Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.l.4049.1 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.23607i | 1.86834i | 0.356822 | + | 0.934172i | \(0.383860\pi\) | ||||
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.23607i | 1.60108i | 0.599277 | + | 0.800542i | \(0.295455\pi\) | ||||
−0.599277 | + | 0.800542i | \(0.704545\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.47214 | −2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.23607i | − 0.620174i | −0.950708 | − | 0.310087i | \(-0.899642\pi\) | ||||
0.950708 | − | 0.310087i | \(-0.100358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.47214i | − 1.56972i | −0.619671 | − | 0.784862i | \(-0.712734\pi\) | ||||
0.619671 | − | 0.784862i | \(-0.287266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.7082 | −2.99138 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 14.4721i | − 2.78516i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76393 | 0.327554 | 0.163777 | − | 0.986497i | \(-0.447632\pi\) | ||||
0.163777 | + | 0.986497i | \(0.447632\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.472136 | 0.0847981 | 0.0423991 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0423991 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607i | 0.563327i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 11.2361i | − 1.84720i | −0.383360 | − | 0.923599i | \(-0.625233\pi\) | ||||
0.383360 | − | 0.923599i | \(-0.374767\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.23607 | 1.15870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.94427 | −0.928339 | −0.464170 | − | 0.885746i | \(-0.653647\pi\) | ||||
−0.464170 | + | 0.885746i | \(0.653647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.52786i | 0.385496i | 0.981248 | + | 0.192748i | \(0.0617399\pi\) | ||||
−0.981248 | + | 0.192748i | \(0.938260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 11.7082i | − 1.70782i | −0.520423 | − | 0.853909i | \(-0.674226\pi\) | ||||
0.520423 | − | 0.853909i | \(-0.325774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.9443 | −1.56347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.9443 | 2.93278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.23607i | 0.169787i | 0.996390 | + | 0.0848935i | \(0.0270550\pi\) | ||||
−0.996390 | + | 0.0848935i | \(0.972945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.23607i | − 0.428628i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.23607 | −0.421300 | −0.210650 | − | 0.977562i | \(-0.567558\pi\) | ||||
−0.210650 | + | 0.977562i | \(0.567558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23607 | −0.926484 | −0.463242 | − | 0.886232i | \(-0.653314\pi\) | ||||
−0.463242 | + | 0.886232i | \(0.653314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 31.6525i | − 3.98784i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.9443i | − 1.58139i | −0.612207 | − | 0.790697i | \(-0.709718\pi\) | ||||
0.612207 | − | 0.790697i | \(-0.290282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.23607 | 0.389577 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 9.47214i | − 1.10863i | −0.832307 | − | 0.554315i | \(-0.812980\pi\) | ||||
0.832307 | − | 0.554315i | \(-0.187020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.23607i | 0.482745i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1803 | −1.70792 | −0.853961 | − | 0.520337i | \(-0.825806\pi\) | ||||
−0.853961 | + | 0.520337i | \(0.825806\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.00000i | 0.987878i | 0.869496 | + | 0.493939i | \(0.164443\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.70820i | 0.611984i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.47214 | 0.992950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52786i | 0.158432i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.18034i | − 0.627518i | −0.949503 | − | 0.313759i | \(-0.898412\pi\) | ||||
0.949503 | − | 0.313759i | \(-0.101588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.47214 | −0.750978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.9443 | −1.88503 | −0.942513 | − | 0.334170i | \(-0.891544\pi\) | ||||
−0.942513 | + | 0.334170i | \(0.891544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.23607i | − 0.220326i | −0.993914 | − | 0.110163i | \(-0.964863\pi\) | ||||
0.993914 | − | 0.110163i | \(-0.0351373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.4164i | 1.87705i | 0.345204 | + | 0.938527i | \(0.387810\pi\) | ||||
−0.345204 | + | 0.938527i | \(0.612190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7639 | 1.22256 | 0.611281 | − | 0.791413i | \(-0.290654\pi\) | ||||
0.611281 | + | 0.791413i | \(0.290654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.3607 | 3.45120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.76393i | 0.636297i | 0.948041 | + | 0.318149i | \(0.103061\pi\) | ||||
−0.948041 | + | 0.318149i | \(0.896939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.7082i | 1.54467i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.4164 | 2.51326 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 19.2361i | − 1.73446i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.18034i | 0.370945i | 0.982649 | + | 0.185473i | \(0.0593816\pi\) | ||||
−0.982649 | + | 0.185473i | \(0.940618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.18034 | −0.720239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9443 | −1.30569 | −0.652844 | − | 0.757493i | \(-0.726424\pi\) | ||||
−0.652844 | + | 0.757493i | \(0.726424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.23607i | − 0.367314i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.5279i | − 0.984892i | −0.870343 | − | 0.492446i | \(-0.836103\pi\) | ||||
0.870343 | − | 0.492446i | \(-0.163897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.8885 | 3.19079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.23607i | − 0.186989i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 35.4164i | − 2.92110i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.9443 | −0.896590 | −0.448295 | − | 0.893886i | \(-0.647969\pi\) | ||||
−0.448295 | + | 0.893886i | \(0.647969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5279 | 0.938124 | 0.469062 | − | 0.883165i | \(-0.344592\pi\) | ||||
0.469062 | + | 0.883165i | \(0.344592\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 48.3607i | 3.90973i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.291796i | − 0.0232879i | −0.999932 | − | 0.0116439i | \(-0.996294\pi\) | ||||
0.999932 | − | 0.0116439i | \(-0.00370646\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.23607 | 0.333849 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.7082i | − 0.917057i | −0.888680 | − | 0.458529i | \(-0.848377\pi\) | ||||
0.888680 | − | 0.458529i | \(-0.151623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.41641i | 0.419134i | 0.977794 | + | 0.209567i | \(0.0672055\pi\) | ||||
−0.977794 | + | 0.209567i | \(0.932795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.00000 | 0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.47214 | 0.571409 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2361i | 1.08235i | 0.840911 | + | 0.541174i | \(0.182020\pi\) | ||||
−0.840911 | + | 0.541174i | \(0.817980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 10.4721i | − 0.787134i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7082 | 1.17409 | 0.587043 | − | 0.809556i | \(-0.300292\pi\) | ||||
0.587043 | + | 0.809556i | \(0.300292\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.944272 | −0.0701872 | −0.0350936 | − | 0.999384i | \(-0.511173\pi\) | ||||
−0.0350936 | + | 0.999384i | \(0.511173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 23.4164i | − 1.73099i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.47214i | − 0.473289i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 61.3050 | 4.45928 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1803 | −1.38784 | −0.693920 | − | 0.720052i | \(-0.744118\pi\) | ||||
−0.693920 | + | 0.720052i | \(0.744118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.94427i | 0.211933i | 0.994370 | + | 0.105967i | \(0.0337937\pi\) | ||||
−0.994370 | + | 0.105967i | \(0.966206\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.23607i | 0.586796i | 0.955990 | + | 0.293398i | \(0.0947860\pi\) | ||||
−0.955990 | + | 0.293398i | \(0.905214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7082 | −0.900861 | −0.450430 | − | 0.892812i | \(-0.648729\pi\) | ||||
−0.450430 | + | 0.892812i | \(0.648729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.8885 | 2.95459 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.47214i | 0.524441i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.47214i | 0.519349i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9443 | −1.02881 | −0.514403 | − | 0.857549i | \(-0.671986\pi\) | ||||
−0.514403 | + | 0.857549i | \(0.671986\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.3607i | 2.21732i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000i | 0.135769i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.6525 | 2.07130 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2361i | 0.886353i | 0.896434 | + | 0.443176i | \(0.146148\pi\) | ||||
−0.896434 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.9443i | − 0.859142i | −0.903033 | − | 0.429571i | \(-0.858665\pi\) | ||||
0.903033 | − | 0.429571i | \(-0.141335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.94427 | −0.458890 | −0.229445 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229445 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.7082 | −0.901934 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.52786i | 0.296630i | 0.988940 | + | 0.148315i | \(0.0473850\pi\) | ||||
−0.988940 | + | 0.148315i | \(0.952615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 49.1246i | − 3.19099i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.76393 | −0.437522 | −0.218761 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218761 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2361 | 1.36794 | 0.683968 | − | 0.729512i | \(-0.260253\pi\) | ||||
0.683968 | + | 0.729512i | \(0.260253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.5967i | 2.28353i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23607i | 0.142278i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.1246 | −1.84570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.52786 | −0.348916 | −0.174458 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174458 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.00000i | − 0.0628695i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000i | 0.873296i | 0.899632 | + | 0.436648i | \(0.143834\pi\) | ||||
−0.899632 | + | 0.436648i | \(0.856166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 47.5967 | 2.95752 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1803 | −0.815843 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.00000i | 0.493301i | 0.969104 | + | 0.246651i | \(0.0793300\pi\) | ||||
−0.969104 | + | 0.246651i | \(0.920670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.47214i | − 0.396088i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.1803 | 1.53527 | 0.767636 | − | 0.640886i | \(-0.221433\pi\) | ||||
0.767636 | + | 0.640886i | \(0.221433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0689 | −1.94805 | −0.974023 | − | 0.226449i | \(-0.927288\pi\) | ||||
−0.974023 | + | 0.226449i | \(0.927288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.6525i | 1.85517i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 14.2361i | − 0.855362i | −0.903930 | − | 0.427681i | \(-0.859331\pi\) | ||||
0.903930 | − | 0.427681i | \(-0.140669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.52786 | −0.211208 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1803 | −1.32317 | −0.661584 | − | 0.749871i | \(-0.730116\pi\) | ||||
−0.661584 | + | 0.749871i | \(0.730116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.3607i | 1.68587i | 0.538017 | + | 0.842934i | \(0.319173\pi\) | ||||
−0.538017 | + | 0.842934i | \(0.680827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 25.1803i | − 1.48635i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.0000 | 1.17242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 14.4721i | − 0.845471i | −0.906253 | − | 0.422736i | \(-0.861070\pi\) | ||||
0.906253 | − | 0.422736i | \(-0.138930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 14.4721i | − 0.839759i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.23607 | −0.129315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7082 | −0.617211 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 61.3050i | − 3.52188i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 24.0000i | − 1.36975i | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||||
0.728659 | − | 0.684876i | \(-0.240144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.23607 | 0.411646 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.23607 | −0.183501 | −0.0917503 | − | 0.995782i | \(-0.529246\pi\) | ||||
−0.0917503 | + | 0.995782i | \(0.529246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 10.6525i | − 0.602114i | −0.953606 | − | 0.301057i | \(-0.902661\pi\) | ||||
0.953606 | − | 0.301057i | \(-0.0973394\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.1246i | 1.24264i | 0.783556 | + | 0.621321i | \(0.213404\pi\) | ||||
−0.783556 | + | 0.621321i | \(0.786596\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.76393 | 0.0987612 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −62.8328 | −3.50699 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.47214i | 0.360119i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.3050i | 2.28417i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 49.5967 | 2.73436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9443 | 1.70085 | 0.850426 | − | 0.526095i | \(-0.176345\pi\) | ||||
0.850426 | + | 0.526095i | \(0.176345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83.9574i | 4.60084i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.6525i | 1.34291i | 0.741047 | + | 0.671453i | \(0.234329\pi\) | ||||
−0.741047 | + | 0.671453i | \(0.765671\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.8885 | −1.18882 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.472136 | 0.0255676 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 16.7082i | − 0.902158i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 3.05573i | − 0.164040i | −0.996631 | − | 0.0820200i | \(-0.973863\pi\) | ||||
0.996631 | − | 0.0820200i | \(-0.0261372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.18034 | 0.277297 | 0.138649 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138649 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.3607 | −1.72729 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 4.88854i | − 0.260191i | −0.991501 | − | 0.130095i | \(-0.958472\pi\) | ||||
0.991501 | − | 0.130095i | \(-0.0415284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 88.7214i | 4.69563i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7639 | −1.04310 | −0.521550 | − | 0.853221i | \(-0.674646\pi\) | ||||
−0.521550 | + | 0.853221i | \(0.674646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 32.3607i | − 1.69850i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.6525i | 1.23465i | 0.786709 | + | 0.617325i | \(0.211783\pi\) | ||||
−0.786709 | + | 0.617325i | \(0.788217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.4164 | 2.31223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.23607 | −0.271843 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.0000i | − 0.621336i | −0.950518 | − | 0.310668i | \(-0.899447\pi\) | ||||
0.950518 | − | 0.310668i | \(-0.100553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.94427i | − 0.203140i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.05573 | −0.156962 | −0.0784811 | − | 0.996916i | \(-0.525007\pi\) | ||||
−0.0784811 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5279 | −0.693053 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 0.236068i | − 0.0120625i | −0.999982 | − | 0.00603126i | \(-0.998080\pi\) | ||||
0.999982 | − | 0.00603126i | \(-0.00191982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 18.8885i | − 0.960159i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.18034 | −0.313356 | −0.156678 | − | 0.987650i | \(-0.550078\pi\) | ||||
−0.156678 | + | 0.987650i | \(0.550078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.47214 | −0.327310 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 48.3607i | − 2.43947i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 22.3607i | − 1.12225i | −0.827731 | − | 0.561125i | \(-0.810369\pi\) | ||||
0.827731 | − | 0.561125i | \(-0.189631\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.7082 | 0.686269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1246 | −0.655412 | −0.327706 | − | 0.944780i | \(-0.606276\pi\) | ||||
−0.327706 | + | 0.944780i | \(0.606276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.05573i | − 0.0525896i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 11.2361i | − 0.556951i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4164 | 1.30621 | 0.653104 | − | 0.757269i | \(-0.273467\pi\) | ||||
0.653104 | + | 0.757269i | \(0.273467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 37.3050 | 1.84012 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.7082i | − 0.674537i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 64.7214i | − 3.16942i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.7771 | 1.79668 | 0.898339 | − | 0.439303i | \(-0.144774\pi\) | ||||
0.898339 | + | 0.439303i | \(0.144774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8885 | 0.774360 | 0.387180 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387180 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 87.4853i | 4.25368i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 30.6525i | − 1.48338i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.23607 | 0.349361 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.9443 | 0.623504 | 0.311752 | − | 0.950164i | \(-0.399084\pi\) | ||||
0.311752 | + | 0.950164i | \(0.399084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 29.1246i | − 1.39964i | −0.714319 | − | 0.699820i | \(-0.753264\pi\) | ||||
0.714319 | − | 0.699820i | \(-0.246736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000i | 0.0478365i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3607 | −0.589943 | −0.294972 | − | 0.955506i | \(-0.595310\pi\) | ||||
−0.294972 | + | 0.955506i | \(0.595310\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 81.7771 | 3.89415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10.0000i | − 0.475114i | −0.971374 | − | 0.237557i | \(-0.923653\pi\) | ||||
0.971374 | − | 0.237557i | \(-0.0763467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 35.4164i | − 1.67514i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.8328 | 1.73825 | 0.869124 | − | 0.494594i | \(-0.164683\pi\) | ||||
0.869124 | + | 0.494594i | \(0.164683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.94427 | −0.279905 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.3050i | 1.75274i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6525i | 0.966082i | 0.875598 | + | 0.483041i | \(0.160468\pi\) | ||||
−0.875598 | + | 0.483041i | \(0.839532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −93.6656 | −4.37194 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.6525 | 1.56735 | 0.783676 | − | 0.621170i | \(-0.213342\pi\) | ||||
0.783676 | + | 0.621170i | \(0.213342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 26.4721i | − 1.23026i | −0.788424 | − | 0.615132i | \(-0.789103\pi\) | ||||
0.788424 | − | 0.615132i | \(-0.210897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000i | 0.786666i | 0.919396 | + | 0.393333i | \(0.128678\pi\) | ||||
−0.919396 | + | 0.393333i | \(0.871322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 54.8328 | 2.53194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.944272 | 0.0435098 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.52786i | 0.116231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 9.23607i | − 0.422891i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1246 | 0.553988 | 0.276994 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276994 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1246 | −1.14558 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.7082i | 0.623745i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1246i | 1.77291i | 0.462819 | + | 0.886453i | \(0.346838\pi\) | ||||
−0.462819 | + | 0.886453i | \(0.653162\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.8885 | 1.71338 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.23607 | −0.146042 | −0.0730209 | − | 0.997330i | \(-0.523264\pi\) | ||||
−0.0730209 | + | 0.997330i | \(0.523264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 11.4164i | − 0.514169i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.3607i | 1.90014i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.5410 | 1.90440 | 0.952199 | − | 0.305479i | \(-0.0988166\pi\) | ||||
0.952199 | + | 0.305479i | \(0.0988166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.5279 | −0.783087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.5967i | 0.740012i | 0.929029 | + | 0.370006i | \(0.120644\pi\) | ||||
−0.929029 | + | 0.370006i | \(0.879356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.8885i | 1.14975i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.3607 | −1.34571 | −0.672857 | − | 0.739773i | \(-0.734933\pi\) | ||||
−0.672857 | + | 0.739773i | \(0.734933\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.1246 | 1.77501 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.4721i | 0.638960i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 11.7082i | − 0.514926i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.0689 | −2.02220 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.34752 | 0.409522 | 0.204761 | − | 0.978812i | \(-0.434358\pi\) | ||||
0.204761 | + | 0.978812i | \(0.434358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.8885i | − 0.825938i | −0.910745 | − | 0.412969i | \(-0.864492\pi\) | ||||
0.910745 | − | 0.412969i | \(-0.135508\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.05573i | − 0.133110i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.1803 | 1.04934 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2918i | 0.575732i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.8328i | 2.19360i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9443 | −0.471403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.70820 | 0.374395 | 0.187197 | − | 0.982322i | \(-0.440060\pi\) | ||||
0.187197 | + | 0.982322i | \(0.440060\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.05573i | − 0.131134i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7082i | 0.671634i | 0.941927 | + | 0.335817i | \(0.109012\pi\) | ||||
−0.941927 | + | 0.335817i | \(0.890988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 54.0689 | 2.30760 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76393 | −0.0751460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 64.3050i | − 2.73452i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 36.1803i | − 1.53301i | −0.642238 | − | 0.766505i | \(-0.721994\pi\) | ||||
0.642238 | − | 0.766505i | \(-0.278006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.65248 | 0.239074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 39.3607i | − 1.65885i | −0.558614 | − | 0.829427i | \(-0.688667\pi\) | ||||
0.558614 | − | 0.829427i | \(-0.311333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 103.430i | 4.34363i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.5836 | −0.527532 | −0.263766 | − | 0.964587i | \(-0.584965\pi\) | ||||
−0.263766 | + | 0.964587i | \(0.584965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000 | 1.00437 | 0.502184 | − | 0.864761i | \(-0.332530\pi\) | ||||
0.502184 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 62.0689i | − 2.59296i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9.00000i | − 0.374675i | −0.982296 | − | 0.187337i | \(-0.940014\pi\) | ||||
0.982296 | − | 0.187337i | \(-0.0599858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.52786 | −0.395965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.1246 | −1.58168 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.23607i | 0.0511927i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 27.5967i | − 1.13904i | −0.821978 | − | 0.569520i | \(-0.807129\pi\) | ||||
0.821978 | − | 0.569520i | \(-0.192871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.472136 | −0.0194540 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.6525 | −1.09634 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.8885i | 1.84335i | 0.387961 | + | 0.921676i | \(0.373180\pi\) | ||||
−0.387961 | + | 0.921676i | \(0.626820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 41.1246i | − 1.68312i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8328 | −0.687770 | −0.343885 | − | 0.939012i | \(-0.611743\pi\) | ||||
−0.343885 | + | 0.939012i | \(0.611743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9443 | −0.609590 | −0.304795 | − | 0.952418i | \(-0.598588\pi\) | ||||
−0.304795 | + | 0.952418i | \(0.598588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 96.7214i | 3.93880i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.1246i | − 0.938599i | −0.883039 | − | 0.469300i | \(-0.844506\pi\) | ||||
0.883039 | − | 0.469300i | \(-0.155494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.1803 | −0.979837 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1803 | −1.05914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 18.0689i | − 0.729795i | −0.931048 | − | 0.364898i | \(-0.881104\pi\) | ||||
0.931048 | − | 0.364898i | \(-0.118896\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 25.3050i | − 1.01874i | −0.860548 | − | 0.509369i | \(-0.829879\pi\) | ||||
0.860548 | − | 0.509369i | \(-0.170121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.52786 | 0.382957 | 0.191479 | − | 0.981497i | \(-0.438672\pi\) | ||||
0.191479 | + | 0.981497i | \(0.438672\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.4721 | −0.580747 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 8.47214i | − 0.339429i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.23607i | − 0.129236i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −72.7214 | −2.89959 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.1246 | −0.960386 | −0.480193 | − | 0.877163i | \(-0.659433\pi\) | ||||
−0.480193 | + | 0.877163i | \(0.659433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 48.3607i | − 1.92216i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.4721i | 0.969621i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −74.7214 | −2.95593 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7771 | 1.09713 | 0.548564 | − | 0.836108i | \(-0.315175\pi\) | ||||
0.548564 | + | 0.836108i | \(0.315175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.94427i | 0.0766746i | 0.999265 | + | 0.0383373i | \(0.0122061\pi\) | ||||
−0.999265 | + | 0.0383373i | \(0.987794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 10.1803i | − 0.400230i | −0.979772 | − | 0.200115i | \(-0.935868\pi\) | ||||
0.979772 | − | 0.200115i | \(-0.0641317\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.23607 | −0.127027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.47214 | −0.253663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 39.5410i | − 1.54736i | −0.633577 | − | 0.773680i | \(-0.718414\pi\) | ||||
0.633577 | − | 0.773680i | \(-0.281586\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70.7771i | 2.76128i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4721 | −0.524800 | −0.262400 | − | 0.964959i | \(-0.584514\pi\) | ||||
−0.262400 | + | 0.964959i | \(0.584514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8197 | −0.848686 | −0.424343 | − | 0.905501i | \(-0.639495\pi\) | ||||
−0.424343 | + | 0.905501i | \(0.639495\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 46.8328i | − 1.81884i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.76393i | − 0.0682997i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.8328 | −1.65601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.23607 | −0.279345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.3050i | 1.86202i | 0.364995 | + | 0.931010i | \(0.381071\pi\) | ||||
−0.364995 | + | 0.931010i | \(0.618929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.7082i | 0.680582i | 0.940320 | + | 0.340291i | \(0.110526\pi\) | ||||
−0.940320 | + | 0.340291i | \(0.889474\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.1803 | 1.00471 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.8885 | 1.60517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.7771i | 1.59856i | 0.600962 | + | 0.799278i | \(0.294784\pi\) | ||||
−0.600962 | + | 0.799278i | \(0.705216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 22.4721i | − 0.857365i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.76393 | 0.105297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.4721 | −1.61572 | −0.807858 | − | 0.589377i | \(-0.799373\pi\) | ||||
−0.807858 | + | 0.589377i | \(0.799373\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 31.6525i | − 1.20238i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.4721i | 1.45724i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.6525 | −0.554208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.5279 | −1.41741 | −0.708704 | − | 0.705506i | \(-0.750720\pi\) | ||||
−0.708704 | + | 0.705506i | \(0.750720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2361i | 0.423776i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 80.2492i | − 3.01808i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.41641 | −0.353641 | −0.176820 | − | 0.984243i | \(-0.556581\pi\) | ||||
−0.176820 | + | 0.984243i | \(0.556581\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 113.430 | 4.25394 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 0.472136i | − 0.0176816i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21.8885i | − 0.817443i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.7082 | −1.40628 | −0.703139 | − | 0.711052i | \(-0.748219\pi\) | ||||
−0.703139 | + | 0.711052i | \(0.748219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.47214 | 0.352761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 68.7214i | 2.55577i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 44.7214i | − 1.65862i | −0.558786 | − | 0.829312i | \(-0.688733\pi\) | ||||
0.558786 | − | 0.829312i | \(-0.311267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.9443 | −1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3607 | 0.605122 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 39.5279i | − 1.45999i | −0.683450 | − | 0.729997i | \(-0.739521\pi\) | ||||
0.683450 | − | 0.729997i | \(-0.260479\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 12.9443i | − 0.476808i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.05573 | −0.333120 | −0.166560 | − | 0.986031i | \(-0.553266\pi\) | ||||
−0.166560 | + | 0.986031i | \(0.553266\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.23607 | −0.265824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.1803i | 1.43739i | 0.695327 | + | 0.718694i | \(0.255260\pi\) | ||||
−0.695327 | + | 0.718694i | \(0.744740\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 67.2492i | − 2.46052i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −82.2492 | −3.00532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5967 | −0.824567 | −0.412284 | − | 0.911056i | \(-0.635269\pi\) | ||||
−0.412284 | + | 0.911056i | \(0.635269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 17.8885i | − 0.651895i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.7639i | 0.609295i | 0.952465 | + | 0.304648i | \(0.0985387\pi\) | ||||
−0.952465 | + | 0.304648i | \(0.901461\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.23607 | 0.117462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.8885 | −1.91721 | −0.958604 | − | 0.284742i | \(-0.908092\pi\) | ||||
−0.958604 | + | 0.284742i | \(0.908092\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 54.0689i | 1.95743i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.23607i | 0.261279i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.0689 | 1.66129 | 0.830643 | − | 0.556805i | \(-0.187973\pi\) | ||||
0.830643 | + | 0.556805i | \(0.187973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.3050 | −1.63162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4.76393i | − 0.171347i | −0.996323 | − | 0.0856734i | \(-0.972696\pi\) | ||||
0.996323 | − | 0.0856734i | \(-0.0273041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 154.026i | 5.52566i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.94427 | 0.212976 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 25.5279i | − 0.912291i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 39.7214i | − 1.41591i | −0.706256 | − | 0.707957i | \(-0.749617\pi\) | ||||
0.706256 | − | 0.707957i | \(-0.250383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.8885 | −0.921657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.6525 | −1.01876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1803i | 0.574581i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 15.2361i | − 0.539689i | −0.962904 | − | 0.269845i | \(-0.913028\pi\) | ||||
0.962904 | − | 0.269845i | \(-0.0869723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.7771 | −2.68080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.9443 | 0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.47214i | − 0.334264i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 81.4853i | 2.86842i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.11146 | 0.320342 | 0.160171 | − | 0.987089i | \(-0.448795\pi\) | ||||
0.160171 | + | 0.987089i | \(0.448795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4164 | 0.541343 | 0.270672 | − | 0.962672i | \(-0.412754\pi\) | ||||
0.270672 | + | 0.962672i | \(0.412754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 103.777i | − 3.63962i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 2.52786i | − 0.0884388i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −70.7771 | −2.47315 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.2361 | −0.776044 | −0.388022 | − | 0.921650i | \(-0.626842\pi\) | ||||
−0.388022 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.94427i | 0.311778i | 0.987775 | + | 0.155889i | \(0.0498242\pi\) | ||||
−0.987775 | + | 0.155889i | \(0.950176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.00000i | − 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.23607 | 0.147125 | 0.0735624 | − | 0.997291i | \(-0.476563\pi\) | ||||
0.0735624 | + | 0.997291i | \(0.476563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 46.0689 | 1.59811 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 70.8328i | 2.45421i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.83282i | − 0.236177i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.59675 | −0.296793 | −0.148396 | − | 0.988928i | \(-0.547411\pi\) | ||||
−0.148396 | + | 0.988928i | \(0.547411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8885 | −0.892708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 71.7771i | − 2.47213i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 42.3607i | − 1.45553i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −91.7771 | −3.14978 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2361 | −0.385167 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2361i | 0.966785i | 0.875404 | + | 0.483392i | \(0.160596\pi\) | ||||
−0.875404 | + | 0.483392i | \(0.839404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.3050i | 1.20599i | 0.797743 | + | 0.602997i | \(0.206027\pi\) | ||||
−0.797743 | + | 0.602997i | \(0.793973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.7082 | 0.740674 | 0.370337 | − | 0.928897i | \(-0.379242\pi\) | ||||
0.370337 | + | 0.928897i | \(0.379242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 81.4853 | 2.77701 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 34.5410i | − 1.17579i | −0.808937 | − | 0.587895i | \(-0.799957\pi\) | ||||
0.808937 | − | 0.587895i | \(-0.200043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 80.5410i | − 2.73532i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1803 | −0.514958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.9443 | −0.980739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.1803i | 1.56297i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.58359i | 0.0872417i | 0.999048 | + | 0.0436209i | \(0.0138894\pi\) | ||||
−0.999048 | + | 0.0436209i | \(0.986111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.8328 | 1.57963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.7082 | 1.27042 | 0.635211 | − | 0.772339i | \(-0.280913\pi\) | ||||
0.635211 | + | 0.772339i | \(0.280913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.05573i | − 0.102833i | −0.998677 | − | 0.0514167i | \(-0.983626\pi\) | ||||
0.998677 | − | 0.0514167i | \(-0.0163737\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3607i | 0.415031i | 0.978232 | + | 0.207516i | \(0.0665377\pi\) | ||||
−0.978232 | + | 0.207516i | \(0.933462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.7082 | −0.593914 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4164 | 0.817980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7082i | 0.391800i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7.23607i | − 0.241605i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.832816 | 0.0277760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 34.6525i | − 1.15316i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.58359i | 0.185400i | 0.995694 | + | 0.0927001i | \(0.0295498\pi\) | ||||
−0.995694 | + | 0.0927001i | \(0.970450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 141.554 | 4.69506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.0689 | −1.02936 | −0.514679 | − | 0.857383i | \(-0.672089\pi\) | ||||
−0.514679 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000i | 0.297857i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 63.3050i | − 2.09051i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.7771 | −1.44407 | −0.722036 | − | 0.691855i | \(-0.756794\pi\) | ||||
−0.722036 | + | 0.691855i | \(0.756794\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 77.6656 | 2.55917 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 22.3607i | − 0.736011i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.7082i | 0.548769i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0000 | −1.01708 | −0.508539 | − | 0.861039i | \(-0.669814\pi\) | ||||
−0.508539 | + | 0.861039i | \(0.669814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9443 | 0.358684 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 10.4721i | − 0.342842i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 7.12461i | − 0.232751i | −0.993205 | − | 0.116375i | \(-0.962872\pi\) | ||||
0.993205 | − | 0.116375i | \(-0.0371276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.4721 | 1.12496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2361 | −0.431483 | −0.215742 | − | 0.976450i | \(-0.569217\pi\) | ||||
−0.215742 | + | 0.976450i | \(0.569217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.94427i | 0.193572i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 45.1935i | − 1.46859i | −0.678830 | − | 0.734296i | \(-0.737513\pi\) | ||||
0.678830 | − | 0.734296i | \(-0.262487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.1803 | −0.687543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −71.5967 | −2.32168 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.34752i | 0.173223i | 0.996242 | + | 0.0866116i | \(0.0276039\pi\) | ||||
−0.996242 | + | 0.0866116i | \(0.972396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.70820i | 0.184520i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.8328 | 1.57689 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7771 | −0.992809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 145.082i | − 4.67520i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 5.88854i | − 0.189363i | −0.995508 | − | 0.0946814i | \(-0.969817\pi\) | ||||
0.995508 | − | 0.0946814i | \(-0.0301832\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.9443 | −0.672827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2492 | 1.19538 | 0.597692 | − | 0.801726i | \(-0.296084\pi\) | ||||
0.597692 | + | 0.801726i | \(0.296084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 84.7214i | − 2.71604i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 22.5410i | − 0.721151i | −0.932730 | − | 0.360576i | \(-0.882580\pi\) | ||||
0.932730 | − | 0.360576i | \(-0.117420\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.3738 | −3.04505 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.6525i | 0.881977i | 0.897513 | + | 0.440989i | \(0.145372\pi\) | ||||
−0.897513 | + | 0.440989i | \(0.854628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 160.498i | 5.10872i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.52786 | 0.0803814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5967 | −1.32136 | −0.660682 | − | 0.750666i | \(-0.729733\pi\) | ||||
−0.660682 | + | 0.750666i | \(0.729733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 100.138i | 3.17778i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.12461i | 0.0672871i | 0.999434 | + | 0.0336436i | \(0.0107111\pi\) | ||||
−0.999434 | + | 0.0336436i | \(0.989289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −162.610 | −5.14475 |
(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 | 4600.2.e.l.4049.4 | 4 | ||
5.2 | odd | 4 | 4600.2.a.u.1.2 | yes | 2 | ||
5.3 | odd | 4 | 4600.2.a.q.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 4600.2.e.l.4049.1 | 4 | ||
20.3 | even | 4 | 9200.2.a.bz.1.2 | 2 | |||
20.7 | even | 4 | 9200.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.q.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
4600.2.a.u.1.2 | yes | 2 | 5.2 | odd | 4 | ||
4600.2.e.l.4049.1 | 4 | 5.4 | even | 2 | inner | ||
4600.2.e.l.4049.4 | 4 | 1.1 | even | 1 | trivial | ||
9200.2.a.bn.1.1 | 2 | 20.7 | even | 4 | |||
9200.2.a.bz.1.2 | 2 | 20.3 | even | 4 |