Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.5 | ||
Root | \(-1.07992 + 0.623490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.361 |
Dual form | 1014.2.i.h.823.5 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.13706i | 0.955724i | 0.878435 | + | 0.477862i | \(0.158588\pi\) | ||||
−0.878435 | + | 0.477862i | \(0.841412\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −0.0423637 | − | 0.0244587i | −0.0160120 | − | 0.00924451i | 0.491973 | − | 0.870611i | \(-0.336276\pi\) |
−0.507985 | + | 0.861366i | \(0.669609\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.06853 | + | 1.85075i | 0.337899 | + | 0.585259i | ||||
\(11\) | −5.45241 | + | 3.14795i | −1.64396 | + | 0.949142i | −0.664557 | + | 0.747237i | \(0.731380\pi\) |
−0.979405 | + | 0.201905i | \(0.935287\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.0489173 | −0.0130737 | ||||||||
\(15\) | −1.85075 | + | 1.06853i | −0.477862 | + | 0.275894i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.44504 | + | 2.50289i | −0.350474 | + | 0.607039i | −0.986333 | − | 0.164767i | \(-0.947313\pi\) |
0.635858 | + | 0.771806i | \(0.280646\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.24210 | + | 3.60388i | 1.43203 | + | 0.826786i | 0.997276 | − | 0.0737611i | \(-0.0235002\pi\) |
0.434759 | + | 0.900547i | \(0.356834\pi\) | |||||||
\(20\) | 1.85075 | + | 1.06853i | 0.413841 | + | 0.238931i | ||||
\(21\) | − | 0.0489173i | − | 0.0106746i | ||||||
\(22\) | −3.14795 | + | 5.45241i | −0.671145 | + | 1.16246i | ||||
\(23\) | 1.35690 | + | 2.35021i | 0.282932 | + | 0.490053i | 0.972106 | − | 0.234543i | \(-0.0753595\pi\) |
−0.689173 | + | 0.724597i | \(0.742026\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0.432960 | 0.0865921 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0423637 | + | 0.0244587i | −0.00800598 | + | 0.00462225i | ||||
\(29\) | −2.45593 | − | 4.25379i | −0.456054 | − | 0.789909i | 0.542694 | − | 0.839931i | \(-0.317404\pi\) |
−0.998748 | + | 0.0500215i | \(0.984071\pi\) | |||||||
\(30\) | −1.06853 | + | 1.85075i | −0.195086 | + | 0.337899i | ||||
\(31\) | 9.00969i | 1.61819i | 0.587679 | + | 0.809094i | \(0.300042\pi\) | ||||
−0.587679 | + | 0.809094i | \(0.699958\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −5.45241 | − | 3.14795i | −0.949142 | − | 0.547987i | ||||
\(34\) | 2.89008i | 0.495645i | ||||||||
\(35\) | 0.0522697 | − | 0.0905338i | 0.00883520 | − | 0.0153030i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 0.152673 | − | 0.0881460i | 0.0250993 | − | 0.0144911i | −0.487398 | − | 0.873180i | \(-0.662054\pi\) |
0.512497 | + | 0.858689i | \(0.328721\pi\) | |||||||
\(38\) | 7.20775 | 1.16925 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.13706 | 0.337899 | ||||||||
\(41\) | −7.44071 | + | 4.29590i | −1.16204 | + | 0.670906i | −0.951793 | − | 0.306741i | \(-0.900761\pi\) |
−0.210251 | + | 0.977647i | \(0.567428\pi\) | |||||||
\(42\) | −0.0244587 | − | 0.0423637i | −0.00377405 | − | 0.00653685i | ||||
\(43\) | 3.35690 | − | 5.81431i | 0.511922 | − | 0.886675i | −0.487983 | − | 0.872853i | \(-0.662267\pi\) |
0.999904 | − | 0.0138213i | \(-0.00439959\pi\) | |||||||
\(44\) | 6.29590i | 0.949142i | ||||||||
\(45\) | −1.85075 | − | 1.06853i | −0.275894 | − | 0.159287i | ||||
\(46\) | 2.35021 | + | 1.35690i | 0.346520 | + | 0.200063i | ||||
\(47\) | − | 7.20775i | − | 1.05136i | −0.850683 | − | 0.525679i | \(-0.823811\pi\) | ||
0.850683 | − | 0.525679i | \(-0.176189\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −3.49880 | − | 6.06011i | −0.499829 | − | 0.865729i | ||||
\(50\) | 0.374955 | − | 0.216480i | 0.0530266 | − | 0.0306149i | ||||
\(51\) | −2.89008 | −0.404693 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.34481 | 1.28361 | 0.641804 | − | 0.766868i | \(-0.278186\pi\) | ||||
0.641804 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −6.72737 | − | 11.6521i | −0.907118 | − | 1.57117i | ||||
\(56\) | −0.0244587 | + | 0.0423637i | −0.00326843 | + | 0.00566108i | ||||
\(57\) | 7.20775i | 0.954690i | ||||||||
\(58\) | −4.25379 | − | 2.45593i | −0.558550 | − | 0.322479i | ||||
\(59\) | −3.69685 | − | 2.13437i | −0.481288 | − | 0.277872i | 0.239665 | − | 0.970856i | \(-0.422962\pi\) |
−0.720953 | + | 0.692984i | \(0.756296\pi\) | |||||||
\(60\) | 2.13706i | 0.275894i | ||||||||
\(61\) | −3.55496 | + | 6.15737i | −0.455166 | + | 0.788370i | −0.998698 | − | 0.0510183i | \(-0.983753\pi\) |
0.543532 | + | 0.839388i | \(0.317087\pi\) | |||||||
\(62\) | 4.50484 | + | 7.80262i | 0.572116 | + | 0.990934i | ||||
\(63\) | 0.0423637 | − | 0.0244587i | 0.00533732 | − | 0.00308150i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.29590 | −0.774971 | ||||||||
\(67\) | 4.66272 | − | 2.69202i | 0.569642 | − | 0.328883i | −0.187365 | − | 0.982290i | \(-0.559995\pi\) |
0.757006 | + | 0.653408i | \(0.226661\pi\) | |||||||
\(68\) | 1.44504 | + | 2.50289i | 0.175237 | + | 0.303520i | ||||
\(69\) | −1.35690 | + | 2.35021i | −0.163351 | + | 0.282932i | ||||
\(70\) | − | 0.104539i | − | 0.0124949i | ||||||
\(71\) | 7.54637 | + | 4.35690i | 0.895589 | + | 0.517068i | 0.875766 | − | 0.482735i | \(-0.160357\pi\) |
0.0198223 | + | 0.999804i | \(0.493690\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 14.9487i | 1.74961i | 0.484474 | + | 0.874806i | \(0.339011\pi\) | ||||
−0.484474 | + | 0.874806i | \(0.660989\pi\) | |||||||
\(74\) | 0.0881460 | − | 0.152673i | 0.0102468 | − | 0.0177479i | ||||
\(75\) | 0.216480 | + | 0.374955i | 0.0249970 | + | 0.0432960i | ||||
\(76\) | 6.24210 | − | 3.60388i | 0.716017 | − | 0.413393i | ||||
\(77\) | 0.307979 | 0.0350974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8291 | 1.55589 | 0.777947 | − | 0.628330i | \(-0.216261\pi\) | ||||
0.777947 | + | 0.628330i | \(0.216261\pi\) | |||||||
\(80\) | 1.85075 | − | 1.06853i | 0.206920 | − | 0.119465i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.29590 | + | 7.44071i | −0.474402 | + | 0.821689i | ||||
\(83\) | − | 11.1347i | − | 1.22219i | −0.791558 | − | 0.611094i | \(-0.790730\pi\) | ||
0.791558 | − | 0.611094i | \(-0.209270\pi\) | |||||||
\(84\) | −0.0423637 | − | 0.0244587i | −0.00462225 | − | 0.00266866i | ||||
\(85\) | −5.34883 | − | 3.08815i | −0.580162 | − | 0.334956i | ||||
\(86\) | − | 6.71379i | − | 0.723967i | ||||||
\(87\) | 2.45593 | − | 4.25379i | 0.263303 | − | 0.456054i | ||||
\(88\) | 3.14795 | + | 5.45241i | 0.335572 | + | 0.581229i | ||||
\(89\) | −3.39616 | + | 1.96077i | −0.359992 | + | 0.207841i | −0.669077 | − | 0.743193i | \(-0.733310\pi\) |
0.309085 | + | 0.951034i | \(0.399977\pi\) | |||||||
\(90\) | −2.13706 | −0.225266 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.71379 | 0.282932 | ||||||||
\(93\) | −7.80262 | + | 4.50484i | −0.809094 | + | 0.467131i | ||||
\(94\) | −3.60388 | − | 6.24210i | −0.371711 | − | 0.643823i | ||||
\(95\) | −7.70171 | + | 13.3398i | −0.790179 | + | 1.36863i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 2.14678 | + | 1.23945i | 0.217973 | + | 0.125847i | 0.605011 | − | 0.796217i | \(-0.293169\pi\) |
−0.387038 | + | 0.922064i | \(0.626502\pi\) | |||||||
\(98\) | −6.06011 | − | 3.49880i | −0.612163 | − | 0.353433i | ||||
\(99\) | − | 6.29590i | − | 0.632761i | ||||||
\(100\) | 0.216480 | − | 0.374955i | 0.0216480 | − | 0.0374955i | ||||
\(101\) | 0.826396 | + | 1.43136i | 0.0822295 | + | 0.142426i | 0.904207 | − | 0.427094i | \(-0.140463\pi\) |
−0.821978 | + | 0.569520i | \(0.807129\pi\) | |||||||
\(102\) | −2.50289 | + | 1.44504i | −0.247823 | + | 0.143080i | ||||
\(103\) | 8.23490 | 0.811409 | 0.405704 | − | 0.914004i | \(-0.367026\pi\) | ||||
0.405704 | + | 0.914004i | \(0.367026\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.104539 | 0.0102020 | ||||||||
\(106\) | 8.09285 | − | 4.67241i | 0.786047 | − | 0.453824i | ||||
\(107\) | 4.18329 | + | 7.24567i | 0.404414 | + | 0.700466i | 0.994253 | − | 0.107055i | \(-0.0341421\pi\) |
−0.589839 | + | 0.807521i | \(0.700809\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 17.4276i | − | 1.66926i | −0.550811 | − | 0.834630i | \(-0.685682\pi\) | ||
0.550811 | − | 0.834630i | \(-0.314318\pi\) | |||||||
\(110\) | −11.6521 | − | 6.72737i | −1.11099 | − | 0.641429i | ||||
\(111\) | 0.152673 | + | 0.0881460i | 0.0144911 | + | 0.00836645i | ||||
\(112\) | 0.0489173i | 0.00462225i | ||||||||
\(113\) | 6.98792 | − | 12.1034i | 0.657368 | − | 1.13859i | −0.323926 | − | 0.946082i | \(-0.605003\pi\) |
0.981294 | − | 0.192513i | \(-0.0616636\pi\) | |||||||
\(114\) | 3.60388 | + | 6.24210i | 0.337534 | + | 0.584626i | ||||
\(115\) | −5.02255 | + | 2.89977i | −0.468355 | + | 0.270405i | ||||
\(116\) | −4.91185 | −0.456054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.26875 | −0.392970 | ||||||||
\(119\) | 0.122435 | − | 0.0706876i | 0.0112236 | − | 0.00647992i | ||||
\(120\) | 1.06853 | + | 1.85075i | 0.0975431 | + | 0.168950i | ||||
\(121\) | 14.3192 | − | 24.8015i | 1.30174 | − | 2.25468i | ||||
\(122\) | 7.10992i | 0.643702i | ||||||||
\(123\) | −7.44071 | − | 4.29590i | −0.670906 | − | 0.387348i | ||||
\(124\) | 7.80262 | + | 4.50484i | 0.700696 | + | 0.404547i | ||||
\(125\) | 11.6106i | 1.03848i | ||||||||
\(126\) | 0.0244587 | − | 0.0423637i | 0.00217895 | − | 0.00377405i | ||||
\(127\) | −3.76055 | − | 6.51347i | −0.333695 | − | 0.577977i | 0.649538 | − | 0.760329i | \(-0.274962\pi\) |
−0.983233 | + | 0.182352i | \(0.941629\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 6.71379 | 0.591116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.12498 | 0.447772 | 0.223886 | − | 0.974615i | \(-0.428126\pi\) | ||||
0.223886 | + | 0.974615i | \(0.428126\pi\) | |||||||
\(132\) | −5.45241 | + | 3.14795i | −0.474571 | + | 0.273994i | ||||
\(133\) | −0.176292 | − | 0.305347i | −0.0152865 | − | 0.0264769i | ||||
\(134\) | 2.69202 | − | 4.66272i | 0.232555 | − | 0.402797i | ||||
\(135\) | − | 2.13706i | − | 0.183929i | ||||||
\(136\) | 2.50289 | + | 1.44504i | 0.214621 | + | 0.123911i | ||||
\(137\) | −3.46410 | − | 2.00000i | −0.295958 | − | 0.170872i | 0.344668 | − | 0.938725i | \(-0.387992\pi\) |
−0.640626 | + | 0.767853i | \(0.721325\pi\) | |||||||
\(138\) | 2.71379i | 0.231013i | ||||||||
\(139\) | −4.34481 | + | 7.52544i | −0.368522 | + | 0.638299i | −0.989335 | − | 0.145660i | \(-0.953470\pi\) |
0.620812 | + | 0.783959i | \(0.286803\pi\) | |||||||
\(140\) | −0.0522697 | − | 0.0905338i | −0.00441760 | − | 0.00765150i | ||||
\(141\) | 6.24210 | − | 3.60388i | 0.525679 | − | 0.303501i | ||||
\(142\) | 8.71379 | 0.731245 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.09062 | − | 5.24847i | 0.754935 | − | 0.435862i | ||||
\(146\) | 7.47434 | + | 12.9459i | 0.618581 | + | 1.07141i | ||||
\(147\) | 3.49880 | − | 6.06011i | 0.288576 | − | 0.499829i | ||||
\(148\) | − | 0.176292i | − | 0.0144911i | ||||||
\(149\) | 4.21608 | + | 2.43416i | 0.345395 | + | 0.199414i | 0.662655 | − | 0.748925i | \(-0.269430\pi\) |
−0.317260 | + | 0.948339i | \(0.602763\pi\) | |||||||
\(150\) | 0.374955 | + | 0.216480i | 0.0306149 | + | 0.0176755i | ||||
\(151\) | − | 14.7463i | − | 1.20004i | −0.799986 | − | 0.600019i | \(-0.795160\pi\) | ||
0.799986 | − | 0.600019i | \(-0.204840\pi\) | |||||||
\(152\) | 3.60388 | − | 6.24210i | 0.292313 | − | 0.506301i | ||||
\(153\) | −1.44504 | − | 2.50289i | −0.116825 | − | 0.202346i | ||||
\(154\) | 0.266717 | − | 0.153989i | 0.0214927 | − | 0.0124088i | ||||
\(155\) | −19.2543 | −1.54654 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7138 | −1.33391 | −0.666953 | − | 0.745100i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745100i | \(0.732402\pi\) | |||||||
\(158\) | 11.9763 | − | 6.91454i | 0.952786 | − | 0.550091i | ||||
\(159\) | 4.67241 | + | 8.09285i | 0.370546 | + | 0.641804i | ||||
\(160\) | 1.06853 | − | 1.85075i | 0.0844748 | − | 0.146315i | ||||
\(161\) | − | 0.132751i | − | 0.0104623i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 4.80608 | + | 2.77479i | 0.376441 | + | 0.217338i | 0.676269 | − | 0.736655i | \(-0.263596\pi\) |
−0.299828 | + | 0.953993i | \(0.596929\pi\) | |||||||
\(164\) | 8.59179i | 0.670906i | ||||||||
\(165\) | 6.72737 | − | 11.6521i | 0.523725 | − | 0.907118i | ||||
\(166\) | −5.56734 | − | 9.64291i | −0.432109 | − | 0.748435i | ||||
\(167\) | 3.39616 | − | 1.96077i | 0.262802 | − | 0.151729i | −0.362810 | − | 0.931863i | \(-0.618183\pi\) |
0.625612 | + | 0.780134i | \(0.284849\pi\) | |||||||
\(168\) | −0.0489173 | −0.00377405 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.17629 | −0.473700 | ||||||||
\(171\) | −6.24210 | + | 3.60388i | −0.477345 | + | 0.275595i | ||||
\(172\) | −3.35690 | − | 5.81431i | −0.255961 | − | 0.443337i | ||||
\(173\) | −1.74214 | + | 3.01747i | −0.132452 | + | 0.229414i | −0.924621 | − | 0.380888i | \(-0.875618\pi\) |
0.792169 | + | 0.610302i | \(0.208952\pi\) | |||||||
\(174\) | − | 4.91185i | − | 0.372367i | ||||||
\(175\) | −0.0183418 | − | 0.0105896i | −0.00138651 | − | 0.000800501i | ||||
\(176\) | 5.45241 | + | 3.14795i | 0.410991 | + | 0.237286i | ||||
\(177\) | − | 4.26875i | − | 0.320859i | ||||||
\(178\) | −1.96077 | + | 3.39616i | −0.146966 | + | 0.254553i | ||||
\(179\) | 1.79440 | + | 3.10800i | 0.134120 | + | 0.232303i | 0.925261 | − | 0.379331i | \(-0.123846\pi\) |
−0.791141 | + | 0.611634i | \(0.790513\pi\) | |||||||
\(180\) | −1.85075 | + | 1.06853i | −0.137947 | + | 0.0796436i | ||||
\(181\) | −5.50604 | −0.409261 | −0.204630 | − | 0.978839i | \(-0.565599\pi\) | ||||
−0.204630 | + | 0.978839i | \(0.565599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.10992 | −0.525580 | ||||||||
\(184\) | 2.35021 | − | 1.35690i | 0.173260 | − | 0.100032i | ||||
\(185\) | 0.188374 | + | 0.326273i | 0.0138495 | + | 0.0239880i | ||||
\(186\) | −4.50484 | + | 7.80262i | −0.330311 | + | 0.572116i | ||||
\(187\) | − | 18.1957i | − | 1.33060i | ||||||
\(188\) | −6.24210 | − | 3.60388i | −0.455252 | − | 0.262840i | ||||
\(189\) | 0.0423637 | + | 0.0244587i | 0.00308150 | + | 0.00177911i | ||||
\(190\) | 15.4034i | 1.11748i | ||||||||
\(191\) | 2.82908 | − | 4.90012i | 0.204705 | − | 0.354560i | −0.745333 | − | 0.666692i | \(-0.767710\pi\) |
0.950039 | + | 0.312132i | \(0.101043\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 11.6077 | − | 6.70171i | 0.835541 | − | 0.482400i | −0.0202053 | − | 0.999796i | \(-0.506432\pi\) |
0.855746 | + | 0.517396i | \(0.173099\pi\) | |||||||
\(194\) | 2.47889 | 0.177974 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99761 | −0.499829 | ||||||||
\(197\) | −17.3042 | + | 9.99061i | −1.23288 | + | 0.711801i | −0.967628 | − | 0.252379i | \(-0.918787\pi\) |
−0.265248 | + | 0.964180i | \(0.585454\pi\) | |||||||
\(198\) | −3.14795 | − | 5.45241i | −0.223715 | − | 0.387486i | ||||
\(199\) | −3.12080 | + | 5.40539i | −0.221228 | + | 0.383178i | −0.955181 | − | 0.296022i | \(-0.904340\pi\) |
0.733953 | + | 0.679200i | \(0.237673\pi\) | |||||||
\(200\) | − | 0.432960i | − | 0.0306149i | ||||||
\(201\) | 4.66272 | + | 2.69202i | 0.328883 | + | 0.189881i | ||||
\(202\) | 1.43136 | + | 0.826396i | 0.100710 | + | 0.0581450i | ||||
\(203\) | 0.240275i | 0.0168640i | ||||||||
\(204\) | −1.44504 | + | 2.50289i | −0.101173 | + | 0.175237i | ||||
\(205\) | −9.18060 | − | 15.9013i | −0.641201 | − | 1.11059i | ||||
\(206\) | 7.13163 | − | 4.11745i | 0.496884 | − | 0.286876i | ||||
\(207\) | −2.71379 | −0.188622 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −45.3793 | −3.13895 | ||||||||
\(210\) | 0.0905338 | − | 0.0522697i | 0.00624743 | − | 0.00360695i | ||||
\(211\) | 2.54288 | + | 4.40439i | 0.175059 | + | 0.303211i | 0.940182 | − | 0.340674i | \(-0.110655\pi\) |
−0.765123 | + | 0.643884i | \(0.777322\pi\) | |||||||
\(212\) | 4.67241 | − | 8.09285i | 0.320902 | − | 0.555819i | ||||
\(213\) | 8.71379i | 0.597059i | ||||||||
\(214\) | 7.24567 | + | 4.18329i | 0.495304 | + | 0.285964i | ||||
\(215\) | 12.4256 | + | 7.17390i | 0.847416 | + | 0.489256i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0.220365 | − | 0.381683i | 0.0149594 | − | 0.0259104i | ||||
\(218\) | −8.71379 | − | 15.0927i | −0.590172 | − | 1.02221i | ||||
\(219\) | −12.9459 | + | 7.47434i | −0.874806 | + | 0.505069i | ||||
\(220\) | −13.4547 | −0.907118 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.176292 | 0.0118319 | ||||||||
\(223\) | 17.7953 | − | 10.2741i | 1.19166 | − | 0.688006i | 0.232979 | − | 0.972482i | \(-0.425153\pi\) |
0.958683 | + | 0.284475i | \(0.0918194\pi\) | |||||||
\(224\) | 0.0244587 | + | 0.0423637i | 0.00163421 | + | 0.00283054i | ||||
\(225\) | −0.216480 | + | 0.374955i | −0.0144320 | + | 0.0249970i | ||||
\(226\) | − | 13.9758i | − | 0.929659i | ||||||
\(227\) | 3.82020 | + | 2.20560i | 0.253556 | + | 0.146390i | 0.621391 | − | 0.783500i | \(-0.286568\pi\) |
−0.367836 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(228\) | 6.24210 | + | 3.60388i | 0.413393 | + | 0.238672i | ||||
\(229\) | 0.230586i | 0.0152376i | 0.999971 | + | 0.00761878i | \(0.00242516\pi\) | ||||
−0.999971 | + | 0.00761878i | \(0.997575\pi\) | |||||||
\(230\) | −2.89977 | + | 5.02255i | −0.191205 | + | 0.331177i | ||||
\(231\) | 0.153989 | + | 0.266717i | 0.0101317 | + | 0.0175487i | ||||
\(232\) | −4.25379 | + | 2.45593i | −0.279275 | + | 0.161240i | ||||
\(233\) | 7.82371 | 0.512548 | 0.256274 | − | 0.966604i | \(-0.417505\pi\) | ||||
0.256274 | + | 0.966604i | \(0.417505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.4034 | 1.00481 | ||||||||
\(236\) | −3.69685 | + | 2.13437i | −0.240644 | + | 0.138936i | ||||
\(237\) | 6.91454 | + | 11.9763i | 0.449148 | + | 0.777947i | ||||
\(238\) | 0.0706876 | − | 0.122435i | 0.00458200 | − | 0.00793625i | ||||
\(239\) | − | 11.1535i | − | 0.721457i | −0.932671 | − | 0.360729i | \(-0.882528\pi\) | ||
0.932671 | − | 0.360729i | \(-0.117472\pi\) | |||||||
\(240\) | 1.85075 | + | 1.06853i | 0.119465 | + | 0.0689734i | ||||
\(241\) | 3.07029 | + | 1.77263i | 0.197775 | + | 0.114185i | 0.595617 | − | 0.803268i | \(-0.296908\pi\) |
−0.397842 | + | 0.917454i | \(0.630241\pi\) | |||||||
\(242\) | − | 28.6383i | − | 1.84094i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 3.55496 | + | 6.15737i | 0.227583 | + | 0.394185i | ||||
\(245\) | 12.9508 | − | 7.47716i | 0.827398 | − | 0.477699i | ||||
\(246\) | −8.59179 | −0.547793 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.00969 | 0.572116 | ||||||||
\(249\) | 9.64291 | − | 5.56734i | 0.611094 | − | 0.352816i | ||||
\(250\) | 5.80529 | + | 10.0551i | 0.367159 | + | 0.635938i | ||||
\(251\) | −2.08546 | + | 3.61212i | −0.131633 | + | 0.227995i | −0.924306 | − | 0.381652i | \(-0.875355\pi\) |
0.792673 | + | 0.609647i | \(0.208689\pi\) | |||||||
\(252\) | − | 0.0489173i | − | 0.00308150i | ||||||
\(253\) | −14.7967 | − | 8.54288i | −0.930260 | − | 0.537086i | ||||
\(254\) | −6.51347 | − | 3.76055i | −0.408691 | − | 0.235958i | ||||
\(255\) | − | 6.17629i | − | 0.386774i | ||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.44504 | − | 9.43109i | −0.339652 | − | 0.588295i | 0.644715 | − | 0.764423i | \(-0.276976\pi\) |
−0.984367 | + | 0.176128i | \(0.943643\pi\) | |||||||
\(258\) | 5.81431 | − | 3.35690i | 0.361983 | − | 0.208991i | ||||
\(259\) | −0.00862374 | −0.000535853 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.91185 | 0.304036 | ||||||||
\(262\) | 4.43836 | − | 2.56249i | 0.274203 | − | 0.158311i | ||||
\(263\) | 15.6136 | + | 27.0435i | 0.962774 | + | 1.66757i | 0.715481 | + | 0.698632i | \(0.246207\pi\) |
0.247292 | + | 0.968941i | \(0.420459\pi\) | |||||||
\(264\) | −3.14795 | + | 5.45241i | −0.193743 | + | 0.335572i | ||||
\(265\) | 19.9705i | 1.22678i | ||||||||
\(266\) | −0.305347 | − | 0.176292i | −0.0187220 | − | 0.0108092i | ||||
\(267\) | −3.39616 | − | 1.96077i | −0.207841 | − | 0.119997i | ||||
\(268\) | − | 5.38404i | − | 0.328883i | ||||||
\(269\) | −7.95862 | + | 13.7847i | −0.485245 | + | 0.840470i | −0.999856 | − | 0.0169542i | \(-0.994603\pi\) |
0.514611 | + | 0.857424i | \(0.327936\pi\) | |||||||
\(270\) | −1.06853 | − | 1.85075i | −0.0650288 | − | 0.112633i | ||||
\(271\) | 3.04937 | − | 1.76055i | 0.185236 | − | 0.106946i | −0.404514 | − | 0.914532i | \(-0.632559\pi\) |
0.589750 | + | 0.807586i | \(0.299226\pi\) | |||||||
\(272\) | 2.89008 | 0.175237 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −2.36068 | + | 1.36294i | −0.142354 | + | 0.0821882i | ||||
\(276\) | 1.35690 | + | 2.35021i | 0.0816755 | + | 0.141466i | ||||
\(277\) | −4.29052 | + | 7.43140i | −0.257792 | + | 0.446509i | −0.965650 | − | 0.259845i | \(-0.916328\pi\) |
0.707858 | + | 0.706355i | \(0.249662\pi\) | |||||||
\(278\) | 8.68963i | 0.521169i | ||||||||
\(279\) | −7.80262 | − | 4.50484i | −0.467131 | − | 0.269698i | ||||
\(280\) | −0.0905338 | − | 0.0522697i | −0.00541043 | − | 0.00312371i | ||||
\(281\) | − | 8.07846i | − | 0.481920i | −0.970535 | − | 0.240960i | \(-0.922538\pi\) | ||
0.970535 | − | 0.240960i | \(-0.0774623\pi\) | |||||||
\(282\) | 3.60388 | − | 6.24210i | 0.214608 | − | 0.371711i | ||||
\(283\) | −8.70171 | − | 15.0718i | −0.517263 | − | 0.895926i | −0.999799 | − | 0.0200496i | \(-0.993618\pi\) |
0.482536 | − | 0.875876i | \(-0.339716\pi\) | |||||||
\(284\) | 7.54637 | − | 4.35690i | 0.447794 | − | 0.258534i | ||||
\(285\) | −15.4034 | −0.912420 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.420288 | 0.0248088 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 4.32371 | + | 7.48888i | 0.254336 | + | 0.440522i | ||||
\(290\) | 5.24847 | − | 9.09062i | 0.308201 | − | 0.533820i | ||||
\(291\) | 2.47889i | 0.145315i | ||||||||
\(292\) | 12.9459 | + | 7.47434i | 0.757604 | + | 0.437403i | ||||
\(293\) | 16.7757 | + | 9.68545i | 0.980046 | + | 0.565830i | 0.902284 | − | 0.431142i | \(-0.141889\pi\) |
0.0777621 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(294\) | − | 6.99761i | − | 0.408109i | ||||||
\(295\) | 4.56129 | − | 7.90039i | 0.265569 | − | 0.459979i | ||||
\(296\) | −0.0881460 | − | 0.152673i | −0.00512338 | − | 0.00887396i | ||||
\(297\) | 5.45241 | − | 3.14795i | 0.316381 | − | 0.182662i | ||||
\(298\) | 4.86831 | 0.282014 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.432960 | 0.0249970 | ||||||||
\(301\) | −0.284421 | + | 0.164210i | −0.0163937 | + | 0.00946493i | ||||
\(302\) | −7.37316 | − | 12.7707i | −0.424278 | − | 0.734870i | ||||
\(303\) | −0.826396 | + | 1.43136i | −0.0474752 | + | 0.0822295i | ||||
\(304\) | − | 7.20775i | − | 0.413393i | ||||||
\(305\) | −13.1587 | − | 7.59717i | −0.753464 | − | 0.435013i | ||||
\(306\) | −2.50289 | − | 1.44504i | −0.143080 | − | 0.0826075i | ||||
\(307\) | − | 12.4263i | − | 0.709204i | −0.935017 | − | 0.354602i | \(-0.884616\pi\) | ||
0.935017 | − | 0.354602i | \(-0.115384\pi\) | |||||||
\(308\) | 0.153989 | − | 0.266717i | 0.00877435 | − | 0.0151976i | ||||
\(309\) | 4.11745 | + | 7.13163i | 0.234233 | + | 0.405704i | ||||
\(310\) | −16.6747 | + | 9.62714i | −0.947059 | + | 0.546785i | ||||
\(311\) | −2.71379 | −0.153885 | −0.0769425 | − | 0.997036i | \(-0.524516\pi\) | ||||
−0.0769425 | + | 0.997036i | \(0.524516\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3884 | 0.869801 | 0.434901 | − | 0.900478i | \(-0.356783\pi\) | ||||
0.434901 | + | 0.900478i | \(0.356783\pi\) | |||||||
\(314\) | −14.4746 | + | 8.35690i | −0.816847 | + | 0.471607i | ||||
\(315\) | 0.0522697 | + | 0.0905338i | 0.00294507 | + | 0.00510100i | ||||
\(316\) | 6.91454 | − | 11.9763i | 0.388973 | − | 0.673722i | ||||
\(317\) | − | 25.6528i | − | 1.44080i | −0.693557 | − | 0.720402i | \(-0.743957\pi\) | ||
0.693557 | − | 0.720402i | \(-0.256043\pi\) | |||||||
\(318\) | 8.09285 | + | 4.67241i | 0.453824 | + | 0.262016i | ||||
\(319\) | 26.7814 | + | 15.4623i | 1.49947 | + | 0.865721i | ||||
\(320\) | − | 2.13706i | − | 0.119465i | ||||||
\(321\) | −4.18329 | + | 7.24567i | −0.233489 | + | 0.404414i | ||||
\(322\) | −0.0663757 | − | 0.114966i | −0.00369898 | − | 0.00640681i | ||||
\(323\) | −18.0402 | + | 10.4155i | −1.00378 | + | 0.579534i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.54958 | 0.307363 | ||||||||
\(327\) | 15.0927 | − | 8.71379i | 0.834630 | − | 0.481874i | ||||
\(328\) | 4.29590 | + | 7.44071i | 0.237201 | + | 0.410845i | ||||
\(329\) | −0.176292 | + | 0.305347i | −0.00971929 | + | 0.0168343i | ||||
\(330\) | − | 13.4547i | − | 0.740659i | ||||||
\(331\) | −3.31143 | − | 1.91185i | −0.182013 | − | 0.105085i | 0.406225 | − | 0.913773i | \(-0.366845\pi\) |
−0.588238 | + | 0.808688i | \(0.700178\pi\) | |||||||
\(332\) | −9.64291 | − | 5.56734i | −0.529223 | − | 0.305547i | ||||
\(333\) | 0.176292i | 0.00966074i | ||||||||
\(334\) | 1.96077 | − | 3.39616i | 0.107289 | − | 0.185829i | ||||
\(335\) | 5.75302 | + | 9.96452i | 0.314321 | + | 0.544420i | ||||
\(336\) | −0.0423637 | + | 0.0244587i | −0.00231113 | + | 0.00133433i | ||||
\(337\) | −20.1304 | −1.09657 | −0.548285 | − | 0.836291i | \(-0.684719\pi\) | ||||
−0.548285 | + | 0.836291i | \(0.684719\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9758 | 0.759063 | ||||||||
\(340\) | −5.34883 | + | 3.08815i | −0.290081 | + | 0.167478i | ||||
\(341\) | −28.3620 | − | 49.1245i | −1.53589 | − | 2.66024i | ||||
\(342\) | −3.60388 | + | 6.24210i | −0.194875 | + | 0.337534i | ||||
\(343\) | 0.684726i | 0.0369717i | ||||||||
\(344\) | −5.81431 | − | 3.35690i | −0.313487 | − | 0.180992i | ||||
\(345\) | −5.02255 | − | 2.89977i | −0.270405 | − | 0.156118i | ||||
\(346\) | 3.48427i | 0.187316i | ||||||||
\(347\) | −1.46950 | + | 2.54525i | −0.0788869 | + | 0.136636i | −0.902770 | − | 0.430124i | \(-0.858470\pi\) |
0.823883 | + | 0.566760i | \(0.191803\pi\) | |||||||
\(348\) | −2.45593 | − | 4.25379i | −0.131652 | − | 0.228027i | ||||
\(349\) | 6.38546 | − | 3.68664i | 0.341806 | − | 0.197342i | −0.319265 | − | 0.947666i | \(-0.603436\pi\) |
0.661070 | + | 0.750324i | \(0.270103\pi\) | |||||||
\(350\) | −0.0211793 | −0.00113208 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.29590 | 0.335572 | ||||||||
\(353\) | 1.74136 | − | 1.00538i | 0.0926834 | − | 0.0535108i | −0.452942 | − | 0.891540i | \(-0.649626\pi\) |
0.545625 | + | 0.838029i | \(0.316292\pi\) | |||||||
\(354\) | −2.13437 | − | 3.69685i | −0.113441 | − | 0.196485i | ||||
\(355\) | −9.31096 | + | 16.1271i | −0.494175 | + | 0.855935i | ||||
\(356\) | 3.92154i | 0.207841i | ||||||||
\(357\) | 0.122435 | + | 0.0706876i | 0.00647992 | + | 0.00374118i | ||||
\(358\) | 3.10800 | + | 1.79440i | 0.164263 | + | 0.0948373i | ||||
\(359\) | 31.4577i | 1.66027i | 0.557559 | + | 0.830137i | \(0.311738\pi\) | ||||
−0.557559 | + | 0.830137i | \(0.688262\pi\) | |||||||
\(360\) | −1.06853 | + | 1.85075i | −0.0563166 | + | 0.0975431i | ||||
\(361\) | 16.4758 | + | 28.5370i | 0.867149 | + | 1.50195i | ||||
\(362\) | −4.76837 | + | 2.75302i | −0.250620 | + | 0.144696i | ||||
\(363\) | 28.6383 | 1.50312 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.9463 | −1.67215 | ||||||||
\(366\) | −6.15737 | + | 3.55496i | −0.321851 | + | 0.185821i | ||||
\(367\) | 2.24967 | + | 3.89654i | 0.117432 | + | 0.203398i | 0.918749 | − | 0.394842i | \(-0.129201\pi\) |
−0.801317 | + | 0.598239i | \(0.795867\pi\) | |||||||
\(368\) | 1.35690 | − | 2.35021i | 0.0707331 | − | 0.122513i | ||||
\(369\) | − | 8.59179i | − | 0.447271i | ||||||
\(370\) | 0.326273 | + | 0.188374i | 0.0169621 | + | 0.00979308i | ||||
\(371\) | −0.395881 | − | 0.228562i | −0.0205531 | − | 0.0118663i | ||||
\(372\) | 9.00969i | 0.467131i | ||||||||
\(373\) | −18.9148 | + | 32.7615i | −0.979373 | + | 1.69632i | −0.314698 | + | 0.949192i | \(0.601903\pi\) |
−0.664676 | + | 0.747132i | \(0.731430\pi\) | |||||||
\(374\) | −9.09783 | − | 15.7579i | −0.470438 | − | 0.814822i | ||||
\(375\) | −10.0551 | + | 5.80529i | −0.519241 | + | 0.299784i | ||||
\(376\) | −7.20775 | −0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.0489173 | 0.00251604 | ||||||||
\(379\) | 7.30896 | − | 4.21983i | 0.375436 | − | 0.216758i | −0.300395 | − | 0.953815i | \(-0.597118\pi\) |
0.675831 | + | 0.737057i | \(0.263785\pi\) | |||||||
\(380\) | 7.70171 | + | 13.3398i | 0.395089 | + | 0.684315i | ||||
\(381\) | 3.76055 | − | 6.51347i | 0.192659 | − | 0.333695i | ||||
\(382\) | − | 5.65817i | − | 0.289497i | ||||||
\(383\) | 1.11389 | + | 0.643104i | 0.0569171 | + | 0.0328611i | 0.528188 | − | 0.849127i | \(-0.322871\pi\) |
−0.471271 | + | 0.881988i | \(0.656205\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0.658170i | 0.0335434i | ||||||||
\(386\) | 6.70171 | − | 11.6077i | 0.341108 | − | 0.590817i | ||||
\(387\) | 3.35690 | + | 5.81431i | 0.170641 | + | 0.295558i | ||||
\(388\) | 2.14678 | − | 1.23945i | 0.108986 | − | 0.0629234i | ||||
\(389\) | −23.3924 | −1.18604 | −0.593021 | − | 0.805187i | \(-0.702065\pi\) | ||||
−0.593021 | + | 0.805187i | \(0.702065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.84309 | −0.396642 | ||||||||
\(392\) | −6.06011 | + | 3.49880i | −0.306082 | + | 0.176716i | ||||
\(393\) | 2.56249 | + | 4.43836i | 0.129261 | + | 0.223886i | ||||
\(394\) | −9.99061 | + | 17.3042i | −0.503320 | + | 0.871775i | ||||
\(395\) | 29.5536i | 1.48700i | ||||||||
\(396\) | −5.45241 | − | 3.14795i | −0.273994 | − | 0.158190i | ||||
\(397\) | −32.1172 | − | 18.5429i | −1.61192 | − | 0.930640i | −0.988926 | − | 0.148411i | \(-0.952584\pi\) |
−0.622990 | − | 0.782229i | \(-0.714082\pi\) | |||||||
\(398\) | 6.24160i | 0.312863i | ||||||||
\(399\) | 0.176292 | − | 0.305347i | 0.00882564 | − | 0.0152865i | ||||
\(400\) | −0.216480 | − | 0.374955i | −0.0108240 | − | 0.0187477i | ||||
\(401\) | 4.21401 | − | 2.43296i | 0.210438 | − | 0.121496i | −0.391077 | − | 0.920358i | \(-0.627897\pi\) |
0.601515 | + | 0.798862i | \(0.294564\pi\) | |||||||
\(402\) | 5.38404 | 0.268532 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.65279 | 0.0822295 | ||||||||
\(405\) | 1.85075 | − | 1.06853i | 0.0919646 | − | 0.0530958i | ||||
\(406\) | 0.120137 | + | 0.208084i | 0.00596232 | + | 0.0103270i | ||||
\(407\) | −0.554958 | + | 0.961216i | −0.0275083 | + | 0.0476457i | ||||
\(408\) | 2.89008i | 0.143080i | ||||||||
\(409\) | −0.385418 | − | 0.222521i | −0.0190577 | − | 0.0110030i | 0.490441 | − | 0.871474i | \(-0.336836\pi\) |
−0.509499 | + | 0.860472i | \(0.670169\pi\) | |||||||
\(410\) | −15.9013 | − | 9.18060i | −0.785308 | − | 0.453398i | ||||
\(411\) | − | 4.00000i | − | 0.197305i | ||||||
\(412\) | 4.11745 | − | 7.13163i | 0.202852 | − | 0.351350i | ||||
\(413\) | 0.104408 | + | 0.180840i | 0.00513758 | + | 0.00889855i | ||||
\(414\) | −2.35021 | + | 1.35690i | −0.115507 | + | 0.0666878i | ||||
\(415\) | 23.7955 | 1.16807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.68963 | −0.425533 | ||||||||
\(418\) | −39.2996 | + | 22.6896i | −1.92221 | + | 1.10979i | ||||
\(419\) | −8.99343 | − | 15.5771i | −0.439358 | − | 0.760990i | 0.558282 | − | 0.829651i | \(-0.311461\pi\) |
−0.997640 | + | 0.0686612i | \(0.978127\pi\) | |||||||
\(420\) | 0.0522697 | − | 0.0905338i | 0.00255050 | − | 0.00441760i | ||||
\(421\) | 21.2814i | 1.03719i | 0.855019 | + | 0.518597i | \(0.173545\pi\) | ||||
−0.855019 | + | 0.518597i | \(0.826455\pi\) | |||||||
\(422\) | 4.40439 | + | 2.54288i | 0.214402 | + | 0.123785i | ||||
\(423\) | 6.24210 | + | 3.60388i | 0.303501 | + | 0.175226i | ||||
\(424\) | − | 9.34481i | − | 0.453824i | ||||||
\(425\) | −0.625646 | + | 1.08365i | −0.0303483 | + | 0.0525648i | ||||
\(426\) | 4.35690 | + | 7.54637i | 0.211092 | + | 0.365623i | ||||
\(427\) | 0.301202 | − | 0.173899i | 0.0145762 | − | 0.00841557i | ||||
\(428\) | 8.36658 | 0.404414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.3478 | 0.691912 | ||||||||
\(431\) | 21.4028 | − | 12.3569i | 1.03094 | − | 0.595211i | 0.113683 | − | 0.993517i | \(-0.463735\pi\) |
0.917252 | + | 0.398306i | \(0.130402\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 16.1087 | − | 27.9011i | 0.774136 | − | 1.34084i | −0.161143 | − | 0.986931i | \(-0.551518\pi\) |
0.935279 | − | 0.353911i | \(-0.115149\pi\) | |||||||
\(434\) | − | 0.440730i | − | 0.0211557i | ||||||
\(435\) | 9.09062 | + | 5.24847i | 0.435862 | + | 0.251645i | ||||
\(436\) | −15.0927 | − | 8.71379i | −0.722811 | − | 0.417315i | ||||
\(437\) | 19.5603i | 0.935698i | ||||||||
\(438\) | −7.47434 | + | 12.9459i | −0.357138 | + | 0.618581i | ||||
\(439\) | 16.0438 | + | 27.7887i | 0.765731 | + | 1.32628i | 0.939859 | + | 0.341561i | \(0.110956\pi\) |
−0.174129 | + | 0.984723i | \(0.555711\pi\) | |||||||
\(440\) | −11.6521 | + | 6.72737i | −0.555494 | + | 0.320715i | ||||
\(441\) | 6.99761 | 0.333219 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5109 | 0.974504 | 0.487252 | − | 0.873261i | \(-0.337999\pi\) | ||||
0.487252 | + | 0.873261i | \(0.337999\pi\) | |||||||
\(444\) | 0.152673 | − | 0.0881460i | 0.00724556 | − | 0.00418322i | ||||
\(445\) | −4.19029 | − | 7.25780i | −0.198639 | − | 0.344053i | ||||
\(446\) | 10.2741 | − | 17.7953i | 0.486494 | − | 0.842632i | ||||
\(447\) | 4.86831i | 0.230263i | ||||||||
\(448\) | 0.0423637 | + | 0.0244587i | 0.00200149 | + | 0.00115556i | ||||
\(449\) | −13.2643 | − | 7.65817i | −0.625983 | − | 0.361411i | 0.153212 | − | 0.988193i | \(-0.451038\pi\) |
−0.779195 | + | 0.626782i | \(0.784372\pi\) | |||||||
\(450\) | 0.432960i | 0.0204099i | ||||||||
\(451\) | 27.0465 | − | 46.8460i | 1.27357 | − | 2.20589i | ||||
\(452\) | −6.98792 | − | 12.1034i | −0.328684 | − | 0.569297i | ||||
\(453\) | 12.7707 | − | 7.37316i | 0.600019 | − | 0.346421i | ||||
\(454\) | 4.41119 | 0.207027 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.20775 | 0.337534 | ||||||||
\(457\) | −16.6155 | + | 9.59299i | −0.777242 | + | 0.448741i | −0.835452 | − | 0.549563i | \(-0.814794\pi\) |
0.0582096 | + | 0.998304i | \(0.481461\pi\) | |||||||
\(458\) | 0.115293 | + | 0.199693i | 0.00538729 | + | 0.00933106i | ||||
\(459\) | 1.44504 | − | 2.50289i | 0.0674488 | − | 0.116825i | ||||
\(460\) | 5.79954i | 0.270405i | ||||||||
\(461\) | −7.19865 | − | 4.15615i | −0.335275 | − | 0.193571i | 0.322906 | − | 0.946431i | \(-0.395340\pi\) |
−0.658181 | + | 0.752860i | \(0.728674\pi\) | |||||||
\(462\) | 0.266717 | + | 0.153989i | 0.0124088 | + | 0.00716423i | ||||
\(463\) | 6.32842i | 0.294107i | 0.989129 | + | 0.147053i | \(0.0469789\pi\) | ||||
−0.989129 | + | 0.147053i | \(0.953021\pi\) | |||||||
\(464\) | −2.45593 | + | 4.25379i | −0.114014 | + | 0.197477i | ||||
\(465\) | −9.62714 | − | 16.6747i | −0.446448 | − | 0.773270i | ||||
\(466\) | 6.77553 | − | 3.91185i | 0.313870 | − | 0.181213i | ||||
\(467\) | 31.1879 | 1.44320 | 0.721602 | − | 0.692308i | \(-0.243406\pi\) | ||||
0.721602 | + | 0.692308i | \(0.243406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.263373 | −0.0121614 | ||||||||
\(470\) | 13.3398 | − | 7.70171i | 0.615317 | − | 0.355253i | ||||
\(471\) | −8.35690 | − | 14.4746i | −0.385065 | − | 0.666953i | ||||
\(472\) | −2.13437 | + | 3.69685i | −0.0982426 | + | 0.170161i | ||||
\(473\) | 42.2693i | 1.94355i | ||||||||
\(474\) | 11.9763 | + | 6.91454i | 0.550091 | + | 0.317595i | ||||
\(475\) | 2.70258 | + | 1.56033i | 0.124003 | + | 0.0715931i | ||||
\(476\) | − | 0.141375i | − | 0.00647992i | ||||||
\(477\) | −4.67241 | + | 8.09285i | −0.213935 | + | 0.370546i | ||||
\(478\) | −5.57673 | − | 9.65918i | −0.255074 | − | 0.441800i | ||||
\(479\) | 15.5298 | − | 8.96615i | 0.709576 | − | 0.409674i | −0.101328 | − | 0.994853i | \(-0.532309\pi\) |
0.810904 | + | 0.585179i | \(0.198976\pi\) | |||||||
\(480\) | 2.13706 | 0.0975431 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.54527 | 0.161483 | ||||||||
\(483\) | 0.114966 | − | 0.0663757i | 0.00523114 | − | 0.00302020i | ||||
\(484\) | −14.3192 | − | 24.8015i | −0.650871 | − | 1.12734i | ||||
\(485\) | −2.64878 | + | 4.58782i | −0.120275 | + | 0.208322i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −26.2648 | − | 15.1640i | −1.19017 | − | 0.687145i | −0.231825 | − | 0.972757i | \(-0.574470\pi\) |
−0.958345 | + | 0.285612i | \(0.907803\pi\) | |||||||
\(488\) | 6.15737 | + | 3.55496i | 0.278731 | + | 0.160925i | ||||
\(489\) | 5.54958i | 0.250961i | ||||||||
\(490\) | 7.47716 | − | 12.9508i | 0.337784 | − | 0.585059i | ||||
\(491\) | 15.0477 | + | 26.0634i | 0.679094 | + | 1.17623i | 0.975254 | + | 0.221087i | \(0.0709605\pi\) |
−0.296160 | + | 0.955138i | \(0.595706\pi\) | |||||||
\(492\) | −7.44071 | + | 4.29590i | −0.335453 | + | 0.193674i | ||||
\(493\) | 14.1957 | 0.639341 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.4547 | 0.604745 | ||||||||
\(496\) | 7.80262 | − | 4.50484i | 0.350348 | − | 0.202273i | ||||
\(497\) | −0.213128 | − | 0.369148i | −0.00956009 | − | 0.0165586i | ||||
\(498\) | 5.56734 | − | 9.64291i | 0.249478 | − | 0.432109i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 10.0551 | + | 5.80529i | 0.449676 | + | 0.259620i | ||||
\(501\) | 3.39616 | + | 1.96077i | 0.151729 | + | 0.0876008i | ||||
\(502\) | 4.17092i | 0.186157i | ||||||||
\(503\) | −16.8756 | + | 29.2294i | −0.752446 | + | 1.30328i | 0.194188 | + | 0.980964i | \(0.437793\pi\) |
−0.946634 | + | 0.322311i | \(0.895540\pi\) | |||||||
\(504\) | −0.0244587 | − | 0.0423637i | −0.00108948 | − | 0.00188703i | ||||
\(505\) | −3.05891 | + | 1.76606i | −0.136120 | + | 0.0785887i | ||||
\(506\) | −17.0858 | −0.759554 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.52111 | −0.333695 | ||||||||
\(509\) | −12.7686 | + | 7.37196i | −0.565959 | + | 0.326756i | −0.755534 | − | 0.655110i | \(-0.772622\pi\) |
0.189575 | + | 0.981866i | \(0.439289\pi\) | |||||||
\(510\) | −3.08815 | − | 5.34883i | −0.136745 | − | 0.236850i | ||||
\(511\) | 0.365625 | − | 0.633281i | 0.0161743 | − | 0.0280147i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.24210 | − | 3.60388i | −0.275595 | − | 0.159115i | ||||
\(514\) | −9.43109 | − | 5.44504i | −0.415988 | − | 0.240171i | ||||
\(515\) | 17.5985i | 0.775483i | ||||||||
\(516\) | 3.35690 | − | 5.81431i | 0.147779 | − | 0.255961i | ||||
\(517\) | 22.6896 | + | 39.2996i | 0.997889 | + | 1.72839i | ||||
\(518\) | −0.00746837 | + | 0.00431187i | −0.000328142 | + | 0.000189453i | ||||
\(519\) | −3.48427 | −0.152943 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1086 | 0.968595 | 0.484297 | − | 0.874903i | \(-0.339075\pi\) | ||||
0.484297 | + | 0.874903i | \(0.339075\pi\) | |||||||
\(522\) | 4.25379 | − | 2.45593i | 0.186183 | − | 0.107493i | ||||
\(523\) | 8.67994 | + | 15.0341i | 0.379547 | + | 0.657395i | 0.990996 | − | 0.133889i | \(-0.0427464\pi\) |
−0.611449 | + | 0.791284i | \(0.709413\pi\) | |||||||
\(524\) | 2.56249 | − | 4.43836i | 0.111943 | − | 0.193891i | ||||
\(525\) | − | 0.0211793i | − | 0.000924339i | ||||||
\(526\) | 27.0435 | + | 15.6136i | 1.17915 | + | 0.680784i | ||||
\(527\) | −22.5502 | − | 13.0194i | −0.982303 | − | 0.567133i | ||||
\(528\) | 6.29590i | 0.273994i | ||||||||
\(529\) | 7.81767 | − | 13.5406i | 0.339899 | − | 0.588722i | ||||
\(530\) | 9.98523 | + | 17.2949i | 0.433731 | + | 0.751244i | ||||
\(531\) | 3.69685 | − | 2.13437i | 0.160429 | − | 0.0926240i | ||||
\(532\) | −0.352584 | −0.0152865 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.92154 | −0.169702 | ||||||||
\(535\) | −15.4845 | + | 8.93996i | −0.669452 | + | 0.386508i | ||||
\(536\) | −2.69202 | − | 4.66272i | −0.116278 | − | 0.201399i | ||||
\(537\) | −1.79440 | + | 3.10800i | −0.0774343 | + | 0.134120i | ||||
\(538\) | 15.9172i | 0.686241i | ||||||||
\(539\) | 38.1538 | + | 22.0281i | 1.64340 | + | 0.948818i | ||||
\(540\) | −1.85075 | − | 1.06853i | −0.0796436 | − | 0.0459823i | ||||
\(541\) | 8.83579i | 0.379880i | 0.981796 | + | 0.189940i | \(0.0608294\pi\) | ||||
−0.981796 | + | 0.189940i | \(0.939171\pi\) | |||||||
\(542\) | 1.76055 | − | 3.04937i | 0.0756222 | − | 0.130982i | ||||
\(543\) | −2.75302 | − | 4.76837i | −0.118143 | − | 0.204630i | ||||
\(544\) | 2.50289 | − | 1.44504i | 0.107310 | − | 0.0619557i | ||||
\(545\) | 37.2438 | 1.59535 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.10859 | −0.346698 | −0.173349 | − | 0.984860i | \(-0.555459\pi\) | ||||
−0.173349 | + | 0.984860i | \(0.555459\pi\) | |||||||
\(548\) | −3.46410 | + | 2.00000i | −0.147979 | + | 0.0854358i | ||||
\(549\) | −3.55496 | − | 6.15737i | −0.151722 | − | 0.262790i | ||||
\(550\) | −1.36294 | + | 2.36068i | −0.0581158 | + | 0.100660i | ||||
\(551\) | − | 35.4034i | − | 1.50824i | ||||||
\(552\) | 2.35021 | + | 1.35690i | 0.100032 | + | 0.0577533i | ||||
\(553\) | −0.585851 | − | 0.338241i | −0.0249129 | − | 0.0143835i | ||||
\(554\) | 8.58104i | 0.364573i | ||||||||
\(555\) | −0.188374 | + | 0.326273i | −0.00799601 | + | 0.0138495i | ||||
\(556\) | 4.34481 | + | 7.52544i | 0.184261 | + | 0.319150i | ||||
\(557\) | 8.27949 | − | 4.78017i | 0.350813 | − | 0.202542i | −0.314230 | − | 0.949347i | \(-0.601746\pi\) |
0.665043 | + | 0.746805i | \(0.268413\pi\) | |||||||
\(558\) | −9.00969 | −0.381411 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.104539 | −0.00441760 | ||||||||
\(561\) | 15.7579 | − | 9.09783i | 0.665300 | − | 0.384111i | ||||
\(562\) | −4.03923 | − | 6.99615i | −0.170385 | − | 0.295115i | ||||
\(563\) | −22.5819 | + | 39.1129i | −0.951712 | + | 1.64841i | −0.209994 | + | 0.977703i | \(0.567344\pi\) |
−0.741719 | + | 0.670711i | \(0.765989\pi\) | |||||||
\(564\) | − | 7.20775i | − | 0.303501i | ||||||
\(565\) | 25.8658 | + | 14.9336i | 1.08818 | + | 0.628262i | ||||
\(566\) | −15.0718 | − | 8.70171i | −0.633515 | − | 0.365760i | ||||
\(567\) | 0.0489173i | 0.00205434i | ||||||||
\(568\) | 4.35690 | − | 7.54637i | 0.182811 | − | 0.316638i | ||||
\(569\) | −1.60388 | − | 2.77799i | −0.0672380 | − | 0.116460i | 0.830447 | − | 0.557098i | \(-0.188085\pi\) |
−0.897685 | + | 0.440639i | \(0.854752\pi\) | |||||||
\(570\) | −13.3398 | + | 7.70171i | −0.558741 | + | 0.322589i | ||||
\(571\) | −0.0241632 | −0.00101120 | −0.000505599 | − | 1.00000i | \(-0.500161\pi\) | ||||
−0.000505599 | 1.00000i | \(0.500161\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.65817 | 0.236373 | ||||||||
\(574\) | 0.363980 | − | 0.210144i | 0.0151922 | − | 0.00877123i | ||||
\(575\) | 0.587482 | + | 1.01755i | 0.0244997 | + | 0.0424347i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 46.0200i | 1.91584i | 0.287041 | + | 0.957918i | \(0.407328\pi\) | ||||
−0.287041 | + | 0.957918i | \(0.592672\pi\) | |||||||
\(578\) | 7.48888 | + | 4.32371i | 0.311496 | + | 0.179843i | ||||
\(579\) | 11.6077 | + | 6.70171i | 0.482400 | + | 0.278514i | ||||
\(580\) | − | 10.4969i | − | 0.435862i | ||||||
\(581\) | −0.272339 | + | 0.471705i | −0.0112985 | + | 0.0195696i | ||||
\(582\) | 1.23945 | + | 2.14678i | 0.0513767 | + | 0.0889871i | ||||
\(583\) | −50.9517 | + | 29.4170i | −2.11020 | + | 1.21833i | ||||
\(584\) | 14.9487 | 0.618581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.3709 | 0.800204 | ||||||||
\(587\) | 22.4634 | − | 12.9693i | 0.927165 | − | 0.535299i | 0.0412510 | − | 0.999149i | \(-0.486866\pi\) |
0.885914 | + | 0.463850i | \(0.153532\pi\) | |||||||
\(588\) | −3.49880 | − | 6.06011i | −0.144288 | − | 0.249915i | ||||
\(589\) | −32.4698 | + | 56.2393i | −1.33789 | + | 2.31730i | ||||
\(590\) | − | 9.12259i | − | 0.375571i | ||||||
\(591\) | −17.3042 | − | 9.99061i | −0.711801 | − | 0.410959i | ||||
\(592\) | −0.152673 | − | 0.0881460i | −0.00627484 | − | 0.00362278i | ||||
\(593\) | − | 8.30691i | − | 0.341124i | −0.985347 | − | 0.170562i | \(-0.945442\pi\) | ||
0.985347 | − | 0.170562i | \(-0.0545583\pi\) | |||||||
\(594\) | 3.14795 | − | 5.45241i | 0.129162 | − | 0.223715i | ||||
\(595\) | 0.151064 | + | 0.261650i | 0.00619302 | + | 0.0107266i | ||||
\(596\) | 4.21608 | − | 2.43416i | 0.172697 | − | 0.0997069i | ||||
\(597\) | −6.24160 | −0.255452 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.1702 | 1.51873 | 0.759366 | − | 0.650664i | \(-0.225509\pi\) | ||||
0.759366 | + | 0.650664i | \(0.225509\pi\) | |||||||
\(600\) | 0.374955 | − | 0.216480i | 0.0153075 | − | 0.00883776i | ||||
\(601\) | 6.28501 | + | 10.8860i | 0.256371 | + | 0.444048i | 0.965267 | − | 0.261265i | \(-0.0841398\pi\) |
−0.708896 | + | 0.705313i | \(0.750806\pi\) | |||||||
\(602\) | −0.164210 | + | 0.284421i | −0.00669272 | + | 0.0115921i | ||||
\(603\) | 5.38404i | 0.219255i | ||||||||
\(604\) | −12.7707 | − | 7.37316i | −0.519632 | − | 0.300010i | ||||
\(605\) | 53.0024 | + | 30.6010i | 2.15485 | + | 1.24411i | ||||
\(606\) | 1.65279i | 0.0671401i | ||||||||
\(607\) | −4.02446 | + | 6.97057i | −0.163348 | + | 0.282927i | −0.936067 | − | 0.351821i | \(-0.885563\pi\) |
0.772720 | + | 0.634748i | \(0.218896\pi\) | |||||||
\(608\) | −3.60388 | − | 6.24210i | −0.146156 | − | 0.253150i | ||||
\(609\) | −0.208084 | + | 0.120137i | −0.00843199 | + | 0.00486821i | ||||
\(610\) | −15.1943 | −0.615201 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.89008 | −0.116825 | ||||||||
\(613\) | −26.3783 | + | 15.2295i | −1.06541 | + | 0.615115i | −0.926924 | − | 0.375250i | \(-0.877557\pi\) |
−0.138486 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(614\) | −6.21313 | − | 10.7615i | −0.250741 | − | 0.434297i | ||||
\(615\) | 9.18060 | − | 15.9013i | 0.370198 | − | 0.641201i | ||||
\(616\) | − | 0.307979i | − | 0.0124088i | ||||||
\(617\) | 4.09904 | + | 2.36658i | 0.165021 | + | 0.0952751i | 0.580236 | − | 0.814448i | \(-0.302960\pi\) |
−0.415215 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(618\) | 7.13163 | + | 4.11745i | 0.286876 | + | 0.165628i | ||||
\(619\) | − | 24.9095i | − | 1.00120i | −0.865680 | − | 0.500598i | \(-0.833114\pi\) | ||
0.865680 | − | 0.500598i | \(-0.166886\pi\) | |||||||
\(620\) | −9.62714 | + | 16.6747i | −0.386635 | + | 0.669672i | ||||
\(621\) | −1.35690 | − | 2.35021i | −0.0544504 | − | 0.0943108i | ||||
\(622\) | −2.35021 | + | 1.35690i | −0.0942349 | + | 0.0544066i | ||||
\(623\) | 0.191831 | 0.00768556 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6477 | −0.905910 | ||||||||
\(626\) | 13.3267 | − | 7.69418i | 0.532642 | − | 0.307521i | ||||
\(627\) | −22.6896 | − | 39.2996i | −0.906136 | − | 1.56947i | ||||
\(628\) | −8.35690 | + | 14.4746i | −0.333476 | + | 0.577598i | ||||
\(629\) | 0.509499i | 0.0203150i | ||||||||
\(630\) | 0.0905338 | + | 0.0522697i | 0.00360695 | + | 0.00208248i | ||||
\(631\) | −21.1566 | − | 12.2148i | −0.842230 | − | 0.486262i | 0.0157918 | − | 0.999875i | \(-0.494973\pi\) |
−0.858022 | + | 0.513614i | \(0.828306\pi\) | |||||||
\(632\) | − | 13.8291i | − | 0.550091i | ||||||
\(633\) | −2.54288 | + | 4.40439i | −0.101070 | + | 0.175059i | ||||
\(634\) | −12.8264 | − | 22.2160i | −0.509401 | − | 0.882309i | ||||
\(635\) | 13.9197 | − | 8.03654i | 0.552386 | − | 0.318920i | ||||
\(636\) | 9.34481 | 0.370546 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 30.9245 | 1.22431 | ||||||||
\(639\) | −7.54637 | + | 4.35690i | −0.298530 | + | 0.172356i | ||||
\(640\) | −1.06853 | − | 1.85075i | −0.0422374 | − | 0.0731574i | ||||
\(641\) | 24.3991 | − | 42.2605i | 0.963707 | − | 1.66919i | 0.250657 | − | 0.968076i | \(-0.419353\pi\) |
0.713050 | − | 0.701113i | \(-0.247313\pi\) | |||||||
\(642\) | 8.36658i | 0.330203i | ||||||||
\(643\) | −24.4820 | − | 14.1347i | −0.965475 | − | 0.557417i | −0.0676209 | − | 0.997711i | \(-0.521541\pi\) |
−0.897854 | + | 0.440294i | \(0.854874\pi\) | |||||||
\(644\) | −0.114966 | − | 0.0663757i | −0.00453030 | − | 0.00261557i | ||||
\(645\) | 14.3478i | 0.564944i | ||||||||
\(646\) | −10.4155 | + | 18.0402i | −0.409792 | + | 0.709781i | ||||
\(647\) | 17.4480 | + | 30.2209i | 0.685953 | + | 1.18810i | 0.973136 | + | 0.230229i | \(0.0739476\pi\) |
−0.287184 | + | 0.957876i | \(0.592719\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 26.8756 | 1.05496 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.440730 | 0.0172736 | ||||||||
\(652\) | 4.80608 | − | 2.77479i | 0.188221 | − | 0.108669i | ||||
\(653\) | 5.85786 | + | 10.1461i | 0.229236 | + | 0.397048i | 0.957582 | − | 0.288162i | \(-0.0930440\pi\) |
−0.728346 | + | 0.685209i | \(0.759711\pi\) | |||||||
\(654\) | 8.71379 | − | 15.0927i | 0.340736 | − | 0.590172i | ||||
\(655\) | 10.9524i | 0.427946i | ||||||||
\(656\) | 7.44071 | + | 4.29590i | 0.290511 | + | 0.167727i | ||||
\(657\) | −12.9459 | − | 7.47434i | −0.505069 | − | 0.291602i | ||||
\(658\) | 0.352584i | 0.0137452i | ||||||||
\(659\) | 3.56734 | − | 6.17881i | 0.138964 | − | 0.240692i | −0.788141 | − | 0.615495i | \(-0.788956\pi\) |
0.927105 | + | 0.374803i | \(0.122290\pi\) | |||||||
\(660\) | −6.72737 | − | 11.6521i | −0.261862 | − | 0.453559i | ||||
\(661\) | −7.38622 | + | 4.26444i | −0.287291 | + | 0.165867i | −0.636719 | − | 0.771096i | \(-0.719709\pi\) |
0.349429 | + | 0.936963i | \(0.386376\pi\) | |||||||
\(662\) | −3.82371 | −0.148613 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.1347 | −0.432109 | ||||||||
\(665\) | 0.652545 | − | 0.376747i | 0.0253046 | − | 0.0146096i | ||||
\(666\) | 0.0881460 | + | 0.152673i | 0.00341559 | + | 0.00591597i | ||||
\(667\) | 6.66487 | − | 11.5439i | 0.258065 | − | 0.446982i | ||||
\(668\) | − | 3.92154i | − | 0.151729i | ||||||
\(669\) | 17.7953 | + | 10.2741i | 0.688006 | + | 0.397221i | ||||
\(670\) | 9.96452 | + | 5.75302i | 0.384963 | + | 0.222259i | ||||
\(671\) | − | 44.7633i | − | 1.72807i | ||||||
\(672\) | −0.0244587 | + | 0.0423637i | −0.000943514 | + | 0.00163421i | ||||
\(673\) | −15.7969 | − | 27.3610i | −0.608924 | − | 1.05469i | −0.991418 | − | 0.130729i | \(-0.958268\pi\) |
0.382494 | − | 0.923958i | \(-0.375065\pi\) | |||||||
\(674\) | −17.4334 | + | 10.0652i | −0.671510 | + | 0.387696i | ||||
\(675\) | −0.432960 | −0.0166646 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.3002 | −0.664901 | −0.332451 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332451 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(678\) | 12.1034 | − | 6.98792i | 0.464829 | − | 0.268369i | ||||
\(679\) | −0.0606304 | − | 0.105015i | −0.00232678 | − | 0.00403011i | ||||
\(680\) | −3.08815 | + | 5.34883i | −0.118425 | + | 0.205118i | ||||
\(681\) | 4.41119i | 0.169037i | ||||||||
\(682\) | −49.1245 | − | 28.3620i | −1.88107 | − | 1.08604i | ||||
\(683\) | −26.3234 | − | 15.1978i | −1.00724 | − | 0.581529i | −0.0968556 | − | 0.995298i | \(-0.530878\pi\) |
−0.910382 | + | 0.413770i | \(0.864212\pi\) | |||||||
\(684\) | 7.20775i | 0.275595i | ||||||||
\(685\) | 4.27413 | − | 7.40300i | 0.163306 | − | 0.282854i | ||||
\(686\) | 0.342363 | + | 0.592990i | 0.0130715 | + | 0.0226405i | ||||
\(687\) | −0.199693 | + | 0.115293i | −0.00761878 | + | 0.00439871i | ||||
\(688\) | −6.71379 | −0.255961 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.79954 | −0.220785 | ||||||||
\(691\) | −30.9447 | + | 17.8659i | −1.17719 | + | 0.679652i | −0.955363 | − | 0.295434i | \(-0.904536\pi\) |
−0.221828 | + | 0.975086i | \(0.571202\pi\) | |||||||
\(692\) | 1.74214 | + | 3.01747i | 0.0662260 | + | 0.114707i | ||||
\(693\) | −0.153989 | + | 0.266717i | −0.00584957 | + | 0.0101317i | ||||
\(694\) | 2.93900i | 0.111563i | ||||||||
\(695\) | −16.0823 | − | 9.28514i | −0.610038 | − | 0.352206i | ||||
\(696\) | −4.25379 | − | 2.45593i | −0.161240 | − | 0.0930917i | ||||
\(697\) | − | 24.8310i | − | 0.940541i | ||||||
\(698\) | 3.68664 | − | 6.38546i | 0.139542 | − | 0.241693i | ||||
\(699\) | 3.91185 | + | 6.77553i | 0.147960 | + | 0.256274i | ||||
\(700\) | −0.0183418 | + | 0.0105896i | −0.000693254 | + | 0.000400250i | ||||
\(701\) | −20.1328 | −0.760404 | −0.380202 | − | 0.924904i | \(-0.624145\pi\) | ||||
−0.380202 | + | 0.924904i | \(0.624145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.27067 | 0.0479242 | ||||||||
\(704\) | 5.45241 | − | 3.14795i | 0.205495 | − | 0.118643i | ||||
\(705\) | 7.70171 | + | 13.3398i | 0.290063 | + | 0.502404i | ||||
\(706\) | 1.00538 | − | 1.74136i | 0.0378379 | − | 0.0655371i | ||||
\(707\) | − | 0.0808502i | − | 0.00304069i | ||||||
\(708\) | −3.69685 | − | 2.13437i | −0.138936 | − | 0.0802147i | ||||
\(709\) | −14.3898 | − | 8.30798i | −0.540422 | − | 0.312013i | 0.204828 | − | 0.978798i | \(-0.434336\pi\) |
−0.745250 | + | 0.666785i | \(0.767670\pi\) | |||||||
\(710\) | 18.6219i | 0.698868i | ||||||||
\(711\) | −6.91454 | + | 11.9763i | −0.259316 | + | 0.449148i | ||||
\(712\) | 1.96077 | + | 3.39616i | 0.0734830 | + | 0.127276i | ||||
\(713\) | −21.1747 | + | 12.2252i | −0.792998 | + | 0.457838i | ||||
\(714\) | 0.141375 | 0.00529083 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.58881 | 0.134120 | ||||||||
\(717\) | 9.65918 | − | 5.57673i | 0.360729 | − | 0.208267i | ||||
\(718\) | 15.7289 | + | 27.2432i | 0.586996 | + | 1.01671i | ||||
\(719\) | 1.02416 | − | 1.77390i | 0.0381948 | − | 0.0661554i | −0.846296 | − | 0.532713i | \(-0.821173\pi\) |
0.884491 | + | 0.466557i | \(0.154506\pi\) | |||||||
\(720\) | 2.13706i | 0.0796436i | ||||||||
\(721\) | −0.348860 | − | 0.201415i | −0.0129922 | − | 0.00750107i | ||||
\(722\) | 28.5370 | + | 16.4758i | 1.06204 | + | 0.613167i | ||||
\(723\) | 3.54527i | 0.131850i | ||||||||
\(724\) | −2.75302 | + | 4.76837i | −0.102315 | + | 0.177215i | ||||
\(725\) | −1.06332 | − | 1.84172i | −0.0394907 | − | 0.0683998i | ||||
\(726\) | 24.8015 | − | 14.3192i | 0.920470 | − | 0.531434i | ||||
\(727\) | −29.9377 | −1.11033 | −0.555163 | − | 0.831741i | \(-0.687344\pi\) | ||||
−0.555163 | + | 0.831741i | \(0.687344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.6663 | + | 15.9731i | −1.02398 | + | 0.591193i | ||||
\(731\) | 9.70171 | + | 16.8039i | 0.358831 | + | 0.621513i | ||||
\(732\) | −3.55496 | + | 6.15737i | −0.131395 | + | 0.227583i | ||||
\(733\) | 1.46250i | 0.0540187i | 0.999635 | + | 0.0270093i | \(0.00859839\pi\) | ||||
−0.999635 | + | 0.0270093i | \(0.991402\pi\) | |||||||
\(734\) | 3.89654 | + | 2.24967i | 0.143824 | + | 0.0830368i | ||||
\(735\) | 12.9508 | + | 7.47716i | 0.477699 | + | 0.275799i | ||||
\(736\) | − | 2.71379i | − | 0.100032i | ||||||
\(737\) | −16.9487 | + | 29.3560i | −0.624313 | + | 1.08134i | ||||
\(738\) | −4.29590 | − | 7.44071i | −0.158134 | − | 0.273896i | ||||
\(739\) | 34.9758 | − | 20.1933i | 1.28660 | − | 0.742822i | 0.308558 | − | 0.951206i | \(-0.400154\pi\) |
0.978047 | + | 0.208384i | \(0.0668203\pi\) | |||||||
\(740\) | 0.376747 | 0.0138495 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.457123 | −0.0167815 | ||||||||
\(743\) | 8.46573 | − | 4.88769i | 0.310577 | − | 0.179312i | −0.336607 | − | 0.941645i | \(-0.609280\pi\) |
0.647185 | + | 0.762333i | \(0.275946\pi\) | |||||||
\(744\) | 4.50484 | + | 7.80262i | 0.165156 | + | 0.286058i | ||||
\(745\) | −5.20195 | + | 9.01004i | −0.190585 | + | 0.330102i | ||||
\(746\) | 37.8297i | 1.38504i | ||||||||
\(747\) | 9.64291 | + | 5.56734i | 0.352816 | + | 0.203698i | ||||
\(748\) | −15.7579 | − | 9.09783i | −0.576166 | − | 0.332650i | ||||
\(749\) | − | 0.409271i | − | 0.0149544i | ||||||
\(750\) | −5.80529 | + | 10.0551i | −0.211979 | + | 0.367159i | ||||
\(751\) | 17.2729 | + | 29.9176i | 0.630298 | + | 1.09171i | 0.987491 | + | 0.157678i | \(0.0504007\pi\) |
−0.357192 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(752\) | −6.24210 | + | 3.60388i | −0.227626 | + | 0.131420i | ||||
\(753\) | −4.17092 | −0.151997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.5138 | 1.14690 | ||||||||
\(756\) | 0.0423637 | − | 0.0244587i | 0.00154075 | − | 0.000889553i | ||||
\(757\) | 2.57242 | + | 4.45556i | 0.0934961 | + | 0.161940i | 0.908980 | − | 0.416840i | \(-0.136862\pi\) |
−0.815484 | + | 0.578780i | \(0.803529\pi\) | |||||||
\(758\) | 4.21983 | − | 7.30896i | 0.153271 | − | 0.265474i | ||||
\(759\) | − | 17.0858i | − | 0.620174i | ||||||
\(760\) | 13.3398 | + | 7.70171i | 0.483884 | + | 0.279370i | ||||
\(761\) | 16.8979 | + | 9.75600i | 0.612548 | + | 0.353655i | 0.773962 | − | 0.633232i | \(-0.218272\pi\) |
−0.161414 | + | 0.986887i | \(0.551605\pi\) | |||||||
\(762\) | − | 7.52111i | − | 0.272461i | ||||||
\(763\) | −0.426256 | + | 0.738296i | −0.0154315 | + | 0.0267281i | ||||
\(764\) | −2.82908 | − | 4.90012i | −0.102353 | − | 0.177280i | ||||
\(765\) | 5.34883 | − | 3.08815i | 0.193387 | − | 0.111652i | ||||
\(766\) | 1.28621 | 0.0464726 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −4.98485 | + | 2.87800i | −0.179758 | + | 0.103783i | −0.587179 | − | 0.809457i | \(-0.699762\pi\) |
0.407421 | + | 0.913241i | \(0.366428\pi\) | |||||||
\(770\) | 0.329085 | + | 0.569992i | 0.0118594 | + | 0.0205411i | ||||
\(771\) | 5.44504 | − | 9.43109i | 0.196098 | − | 0.339652i | ||||
\(772\) | − | 13.4034i | − | 0.482400i | ||||||
\(773\) | −3.57441 | − | 2.06369i | −0.128563 | − | 0.0742257i | 0.434339 | − | 0.900749i | \(-0.356982\pi\) |
−0.562902 | + | 0.826524i | \(0.690315\pi\) | |||||||
\(774\) | 5.81431 | + | 3.35690i | 0.208991 | + | 0.120661i | ||||
\(775\) | 3.90084i | 0.140122i | ||||||||
\(776\) | 1.23945 | − | 2.14678i | 0.0444935 | − | 0.0770651i | ||||
\(777\) | −0.00431187 | − | 0.00746837i | −0.000154687 | − | 0.000267926i | ||||
\(778\) | −20.2584 | + | 11.6962i | −0.726299 | + | 0.419329i | ||||
\(779\) | −61.9275 | −2.21878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.8611 | −1.96309 | ||||||||
\(782\) | −6.79231 | + | 3.92154i | −0.242893 | + | 0.140234i | ||||
\(783\) | 2.45593 | + | 4.25379i | 0.0877677 | + | 0.152018i | ||||
\(784\) | −3.49880 | + | 6.06011i | −0.124957 | + | 0.216432i | ||||
\(785\) | − | 35.7184i | − | 1.27485i | ||||||
\(786\) | 4.43836 | + | 2.56249i | 0.158311 | + | 0.0914010i | ||||
\(787\) | 14.0636 | + | 8.11960i | 0.501312 | + | 0.289433i | 0.729255 | − | 0.684242i | \(-0.239867\pi\) |
−0.227943 | + | 0.973674i | \(0.573200\pi\) | |||||||
\(788\) | 19.9812i | 0.711801i | ||||||||
\(789\) | −15.6136 | + | 27.0435i | −0.555858 | + | 0.962774i | ||||
\(790\) | 14.7768 | + | 25.5942i | 0.525735 | + | 0.910601i | ||||
\(791\) | −0.592068 | + | 0.341830i | −0.0210515 | + | 0.0121541i | ||||
\(792\) | −6.29590 | −0.223715 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −37.0858 | −1.31612 | ||||||||
\(795\) | −17.2949 | + | 9.98523i | −0.613388 | + | 0.354140i | ||||
\(796\) | 3.12080 | + | 5.40539i | 0.110614 | + | 0.191589i | ||||
\(797\) | 8.05741 | − | 13.9558i | 0.285408 | − | 0.494341i | −0.687300 | − | 0.726374i | \(-0.741204\pi\) |
0.972708 | + | 0.232032i | \(0.0745375\pi\) | |||||||
\(798\) | − | 0.352584i | − | 0.0124813i | ||||||
\(799\) | 18.0402 | + | 10.4155i | 0.638216 | + | 0.368474i | ||||
\(800\) | −0.374955 | − | 0.216480i | −0.0132566 | − | 0.00765373i | ||||
\(801\) | − | 3.92154i | − | 0.138561i | ||||||
\(802\) | 2.43296 | − | 4.21401i | 0.0859108 | − | 0.148802i | ||||
\(803\) | −47.0577 | − | 81.5063i | −1.66063 | − | 2.87630i | ||||
\(804\) | 4.66272 | − | 2.69202i | 0.164441 | − | 0.0949403i | ||||
\(805\) | 0.283698 | 0.00999905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.9172 | −0.560313 | ||||||||
\(808\) | 1.43136 | − | 0.826396i | 0.0503551 | − | 0.0290725i | ||||
\(809\) | −20.0761 | − | 34.7728i | −0.705837 | − | 1.22255i | −0.966389 | − | 0.257085i | \(-0.917238\pi\) |
0.260552 | − | 0.965460i | \(-0.416096\pi\) | |||||||
\(810\) | 1.06853 | − | 1.85075i | 0.0375444 | − | 0.0650288i | ||||
\(811\) | − | 39.8646i | − | 1.39984i | −0.714224 | − | 0.699918i | \(-0.753220\pi\) | ||
0.714224 | − | 0.699918i | \(-0.246780\pi\) | |||||||
\(812\) | 0.208084 | + | 0.120137i | 0.00730232 | + | 0.00421600i | ||||
\(813\) | 3.04937 | + | 1.76055i | 0.106946 | + | 0.0617453i | ||||
\(814\) | 1.10992i | 0.0389025i | ||||||||
\(815\) | −5.92990 | + | 10.2709i | −0.207715 | + | 0.359774i | ||||
\(816\) | 1.44504 | + | 2.50289i | 0.0505866 | + | 0.0876185i | ||||
\(817\) | 41.9081 | − | 24.1957i | 1.46618 | − | 0.846499i | ||||
\(818\) | −0.445042 | −0.0155605 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.3612 | −0.641201 | ||||||||
\(821\) | 5.41636 | − | 3.12714i | 0.189032 | − | 0.109138i | −0.402497 | − | 0.915421i | \(-0.631858\pi\) |
0.591529 | + | 0.806283i | \(0.298524\pi\) | |||||||
\(822\) | −2.00000 | − | 3.46410i | −0.0697580 | − | 0.120824i | ||||
\(823\) | −2.37167 | + | 4.10785i | −0.0826711 | + | 0.143191i | −0.904396 | − | 0.426693i | \(-0.859678\pi\) |
0.821725 | + | 0.569884i | \(0.193012\pi\) | |||||||
\(824\) | − | 8.23490i | − | 0.286876i | ||||||
\(825\) | −2.36068 | − | 1.36294i | −0.0821882 | − | 0.0474514i | ||||
\(826\) | 0.180840 | + | 0.104408i | 0.00629222 | + | 0.00363282i | ||||
\(827\) | − | 0.716185i | − | 0.0249042i | −0.999922 | − | 0.0124521i | \(-0.996036\pi\) | ||
0.999922 | − | 0.0124521i | \(-0.00396373\pi\) | |||||||
\(828\) | −1.35690 | + | 2.35021i | −0.0471554 | + | 0.0816755i | ||||
\(829\) | −18.0030 | − | 31.1821i | −0.625269 | − | 1.08300i | −0.988489 | − | 0.151295i | \(-0.951656\pi\) |
0.363219 | − | 0.931704i | \(-0.381678\pi\) | |||||||
\(830\) | 20.6075 | − | 11.8977i | 0.715297 | − | 0.412977i | ||||
\(831\) | −8.58104 | −0.297673 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2237 | 0.700709 | ||||||||
\(834\) | −7.52544 | + | 4.34481i | −0.260585 | + | 0.150449i | ||||
\(835\) | 4.19029 | + | 7.25780i | 0.145011 | + | 0.251167i | ||||
\(836\) | −22.6896 | + | 39.2996i | −0.784737 | + | 1.35920i | ||||
\(837\) | − | 9.00969i | − | 0.311420i | ||||||
\(838\) | −15.5771 | − | 8.99343i | −0.538101 | − | 0.310673i | ||||
\(839\) | 18.6677 | + | 10.7778i | 0.644479 | + | 0.372090i | 0.786338 | − | 0.617797i | \(-0.211975\pi\) |
−0.141859 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(840\) | − | 0.104539i | − | 0.00360695i | ||||||
\(841\) | 2.43685 | − | 4.22074i | 0.0840291 | − | 0.145543i | ||||
\(842\) | 10.6407 | + | 18.4303i | 0.366703 | + | 0.635148i | ||||
\(843\) | 6.99615 | − | 4.03923i | 0.240960 | − | 0.139118i | ||||
\(844\) | 5.08575 | 0.175059 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.20775 | 0.247808 | ||||||||
\(847\) | −1.21322 | + | 0.700455i | −0.0416869 | + | 0.0240679i | ||||
\(848\) | −4.67241 | − | 8.09285i | −0.160451 | − | 0.277909i | ||||
\(849\) | 8.70171 | − | 15.0718i | 0.298642 | − | 0.517263i | ||||
\(850\) | 1.25129i | 0.0429189i | ||||||||
\(851\) | 0.414324 | + | 0.239210i | 0.0142028 | + | 0.00820001i | ||||
\(852\) | 7.54637 | + | 4.35690i | 0.258534 | + | 0.149265i | ||||
\(853\) | 37.8237i | 1.29506i | 0.762040 | + | 0.647530i | \(0.224198\pi\) | ||||
−0.762040 | + | 0.647530i | \(0.775802\pi\) | |||||||
\(854\) | 0.173899 | − | 0.301202i | 0.00595070 | − | 0.0103069i | ||||
\(855\) | −7.70171 | − | 13.3398i | −0.263393 | − | 0.456210i | ||||
\(856\) | 7.24567 | − | 4.18329i | 0.247652 | − | 0.142982i | ||||
\(857\) | 6.58317 | 0.224877 | 0.112438 | − | 0.993659i | \(-0.464134\pi\) | ||||
0.112438 | + | 0.993659i | \(0.464134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6246 | −0.703702 | −0.351851 | − | 0.936056i | \(-0.614448\pi\) | ||||
−0.351851 | + | 0.936056i | \(0.614448\pi\) | |||||||
\(860\) | 12.4256 | − | 7.17390i | 0.423708 | − | 0.244628i | ||||
\(861\) | 0.210144 | + | 0.363980i | 0.00716168 | + | 0.0124044i | ||||
\(862\) | 12.3569 | − | 21.4028i | 0.420878 | − | 0.728981i | ||||
\(863\) | 15.9081i | 0.541519i | 0.962647 | + | 0.270760i | \(0.0872748\pi\) | ||||
−0.962647 | + | 0.270760i | \(0.912725\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −6.44852 | − | 3.72305i | −0.219256 | − | 0.126588i | ||||
\(866\) | − | 32.2174i | − | 1.09479i | ||||||
\(867\) | −4.32371 | + | 7.48888i | −0.146841 | + | 0.254336i | ||||
\(868\) | −0.220365 | − | 0.381683i | −0.00747968 | − | 0.0129552i | ||||
\(869\) | −75.4018 | + | 43.5332i | −2.55783 | + | 1.47676i | ||||
\(870\) | 10.4969 | 0.355880 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.4276 | −0.590172 | ||||||||
\(873\) | −2.14678 | + | 1.23945i | −0.0726577 | + | 0.0419489i | ||||
\(874\) | 9.78017 | + | 16.9397i | 0.330819 | + | 0.572995i | ||||
\(875\) | 0.283979 | − | 0.491867i | 0.00960025 | − | 0.0166281i | ||||
\(876\) | 14.9487i | 0.505069i | ||||||||
\(877\) | 13.5134 | + | 7.80194i | 0.456313 | + | 0.263453i | 0.710493 | − | 0.703704i | \(-0.248472\pi\) |
−0.254179 | + | 0.967157i | \(0.581805\pi\) | |||||||
\(878\) | 27.7887 | + | 16.0438i | 0.937825 | + | 0.541453i | ||||
\(879\) | 19.3709i | 0.653364i | ||||||||
\(880\) | −6.72737 | + | 11.6521i | −0.226779 | + | 0.392794i | ||||
\(881\) | −7.12737 | − | 12.3450i | −0.240127 | − | 0.415913i | 0.720623 | − | 0.693327i | \(-0.243856\pi\) |
−0.960750 | + | 0.277414i | \(0.910523\pi\) | |||||||
\(882\) | 6.06011 | − | 3.49880i | 0.204054 | − | 0.117811i | ||||
\(883\) | −1.65817 | −0.0558019 | −0.0279009 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0279009 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.12259 | 0.306652 | ||||||||
\(886\) | 17.7630 | − | 10.2555i | 0.596760 | − | 0.344539i | ||||
\(887\) | 9.60148 | + | 16.6303i | 0.322386 | + | 0.558389i | 0.980980 | − | 0.194109i | \(-0.0621817\pi\) |
−0.658594 | + | 0.752499i | \(0.728848\pi\) | |||||||
\(888\) | 0.0881460 | − | 0.152673i | 0.00295799 | − | 0.00512338i | ||||
\(889\) | 0.367913i | 0.0123394i | ||||||||
\(890\) | −7.25780 | − | 4.19029i | −0.243282 | − | 0.140459i | ||||
\(891\) | 5.45241 | + | 3.14795i | 0.182662 | + | 0.105460i | ||||
\(892\) | − | 20.5483i | − | 0.688006i | ||||||
\(893\) | 25.9758 | − | 44.9915i | 0.869248 | − | 1.50558i | ||||
\(894\) | 2.43416 | + | 4.21608i | 0.0814104 | + | 0.141007i | ||||
\(895\) | −6.64199 | + | 3.83476i | −0.222017 | + | 0.128182i | ||||
\(896\) | 0.0489173 | 0.00163421 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.3163 | −0.511113 | ||||||||
\(899\) | 38.3253 | − | 22.1271i | 1.27822 | − | 0.737981i | ||||
\(900\) | 0.216480 | + | 0.374955i | 0.00721600 | + | 0.0124985i | ||||
\(901\) | −13.5036 | + | 23.3890i | −0.449872 | + | 0.779201i | ||||
\(902\) | − | 54.0930i | − | 1.80110i | ||||||
\(903\) | −0.284421 | − | 0.164210i | −0.00946493 | − | 0.00546458i | ||||
\(904\) | −12.1034 | − | 6.98792i | −0.402554 | − | 0.232415i | ||||
\(905\) | − | 11.7668i | − | 0.391140i | ||||||
\(906\) | 7.37316 | − | 12.7707i | 0.244957 | − | 0.424278i | ||||
\(907\) | −16.1836 | − | 28.0308i | −0.537367 | − | 0.930747i | −0.999045 | − | 0.0436995i | \(-0.986086\pi\) |
0.461678 | − | 0.887048i | \(-0.347248\pi\) | |||||||
\(908\) | 3.82020 | − | 2.20560i | 0.126778 | − | 0.0731952i | ||||
\(909\) | −1.65279 | −0.0548197 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.9624 | −1.12523 | −0.562613 | − | 0.826721i | \(-0.690204\pi\) | ||||
−0.562613 | + | 0.826721i | \(0.690204\pi\) | |||||||
\(912\) | 6.24210 | − | 3.60388i | 0.206696 | − | 0.119336i | ||||
\(913\) | 35.0514 | + | 60.7108i | 1.16003 | + | 2.00923i | ||||
\(914\) | −9.59299 | + | 16.6155i | −0.317308 | + | 0.549593i | ||||
\(915\) | − | 15.1943i | − | 0.502309i | ||||||
\(916\) | 0.199693 | + | 0.115293i | 0.00659806 | + | 0.00380939i | ||||
\(917\) | −0.217113 | − | 0.125350i | −0.00716970 | − | 0.00413943i | ||||
\(918\) | − | 2.89008i | − | 0.0953870i | ||||||
\(919\) | 10.0390 | − | 17.3880i | 0.331156 | − | 0.573579i | −0.651583 | − | 0.758577i | \(-0.725895\pi\) |
0.982739 | + | 0.184999i | \(0.0592281\pi\) | |||||||
\(920\) | 2.89977 | + | 5.02255i | 0.0956027 | + | 0.165589i | ||||
\(921\) | 10.7615 | − | 6.21313i | 0.354602 | − | 0.204730i | ||||
\(922\) | −8.31229 | −0.273751 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.307979 | 0.0101317 | ||||||||
\(925\) | 0.0661015 | − | 0.0381637i | 0.00217340 | − | 0.00125482i | ||||
\(926\) | 3.16421 | + | 5.48057i | 0.103982 | + | 0.180103i | ||||
\(927\) | −4.11745 | + | 7.13163i | −0.135235 | + | 0.234233i | ||||
\(928\) | 4.91185i | 0.161240i | ||||||||
\(929\) | −48.6082 | − | 28.0640i | −1.59478 | − | 0.920749i | −0.992470 | − | 0.122491i | \(-0.960912\pi\) |
−0.602315 | − | 0.798258i | \(-0.705755\pi\) | |||||||
\(930\) | −16.6747 | − | 9.62714i | −0.546785 | − | 0.315686i | ||||
\(931\) | − | 50.4370i | − | 1.65301i | ||||||
\(932\) | 3.91185 | − | 6.77553i | 0.128137 | − | 0.221940i | ||||
\(933\) | −1.35690 | − | 2.35021i | −0.0444228 | − | 0.0769425i | ||||
\(934\) | 27.0095 | − | 15.5939i | 0.883778 | − | 0.510250i | ||||
\(935\) | 38.8853 | 1.27169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0291 | 0.883001 | 0.441501 | − | 0.897261i | \(-0.354446\pi\) | ||||
0.441501 | + | 0.897261i | \(0.354446\pi\) | |||||||
\(938\) | −0.228088 | + | 0.131687i | −0.00744733 | + | 0.00429972i | ||||
\(939\) | 7.69418 | + | 13.3267i | 0.251090 | + | 0.434901i | ||||
\(940\) | 7.70171 | − | 13.3398i | 0.251202 | − | 0.435095i | ||||
\(941\) | − | 24.0277i | − | 0.783282i | −0.920118 | − | 0.391641i | \(-0.871908\pi\) | ||
0.920118 | − | 0.391641i | \(-0.128092\pi\) | |||||||
\(942\) | −14.4746 | − | 8.35690i | −0.471607 | − | 0.272282i | ||||
\(943\) | −20.1925 | − | 11.6582i | −0.657560 | − | 0.379642i | ||||
\(944\) | 4.26875i | 0.138936i | ||||||||
\(945\) | −0.0522697 | + | 0.0905338i | −0.00170033 | + | 0.00294507i | ||||
\(946\) | 21.1347 | + | 36.6063i | 0.687147 | + | 1.19017i | ||||
\(947\) | 23.2065 | − | 13.3983i | 0.754110 | − | 0.435386i | −0.0730670 | − | 0.997327i | \(-0.523279\pi\) |
0.827177 | + | 0.561941i | \(0.189945\pi\) | |||||||
\(948\) | 13.8291 | 0.449148 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.12067 | 0.101248 | ||||||||
\(951\) | 22.2160 | − | 12.8264i | 0.720402 | − | 0.415924i | ||||
\(952\) | −0.0706876 | − | 0.122435i | −0.00229100 | − | 0.00396813i | ||||
\(953\) | 17.2107 | − | 29.8099i | 0.557510 | − | 0.965636i | −0.440193 | − | 0.897903i | \(-0.645090\pi\) |
0.997703 | − | 0.0677332i | \(-0.0215767\pi\) | |||||||
\(954\) | 9.34481i | 0.302550i | ||||||||
\(955\) | 10.4719 | + | 6.04593i | 0.338862 | + | 0.195642i | ||||
\(956\) | −9.65918 | − | 5.57673i | −0.312400 | − | 0.180364i | ||||
\(957\) | 30.9245i | 0.999648i | ||||||||
\(958\) | 8.96615 | − | 15.5298i | 0.289683 | − | 0.501746i | ||||
\(959\) | 0.0978347 | + | 0.169455i | 0.00315925 | + | 0.00547198i | ||||
\(960\) | 1.85075 | − | 1.06853i | 0.0597327 | − | 0.0344867i | ||||
\(961\) | −50.1745 | −1.61853 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.36658 | −0.269609 | ||||||||
\(964\) | 3.07029 | − | 1.77263i | 0.0988875 | − | 0.0570927i | ||||
\(965\) | 14.3220 | + | 24.8064i | 0.461041 | + | 0.798546i | ||||
\(966\) | 0.0663757 | − | 0.114966i | 0.00213560 | − | 0.00369898i | ||||
\(967\) | 26.2631i | 0.844565i | 0.906464 | + | 0.422282i | \(0.138771\pi\) | ||||
−0.906464 | + | 0.422282i | \(0.861229\pi\) | |||||||
\(968\) | −24.8015 | − | 14.3192i | −0.797151 | − | 0.460235i | ||||
\(969\) | −18.0402 | − | 10.4155i | −0.579534 | − | 0.334594i | ||||
\(970\) | 5.29755i | 0.170094i | ||||||||
\(971\) | 19.9921 | − | 34.6273i | 0.641577 | − | 1.11124i | −0.343504 | − | 0.939151i | \(-0.611614\pi\) |
0.985081 | − | 0.172093i | \(-0.0550528\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 0.368124 | − | 0.212537i | 0.0118015 | − | 0.00681362i | ||||
\(974\) | −30.3279 | −0.971770 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.10992 | 0.227583 | ||||||||
\(977\) | 3.96914 | − | 2.29159i | 0.126984 | − | 0.0733143i | −0.435162 | − | 0.900352i | \(-0.643309\pi\) |
0.562146 | + | 0.827038i | \(0.309976\pi\) | |||||||
\(978\) | 2.77479 | + | 4.80608i | 0.0887280 | + | 0.153681i | ||||
\(979\) | 12.3448 | − | 21.3818i | 0.394542 | − | 0.683367i | ||||
\(980\) | − | 14.9543i | − | 0.477699i | ||||||
\(981\) | 15.0927 | + | 8.71379i | 0.481874 | + | 0.278210i | ||||
\(982\) | 26.0634 | + | 15.0477i | 0.831717 | + | 0.480192i | ||||
\(983\) | 10.6848i | 0.340794i | 0.985376 | + | 0.170397i | \(0.0545049\pi\) | ||||
−0.985376 | + | 0.170397i | \(0.945495\pi\) | |||||||
\(984\) | −4.29590 | + | 7.44071i | −0.136948 | + | 0.237201i | ||||
\(985\) | −21.3506 | − | 36.9803i | −0.680285 | − | 1.17829i | ||||
\(986\) | 12.2938 | − | 7.09783i | 0.391515 | − | 0.226041i | ||||
\(987\) | −0.352584 | −0.0112229 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.2198 | 0.579357 | ||||||||
\(990\) | 11.6521 | − | 6.72737i | 0.370329 | − | 0.213810i | ||||
\(991\) | −25.3010 | − | 43.8227i | −0.803714 | − | 1.39207i | −0.917156 | − | 0.398529i | \(-0.869521\pi\) |
0.113442 | − | 0.993545i | \(-0.463812\pi\) | |||||||
\(992\) | 4.50484 | − | 7.80262i | 0.143029 | − | 0.247733i | ||||
\(993\) | − | 3.82371i | − | 0.121342i | ||||||
\(994\) | −0.369148 | − | 0.213128i | −0.0117087 | − | 0.00676000i | ||||
\(995\) | −11.5517 | − | 6.66935i | −0.366212 | − | 0.211433i | ||||
\(996\) | − | 11.1347i | − | 0.352816i | ||||||
\(997\) | 17.9801 | − | 31.1425i | 0.569437 | − | 0.986294i | −0.427185 | − | 0.904164i | \(-0.640495\pi\) |
0.996622 | − | 0.0821294i | \(-0.0261721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.152673 | + | 0.0881460i | −0.00483037 | + | 0.00278882i |
(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.i.h.361.5 | 12 | ||
13.2 | odd | 12 | 1014.2.a.n.1.2 | yes | 3 | ||
13.3 | even | 3 | 1014.2.b.f.337.5 | 6 | |||
13.4 | even | 6 | inner | 1014.2.i.h.823.5 | 12 | ||
13.5 | odd | 4 | 1014.2.e.l.991.2 | 6 | |||
13.6 | odd | 12 | 1014.2.e.l.529.2 | 6 | |||
13.7 | odd | 12 | 1014.2.e.n.529.2 | 6 | |||
13.8 | odd | 4 | 1014.2.e.n.991.2 | 6 | |||
13.9 | even | 3 | inner | 1014.2.i.h.823.2 | 12 | ||
13.10 | even | 6 | 1014.2.b.f.337.2 | 6 | |||
13.11 | odd | 12 | 1014.2.a.l.1.2 | ✓ | 3 | ||
13.12 | even | 2 | inner | 1014.2.i.h.361.2 | 12 | ||
39.2 | even | 12 | 3042.2.a.ba.1.2 | 3 | |||
39.11 | even | 12 | 3042.2.a.bh.1.2 | 3 | |||
39.23 | odd | 6 | 3042.2.b.o.1351.5 | 6 | |||
39.29 | odd | 6 | 3042.2.b.o.1351.2 | 6 | |||
52.11 | even | 12 | 8112.2.a.cj.1.2 | 3 | |||
52.15 | even | 12 | 8112.2.a.cm.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.l.1.2 | ✓ | 3 | 13.11 | odd | 12 | ||
1014.2.a.n.1.2 | yes | 3 | 13.2 | odd | 12 | ||
1014.2.b.f.337.2 | 6 | 13.10 | even | 6 | |||
1014.2.b.f.337.5 | 6 | 13.3 | even | 3 | |||
1014.2.e.l.529.2 | 6 | 13.6 | odd | 12 | |||
1014.2.e.l.991.2 | 6 | 13.5 | odd | 4 | |||
1014.2.e.n.529.2 | 6 | 13.7 | odd | 12 | |||
1014.2.e.n.991.2 | 6 | 13.8 | odd | 4 | |||
1014.2.i.h.361.2 | 12 | 13.12 | even | 2 | inner | ||
1014.2.i.h.361.5 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.i.h.823.2 | 12 | 13.9 | even | 3 | inner | ||
1014.2.i.h.823.5 | 12 | 13.4 | even | 6 | inner | ||
3042.2.a.ba.1.2 | 3 | 39.2 | even | 12 | |||
3042.2.a.bh.1.2 | 3 | 39.11 | even | 12 | |||
3042.2.b.o.1351.2 | 6 | 39.29 | odd | 6 | |||
3042.2.b.o.1351.5 | 6 | 39.23 | odd | 6 | |||
8112.2.a.cj.1.2 | 3 | 52.11 | even | 12 | |||
8112.2.a.cm.1.2 | 3 | 52.15 | even | 12 |