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.1825 | −0.521710 | −0.260855 | − | 0.965378i | \(-0.584004\pi\) | ||||
−0.260855 | + | 0.965378i | \(0.584004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.20543 | −0.301434 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5740 | −0.828159 | −0.414079 | − | 0.910241i | \(-0.635896\pi\) | ||||
−0.414079 | + | 0.910241i | \(0.635896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.47787 | 0.163837 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.3334 | 0.960921 | 0.480460 | − | 0.877016i | \(-0.340470\pi\) | ||||
0.480460 | + | 0.877016i | \(0.340470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.306496 | −0.0111693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0442 | 0.692173 | 0.346086 | − | 0.938203i | \(-0.387510\pi\) | ||||
0.346086 | + | 0.938203i | \(0.387510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −71.4218 | −2.59245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.85917 | 0.176145 | 0.0880723 | − | 0.996114i | \(-0.471929\pi\) | ||||
0.0880723 | + | 0.996114i | \(0.471929\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.98326 | −0.0716114 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8462 | 0.391124 | 0.195562 | − | 0.980691i | \(-0.437347\pi\) | ||||
0.195562 | + | 0.980691i | \(0.437347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1758 | −0.726614 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.4664 | −0.664192 | −0.332096 | − | 0.943246i | \(-0.607756\pi\) | ||||
−0.332096 | + | 0.943246i | \(0.607756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 69.5088 | 2.49041 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.9521 | −2.18104 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.5557 | −0.770339 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.5397 | 0.874746 | 0.437373 | − | 0.899280i | \(-0.355909\pi\) | ||||
0.437373 | + | 0.899280i | \(0.355909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.4291 | 0.442487 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.35674 | 0.119201 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3424 | 0.578876 | 0.289438 | − | 0.957197i | \(-0.406532\pi\) | ||||
0.289438 | + | 0.957197i | \(0.406532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.0974 | 1.34779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.08948 | −0.144495 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 86.1720 | 3.04094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3538 | −0.646083 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.6799 | 1.46539 | 0.732693 | − | 0.680559i | \(-0.238263\pi\) | ||||
0.732693 | + | 0.680559i | \(0.238263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.9750 | 0.771645 | 0.385823 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385823 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.4766 | 1.13900 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.9752 | 1.32858 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9383 | 1.84756 | 0.923780 | − | 0.382923i | \(-0.125082\pi\) | ||||
0.923780 | + | 0.382923i | \(0.125082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7583 | −0.723588 | −0.361794 | − | 0.932258i | \(-0.617836\pi\) | ||||
−0.361794 | + | 0.932258i | \(0.617836\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.0645 | 1.21931 | 0.609656 | − | 0.792666i | \(-0.291308\pi\) | ||||
0.609656 | + | 0.792666i | \(0.291308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.6035 | 1.58388 | 0.791938 | − | 0.610602i | \(-0.209072\pi\) | ||||
0.791938 | + | 0.610602i | \(0.209072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.04395 | −0.279041 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.0940 | −1.28216 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.7589 | −1.16549 | −0.582744 | − | 0.812656i | \(-0.698021\pi\) | ||||
−0.582744 | + | 0.812656i | \(0.698021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0026 | −0.482849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.9768 | −0.515828 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.5747 | 0.637481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.5170 | −0.429079 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.05793 | 0.104701 | 0.0523507 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523507 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.1290 | −0.721752 | −0.360876 | − | 0.932614i | \(-0.617522\pi\) | ||||
−0.360876 | + | 0.932614i | \(0.617522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.5617 | 0.667436 | 0.333718 | − | 0.942673i | \(-0.391697\pi\) | ||||
0.333718 | + | 0.942673i | \(0.391697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.23960 | −0.0762369 | −0.0381184 | − | 0.999273i | \(-0.512136\pi\) | ||||
−0.0381184 | + | 0.999273i | \(0.512136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.14741 | 0.140853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.8578 | −2.03054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.15034 | −0.106745 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.34192 | −0.282331 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.5582 | 1.26825 | 0.634125 | − | 0.773231i | \(-0.281361\pi\) | ||||
0.634125 | + | 0.773231i | \(0.281361\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.3102 | −0.583858 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.2210 | 0.445426 | 0.222713 | − | 0.974884i | \(-0.428509\pi\) | ||||
0.222713 | + | 0.974884i | \(0.428509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.9332 | −1.04098 | −0.520492 | − | 0.853867i | \(-0.674251\pi\) | ||||
−0.520492 | + | 0.853867i | \(0.674251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.3034 | 0.983912 | 0.491956 | − | 0.870620i | \(-0.336282\pi\) | ||||
0.491956 | + | 0.870620i | \(0.336282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.3113 | −0.613452 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −49.6844 | −1.66262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.2601 | 0.409352 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.8082 | 0.860750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.46031 | 0.115280 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.4249 | 0.611788 | 0.305894 | − | 0.952066i | \(-0.401045\pi\) | ||||
0.305894 | + | 0.952066i | \(0.401045\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.7009 | −0.487598 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.5402 | 0.680527 | 0.340263 | − | 0.940330i | \(-0.389484\pi\) | ||||
0.340263 | + | 0.940330i | \(0.389484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.5915 | −0.681478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.4469 | −0.740454 | −0.370227 | − | 0.928941i | \(-0.620720\pi\) | ||||
−0.370227 | + | 0.928941i | \(0.620720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.0965 | 0.892860 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4629 | 0.344390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.7441 | −0.418571 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0782 | −1.01964 | −0.509822 | − | 0.860280i | \(-0.670289\pi\) | ||||
−0.509822 | + | 0.860280i | \(0.670289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.6598 | 1.03649 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.7564 | 0.972098 | 0.486049 | − | 0.873931i | \(-0.338438\pi\) | ||||
0.486049 | + | 0.873931i | \(0.338438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.11556 | 0.297475 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.9577 | −1.59598 | −0.797988 | − | 0.602673i | \(-0.794102\pi\) | ||||
−0.797988 | + | 0.602673i | \(0.794102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −103.856 | −3.38202 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7245 | −0.868429 | −0.434214 | − | 0.900810i | \(-0.642974\pi\) | ||||
−0.434214 | + | 0.900810i | \(0.642974\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.7921 | −0.480171 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.7346 | 0.348094 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.5373 | −0.859627 | −0.429814 | − | 0.902918i | \(-0.641421\pi\) | ||||
−0.429814 | + | 0.902918i | \(0.641421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.5219 | 1.01896 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4118 | 0.432640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.7488 | 0.378600 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3042 | −0.942358 | −0.471179 | − | 0.882038i | \(-0.656171\pi\) | ||||
−0.471179 | + | 0.882038i | \(0.656171\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.4624 | −1.07497 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.7835 | −0.891616 | −0.445808 | − | 0.895129i | \(-0.647084\pi\) | ||||
−0.445808 | + | 0.895129i | \(0.647084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3268 | −0.938248 | −0.469124 | − | 0.883132i | \(-0.655430\pi\) | ||||
−0.469124 | + | 0.883132i | \(0.655430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8055 | 0.601026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.77114 | −0.216186 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.85139 | 0.186631 | 0.0933153 | − | 0.995637i | \(-0.470254\pi\) | ||||
0.0933153 | + | 0.995637i | \(0.470254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.7403 | −1.80424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3870 | 0.393486 | 0.196743 | − | 0.980455i | \(-0.436963\pi\) | ||||
0.196743 | + | 0.980455i | \(0.436963\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.40294 | 0.0445209 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2259 | 0.672231 | 0.336116 | − | 0.941821i | \(-0.390887\pi\) | ||||
0.336116 | + | 0.941821i | \(0.390887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.94018 | −0.251216 |
(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 | 9800.2.a.cu.1.3 | 4 | ||
5.4 | even | 2 | 9800.2.a.ck.1.2 | 4 | |||
7.3 | odd | 6 | 1400.2.q.m.401.3 | yes | 8 | ||
7.5 | odd | 6 | 1400.2.q.m.1201.3 | yes | 8 | ||
7.6 | odd | 2 | 9800.2.a.cj.1.2 | 4 | |||
35.3 | even | 12 | 1400.2.bh.j.849.3 | 16 | |||
35.12 | even | 12 | 1400.2.bh.j.249.3 | 16 | |||
35.17 | even | 12 | 1400.2.bh.j.849.6 | 16 | |||
35.19 | odd | 6 | 1400.2.q.l.1201.2 | yes | 8 | ||
35.24 | odd | 6 | 1400.2.q.l.401.2 | ✓ | 8 | ||
35.33 | even | 12 | 1400.2.bh.j.249.6 | 16 | |||
35.34 | odd | 2 | 9800.2.a.ct.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.l.401.2 | ✓ | 8 | 35.24 | odd | 6 | ||
1400.2.q.l.1201.2 | yes | 8 | 35.19 | odd | 6 | ||
1400.2.q.m.401.3 | yes | 8 | 7.3 | odd | 6 | ||
1400.2.q.m.1201.3 | yes | 8 | 7.5 | odd | 6 | ||
1400.2.bh.j.249.3 | 16 | 35.12 | even | 12 | |||
1400.2.bh.j.249.6 | 16 | 35.33 | even | 12 | |||
1400.2.bh.j.849.3 | 16 | 35.3 | even | 12 | |||
1400.2.bh.j.849.6 | 16 | 35.17 | even | 12 | |||
9800.2.a.cj.1.2 | 4 | 7.6 | odd | 2 | |||
9800.2.a.ck.1.2 | 4 | 5.4 | even | 2 | |||
9800.2.a.ct.1.3 | 4 | 35.34 | odd | 2 | |||
9800.2.a.cu.1.3 | 4 | 1.1 | even | 1 | trivial |