Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [238,2,Mod(67,238)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(238, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("238.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 238 = 2 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 238.j (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: | \(1.90043956811\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 135.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 238.135 |
Dual form | 238.2.j.a.67.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/238\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(171\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 2.59808 | − | 1.50000i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | − | 3.00000i | − | 1.22474i | ||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 1.50000i | −0.783349 | + | 0.452267i | −0.837616 | − | 0.546259i | \(-0.816051\pi\) |
0.0542666 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(12\) | −2.59808 | − | 1.50000i | −0.750000 | − | 0.433013i | ||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0.866025 | + | 2.50000i | 0.231455 | + | 0.668153i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.96410 | + | 1.13397i | −0.961436 | + | 0.275029i | ||||
\(18\) | −3.00000 | − | 5.19615i | −0.707107 | − | 1.22474i | ||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | + | 7.79423i | −0.327327 | + | 1.70084i | ||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | 3.46410 | + | 2.00000i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932891 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(24\) | −2.59808 | + | 1.50000i | −0.530330 | + | 0.306186i | ||||
\(25\) | −2.50000 | − | 4.33013i | −0.500000 | − | 0.866025i | ||||
\(26\) | 2.50000 | − | 4.33013i | 0.490290 | − | 0.849208i | ||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 2.59808 | + | 0.500000i | 0.490990 | + | 0.0944911i | ||||
\(29\) | 4.00000i | 0.742781i | 0.928477 | + | 0.371391i | \(0.121119\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | − | 2.00000i | 0.622171 | − | 0.359211i | −0.155543 | − | 0.987829i | \(-0.549713\pi\) |
0.777714 | + | 0.628619i | \(0.216379\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −4.50000 | + | 7.79423i | −0.783349 | + | 1.35680i | ||||
\(34\) | −1.00000 | + | 4.00000i | −0.171499 | + | 0.685994i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | −6.92820 | − | 4.00000i | −1.13899 | − | 0.657596i | −0.192809 | − | 0.981236i | \(-0.561760\pi\) |
−0.946180 | + | 0.323640i | \(0.895093\pi\) | |||||||
\(38\) | 2.00000 | + | 3.46410i | 0.324443 | + | 0.561951i | ||||
\(39\) | 12.9904 | − | 7.50000i | 2.08013 | − | 1.20096i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | 6.00000 | + | 5.19615i | 0.925820 | + | 0.801784i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 2.59808 | + | 1.50000i | 0.391675 | + | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.46410 | − | 2.00000i | 0.510754 | − | 0.294884i | ||||
\(47\) | −2.00000 | + | 3.46410i | −0.291730 | + | 0.505291i | −0.974219 | − | 0.225605i | \(-0.927564\pi\) |
0.682489 | + | 0.730896i | \(0.260898\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | −8.59808 | + | 8.89230i | −1.20397 | + | 1.24517i | ||||
\(52\) | −2.50000 | − | 4.33013i | −0.346688 | − | 0.600481i | ||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | −7.79423 | − | 4.50000i | −1.06066 | − | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.73205 | − | 2.00000i | 0.231455 | − | 0.267261i | ||||
\(57\) | 12.0000i | 1.58944i | ||||||||
\(58\) | 3.46410 | + | 2.00000i | 0.454859 | + | 0.262613i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 5.19615 | + | 15.0000i | 0.654654 | + | 1.88982i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50000 | + | 7.79423i | 0.553912 | + | 0.959403i | ||||
\(67\) | 8.00000 | + | 13.8564i | 0.977356 | + | 1.69283i | 0.671932 | + | 0.740613i | \(0.265465\pi\) |
0.305424 | + | 0.952217i | \(0.401202\pi\) | |||||||
\(68\) | 2.96410 | + | 2.86603i | 0.359450 | + | 0.347557i | ||||
\(69\) | 12.0000 | 1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.00000i | − | 0.118678i | −0.998238 | − | 0.0593391i | \(-0.981101\pi\) | ||
0.998238 | − | 0.0593391i | \(-0.0188993\pi\) | |||||||
\(72\) | −3.00000 | + | 5.19615i | −0.353553 | + | 0.612372i | ||||
\(73\) | −6.92820 | + | 4.00000i | −0.810885 | + | 0.468165i | −0.847263 | − | 0.531174i | \(-0.821751\pi\) |
0.0363782 | + | 0.999338i | \(0.488418\pi\) | |||||||
\(74\) | −6.92820 | + | 4.00000i | −0.805387 | + | 0.464991i | ||||
\(75\) | −12.9904 | − | 7.50000i | −1.50000 | − | 0.866025i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | − | 15.0000i | − | 1.69842i | ||||||
\(79\) | 6.06218 | + | 3.50000i | 0.682048 | + | 0.393781i | 0.800626 | − | 0.599164i | \(-0.204500\pi\) |
−0.118578 | + | 0.992945i | \(0.537834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −3.46410 | − | 2.00000i | −0.382546 | − | 0.220863i | ||||
\(83\) | −16.0000 | −1.75623 | −0.878114 | − | 0.478451i | \(-0.841198\pi\) | ||||
−0.878114 | + | 0.478451i | \(0.841198\pi\) | |||||||
\(84\) | 7.50000 | − | 2.59808i | 0.818317 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 6.00000 | + | 10.3923i | 0.643268 | + | 1.11417i | ||||
\(88\) | 2.59808 | − | 1.50000i | 0.276956 | − | 0.159901i | ||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.66025 | + | 10.0000i | −0.907841 | + | 1.04828i | ||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | 6.00000 | − | 10.3923i | 0.622171 | − | 1.07763i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.59808 | + | 1.50000i | 0.265165 | + | 0.153093i | ||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 18.0000i | 1.80907i | ||||||||
\(100\) | −2.50000 | + | 4.33013i | −0.250000 | + | 0.433013i | ||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | 3.40192 | + | 11.8923i | 0.336841 | + | 1.17751i | ||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −2.59808 | − | 1.50000i | −0.251166 | − | 0.145010i | 0.369132 | − | 0.929377i | \(-0.379655\pi\) |
−0.620298 | + | 0.784366i | \(0.712988\pi\) | |||||||
\(108\) | −7.79423 | + | 4.50000i | −0.750000 | + | 0.433013i | ||||
\(109\) | 17.3205 | − | 10.0000i | 1.65900 | − | 0.957826i | 0.685828 | − | 0.727764i | \(-0.259440\pi\) |
0.973176 | − | 0.230063i | \(-0.0738931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.0000 | −2.27798 | ||||||||
\(112\) | −0.866025 | − | 2.50000i | −0.0818317 | − | 0.236228i | ||||
\(113\) | − | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | \(-0.809095\pi\) | ||
0.825479 | − | 0.564433i | \(-0.190905\pi\) | |||||||
\(114\) | 10.3923 | + | 6.00000i | 0.973329 | + | 0.561951i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.46410 | − | 2.00000i | 0.321634 | − | 0.185695i | ||||
\(117\) | 15.0000 | − | 25.9808i | 1.38675 | − | 2.40192i | ||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 4.59808 | − | 9.89230i | 0.421505 | − | 0.906826i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | − | 10.3923i | −0.541002 | − | 0.937043i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 15.5885 | + | 3.00000i | 1.38873 | + | 0.267261i | ||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 20.7846 | − | 12.0000i | 1.82998 | − | 1.05654i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.92820 | − | 4.00000i | −0.605320 | − | 0.349482i | 0.165812 | − | 0.986157i | \(-0.446976\pi\) |
−0.771132 | + | 0.636676i | \(0.780309\pi\) | |||||||
\(132\) | 9.00000 | 0.783349 | ||||||||
\(133\) | −3.46410 | − | 10.0000i | −0.300376 | − | 0.867110i | ||||
\(134\) | 16.0000 | 1.38219 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.96410 | − | 1.13397i | 0.339919 | − | 0.0972375i | ||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 6.00000 | − | 10.3923i | 0.510754 | − | 0.884652i | ||||
\(139\) | − | 11.0000i | − | 0.933008i | −0.884519 | − | 0.466504i | \(-0.845513\pi\) | ||
0.884519 | − | 0.466504i | \(-0.154487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000i | 1.01058i | ||||||||
\(142\) | −0.866025 | − | 0.500000i | −0.0726752 | − | 0.0419591i | ||||
\(143\) | −12.9904 | + | 7.50000i | −1.08631 | + | 0.627182i | ||||
\(144\) | 3.00000 | + | 5.19615i | 0.250000 | + | 0.433013i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00000i | 0.662085i | ||||||||
\(147\) | −12.9904 | − | 16.5000i | −1.07143 | − | 1.36090i | ||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | −5.50000 | + | 9.52628i | −0.450578 | + | 0.780423i | −0.998422 | − | 0.0561570i | \(-0.982115\pi\) |
0.547844 | + | 0.836580i | \(0.315449\pi\) | |||||||
\(150\) | −12.9904 | + | 7.50000i | −1.06066 | + | 0.612372i | ||||
\(151\) | 6.00000 | + | 10.3923i | 0.488273 | + | 0.845714i | 0.999909 | − | 0.0134886i | \(-0.00429367\pi\) |
−0.511636 | + | 0.859202i | \(0.670960\pi\) | |||||||
\(152\) | 2.00000 | − | 3.46410i | 0.162221 | − | 0.280976i | ||||
\(153\) | −6.00000 | + | 24.0000i | −0.485071 | + | 1.94029i | ||||
\(154\) | −6.00000 | − | 5.19615i | −0.483494 | − | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.9904 | − | 7.50000i | −1.04006 | − | 0.600481i | ||||
\(157\) | −1.50000 | − | 2.59808i | −0.119713 | − | 0.207349i | 0.799941 | − | 0.600079i | \(-0.204864\pi\) |
−0.919654 | + | 0.392730i | \(0.871531\pi\) | |||||||
\(158\) | 6.06218 | − | 3.50000i | 0.482281 | − | 0.278445i | ||||
\(159\) | 2.59808 | + | 1.50000i | 0.206041 | + | 0.118958i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0000 | + | 3.46410i | −0.788110 | + | 0.273009i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −13.8564 | − | 8.00000i | −1.08532 | − | 0.626608i | −0.152992 | − | 0.988227i | \(-0.548891\pi\) |
−0.932326 | + | 0.361619i | \(0.882224\pi\) | |||||||
\(164\) | −3.46410 | + | 2.00000i | −0.270501 | + | 0.156174i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00000 | + | 13.8564i | −0.620920 | + | 1.07547i | ||||
\(167\) | 25.0000i | 1.93456i | 0.253715 | + | 0.967279i | \(0.418347\pi\) | ||||
−0.253715 | + | 0.967279i | \(0.581653\pi\) | |||||||
\(168\) | 1.50000 | − | 7.79423i | 0.115728 | − | 0.601338i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.0000 | + | 20.7846i | 0.917663 | + | 1.58944i | ||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | −3.46410 | − | 2.00000i | −0.263371 | − | 0.152057i | 0.362500 | − | 0.931984i | \(-0.381923\pi\) |
−0.625871 | + | 0.779926i | \(0.715256\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 12.9904 | + | 2.50000i | 0.981981 | + | 0.188982i | ||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | −31.1769 | − | 18.0000i | −2.34340 | − | 1.35296i | ||||
\(178\) | 4.50000 | + | 7.79423i | 0.337289 | + | 0.584202i | ||||
\(179\) | 8.00000 | + | 13.8564i | 0.597948 | + | 1.03568i | 0.993124 | + | 0.117071i | \(0.0373504\pi\) |
−0.395175 | + | 0.918606i | \(0.629316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.00000i | − | 0.297318i | −0.988889 | − | 0.148659i | \(-0.952504\pi\) | ||
0.988889 | − | 0.148659i | \(-0.0474956\pi\) | |||||||
\(182\) | 4.33013 | + | 12.5000i | 0.320970 | + | 0.926562i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.46410 | − | 2.00000i | −0.255377 | − | 0.147442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.00000 | − | 10.3923i | −0.439941 | − | 0.762001i | ||||
\(187\) | 8.59808 | − | 8.89230i | 0.628754 | − | 0.650270i | ||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | 18.0000 | + | 15.5885i | 1.30931 | + | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 2.59808 | − | 1.50000i | 0.187500 | − | 0.108253i | ||||
\(193\) | 3.46410 | − | 2.00000i | 0.249351 | − | 0.143963i | −0.370116 | − | 0.928986i | \(-0.620682\pi\) |
0.619467 | + | 0.785022i | \(0.287349\pi\) | |||||||
\(194\) | −6.92820 | − | 4.00000i | −0.497416 | − | 0.287183i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.50000 | + | 4.33013i | −0.392857 | + | 0.309295i | ||||
\(197\) | − | 16.0000i | − | 1.13995i | −0.821661 | − | 0.569976i | \(-0.806952\pi\) | ||
0.821661 | − | 0.569976i | \(-0.193048\pi\) | |||||||
\(198\) | 15.5885 | + | 9.00000i | 1.10782 | + | 0.639602i | ||||
\(199\) | −2.59808 | + | 1.50000i | −0.184173 | + | 0.106332i | −0.589252 | − | 0.807950i | \(-0.700577\pi\) |
0.405079 | + | 0.914282i | \(0.367244\pi\) | |||||||
\(200\) | 2.50000 | + | 4.33013i | 0.176777 | + | 0.306186i | ||||
\(201\) | 41.5692 | + | 24.0000i | 2.93207 | + | 1.69283i | ||||
\(202\) | −10.0000 | −0.703598 | ||||||||
\(203\) | −8.00000 | − | 6.92820i | −0.561490 | − | 0.486265i | ||||
\(204\) | 12.0000 | + | 3.00000i | 0.840168 | + | 0.210042i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 20.7846 | − | 12.0000i | 1.44463 | − | 0.834058i | ||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | − | 12.0000i | − | 0.830057i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.0000i | 1.65223i | 0.563503 | + | 0.826114i | \(0.309453\pi\) | ||||
−0.563503 | + | 0.826114i | \(0.690547\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | −1.50000 | − | 2.59808i | −0.102778 | − | 0.178017i | ||||
\(214\) | −2.59808 | + | 1.50000i | −0.177601 | + | 0.102538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000i | 0.612372i | ||||||||
\(217\) | −2.00000 | + | 10.3923i | −0.135769 | + | 0.705476i | ||||
\(218\) | − | 20.0000i | − | 1.35457i | ||||||
\(219\) | −12.0000 | + | 20.7846i | −0.810885 | + | 1.40449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.8205 | + | 5.66987i | −1.33327 | + | 0.381397i | ||||
\(222\) | −12.0000 | + | 20.7846i | −0.805387 | + | 1.39497i | ||||
\(223\) | 12.0000 | 0.803579 | 0.401790 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401790 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(224\) | −2.59808 | − | 0.500000i | −0.173591 | − | 0.0334077i | ||||
\(225\) | −30.0000 | −2.00000 | ||||||||
\(226\) | −10.3923 | − | 6.00000i | −0.691286 | − | 0.399114i | ||||
\(227\) | 18.1865 | − | 10.5000i | 1.20708 | − | 0.696909i | 0.244962 | − | 0.969533i | \(-0.421225\pi\) |
0.962121 | + | 0.272623i | \(0.0878913\pi\) | |||||||
\(228\) | 10.3923 | − | 6.00000i | 0.688247 | − | 0.397360i | ||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.79423 | − | 22.5000i | −0.512823 | − | 1.48039i | ||||
\(232\) | − | 4.00000i | − | 0.262613i | ||||||
\(233\) | 13.8564 | + | 8.00000i | 0.907763 | + | 0.524097i | 0.879711 | − | 0.475509i | \(-0.157736\pi\) |
0.0280525 | + | 0.999606i | \(0.491069\pi\) | |||||||
\(234\) | −15.0000 | − | 25.9808i | −0.980581 | − | 1.69842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 21.0000 | 1.36410 | ||||||||
\(238\) | −6.26795 | − | 8.92820i | −0.406291 | − | 0.578729i | ||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3923 | − | 6.00000i | 0.669427 | − | 0.386494i | −0.126432 | − | 0.991975i | \(-0.540353\pi\) |
0.795860 | + | 0.605481i | \(0.207019\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.0000 | −0.765092 | ||||||||
\(247\) | −10.0000 | + | 17.3205i | −0.636285 | + | 1.10208i | ||||
\(248\) | −3.46410 | + | 2.00000i | −0.219971 | + | 0.127000i | ||||
\(249\) | −41.5692 | + | 24.0000i | −2.63434 | + | 1.52094i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0000 | 1.00991 | 0.504956 | − | 0.863145i | \(-0.331509\pi\) | ||||
0.504956 | + | 0.863145i | \(0.331509\pi\) | |||||||
\(252\) | 10.3923 | − | 12.0000i | 0.654654 | − | 0.755929i | ||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.50000 | − | 6.06218i | 0.218324 | − | 0.378148i | −0.735972 | − | 0.677012i | \(-0.763274\pi\) |
0.954296 | + | 0.298864i | \(0.0966077\pi\) | |||||||
\(258\) | − | 24.0000i | − | 1.49417i | ||||||
\(259\) | 20.0000 | − | 6.92820i | 1.24274 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7846 | + | 12.0000i | 1.28654 | + | 0.742781i | ||||
\(262\) | −6.92820 | + | 4.00000i | −0.428026 | + | 0.247121i | ||||
\(263\) | −2.00000 | − | 3.46410i | −0.123325 | − | 0.213606i | 0.797752 | − | 0.602986i | \(-0.206023\pi\) |
−0.921077 | + | 0.389380i | \(0.872689\pi\) | |||||||
\(264\) | 4.50000 | − | 7.79423i | 0.276956 | − | 0.479702i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.3923 | − | 2.00000i | −0.637193 | − | 0.122628i | ||||
\(267\) | 27.0000i | 1.65237i | ||||||||
\(268\) | 8.00000 | − | 13.8564i | 0.488678 | − | 0.846415i | ||||
\(269\) | 3.46410 | − | 2.00000i | 0.211210 | − | 0.121942i | −0.390664 | − | 0.920534i | \(-0.627754\pi\) |
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.00000 | + | 10.3923i | −0.364474 | + | 0.631288i | −0.988692 | − | 0.149963i | \(-0.952085\pi\) |
0.624218 | + | 0.781251i | \(0.285418\pi\) | |||||||
\(272\) | 1.00000 | − | 4.00000i | 0.0606339 | − | 0.242536i | ||||
\(273\) | −7.50000 | + | 38.9711i | −0.453921 | + | 2.35864i | ||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | 12.9904 | + | 7.50000i | 0.783349 | + | 0.452267i | ||||
\(276\) | −6.00000 | − | 10.3923i | −0.361158 | − | 0.625543i | ||||
\(277\) | −3.46410 | + | 2.00000i | −0.208138 | + | 0.120168i | −0.600446 | − | 0.799666i | \(-0.705010\pi\) |
0.392308 | + | 0.919834i | \(0.371677\pi\) | |||||||
\(278\) | −9.52628 | − | 5.50000i | −0.571348 | − | 0.329868i | ||||
\(279\) | − | 24.0000i | − | 1.43684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | 10.3923 | + | 6.00000i | 0.618853 | + | 0.357295i | ||||
\(283\) | 9.52628 | − | 5.50000i | 0.566279 | − | 0.326941i | −0.189383 | − | 0.981903i | \(-0.560649\pi\) |
0.755662 | + | 0.654962i | \(0.227315\pi\) | |||||||
\(284\) | −0.866025 | + | 0.500000i | −0.0513892 | + | 0.0296695i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000i | 0.886969i | ||||||||
\(287\) | 8.00000 | + | 6.92820i | 0.472225 | + | 0.408959i | ||||
\(288\) | 6.00000 | 0.353553 | ||||||||
\(289\) | 14.4282 | − | 8.99038i | 0.848718 | − | 0.528846i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | − | 20.7846i | −0.703452 | − | 1.21842i | ||||
\(292\) | 6.92820 | + | 4.00000i | 0.405442 | + | 0.234082i | ||||
\(293\) | 23.0000 | 1.34367 | 0.671837 | − | 0.740699i | \(-0.265505\pi\) | ||||
0.671837 | + | 0.740699i | \(0.265505\pi\) | |||||||
\(294\) | −20.7846 | + | 3.00000i | −1.21218 | + | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820 | + | 4.00000i | 0.402694 | + | 0.232495i | ||||
\(297\) | 13.5000 | + | 23.3827i | 0.783349 | + | 1.35680i | ||||
\(298\) | 5.50000 | + | 9.52628i | 0.318606 | + | 0.551843i | ||||
\(299\) | 17.3205 | + | 10.0000i | 1.00167 | + | 0.578315i | ||||
\(300\) | 15.0000i | 0.866025i | ||||||||
\(301\) | −13.8564 | + | 16.0000i | −0.798670 | + | 0.922225i | ||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −25.9808 | − | 15.0000i | −1.49256 | − | 0.861727i | ||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 17.7846 | + | 17.1962i | 1.01668 | + | 0.983039i | ||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −7.50000 | + | 2.59808i | −0.427352 | + | 0.148039i | ||||
\(309\) | − | 24.0000i | − | 1.36531i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.1865 | + | 10.5000i | −1.03126 | + | 0.595400i | −0.917346 | − | 0.398090i | \(-0.869673\pi\) |
−0.113917 | + | 0.993490i | \(0.536340\pi\) | |||||||
\(312\) | −12.9904 | + | 7.50000i | −0.735436 | + | 0.424604i | ||||
\(313\) | −17.3205 | − | 10.0000i | −0.979013 | − | 0.565233i | −0.0770410 | − | 0.997028i | \(-0.524547\pi\) |
−0.901972 | + | 0.431795i | \(0.857881\pi\) | |||||||
\(314\) | −3.00000 | −0.169300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 7.00000i | − | 0.393781i | ||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 2.59808 | − | 1.50000i | 0.145693 | − | 0.0841158i | ||||
\(319\) | −6.00000 | − | 10.3923i | −0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | −2.00000 | + | 10.3923i | −0.111456 | + | 0.579141i | ||||
\(323\) | 4.00000 | − | 16.0000i | 0.222566 | − | 0.890264i | ||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | −12.5000 | − | 21.6506i | −0.693375 | − | 1.20096i | ||||
\(326\) | −13.8564 | + | 8.00000i | −0.767435 | + | 0.443079i | ||||
\(327\) | 30.0000 | − | 51.9615i | 1.65900 | − | 2.87348i | ||||
\(328\) | 4.00000i | 0.220863i | ||||||||
\(329\) | −3.46410 | − | 10.0000i | −0.190982 | − | 0.551318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | 8.00000 | + | 13.8564i | 0.439057 | + | 0.760469i | ||||
\(333\) | −41.5692 | + | 24.0000i | −2.27798 | + | 1.31519i | ||||
\(334\) | 21.6506 | + | 12.5000i | 1.18467 | + | 0.683970i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | − | 5.19615i | −0.327327 | − | 0.283473i | ||||
\(337\) | 8.00000i | 0.435788i | 0.975972 | + | 0.217894i | \(0.0699187\pi\) | ||||
−0.975972 | + | 0.217894i | \(0.930081\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | −18.0000 | − | 31.1769i | −0.977626 | − | 1.69330i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 24.0000 | 1.29777 | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.46410 | + | 2.00000i | −0.186231 | + | 0.107521i | ||||
\(347\) | 27.7128 | − | 16.0000i | 1.48770 | − | 0.858925i | 0.487800 | − | 0.872955i | \(-0.337799\pi\) |
0.999902 | + | 0.0140303i | \(0.00446613\pi\) | |||||||
\(348\) | 6.00000 | − | 10.3923i | 0.321634 | − | 0.557086i | ||||
\(349\) | 30.0000 | 1.60586 | 0.802932 | − | 0.596071i | \(-0.203272\pi\) | ||||
0.802932 | + | 0.596071i | \(0.203272\pi\) | |||||||
\(350\) | 8.66025 | − | 10.0000i | 0.462910 | − | 0.534522i | ||||
\(351\) | − | 45.0000i | − | 2.40192i | ||||||
\(352\) | −2.59808 | − | 1.50000i | −0.138478 | − | 0.0799503i | ||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | −31.1769 | + | 18.0000i | −1.65703 | + | 0.956689i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.00000 | 0.476999 | ||||||||
\(357\) | −2.89230 | − | 32.5981i | −0.153077 | − | 1.72527i | ||||
\(358\) | 16.0000 | 0.845626 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −3.46410 | − | 2.00000i | −0.182069 | − | 0.105118i | ||||
\(363\) | 6.00000i | 0.314918i | ||||||||
\(364\) | 12.9904 | + | 2.50000i | 0.680881 | + | 0.131036i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.06218 | + | 3.50000i | −0.316443 | + | 0.182699i | −0.649806 | − | 0.760100i | \(-0.725150\pi\) |
0.333363 | + | 0.942799i | \(0.391817\pi\) | |||||||
\(368\) | −3.46410 | + | 2.00000i | −0.180579 | + | 0.104257i | ||||
\(369\) | −20.7846 | − | 12.0000i | −1.08200 | − | 0.624695i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.59808 | − | 0.500000i | −0.134885 | − | 0.0259587i | ||||
\(372\) | −12.0000 | −0.622171 | ||||||||
\(373\) | 9.50000 | − | 16.4545i | 0.491891 | − | 0.851981i | −0.508065 | − | 0.861319i | \(-0.669639\pi\) |
0.999956 | + | 0.00933789i | \(0.00297238\pi\) | |||||||
\(374\) | −3.40192 | − | 11.8923i | −0.175909 | − | 0.614936i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.00000 | − | 3.46410i | 0.103142 | − | 0.178647i | ||||
\(377\) | 20.0000i | 1.03005i | ||||||||
\(378\) | 22.5000 | − | 7.79423i | 1.15728 | − | 0.400892i | ||||
\(379\) | − | 1.00000i | − | 0.0513665i | −0.999670 | − | 0.0256833i | \(-0.991824\pi\) | ||
0.999670 | − | 0.0256833i | \(-0.00817614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.7846 | − | 12.0000i | 1.06483 | − | 0.614779i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | −12.0000 | + | 20.7846i | −0.613171 | + | 1.06204i | 0.377531 | + | 0.925997i | \(0.376773\pi\) |
−0.990702 | + | 0.136047i | \(0.956560\pi\) | |||||||
\(384\) | − | 3.00000i | − | 0.153093i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.00000i | − | 0.203595i | ||||||
\(387\) | 24.0000 | − | 41.5692i | 1.21999 | − | 2.11308i | ||||
\(388\) | −6.92820 | + | 4.00000i | −0.351726 | + | 0.203069i | ||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | − | 4.00000i | −0.809155 | − | 0.202289i | ||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | −24.0000 | −1.21064 | ||||||||
\(394\) | −13.8564 | − | 8.00000i | −0.698076 | − | 0.403034i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.5885 | − | 9.00000i | 0.783349 | − | 0.452267i | ||||
\(397\) | 27.7128 | + | 16.0000i | 1.39087 | + | 0.803017i | 0.993411 | − | 0.114605i | \(-0.0365601\pi\) |
0.397455 | + | 0.917622i | \(0.369893\pi\) | |||||||
\(398\) | 3.00000i | 0.150376i | ||||||||
\(399\) | −24.0000 | − | 20.7846i | −1.20150 | − | 1.04053i | ||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 17.3205 | + | 10.0000i | 0.864945 | + | 0.499376i | 0.865665 | − | 0.500624i | \(-0.166896\pi\) |
−0.000720188 | 1.00000i | \(0.500229\pi\) | ||||||||
\(402\) | 41.5692 | − | 24.0000i | 2.07328 | − | 1.19701i | ||||
\(403\) | 17.3205 | − | 10.0000i | 0.862796 | − | 0.498135i | ||||
\(404\) | −5.00000 | + | 8.66025i | −0.248759 | + | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0000 | + | 3.46410i | −0.496292 | + | 0.171920i | ||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 8.59808 | − | 8.89230i | 0.425668 | − | 0.440235i | ||||
\(409\) | −9.50000 | − | 16.4545i | −0.469745 | − | 0.813622i | 0.529657 | − | 0.848212i | \(-0.322321\pi\) |
−0.999402 | + | 0.0345902i | \(0.988987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.3827 | − | 13.5000i | −1.15338 | − | 0.665906i | ||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 31.1769 | + | 6.00000i | 1.53412 | + | 0.295241i | ||||
\(414\) | − | 24.0000i | − | 1.17954i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.50000 | + | 4.33013i | 0.122573 | + | 0.212302i | ||||
\(417\) | −16.5000 | − | 28.5788i | −0.808008 | − | 1.39951i | ||||
\(418\) | −10.3923 | − | 6.00000i | −0.508304 | − | 0.293470i | ||||
\(419\) | 5.00000i | 0.244266i | 0.992514 | + | 0.122133i | \(0.0389734\pi\) | ||||
−0.992514 | + | 0.122133i | \(0.961027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 20.7846 | + | 12.0000i | 1.01178 | + | 0.584151i | ||||
\(423\) | 12.0000 | + | 20.7846i | 0.583460 | + | 1.01058i | ||||
\(424\) | −0.500000 | − | 0.866025i | −0.0242821 | − | 0.0420579i | ||||
\(425\) | 14.8205 | + | 14.3301i | 0.718900 | + | 0.695113i | ||||
\(426\) | −3.00000 | −0.145350 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.00000i | 0.145010i | ||||||||
\(429\) | −22.5000 | + | 38.9711i | −1.08631 | + | 1.88154i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.1865 | + | 10.5000i | −0.876014 | + | 0.505767i | −0.869342 | − | 0.494211i | \(-0.835457\pi\) |
−0.00667224 | + | 0.999978i | \(0.502124\pi\) | |||||||
\(432\) | 7.79423 | + | 4.50000i | 0.375000 | + | 0.216506i | ||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | 8.00000 | + | 6.92820i | 0.384012 | + | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.3205 | − | 10.0000i | −0.829502 | − | 0.478913i | ||||
\(437\) | −13.8564 | + | 8.00000i | −0.662842 | + | 0.382692i | ||||
\(438\) | 12.0000 | + | 20.7846i | 0.573382 | + | 0.993127i | ||||
\(439\) | 0.866025 | + | 0.500000i | 0.0413331 | + | 0.0238637i | 0.520524 | − | 0.853847i | \(-0.325737\pi\) |
−0.479191 | + | 0.877711i | \(0.659070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0000 | − | 15.5885i | −1.85714 | − | 0.742307i | ||||
\(442\) | −5.00000 | + | 20.0000i | −0.237826 | + | 0.951303i | ||||
\(443\) | 8.00000 | − | 13.8564i | 0.380091 | − | 0.658338i | −0.610984 | − | 0.791643i | \(-0.709226\pi\) |
0.991075 | + | 0.133306i | \(0.0425592\pi\) | |||||||
\(444\) | 12.0000 | + | 20.7846i | 0.569495 | + | 0.986394i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | − | 10.3923i | 0.284108 | − | 0.492090i | ||||
\(447\) | 33.0000i | 1.56085i | ||||||||
\(448\) | −1.73205 | + | 2.00000i | −0.0818317 | + | 0.0944911i | ||||
\(449\) | − | 4.00000i | − | 0.188772i | −0.995536 | − | 0.0943858i | \(-0.969911\pi\) | ||
0.995536 | − | 0.0943858i | \(-0.0300887\pi\) | |||||||
\(450\) | −15.0000 | + | 25.9808i | −0.707107 | + | 1.22474i | ||||
\(451\) | 6.00000 | + | 10.3923i | 0.282529 | + | 0.489355i | ||||
\(452\) | −10.3923 | + | 6.00000i | −0.488813 | + | 0.282216i | ||||
\(453\) | 31.1769 | + | 18.0000i | 1.46482 | + | 0.845714i | ||||
\(454\) | − | 21.0000i | − | 0.985579i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 12.0000i | − | 0.561951i | ||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | 10.2058 | + | 35.6769i | 0.476365 | + | 1.66526i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.00000 | −0.0465746 | −0.0232873 | − | 0.999729i | \(-0.507413\pi\) | ||||
−0.0232873 | + | 0.999729i | \(0.507413\pi\) | |||||||
\(462\) | −23.3827 | − | 4.50000i | −1.08786 | − | 0.209359i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | −3.46410 | − | 2.00000i | −0.160817 | − | 0.0928477i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.8564 | − | 8.00000i | 0.641886 | − | 0.370593i | ||||
\(467\) | 12.0000 | − | 20.7846i | 0.555294 | − | 0.961797i | −0.442587 | − | 0.896726i | \(-0.645939\pi\) |
0.997881 | − | 0.0650714i | \(-0.0207275\pi\) | |||||||
\(468\) | −30.0000 | −1.38675 | ||||||||
\(469\) | −41.5692 | − | 8.00000i | −1.91949 | − | 0.369406i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.79423 | − | 4.50000i | −0.359139 | − | 0.207349i | ||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | −20.7846 | + | 12.0000i | −0.955677 | + | 0.551761i | ||||
\(474\) | 10.5000 | − | 18.1865i | 0.482281 | − | 0.835335i | ||||
\(475\) | 20.0000 | 0.917663 | ||||||||
\(476\) | −10.8660 | + | 0.964102i | −0.498043 | + | 0.0441895i | ||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | −8.00000 | + | 13.8564i | −0.365911 | + | 0.633777i | ||||
\(479\) | −31.1769 | + | 18.0000i | −1.42451 | + | 0.822441i | −0.996680 | − | 0.0814184i | \(-0.974055\pi\) |
−0.427830 | + | 0.903859i | \(0.640722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.6410 | − | 20.0000i | −1.57949 | − | 0.911922i | ||||
\(482\) | − | 12.0000i | − | 0.546585i | ||||||
\(483\) | −20.7846 | + | 24.0000i | −0.945732 | + | 1.09204i | ||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4545 | + | 9.50000i | −0.745624 | + | 0.430486i | −0.824110 | − | 0.566429i | \(-0.808325\pi\) |
0.0784867 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.0000 | −2.17064 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | −6.00000 | + | 10.3923i | −0.270501 | + | 0.468521i | ||||
\(493\) | −4.53590 | − | 15.8564i | −0.204287 | − | 0.714137i | ||||
\(494\) | 10.0000 | + | 17.3205i | 0.449921 | + | 0.779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000i | 0.179605i | ||||||||
\(497\) | 2.00000 | + | 1.73205i | 0.0897123 | + | 0.0776931i | ||||
\(498\) | 48.0000i | 2.15093i | ||||||||
\(499\) | 21.6506 | + | 12.5000i | 0.969216 | + | 0.559577i | 0.898997 | − | 0.437955i | \(-0.144297\pi\) |
0.0702185 | + | 0.997532i | \(0.477630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.5000 | + | 64.9519i | 1.67538 | + | 2.90184i | ||||
\(502\) | 8.00000 | − | 13.8564i | 0.357057 | − | 0.618442i | ||||
\(503\) | − | 1.00000i | − | 0.0445878i | −0.999751 | − | 0.0222939i | \(-0.992903\pi\) | ||
0.999751 | − | 0.0222939i | \(-0.00709696\pi\) | |||||||
\(504\) | −5.19615 | − | 15.0000i | −0.231455 | − | 0.668153i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.00000 | + | 10.3923i | −0.266733 | + | 0.461994i | ||||
\(507\) | 31.1769 | − | 18.0000i | 1.38462 | − | 0.799408i | ||||
\(508\) | −4.00000 | − | 6.92820i | −0.177471 | − | 0.307389i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | − | 20.7846i | 0.176950 | − | 0.919457i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 31.1769 | + | 18.0000i | 1.37649 | + | 0.794719i | ||||
\(514\) | −3.50000 | − | 6.06218i | −0.154378 | − | 0.267391i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −20.7846 | − | 12.0000i | −0.914991 | − | 0.528271i | ||||
\(517\) | − | 12.0000i | − | 0.527759i | ||||||
\(518\) | 4.00000 | − | 20.7846i | 0.175750 | − | 0.913223i | ||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 20.7846 | − | 12.0000i | 0.909718 | − | 0.525226i | ||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 8.00000i | 0.349482i | ||||||||
\(525\) | 37.5000 | − | 12.9904i | 1.63663 | − | 0.566947i | ||||
\(526\) | −4.00000 | −0.174408 | ||||||||
\(527\) | −11.4641 | + | 11.8564i | −0.499384 | + | 0.516473i | ||||
\(528\) | −4.50000 | − | 7.79423i | −0.195837 | − | 0.339200i | ||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −72.0000 | −3.12453 | ||||||||
\(532\) | −6.92820 | + | 8.00000i | −0.300376 | + | 0.346844i | ||||
\(533\) | − | 20.0000i | − | 0.866296i | ||||||
\(534\) | 23.3827 | + | 13.5000i | 1.01187 | + | 0.584202i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.00000 | − | 13.8564i | −0.345547 | − | 0.598506i | ||||
\(537\) | 41.5692 | + | 24.0000i | 1.79384 | + | 1.03568i | ||||
\(538\) | − | 4.00000i | − | 0.172452i | ||||||
\(539\) | 12.9904 | + | 16.5000i | 0.559535 | + | 0.710705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.7128 | + | 16.0000i | 1.19147 | + | 0.687894i | 0.958639 | − | 0.284624i | \(-0.0918688\pi\) |
0.232828 | + | 0.972518i | \(0.425202\pi\) | |||||||
\(542\) | 6.00000 | + | 10.3923i | 0.257722 | + | 0.446388i | ||||
\(543\) | −6.00000 | − | 10.3923i | −0.257485 | − | 0.445976i | ||||
\(544\) | −2.96410 | − | 2.86603i | −0.127085 | − | 0.122880i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.0000 | + | 25.9808i | 1.28388 | + | 1.11187i | ||||
\(547\) | 9.00000i | 0.384812i | 0.981315 | + | 0.192406i | \(0.0616291\pi\) | ||||
−0.981315 | + | 0.192406i | \(0.938371\pi\) | |||||||
\(548\) | −4.50000 | + | 7.79423i | −0.192230 | + | 0.332953i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.9904 | − | 7.50000i | 0.553912 | − | 0.319801i | ||||
\(551\) | −13.8564 | − | 8.00000i | −0.590303 | − | 0.340811i | ||||
\(552\) | −12.0000 | −0.510754 | ||||||||
\(553\) | −17.5000 | + | 6.06218i | −0.744176 | + | 0.257790i | ||||
\(554\) | 4.00000i | 0.169944i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.52628 | + | 5.50000i | −0.404004 | + | 0.233252i | ||||
\(557\) | 19.5000 | + | 33.7750i | 0.826242 | + | 1.43109i | 0.900967 | + | 0.433888i | \(0.142859\pi\) |
−0.0747252 | + | 0.997204i | \(0.523808\pi\) | |||||||
\(558\) | −20.7846 | − | 12.0000i | −0.879883 | − | 0.508001i | ||||
\(559\) | 40.0000 | 1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 36.0000i | 0.379980 | − | 1.51992i | ||||
\(562\) | 3.50000 | − | 6.06218i | 0.147639 | − | 0.255718i | ||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 10.3923 | − | 6.00000i | 0.437595 | − | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 11.0000i | − | 0.462364i | ||||||
\(567\) | 23.3827 | + | 4.50000i | 0.981981 | + | 0.188982i | ||||
\(568\) | 1.00000i | 0.0419591i | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8564 | + | 8.00000i | −0.579873 | + | 0.334790i | −0.761083 | − | 0.648655i | \(-0.775332\pi\) |
0.181210 | + | 0.983444i | \(0.441999\pi\) | |||||||
\(572\) | 12.9904 | + | 7.50000i | 0.543155 | + | 0.313591i | ||||
\(573\) | − | 36.0000i | − | 1.50392i | ||||||
\(574\) | 10.0000 | − | 3.46410i | 0.417392 | − | 0.144589i | ||||
\(575\) | − | 20.0000i | − | 0.834058i | ||||||
\(576\) | 3.00000 | − | 5.19615i | 0.125000 | − | 0.216506i | ||||
\(577\) | −8.50000 | − | 14.7224i | −0.353860 | − | 0.612903i | 0.633062 | − | 0.774101i | \(-0.281798\pi\) |
−0.986922 | + | 0.161198i | \(0.948464\pi\) | |||||||
\(578\) | −0.571797 | − | 16.9904i | −0.0237836 | − | 0.706707i | ||||
\(579\) | 6.00000 | − | 10.3923i | 0.249351 | − | 0.431889i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.7128 | − | 32.0000i | 1.14972 | − | 1.32758i | ||||
\(582\) | −24.0000 | −0.994832 | ||||||||
\(583\) | −2.59808 | − | 1.50000i | −0.107601 | − | 0.0621237i | ||||
\(584\) | 6.92820 | − | 4.00000i | 0.286691 | − | 0.165521i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5000 | − | 19.9186i | 0.475061 | − | 0.822829i | ||||
\(587\) | 8.00000 | 0.330195 | 0.165098 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165098 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(588\) | −7.79423 | + | 19.5000i | −0.321429 | + | 0.804166i | ||||
\(589\) | 16.0000i | 0.659269i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0000 | − | 41.5692i | −0.987228 | − | 1.70993i | ||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | 4.50000 | − | 7.79423i | 0.184793 | − | 0.320071i | −0.758714 | − | 0.651424i | \(-0.774172\pi\) |
0.943507 | + | 0.331353i | \(0.107505\pi\) | |||||||
\(594\) | 27.0000 | 1.10782 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.0000 | 0.450578 | ||||||||
\(597\) | −4.50000 | + | 7.79423i | −0.184173 | + | 0.318997i | ||||
\(598\) | 17.3205 | − | 10.0000i | 0.708288 | − | 0.408930i | ||||
\(599\) | 20.0000 | + | 34.6410i | 0.817178 | + | 1.41539i | 0.907754 | + | 0.419504i | \(0.137796\pi\) |
−0.0905757 | + | 0.995890i | \(0.528871\pi\) | |||||||
\(600\) | 12.9904 | + | 7.50000i | 0.530330 | + | 0.306186i | ||||
\(601\) | 8.00000i | 0.326327i | 0.986599 | + | 0.163163i | \(0.0521698\pi\) | ||||
−0.986599 | + | 0.163163i | \(0.947830\pi\) | |||||||
\(602\) | 6.92820 | + | 20.0000i | 0.282372 | + | 0.815139i | ||||
\(603\) | 96.0000 | 3.90942 | ||||||||
\(604\) | 6.00000 | − | 10.3923i | 0.244137 | − | 0.422857i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −25.9808 | + | 15.0000i | −1.05540 | + | 0.609333i | ||||
\(607\) | −32.0429 | − | 18.5000i | −1.30058 | − | 0.750892i | −0.320079 | − | 0.947391i | \(-0.603709\pi\) |
−0.980504 | + | 0.196499i | \(0.937043\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | −31.1769 | − | 6.00000i | −1.26335 | − | 0.243132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0000 | + | 17.3205i | −0.404557 | + | 0.700713i | ||||
\(612\) | 23.7846 | − | 6.80385i | 0.961436 | − | 0.275029i | ||||
\(613\) | −13.5000 | − | 23.3827i | −0.545260 | − | 0.944418i | −0.998591 | − | 0.0530754i | \(-0.983098\pi\) |
0.453331 | − | 0.891342i | \(-0.350236\pi\) | |||||||
\(614\) | −8.00000 | + | 13.8564i | −0.322854 | + | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50000 | + | 7.79423i | −0.0604367 | + | 0.314038i | ||||
\(617\) | − | 48.0000i | − | 1.93241i | −0.257780 | − | 0.966204i | \(-0.582991\pi\) | ||
0.257780 | − | 0.966204i | \(-0.417009\pi\) | |||||||
\(618\) | −20.7846 | − | 12.0000i | −0.836080 | − | 0.482711i | ||||
\(619\) | 6.06218 | − | 3.50000i | 0.243659 | − | 0.140677i | −0.373198 | − | 0.927752i | \(-0.621739\pi\) |
0.616858 | + | 0.787075i | \(0.288405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | − | 31.1769i | 0.722315 | − | 1.25109i | ||||
\(622\) | 21.0000i | 0.842023i | ||||||||
\(623\) | −7.79423 | − | 22.5000i | −0.312269 | − | 0.901443i | ||||
\(624\) | 15.0000i | 0.600481i | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | −17.3205 | + | 10.0000i | −0.692267 | + | 0.399680i | ||||
\(627\) | −18.0000 | − | 31.1769i | −0.718851 | − | 1.24509i | ||||
\(628\) | −1.50000 | + | 2.59808i | −0.0598565 | + | 0.103675i | ||||
\(629\) | 32.0000 | + | 8.00000i | 1.27592 | + | 0.318981i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0000 | −1.43314 | −0.716569 | − | 0.697517i | \(-0.754288\pi\) | ||||
−0.716569 | + | 0.697517i | \(0.754288\pi\) | |||||||
\(632\) | −6.06218 | − | 3.50000i | −0.241140 | − | 0.139223i | ||||
\(633\) | 36.0000 | + | 62.3538i | 1.43087 | + | 2.47834i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 3.00000i | − | 0.118958i | ||||||
\(637\) | −5.00000 | − | 34.6410i | −0.198107 | − | 1.37253i | ||||
\(638\) | −12.0000 | −0.475085 | ||||||||
\(639\) | −5.19615 | − | 3.00000i | −0.205557 | − | 0.118678i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.3923 | − | 6.00000i | 0.410471 | − | 0.236986i | −0.280521 | − | 0.959848i | \(-0.590507\pi\) |
0.690992 | + | 0.722862i | \(0.257174\pi\) | |||||||
\(642\) | −4.50000 | + | 7.79423i | −0.177601 | + | 0.307614i | ||||
\(643\) | − | 43.0000i | − | 1.69575i | −0.530193 | − | 0.847877i | \(-0.677880\pi\) | ||
0.530193 | − | 0.847877i | \(-0.322120\pi\) | |||||||
\(644\) | 8.00000 | + | 6.92820i | 0.315244 | + | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.8564 | − | 11.4641i | −0.466484 | − | 0.451049i | ||||
\(647\) | −6.00000 | − | 10.3923i | −0.235884 | − | 0.408564i | 0.723645 | − | 0.690172i | \(-0.242465\pi\) |
−0.959529 | + | 0.281609i | \(0.909132\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | 31.1769 | + | 18.0000i | 1.22380 | + | 0.706562i | ||||
\(650\) | −25.0000 | −0.980581 | ||||||||
\(651\) | 10.3923 | + | 30.0000i | 0.407307 | + | 1.17579i | ||||
\(652\) | 16.0000i | 0.626608i | ||||||||
\(653\) | −31.1769 | − | 18.0000i | −1.22005 | − | 0.704394i | −0.255119 | − | 0.966910i | \(-0.582115\pi\) |
−0.964928 | + | 0.262515i | \(0.915448\pi\) | |||||||
\(654\) | −30.0000 | − | 51.9615i | −1.17309 | − | 2.03186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.46410 | + | 2.00000i | 0.135250 | + | 0.0780869i | ||||
\(657\) | 48.0000i | 1.87266i | ||||||||
\(658\) | −10.3923 | − | 2.00000i | −0.405134 | − | 0.0779681i | ||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | − | 19.0526i | −0.427850 | − | 0.741059i | 0.568831 | − | 0.822454i | \(-0.307396\pi\) |
−0.996682 | + | 0.0813955i | \(0.974062\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | −42.9904 | + | 44.4615i | −1.66961 | + | 1.72674i | ||||
\(664\) | 16.0000 | 0.620920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 48.0000i | 1.85996i | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 21.6506 | − | 12.5000i | 0.837688 | − | 0.483640i | ||||
\(669\) | 31.1769 | − | 18.0000i | 1.20537 | − | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −7.50000 | + | 2.59808i | −0.289319 | + | 0.100223i | ||||
\(673\) | 4.00000i | 0.154189i | 0.997024 | + | 0.0770943i | \(0.0245643\pi\) | ||||
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(674\) | 6.92820 | + | 4.00000i | 0.266864 | + | 0.154074i | ||||
\(675\) | −38.9711 | + | 22.5000i | −1.50000 | + | 0.866025i | ||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | −17.3205 | − | 10.0000i | −0.665681 | − | 0.384331i | 0.128757 | − | 0.991676i | \(-0.458901\pi\) |
−0.794438 | + | 0.607345i | \(0.792235\pi\) | |||||||
\(678\) | −36.0000 | −1.38257 | ||||||||
\(679\) | 16.0000 | + | 13.8564i | 0.614024 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.5000 | − | 54.5596i | 1.20708 | − | 2.09073i | ||||
\(682\) | 6.00000 | + | 10.3923i | 0.229752 | + | 0.397942i | ||||
\(683\) | 7.79423 | − | 4.50000i | 0.298238 | − | 0.172188i | −0.343413 | − | 0.939184i | \(-0.611583\pi\) |
0.641651 | + | 0.766997i | \(0.278250\pi\) | |||||||
\(684\) | 12.0000 | − | 20.7846i | 0.458831 | − | 0.794719i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.4545 | − | 8.50000i | 0.628235 | − | 0.324532i | ||||
\(687\) | 78.0000i | 2.97589i | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 2.50000 | + | 4.33013i | 0.0952424 | + | 0.164965i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.92820 | − | 4.00000i | −0.263561 | − | 0.152167i | 0.362397 | − | 0.932024i | \(-0.381959\pi\) |
−0.625958 | + | 0.779857i | \(0.715292\pi\) | |||||||
\(692\) | 4.00000i | 0.152057i | ||||||||
\(693\) | −36.0000 | − | 31.1769i | −1.36753 | − | 1.18431i | ||||
\(694\) | − | 32.0000i | − | 1.21470i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | − | 10.3923i | −0.227429 | − | 0.393919i | ||||
\(697\) | 4.53590 | + | 15.8564i | 0.171809 | + | 0.600604i | ||||
\(698\) | 15.0000 | − | 25.9808i | 0.567758 | − | 0.983386i | ||||
\(699\) | 48.0000 | 1.81553 | ||||||||
\(700\) | −4.33013 | − | 12.5000i | −0.163663 | − | 0.472456i | ||||
\(701\) | 1.00000 | 0.0377695 | 0.0188847 | − | 0.999822i | \(-0.493988\pi\) | ||||
0.0188847 | + | 0.999822i | \(0.493988\pi\) | |||||||
\(702\) | −38.9711 | − | 22.5000i | −1.47087 | − | 0.849208i | ||||
\(703\) | 27.7128 | − | 16.0000i | 1.04521 | − | 0.603451i | ||||
\(704\) | −2.59808 | + | 1.50000i | −0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.0000 | 0.790345 | ||||||||
\(707\) | 25.9808 | + | 5.00000i | 0.977107 | + | 0.188044i | ||||
\(708\) | 36.0000i | 1.35296i | ||||||||
\(709\) | −41.5692 | − | 24.0000i | −1.56116 | − | 0.901339i | −0.997140 | − | 0.0755813i | \(-0.975919\pi\) |
−0.564025 | − | 0.825758i | \(-0.690748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.3731 | − | 21.0000i | 1.36410 | − | 0.787562i | ||||
\(712\) | 4.50000 | − | 7.79423i | 0.168645 | − | 0.292101i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | −29.6769 | − | 13.7942i | −1.11063 | − | 0.516236i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.00000 | − | 13.8564i | 0.298974 | − | 0.517838i | ||||
\(717\) | −41.5692 | + | 24.0000i | −1.55243 | + | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.79423 | − | 4.50000i | −0.290676 | − | 0.167822i | 0.347571 | − | 0.937654i | \(-0.387007\pi\) |
−0.638247 | + | 0.769832i | \(0.720340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.92820 | + | 20.0000i | 0.258020 | + | 0.744839i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 18.0000 | − | 31.1769i | 0.669427 | − | 1.15948i | ||||
\(724\) | −3.46410 | + | 2.00000i | −0.128742 | + | 0.0743294i | ||||
\(725\) | 17.3205 | − | 10.0000i | 0.643268 | − | 0.371391i | ||||
\(726\) | 5.19615 | + | 3.00000i | 0.192847 | + | 0.111340i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 8.66025 | − | 10.0000i | 0.320970 | − | 0.370625i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.7128 | + | 9.07180i | −1.17294 | + | 0.335533i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5000 | − | 25.1147i | 0.535570 | − | 0.927634i | −0.463566 | − | 0.886062i | \(-0.653430\pi\) |
0.999136 | − | 0.0415715i | \(-0.0132364\pi\) | |||||||
\(734\) | 7.00000i | 0.258375i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | −41.5692 | − | 24.0000i | −1.53122 | − | 0.884051i | ||||
\(738\) | −20.7846 | + | 12.0000i | −0.765092 | + | 0.441726i | ||||
\(739\) | −10.0000 | − | 17.3205i | −0.367856 | − | 0.637145i | 0.621374 | − | 0.783514i | \(-0.286575\pi\) |
−0.989230 | + | 0.146369i | \(0.953241\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 60.0000i | 2.20416i | ||||||||
\(742\) | −1.73205 | + | 2.00000i | −0.0635856 | + | 0.0734223i | ||||
\(743\) | 33.0000i | 1.21065i | 0.795977 | + | 0.605326i | \(0.206957\pi\) | ||||
−0.795977 | + | 0.605326i | \(0.793043\pi\) | |||||||
\(744\) | −6.00000 | + | 10.3923i | −0.219971 | + | 0.381000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.50000 | − | 16.4545i | −0.347820 | − | 0.602441i | ||||
\(747\) | −48.0000 | + | 83.1384i | −1.75623 | + | 3.04188i | ||||
\(748\) | −12.0000 | − | 3.00000i | −0.438763 | − | 0.109691i | ||||
\(749\) | 7.50000 | − | 2.59808i | 0.274044 | − | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2583 | + | 6.50000i | 0.410822 | + | 0.237188i | 0.691143 | − | 0.722718i | \(-0.257107\pi\) |
−0.280321 | + | 0.959906i | \(0.590441\pi\) | |||||||
\(752\) | −2.00000 | − | 3.46410i | −0.0729325 | − | 0.126323i | ||||
\(753\) | 41.5692 | − | 24.0000i | 1.51487 | − | 0.874609i | ||||
\(754\) | 17.3205 | + | 10.0000i | 0.630776 | + | 0.364179i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.50000 | − | 23.3827i | 0.163663 | − | 0.850420i | ||||
\(757\) | −39.0000 | −1.41748 | −0.708740 | − | 0.705470i | \(-0.750736\pi\) | ||||
−0.708740 | + | 0.705470i | \(0.750736\pi\) | |||||||
\(758\) | −0.866025 | − | 0.500000i | −0.0314555 | − | 0.0181608i | ||||
\(759\) | −31.1769 | + | 18.0000i | −1.13165 | + | 0.653359i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.50000 | − | 12.9904i | 0.271875 | − | 0.470901i | −0.697467 | − | 0.716617i | \(-0.745690\pi\) |
0.969342 | + | 0.245716i | \(0.0790230\pi\) | |||||||
\(762\) | − | 24.0000i | − | 0.869428i | ||||||
\(763\) | −10.0000 | + | 51.9615i | −0.362024 | + | 1.88113i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | + | 20.7846i | 0.433578 | + | 0.750978i | ||||
\(767\) | −30.0000 | − | 51.9615i | −1.08324 | − | 1.87622i | ||||
\(768\) | −2.59808 | − | 1.50000i | −0.0937500 | − | 0.0541266i | ||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 21.0000i | − | 0.756297i | ||||||
\(772\) | −3.46410 | − | 2.00000i | −0.124676 | − | 0.0719816i | ||||
\(773\) | −0.500000 | − | 0.866025i | −0.0179838 | − | 0.0311488i | 0.856893 | − | 0.515494i | \(-0.172391\pi\) |
−0.874877 | + | 0.484345i | \(0.839058\pi\) | |||||||
\(774\) | −24.0000 | − | 41.5692i | −0.862662 | − | 1.49417i | ||||
\(775\) | −17.3205 | − | 10.0000i | −0.622171 | − | 0.359211i | ||||
\(776\) | 8.00000i | 0.287183i | ||||||||
\(777\) | 41.5692 | − | 48.0000i | 1.49129 | − | 1.72199i | ||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 13.8564 | + | 8.00000i | 0.496457 | + | 0.286630i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50000 | + | 2.59808i | 0.0536742 | + | 0.0929665i | ||||
\(782\) | −11.4641 | + | 11.8564i | −0.409955 | + | 0.423984i | ||||
\(783\) | 36.0000 | 1.28654 | ||||||||
\(784\) | 6.50000 | + | 2.59808i | 0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.0000 | + | 20.7846i | −0.428026 | + | 0.741362i | ||||
\(787\) | −20.7846 | + | 12.0000i | −0.740891 | + | 0.427754i | −0.822393 | − | 0.568919i | \(-0.807362\pi\) |
0.0815020 | + | 0.996673i | \(0.474028\pi\) | |||||||
\(788\) | −13.8564 | + | 8.00000i | −0.493614 | + | 0.284988i | ||||
\(789\) | −10.3923 | − | 6.00000i | −0.369976 | − | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | + | 20.7846i | 0.853342 | + | 0.739016i | ||||
\(792\) | − | 18.0000i | − | 0.639602i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 27.7128 | − | 16.0000i | 0.983491 | − | 0.567819i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.59808 | + | 1.50000i | 0.0920864 | + | 0.0531661i | ||||
\(797\) | −9.00000 | −0.318796 | −0.159398 | − | 0.987214i | \(-0.550955\pi\) | ||||
−0.159398 | + | 0.987214i | \(0.550955\pi\) | |||||||
\(798\) | −30.0000 | + | 10.3923i | −1.06199 | + | 0.367884i | ||||
\(799\) | 4.00000 | − | 16.0000i | 0.141510 | − | 0.566039i | ||||
\(800\) | 2.50000 | − | 4.33013i | 0.0883883 | − | 0.153093i | ||||
\(801\) | 27.0000 | + | 46.7654i | 0.953998 | + | 1.65237i | ||||
\(802\) | 17.3205 | − | 10.0000i | 0.611608 | − | 0.353112i | ||||
\(803\) | 12.0000 | − | 20.7846i | 0.423471 | − | 0.733473i | ||||
\(804\) | − | 48.0000i | − | 1.69283i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 20.0000i | − | 0.704470i | ||||||
\(807\) | 6.00000 | − | 10.3923i | 0.211210 | − | 0.365826i | ||||
\(808\) | 5.00000 | + | 8.66025i | 0.175899 | + | 0.304667i | ||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.0000i | − | 1.15879i | −0.815048 | − | 0.579393i | \(-0.803290\pi\) | ||
0.815048 | − | 0.579393i | \(-0.196710\pi\) | |||||||
\(812\) | −2.00000 | + | 10.3923i | −0.0701862 | + | 0.364698i | ||||
\(813\) | 36.0000i | 1.26258i | ||||||||
\(814\) | 12.0000 | − | 20.7846i | 0.420600 | − | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.40192 | − | 11.8923i | −0.119091 | − | 0.416314i | ||||
\(817\) | −16.0000 | + | 27.7128i | −0.559769 | + | 0.969549i | ||||
\(818\) | −19.0000 | −0.664319 | ||||||||
\(819\) | 25.9808 | + | 75.0000i | 0.907841 | + | 2.62071i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.5692 | + | 24.0000i | 1.45078 | + | 0.837606i | 0.998525 | − | 0.0542853i | \(-0.0172880\pi\) |
0.452250 | + | 0.891891i | \(0.350621\pi\) | |||||||
\(822\) | −23.3827 | + | 13.5000i | −0.815565 | + | 0.470867i | ||||
\(823\) | 12.9904 | − | 7.50000i | 0.452816 | − | 0.261434i | −0.256203 | − | 0.966623i | \(-0.582471\pi\) |
0.709019 | + | 0.705190i | \(0.249138\pi\) | |||||||
\(824\) | −4.00000 | + | 6.92820i | −0.139347 | + | 0.241355i | ||||
\(825\) | 45.0000 | 1.56670 | ||||||||
\(826\) | 20.7846 | − | 24.0000i | 0.723189 | − | 0.835067i | ||||
\(827\) | − | 43.0000i | − | 1.49526i | −0.664117 | − | 0.747628i | \(-0.731193\pi\) | ||
0.664117 | − | 0.747628i | \(-0.268807\pi\) | |||||||
\(828\) | −20.7846 | − | 12.0000i | −0.722315 | − | 0.417029i | ||||
\(829\) | −3.50000 | − | 6.06218i | −0.121560 | − | 0.210548i | 0.798823 | − | 0.601566i | \(-0.205456\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.00000 | + | 10.3923i | −0.208138 | + | 0.360505i | ||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | 11.8205 | + | 26.3301i | 0.409556 | + | 0.912285i | ||||
\(834\) | −33.0000 | −1.14270 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.3923 | + | 6.00000i | −0.359425 | + | 0.207514i | ||||
\(837\) | −18.0000 | − | 31.1769i | −0.622171 | − | 1.07763i | ||||
\(838\) | 4.33013 | + | 2.50000i | 0.149582 | + | 0.0863611i | ||||
\(839\) | − | 12.0000i | − | 0.414286i | −0.978311 | − | 0.207143i | \(-0.933583\pi\) | ||
0.978311 | − | 0.207143i | \(-0.0664165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 5.00000 | − | 8.66025i | 0.172311 | − | 0.298452i | ||||
\(843\) | 18.1865 | − | 10.5000i | 0.626377 | − | 0.361639i | ||||
\(844\) | 20.7846 | − | 12.0000i | 0.715436 | − | 0.413057i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.0000 | 0.825137 | ||||||||
\(847\) | −1.73205 | − | 5.00000i | −0.0595140 | − | 0.171802i | ||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 16.5000 | − | 28.5788i | 0.566279 | − | 0.980823i | ||||
\(850\) | 19.8205 | − | 5.66987i | 0.679838 | − | 0.194475i | ||||
\(851\) | −16.0000 | − | 27.7128i | −0.548473 | − | 0.949983i | ||||
\(852\) | −1.50000 | + | 2.59808i | −0.0513892 | + | 0.0890086i | ||||
\(853\) | 4.00000i | 0.136957i | 0.997653 | + | 0.0684787i | \(0.0218145\pi\) | ||||
−0.997653 | + | 0.0684787i | \(0.978185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.59808 | + | 1.50000i | 0.0888004 | + | 0.0512689i | ||||
\(857\) | −20.7846 | + | 12.0000i | −0.709989 | + | 0.409912i | −0.811057 | − | 0.584967i | \(-0.801107\pi\) |
0.101068 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(858\) | 22.5000 | + | 38.9711i | 0.768137 | + | 1.33045i | ||||
\(859\) | 6.00000 | − | 10.3923i | 0.204717 | − | 0.354581i | −0.745325 | − | 0.666701i | \(-0.767706\pi\) |
0.950043 | + | 0.312120i | \(0.101039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.1769 | + | 6.00000i | 1.06251 | + | 0.204479i | ||||
\(862\) | 21.0000i | 0.715263i | ||||||||
\(863\) | 18.0000 | − | 31.1769i | 0.612727 | − | 1.06127i | −0.378052 | − | 0.925785i | \(-0.623406\pi\) |
0.990779 | − | 0.135490i | \(-0.0432609\pi\) | |||||||
\(864\) | 7.79423 | − | 4.50000i | 0.265165 | − | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.0000 | + | 29.4449i | −0.577684 | + | 1.00058i | ||||
\(867\) | 24.0000 | − | 45.0000i | 0.815083 | − | 1.52828i | ||||
\(868\) | 10.0000 | − | 3.46410i | 0.339422 | − | 0.117579i | ||||
\(869\) | −21.0000 | −0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.0000 | + | 69.2820i | 1.35535 | + | 2.34753i | ||||
\(872\) | −17.3205 | + | 10.0000i | −0.586546 | + | 0.338643i | ||||
\(873\) | −41.5692 | − | 24.0000i | −1.40690 | − | 0.812277i | ||||
\(874\) | 16.0000i | 0.541208i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.0000 | 0.810885 | ||||||||
\(877\) | −10.3923 | − | 6.00000i | −0.350923 | − | 0.202606i | 0.314169 | − | 0.949367i | \(-0.398274\pi\) |
−0.665092 | + | 0.746762i | \(0.731608\pi\) | |||||||
\(878\) | 0.866025 | − | 0.500000i | 0.0292269 | − | 0.0168742i | ||||
\(879\) | 59.7558 | − | 34.5000i | 2.01551 | − | 1.16366i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000i | 0.404290i | 0.979356 | + | 0.202145i | \(0.0647913\pi\) | ||||
−0.979356 | + | 0.202145i | \(0.935209\pi\) | |||||||
\(882\) | −33.0000 | + | 25.9808i | −1.11117 | + | 0.874818i | ||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | 14.8205 | + | 14.3301i | 0.498468 | + | 0.481974i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.00000 | − | 13.8564i | −0.268765 | − | 0.465515i | ||||
\(887\) | −11.2583 | − | 6.50000i | −0.378018 | − | 0.218249i | 0.298938 | − | 0.954273i | \(-0.403368\pi\) |
−0.676955 | + | 0.736024i | \(0.736701\pi\) | |||||||
\(888\) | 24.0000 | 0.805387 | ||||||||
\(889\) | −13.8564 | + | 16.0000i | −0.464729 | + | 0.536623i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.3827 | + | 13.5000i | 0.783349 | + | 0.452267i | ||||
\(892\) | −6.00000 | − | 10.3923i | −0.200895 | − | 0.347960i | ||||
\(893\) | −8.00000 | − | 13.8564i | −0.267710 | − | 0.463687i | ||||
\(894\) | 28.5788 | + | 16.5000i | 0.955819 | + | 0.551843i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.866025 | + | 2.50000i | 0.0289319 | + | 0.0835191i | ||||
\(897\) | 60.0000 | 2.00334 | ||||||||
\(898\) | −3.46410 | − | 2.00000i | −0.115599 | − | 0.0667409i | ||||
\(899\) | 8.00000 | + | 13.8564i | 0.266815 | + | 0.462137i | ||||
\(900\) | 15.0000 | + | 25.9808i | 0.500000 | + | 0.866025i | ||||
\(901\) | −2.96410 | − | 2.86603i | −0.0987485 | − | 0.0954811i | ||||
\(902\) | 12.0000 | 0.399556 | ||||||||
\(903\) | −12.0000 | + | 62.3538i | −0.399335 | + | 2.07501i | ||||
\(904\) | 12.0000i | 0.399114i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 31.1769 | − | 18.0000i | 1.03578 | − | 0.598010i | ||||
\(907\) | 6.92820 | − | 4.00000i | 0.230047 | − | 0.132818i | −0.380547 | − | 0.924762i | \(-0.624264\pi\) |
0.610594 | + | 0.791944i | \(0.290931\pi\) | |||||||
\(908\) | −18.1865 | − | 10.5000i | −0.603541 | − | 0.348455i | ||||
\(909\) | −60.0000 | −1.99007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000i | 1.19273i | 0.802712 | + | 0.596367i | \(0.203390\pi\) | ||||
−0.802712 | + | 0.596367i | \(0.796610\pi\) | |||||||
\(912\) | −10.3923 | − | 6.00000i | −0.344124 | − | 0.198680i | ||||
\(913\) | 41.5692 | − | 24.0000i | 1.37574 | − | 0.794284i | ||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 20.0000 | − | 6.92820i | 0.660458 | − | 0.228789i | ||||
\(918\) | 36.0000 | + | 9.00000i | 1.18818 | + | 0.297044i | ||||
\(919\) | −22.0000 | + | 38.1051i | −0.725713 | + | 1.25697i | 0.232967 | + | 0.972485i | \(0.425157\pi\) |
−0.958680 | + | 0.284487i | \(0.908177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.5692 | + | 24.0000i | −1.36975 | + | 0.790827i | ||||
\(922\) | −0.500000 | + | 0.866025i | −0.0164666 | + | 0.0285210i | ||||
\(923\) | − | 5.00000i | − | 0.164577i | ||||||
\(924\) | −15.5885 | + | 18.0000i | −0.512823 | + | 0.592157i | ||||
\(925\) | 40.0000i | 1.31519i | ||||||||
\(926\) | 10.0000 | − | 17.3205i | 0.328620 | − | 0.569187i | ||||
\(927\) | −24.0000 | − | 41.5692i | −0.788263 | − | 1.36531i | ||||
\(928\) | −3.46410 | + | 2.00000i | −0.113715 | + | 0.0656532i | ||||
\(929\) | −34.6410 | − | 20.0000i | −1.13653 | − | 0.656179i | −0.190965 | − | 0.981597i | \(-0.561162\pi\) |
−0.945570 | + | 0.325418i | \(0.894495\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.0000 | + | 10.3923i | 0.852116 | + | 0.340594i | ||||
\(932\) | − | 16.0000i | − | 0.524097i | ||||||
\(933\) | −31.5000 | + | 54.5596i | −1.03126 | + | 1.78620i | ||||
\(934\) | −12.0000 | − | 20.7846i | −0.392652 | − | 0.680093i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.0000 | + | 25.9808i | −0.490290 | + | 0.849208i | ||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | −27.7128 | + | 32.0000i | −0.904855 | + | 1.04484i | ||||
\(939\) | −60.0000 | −1.95803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.9615 | + | 30.0000i | −1.69390 | + | 0.977972i | −0.742581 | + | 0.669757i | \(0.766398\pi\) |
−0.951317 | + | 0.308215i | \(0.900268\pi\) | |||||||
\(942\) | −7.79423 | + | 4.50000i | −0.253950 | + | 0.146618i | ||||
\(943\) | 8.00000 | − | 13.8564i | 0.260516 | − | 0.451227i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0000i | 0.780307i | ||||||||
\(947\) | 0.866025 | + | 0.500000i | 0.0281420 | + | 0.0162478i | 0.514005 | − | 0.857787i | \(-0.328161\pi\) |
−0.485863 | + | 0.874035i | \(0.661495\pi\) | |||||||
\(948\) | −10.5000 | − | 18.1865i | −0.341024 | − | 0.590671i | ||||
\(949\) | −34.6410 | + | 20.0000i | −1.12449 | + | 0.649227i | ||||
\(950\) | 10.0000 | − | 17.3205i | 0.324443 | − | 0.561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.59808 | + | 9.89230i | −0.149025 | + | 0.320611i | ||||
\(953\) | −27.0000 | −0.874616 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(954\) | 3.00000 | − | 5.19615i | 0.0971286 | − | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.00000 | + | 13.8564i | 0.258738 | + | 0.448148i | ||||
\(957\) | −31.1769 | − | 18.0000i | −1.00781 | − | 0.581857i | ||||
\(958\) | 36.0000i | 1.16311i | ||||||||
\(959\) | 23.3827 | + | 4.50000i | 0.755066 | + | 0.145313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.50000 | + | 12.9904i | −0.241935 | + | 0.419045i | ||||
\(962\) | −34.6410 | + | 20.0000i | −1.11687 | + | 0.644826i | ||||
\(963\) | −15.5885 | + | 9.00000i | −0.502331 | + | 0.290021i | ||||
\(964\) | −10.3923 | − | 6.00000i | −0.334714 | − | 0.193247i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 10.3923 | + | 30.0000i | 0.334367 | + | 0.965234i | ||||
\(967\) | −4.00000 | −0.128631 | −0.0643157 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643157 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | −13.6077 | − | 47.5692i | −0.437142 | − | 1.52814i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.00000 | − | 3.46410i | 0.0641831 | − | 0.111168i | −0.832148 | − | 0.554553i | \(-0.812889\pi\) |
0.896331 | + | 0.443385i | \(0.146223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0000 | + | 19.0526i | 0.705288 | + | 0.610797i | ||||
\(974\) | 19.0000i | 0.608799i | ||||||||
\(975\) | −64.9519 | − | 37.5000i | −2.08013 | − | 1.20096i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.0000 | + | 25.9808i | 0.479893 | + | 0.831198i | 0.999734 | − | 0.0230645i | \(-0.00734232\pi\) |
−0.519841 | + | 0.854263i | \(0.674009\pi\) | |||||||
\(978\) | −24.0000 | + | 41.5692i | −0.767435 | + | 1.32924i | ||||
\(979\) | − | 27.0000i | − | 0.862924i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 120.000i | − | 3.83131i | ||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | 19.9186 | − | 11.5000i | 0.635304 | − | 0.366793i | −0.147499 | − | 0.989062i | \(-0.547122\pi\) |
0.782803 | + | 0.622269i | \(0.213789\pi\) | |||||||
\(984\) | 6.00000 | + | 10.3923i | 0.191273 | + | 0.331295i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.0000 | − | 4.00000i | −0.509544 | − | 0.127386i | ||||
\(987\) | −24.0000 | − | 20.7846i | −0.763928 | − | 0.661581i | ||||
\(988\) | 20.0000 | 0.636285 | ||||||||
\(989\) | 27.7128 | + | 16.0000i | 0.881216 | + | 0.508770i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.7032 | + | 23.5000i | −1.29298 | + | 0.746502i | −0.979181 | − | 0.202988i | \(-0.934935\pi\) |
−0.313798 | + | 0.949490i | \(0.601602\pi\) | |||||||
\(992\) | 3.46410 | + | 2.00000i | 0.109985 | + | 0.0635001i | ||||
\(993\) | − | 12.0000i | − | 0.380808i | ||||||
\(994\) | 2.50000 | − | 0.866025i | 0.0792952 | − | 0.0274687i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 41.5692 | + | 24.0000i | 1.31717 | + | 0.760469i | ||||
\(997\) | 13.8564 | − | 8.00000i | 0.438837 | − | 0.253363i | −0.264267 | − | 0.964449i | \(-0.585130\pi\) |
0.703104 | + | 0.711087i | \(0.251797\pi\) | |||||||
\(998\) | 21.6506 | − | 12.5000i | 0.685339 | − | 0.395681i | ||||
\(999\) | −36.0000 | + | 62.3538i | −1.13899 | + | 1.97279i |
(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 | 238.2.j.a.135.2 | yes | 4 | |
7.2 | even | 3 | 1666.2.b.b.883.2 | 2 | |||
7.4 | even | 3 | inner | 238.2.j.a.67.1 | ✓ | 4 | |
7.5 | odd | 6 | 1666.2.b.a.883.1 | 2 | |||
17.16 | even | 2 | inner | 238.2.j.a.135.1 | yes | 4 | |
119.16 | even | 6 | 1666.2.b.b.883.1 | 2 | |||
119.33 | odd | 6 | 1666.2.b.a.883.2 | 2 | |||
119.67 | even | 6 | inner | 238.2.j.a.67.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
238.2.j.a.67.1 | ✓ | 4 | 7.4 | even | 3 | inner | |
238.2.j.a.67.2 | yes | 4 | 119.67 | even | 6 | inner | |
238.2.j.a.135.1 | yes | 4 | 17.16 | even | 2 | inner | |
238.2.j.a.135.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1666.2.b.a.883.1 | 2 | 7.5 | odd | 6 | |||
1666.2.b.a.883.2 | 2 | 119.33 | odd | 6 | |||
1666.2.b.b.883.1 | 2 | 119.16 | even | 6 | |||
1666.2.b.b.883.2 | 2 | 7.2 | even | 3 |