Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.c.369.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 0.618034i | − 0.356822i | −0.983956 | − | 0.178411i | \(-0.942904\pi\) | ||||
0.983956 | − | 0.178411i | \(-0.0570957\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.85410i | − 1.83468i | −0.398107 | − | 0.917339i | \(-0.630333\pi\) | ||||
0.398107 | − | 0.917339i | \(-0.369667\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | − 0.381966i | − 0.105938i | −0.998596 | − | 0.0529692i | \(-0.983131\pi\) | ||||
0.998596 | − | 0.0529692i | \(-0.0168685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 1.38197i | − 0.356822i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.85410i | − 1.41983i | −0.704288 | − | 0.709914i | \(-0.748734\pi\) | ||||
0.704288 | − | 0.709914i | \(-0.251266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.85410 | −1.57244 | −0.786219 | − | 0.617947i | \(-0.787964\pi\) | ||||
−0.786219 | + | 0.617947i | \(0.787964\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3.47214i | − 0.668213i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.70820 | −0.688596 | −0.344298 | − | 0.938860i | \(-0.611883\pi\) | ||||
−0.344298 | + | 0.938860i | \(0.611883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.85410 | 1.59024 | 0.795122 | − | 0.606450i | \(-0.207407\pi\) | ||||
0.795122 | + | 0.606450i | \(0.207407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.09017i | − 0.363852i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 10.8541i | − 1.83468i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70820i | 0.609625i | 0.952412 | + | 0.304812i | \(0.0985938\pi\) | ||||
−0.952412 | + | 0.304812i | \(0.901406\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 6.76393i | 1.03149i | 0.856742 | + | 0.515745i | \(0.172485\pi\) | ||||
−0.856742 | + | 0.515745i | \(0.827515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.85410 | 0.872678 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7082i | 1.70782i | 0.520423 | + | 0.853909i | \(0.325774\pi\) | ||||
−0.520423 | + | 0.853909i | \(0.674226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.5623 | −2.36604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.61803 | −0.506626 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.56231 | 1.01970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.23607i | 0.561081i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85410 | −0.493467 | −0.246734 | − | 0.969083i | \(-0.579357\pi\) | ||||
−0.246734 | + | 0.969083i | \(0.579357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 12.7082i | − 1.60108i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.854102i | − 0.105938i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.763932i | − 0.0933292i | −0.998911 | − | 0.0466646i | \(-0.985141\pi\) | ||||
0.998911 | − | 0.0466646i | \(-0.0148592\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 7.52786i | 0.881070i | 0.897735 | + | 0.440535i | \(0.145211\pi\) | ||||
−0.897735 | + | 0.440535i | \(0.854789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.09017i | − 0.356822i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 16.4164i | − 1.87082i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.70820 | 0.642223 | 0.321112 | − | 0.947041i | \(-0.395944\pi\) | ||||
0.321112 | + | 0.947041i | \(0.395944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.70820i | − 0.626557i | −0.949661 | − | 0.313278i | \(-0.898573\pi\) | ||||
0.949661 | − | 0.313278i | \(-0.101427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.0902i | − 1.41983i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.29180i | 0.245706i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.70820 | 1.02907 | 0.514534 | − | 0.857470i | \(-0.327965\pi\) | ||||
0.514534 | + | 0.857470i | \(0.327965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.85410 | −0.194363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 5.47214i | − 0.567434i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.3262 | −1.57244 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.0344i | − 1.62805i | −0.580829 | − | 0.814025i | \(-0.697272\pi\) | ||||
0.580829 | − | 0.814025i | \(-0.302728\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 4.14590i | 0.408507i | 0.978918 | + | 0.204254i | \(0.0654768\pi\) | ||||
−0.978918 | + | 0.204254i | \(0.934523\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.70820 | −0.654654 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.70820i | 0.165138i | 0.996585 | + | 0.0825692i | \(0.0263125\pi\) | ||||
−0.996585 | + | 0.0825692i | \(0.973687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5623 | 1.20325 | 0.601625 | − | 0.798778i | \(-0.294520\pi\) | ||||
0.601625 | + | 0.798778i | \(0.294520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.29180 | 0.217528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.4164i | − 1.26211i | −0.775738 | − | 0.631055i | \(-0.782622\pi\) | ||||
0.775738 | − | 0.631055i | \(-0.217378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.23607i | 0.208514i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.4164 | −2.60493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.437694 | 0.0397904 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.09017i | 0.188464i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.70820i | − 0.329050i | −0.986373 | − | 0.164525i | \(-0.947391\pi\) | ||||
0.986373 | − | 0.164525i | \(-0.0526091\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 33.2705i | 2.88492i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 7.76393i | − 0.668213i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 7.14590i | − 0.610515i | −0.952270 | − | 0.305258i | \(-0.901257\pi\) | ||||
0.952270 | − | 0.305258i | \(-0.0987426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7082 | 1.50199 | 0.750995 | − | 0.660308i | \(-0.229574\pi\) | ||||
0.750995 | + | 0.660308i | \(0.229574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.23607 | 0.609387 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.29180i | − 0.108025i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.29180 | −0.688596 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.2361i | 0.844257i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.381966 | 0.0312919 | 0.0156459 | − | 0.999878i | \(-0.495020\pi\) | ||||
0.0156459 | + | 0.999878i | \(0.495020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2705 | 1.56821 | 0.784106 | − | 0.620627i | \(-0.213122\pi\) | ||||
0.784106 | + | 0.620627i | \(0.213122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 15.3262i | − 1.23905i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.7984 | 1.59024 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7082i | 1.25365i | 0.779160 | + | 0.626826i | \(0.215646\pi\) | ||||
−0.779160 | + | 0.626826i | \(0.784354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.23607 | 0.0980266 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.85410 | 0.382557 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.03444i | 0.550980i | 0.961304 | + | 0.275490i | \(0.0888401\pi\) | ||||
−0.961304 | + | 0.275490i | \(0.911160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 4.67376i | − 0.363852i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3.70820i | − 0.286949i | −0.989654 | − | 0.143475i | \(-0.954172\pi\) | ||||
0.989654 | − | 0.143475i | \(-0.0458276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8541 | 0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.9443 | −1.37223 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.56231i | 0.270837i | 0.990788 | + | 0.135419i | \(0.0432379\pi\) | ||||
−0.990788 | + | 0.135419i | \(0.956762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 24.2705i | − 1.83468i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.70820i | 0.278726i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.4721 | 1.23119 | 0.615593 | − | 0.788065i | \(-0.288917\pi\) | ||||
0.615593 | + | 0.788065i | \(0.288917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.56231 | −0.339114 | −0.169557 | − | 0.985520i | \(-0.554234\pi\) | ||||
−0.169557 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.38197i | 0.176080i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.29180i | 0.609625i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 19.7984i | − 1.44780i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 2.29180i | 0.164967i | 0.996592 | + | 0.0824835i | \(0.0262852\pi\) | ||||
−0.996592 | + | 0.0824835i | \(0.973715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.527864 | −0.0378011 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.437694i | − 0.0311844i | −0.999878 | − | 0.0155922i | \(-0.995037\pi\) | ||||
0.999878 | − | 0.0155922i | \(-0.00496335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4164 | −1.09284 | −0.546420 | − | 0.837511i | \(-0.684010\pi\) | ||||
−0.546420 | + | 0.837511i | \(0.684010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.472136 | −0.0333019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0000i | 1.26335i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.56231 | −0.528174 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.61803i | 0.181966i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 1.61803i | 0.110866i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.1246i | 1.03149i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 42.9787i | − 2.91759i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.65248 | 0.314385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.23607 | −0.150414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 22.3607i | − 1.49738i | −0.662919 | − | 0.748691i | \(-0.730683\pi\) | ||||
0.662919 | − | 0.748691i | \(-0.269317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0902 | 0.872678 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.7082i | − 1.57357i | −0.617228 | − | 0.786784i | \(-0.711744\pi\) | ||||
0.617228 | − | 0.786784i | \(-0.288256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.1459 | −0.667551 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1246i | 1.25289i | 0.779464 | + | 0.626447i | \(0.215492\pi\) | ||||
−0.779464 | + | 0.626447i | \(0.784508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.1803i | 1.70782i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.52786i | − 0.229159i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.52786 | −0.0988293 | −0.0494147 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494147 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 13.9443i | − 0.894525i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −37.0344 | −2.36604 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.61803i | 0.166582i | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 3.38197i | 0.212622i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.09017 | −0.506626 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4164i | 0.961649i | 0.876817 | + | 0.480825i | \(0.159663\pi\) | ||||
−0.876817 | + | 0.480825i | \(0.840337\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.0000 | 1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.70820 | −0.600923 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2705i | 0.941620i | 0.882235 | + | 0.470810i | \(0.156038\pi\) | ||||
−0.882235 | + | 0.470810i | \(0.843962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.47214i | 0.274721i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.00000i | − 0.367194i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.4721 | 0.638497 | 0.319249 | − | 0.947671i | \(-0.396569\pi\) | ||||
0.319249 | + | 0.947671i | \(0.396569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1459 | −1.16303 | −0.581515 | − | 0.813536i | \(-0.697540\pi\) | ||||
−0.581515 | + | 0.813536i | \(0.697540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.14590i | 0.0693529i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.9098 | 1.01970 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4721i | 0.989715i | 0.868974 | + | 0.494857i | \(0.164780\pi\) | ||||
−0.868974 | + | 0.494857i | \(0.835220\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 3.05573i | 0.181644i | 0.995867 | + | 0.0908221i | \(0.0289495\pi\) | ||||
−0.995867 | + | 0.0908221i | \(0.971051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.47214i | 0.561081i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.4164i | 0.969030i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.2705 | −1.01591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.90983 | −0.580925 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.7082i | 1.61873i | 0.587306 | + | 0.809365i | \(0.300189\pi\) | ||||
−0.587306 | + | 0.809365i | \(0.699811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4164 | −0.781133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 11.7426i | − 0.681377i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.381966 | 0.0220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.8328 | 1.89245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.47214i | 0.371814i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.61803 | −0.493467 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 10.1459i | − 0.579057i | −0.957169 | − | 0.289528i | \(-0.906502\pi\) | ||||
0.957169 | − | 0.289528i | \(-0.0934985\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | − 19.1459i | − 1.08219i | −0.840961 | − | 0.541095i | \(-0.818010\pi\) | ||||
0.840961 | − | 0.541095i | \(-0.181990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 28.4164i | − 1.60108i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.2705i | 1.47550i | 0.675075 | + | 0.737749i | \(0.264111\pi\) | ||||
−0.675075 | + | 0.737749i | \(0.735889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5410 | −0.702162 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05573 | 0.0589250 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.1246i | 2.23259i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.90983i | − 0.105938i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 7.76393i | − 0.429346i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 9.70820i | 0.532006i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.70820i | − 0.0933292i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 5.61803i | − 0.306034i | −0.988224 | − | 0.153017i | \(-0.951101\pi\) | ||||
0.988224 | − | 0.153017i | \(-0.0488989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.29180 | −0.450349 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.9443 | 1.62157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 46.4164i | 2.50625i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.38197 | 0.0744025 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.56231i | 0.298600i | 0.988792 | + | 0.149300i | \(0.0477021\pi\) | ||||
−0.988792 | + | 0.149300i | \(0.952298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.2918 | −0.765022 | −0.382511 | − | 0.923951i | \(-0.624941\pi\) | ||||
−0.382511 | + | 0.923951i | \(0.624941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.32624 | −0.0707893 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.00000i | − 0.425797i | −0.977074 | − | 0.212899i | \(-0.931710\pi\) | ||||
0.977074 | − | 0.212899i | \(-0.0682904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.85410 | −0.310703 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5623i | 0.929496i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4164 | 0.708091 | 0.354045 | − | 0.935228i | \(-0.384806\pi\) | ||||
0.354045 | + | 0.935228i | \(0.384806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.9787 | 1.47256 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 0.270510i | − 0.0141981i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8328i | 0.881070i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.0000i | − 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.85410 | −0.460926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.70820 | 0.504025 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.05573i | 0.158220i | 0.996866 | + | 0.0791098i | \(0.0252078\pi\) | ||||
−0.996866 | + | 0.0791098i | \(0.974792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 6.90983i | − 0.356822i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.41641i | 0.0729487i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.27051 | 0.476194 | 0.238097 | − | 0.971241i | \(-0.423476\pi\) | ||||
0.238097 | + | 0.971241i | \(0.423476\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.29180 | −0.117412 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.4164i | 1.40091i | 0.713695 | + | 0.700456i | \(0.247020\pi\) | ||||
−0.713695 | + | 0.700456i | \(0.752980\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 36.7082i | − 1.87082i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.7082i | 0.900159i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.67376 | 0.287671 | 0.143836 | − | 0.989602i | \(-0.454056\pi\) | ||||
0.143836 | + | 0.989602i | \(0.454056\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.85410 | 0.296055 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.05573i | 0.255028i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7639 | 0.642223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.5623i | 1.78482i | 0.451224 | + | 0.892410i | \(0.350987\pi\) | ||||
−0.451224 | + | 0.892410i | \(0.649013\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 3.38197i | − 0.168468i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7639 | 0.634245 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.5410i | 0.621635i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.56231 | 0.324485 | 0.162243 | − | 0.986751i | \(-0.448127\pi\) | ||||
0.162243 | + | 0.986751i | \(0.448127\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.41641 | −0.217845 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.1246i | 1.43313i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 12.7639i | − 0.626557i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 10.9443i | − 0.535943i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.88854 | 0.287674 | 0.143837 | − | 0.989601i | \(-0.454056\pi\) | ||||
0.143837 | + | 0.989601i | \(0.454056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.85410 | 0.334048 | 0.167024 | − | 0.985953i | \(-0.446584\pi\) | ||||
0.167024 | + | 0.985953i | \(0.446584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.6525i | 1.49037i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 29.2705i | − 1.41983i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.7082i | 0.905353i | ||||||||
\(428\) | 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 | ||||||||
\(433\) | 29.6180i | 1.42335i | 0.702508 | + | 0.711676i | \(0.252064\pi\) | ||||
−0.702508 | + | 0.711676i | \(0.747936\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.12461i | 0.245706i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.85410i | − 0.327876i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.270510 | −0.0129107 | −0.00645536 | − | 0.999979i | \(-0.502055\pi\) | ||||
−0.00645536 | + | 0.999979i | \(0.502055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.3607 | −2.06479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.85410i | 0.325648i | 0.986655 | + | 0.162824i | \(0.0520603\pi\) | ||||
−0.986655 | + | 0.162824i | \(0.947940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.7082 | 1.02907 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 0.236068i | − 0.0111656i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.56231 | −0.120923 | −0.0604613 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604613 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4377 | −0.538580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 11.9098i | − 0.559573i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.14590 | −0.194363 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 25.4164i | − 1.18893i | −0.804122 | − | 0.594465i | \(-0.797364\pi\) | ||||
0.804122 | − | 0.594465i | \(-0.202636\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | − 2.29180i | − 0.106509i | −0.998581 | − | 0.0532544i | \(-0.983041\pi\) | ||||
0.998581 | − | 0.0532544i | \(-0.0169594\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 12.2361i | − 0.567434i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1246i | 0.792433i | 0.918157 | + | 0.396216i | \(0.129677\pi\) | ||||
−0.918157 | + | 0.396216i | \(0.870323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.70820 | −0.171229 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.70820 | 0.447330 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.8754i | 1.05181i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.2705 | −1.57244 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.23607i | 0.239743i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5279 | −0.892251 | −0.446125 | − | 0.894970i | \(-0.647196\pi\) | ||||
−0.446125 | + | 0.894970i | \(0.647196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.41641 | 0.0645826 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.00000i | − 0.136505i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 35.8541i | − 1.62805i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.7082i | 0.983693i | 0.870682 | + | 0.491846i | \(0.163678\pi\) | ||||
−0.870682 | + | 0.491846i | \(0.836322\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 21.7082i | 0.977688i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.7984 | 0.889871 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7082i | 0.570041i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4164 | 0.511069 | 0.255534 | − | 0.966800i | \(-0.417749\pi\) | ||||
0.255534 | + | 0.966800i | \(0.417749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.29180 | −0.102390 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8541i | 0.751487i | 0.926724 | + | 0.375744i | \(0.122613\pi\) | ||||
−0.926724 | + | 0.375744i | \(0.877387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.4164 | −1.04202 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7.94427i | − 0.352818i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6525 | 1.09270 | 0.546351 | − | 0.837556i | \(-0.316017\pi\) | ||||
0.546351 | + | 0.837556i | \(0.316017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.5410 | 1.61648 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.7984i | 1.05072i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.27051i | 0.408507i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.5967i | 1.74146i | ||||||||
\(518\) | 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 | ||||||||
\(523\) | − 40.3607i | − 1.76485i | −0.470454 | − | 0.882425i | \(-0.655910\pi\) | ||||
0.470454 | − | 0.882425i | \(-0.344090\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15.0000 | −0.654654 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 51.8328i | − 2.25787i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.7082 | −0.681678 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.29180i | 0.0559539i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.81966i | 0.165138i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 10.1803i | − 0.439314i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 2.81966i | 0.121003i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.0902 | 1.20325 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14590i | 0.0489951i | 0.999700 | + | 0.0244975i | \(0.00779859\pi\) | ||||
−0.999700 | + | 0.0244975i | \(0.992201\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0902 | −0.430638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.4164 | 1.08278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 27.7082i | − 1.17827i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.12461 | 0.217528 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 30.0000i | − 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.58359 | 0.109274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2361 | −0.516607 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.29180i | − 0.0965877i | −0.998833 | − | 0.0482938i | \(-0.984622\pi\) | ||||
0.998833 | − | 0.0482938i | \(-0.0153784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 30.0000i | − 1.26211i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 27.7082i | − 1.16364i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.3607 | −1.18894 | −0.594471 | − | 0.804117i | \(-0.702638\pi\) | ||||
−0.594471 | + | 0.804117i | \(0.702638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.2705 | 1.05754 | 0.528769 | − | 0.848766i | \(-0.322654\pi\) | ||||
0.528769 | + | 0.848766i | \(0.322654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 0.875388i | − 0.0365699i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.00000i | 0.208514i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26.2918i | − 1.09454i | −0.836956 | − | 0.547271i | \(-0.815667\pi\) | ||||
0.836956 | − | 0.547271i | \(-0.184333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.41641 | 0.0588639 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.7082 | −1.14953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.76393i | 0.280133i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − 2.23607i | − 0.0924500i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.14590i | 0.0885707i | 0.999019 | + | 0.0442853i | \(0.0141011\pi\) | ||||
−0.999019 | + | 0.0442853i | \(0.985899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.6869 | −2.50056 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.270510 | −0.0111273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 33.4164i | − 1.37225i | −0.727485 | − | 0.686124i | \(-0.759311\pi\) | ||||
0.727485 | − | 0.686124i | \(-0.240689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −63.5410 | −2.60493 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.52786i | 0.389950i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3820 | 0.873643 | 0.436822 | − | 0.899548i | \(-0.356104\pi\) | ||||
0.436822 | + | 0.899548i | \(0.356104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.14590 | −0.128324 | −0.0641619 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641619 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.00000i | − 0.0814463i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.978714 | 0.0397904 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 38.9443i | − 1.58070i | −0.612656 | − | 0.790350i | \(-0.709899\pi\) | ||||
0.612656 | − | 0.790350i | \(-0.290101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.1246 | 0.450792 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.47214 | 0.180923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.23607i | 0.211483i | 0.994394 | + | 0.105741i | \(0.0337216\pi\) | ||||
−0.994394 | + | 0.105741i | \(0.966278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.67376i | 0.188464i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5623i | 0.707032i | 0.935429 | + | 0.353516i | \(0.115014\pi\) | ||||
−0.935429 | + | 0.353516i | \(0.884986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.1459 | −0.849925 | −0.424963 | − | 0.905211i | \(-0.639713\pi\) | ||||
−0.424963 | + | 0.905211i | \(0.639713\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.47214 | 0.139332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 47.1246i | − 1.88801i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3262i | 0.572135i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 3.52786i | 0.140220i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.29180i | − 0.329050i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.32624i | 0.250655i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 35.0132i | 1.38078i | 0.723435 | + | 0.690392i | \(0.242562\pi\) | ||||
−0.723435 | + | 0.690392i | \(0.757438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.34752 | 0.368058 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.291796i | 0.0114717i | 0.999984 | + | 0.00573584i | \(0.00182579\pi\) | ||||
−0.999984 | + | 0.00573584i | \(0.998174\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.2918 | −0.796523 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.5623 | −1.04106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.9787i | 0.468763i | 0.972145 | + | 0.234382i | \(0.0753065\pi\) | ||||
−0.972145 | + | 0.234382i | \(0.924693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.2918 | −0.714720 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.7082i | 0.768890i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3951 | 1.33782 | 0.668908 | − | 0.743346i | \(-0.266762\pi\) | ||||
0.668908 | + | 0.743346i | \(0.266762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.38197i | 0.0536711i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 74.3951i | 2.88492i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.70820i | − 0.143582i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.8197 | −0.534299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0344 | −0.503189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2918i | 0.550908i | 0.961314 | + | 0.275454i | \(0.0888282\pi\) | ||||
−0.961314 | + | 0.275454i | \(0.911172\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 17.3607i | − 0.668213i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000i | 1.61419i | 0.590421 | + | 0.807096i | \(0.298962\pi\) | ||||
−0.590421 | + | 0.807096i | \(0.701038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −77.8328 | −2.98695 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6525 | −0.561484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9787i | 1.37669i | 0.725385 | + | 0.688344i | \(0.241662\pi\) | ||||
−0.725385 | + | 0.688344i | \(0.758338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 15.9787i | − 0.610515i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 6.18034i | − 0.235795i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | − 42.9787i | − 1.63263i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.5967 | 1.50199 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7984i | 0.749917i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | − 25.4164i | − 0.958598i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.1803 | 0.609387 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.8328i | 1.91176i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5623 | 0.434232 | 0.217116 | − | 0.976146i | \(-0.430335\pi\) | ||||
0.217116 | + | 0.976146i | \(0.430335\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9443 | 0.560454 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.85410i | 0.331589i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.88854i | − 0.108025i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.944272i | 0.0352645i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.4508 | −1.21021 | −0.605106 | − | 0.796145i | \(-0.706869\pi\) | ||||
−0.605106 | + | 0.796145i | \(0.706869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.1246 | 0.749480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23607i | 0.0459699i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.5410 | −0.688596 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.74265i | 0.0646312i | 0.999478 | + | 0.0323156i | \(0.0102882\pi\) | ||||
−0.999478 | + | 0.0323156i | \(0.989712\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.50658 | 0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.5967 | 1.46454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 35.8885i | − 1.32557i | −0.748808 | − | 0.662787i | \(-0.769374\pi\) | ||||
0.748808 | − | 0.662787i | \(-0.230626\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.8885i | 0.844257i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.58359i | − 0.0951678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5410 | −1.19704 | −0.598520 | − | 0.801108i | \(-0.704244\pi\) | ||||
−0.598520 | + | 0.801108i | \(0.704244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.61803 | 0.0594400 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 9.97871i | − 0.366084i | −0.983105 | − | 0.183042i | \(-0.941406\pi\) | ||||
0.983105 | − | 0.183042i | \(-0.0585944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.854102 | 0.0312919 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 14.9443i | − 0.546782i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 4.81966i | 0.175638i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.0902 | 1.56821 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.0132i | − 1.70872i | −0.519680 | − | 0.854361i | \(-0.673949\pi\) | ||||
0.519680 | − | 0.854361i | \(-0.326051\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | − 60.9787i | − 2.20758i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 34.2705i | − 1.23905i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.29180i | 0.0827520i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.2918 | 1.23659 | 0.618297 | − | 0.785945i | \(-0.287823\pi\) | ||||
0.618297 | + | 0.785945i | \(0.287823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.52786 | 0.343138 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 14.0000i | − 0.503545i | −0.967786 | − | 0.251773i | \(-0.918987\pi\) | ||||
0.967786 | − | 0.251773i | \(-0.0810135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.2705 | 1.59024 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 11.1246i | − 0.399093i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.1803 | 0.830522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.85410 | −0.316825 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.8754i | 0.460129i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.1246i | 1.25365i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 31.4164i | − 1.11987i | −0.828535 | − | 0.559937i | \(-0.810825\pi\) | ||||
0.828535 | − | 0.559937i | \(-0.189175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.43769 | 0.335991 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −65.1246 | −2.31556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.47214i | 0.0522771i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.76393 | 0.0980266 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5836i | 0.658265i | 0.944284 | + | 0.329132i | \(0.106756\pi\) | ||||
−0.944284 | + | 0.329132i | \(0.893244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.5410 | 2.42481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4164 | 0.898045 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.4590i | 0.898428i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.8541 | 0.382557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6.47214i | − 0.227830i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.1591 | −0.954861 | −0.477431 | − | 0.878669i | \(-0.658432\pi\) | ||||
−0.477431 | + | 0.878669i | \(0.658432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.70820 | 0.270672 | 0.135336 | − | 0.990800i | \(-0.456789\pi\) | ||||
0.135336 | + | 0.990800i | \(0.456789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.8328i | 0.414995i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7295i | 0.550980i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 46.3607i | − 1.62195i | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 20.8328i | 0.726186i | 0.931753 | + | 0.363093i | \(0.118279\pi\) | ||||
−0.931753 | + | 0.363093i | \(0.881721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 10.4508i | − 0.363852i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 48.2492i | − 1.67779i | −0.544293 | − | 0.838895i | \(-0.683202\pi\) | ||||
0.544293 | − | 0.838895i | \(-0.316798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.5410 | −1.13020 | −0.565098 | − | 0.825024i | \(-0.691162\pi\) | ||||
−0.565098 | + | 0.825024i | \(0.691162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1803 | 0.353152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 96.9574i | 3.35938i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.29180i | − 0.286949i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 30.7426i | − 1.06262i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.76393 | −0.233517 | −0.116758 | − | 0.993160i | \(-0.537250\pi\) | ||||
−0.116758 | + | 0.993160i | \(0.537250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2492 | −0.525835 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.403252i | 0.0138887i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.7426 | 0.988777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.12461i | − 0.0730025i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.88854 | 0.0648147 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.70820 | −0.127116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.2148i | 1.75356i | 0.480891 | + | 0.876780i | \(0.340313\pi\) | ||||
−0.480891 | + | 0.876780i | \(0.659687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −40.1246 | −1.37223 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 36.0000i | − 1.22974i | −0.788630 | − | 0.614868i | \(-0.789209\pi\) | ||||
0.788630 | − | 0.614868i | \(-0.210791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.1459 | 0.345771 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.96556i | 0.270837i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.6738i | 0.362500i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.3050 | 0.654876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.291796 | −0.00988713 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 41.9787i | − 1.42076i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 54.2705i | − 1.83468i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34.6869i | − 1.17129i | −0.810566 | − | 0.585647i | \(-0.800840\pi\) | ||||
0.810566 | − | 0.585647i | \(-0.199160\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 17.7295i | − 0.596645i | −0.954465 | − | 0.298322i | \(-0.903573\pi\) | ||||
0.954465 | − | 0.298322i | \(-0.0964271\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.29180i | 0.278726i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5410i | 1.22693i | 0.789723 | + | 0.613464i | \(0.210224\pi\) | ||||
−0.789723 | + | 0.613464i | \(0.789776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | −0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.3050 | 0.646740 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 80.2492i | − 2.68544i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.8328 | 1.23119 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 0.236068i | − 0.00788208i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.8328 | −1.09504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.7082 | 0.390057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 20.2918i | − 0.675269i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.2016 | −0.339114 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30.5410i | − 1.01410i | −0.861917 | − | 0.507049i | \(-0.830736\pi\) | ||||
0.861917 | − | 0.507049i | \(-0.169264\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − 19.3050i | − 0.638901i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.32624i | 0.176080i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.7082i | 1.31128i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.5836 | −0.481068 | −0.240534 | − | 0.970641i | \(-0.577323\pi\) | ||||
−0.240534 | + | 0.970641i | \(0.577323\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.27051 | −0.206620 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.00000i | 0.0329154i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.5410i | 0.609625i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.8541i | 0.356495i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3050 | −0.633375 | −0.316687 | − | 0.948530i | \(-0.602571\pi\) | ||||
−0.316687 | + | 0.948530i | \(0.602571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 113.520 | 3.72046 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.36068i | − 0.273716i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 44.2705i | − 1.44780i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 8.67376i | − 0.283359i | −0.989913 | − | 0.141680i | \(-0.954750\pi\) | ||||
0.989913 | − | 0.141680i | \(-0.0452503\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − 3.38197i | − 0.110132i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −37.6869 | −1.22596 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.3951i | 1.54013i | 0.637963 | + | 0.770067i | \(0.279777\pi\) | ||||
−0.637963 | + | 0.770067i | \(0.720223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.87539 | 0.0933391 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.2361 | 0.526491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.3951i | 1.17895i | 0.807785 | + | 0.589477i | \(0.200666\pi\) | ||||
−0.807785 | + | 0.589477i | \(0.799334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.16718 | 0.102488 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.75078i | 0.250547i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.6869 | −1.12010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.3951 | 1.52887 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.47214i | 0.144113i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.12461i | 0.164967i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 24.7639i | − 0.796354i | −0.917309 | − | 0.398177i | \(-0.869643\pi\) | ||||
0.917309 | − | 0.398177i | \(-0.130357\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | − 85.9574i | − 2.75567i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.18034 | −0.0378011 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 32.2705i | − 1.03243i | −0.856461 | − | 0.516213i | \(-0.827341\pi\) | ||||
0.856461 | − | 0.516213i | \(-0.172659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.8328 | 1.04934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.8885 | 1.05005 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.3951i | 0.841874i | 0.907090 | + | 0.420937i | \(0.138299\pi\) | ||||
−0.907090 | + | 0.420937i | \(0.861701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 0.978714i | − 0.0311844i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 35.1246i | − 1.11803i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 9.34752i | 0.296635i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.4721 | −1.09284 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.7214i | 0.846274i | 0.906066 | + | 0.423137i | \(0.139071\pi\) | ||||
−0.906066 | + | 0.423137i | \(0.860929\pi\) | |||||||
\(998\) | 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 | 1840.2.e.c.369.2 | 4 | ||
4.3 | odd | 2 | 230.2.b.a.139.2 | ✓ | 4 | ||
5.2 | odd | 4 | 9200.2.a.by.1.1 | 2 | |||
5.3 | odd | 4 | 9200.2.a.bo.1.2 | 2 | |||
5.4 | even | 2 | inner | 1840.2.e.c.369.3 | 4 | ||
12.11 | even | 2 | 2070.2.d.c.829.3 | 4 | |||
20.3 | even | 4 | 1150.2.a.l.1.1 | 2 | |||
20.7 | even | 4 | 1150.2.a.n.1.2 | 2 | |||
20.19 | odd | 2 | 230.2.b.a.139.3 | yes | 4 | ||
60.59 | even | 2 | 2070.2.d.c.829.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.a.139.2 | ✓ | 4 | 4.3 | odd | 2 | ||
230.2.b.a.139.3 | yes | 4 | 20.19 | odd | 2 | ||
1150.2.a.l.1.1 | 2 | 20.3 | even | 4 | |||
1150.2.a.n.1.2 | 2 | 20.7 | even | 4 | |||
1840.2.e.c.369.2 | 4 | 1.1 | even | 1 | trivial | ||
1840.2.e.c.369.3 | 4 | 5.4 | even | 2 | inner | ||
2070.2.d.c.829.1 | 4 | 60.59 | even | 2 | |||
2070.2.d.c.829.3 | 4 | 12.11 | even | 2 | |||
9200.2.a.bo.1.2 | 2 | 5.3 | odd | 4 | |||
9200.2.a.by.1.1 | 2 | 5.2 | odd | 4 |