Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1009,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1680.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.1 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.k.1009.4 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48119 | + | 1.67513i | −0.662410 | + | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.35026i | − | 0.374495i | −0.982313 | − | 0.187248i | \(-0.940043\pi\) | ||
0.982313 | − | 0.187248i | \(-0.0599567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.67513 | + | 1.48119i | 0.432517 | + | 0.382443i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.35026i | − | 0.812558i | −0.913749 | − | 0.406279i | \(-0.866826\pi\) | ||
0.913749 | − | 0.406279i | \(-0.133174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.35026 | 1.22743 | 0.613717 | − | 0.789526i | \(-0.289674\pi\) | ||||
0.613717 | + | 0.789526i | \(0.289674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.96239i | 1.03473i | 0.855765 | + | 0.517365i | \(0.173087\pi\) | ||||
−0.855765 | + | 0.517365i | \(0.826913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92478 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.57452 | −0.821607 | −0.410804 | − | 0.911724i | \(-0.634752\pi\) | ||||
−0.410804 | + | 0.911724i | \(0.634752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.67513 | − | 1.48119i | −0.283149 | − | 0.250368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.775746i | − | 0.127532i | −0.997965 | − | 0.0637660i | \(-0.979689\pi\) | ||
0.997965 | − | 0.0637660i | \(-0.0203111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.35026 | −0.216215 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.73813 | 0.583799 | 0.291899 | − | 0.956449i | \(-0.405713\pi\) | ||||
0.291899 | + | 0.956449i | \(0.405713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.6253i | − | 1.92534i | −0.270677 | − | 0.962670i | \(-0.587248\pi\) | ||
0.270677 | − | 0.962670i | \(-0.412752\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.48119 | − | 1.67513i | 0.220803 | − | 0.249714i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.92478i | − | 1.44768i | −0.689969 | − | 0.723839i | \(-0.742376\pi\) | ||
0.689969 | − | 0.723839i | \(-0.257624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.35026 | −0.469130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.57452i | − | 1.17780i | −0.808206 | − | 0.588900i | \(-0.799561\pi\) | ||
0.808206 | − | 0.588900i | \(-0.200439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.96239 | − | 3.35026i | 0.399448 | − | 0.451749i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.35026i | − | 0.708659i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.62530 | −1.12292 | −0.561459 | − | 0.827504i | \(-0.689760\pi\) | ||||
−0.561459 | + | 0.827504i | \(0.689760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.70052 | −1.11399 | −0.556994 | − | 0.830517i | \(-0.688045\pi\) | ||||
−0.556994 | + | 0.830517i | \(0.688045\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.26187 | + | 2.00000i | 0.280550 | + | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.92478i | − | 1.21250i | −0.795272 | − | 0.606252i | \(-0.792672\pi\) | ||
0.795272 | − | 0.606252i | \(-0.207328\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.96239 | 0.597401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.35026i | 1.09437i | 0.837013 | + | 0.547183i | \(0.184300\pi\) | ||||
−0.837013 | + | 0.547183i | \(0.815700\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.96239 | + | 0.612127i | −0.573007 | + | 0.0706823i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7005 | 1.20390 | 0.601951 | − | 0.798533i | \(-0.294390\pi\) | ||||
0.601951 | + | 0.798533i | \(0.294390\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.22425i | 0.353908i | 0.984219 | + | 0.176954i | \(0.0566244\pi\) | ||||
−0.984219 | + | 0.176954i | \(0.943376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61213 | + | 4.96239i | 0.608721 | + | 0.538247i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.92478i | 0.849625i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.03761 | −0.109987 | −0.0549933 | − | 0.998487i | \(-0.517514\pi\) | ||||
−0.0549933 | + | 0.998487i | \(0.517514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.35026 | 0.141546 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.57452i | 0.474355i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.92478 | + | 8.96239i | −0.813065 | + | 0.919522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.4993i | − | 1.87832i | −0.343482 | − | 0.939159i | \(-0.611606\pi\) | ||
0.343482 | − | 0.939159i | \(-0.388394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.6629 | −1.75753 | −0.878763 | − | 0.477259i | \(-0.841630\pi\) | ||||
−0.878763 | + | 0.477259i | \(0.841630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.70052i | 0.660222i | 0.943942 | + | 0.330111i | \(0.107086\pi\) | ||||
−0.943942 | + | 0.330111i | \(0.892914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.48119 | + | 1.67513i | −0.144550 | + | 0.163476i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.7381i | − | 1.32812i | −0.747681 | − | 0.664058i | \(-0.768833\pi\) | ||
0.747681 | − | 0.664058i | \(-0.231167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.77575 | 0.265868 | 0.132934 | − | 0.991125i | \(-0.457560\pi\) | ||||
0.132934 | + | 0.991125i | \(0.457560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.775746 | −0.0736306 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.0508i | − | 1.13364i | −0.823841 | − | 0.566821i | \(-0.808173\pi\) | ||
0.823841 | − | 0.566821i | \(-0.191827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.31265 | − | 7.35026i | −0.775159 | − | 0.685415i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.35026i | 0.124832i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.35026 | 0.307118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.73813i | − | 0.337056i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21933 | + | 6.32487i | 0.824602 | + | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.70052i | − | 0.239633i | −0.992796 | − | 0.119816i | \(-0.961769\pi\) | ||
0.992796 | − | 0.119816i | \(-0.0382306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.6253 | −1.11160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.6253 | −1.80204 | −0.901020 | − | 0.433777i | \(-0.857181\pi\) | ||||
−0.901020 | + | 0.433777i | \(0.857181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.35026i | 0.463927i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.67513 | − | 1.48119i | −0.144172 | − | 0.127481i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.4993i | 1.92224i | 0.276124 | + | 0.961122i | \(0.410950\pi\) | ||||
−0.276124 | + | 0.961122i | \(0.589050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.27504 | −0.277785 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.92478 | −0.835817 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.70052i | 0.225829i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7381 | − | 13.2750i | 0.974799 | − | 1.10243i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.44851 | 0.364436 | 0.182218 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182218 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.29948 | −0.105750 | −0.0528749 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528749 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.35026i | 0.270853i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.77575 | − | 7.66291i | 0.544241 | − | 0.615500i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.64974i | − | 0.211472i | −0.994394 | − | 0.105736i | \(-0.966280\pi\) | ||
0.994394 | − | 0.105736i | \(-0.0337199\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.57452 | −0.680003 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.96239 | −0.391091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.29948i | 0.415087i | 0.978226 | + | 0.207544i | \(0.0665469\pi\) | ||||
−0.978226 | + | 0.207544i | \(0.933453\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.35026 | − | 2.96239i | −0.260818 | − | 0.230622i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5501i | 1.12592i | 0.826485 | + | 0.562959i | \(0.190337\pi\) | ||||
−0.826485 | + | 0.562959i | \(0.809663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1768 | 0.859753 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.35026 | −0.409145 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.49929i | 0.342075i | 0.985265 | + | 0.171037i | \(0.0547119\pi\) | ||||
−0.985265 | + | 0.171037i | \(0.945288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.96239 | − | 0.612127i | 0.375121 | − | 0.0462724i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.62530i | 0.648317i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6253 | 0.789772 | 0.394886 | − | 0.918730i | \(-0.370784\pi\) | ||||
0.394886 | + | 0.918730i | \(0.370784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.70052i | 0.643161i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.29948 | + | 1.14903i | 0.0955394 | + | 0.0844784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70052i | 0.489991i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8496 | 1.00212 | 0.501059 | − | 0.865413i | \(-0.332944\pi\) | ||||
0.501059 | + | 0.865413i | \(0.332944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.3258i | − | 1.10318i | −0.834116 | − | 0.551588i | \(-0.814022\pi\) | ||
0.834116 | − | 0.551588i | \(-0.185978\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000 | − | 2.26187i | 0.143223 | − | 0.161976i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.574515i | − | 0.0409325i | −0.999791 | − | 0.0204663i | \(-0.993485\pi\) | ||
0.999791 | − | 0.0204663i | \(-0.00651507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.201231 | −0.0142649 | −0.00713244 | − | 0.999975i | \(-0.502270\pi\) | ||||
−0.00713244 | + | 0.999975i | \(0.502270\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.92478 | −0.700040 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.92478i | − | 0.556210i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.53690 | + | 6.26187i | −0.386714 | + | 0.437348i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.96239i | − | 0.344910i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7005 | −0.740171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.44851 | −0.443934 | −0.221967 | − | 0.975054i | \(-0.571248\pi\) | ||||
−0.221967 | + | 0.975054i | \(0.571248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00000i | 0.137038i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.1490 | + | 18.7005i | 1.44235 | + | 1.27537i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.57452i | − | 0.310538i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.35026 | 0.631832 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.52373 | −0.304299 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.55149i | 0.103896i | 0.998650 | + | 0.0519478i | \(0.0165429\pi\) | ||||
−0.998650 | + | 0.0519478i | \(0.983457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.612127 | + | 4.96239i | 0.0408085 | + | 0.330826i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1490i | 0.872732i | 0.899769 | + | 0.436366i | \(0.143735\pi\) | ||||
−0.899769 | + | 0.436366i | \(0.856265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.77575 | −0.183426 | −0.0917132 | − | 0.995785i | \(-0.529234\pi\) | ||||
−0.0917132 | + | 0.995785i | \(0.529234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.0507852i | 0.00332705i | 0.999999 | + | 0.00166353i | \(0.000529517\pi\) | ||||
−0.999999 | + | 0.00166353i | \(0.999470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.6253 | + | 14.7005i | 1.08452 | + | 0.958956i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.7005i | − | 0.695074i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.84955 | 0.378376 | 0.189188 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189188 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0752228 | −0.00484553 | −0.00242276 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242276 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.48119 | − | 1.67513i | 0.0946300 | − | 0.107020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.22425i | − | 0.459668i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.22425 | 0.204329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.2243 | −1.21342 | −0.606712 | − | 0.794922i | \(-0.707512\pi\) | ||||
−0.606712 | + | 0.794922i | \(0.707512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.92478i | − | 0.623965i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.96239 | − | 5.61213i | 0.310757 | − | 0.351445i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.35026i | 0.458497i | 0.973368 | + | 0.229248i | \(0.0736268\pi\) | ||||
−0.973368 | + | 0.229248i | \(0.926373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.775746 | 0.0482025 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.92478 | 0.490531 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.9624i | − | 0.799295i | −0.916669 | − | 0.399648i | \(-0.869133\pi\) | ||
0.916669 | − | 0.399648i | \(-0.130867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.3634 | + | 12.7005i | 0.882339 | + | 0.780187i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.03761i | 0.0635008i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.11142 | −0.250678 | −0.125339 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125339 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4241 | 0.997691 | 0.498846 | − | 0.866691i | \(-0.333757\pi\) | ||||
0.498846 | + | 0.866691i | \(0.333757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.35026i | − | 0.0817216i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.22425 | + | 9.92478i | 0.0738253 | + | 0.598487i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.0738i | − | 0.665361i | −0.943040 | − | 0.332680i | \(-0.892047\pi\) | ||
0.943040 | − | 0.332680i | \(-0.107953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.57452 | 0.273869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3733 | 0.857438 | 0.428719 | − | 0.903438i | \(-0.358965\pi\) | ||||
0.428719 | + | 0.903438i | \(0.358965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.14903i | 0.0683028i | 0.999417 | + | 0.0341514i | \(0.0108728\pi\) | ||||
−0.999417 | + | 0.0341514i | \(0.989127\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.96239 | + | 7.92478i | 0.530886 | + | 0.469423i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.73813i | 0.220655i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77575 | 0.339750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4993 | −1.08445 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 0.649738i | − | 0.0379581i | −0.999820 | − | 0.0189791i | \(-0.993958\pi\) | ||
0.999820 | − | 0.0189791i | \(-0.00604158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7757 | − | 14.4485i | 0.743833 | − | 0.841225i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.00000i | − | 0.116052i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.70052 | 0.387501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6253 | 0.727710 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.6629i | 1.01471i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.8872 | − | 14.5745i | 0.737917 | − | 0.834534i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.1016i | − | 1.37555i | −0.725924 | − | 0.687775i | \(-0.758588\pi\) | ||
0.725924 | − | 0.687775i | \(-0.241412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.70052 | 0.381179 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.25202 | −0.467929 | −0.233964 | − | 0.972245i | \(-0.575170\pi\) | ||||
−0.233964 | + | 0.972245i | \(0.575170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9018i | 0.842297i | 0.906992 | + | 0.421148i | \(0.138373\pi\) | ||||
−0.906992 | + | 0.421148i | \(0.861627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67513 | + | 1.48119i | 0.0943829 | + | 0.0834558i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1260i | 0.568733i | 0.958716 | + | 0.284367i | \(0.0917833\pi\) | ||||
−0.958716 | + | 0.284367i | \(0.908217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.8496 | 0.887405 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7381 | −0.766788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 17.9248i | − | 0.997361i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.70052 | + | 0.826531i | −0.371678 | + | 0.0458477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.77575i | − | 0.153499i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.92478 | 0.547171 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.8496 | −1.53075 | −0.765375 | − | 0.643585i | \(-0.777446\pi\) | ||||
−0.765375 | + | 0.643585i | \(0.777446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.775746i | 0.0425106i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.6253 | + | 14.7005i | 0.908337 | + | 0.803175i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.84955i | − | 0.209699i | −0.994488 | − | 0.104849i | \(-0.966564\pi\) | ||
0.994488 | − | 0.104849i | \(-0.0334360\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0508 | −0.654509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.14903 | 0.495448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.35026 | + | 8.31265i | −0.395725 | + | 0.447538i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 9.58769i | − | 0.514694i | −0.966319 | − | 0.257347i | \(-0.917152\pi\) | ||
0.966319 | − | 0.257347i | \(-0.0828484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.1490 | 0.810909 | 0.405455 | − | 0.914115i | \(-0.367113\pi\) | ||||
0.405455 | + | 0.914115i | \(0.367113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.35026 | 0.0720716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.3488i | 1.08306i | 0.840681 | + | 0.541530i | \(0.182155\pi\) | ||||
−0.840681 | + | 0.541530i | \(0.817845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96239 | − | 3.35026i | 0.157227 | − | 0.177813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.35026i | − | 0.177315i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.4010 | −1.65728 | −0.828642 | − | 0.559779i | \(-0.810886\pi\) | ||||
−0.828642 | + | 0.559779i | \(0.810886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.62530 | 0.506595 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6629 | − | 13.8496i | −0.819834 | − | 0.724919i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.4010i | 1.53472i | 0.641215 | + | 0.767361i | \(0.278431\pi\) | ||||
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.73813 | −0.194600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.57452 | 0.445167 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.0000i | − | 0.828449i | −0.910175 | − | 0.414224i | \(-0.864053\pi\) | ||
0.910175 | − | 0.414224i | \(-0.135947\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.32487 | − | 9.21933i | 0.326615 | − | 0.476084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.7005i | 0.551105i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7005 | 0.549649 | 0.274824 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274824 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.70052 | −0.138352 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.7757i | − | 0.857201i | −0.903494 | − | 0.428600i | \(-0.859007\pi\) | ||
0.903494 | − | 0.428600i | \(-0.140993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.35026 | + | 2.96239i | 0.170745 | + | 0.150977i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.6253i | 0.641780i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3258 | 1.48688 | 0.743439 | − | 0.668804i | \(-0.233193\pi\) | ||||
0.743439 | + | 0.668804i | \(0.233193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6253 | 0.840778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6253i | 1.04041i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.8496 | + | 17.9248i | −0.797478 | + | 0.901893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3488i | 0.920902i | 0.887685 | + | 0.460451i | \(0.152312\pi\) | ||||
−0.887685 | + | 0.460451i | \(0.847688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.35026 | 0.267848 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.3258 | −1.86396 | −0.931981 | − | 0.362506i | \(-0.881921\pi\) | ||||
−0.931981 | + | 0.362506i | \(0.881921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.17679i | 0.307688i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.48119 | + | 1.67513i | −0.0736011 | + | 0.0832379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.55149i | 0.0769046i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.3733 | 1.10629 | 0.553144 | − | 0.833086i | \(-0.313428\pi\) | ||||
0.553144 | + | 0.833086i | \(0.313428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.4993 | 1.10981 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.62530i | − | 0.424423i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.40105 | − | 4.77575i | −0.265127 | − | 0.234432i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.27504i | 0.160379i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4763 | 1.14689 | 0.573445 | − | 0.819244i | \(-0.305606\pi\) | ||||
0.573445 | + | 0.819244i | \(0.305606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2243 | −1.22935 | −0.614677 | − | 0.788779i | \(-0.710714\pi\) | ||||
−0.614677 | + | 0.788779i | \(0.710714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.92478i | 0.482559i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.6253 | + | 2.05079i | −0.806446 | + | 0.0994777i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.70052i | − | 0.421048i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.70052 | 0.130383 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.4010 | 0.934516 | 0.467258 | − | 0.884121i | \(-0.345242\pi\) | ||||
0.467258 | + | 0.884121i | \(0.345242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.49929i | − | 0.312336i | −0.987731 | − | 0.156168i | \(-0.950086\pi\) | ||
0.987731 | − | 0.156168i | \(-0.0499141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.2750 | − | 11.7381i | −0.636489 | − | 0.562800i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.5501i | 1.27006i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6497 | −0.699194 | −0.349597 | − | 0.936900i | \(-0.613681\pi\) | ||||
−0.349597 | + | 0.936900i | \(0.613681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1392i | 0.909330i | 0.890663 | + | 0.454665i | \(0.150241\pi\) | ||||
−0.890663 | + | 0.454665i | \(0.849759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.53690 | − | 1.73813i | 0.0728562 | − | 0.0823955i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.44851i | − | 0.210407i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.8021 | 1.54803 | 0.774013 | − | 0.633169i | \(-0.218246\pi\) | ||||
0.774013 | + | 0.633169i | \(0.218246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.47627 | −0.352044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.29948i | 0.0610547i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | + | 2.26187i | −0.0937614 | + | 0.106038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.7005i | − | 0.874774i | −0.899273 | − | 0.437387i | \(-0.855904\pi\) | ||
0.899273 | − | 0.437387i | \(-0.144096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.35026 | 0.156377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.96239 | −0.324271 | −0.162135 | − | 0.986769i | \(-0.551838\pi\) | ||||
−0.162135 | + | 0.986769i | \(0.551838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.29948i | 0.246288i | 0.992389 | + | 0.123144i | \(0.0392976\pi\) | ||||
−0.992389 | + | 0.123144i | \(0.960702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.66291 | − | 6.77575i | −0.355359 | − | 0.314218i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1490i | 0.608465i | 0.952598 | + | 0.304232i | \(0.0983999\pi\) | ||||
−0.952598 | + | 0.304232i | \(0.901600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.92478 | 0.458284 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.64974 | −0.122093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.2506i | 1.16102i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.27504 | − | 26.5501i | −0.150269 | − | 1.21820i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.57452i | 0.392600i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.14903 | 0.235265 | 0.117633 | − | 0.993057i | \(-0.462469\pi\) | ||||
0.117633 | + | 0.993057i | \(0.462469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04746 | −0.0477601 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.96239i | 0.225797i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.9887 | + | 27.4010i | 1.40713 | + | 1.24422i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.1768i | 1.00493i | 0.864599 | + | 0.502463i | \(0.167573\pi\) | ||||
−0.864599 | + | 0.502463i | \(0.832427\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.29948 | 0.239651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.00000 | −0.0902587 | −0.0451294 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.5501i | 1.19576i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.96239 | + | 3.35026i | −0.133149 | + | 0.150583i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.00000i | − | 0.0897123i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.55008 | −0.293222 | −0.146611 | − | 0.989194i | \(-0.546837\pi\) | ||||
−0.146611 | + | 0.989194i | \(0.546837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5501 | 0.650050 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.77575i | 0.391291i | 0.980675 | + | 0.195646i | \(0.0626802\pi\) | ||||
−0.980675 | + | 0.195646i | \(0.937320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1622 | − | 29.5877i | 1.16420 | − | 1.31663i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 11.1768i | − | 0.496379i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.1392 | −0.582384 | −0.291192 | − | 0.956665i | \(-0.594052\pi\) | ||||
−0.291192 | + | 0.956665i | \(0.594052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.35026 | −0.413631 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.35026i | 0.236220i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2243 | − | 9.92478i | −0.494600 | − | 0.437338i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8496i | 0.872982i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.49929 | 0.197497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.6629 | −1.65004 | −0.825021 | − | 0.565102i | \(-0.808837\pi\) | ||||
−0.825021 | + | 0.565102i | \(0.808837\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.612127 | − | 4.96239i | −0.0267154 | − | 0.216576i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.3258i | 0.667603i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.62530 | −0.0706652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.62530 | 0.374306 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.04746i | − | 0.218630i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.0132 | + | 20.3488i | 0.994946 | + | 0.879757i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10.0000i | − | 0.431532i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.4749 | −0.966269 | −0.483135 | − | 0.875546i | \(-0.660502\pi\) | ||||
−0.483135 | + | 0.875546i | \(0.660502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 10.6253i | − | 0.455975i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.11142 | + | 4.64974i | −0.176114 | + | 0.199173i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9248i | 1.10846i | 0.832362 | + | 0.554232i | \(0.186988\pi\) | ||||
−0.832362 | + | 0.554232i | \(0.813012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.70052 | 0.371329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.3996 | −1.80629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.7005i | 0.455033i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.14903 | − | 1.29948i | 0.0487736 | − | 0.0551597i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 28.5256i | − | 1.20867i | −0.796730 | − | 0.604335i | \(-0.793439\pi\) | ||
0.796730 | − | 0.604335i | \(-0.206561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.0475 | −0.721031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.70052 | 0.282896 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 11.6267i | − | 0.490008i | −0.969522 | − | 0.245004i | \(-0.921211\pi\) | ||
0.969522 | − | 0.245004i | \(-0.0787892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.1866 | + | 17.8496i | 0.849258 | + | 0.750936i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.32582 | −0.390959 | −0.195479 | − | 0.980708i | \(-0.562626\pi\) | ||||
−0.195479 | + | 0.980708i | \(0.562626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6991 | 0.824382 | 0.412191 | − | 0.911097i | \(-0.364764\pi\) | ||||
0.412191 | + | 0.911097i | \(0.364764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.8496i | − | 0.578573i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.6253 | − | 3.03761i | 1.02695 | − | 0.126677i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.7974i | 1.36537i | 0.730712 | + | 0.682686i | \(0.239188\pi\) | ||||
−0.730712 | + | 0.682686i | \(0.760812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.3258 | −0.636920 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.22425 | −0.133765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1490i | 0.710240i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.26187 | − | 2.00000i | −0.0935166 | − | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.8218i | − | 0.776859i | −0.921479 | − | 0.388429i | \(-0.873018\pi\) | ||
0.921479 | − | 0.388429i | \(-0.126982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.4749 | −1.00847 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.574515 | −0.0236324 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.7499i | − | 1.38594i | −0.720965 | − | 0.692971i | \(-0.756301\pi\) | ||
0.720965 | − | 0.692971i | \(-0.243699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.96239 | + | 5.61213i | −0.203438 | + | 0.230075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.201231i | 0.00823583i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.2981 | −0.829356 | −0.414678 | − | 0.909968i | \(-0.636106\pi\) | ||||
−0.414678 | + | 0.909968i | \(0.636106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8496 | −0.564935 | −0.282468 | − | 0.959277i | \(-0.591153\pi\) | ||||
−0.282468 | + | 0.959277i | \(0.591153\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.92478i | 0.404168i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3684 | − | 11.7259i | 0.421534 | − | 0.476726i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.2506i | 1.02489i | 0.858720 | + | 0.512445i | \(0.171260\pi\) | ||||
−0.858720 | + | 0.512445i | \(0.828740\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.92478 | −0.321128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4010 | −0.542148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.14903i | 0.369526i | 0.982783 | + | 0.184763i | \(0.0591517\pi\) | ||||
−0.982783 | + | 0.184763i | \(0.940848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.26187 | + | 5.53690i | 0.252503 | + | 0.223270i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9492i | 0.642091i | 0.947064 | + | 0.321046i | \(0.104034\pi\) | ||||
−0.947064 | + | 0.321046i | \(0.895966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1735 | 0.449100 | 0.224550 | − | 0.974463i | \(-0.427909\pi\) | ||||
0.224550 | + | 0.974463i | \(0.427909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.96239 | −0.199134 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.03761i | − | 0.0415710i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.7005i | 0.427338i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.59895 | −0.103627 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5501 | 0.579229 | 0.289615 | − | 0.957143i | \(-0.406473\pi\) | ||||
0.289615 | + | 0.957143i | \(0.406473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.44851i | 0.256305i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.52373 | + | 4.00000i | 0.179519 | + | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.35026i | 0.0534993i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7269 | −1.52962 | −0.764810 | − | 0.644256i | \(-0.777167\pi\) | ||||
−0.764810 | + | 0.644256i | \(0.777167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.9511i | − | 0.471306i | −0.971837 | − | 0.235653i | \(-0.924277\pi\) | ||
0.971837 | − | 0.235653i | \(-0.0757229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.7005 | − | 21.1490i | 0.736332 | − | 0.832742i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5501i | 0.572023i | 0.958226 | + | 0.286011i | \(0.0923295\pi\) | ||||
−0.958226 | + | 0.286011i | \(0.907671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2506 | 0.677145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.57452 | −0.179289 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 49.9756i | − | 1.95569i | −0.209319 | − | 0.977847i | \(-0.567125\pi\) | ||
0.209319 | − | 0.977847i | \(-0.432875\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.5501 | − | 34.5501i | 1.19369 | − | 1.34998i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9.35026i | − | 0.364788i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9525 | −0.660377 | −0.330189 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330189 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6531 | −0.608834 | −0.304417 | − | 0.952539i | \(-0.598462\pi\) | ||||
−0.304417 | + | 0.952539i | \(0.598462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.52373i | 0.175687i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.96239 | − | 7.92478i | −0.347547 | − | 0.307310i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 39.3258i | − | 1.52270i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.55149 | 0.0599842 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4010 | 0.671760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 26.0263i | − | 1.00324i | −0.865088 | − | 0.501621i | \(-0.832737\pi\) | ||
0.865088 | − | 0.501621i | \(-0.167263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.96239 | − | 0.612127i | 0.191002 | − | 0.0235608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 35.4518i | − | 1.36252i | −0.732039 | − | 0.681262i | \(-0.761431\pi\) | ||
0.732039 | − | 0.681262i | \(-0.238569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4993 | 0.709938 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1490 | 0.503872 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 23.6629i | − | 0.905436i | −0.891654 | − | 0.452718i | \(-0.850454\pi\) | ||
0.891654 | − | 0.452718i | \(-0.149546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.6893 | − | 33.3258i | −1.44003 | − | 1.27331i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.77575i | 0.105901i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.5778 | −0.441081 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.574515 | 0.0218556 | 0.0109278 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109278 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.00000i | 0.0759737i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.85097 | − | 5.48612i | 0.184008 | − | 0.208100i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.5237i | − | 0.474370i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.0507852 | 0.00192087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7269 | 1.61377 | 0.806886 | − | 0.590707i | \(-0.201151\pi\) | ||||
0.806886 | + | 0.590707i | \(0.201151\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.15045i | − | 0.156537i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7005 | − | 16.6253i | 0.553654 | − | 0.626145i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 17.6629i | − | 0.664282i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.2506 | −1.02342 | −0.511709 | − | 0.859159i | \(-0.670987\pi\) | ||||
−0.511709 | + | 0.859159i | \(0.670987\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.7005 | −0.401301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 22.7005i | − | 0.850141i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.52373 | − | 4.00000i | −0.169178 | − | 0.149592i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 5.84955i | − | 0.218456i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7005 | −0.399062 | −0.199531 | − | 0.979891i | \(-0.563942\pi\) | ||||
−0.199531 | + | 0.979891i | \(0.563942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.70052 | −0.249541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0752228i | 0.00279757i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.85097 | + | 39.3258i | 0.180160 | + | 1.46052i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.9511i | − | 1.48171i | −0.671668 | − | 0.740853i | \(-0.734422\pi\) | ||
0.671668 | − | 0.740853i | \(-0.265578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.2981 | −1.56445 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.3488i | 1.12096i | 0.828168 | + | 0.560480i | \(0.189383\pi\) | ||||
−0.828168 | + | 0.560480i | \(0.810617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.67513 | − | 1.48119i | −0.0617881 | − | 0.0546347i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.8496i | 0.731168i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.2506 | 1.37029 | 0.685143 | − | 0.728409i | \(-0.259740\pi\) | ||||
0.685143 | + | 0.728409i | \(0.259740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.22425 | −0.265390 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3634i | 0.967181i | 0.875294 | + | 0.483590i | \(0.160668\pi\) | ||||
−0.875294 | + | 0.483590i | \(0.839332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.58910 | + | 7.45183i | −0.241406 | + | 0.273014i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 3.22425i | − | 0.117969i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7381 | 0.501981 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.6516 | −1.84830 | −0.924152 | − | 0.382024i | \(-0.875227\pi\) | ||||
−0.924152 | + | 0.382024i | \(0.875227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.2243i | 0.700571i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.92478 | − | 2.17679i | 0.0700498 | − | 0.0792216i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.9525i | 1.41575i | 0.706336 | + | 0.707877i | \(0.250347\pi\) | ||||
−0.706336 | + | 0.707877i | \(0.749653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.92478 | −0.360247 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.2130 | 1.74772 | 0.873860 | − | 0.486178i | \(-0.161609\pi\) | ||||
0.873860 | + | 0.486178i | \(0.161609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77575i | 0.100489i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.61213 | − | 4.96239i | −0.202907 | − | 0.179416i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.6464i | 0.420528i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.44851 | −0.160417 | −0.0802086 | − | 0.996778i | \(-0.525559\pi\) | ||||
−0.0802086 | + | 0.996778i | \(0.525559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.35026 | 0.264713 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 39.3014i | − | 1.41357i | −0.707427 | − | 0.706786i | \(-0.750144\pi\) | ||
0.707427 | − | 0.706786i | \(-0.249856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.80018 | + | 22.7005i | 0.100586 | + | 0.815427i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 0.775746i | − | 0.0278297i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.92478i | − | 0.283208i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.43866 | + | 3.92478i | 0.158423 | + | 0.140081i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.897015i | − | 0.0319751i | −0.999872 | − | 0.0159876i | \(-0.994911\pi\) | ||
0.999872 | − | 0.0159876i | \(-0.00508922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.9624 | −0.461473 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0508 | 0.428477 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7480i | 0.417183i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7005 | − | 14.3634i | 0.450441 | − | 0.509419i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.19982i | 0.113343i | 0.998393 | + | 0.0566717i | \(0.0180488\pi\) | ||||
−0.998393 | + | 0.0566717i | \(0.981951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.2506 | −1.17632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.03761 | 0.0366622 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 18.7005i | − | 0.659927i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.35026 | − | 8.31265i | 0.259063 | − | 0.292982i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.11142i | 0.144729i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.44851 | −0.156401 | −0.0782006 | − | 0.996938i | \(-0.524917\pi\) | ||||
−0.0782006 | + | 0.996938i | \(0.524917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6747 | −1.32294 | −0.661468 | − | 0.749973i | \(-0.730066\pi\) | ||||
−0.661468 | + | 0.749973i | \(0.730066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.4241i | − | 0.576017i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.87732 | − | 7.84955i | −0.310959 | − | 0.274958i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 67.5487i | − | 2.36323i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.35026 | −0.0471820 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.749399 | −0.0261542 | −0.0130771 | − | 0.999914i | \(-0.504163\pi\) | ||||
−0.0130771 | + | 0.999914i | \(0.504163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3996i | − | 0.920233i | −0.887858 | − | 0.460117i | \(-0.847808\pi\) | ||
0.887858 | − | 0.460117i | \(-0.152192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.92478 | − | 1.22425i | 0.345536 | − | 0.0426230i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.43724i | − | 0.189071i | −0.995521 | − | 0.0945357i | \(-0.969863\pi\) | ||
0.995521 | − | 0.0945357i | \(-0.0301367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7757 | −0.791034 | −0.395517 | − | 0.918459i | \(-0.629435\pi\) | ||||
−0.395517 | + | 0.918459i | \(0.629435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.0738 | −0.384146 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.35026i | 0.116080i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.3733 | − | 21.5515i | −0.843472 | − | 0.745820i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.57452i | − | 0.158118i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8496 | 0.547187 | 0.273594 | − | 0.961845i | \(-0.411788\pi\) | ||||
0.273594 | + | 0.961845i | \(0.411788\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 14.3733i | − | 0.495042i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.5550 | + | 18.7226i | −0.569509 | + | 0.644077i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14903 | 0.0394346 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.84955 | 0.131961 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0494i | 0.720717i | 0.932814 | + | 0.360358i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.92478 | − | 8.96239i | 0.271022 | − | 0.306507i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.1524i | 1.71317i | 0.516004 | + | 0.856586i | \(0.327419\pi\) | ||||
−0.516004 | + | 0.856586i | \(0.672581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.35026 | −0.182549 | −0.0912743 | − | 0.995826i | \(-0.529094\pi\) | ||||
−0.0912743 | + | 0.995826i | \(0.529094\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.73813 | 0.127395 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 33.6893i | − | 1.14680i | −0.819277 | − | 0.573398i | \(-0.805625\pi\) | ||
0.819277 | − | 0.573398i | \(-0.194375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.53690 | − | 6.66433i | −0.256262 | − | 0.226594i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.77575i | − | 0.196155i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.4010 | −0.725981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4010 | −0.454077 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.4993i | 0.626106i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.32487 | + | 9.21933i | −0.213820 | + | 0.311670i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.5026i | − | 0.726092i | −0.931771 | − | 0.363046i | \(-0.881737\pi\) | ||
0.931771 | − | 0.363046i | \(-0.118263\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.649738 | −0.0219151 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.3634 | 1.09035 | 0.545176 | − | 0.838322i | \(-0.316463\pi\) | ||||
0.545176 | + | 0.838322i | \(0.316463\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.59895i | − | 0.0874617i | −0.999043 | − | 0.0437309i | \(-0.986076\pi\) | ||
0.999043 | − | 0.0437309i | \(-0.0139244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.4485 | − | 12.7757i | −0.485681 | − | 0.429452i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 38.2784i | − | 1.28526i | −0.766176 | − | 0.642631i | \(-0.777843\pi\) | ||
0.766176 | − | 0.642631i | \(-0.222157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.70052 | 0.0905727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 53.1002i | − | 1.77693i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8119 | + | 16.7513i | −0.495109 | + | 0.559934i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.70052i | − | 0.223724i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.2520 | 1.20907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.7269 | −0.957031 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 12.6253i | − | 0.420144i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.7381 | + | 17.7988i | −0.523153 | + | 0.591651i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.9972i | 1.66013i | 0.557668 | + | 0.830064i | \(0.311696\pi\) | ||||
−0.557668 | + | 0.830064i | \(0.688304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.6629 | 0.585842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9525 | 0.826715 | 0.413357 | − | 0.910569i | \(-0.364356\pi\) | ||||
0.413357 | + | 0.910569i | \(0.364356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 6.44851i | − | 0.213414i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.5745 | − | 12.8872i | −0.481819 | − | 0.426037i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 20.6253i | − | 0.681107i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6991 | −0.385918 | −0.192959 | − | 0.981207i | \(-0.561808\pi\) | ||||
−0.192959 | + | 0.981207i | \(0.561808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.1016 | −0.794174 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.70052i | 0.0888888i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.84955 | + | 0.474855i | −0.126573 | + | 0.0156131i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 6.70052i | − | 0.220074i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7090 | −0.777866 | −0.388933 | − | 0.921266i | \(-0.627156\pi\) | ||||
−0.388933 | + | 0.921266i | \(0.627156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.35026 | −0.175348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.25202i | 0.270159i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.2243 | − | 9.92478i | −0.367072 | − | 0.324575i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.9003i | − | 0.650116i | −0.945694 | − | 0.325058i | \(-0.894616\pi\) | ||
0.945694 | − | 0.325058i | \(-0.105384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.9018 | 0.486300 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.28821 | −0.204990 | −0.102495 | − | 0.994734i | \(-0.532683\pi\) | ||||
−0.102495 | + | 0.994734i | \(0.532683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.5501i | 0.604074i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.48119 | − | 1.67513i | 0.0481833 | − | 0.0544920i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.0362i | 1.30100i | 0.759506 | + | 0.650501i | \(0.225441\pi\) | ||||
−0.759506 | + | 0.650501i | \(0.774559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6253 | 0.409835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.1260 | 0.328358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.9478i | − | 1.32643i | −0.748429 | − | 0.663215i | \(-0.769192\pi\) | ||
0.748429 | − | 0.663215i | \(-0.230808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.5139 | + | 23.1998i | −0.663814 | + | 0.750728i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 15.8496i | − | 0.512343i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.4993 | −0.726540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0738 | −0.324962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.7381i | 0.442705i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.6728 | + | 22.7005i | 0.826435 | + | 0.730756i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.2784i | − | 1.23095i | −0.788157 | − | 0.615475i | \(-0.788964\pi\) | ||
0.788157 | − | 0.615475i | \(-0.211036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.9248 | −0.575827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.7269 | 0.921889 | 0.460945 | − | 0.887429i | \(-0.347511\pi\) | ||||
0.460945 | + | 0.887429i | \(0.347511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.27504i | − | 0.104993i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.826531 | + | 6.70052i | 0.0264702 | + | 0.214588i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 41.3014i | − | 1.32135i | −0.750673 | − | 0.660674i | \(-0.770270\pi\) | ||
0.750673 | − | 0.660674i | \(-0.229730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.07522 | 0.0663244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.77575 | −0.0886228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.962389 | + | 0.850969i | 0.0306643 | + | 0.0271141i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 9.92478i | − | 0.315909i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.6516 | 1.99221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1002 | −0.797333 | −0.398666 | − | 0.917096i | \(-0.630527\pi\) | ||||
−0.398666 | + | 0.917096i | \(0.630527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8496i | 0.883779i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.298062 | − | 0.337088i | 0.00944920 | − | 0.0106864i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7974i | 1.03870i | 0.854561 | + | 0.519351i | \(0.173826\pi\) | ||||
−0.854561 | + | 0.519351i | \(0.826174\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.775746 | 0.0245435 |
(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 | 1680.2.t.k.1009.1 | 6 | ||
3.2 | odd | 2 | 5040.2.t.v.1009.5 | 6 | |||
4.3 | odd | 2 | 105.2.d.b.64.4 | yes | 6 | ||
5.2 | odd | 4 | 8400.2.a.dg.1.1 | 3 | |||
5.3 | odd | 4 | 8400.2.a.dj.1.3 | 3 | |||
5.4 | even | 2 | inner | 1680.2.t.k.1009.4 | 6 | ||
12.11 | even | 2 | 315.2.d.e.64.3 | 6 | |||
15.14 | odd | 2 | 5040.2.t.v.1009.6 | 6 | |||
20.3 | even | 4 | 525.2.a.k.1.2 | 3 | |||
20.7 | even | 4 | 525.2.a.j.1.2 | 3 | |||
20.19 | odd | 2 | 105.2.d.b.64.3 | ✓ | 6 | ||
28.3 | even | 6 | 735.2.q.f.79.3 | 12 | |||
28.11 | odd | 6 | 735.2.q.e.79.3 | 12 | |||
28.19 | even | 6 | 735.2.q.f.214.4 | 12 | |||
28.23 | odd | 6 | 735.2.q.e.214.4 | 12 | |||
28.27 | even | 2 | 735.2.d.b.589.4 | 6 | |||
60.23 | odd | 4 | 1575.2.a.w.1.2 | 3 | |||
60.47 | odd | 4 | 1575.2.a.x.1.2 | 3 | |||
60.59 | even | 2 | 315.2.d.e.64.4 | 6 | |||
84.83 | odd | 2 | 2205.2.d.l.1324.3 | 6 | |||
140.19 | even | 6 | 735.2.q.f.214.3 | 12 | |||
140.27 | odd | 4 | 3675.2.a.bi.1.2 | 3 | |||
140.39 | odd | 6 | 735.2.q.e.79.4 | 12 | |||
140.59 | even | 6 | 735.2.q.f.79.4 | 12 | |||
140.79 | odd | 6 | 735.2.q.e.214.3 | 12 | |||
140.83 | odd | 4 | 3675.2.a.bj.1.2 | 3 | |||
140.139 | even | 2 | 735.2.d.b.589.3 | 6 | |||
420.419 | odd | 2 | 2205.2.d.l.1324.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.3 | ✓ | 6 | 20.19 | odd | 2 | ||
105.2.d.b.64.4 | yes | 6 | 4.3 | odd | 2 | ||
315.2.d.e.64.3 | 6 | 12.11 | even | 2 | |||
315.2.d.e.64.4 | 6 | 60.59 | even | 2 | |||
525.2.a.j.1.2 | 3 | 20.7 | even | 4 | |||
525.2.a.k.1.2 | 3 | 20.3 | even | 4 | |||
735.2.d.b.589.3 | 6 | 140.139 | even | 2 | |||
735.2.d.b.589.4 | 6 | 28.27 | even | 2 | |||
735.2.q.e.79.3 | 12 | 28.11 | odd | 6 | |||
735.2.q.e.79.4 | 12 | 140.39 | odd | 6 | |||
735.2.q.e.214.3 | 12 | 140.79 | odd | 6 | |||
735.2.q.e.214.4 | 12 | 28.23 | odd | 6 | |||
735.2.q.f.79.3 | 12 | 28.3 | even | 6 | |||
735.2.q.f.79.4 | 12 | 140.59 | even | 6 | |||
735.2.q.f.214.3 | 12 | 140.19 | even | 6 | |||
735.2.q.f.214.4 | 12 | 28.19 | even | 6 | |||
1575.2.a.w.1.2 | 3 | 60.23 | odd | 4 | |||
1575.2.a.x.1.2 | 3 | 60.47 | odd | 4 | |||
1680.2.t.k.1009.1 | 6 | 1.1 | even | 1 | trivial | ||
1680.2.t.k.1009.4 | 6 | 5.4 | even | 2 | inner | ||
2205.2.d.l.1324.3 | 6 | 84.83 | odd | 2 | |||
2205.2.d.l.1324.4 | 6 | 420.419 | odd | 2 | |||
3675.2.a.bi.1.2 | 3 | 140.27 | odd | 4 | |||
3675.2.a.bj.1.2 | 3 | 140.83 | odd | 4 | |||
5040.2.t.v.1009.5 | 6 | 3.2 | odd | 2 | |||
5040.2.t.v.1009.6 | 6 | 15.14 | odd | 2 | |||
8400.2.a.dg.1.1 | 3 | 5.2 | odd | 4 | |||
8400.2.a.dj.1.3 | 3 | 5.3 | odd | 4 |