Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (of order \(3\), degree \(2\), 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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(0.222521 + 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.529 |
Dual form | 1014.2.e.n.991.2 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.13706 | −0.955724 | −0.477862 | − | 0.878435i | \(-0.658588\pi\) | ||||
−0.477862 | + | 0.878435i | \(0.658588\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −0.0244587 | − | 0.0423637i | −0.00924451 | − | 0.0160120i | 0.861366 | − | 0.507985i | \(-0.169609\pi\) |
−0.870611 | + | 0.491973i | \(0.836276\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.06853 | + | 1.85075i | −0.337899 | + | 0.585259i | ||||
\(11\) | 3.14795 | − | 5.45241i | 0.949142 | − | 1.64396i | 0.201905 | − | 0.979405i | \(-0.435287\pi\) |
0.747237 | − | 0.664557i | \(-0.231380\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.0489173 | −0.0130737 | ||||||||
\(15\) | −1.06853 | + | 1.85075i | −0.275894 | + | 0.477862i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.44504 | + | 2.50289i | 0.350474 | + | 0.607039i | 0.986333 | − | 0.164767i | \(-0.0526871\pi\) |
−0.635858 | + | 0.771806i | \(0.719354\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.60388 | − | 6.24210i | −0.826786 | − | 1.43203i | −0.900547 | − | 0.434759i | \(-0.856834\pi\) |
0.0737611 | − | 0.997276i | \(-0.476500\pi\) | |||||||
\(20\) | 1.06853 | + | 1.85075i | 0.238931 | + | 0.413841i | ||||
\(21\) | −0.0489173 | −0.0106746 | ||||||||
\(22\) | −3.14795 | − | 5.45241i | −0.671145 | − | 1.16246i | ||||
\(23\) | −1.35690 | + | 2.35021i | −0.282932 | + | 0.490053i | −0.972106 | − | 0.234543i | \(-0.924641\pi\) |
0.689173 | + | 0.724597i | \(0.257974\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.432960 | −0.0865921 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0244587 | + | 0.0423637i | −0.00462225 | + | 0.00800598i | ||||
\(29\) | −2.45593 | + | 4.25379i | −0.456054 | + | 0.789909i | −0.998748 | − | 0.0500215i | \(-0.984071\pi\) |
0.542694 | + | 0.839931i | \(0.317404\pi\) | |||||||
\(30\) | 1.06853 | + | 1.85075i | 0.195086 | + | 0.337899i | ||||
\(31\) | −9.00969 | −1.61819 | −0.809094 | − | 0.587679i | \(-0.800042\pi\) | ||||
−0.809094 | + | 0.587679i | \(0.800042\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −3.14795 | − | 5.45241i | −0.547987 | − | 0.949142i | ||||
\(34\) | 2.89008 | 0.495645 | ||||||||
\(35\) | 0.0522697 | + | 0.0905338i | 0.00883520 | + | 0.0153030i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −0.0881460 | + | 0.152673i | −0.0144911 | + | 0.0250993i | −0.873180 | − | 0.487398i | \(-0.837946\pi\) |
0.858689 | + | 0.512497i | \(0.171279\pi\) | |||||||
\(38\) | −7.20775 | −1.16925 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.13706 | 0.337899 | ||||||||
\(41\) | −4.29590 | + | 7.44071i | −0.670906 | + | 1.16204i | 0.306741 | + | 0.951793i | \(0.400761\pi\) |
−0.977647 | + | 0.210251i | \(0.932572\pi\) | |||||||
\(42\) | −0.0244587 | + | 0.0423637i | −0.00377405 | + | 0.00653685i | ||||
\(43\) | −3.35690 | − | 5.81431i | −0.511922 | − | 0.886675i | −0.999904 | − | 0.0138213i | \(-0.995600\pi\) |
0.487983 | − | 0.872853i | \(-0.337733\pi\) | |||||||
\(44\) | −6.29590 | −0.949142 | ||||||||
\(45\) | 1.06853 | + | 1.85075i | 0.159287 | + | 0.275894i | ||||
\(46\) | 1.35690 | + | 2.35021i | 0.200063 | + | 0.346520i | ||||
\(47\) | −7.20775 | −1.05136 | −0.525679 | − | 0.850683i | \(-0.676189\pi\) | ||||
−0.525679 | + | 0.850683i | \(0.676189\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 3.49880 | − | 6.06011i | 0.499829 | − | 0.865729i | ||||
\(50\) | −0.216480 | + | 0.374955i | −0.0306149 | + | 0.0530266i | ||||
\(51\) | 2.89008 | 0.404693 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.34481 | 1.28361 | 0.641804 | − | 0.766868i | \(-0.278186\pi\) | ||||
0.641804 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −6.72737 | + | 11.6521i | −0.907118 | + | 1.57117i | ||||
\(56\) | 0.0244587 | + | 0.0423637i | 0.00326843 | + | 0.00566108i | ||||
\(57\) | −7.20775 | −0.954690 | ||||||||
\(58\) | 2.45593 | + | 4.25379i | 0.322479 | + | 0.558550i | ||||
\(59\) | −2.13437 | − | 3.69685i | −0.277872 | − | 0.481288i | 0.692984 | − | 0.720953i | \(-0.256296\pi\) |
−0.970856 | + | 0.239665i | \(0.922962\pi\) | |||||||
\(60\) | 2.13706 | 0.275894 | ||||||||
\(61\) | −3.55496 | − | 6.15737i | −0.455166 | − | 0.788370i | 0.543532 | − | 0.839388i | \(-0.317087\pi\) |
−0.998698 | + | 0.0510183i | \(0.983753\pi\) | |||||||
\(62\) | −4.50484 | + | 7.80262i | −0.572116 | + | 0.990934i | ||||
\(63\) | −0.0244587 | + | 0.0423637i | −0.00308150 | + | 0.00533732i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.29590 | −0.774971 | ||||||||
\(67\) | 2.69202 | − | 4.66272i | 0.328883 | − | 0.569642i | −0.653408 | − | 0.757006i | \(-0.726661\pi\) |
0.982290 | + | 0.187365i | \(0.0599946\pi\) | |||||||
\(68\) | 1.44504 | − | 2.50289i | 0.175237 | − | 0.303520i | ||||
\(69\) | 1.35690 | + | 2.35021i | 0.163351 | + | 0.282932i | ||||
\(70\) | 0.104539 | 0.0124949 | ||||||||
\(71\) | −4.35690 | − | 7.54637i | −0.517068 | − | 0.895589i | −0.999804 | − | 0.0198223i | \(-0.993690\pi\) |
0.482735 | − | 0.875766i | \(-0.339643\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 14.9487 | 1.74961 | 0.874806 | − | 0.484474i | \(-0.160989\pi\) | ||||
0.874806 | + | 0.484474i | \(0.160989\pi\) | |||||||
\(74\) | 0.0881460 | + | 0.152673i | 0.0102468 | + | 0.0177479i | ||||
\(75\) | −0.216480 | + | 0.374955i | −0.0249970 | + | 0.0432960i | ||||
\(76\) | −3.60388 | + | 6.24210i | −0.413393 | + | 0.716017i | ||||
\(77\) | −0.307979 | −0.0350974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8291 | 1.55589 | 0.777947 | − | 0.628330i | \(-0.216261\pi\) | ||||
0.777947 | + | 0.628330i | \(0.216261\pi\) | |||||||
\(80\) | 1.06853 | − | 1.85075i | 0.119465 | − | 0.206920i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.29590 | + | 7.44071i | 0.474402 | + | 0.821689i | ||||
\(83\) | 11.1347 | 1.22219 | 0.611094 | − | 0.791558i | \(-0.290730\pi\) | ||||
0.611094 | + | 0.791558i | \(0.290730\pi\) | |||||||
\(84\) | 0.0244587 | + | 0.0423637i | 0.00266866 | + | 0.00462225i | ||||
\(85\) | −3.08815 | − | 5.34883i | −0.334956 | − | 0.580162i | ||||
\(86\) | −6.71379 | −0.723967 | ||||||||
\(87\) | 2.45593 | + | 4.25379i | 0.263303 | + | 0.456054i | ||||
\(88\) | −3.14795 | + | 5.45241i | −0.335572 | + | 0.581229i | ||||
\(89\) | 1.96077 | − | 3.39616i | 0.207841 | − | 0.359992i | −0.743193 | − | 0.669077i | \(-0.766690\pi\) |
0.951034 | + | 0.309085i | \(0.100023\pi\) | |||||||
\(90\) | 2.13706 | 0.225266 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.71379 | 0.282932 | ||||||||
\(93\) | −4.50484 | + | 7.80262i | −0.467131 | + | 0.809094i | ||||
\(94\) | −3.60388 | + | 6.24210i | −0.371711 | + | 0.643823i | ||||
\(95\) | 7.70171 | + | 13.3398i | 0.790179 | + | 1.36863i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.23945 | − | 2.14678i | −0.125847 | − | 0.217973i | 0.796217 | − | 0.605011i | \(-0.206831\pi\) |
−0.922064 | + | 0.387038i | \(0.873498\pi\) | |||||||
\(98\) | −3.49880 | − | 6.06011i | −0.353433 | − | 0.612163i | ||||
\(99\) | −6.29590 | −0.632761 | ||||||||
\(100\) | 0.216480 | + | 0.374955i | 0.0216480 | + | 0.0374955i | ||||
\(101\) | −0.826396 | + | 1.43136i | −0.0822295 | + | 0.142426i | −0.904207 | − | 0.427094i | \(-0.859537\pi\) |
0.821978 | + | 0.569520i | \(0.192871\pi\) | |||||||
\(102\) | 1.44504 | − | 2.50289i | 0.143080 | − | 0.247823i | ||||
\(103\) | −8.23490 | −0.811409 | −0.405704 | − | 0.914004i | \(-0.632974\pi\) | ||||
−0.405704 | + | 0.914004i | \(0.632974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.104539 | 0.0102020 | ||||||||
\(106\) | 4.67241 | − | 8.09285i | 0.453824 | − | 0.786047i | ||||
\(107\) | 4.18329 | − | 7.24567i | 0.404414 | − | 0.700466i | −0.589839 | − | 0.807521i | \(-0.700809\pi\) |
0.994253 | + | 0.107055i | \(0.0341421\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 17.4276 | 1.66926 | 0.834630 | − | 0.550811i | \(-0.185682\pi\) | ||||
0.834630 | + | 0.550811i | \(0.185682\pi\) | |||||||
\(110\) | 6.72737 | + | 11.6521i | 0.641429 | + | 1.11099i | ||||
\(111\) | 0.0881460 | + | 0.152673i | 0.00836645 | + | 0.0144911i | ||||
\(112\) | 0.0489173 | 0.00462225 | ||||||||
\(113\) | 6.98792 | + | 12.1034i | 0.657368 | + | 1.13859i | 0.981294 | + | 0.192513i | \(0.0616636\pi\) |
−0.323926 | + | 0.946082i | \(0.605003\pi\) | |||||||
\(114\) | −3.60388 | + | 6.24210i | −0.337534 | + | 0.584626i | ||||
\(115\) | 2.89977 | − | 5.02255i | 0.270405 | − | 0.468355i | ||||
\(116\) | 4.91185 | 0.456054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.26875 | −0.392970 | ||||||||
\(119\) | 0.0706876 | − | 0.122435i | 0.00647992 | − | 0.0112236i | ||||
\(120\) | 1.06853 | − | 1.85075i | 0.0975431 | − | 0.168950i | ||||
\(121\) | −14.3192 | − | 24.8015i | −1.30174 | − | 2.25468i | ||||
\(122\) | −7.10992 | −0.643702 | ||||||||
\(123\) | 4.29590 | + | 7.44071i | 0.387348 | + | 0.670906i | ||||
\(124\) | 4.50484 | + | 7.80262i | 0.404547 | + | 0.700696i | ||||
\(125\) | 11.6106 | 1.03848 | ||||||||
\(126\) | 0.0244587 | + | 0.0423637i | 0.00217895 | + | 0.00377405i | ||||
\(127\) | 3.76055 | − | 6.51347i | 0.333695 | − | 0.577977i | −0.649538 | − | 0.760329i | \(-0.725038\pi\) |
0.983233 | + | 0.182352i | \(0.0583711\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −6.71379 | −0.591116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.12498 | 0.447772 | 0.223886 | − | 0.974615i | \(-0.428126\pi\) | ||||
0.223886 | + | 0.974615i | \(0.428126\pi\) | |||||||
\(132\) | −3.14795 | + | 5.45241i | −0.273994 | + | 0.474571i | ||||
\(133\) | −0.176292 | + | 0.305347i | −0.0152865 | + | 0.0264769i | ||||
\(134\) | −2.69202 | − | 4.66272i | −0.232555 | − | 0.402797i | ||||
\(135\) | 2.13706 | 0.183929 | ||||||||
\(136\) | −1.44504 | − | 2.50289i | −0.123911 | − | 0.214621i | ||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 2.71379 | 0.231013 | ||||||||
\(139\) | −4.34481 | − | 7.52544i | −0.368522 | − | 0.638299i | 0.620812 | − | 0.783959i | \(-0.286803\pi\) |
−0.989335 | + | 0.145660i | \(0.953470\pi\) | |||||||
\(140\) | 0.0522697 | − | 0.0905338i | 0.00441760 | − | 0.00765150i | ||||
\(141\) | −3.60388 | + | 6.24210i | −0.303501 | + | 0.525679i | ||||
\(142\) | −8.71379 | −0.731245 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.24847 | − | 9.09062i | 0.435862 | − | 0.754935i | ||||
\(146\) | 7.47434 | − | 12.9459i | 0.618581 | − | 1.07141i | ||||
\(147\) | −3.49880 | − | 6.06011i | −0.288576 | − | 0.499829i | ||||
\(148\) | 0.176292 | 0.0144911 | ||||||||
\(149\) | −2.43416 | − | 4.21608i | −0.199414 | − | 0.345395i | 0.748925 | − | 0.662655i | \(-0.230570\pi\) |
−0.948339 | + | 0.317260i | \(0.897237\pi\) | |||||||
\(150\) | 0.216480 | + | 0.374955i | 0.0176755 | + | 0.0306149i | ||||
\(151\) | −14.7463 | −1.20004 | −0.600019 | − | 0.799986i | \(-0.704840\pi\) | ||||
−0.600019 | + | 0.799986i | \(0.704840\pi\) | |||||||
\(152\) | 3.60388 | + | 6.24210i | 0.292313 | + | 0.506301i | ||||
\(153\) | 1.44504 | − | 2.50289i | 0.116825 | − | 0.202346i | ||||
\(154\) | −0.153989 | + | 0.266717i | −0.0124088 | + | 0.0214927i | ||||
\(155\) | 19.2543 | 1.54654 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7138 | −1.33391 | −0.666953 | − | 0.745100i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745100i | \(0.732402\pi\) | |||||||
\(158\) | 6.91454 | − | 11.9763i | 0.550091 | − | 0.952786i | ||||
\(159\) | 4.67241 | − | 8.09285i | 0.370546 | − | 0.641804i | ||||
\(160\) | −1.06853 | − | 1.85075i | −0.0844748 | − | 0.146315i | ||||
\(161\) | 0.132751 | 0.0104623 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 2.77479 | + | 4.80608i | 0.217338 | + | 0.376441i | 0.953993 | − | 0.299828i | \(-0.0969292\pi\) |
−0.736655 | + | 0.676269i | \(0.763596\pi\) | |||||||
\(164\) | 8.59179 | 0.670906 | ||||||||
\(165\) | 6.72737 | + | 11.6521i | 0.523725 | + | 0.907118i | ||||
\(166\) | 5.56734 | − | 9.64291i | 0.432109 | − | 0.748435i | ||||
\(167\) | −1.96077 | + | 3.39616i | −0.151729 | + | 0.262802i | −0.931863 | − | 0.362810i | \(-0.881817\pi\) |
0.780134 | + | 0.625612i | \(0.215151\pi\) | |||||||
\(168\) | 0.0489173 | 0.00377405 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.17629 | −0.473700 | ||||||||
\(171\) | −3.60388 | + | 6.24210i | −0.275595 | + | 0.477345i | ||||
\(172\) | −3.35690 | + | 5.81431i | −0.255961 | + | 0.443337i | ||||
\(173\) | 1.74214 | + | 3.01747i | 0.132452 | + | 0.229414i | 0.924621 | − | 0.380888i | \(-0.124382\pi\) |
−0.792169 | + | 0.610302i | \(0.791048\pi\) | |||||||
\(174\) | 4.91185 | 0.372367 | ||||||||
\(175\) | 0.0105896 | + | 0.0183418i | 0.000800501 | + | 0.00138651i | ||||
\(176\) | 3.14795 | + | 5.45241i | 0.237286 | + | 0.410991i | ||||
\(177\) | −4.26875 | −0.320859 | ||||||||
\(178\) | −1.96077 | − | 3.39616i | −0.146966 | − | 0.254553i | ||||
\(179\) | −1.79440 | + | 3.10800i | −0.134120 | + | 0.232303i | −0.925261 | − | 0.379331i | \(-0.876154\pi\) |
0.791141 | + | 0.611634i | \(0.209487\pi\) | |||||||
\(180\) | 1.06853 | − | 1.85075i | 0.0796436 | − | 0.137947i | ||||
\(181\) | 5.50604 | 0.409261 | 0.204630 | − | 0.978839i | \(-0.434401\pi\) | ||||
0.204630 | + | 0.978839i | \(0.434401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.10992 | −0.525580 | ||||||||
\(184\) | 1.35690 | − | 2.35021i | 0.100032 | − | 0.173260i | ||||
\(185\) | 0.188374 | − | 0.326273i | 0.0138495 | − | 0.0239880i | ||||
\(186\) | 4.50484 | + | 7.80262i | 0.330311 | + | 0.572116i | ||||
\(187\) | 18.1957 | 1.33060 | ||||||||
\(188\) | 3.60388 | + | 6.24210i | 0.262840 | + | 0.455252i | ||||
\(189\) | 0.0244587 | + | 0.0423637i | 0.00177911 | + | 0.00308150i | ||||
\(190\) | 15.4034 | 1.11748 | ||||||||
\(191\) | 2.82908 | + | 4.90012i | 0.204705 | + | 0.354560i | 0.950039 | − | 0.312132i | \(-0.101043\pi\) |
−0.745333 | + | 0.666692i | \(0.767710\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −6.70171 | + | 11.6077i | −0.482400 | + | 0.835541i | −0.999796 | − | 0.0202053i | \(-0.993568\pi\) |
0.517396 | + | 0.855746i | \(0.326901\pi\) | |||||||
\(194\) | −2.47889 | −0.177974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99761 | −0.499829 | ||||||||
\(197\) | −9.99061 | + | 17.3042i | −0.711801 | + | 1.23288i | 0.252379 | + | 0.967628i | \(0.418787\pi\) |
−0.964180 | + | 0.265248i | \(0.914546\pi\) | |||||||
\(198\) | −3.14795 | + | 5.45241i | −0.223715 | + | 0.387486i | ||||
\(199\) | 3.12080 | + | 5.40539i | 0.221228 | + | 0.383178i | 0.955181 | − | 0.296022i | \(-0.0956603\pi\) |
−0.733953 | + | 0.679200i | \(0.762327\pi\) | |||||||
\(200\) | 0.432960 | 0.0306149 | ||||||||
\(201\) | −2.69202 | − | 4.66272i | −0.189881 | − | 0.328883i | ||||
\(202\) | 0.826396 | + | 1.43136i | 0.0581450 | + | 0.100710i | ||||
\(203\) | 0.240275 | 0.0168640 | ||||||||
\(204\) | −1.44504 | − | 2.50289i | −0.101173 | − | 0.175237i | ||||
\(205\) | 9.18060 | − | 15.9013i | 0.641201 | − | 1.11059i | ||||
\(206\) | −4.11745 | + | 7.13163i | −0.286876 | + | 0.496884i | ||||
\(207\) | 2.71379 | 0.188622 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −45.3793 | −3.13895 | ||||||||
\(210\) | 0.0522697 | − | 0.0905338i | 0.00360695 | − | 0.00624743i | ||||
\(211\) | 2.54288 | − | 4.40439i | 0.175059 | − | 0.303211i | −0.765123 | − | 0.643884i | \(-0.777322\pi\) |
0.940182 | + | 0.340674i | \(0.110655\pi\) | |||||||
\(212\) | −4.67241 | − | 8.09285i | −0.320902 | − | 0.555819i | ||||
\(213\) | −8.71379 | −0.597059 | ||||||||
\(214\) | −4.18329 | − | 7.24567i | −0.285964 | − | 0.495304i | ||||
\(215\) | 7.17390 | + | 12.4256i | 0.489256 | + | 0.847416i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.220365 | + | 0.381683i | 0.0149594 | + | 0.0259104i | ||||
\(218\) | 8.71379 | − | 15.0927i | 0.590172 | − | 1.02221i | ||||
\(219\) | 7.47434 | − | 12.9459i | 0.505069 | − | 0.874806i | ||||
\(220\) | 13.4547 | 0.907118 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.176292 | 0.0118319 | ||||||||
\(223\) | 10.2741 | − | 17.7953i | 0.688006 | − | 1.19166i | −0.284475 | − | 0.958683i | \(-0.591819\pi\) |
0.972482 | − | 0.232979i | \(-0.0748473\pi\) | |||||||
\(224\) | 0.0244587 | − | 0.0423637i | 0.00163421 | − | 0.00283054i | ||||
\(225\) | 0.216480 | + | 0.374955i | 0.0144320 | + | 0.0249970i | ||||
\(226\) | 13.9758 | 0.929659 | ||||||||
\(227\) | −2.20560 | − | 3.82020i | −0.146390 | − | 0.253556i | 0.783500 | − | 0.621391i | \(-0.213432\pi\) |
−0.929891 | + | 0.367836i | \(0.880099\pi\) | |||||||
\(228\) | 3.60388 | + | 6.24210i | 0.238672 | + | 0.413393i | ||||
\(229\) | 0.230586 | 0.0152376 | 0.00761878 | − | 0.999971i | \(-0.497575\pi\) | ||||
0.00761878 | + | 0.999971i | \(0.497575\pi\) | |||||||
\(230\) | −2.89977 | − | 5.02255i | −0.191205 | − | 0.331177i | ||||
\(231\) | −0.153989 | + | 0.266717i | −0.0101317 | + | 0.0175487i | ||||
\(232\) | 2.45593 | − | 4.25379i | 0.161240 | − | 0.279275i | ||||
\(233\) | −7.82371 | −0.512548 | −0.256274 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256274 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4034 | 1.00481 | ||||||||
\(236\) | −2.13437 | + | 3.69685i | −0.138936 | + | 0.240644i | ||||
\(237\) | 6.91454 | − | 11.9763i | 0.449148 | − | 0.777947i | ||||
\(238\) | −0.0706876 | − | 0.122435i | −0.00458200 | − | 0.00793625i | ||||
\(239\) | 11.1535 | 0.721457 | 0.360729 | − | 0.932671i | \(-0.382528\pi\) | ||||
0.360729 | + | 0.932671i | \(0.382528\pi\) | |||||||
\(240\) | −1.06853 | − | 1.85075i | −0.0689734 | − | 0.119465i | ||||
\(241\) | 1.77263 | + | 3.07029i | 0.114185 | + | 0.197775i | 0.917454 | − | 0.397842i | \(-0.130241\pi\) |
−0.803268 | + | 0.595617i | \(0.796908\pi\) | |||||||
\(242\) | −28.6383 | −1.84094 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.55496 | + | 6.15737i | −0.227583 | + | 0.394185i | ||||
\(245\) | −7.47716 | + | 12.9508i | −0.477699 | + | 0.827398i | ||||
\(246\) | 8.59179 | 0.547793 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.00969 | 0.572116 | ||||||||
\(249\) | 5.56734 | − | 9.64291i | 0.352816 | − | 0.611094i | ||||
\(250\) | 5.80529 | − | 10.0551i | 0.367159 | − | 0.635938i | ||||
\(251\) | 2.08546 | + | 3.61212i | 0.131633 | + | 0.227995i | 0.924306 | − | 0.381652i | \(-0.124645\pi\) |
−0.792673 | + | 0.609647i | \(0.791311\pi\) | |||||||
\(252\) | 0.0489173 | 0.00308150 | ||||||||
\(253\) | 8.54288 | + | 14.7967i | 0.537086 | + | 0.930260i | ||||
\(254\) | −3.76055 | − | 6.51347i | −0.235958 | − | 0.408691i | ||||
\(255\) | −6.17629 | −0.386774 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.44504 | − | 9.43109i | 0.339652 | − | 0.588295i | −0.644715 | − | 0.764423i | \(-0.723024\pi\) |
0.984367 | + | 0.176128i | \(0.0563572\pi\) | |||||||
\(258\) | −3.35690 | + | 5.81431i | −0.208991 | + | 0.361983i | ||||
\(259\) | 0.00862374 | 0.000535853 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.91185 | 0.304036 | ||||||||
\(262\) | 2.56249 | − | 4.43836i | 0.158311 | − | 0.274203i | ||||
\(263\) | 15.6136 | − | 27.0435i | 0.962774 | − | 1.66757i | 0.247292 | − | 0.968941i | \(-0.420459\pi\) |
0.715481 | − | 0.698632i | \(-0.246207\pi\) | |||||||
\(264\) | 3.14795 | + | 5.45241i | 0.193743 | + | 0.335572i | ||||
\(265\) | −19.9705 | −1.22678 | ||||||||
\(266\) | 0.176292 | + | 0.305347i | 0.0108092 | + | 0.0187220i | ||||
\(267\) | −1.96077 | − | 3.39616i | −0.119997 | − | 0.207841i | ||||
\(268\) | −5.38404 | −0.328883 | ||||||||
\(269\) | −7.95862 | − | 13.7847i | −0.485245 | − | 0.840470i | 0.514611 | − | 0.857424i | \(-0.327936\pi\) |
−0.999856 | + | 0.0169542i | \(0.994603\pi\) | |||||||
\(270\) | 1.06853 | − | 1.85075i | 0.0650288 | − | 0.112633i | ||||
\(271\) | −1.76055 | + | 3.04937i | −0.106946 | + | 0.185236i | −0.914532 | − | 0.404514i | \(-0.867441\pi\) |
0.807586 | + | 0.589750i | \(0.200774\pi\) | |||||||
\(272\) | −2.89008 | −0.175237 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −1.36294 | + | 2.36068i | −0.0821882 | + | 0.142354i | ||||
\(276\) | 1.35690 | − | 2.35021i | 0.0816755 | − | 0.141466i | ||||
\(277\) | 4.29052 | + | 7.43140i | 0.257792 | + | 0.446509i | 0.965650 | − | 0.259845i | \(-0.0836716\pi\) |
−0.707858 | + | 0.706355i | \(0.750338\pi\) | |||||||
\(278\) | −8.68963 | −0.521169 | ||||||||
\(279\) | 4.50484 | + | 7.80262i | 0.269698 | + | 0.467131i | ||||
\(280\) | −0.0522697 | − | 0.0905338i | −0.00312371 | − | 0.00541043i | ||||
\(281\) | −8.07846 | −0.481920 | −0.240960 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240960 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(282\) | 3.60388 | + | 6.24210i | 0.214608 | + | 0.371711i | ||||
\(283\) | 8.70171 | − | 15.0718i | 0.517263 | − | 0.895926i | −0.482536 | − | 0.875876i | \(-0.660284\pi\) |
0.999799 | − | 0.0200496i | \(-0.00638242\pi\) | |||||||
\(284\) | −4.35690 | + | 7.54637i | −0.258534 | + | 0.447794i | ||||
\(285\) | 15.4034 | 0.912420 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.420288 | 0.0248088 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 4.32371 | − | 7.48888i | 0.254336 | − | 0.440522i | ||||
\(290\) | −5.24847 | − | 9.09062i | −0.308201 | − | 0.533820i | ||||
\(291\) | −2.47889 | −0.145315 | ||||||||
\(292\) | −7.47434 | − | 12.9459i | −0.437403 | − | 0.757604i | ||||
\(293\) | 9.68545 | + | 16.7757i | 0.565830 | + | 0.980046i | 0.996972 | + | 0.0777621i | \(0.0247775\pi\) |
−0.431142 | + | 0.902284i | \(0.641889\pi\) | |||||||
\(294\) | −6.99761 | −0.408109 | ||||||||
\(295\) | 4.56129 | + | 7.90039i | 0.265569 | + | 0.459979i | ||||
\(296\) | 0.0881460 | − | 0.152673i | 0.00512338 | − | 0.00887396i | ||||
\(297\) | −3.14795 | + | 5.45241i | −0.182662 | + | 0.316381i | ||||
\(298\) | −4.86831 | −0.282014 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.432960 | 0.0249970 | ||||||||
\(301\) | −0.164210 | + | 0.284421i | −0.00946493 | + | 0.0163937i | ||||
\(302\) | −7.37316 | + | 12.7707i | −0.424278 | + | 0.734870i | ||||
\(303\) | 0.826396 | + | 1.43136i | 0.0474752 | + | 0.0822295i | ||||
\(304\) | 7.20775 | 0.413393 | ||||||||
\(305\) | 7.59717 | + | 13.1587i | 0.435013 | + | 0.753464i | ||||
\(306\) | −1.44504 | − | 2.50289i | −0.0826075 | − | 0.143080i | ||||
\(307\) | −12.4263 | −0.709204 | −0.354602 | − | 0.935017i | \(-0.615384\pi\) | ||||
−0.354602 | + | 0.935017i | \(0.615384\pi\) | |||||||
\(308\) | 0.153989 | + | 0.266717i | 0.00877435 | + | 0.0151976i | ||||
\(309\) | −4.11745 | + | 7.13163i | −0.234233 | + | 0.405704i | ||||
\(310\) | 9.62714 | − | 16.6747i | 0.546785 | − | 0.947059i | ||||
\(311\) | 2.71379 | 0.153885 | 0.0769425 | − | 0.997036i | \(-0.475484\pi\) | ||||
0.0769425 | + | 0.997036i | \(0.475484\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3884 | 0.869801 | 0.434901 | − | 0.900478i | \(-0.356783\pi\) | ||||
0.434901 | + | 0.900478i | \(0.356783\pi\) | |||||||
\(314\) | −8.35690 | + | 14.4746i | −0.471607 | + | 0.816847i | ||||
\(315\) | 0.0522697 | − | 0.0905338i | 0.00294507 | − | 0.00510100i | ||||
\(316\) | −6.91454 | − | 11.9763i | −0.388973 | − | 0.673722i | ||||
\(317\) | 25.6528 | 1.44080 | 0.720402 | − | 0.693557i | \(-0.243957\pi\) | ||||
0.720402 | + | 0.693557i | \(0.243957\pi\) | |||||||
\(318\) | −4.67241 | − | 8.09285i | −0.262016 | − | 0.453824i | ||||
\(319\) | 15.4623 | + | 26.7814i | 0.865721 | + | 1.49947i | ||||
\(320\) | −2.13706 | −0.119465 | ||||||||
\(321\) | −4.18329 | − | 7.24567i | −0.233489 | − | 0.404414i | ||||
\(322\) | 0.0663757 | − | 0.114966i | 0.00369898 | − | 0.00640681i | ||||
\(323\) | 10.4155 | − | 18.0402i | 0.579534 | − | 1.00378i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.54958 | 0.307363 | ||||||||
\(327\) | 8.71379 | − | 15.0927i | 0.481874 | − | 0.834630i | ||||
\(328\) | 4.29590 | − | 7.44071i | 0.237201 | − | 0.410845i | ||||
\(329\) | 0.176292 | + | 0.305347i | 0.00971929 | + | 0.0168343i | ||||
\(330\) | 13.4547 | 0.740659 | ||||||||
\(331\) | 1.91185 | + | 3.31143i | 0.105085 | + | 0.182013i | 0.913773 | − | 0.406225i | \(-0.133155\pi\) |
−0.808688 | + | 0.588238i | \(0.799822\pi\) | |||||||
\(332\) | −5.56734 | − | 9.64291i | −0.305547 | − | 0.529223i | ||||
\(333\) | 0.176292 | 0.00966074 | ||||||||
\(334\) | 1.96077 | + | 3.39616i | 0.107289 | + | 0.185829i | ||||
\(335\) | −5.75302 | + | 9.96452i | −0.314321 | + | 0.544420i | ||||
\(336\) | 0.0244587 | − | 0.0423637i | 0.00133433 | − | 0.00231113i | ||||
\(337\) | 20.1304 | 1.09657 | 0.548285 | − | 0.836291i | \(-0.315281\pi\) | ||||
0.548285 | + | 0.836291i | \(0.315281\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9758 | 0.759063 | ||||||||
\(340\) | −3.08815 | + | 5.34883i | −0.167478 | + | 0.290081i | ||||
\(341\) | −28.3620 | + | 49.1245i | −1.53589 | + | 2.66024i | ||||
\(342\) | 3.60388 | + | 6.24210i | 0.194875 | + | 0.337534i | ||||
\(343\) | −0.684726 | −0.0369717 | ||||||||
\(344\) | 3.35690 | + | 5.81431i | 0.180992 | + | 0.313487i | ||||
\(345\) | −2.89977 | − | 5.02255i | −0.156118 | − | 0.270405i | ||||
\(346\) | 3.48427 | 0.187316 | ||||||||
\(347\) | −1.46950 | − | 2.54525i | −0.0788869 | − | 0.136636i | 0.823883 | − | 0.566760i | \(-0.191803\pi\) |
−0.902770 | + | 0.430124i | \(0.858470\pi\) | |||||||
\(348\) | 2.45593 | − | 4.25379i | 0.131652 | − | 0.228027i | ||||
\(349\) | −3.68664 | + | 6.38546i | −0.197342 | + | 0.341806i | −0.947666 | − | 0.319265i | \(-0.896564\pi\) |
0.750324 | + | 0.661070i | \(0.229897\pi\) | |||||||
\(350\) | 0.0211793 | 0.00113208 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.29590 | 0.335572 | ||||||||
\(353\) | 1.00538 | − | 1.74136i | 0.0535108 | − | 0.0926834i | −0.838029 | − | 0.545625i | \(-0.816292\pi\) |
0.891540 | + | 0.452942i | \(0.149626\pi\) | |||||||
\(354\) | −2.13437 | + | 3.69685i | −0.113441 | + | 0.196485i | ||||
\(355\) | 9.31096 | + | 16.1271i | 0.494175 | + | 0.855935i | ||||
\(356\) | −3.92154 | −0.207841 | ||||||||
\(357\) | −0.0706876 | − | 0.122435i | −0.00374118 | − | 0.00647992i | ||||
\(358\) | 1.79440 | + | 3.10800i | 0.0948373 | + | 0.164263i | ||||
\(359\) | 31.4577 | 1.66027 | 0.830137 | − | 0.557559i | \(-0.188262\pi\) | ||||
0.830137 | + | 0.557559i | \(0.188262\pi\) | |||||||
\(360\) | −1.06853 | − | 1.85075i | −0.0563166 | − | 0.0975431i | ||||
\(361\) | −16.4758 | + | 28.5370i | −0.867149 | + | 1.50195i | ||||
\(362\) | 2.75302 | − | 4.76837i | 0.144696 | − | 0.250620i | ||||
\(363\) | −28.6383 | −1.50312 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.9463 | −1.67215 | ||||||||
\(366\) | −3.55496 | + | 6.15737i | −0.185821 | + | 0.321851i | ||||
\(367\) | 2.24967 | − | 3.89654i | 0.117432 | − | 0.203398i | −0.801317 | − | 0.598239i | \(-0.795867\pi\) |
0.918749 | + | 0.394842i | \(0.129201\pi\) | |||||||
\(368\) | −1.35690 | − | 2.35021i | −0.0707331 | − | 0.122513i | ||||
\(369\) | 8.59179 | 0.447271 | ||||||||
\(370\) | −0.188374 | − | 0.326273i | −0.00979308 | − | 0.0169621i | ||||
\(371\) | −0.228562 | − | 0.395881i | −0.0118663 | − | 0.0205531i | ||||
\(372\) | 9.00969 | 0.467131 | ||||||||
\(373\) | −18.9148 | − | 32.7615i | −0.979373 | − | 1.69632i | −0.664676 | − | 0.747132i | \(-0.731430\pi\) |
−0.314698 | − | 0.949192i | \(-0.601903\pi\) | |||||||
\(374\) | 9.09783 | − | 15.7579i | 0.470438 | − | 0.814822i | ||||
\(375\) | 5.80529 | − | 10.0551i | 0.299784 | − | 0.519241i | ||||
\(376\) | 7.20775 | 0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0489173 | 0.00251604 | ||||||||
\(379\) | 4.21983 | − | 7.30896i | 0.216758 | − | 0.375436i | −0.737057 | − | 0.675831i | \(-0.763785\pi\) |
0.953815 | + | 0.300395i | \(0.0971183\pi\) | |||||||
\(380\) | 7.70171 | − | 13.3398i | 0.395089 | − | 0.684315i | ||||
\(381\) | −3.76055 | − | 6.51347i | −0.192659 | − | 0.333695i | ||||
\(382\) | 5.65817 | 0.289497 | ||||||||
\(383\) | −0.643104 | − | 1.11389i | −0.0328611 | − | 0.0569171i | 0.849127 | − | 0.528188i | \(-0.177129\pi\) |
−0.881988 | + | 0.471271i | \(0.843795\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0.658170 | 0.0335434 | ||||||||
\(386\) | 6.70171 | + | 11.6077i | 0.341108 | + | 0.590817i | ||||
\(387\) | −3.35690 | + | 5.81431i | −0.170641 | + | 0.295558i | ||||
\(388\) | −1.23945 | + | 2.14678i | −0.0629234 | + | 0.108986i | ||||
\(389\) | 23.3924 | 1.18604 | 0.593021 | − | 0.805187i | \(-0.297935\pi\) | ||||
0.593021 | + | 0.805187i | \(0.297935\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.84309 | −0.396642 | ||||||||
\(392\) | −3.49880 | + | 6.06011i | −0.176716 | + | 0.306082i | ||||
\(393\) | 2.56249 | − | 4.43836i | 0.129261 | − | 0.223886i | ||||
\(394\) | 9.99061 | + | 17.3042i | 0.503320 | + | 0.871775i | ||||
\(395\) | −29.5536 | −1.48700 | ||||||||
\(396\) | 3.14795 | + | 5.45241i | 0.158190 | + | 0.273994i | ||||
\(397\) | −18.5429 | − | 32.1172i | −0.930640 | − | 1.61192i | −0.782229 | − | 0.622990i | \(-0.785918\pi\) |
−0.148411 | − | 0.988926i | \(-0.547416\pi\) | |||||||
\(398\) | 6.24160 | 0.312863 | ||||||||
\(399\) | 0.176292 | + | 0.305347i | 0.00882564 | + | 0.0152865i | ||||
\(400\) | 0.216480 | − | 0.374955i | 0.0108240 | − | 0.0187477i | ||||
\(401\) | −2.43296 | + | 4.21401i | −0.121496 | + | 0.210438i | −0.920358 | − | 0.391077i | \(-0.872103\pi\) |
0.798862 | + | 0.601515i | \(0.205436\pi\) | |||||||
\(402\) | −5.38404 | −0.268532 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.65279 | 0.0822295 | ||||||||
\(405\) | 1.06853 | − | 1.85075i | 0.0530958 | − | 0.0919646i | ||||
\(406\) | 0.120137 | − | 0.208084i | 0.00596232 | − | 0.0103270i | ||||
\(407\) | 0.554958 | + | 0.961216i | 0.0275083 | + | 0.0476457i | ||||
\(408\) | −2.89008 | −0.143080 | ||||||||
\(409\) | 0.222521 | + | 0.385418i | 0.0110030 | + | 0.0190577i | 0.871474 | − | 0.490441i | \(-0.163164\pi\) |
−0.860472 | + | 0.509499i | \(0.829831\pi\) | |||||||
\(410\) | −9.18060 | − | 15.9013i | −0.453398 | − | 0.785308i | ||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 4.11745 | + | 7.13163i | 0.202852 | + | 0.351350i | ||||
\(413\) | −0.104408 | + | 0.180840i | −0.00513758 | + | 0.00889855i | ||||
\(414\) | 1.35690 | − | 2.35021i | 0.0666878 | − | 0.115507i | ||||
\(415\) | −23.7955 | −1.16807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.68963 | −0.425533 | ||||||||
\(418\) | −22.6896 | + | 39.2996i | −1.10979 | + | 1.92221i | ||||
\(419\) | −8.99343 | + | 15.5771i | −0.439358 | + | 0.760990i | −0.997640 | − | 0.0686612i | \(-0.978127\pi\) |
0.558282 | + | 0.829651i | \(0.311461\pi\) | |||||||
\(420\) | −0.0522697 | − | 0.0905338i | −0.00255050 | − | 0.00441760i | ||||
\(421\) | −21.2814 | −1.03719 | −0.518597 | − | 0.855019i | \(-0.673545\pi\) | ||||
−0.518597 | + | 0.855019i | \(0.673545\pi\) | |||||||
\(422\) | −2.54288 | − | 4.40439i | −0.123785 | − | 0.214402i | ||||
\(423\) | 3.60388 | + | 6.24210i | 0.175226 | + | 0.303501i | ||||
\(424\) | −9.34481 | −0.453824 | ||||||||
\(425\) | −0.625646 | − | 1.08365i | −0.0303483 | − | 0.0525648i | ||||
\(426\) | −4.35690 | + | 7.54637i | −0.211092 | + | 0.365623i | ||||
\(427\) | −0.173899 | + | 0.301202i | −0.00841557 | + | 0.0145762i | ||||
\(428\) | −8.36658 | −0.404414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.3478 | 0.691912 | ||||||||
\(431\) | 12.3569 | − | 21.4028i | 0.595211 | − | 1.03094i | −0.398306 | − | 0.917252i | \(-0.630402\pi\) |
0.993517 | − | 0.113683i | \(-0.0362648\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −16.1087 | − | 27.9011i | −0.774136 | − | 1.34084i | −0.935279 | − | 0.353911i | \(-0.884851\pi\) |
0.161143 | − | 0.986931i | \(-0.448482\pi\) | |||||||
\(434\) | 0.440730 | 0.0211557 | ||||||||
\(435\) | −5.24847 | − | 9.09062i | −0.251645 | − | 0.435862i | ||||
\(436\) | −8.71379 | − | 15.0927i | −0.417315 | − | 0.722811i | ||||
\(437\) | 19.5603 | 0.935698 | ||||||||
\(438\) | −7.47434 | − | 12.9459i | −0.357138 | − | 0.618581i | ||||
\(439\) | −16.0438 | + | 27.7887i | −0.765731 | + | 1.32628i | 0.174129 | + | 0.984723i | \(0.444289\pi\) |
−0.939859 | + | 0.341561i | \(0.889044\pi\) | |||||||
\(440\) | 6.72737 | − | 11.6521i | 0.320715 | − | 0.555494i | ||||
\(441\) | −6.99761 | −0.333219 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5109 | 0.974504 | 0.487252 | − | 0.873261i | \(-0.337999\pi\) | ||||
0.487252 | + | 0.873261i | \(0.337999\pi\) | |||||||
\(444\) | 0.0881460 | − | 0.152673i | 0.00418322 | − | 0.00724556i | ||||
\(445\) | −4.19029 | + | 7.25780i | −0.198639 | + | 0.344053i | ||||
\(446\) | −10.2741 | − | 17.7953i | −0.486494 | − | 0.842632i | ||||
\(447\) | −4.86831 | −0.230263 | ||||||||
\(448\) | −0.0244587 | − | 0.0423637i | −0.00115556 | − | 0.00200149i | ||||
\(449\) | −7.65817 | − | 13.2643i | −0.361411 | − | 0.625983i | 0.626782 | − | 0.779195i | \(-0.284372\pi\) |
−0.988193 | + | 0.153212i | \(0.951038\pi\) | |||||||
\(450\) | 0.432960 | 0.0204099 | ||||||||
\(451\) | 27.0465 | + | 46.8460i | 1.27357 | + | 2.20589i | ||||
\(452\) | 6.98792 | − | 12.1034i | 0.328684 | − | 0.569297i | ||||
\(453\) | −7.37316 | + | 12.7707i | −0.346421 | + | 0.600019i | ||||
\(454\) | −4.41119 | −0.207027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.20775 | 0.337534 | ||||||||
\(457\) | −9.59299 | + | 16.6155i | −0.448741 | + | 0.777242i | −0.998304 | − | 0.0582096i | \(-0.981461\pi\) |
0.549563 | + | 0.835452i | \(0.314794\pi\) | |||||||
\(458\) | 0.115293 | − | 0.199693i | 0.00538729 | − | 0.00933106i | ||||
\(459\) | −1.44504 | − | 2.50289i | −0.0674488 | − | 0.116825i | ||||
\(460\) | −5.79954 | −0.270405 | ||||||||
\(461\) | 4.15615 | + | 7.19865i | 0.193571 | + | 0.335275i | 0.946431 | − | 0.322906i | \(-0.104660\pi\) |
−0.752860 | + | 0.658181i | \(0.771326\pi\) | |||||||
\(462\) | 0.153989 | + | 0.266717i | 0.00716423 | + | 0.0124088i | ||||
\(463\) | 6.32842 | 0.294107 | 0.147053 | − | 0.989129i | \(-0.453021\pi\) | ||||
0.147053 | + | 0.989129i | \(0.453021\pi\) | |||||||
\(464\) | −2.45593 | − | 4.25379i | −0.114014 | − | 0.197477i | ||||
\(465\) | 9.62714 | − | 16.6747i | 0.446448 | − | 0.773270i | ||||
\(466\) | −3.91185 | + | 6.77553i | −0.181213 | + | 0.313870i | ||||
\(467\) | −31.1879 | −1.44320 | −0.721602 | − | 0.692308i | \(-0.756594\pi\) | ||||
−0.721602 | + | 0.692308i | \(0.756594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.263373 | −0.0121614 | ||||||||
\(470\) | 7.70171 | − | 13.3398i | 0.355253 | − | 0.615317i | ||||
\(471\) | −8.35690 | + | 14.4746i | −0.385065 | + | 0.666953i | ||||
\(472\) | 2.13437 | + | 3.69685i | 0.0982426 | + | 0.170161i | ||||
\(473\) | −42.2693 | −1.94355 | ||||||||
\(474\) | −6.91454 | − | 11.9763i | −0.317595 | − | 0.550091i | ||||
\(475\) | 1.56033 | + | 2.70258i | 0.0715931 | + | 0.124003i | ||||
\(476\) | −0.141375 | −0.00647992 | ||||||||
\(477\) | −4.67241 | − | 8.09285i | −0.213935 | − | 0.370546i | ||||
\(478\) | 5.57673 | − | 9.65918i | 0.255074 | − | 0.441800i | ||||
\(479\) | −8.96615 | + | 15.5298i | −0.409674 | + | 0.709576i | −0.994853 | − | 0.101328i | \(-0.967691\pi\) |
0.585179 | + | 0.810904i | \(0.301024\pi\) | |||||||
\(480\) | −2.13706 | −0.0975431 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.54527 | 0.161483 | ||||||||
\(483\) | 0.0663757 | − | 0.114966i | 0.00302020 | − | 0.00523114i | ||||
\(484\) | −14.3192 | + | 24.8015i | −0.650871 | + | 1.12734i | ||||
\(485\) | 2.64878 | + | 4.58782i | 0.120275 | + | 0.208322i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 15.1640 | + | 26.2648i | 0.687145 | + | 1.19017i | 0.972757 | + | 0.231825i | \(0.0744697\pi\) |
−0.285612 | + | 0.958345i | \(0.592197\pi\) | |||||||
\(488\) | 3.55496 | + | 6.15737i | 0.160925 | + | 0.278731i | ||||
\(489\) | 5.54958 | 0.250961 | ||||||||
\(490\) | 7.47716 | + | 12.9508i | 0.337784 | + | 0.585059i | ||||
\(491\) | −15.0477 | + | 26.0634i | −0.679094 | + | 1.17623i | 0.296160 | + | 0.955138i | \(0.404294\pi\) |
−0.975254 | + | 0.221087i | \(0.929039\pi\) | |||||||
\(492\) | 4.29590 | − | 7.44071i | 0.193674 | − | 0.335453i | ||||
\(493\) | −14.1957 | −0.639341 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.4547 | 0.604745 | ||||||||
\(496\) | 4.50484 | − | 7.80262i | 0.202273 | − | 0.350348i | ||||
\(497\) | −0.213128 | + | 0.369148i | −0.00956009 | + | 0.0165586i | ||||
\(498\) | −5.56734 | − | 9.64291i | −0.249478 | − | 0.432109i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | −5.80529 | − | 10.0551i | −0.259620 | − | 0.449676i | ||||
\(501\) | 1.96077 | + | 3.39616i | 0.0876008 | + | 0.151729i | ||||
\(502\) | 4.17092 | 0.186157 | ||||||||
\(503\) | −16.8756 | − | 29.2294i | −0.752446 | − | 1.30328i | −0.946634 | − | 0.322311i | \(-0.895540\pi\) |
0.194188 | − | 0.980964i | \(-0.437793\pi\) | |||||||
\(504\) | 0.0244587 | − | 0.0423637i | 0.00108948 | − | 0.00188703i | ||||
\(505\) | 1.76606 | − | 3.05891i | 0.0785887 | − | 0.136120i | ||||
\(506\) | 17.0858 | 0.759554 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.52111 | −0.333695 | ||||||||
\(509\) | −7.37196 | + | 12.7686i | −0.326756 | + | 0.565959i | −0.981866 | − | 0.189575i | \(-0.939289\pi\) |
0.655110 | + | 0.755534i | \(0.272622\pi\) | |||||||
\(510\) | −3.08815 | + | 5.34883i | −0.136745 | + | 0.236850i | ||||
\(511\) | −0.365625 | − | 0.633281i | −0.0161743 | − | 0.0280147i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.60388 | + | 6.24210i | 0.159115 | + | 0.275595i | ||||
\(514\) | −5.44504 | − | 9.43109i | −0.240171 | − | 0.415988i | ||||
\(515\) | 17.5985 | 0.775483 | ||||||||
\(516\) | 3.35690 | + | 5.81431i | 0.147779 | + | 0.255961i | ||||
\(517\) | −22.6896 | + | 39.2996i | −0.997889 | + | 1.72839i | ||||
\(518\) | 0.00431187 | − | 0.00746837i | 0.000189453 | − | 0.000328142i | ||||
\(519\) | 3.48427 | 0.152943 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1086 | 0.968595 | 0.484297 | − | 0.874903i | \(-0.339075\pi\) | ||||
0.484297 | + | 0.874903i | \(0.339075\pi\) | |||||||
\(522\) | 2.45593 | − | 4.25379i | 0.107493 | − | 0.186183i | ||||
\(523\) | 8.67994 | − | 15.0341i | 0.379547 | − | 0.657395i | −0.611449 | − | 0.791284i | \(-0.709413\pi\) |
0.990996 | + | 0.133889i | \(0.0427464\pi\) | |||||||
\(524\) | −2.56249 | − | 4.43836i | −0.111943 | − | 0.193891i | ||||
\(525\) | 0.0211793 | 0.000924339 | ||||||||
\(526\) | −15.6136 | − | 27.0435i | −0.680784 | − | 1.17915i | ||||
\(527\) | −13.0194 | − | 22.5502i | −0.567133 | − | 0.982303i | ||||
\(528\) | 6.29590 | 0.273994 | ||||||||
\(529\) | 7.81767 | + | 13.5406i | 0.339899 | + | 0.588722i | ||||
\(530\) | −9.98523 | + | 17.2949i | −0.433731 | + | 0.751244i | ||||
\(531\) | −2.13437 | + | 3.69685i | −0.0926240 | + | 0.160429i | ||||
\(532\) | 0.352584 | 0.0152865 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.92154 | −0.169702 | ||||||||
\(535\) | −8.93996 | + | 15.4845i | −0.386508 | + | 0.669452i | ||||
\(536\) | −2.69202 | + | 4.66272i | −0.116278 | + | 0.201399i | ||||
\(537\) | 1.79440 | + | 3.10800i | 0.0774343 | + | 0.134120i | ||||
\(538\) | −15.9172 | −0.686241 | ||||||||
\(539\) | −22.0281 | − | 38.1538i | −0.948818 | − | 1.64340i | ||||
\(540\) | −1.06853 | − | 1.85075i | −0.0459823 | − | 0.0796436i | ||||
\(541\) | 8.83579 | 0.379880 | 0.189940 | − | 0.981796i | \(-0.439171\pi\) | ||||
0.189940 | + | 0.981796i | \(0.439171\pi\) | |||||||
\(542\) | 1.76055 | + | 3.04937i | 0.0756222 | + | 0.130982i | ||||
\(543\) | 2.75302 | − | 4.76837i | 0.118143 | − | 0.204630i | ||||
\(544\) | −1.44504 | + | 2.50289i | −0.0619557 | + | 0.107310i | ||||
\(545\) | −37.2438 | −1.59535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.10859 | −0.346698 | −0.173349 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173349 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(548\) | −2.00000 | + | 3.46410i | −0.0854358 | + | 0.147979i | ||||
\(549\) | −3.55496 | + | 6.15737i | −0.151722 | + | 0.262790i | ||||
\(550\) | 1.36294 | + | 2.36068i | 0.0581158 | + | 0.100660i | ||||
\(551\) | 35.4034 | 1.50824 | ||||||||
\(552\) | −1.35690 | − | 2.35021i | −0.0577533 | − | 0.100032i | ||||
\(553\) | −0.338241 | − | 0.585851i | −0.0143835 | − | 0.0249129i | ||||
\(554\) | 8.58104 | 0.364573 | ||||||||
\(555\) | −0.188374 | − | 0.326273i | −0.00799601 | − | 0.0138495i | ||||
\(556\) | −4.34481 | + | 7.52544i | −0.184261 | + | 0.319150i | ||||
\(557\) | −4.78017 | + | 8.27949i | −0.202542 | + | 0.350813i | −0.949347 | − | 0.314230i | \(-0.898254\pi\) |
0.746805 | + | 0.665043i | \(0.231587\pi\) | |||||||
\(558\) | 9.00969 | 0.381411 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.104539 | −0.00441760 | ||||||||
\(561\) | 9.09783 | − | 15.7579i | 0.384111 | − | 0.665300i | ||||
\(562\) | −4.03923 | + | 6.99615i | −0.170385 | + | 0.295115i | ||||
\(563\) | 22.5819 | + | 39.1129i | 0.951712 | + | 1.64841i | 0.741719 | + | 0.670711i | \(0.234011\pi\) |
0.209994 | + | 0.977703i | \(0.432656\pi\) | |||||||
\(564\) | 7.20775 | 0.303501 | ||||||||
\(565\) | −14.9336 | − | 25.8658i | −0.628262 | − | 1.08818i | ||||
\(566\) | −8.70171 | − | 15.0718i | −0.365760 | − | 0.633515i | ||||
\(567\) | 0.0489173 | 0.00205434 | ||||||||
\(568\) | 4.35690 | + | 7.54637i | 0.182811 | + | 0.316638i | ||||
\(569\) | 1.60388 | − | 2.77799i | 0.0672380 | − | 0.116460i | −0.830447 | − | 0.557098i | \(-0.811915\pi\) |
0.897685 | + | 0.440639i | \(0.145248\pi\) | |||||||
\(570\) | 7.70171 | − | 13.3398i | 0.322589 | − | 0.558741i | ||||
\(571\) | 0.0241632 | 0.00101120 | 0.000505599 | − | 1.00000i | \(-0.499839\pi\) | ||||
0.000505599 | 1.00000i | \(0.499839\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.65817 | 0.236373 | ||||||||
\(574\) | 0.210144 | − | 0.363980i | 0.00877123 | − | 0.0151922i | ||||
\(575\) | 0.587482 | − | 1.01755i | 0.0244997 | − | 0.0424347i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −46.0200 | −1.91584 | −0.957918 | − | 0.287041i | \(-0.907328\pi\) | ||||
−0.957918 | + | 0.287041i | \(0.907328\pi\) | |||||||
\(578\) | −4.32371 | − | 7.48888i | −0.179843 | − | 0.311496i | ||||
\(579\) | 6.70171 | + | 11.6077i | 0.278514 | + | 0.482400i | ||||
\(580\) | −10.4969 | −0.435862 | ||||||||
\(581\) | −0.272339 | − | 0.471705i | −0.0112985 | − | 0.0195696i | ||||
\(582\) | −1.23945 | + | 2.14678i | −0.0513767 | + | 0.0889871i | ||||
\(583\) | 29.4170 | − | 50.9517i | 1.21833 | − | 2.11020i | ||||
\(584\) | −14.9487 | −0.618581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.3709 | 0.800204 | ||||||||
\(587\) | 12.9693 | − | 22.4634i | 0.535299 | − | 0.927165i | −0.463850 | − | 0.885914i | \(-0.653532\pi\) |
0.999149 | − | 0.0412510i | \(-0.0131343\pi\) | |||||||
\(588\) | −3.49880 | + | 6.06011i | −0.144288 | + | 0.249915i | ||||
\(589\) | 32.4698 | + | 56.2393i | 1.33789 | + | 2.31730i | ||||
\(590\) | 9.12259 | 0.375571 | ||||||||
\(591\) | 9.99061 | + | 17.3042i | 0.410959 | + | 0.711801i | ||||
\(592\) | −0.0881460 | − | 0.152673i | −0.00362278 | − | 0.00627484i | ||||
\(593\) | −8.30691 | −0.341124 | −0.170562 | − | 0.985347i | \(-0.554558\pi\) | ||||
−0.170562 | + | 0.985347i | \(0.554558\pi\) | |||||||
\(594\) | 3.14795 | + | 5.45241i | 0.129162 | + | 0.223715i | ||||
\(595\) | −0.151064 | + | 0.261650i | −0.00619302 | + | 0.0107266i | ||||
\(596\) | −2.43416 | + | 4.21608i | −0.0997069 | + | 0.172697i | ||||
\(597\) | 6.24160 | 0.255452 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.1702 | 1.51873 | 0.759366 | − | 0.650664i | \(-0.225509\pi\) | ||||
0.759366 | + | 0.650664i | \(0.225509\pi\) | |||||||
\(600\) | 0.216480 | − | 0.374955i | 0.00883776 | − | 0.0153075i | ||||
\(601\) | 6.28501 | − | 10.8860i | 0.256371 | − | 0.444048i | −0.708896 | − | 0.705313i | \(-0.750806\pi\) |
0.965267 | + | 0.261265i | \(0.0841398\pi\) | |||||||
\(602\) | 0.164210 | + | 0.284421i | 0.00669272 | + | 0.0115921i | ||||
\(603\) | −5.38404 | −0.219255 | ||||||||
\(604\) | 7.37316 | + | 12.7707i | 0.300010 | + | 0.519632i | ||||
\(605\) | 30.6010 | + | 53.0024i | 1.24411 | + | 2.15485i | ||||
\(606\) | 1.65279 | 0.0671401 | ||||||||
\(607\) | −4.02446 | − | 6.97057i | −0.163348 | − | 0.282927i | 0.772720 | − | 0.634748i | \(-0.218896\pi\) |
−0.936067 | + | 0.351821i | \(0.885563\pi\) | |||||||
\(608\) | 3.60388 | − | 6.24210i | 0.146156 | − | 0.253150i | ||||
\(609\) | 0.120137 | − | 0.208084i | 0.00486821 | − | 0.00843199i | ||||
\(610\) | 15.1943 | 0.615201 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.89008 | −0.116825 | ||||||||
\(613\) | −15.2295 | + | 26.3783i | −0.615115 | + | 1.06541i | 0.375250 | + | 0.926924i | \(0.377557\pi\) |
−0.990364 | + | 0.138486i | \(0.955776\pi\) | |||||||
\(614\) | −6.21313 | + | 10.7615i | −0.250741 | + | 0.434297i | ||||
\(615\) | −9.18060 | − | 15.9013i | −0.370198 | − | 0.641201i | ||||
\(616\) | 0.307979 | 0.0124088 | ||||||||
\(617\) | −2.36658 | − | 4.09904i | −0.0952751 | − | 0.165021i | 0.814448 | − | 0.580236i | \(-0.197040\pi\) |
−0.909723 | + | 0.415215i | \(0.863706\pi\) | |||||||
\(618\) | 4.11745 | + | 7.13163i | 0.165628 | + | 0.286876i | ||||
\(619\) | −24.9095 | −1.00120 | −0.500598 | − | 0.865680i | \(-0.666886\pi\) | ||||
−0.500598 | + | 0.865680i | \(0.666886\pi\) | |||||||
\(620\) | −9.62714 | − | 16.6747i | −0.386635 | − | 0.669672i | ||||
\(621\) | 1.35690 | − | 2.35021i | 0.0544504 | − | 0.0943108i | ||||
\(622\) | 1.35690 | − | 2.35021i | 0.0544066 | − | 0.0942349i | ||||
\(623\) | −0.191831 | −0.00768556 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6477 | −0.905910 | ||||||||
\(626\) | 7.69418 | − | 13.3267i | 0.307521 | − | 0.532642i | ||||
\(627\) | −22.6896 | + | 39.2996i | −0.906136 | + | 1.56947i | ||||
\(628\) | 8.35690 | + | 14.4746i | 0.333476 | + | 0.577598i | ||||
\(629\) | −0.509499 | −0.0203150 | ||||||||
\(630\) | −0.0522697 | − | 0.0905338i | −0.00208248 | − | 0.00360695i | ||||
\(631\) | −12.2148 | − | 21.1566i | −0.486262 | − | 0.842230i | 0.513614 | − | 0.858022i | \(-0.328306\pi\) |
−0.999875 | + | 0.0157918i | \(0.994973\pi\) | |||||||
\(632\) | −13.8291 | −0.550091 | ||||||||
\(633\) | −2.54288 | − | 4.40439i | −0.101070 | − | 0.175059i | ||||
\(634\) | 12.8264 | − | 22.2160i | 0.509401 | − | 0.882309i | ||||
\(635\) | −8.03654 | + | 13.9197i | −0.318920 | + | 0.552386i | ||||
\(636\) | −9.34481 | −0.370546 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 30.9245 | 1.22431 | ||||||||
\(639\) | −4.35690 | + | 7.54637i | −0.172356 | + | 0.298530i | ||||
\(640\) | −1.06853 | + | 1.85075i | −0.0422374 | + | 0.0731574i | ||||
\(641\) | −24.3991 | − | 42.2605i | −0.963707 | − | 1.66919i | −0.713050 | − | 0.701113i | \(-0.752687\pi\) |
−0.250657 | − | 0.968076i | \(-0.580647\pi\) | |||||||
\(642\) | −8.36658 | −0.330203 | ||||||||
\(643\) | 14.1347 | + | 24.4820i | 0.557417 | + | 0.965475i | 0.997711 | + | 0.0676209i | \(0.0215408\pi\) |
−0.440294 | + | 0.897854i | \(0.645126\pi\) | |||||||
\(644\) | −0.0663757 | − | 0.114966i | −0.00261557 | − | 0.00453030i | ||||
\(645\) | 14.3478 | 0.564944 | ||||||||
\(646\) | −10.4155 | − | 18.0402i | −0.409792 | − | 0.709781i | ||||
\(647\) | −17.4480 | + | 30.2209i | −0.685953 | + | 1.18810i | 0.287184 | + | 0.957876i | \(0.407281\pi\) |
−0.973136 | + | 0.230229i | \(0.926052\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −26.8756 | −1.05496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.440730 | 0.0172736 | ||||||||
\(652\) | 2.77479 | − | 4.80608i | 0.108669 | − | 0.188221i | ||||
\(653\) | 5.85786 | − | 10.1461i | 0.229236 | − | 0.397048i | −0.728346 | − | 0.685209i | \(-0.759711\pi\) |
0.957582 | + | 0.288162i | \(0.0930440\pi\) | |||||||
\(654\) | −8.71379 | − | 15.0927i | −0.340736 | − | 0.590172i | ||||
\(655\) | −10.9524 | −0.427946 | ||||||||
\(656\) | −4.29590 | − | 7.44071i | −0.167727 | − | 0.290511i | ||||
\(657\) | −7.47434 | − | 12.9459i | −0.291602 | − | 0.505069i | ||||
\(658\) | 0.352584 | 0.0137452 | ||||||||
\(659\) | 3.56734 | + | 6.17881i | 0.138964 | + | 0.240692i | 0.927105 | − | 0.374803i | \(-0.122290\pi\) |
−0.788141 | + | 0.615495i | \(0.788956\pi\) | |||||||
\(660\) | 6.72737 | − | 11.6521i | 0.261862 | − | 0.453559i | ||||
\(661\) | 4.26444 | − | 7.38622i | 0.165867 | − | 0.287291i | −0.771096 | − | 0.636719i | \(-0.780291\pi\) |
0.936963 | + | 0.349429i | \(0.113624\pi\) | |||||||
\(662\) | 3.82371 | 0.148613 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.1347 | −0.432109 | ||||||||
\(665\) | 0.376747 | − | 0.652545i | 0.0146096 | − | 0.0253046i | ||||
\(666\) | 0.0881460 | − | 0.152673i | 0.00341559 | − | 0.00591597i | ||||
\(667\) | −6.66487 | − | 11.5439i | −0.258065 | − | 0.446982i | ||||
\(668\) | 3.92154 | 0.151729 | ||||||||
\(669\) | −10.2741 | − | 17.7953i | −0.397221 | − | 0.688006i | ||||
\(670\) | 5.75302 | + | 9.96452i | 0.222259 | + | 0.384963i | ||||
\(671\) | −44.7633 | −1.72807 | ||||||||
\(672\) | −0.0244587 | − | 0.0423637i | −0.000943514 | − | 0.00163421i | ||||
\(673\) | 15.7969 | − | 27.3610i | 0.608924 | − | 1.05469i | −0.382494 | − | 0.923958i | \(-0.624935\pi\) |
0.991418 | − | 0.130729i | \(-0.0417319\pi\) | |||||||
\(674\) | 10.0652 | − | 17.4334i | 0.387696 | − | 0.671510i | ||||
\(675\) | 0.432960 | 0.0166646 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.3002 | −0.664901 | −0.332451 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332451 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(678\) | 6.98792 | − | 12.1034i | 0.268369 | − | 0.464829i | ||||
\(679\) | −0.0606304 | + | 0.105015i | −0.00232678 | + | 0.00403011i | ||||
\(680\) | 3.08815 | + | 5.34883i | 0.118425 | + | 0.205118i | ||||
\(681\) | −4.41119 | −0.169037 | ||||||||
\(682\) | 28.3620 | + | 49.1245i | 1.08604 | + | 1.88107i | ||||
\(683\) | −15.1978 | − | 26.3234i | −0.581529 | − | 1.00724i | −0.995298 | − | 0.0968556i | \(-0.969122\pi\) |
0.413770 | − | 0.910382i | \(-0.364212\pi\) | |||||||
\(684\) | 7.20775 | 0.275595 | ||||||||
\(685\) | 4.27413 | + | 7.40300i | 0.163306 | + | 0.282854i | ||||
\(686\) | −0.342363 | + | 0.592990i | −0.0130715 | + | 0.0226405i | ||||
\(687\) | 0.115293 | − | 0.199693i | 0.00439871 | − | 0.00761878i | ||||
\(688\) | 6.71379 | 0.255961 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.79954 | −0.220785 | ||||||||
\(691\) | −17.8659 | + | 30.9447i | −0.679652 | + | 1.17719i | 0.295434 | + | 0.955363i | \(0.404536\pi\) |
−0.975086 | + | 0.221828i | \(0.928798\pi\) | |||||||
\(692\) | 1.74214 | − | 3.01747i | 0.0662260 | − | 0.114707i | ||||
\(693\) | 0.153989 | + | 0.266717i | 0.00584957 | + | 0.0101317i | ||||
\(694\) | −2.93900 | −0.111563 | ||||||||
\(695\) | 9.28514 | + | 16.0823i | 0.352206 | + | 0.610038i | ||||
\(696\) | −2.45593 | − | 4.25379i | −0.0930917 | − | 0.161240i | ||||
\(697\) | −24.8310 | −0.940541 | ||||||||
\(698\) | 3.68664 | + | 6.38546i | 0.139542 | + | 0.241693i | ||||
\(699\) | −3.91185 | + | 6.77553i | −0.147960 | + | 0.256274i | ||||
\(700\) | 0.0105896 | − | 0.0183418i | 0.000400250 | − | 0.000693254i | ||||
\(701\) | 20.1328 | 0.760404 | 0.380202 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380202 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.27067 | 0.0479242 | ||||||||
\(704\) | 3.14795 | − | 5.45241i | 0.118643 | − | 0.205495i | ||||
\(705\) | 7.70171 | − | 13.3398i | 0.290063 | − | 0.502404i | ||||
\(706\) | −1.00538 | − | 1.74136i | −0.0378379 | − | 0.0655371i | ||||
\(707\) | 0.0808502 | 0.00304069 | ||||||||
\(708\) | 2.13437 | + | 3.69685i | 0.0802147 | + | 0.138936i | ||||
\(709\) | −8.30798 | − | 14.3898i | −0.312013 | − | 0.540422i | 0.666785 | − | 0.745250i | \(-0.267670\pi\) |
−0.978798 | + | 0.204828i | \(0.934336\pi\) | |||||||
\(710\) | 18.6219 | 0.698868 | ||||||||
\(711\) | −6.91454 | − | 11.9763i | −0.259316 | − | 0.449148i | ||||
\(712\) | −1.96077 | + | 3.39616i | −0.0734830 | + | 0.127276i | ||||
\(713\) | 12.2252 | − | 21.1747i | 0.457838 | − | 0.792998i | ||||
\(714\) | −0.141375 | −0.00529083 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.58881 | 0.134120 | ||||||||
\(717\) | 5.57673 | − | 9.65918i | 0.208267 | − | 0.360729i | ||||
\(718\) | 15.7289 | − | 27.2432i | 0.586996 | − | 1.01671i | ||||
\(719\) | −1.02416 | − | 1.77390i | −0.0381948 | − | 0.0661554i | 0.846296 | − | 0.532713i | \(-0.178827\pi\) |
−0.884491 | + | 0.466557i | \(0.845494\pi\) | |||||||
\(720\) | −2.13706 | −0.0796436 | ||||||||
\(721\) | 0.201415 | + | 0.348860i | 0.00750107 | + | 0.0129922i | ||||
\(722\) | 16.4758 | + | 28.5370i | 0.613167 | + | 1.06204i | ||||
\(723\) | 3.54527 | 0.131850 | ||||||||
\(724\) | −2.75302 | − | 4.76837i | −0.102315 | − | 0.177215i | ||||
\(725\) | 1.06332 | − | 1.84172i | 0.0394907 | − | 0.0683998i | ||||
\(726\) | −14.3192 | + | 24.8015i | −0.531434 | + | 0.920470i | ||||
\(727\) | 29.9377 | 1.11033 | 0.555163 | − | 0.831741i | \(-0.312656\pi\) | ||||
0.555163 | + | 0.831741i | \(0.312656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.9731 | + | 27.6663i | −0.591193 | + | 1.02398i | ||||
\(731\) | 9.70171 | − | 16.8039i | 0.358831 | − | 0.621513i | ||||
\(732\) | 3.55496 | + | 6.15737i | 0.131395 | + | 0.227583i | ||||
\(733\) | −1.46250 | −0.0540187 | −0.0270093 | − | 0.999635i | \(-0.508598\pi\) | ||||
−0.0270093 | + | 0.999635i | \(0.508598\pi\) | |||||||
\(734\) | −2.24967 | − | 3.89654i | −0.0830368 | − | 0.143824i | ||||
\(735\) | 7.47716 | + | 12.9508i | 0.275799 | + | 0.477699i | ||||
\(736\) | −2.71379 | −0.100032 | ||||||||
\(737\) | −16.9487 | − | 29.3560i | −0.624313 | − | 1.08134i | ||||
\(738\) | 4.29590 | − | 7.44071i | 0.158134 | − | 0.273896i | ||||
\(739\) | −20.1933 | + | 34.9758i | −0.742822 | + | 1.28660i | 0.208384 | + | 0.978047i | \(0.433180\pi\) |
−0.951206 | + | 0.308558i | \(0.900154\pi\) | |||||||
\(740\) | −0.376747 | −0.0138495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.457123 | −0.0167815 | ||||||||
\(743\) | 4.88769 | − | 8.46573i | 0.179312 | − | 0.310577i | −0.762333 | − | 0.647185i | \(-0.775946\pi\) |
0.941645 | + | 0.336607i | \(0.109280\pi\) | |||||||
\(744\) | 4.50484 | − | 7.80262i | 0.165156 | − | 0.286058i | ||||
\(745\) | 5.20195 | + | 9.01004i | 0.190585 | + | 0.330102i | ||||
\(746\) | −37.8297 | −1.38504 | ||||||||
\(747\) | −5.56734 | − | 9.64291i | −0.203698 | − | 0.352816i | ||||
\(748\) | −9.09783 | − | 15.7579i | −0.332650 | − | 0.576166i | ||||
\(749\) | −0.409271 | −0.0149544 | ||||||||
\(750\) | −5.80529 | − | 10.0551i | −0.211979 | − | 0.367159i | ||||
\(751\) | −17.2729 | + | 29.9176i | −0.630298 | + | 1.09171i | 0.357192 | + | 0.934031i | \(0.383734\pi\) |
−0.987491 | + | 0.157678i | \(0.949599\pi\) | |||||||
\(752\) | 3.60388 | − | 6.24210i | 0.131420 | − | 0.227626i | ||||
\(753\) | 4.17092 | 0.151997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.5138 | 1.14690 | ||||||||
\(756\) | 0.0244587 | − | 0.0423637i | 0.000889553 | − | 0.00154075i | ||||
\(757\) | 2.57242 | − | 4.45556i | 0.0934961 | − | 0.161940i | −0.815484 | − | 0.578780i | \(-0.803529\pi\) |
0.908980 | + | 0.416840i | \(0.136862\pi\) | |||||||
\(758\) | −4.21983 | − | 7.30896i | −0.153271 | − | 0.265474i | ||||
\(759\) | 17.0858 | 0.620174 | ||||||||
\(760\) | −7.70171 | − | 13.3398i | −0.279370 | − | 0.483884i | ||||
\(761\) | 9.75600 | + | 16.8979i | 0.353655 | + | 0.612548i | 0.986887 | − | 0.161414i | \(-0.0516054\pi\) |
−0.633232 | + | 0.773962i | \(0.718272\pi\) | |||||||
\(762\) | −7.52111 | −0.272461 | ||||||||
\(763\) | −0.426256 | − | 0.738296i | −0.0154315 | − | 0.0267281i | ||||
\(764\) | 2.82908 | − | 4.90012i | 0.102353 | − | 0.177280i | ||||
\(765\) | −3.08815 | + | 5.34883i | −0.111652 | + | 0.193387i | ||||
\(766\) | −1.28621 | −0.0464726 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −2.87800 | + | 4.98485i | −0.103783 | + | 0.179758i | −0.913241 | − | 0.407421i | \(-0.866428\pi\) |
0.809457 | + | 0.587179i | \(0.199762\pi\) | |||||||
\(770\) | 0.329085 | − | 0.569992i | 0.0118594 | − | 0.0205411i | ||||
\(771\) | −5.44504 | − | 9.43109i | −0.196098 | − | 0.339652i | ||||
\(772\) | 13.4034 | 0.482400 | ||||||||
\(773\) | 2.06369 | + | 3.57441i | 0.0742257 | + | 0.128563i | 0.900749 | − | 0.434339i | \(-0.143018\pi\) |
−0.826524 | + | 0.562902i | \(0.809685\pi\) | |||||||
\(774\) | 3.35690 | + | 5.81431i | 0.120661 | + | 0.208991i | ||||
\(775\) | 3.90084 | 0.140122 | ||||||||
\(776\) | 1.23945 | + | 2.14678i | 0.0444935 | + | 0.0770651i | ||||
\(777\) | 0.00431187 | − | 0.00746837i | 0.000154687 | − | 0.000267926i | ||||
\(778\) | 11.6962 | − | 20.2584i | 0.419329 | − | 0.726299i | ||||
\(779\) | 61.9275 | 2.21878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.8611 | −1.96309 | ||||||||
\(782\) | −3.92154 | + | 6.79231i | −0.140234 | + | 0.242893i | ||||
\(783\) | 2.45593 | − | 4.25379i | 0.0877677 | − | 0.152018i | ||||
\(784\) | 3.49880 | + | 6.06011i | 0.124957 | + | 0.216432i | ||||
\(785\) | 35.7184 | 1.27485 | ||||||||
\(786\) | −2.56249 | − | 4.43836i | −0.0914010 | − | 0.158311i | ||||
\(787\) | 8.11960 | + | 14.0636i | 0.289433 | + | 0.501312i | 0.973674 | − | 0.227943i | \(-0.0732000\pi\) |
−0.684242 | + | 0.729255i | \(0.739867\pi\) | |||||||
\(788\) | 19.9812 | 0.711801 | ||||||||
\(789\) | −15.6136 | − | 27.0435i | −0.555858 | − | 0.962774i | ||||
\(790\) | −14.7768 | + | 25.5942i | −0.525735 | + | 0.910601i | ||||
\(791\) | 0.341830 | − | 0.592068i | 0.0121541 | − | 0.0210515i | ||||
\(792\) | 6.29590 | 0.223715 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −37.0858 | −1.31612 | ||||||||
\(795\) | −9.98523 | + | 17.2949i | −0.354140 | + | 0.613388i | ||||
\(796\) | 3.12080 | − | 5.40539i | 0.110614 | − | 0.191589i | ||||
\(797\) | −8.05741 | − | 13.9558i | −0.285408 | − | 0.494341i | 0.687300 | − | 0.726374i | \(-0.258796\pi\) |
−0.972708 | + | 0.232032i | \(0.925462\pi\) | |||||||
\(798\) | 0.352584 | 0.0124813 | ||||||||
\(799\) | −10.4155 | − | 18.0402i | −0.368474 | − | 0.638216i | ||||
\(800\) | −0.216480 | − | 0.374955i | −0.00765373 | − | 0.0132566i | ||||
\(801\) | −3.92154 | −0.138561 | ||||||||
\(802\) | 2.43296 | + | 4.21401i | 0.0859108 | + | 0.148802i | ||||
\(803\) | 47.0577 | − | 81.5063i | 1.66063 | − | 2.87630i | ||||
\(804\) | −2.69202 | + | 4.66272i | −0.0949403 | + | 0.164441i | ||||
\(805\) | −0.283698 | −0.00999905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.9172 | −0.560313 | ||||||||
\(808\) | 0.826396 | − | 1.43136i | 0.0290725 | − | 0.0503551i | ||||
\(809\) | −20.0761 | + | 34.7728i | −0.705837 | + | 1.22255i | 0.260552 | + | 0.965460i | \(0.416096\pi\) |
−0.966389 | + | 0.257085i | \(0.917238\pi\) | |||||||
\(810\) | −1.06853 | − | 1.85075i | −0.0375444 | − | 0.0650288i | ||||
\(811\) | 39.8646 | 1.39984 | 0.699918 | − | 0.714224i | \(-0.253220\pi\) | ||||
0.699918 | + | 0.714224i | \(0.253220\pi\) | |||||||
\(812\) | −0.120137 | − | 0.208084i | −0.00421600 | − | 0.00730232i | ||||
\(813\) | 1.76055 | + | 3.04937i | 0.0617453 | + | 0.106946i | ||||
\(814\) | 1.10992 | 0.0389025 | ||||||||
\(815\) | −5.92990 | − | 10.2709i | −0.207715 | − | 0.359774i | ||||
\(816\) | −1.44504 | + | 2.50289i | −0.0505866 | + | 0.0876185i | ||||
\(817\) | −24.1957 | + | 41.9081i | −0.846499 | + | 1.46618i | ||||
\(818\) | 0.445042 | 0.0155605 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.3612 | −0.641201 | ||||||||
\(821\) | 3.12714 | − | 5.41636i | 0.109138 | − | 0.189032i | −0.806283 | − | 0.591529i | \(-0.798524\pi\) |
0.915421 | + | 0.402497i | \(0.131858\pi\) | |||||||
\(822\) | −2.00000 | + | 3.46410i | −0.0697580 | + | 0.120824i | ||||
\(823\) | 2.37167 | + | 4.10785i | 0.0826711 | + | 0.143191i | 0.904396 | − | 0.426693i | \(-0.140322\pi\) |
−0.821725 | + | 0.569884i | \(0.806988\pi\) | |||||||
\(824\) | 8.23490 | 0.286876 | ||||||||
\(825\) | 1.36294 | + | 2.36068i | 0.0474514 | + | 0.0821882i | ||||
\(826\) | 0.104408 | + | 0.180840i | 0.00363282 | + | 0.00629222i | ||||
\(827\) | −0.716185 | −0.0249042 | −0.0124521 | − | 0.999922i | \(-0.503964\pi\) | ||||
−0.0124521 | + | 0.999922i | \(0.503964\pi\) | |||||||
\(828\) | −1.35690 | − | 2.35021i | −0.0471554 | − | 0.0816755i | ||||
\(829\) | 18.0030 | − | 31.1821i | 0.625269 | − | 1.08300i | −0.363219 | − | 0.931704i | \(-0.618322\pi\) |
0.988489 | − | 0.151295i | \(-0.0483443\pi\) | |||||||
\(830\) | −11.8977 | + | 20.6075i | −0.412977 | + | 0.715297i | ||||
\(831\) | 8.58104 | 0.297673 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2237 | 0.700709 | ||||||||
\(834\) | −4.34481 | + | 7.52544i | −0.150449 | + | 0.260585i | ||||
\(835\) | 4.19029 | − | 7.25780i | 0.145011 | − | 0.251167i | ||||
\(836\) | 22.6896 | + | 39.2996i | 0.784737 | + | 1.35920i | ||||
\(837\) | 9.00969 | 0.311420 | ||||||||
\(838\) | 8.99343 | + | 15.5771i | 0.310673 | + | 0.538101i | ||||
\(839\) | 10.7778 | + | 18.6677i | 0.372090 | + | 0.644479i | 0.989887 | − | 0.141859i | \(-0.0453079\pi\) |
−0.617797 | + | 0.786338i | \(0.711975\pi\) | |||||||
\(840\) | −0.104539 | −0.00360695 | ||||||||
\(841\) | 2.43685 | + | 4.22074i | 0.0840291 | + | 0.145543i | ||||
\(842\) | −10.6407 | + | 18.4303i | −0.366703 | + | 0.635148i | ||||
\(843\) | −4.03923 | + | 6.99615i | −0.139118 | + | 0.240960i | ||||
\(844\) | −5.08575 | −0.175059 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.20775 | 0.247808 | ||||||||
\(847\) | −0.700455 | + | 1.21322i | −0.0240679 | + | 0.0416869i | ||||
\(848\) | −4.67241 | + | 8.09285i | −0.160451 | + | 0.277909i | ||||
\(849\) | −8.70171 | − | 15.0718i | −0.298642 | − | 0.517263i | ||||
\(850\) | −1.25129 | −0.0429189 | ||||||||
\(851\) | −0.239210 | − | 0.414324i | −0.00820001 | − | 0.0142028i | ||||
\(852\) | 4.35690 | + | 7.54637i | 0.149265 | + | 0.258534i | ||||
\(853\) | 37.8237 | 1.29506 | 0.647530 | − | 0.762040i | \(-0.275802\pi\) | ||||
0.647530 | + | 0.762040i | \(0.275802\pi\) | |||||||
\(854\) | 0.173899 | + | 0.301202i | 0.00595070 | + | 0.0103069i | ||||
\(855\) | 7.70171 | − | 13.3398i | 0.263393 | − | 0.456210i | ||||
\(856\) | −4.18329 | + | 7.24567i | −0.142982 | + | 0.247652i | ||||
\(857\) | −6.58317 | −0.224877 | −0.112438 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112438 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6246 | −0.703702 | −0.351851 | − | 0.936056i | \(-0.614448\pi\) | ||||
−0.351851 | + | 0.936056i | \(0.614448\pi\) | |||||||
\(860\) | 7.17390 | − | 12.4256i | 0.244628 | − | 0.423708i | ||||
\(861\) | 0.210144 | − | 0.363980i | 0.00716168 | − | 0.0124044i | ||||
\(862\) | −12.3569 | − | 21.4028i | −0.420878 | − | 0.728981i | ||||
\(863\) | −15.9081 | −0.541519 | −0.270760 | − | 0.962647i | \(-0.587275\pi\) | ||||
−0.270760 | + | 0.962647i | \(0.587275\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −3.72305 | − | 6.44852i | −0.126588 | − | 0.219256i | ||||
\(866\) | −32.2174 | −1.09479 | ||||||||
\(867\) | −4.32371 | − | 7.48888i | −0.146841 | − | 0.254336i | ||||
\(868\) | 0.220365 | − | 0.381683i | 0.00747968 | − | 0.0129552i | ||||
\(869\) | 43.5332 | − | 75.4018i | 1.47676 | − | 2.55783i | ||||
\(870\) | −10.4969 | −0.355880 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.4276 | −0.590172 | ||||||||
\(873\) | −1.23945 | + | 2.14678i | −0.0419489 | + | 0.0726577i | ||||
\(874\) | 9.78017 | − | 16.9397i | 0.330819 | − | 0.572995i | ||||
\(875\) | −0.283979 | − | 0.491867i | −0.00960025 | − | 0.0166281i | ||||
\(876\) | −14.9487 | −0.505069 | ||||||||
\(877\) | −7.80194 | − | 13.5134i | −0.263453 | − | 0.456313i | 0.703704 | − | 0.710493i | \(-0.251528\pi\) |
−0.967157 | + | 0.254179i | \(0.918195\pi\) | |||||||
\(878\) | 16.0438 | + | 27.7887i | 0.541453 | + | 0.937825i | ||||
\(879\) | 19.3709 | 0.653364 | ||||||||
\(880\) | −6.72737 | − | 11.6521i | −0.226779 | − | 0.392794i | ||||
\(881\) | 7.12737 | − | 12.3450i | 0.240127 | − | 0.415913i | −0.720623 | − | 0.693327i | \(-0.756144\pi\) |
0.960750 | + | 0.277414i | \(0.0894775\pi\) | |||||||
\(882\) | −3.49880 | + | 6.06011i | −0.117811 | + | 0.204054i | ||||
\(883\) | 1.65817 | 0.0558019 | 0.0279009 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0279009 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.12259 | 0.306652 | ||||||||
\(886\) | 10.2555 | − | 17.7630i | 0.344539 | − | 0.596760i | ||||
\(887\) | 9.60148 | − | 16.6303i | 0.322386 | − | 0.558389i | −0.658594 | − | 0.752499i | \(-0.728848\pi\) |
0.980980 | + | 0.194109i | \(0.0621817\pi\) | |||||||
\(888\) | −0.0881460 | − | 0.152673i | −0.00295799 | − | 0.00512338i | ||||
\(889\) | −0.367913 | −0.0123394 | ||||||||
\(890\) | 4.19029 | + | 7.25780i | 0.140459 | + | 0.243282i | ||||
\(891\) | 3.14795 | + | 5.45241i | 0.105460 | + | 0.182662i | ||||
\(892\) | −20.5483 | −0.688006 | ||||||||
\(893\) | 25.9758 | + | 44.9915i | 0.869248 | + | 1.50558i | ||||
\(894\) | −2.43416 | + | 4.21608i | −0.0814104 | + | 0.141007i | ||||
\(895\) | 3.83476 | − | 6.64199i | 0.128182 | − | 0.222017i | ||||
\(896\) | −0.0489173 | −0.00163421 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.3163 | −0.511113 | ||||||||
\(899\) | 22.1271 | − | 38.3253i | 0.737981 | − | 1.27822i | ||||
\(900\) | 0.216480 | − | 0.374955i | 0.00721600 | − | 0.0124985i | ||||
\(901\) | 13.5036 | + | 23.3890i | 0.449872 | + | 0.779201i | ||||
\(902\) | 54.0930 | 1.80110 | ||||||||
\(903\) | 0.164210 | + | 0.284421i | 0.00546458 | + | 0.00946493i | ||||
\(904\) | −6.98792 | − | 12.1034i | −0.232415 | − | 0.402554i | ||||
\(905\) | −11.7668 | −0.391140 | ||||||||
\(906\) | 7.37316 | + | 12.7707i | 0.244957 | + | 0.424278i | ||||
\(907\) | 16.1836 | − | 28.0308i | 0.537367 | − | 0.930747i | −0.461678 | − | 0.887048i | \(-0.652752\pi\) |
0.999045 | − | 0.0436995i | \(-0.0139144\pi\) | |||||||
\(908\) | −2.20560 | + | 3.82020i | −0.0731952 | + | 0.126778i | ||||
\(909\) | 1.65279 | 0.0548197 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9624 | −1.12523 | −0.562613 | − | 0.826721i | \(-0.690204\pi\) | ||||
−0.562613 | + | 0.826721i | \(0.690204\pi\) | |||||||
\(912\) | 3.60388 | − | 6.24210i | 0.119336 | − | 0.206696i | ||||
\(913\) | 35.0514 | − | 60.7108i | 1.16003 | − | 2.00923i | ||||
\(914\) | 9.59299 | + | 16.6155i | 0.317308 | + | 0.549593i | ||||
\(915\) | 15.1943 | 0.502309 | ||||||||
\(916\) | −0.115293 | − | 0.199693i | −0.00380939 | − | 0.00659806i | ||||
\(917\) | −0.125350 | − | 0.217113i | −0.00413943 | − | 0.00716970i | ||||
\(918\) | −2.89008 | −0.0953870 | ||||||||
\(919\) | 10.0390 | + | 17.3880i | 0.331156 | + | 0.573579i | 0.982739 | − | 0.184999i | \(-0.0592281\pi\) |
−0.651583 | + | 0.758577i | \(0.725895\pi\) | |||||||
\(920\) | −2.89977 | + | 5.02255i | −0.0956027 | + | 0.165589i | ||||
\(921\) | −6.21313 | + | 10.7615i | −0.204730 | + | 0.354602i | ||||
\(922\) | 8.31229 | 0.273751 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.307979 | 0.0101317 | ||||||||
\(925\) | 0.0381637 | − | 0.0661015i | 0.00125482 | − | 0.00217340i | ||||
\(926\) | 3.16421 | − | 5.48057i | 0.103982 | − | 0.180103i | ||||
\(927\) | 4.11745 | + | 7.13163i | 0.135235 | + | 0.234233i | ||||
\(928\) | −4.91185 | −0.161240 | ||||||||
\(929\) | 28.0640 | + | 48.6082i | 0.920749 | + | 1.59478i | 0.798258 | + | 0.602315i | \(0.205755\pi\) |
0.122491 | + | 0.992470i | \(0.460912\pi\) | |||||||
\(930\) | −9.62714 | − | 16.6747i | −0.315686 | − | 0.546785i | ||||
\(931\) | −50.4370 | −1.65301 | ||||||||
\(932\) | 3.91185 | + | 6.77553i | 0.128137 | + | 0.221940i | ||||
\(933\) | 1.35690 | − | 2.35021i | 0.0444228 | − | 0.0769425i | ||||
\(934\) | −15.5939 | + | 27.0095i | −0.510250 | + | 0.883778i | ||||
\(935\) | −38.8853 | −1.27169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0291 | 0.883001 | 0.441501 | − | 0.897261i | \(-0.354446\pi\) | ||||
0.441501 | + | 0.897261i | \(0.354446\pi\) | |||||||
\(938\) | −0.131687 | + | 0.228088i | −0.00429972 | + | 0.00744733i | ||||
\(939\) | 7.69418 | − | 13.3267i | 0.251090 | − | 0.434901i | ||||
\(940\) | −7.70171 | − | 13.3398i | −0.251202 | − | 0.435095i | ||||
\(941\) | 24.0277 | 0.783282 | 0.391641 | − | 0.920118i | \(-0.371908\pi\) | ||||
0.391641 | + | 0.920118i | \(0.371908\pi\) | |||||||
\(942\) | 8.35690 | + | 14.4746i | 0.272282 | + | 0.471607i | ||||
\(943\) | −11.6582 | − | 20.1925i | −0.379642 | − | 0.657560i | ||||
\(944\) | 4.26875 | 0.138936 | ||||||||
\(945\) | −0.0522697 | − | 0.0905338i | −0.00170033 | − | 0.00294507i | ||||
\(946\) | −21.1347 | + | 36.6063i | −0.687147 | + | 1.19017i | ||||
\(947\) | −13.3983 | + | 23.2065i | −0.435386 | + | 0.754110i | −0.997327 | − | 0.0730670i | \(-0.976721\pi\) |
0.561941 | + | 0.827177i | \(0.310055\pi\) | |||||||
\(948\) | −13.8291 | −0.449148 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.12067 | 0.101248 | ||||||||
\(951\) | 12.8264 | − | 22.2160i | 0.415924 | − | 0.720402i | ||||
\(952\) | −0.0706876 | + | 0.122435i | −0.00229100 | + | 0.00396813i | ||||
\(953\) | −17.2107 | − | 29.8099i | −0.557510 | − | 0.965636i | −0.997703 | − | 0.0677332i | \(-0.978423\pi\) |
0.440193 | − | 0.897903i | \(-0.354910\pi\) | |||||||
\(954\) | −9.34481 | −0.302550 | ||||||||
\(955\) | −6.04593 | − | 10.4719i | −0.195642 | − | 0.338862i | ||||
\(956\) | −5.57673 | − | 9.65918i | −0.180364 | − | 0.312400i | ||||
\(957\) | 30.9245 | 0.999648 | ||||||||
\(958\) | 8.96615 | + | 15.5298i | 0.289683 | + | 0.501746i | ||||
\(959\) | −0.0978347 | + | 0.169455i | −0.00315925 | + | 0.00547198i | ||||
\(960\) | −1.06853 | + | 1.85075i | −0.0344867 | + | 0.0597327i | ||||
\(961\) | 50.1745 | 1.61853 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.36658 | −0.269609 | ||||||||
\(964\) | 1.77263 | − | 3.07029i | 0.0570927 | − | 0.0988875i | ||||
\(965\) | 14.3220 | − | 24.8064i | 0.461041 | − | 0.798546i | ||||
\(966\) | −0.0663757 | − | 0.114966i | −0.00213560 | − | 0.00369898i | ||||
\(967\) | −26.2631 | −0.844565 | −0.422282 | − | 0.906464i | \(-0.638771\pi\) | ||||
−0.422282 | + | 0.906464i | \(0.638771\pi\) | |||||||
\(968\) | 14.3192 | + | 24.8015i | 0.460235 | + | 0.797151i | ||||
\(969\) | −10.4155 | − | 18.0402i | −0.334594 | − | 0.579534i | ||||
\(970\) | 5.29755 | 0.170094 | ||||||||
\(971\) | 19.9921 | + | 34.6273i | 0.641577 | + | 1.11124i | 0.985081 | + | 0.172093i | \(0.0550528\pi\) |
−0.343504 | + | 0.939151i | \(0.611614\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −0.212537 | + | 0.368124i | −0.00681362 | + | 0.0118015i | ||||
\(974\) | 30.3279 | 0.971770 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.10992 | 0.227583 | ||||||||
\(977\) | 2.29159 | − | 3.96914i | 0.0733143 | − | 0.126984i | −0.827038 | − | 0.562146i | \(-0.809976\pi\) |
0.900352 | + | 0.435162i | \(0.143309\pi\) | |||||||
\(978\) | 2.77479 | − | 4.80608i | 0.0887280 | − | 0.153681i | ||||
\(979\) | −12.3448 | − | 21.3818i | −0.394542 | − | 0.683367i | ||||
\(980\) | 14.9543 | 0.477699 | ||||||||
\(981\) | −8.71379 | − | 15.0927i | −0.278210 | − | 0.481874i | ||||
\(982\) | 15.0477 | + | 26.0634i | 0.480192 | + | 0.831717i | ||||
\(983\) | 10.6848 | 0.340794 | 0.170397 | − | 0.985376i | \(-0.445495\pi\) | ||||
0.170397 | + | 0.985376i | \(0.445495\pi\) | |||||||
\(984\) | −4.29590 | − | 7.44071i | −0.136948 | − | 0.237201i | ||||
\(985\) | 21.3506 | − | 36.9803i | 0.680285 | − | 1.17829i | ||||
\(986\) | −7.09783 | + | 12.2938i | −0.226041 | + | 0.391515i | ||||
\(987\) | 0.352584 | 0.0112229 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.2198 | 0.579357 | ||||||||
\(990\) | 6.72737 | − | 11.6521i | 0.213810 | − | 0.370329i | ||||
\(991\) | −25.3010 | + | 43.8227i | −0.803714 | + | 1.39207i | 0.113442 | + | 0.993545i | \(0.463812\pi\) |
−0.917156 | + | 0.398529i | \(0.869521\pi\) | |||||||
\(992\) | −4.50484 | − | 7.80262i | −0.143029 | − | 0.247733i | ||||
\(993\) | 3.82371 | 0.121342 | ||||||||
\(994\) | 0.213128 | + | 0.369148i | 0.00676000 | + | 0.0117087i | ||||
\(995\) | −6.66935 | − | 11.5517i | −0.211433 | − | 0.366212i | ||||
\(996\) | −11.1347 | −0.352816 | ||||||||
\(997\) | 17.9801 | + | 31.1425i | 0.569437 | + | 0.986294i | 0.996622 | + | 0.0821294i | \(0.0261721\pi\) |
−0.427185 | + | 0.904164i | \(0.640495\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0881460 | − | 0.152673i | 0.00278882 | − | 0.00483037i |
(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 | 1014.2.e.n.529.2 | 6 | ||
13.2 | odd | 12 | 1014.2.i.h.361.5 | 12 | |||
13.3 | even | 3 | inner | 1014.2.e.n.991.2 | 6 | ||
13.4 | even | 6 | 1014.2.a.n.1.2 | yes | 3 | ||
13.5 | odd | 4 | 1014.2.i.h.823.2 | 12 | |||
13.6 | odd | 12 | 1014.2.b.f.337.5 | 6 | |||
13.7 | odd | 12 | 1014.2.b.f.337.2 | 6 | |||
13.8 | odd | 4 | 1014.2.i.h.823.5 | 12 | |||
13.9 | even | 3 | 1014.2.a.l.1.2 | ✓ | 3 | ||
13.10 | even | 6 | 1014.2.e.l.991.2 | 6 | |||
13.11 | odd | 12 | 1014.2.i.h.361.2 | 12 | |||
13.12 | even | 2 | 1014.2.e.l.529.2 | 6 | |||
39.17 | odd | 6 | 3042.2.a.ba.1.2 | 3 | |||
39.20 | even | 12 | 3042.2.b.o.1351.5 | 6 | |||
39.32 | even | 12 | 3042.2.b.o.1351.2 | 6 | |||
39.35 | odd | 6 | 3042.2.a.bh.1.2 | 3 | |||
52.35 | odd | 6 | 8112.2.a.cj.1.2 | 3 | |||
52.43 | odd | 6 | 8112.2.a.cm.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.2 | ✓ | 3 | 13.9 | even | 3 | ||
1014.2.a.n.1.2 | yes | 3 | 13.4 | even | 6 | ||
1014.2.b.f.337.2 | 6 | 13.7 | odd | 12 | |||
1014.2.b.f.337.5 | 6 | 13.6 | odd | 12 | |||
1014.2.e.l.529.2 | 6 | 13.12 | even | 2 | |||
1014.2.e.l.991.2 | 6 | 13.10 | even | 6 | |||
1014.2.e.n.529.2 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.e.n.991.2 | 6 | 13.3 | even | 3 | inner | ||
1014.2.i.h.361.2 | 12 | 13.11 | odd | 12 | |||
1014.2.i.h.361.5 | 12 | 13.2 | odd | 12 | |||
1014.2.i.h.823.2 | 12 | 13.5 | odd | 4 | |||
1014.2.i.h.823.5 | 12 | 13.8 | odd | 4 | |||
3042.2.a.ba.1.2 | 3 | 39.17 | odd | 6 | |||
3042.2.a.bh.1.2 | 3 | 39.35 | odd | 6 | |||
3042.2.b.o.1351.2 | 6 | 39.32 | even | 12 | |||
3042.2.b.o.1351.5 | 6 | 39.20 | even | 12 | |||
8112.2.a.cj.1.2 | 3 | 52.35 | odd | 6 | |||
8112.2.a.cm.1.2 | 3 | 52.43 | odd | 6 |