Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8496,2,Mod(1,8496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8496, 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("8496.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8496 = 2^{4} \cdot 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8496.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: | \(67.8409015573\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8496.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.32340 | 1.48627 | 0.743136 | − | 0.669141i | \(-0.233338\pi\) | ||||
0.743136 | + | 0.669141i | \(0.233338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.13919 | −0.430575 | −0.215287 | − | 0.976551i | \(-0.569069\pi\) | ||||
−0.215287 | + | 0.976551i | \(0.569069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.398207 | 0.120064 | 0.0600320 | − | 0.998196i | \(-0.480880\pi\) | ||||
0.0600320 | + | 0.998196i | \(0.480880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.39821 | 0.665143 | 0.332572 | − | 0.943078i | \(-0.392084\pi\) | ||||
0.332572 | + | 0.943078i | \(0.392084\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.10941 | −1.72428 | −0.862142 | − | 0.506666i | \(-0.830878\pi\) | ||||
−0.862142 | + | 0.506666i | \(0.830878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.53740 | −0.352704 | −0.176352 | − | 0.984327i | \(-0.556430\pi\) | ||||
−0.176352 | + | 0.984327i | \(0.556430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.25901 | 0.679551 | 0.339776 | − | 0.940507i | \(-0.389649\pi\) | ||||
0.339776 | + | 0.940507i | \(0.389649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.04502 | 1.20900 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.93561 | 0.730824 | 0.365412 | − | 0.930846i | \(-0.380928\pi\) | ||||
0.365412 | + | 0.930846i | \(0.380928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.78600 | −1.39841 | −0.699204 | − | 0.714923i | \(-0.746462\pi\) | ||||
−0.699204 | + | 0.714923i | \(0.746462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.78600 | −0.639951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.25901 | 0.206981 | 0.103490 | − | 0.994630i | \(-0.466999\pi\) | ||||
0.103490 | + | 0.994630i | \(0.466999\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.50761 | 1.17249 | 0.586246 | − | 0.810133i | \(-0.300605\pi\) | ||||
0.586246 | + | 0.810133i | \(0.300605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.69182 | 1.47799 | 0.738995 | − | 0.673711i | \(-0.235301\pi\) | ||||
0.738995 | + | 0.673711i | \(0.235301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.71120 | 1.27066 | 0.635330 | − | 0.772241i | \(-0.280864\pi\) | ||||
0.635330 | + | 0.772241i | \(0.280864\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.70224 | −0.814605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7666 | −1.47891 | −0.739455 | − | 0.673206i | \(-0.764917\pi\) | ||||
−0.739455 | + | 0.673206i | \(0.764917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.32340 | 0.178448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.989588 | 0.126704 | 0.0633519 | − | 0.997991i | \(-0.479821\pi\) | ||||
0.0633519 | + | 0.997991i | \(0.479821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.97021 | 0.988583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.45219 | −0.666091 | −0.333045 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333045 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0450 | 1.78551 | 0.892757 | − | 0.450538i | \(-0.148768\pi\) | ||||
0.892757 | + | 0.450538i | \(0.148768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.73202 | 0.553842 | 0.276921 | − | 0.960893i | \(-0.410686\pi\) | ||||
0.276921 | + | 0.960893i | \(0.410686\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.453636 | −0.0516966 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.04502 | −0.792626 | −0.396313 | − | 0.918115i | \(-0.629711\pi\) | ||||
−0.396313 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0796 | 1.43567 | 0.717837 | − | 0.696211i | \(-0.245132\pi\) | ||||
0.717837 | + | 0.696211i | \(0.245132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.6274 | −2.56275 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.4328 | 1.74187 | 0.870937 | − | 0.491394i | \(-0.163513\pi\) | ||||
0.870937 | + | 0.491394i | \(0.163513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.73202 | −0.286394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.10941 | −0.524214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.7666 | 1.49932 | 0.749662 | − | 0.661821i | \(-0.230216\pi\) | ||||
0.749662 | + | 0.661821i | \(0.230216\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.278388 | 0.0277007 | 0.0138503 | − | 0.999904i | \(-0.495591\pi\) | ||||
0.0138503 | + | 0.999904i | \(0.495591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0152 | 1.47949 | 0.739747 | − | 0.672885i | \(-0.234945\pi\) | ||||
0.739747 | + | 0.672885i | \(0.234945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.16898 | 0.113010 | 0.0565048 | − | 0.998402i | \(-0.482004\pi\) | ||||
0.0565048 | + | 0.998402i | \(0.482004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.89059 | −0.468434 | −0.234217 | − | 0.972184i | \(-0.575253\pi\) | ||||
−0.234217 | + | 0.972184i | \(0.575253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5630 | 1.46405 | 0.732024 | − | 0.681279i | \(-0.238576\pi\) | ||||
0.732024 | + | 0.681279i | \(0.238576\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8310 | 1.01000 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.09899 | 0.742434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8414 | −0.985585 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.47301 | 0.310636 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.39821 | −0.390278 | −0.195139 | − | 0.980776i | \(-0.562516\pi\) | ||||
−0.195139 | + | 0.980776i | \(0.562516\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6620 | 1.54314 | 0.771570 | − | 0.636145i | \(-0.219472\pi\) | ||||
0.771570 | + | 0.636145i | \(0.219472\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.75140 | 0.151866 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7666 | 0.919855 | 0.459928 | − | 0.887956i | \(-0.347875\pi\) | ||||
0.459928 | + | 0.887956i | \(0.347875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.82061 | −0.832973 | −0.416486 | − | 0.909142i | \(-0.636739\pi\) | ||||
−0.416486 | + | 0.909142i | \(0.636739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.954984 | 0.0798598 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.0796 | 1.08620 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.01938 | 0.411203 | 0.205602 | − | 0.978636i | \(-0.434085\pi\) | ||||
0.205602 | + | 0.978636i | \(0.434085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.35801 | −0.598786 | −0.299393 | − | 0.954130i | \(-0.596784\pi\) | ||||
−0.299393 | + | 0.954130i | \(0.596784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.8760 | −2.07841 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.73057 | −0.138115 | −0.0690574 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690574 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.71265 | −0.292598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.58242 | 0.672227 | 0.336113 | − | 0.941822i | \(-0.390887\pi\) | ||||
0.336113 | + | 0.941822i | \(0.390887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.49239 | 0.502396 | 0.251198 | − | 0.967936i | \(-0.419175\pi\) | ||||
0.251198 | + | 0.967936i | \(0.419175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.24860 | −0.557585 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.5437 | 1.56191 | 0.780953 | − | 0.624590i | \(-0.214734\pi\) | ||||
0.780953 | + | 0.624590i | \(0.214734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.88645 | −0.520566 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.9702 | −1.79162 | −0.895809 | − | 0.444439i | \(-0.853403\pi\) | ||||
−0.895809 | + | 0.444439i | \(0.853403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7112 | 1.09347 | 0.546737 | − | 0.837304i | \(-0.315870\pi\) | ||||
0.546737 | + | 0.837304i | \(0.315870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.18421 | 0.307629 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.83102 | −0.207025 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.91623 | 0.211011 | 0.105506 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105506 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.646809 | −0.0465583 | −0.0232791 | − | 0.999729i | \(-0.507411\pi\) | ||||
−0.0232791 | + | 0.999729i | \(0.507411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.87122 | 0.418307 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1004 | −0.786890 | −0.393445 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.48342 | −0.314675 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.9508 | 1.74264 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.612205 | −0.0423471 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4778 | 0.927852 | 0.463926 | − | 0.885874i | \(-0.346440\pi\) | ||||
0.463926 | + | 0.885874i | \(0.346440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.2099 | 2.19669 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.86977 | 0.602119 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.0498 | −1.14690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7368 | −1.12078 | −0.560391 | − | 0.828228i | \(-0.689349\pi\) | ||||
−0.560391 | + | 0.828228i | \(0.689349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0346 | −0.931509 | −0.465755 | − | 0.884914i | \(-0.654217\pi\) | ||||
−0.465755 | + | 0.884914i | \(0.654217\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2445 | −0.809136 | −0.404568 | − | 0.914508i | \(-0.632578\pi\) | ||||
−0.404568 | + | 0.914508i | \(0.632578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.87122 | −0.122588 | −0.0612938 | − | 0.998120i | \(-0.519523\pi\) | ||||
−0.0612938 | + | 0.998120i | \(0.519523\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.9508 | 1.88854 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.9910 | −0.905005 | −0.452502 | − | 0.891763i | \(-0.649469\pi\) | ||||
−0.452502 | + | 0.891763i | \(0.649469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5333 | 1.77357 | 0.886786 | − | 0.462179i | \(-0.152932\pi\) | ||||
0.886786 | + | 0.462179i | \(0.152932\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.9508 | −1.21072 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.68701 | −0.234599 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.61702 | −0.165185 | −0.0825925 | − | 0.996583i | \(-0.526320\pi\) | ||||
−0.0825925 | + | 0.996583i | \(0.526320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.29776 | 0.0815897 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3892 | −1.27185 | −0.635923 | − | 0.771752i | \(-0.719380\pi\) | ||||
−0.635923 | + | 0.771752i | \(0.719380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.43426 | −0.0891206 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.8552 | −1.47098 | −0.735488 | − | 0.677538i | \(-0.763047\pi\) | ||||
−0.735488 | + | 0.677538i | \(0.763047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.7819 | −2.19806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.2999 | 1.72547 | 0.862737 | − | 0.505653i | \(-0.168748\pi\) | ||||
0.862737 | + | 0.505653i | \(0.168748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4134 | 1.42226 | 0.711132 | − | 0.703058i | \(-0.248183\pi\) | ||||
0.711132 | + | 0.703058i | \(0.248183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.40717 | 0.145158 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.6918 | 0.942830 | 0.471415 | − | 0.881911i | \(-0.343743\pi\) | ||||
0.471415 | + | 0.881911i | \(0.343743\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63158 | 0.335952 | 0.167976 | − | 0.985791i | \(-0.446277\pi\) | ||||
0.167976 | + | 0.985791i | \(0.446277\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8310 | −0.643837 | −0.321919 | − | 0.946767i | \(-0.604328\pi\) | ||||
−0.321919 | + | 0.946767i | \(0.604328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.55263 | −0.504846 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.5437 | 1.97316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.9959 | −1.98606 | −0.993029 | − | 0.117866i | \(-0.962395\pi\) | ||||
−0.993029 | + | 0.117866i | \(0.962395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.32340 | 0.193496 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.81579 | 0.451999 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0409 | −0.636385 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.28880 | 0.188316 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.25756 | 0.242992 | 0.121496 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121496 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5374 | 1.22127 | 0.610637 | − | 0.791911i | \(-0.290913\pi\) | ||||
0.610637 | + | 0.791911i | \(0.290913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.96540 | −0.224137 | −0.112069 | − | 0.993700i | \(-0.535748\pi\) | ||||
−0.112069 | + | 0.993700i | \(0.535748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.58097 | −0.425790 | −0.212895 | − | 0.977075i | \(-0.568289\pi\) | ||||
−0.212895 | + | 0.977075i | \(0.568289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56719 | 0.0877457 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.9300 | 0.608162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.4972 | 0.804160 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.92375 | −0.547114 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.667633 | 0.0366964 | 0.0183482 | − | 0.999832i | \(-0.494159\pi\) | ||||
0.0183482 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.1198 | −0.989991 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.47783 | 0.407343 | 0.203672 | − | 0.979039i | \(-0.434713\pi\) | ||||
0.203672 | + | 0.979039i | \(0.434713\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.10044 | −0.167898 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4703 | 0.781323 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.0200 | −1.55788 | −0.778939 | − | 0.627100i | \(-0.784242\pi\) | ||||
−0.778939 | + | 0.627100i | \(0.784242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8746 | −0.903276 | −0.451638 | − | 0.892201i | \(-0.649160\pi\) | ||||
−0.451638 | + | 0.892201i | \(0.649160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.98062 | 0.158643 | 0.0793213 | − | 0.996849i | \(-0.474725\pi\) | ||||
0.0793213 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.0007 | 2.65376 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.85039 | −0.0976600 | −0.0488300 | − | 0.998807i | \(-0.515549\pi\) | ||||
−0.0488300 | + | 0.998807i | \(0.515549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6364 | −0.875600 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7264 | 0.823159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.97021 | −0.416042 | −0.208021 | − | 0.978124i | \(-0.566702\pi\) | ||||
−0.208021 | + | 0.978124i | \(0.566702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2653 | 0.636782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.31859 | 0.0682739 | 0.0341369 | − | 0.999417i | \(-0.489132\pi\) | ||||
0.0341369 | + | 0.999417i | \(0.489132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.43841 | 0.486103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5783 | −1.05703 | −0.528517 | − | 0.848922i | \(-0.677252\pi\) | ||||
−0.528517 | + | 0.848922i | \(0.677252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8802 | 1.11803 | 0.559013 | − | 0.829159i | \(-0.311180\pi\) | ||||
0.559013 | + | 0.829159i | \(0.311180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50761 | −0.0768351 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.29921 | 0.319383 | 0.159691 | − | 0.987167i | \(-0.448950\pi\) | ||||
0.159691 | + | 0.987167i | \(0.448950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.1697 | −1.17174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.4134 | −1.17806 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1198 | −0.608276 | −0.304138 | − | 0.952628i | \(-0.598368\pi\) | ||||
−0.304138 | + | 0.952628i | \(0.598368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3338 | 0.815672 | 0.407836 | − | 0.913055i | \(-0.366284\pi\) | ||||
0.407836 | + | 0.913055i | \(0.366284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6724 | −0.930141 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.501348 | 0.0248509 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0665 | 1.83282 | 0.916410 | − | 0.400240i | \(-0.131073\pi\) | ||||
0.916410 | + | 0.400240i | \(0.131073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.13919 | −0.0560561 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.4689 | 2.13380 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6468 | 0.715543 | 0.357772 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357772 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.32340 | −0.161973 | −0.0809864 | − | 0.996715i | \(-0.525807\pi\) | ||||
−0.0809864 | + | 0.996715i | \(0.525807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −42.9765 | −2.08467 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.12733 | −0.0545555 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.73202 | 0.131597 | 0.0657985 | − | 0.997833i | \(-0.479041\pi\) | ||||
0.0657985 | + | 0.997833i | \(0.479041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.1038 | −1.73504 | −0.867519 | − | 0.497404i | \(-0.834287\pi\) | ||||
−0.867519 | + | 0.497404i | \(0.834287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.01041 | −0.239681 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.9571 | 1.81159 | 0.905797 | − | 0.423712i | \(-0.139273\pi\) | ||||
0.905797 | + | 0.423712i | \(0.139273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.84625 | 0.0877179 | 0.0438589 | − | 0.999038i | \(-0.486035\pi\) | ||||
0.0438589 | + | 0.999038i | \(0.486035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 54.6129 | 2.58890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.9494 | −1.31901 | −0.659507 | − | 0.751699i | \(-0.729235\pi\) | ||||
−0.659507 | + | 0.751699i | \(0.729235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.98959 | 0.140774 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.07962 | −0.425659 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2501 | −1.08759 | −0.543796 | − | 0.839218i | \(-0.683013\pi\) | ||||
−0.543796 | + | 0.839218i | \(0.683013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.4447 | −0.952203 | −0.476102 | − | 0.879390i | \(-0.657951\pi\) | ||||
−0.476102 | + | 0.879390i | \(0.657951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6122 | 0.586139 | 0.293069 | − | 0.956091i | \(-0.405323\pi\) | ||||
0.293069 | + | 0.956091i | \(0.405323\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.89204 | −0.0875533 | −0.0437766 | − | 0.999041i | \(-0.513939\pi\) | ||||
−0.0437766 | + | 0.999041i | \(0.513939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.21110 | 0.286802 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.85936 | 0.177453 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.29362 | −0.426420 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.51658 | −0.160677 | −0.0803383 | − | 0.996768i | \(-0.525600\pi\) | ||||
−0.0803383 | + | 0.996768i | \(0.525600\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.01938 | 0.137672 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 49.0755 | 2.22840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.2203 | −0.961582 | −0.480791 | − | 0.876835i | \(-0.659650\pi\) | ||||
−0.480791 | + | 0.876835i | \(0.659650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.4536 | 0.562025 | 0.281012 | − | 0.959704i | \(-0.409330\pi\) | ||||
0.281012 | + | 0.959704i | \(0.409330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.9798 | −1.26015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1392 | −0.768798 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.0755 | −1.48066 | −0.740331 | − | 0.672243i | \(-0.765331\pi\) | ||||
−0.740331 | + | 0.672243i | \(0.765331\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5824 | 0.561022 | 0.280511 | − | 0.959851i | \(-0.409496\pi\) | ||||
0.280511 | + | 0.959851i | \(0.409496\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.925197 | 0.0411707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.0465 | −1.24314 | −0.621569 | − | 0.783360i | \(-0.713504\pi\) | ||||
−0.621569 | + | 0.783360i | \(0.713504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.39069 | −0.238470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.9017 | 2.19893 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.46886 | 0.152560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.7956 | 1.65586 | 0.827928 | − | 0.560834i | \(-0.189519\pi\) | ||||
0.827928 | + | 0.560834i | \(0.189519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.1946 | 0.751868 | 0.375934 | − | 0.926646i | \(-0.377322\pi\) | ||||
0.375934 | + | 0.926646i | \(0.377322\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 55.3539 | 2.41125 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.3788 | −0.538210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.0048 | 0.779875 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.88500 | 0.167963 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.27067 | −0.0978048 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.94939 | −0.169797 | −0.0848987 | − | 0.996390i | \(-0.527057\pi\) | ||||
−0.0848987 | + | 0.996390i | \(0.527057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.2534 | −0.696220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1094 | −0.731545 | −0.365773 | − | 0.930704i | \(-0.619195\pi\) | ||||
−0.365773 | + | 0.930704i | \(0.619195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.05061 | −0.257765 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.02564 | 0.341285 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.29362 | −0.139555 | −0.0697775 | − | 0.997563i | \(-0.522229\pi\) | ||||
−0.0697775 | + | 0.997563i | \(0.522229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.2430 | 0.983074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.10459 | 0.130843 | 0.0654214 | − | 0.997858i | \(-0.479161\pi\) | ||||
0.0654214 | + | 0.997858i | \(0.479161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51.7223 | 2.17597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4024 | −0.603778 | −0.301889 | − | 0.953343i | \(-0.597617\pi\) | ||||
−0.301889 | + | 0.953343i | \(0.597617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.1198 | 1.42787 | 0.713935 | − | 0.700212i | \(-0.246911\pi\) | ||||
0.713935 | + | 0.700212i | \(0.246911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.7008 | 0.821580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.6143 | −1.81569 | −0.907844 | − | 0.419308i | \(-0.862273\pi\) | ||||
−0.907844 | + | 0.419308i | \(0.862273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.9002 | −0.618166 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.28735 | −0.177564 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.6170 | 0.438211 | 0.219106 | − | 0.975701i | \(-0.429686\pi\) | ||||
0.219106 | + | 0.975701i | \(0.429686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9702 | 0.493224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.621168 | 0.0255083 | 0.0127541 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127541 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.9162 | 1.10346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.01523 | 0.123199 | 0.0615995 | − | 0.998101i | \(-0.480380\pi\) | ||||
0.0615995 | + | 0.998101i | \(0.480380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.24378 | −0.254689 | −0.127345 | − | 0.991859i | \(-0.540645\pi\) | ||||
−0.127345 | + | 0.991859i | \(0.540645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.0305 | −1.46485 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.526989 | 0.0213898 | 0.0106949 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106949 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.8913 | 0.845170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.6564 | 1.80366 | 0.901828 | − | 0.432094i | \(-0.142225\pi\) | ||||
0.901828 | + | 0.432094i | \(0.142225\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.5831 | 1.79485 | 0.897424 | − | 0.441170i | \(-0.145436\pi\) | ||||
0.897424 | + | 0.441170i | \(0.145436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.6531 | 1.59379 | 0.796896 | − | 0.604117i | \(-0.206474\pi\) | ||||
0.796896 | + | 0.604117i | \(0.206474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.7202 | −0.750007 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.6829 | −0.747314 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.95084 | −0.356893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.30818 | 0.251125 | 0.125562 | − | 0.992086i | \(-0.459927\pi\) | ||||
0.125562 | + | 0.992086i | \(0.459927\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.6170 | −0.580059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.6751 | −0.541829 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5062 | −0.651954 | −0.325977 | − | 0.945378i | \(-0.605693\pi\) | ||||
−0.325977 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1455 | 0.873332 | 0.436666 | − | 0.899624i | \(-0.356159\pi\) | ||||
0.436666 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.4376 | −0.488974 | −0.244487 | − | 0.969653i | \(-0.578619\pi\) | ||||
−0.244487 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.398207 | 0.0156310 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3941 | 0.406751 | 0.203376 | − | 0.979101i | \(-0.434809\pi\) | ||||
0.203376 | + | 0.979101i | \(0.434809\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.6981 | 2.29352 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.5139 | −1.81192 | −0.905962 | − | 0.423360i | \(-0.860851\pi\) | ||||
−0.905962 | + | 0.423360i | \(0.860851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.3788 | −1.22050 | −0.610248 | − | 0.792211i | \(-0.708930\pi\) | ||||
−0.610248 | + | 0.792211i | \(0.708930\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.82061 | 0.225713 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.8262 | 0.496633 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.394061 | 0.0152126 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2936 | 0.897903 | 0.448951 | − | 0.893556i | \(-0.351798\pi\) | ||||
0.448951 | + | 0.893556i | \(0.351798\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.775591 | 0.0298084 | 0.0149042 | − | 0.999889i | \(-0.495256\pi\) | ||||
0.0149042 | + | 0.999889i | \(0.495256\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.8221 | −0.645571 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5810 | −0.519661 | −0.259831 | − | 0.965654i | \(-0.583667\pi\) | ||||
−0.259831 | + | 0.965654i | \(0.583667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.7819 | 1.36715 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.8206 | −0.983687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6981 | −0.711309 | −0.355654 | − | 0.934618i | \(-0.615742\pi\) | ||||
−0.355654 | + | 0.934618i | \(0.615742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.6378 | −1.23802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.3747 | −2.02171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7625 | 1.76619 | 0.883097 | − | 0.469190i | \(-0.155454\pi\) | ||||
0.883097 | + | 0.469190i | \(0.155454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.93561 | −0.0730029 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.317138 | −0.0119272 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.98477 | 0.112095 | 0.0560477 | − | 0.998428i | \(-0.482150\pi\) | ||||
0.0560477 | + | 0.998428i | \(0.482150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.3747 | −0.950289 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.17380 | 0.118693 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.0915 | −1.23410 | −0.617052 | − | 0.786922i | \(-0.711673\pi\) | ||||
−0.617052 | + | 0.786922i | \(0.711673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.1053 | −0.637033 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.7908 | 0.883569 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9100 | −0.960948 | −0.480474 | − | 0.877009i | \(-0.659535\pi\) | ||||
−0.480474 | + | 0.877009i | \(0.659535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68.9031 | −2.54847 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.43426 | −0.126847 | −0.0634237 | − | 0.997987i | \(-0.520202\pi\) | ||||
−0.0634237 | + | 0.997987i | \(0.520202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.17110 | −0.0799735 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0014 | −0.698980 | −0.349490 | − | 0.936940i | \(-0.613645\pi\) | ||||
−0.349490 | + | 0.936940i | \(0.613645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.1607 | −0.482819 | −0.241409 | − | 0.970423i | \(-0.577610\pi\) | ||||
−0.241409 | + | 0.970423i | \(0.577610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.6814 | 0.611160 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.33170 | −0.0486591 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6981 | 0.536341 | 0.268170 | − | 0.963371i | \(-0.413581\pi\) | ||||
0.268170 | + | 0.963371i | \(0.413581\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4536 | −0.889959 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.27984 | 0.119208 | 0.0596039 | − | 0.998222i | \(-0.481016\pi\) | ||||
0.0596039 | + | 0.998222i | \(0.481016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5810 | 0.564810 | 0.282405 | − | 0.959295i | \(-0.408868\pi\) | ||||
0.282405 | + | 0.959295i | \(0.408868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.57133 | 0.201696 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.39821 | 0.0865943 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.0402 | 0.398120 | 0.199060 | − | 0.979987i | \(-0.436211\pi\) | ||||
0.199060 | + | 0.979987i | \(0.436211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.8600 | −1.43367 | −0.716833 | − | 0.697245i | \(-0.754409\pi\) | ||||
−0.716833 | + | 0.697245i | \(0.754409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.0665 | −1.69068 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5422 | −0.413543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.99104 | 0.214376 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.75140 | −0.205276 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.0692 | −0.857975 | −0.428987 | − | 0.903311i | \(-0.641129\pi\) | ||||
−0.428987 | + | 0.903311i | \(0.641129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.7293 | −0.630382 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.37324 | 0.0842761 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.3088 | −0.365158 | −0.182579 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182579 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.9315 | −2.19098 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.88433 | 0.0664965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.3386 | −0.434880 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.7119 | −0.868823 | −0.434412 | − | 0.900715i | \(-0.643044\pi\) | ||||
−0.434412 | + | 0.900715i | \(0.643044\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3088 | 0.572681 | 0.286341 | − | 0.958128i | \(-0.407561\pi\) | ||||
0.286341 | + | 0.958128i | \(0.407561\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.5228 | 0.999112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.9002 | −0.521293 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.5076 | 1.37883 | 0.689413 | − | 0.724369i | \(-0.257869\pi\) | ||||
0.689413 | + | 0.724369i | \(0.257869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.655771 | 0.0228588 | 0.0114294 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114294 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.5035 | 1.16503 | 0.582515 | − | 0.812820i | \(-0.302069\pi\) | ||||
0.582515 | + | 0.812820i | \(0.302069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.1752 | 0.978567 | 0.489283 | − | 0.872125i | \(-0.337258\pi\) | ||||
0.489283 | + | 0.872125i | \(0.337258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.5395 | 1.40461 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.5768 | 0.746697 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.9315 | −0.757158 | −0.378579 | − | 0.925569i | \(-0.623587\pi\) | ||||
−0.378579 | + | 0.925569i | \(0.623587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5110 | −0.465896 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0900 | −0.828722 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.3505 | 0.424368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10314 | 0.140654 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.9903 | −0.787171 | −0.393586 | − | 0.919288i | \(-0.628766\pi\) | ||||
−0.393586 | + | 0.919288i | \(0.628766\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5574 | 0.565592 | 0.282796 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282796 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50280 | 0.119514 | 0.0597570 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597570 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.1994 | −0.653557 | −0.326778 | − | 0.945101i | \(-0.605963\pi\) | ||||
−0.326778 | + | 0.945101i | \(0.605963\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.2749 | 2.32142 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.80538 | −0.0951659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.0755 | −0.443046 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.95643 | −0.133752 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.8864 | 1.78585 | 0.892924 | − | 0.450207i | \(-0.148650\pi\) | ||||
0.892924 | + | 0.450207i | \(0.148650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.86562 | 0.231309 | 0.115654 | − | 0.993290i | \(-0.463104\pi\) | ||||
0.115654 | + | 0.993290i | \(0.463104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.6233 | 1.73726 | 0.868631 | − | 0.495460i | \(-0.165000\pi\) | ||||
0.868631 | + | 0.495460i | \(0.165000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.7126 | 0.661886 | 0.330943 | − | 0.943651i | \(-0.392633\pi\) | ||||
0.330943 | + | 0.943651i | \(0.392633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.01041 | 0.168044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.3926 | −0.448167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −79.6627 | −2.66283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.6427 | −1.02199 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 76.5443 | 2.55006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.8913 | 1.62520 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.5366 | 1.34600 | 0.672998 | − | 0.739644i | \(-0.265006\pi\) | ||||
0.672998 | + | 0.739644i | \(0.265006\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.5949 | 1.80881 | 0.904406 | − | 0.426674i | \(-0.140315\pi\) | ||||
0.904406 | + | 0.426674i | \(0.140315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.20840 | 0.172373 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.1205 | −0.664437 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.95565 | 0.229446 | 0.114723 | − | 0.993398i | \(-0.463402\pi\) | ||||
0.114723 | + | 0.993398i | \(0.463402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0811 | 1.18762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.61076 | 0.250240 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.5478 | −0.542916 | −0.271458 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271458 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.76663 | 0.287315 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.40862 | −0.307695 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6766 | −0.936824 | −0.468412 | − | 0.883510i | \(-0.655174\pi\) | ||||
−0.468412 | + | 0.883510i | \(0.655174\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.1198 | 0.786284 | 0.393142 | − | 0.919478i | \(-0.371388\pi\) | ||||
0.393142 | + | 0.919478i | \(0.371388\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.4674 | 0.796769 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.0617 | 1.07436 | 0.537180 | − | 0.843467i | \(-0.319489\pi\) | ||||
0.537180 | + | 0.843467i | \(0.319489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3484 | 0.368384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.79641 | 0.220157 | 0.110079 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110079 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.69182 | 0.313620 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.2653 | −0.396067 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6218 | 0.955543 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.14961 | −0.0691983 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.7479 | 1.40684 | 0.703419 | − | 0.710775i | \(-0.251656\pi\) | ||||
0.703419 | + | 0.710775i | \(0.251656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.3434 | 0.973768 | 0.486884 | − | 0.873467i | \(-0.338134\pi\) | ||||
0.486884 | + | 0.873467i | \(0.338134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.1876 | 0.358657 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.2638 | −1.51210 | −0.756052 | − | 0.654512i | \(-0.772874\pi\) | ||||
−0.756052 | + | 0.654512i | \(0.772874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.54367 | 0.209137 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.9854 | 0.988282 | 0.494141 | − | 0.869382i | \(-0.335483\pi\) | ||||
0.494141 | + | 0.869382i | \(0.335483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.5124 | 0.621718 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.5858 | 1.00437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.8131 | 0.597618 | 0.298809 | − | 0.954313i | \(-0.403411\pi\) | ||||
0.298809 | + | 0.954313i | \(0.403411\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.8913 | −1.16953 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.5020 | 0.522624 | 0.261312 | − | 0.965254i | \(-0.415845\pi\) | ||||
0.261312 | + | 0.965254i | \(0.415845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8496.2.a.bl.1.3 | 3 | ||
3.2 | odd | 2 | 2832.2.a.t.1.1 | 3 | |||
4.3 | odd | 2 | 531.2.a.d.1.3 | 3 | |||
12.11 | even | 2 | 177.2.a.d.1.1 | ✓ | 3 | ||
60.59 | even | 2 | 4425.2.a.w.1.3 | 3 | |||
84.83 | odd | 2 | 8673.2.a.s.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.a.d.1.1 | ✓ | 3 | 12.11 | even | 2 | ||
531.2.a.d.1.3 | 3 | 4.3 | odd | 2 | |||
2832.2.a.t.1.1 | 3 | 3.2 | odd | 2 | |||
4425.2.a.w.1.3 | 3 | 60.59 | even | 2 | |||
8496.2.a.bl.1.3 | 3 | 1.1 | even | 1 | trivial | ||
8673.2.a.s.1.1 | 3 | 84.83 | odd | 2 |