Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (of order \(2\), degree \(1\), 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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.2 | ||
Root | \(0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.f.881.7 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | − 0.930151i | − 0.280451i | −0.990120 | − | 0.140226i | \(-0.955217\pi\) | ||||
0.990120 | − | 0.140226i | \(-0.0447828\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.331821i | − 0.0920307i | −0.998941 | − | 0.0460153i | \(-0.985348\pi\) | ||||
0.998941 | − | 0.0460153i | \(-0.0146523\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.26197 | 0.791145 | 0.395572 | − | 0.918435i | \(-0.370546\pi\) | ||||
0.395572 | + | 0.918435i | \(0.370546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.547123i | 0.125519i | 0.998029 | + | 0.0627593i | \(0.0199900\pi\) | ||||
−0.998029 | + | 0.0627593i | \(0.980010\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.930151 | −0.198309 | ||||||||
\(23\) | 0.801088i | 0.167038i | 0.996506 | + | 0.0835192i | \(0.0266160\pi\) | ||||
−0.996506 | + | 0.0835192i | \(0.973384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.331821 | −0.0650755 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.37170i | 1.18320i | 0.806233 | + | 0.591598i | \(0.201503\pi\) | ||||
−0.806233 | + | 0.591598i | \(0.798497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.101724i | 0.0182702i | 0.999958 | + | 0.00913510i | \(0.00290783\pi\) | ||||
−0.999958 | + | 0.00913510i | \(0.997092\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 3.26197i | − 0.559424i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.29385 | 1.36350 | 0.681750 | − | 0.731585i | \(-0.261219\pi\) | ||||
0.681750 | + | 0.731585i | \(0.261219\pi\) | |||||||
\(38\) | 0.547123 | 0.0887550 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −6.57446 | −1.02676 | −0.513379 | − | 0.858162i | \(-0.671607\pi\) | ||||
−0.513379 | + | 0.858162i | \(0.671607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.49501 | 0.227987 | 0.113994 | − | 0.993481i | \(-0.463636\pi\) | ||||
0.113994 | + | 0.993481i | \(0.463636\pi\) | |||||||
\(44\) | 0.930151i | 0.140226i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.801088 | 0.118114 | ||||||||
\(47\) | 6.57741 | 0.959413 | 0.479707 | − | 0.877429i | \(-0.340743\pi\) | ||||
0.479707 | + | 0.877429i | \(0.340743\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.331821i | 0.0460153i | ||||||||
\(53\) | − 6.38009i | − 0.876372i | −0.898884 | − | 0.438186i | \(-0.855621\pi\) | ||||
0.898884 | − | 0.438186i | \(-0.144379\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.930151i | − 0.125422i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.37170 | 0.836646 | ||||||||
\(59\) | 6.11652 | 0.796303 | 0.398152 | − | 0.917320i | \(-0.369652\pi\) | ||||
0.398152 | + | 0.917320i | \(0.369652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.28130i | 0.548165i | 0.961706 | + | 0.274082i | \(0.0883741\pi\) | ||||
−0.961706 | + | 0.274082i | \(0.911626\pi\) | |||||||
\(62\) | 0.101724 | 0.0129190 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 0.331821i | − 0.0411574i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.25102 | −0.275006 | −0.137503 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137503 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(68\) | −3.26197 | −0.395572 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.64725i | 0.432849i | 0.976299 | + | 0.216425i | \(0.0694396\pi\) | ||||
−0.976299 | + | 0.216425i | \(0.930560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.28356i | 0.267270i | 0.991031 | + | 0.133635i | \(0.0426650\pi\) | ||||
−0.991031 | + | 0.133635i | \(0.957335\pi\) | |||||||
\(74\) | − 8.29385i | − 0.964140i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 0.547123i | − 0.0627593i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.32957 | 0.487115 | 0.243557 | − | 0.969887i | \(-0.421686\pi\) | ||||
0.243557 | + | 0.969887i | \(0.421686\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.57446i | 0.726028i | ||||||||
\(83\) | −15.4785 | −1.69899 | −0.849493 | − | 0.527600i | \(-0.823092\pi\) | ||||
−0.849493 | + | 0.527600i | \(0.823092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.26197 | 0.353811 | ||||||||
\(86\) | − 1.49501i | − 0.161211i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.930151 | 0.0991545 | ||||||||
\(89\) | −0.219463 | −0.0232631 | −0.0116315 | − | 0.999932i | \(-0.503703\pi\) | ||||
−0.0116315 | + | 0.999932i | \(0.503703\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 0.801088i | − 0.0835192i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 6.57741i | − 0.678408i | ||||||||
\(95\) | 0.547123i | 0.0561336i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.65685i | − 0.371297i | −0.982616 | − | 0.185649i | \(-0.940561\pi\) | ||||
0.982616 | − | 0.185649i | \(-0.0594386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 10.7119 | 1.06587 | 0.532937 | − | 0.846155i | \(-0.321088\pi\) | ||||
0.532937 | + | 0.846155i | \(0.321088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.91082i | 0.188279i | 0.995559 | + | 0.0941393i | \(0.0300099\pi\) | ||||
−0.995559 | + | 0.0941393i | \(0.969990\pi\) | |||||||
\(104\) | 0.331821 | 0.0325378 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.38009 | −0.619689 | ||||||||
\(107\) | − 0.972287i | − 0.0939945i | −0.998895 | − | 0.0469973i | \(-0.985035\pi\) | ||||
0.998895 | − | 0.0469973i | \(-0.0149652\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.4020 | 1.76259 | 0.881295 | − | 0.472566i | \(-0.156672\pi\) | ||||
0.881295 | + | 0.472566i | \(0.156672\pi\) | |||||||
\(110\) | −0.930151 | −0.0886864 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.16160i | 0.391490i | 0.980655 | + | 0.195745i | \(0.0627125\pi\) | ||||
−0.980655 | + | 0.195745i | \(0.937287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.801088i | 0.0747018i | ||||||||
\(116\) | − 6.37170i | − 0.591598i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 6.11652i | − 0.563071i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.1348 | 0.921347 | ||||||||
\(122\) | 4.28130 | 0.387611 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 0.101724i | − 0.00913510i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9832 | 1.41828 | 0.709141 | − | 0.705066i | \(-0.249083\pi\) | ||||
0.709141 | + | 0.705066i | \(0.249083\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.331821 | −0.0291027 | ||||||||
\(131\) | −5.82805 | −0.509199 | −0.254600 | − | 0.967047i | \(-0.581944\pi\) | ||||
−0.254600 | + | 0.967047i | \(0.581944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.25102i | 0.194459i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.26197i | 0.279712i | ||||||||
\(137\) | − 5.58316i | − 0.477002i | −0.971142 | − | 0.238501i | \(-0.923344\pi\) | ||||
0.971142 | − | 0.238501i | \(-0.0766560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 12.8599i | − 1.09076i | −0.838187 | − | 0.545382i | \(-0.816384\pi\) | ||||
0.838187 | − | 0.545382i | \(-0.183616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.64725 | 0.306071 | ||||||||
\(143\) | −0.308644 | −0.0258101 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.37170i | 0.529141i | ||||||||
\(146\) | 2.28356 | 0.188989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.29385 | −0.681750 | ||||||||
\(149\) | − 7.93694i | − 0.650219i | −0.945676 | − | 0.325110i | \(-0.894599\pi\) | ||||
0.945676 | − | 0.325110i | \(-0.105401\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5236 | 1.10053 | 0.550266 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550266 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(152\) | −0.547123 | −0.0443775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.101724i | 0.00817068i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3196i | 1.22264i | 0.791385 | + | 0.611318i | \(0.209361\pi\) | ||||
−0.791385 | + | 0.611318i | \(0.790639\pi\) | |||||||
\(158\) | − 4.32957i | − 0.344442i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2661 | 1.03908 | 0.519542 | − | 0.854445i | \(-0.326103\pi\) | ||||
0.519542 | + | 0.854445i | \(0.326103\pi\) | |||||||
\(164\) | 6.57446 | 0.513379 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.4785i | 1.20136i | ||||||||
\(167\) | −15.3462 | −1.18753 | −0.593764 | − | 0.804639i | \(-0.702359\pi\) | ||||
−0.593764 | + | 0.804639i | \(0.702359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8899 | 0.991530 | ||||||||
\(170\) | − 3.26197i | − 0.250182i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.49501 | −0.113994 | ||||||||
\(173\) | 7.23532 | 0.550091 | 0.275046 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275046 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 0.930151i | − 0.0701128i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.219463i | 0.0164495i | ||||||||
\(179\) | − 14.8082i | − 1.10682i | −0.832910 | − | 0.553408i | \(-0.813327\pi\) | ||||
0.832910 | − | 0.553408i | \(-0.186673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0930i | 1.12185i | 0.827866 | + | 0.560926i | \(0.189555\pi\) | ||||
−0.827866 | + | 0.560926i | \(0.810445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.801088 | −0.0590570 | ||||||||
\(185\) | 8.29385 | 0.609776 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.03413i | − 0.221877i | ||||||||
\(188\) | −6.57741 | −0.479707 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.547123 | 0.0396924 | ||||||||
\(191\) | − 20.9314i | − 1.51454i | −0.653101 | − | 0.757270i | \(-0.726533\pi\) | ||||
0.653101 | − | 0.757270i | \(-0.273467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6014 | 1.12302 | 0.561508 | − | 0.827472i | \(-0.310222\pi\) | ||||
0.561508 | + | 0.827472i | \(0.310222\pi\) | |||||||
\(194\) | −3.65685 | −0.262547 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.65498i | − 0.189159i | −0.995517 | − | 0.0945796i | \(-0.969849\pi\) | ||||
0.995517 | − | 0.0945796i | \(-0.0301507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.6840i | − 0.828253i | −0.910219 | − | 0.414127i | \(-0.864087\pi\) | ||||
0.910219 | − | 0.414127i | \(-0.135913\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 10.7119i | − 0.753687i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.57446 | −0.459180 | ||||||||
\(206\) | 1.91082 | 0.133133 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 0.331821i | − 0.0230077i | ||||||||
\(209\) | 0.508907 | 0.0352018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.36407 | −0.300435 | −0.150218 | − | 0.988653i | \(-0.547997\pi\) | ||||
−0.150218 | + | 0.988653i | \(0.547997\pi\) | |||||||
\(212\) | 6.38009i | 0.438186i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.972287 | −0.0664642 | ||||||||
\(215\) | 1.49501 | 0.101959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 18.4020i | − 1.24634i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.930151i | 0.0627108i | ||||||||
\(221\) | − 1.08239i | − 0.0728096i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2623i | 1.62472i | 0.583154 | + | 0.812362i | \(0.301818\pi\) | ||||
−0.583154 | + | 0.812362i | \(0.698182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.16160 | 0.276825 | ||||||||
\(227\) | 29.2809 | 1.94344 | 0.971722 | − | 0.236129i | \(-0.0758787\pi\) | ||||
0.971722 | + | 0.236129i | \(0.0758787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.84710i | − 0.320305i | −0.987092 | − | 0.160153i | \(-0.948801\pi\) | ||||
0.987092 | − | 0.160153i | \(-0.0511987\pi\) | |||||||
\(230\) | 0.801088 | 0.0528222 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.37170 | −0.418323 | ||||||||
\(233\) | 2.66683i | 0.174710i | 0.996177 | + | 0.0873549i | \(0.0278414\pi\) | ||||
−0.996177 | + | 0.0873549i | \(0.972159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.57741 | 0.429063 | ||||||||
\(236\) | −6.11652 | −0.398152 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9906i | 1.22840i | 0.789152 | + | 0.614198i | \(0.210521\pi\) | ||||
−0.789152 | + | 0.614198i | \(0.789479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4045i | 0.927874i | 0.885868 | + | 0.463937i | \(0.153564\pi\) | ||||
−0.885868 | + | 0.463937i | \(0.846436\pi\) | |||||||
\(242\) | − 10.1348i | − 0.651491i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 4.28130i | − 0.274082i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.181547 | 0.0115516 | ||||||||
\(248\) | −0.101724 | −0.00645949 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | −20.5072 | −1.29440 | −0.647201 | − | 0.762319i | \(-0.724061\pi\) | ||||
−0.647201 | + | 0.762319i | \(0.724061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.745133 | 0.0468461 | ||||||||
\(254\) | − 15.9832i | − 1.00288i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.5842 | 0.847359 | 0.423679 | − | 0.905812i | \(-0.360738\pi\) | ||||
0.423679 | + | 0.905812i | \(0.360738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.331821i | 0.0205787i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.82805i | 0.360058i | ||||||||
\(263\) | − 27.6507i | − 1.70501i | −0.522716 | − | 0.852507i | \(-0.675081\pi\) | ||||
0.522716 | − | 0.852507i | \(-0.324919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 6.38009i | − 0.391926i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.25102 | 0.137503 | ||||||||
\(269\) | −13.1708 | −0.803039 | −0.401520 | − | 0.915850i | \(-0.631518\pi\) | ||||
−0.401520 | + | 0.915850i | \(0.631518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 13.1590i | − 0.799354i | −0.916656 | − | 0.399677i | \(-0.869122\pi\) | ||||
0.916656 | − | 0.399677i | \(-0.130878\pi\) | |||||||
\(272\) | 3.26197 | 0.197786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.58316 | −0.337291 | ||||||||
\(275\) | − 0.930151i | − 0.0560902i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0071 | 0.601269 | 0.300634 | − | 0.953739i | \(-0.402802\pi\) | ||||
0.300634 | + | 0.953739i | \(0.402802\pi\) | |||||||
\(278\) | −12.8599 | −0.771287 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 3.54033i | − 0.211199i | −0.994409 | − | 0.105599i | \(-0.966324\pi\) | ||||
0.994409 | − | 0.105599i | \(-0.0336761\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5581i | 0.924831i | 0.886663 | + | 0.462416i | \(0.153017\pi\) | ||||
−0.886663 | + | 0.462416i | \(0.846983\pi\) | |||||||
\(284\) | − 3.64725i | − 0.216425i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.308644i | 0.0182505i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.35953 | −0.374090 | ||||||||
\(290\) | 6.37170 | 0.374159 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 2.28356i | − 0.133635i | ||||||||
\(293\) | −4.25813 | −0.248762 | −0.124381 | − | 0.992235i | \(-0.539695\pi\) | ||||
−0.124381 | + | 0.992235i | \(0.539695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.11652 | 0.356118 | ||||||||
\(296\) | 8.29385i | 0.482070i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.93694 | −0.459775 | ||||||||
\(299\) | 0.265818 | 0.0153727 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 13.5236i | − 0.778194i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.547123i | 0.0313796i | ||||||||
\(305\) | 4.28130i | 0.245147i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.65097i | 0.208372i | 0.994558 | + | 0.104186i | \(0.0332237\pi\) | ||||
−0.994558 | + | 0.104186i | \(0.966776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.101724 | 0.00577754 | ||||||||
\(311\) | −8.15121 | −0.462213 | −0.231106 | − | 0.972929i | \(-0.574235\pi\) | ||||
−0.231106 | + | 0.972929i | \(0.574235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 7.07921i | − 0.400140i | −0.979782 | − | 0.200070i | \(-0.935883\pi\) | ||||
0.979782 | − | 0.200070i | \(-0.0641170\pi\) | |||||||
\(314\) | 15.3196 | 0.864535 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.32957 | −0.243557 | ||||||||
\(317\) | 0.0850185i | 0.00477511i | 0.999997 | + | 0.00238756i | \(0.000759984\pi\) | ||||
−0.999997 | + | 0.00238756i | \(0.999240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.92665 | 0.331829 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.78470i | 0.0993033i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 0.331821i | − 0.0184061i | ||||||||
\(326\) | − 13.2661i | − 0.734743i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 6.57446i | − 0.363014i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.64860 | −0.365440 | −0.182720 | − | 0.983165i | \(-0.558490\pi\) | ||||
−0.182720 | + | 0.983165i | \(0.558490\pi\) | |||||||
\(332\) | 15.4785 | 0.849493 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.3462i | 0.839709i | ||||||||
\(335\) | −2.25102 | −0.122986 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.65367 | −0.307975 | −0.153987 | − | 0.988073i | \(-0.549212\pi\) | ||||
−0.153987 | + | 0.988073i | \(0.549212\pi\) | |||||||
\(338\) | − 12.8899i | − 0.701118i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.26197 | −0.176905 | ||||||||
\(341\) | 0.0946188 | 0.00512390 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.49501i | 0.0806057i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 7.23532i | − 0.388973i | ||||||||
\(347\) | 13.0479i | 0.700447i | 0.936666 | + | 0.350224i | \(0.113894\pi\) | ||||
−0.936666 | + | 0.350224i | \(0.886106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 32.2182i | − 1.72460i | −0.506398 | − | 0.862300i | \(-0.669023\pi\) | ||||
0.506398 | − | 0.862300i | \(-0.330977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.930151 | −0.0495772 | ||||||||
\(353\) | −18.2963 | −0.973813 | −0.486907 | − | 0.873454i | \(-0.661875\pi\) | ||||
−0.486907 | + | 0.873454i | \(0.661875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.64725i | 0.193576i | ||||||||
\(356\) | 0.219463 | 0.0116315 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8082 | −0.782637 | ||||||||
\(359\) | − 36.9146i | − 1.94828i | −0.225949 | − | 0.974139i | \(-0.572548\pi\) | ||||
0.225949 | − | 0.974139i | \(-0.427452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7007 | 0.984245 | ||||||||
\(362\) | 15.0930 | 0.793269 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.28356i | 0.119527i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2459i | 0.848028i | 0.905656 | + | 0.424014i | \(0.139379\pi\) | ||||
−0.905656 | + | 0.424014i | \(0.860621\pi\) | |||||||
\(368\) | 0.801088i | 0.0417596i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 8.29385i | − 0.431177i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2333 | 0.633415 | 0.316708 | − | 0.948523i | \(-0.397423\pi\) | ||||
0.316708 | + | 0.948523i | \(0.397423\pi\) | |||||||
\(374\) | −3.03413 | −0.156891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.57741i | 0.339204i | ||||||||
\(377\) | 2.11427 | 0.108890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.8754 | 1.27776 | 0.638882 | − | 0.769305i | \(-0.279397\pi\) | ||||
0.638882 | + | 0.769305i | \(0.279397\pi\) | |||||||
\(380\) | − 0.547123i | − 0.0280668i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.9314 | −1.07094 | ||||||||
\(383\) | 18.0549 | 0.922563 | 0.461282 | − | 0.887254i | \(-0.347390\pi\) | ||||
0.461282 | + | 0.887254i | \(0.347390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 15.6014i | − 0.794092i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.65685i | 0.185649i | ||||||||
\(389\) | − 9.78892i | − 0.496318i | −0.968719 | − | 0.248159i | \(-0.920174\pi\) | ||||
0.968719 | − | 0.248159i | \(-0.0798255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61313i | 0.132151i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.65498 | −0.133756 | ||||||||
\(395\) | 4.32957 | 0.217844 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.0160i | − 0.703444i | −0.936105 | − | 0.351722i | \(-0.885596\pi\) | ||||
0.936105 | − | 0.351722i | \(-0.114404\pi\) | |||||||
\(398\) | −11.6840 | −0.585664 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.34596i | 0.466715i | 0.972391 | + | 0.233357i | \(0.0749712\pi\) | ||||
−0.972391 | + | 0.233357i | \(0.925029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0337542 | 0.00168142 | ||||||||
\(404\) | −10.7119 | −0.532937 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 7.71453i | − 0.382395i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 17.7620i | − 0.878274i | −0.898420 | − | 0.439137i | \(-0.855284\pi\) | ||||
0.898420 | − | 0.439137i | \(-0.144716\pi\) | |||||||
\(410\) | 6.57446i | 0.324690i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 1.91082i | − 0.0941393i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.4785 | −0.759809 | ||||||||
\(416\) | −0.331821 | −0.0162689 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.508907i | − 0.0248914i | ||||||||
\(419\) | 17.3073 | 0.845519 | 0.422759 | − | 0.906242i | \(-0.361062\pi\) | ||||
0.422759 | + | 0.906242i | \(0.361062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.79621 | 0.185016 | 0.0925079 | − | 0.995712i | \(-0.470512\pi\) | ||||
0.0925079 | + | 0.995712i | \(0.470512\pi\) | |||||||
\(422\) | 4.36407i | 0.212440i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.38009 | 0.309844 | ||||||||
\(425\) | 3.26197 | 0.158229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.972287i | 0.0469973i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 1.49501i | − 0.0720959i | ||||||||
\(431\) | 1.92214i | 0.0925864i | 0.998928 | + | 0.0462932i | \(0.0147409\pi\) | ||||
−0.998928 | + | 0.0462932i | \(0.985259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.5127i | 0.841604i | 0.907152 | + | 0.420802i | \(0.138251\pi\) | ||||
−0.907152 | + | 0.420802i | \(0.861749\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.4020 | −0.881295 | ||||||||
\(437\) | −0.438293 | −0.0209664 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 40.3613i | − 1.92634i | −0.268893 | − | 0.963170i | \(-0.586658\pi\) | ||||
0.268893 | − | 0.963170i | \(-0.413342\pi\) | |||||||
\(440\) | 0.930151 | 0.0443432 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.08239 | −0.0514841 | ||||||||
\(443\) | 8.00694i | 0.380421i | 0.981743 | + | 0.190211i | \(0.0609171\pi\) | ||||
−0.981743 | + | 0.190211i | \(0.939083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.219463 | −0.0104036 | ||||||||
\(446\) | 24.2623 | 1.14885 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.4212i | 1.29408i | 0.762454 | + | 0.647042i | \(0.223994\pi\) | ||||
−0.762454 | + | 0.647042i | \(0.776006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.11524i | 0.287956i | ||||||||
\(452\) | − 4.16160i | − 0.195745i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 29.2809i | − 1.37422i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.49526 | −0.163501 | −0.0817506 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817506 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(458\) | −4.84710 | −0.226490 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 0.801088i | − 0.0373509i | ||||||||
\(461\) | −28.4061 | −1.32301 | −0.661503 | − | 0.749942i | \(-0.730081\pi\) | ||||
−0.661503 | + | 0.749942i | \(0.730081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.4813 | −1.97428 | −0.987138 | − | 0.159871i | \(-0.948892\pi\) | ||||
−0.987138 | + | 0.159871i | \(0.948892\pi\) | |||||||
\(464\) | 6.37170i | 0.295799i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.66683 | 0.123538 | ||||||||
\(467\) | 11.8480 | 0.548262 | 0.274131 | − | 0.961692i | \(-0.411610\pi\) | ||||
0.274131 | + | 0.961692i | \(0.411610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 6.57741i | − 0.303393i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.11652i | 0.281536i | ||||||||
\(473\) | − 1.39059i | − 0.0639393i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.547123i | 0.0251037i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.9906 | 0.868608 | ||||||||
\(479\) | 11.4231 | 0.521933 | 0.260967 | − | 0.965348i | \(-0.415959\pi\) | ||||
0.260967 | + | 0.965348i | \(0.415959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 2.75208i | − 0.125484i | ||||||||
\(482\) | 14.4045 | 0.656106 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.1348 | −0.460674 | ||||||||
\(485\) | − 3.65685i | − 0.166049i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0897 | −0.865039 | −0.432519 | − | 0.901625i | \(-0.642375\pi\) | ||||
−0.432519 | + | 0.901625i | \(0.642375\pi\) | |||||||
\(488\) | −4.28130 | −0.193806 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.04288i | − 0.182453i | −0.995830 | − | 0.0912264i | \(-0.970921\pi\) | ||||
0.995830 | − | 0.0912264i | \(-0.0290787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.7843i | 0.936079i | ||||||||
\(494\) | − 0.181547i | − 0.00816818i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.101724i | 0.00456755i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.4594 | −1.36355 | −0.681776 | − | 0.731561i | \(-0.738792\pi\) | ||||
−0.681776 | + | 0.731561i | \(0.738792\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.5072i | 0.915280i | ||||||||
\(503\) | −1.83400 | −0.0817739 | −0.0408869 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408869 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7119 | 0.476674 | ||||||||
\(506\) | − 0.745133i | − 0.0331252i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.9832 | −0.709141 | ||||||||
\(509\) | −5.75147 | −0.254930 | −0.127465 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127465 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 13.5842i | − 0.599173i | ||||||||
\(515\) | 1.91082i | 0.0842008i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.11798i | − 0.269069i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.331821 | 0.0145513 | ||||||||
\(521\) | −30.8399 | −1.35112 | −0.675561 | − | 0.737304i | \(-0.736099\pi\) | ||||
−0.675561 | + | 0.737304i | \(0.736099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 16.2217i | − 0.709326i | −0.934994 | − | 0.354663i | \(-0.884596\pi\) | ||||
0.934994 | − | 0.354663i | \(-0.115404\pi\) | |||||||
\(524\) | 5.82805 | 0.254600 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.6507 | −1.20563 | ||||||||
\(527\) | 0.331821i | 0.0144544i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3583 | 0.972098 | ||||||||
\(530\) | −6.38009 | −0.277133 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.18155i | 0.0944933i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 0.972287i | − 0.0420356i | ||||||||
\(536\) | − 2.25102i | − 0.0972293i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.1708i | 0.567835i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6951 | 0.932746 | 0.466373 | − | 0.884588i | \(-0.345561\pi\) | ||||
0.466373 | + | 0.884588i | \(0.345561\pi\) | |||||||
\(542\) | −13.1590 | −0.565229 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 3.26197i | − 0.139856i | ||||||||
\(545\) | 18.4020 | 0.788255 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.2142 | 1.07808 | 0.539041 | − | 0.842279i | \(-0.318787\pi\) | ||||
0.539041 | + | 0.842279i | \(0.318787\pi\) | |||||||
\(548\) | 5.58316i | 0.238501i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.930151 | −0.0396618 | ||||||||
\(551\) | −3.48610 | −0.148513 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 10.0071i | − 0.425161i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8599i | 0.545382i | ||||||||
\(557\) | 36.5741i | 1.54970i | 0.632148 | + | 0.774848i | \(0.282173\pi\) | ||||
−0.632148 | + | 0.774848i | \(0.717827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.496077i | − 0.0209818i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.54033 | −0.149340 | ||||||||
\(563\) | −32.4995 | −1.36969 | −0.684845 | − | 0.728689i | \(-0.740130\pi\) | ||||
−0.684845 | + | 0.728689i | \(0.740130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.16160i | 0.175080i | ||||||||
\(566\) | 15.5581 | 0.653955 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.64725 | −0.153035 | ||||||||
\(569\) | − 11.4915i | − 0.481750i | −0.970556 | − | 0.240875i | \(-0.922566\pi\) | ||||
0.970556 | − | 0.240875i | \(-0.0774345\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0006 | −1.59028 | −0.795139 | − | 0.606428i | \(-0.792602\pi\) | ||||
−0.795139 | + | 0.606428i | \(0.792602\pi\) | |||||||
\(572\) | 0.308644 | 0.0129051 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.801088i | 0.0334077i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.6416i | 1.40052i | 0.713890 | + | 0.700258i | \(0.246932\pi\) | ||||
−0.713890 | + | 0.700258i | \(0.753068\pi\) | |||||||
\(578\) | 6.35953i | 0.264522i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 6.37170i | − 0.264571i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.93444 | −0.245780 | ||||||||
\(584\) | −2.28356 | −0.0944943 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.25813i | 0.175902i | ||||||||
\(587\) | −26.2459 | −1.08328 | −0.541641 | − | 0.840610i | \(-0.682197\pi\) | ||||
−0.541641 | + | 0.840610i | \(0.682197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0556556 | −0.00229325 | ||||||||
\(590\) | − 6.11652i | − 0.251813i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.29385 | 0.340875 | ||||||||
\(593\) | 19.2070 | 0.788735 | 0.394367 | − | 0.918953i | \(-0.370964\pi\) | ||||
0.394367 | + | 0.918953i | \(0.370964\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.93694i | 0.325110i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 0.265818i | − 0.0108701i | ||||||||
\(599\) | 26.6429i | 1.08860i | 0.838891 | + | 0.544300i | \(0.183205\pi\) | ||||
−0.838891 | + | 0.544300i | \(0.816795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 2.45770i | − 0.100252i | −0.998743 | − | 0.0501258i | \(-0.984038\pi\) | ||||
0.998743 | − | 0.0501258i | \(-0.0159622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.5236 | −0.550266 | ||||||||
\(605\) | 10.1348 | 0.412039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.93681i | 0.362734i | 0.983415 | + | 0.181367i | \(0.0580522\pi\) | ||||
−0.983415 | + | 0.181367i | \(0.941948\pi\) | |||||||
\(608\) | 0.547123 | 0.0221887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.28130 | 0.173345 | ||||||||
\(611\) | − 2.18252i | − 0.0882955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.9482 | 1.12882 | 0.564409 | − | 0.825495i | \(-0.309104\pi\) | ||||
0.564409 | + | 0.825495i | \(0.309104\pi\) | |||||||
\(614\) | 3.65097 | 0.147341 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.4353i | − 0.500626i | −0.968165 | − | 0.250313i | \(-0.919466\pi\) | ||||
0.968165 | − | 0.250313i | \(-0.0805335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 41.9175i | − 1.68481i | −0.538849 | − | 0.842403i | \(-0.681141\pi\) | ||||
0.538849 | − | 0.842403i | \(-0.318859\pi\) | |||||||
\(620\) | − 0.101724i | − 0.00408534i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.15121i | 0.326834i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.07921 | −0.282942 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 15.3196i | − 0.611318i | ||||||||
\(629\) | 27.0543 | 1.07873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.24943 | −0.208976 | −0.104488 | − | 0.994526i | \(-0.533320\pi\) | ||||
−0.104488 | + | 0.994526i | \(0.533320\pi\) | |||||||
\(632\) | 4.32957i | 0.172221i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0850185 | 0.00337652 | ||||||||
\(635\) | 15.9832 | 0.634275 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 5.92665i | − 0.234638i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 30.4266i | 1.20178i | 0.799332 | + | 0.600890i | \(0.205187\pi\) | ||||
−0.799332 | + | 0.600890i | \(0.794813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.6780i | 1.68306i | 0.540212 | + | 0.841529i | \(0.318344\pi\) | ||||
−0.540212 | + | 0.841529i | \(0.681656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.78470 | 0.0702180 | ||||||||
\(647\) | −18.2966 | −0.719315 | −0.359657 | − | 0.933084i | \(-0.617106\pi\) | ||||
−0.359657 | + | 0.933084i | \(0.617106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 5.68929i | − 0.223324i | ||||||||
\(650\) | −0.331821 | −0.0130151 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.2661 | −0.519542 | ||||||||
\(653\) | 44.1790i | 1.72886i | 0.502755 | + | 0.864429i | \(0.332320\pi\) | ||||
−0.502755 | + | 0.864429i | \(0.667680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.82805 | −0.227721 | ||||||||
\(656\) | −6.57446 | −0.256690 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.0063i | 1.55842i | 0.626760 | + | 0.779212i | \(0.284381\pi\) | ||||
−0.626760 | + | 0.779212i | \(0.715619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.14596i | 0.200155i | 0.994980 | + | 0.100077i | \(0.0319090\pi\) | ||||
−0.994980 | + | 0.100077i | \(0.968091\pi\) | |||||||
\(662\) | 6.64860i | 0.258405i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 15.4785i | − 0.600682i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.10429 | −0.197639 | ||||||||
\(668\) | 15.3462 | 0.593764 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.25102i | 0.0869646i | ||||||||
\(671\) | 3.98226 | 0.153733 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7124 | −0.952594 | −0.476297 | − | 0.879284i | \(-0.658021\pi\) | ||||
−0.476297 | + | 0.879284i | \(0.658021\pi\) | |||||||
\(674\) | 5.65367i | 0.217771i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8899 | −0.495765 | ||||||||
\(677\) | 22.5424 | 0.866375 | 0.433187 | − | 0.901304i | \(-0.357389\pi\) | ||||
0.433187 | + | 0.901304i | \(0.357389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.26197i | 0.125091i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 0.0946188i | − 0.00362314i | ||||||||
\(683\) | 4.15882i | 0.159133i | 0.996830 | + | 0.0795664i | \(0.0253536\pi\) | ||||
−0.996830 | + | 0.0795664i | \(0.974646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 5.58316i | − 0.213322i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.49501 | 0.0569968 | ||||||||
\(689\) | −2.11705 | −0.0806531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 27.1058i | − 1.03115i | −0.856843 | − | 0.515577i | \(-0.827578\pi\) | ||||
0.856843 | − | 0.515577i | \(-0.172422\pi\) | |||||||
\(692\) | −7.23532 | −0.275046 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0479 | 0.495291 | ||||||||
\(695\) | − 12.8599i | − 0.487805i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.4457 | −0.812314 | ||||||||
\(698\) | −32.2182 | −1.21948 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 6.04705i | − 0.228394i | −0.993458 | − | 0.114197i | \(-0.963571\pi\) | ||||
0.993458 | − | 0.114197i | \(-0.0364295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.53775i | 0.171145i | ||||||||
\(704\) | 0.930151i | 0.0350564i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.2963i | 0.688590i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.3571 | −1.59075 | −0.795377 | − | 0.606115i | \(-0.792727\pi\) | ||||
−0.795377 | + | 0.606115i | \(0.792727\pi\) | |||||||
\(710\) | 3.64725 | 0.136879 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 0.219463i | − 0.00822474i | ||||||||
\(713\) | −0.0814900 | −0.00305182 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.308644 | −0.0115426 | ||||||||
\(716\) | 14.8082i | 0.553408i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −36.9146 | −1.37764 | ||||||||
\(719\) | −23.8704 | −0.890214 | −0.445107 | − | 0.895477i | \(-0.646834\pi\) | ||||
−0.445107 | + | 0.895477i | \(0.646834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 18.7007i | − 0.695966i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 15.0930i | − 0.560926i | ||||||||
\(725\) | 6.37170i | 0.236639i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6041i | 0.393283i | 0.980475 | + | 0.196641i | \(0.0630034\pi\) | ||||
−0.980475 | + | 0.196641i | \(0.936997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.28356 | 0.0845182 | ||||||||
\(731\) | 4.87669 | 0.180371 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.8949i | 1.06726i | 0.845719 | + | 0.533628i | \(0.179172\pi\) | ||||
−0.845719 | + | 0.533628i | \(0.820828\pi\) | |||||||
\(734\) | 16.2459 | 0.599646 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.801088 | 0.0295285 | ||||||||
\(737\) | 2.09379i | 0.0771258i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.21872 | −0.155188 | −0.0775940 | − | 0.996985i | \(-0.524724\pi\) | ||||
−0.0775940 | + | 0.996985i | \(0.524724\pi\) | |||||||
\(740\) | −8.29385 | −0.304888 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.75683i | 0.0644519i | 0.999481 | + | 0.0322259i | \(0.0102596\pi\) | ||||
−0.999481 | + | 0.0322259i | \(0.989740\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 7.93694i | − 0.290787i | ||||||||
\(746\) | − 12.2333i | − 0.447892i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.03413i | 0.110939i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.16801 | −0.298055 | −0.149028 | − | 0.988833i | \(-0.547614\pi\) | ||||
−0.149028 | + | 0.988833i | \(0.547614\pi\) | |||||||
\(752\) | 6.57741 | 0.239853 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 2.11427i | − 0.0769971i | ||||||||
\(755\) | 13.5236 | 0.492173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.7897 | 0.864653 | 0.432326 | − | 0.901717i | \(-0.357693\pi\) | ||||
0.432326 | + | 0.901717i | \(0.357693\pi\) | |||||||
\(758\) | − 24.8754i | − 0.903516i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.547123 | −0.0198462 | ||||||||
\(761\) | −29.0511 | −1.05310 | −0.526550 | − | 0.850144i | \(-0.676515\pi\) | ||||
−0.526550 | + | 0.850144i | \(0.676515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.9314i | 0.757270i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 18.0549i | − 0.652351i | ||||||||
\(767\) | − 2.02959i | − 0.0732843i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 37.9013i | − 1.36676i | −0.730064 | − | 0.683379i | \(-0.760510\pi\) | ||||
0.730064 | − | 0.683379i | \(-0.239490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.6014 | −0.561508 | ||||||||
\(773\) | −34.8149 | −1.25220 | −0.626102 | − | 0.779742i | \(-0.715350\pi\) | ||||
−0.626102 | + | 0.779742i | \(0.715350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.101724i | 0.00365404i | ||||||||
\(776\) | 3.65685 | 0.131273 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.78892 | −0.350950 | ||||||||
\(779\) | − 3.59704i | − 0.128877i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.39250 | 0.121393 | ||||||||
\(782\) | 2.61313 | 0.0934452 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.3196i | 0.546780i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 44.7309i | − 1.59448i | −0.603660 | − | 0.797242i | \(-0.706291\pi\) | ||||
0.603660 | − | 0.797242i | \(-0.293709\pi\) | |||||||
\(788\) | 2.65498i | 0.0945796i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 4.32957i | − 0.154039i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.42063 | 0.0504480 | ||||||||
\(794\) | −14.0160 | −0.497410 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6840i | 0.414127i | ||||||||
\(797\) | 15.9485 | 0.564925 | 0.282463 | − | 0.959278i | \(-0.408849\pi\) | ||||
0.282463 | + | 0.959278i | \(0.408849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.4553 | 0.759035 | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.34596 | 0.330017 | ||||||||
\(803\) | 2.12405 | 0.0749562 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 0.0337542i | − 0.00118894i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.7119i | 0.376844i | ||||||||
\(809\) | 31.5898i | 1.11064i | 0.831638 | + | 0.555318i | \(0.187404\pi\) | ||||
−0.831638 | + | 0.555318i | \(0.812596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.5850i | 1.77628i | 0.459572 | + | 0.888140i | \(0.348003\pi\) | ||||
−0.459572 | + | 0.888140i | \(0.651997\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.71453 | −0.270394 | ||||||||
\(815\) | 13.2661 | 0.464692 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.817955i | 0.0286166i | ||||||||
\(818\) | −17.7620 | −0.621034 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.57446 | 0.229590 | ||||||||
\(821\) | 10.9221i | 0.381182i | 0.981669 | + | 0.190591i | \(0.0610405\pi\) | ||||
−0.981669 | + | 0.190591i | \(0.938960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.5641 | −1.16997 | −0.584986 | − | 0.811043i | \(-0.698900\pi\) | ||||
−0.584986 | + | 0.811043i | \(0.698900\pi\) | |||||||
\(824\) | −1.91082 | −0.0665665 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 33.7958i | − 1.17520i | −0.809153 | − | 0.587598i | \(-0.800074\pi\) | ||||
0.809153 | − | 0.587598i | \(-0.199926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 23.2218i | − 0.806526i | −0.915084 | − | 0.403263i | \(-0.867876\pi\) | ||||
0.915084 | − | 0.403263i | \(-0.132124\pi\) | |||||||
\(830\) | 15.4785i | 0.537266i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.331821i | 0.0115038i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.3462 | −0.531079 | ||||||||
\(836\) | −0.508907 | −0.0176009 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 17.3073i | − 0.597872i | ||||||||
\(839\) | 22.7535 | 0.785537 | 0.392768 | − | 0.919637i | \(-0.371517\pi\) | ||||
0.392768 | + | 0.919637i | \(0.371517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5986 | −0.399952 | ||||||||
\(842\) | − 3.79621i | − 0.130826i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.36407 | 0.150218 | ||||||||
\(845\) | 12.8899 | 0.443426 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 6.38009i | − 0.219093i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 3.26197i | − 0.111885i | ||||||||
\(851\) | 6.64410i | 0.227757i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 58.0358i | 1.98711i | 0.113353 | + | 0.993555i | \(0.463841\pi\) | ||||
−0.113353 | + | 0.993555i | \(0.536159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.972287 | 0.0332321 | ||||||||
\(857\) | 14.2966 | 0.488364 | 0.244182 | − | 0.969729i | \(-0.421481\pi\) | ||||
0.244182 | + | 0.969729i | \(0.421481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.3580i | 1.47936i | 0.672960 | + | 0.739679i | \(0.265022\pi\) | ||||
−0.672960 | + | 0.739679i | \(0.734978\pi\) | |||||||
\(860\) | −1.49501 | −0.0509795 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.92214 | 0.0654685 | ||||||||
\(863\) | 22.8329i | 0.777242i | 0.921398 | + | 0.388621i | \(0.127048\pi\) | ||||
−0.921398 | + | 0.388621i | \(0.872952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.23532 | 0.246008 | ||||||||
\(866\) | 17.5127 | 0.595104 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.02715i | − 0.136612i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.746937i | 0.0253090i | ||||||||
\(872\) | 18.4020i | 0.623170i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.438293i | 0.0148255i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7859 | 0.397982 | 0.198991 | − | 0.980001i | \(-0.436234\pi\) | ||||
0.198991 | + | 0.980001i | \(0.436234\pi\) | |||||||
\(878\) | −40.3613 | −1.36213 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 0.930151i | − 0.0313554i | ||||||||
\(881\) | 14.1084 | 0.475323 | 0.237662 | − | 0.971348i | \(-0.423619\pi\) | ||||
0.237662 | + | 0.971348i | \(0.423619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.9258 | 0.872474 | 0.436237 | − | 0.899832i | \(-0.356311\pi\) | ||||
0.436237 | + | 0.899832i | \(0.356311\pi\) | |||||||
\(884\) | 1.08239i | 0.0364048i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.00694 | 0.268999 | ||||||||
\(887\) | −33.2065 | −1.11497 | −0.557483 | − | 0.830188i | \(-0.688233\pi\) | ||||
−0.557483 | + | 0.830188i | \(0.688233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.219463i | 0.00735643i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 24.2623i | − 0.812362i | ||||||||
\(893\) | 3.59865i | 0.120424i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 14.8082i | − 0.494983i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.4212 | 0.915056 | ||||||||
\(899\) | −0.648156 | −0.0216172 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 20.8117i | − 0.693337i | ||||||||
\(902\) | 6.11524 | 0.203615 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.16160 | −0.138413 | ||||||||
\(905\) | 15.0930i | 0.501707i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.9492 | −0.396768 | −0.198384 | − | 0.980124i | \(-0.563569\pi\) | ||||
−0.198384 | + | 0.980124i | \(0.563569\pi\) | |||||||
\(908\) | −29.2809 | −0.971722 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 20.2523i | − 0.670988i | −0.942042 | − | 0.335494i | \(-0.891097\pi\) | ||||
0.942042 | − | 0.335494i | \(-0.108903\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3973i | 0.476482i | ||||||||
\(914\) | 3.49526i | 0.115613i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.84710i | 0.160153i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.6974 | −1.04560 | −0.522801 | − | 0.852455i | \(-0.675113\pi\) | ||||
−0.522801 | + | 0.852455i | \(0.675113\pi\) | |||||||
\(920\) | −0.801088 | −0.0264111 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.4061i | 0.935507i | ||||||||
\(923\) | 1.21024 | 0.0398354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.29385 | 0.272700 | ||||||||
\(926\) | 42.4813i | 1.39602i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.37170 | 0.209161 | ||||||||
\(929\) | −20.5149 | −0.673073 | −0.336537 | − | 0.941670i | \(-0.609256\pi\) | ||||
−0.336537 | + | 0.941670i | \(0.609256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 2.66683i | − 0.0873549i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 11.8480i | − 0.387680i | ||||||||
\(935\) | − 3.03413i | − 0.0992266i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3157i | 0.957701i | 0.877896 | + | 0.478850i | \(0.158946\pi\) | ||||
−0.877896 | + | 0.478850i | \(0.841054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.57741 | −0.214531 | ||||||||
\(941\) | −32.6165 | −1.06327 | −0.531634 | − | 0.846974i | \(-0.678422\pi\) | ||||
−0.531634 | + | 0.846974i | \(0.678422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.26672i | − 0.171508i | ||||||||
\(944\) | 6.11652 | 0.199076 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.39059 | −0.0452119 | ||||||||
\(947\) | 32.0156i | 1.04037i | 0.854054 | + | 0.520184i | \(0.174137\pi\) | ||||
−0.854054 | + | 0.520184i | \(0.825863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.757733 | 0.0245971 | ||||||||
\(950\) | 0.547123 | 0.0177510 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 35.3686i | − 1.14570i | −0.819660 | − | 0.572850i | \(-0.805838\pi\) | ||||
0.819660 | − | 0.572850i | \(-0.194162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 20.9314i | − 0.677323i | ||||||||
\(956\) | − 18.9906i | − 0.614198i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 11.4231i | − 0.369063i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9897 | 0.999666 | ||||||||
\(962\) | −2.75208 | −0.0887305 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 14.4045i | − 0.463937i | ||||||||
\(965\) | 15.6014 | 0.502228 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.3515 | −0.976037 | −0.488019 | − | 0.872833i | \(-0.662280\pi\) | ||||
−0.488019 | + | 0.872833i | \(0.662280\pi\) | |||||||
\(968\) | 10.1348i | 0.325745i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.65685 | −0.117415 | ||||||||
\(971\) | 8.15046 | 0.261561 | 0.130780 | − | 0.991411i | \(-0.458252\pi\) | ||||
0.130780 | + | 0.991411i | \(0.458252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.0897i | 0.611675i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.28130i | 0.137041i | ||||||||
\(977\) | 62.0995i | 1.98674i | 0.114960 | + | 0.993370i | \(0.463326\pi\) | ||||
−0.114960 | + | 0.993370i | \(0.536674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.204134i | 0.00652416i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.04288 | −0.129014 | ||||||||
\(983\) | 20.2029 | 0.644374 | 0.322187 | − | 0.946676i | \(-0.395582\pi\) | ||||
0.322187 | + | 0.946676i | \(0.395582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 2.65498i | − 0.0845946i | ||||||||
\(986\) | 20.7843 | 0.661908 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.181547 | −0.00577578 | ||||||||
\(989\) | 1.19764i | 0.0380826i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.7136 | −1.61097 | −0.805485 | − | 0.592616i | \(-0.798095\pi\) | ||||
−0.805485 | + | 0.592616i | \(0.798095\pi\) | |||||||
\(992\) | 0.101724 | 0.00322974 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 11.6840i | − 0.370406i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.7493i | 0.467115i | 0.972343 | + | 0.233557i | \(0.0750367\pi\) | ||||
−0.972343 | + | 0.233557i | \(0.924963\pi\) | |||||||
\(998\) | 30.4594i | 0.964177i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4410.2.b.f.881.2 | yes | 8 | |
3.2 | odd | 2 | 4410.2.b.c.881.7 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.c.881.2 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.f.881.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.b.c.881.2 | ✓ | 8 | 7.6 | odd | 2 | ||
4410.2.b.c.881.7 | yes | 8 | 3.2 | odd | 2 | ||
4410.2.b.f.881.2 | yes | 8 | 1.1 | even | 1 | trivial | |
4410.2.b.f.881.7 | yes | 8 | 21.20 | even | 2 | inner |