Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(79,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.n (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.7652750400000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} - 112 x^{3} + 288 x^{2} - 192 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.5 | ||
Root | \(-1.45845 - 1.45845i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.79 |
Dual form | 1470.2.n.j.949.5 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.806615 | − | 2.08551i | 0.360729 | − | 0.932671i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.74131 | − | 1.40280i | 0.550649 | − | 0.443605i | ||||
\(11\) | −3.05362 | − | 5.28903i | −0.920703 | − | 1.59470i | −0.798331 | − | 0.602219i | \(-0.794283\pi\) |
−0.122372 | − | 0.992484i | \(-0.539050\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 1.68842i | − | 0.468283i | −0.972203 | − | 0.234141i | \(-0.924772\pi\) | ||
0.972203 | − | 0.234141i | \(-0.0752278\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.344208 | + | 2.20942i | 0.0888742 | + | 0.570469i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.92159 | + | 3.41883i | −1.43620 | + | 0.829189i | −0.997583 | − | 0.0694868i | \(-0.977864\pi\) |
−0.438614 | + | 0.898675i | \(0.644530\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −0.844208 | + | 1.46221i | −0.193675 | + | 0.335454i | −0.946465 | − | 0.322806i | \(-0.895374\pi\) |
0.752791 | + | 0.658260i | \(0.228707\pi\) | |||||||
\(20\) | 2.20942 | − | 0.344208i | 0.494041 | − | 0.0769673i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 6.10725i | − | 1.30207i | ||||||
\(23\) | −2.00189 | − | 1.15579i | −0.417423 | − | 0.240999i | 0.276551 | − | 0.960999i | \(-0.410808\pi\) |
−0.693974 | + | 0.720000i | \(0.744142\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −3.69874 | − | 3.36441i | −0.739749 | − | 0.672883i | ||||
\(26\) | 0.844208 | − | 1.46221i | 0.165563 | − | 0.286763i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.41883 | −1.56334 | −0.781669 | − | 0.623694i | \(-0.785631\pi\) | ||||
−0.781669 | + | 0.623694i | \(0.785631\pi\) | |||||||
\(30\) | −0.806615 | + | 2.08551i | −0.147267 | + | 0.380761i | ||||
\(31\) | −0.344208 | − | 0.596186i | −0.0618217 | − | 0.107078i | 0.833458 | − | 0.552583i | \(-0.186358\pi\) |
−0.895280 | + | 0.445504i | \(0.853024\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 5.28903 | + | 3.05362i | 0.920703 | + | 0.531568i | ||||
\(34\) | −6.83767 | −1.17265 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00189 | + | 1.15579i | 0.329109 | + | 0.190011i | 0.655445 | − | 0.755243i | \(-0.272481\pi\) |
−0.326337 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(38\) | −1.46221 | + | 0.844208i | −0.237202 | + | 0.136949i | ||||
\(39\) | 0.844208 | + | 1.46221i | 0.135182 | + | 0.234141i | ||||
\(40\) | 2.08551 | + | 0.806615i | 0.329749 | + | 0.127537i | ||||
\(41\) | −5.14925 | −0.804178 | −0.402089 | − | 0.915601i | \(-0.631716\pi\) | ||||
−0.402089 | + | 0.915601i | \(0.631716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 3.05362 | − | 5.28903i | 0.460351 | − | 0.797352i | ||||
\(45\) | −1.40280 | − | 1.74131i | −0.209117 | − | 0.259579i | ||||
\(46\) | −1.15579 | − | 2.00189i | −0.170412 | − | 0.295163i | ||||
\(47\) | 2.65458 | + | 1.53263i | 0.387211 | + | 0.223556i | 0.680951 | − | 0.732329i | \(-0.261567\pi\) |
−0.293740 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.52100 | − | 4.76304i | −0.215102 | − | 0.673596i | ||||
\(51\) | 3.41883 | − | 5.92159i | 0.478732 | − | 0.829189i | ||||
\(52\) | 1.46221 | − | 0.844208i | 0.202772 | − | 0.117071i | ||||
\(53\) | −9.05935 | + | 5.23042i | −1.24440 | + | 0.718453i | −0.969986 | − | 0.243160i | \(-0.921816\pi\) |
−0.274411 | + | 0.961613i | \(0.588483\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −13.4935 | + | 2.10217i | −1.81946 | + | 0.283456i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.68842i | − | 0.223636i | ||||||
\(58\) | −7.29092 | − | 4.20942i | −0.957345 | − | 0.552723i | ||||
\(59\) | 3.52100 | + | 6.09855i | 0.458395 | + | 0.793964i | 0.998876 | − | 0.0473925i | \(-0.0150911\pi\) |
−0.540481 | + | 0.841356i | \(0.681758\pi\) | |||||||
\(60\) | −1.74131 | + | 1.40280i | −0.224802 | + | 0.181101i | ||||
\(61\) | 4.73042 | − | 8.19332i | 0.605668 | − | 1.04905i | −0.386278 | − | 0.922382i | \(-0.626239\pi\) |
0.991946 | − | 0.126665i | \(-0.0404272\pi\) | |||||||
\(62\) | − | 0.688417i | − | 0.0874290i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.52122 | − | 1.36190i | −0.436753 | − | 0.168923i | ||||
\(66\) | 3.05362 | + | 5.28903i | 0.375875 | + | 0.651035i | ||||
\(67\) | 10.5781 | − | 6.10725i | 1.29232 | − | 0.746119i | 0.313252 | − | 0.949670i | \(-0.398582\pi\) |
0.979064 | + | 0.203551i | \(0.0652482\pi\) | |||||||
\(68\) | −5.92159 | − | 3.41883i | −0.718098 | − | 0.414594i | ||||
\(69\) | 2.31158 | 0.278282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −3.46410 | + | 2.00000i | −0.405442 | + | 0.234082i | −0.688830 | − | 0.724923i | \(-0.741875\pi\) |
0.283387 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(74\) | 1.15579 | + | 2.00189i | 0.134358 | + | 0.232715i | ||||
\(75\) | 4.88541 | + | 1.06430i | 0.564119 | + | 0.122894i | ||||
\(76\) | −1.68842 | −0.193675 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.68842i | 0.191176i | ||||||||
\(79\) | 3.65579 | − | 6.33202i | 0.411309 | − | 0.712408i | −0.583724 | − | 0.811952i | \(-0.698405\pi\) |
0.995033 | + | 0.0995443i | \(0.0317385\pi\) | |||||||
\(80\) | 1.40280 | + | 1.74131i | 0.156838 | + | 0.194684i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.45938 | − | 2.57462i | −0.492456 | − | 0.284320i | ||||
\(83\) | − | 13.5261i | − | 1.48468i | −0.670023 | − | 0.742340i | \(-0.733716\pi\) | ||
0.670023 | − | 0.742340i | \(-0.266284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.35358 | + | 15.1072i | 0.255282 | + | 1.63861i | ||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | 7.29092 | − | 4.20942i | 0.781669 | − | 0.451297i | ||||
\(88\) | 5.28903 | − | 3.05362i | 0.563813 | − | 0.325517i | ||||
\(89\) | 6.10725 | − | 10.5781i | 0.647367 | − | 1.12127i | −0.336382 | − | 0.941726i | \(-0.609203\pi\) |
0.983749 | − | 0.179547i | \(-0.0574633\pi\) | |||||||
\(90\) | −0.344208 | − | 2.20942i | −0.0362828 | − | 0.232893i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2.31158i | − | 0.240999i | ||||||
\(93\) | 0.596186 | + | 0.344208i | 0.0618217 | + | 0.0356928i | ||||
\(94\) | 1.53263 | + | 2.65458i | 0.158078 | + | 0.273800i | ||||
\(95\) | 2.36851 | + | 2.94005i | 0.243004 | + | 0.301643i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 4.95800i | − | 0.503409i | −0.967804 | − | 0.251704i | \(-0.919009\pi\) | ||
0.967804 | − | 0.251704i | \(-0.0809911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.10725 | −0.613802 | ||||||||
\(100\) | 1.06430 | − | 4.88541i | 0.106430 | − | 0.488541i | ||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | 5.92159 | − | 3.41883i | 0.586325 | − | 0.338515i | ||||
\(103\) | 0.725439 | + | 0.418833i | 0.0714797 | + | 0.0412688i | 0.535314 | − | 0.844653i | \(-0.320193\pi\) |
−0.463834 | + | 0.885922i | \(0.653527\pi\) | |||||||
\(104\) | 1.68842 | 0.165563 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4608 | −1.01605 | ||||||||
\(107\) | 13.4460 | + | 7.76304i | 1.29987 | + | 0.750482i | 0.980382 | − | 0.197108i | \(-0.0631550\pi\) |
0.319490 | + | 0.947590i | \(0.396488\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −5.83767 | − | 10.1111i | −0.559147 | − | 0.968471i | −0.997568 | − | 0.0697012i | \(-0.977795\pi\) |
0.438421 | − | 0.898770i | \(-0.355538\pi\) | |||||||
\(110\) | −12.7368 | − | 4.92620i | −1.21440 | − | 0.469695i | ||||
\(111\) | −2.31158 | −0.219406 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.37683i | − | 0.317666i | −0.987305 | − | 0.158833i | \(-0.949227\pi\) | ||
0.987305 | − | 0.158833i | \(-0.0507731\pi\) | |||||||
\(114\) | 0.844208 | − | 1.46221i | 0.0790674 | − | 0.136949i | ||||
\(115\) | −4.02517 | + | 3.24269i | −0.375349 | + | 0.302383i | ||||
\(116\) | −4.20942 | − | 7.29092i | −0.390834 | − | 0.676945i | ||||
\(117\) | −1.46221 | − | 0.844208i | −0.135182 | − | 0.0780471i | ||||
\(118\) | 7.04200i | 0.648269i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.20942 | + | 0.344208i | −0.201691 | + | 0.0314218i | ||||
\(121\) | −13.1492 | + | 22.7752i | −1.19539 | + | 2.07047i | ||||
\(122\) | 8.19332 | − | 4.73042i | 0.741788 | − | 0.428272i | ||||
\(123\) | 4.45938 | − | 2.57462i | 0.402089 | − | 0.232146i | ||||
\(124\) | 0.344208 | − | 0.596186i | 0.0309108 | − | 0.0535391i | ||||
\(125\) | −10.0000 | + | 5.00000i | −0.894427 | + | 0.447214i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.94491i | 0.438790i | 0.975636 | + | 0.219395i | \(0.0704084\pi\) | ||||
−0.975636 | + | 0.219395i | \(0.929592\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | −2.36851 | − | 2.94005i | −0.207732 | − | 0.257860i | ||||
\(131\) | −3.36521 | + | 5.82871i | −0.294020 | + | 0.509257i | −0.974756 | − | 0.223271i | \(-0.928326\pi\) |
0.680737 | + | 0.732528i | \(0.261660\pi\) | |||||||
\(132\) | 6.10725i | 0.531568i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.2145 | 1.05517 | ||||||||
\(135\) | 2.08551 | + | 0.806615i | 0.179493 | + | 0.0694224i | ||||
\(136\) | −3.41883 | − | 5.92159i | −0.293162 | − | 0.507772i | ||||
\(137\) | −16.4997 | + | 9.52608i | −1.40966 | + | 0.813868i | −0.995355 | − | 0.0962697i | \(-0.969309\pi\) |
−0.414306 | + | 0.910138i | \(0.635976\pi\) | |||||||
\(138\) | 2.00189 | + | 1.15579i | 0.170412 | + | 0.0983875i | ||||
\(139\) | 13.3768 | 1.13461 | 0.567304 | − | 0.823508i | \(-0.307986\pi\) | ||||
0.567304 | + | 0.823508i | \(0.307986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06525 | −0.258141 | ||||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | −8.93009 | + | 5.15579i | −0.746772 | + | 0.431149i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.79076 | + | 17.5576i | −0.563942 | + | 1.45808i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.31158i | 0.190011i | ||||||||
\(149\) | 6.31158 | − | 10.9320i | 0.517065 | − | 0.895583i | −0.482739 | − | 0.875765i | \(-0.660358\pi\) |
0.999804 | − | 0.0198184i | \(-0.00630881\pi\) | |||||||
\(150\) | 3.69874 | + | 3.36441i | 0.302001 | + | 0.274703i | ||||
\(151\) | −0.967375 | − | 1.67554i | −0.0787238 | − | 0.136354i | 0.823976 | − | 0.566625i | \(-0.191751\pi\) |
−0.902700 | + | 0.430271i | \(0.858418\pi\) | |||||||
\(152\) | −1.46221 | − | 0.844208i | −0.118601 | − | 0.0684743i | ||||
\(153\) | 6.83767i | 0.552792i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.52100 | + | 0.236959i | −0.122170 | + | 0.0190330i | ||||
\(156\) | −0.844208 | + | 1.46221i | −0.0675908 | + | 0.117071i | ||||
\(157\) | 14.8517 | − | 8.57462i | 1.18529 | − | 0.684330i | 0.228060 | − | 0.973647i | \(-0.426762\pi\) |
0.957233 | + | 0.289317i | \(0.0934283\pi\) | |||||||
\(158\) | 6.33202 | − | 3.65579i | 0.503748 | − | 0.290839i | ||||
\(159\) | 5.23042 | − | 9.05935i | 0.414799 | − | 0.718453i | ||||
\(160\) | 0.344208 | + | 2.20942i | 0.0272121 | + | 0.174670i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −0.466934 | − | 0.269584i | −0.0365731 | − | 0.0211155i | 0.481602 | − | 0.876390i | \(-0.340055\pi\) |
−0.518175 | + | 0.855275i | \(0.673388\pi\) | |||||||
\(164\) | −2.57462 | − | 4.45938i | −0.201044 | − | 0.348219i | ||||
\(165\) | 10.6346 | − | 8.56726i | 0.827902 | − | 0.666960i | ||||
\(166\) | 6.76304 | − | 11.7139i | 0.524914 | − | 0.909177i | ||||
\(167\) | − | 3.14925i | − | 0.243696i | −0.992549 | − | 0.121848i | \(-0.961118\pi\) | ||
0.992549 | − | 0.121848i | \(-0.0388821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1492 | 0.780711 | ||||||||
\(170\) | −5.51536 | + | 14.2601i | −0.423009 | + | 1.09370i | ||||
\(171\) | 0.844208 | + | 1.46221i | 0.0645582 | + | 0.111818i | ||||
\(172\) | 1.73205 | − | 1.00000i | 0.132068 | − | 0.0762493i | ||||
\(173\) | −9.11585 | − | 5.26304i | −0.693066 | − | 0.400142i | 0.111694 | − | 0.993743i | \(-0.464372\pi\) |
−0.804759 | + | 0.593601i | \(0.797706\pi\) | |||||||
\(174\) | 8.41883 | 0.638230 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.10725 | 0.460351 | ||||||||
\(177\) | −6.09855 | − | 3.52100i | −0.458395 | − | 0.264655i | ||||
\(178\) | 10.5781 | − | 6.10725i | 0.792860 | − | 0.457758i | ||||
\(179\) | 2.46737 | + | 4.27362i | 0.184420 | + | 0.319425i | 0.943381 | − | 0.331711i | \(-0.107626\pi\) |
−0.758961 | + | 0.651136i | \(0.774293\pi\) | |||||||
\(180\) | 0.806615 | − | 2.08551i | 0.0601215 | − | 0.155445i | ||||
\(181\) | −6.13050 | −0.455677 | −0.227838 | − | 0.973699i | \(-0.573166\pi\) | ||||
−0.227838 | + | 0.973699i | \(0.573166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.46083i | 0.699365i | ||||||||
\(184\) | 1.15579 | − | 2.00189i | 0.0852061 | − | 0.147581i | ||||
\(185\) | 4.02517 | − | 3.24269i | 0.295937 | − | 0.238407i | ||||
\(186\) | 0.344208 | + | 0.596186i | 0.0252386 | + | 0.0437145i | ||||
\(187\) | 36.1646 | + | 20.8797i | 2.64462 | + | 1.52687i | ||||
\(188\) | 3.06525i | 0.223556i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.581167 | + | 3.73042i | 0.0421623 | + | 0.270633i | ||||
\(191\) | 7.46083 | − | 12.9225i | 0.539847 | − | 0.935042i | −0.459065 | − | 0.888403i | \(-0.651815\pi\) |
0.998912 | − | 0.0466394i | \(-0.0148512\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −4.83343 | + | 2.79058i | −0.347918 | + | 0.200871i | −0.663768 | − | 0.747939i | \(-0.731044\pi\) |
0.315850 | + | 0.948809i | \(0.397710\pi\) | |||||||
\(194\) | 2.47900 | − | 4.29375i | 0.177982 | − | 0.308274i | ||||
\(195\) | 3.73042 | − | 0.581167i | 0.267141 | − | 0.0416183i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.5261i | − | 1.03494i | −0.855701 | − | 0.517470i | \(-0.826874\pi\) | ||
0.855701 | − | 0.517470i | \(-0.173126\pi\) | |||||||
\(198\) | −5.28903 | − | 3.05362i | −0.375875 | − | 0.217012i | ||||
\(199\) | 4.31158 | + | 7.46788i | 0.305640 | + | 0.529384i | 0.977404 | − | 0.211382i | \(-0.0677963\pi\) |
−0.671764 | + | 0.740766i | \(0.734463\pi\) | |||||||
\(200\) | 3.36441 | − | 3.69874i | 0.237900 | − | 0.261541i | ||||
\(201\) | −6.10725 | + | 10.5781i | −0.430772 | + | 0.746119i | ||||
\(202\) | − | 8.00000i | − | 0.562878i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.83767 | 0.478732 | ||||||||
\(205\) | −4.15346 | + | 10.7388i | −0.290090 | + | 0.750033i | ||||
\(206\) | 0.418833 | + | 0.725439i | 0.0291815 | + | 0.0505438i | ||||
\(207\) | −2.00189 | + | 1.15579i | −0.139141 | + | 0.0803331i | ||||
\(208\) | 1.46221 | + | 0.844208i | 0.101386 | + | 0.0585353i | ||||
\(209\) | 10.3116 | 0.713267 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68842 | −0.529292 | −0.264646 | − | 0.964346i | \(-0.585255\pi\) | ||||
−0.264646 | + | 0.964346i | \(0.585255\pi\) | |||||||
\(212\) | −9.05935 | − | 5.23042i | −0.622198 | − | 0.359226i | ||||
\(213\) | −5.19615 | + | 3.00000i | −0.356034 | + | 0.205557i | ||||
\(214\) | 7.76304 | + | 13.4460i | 0.530671 | + | 0.919148i | ||||
\(215\) | −4.17103 | − | 1.61323i | −0.284462 | − | 0.110021i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 11.6753i | − | 0.790753i | ||||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | −8.56726 | − | 10.6346i | −0.577604 | − | 0.716984i | ||||
\(221\) | 5.77241 | + | 9.99812i | 0.388295 | + | 0.672546i | ||||
\(222\) | −2.00189 | − | 1.15579i | −0.134358 | − | 0.0775717i | ||||
\(223\) | 11.1725i | 0.748166i | 0.927395 | + | 0.374083i | \(0.122042\pi\) | ||||
−0.927395 | + | 0.374083i | \(0.877958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.76304 | + | 1.52100i | −0.317536 | + | 0.101400i | ||||
\(226\) | 1.68842 | − | 2.92442i | 0.112312 | − | 0.194530i | ||||
\(227\) | 3.33485 | − | 1.92538i | 0.221342 | − | 0.127792i | −0.385230 | − | 0.922821i | \(-0.625878\pi\) |
0.606571 | + | 0.795029i | \(0.292544\pi\) | |||||||
\(228\) | 1.46221 | − | 0.844208i | 0.0968373 | − | 0.0559091i | ||||
\(229\) | −2.83767 | + | 4.91498i | −0.187518 | + | 0.324791i | −0.944422 | − | 0.328735i | \(-0.893378\pi\) |
0.756904 | + | 0.653526i | \(0.226711\pi\) | |||||||
\(230\) | −5.10725 | + | 0.795666i | −0.336762 | + | 0.0524647i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.41883i | − | 0.552723i | ||||||
\(233\) | 9.92537 | + | 5.73042i | 0.650233 | + | 0.375412i | 0.788545 | − | 0.614977i | \(-0.210835\pi\) |
−0.138313 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(234\) | −0.844208 | − | 1.46221i | −0.0551876 | − | 0.0955878i | ||||
\(235\) | 5.33754 | − | 4.29994i | 0.348183 | − | 0.280497i | ||||
\(236\) | −3.52100 | + | 6.09855i | −0.229198 | + | 0.396982i | ||||
\(237\) | 7.31158i | 0.474938i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4608 | −1.00008 | −0.500039 | − | 0.866003i | \(-0.666681\pi\) | ||||
−0.500039 | + | 0.866003i | \(0.666681\pi\) | |||||||
\(240\) | −2.08551 | − | 0.806615i | −0.134619 | − | 0.0520668i | ||||
\(241\) | 2.18842 | + | 3.79045i | 0.140968 | + | 0.244164i | 0.927862 | − | 0.372925i | \(-0.121645\pi\) |
−0.786893 | + | 0.617089i | \(0.788312\pi\) | |||||||
\(242\) | −22.7752 | + | 13.1492i | −1.46404 | + | 0.845266i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 9.46083 | 0.605668 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.14925 | 0.328304 | ||||||||
\(247\) | 2.46882 | + | 1.42538i | 0.157087 | + | 0.0906945i | ||||
\(248\) | 0.596186 | − | 0.344208i | 0.0378579 | − | 0.0218573i | ||||
\(249\) | 6.76304 | + | 11.7139i | 0.428590 | + | 0.742340i | ||||
\(250\) | −11.1603 | − | 0.669873i | −0.705836 | − | 0.0423665i | ||||
\(251\) | 26.5362 | 1.67495 | 0.837477 | − | 0.546473i | \(-0.184030\pi\) | ||||
0.837477 | + | 0.546473i | \(0.184030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.1174i | 0.887554i | ||||||||
\(254\) | −2.47246 | + | 4.28242i | −0.155136 | + | 0.268703i | ||||
\(255\) | −9.59189 | − | 11.9065i | −0.600667 | − | 0.745612i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −19.4241 | − | 11.2145i | −1.21164 | − | 0.699541i | −0.248524 | − | 0.968626i | \(-0.579946\pi\) |
−0.963117 | + | 0.269084i | \(0.913279\pi\) | |||||||
\(258\) | 2.00000i | 0.124515i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.581167 | − | 3.73042i | −0.0360425 | − | 0.231351i | ||||
\(261\) | −4.20942 | + | 7.29092i | −0.260556 | + | 0.451297i | ||||
\(262\) | −5.82871 | + | 3.36521i | −0.360099 | + | 0.207903i | ||||
\(263\) | −16.9666 | + | 9.79567i | −1.04620 | + | 0.604027i | −0.921584 | − | 0.388178i | \(-0.873105\pi\) |
−0.124620 | + | 0.992204i | \(0.539771\pi\) | |||||||
\(264\) | −3.05362 | + | 5.28903i | −0.187938 | + | 0.325517i | ||||
\(265\) | 3.60071 | + | 23.1123i | 0.221190 | + | 1.41978i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2145i | 0.747515i | ||||||||
\(268\) | 10.5781 | + | 6.10725i | 0.646158 | + | 0.373060i | ||||
\(269\) | 3.47900 | + | 6.02581i | 0.212118 | + | 0.367400i | 0.952377 | − | 0.304922i | \(-0.0986304\pi\) |
−0.740259 | + | 0.672322i | \(0.765297\pi\) | |||||||
\(270\) | 1.40280 | + | 1.74131i | 0.0853718 | + | 0.105973i | ||||
\(271\) | −14.1819 | + | 24.5637i | −0.861487 | + | 1.49214i | 0.00900561 | + | 0.999959i | \(0.497133\pi\) |
−0.870493 | + | 0.492181i | \(0.836200\pi\) | |||||||
\(272\) | − | 6.83767i | − | 0.414594i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.0522 | −1.15098 | ||||||||
\(275\) | −6.49992 | + | 29.8364i | −0.391960 | + | 1.79921i | ||||
\(276\) | 1.15579 | + | 2.00189i | 0.0695705 | + | 0.120500i | ||||
\(277\) | −4.37530 | + | 2.52608i | −0.262886 | + | 0.151778i | −0.625651 | − | 0.780103i | \(-0.715166\pi\) |
0.362764 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(278\) | 11.5847 | + | 6.68842i | 0.694803 | + | 0.401145i | ||||
\(279\) | −0.688417 | −0.0412144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.68842 | 0.458652 | 0.229326 | − | 0.973350i | \(-0.426348\pi\) | ||||
0.229326 | + | 0.973350i | \(0.426348\pi\) | |||||||
\(282\) | −2.65458 | − | 1.53263i | −0.158078 | − | 0.0912665i | ||||
\(283\) | −15.9600 | + | 9.21450i | −0.948722 | + | 0.547745i | −0.892684 | − | 0.450683i | \(-0.851180\pi\) |
−0.0560386 | + | 0.998429i | \(0.517847\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | −3.52122 | − | 1.36190i | −0.208579 | − | 0.0806721i | ||||
\(286\) | −10.3116 | −0.609737 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 14.8768 | − | 25.7674i | 0.875108 | − | 1.51573i | ||||
\(290\) | −14.6598 | + | 11.8100i | −0.860851 | + | 0.693504i | ||||
\(291\) | 2.47900 | + | 4.29375i | 0.145322 | + | 0.251704i | ||||
\(292\) | −3.46410 | − | 2.00000i | −0.202721 | − | 0.117041i | ||||
\(293\) | 1.83767i | 0.107358i | 0.998558 | + | 0.0536788i | \(0.0170947\pi\) | ||||
−0.998558 | + | 0.0536788i | \(0.982905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5587 | − | 2.42392i | 0.905863 | − | 0.141126i | ||||
\(296\) | −1.15579 | + | 2.00189i | −0.0671790 | + | 0.116357i | ||||
\(297\) | 5.28903 | − | 3.05362i | 0.306901 | − | 0.177189i | ||||
\(298\) | 10.9320 | − | 6.31158i | 0.633273 | − | 0.365620i | ||||
\(299\) | −1.95146 | + | 3.38002i | −0.112856 | + | 0.195472i | ||||
\(300\) | 1.52100 | + | 4.76304i | 0.0878149 | + | 0.274994i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1.93475i | − | 0.111332i | ||||||
\(303\) | 6.92820 | + | 4.00000i | 0.398015 | + | 0.229794i | ||||
\(304\) | −0.844208 | − | 1.46221i | −0.0484187 | − | 0.0838636i | ||||
\(305\) | −13.2717 | − | 16.4742i | −0.759933 | − | 0.943310i | ||||
\(306\) | −3.41883 | + | 5.92159i | −0.195442 | + | 0.338515i | ||||
\(307\) | − | 16.0840i | − | 0.917962i | −0.888446 | − | 0.458981i | \(-0.848215\pi\) | ||
0.888446 | − | 0.458981i | \(-0.151785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.837665 | −0.0476531 | ||||||||
\(310\) | −1.43570 | − | 0.555287i | −0.0815425 | − | 0.0315382i | ||||
\(311\) | −7.68842 | − | 13.3167i | −0.435970 | − | 0.755122i | 0.561404 | − | 0.827542i | \(-0.310261\pi\) |
−0.997374 | + | 0.0724194i | \(0.976928\pi\) | |||||||
\(312\) | −1.46221 | + | 0.844208i | −0.0827814 | + | 0.0477939i | ||||
\(313\) | −19.4153 | − | 11.2094i | −1.09742 | − | 0.633594i | −0.161875 | − | 0.986811i | \(-0.551754\pi\) |
−0.935541 | + | 0.353218i | \(0.885088\pi\) | |||||||
\(314\) | 17.1492 | 0.967788 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.31158 | 0.411309 | ||||||||
\(317\) | −8.71676 | − | 5.03263i | −0.489582 | − | 0.282660i | 0.234819 | − | 0.972039i | \(-0.424550\pi\) |
−0.724401 | + | 0.689379i | \(0.757884\pi\) | |||||||
\(318\) | 9.05935 | − | 5.23042i | 0.508023 | − | 0.293307i | ||||
\(319\) | 25.7080 | + | 44.5275i | 1.43937 | + | 2.49306i | ||||
\(320\) | −0.806615 | + | 2.08551i | −0.0450911 | + | 0.116584i | ||||
\(321\) | −15.5261 | −0.866581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.5448i | − | 0.642371i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −5.68053 | + | 6.24502i | −0.315099 | + | 0.346412i | ||||
\(326\) | −0.269584 | − | 0.466934i | −0.0149309 | − | 0.0258611i | ||||
\(327\) | 10.1111 | + | 5.83767i | 0.559147 | + | 0.322824i | ||||
\(328\) | − | 5.14925i | − | 0.284320i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13.4935 | − | 2.10217i | 0.742790 | − | 0.115720i | ||||
\(331\) | −11.6399 | + | 20.1609i | −0.639785 | + | 1.10814i | 0.345694 | + | 0.938347i | \(0.387643\pi\) |
−0.985480 | + | 0.169794i | \(0.945690\pi\) | |||||||
\(332\) | 11.7139 | − | 6.76304i | 0.642885 | − | 0.371170i | ||||
\(333\) | 2.00189 | − | 1.15579i | 0.109703 | − | 0.0633370i | ||||
\(334\) | 1.57462 | − | 2.72733i | 0.0861596 | − | 0.149233i | ||||
\(335\) | −4.20433 | − | 26.9869i | −0.229707 | − | 1.47445i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.17250i | 0.281764i | 0.990026 | + | 0.140882i | \(0.0449938\pi\) | ||||
−0.990026 | + | 0.140882i | \(0.955006\pi\) | |||||||
\(338\) | 8.78951 | + | 5.07462i | 0.478086 | + | 0.276023i | ||||
\(339\) | 1.68842 | + | 2.92442i | 0.0917022 | + | 0.158833i | ||||
\(340\) | −11.9065 | + | 9.59189i | −0.645719 | + | 0.520193i | ||||
\(341\) | −2.10217 | + | 3.64106i | −0.113839 | + | 0.197174i | ||||
\(342\) | 1.68842i | 0.0912991i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 1.86456 | − | 4.82084i | 0.100384 | − | 0.259545i | ||||
\(346\) | −5.26304 | − | 9.11585i | −0.282943 | − | 0.490071i | ||||
\(347\) | 8.37908 | − | 4.83767i | 0.449813 | − | 0.259699i | −0.257938 | − | 0.966161i | \(-0.583043\pi\) |
0.707751 | + | 0.706462i | \(0.249710\pi\) | |||||||
\(348\) | 7.29092 | + | 4.20942i | 0.390834 | + | 0.225648i | ||||
\(349\) | 28.2985 | 1.51478 | 0.757392 | − | 0.652961i | \(-0.226473\pi\) | ||||
0.757392 | + | 0.652961i | \(0.226473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.68842 | 0.0901210 | ||||||||
\(352\) | 5.28903 | + | 3.05362i | 0.281906 | + | 0.162759i | ||||
\(353\) | −15.3073 | + | 8.83767i | −0.814725 | + | 0.470381i | −0.848594 | − | 0.529045i | \(-0.822550\pi\) |
0.0338693 | + | 0.999426i | \(0.489217\pi\) | |||||||
\(354\) | −3.52100 | − | 6.09855i | −0.187139 | − | 0.324134i | ||||
\(355\) | 4.83969 | − | 12.5131i | 0.256864 | − | 0.664126i | ||||
\(356\) | 12.2145 | 0.647367 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.93475i | 0.260810i | ||||||||
\(359\) | −2.41883 | + | 4.18954i | −0.127661 | + | 0.221116i | −0.922770 | − | 0.385351i | \(-0.874080\pi\) |
0.795109 | + | 0.606467i | \(0.207414\pi\) | |||||||
\(360\) | 1.74131 | − | 1.40280i | 0.0917749 | − | 0.0739341i | ||||
\(361\) | 8.07462 | + | 13.9857i | 0.424980 | + | 0.736087i | ||||
\(362\) | −5.30917 | − | 3.06525i | −0.279044 | − | 0.161106i | ||||
\(363\) | − | 26.2985i | − | 1.38031i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.37683 | + | 8.83767i | 0.0720668 | + | 0.462585i | ||||
\(366\) | −4.73042 | + | 8.19332i | −0.247263 | + | 0.428272i | ||||
\(367\) | −9.22007 | + | 5.32321i | −0.481284 | + | 0.277869i | −0.720951 | − | 0.692986i | \(-0.756295\pi\) |
0.239668 | + | 0.970855i | \(0.422962\pi\) | |||||||
\(368\) | 2.00189 | − | 1.15579i | 0.104356 | − | 0.0602498i | ||||
\(369\) | −2.57462 | + | 4.45938i | −0.134030 | + | 0.232146i | ||||
\(370\) | 5.10725 | − | 0.795666i | 0.265513 | − | 0.0413647i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.688417i | 0.0356928i | ||||||||
\(373\) | −30.0749 | − | 17.3637i | −1.55722 | − | 0.899061i | −0.997521 | − | 0.0703638i | \(-0.977584\pi\) |
−0.559698 | − | 0.828697i | \(-0.689083\pi\) | |||||||
\(374\) | 20.8797 | + | 36.1646i | 1.07966 | + | 1.87003i | ||||
\(375\) | 6.16025 | − | 9.33013i | 0.318114 | − | 0.481806i | ||||
\(376\) | −1.53263 | + | 2.65458i | −0.0790391 | + | 0.136900i | ||||
\(377\) | 14.2145i | 0.732084i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4477 | 0.998964 | 0.499482 | − | 0.866324i | \(-0.333524\pi\) | ||||
0.499482 | + | 0.866324i | \(0.333524\pi\) | |||||||
\(380\) | −1.36190 | + | 3.52122i | −0.0698641 | + | 0.180635i | ||||
\(381\) | −2.47246 | − | 4.28242i | −0.126668 | − | 0.219395i | ||||
\(382\) | 12.9225 | − | 7.46083i | 0.661175 | − | 0.381729i | ||||
\(383\) | −0.736772 | − | 0.425376i | −0.0376473 | − | 0.0217357i | 0.481058 | − | 0.876689i | \(-0.340253\pi\) |
−0.518706 | + | 0.854953i | \(0.673586\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.58117 | −0.284074 | ||||||||
\(387\) | −1.73205 | − | 1.00000i | −0.0880451 | − | 0.0508329i | ||||
\(388\) | 4.29375 | − | 2.47900i | 0.217982 | − | 0.125852i | ||||
\(389\) | 13.1492 | + | 22.7752i | 0.666693 | + | 1.15475i | 0.978823 | + | 0.204707i | \(0.0656243\pi\) |
−0.312130 | + | 0.950039i | \(0.601042\pi\) | |||||||
\(390\) | 3.52122 | + | 1.36190i | 0.178304 | + | 0.0689626i | ||||
\(391\) | 15.8058 | 0.799335 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.73042i | − | 0.339505i | ||||||
\(394\) | 7.26304 | − | 12.5800i | 0.365907 | − | 0.633769i | ||||
\(395\) | −10.2567 | − | 12.7317i | −0.516071 | − | 0.640602i | ||||
\(396\) | −3.05362 | − | 5.28903i | −0.153450 | − | 0.265784i | ||||
\(397\) | 1.47354 | + | 0.850752i | 0.0739551 | + | 0.0426980i | 0.536522 | − | 0.843887i | \(-0.319738\pi\) |
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(398\) | 8.62317i | 0.432240i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.76304 | − | 1.52100i | 0.238152 | − | 0.0760500i | ||||
\(401\) | −1.50937 | + | 2.61431i | −0.0753745 | + | 0.130553i | −0.901249 | − | 0.433301i | \(-0.857349\pi\) |
0.825875 | + | 0.563854i | \(0.190682\pi\) | |||||||
\(402\) | −10.5781 | + | 6.10725i | −0.527586 | + | 0.304602i | ||||
\(403\) | −1.00661 | + | 0.581167i | −0.0501429 | + | 0.0289500i | ||||
\(404\) | 4.00000 | − | 6.92820i | 0.199007 | − | 0.344691i | ||||
\(405\) | −2.20942 | + | 0.344208i | −0.109787 | + | 0.0171039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.1174i | − | 0.699774i | ||||||
\(408\) | 5.92159 | + | 3.41883i | 0.293162 | + | 0.169257i | ||||
\(409\) | 2.07462 | + | 3.59335i | 0.102584 | + | 0.177680i | 0.912748 | − | 0.408522i | \(-0.133956\pi\) |
−0.810165 | + | 0.586202i | \(0.800622\pi\) | |||||||
\(410\) | −8.96642 | + | 7.22337i | −0.442820 | + | 0.356737i | ||||
\(411\) | 9.52608 | − | 16.4997i | 0.469887 | − | 0.813868i | ||||
\(412\) | 0.837665i | 0.0412688i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.31158 | −0.113608 | ||||||||
\(415\) | −28.2088 | − | 10.9103i | −1.38472 | − | 0.535568i | ||||
\(416\) | 0.844208 | + | 1.46221i | 0.0413907 | + | 0.0716908i | ||||
\(417\) | −11.5847 | + | 6.68842i | −0.567304 | + | 0.327533i | ||||
\(418\) | 8.93009 | + | 5.15579i | 0.436785 | + | 0.252178i | ||||
\(419\) | 13.8189 | 0.675098 | 0.337549 | − | 0.941308i | \(-0.390402\pi\) | ||||
0.337549 | + | 0.941308i | \(0.390402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2667 | 1.23142 | 0.615711 | − | 0.787972i | \(-0.288869\pi\) | ||||
0.615711 | + | 0.787972i | \(0.288869\pi\) | |||||||
\(422\) | −6.65836 | − | 3.84421i | −0.324124 | − | 0.187133i | ||||
\(423\) | 2.65458 | − | 1.53263i | 0.129070 | − | 0.0745188i | ||||
\(424\) | −5.23042 | − | 9.05935i | −0.254011 | − | 0.439961i | ||||
\(425\) | 33.4048 | + | 7.27730i | 1.62037 | + | 0.353001i | ||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.5261i | 0.750482i | ||||||||
\(429\) | 5.15579 | − | 8.93009i | 0.248924 | − | 0.431149i | ||||
\(430\) | −2.80560 | − | 3.48261i | −0.135298 | − | 0.167947i | ||||
\(431\) | −9.77241 | − | 16.9263i | −0.470721 | − | 0.815312i | 0.528719 | − | 0.848797i | \(-0.322673\pi\) |
−0.999439 | + | 0.0334851i | \(0.989339\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 14.7537i | 0.709016i | 0.935053 | + | 0.354508i | \(0.115352\pi\) | ||||
−0.935053 | + | 0.354508i | \(0.884648\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.89783 | − | 18.6007i | −0.138940 | − | 0.891836i | ||||
\(436\) | 5.83767 | − | 10.1111i | 0.279573 | − | 0.484235i | ||||
\(437\) | 3.38002 | − | 1.95146i | 0.161688 | − | 0.0933509i | ||||
\(438\) | 3.46410 | − | 2.00000i | 0.165521 | − | 0.0955637i | ||||
\(439\) | 7.96737 | − | 13.7999i | 0.380262 | − | 0.658633i | −0.610838 | − | 0.791756i | \(-0.709167\pi\) |
0.991100 | + | 0.133123i | \(0.0425005\pi\) | |||||||
\(440\) | −2.10217 | − | 13.4935i | −0.100217 | − | 0.643275i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.5448i | 0.549132i | ||||||||
\(443\) | −18.9006 | − | 10.9123i | −0.897997 | − | 0.518459i | −0.0214469 | − | 0.999770i | \(-0.506827\pi\) |
−0.876550 | + | 0.481311i | \(0.840161\pi\) | |||||||
\(444\) | −1.15579 | − | 2.00189i | −0.0548514 | − | 0.0950055i | ||||
\(445\) | −17.1345 | − | 21.2692i | −0.812254 | − | 1.00826i | ||||
\(446\) | −5.58625 | + | 9.67567i | −0.264517 | + | 0.458156i | ||||
\(447\) | 12.6232i | 0.597055i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3637 | 0.536288 | 0.268144 | − | 0.963379i | \(-0.413590\pi\) | ||||
0.268144 | + | 0.963379i | \(0.413590\pi\) | |||||||
\(450\) | −4.88541 | − | 1.06430i | −0.230301 | − | 0.0501714i | ||||
\(451\) | 15.7239 | + | 27.2345i | 0.740408 | + | 1.28242i | ||||
\(452\) | 2.92442 | − | 1.68842i | 0.137553 | − | 0.0794164i | ||||
\(453\) | 1.67554 | + | 0.967375i | 0.0787238 | + | 0.0454512i | ||||
\(454\) | 3.85075 | 0.180725 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.68842 | 0.0790674 | ||||||||
\(457\) | 5.55887 | + | 3.20942i | 0.260033 | + | 0.150130i | 0.624350 | − | 0.781145i | \(-0.285364\pi\) |
−0.364317 | + | 0.931275i | \(0.618697\pi\) | |||||||
\(458\) | −4.91498 | + | 2.83767i | −0.229662 | + | 0.132595i | ||||
\(459\) | −3.41883 | − | 5.92159i | −0.159577 | − | 0.276396i | ||||
\(460\) | −4.82084 | − | 1.86456i | −0.224773 | − | 0.0869354i | ||||
\(461\) | −1.50733 | −0.0702036 | −0.0351018 | − | 0.999384i | \(-0.511176\pi\) | ||||
−0.0351018 | + | 0.999384i | \(0.511176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.1174i | − | 1.12083i | −0.828211 | − | 0.560416i | \(-0.810641\pi\) | ||
0.828211 | − | 0.560416i | \(-0.189359\pi\) | |||||||
\(464\) | 4.20942 | − | 7.29092i | 0.195417 | − | 0.338473i | ||||
\(465\) | 1.19874 | − | 0.965712i | 0.0555905 | − | 0.0447838i | ||||
\(466\) | 5.73042 | + | 9.92537i | 0.265456 | + | 0.459784i | ||||
\(467\) | −20.3904 | − | 11.7724i | −0.943556 | − | 0.544762i | −0.0524828 | − | 0.998622i | \(-0.516713\pi\) |
−0.891073 | + | 0.453859i | \(0.850047\pi\) | |||||||
\(468\) | − | 1.68842i | − | 0.0780471i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.77241 | − | 1.05509i | 0.312388 | − | 0.0486674i | ||||
\(471\) | −8.57462 | + | 14.8517i | −0.395098 | + | 0.684330i | ||||
\(472\) | −6.09855 | + | 3.52100i | −0.280709 | + | 0.162067i | ||||
\(473\) | −10.5781 | + | 6.10725i | −0.486380 | + | 0.280812i | ||||
\(474\) | −3.65579 | + | 6.33202i | −0.167916 | + | 0.290839i | ||||
\(475\) | 8.04200 | − | 2.56808i | 0.368992 | − | 0.117832i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4608i | 0.478969i | ||||||||
\(478\) | −13.3895 | − | 7.73042i | −0.612420 | − | 0.353581i | ||||
\(479\) | −14.9869 | − | 25.9581i | −0.684770 | − | 1.18606i | −0.973509 | − | 0.228648i | \(-0.926570\pi\) |
0.288740 | − | 0.957408i | \(-0.406764\pi\) | |||||||
\(480\) | −1.40280 | − | 1.74131i | −0.0640288 | − | 0.0794794i | ||||
\(481\) | 1.95146 | − | 3.38002i | 0.0889788 | − | 0.154116i | ||||
\(482\) | 4.37683i | 0.199359i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.2985 | −1.19539 | ||||||||
\(485\) | −10.3400 | − | 3.99920i | −0.469515 | − | 0.181594i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 26.4162 | − | 15.2514i | 1.19703 | − | 0.691108i | 0.237141 | − | 0.971475i | \(-0.423790\pi\) |
0.959893 | + | 0.280368i | \(0.0904564\pi\) | |||||||
\(488\) | 8.19332 | + | 4.73042i | 0.370894 | + | 0.214136i | ||||
\(489\) | 0.539168 | 0.0243820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.87966 | −0.175087 | −0.0875434 | − | 0.996161i | \(-0.527902\pi\) | ||||
−0.0875434 | + | 0.996161i | \(0.527902\pi\) | |||||||
\(492\) | 4.45938 | + | 2.57462i | 0.201044 | + | 0.116073i | ||||
\(493\) | 49.8529 | − | 28.7826i | 2.24526 | − | 1.29630i | ||||
\(494\) | 1.42538 | + | 2.46882i | 0.0641307 | + | 0.111078i | ||||
\(495\) | −4.92620 | + | 12.7368i | −0.221416 | + | 0.572475i | ||||
\(496\) | 0.688417 | 0.0309108 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.5261i | 0.606118i | ||||||||
\(499\) | 4.68842 | − | 8.12058i | 0.209882 | − | 0.363527i | −0.741795 | − | 0.670627i | \(-0.766025\pi\) |
0.951677 | + | 0.307100i | \(0.0993586\pi\) | |||||||
\(500\) | −9.33013 | − | 6.16025i | −0.417256 | − | 0.275495i | ||||
\(501\) | 1.57462 | + | 2.72733i | 0.0703490 | + | 0.121848i | ||||
\(502\) | 22.9811 | + | 13.2681i | 1.02570 | + | 0.592185i | ||||
\(503\) | − | 14.2145i | − | 0.633793i | −0.948460 | − | 0.316897i | \(-0.897359\pi\) | ||
0.948460 | − | 0.316897i | \(-0.102641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6753 | + | 2.75367i | −0.786542 | + | 0.122537i | ||||
\(506\) | −7.05871 | + | 12.2260i | −0.313798 | + | 0.543514i | ||||
\(507\) | −8.78951 | + | 5.07462i | −0.390356 | + | 0.225372i | ||||
\(508\) | −4.28242 | + | 2.47246i | −0.190002 | + | 0.109698i | ||||
\(509\) | −15.9818 | + | 27.6813i | −0.708382 | + | 1.22695i | 0.257075 | + | 0.966392i | \(0.417241\pi\) |
−0.965457 | + | 0.260562i | \(0.916092\pi\) | |||||||
\(510\) | −2.35358 | − | 15.1072i | −0.104218 | − | 0.668960i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −1.46221 | − | 0.844208i | −0.0645582 | − | 0.0372727i | ||||
\(514\) | −11.2145 | − | 19.4241i | −0.494650 | − | 0.856760i | ||||
\(515\) | 1.45863 | − | 1.17508i | 0.0642750 | − | 0.0517801i | ||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | − | 18.7203i | − | 0.823316i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.5261 | 0.462044 | ||||||||
\(520\) | 1.36190 | − | 3.52122i | 0.0597234 | − | 0.154416i | ||||
\(521\) | −18.1007 | − | 31.3513i | −0.793006 | − | 1.37353i | −0.924097 | − | 0.382157i | \(-0.875181\pi\) |
0.131091 | − | 0.991370i | \(-0.458152\pi\) | |||||||
\(522\) | −7.29092 | + | 4.20942i | −0.319115 | + | 0.184241i | ||||
\(523\) | −32.0154 | − | 18.4841i | −1.39993 | − | 0.808253i | −0.405549 | − | 0.914073i | \(-0.632920\pi\) |
−0.994385 | + | 0.105821i | \(0.966253\pi\) | |||||||
\(524\) | −6.73042 | −0.294020 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.5913 | −0.854223 | ||||||||
\(527\) | 4.07652 | + | 2.35358i | 0.177576 | + | 0.102524i | ||||
\(528\) | −5.28903 | + | 3.05362i | −0.230176 | + | 0.132892i | ||||
\(529\) | −8.82829 | − | 15.2910i | −0.383839 | − | 0.664828i | ||||
\(530\) | −8.43786 | + | 21.8162i | −0.366517 | + | 0.947636i | ||||
\(531\) | 7.04200 | 0.305597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.69408i | 0.376582i | ||||||||
\(534\) | −6.10725 | + | 10.5781i | −0.264287 | + | 0.457758i | ||||
\(535\) | 27.0357 | − | 21.7800i | 1.16885 | − | 0.941632i | ||||
\(536\) | 6.10725 | + | 10.5781i | 0.263793 | + | 0.456903i | ||||
\(537\) | −4.27362 | − | 2.46737i | −0.184420 | − | 0.106475i | ||||
\(538\) | 6.95800i | 0.299981i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.344208 | + | 2.20942i | 0.0148124 | + | 0.0950781i | ||||
\(541\) | 8.63333 | − | 14.9534i | 0.371176 | − | 0.642896i | −0.618571 | − | 0.785729i | \(-0.712288\pi\) |
0.989747 | + | 0.142834i | \(0.0456213\pi\) | |||||||
\(542\) | −24.5637 | + | 14.1819i | −1.05510 | + | 0.609164i | ||||
\(543\) | 5.30917 | − | 3.06525i | 0.227838 | − | 0.131542i | ||||
\(544\) | 3.41883 | − | 5.92159i | 0.146581 | − | 0.253886i | ||||
\(545\) | −25.7957 | + | 4.01875i | −1.10496 | + | 0.172144i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.4347i | − | 1.68610i | −0.537832 | − | 0.843052i | \(-0.680756\pi\) | ||
0.537832 | − | 0.843052i | \(-0.319244\pi\) | |||||||
\(548\) | −16.4997 | − | 9.52608i | −0.704830 | − | 0.406934i | ||||
\(549\) | −4.73042 | − | 8.19332i | −0.201889 | − | 0.349682i | ||||
\(550\) | −20.5473 | + | 22.5892i | −0.876141 | + | 0.963205i | ||||
\(551\) | 7.10725 | − | 12.3101i | 0.302779 | − | 0.524429i | ||||
\(552\) | 2.31158i | 0.0983875i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.05216 | −0.214646 | ||||||||
\(555\) | −1.86456 | + | 4.82084i | −0.0791461 | + | 0.204633i | ||||
\(556\) | 6.68842 | + | 11.5847i | 0.283652 | + | 0.491300i | ||||
\(557\) | 28.4834 | − | 16.4449i | 1.20688 | − | 0.696793i | 0.244805 | − | 0.969572i | \(-0.421276\pi\) |
0.962077 | + | 0.272779i | \(0.0879428\pi\) | |||||||
\(558\) | −0.596186 | − | 0.344208i | −0.0252386 | − | 0.0145715i | ||||
\(559\) | −3.37683 | −0.142825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.7593 | −1.76308 | ||||||||
\(562\) | 6.65836 | + | 3.84421i | 0.280866 | + | 0.162158i | ||||
\(563\) | 30.4853 | − | 17.6007i | 1.28480 | − | 0.741781i | 0.307081 | − | 0.951684i | \(-0.400648\pi\) |
0.977722 | + | 0.209902i | \(0.0673146\pi\) | |||||||
\(564\) | −1.53263 | − | 2.65458i | −0.0645352 | − | 0.111778i | ||||
\(565\) | −7.04244 | − | 2.72380i | −0.296278 | − | 0.114591i | ||||
\(566\) | −18.4290 | −0.774629 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 8.74712 | − | 15.1505i | 0.366699 | − | 0.635140i | −0.622349 | − | 0.782740i | \(-0.713821\pi\) |
0.989047 | + | 0.147600i | \(0.0471547\pi\) | |||||||
\(570\) | −2.36851 | − | 2.94005i | −0.0992061 | − | 0.123145i | ||||
\(571\) | −4.41883 | − | 7.65364i | −0.184922 | − | 0.320295i | 0.758628 | − | 0.651524i | \(-0.225870\pi\) |
−0.943550 | + | 0.331229i | \(0.892537\pi\) | |||||||
\(572\) | −8.93009 | − | 5.15579i | −0.373386 | − | 0.215574i | ||||
\(573\) | 14.9217i | 0.623361i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.51592 | + | 11.0102i | 0.146624 | + | 0.459156i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −34.9083 | + | 20.1543i | −1.45325 | + | 0.839036i | −0.998664 | − | 0.0516659i | \(-0.983547\pi\) |
−0.454588 | + | 0.890702i | \(0.650214\pi\) | |||||||
\(578\) | 25.7674 | − | 14.8768i | 1.07178 | − | 0.618795i | ||||
\(579\) | 2.79058 | − | 4.83343i | 0.115973 | − | 0.200871i | ||||
\(580\) | −18.6007 | + | 2.89783i | −0.772352 | + | 0.120326i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.95800i | 0.205516i | ||||||||
\(583\) | 55.3277 | + | 31.9435i | 2.29144 | + | 1.32296i | ||||
\(584\) | −2.00000 | − | 3.46410i | −0.0827606 | − | 0.143346i | ||||
\(585\) | −2.94005 | + | 2.36851i | −0.121556 | + | 0.0979260i | ||||
\(586\) | −0.918833 | + | 1.59146i | −0.0379566 | + | 0.0657428i | ||||
\(587\) | 36.1492i | 1.49204i | 0.665924 | + | 0.746020i | \(0.268037\pi\) | ||||
−0.665924 | + | 0.746020i | \(0.731963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.16233 | 0.0478932 | ||||||||
\(590\) | 14.6862 | + | 5.68018i | 0.604621 | + | 0.233849i | ||||
\(591\) | 7.26304 | + | 12.5800i | 0.298762 | + | 0.517470i | ||||
\(592\) | −2.00189 | + | 1.15579i | −0.0822772 | + | 0.0475027i | ||||
\(593\) | −3.53685 | − | 2.04200i | −0.145241 | − | 0.0838548i | 0.425619 | − | 0.904903i | \(-0.360057\pi\) |
−0.570859 | + | 0.821048i | \(0.693390\pi\) | |||||||
\(594\) | 6.10725 | 0.250583 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.6232 | 0.517065 | ||||||||
\(597\) | −7.46788 | − | 4.31158i | −0.305640 | − | 0.176461i | ||||
\(598\) | −3.38002 | + | 1.95146i | −0.138219 | + | 0.0798011i | ||||
\(599\) | −9.87966 | − | 17.1121i | −0.403672 | − | 0.699181i | 0.590494 | − | 0.807042i | \(-0.298933\pi\) |
−0.994166 | + | 0.107862i | \(0.965600\pi\) | |||||||
\(600\) | −1.06430 | + | 4.88541i | −0.0434497 | + | 0.199446i | ||||
\(601\) | −3.72025 | −0.151752 | −0.0758761 | − | 0.997117i | \(-0.524175\pi\) | ||||
−0.0758761 | + | 0.997117i | \(0.524175\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.2145i | − | 0.497413i | ||||||
\(604\) | 0.967375 | − | 1.67554i | 0.0393619 | − | 0.0681768i | ||||
\(605\) | 36.8916 | + | 45.7937i | 1.49986 | + | 1.86178i | ||||
\(606\) | 4.00000 | + | 6.92820i | 0.162489 | + | 0.281439i | ||||
\(607\) | −9.73708 | − | 5.62171i | −0.395216 | − | 0.228178i | 0.289202 | − | 0.957268i | \(-0.406610\pi\) |
−0.684418 | + | 0.729090i | \(0.739943\pi\) | |||||||
\(608\) | − | 1.68842i | − | 0.0684743i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.25650 | − | 20.9029i | −0.131852 | − | 0.846334i | ||||
\(611\) | 2.58771 | − | 4.48205i | 0.104688 | − | 0.181324i | ||||
\(612\) | −5.92159 | + | 3.41883i | −0.239366 | + | 0.138198i | ||||
\(613\) | −23.3262 | + | 13.4674i | −0.942135 | + | 0.543942i | −0.890629 | − | 0.454731i | \(-0.849736\pi\) |
−0.0515063 | + | 0.998673i | \(0.516402\pi\) | |||||||
\(614\) | 8.04200 | − | 13.9292i | 0.324549 | − | 0.562135i | ||||
\(615\) | −1.77241 | − | 11.3768i | −0.0714707 | − | 0.458758i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4608i | 1.34708i | 0.739150 | + | 0.673541i | \(0.235228\pi\) | ||||
−0.739150 | + | 0.673541i | \(0.764772\pi\) | |||||||
\(618\) | −0.725439 | − | 0.418833i | −0.0291815 | − | 0.0168479i | ||||
\(619\) | 17.4355 | + | 30.1992i | 0.700794 | + | 1.21381i | 0.968188 | + | 0.250223i | \(0.0805039\pi\) |
−0.267395 | + | 0.963587i | \(0.586163\pi\) | |||||||
\(620\) | −0.965712 | − | 1.19874i | −0.0387839 | − | 0.0481427i | ||||
\(621\) | 1.15579 | − | 2.00189i | 0.0463803 | − | 0.0803331i | ||||
\(622\) | − | 15.3768i | − | 0.616555i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.68842 | −0.0675908 | ||||||||
\(625\) | 2.36143 | + | 24.8882i | 0.0944570 | + | 0.995529i | ||||
\(626\) | −11.2094 | − | 19.4153i | −0.448018 | − | 0.775991i | ||||
\(627\) | −8.93009 | + | 5.15579i | −0.356634 | + | 0.205902i | ||||
\(628\) | 14.8517 | + | 8.57462i | 0.592647 | + | 0.342165i | ||||
\(629\) | −15.8058 | −0.630220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4942 | −0.417769 | −0.208885 | − | 0.977940i | \(-0.566983\pi\) | ||||
−0.208885 | + | 0.977940i | \(0.566983\pi\) | |||||||
\(632\) | 6.33202 | + | 3.65579i | 0.251874 | + | 0.145420i | ||||
\(633\) | 6.65836 | − | 3.84421i | 0.264646 | − | 0.152794i | ||||
\(634\) | −5.03263 | − | 8.71676i | −0.199871 | − | 0.346187i | ||||
\(635\) | 10.3127 | + | 3.98864i | 0.409247 | + | 0.158284i | ||||
\(636\) | 10.4608 | 0.414799 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 51.4159i | 2.03558i | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | −1.74131 | + | 1.40280i | −0.0688312 | + | 0.0554506i | ||||
\(641\) | −3.88621 | − | 6.73111i | −0.153496 | − | 0.265863i | 0.779014 | − | 0.627006i | \(-0.215720\pi\) |
−0.932510 | + | 0.361143i | \(0.882387\pi\) | |||||||
\(642\) | −13.4460 | − | 7.76304i | −0.530671 | − | 0.306383i | ||||
\(643\) | − | 21.7218i | − | 0.856626i | −0.903631 | − | 0.428313i | \(-0.859108\pi\) | ||
0.903631 | − | 0.428313i | \(-0.140892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.41883 | − | 0.688417i | 0.173991 | − | 0.0271064i | ||||
\(646\) | 5.77241 | − | 9.99812i | 0.227113 | − | 0.393371i | ||||
\(647\) | −8.27740 | + | 4.77896i | −0.325418 | + | 0.187880i | −0.653805 | − | 0.756663i | \(-0.726828\pi\) |
0.328387 | + | 0.944543i | \(0.393495\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 21.5036 | − | 37.2454i | 0.844091 | − | 1.46201i | ||||
\(650\) | −8.04200 | + | 2.56808i | −0.315433 | + | 0.100728i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 0.539168i | − | 0.0211155i | ||||||
\(653\) | 43.5322 | + | 25.1333i | 1.70355 | + | 0.983543i | 0.942110 | + | 0.335304i | \(0.108839\pi\) |
0.761437 | + | 0.648239i | \(0.224494\pi\) | |||||||
\(654\) | 5.83767 | + | 10.1111i | 0.228271 | + | 0.395377i | ||||
\(655\) | 9.44144 | + | 11.7197i | 0.368907 | + | 0.457927i | ||||
\(656\) | 2.57462 | − | 4.45938i | 0.100522 | − | 0.174110i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1623 | −0.434823 | −0.217411 | − | 0.976080i | \(-0.569761\pi\) | ||||
−0.217411 | + | 0.976080i | \(0.569761\pi\) | |||||||
\(660\) | 12.7368 | + | 4.92620i | 0.495778 | + | 0.191752i | ||||
\(661\) | 7.17250 | + | 12.4231i | 0.278978 | + | 0.483204i | 0.971131 | − | 0.238547i | \(-0.0766710\pi\) |
−0.692153 | + | 0.721751i | \(0.743338\pi\) | |||||||
\(662\) | −20.1609 | + | 11.6399i | −0.783574 | + | 0.452397i | ||||
\(663\) | −9.99812 | − | 5.77241i | −0.388295 | − | 0.224182i | ||||
\(664\) | 13.5261 | 0.524914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.31158 | 0.0895720 | ||||||||
\(667\) | 16.8536 | + | 9.73042i | 0.652573 | + | 0.376763i | ||||
\(668\) | 2.72733 | − | 1.57462i | 0.105524 | − | 0.0609240i | ||||
\(669\) | −5.58625 | − | 9.67567i | −0.215977 | − | 0.374083i | ||||
\(670\) | 9.85240 | − | 25.4735i | 0.380631 | − | 0.984128i | ||||
\(671\) | −57.7797 | −2.23056 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.8013i | − | 1.18730i | −0.804722 | − | 0.593652i | \(-0.797686\pi\) | ||
0.804722 | − | 0.593652i | \(-0.202314\pi\) | |||||||
\(674\) | −2.58625 | + | 4.47952i | −0.0996186 | + | 0.172545i | ||||
\(675\) | 3.36441 | − | 3.69874i | 0.129496 | − | 0.142365i | ||||
\(676\) | 5.07462 | + | 8.78951i | 0.195178 | + | 0.338058i | ||||
\(677\) | −12.2649 | − | 7.08117i | −0.471380 | − | 0.272151i | 0.245437 | − | 0.969412i | \(-0.421068\pi\) |
−0.716817 | + | 0.697261i | \(0.754402\pi\) | |||||||
\(678\) | 3.37683i | 0.129687i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15.1072 | + | 2.35358i | −0.579337 | + | 0.0902558i | ||||
\(681\) | −1.92538 | + | 3.33485i | −0.0737806 | + | 0.127792i | ||||
\(682\) | −3.64106 | + | 2.10217i | −0.139423 | + | 0.0804961i | ||||
\(683\) | 26.5946 | − | 15.3544i | 1.01761 | − | 0.587519i | 0.104201 | − | 0.994556i | \(-0.466771\pi\) |
0.913411 | + | 0.407037i | \(0.133438\pi\) | |||||||
\(684\) | −0.844208 | + | 1.46221i | −0.0322791 | + | 0.0559091i | ||||
\(685\) | 6.55792 | + | 42.0942i | 0.250565 | + | 1.60834i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.67533i | − | 0.216527i | ||||||
\(688\) | 1.73205 | + | 1.00000i | 0.0660338 | + | 0.0381246i | ||||
\(689\) | 8.83112 | + | 15.2960i | 0.336439 | + | 0.582729i | ||||
\(690\) | 4.02517 | − | 3.24269i | 0.153236 | − | 0.123447i | ||||
\(691\) | −19.6753 | + | 34.0787i | −0.748485 | + | 1.29641i | 0.200064 | + | 0.979783i | \(0.435885\pi\) |
−0.948549 | + | 0.316631i | \(0.897448\pi\) | |||||||
\(692\) | − | 10.5261i | − | 0.400142i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.67533 | 0.367271 | ||||||||
\(695\) | 10.7900 | − | 27.8976i | 0.409286 | − | 1.05822i | ||||
\(696\) | 4.20942 | + | 7.29092i | 0.159558 | + | 0.276362i | ||||
\(697\) | 30.4917 | − | 17.6044i | 1.15496 | − | 0.666815i | ||||
\(698\) | 24.5072 | + | 14.1492i | 0.927612 | + | 0.535557i | ||||
\(699\) | −11.4608 | −0.433488 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.79567 | −0.143360 | −0.0716802 | − | 0.997428i | \(-0.522836\pi\) | ||||
−0.0716802 | + | 0.997428i | \(0.522836\pi\) | |||||||
\(702\) | 1.46221 | + | 0.844208i | 0.0551876 | + | 0.0318626i | ||||
\(703\) | −3.38002 | + | 1.95146i | −0.127480 | + | 0.0736006i | ||||
\(704\) | 3.05362 | + | 5.28903i | 0.115088 | + | 0.199338i | ||||
\(705\) | −2.47248 | + | 6.39263i | −0.0931189 | + | 0.240760i | ||||
\(706\) | −17.6753 | −0.665220 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 7.04200i | − | 0.264655i | ||||||
\(709\) | −10.2797 | + | 17.8050i | −0.386064 | + | 0.668683i | −0.991916 | − | 0.126895i | \(-0.959499\pi\) |
0.605852 | + | 0.795577i | \(0.292832\pi\) | |||||||
\(710\) | 10.4478 | − | 8.41681i | 0.392100 | − | 0.315877i | ||||
\(711\) | −3.65579 | − | 6.33202i | −0.137103 | − | 0.237469i | ||||
\(712\) | 10.5781 | + | 6.10725i | 0.396430 | + | 0.228879i | ||||
\(713\) | 1.59133i | 0.0595959i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.54933 | + | 22.7826i | 0.132738 | + | 0.852020i | ||||
\(716\) | −2.46737 | + | 4.27362i | −0.0922101 | + | 0.159713i | ||||
\(717\) | 13.3895 | − | 7.73042i | 0.500039 | − | 0.288698i | ||||
\(718\) | −4.18954 | + | 2.41883i | −0.156352 | + | 0.0902700i | ||||
\(719\) | 12.4057 | − | 21.4874i | 0.462656 | − | 0.801344i | −0.536436 | − | 0.843941i | \(-0.680230\pi\) |
0.999092 | + | 0.0425968i | \(0.0135631\pi\) | |||||||
\(720\) | 2.20942 | − | 0.344208i | 0.0823401 | − | 0.0128279i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.1492i | 0.601013i | ||||||||
\(723\) | −3.79045 | − | 2.18842i | −0.140968 | − | 0.0813881i | ||||
\(724\) | −3.06525 | − | 5.30917i | −0.113919 | − | 0.197314i | ||||
\(725\) | 31.1391 | + | 28.3244i | 1.15648 | + | 1.05194i | ||||
\(726\) | 13.1492 | − | 22.7752i | 0.488014 | − | 0.845266i | ||||
\(727\) | − | 39.2899i | − | 1.45718i | −0.684949 | − | 0.728591i | \(-0.740175\pi\) | ||
0.684949 | − | 0.728591i | \(-0.259825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.22646 | + | 8.34206i | −0.119417 | + | 0.308753i | ||||
\(731\) | 6.83767 | + | 11.8432i | 0.252900 | + | 0.438036i | ||||
\(732\) | −8.19332 | + | 4.73042i | −0.302834 | + | 0.174841i | ||||
\(733\) | −7.81046 | − | 4.50937i | −0.288486 | − | 0.166558i | 0.348773 | − | 0.937207i | \(-0.386598\pi\) |
−0.637259 | + | 0.770650i | \(0.719932\pi\) | |||||||
\(734\) | −10.6464 | −0.392966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.31158 | 0.0852061 | ||||||||
\(737\) | −64.6029 | − | 37.2985i | −2.37968 | − | 1.37391i | ||||
\(738\) | −4.45938 | + | 2.57462i | −0.164152 | + | 0.0947732i | ||||
\(739\) | −7.03546 | − | 12.1858i | −0.258803 | − | 0.448261i | 0.707118 | − | 0.707095i | \(-0.249995\pi\) |
−0.965922 | + | 0.258835i | \(0.916662\pi\) | |||||||
\(740\) | 4.82084 | + | 1.86456i | 0.177218 | + | 0.0685425i | ||||
\(741\) | −2.85075 | −0.104725 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 39.1492i | − | 1.43625i | −0.695916 | − | 0.718123i | \(-0.745001\pi\) | ||
0.695916 | − | 0.718123i | \(-0.254999\pi\) | |||||||
\(744\) | −0.344208 | + | 0.596186i | −0.0126193 | + | 0.0218573i | ||||
\(745\) | −17.7078 | − | 21.9808i | −0.648763 | − | 0.805314i | ||||
\(746\) | −17.3637 | − | 30.0749i | −0.635732 | − | 1.10112i | ||||
\(747\) | −11.7139 | − | 6.76304i | −0.428590 | − | 0.247447i | ||||
\(748\) | 41.7593i | 1.52687i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.0000 | − | 5.00000i | 0.365148 | − | 0.182574i | ||||
\(751\) | 19.6427 | − | 34.0222i | 0.716773 | − | 1.24149i | −0.245499 | − | 0.969397i | \(-0.578952\pi\) |
0.962272 | − | 0.272090i | \(-0.0877147\pi\) | |||||||
\(752\) | −2.65458 | + | 1.53263i | −0.0968028 | + | 0.0558891i | ||||
\(753\) | −22.9811 | + | 13.2681i | −0.837477 | + | 0.483517i | ||||
\(754\) | −7.10725 | + | 12.3101i | −0.258831 | + | 0.448308i | ||||
\(755\) | −4.27467 | + | 0.665957i | −0.155571 | + | 0.0242367i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.9217i | 1.05118i | 0.850739 | + | 0.525588i | \(0.176155\pi\) | ||||
−0.850739 | + | 0.525588i | \(0.823845\pi\) | |||||||
\(758\) | 16.8422 | + | 9.72387i | 0.611738 | + | 0.353187i | ||||
\(759\) | −7.05871 | − | 12.2260i | −0.256215 | − | 0.443777i | ||||
\(760\) | −2.94005 | + | 2.36851i | −0.106647 | + | 0.0859150i | ||||
\(761\) | 7.77896 | − | 13.4736i | 0.281987 | − | 0.488416i | −0.689887 | − | 0.723917i | \(-0.742340\pi\) |
0.971874 | + | 0.235501i | \(0.0756732\pi\) | |||||||
\(762\) | − | 4.94491i | − | 0.179135i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.9217 | 0.539847 | ||||||||
\(765\) | 14.2601 | + | 5.51536i | 0.515573 | + | 0.199408i | ||||
\(766\) | −0.425376 | − | 0.736772i | −0.0153695 | − | 0.0266207i | ||||
\(767\) | 10.2969 | − | 5.94491i | 0.371799 | − | 0.214658i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −4.05216 | −0.146125 | −0.0730624 | − | 0.997327i | \(-0.523277\pi\) | ||||
−0.0730624 | + | 0.997327i | \(0.523277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4290 | 0.807761 | ||||||||
\(772\) | −4.83343 | − | 2.79058i | −0.173959 | − | 0.100435i | ||||
\(773\) | 18.5743 | − | 10.7239i | 0.668071 | − | 0.385711i | −0.127274 | − | 0.991868i | \(-0.540623\pi\) |
0.795345 | + | 0.606157i | \(0.207290\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | −0.732680 | + | 3.36320i | −0.0263186 | + | 0.120810i | ||||
\(776\) | 4.95800 | 0.177982 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.2985i | 0.942847i | ||||||||
\(779\) | 4.34704 | − | 7.52929i | 0.155749 | − | 0.269765i | ||||
\(780\) | 2.36851 | + | 2.94005i | 0.0848064 | + | 0.105271i | ||||
\(781\) | −18.3217 | − | 31.7342i | −0.655604 | − | 1.13554i | ||||
\(782\) | 13.6883 | + | 7.90292i | 0.489491 | + | 0.282608i | ||||
\(783\) | − | 8.41883i | − | 0.300865i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.90292 | − | 37.8898i | −0.210684 | − | 1.35235i | ||||
\(786\) | 3.36521 | − | 5.82871i | 0.120033 | − | 0.207903i | ||||
\(787\) | −3.74527 | + | 2.16233i | −0.133505 | + | 0.0770789i | −0.565265 | − | 0.824910i | \(-0.691226\pi\) |
0.431760 | + | 0.901988i | \(0.357893\pi\) | |||||||
\(788\) | 12.5800 | − | 7.26304i | 0.448142 | − | 0.258735i | ||||
\(789\) | 9.79567 | − | 16.9666i | 0.348735 | − | 0.604027i | ||||
\(790\) | −2.51671 | − | 16.1543i | −0.0895405 | − | 0.574745i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 6.10725i | − | 0.217012i | ||||||
\(793\) | −13.8337 | − | 7.98691i | −0.491251 | − | 0.283624i | ||||
\(794\) | 0.850752 | + | 1.47354i | 0.0301920 | + | 0.0522941i | ||||
\(795\) | −14.6745 | − | 18.2155i | −0.520450 | − | 0.646038i | ||||
\(796\) | −4.31158 | + | 7.46788i | −0.152820 | + | 0.264692i | ||||
\(797\) | 41.1549i | 1.45778i | 0.684630 | + | 0.728891i | \(0.259964\pi\) | ||||
−0.684630 | + | 0.728891i | \(0.740036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.9592 | −0.741482 | ||||||||
\(800\) | 4.88541 | + | 1.06430i | 0.172725 | + | 0.0376286i | ||||
\(801\) | −6.10725 | − | 10.5781i | −0.215789 | − | 0.373758i | ||||
\(802\) | −2.61431 | + | 1.50937i | −0.0923146 | + | 0.0532978i | ||||
\(803\) | 21.1561 | + | 12.2145i | 0.746584 | + | 0.431040i | ||||
\(804\) | −12.2145 | −0.430772 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.16233 | −0.0409415 | ||||||||
\(807\) | −6.02581 | − | 3.47900i | −0.212118 | − | 0.122467i | ||||
\(808\) | 6.92820 | − | 4.00000i | 0.243733 | − | 0.140720i | ||||
\(809\) | −8.88621 | − | 15.3914i | −0.312422 | − | 0.541131i | 0.666464 | − | 0.745537i | \(-0.267807\pi\) |
−0.978886 | + | 0.204406i | \(0.934474\pi\) | |||||||
\(810\) | −2.08551 | − | 0.806615i | −0.0732775 | − | 0.0283416i | ||||
\(811\) | −47.1231 | −1.65472 | −0.827358 | − | 0.561676i | \(-0.810157\pi\) | ||||
−0.827358 | + | 0.561676i | \(0.810157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 28.3637i | − | 0.994760i | ||||||
\(814\) | 7.05871 | − | 12.2260i | 0.247408 | − | 0.428522i | ||||
\(815\) | −0.938857 | + | 0.756346i | −0.0328867 | + | 0.0264937i | ||||
\(816\) | 3.41883 | + | 5.92159i | 0.119683 | + | 0.207297i | ||||
\(817\) | 2.92442 | + | 1.68842i | 0.102313 | + | 0.0590702i | ||||
\(818\) | 4.14925i | 0.145075i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.3768 | + | 1.77241i | −0.397296 | + | 0.0618954i | ||||
\(821\) | −2.85583 | + | 4.94645i | −0.0996693 | + | 0.172632i | −0.911548 | − | 0.411194i | \(-0.865112\pi\) |
0.811878 | + | 0.583826i | \(0.198445\pi\) | |||||||
\(822\) | 16.4997 | − | 9.52608i | 0.575492 | − | 0.332260i | ||||
\(823\) | −26.2795 | + | 15.1725i | −0.916047 | + | 0.528880i | −0.882372 | − | 0.470553i | \(-0.844055\pi\) |
−0.0336753 | + | 0.999433i | \(0.510721\pi\) | |||||||
\(824\) | −0.418833 | + | 0.725439i | −0.0145907 | + | 0.0252719i | ||||
\(825\) | −9.28912 | − | 29.0891i | −0.323406 | − | 1.01275i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2014i | 0.945886i | 0.881093 | + | 0.472943i | \(0.156808\pi\) | ||||
−0.881093 | + | 0.472943i | \(0.843192\pi\) | |||||||
\(828\) | −2.00189 | − | 1.15579i | −0.0695705 | − | 0.0401665i | ||||
\(829\) | −5.41883 | − | 9.38569i | −0.188204 | − | 0.325979i | 0.756448 | − | 0.654054i | \(-0.226933\pi\) |
−0.944651 | + | 0.328076i | \(0.893600\pi\) | |||||||
\(830\) | −18.9744 | − | 23.5531i | −0.658611 | − | 0.817538i | ||||
\(831\) | 2.52608 | − | 4.37530i | 0.0876288 | − | 0.151778i | ||||
\(832\) | 1.68842i | 0.0585353i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.3768 | −0.463202 | ||||||||
\(835\) | −6.56780 | − | 2.54023i | −0.227288 | − | 0.0879083i | ||||
\(836\) | 5.15579 | + | 8.93009i | 0.178317 | + | 0.308854i | ||||
\(837\) | 0.596186 | − | 0.344208i | 0.0206072 | − | 0.0118976i | ||||
\(838\) | 11.9675 | + | 6.90946i | 0.413412 | + | 0.238683i | ||||
\(839\) | −1.59133 | −0.0549389 | −0.0274695 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274695 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.8767 | 1.44403 | ||||||||
\(842\) | 21.8816 | + | 12.6333i | 0.754089 | + | 0.435373i | ||||
\(843\) | −6.65836 | + | 3.84421i | −0.229326 | + | 0.132402i | ||||
\(844\) | −3.84421 | − | 6.65836i | −0.132323 | − | 0.229190i | ||||
\(845\) | 8.18654 | − | 21.1664i | 0.281625 | − | 0.728147i | ||||
\(846\) | 3.06525 | 0.105385 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 10.4608i | − | 0.359226i | ||||||
\(849\) | 9.21450 | − | 15.9600i | 0.316241 | − | 0.547745i | ||||
\(850\) | 25.2908 | + | 23.0047i | 0.867467 | + | 0.789056i | ||||
\(851\) | −2.67171 | − | 4.62753i | −0.0915850 | − | 0.158630i | ||||
\(852\) | −5.19615 | − | 3.00000i | −0.178017 | − | 0.102778i | ||||
\(853\) | 29.9869i | 1.02673i | 0.858170 | + | 0.513366i | \(0.171602\pi\) | ||||
−0.858170 | + | 0.513366i | \(0.828398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.73042 | − | 0.581167i | 0.127578 | − | 0.0198755i | ||||
\(856\) | −7.76304 | + | 13.4460i | −0.265335 | + | 0.459574i | ||||
\(857\) | 32.0478 | − | 18.5028i | 1.09473 | − | 0.632045i | 0.159901 | − | 0.987133i | \(-0.448883\pi\) |
0.934833 | + | 0.355088i | \(0.115549\pi\) | |||||||
\(858\) | 8.93009 | − | 5.15579i | 0.304868 | − | 0.176016i | ||||
\(859\) | −13.8797 | + | 24.0403i | −0.473568 | + | 0.820244i | −0.999542 | − | 0.0302567i | \(-0.990368\pi\) |
0.525974 | + | 0.850501i | \(0.323701\pi\) | |||||||
\(860\) | −0.688417 | − | 4.41883i | −0.0234748 | − | 0.150681i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.5448i | − | 0.665700i | ||||||
\(863\) | 3.12152 | + | 1.80221i | 0.106258 | + | 0.0613479i | 0.552187 | − | 0.833720i | \(-0.313793\pi\) |
−0.445929 | + | 0.895068i | \(0.647127\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −18.3291 | + | 14.7660i | −0.623209 | + | 0.502059i | ||||
\(866\) | −7.37683 | + | 12.7771i | −0.250675 | + | 0.434182i | ||||
\(867\) | 29.7537i | 1.01049i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.6537 | −1.51477 | ||||||||
\(870\) | 6.79076 | − | 17.5576i | 0.230228 | − | 0.595258i | ||||
\(871\) | −10.3116 | − | 17.8602i | −0.349395 | − | 0.605169i | ||||
\(872\) | 10.1111 | − | 5.83767i | 0.342406 | − | 0.197688i | ||||
\(873\) | −4.29375 | − | 2.47900i | −0.145322 | − | 0.0839015i | ||||
\(874\) | 3.90292 | 0.132018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | −10.4764 | − | 6.04854i | −0.353762 | − | 0.204245i | 0.312579 | − | 0.949892i | \(-0.398807\pi\) |
−0.666341 | + | 0.745647i | \(0.732141\pi\) | |||||||
\(878\) | 13.7999 | − | 7.96737i | 0.465724 | − | 0.268886i | ||||
\(879\) | −0.918833 | − | 1.59146i | −0.0309915 | − | 0.0536788i | ||||
\(880\) | 4.92620 | − | 12.7368i | 0.166062 | − | 0.429356i | ||||
\(881\) | 44.7406 | 1.50735 | 0.753674 | − | 0.657248i | \(-0.228280\pi\) | ||||
0.753674 | + | 0.657248i | \(0.228280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.5970i | 1.23159i | 0.787908 | + | 0.615793i | \(0.211164\pi\) | ||||
−0.787908 | + | 0.615793i | \(0.788836\pi\) | |||||||
\(884\) | −5.77241 | + | 9.99812i | −0.194147 | + | 0.336273i | ||||
\(885\) | −12.2623 | + | 9.87853i | −0.412192 | + | 0.332063i | ||||
\(886\) | −10.9123 | − | 18.9006i | −0.366606 | − | 0.634979i | ||||
\(887\) | 48.5475 | + | 28.0289i | 1.63007 | + | 0.941119i | 0.984071 | + | 0.177777i | \(0.0568905\pi\) |
0.645995 | + | 0.763342i | \(0.276443\pi\) | |||||||
\(888\) | − | 2.31158i | − | 0.0775717i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.20433 | − | 26.9869i | −0.140930 | − | 0.904603i | ||||
\(891\) | −3.05362 | + | 5.28903i | −0.102300 | + | 0.177189i | ||||
\(892\) | −9.67567 | + | 5.58625i | −0.323965 | + | 0.187041i | ||||
\(893\) | −4.48205 | + | 2.58771i | −0.149986 | + | 0.0865944i | ||||
\(894\) | −6.31158 | + | 10.9320i | −0.211091 | + | 0.365620i | ||||
\(895\) | 10.9029 | − | 1.69858i | 0.364444 | − | 0.0567773i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 3.90292i | − | 0.130315i | ||||||
\(898\) | 9.84129 | + | 5.68187i | 0.328408 | + | 0.189607i | ||||
\(899\) | 2.89783 | + | 5.01919i | 0.0966481 | + | 0.167400i | ||||
\(900\) | −3.69874 | − | 3.36441i | −0.123291 | − | 0.112147i | ||||
\(901\) | 35.7638 | − | 61.9448i | 1.19147 | − | 2.06368i | ||||
\(902\) | 31.4477i | 1.04710i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.37683 | 0.112312 | ||||||||
\(905\) | −4.94495 | + | 12.7853i | −0.164376 | + | 0.424996i | ||||
\(906\) | 0.967375 | + | 1.67554i | 0.0321389 | + | 0.0556662i | ||||
\(907\) | −16.1457 | + | 9.32175i | −0.536111 | + | 0.309524i | −0.743501 | − | 0.668735i | \(-0.766836\pi\) |
0.207391 | + | 0.978258i | \(0.433503\pi\) | |||||||
\(908\) | 3.33485 | + | 1.92538i | 0.110671 | + | 0.0638958i | ||||
\(909\) | −8.00000 | −0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 1.46221 | + | 0.844208i | 0.0484187 | + | 0.0279545i | ||||
\(913\) | −71.5399 | + | 41.3036i | −2.36763 | + | 1.36695i | ||||
\(914\) | 3.20942 | + | 5.55887i | 0.106158 | + | 0.183871i | ||||
\(915\) | 19.7307 | + | 7.63125i | 0.652277 | + | 0.252281i | ||||
\(916\) | −5.67533 | −0.187518 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 6.83767i | − | 0.225677i | ||||||
\(919\) | −19.4608 | + | 33.7071i | −0.641954 | + | 1.11190i | 0.343043 | + | 0.939320i | \(0.388542\pi\) |
−0.984996 | + | 0.172576i | \(0.944791\pi\) | |||||||
\(920\) | −3.24269 | − | 4.02517i | −0.106908 | − | 0.132706i | ||||
\(921\) | 8.04200 | + | 13.9292i | 0.264993 | + | 0.458981i | ||||
\(922\) | −1.30539 | − | 0.753667i | −0.0429907 | − | 0.0248207i | ||||
\(923\) | − | 10.1305i | − | 0.333450i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.51592 | − | 11.0102i | −0.115603 | − | 0.362012i | ||||
\(926\) | 12.0587 | − | 20.8863i | 0.396274 | − | 0.686366i | ||||
\(927\) | 0.725439 | − | 0.418833i | 0.0238266 | − | 0.0137563i | ||||
\(928\) | 7.29092 | − | 4.20942i | 0.239336 | − | 0.138181i | ||||
\(929\) | −6.86746 | + | 11.8948i | −0.225314 | + | 0.390255i | −0.956414 | − | 0.292015i | \(-0.905674\pi\) |
0.731100 | + | 0.682271i | \(0.239007\pi\) | |||||||
\(930\) | 1.52100 | − | 0.236959i | 0.0498755 | − | 0.00777019i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.4608i | 0.375412i | ||||||||
\(933\) | 13.3167 | + | 7.68842i | 0.435970 | + | 0.251707i | ||||
\(934\) | −11.7724 | − | 20.3904i | −0.385205 | − | 0.667195i | ||||
\(935\) | 72.7158 | − | 58.5800i | 2.37806 | − | 1.91577i | ||||
\(936\) | 0.844208 | − | 1.46221i | 0.0275938 | − | 0.0477939i | ||||
\(937\) | − | 20.7435i | − | 0.677661i | −0.940847 | − | 0.338830i | \(-0.889969\pi\) | ||
0.940847 | − | 0.338830i | \(-0.110031\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.4188 | 0.731611 | ||||||||
\(940\) | 6.39263 | + | 2.47248i | 0.208504 | + | 0.0806433i | ||||
\(941\) | 6.54425 | + | 11.3350i | 0.213336 | + | 0.369510i | 0.952757 | − | 0.303735i | \(-0.0982336\pi\) |
−0.739420 | + | 0.673244i | \(0.764900\pi\) | |||||||
\(942\) | −14.8517 | + | 8.57462i | −0.483894 | + | 0.279376i | ||||
\(943\) | 10.3082 | + | 5.95146i | 0.335682 | + | 0.193806i | ||||
\(944\) | −7.04200 | −0.229198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2145 | −0.397128 | ||||||||
\(947\) | 17.5465 | + | 10.1305i | 0.570186 | + | 0.329197i | 0.757224 | − | 0.653156i | \(-0.226555\pi\) |
−0.187038 | + | 0.982353i | \(0.559889\pi\) | |||||||
\(948\) | −6.33202 | + | 3.65579i | −0.205654 | + | 0.118735i | ||||
\(949\) | 3.37683 | + | 5.84885i | 0.109617 | + | 0.189862i | ||||
\(950\) | 8.24862 | + | 1.79698i | 0.267620 | + | 0.0583016i | ||||
\(951\) | 10.0653 | 0.326388 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.65500i | 0.0536107i | 0.999641 | + | 0.0268053i | \(0.00853343\pi\) | ||||
−0.999641 | + | 0.0268053i | \(0.991467\pi\) | |||||||
\(954\) | −5.23042 | + | 9.05935i | −0.169341 | + | 0.293307i | ||||
\(955\) | −20.9321 | − | 25.9832i | −0.677348 | − | 0.840796i | ||||
\(956\) | −7.73042 | − | 13.3895i | −0.250020 | − | 0.433047i | ||||
\(957\) | −44.5275 | − | 25.7080i | −1.43937 | − | 0.831020i | ||||
\(958\) | − | 29.9738i | − | 0.968410i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.344208 | − | 2.20942i | −0.0111093 | − | 0.0713086i | ||||
\(961\) | 15.2630 | − | 26.4364i | 0.492356 | − | 0.852786i | ||||
\(962\) | 3.38002 | − | 1.95146i | 0.108976 | − | 0.0629175i | ||||
\(963\) | 13.4460 | − | 7.76304i | 0.433291 | − | 0.250161i | ||||
\(964\) | −2.18842 | + | 3.79045i | −0.0704842 | + | 0.122082i | ||||
\(965\) | 1.92108 | + | 12.3311i | 0.0618419 | + | 0.396953i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.3405i | 0.493317i | 0.969102 | + | 0.246659i | \(0.0793326\pi\) | ||||
−0.969102 | + | 0.246659i | \(0.920667\pi\) | |||||||
\(968\) | −22.7752 | − | 13.1492i | −0.732022 | − | 0.422633i | ||||
\(969\) | 5.77241 | + | 9.99812i | 0.185437 | + | 0.321186i | ||||
\(970\) | −6.95509 | − | 8.63340i | −0.223315 | − | 0.277202i | ||||
\(971\) | 23.5565 | − | 40.8010i | 0.755963 | − | 1.30937i | −0.188932 | − | 0.981990i | \(-0.560502\pi\) |
0.944894 | − | 0.327375i | \(-0.106164\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.5028 | 0.977374 | ||||||||
\(975\) | 1.79698 | − | 8.24862i | 0.0575493 | − | 0.264167i | ||||
\(976\) | 4.73042 | + | 8.19332i | 0.151417 | + | 0.262262i | ||||
\(977\) | −25.8854 | + | 14.9449i | −0.828146 | + | 0.478130i | −0.853217 | − | 0.521555i | \(-0.825352\pi\) |
0.0250716 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(978\) | 0.466934 | + | 0.269584i | 0.0149309 | + | 0.00862035i | ||||
\(979\) | −74.5970 | −2.38413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6753 | −0.372765 | ||||||||
\(982\) | −3.35989 | − | 1.93983i | −0.107218 | − | 0.0619025i | ||||
\(983\) | −4.45938 | + | 2.57462i | −0.142232 | + | 0.0821178i | −0.569427 | − | 0.822042i | \(-0.692835\pi\) |
0.427195 | + | 0.904159i | \(0.359502\pi\) | |||||||
\(984\) | 2.57462 | + | 4.45938i | 0.0820760 | + | 0.142160i | ||||
\(985\) | −30.2944 | − | 11.7170i | −0.965259 | − | 0.373333i | ||||
\(986\) | 57.5652 | 1.83325 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.85075i | 0.0906945i | ||||||||
\(989\) | −2.31158 | + | 4.00378i | −0.0735041 | + | 0.127313i | ||||
\(990\) | −10.6346 | + | 8.56726i | −0.337990 | + | 0.272285i | ||||
\(991\) | −3.40946 | − | 5.90536i | −0.108305 | − | 0.187590i | 0.806779 | − | 0.590854i | \(-0.201209\pi\) |
−0.915084 | + | 0.403264i | \(0.867876\pi\) | |||||||
\(992\) | 0.596186 | + | 0.344208i | 0.0189289 | + | 0.0109286i | ||||
\(993\) | − | 23.2797i | − | 0.738761i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.0522 | − | 2.96817i | 0.603994 | − | 0.0940972i | ||||
\(996\) | −6.76304 | + | 11.7139i | −0.214295 | + | 0.371170i | ||||
\(997\) | 44.6567 | − | 25.7826i | 1.41429 | − | 0.816543i | 0.418504 | − | 0.908215i | \(-0.362555\pi\) |
0.995789 | + | 0.0916725i | \(0.0292213\pi\) | |||||||
\(998\) | 8.12058 | − | 4.68842i | 0.257052 | − | 0.148409i | ||||
\(999\) | −1.15579 | + | 2.00189i | −0.0365676 | + | 0.0633370i |
(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 | 1470.2.n.j.79.5 | 12 | ||
5.4 | even | 2 | inner | 1470.2.n.j.79.3 | 12 | ||
7.2 | even | 3 | 1470.2.g.h.589.1 | 6 | |||
7.3 | odd | 6 | 210.2.n.b.109.1 | yes | 12 | ||
7.4 | even | 3 | inner | 1470.2.n.j.949.3 | 12 | ||
7.5 | odd | 6 | 1470.2.g.i.589.3 | 6 | |||
7.6 | odd | 2 | 210.2.n.b.79.5 | yes | 12 | ||
21.17 | even | 6 | 630.2.u.f.109.6 | 12 | |||
21.20 | even | 2 | 630.2.u.f.289.2 | 12 | |||
28.3 | even | 6 | 1680.2.di.c.529.4 | 12 | |||
28.27 | even | 2 | 1680.2.di.c.289.2 | 12 | |||
35.2 | odd | 12 | 7350.2.a.dp.1.3 | 3 | |||
35.3 | even | 12 | 1050.2.i.v.151.3 | 6 | |||
35.4 | even | 6 | inner | 1470.2.n.j.949.5 | 12 | ||
35.9 | even | 6 | 1470.2.g.h.589.4 | 6 | |||
35.12 | even | 12 | 7350.2.a.dq.1.3 | 3 | |||
35.13 | even | 4 | 1050.2.i.v.751.3 | 6 | |||
35.17 | even | 12 | 1050.2.i.u.151.1 | 6 | |||
35.19 | odd | 6 | 1470.2.g.i.589.6 | 6 | |||
35.23 | odd | 12 | 7350.2.a.do.1.3 | 3 | |||
35.24 | odd | 6 | 210.2.n.b.109.5 | yes | 12 | ||
35.27 | even | 4 | 1050.2.i.u.751.1 | 6 | |||
35.33 | even | 12 | 7350.2.a.dn.1.3 | 3 | |||
35.34 | odd | 2 | 210.2.n.b.79.1 | ✓ | 12 | ||
105.59 | even | 6 | 630.2.u.f.109.2 | 12 | |||
105.104 | even | 2 | 630.2.u.f.289.6 | 12 | |||
140.59 | even | 6 | 1680.2.di.c.529.2 | 12 | |||
140.139 | even | 2 | 1680.2.di.c.289.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.b.79.1 | ✓ | 12 | 35.34 | odd | 2 | ||
210.2.n.b.79.5 | yes | 12 | 7.6 | odd | 2 | ||
210.2.n.b.109.1 | yes | 12 | 7.3 | odd | 6 | ||
210.2.n.b.109.5 | yes | 12 | 35.24 | odd | 6 | ||
630.2.u.f.109.2 | 12 | 105.59 | even | 6 | |||
630.2.u.f.109.6 | 12 | 21.17 | even | 6 | |||
630.2.u.f.289.2 | 12 | 21.20 | even | 2 | |||
630.2.u.f.289.6 | 12 | 105.104 | even | 2 | |||
1050.2.i.u.151.1 | 6 | 35.17 | even | 12 | |||
1050.2.i.u.751.1 | 6 | 35.27 | even | 4 | |||
1050.2.i.v.151.3 | 6 | 35.3 | even | 12 | |||
1050.2.i.v.751.3 | 6 | 35.13 | even | 4 | |||
1470.2.g.h.589.1 | 6 | 7.2 | even | 3 | |||
1470.2.g.h.589.4 | 6 | 35.9 | even | 6 | |||
1470.2.g.i.589.3 | 6 | 7.5 | odd | 6 | |||
1470.2.g.i.589.6 | 6 | 35.19 | odd | 6 | |||
1470.2.n.j.79.3 | 12 | 5.4 | even | 2 | inner | ||
1470.2.n.j.79.5 | 12 | 1.1 | even | 1 | trivial | ||
1470.2.n.j.949.3 | 12 | 7.4 | even | 3 | inner | ||
1470.2.n.j.949.5 | 12 | 35.4 | even | 6 | inner | ||
1680.2.di.c.289.2 | 12 | 28.27 | even | 2 | |||
1680.2.di.c.289.4 | 12 | 140.139 | even | 2 | |||
1680.2.di.c.529.2 | 12 | 140.59 | even | 6 | |||
1680.2.di.c.529.4 | 12 | 28.3 | even | 6 | |||
7350.2.a.dn.1.3 | 3 | 35.33 | even | 12 | |||
7350.2.a.do.1.3 | 3 | 35.23 | odd | 12 | |||
7350.2.a.dp.1.3 | 3 | 35.2 | odd | 12 | |||
7350.2.a.dq.1.3 | 3 | 35.12 | even | 12 |