Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(4,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.k (of order \(6\), degree \(2\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.4 |
Dual form | 91.2.k.a.23.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.73205i | − | 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | −4.50000 | + | 2.59808i | −1.35680 | + | 0.783349i | −0.989191 | − | 0.146631i | \(-0.953157\pi\) |
−0.367610 | + | 0.929980i | \(0.619824\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | 3.00000 | + | 3.46410i | 0.801784 | + | 0.925820i | ||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | −3.00000 | − | 1.73205i | −0.707107 | − | 0.408248i | ||||
\(19\) | −1.50000 | − | 0.866025i | −0.344124 | − | 0.198680i | 0.317970 | − | 0.948101i | \(-0.396999\pi\) |
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(20\) | −1.50000 | + | 0.866025i | −0.335410 | + | 0.193649i | ||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | 4.50000 | + | 7.79423i | 0.959403 | + | 1.66174i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 1.50000 | − | 0.866025i | 0.306186 | − | 0.176777i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 6.00000 | + | 1.73205i | 1.17670 | + | 0.339683i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 2.00000 | − | 1.73205i | 0.377964 | − | 0.327327i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | −1.50000 | + | 4.33013i | −0.253546 | + | 0.731925i | ||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −1.50000 | + | 2.59808i | −0.243332 | + | 0.421464i | ||||
\(39\) | −3.50000 | + | 0.866025i | −0.560449 | + | 0.138675i | ||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | −4.50000 | − | 2.59808i | −0.702782 | − | 0.405751i | 0.105601 | − | 0.994409i | \(-0.466323\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(42\) | −1.50000 | + | 4.33013i | −0.231455 | + | 0.668153i | ||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 4.50000 | − | 2.59808i | 0.678401 | − | 0.391675i | ||||
\(45\) | − | 3.46410i | − | 0.516398i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.50000 | − | 4.33013i | 1.09399 | − | 0.631614i | 0.159352 | − | 0.987222i | \(-0.449059\pi\) |
0.934635 | + | 0.355608i | \(0.115726\pi\) | |||||||
\(48\) | −2.50000 | − | 4.33013i | −0.360844 | − | 0.625000i | ||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 3.00000 | + | 1.73205i | 0.424264 | + | 0.244949i | ||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 1.00000 | − | 3.46410i | 0.138675 | − | 0.480384i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | − | 8.66025i | − | 1.17851i | ||||||
\(55\) | −4.50000 | + | 7.79423i | −0.606780 | + | 1.05097i | ||||
\(56\) | 3.00000 | + | 3.46410i | 0.400892 | + | 0.462910i | ||||
\(57\) | − | 1.73205i | − | 0.229416i | ||||||
\(58\) | 4.50000 | + | 2.59808i | 0.590879 | + | 0.341144i | ||||
\(59\) | 3.46410i | 0.450988i | 0.974245 | + | 0.225494i | \(0.0723995\pi\) | ||||
−0.974245 | + | 0.225494i | \(0.927600\pi\) | |||||||
\(60\) | −1.50000 | − | 0.866025i | −0.193649 | − | 0.111803i | ||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | −1.50000 | + | 2.59808i | −0.190500 | + | 0.329956i | ||||
\(63\) | 1.00000 | + | 5.19615i | 0.125988 | + | 0.654654i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.50000 | + | 6.06218i | 0.186052 | + | 0.751921i | ||||
\(66\) | −4.50000 | + | 7.79423i | −0.553912 | + | 0.959403i | ||||
\(67\) | 7.50000 | − | 4.33013i | 0.916271 | − | 0.529009i | 0.0338274 | − | 0.999428i | \(-0.489230\pi\) |
0.882443 | + | 0.470418i | \(0.155897\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.50000 | + | 2.59808i | 0.896421 | + | 0.310530i | ||||
\(71\) | 1.50000 | − | 0.866025i | 0.178017 | − | 0.102778i | −0.408344 | − | 0.912828i | \(-0.633893\pi\) |
0.586361 | + | 0.810050i | \(0.300560\pi\) | |||||||
\(72\) | −3.00000 | − | 1.73205i | −0.353553 | − | 0.204124i | ||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | −0.230940 | ||||||||
\(76\) | 1.50000 | + | 0.866025i | 0.172062 | + | 0.0993399i | ||||
\(77\) | 4.50000 | − | 12.9904i | 0.512823 | − | 1.48039i | ||||
\(78\) | 1.50000 | + | 6.06218i | 0.169842 | + | 0.686406i | ||||
\(79\) | 2.50000 | + | 4.33013i | 0.281272 | + | 0.487177i | 0.971698 | − | 0.236225i | \(-0.0759104\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(80\) | −7.50000 | + | 4.33013i | −0.838525 | + | 0.484123i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.50000 | + | 7.79423i | −0.496942 | + | 0.860729i | ||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 2.50000 | + | 0.866025i | 0.272772 | + | 0.0944911i | ||||
\(85\) | 9.00000 | − | 5.19615i | 0.976187 | − | 0.563602i | ||||
\(86\) | −16.5000 | + | 9.52628i | −1.77924 | + | 1.02725i | ||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 4.50000 | + | 7.79423i | 0.479702 | + | 0.830868i | ||||
\(89\) | − | 6.92820i | − | 0.734388i | −0.930144 | − | 0.367194i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367194i | \(-0.119682\pi\) | |||||||
\(90\) | −6.00000 | −0.632456 | ||||||||
\(91\) | −4.00000 | − | 8.66025i | −0.419314 | − | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.73205i | − | 0.179605i | ||||||
\(94\) | −7.50000 | − | 12.9904i | −0.773566 | − | 1.33986i | ||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | −4.50000 | + | 2.59808i | −0.459279 | + | 0.265165i | ||||
\(97\) | −4.50000 | + | 2.59808i | −0.456906 | + | 0.263795i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −12.0000 | − | 1.73205i | −1.21218 | − | 0.174964i | ||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | 1.00000 | − | 1.73205i | 0.100000 | − | 0.173205i | ||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | 9.00000 | − | 5.19615i | 0.891133 | − | 0.514496i | ||||
\(103\) | 6.50000 | + | 11.2583i | 0.640464 | + | 1.10932i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | ||||
\(105\) | −4.50000 | + | 0.866025i | −0.439155 | + | 0.0845154i | ||||
\(106\) | −13.5000 | − | 7.79423i | −1.31124 | − | 0.757042i | ||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | −4.50000 | − | 2.59808i | −0.431022 | − | 0.248851i | 0.268760 | − | 0.963207i | \(-0.413386\pi\) |
−0.699782 | + | 0.714357i | \(0.746719\pi\) | |||||||
\(110\) | 13.5000 | + | 7.79423i | 1.28717 | + | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0000 | − | 8.66025i | 0.944911 | − | 0.818317i | ||||
\(113\) | −7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) |
0.260955 | − | 0.965351i | \(-0.415962\pi\) | |||||||
\(114\) | −3.00000 | −0.280976 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | 5.00000 | + | 5.19615i | 0.462250 | + | 0.480384i | ||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | −12.0000 | + | 10.3923i | −1.10004 | + | 0.952661i | ||||
\(120\) | 1.50000 | − | 2.59808i | 0.136931 | − | 0.237171i | ||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 10.5000 | + | 6.06218i | 0.950625 | + | 0.548844i | ||||
\(123\) | − | 5.19615i | − | 0.468521i | ||||||
\(124\) | 1.50000 | + | 0.866025i | 0.134704 | + | 0.0777714i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 9.00000 | − | 1.73205i | 0.801784 | − | 0.154303i | ||||
\(127\) | −6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | \(0.362358\pi\) |
−0.995846 | + | 0.0910585i | \(0.970975\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | 5.50000 | − | 9.52628i | 0.484248 | − | 0.838742i | ||||
\(130\) | 10.5000 | − | 2.59808i | 0.920911 | − | 0.227866i | ||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 4.50000 | + | 2.59808i | 0.391675 | + | 0.226134i | ||||
\(133\) | 4.50000 | − | 0.866025i | 0.390199 | − | 0.0750939i | ||||
\(134\) | −7.50000 | − | 12.9904i | −0.647901 | − | 1.12220i | ||||
\(135\) | 7.50000 | − | 4.33013i | 0.645497 | − | 0.372678i | ||||
\(136\) | − | 10.3923i | − | 0.891133i | ||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | + | 11.2583i | 0.551323 | + | 0.954919i | 0.998179 | + | 0.0603135i | \(0.0192101\pi\) |
−0.446857 | + | 0.894606i | \(0.647457\pi\) | |||||||
\(140\) | 1.50000 | − | 4.33013i | 0.126773 | − | 0.365963i | ||||
\(141\) | 7.50000 | + | 4.33013i | 0.631614 | + | 0.364662i | ||||
\(142\) | −1.50000 | − | 2.59808i | −0.125877 | − | 0.218026i | ||||
\(143\) | −4.50000 | − | 18.1865i | −0.376309 | − | 1.52083i | ||||
\(144\) | −5.00000 | + | 8.66025i | −0.416667 | + | 0.721688i | ||||
\(145\) | 5.19615i | 0.431517i | ||||||||
\(146\) | 7.50000 | − | 12.9904i | 0.620704 | − | 1.07509i | ||||
\(147\) | 6.50000 | − | 2.59808i | 0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5000 | − | 9.52628i | −1.35173 | − | 0.780423i | −0.363241 | − | 0.931695i | \(-0.618330\pi\) |
−0.988492 | + | 0.151272i | \(0.951663\pi\) | |||||||
\(150\) | 3.46410i | 0.282843i | ||||||||
\(151\) | 10.5000 | + | 6.06218i | 0.854478 | + | 0.493333i | 0.862159 | − | 0.506637i | \(-0.169112\pi\) |
−0.00768132 | + | 0.999970i | \(0.502445\pi\) | |||||||
\(152\) | −1.50000 | + | 2.59808i | −0.121666 | + | 0.210732i | ||||
\(153\) | 6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | ||||
\(154\) | −22.5000 | − | 7.79423i | −1.81310 | − | 0.628077i | ||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | 3.50000 | − | 0.866025i | 0.280224 | − | 0.0693375i | ||||
\(157\) | −11.5000 | + | 19.9186i | −0.917800 | + | 1.58968i | −0.115050 | + | 0.993360i | \(0.536703\pi\) |
−0.802749 | + | 0.596316i | \(0.796630\pi\) | |||||||
\(158\) | 7.50000 | − | 4.33013i | 0.596668 | − | 0.344486i | ||||
\(159\) | 9.00000 | 0.713746 | ||||||||
\(160\) | 4.50000 | + | 7.79423i | 0.355756 | + | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.50000 | + | 0.866025i | −0.117851 | + | 0.0680414i | ||||
\(163\) | 10.5000 | + | 6.06218i | 0.822423 | + | 0.474826i | 0.851251 | − | 0.524758i | \(-0.175844\pi\) |
−0.0288280 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(164\) | 4.50000 | + | 2.59808i | 0.351391 | + | 0.202876i | ||||
\(165\) | −9.00000 | −0.700649 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −1.50000 | − | 0.866025i | −0.116073 | − | 0.0670151i | 0.440839 | − | 0.897586i | \(-0.354681\pi\) |
−0.556913 | + | 0.830571i | \(0.688014\pi\) | |||||||
\(168\) | −1.50000 | + | 4.33013i | −0.115728 | + | 0.334077i | ||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | −9.00000 | − | 15.5885i | −0.690268 | − | 1.19558i | ||||
\(171\) | −3.00000 | + | 1.73205i | −0.229416 | + | 0.132453i | ||||
\(172\) | 5.50000 | + | 9.52628i | 0.419371 | + | 0.726372i | ||||
\(173\) | −7.50000 | + | 12.9904i | −0.570214 | + | 0.987640i | 0.426329 | + | 0.904568i | \(0.359807\pi\) |
−0.996544 | + | 0.0830722i | \(0.973527\pi\) | |||||||
\(174\) | 5.19615i | 0.393919i | ||||||||
\(175\) | −1.00000 | − | 5.19615i | −0.0755929 | − | 0.392792i | ||||
\(176\) | 22.5000 | − | 12.9904i | 1.69600 | − | 0.979187i | ||||
\(177\) | −3.00000 | + | 1.73205i | −0.225494 | + | 0.130189i | ||||
\(178\) | −12.0000 | −0.899438 | ||||||||
\(179\) | −1.50000 | − | 2.59808i | −0.112115 | − | 0.194189i | 0.804508 | − | 0.593942i | \(-0.202429\pi\) |
−0.916623 | + | 0.399753i | \(0.869096\pi\) | |||||||
\(180\) | 3.46410i | 0.258199i | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −15.0000 | + | 6.92820i | −1.11187 | + | 0.513553i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | −0.219971 | ||||||||
\(187\) | −27.0000 | + | 15.5885i | −1.97444 | + | 1.13994i | ||||
\(188\) | −7.50000 | + | 4.33013i | −0.546994 | + | 0.315807i | ||||
\(189\) | −10.0000 | + | 8.66025i | −0.727393 | + | 0.629941i | ||||
\(190\) | 5.19615i | 0.376969i | ||||||||
\(191\) | 7.50000 | − | 12.9904i | 0.542681 | − | 0.939951i | −0.456068 | − | 0.889945i | \(-0.650743\pi\) |
0.998749 | − | 0.0500060i | \(-0.0159241\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 1.50000 | − | 0.866025i | 0.107972 | − | 0.0623379i | −0.445041 | − | 0.895510i | \(-0.646811\pi\) |
0.553014 | + | 0.833172i | \(0.313478\pi\) | |||||||
\(194\) | 4.50000 | + | 7.79423i | 0.323081 | + | 0.559593i | ||||
\(195\) | −4.50000 | + | 4.33013i | −0.322252 | + | 0.310087i | ||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | 19.5000 | + | 11.2583i | 1.38932 | + | 0.802123i | 0.993238 | − | 0.116094i | \(-0.0370372\pi\) |
0.396079 | + | 0.918216i | \(0.370371\pi\) | |||||||
\(198\) | 18.0000 | 1.27920 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 3.00000 | + | 1.73205i | 0.212132 | + | 0.122474i | ||||
\(201\) | 7.50000 | + | 4.33013i | 0.529009 | + | 0.305424i | ||||
\(202\) | 13.5000 | − | 7.79423i | 0.949857 | − | 0.548400i | ||||
\(203\) | −1.50000 | − | 7.79423i | −0.105279 | − | 0.547048i | ||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 19.5000 | − | 11.2583i | 1.35863 | − | 0.784405i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000 | − | 17.3205i | 0.346688 | − | 1.20096i | ||||
\(209\) | 9.00000 | 0.622543 | ||||||||
\(210\) | 1.50000 | + | 7.79423i | 0.103510 | + | 0.537853i | ||||
\(211\) | −6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | −4.50000 | + | 7.79423i | −0.309061 | + | 0.535310i | ||||
\(213\) | 1.50000 | + | 0.866025i | 0.102778 | + | 0.0593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.5000 | − | 9.52628i | −1.12529 | − | 0.649687i | ||||
\(216\) | − | 8.66025i | − | 0.589256i | ||||||
\(217\) | 4.50000 | − | 0.866025i | 0.305480 | − | 0.0587896i | ||||
\(218\) | −4.50000 | + | 7.79423i | −0.304778 | + | 0.527892i | ||||
\(219\) | 8.66025i | 0.585206i | ||||||||
\(220\) | 4.50000 | − | 7.79423i | 0.303390 | − | 0.525487i | ||||
\(221\) | −6.00000 | + | 20.7846i | −0.403604 | + | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | + | 2.59808i | 0.301342 | + | 0.173980i | 0.643046 | − | 0.765828i | \(-0.277671\pi\) |
−0.341703 | + | 0.939808i | \(0.611004\pi\) | |||||||
\(224\) | −9.00000 | − | 10.3923i | −0.601338 | − | 0.694365i | ||||
\(225\) | 2.00000 | + | 3.46410i | 0.133333 | + | 0.230940i | ||||
\(226\) | −22.5000 | + | 12.9904i | −1.49668 | + | 0.864107i | ||||
\(227\) | 17.3205i | 1.14960i | 0.818293 | + | 0.574801i | \(0.194921\pi\) | ||||
−0.818293 | + | 0.574801i | \(0.805079\pi\) | |||||||
\(228\) | 1.73205i | 0.114708i | ||||||||
\(229\) | −10.5000 | + | 6.06218i | −0.693860 | + | 0.400600i | −0.805056 | − | 0.593198i | \(-0.797865\pi\) |
0.111197 | + | 0.993798i | \(0.464532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.5000 | − | 2.59808i | 0.888235 | − | 0.170941i | ||||
\(232\) | 4.50000 | + | 2.59808i | 0.295439 | + | 0.170572i | ||||
\(233\) | −1.50000 | − | 2.59808i | −0.0982683 | − | 0.170206i | 0.812700 | − | 0.582683i | \(-0.197997\pi\) |
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(234\) | 9.00000 | − | 8.66025i | 0.588348 | − | 0.566139i | ||||
\(235\) | 7.50000 | − | 12.9904i | 0.489246 | − | 0.847399i | ||||
\(236\) | − | 3.46410i | − | 0.225494i | ||||||
\(237\) | −2.50000 | + | 4.33013i | −0.162392 | + | 0.281272i | ||||
\(238\) | 18.0000 | + | 20.7846i | 1.16677 | + | 1.34727i | ||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | −7.50000 | − | 4.33013i | −0.484123 | − | 0.279508i | ||||
\(241\) | 6.92820i | 0.446285i | 0.974786 | + | 0.223142i | \(0.0716315\pi\) | ||||
−0.974786 | + | 0.223142i | \(0.928369\pi\) | |||||||
\(242\) | −24.0000 | − | 13.8564i | −1.54278 | − | 0.890724i | ||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 3.50000 | − | 6.06218i | 0.224065 | − | 0.388091i | ||||
\(245\) | −4.50000 | − | 11.2583i | −0.287494 | − | 0.719268i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 4.50000 | − | 4.33013i | 0.286328 | − | 0.275519i | ||||
\(248\) | −1.50000 | + | 2.59808i | −0.0952501 | + | 0.164978i | ||||
\(249\) | 3.00000 | − | 1.73205i | 0.190117 | − | 0.109764i | ||||
\(250\) | 21.0000 | 1.32816 | ||||||||
\(251\) | −1.50000 | − | 2.59808i | −0.0946792 | − | 0.163989i | 0.814795 | − | 0.579748i | \(-0.196849\pi\) |
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(252\) | −1.00000 | − | 5.19615i | −0.0629941 | − | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.5000 | + | 11.2583i | 1.22354 | + | 0.706410i | ||||
\(255\) | 9.00000 | + | 5.19615i | 0.563602 | + | 0.325396i | ||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | 30.0000 | 1.87135 | 0.935674 | − | 0.352865i | \(-0.114792\pi\) | ||||
0.935674 | + | 0.352865i | \(0.114792\pi\) | |||||||
\(258\) | −16.5000 | − | 9.52628i | −1.02725 | − | 0.593080i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.50000 | − | 6.06218i | −0.0930261 | − | 0.375960i | ||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | −22.5000 | + | 12.9904i | −1.39005 | + | 0.802548i | ||||
\(263\) | −1.50000 | − | 2.59808i | −0.0924940 | − | 0.160204i | 0.816066 | − | 0.577959i | \(-0.196151\pi\) |
−0.908560 | + | 0.417755i | \(0.862817\pi\) | |||||||
\(264\) | −4.50000 | + | 7.79423i | −0.276956 | + | 0.479702i | ||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | −1.50000 | − | 7.79423i | −0.0919709 | − | 0.477895i | ||||
\(267\) | 6.00000 | − | 3.46410i | 0.367194 | − | 0.212000i | ||||
\(268\) | −7.50000 | + | 4.33013i | −0.458135 | + | 0.264505i | ||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | −7.50000 | − | 12.9904i | −0.456435 | − | 0.790569i | ||||
\(271\) | − | 17.3205i | − | 1.05215i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||
0.850439 | − | 0.526073i | \(-0.176336\pi\) | |||||||
\(272\) | −30.0000 | −1.81902 | ||||||||
\(273\) | 5.50000 | − | 7.79423i | 0.332875 | − | 0.471728i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 10.3923i | − | 0.626680i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 19.5000 | − | 11.2583i | 1.16953 | − | 0.675230i | ||||
\(279\) | −3.00000 | + | 1.73205i | −0.179605 | + | 0.103695i | ||||
\(280\) | 7.50000 | + | 2.59808i | 0.448211 | + | 0.155265i | ||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | 7.50000 | − | 12.9904i | 0.446619 | − | 0.773566i | ||||
\(283\) | −9.50000 | − | 16.4545i | −0.564716 | − | 0.978117i | −0.997076 | − | 0.0764162i | \(-0.975652\pi\) |
0.432360 | − | 0.901701i | \(-0.357681\pi\) | |||||||
\(284\) | −1.50000 | + | 0.866025i | −0.0890086 | + | 0.0513892i | ||||
\(285\) | −1.50000 | − | 2.59808i | −0.0888523 | − | 0.153897i | ||||
\(286\) | −31.5000 | + | 7.79423i | −1.86263 | + | 0.460882i | ||||
\(287\) | 13.5000 | − | 2.59808i | 0.796880 | − | 0.153360i | ||||
\(288\) | 9.00000 | + | 5.19615i | 0.530330 | + | 0.306186i | ||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 9.00000 | 0.528498 | ||||||||
\(291\) | −4.50000 | − | 2.59808i | −0.263795 | − | 0.152302i | ||||
\(292\) | −7.50000 | − | 4.33013i | −0.438904 | − | 0.253402i | ||||
\(293\) | −22.5000 | + | 12.9904i | −1.31446 | + | 0.758906i | −0.982832 | − | 0.184503i | \(-0.940933\pi\) |
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(294\) | −4.50000 | − | 11.2583i | −0.262445 | − | 0.656599i | ||||
\(295\) | 3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.5000 | + | 12.9904i | −1.30558 | + | 0.753778i | ||||
\(298\) | −16.5000 | + | 28.5788i | −0.955819 | + | 1.65553i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | 27.5000 | + | 9.52628i | 1.58507 | + | 0.549086i | ||||
\(302\) | 10.5000 | − | 18.1865i | 0.604207 | − | 1.04652i | ||||
\(303\) | −4.50000 | + | 7.79423i | −0.258518 | + | 0.447767i | ||||
\(304\) | 7.50000 | + | 4.33013i | 0.430155 | + | 0.248350i | ||||
\(305\) | 12.1244i | 0.694239i | ||||||||
\(306\) | −18.0000 | − | 10.3923i | −1.02899 | − | 0.594089i | ||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | −4.50000 | + | 12.9904i | −0.256411 | + | 0.740196i | ||||
\(309\) | −6.50000 | + | 11.2583i | −0.369772 | + | 0.640464i | ||||
\(310\) | 5.19615i | 0.295122i | ||||||||
\(311\) | 7.50000 | − | 12.9904i | 0.425286 | − | 0.736617i | −0.571161 | − | 0.820838i | \(-0.693507\pi\) |
0.996447 | + | 0.0842210i | \(0.0268402\pi\) | |||||||
\(312\) | 1.50000 | + | 6.06218i | 0.0849208 | + | 0.343203i | ||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | 34.5000 | + | 19.9186i | 1.94695 | + | 1.12407i | ||||
\(315\) | 6.00000 | + | 6.92820i | 0.338062 | + | 0.390360i | ||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | −4.50000 | + | 2.59808i | −0.252745 | + | 0.145922i | −0.621021 | − | 0.783794i | \(-0.713282\pi\) |
0.368275 | + | 0.929717i | \(0.379948\pi\) | |||||||
\(318\) | − | 15.5885i | − | 0.874157i | ||||||
\(319\) | − | 15.5885i | − | 0.872786i | ||||||
\(320\) | −1.50000 | + | 0.866025i | −0.0838525 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00000 | − | 5.19615i | −0.500773 | − | 0.289122i | ||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −5.00000 | − | 5.19615i | −0.277350 | − | 0.288231i | ||||
\(326\) | 10.5000 | − | 18.1865i | 0.581541 | − | 1.00726i | ||||
\(327\) | − | 5.19615i | − | 0.287348i | ||||||
\(328\) | −4.50000 | + | 7.79423i | −0.248471 | + | 0.430364i | ||||
\(329\) | −7.50000 | + | 21.6506i | −0.413488 | + | 1.19364i | ||||
\(330\) | 15.5885i | 0.858116i | ||||||||
\(331\) | 28.5000 | + | 16.4545i | 1.56650 | + | 0.904420i | 0.996572 | + | 0.0827265i | \(0.0263628\pi\) |
0.569929 | + | 0.821694i | \(0.306971\pi\) | |||||||
\(332\) | 3.46410i | 0.190117i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.50000 | + | 2.59808i | −0.0820763 | + | 0.142160i | ||||
\(335\) | 7.50000 | − | 12.9904i | 0.409769 | − | 0.709740i | ||||
\(336\) | 12.5000 | + | 4.33013i | 0.681931 | + | 0.236228i | ||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | −12.0000 | + | 19.0526i | −0.652714 | + | 1.03632i | ||||
\(339\) | 7.50000 | − | 12.9904i | 0.407344 | − | 0.705541i | ||||
\(340\) | −9.00000 | + | 5.19615i | −0.488094 | + | 0.281801i | ||||
\(341\) | 9.00000 | 0.487377 | ||||||||
\(342\) | 3.00000 | + | 5.19615i | 0.162221 | + | 0.280976i | ||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −16.5000 | + | 9.52628i | −0.889620 | + | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.5000 | + | 12.9904i | 1.20961 | + | 0.698367i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | −4.50000 | − | 2.59808i | −0.240879 | − | 0.139072i | 0.374701 | − | 0.927146i | \(-0.377745\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | −9.00000 | + | 1.73205i | −0.481070 | + | 0.0925820i | ||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | −13.5000 | − | 23.3827i | −0.719552 | − | 1.24630i | ||||
\(353\) | 1.50000 | − | 0.866025i | 0.0798369 | − | 0.0460939i | −0.459550 | − | 0.888152i | \(-0.651989\pi\) |
0.539387 | + | 0.842058i | \(0.318656\pi\) | |||||||
\(354\) | 3.00000 | + | 5.19615i | 0.159448 | + | 0.276172i | ||||
\(355\) | 1.50000 | − | 2.59808i | 0.0796117 | − | 0.137892i | ||||
\(356\) | 6.92820i | 0.367194i | ||||||||
\(357\) | −15.0000 | − | 5.19615i | −0.793884 | − | 0.275010i | ||||
\(358\) | −4.50000 | + | 2.59808i | −0.237832 | + | 0.137313i | ||||
\(359\) | −16.5000 | + | 9.52628i | −0.870837 | + | 0.502778i | −0.867626 | − | 0.497217i | \(-0.834355\pi\) |
−0.00321050 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(360\) | −6.00000 | −0.316228 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | − | 3.46410i | − | 0.182069i | ||||||
\(363\) | 16.0000 | 0.839782 | ||||||||
\(364\) | 4.00000 | + | 8.66025i | 0.209657 | + | 0.453921i | ||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 12.1244i | 0.633750i | ||||||||
\(367\) | −11.5000 | − | 19.9186i | −0.600295 | − | 1.03974i | −0.992776 | − | 0.119982i | \(-0.961716\pi\) |
0.392481 | − | 0.919760i | \(-0.371617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | + | 5.19615i | −0.468521 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | + | 23.3827i | 0.233628 | + | 1.21397i | ||||
\(372\) | 1.73205i | 0.0898027i | ||||||||
\(373\) | −9.50000 | + | 16.4545i | −0.491891 | + | 0.851981i | −0.999956 | − | 0.00933789i | \(-0.997028\pi\) |
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(374\) | 27.0000 | + | 46.7654i | 1.39614 | + | 2.41818i | ||||
\(375\) | −10.5000 | + | 6.06218i | −0.542218 | + | 0.313050i | ||||
\(376\) | −7.50000 | − | 12.9904i | −0.386783 | − | 0.669928i | ||||
\(377\) | −7.50000 | − | 7.79423i | −0.386270 | − | 0.401423i | ||||
\(378\) | 15.0000 | + | 17.3205i | 0.771517 | + | 0.890871i | ||||
\(379\) | −1.50000 | − | 0.866025i | −0.0770498 | − | 0.0444847i | 0.460980 | − | 0.887410i | \(-0.347498\pi\) |
−0.538030 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(380\) | 3.00000 | 0.153897 | ||||||||
\(381\) | −13.0000 | −0.666010 | ||||||||
\(382\) | −22.5000 | − | 12.9904i | −1.15120 | − | 0.664646i | ||||
\(383\) | −13.5000 | − | 7.79423i | −0.689818 | − | 0.398266i | 0.113726 | − | 0.993512i | \(-0.463721\pi\) |
−0.803544 | + | 0.595246i | \(0.797055\pi\) | |||||||
\(384\) | −10.5000 | + | 6.06218i | −0.535826 | + | 0.309359i | ||||
\(385\) | −4.50000 | − | 23.3827i | −0.229341 | − | 1.19169i | ||||
\(386\) | −1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | ||||
\(387\) | −22.0000 | −1.11832 | ||||||||
\(388\) | 4.50000 | − | 2.59808i | 0.228453 | − | 0.131897i | ||||
\(389\) | −1.50000 | + | 2.59808i | −0.0760530 | + | 0.131728i | −0.901544 | − | 0.432688i | \(-0.857565\pi\) |
0.825491 | + | 0.564416i | \(0.190898\pi\) | |||||||
\(390\) | 7.50000 | + | 7.79423i | 0.379777 | + | 0.394676i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −12.0000 | − | 1.73205i | −0.606092 | − | 0.0874818i | ||||
\(393\) | 7.50000 | − | 12.9904i | 0.378325 | − | 0.655278i | ||||
\(394\) | 19.5000 | − | 33.7750i | 0.982396 | − | 1.70156i | ||||
\(395\) | 7.50000 | + | 4.33013i | 0.377366 | + | 0.217872i | ||||
\(396\) | − | 10.3923i | − | 0.522233i | ||||||
\(397\) | 31.5000 | + | 18.1865i | 1.58094 | + | 0.912756i | 0.994722 | + | 0.102602i | \(0.0327168\pi\) |
0.586217 | + | 0.810154i | \(0.300617\pi\) | |||||||
\(398\) | − | 6.92820i | − | 0.347279i | ||||||
\(399\) | 3.00000 | + | 3.46410i | 0.150188 | + | 0.173422i | ||||
\(400\) | 5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | ||||
\(401\) | − | 6.92820i | − | 0.345978i | −0.984924 | − | 0.172989i | \(-0.944657\pi\) | ||
0.984924 | − | 0.172989i | \(-0.0553425\pi\) | |||||||
\(402\) | 7.50000 | − | 12.9904i | 0.374066 | − | 0.647901i | ||||
\(403\) | 4.50000 | − | 4.33013i | 0.224161 | − | 0.215699i | ||||
\(404\) | −4.50000 | − | 7.79423i | −0.223883 | − | 0.387777i | ||||
\(405\) | −1.50000 | − | 0.866025i | −0.0745356 | − | 0.0430331i | ||||
\(406\) | −13.5000 | + | 2.59808i | −0.669994 | + | 0.128940i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.00000 | − | 5.19615i | 0.445566 | − | 0.257248i | ||||
\(409\) | − | 6.92820i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547931\pi\) | |||||||
\(410\) | 15.5885i | 0.769859i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.50000 | − | 11.2583i | −0.320232 | − | 0.554658i | ||||
\(413\) | −6.00000 | − | 6.92820i | −0.295241 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 5.19615i | −0.147264 | − | 0.255069i | ||||
\(416\) | −18.0000 | − | 5.19615i | −0.882523 | − | 0.254762i | ||||
\(417\) | −6.50000 | + | 11.2583i | −0.318306 | + | 0.551323i | ||||
\(418\) | − | 15.5885i | − | 0.762456i | ||||||
\(419\) | −10.5000 | + | 18.1865i | −0.512959 | + | 0.888470i | 0.486928 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(420\) | 4.50000 | − | 0.866025i | 0.219578 | − | 0.0422577i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 19.5000 | + | 11.2583i | 0.949245 | + | 0.548047i | ||||
\(423\) | − | 17.3205i | − | 0.842152i | ||||||
\(424\) | −13.5000 | − | 7.79423i | −0.655618 | − | 0.378521i | ||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 1.50000 | − | 2.59808i | 0.0726752 | − | 0.125877i | ||||
\(427\) | −3.50000 | − | 18.1865i | −0.169377 | − | 0.880108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.5000 | − | 12.9904i | 0.651786 | − | 0.627182i | ||||
\(430\) | −16.5000 | + | 28.5788i | −0.795701 | + | 1.37819i | ||||
\(431\) | −28.5000 | + | 16.4545i | −1.37280 | + | 0.792585i | −0.991279 | − | 0.131777i | \(-0.957932\pi\) |
−0.381517 | + | 0.924362i | \(0.624598\pi\) | |||||||
\(432\) | −25.0000 | −1.20281 | ||||||||
\(433\) | −9.50000 | − | 16.4545i | −0.456541 | − | 0.790752i | 0.542234 | − | 0.840227i | \(-0.317578\pi\) |
−0.998775 | + | 0.0494752i | \(0.984245\pi\) | |||||||
\(434\) | −1.50000 | − | 7.79423i | −0.0720023 | − | 0.374135i | ||||
\(435\) | −4.50000 | + | 2.59808i | −0.215758 | + | 0.124568i | ||||
\(436\) | 4.50000 | + | 2.59808i | 0.215511 | + | 0.124425i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 15.0000 | 0.716728 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 13.5000 | + | 7.79423i | 0.643587 | + | 0.371575i | ||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 36.0000 | + | 10.3923i | 1.71235 | + | 0.494312i | ||||
\(443\) | −7.50000 | − | 12.9904i | −0.356336 | − | 0.617192i | 0.631010 | − | 0.775775i | \(-0.282641\pi\) |
−0.987346 | + | 0.158583i | \(0.949307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | − | 10.3923i | −0.284427 | − | 0.492642i | ||||
\(446\) | 4.50000 | − | 7.79423i | 0.213081 | − | 0.369067i | ||||
\(447\) | − | 19.0526i | − | 0.901155i | ||||||
\(448\) | 2.00000 | − | 1.73205i | 0.0944911 | − | 0.0818317i | ||||
\(449\) | 1.50000 | − | 0.866025i | 0.0707894 | − | 0.0408703i | −0.464188 | − | 0.885737i | \(-0.653654\pi\) |
0.534977 | + | 0.844867i | \(0.320320\pi\) | |||||||
\(450\) | 6.00000 | − | 3.46410i | 0.282843 | − | 0.163299i | ||||
\(451\) | 27.0000 | 1.27138 | ||||||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | 12.1244i | 0.569652i | ||||||||
\(454\) | 30.0000 | 1.40797 | ||||||||
\(455\) | −13.5000 | − | 9.52628i | −0.632890 | − | 0.446599i | ||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | − | 34.6410i | − | 1.62044i | −0.586127 | − | 0.810219i | \(-0.699348\pi\) | ||
0.586127 | − | 0.810219i | \(-0.300652\pi\) | |||||||
\(458\) | 10.5000 | + | 18.1865i | 0.490633 | + | 0.849801i | ||||
\(459\) | 30.0000 | 1.40028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.5000 | − | 14.7224i | 1.18765 | − | 0.685692i | 0.229881 | − | 0.973219i | \(-0.426166\pi\) |
0.957773 | + | 0.287527i | \(0.0928330\pi\) | |||||||
\(462\) | −4.50000 | − | 23.3827i | −0.209359 | − | 1.08786i | ||||
\(463\) | 24.2487i | 1.12693i | 0.826139 | + | 0.563467i | \(0.190533\pi\) | ||||
−0.826139 | + | 0.563467i | \(0.809467\pi\) | |||||||
\(464\) | 7.50000 | − | 12.9904i | 0.348179 | − | 0.603063i | ||||
\(465\) | −1.50000 | − | 2.59808i | −0.0695608 | − | 0.120483i | ||||
\(466\) | −4.50000 | + | 2.59808i | −0.208458 | + | 0.120354i | ||||
\(467\) | 10.5000 | + | 18.1865i | 0.485882 | + | 0.841572i | 0.999868 | − | 0.0162260i | \(-0.00516512\pi\) |
−0.513986 | + | 0.857798i | \(0.671832\pi\) | |||||||
\(468\) | −5.00000 | − | 5.19615i | −0.231125 | − | 0.240192i | ||||
\(469\) | −7.50000 | + | 21.6506i | −0.346318 | + | 0.999733i | ||||
\(470\) | −22.5000 | − | 12.9904i | −1.03785 | − | 0.599202i | ||||
\(471\) | −23.0000 | −1.05978 | ||||||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | 49.5000 | + | 28.5788i | 2.27601 | + | 1.31406i | ||||
\(474\) | 7.50000 | + | 4.33013i | 0.344486 | + | 0.198889i | ||||
\(475\) | 3.00000 | − | 1.73205i | 0.137649 | − | 0.0794719i | ||||
\(476\) | 12.0000 | − | 10.3923i | 0.550019 | − | 0.476331i | ||||
\(477\) | −9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | ||||
\(478\) | −18.0000 | −0.823301 | ||||||||
\(479\) | 25.5000 | − | 14.7224i | 1.16512 | − | 0.672685i | 0.212598 | − | 0.977140i | \(-0.431808\pi\) |
0.952527 | + | 0.304455i | \(0.0984742\pi\) | |||||||
\(480\) | −4.50000 | + | 7.79423i | −0.205396 | + | 0.355756i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12.0000 | 0.546585 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | + | 13.8564i | −0.363636 | + | 0.629837i | ||||
\(485\) | −4.50000 | + | 7.79423i | −0.204334 | + | 0.353918i | ||||
\(486\) | −24.0000 | − | 13.8564i | −1.08866 | − | 0.628539i | ||||
\(487\) | 24.2487i | 1.09881i | 0.835555 | + | 0.549407i | \(0.185146\pi\) | ||||
−0.835555 | + | 0.549407i | \(0.814854\pi\) | |||||||
\(488\) | 10.5000 | + | 6.06218i | 0.475313 | + | 0.274422i | ||||
\(489\) | 12.1244i | 0.548282i | ||||||||
\(490\) | −19.5000 | + | 7.79423i | −0.880920 | + | 0.352107i | ||||
\(491\) | 13.5000 | − | 23.3827i | 0.609246 | − | 1.05525i | −0.382118 | − | 0.924113i | \(-0.624805\pi\) |
0.991365 | − | 0.131132i | \(-0.0418613\pi\) | |||||||
\(492\) | 5.19615i | 0.234261i | ||||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | −7.50000 | − | 7.79423i | −0.337441 | − | 0.350679i | ||||
\(495\) | 9.00000 | + | 15.5885i | 0.404520 | + | 0.700649i | ||||
\(496\) | 7.50000 | + | 4.33013i | 0.336760 | + | 0.194428i | ||||
\(497\) | −1.50000 | + | 4.33013i | −0.0672842 | + | 0.194233i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | 1.50000 | − | 0.866025i | 0.0671492 | − | 0.0387686i | −0.466049 | − | 0.884759i | \(-0.654323\pi\) |
0.533199 | + | 0.845990i | \(0.320990\pi\) | |||||||
\(500\) | − | 12.1244i | − | 0.542218i | ||||||
\(501\) | − | 1.73205i | − | 0.0773823i | ||||||
\(502\) | −4.50000 | + | 2.59808i | −0.200845 | + | 0.115958i | ||||
\(503\) | 4.50000 | + | 7.79423i | 0.200645 | + | 0.347527i | 0.948736 | − | 0.316068i | \(-0.102363\pi\) |
−0.748091 | + | 0.663596i | \(0.769030\pi\) | |||||||
\(504\) | 9.00000 | − | 1.73205i | 0.400892 | − | 0.0771517i | ||||
\(505\) | 13.5000 | + | 7.79423i | 0.600742 | + | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.500000 | − | 12.9904i | 0.0222058 | − | 0.576923i | ||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | − | 6.92820i | − | 0.307087i | −0.988142 | − | 0.153544i | \(-0.950931\pi\) | ||
0.988142 | − | 0.153544i | \(-0.0490686\pi\) | |||||||
\(510\) | 9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | ||||
\(511\) | −22.5000 | + | 4.33013i | −0.995341 | + | 0.191554i | ||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | −7.50000 | − | 4.33013i | −0.331133 | − | 0.191180i | ||||
\(514\) | − | 51.9615i | − | 2.29192i | ||||||
\(515\) | 19.5000 | + | 11.2583i | 0.859273 | + | 0.496101i | ||||
\(516\) | −5.50000 | + | 9.52628i | −0.242124 | + | 0.419371i | ||||
\(517\) | −22.5000 | + | 38.9711i | −0.989549 | + | 1.71395i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 10.5000 | − | 2.59808i | 0.460455 | − | 0.113933i | ||||
\(521\) | −19.5000 | + | 33.7750i | −0.854311 | + | 1.47971i | 0.0229727 | + | 0.999736i | \(0.492687\pi\) |
−0.877283 | + | 0.479973i | \(0.840646\pi\) | |||||||
\(522\) | 9.00000 | − | 5.19615i | 0.393919 | − | 0.227429i | ||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 7.50000 | + | 12.9904i | 0.327639 | + | 0.567487i | ||||
\(525\) | 4.00000 | − | 3.46410i | 0.174574 | − | 0.151186i | ||||
\(526\) | −4.50000 | + | 2.59808i | −0.196209 | + | 0.113282i | ||||
\(527\) | −9.00000 | − | 5.19615i | −0.392046 | − | 0.226348i | ||||
\(528\) | 22.5000 | + | 12.9904i | 0.979187 | + | 0.565334i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −27.0000 | −1.17281 | ||||||||
\(531\) | 6.00000 | + | 3.46410i | 0.260378 | + | 0.150329i | ||||
\(532\) | −4.50000 | + | 0.866025i | −0.195100 | + | 0.0375470i | ||||
\(533\) | 13.5000 | − | 12.9904i | 0.584750 | − | 0.562676i | ||||
\(534\) | −6.00000 | − | 10.3923i | −0.259645 | − | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.50000 | − | 12.9904i | −0.323951 | − | 0.561099i | ||||
\(537\) | 1.50000 | − | 2.59808i | 0.0647298 | − | 0.112115i | ||||
\(538\) | 10.3923i | 0.448044i | ||||||||
\(539\) | 13.5000 | + | 33.7750i | 0.581486 | + | 1.45479i | ||||
\(540\) | −7.50000 | + | 4.33013i | −0.322749 | + | 0.186339i | ||||
\(541\) | −10.5000 | + | 6.06218i | −0.451430 | + | 0.260633i | −0.708434 | − | 0.705777i | \(-0.750598\pi\) |
0.257004 | + | 0.966410i | \(0.417265\pi\) | |||||||
\(542\) | −30.0000 | −1.28861 | ||||||||
\(543\) | 1.00000 | + | 1.73205i | 0.0429141 | + | 0.0743294i | ||||
\(544\) | 31.1769i | 1.33670i | ||||||||
\(545\) | −9.00000 | −0.385518 | ||||||||
\(546\) | −13.5000 | − | 9.52628i | −0.577747 | − | 0.407687i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.00000 | + | 12.1244i | 0.298753 | + | 0.517455i | ||||
\(550\) | −18.0000 | −0.767523 | ||||||||
\(551\) | 4.50000 | − | 2.59808i | 0.191706 | − | 0.110682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5000 | − | 4.33013i | −0.531554 | − | 0.184136i | ||||
\(554\) | 17.3205i | 0.735878i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.50000 | − | 11.2583i | −0.275661 | − | 0.477460i | ||||
\(557\) | 13.5000 | − | 7.79423i | 0.572013 | − | 0.330252i | −0.185940 | − | 0.982561i | \(-0.559533\pi\) |
0.757953 | + | 0.652309i | \(0.226200\pi\) | |||||||
\(558\) | 3.00000 | + | 5.19615i | 0.127000 | + | 0.219971i | ||||
\(559\) | 38.5000 | − | 9.52628i | 1.62838 | − | 0.402919i | ||||
\(560\) | 7.50000 | − | 21.6506i | 0.316933 | − | 0.914906i | ||||
\(561\) | −27.0000 | − | 15.5885i | −1.13994 | − | 0.658145i | ||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | −36.0000 | −1.51722 | −0.758610 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758610 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(564\) | −7.50000 | − | 4.33013i | −0.315807 | − | 0.182331i | ||||
\(565\) | −22.5000 | − | 12.9904i | −0.946582 | − | 0.546509i | ||||
\(566\) | −28.5000 | + | 16.4545i | −1.19794 | + | 0.691633i | ||||
\(567\) | 2.50000 | + | 0.866025i | 0.104990 | + | 0.0363696i | ||||
\(568\) | −1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | ||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | −4.50000 | + | 2.59808i | −0.188484 | + | 0.108821i | ||||
\(571\) | 11.5000 | − | 19.9186i | 0.481260 | − | 0.833567i | −0.518509 | − | 0.855072i | \(-0.673513\pi\) |
0.999769 | + | 0.0215055i | \(0.00684595\pi\) | |||||||
\(572\) | 4.50000 | + | 18.1865i | 0.188154 | + | 0.760417i | ||||
\(573\) | 15.0000 | 0.626634 | ||||||||
\(574\) | −4.50000 | − | 23.3827i | −0.187826 | − | 0.975974i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | + | 1.73205i | −0.0416667 | + | 0.0721688i | ||||
\(577\) | 13.5000 | + | 7.79423i | 0.562012 | + | 0.324478i | 0.753953 | − | 0.656929i | \(-0.228145\pi\) |
−0.191940 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(578\) | − | 32.9090i | − | 1.36883i | ||||||
\(579\) | 1.50000 | + | 0.866025i | 0.0623379 | + | 0.0359908i | ||||
\(580\) | − | 5.19615i | − | 0.215758i | ||||||
\(581\) | 6.00000 | + | 6.92820i | 0.248922 | + | 0.287430i | ||||
\(582\) | −4.50000 | + | 7.79423i | −0.186531 | + | 0.323081i | ||||
\(583\) | 46.7654i | 1.93682i | ||||||||
\(584\) | 7.50000 | − | 12.9904i | 0.310352 | − | 0.537546i | ||||
\(585\) | 12.0000 | + | 3.46410i | 0.496139 | + | 0.143223i | ||||
\(586\) | 22.5000 | + | 38.9711i | 0.929466 | + | 1.60988i | ||||
\(587\) | −13.5000 | − | 7.79423i | −0.557205 | − | 0.321702i | 0.194818 | − | 0.980839i | \(-0.437588\pi\) |
−0.752023 | + | 0.659137i | \(0.770922\pi\) | |||||||
\(588\) | −6.50000 | + | 2.59808i | −0.268055 | + | 0.107143i | ||||
\(589\) | 1.50000 | + | 2.59808i | 0.0618064 | + | 0.107052i | ||||
\(590\) | 9.00000 | − | 5.19615i | 0.370524 | − | 0.213922i | ||||
\(591\) | 22.5167i | 0.926212i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.50000 | + | 2.59808i | −0.184793 | + | 0.106690i | −0.589543 | − | 0.807737i | \(-0.700692\pi\) |
0.404750 | + | 0.914428i | \(0.367359\pi\) | |||||||
\(594\) | 22.5000 | + | 38.9711i | 0.923186 | + | 1.59901i | ||||
\(595\) | −9.00000 | + | 25.9808i | −0.368964 | + | 1.06511i | ||||
\(596\) | 16.5000 | + | 9.52628i | 0.675866 | + | 0.390212i | ||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | + | 7.79423i | −0.183865 | + | 0.318464i | −0.943193 | − | 0.332244i | \(-0.892194\pi\) |
0.759328 | + | 0.650708i | \(0.225528\pi\) | |||||||
\(600\) | 3.46410i | 0.141421i | ||||||||
\(601\) | −9.50000 | + | 16.4545i | −0.387513 | + | 0.671192i | −0.992114 | − | 0.125336i | \(-0.959999\pi\) |
0.604601 | + | 0.796528i | \(0.293332\pi\) | |||||||
\(602\) | 16.5000 | − | 47.6314i | 0.672490 | − | 1.94131i | ||||
\(603\) | − | 17.3205i | − | 0.705346i | ||||||
\(604\) | −10.5000 | − | 6.06218i | −0.427239 | − | 0.246667i | ||||
\(605\) | − | 27.7128i | − | 1.12669i | ||||||
\(606\) | 13.5000 | + | 7.79423i | 0.548400 | + | 0.316619i | ||||
\(607\) | 21.5000 | − | 37.2391i | 0.872658 | − | 1.51149i | 0.0134214 | − | 0.999910i | \(-0.495728\pi\) |
0.859237 | − | 0.511578i | \(-0.170939\pi\) | |||||||
\(608\) | 4.50000 | − | 7.79423i | 0.182499 | − | 0.316098i | ||||
\(609\) | 6.00000 | − | 5.19615i | 0.243132 | − | 0.210559i | ||||
\(610\) | 21.0000 | 0.850265 | ||||||||
\(611\) | 7.50000 | + | 30.3109i | 0.303418 | + | 1.22625i | ||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | 31.5000 | − | 18.1865i | 1.27227 | − | 0.734547i | 0.296858 | − | 0.954922i | \(-0.404061\pi\) |
0.975415 | + | 0.220375i | \(0.0707280\pi\) | |||||||
\(614\) | −42.0000 | −1.69498 | ||||||||
\(615\) | −4.50000 | − | 7.79423i | −0.181458 | − | 0.314294i | ||||
\(616\) | −22.5000 | − | 7.79423i | −0.906551 | − | 0.314038i | ||||
\(617\) | 37.5000 | − | 21.6506i | 1.50969 | − | 0.871622i | 0.509757 | − | 0.860318i | \(-0.329735\pi\) |
0.999936 | − | 0.0113033i | \(-0.00359804\pi\) | |||||||
\(618\) | 19.5000 | + | 11.2583i | 0.784405 | + | 0.452876i | ||||
\(619\) | 16.5000 | + | 9.52628i | 0.663191 | + | 0.382893i | 0.793492 | − | 0.608581i | \(-0.208261\pi\) |
−0.130301 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(620\) | 3.00000 | 0.120483 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.5000 | − | 12.9904i | −0.902168 | − | 0.520867i | ||||
\(623\) | 12.0000 | + | 13.8564i | 0.480770 | + | 0.555145i | ||||
\(624\) | 17.5000 | − | 4.33013i | 0.700561 | − | 0.173344i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −28.5000 | + | 16.4545i | −1.13909 | + | 0.657653i | ||||
\(627\) | 4.50000 | + | 7.79423i | 0.179713 | + | 0.311272i | ||||
\(628\) | 11.5000 | − | 19.9186i | 0.458900 | − | 0.794838i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 12.0000 | − | 10.3923i | 0.478091 | − | 0.414039i | ||||
\(631\) | −40.5000 | + | 23.3827i | −1.61228 | + | 0.930850i | −0.623439 | + | 0.781872i | \(0.714265\pi\) |
−0.988841 | + | 0.148978i | \(0.952402\pi\) | |||||||
\(632\) | 7.50000 | − | 4.33013i | 0.298334 | − | 0.172243i | ||||
\(633\) | −13.0000 | −0.516704 | ||||||||
\(634\) | 4.50000 | + | 7.79423i | 0.178718 | + | 0.309548i | ||||
\(635\) | 22.5167i | 0.893546i | ||||||||
\(636\) | −9.00000 | −0.356873 | ||||||||
\(637\) | 23.0000 | + | 10.3923i | 0.911293 | + | 0.411758i | ||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | − | 3.46410i | − | 0.137038i | ||||||
\(640\) | 10.5000 | + | 18.1865i | 0.415049 | + | 0.718886i | ||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.50000 | + | 2.59808i | −0.177463 | + | 0.102458i | −0.586100 | − | 0.810239i | \(-0.699337\pi\) |
0.408637 | + | 0.912697i | \(0.366004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 19.0526i | − | 0.750194i | ||||||
\(646\) | −9.00000 | + | 15.5885i | −0.354100 | + | 0.613320i | ||||
\(647\) | 4.50000 | + | 7.79423i | 0.176913 | + | 0.306423i | 0.940822 | − | 0.338902i | \(-0.110055\pi\) |
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(648\) | −1.50000 | + | 0.866025i | −0.0589256 | + | 0.0340207i | ||||
\(649\) | −9.00000 | − | 15.5885i | −0.353281 | − | 0.611900i | ||||
\(650\) | −9.00000 | + | 8.66025i | −0.353009 | + | 0.339683i | ||||
\(651\) | 3.00000 | + | 3.46410i | 0.117579 | + | 0.135769i | ||||
\(652\) | −10.5000 | − | 6.06218i | −0.411212 | − | 0.237413i | ||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | −9.00000 | −0.351928 | ||||||||
\(655\) | −22.5000 | − | 12.9904i | −0.879148 | − | 0.507576i | ||||
\(656\) | 22.5000 | + | 12.9904i | 0.878477 | + | 0.507189i | ||||
\(657\) | 15.0000 | − | 8.66025i | 0.585206 | − | 0.337869i | ||||
\(658\) | 37.5000 | + | 12.9904i | 1.46190 | + | 0.506418i | ||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | 9.00000 | 0.350325 | ||||||||
\(661\) | 31.5000 | − | 18.1865i | 1.22521 | − | 0.707374i | 0.259184 | − | 0.965828i | \(-0.416546\pi\) |
0.966024 | + | 0.258454i | \(0.0832129\pi\) | |||||||
\(662\) | 28.5000 | − | 49.3634i | 1.10768 | − | 1.91856i | ||||
\(663\) | −21.0000 | + | 5.19615i | −0.815572 | + | 0.201802i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 6.00000 | − | 5.19615i | 0.232670 | − | 0.201498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.50000 | + | 0.866025i | 0.0580367 | + | 0.0335075i | ||||
\(669\) | 5.19615i | 0.200895i | ||||||||
\(670\) | −22.5000 | − | 12.9904i | −0.869251 | − | 0.501862i | ||||
\(671\) | − | 36.3731i | − | 1.40417i | ||||||
\(672\) | 4.50000 | − | 12.9904i | 0.173591 | − | 0.501115i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | − | 38.1051i | − | 1.46775i | ||||||
\(675\) | −5.00000 | + | 8.66025i | −0.192450 | + | 0.333333i | ||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | −13.5000 | − | 23.3827i | −0.518847 | − | 0.898670i | −0.999760 | − | 0.0219013i | \(-0.993028\pi\) |
0.480913 | − | 0.876768i | \(-0.340305\pi\) | |||||||
\(678\) | −22.5000 | − | 12.9904i | −0.864107 | − | 0.498893i | ||||
\(679\) | 4.50000 | − | 12.9904i | 0.172694 | − | 0.498525i | ||||
\(680\) | −9.00000 | − | 15.5885i | −0.345134 | − | 0.597790i | ||||
\(681\) | −15.0000 | + | 8.66025i | −0.574801 | + | 0.331862i | ||||
\(682\) | − | 15.5885i | − | 0.596913i | ||||||
\(683\) | − | 24.2487i | − | 0.927851i | −0.885874 | − | 0.463926i | \(-0.846441\pi\) | ||
0.885874 | − | 0.463926i | \(-0.153559\pi\) | |||||||
\(684\) | 3.00000 | − | 1.73205i | 0.114708 | − | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.0000 | − | 17.3205i | 1.03086 | − | 0.661300i | ||||
\(687\) | −10.5000 | − | 6.06218i | −0.400600 | − | 0.231287i | ||||
\(688\) | 27.5000 | + | 47.6314i | 1.04843 | + | 1.81593i | ||||
\(689\) | 22.5000 | + | 23.3827i | 0.857182 | + | 0.890809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1769i | 1.18603i | 0.805193 | + | 0.593013i | \(0.202062\pi\) | ||||
−0.805193 | + | 0.593013i | \(0.797938\pi\) | |||||||
\(692\) | 7.50000 | − | 12.9904i | 0.285107 | − | 0.493820i | ||||
\(693\) | −18.0000 | − | 20.7846i | −0.683763 | − | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.5000 | + | 11.2583i | 0.739677 | + | 0.427053i | ||||
\(696\) | 5.19615i | 0.196960i | ||||||||
\(697\) | −27.0000 | − | 15.5885i | −1.02270 | − | 0.590455i | ||||
\(698\) | −4.50000 | + | 7.79423i | −0.170328 | + | 0.295016i | ||||
\(699\) | 1.50000 | − | 2.59808i | 0.0567352 | − | 0.0982683i | ||||
\(700\) | 1.00000 | + | 5.19615i | 0.0377964 | + | 0.196396i | ||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 30.0000 | + | 8.66025i | 1.13228 | + | 0.326860i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.50000 | − | 2.59808i | 0.169600 | − | 0.0979187i | ||||
\(705\) | 15.0000 | 0.564933 | ||||||||
\(706\) | −1.50000 | − | 2.59808i | −0.0564532 | − | 0.0977799i | ||||
\(707\) | −22.5000 | − | 7.79423i | −0.846200 | − | 0.293132i | ||||
\(708\) | 3.00000 | − | 1.73205i | 0.112747 | − | 0.0650945i | ||||
\(709\) | −10.5000 | − | 6.06218i | −0.394336 | − | 0.227670i | 0.289701 | − | 0.957117i | \(-0.406444\pi\) |
−0.684037 | + | 0.729447i | \(0.739777\pi\) | |||||||
\(710\) | −4.50000 | − | 2.59808i | −0.168882 | − | 0.0975041i | ||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | −12.0000 | −0.449719 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −9.00000 | + | 25.9808i | −0.336817 | + | 0.972306i | ||||
\(715\) | −22.5000 | − | 23.3827i | −0.841452 | − | 0.874463i | ||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | 9.00000 | − | 5.19615i | 0.336111 | − | 0.194054i | ||||
\(718\) | 16.5000 | + | 28.5788i | 0.615775 | + | 1.06655i | ||||
\(719\) | 7.50000 | − | 12.9904i | 0.279703 | − | 0.484459i | −0.691608 | − | 0.722273i | \(-0.743097\pi\) |
0.971311 | + | 0.237814i | \(0.0764307\pi\) | |||||||
\(720\) | 17.3205i | 0.645497i | ||||||||
\(721\) | −32.5000 | − | 11.2583i | −1.21036 | − | 0.419282i | ||||
\(722\) | −24.0000 | + | 13.8564i | −0.893188 | + | 0.515682i | ||||
\(723\) | −6.00000 | + | 3.46410i | −0.223142 | + | 0.128831i | ||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | − | 27.7128i | − | 1.02852i | ||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | −15.0000 | + | 6.92820i | −0.555937 | + | 0.256776i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | − | 25.9808i | − | 0.961591i | ||||||
\(731\) | −33.0000 | − | 57.1577i | −1.22055 | − | 2.11405i | ||||
\(732\) | 7.00000 | 0.258727 | ||||||||
\(733\) | 43.5000 | − | 25.1147i | 1.60671 | − | 0.927634i | 0.616609 | − | 0.787269i | \(-0.288506\pi\) |
0.990100 | − | 0.140365i | \(-0.0448275\pi\) | |||||||
\(734\) | −34.5000 | + | 19.9186i | −1.27342 | + | 0.735208i | ||||
\(735\) | 7.50000 | − | 9.52628i | 0.276642 | − | 0.351382i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.5000 | + | 38.9711i | −0.828798 | + | 1.43552i | ||||
\(738\) | 9.00000 | + | 15.5885i | 0.331295 | + | 0.573819i | ||||
\(739\) | −34.5000 | + | 19.9186i | −1.26910 | + | 0.732717i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | + | 1.73205i | 0.220416 | + | 0.0636285i | ||||
\(742\) | 40.5000 | − | 7.79423i | 1.48680 | − | 0.286135i | ||||
\(743\) | −1.50000 | − | 0.866025i | −0.0550297 | − | 0.0317714i | 0.472233 | − | 0.881474i | \(-0.343448\pi\) |
−0.527262 | + | 0.849703i | \(0.676782\pi\) | |||||||
\(744\) | −3.00000 | −0.109985 | ||||||||
\(745\) | −33.0000 | −1.20903 | ||||||||
\(746\) | 28.5000 | + | 16.4545i | 1.04346 | + | 0.602441i | ||||
\(747\) | −6.00000 | − | 3.46410i | −0.219529 | − | 0.126745i | ||||
\(748\) | 27.0000 | − | 15.5885i | 0.987218 | − | 0.569970i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.5000 | + | 18.1865i | 0.383406 | + | 0.664078i | ||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | −37.5000 | + | 21.6506i | −1.36748 | + | 0.789517i | ||||
\(753\) | 1.50000 | − | 2.59808i | 0.0546630 | − | 0.0946792i | ||||
\(754\) | −13.5000 | + | 12.9904i | −0.491641 | + | 0.473082i | ||||
\(755\) | 21.0000 | 0.764268 | ||||||||
\(756\) | 10.0000 | − | 8.66025i | 0.363696 | − | 0.314970i | ||||
\(757\) | 8.50000 | − | 14.7224i | 0.308938 | − | 0.535096i | −0.669193 | − | 0.743089i | \(-0.733360\pi\) |
0.978130 | + | 0.207993i | \(0.0666932\pi\) | |||||||
\(758\) | −1.50000 | + | 2.59808i | −0.0544825 | + | 0.0943664i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.19615i | 0.188484i | ||||||||
\(761\) | 25.5000 | + | 14.7224i | 0.924374 | + | 0.533688i | 0.885028 | − | 0.465538i | \(-0.154139\pi\) |
0.0393463 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(762\) | 22.5167i | 0.815693i | ||||||||
\(763\) | 13.5000 | − | 2.59808i | 0.488733 | − | 0.0940567i | ||||
\(764\) | −7.50000 | + | 12.9904i | −0.271340 | + | 0.469975i | ||||
\(765\) | − | 20.7846i | − | 0.751469i | ||||||
\(766\) | −13.5000 | + | 23.3827i | −0.487775 | + | 0.844851i | ||||
\(767\) | −12.0000 | − | 3.46410i | −0.433295 | − | 0.125081i | ||||
\(768\) | 9.50000 | + | 16.4545i | 0.342802 | + | 0.593750i | ||||
\(769\) | −16.5000 | − | 9.52628i | −0.595005 | − | 0.343526i | 0.172069 | − | 0.985085i | \(-0.444955\pi\) |
−0.767074 | + | 0.641558i | \(0.778288\pi\) | |||||||
\(770\) | −40.5000 | + | 7.79423i | −1.45952 | + | 0.280885i | ||||
\(771\) | 15.0000 | + | 25.9808i | 0.540212 | + | 0.935674i | ||||
\(772\) | −1.50000 | + | 0.866025i | −0.0539862 | + | 0.0311689i | ||||
\(773\) | 13.8564i | 0.498380i | 0.968455 | + | 0.249190i | \(0.0801644\pi\) | ||||
−0.968455 | + | 0.249190i | \(0.919836\pi\) | |||||||
\(774\) | 38.1051i | 1.36966i | ||||||||
\(775\) | 3.00000 | − | 1.73205i | 0.107763 | − | 0.0622171i | ||||
\(776\) | 4.50000 | + | 7.79423i | 0.161541 | + | 0.279797i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | + | 2.59808i | 0.161333 | + | 0.0931455i | ||||
\(779\) | 4.50000 | + | 7.79423i | 0.161229 | + | 0.279257i | ||||
\(780\) | 4.50000 | − | 4.33013i | 0.161126 | − | 0.155043i | ||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.50000 | + | 12.9904i | −0.268028 | + | 0.464238i | ||||
\(784\) | −5.00000 | + | 34.6410i | −0.178571 | + | 1.23718i | ||||
\(785\) | 39.8372i | 1.42185i | ||||||||
\(786\) | −22.5000 | − | 12.9904i | −0.802548 | − | 0.463352i | ||||
\(787\) | 31.1769i | 1.11134i | 0.831404 | + | 0.555668i | \(0.187538\pi\) | ||||
−0.831404 | + | 0.555668i | \(0.812462\pi\) | |||||||
\(788\) | −19.5000 | − | 11.2583i | −0.694659 | − | 0.401061i | ||||
\(789\) | 1.50000 | − | 2.59808i | 0.0534014 | − | 0.0924940i | ||||
\(790\) | 7.50000 | − | 12.9904i | 0.266838 | − | 0.462177i | ||||
\(791\) | 37.5000 | + | 12.9904i | 1.33335 | + | 0.461885i | ||||
\(792\) | 18.0000 | 0.639602 | ||||||||
\(793\) | −17.5000 | − | 18.1865i | −0.621443 | − | 0.645823i | ||||
\(794\) | 31.5000 | − | 54.5596i | 1.11789 | − | 1.93625i | ||||
\(795\) | 13.5000 | − | 7.79423i | 0.478796 | − | 0.276433i | ||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | 16.5000 | + | 28.5788i | 0.584460 | + | 1.01231i | 0.994943 | + | 0.100446i | \(0.0320269\pi\) |
−0.410483 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(798\) | 6.00000 | − | 5.19615i | 0.212398 | − | 0.183942i | ||||
\(799\) | 45.0000 | − | 25.9808i | 1.59199 | − | 0.919133i | ||||
\(800\) | −9.00000 | − | 5.19615i | −0.318198 | − | 0.183712i | ||||
\(801\) | −12.0000 | − | 6.92820i | −0.423999 | − | 0.244796i | ||||
\(802\) | −12.0000 | −0.423735 | ||||||||
\(803\) | −45.0000 | −1.58802 | ||||||||
\(804\) | −7.50000 | − | 4.33013i | −0.264505 | − | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.50000 | − | 7.79423i | −0.264176 | − | 0.274540i | ||||
\(807\) | −3.00000 | − | 5.19615i | −0.105605 | − | 0.182913i | ||||
\(808\) | 13.5000 | − | 7.79423i | 0.474928 | − | 0.274200i | ||||
\(809\) | 10.5000 | + | 18.1865i | 0.369160 | + | 0.639404i | 0.989434 | − | 0.144981i | \(-0.0463120\pi\) |
−0.620274 | + | 0.784385i | \(0.712979\pi\) | |||||||
\(810\) | −1.50000 | + | 2.59808i | −0.0527046 | + | 0.0912871i | ||||
\(811\) | 3.46410i | 0.121641i | 0.998149 | + | 0.0608205i | \(0.0193717\pi\) | ||||
−0.998149 | + | 0.0608205i | \(0.980628\pi\) | |||||||
\(812\) | 1.50000 | + | 7.79423i | 0.0526397 | + | 0.273524i | ||||
\(813\) | 15.0000 | − | 8.66025i | 0.526073 | − | 0.303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0000 | 0.735598 | ||||||||
\(816\) | −15.0000 | − | 25.9808i | −0.525105 | − | 0.909509i | ||||
\(817\) | 19.0526i | 0.666565i | ||||||||
\(818\) | −12.0000 | −0.419570 | ||||||||
\(819\) | −19.0000 | − | 1.73205i | −0.663914 | − | 0.0605228i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 19.5000 | − | 11.2583i | 0.679315 | − | 0.392203i | ||||
\(825\) | 9.00000 | − | 5.19615i | 0.313340 | − | 0.180907i | ||||
\(826\) | −12.0000 | + | 10.3923i | −0.417533 | + | 0.361595i | ||||
\(827\) | − | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | \(-0.942168\pi\) | ||
0.983540 | − | 0.180688i | \(-0.0578324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.50000 | − | 6.06218i | −0.121560 | − | 0.210548i | 0.798823 | − | 0.601566i | \(-0.205456\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | −9.00000 | + | 5.19615i | −0.312395 | + | 0.180361i | ||||
\(831\) | −5.00000 | − | 8.66025i | −0.173448 | − | 0.300421i | ||||
\(832\) | 1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | ||||
\(833\) | 6.00000 | − | 41.5692i | 0.207888 | − | 1.44029i | ||||
\(834\) | 19.5000 | + | 11.2583i | 0.675230 | + | 0.389844i | ||||
\(835\) | −3.00000 | −0.103819 | ||||||||
\(836\) | −9.00000 | −0.311272 | ||||||||
\(837\) | −7.50000 | − | 4.33013i | −0.259238 | − | 0.149671i | ||||
\(838\) | 31.5000 | + | 18.1865i | 1.08815 | + | 0.628243i | ||||
\(839\) | 1.50000 | − | 0.866025i | 0.0517858 | − | 0.0298985i | −0.473884 | − | 0.880587i | \(-0.657148\pi\) |
0.525669 | + | 0.850689i | \(0.323815\pi\) | |||||||
\(840\) | 1.50000 | + | 7.79423i | 0.0517549 | + | 0.268926i | ||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | + | 3.46410i | −0.206651 | + | 0.119310i | ||||
\(844\) | 6.50000 | − | 11.2583i | 0.223739 | − | 0.387528i | ||||
\(845\) | −22.5000 | − | 0.866025i | −0.774024 | − | 0.0297922i | ||||
\(846\) | −30.0000 | −1.03142 | ||||||||
\(847\) | 8.00000 | + | 41.5692i | 0.274883 | + | 1.42834i | ||||
\(848\) | −22.5000 | + | 38.9711i | −0.772653 | + | 1.33827i | ||||
\(849\) | 9.50000 | − | 16.4545i | 0.326039 | − | 0.564716i | ||||
\(850\) | 18.0000 | + | 10.3923i | 0.617395 | + | 0.356453i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −1.50000 | − | 0.866025i | −0.0513892 | − | 0.0296695i | ||||
\(853\) | − | 41.5692i | − | 1.42330i | −0.702533 | − | 0.711651i | \(-0.747948\pi\) | ||
0.702533 | − | 0.711651i | \(-0.252052\pi\) | |||||||
\(854\) | −31.5000 | + | 6.06218i | −1.07791 | + | 0.207443i | ||||
\(855\) | −3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5000 | − | 28.5788i | 0.563629 | − | 0.976235i | −0.433546 | − | 0.901131i | \(-0.642738\pi\) |
0.997176 | − | 0.0751033i | \(-0.0239287\pi\) | |||||||
\(858\) | −22.5000 | − | 23.3827i | −0.768137 | − | 0.798272i | ||||
\(859\) | 14.5000 | + | 25.1147i | 0.494734 | + | 0.856904i | 0.999982 | − | 0.00607046i | \(-0.00193230\pi\) |
−0.505248 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(860\) | 16.5000 | + | 9.52628i | 0.562645 | + | 0.324843i | ||||
\(861\) | 9.00000 | + | 10.3923i | 0.306719 | + | 0.354169i | ||||
\(862\) | 28.5000 | + | 49.3634i | 0.970714 | + | 1.68133i | ||||
\(863\) | 1.50000 | − | 0.866025i | 0.0510606 | − | 0.0294798i | −0.474252 | − | 0.880389i | \(-0.657282\pi\) |
0.525313 | + | 0.850909i | \(0.323948\pi\) | |||||||
\(864\) | 25.9808i | 0.883883i | ||||||||
\(865\) | 25.9808i | 0.883372i | ||||||||
\(866\) | −28.5000 | + | 16.4545i | −0.968469 | + | 0.559146i | ||||
\(867\) | 9.50000 | + | 16.4545i | 0.322637 | + | 0.558824i | ||||
\(868\) | −4.50000 | + | 0.866025i | −0.152740 | + | 0.0293948i | ||||
\(869\) | −22.5000 | − | 12.9904i | −0.763260 | − | 0.440668i | ||||
\(870\) | 4.50000 | + | 7.79423i | 0.152564 | + | 0.264249i | ||||
\(871\) | 7.50000 | + | 30.3109i | 0.254128 | + | 1.02705i | ||||
\(872\) | −4.50000 | + | 7.79423i | −0.152389 | + | 0.263946i | ||||
\(873\) | 10.3923i | 0.351726i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.0000 | − | 24.2487i | −0.709930 | − | 0.819756i | ||||
\(876\) | − | 8.66025i | − | 0.292603i | ||||||
\(877\) | 1.50000 | + | 0.866025i | 0.0506514 | + | 0.0292436i | 0.525112 | − | 0.851033i | \(-0.324023\pi\) |
−0.474460 | + | 0.880277i | \(0.657357\pi\) | |||||||
\(878\) | − | 13.8564i | − | 0.467631i | ||||||
\(879\) | −22.5000 | − | 12.9904i | −0.758906 | − | 0.438155i | ||||
\(880\) | 22.5000 | − | 38.9711i | 0.758475 | − | 1.31372i | ||||
\(881\) | 16.5000 | − | 28.5788i | 0.555899 | − | 0.962846i | −0.441934 | − | 0.897048i | \(-0.645707\pi\) |
0.997833 | − | 0.0657979i | \(-0.0209593\pi\) | |||||||
\(882\) | −15.0000 | + | 19.0526i | −0.505076 | + | 0.641533i | ||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 6.00000 | − | 20.7846i | 0.201802 | − | 0.699062i | ||||
\(885\) | −3.00000 | + | 5.19615i | −0.100844 | + | 0.174667i | ||||
\(886\) | −22.5000 | + | 12.9904i | −0.755902 | + | 0.436420i | ||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | − | 33.7750i | −0.218003 | − | 1.13278i | ||||
\(890\) | −18.0000 | + | 10.3923i | −0.603361 | + | 0.348351i | ||||
\(891\) | 4.50000 | + | 2.59808i | 0.150756 | + | 0.0870388i | ||||
\(892\) | −4.50000 | − | 2.59808i | −0.150671 | − | 0.0869900i | ||||
\(893\) | −15.0000 | −0.501956 | ||||||||
\(894\) | −33.0000 | −1.10369 | ||||||||
\(895\) | −4.50000 | − | 2.59808i | −0.150418 | − | 0.0868441i | ||||
\(896\) | −21.0000 | − | 24.2487i | −0.701561 | − | 0.810093i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.50000 | − | 2.59808i | −0.0500556 | − | 0.0866989i | ||||
\(899\) | 4.50000 | − | 2.59808i | 0.150083 | − | 0.0866507i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 27.0000 | − | 46.7654i | 0.899500 | − | 1.55798i | ||||
\(902\) | − | 46.7654i | − | 1.55712i | ||||||
\(903\) | 5.50000 | + | 28.5788i | 0.183029 | + | 0.951044i | ||||
\(904\) | −22.5000 | + | 12.9904i | −0.748339 | + | 0.432054i | ||||
\(905\) | 3.00000 | − | 1.73205i | 0.0997234 | − | 0.0575753i | ||||
\(906\) | 21.0000 | 0.697678 | ||||||||
\(907\) | 14.5000 | + | 25.1147i | 0.481465 | + | 0.833921i | 0.999774 | − | 0.0212722i | \(-0.00677166\pi\) |
−0.518309 | + | 0.855193i | \(0.673438\pi\) | |||||||
\(908\) | − | 17.3205i | − | 0.574801i | ||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | −16.5000 | + | 23.3827i | −0.546970 | + | 0.775128i | ||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 8.66025i | 0.286770i | ||||||||
\(913\) | 9.00000 | + | 15.5885i | 0.297857 | + | 0.515903i | ||||
\(914\) | −60.0000 | −1.98462 | ||||||||
\(915\) | −10.5000 | + | 6.06218i | −0.347119 | + | 0.200409i | ||||
\(916\) | 10.5000 | − | 6.06218i | 0.346930 | − | 0.200300i | ||||
\(917\) | 37.5000 | + | 12.9904i | 1.23836 | + | 0.428980i | ||||
\(918\) | − | 51.9615i | − | 1.71499i | ||||||
\(919\) | 23.5000 | − | 40.7032i | 0.775193 | − | 1.34267i | −0.159492 | − | 0.987199i | \(-0.550986\pi\) |
0.934686 | − | 0.355475i | \(-0.115681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.0000 | − | 12.1244i | 0.691974 | − | 0.399511i | ||||
\(922\) | −25.5000 | − | 44.1673i | −0.839798 | − | 1.45457i | ||||
\(923\) | 1.50000 | + | 6.06218i | 0.0493731 | + | 0.199539i | ||||
\(924\) | −13.5000 | + | 2.59808i | −0.444117 | + | 0.0854704i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 42.0000 | 1.38021 | ||||||||
\(927\) | 26.0000 | 0.853952 | ||||||||
\(928\) | −13.5000 | − | 7.79423i | −0.443159 | − | 0.255858i | ||||
\(929\) | −40.5000 | − | 23.3827i | −1.32876 | − | 0.767161i | −0.343654 | − | 0.939096i | \(-0.611665\pi\) |
−0.985108 | + | 0.171935i | \(0.944998\pi\) | |||||||
\(930\) | −4.50000 | + | 2.59808i | −0.147561 | + | 0.0851943i | ||||
\(931\) | −7.50000 | + | 9.52628i | −0.245803 | + | 0.312211i | ||||
\(932\) | 1.50000 | + | 2.59808i | 0.0491341 | + | 0.0851028i | ||||
\(933\) | 15.0000 | 0.491078 | ||||||||
\(934\) | 31.5000 | − | 18.1865i | 1.03071 | − | 0.595082i | ||||
\(935\) | −27.0000 | + | 46.7654i | −0.882994 | + | 1.52939i | ||||
\(936\) | 9.00000 | − | 8.66025i | 0.294174 | − | 0.283069i | ||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 37.5000 | + | 12.9904i | 1.22442 | + | 0.424151i | ||||
\(939\) | 9.50000 | − | 16.4545i | 0.310021 | − | 0.536972i | ||||
\(940\) | −7.50000 | + | 12.9904i | −0.244623 | + | 0.423700i | ||||
\(941\) | −4.50000 | − | 2.59808i | −0.146696 | − | 0.0846949i | 0.424856 | − | 0.905261i | \(-0.360325\pi\) |
−0.571551 | + | 0.820566i | \(0.693658\pi\) | |||||||
\(942\) | 39.8372i | 1.29797i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 17.3205i | − | 0.563735i | ||||||
\(945\) | −7.50000 | + | 21.6506i | −0.243975 | + | 0.704295i | ||||
\(946\) | 49.5000 | − | 85.7365i | 1.60938 | − | 2.78753i | ||||
\(947\) | − | 38.1051i | − | 1.23825i | −0.785292 | − | 0.619125i | \(-0.787487\pi\) | ||
0.785292 | − | 0.619125i | \(-0.212513\pi\) | |||||||
\(948\) | 2.50000 | − | 4.33013i | 0.0811962 | − | 0.140636i | ||||
\(949\) | −22.5000 | + | 21.6506i | −0.730381 | + | 0.702809i | ||||
\(950\) | −3.00000 | − | 5.19615i | −0.0973329 | − | 0.168585i | ||||
\(951\) | −4.50000 | − | 2.59808i | −0.145922 | − | 0.0842484i | ||||
\(952\) | 18.0000 | + | 20.7846i | 0.583383 | + | 0.673633i | ||||
\(953\) | 28.5000 | + | 49.3634i | 0.923206 | + | 1.59904i | 0.794422 | + | 0.607366i | \(0.207774\pi\) |
0.128784 | + | 0.991673i | \(0.458893\pi\) | |||||||
\(954\) | −27.0000 | + | 15.5885i | −0.874157 | + | 0.504695i | ||||
\(955\) | − | 25.9808i | − | 0.840718i | ||||||
\(956\) | 10.3923i | 0.336111i | ||||||||
\(957\) | 13.5000 | − | 7.79423i | 0.436393 | − | 0.251952i | ||||
\(958\) | −25.5000 | − | 44.1673i | −0.823868 | − | 1.42698i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.50000 | − | 0.866025i | −0.0484123 | − | 0.0279508i | ||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 6.92820i | − | 0.223142i | ||||||
\(965\) | 1.50000 | − | 2.59808i | 0.0482867 | − | 0.0836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3923i | 0.334194i | 0.985940 | + | 0.167097i | \(0.0534393\pi\) | ||||
−0.985940 | + | 0.167097i | \(0.946561\pi\) | |||||||
\(968\) | −24.0000 | − | 13.8564i | −0.771389 | − | 0.445362i | ||||
\(969\) | − | 10.3923i | − | 0.333849i | ||||||
\(970\) | 13.5000 | + | 7.79423i | 0.433459 | + | 0.250258i | ||||
\(971\) | −10.5000 | + | 18.1865i | −0.336961 | + | 0.583634i | −0.983860 | − | 0.178942i | \(-0.942732\pi\) |
0.646899 | + | 0.762576i | \(0.276066\pi\) | |||||||
\(972\) | −8.00000 | + | 13.8564i | −0.256600 | + | 0.444444i | ||||
\(973\) | −32.5000 | − | 11.2583i | −1.04190 | − | 0.360925i | ||||
\(974\) | 42.0000 | 1.34577 | ||||||||
\(975\) | 2.00000 | − | 6.92820i | 0.0640513 | − | 0.221880i | ||||
\(976\) | 17.5000 | − | 30.3109i | 0.560161 | − | 0.970228i | ||||
\(977\) | −16.5000 | + | 9.52628i | −0.527882 | + | 0.304773i | −0.740153 | − | 0.672438i | \(-0.765247\pi\) |
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(978\) | 21.0000 | 0.671506 | ||||||||
\(979\) | 18.0000 | + | 31.1769i | 0.575282 | + | 0.996419i | ||||
\(980\) | 4.50000 | + | 11.2583i | 0.143747 | + | 0.359634i | ||||
\(981\) | −9.00000 | + | 5.19615i | −0.287348 | + | 0.165900i | ||||
\(982\) | −40.5000 | − | 23.3827i | −1.29241 | − | 0.746171i | ||||
\(983\) | −31.5000 | − | 18.1865i | −1.00469 | − | 0.580060i | −0.0950602 | − | 0.995472i | \(-0.530304\pi\) |
−0.909634 | + | 0.415411i | \(0.863638\pi\) | |||||||
\(984\) | −9.00000 | −0.286910 | ||||||||
\(985\) | 39.0000 | 1.24264 | ||||||||
\(986\) | 27.0000 | + | 15.5885i | 0.859855 | + | 0.496438i | ||||
\(987\) | −22.5000 | + | 4.33013i | −0.716183 | + | 0.137829i | ||||
\(988\) | −4.50000 | + | 4.33013i | −0.143164 | + | 0.137760i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 27.0000 | − | 15.5885i | 0.858116 | − | 0.495434i | ||||
\(991\) | −29.5000 | − | 51.0955i | −0.937098 | − | 1.62310i | −0.770849 | − | 0.637018i | \(-0.780168\pi\) |
−0.166250 | − | 0.986084i | \(-0.553166\pi\) | |||||||
\(992\) | 4.50000 | − | 7.79423i | 0.142875 | − | 0.247467i | ||||
\(993\) | 32.9090i | 1.04433i | ||||||||
\(994\) | 7.50000 | + | 2.59808i | 0.237886 | + | 0.0824060i | ||||
\(995\) | 6.00000 | − | 3.46410i | 0.190213 | − | 0.109819i | ||||
\(996\) | −3.00000 | + | 1.73205i | −0.0950586 | + | 0.0548821i | ||||
\(997\) | 2.00000 | 0.0633406 | 0.0316703 | − | 0.999498i | \(-0.489917\pi\) | ||||
0.0316703 | + | 0.999498i | \(0.489917\pi\) | |||||||
\(998\) | −1.50000 | − | 2.59808i | −0.0474817 | − | 0.0822407i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 91.2.k.a.4.1 | ✓ | 2 | |
3.2 | odd | 2 | 819.2.bm.a.550.1 | 2 | |||
7.2 | even | 3 | 91.2.u.a.30.1 | yes | 2 | ||
7.3 | odd | 6 | 637.2.q.b.589.1 | 2 | |||
7.4 | even | 3 | 637.2.q.c.589.1 | 2 | |||
7.5 | odd | 6 | 637.2.u.a.30.1 | 2 | |||
7.6 | odd | 2 | 637.2.k.b.459.1 | 2 | |||
13.6 | odd | 12 | 1183.2.e.e.508.2 | 4 | |||
13.7 | odd | 12 | 1183.2.e.e.508.1 | 4 | |||
13.10 | even | 6 | 91.2.u.a.88.1 | yes | 2 | ||
21.2 | odd | 6 | 819.2.do.c.667.1 | 2 | |||
39.23 | odd | 6 | 819.2.do.c.361.1 | 2 | |||
91.10 | odd | 6 | 637.2.q.b.491.1 | 2 | |||
91.23 | even | 6 | inner | 91.2.k.a.23.1 | yes | 2 | |
91.32 | odd | 12 | 8281.2.a.s.1.1 | 2 | |||
91.45 | even | 12 | 8281.2.a.w.1.1 | 2 | |||
91.46 | odd | 12 | 8281.2.a.s.1.2 | 2 | |||
91.58 | odd | 12 | 1183.2.e.e.170.2 | 4 | |||
91.59 | even | 12 | 8281.2.a.w.1.2 | 2 | |||
91.62 | odd | 6 | 637.2.u.a.361.1 | 2 | |||
91.72 | odd | 12 | 1183.2.e.e.170.1 | 4 | |||
91.75 | odd | 6 | 637.2.k.b.569.1 | 2 | |||
91.88 | even | 6 | 637.2.q.c.491.1 | 2 | |||
273.23 | odd | 6 | 819.2.bm.a.478.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.a.4.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
91.2.k.a.23.1 | yes | 2 | 91.23 | even | 6 | inner | |
91.2.u.a.30.1 | yes | 2 | 7.2 | even | 3 | ||
91.2.u.a.88.1 | yes | 2 | 13.10 | even | 6 | ||
637.2.k.b.459.1 | 2 | 7.6 | odd | 2 | |||
637.2.k.b.569.1 | 2 | 91.75 | odd | 6 | |||
637.2.q.b.491.1 | 2 | 91.10 | odd | 6 | |||
637.2.q.b.589.1 | 2 | 7.3 | odd | 6 | |||
637.2.q.c.491.1 | 2 | 91.88 | even | 6 | |||
637.2.q.c.589.1 | 2 | 7.4 | even | 3 | |||
637.2.u.a.30.1 | 2 | 7.5 | odd | 6 | |||
637.2.u.a.361.1 | 2 | 91.62 | odd | 6 | |||
819.2.bm.a.478.1 | 2 | 273.23 | odd | 6 | |||
819.2.bm.a.550.1 | 2 | 3.2 | odd | 2 | |||
819.2.do.c.361.1 | 2 | 39.23 | odd | 6 | |||
819.2.do.c.667.1 | 2 | 21.2 | odd | 6 | |||
1183.2.e.e.170.1 | 4 | 91.72 | odd | 12 | |||
1183.2.e.e.170.2 | 4 | 91.58 | odd | 12 | |||
1183.2.e.e.508.1 | 4 | 13.7 | odd | 12 | |||
1183.2.e.e.508.2 | 4 | 13.6 | odd | 12 | |||
8281.2.a.s.1.1 | 2 | 91.32 | odd | 12 | |||
8281.2.a.s.1.2 | 2 | 91.46 | odd | 12 | |||
8281.2.a.w.1.1 | 2 | 91.45 | even | 12 | |||
8281.2.a.w.1.2 | 2 | 91.59 | even | 12 |