Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.85410 | −1.83468 | −0.917339 | − | 0.398107i | \(-0.869667\pi\) | ||||
−0.917339 | + | 0.398107i | \(0.869667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.38197 | 1.01970 | 0.509851 | − | 0.860263i | \(-0.329701\pi\) | ||||
0.509851 | + | 0.860263i | \(0.329701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.381966 | 0.105938 | 0.0529692 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529692 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.85410 | −1.41983 | −0.709914 | − | 0.704288i | \(-0.751266\pi\) | ||||
−0.709914 | + | 0.704288i | \(0.751266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.85410 | 1.57244 | 0.786219 | − | 0.617947i | \(-0.212036\pi\) | ||||
0.786219 | + | 0.617947i | \(0.212036\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70820 | 0.688596 | 0.344298 | − | 0.938860i | \(-0.388117\pi\) | ||||
0.344298 | + | 0.938860i | \(0.388117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.85410 | 1.59024 | 0.795122 | − | 0.606450i | \(-0.207407\pi\) | ||||
0.795122 | + | 0.606450i | \(0.207407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.09017 | 0.363852 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70820 | 0.609625 | 0.304812 | − | 0.952412i | \(-0.401406\pi\) | ||||
0.304812 | + | 0.952412i | \(0.401406\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.236068 | 0.0378011 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.38197 | −0.528174 | −0.264087 | − | 0.964499i | \(-0.585071\pi\) | ||||
−0.264087 | + | 0.964499i | \(0.585071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.76393 | −1.03149 | −0.515745 | − | 0.856742i | \(-0.672485\pi\) | ||||
−0.515745 | + | 0.856742i | \(0.672485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7082 | 1.70782 | 0.853909 | − | 0.520423i | \(-0.174226\pi\) | ||||
0.853909 | + | 0.520423i | \(0.174226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.5623 | 2.36604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.61803 | −0.506626 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.23607 | 0.561081 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85410 | −0.493467 | −0.246734 | − | 0.969083i | \(-0.579357\pi\) | ||||
−0.246734 | + | 0.969083i | \(0.579357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.7082 | 1.60108 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.763932 | −0.0933292 | −0.0466646 | − | 0.998911i | \(-0.514859\pi\) | ||||
−0.0466646 | + | 0.998911i | \(0.514859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.618034 | −0.0744025 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.61803 | −0.310703 | −0.155352 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155352 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.52786 | −0.881070 | −0.440535 | − | 0.897735i | \(-0.645211\pi\) | ||||
−0.440535 | + | 0.897735i | \(0.645211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.4164 | −1.87082 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.70820 | −0.642223 | −0.321112 | − | 0.947041i | \(-0.604056\pi\) | ||||
−0.321112 | + | 0.947041i | \(0.604056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.70820 | 0.626557 | 0.313278 | − | 0.949661i | \(-0.398573\pi\) | ||||
0.313278 | + | 0.949661i | \(0.398573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.29180 | 0.245706 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.70820 | −1.02907 | −0.514534 | − | 0.857470i | \(-0.672035\pi\) | ||||
−0.514534 | + | 0.857470i | \(0.672035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85410 | −0.194363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.47214 | 0.567434 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0344 | −1.62805 | −0.814025 | − | 0.580829i | \(-0.802728\pi\) | ||||
−0.814025 | + | 0.580829i | \(0.802728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.85410 | −0.889871 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4721 | −1.04202 | −0.521008 | − | 0.853552i | \(-0.674444\pi\) | ||||
−0.521008 | + | 0.853552i | \(0.674444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.14590 | −0.408507 | −0.204254 | − | 0.978918i | \(-0.565477\pi\) | ||||
−0.204254 | + | 0.978918i | \(0.565477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.70820 | 0.165138 | 0.0825692 | − | 0.996585i | \(-0.473687\pi\) | ||||
0.0825692 | + | 0.996585i | \(0.473687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5623 | −1.20325 | −0.601625 | − | 0.798778i | \(-0.705480\pi\) | ||||
−0.601625 | + | 0.798778i | \(0.705480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29180 | 0.217528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4164 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.4164 | 2.60493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.437694 | 0.0397904 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.09017 | −0.188464 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.70820 | −0.329050 | −0.164525 | − | 0.986373i | \(-0.552609\pi\) | ||||
−0.164525 | + | 0.986373i | \(0.552609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.18034 | −0.368058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.18034 | −0.714720 | −0.357360 | − | 0.933967i | \(-0.616323\pi\) | ||||
−0.357360 | + | 0.933967i | \(0.616323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −33.2705 | −2.88492 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.14590 | −0.610515 | −0.305258 | − | 0.952270i | \(-0.598743\pi\) | ||||
−0.305258 | + | 0.952270i | \(0.598743\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.7082 | −1.50199 | −0.750995 | − | 0.660308i | \(-0.770426\pi\) | ||||
−0.750995 | + | 0.660308i | \(0.770426\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.23607 | 0.609387 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.29180 | 0.108025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.2361 | 0.844257 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.381966 | −0.0312919 | −0.0156459 | − | 0.999878i | \(-0.504980\pi\) | ||||
−0.0156459 | + | 0.999878i | \(0.504980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2705 | 1.56821 | 0.784106 | − | 0.620627i | \(-0.213122\pi\) | ||||
0.784106 | + | 0.620627i | \(0.213122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.3262 | 1.23905 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7082 | 1.25365 | 0.626826 | − | 0.779160i | \(-0.284354\pi\) | ||||
0.626826 | + | 0.779160i | \(0.284354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.23607 | −0.0980266 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.85410 | 0.382557 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.03444 | −0.550980 | −0.275490 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275490 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.70820 | −0.286949 | −0.143475 | − | 0.989654i | \(-0.545828\pi\) | ||||
−0.143475 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8541 | −0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.9443 | −1.37223 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.56231 | −0.270837 | −0.135419 | − | 0.990788i | \(-0.543238\pi\) | ||||
−0.135419 | + | 0.990788i | \(0.543238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.70820 | 0.278726 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.4721 | −1.23119 | −0.615593 | − | 0.788065i | \(-0.711083\pi\) | ||||
−0.615593 | + | 0.788065i | \(0.711083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.56231 | −0.339114 | −0.169557 | − | 0.985520i | \(-0.554234\pi\) | ||||
−0.169557 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.38197 | −0.176080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.7984 | −1.44780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.8541 | 1.22596 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41641 | 0.102488 | 0.0512438 | − | 0.998686i | \(-0.483681\pi\) | ||||
0.0512438 | + | 0.998686i | \(0.483681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.29180 | −0.164967 | −0.0824835 | − | 0.996592i | \(-0.526285\pi\) | ||||
−0.0824835 | + | 0.996592i | \(0.526285\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.437694 | −0.0311844 | −0.0155922 | − | 0.999878i | \(-0.504963\pi\) | ||||
−0.0155922 | + | 0.999878i | \(0.504963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4164 | 1.09284 | 0.546420 | − | 0.837511i | \(-0.315990\pi\) | ||||
0.546420 | + | 0.837511i | \(0.315990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.472136 | −0.0333019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.0000 | −1.26335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.61803 | 0.181966 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1803 | 1.60342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.70820 | −0.392969 | −0.196484 | − | 0.980507i | \(-0.562953\pi\) | ||||
−0.196484 | + | 0.980507i | \(0.562953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.61803 | −0.110866 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −42.9787 | −2.91759 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.65248 | −0.314385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.23607 | −0.150414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3607 | 1.49738 | 0.748691 | − | 0.662919i | \(-0.230683\pi\) | ||||
0.748691 | + | 0.662919i | \(0.230683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.7082 | −1.57357 | −0.786784 | − | 0.617228i | \(-0.788256\pi\) | ||||
−0.786784 | + | 0.617228i | \(0.788256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.1459 | −0.667551 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.1246 | −1.25289 | −0.626447 | − | 0.779464i | \(-0.715492\pi\) | ||||
−0.626447 | + | 0.779464i | \(0.715492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.52786 | −0.229159 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.52786 | 0.0988293 | 0.0494147 | − | 0.998778i | \(-0.484264\pi\) | ||||
0.0494147 | + | 0.998778i | \(0.484264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.61803 | 0.166582 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.52786 | 0.223569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.79837 | −0.492229 | −0.246114 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246114 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.38197 | −0.212622 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4164 | 0.961649 | 0.480825 | − | 0.876817i | \(-0.340337\pi\) | ||||
0.480825 | + | 0.876817i | \(0.340337\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.70820 | −0.600923 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.2705 | −0.941620 | −0.470810 | − | 0.882235i | \(-0.656038\pi\) | ||||
−0.470810 | + | 0.882235i | \(0.656038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4721 | −0.638497 | −0.319249 | − | 0.947671i | \(-0.603431\pi\) | ||||
−0.319249 | + | 0.947671i | \(0.603431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1459 | −1.16303 | −0.581515 | − | 0.813536i | \(-0.697540\pi\) | ||||
−0.581515 | + | 0.813536i | \(0.697540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.14590 | −0.0693529 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4721 | 0.989715 | 0.494857 | − | 0.868974i | \(-0.335220\pi\) | ||||
0.494857 | + | 0.868974i | \(0.335220\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.1803 | −1.38777 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.652476 | −0.0389234 | −0.0194617 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194617 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.05573 | −0.181644 | −0.0908221 | − | 0.995867i | \(-0.528949\pi\) | ||||
−0.0908221 | + | 0.995867i | \(0.528949\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.4164 | 0.969030 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.2705 | 1.01591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.90983 | −0.580925 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.7082 | −1.61873 | −0.809365 | − | 0.587306i | \(-0.800189\pi\) | ||||
−0.809365 | + | 0.587306i | \(0.800189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.7426 | −0.681377 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.381966 | −0.0220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.8328 | 1.89245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.47214 | −0.371814 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.1459 | −0.579057 | −0.289528 | − | 0.957169i | \(-0.593498\pi\) | ||||
−0.289528 | + | 0.957169i | \(0.593498\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.56231 | −0.145764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5279 | 0.767095 | 0.383547 | − | 0.923521i | \(-0.374702\pi\) | ||||
0.383547 | + | 0.923521i | \(0.374702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1459 | 1.08219 | 0.541095 | − | 0.840961i | \(-0.318010\pi\) | ||||
0.541095 | + | 0.840961i | \(0.318010\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.2705 | 1.47550 | 0.737749 | − | 0.675075i | \(-0.235889\pi\) | ||||
0.737749 | + | 0.675075i | \(0.235889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5410 | 0.702162 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05573 | 0.0589250 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −40.1246 | −2.23259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.76393 | −0.429346 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −56.8328 | −3.13329 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.1246 | −0.831324 | −0.415662 | − | 0.909519i | \(-0.636450\pi\) | ||||
−0.415662 | + | 0.909519i | \(0.636450\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.70820 | −0.532006 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.61803 | −0.306034 | −0.153017 | − | 0.988224i | \(-0.548899\pi\) | ||||
−0.153017 | + | 0.988224i | \(0.548899\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.29180 | 0.450349 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.9443 | 1.62157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −46.4164 | −2.50625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.56231 | 0.298600 | 0.149300 | − | 0.988792i | \(-0.452298\pi\) | ||||
0.149300 | + | 0.988792i | \(0.452298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.2918 | 0.765022 | 0.382511 | − | 0.923951i | \(-0.375059\pi\) | ||||
0.382511 | + | 0.923951i | \(0.375059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.32624 | −0.0707893 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.00000 | 0.425797 | 0.212899 | − | 0.977074i | \(-0.431710\pi\) | ||||
0.212899 | + | 0.977074i | \(0.431710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5623 | 0.929496 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.9787 | 1.47256 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.270510 | 0.0141981 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.0000 | −0.626395 | −0.313197 | − | 0.949688i | \(-0.601400\pi\) | ||||
−0.313197 | + | 0.949688i | \(0.601400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.85410 | 0.460926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.70820 | 0.504025 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.05573 | −0.158220 | −0.0791098 | − | 0.996866i | \(-0.525208\pi\) | ||||
−0.0791098 | + | 0.996866i | \(0.525208\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.41641 | 0.0729487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.27051 | −0.476194 | −0.238097 | − | 0.971241i | \(-0.576524\pi\) | ||||
−0.238097 | + | 0.971241i | \(0.576524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.29180 | −0.117412 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.4164 | −1.40091 | −0.700456 | − | 0.713695i | \(-0.747020\pi\) | ||||
−0.700456 | + | 0.713695i | \(0.747020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.7082 | 0.900159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.67376 | −0.287671 | −0.143836 | − | 0.989602i | \(-0.545944\pi\) | ||||
−0.143836 | + | 0.989602i | \(0.545944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.85410 | 0.296055 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.05573 | −0.255028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.5623 | 1.78482 | 0.892410 | − | 0.451224i | \(-0.149013\pi\) | ||||
0.892410 | + | 0.451224i | \(0.149013\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.5623 | −1.02940 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.4721 | −1.72146 | −0.860728 | − | 0.509065i | \(-0.829991\pi\) | ||||
−0.860728 | + | 0.509065i | \(0.829991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.38197 | 0.168468 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.5410 | 0.621635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.56231 | −0.324485 | −0.162243 | − | 0.986751i | \(-0.551873\pi\) | ||||
−0.162243 | + | 0.986751i | \(0.551873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.41641 | −0.217845 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.1246 | −1.43313 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.9443 | −0.535943 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.88854 | −0.287674 | −0.143837 | − | 0.989601i | \(-0.545944\pi\) | ||||
−0.143837 | + | 0.989601i | \(0.545944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.85410 | 0.334048 | 0.167024 | − | 0.985953i | \(-0.446584\pi\) | ||||
0.167024 | + | 0.985953i | \(0.446584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.6525 | −1.49037 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.7082 | 0.905353 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.798374 | 0.0385459 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.76393 | 0.325807 | 0.162904 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162904 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6180 | −1.42335 | −0.711676 | − | 0.702508i | \(-0.752064\pi\) | ||||
−0.711676 | + | 0.702508i | \(0.752064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.85410 | −0.327876 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.270510 | 0.0129107 | 0.00645536 | − | 0.999979i | \(-0.497945\pi\) | ||||
0.00645536 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.3607 | −2.06479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.85410 | −0.325648 | −0.162824 | − | 0.986655i | \(-0.552060\pi\) | ||||
−0.162824 | + | 0.986655i | \(0.552060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.236068 | −0.0111656 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.56231 | 0.120923 | 0.0604613 | − | 0.998171i | \(-0.480743\pi\) | ||||
0.0604613 | + | 0.998171i | \(0.480743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4377 | −0.538580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9098 | 0.559573 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.4164 | −1.18893 | −0.594465 | − | 0.804122i | \(-0.702636\pi\) | ||||
−0.594465 | + | 0.804122i | \(0.702636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.3262 | 0.948748 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.3050 | −1.17857 | −0.589285 | − | 0.807926i | \(-0.700590\pi\) | ||||
−0.589285 | + | 0.807926i | \(0.700590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.29180 | 0.106509 | 0.0532544 | − | 0.998581i | \(-0.483041\pi\) | ||||
0.0532544 | + | 0.998581i | \(0.483041\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1246 | 0.792433 | 0.396216 | − | 0.918157i | \(-0.370323\pi\) | ||||
0.396216 | + | 0.918157i | \(0.370323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.70820 | 0.171229 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.70820 | 0.447330 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.8754 | −1.05181 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.23607 | 0.239743 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5279 | 0.892251 | 0.446125 | − | 0.894970i | \(-0.352804\pi\) | ||||
0.446125 | + | 0.894970i | \(0.352804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.41641 | 0.0645826 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.00000 | 0.136505 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.7082 | 0.983693 | 0.491846 | − | 0.870682i | \(-0.336322\pi\) | ||||
0.491846 | + | 0.870682i | \(0.336322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.34752 | −0.196602 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.8328 | 1.21095 | 0.605474 | − | 0.795865i | \(-0.292984\pi\) | ||||
0.605474 | + | 0.795865i | \(0.292984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.7082 | −0.977688 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7082 | 0.570041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.4164 | −0.511069 | −0.255534 | − | 0.966800i | \(-0.582251\pi\) | ||||
−0.255534 | + | 0.966800i | \(0.582251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.29180 | −0.102390 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.8541 | −0.751487 | −0.375744 | − | 0.926724i | \(-0.622613\pi\) | ||||
−0.375744 | + | 0.926724i | \(0.622613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.94427 | −0.352818 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.6525 | −1.09270 | −0.546351 | − | 0.837556i | \(-0.683983\pi\) | ||||
−0.546351 | + | 0.837556i | \(0.683983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.5410 | 1.61648 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.7984 | −1.05072 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.5967 | 1.74146 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.20163 | −0.0966407 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0689 | 0.879234 | 0.439617 | − | 0.898185i | \(-0.355114\pi\) | ||||
0.439617 | + | 0.898185i | \(0.355114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.3607 | 1.76485 | 0.882425 | − | 0.470454i | \(-0.155910\pi\) | ||||
0.882425 | + | 0.470454i | \(0.155910\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.8328 | −2.25787 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.7082 | −0.681678 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.29180 | −0.0559539 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.1803 | −0.439314 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 56.0132 | 2.41266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.4164 | −1.17872 | −0.589362 | − | 0.807869i | \(-0.700621\pi\) | ||||
−0.589362 | + | 0.807869i | \(0.700621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.81966 | −0.121003 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14590 | 0.0489951 | 0.0244975 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0244975 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0902 | 0.430638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.4164 | 1.08278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.7082 | 1.17827 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.58359 | −0.109274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2361 | −0.516607 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.29180 | 0.0965877 | 0.0482938 | − | 0.998833i | \(-0.484622\pi\) | ||||
0.0482938 | + | 0.998833i | \(0.484622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.7082 | −1.16364 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3607 | 1.18894 | 0.594471 | − | 0.804117i | \(-0.297362\pi\) | ||||
0.594471 | + | 0.804117i | \(0.297362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2705 | 1.05754 | 0.528769 | − | 0.848766i | \(-0.322654\pi\) | ||||
0.528769 | + | 0.848766i | \(0.322654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.875388 | 0.0365699 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.2918 | −1.09454 | −0.547271 | − | 0.836956i | \(-0.684333\pi\) | ||||
−0.547271 | + | 0.836956i | \(0.684333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.41641 | −0.0588639 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.7082 | −1.14953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.76393 | −0.280133 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.14590 | 0.0885707 | 0.0442853 | − | 0.999019i | \(-0.485899\pi\) | ||||
0.0442853 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.6869 | 2.50056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.270510 | −0.0111273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.4164 | 1.37225 | 0.686124 | − | 0.727485i | \(-0.259311\pi\) | ||||
0.686124 | + | 0.727485i | \(0.259311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.52786 | 0.389950 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3820 | −0.873643 | −0.436822 | − | 0.899548i | \(-0.643896\pi\) | ||||
−0.436822 | + | 0.899548i | \(0.643896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.14590 | −0.128324 | −0.0641619 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641619 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.9443 | −1.58070 | −0.790350 | − | 0.612656i | \(-0.790101\pi\) | ||||
−0.790350 | + | 0.612656i | \(0.790101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.1246 | −0.450792 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.47214 | 0.180923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.23607 | −0.211483 | −0.105741 | − | 0.994394i | \(-0.533722\pi\) | ||||
−0.105741 | + | 0.994394i | \(0.533722\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5623 | 0.707032 | 0.353516 | − | 0.935429i | \(-0.384986\pi\) | ||||
0.353516 | + | 0.935429i | \(0.384986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1459 | 0.849925 | 0.424963 | − | 0.905211i | \(-0.360287\pi\) | ||||
0.424963 | + | 0.905211i | \(0.360287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.47214 | 0.139332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.1246 | 1.88801 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3262 | 0.572135 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.7082 | −0.865563 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.41641 | −0.136005 | −0.0680025 | − | 0.997685i | \(-0.521663\pi\) | ||||
−0.0680025 | + | 0.997685i | \(0.521663\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.52786 | −0.140220 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.32624 | 0.250655 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.85410 | 0.271144 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.6525 | 1.21070 | 0.605350 | − | 0.795959i | \(-0.293033\pi\) | ||||
0.605350 | + | 0.795959i | \(0.293033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.0132 | −1.38078 | −0.690392 | − | 0.723435i | \(-0.742562\pi\) | ||||
−0.690392 | + | 0.723435i | \(0.742562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.291796 | 0.0114717 | 0.00573584 | − | 0.999984i | \(-0.498174\pi\) | ||||
0.00573584 | + | 0.999984i | \(0.498174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2918 | 0.796523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.5623 | −1.04106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.9787 | −0.468763 | −0.234382 | − | 0.972145i | \(-0.575307\pi\) | ||||
−0.234382 | + | 0.972145i | \(0.575307\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.7082 | 0.768890 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3951 | 1.33782 | 0.668908 | − | 0.743346i | \(-0.266762\pi\) | ||||
0.668908 | + | 0.743346i | \(0.266762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.38197 | −0.0536711 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.70820 | −0.143582 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.8197 | 0.534299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0344 | −0.503189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.2918 | −0.550908 | −0.275454 | − | 0.961314i | \(-0.588828\pi\) | ||||
−0.275454 | + | 0.961314i | \(0.588828\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000 | 1.61419 | 0.807096 | − | 0.590421i | \(-0.201038\pi\) | ||||
0.807096 | + | 0.590421i | \(0.201038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 77.8328 | 2.98695 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6525 | −0.561484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.9787 | −1.37669 | −0.688344 | − | 0.725385i | \(-0.741662\pi\) | ||||
−0.688344 | + | 0.725385i | \(0.741662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.18034 | −0.235795 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.763932 | −0.0291035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1246 | −0.727535 | −0.363767 | − | 0.931490i | \(-0.618510\pi\) | ||||
−0.363767 | + | 0.931490i | \(0.618510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.9787 | 1.63263 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7984 | 0.749917 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.8197 | −0.447061 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9230 | 1.39456 | 0.697281 | − | 0.716798i | \(-0.254393\pi\) | ||||
0.697281 | + | 0.716798i | \(0.254393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4164 | 0.958598 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.8328 | 1.91176 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5623 | −0.434232 | −0.217116 | − | 0.976146i | \(-0.569665\pi\) | ||||
−0.217116 | + | 0.976146i | \(0.569665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9443 | 0.560454 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.85410 | −0.331589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.944272 | 0.0352645 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.4508 | 1.21021 | 0.605106 | − | 0.796145i | \(-0.293131\pi\) | ||||
0.605106 | + | 0.796145i | \(0.293131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.1246 | 0.749480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.23607 | −0.0459699 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.74265 | 0.0646312 | 0.0323156 | − | 0.999478i | \(-0.489712\pi\) | ||||
0.0323156 | + | 0.999478i | \(0.489712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.5967 | 1.46454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8885 | 1.32557 | 0.662787 | − | 0.748808i | \(-0.269374\pi\) | ||||
0.662787 | + | 0.748808i | \(0.269374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.58359 | −0.0951678 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.5410 | 1.19704 | 0.598520 | − | 0.801108i | \(-0.295756\pi\) | ||||
0.598520 | + | 0.801108i | \(0.295756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.61803 | 0.0594400 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.97871 | 0.366084 | 0.183042 | − | 0.983105i | \(-0.441406\pi\) | ||||
0.183042 | + | 0.983105i | \(0.441406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.9443 | −0.546782 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.29180 | −0.302976 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.1246 | 1.50066 | 0.750329 | − | 0.661064i | \(-0.229895\pi\) | ||||
0.750329 | + | 0.661064i | \(0.229895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.81966 | −0.175638 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.0132 | −1.70872 | −0.854361 | − | 0.519680i | \(-0.826051\pi\) | ||||
−0.854361 | + | 0.519680i | \(0.826051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.09017 | −0.0758684 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5066 | −0.417113 | −0.208557 | − | 0.978010i | \(-0.566877\pi\) | ||||
−0.208557 | + | 0.978010i | \(0.566877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60.9787 | 2.20758 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.29180 | 0.0827520 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.2918 | −1.23659 | −0.618297 | − | 0.785945i | \(-0.712177\pi\) | ||||
−0.618297 | + | 0.785945i | \(0.712177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.52786 | 0.343138 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.0000 | 0.503545 | 0.251773 | − | 0.967786i | \(-0.418987\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.1246 | −0.399093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.1803 | −0.830522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.85410 | −0.316825 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.8754 | −0.460129 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.4164 | −1.11987 | −0.559937 | − | 0.828535i | \(-0.689175\pi\) | ||||
−0.559937 | + | 0.828535i | \(0.689175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.43769 | −0.335991 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.1246 | −2.31556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.47214 | −0.0522771 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5836 | 0.658265 | 0.329132 | − | 0.944284i | \(-0.393244\pi\) | ||||
0.329132 | + | 0.944284i | \(0.393244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.5410 | −2.42481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4164 | 0.898045 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.4590 | −0.898428 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.47214 | −0.227830 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.1591 | 0.954861 | 0.477431 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477431 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.70820 | 0.270672 | 0.135336 | − | 0.990800i | \(-0.456789\pi\) | ||||
0.135336 | + | 0.990800i | \(0.456789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8328 | −0.414995 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.3607 | −1.62195 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.85410 | 0.169616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.94427 | −0.102756 | −0.0513779 | − | 0.998679i | \(-0.516361\pi\) | ||||
−0.0513779 | + | 0.998679i | \(0.516361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.8328 | −0.726186 | −0.363093 | − | 0.931753i | \(-0.618279\pi\) | ||||
−0.363093 | + | 0.931753i | \(0.618279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.2492 | −1.67779 | −0.838895 | − | 0.544293i | \(-0.816798\pi\) | ||||
−0.838895 | + | 0.544293i | \(0.816798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.5410 | 1.13020 | 0.565098 | − | 0.825024i | \(-0.308838\pi\) | ||||
0.565098 | + | 0.825024i | \(0.308838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1803 | 0.353152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −96.9574 | −3.35938 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.7426 | −1.06262 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.76393 | 0.233517 | 0.116758 | − | 0.993160i | \(-0.462750\pi\) | ||||
0.116758 | + | 0.993160i | \(0.462750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2492 | −0.525835 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.403252 | −0.0138887 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.12461 | −0.0730025 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.88854 | −0.0648147 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.70820 | −0.127116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.2148 | −1.75356 | −0.876780 | − | 0.480891i | \(-0.840313\pi\) | ||||
−0.876780 | + | 0.480891i | \(0.840313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.0000 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.1459 | 0.345771 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.6738 | 0.362500 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.3050 | −0.654876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.291796 | −0.00988713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.9787 | 1.42076 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.6869 | −1.17129 | −0.585647 | − | 0.810566i | \(-0.699160\pi\) | ||||
−0.585647 | + | 0.810566i | \(0.699160\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1246 | −0.577599 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.2918 | −1.29008 | −0.645042 | − | 0.764147i | \(-0.723160\pi\) | ||||
−0.645042 | + | 0.764147i | \(0.723160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7295 | 0.596645 | 0.298322 | − | 0.954465i | \(-0.403573\pi\) | ||||
0.298322 | + | 0.954465i | \(0.403573\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5410 | 1.22693 | 0.613464 | − | 0.789723i | \(-0.289776\pi\) | ||||
0.613464 | + | 0.789723i | \(0.289776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3050 | 0.646740 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 80.2492 | 2.68544 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.236068 | −0.00788208 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.8328 | 1.09504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.7082 | 0.390057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.2918 | 0.675269 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.5410 | −1.01410 | −0.507049 | − | 0.861917i | \(-0.669264\pi\) | ||||
−0.507049 | + | 0.861917i | \(0.669264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.4164 | 0.909345 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.3607 | −0.740842 | −0.370421 | − | 0.928864i | \(-0.620787\pi\) | ||||
−0.370421 | + | 0.928864i | \(0.620787\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.3050 | 0.638901 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.7082 | 1.31128 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5836 | 0.481068 | 0.240534 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240534 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.27051 | −0.206620 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.00000 | −0.0329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8541 | 0.356495 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.3050 | 0.633375 | 0.316687 | − | 0.948530i | \(-0.397429\pi\) | ||||
0.316687 | + | 0.948530i | \(0.397429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 113.520 | 3.72046 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.36068 | 0.273716 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.67376 | −0.283359 | −0.141680 | − | 0.989913i | \(-0.545250\pi\) | ||||
−0.141680 | + | 0.989913i | \(0.545250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.8328 | 0.386149 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2148 | −0.789379 | −0.394690 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394690 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.38197 | 0.110132 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.3951 | 1.54013 | 0.770067 | − | 0.637963i | \(-0.220223\pi\) | ||||
0.770067 | + | 0.637963i | \(0.220223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.87539 | −0.0933391 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2361 | 0.526491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.3951 | −1.17895 | −0.589477 | − | 0.807785i | \(-0.700666\pi\) | ||||
−0.589477 | + | 0.807785i | \(0.700666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.75078 | 0.250547 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.6869 | 1.12010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.3951 | 1.52887 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.47214 | −0.144113 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.7639 | −0.796354 | −0.398177 | − | 0.917309i | \(-0.630357\pi\) | ||||
−0.398177 | + | 0.917309i | \(0.630357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.7984 | −0.796639 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8541 | −0.829698 | −0.414849 | − | 0.909890i | \(-0.636166\pi\) | ||||
−0.414849 | + | 0.909890i | \(0.636166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 85.9574 | 2.75567 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.2705 | −1.03243 | −0.516213 | − | 0.856461i | \(-0.672659\pi\) | ||||
−0.516213 | + | 0.856461i | \(0.672659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.8328 | −1.04934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.8885 | 1.05005 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.3951 | −0.841874 | −0.420937 | − | 0.907090i | \(-0.638299\pi\) | ||||
−0.420937 | + | 0.907090i | \(0.638299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.1246 | −1.11803 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.76393 | 0.215081 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.2705 | −1.62866 | −0.814331 | − | 0.580401i | \(-0.802896\pi\) | ||||
−0.814331 | + | 0.580401i | \(0.802896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.34752 | −0.296635 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.7214 | 0.846274 | 0.423137 | − | 0.906066i | \(-0.360929\pi\) | ||||
0.423137 | + | 0.906066i | \(0.360929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.8754 | −0.407359 |
(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 | 9200.2.a.bo.1.2 | 2 | ||
4.3 | odd | 2 | 1150.2.a.l.1.1 | 2 | |||
5.2 | odd | 4 | 1840.2.e.c.369.2 | 4 | |||
5.3 | odd | 4 | 1840.2.e.c.369.3 | 4 | |||
5.4 | even | 2 | 9200.2.a.by.1.1 | 2 | |||
20.3 | even | 4 | 230.2.b.a.139.3 | yes | 4 | ||
20.7 | even | 4 | 230.2.b.a.139.2 | ✓ | 4 | ||
20.19 | odd | 2 | 1150.2.a.n.1.2 | 2 | |||
60.23 | odd | 4 | 2070.2.d.c.829.1 | 4 | |||
60.47 | odd | 4 | 2070.2.d.c.829.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.a.139.2 | ✓ | 4 | 20.7 | even | 4 | ||
230.2.b.a.139.3 | yes | 4 | 20.3 | even | 4 | ||
1150.2.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
1150.2.a.n.1.2 | 2 | 20.19 | odd | 2 | |||
1840.2.e.c.369.2 | 4 | 5.2 | odd | 4 | |||
1840.2.e.c.369.3 | 4 | 5.3 | odd | 4 | |||
2070.2.d.c.829.1 | 4 | 60.23 | odd | 4 | |||
2070.2.d.c.829.3 | 4 | 60.47 | odd | 4 | |||
9200.2.a.bo.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9200.2.a.by.1.1 | 2 | 5.4 | even | 2 |