Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7744,2,Mod(1,7744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7744 = 2^{6} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7744.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: | \(61.8361513253\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.26498\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7744.1 |
$q$-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 | ||||||||
\(3\) | −2.04678 | −1.18171 | −0.590853 | − | 0.806779i | \(-0.701209\pi\) | ||||
−0.590853 | + | 0.806779i | \(0.701209\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.163765 | 0.0732379 | 0.0366189 | − | 0.999329i | \(-0.488341\pi\) | ||||
0.0366189 | + | 0.999329i | \(0.488341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50105 | 1.32327 | 0.661635 | − | 0.749826i | \(-0.269863\pi\) | ||||
0.661635 | + | 0.749826i | \(0.269863\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.18929 | 0.396431 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.69372 | 0.747103 | 0.373552 | − | 0.927609i | \(-0.378140\pi\) | ||||
0.373552 | + | 0.927609i | \(0.378140\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.335190 | −0.0865457 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.57673 | 1.83763 | 0.918814 | − | 0.394692i | \(-0.129149\pi\) | ||||
0.918814 | + | 0.394692i | \(0.129149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.61803 | −1.05945 | −0.529725 | − | 0.848170i | \(-0.677705\pi\) | ||||
−0.529725 | + | 0.848170i | \(0.677705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.16586 | −1.56372 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.706114 | 0.147235 | 0.0736174 | − | 0.997287i | \(-0.476546\pi\) | ||||
0.0736174 | + | 0.997287i | \(0.476546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97318 | −0.994636 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.70611 | 0.713242 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.02891 | −0.191064 | −0.0955318 | − | 0.995426i | \(-0.530455\pi\) | ||||
−0.0955318 | + | 0.995426i | \(0.530455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.39983 | −0.969839 | −0.484919 | − | 0.874559i | \(-0.661151\pi\) | ||||
−0.484919 | + | 0.874559i | \(0.661151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.573348 | 0.0969135 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.5946 | −1.90614 | −0.953070 | − | 0.302750i | \(-0.902095\pi\) | ||||
−0.953070 | + | 0.302750i | \(0.902095\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.51344 | −0.882857 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.280754 | 0.0438464 | 0.0219232 | − | 0.999760i | \(-0.493021\pi\) | ||||
0.0219232 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.31175 | −0.657536 | −0.328768 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328768 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.194764 | 0.0290337 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.82857 | −0.850185 | −0.425093 | − | 0.905150i | \(-0.639758\pi\) | ||||
−0.425093 | + | 0.905150i | \(0.639758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.25732 | 0.751045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.5079 | −2.17154 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.87197 | −1.35602 | −0.678010 | − | 0.735053i | \(-0.737157\pi\) | ||||
−0.678010 | + | 0.735053i | \(0.737157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.45208 | 1.25196 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.09017 | −0.402306 | −0.201153 | − | 0.979560i | \(-0.564469\pi\) | ||||
−0.201153 | + | 0.979560i | \(0.564469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.93188 | 0.887536 | 0.443768 | − | 0.896142i | \(-0.353641\pi\) | ||||
0.443768 | + | 0.896142i | \(0.353641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.16376 | 0.524585 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.441137 | 0.0547163 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.91665 | 0.234157 | 0.117078 | − | 0.993123i | \(-0.462647\pi\) | ||||
0.117078 | + | 0.993123i | \(0.462647\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.44526 | −0.173988 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1679 | −1.44407 | −0.722035 | − | 0.691857i | \(-0.756793\pi\) | ||||
−0.722035 | + | 0.691857i | \(0.756793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3764 | 1.33151 | 0.665753 | − | 0.746172i | \(-0.268110\pi\) | ||||
0.665753 | + | 0.746172i | \(0.268110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.1790 | 1.17537 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.72736 | −0.194343 | −0.0971717 | − | 0.995268i | \(-0.530980\pi\) | ||||
−0.0971717 | + | 0.995268i | \(0.530980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1535 | −1.23927 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.70950 | −0.516934 | −0.258467 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258467 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.24080 | 0.134584 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.10595 | 0.225781 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.31175 | 0.669044 | 0.334522 | − | 0.942388i | \(-0.391425\pi\) | ||||
0.334522 | + | 0.942388i | \(0.391425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.43083 | 0.988620 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.0522 | 1.14606 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.756272 | −0.0775918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00547 | 0.711298 | 0.355649 | − | 0.934620i | \(-0.384260\pi\) | ||||
0.355649 | + | 0.934620i | \(0.384260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.02334 | 0.400337 | 0.200169 | − | 0.979761i | \(-0.435851\pi\) | ||||
0.200169 | + | 0.979761i | \(0.435851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0646 | −1.48436 | −0.742182 | − | 0.670199i | \(-0.766209\pi\) | ||||
−0.742182 | + | 0.670199i | \(0.766209\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17352 | −0.114523 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.518912 | 0.0501651 | 0.0250826 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250826 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.285032 | −0.0273011 | −0.0136506 | − | 0.999907i | \(-0.504345\pi\) | ||||
−0.0136506 | + | 0.999907i | \(0.504345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.7315 | 2.25250 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5691 | −1.08833 | −0.544163 | − | 0.838979i | \(-0.683153\pi\) | ||||
−0.544163 | + | 0.838979i | \(0.683153\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.115637 | 0.0107832 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.20362 | 0.296175 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.5265 | 2.43168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.574640 | −0.0518135 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.63326 | −0.146083 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1190 | −1.51906 | −0.759532 | − | 0.650470i | \(-0.774572\pi\) | ||||
−0.759532 | + | 0.650470i | \(0.774572\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.82519 | 0.777015 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.02344 | −0.438900 | −0.219450 | − | 0.975624i | \(-0.570426\pi\) | ||||
−0.219450 | + | 0.975624i | \(0.570426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.1679 | −1.40194 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.606931 | 0.0522363 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00547 | 0.256775 | 0.128387 | − | 0.991724i | \(-0.459020\pi\) | ||||
0.128387 | + | 0.991724i | \(0.459020\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.36062 | 0.454682 | 0.227341 | − | 0.973815i | \(-0.426997\pi\) | ||||
0.227341 | + | 0.973815i | \(0.426997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9298 | 1.00467 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.168499 | −0.0139931 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.7605 | −0.887515 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.82091 | 0.476868 | 0.238434 | − | 0.971159i | \(-0.423366\pi\) | ||||
0.238434 | + | 0.971159i | \(0.423366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.64565 | 0.296679 | 0.148339 | − | 0.988937i | \(-0.452607\pi\) | ||||
0.148339 | + | 0.988937i | \(0.452607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.01094 | 0.728492 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.884303 | −0.0710289 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.145160 | −0.0115850 | −0.00579252 | − | 0.999983i | \(-0.501844\pi\) | ||||
−0.00579252 | + | 0.999983i | \(0.501844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.2057 | 1.60242 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.47214 | 0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.4384 | −1.13090 | −0.565451 | − | 0.824782i | \(-0.691298\pi\) | ||||
−0.565451 | + | 0.824782i | \(0.691298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4397 | 1.34953 | 0.674764 | − | 0.738034i | \(-0.264245\pi\) | ||||
0.674764 | + | 0.738034i | \(0.264245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.74388 | −0.441837 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.49219 | −0.419998 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2429 | −1.38698 | −0.693491 | − | 0.720466i | \(-0.743928\pi\) | ||||
−0.693491 | + | 0.720466i | \(0.743928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.4113 | −1.31617 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.32489 | 0.475408 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.14799 | −0.683753 | −0.341876 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341876 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6401 | 1.23685 | 0.618424 | − | 0.785845i | \(-0.287772\pi\) | ||||
0.618424 | + | 0.785845i | \(0.287772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1880 | −1.04881 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.89879 | −0.139602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9753 | 0.943812 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.67720 | 0.555503 | 0.277752 | − | 0.960653i | \(-0.410411\pi\) | ||||
0.277752 | + | 0.960653i | \(0.410411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.6695 | −1.41584 | −0.707922 | − | 0.706290i | \(-0.750367\pi\) | ||||
−0.707922 | + | 0.706290i | \(0.750367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.902908 | −0.0646586 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.7460 | 1.62059 | 0.810294 | − | 0.586024i | \(-0.199308\pi\) | ||||
0.810294 | + | 0.586024i | \(0.199308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.85748 | −0.486114 | −0.243057 | − | 0.970012i | \(-0.578150\pi\) | ||||
−0.243057 | + | 0.970012i | \(0.578150\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.92296 | −0.276704 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.60226 | −0.252829 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0459776 | 0.00321122 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.839775 | 0.0583684 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5024 | 0.791858 | 0.395929 | − | 0.918281i | \(-0.370423\pi\) | ||||
0.395929 | + | 0.918281i | \(0.370423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.9051 | 1.70647 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.706114 | −0.0481566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.9051 | −1.28336 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.2849 | −1.57345 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.4096 | 1.37290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.2692 | −1.08946 | −0.544732 | − | 0.838610i | \(-0.683368\pi\) | ||||
−0.544732 | + | 0.838610i | \(0.683368\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.91456 | −0.394304 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.20790 | −0.412033 | −0.206016 | − | 0.978549i | \(-0.566050\pi\) | ||||
−0.206016 | + | 0.978549i | \(0.566050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.6401 | 1.36393 | 0.681967 | − | 0.731382i | \(-0.261125\pi\) | ||||
0.681967 | + | 0.731382i | \(0.261125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.2731 | 0.673013 | 0.336506 | − | 0.941681i | \(-0.390755\pi\) | ||||
0.336506 | + | 0.941681i | \(0.390755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.954516 | −0.0622657 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.53552 | 0.229657 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0419 | −1.29641 | −0.648203 | − | 0.761468i | \(-0.724479\pi\) | ||||
−0.648203 | + | 0.761468i | \(0.724479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.87625 | 0.442938 | 0.221469 | − | 0.975167i | \(-0.428915\pi\) | ||||
0.221469 | + | 0.975167i | \(0.428915\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7103 | 0.751216 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.860964 | 0.0550050 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.4397 | −0.791518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.63928 | 0.610865 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.20159 | 0.328321 | 0.164161 | − | 0.986434i | \(-0.447508\pi\) | ||||
0.164161 | + | 0.986434i | \(0.447508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.53964 | −0.159039 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.5971 | 1.16006 | 0.580029 | − | 0.814596i | \(-0.303041\pi\) | ||||
0.580029 | + | 0.814596i | \(0.303041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.5932 | −2.52234 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22367 | −0.0757435 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.27857 | 0.0788397 | 0.0394199 | − | 0.999223i | \(-0.487449\pi\) | ||||
0.0394199 | + | 0.999223i | \(0.487449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.61668 | −0.0993120 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9187 | −0.790614 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.69372 | −0.164239 | −0.0821195 | − | 0.996622i | \(-0.526169\pi\) | ||||
−0.0821195 | + | 0.996622i | \(0.526169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.3875 | −0.630996 | −0.315498 | − | 0.948926i | \(-0.602171\pi\) | ||||
−0.315498 | + | 0.948926i | \(0.602171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.3028 | −1.16826 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.31046 | −0.439243 | −0.219622 | − | 0.975585i | \(-0.570482\pi\) | ||||
−0.219622 | + | 0.975585i | \(0.570482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.42198 | −0.384474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7452 | 0.998937 | 0.499468 | − | 0.866332i | \(-0.333529\pi\) | ||||
0.499468 | + | 0.866332i | \(0.333529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4783 | 1.21731 | 0.608656 | − | 0.793434i | \(-0.291709\pi\) | ||||
0.608656 | + | 0.793434i | \(0.291709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.54792 | 0.0916908 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.982932 | 0.0580206 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.4068 | 2.37687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.3386 | −0.840546 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.6613 | −1.09020 | −0.545102 | − | 0.838370i | \(-0.683509\pi\) | ||||
−0.545102 | + | 0.838370i | \(0.683509\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.506061 | −0.0294640 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.90207 | 0.110000 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0956 | −0.870098 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.23487 | −0.473081 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.13520 | 0.0650012 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2802 | 0.929160 | 0.464580 | − | 0.885531i | \(-0.346205\pi\) | ||||
0.464580 | + | 0.885531i | \(0.346205\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.8339 | 1.75408 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4521 | −0.592683 | −0.296342 | − | 0.955082i | \(-0.595767\pi\) | ||||
−0.296342 | + | 0.955082i | \(0.595767\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.42327 | 0.476111 | 0.238056 | − | 0.971252i | \(-0.423490\pi\) | ||||
0.238056 | + | 0.971252i | \(0.423490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.681878 | 0.0384195 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.4686 | −1.20580 | −0.602898 | − | 0.797818i | \(-0.705988\pi\) | ||||
−0.602898 | + | 0.797818i | \(0.705988\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.06210 | −0.0592804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.9896 | −1.94687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.3964 | −0.743096 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.583397 | 0.0322619 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.4061 | −1.12502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5452 | 1.18423 | 0.592117 | − | 0.805852i | \(-0.298292\pi\) | ||||
0.592117 | + | 0.805852i | \(0.298292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7894 | −0.755652 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.313881 | 0.0171491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2058 | −0.610419 | −0.305210 | − | 0.952285i | \(-0.598727\pi\) | ||||
−0.305210 | + | 0.952285i | \(0.598727\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.6793 | 1.28608 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.10121 | −0.329434 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.236682 | −0.0127425 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5363 | −0.672985 | −0.336493 | − | 0.941686i | \(-0.609241\pi\) | ||||
−0.336493 | + | 0.941686i | \(0.609241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0821 | 0.860853 | 0.430426 | − | 0.902626i | \(-0.358363\pi\) | ||||
0.430426 | + | 0.902626i | \(0.358363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.98323 | 0.532865 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.9450 | −0.901892 | −0.450946 | − | 0.892551i | \(-0.648913\pi\) | ||||
−0.450946 | + | 0.892551i | \(0.648913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.99268 | −0.105761 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −54.2938 | −2.87353 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.6740 | −1.30224 | −0.651122 | − | 0.758973i | \(-0.725701\pi\) | ||||
−0.651122 | + | 0.758973i | \(0.725701\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32624 | 0.122434 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.86305 | 0.0975167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9490 | −1.61552 | −0.807762 | − | 0.589508i | \(-0.799322\pi\) | ||||
−0.807762 | + | 0.589508i | \(0.799322\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.333898 | 0.0173820 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.5622 | −1.79438 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6908 | −0.864217 | −0.432108 | − | 0.901822i | \(-0.642230\pi\) | ||||
−0.432108 | + | 0.901822i | \(0.642230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.34291 | 0.172627 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.77159 | −0.142744 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.6090 | −0.853146 | −0.426573 | − | 0.904453i | \(-0.640279\pi\) | ||||
−0.426573 | + | 0.904453i | \(0.640279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.0387 | 1.79509 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.72945 | −0.139469 | −0.0697343 | − | 0.997566i | \(-0.522215\pi\) | ||||
−0.0697343 | + | 0.997566i | \(0.522215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.12793 | −0.260668 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2712 | 0.774283 | 0.387141 | − | 0.922020i | \(-0.373462\pi\) | ||||
0.387141 | + | 0.922020i | \(0.373462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.35003 | 0.270563 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2819 | 0.518651 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.282881 | −0.0142333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.4810 | −1.07810 | −0.539050 | − | 0.842274i | \(-0.681217\pi\) | ||||
−0.539050 | + | 0.842274i | \(0.681217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.0922 | 1.65668 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.7778 | −1.78666 | −0.893328 | − | 0.449405i | \(-0.851636\pi\) | ||||
−0.893328 | + | 0.449405i | \(0.851636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5456 | −0.724570 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.82655 | −0.0907618 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5601 | −0.522161 | −0.261081 | − | 0.965317i | \(-0.584079\pi\) | ||||
−0.261081 | + | 0.965317i | \(0.584079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.15153 | −0.303433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.8188 | −0.532360 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.771250 | −0.0378592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.9720 | −0.537301 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.9952 | 1.46536 | 0.732680 | − | 0.680573i | \(-0.238269\pi\) | ||||
0.732680 | + | 0.680573i | \(0.238269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.2049 | 1.03346 | 0.516731 | − | 0.856148i | \(-0.327149\pi\) | ||||
0.516731 | + | 0.856148i | \(0.327149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.93188 | −0.337039 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.6805 | −1.82777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.2688 | 1.17445 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.4577 | −0.648232 | −0.324116 | − | 0.946017i | \(-0.605067\pi\) | ||||
−0.324116 | + | 0.946017i | \(0.605067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9161 | 1.43768 | 0.718838 | − | 0.695178i | \(-0.244674\pi\) | ||||
0.718838 | + | 0.695178i | \(0.244674\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.344880 | 0.0165357 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.26086 | −0.155988 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.1644 | −1.58285 | −0.791425 | − | 0.611266i | \(-0.790661\pi\) | ||||
−0.791425 | + | 0.611266i | \(0.790661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.25248 | 0.297737 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.8197 | −1.32175 | −0.660877 | − | 0.750495i | \(-0.729815\pi\) | ||||
−0.660877 | + | 0.750495i | \(0.729815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03364 | 0.0489994 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.9141 | −0.563518 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.29588 | −0.344314 | −0.172157 | − | 0.985070i | \(-0.555074\pi\) | ||||
−0.172157 | + | 0.985070i | \(0.555074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.46183 | −0.350587 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.54444 | 0.0724044 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.1301 | 0.754534 | 0.377267 | − | 0.926105i | \(-0.376864\pi\) | ||||
0.377267 | + | 0.926105i | \(0.376864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.0802 | 1.31067 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.4253 | −0.671851 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7906 | 0.919748 | 0.459874 | − | 0.887984i | \(-0.347895\pi\) | ||||
0.459874 | + | 0.887984i | \(0.347895\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.80997 | 0.0839354 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.8183 | 1.75002 | 0.875012 | − | 0.484102i | \(-0.160853\pi\) | ||||
0.875012 | + | 0.484102i | \(0.160853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.71029 | 0.309853 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.297110 | 0.0136901 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.9663 | 1.05377 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.7407 | −0.537568 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.3330 | −1.75148 | −0.875739 | − | 0.482785i | \(-0.839625\pi\) | ||||
−0.875739 | + | 0.482785i | \(0.839625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.2326 | −1.42408 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.05991 | −0.230234 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.14725 | 0.0520940 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4584 | 0.519227 | 0.259614 | − | 0.965713i | \(-0.416405\pi\) | ||||
0.259614 | + | 0.965713i | \(0.416405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.5522 | 1.33639 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.4874 | −1.10510 | −0.552550 | − | 0.833480i | \(-0.686345\pi\) | ||||
−0.552550 | + | 0.833480i | \(0.686345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.79577 | −0.351104 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.6005 | −1.91089 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.2088 | 0.680839 | 0.340420 | − | 0.940274i | \(-0.389431\pi\) | ||||
0.340420 | + | 0.940274i | \(0.389431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.6953 | −1.59475 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.6392 | 1.18778 | 0.593891 | − | 0.804545i | \(-0.297591\pi\) | ||||
0.593891 | + | 0.804545i | \(0.297591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.658882 | 0.0293198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.7564 | 0.522121 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.2919 | −0.677800 | −0.338900 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338900 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.8293 | 1.76194 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.1150 | −0.755644 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.46706 | −0.108712 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 37.3391 | 1.63901 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.6400 | −1.51761 | −0.758804 | − | 0.651319i | \(-0.774216\pi\) | ||||
−0.758804 | + | 0.651319i | \(0.774216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7107 | 0.730707 | 0.365354 | − | 0.930869i | \(-0.380948\pi\) | ||||
0.365354 | + | 0.930869i | \(0.380948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 35.6371 | 1.55533 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −40.9131 | −1.78220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5014 | −0.978322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.67511 | −0.159486 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.756272 | 0.0327578 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0849796 | 0.00367399 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.7239 | 0.807995 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9233 | −0.555617 | −0.277808 | − | 0.960636i | \(-0.589608\pi\) | ||||
−0.277808 | + | 0.960636i | \(0.589608\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.0585 | −1.46159 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0466782 | −0.00199948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.22204 | −0.223278 | −0.111639 | − | 0.993749i | \(-0.535610\pi\) | ||||
−0.111639 | + | 0.993749i | \(0.535610\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.24403 | 0.351846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.75154 | 0.202422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.04757 | −0.257169 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.88639 | 0.164968 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.8023 | −0.500080 | −0.250040 | − | 0.968236i | \(-0.580444\pi\) | ||||
−0.250040 | + | 0.968236i | \(0.580444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.6147 | −0.491247 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.8583 | −1.55339 | −0.776696 | − | 0.629876i | \(-0.783106\pi\) | ||||
−0.776696 | + | 0.629876i | \(0.783106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.89461 | −0.0797067 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −39.0488 | −1.63989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9651 | 1.13043 | 0.565217 | − | 0.824942i | \(-0.308792\pi\) | ||||
0.565217 | + | 0.824942i | \(0.308792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.3565 | 0.600801 | 0.300400 | − | 0.953813i | \(-0.402880\pi\) | ||||
0.300400 | + | 0.953813i | \(0.402880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.7135 | −0.656442 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.51163 | −0.146445 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5941 | 0.441040 | 0.220520 | − | 0.975382i | \(-0.429225\pi\) | ||||
0.220520 | + | 0.975382i | \(0.429225\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 40.2592 | 1.67311 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.4882 | −0.684044 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.524640 | 0.0216912 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.9943 | 0.825254 | 0.412627 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412627 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9366 | 1.02750 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.5560 | −1.91506 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.8414 | −0.527334 | −0.263667 | − | 0.964614i | \(-0.584932\pi\) | ||||
−0.263667 | + | 0.964614i | \(0.584932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.34410 | 0.178091 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0357 | 0.574444 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3058 | −0.747954 | −0.373977 | − | 0.927438i | \(-0.622006\pi\) | ||||
−0.373977 | + | 0.927438i | \(0.622006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1250 | −0.657753 | −0.328876 | − | 0.944373i | \(-0.606670\pi\) | ||||
−0.328876 | + | 0.944373i | \(0.606670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.27946 | 0.0928269 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.99855 | −0.405829 | −0.202914 | − | 0.979196i | \(-0.565041\pi\) | ||||
−0.202914 | + | 0.979196i | \(0.565041\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.37301 | 0.298770 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.7005 | −0.635176 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.9553 | 1.61378 | 0.806889 | − | 0.590703i | \(-0.201149\pi\) | ||||
0.806889 | + | 0.590703i | \(0.201149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0941059 | −0.00379471 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5485 | −1.14932 | −0.574660 | − | 0.818392i | \(-0.694866\pi\) | ||||
−0.574660 | + | 0.818392i | \(0.694866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0229 | 0.523434 | 0.261717 | − | 0.965145i | \(-0.415711\pi\) | ||||
0.261717 | + | 0.965145i | \(0.415711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.61694 | 0.105014 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.0977 | 0.885327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5984 | 0.983937 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −87.8491 | −3.50277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4294 | 0.773471 | 0.386736 | − | 0.922191i | \(-0.373603\pi\) | ||||
0.386736 | + | 0.922191i | \(0.373603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.5428 | −0.935744 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.80349 | −0.111253 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.1617 | 0.561108 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.4712 | −0.572473 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.5658 | −0.575314 | −0.287657 | − | 0.957734i | \(-0.592876\pi\) | ||||
−0.287657 | + | 0.957734i | \(0.592876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.61127 | −0.142415 | −0.0712073 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712073 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44526 | 0.0569069 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.65811 | 0.261757 | 0.130879 | − | 0.991398i | \(-0.458220\pi\) | ||||
0.130879 | + | 0.991398i | \(0.458220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.6944 | 1.51655 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.63680 | −0.103186 | −0.0515929 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515929 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.822663 | −0.0321441 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.5299 | 0.527850 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2059 | −0.709200 | −0.354600 | − | 0.935018i | \(-0.615383\pi\) | ||||
−0.354600 | + | 0.935018i | \(0.615383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.6750 | −1.46539 | −0.732693 | − | 0.680559i | \(-0.761737\pi\) | ||||
−0.732693 | + | 0.680559i | \(0.761737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −41.7738 | −1.62236 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.64774 | −0.102675 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.726527 | −0.0281312 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.2993 | 1.28743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3044 | −0.667037 | −0.333518 | − | 0.942744i | \(-0.608236\pi\) | ||||
−0.333518 | + | 0.942744i | \(0.608236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.4312 | −0.709416 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.61579 | 0.369565 | 0.184782 | − | 0.982779i | \(-0.440842\pi\) | ||||
0.184782 | + | 0.982779i | \(0.440842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.5265 | 0.941240 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.7062 | 0.486902 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.2554 | −1.27248 | −0.636241 | − | 0.771491i | \(-0.719511\pi\) | ||||
−0.636241 | + | 0.771491i | \(0.719511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.492191 | 0.0188056 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −42.2456 | −1.61177 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.5923 | −1.01309 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0510 | 0.648649 | 0.324324 | − | 0.945946i | \(-0.394863\pi\) | ||||
0.324324 | + | 0.945946i | \(0.394863\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.877881 | 0.0332999 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.12720 | 0.0805733 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.0267 | −0.795304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.6213 | −1.38317 | −0.691583 | − | 0.722297i | \(-0.743087\pi\) | ||||
−0.691583 | + | 0.722297i | \(0.743087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 53.5442 | 2.01946 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.95368 | 0.0735798 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0859 | 0.529754 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5539 | −0.734362 | −0.367181 | − | 0.930149i | \(-0.619677\pi\) | ||||
−0.367181 | + | 0.930149i | \(0.619677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.05434 | −0.0770437 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.81290 | −0.142794 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.0214 | 1.53197 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.53407 | −0.131799 | −0.0658994 | − | 0.997826i | \(-0.520992\pi\) | ||||
−0.0658994 | + | 0.997826i | \(0.520992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.7420 | −1.96421 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0741 | −0.523423 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.11695 | 0.190039 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.02836 | −0.186491 | −0.0932457 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932457 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.49203 | 0.351557 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.6690 | −1.20831 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4073 | −0.421338 | −0.210669 | − | 0.977557i | \(-0.567564\pi\) | ||||
−0.210669 | + | 0.977557i | \(0.567564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.76220 | −0.0649997 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.52359 | −0.166403 | −0.0832014 | − | 0.996533i | \(-0.526514\pi\) | ||||
−0.0832014 | + | 0.996533i | \(0.526514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.4613 | 0.935342 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.1484 | 0.885921 | 0.442960 | − | 0.896541i | \(-0.353928\pi\) | ||||
0.442960 | + | 0.896541i | \(0.353928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.953261 | 0.0349248 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.60097 | −0.204929 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.81673 | 0.0663820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.7617 | −0.538662 | −0.269331 | − | 0.963048i | \(-0.586803\pi\) | ||||
−0.269331 | + | 0.963048i | \(0.586803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.6465 | −0.387980 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.597030 | 0.0217281 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6153 | −0.458511 | −0.229255 | − | 0.973366i | \(-0.573629\pi\) | ||||
−0.229255 | + | 0.973366i | \(0.573629\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.7387 | 0.896779 | 0.448389 | − | 0.893838i | \(-0.351998\pi\) | ||||
0.448389 | + | 0.893838i | \(0.351998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.997910 | −0.0361268 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.47568 | 0.0533532 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.32405 | −0.300564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.37741 | 0.193914 | 0.0969571 | − | 0.995289i | \(-0.469089\pi\) | ||||
0.0969571 | + | 0.995289i | \(0.469089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.0642 | −1.37085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2677 | −0.585108 | −0.292554 | − | 0.956249i | \(-0.594505\pi\) | ||||
−0.292554 | + | 0.956249i | \(0.594505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.8543 | 0.964637 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 83.0852 | 2.98067 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.29653 | −0.0464530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.81325 | −0.136275 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0237721 | −0.000848463 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5653 | 0.661781 | 0.330891 | − | 0.943669i | \(-0.392651\pi\) | ||||
0.330891 | + | 0.943669i | \(0.392651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.61694 | −0.0931654 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.5038 | −1.44015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.6725 | 0.663081 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.30899 | 0.117358 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.1721 | 1.13960 | 0.569798 | − | 0.821785i | \(-0.307022\pi\) | ||||
0.569798 | + | 0.821785i | \(0.307022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.1615 | −1.56232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.50652 | 0.265230 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.404849 | 0.0142691 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.51344 | 0.194082 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.9394 | 1.01745 | 0.508727 | − | 0.860928i | \(-0.330116\pi\) | ||||
0.508727 | + | 0.860928i | \(0.330116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.0382 | −0.352490 | −0.176245 | − | 0.984346i | \(-0.556395\pi\) | ||||
−0.176245 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.2609 | 0.745652 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.36450 | −0.0828249 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.9118 | 0.696626 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.2160 | 0.391919 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0266 | −1.04794 | −0.523968 | − | 0.851738i | \(-0.675549\pi\) | ||||
−0.523968 | + | 0.851738i | \(0.675549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5575 | 1.06517 | 0.532583 | − | 0.846378i | \(-0.321221\pi\) | ||||
0.532583 | + | 0.846378i | \(0.321221\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.87708 | 0.204366 | 0.102183 | − | 0.994766i | \(-0.467417\pi\) | ||||
0.102183 | + | 0.994766i | \(0.467417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.4742 | 0.363783 | 0.181891 | − | 0.983319i | \(-0.441778\pi\) | ||||
0.181891 | + | 0.983319i | \(0.441778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9629 | 0.519056 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.8333 | 1.38014 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.85602 | 0.0988366 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0124 | −0.691730 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.3400 | 1.15102 | 0.575512 | − | 0.817793i | \(-0.304803\pi\) | ||||
0.575512 | + | 0.817793i | \(0.304803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9413 | −0.963495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −34.2737 | −1.18045 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.940645 | −0.0323592 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.9146 | −1.43850 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.18710 | −0.280650 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.6967 | −0.948318 | −0.474159 | − | 0.880439i | \(-0.657248\pi\) | ||||
−0.474159 | + | 0.880439i | \(0.657248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.899428 | −0.0307598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.13818 | 0.0730387 | 0.0365194 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365194 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.06982 | −0.207099 | −0.103550 | − | 0.994624i | \(-0.533020\pi\) | ||||
−0.103550 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.01184 | −0.0685633 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.7979 | −1.01433 | −0.507166 | − | 0.861848i | \(-0.669307\pi\) | ||||
−0.507166 | + | 0.861848i | \(0.669307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.98755 | −0.101580 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −82.7038 | −2.80877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.16293 | 0.174939 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.33155 | 0.281980 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.71811 | −0.193307 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.0577 | −1.25135 | −0.625675 | − | 0.780084i | \(-0.715176\pi\) | ||||
−0.625675 | + | 0.780084i | \(0.715176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.1954 | 1.28830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.6956 | −0.360345 | −0.180172 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180172 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0960 | −0.541675 | −0.270837 | − | 0.962625i | \(-0.587301\pi\) | ||||
−0.270837 | + | 0.962625i | \(0.587301\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.03579 | 0.0348178 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.2843 | 0.882540 | 0.441270 | − | 0.897374i | \(-0.354528\pi\) | ||||
0.441270 | + | 0.897374i | \(0.354528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.9343 | −2.01013 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.9166 | 0.900728 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.49812 | −0.0500766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.89312 | −0.129987 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.55594 | 0.185301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.7972 | −2.49186 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.8974 | 1.02820 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.72506 | 0.0905841 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.59235 | −0.218895 | −0.109448 | − | 0.993993i | \(-0.534908\pi\) | ||||
−0.109448 | + | 0.993993i | \(0.534908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.78492 | 0.158706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.1679 | 1.46335 | 0.731675 | − | 0.681654i | \(-0.238739\pi\) | ||||
0.731675 | + | 0.681654i | \(0.238739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.32350 | −0.0768124 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.5873 | −0.580783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.4754 | 1.03828 | 0.519138 | − | 0.854690i | \(-0.326253\pi\) | ||||
0.519138 | + | 0.854690i | \(0.326253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.3219 | −1.09799 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.7770 | −1.07887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.6620 | 1.89592 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.9163 | −0.588447 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.4685 | −1.06526 | −0.532628 | − | 0.846349i | \(-0.678796\pi\) | ||||
−0.532628 | + | 0.846349i | \(0.678796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.2785 | −0.795695 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.3931 | 0.700378 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0094 | 0.947695 | 0.473847 | − | 0.880607i | \(-0.342865\pi\) | ||||
0.473847 | + | 0.880607i | \(0.342865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.2405 | −0.562624 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.88999 | 0.192008 | 0.0960042 | − | 0.995381i | \(-0.469394\pi\) | ||||
0.0960042 | + | 0.995381i | \(0.469394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.198244 | 0.00645572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.12489 | 0.0691228 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.2319 | 1.69731 | 0.848655 | − | 0.528947i | \(-0.177413\pi\) | ||||
0.848655 | + | 0.528947i | \(0.177413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.6448 | 0.994773 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.9414 | 1.42490 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.4195 | 1.24453 | 0.622265 | − | 0.782807i | \(-0.286213\pi\) | ||||
0.622265 | + | 0.782807i | \(0.286213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.25726 | 0.0406839 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5223 | 0.339783 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.84181 | −0.0594131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.617138 | 0.0198870 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.22118 | −0.103693 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.8436 | 1.63502 | 0.817509 | − | 0.575915i | \(-0.195354\pi\) | ||||
0.817509 | + | 0.575915i | \(0.195354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 71.6159 | 2.30063 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.89992 | −0.253521 | −0.126760 | − | 0.991933i | \(-0.540458\pi\) | ||||
−0.126760 | + | 0.991933i | \(0.540458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7678 | 0.601667 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.4193 | 0.878121 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0190 | −0.512492 | −0.256246 | − | 0.966612i | \(-0.582486\pi\) | ||||
−0.256246 | + | 0.966612i | \(0.582486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.338986 | −0.0108230 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.4809 | 1.86525 | 0.932625 | − | 0.360848i | \(-0.117513\pi\) | ||||
0.932625 | + | 0.360848i | \(0.117513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.72500 | 0.118688 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.7667 | 1.32945 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.04459 | −0.0968123 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.1741 | 0.545552 | 0.272776 | − | 0.962078i | \(-0.412058\pi\) | ||||
0.272776 | + | 0.962078i | \(0.412058\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44.0983 | −1.39942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.12302 | −0.0356020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.5451 | −1.31575 | −0.657874 | − | 0.753128i | \(-0.728544\pi\) | ||||
−0.657874 | + | 0.753128i | \(0.728544\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −42.9709 | −1.35954 |
(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 | 7744.2.a.ds.1.1 | 4 | ||
4.3 | odd | 2 | 7744.2.a.dh.1.4 | 4 | |||
8.3 | odd | 2 | 968.2.a.m.1.1 | 4 | |||
8.5 | even | 2 | 1936.2.a.bc.1.4 | 4 | |||
11.2 | odd | 10 | 704.2.m.i.257.1 | 8 | |||
11.6 | odd | 10 | 704.2.m.i.641.1 | 8 | |||
11.10 | odd | 2 | 7744.2.a.dr.1.1 | 4 | |||
24.11 | even | 2 | 8712.2.a.cd.1.3 | 4 | |||
44.35 | even | 10 | 704.2.m.l.257.2 | 8 | |||
44.39 | even | 10 | 704.2.m.l.641.2 | 8 | |||
44.43 | even | 2 | 7744.2.a.di.1.4 | 4 | |||
88.3 | odd | 10 | 968.2.i.t.9.2 | 8 | |||
88.13 | odd | 10 | 176.2.m.d.81.2 | 8 | |||
88.19 | even | 10 | 968.2.i.s.9.2 | 8 | |||
88.21 | odd | 2 | 1936.2.a.bb.1.4 | 4 | |||
88.27 | odd | 10 | 968.2.i.p.729.1 | 8 | |||
88.35 | even | 10 | 88.2.i.b.81.1 | yes | 8 | ||
88.43 | even | 2 | 968.2.a.n.1.1 | 4 | |||
88.51 | even | 10 | 968.2.i.s.753.2 | 8 | |||
88.59 | odd | 10 | 968.2.i.t.753.2 | 8 | |||
88.61 | odd | 10 | 176.2.m.d.113.2 | 8 | |||
88.75 | odd | 10 | 968.2.i.p.81.1 | 8 | |||
88.83 | even | 10 | 88.2.i.b.25.1 | ✓ | 8 | ||
264.35 | odd | 10 | 792.2.r.g.433.1 | 8 | |||
264.83 | odd | 10 | 792.2.r.g.289.1 | 8 | |||
264.131 | odd | 2 | 8712.2.a.ce.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.2.i.b.25.1 | ✓ | 8 | 88.83 | even | 10 | ||
88.2.i.b.81.1 | yes | 8 | 88.35 | even | 10 | ||
176.2.m.d.81.2 | 8 | 88.13 | odd | 10 | |||
176.2.m.d.113.2 | 8 | 88.61 | odd | 10 | |||
704.2.m.i.257.1 | 8 | 11.2 | odd | 10 | |||
704.2.m.i.641.1 | 8 | 11.6 | odd | 10 | |||
704.2.m.l.257.2 | 8 | 44.35 | even | 10 | |||
704.2.m.l.641.2 | 8 | 44.39 | even | 10 | |||
792.2.r.g.289.1 | 8 | 264.83 | odd | 10 | |||
792.2.r.g.433.1 | 8 | 264.35 | odd | 10 | |||
968.2.a.m.1.1 | 4 | 8.3 | odd | 2 | |||
968.2.a.n.1.1 | 4 | 88.43 | even | 2 | |||
968.2.i.p.81.1 | 8 | 88.75 | odd | 10 | |||
968.2.i.p.729.1 | 8 | 88.27 | odd | 10 | |||
968.2.i.s.9.2 | 8 | 88.19 | even | 10 | |||
968.2.i.s.753.2 | 8 | 88.51 | even | 10 | |||
968.2.i.t.9.2 | 8 | 88.3 | odd | 10 | |||
968.2.i.t.753.2 | 8 | 88.59 | odd | 10 | |||
1936.2.a.bb.1.4 | 4 | 88.21 | odd | 2 | |||
1936.2.a.bc.1.4 | 4 | 8.5 | even | 2 | |||
7744.2.a.dh.1.4 | 4 | 4.3 | odd | 2 | |||
7744.2.a.di.1.4 | 4 | 44.43 | even | 2 | |||
7744.2.a.dr.1.1 | 4 | 11.10 | odd | 2 | |||
7744.2.a.ds.1.1 | 4 | 1.1 | even | 1 | trivial | ||
8712.2.a.cd.1.3 | 4 | 24.11 | even | 2 | |||
8712.2.a.ce.1.3 | 4 | 264.131 | odd | 2 |