Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.i (of order \(3\), 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: | \(1.67685844245\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.151 |
Dual form | 210.2.i.d.121.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 1.50000 | + | 2.59808i | 0.344124 | + | 0.596040i | 0.985194 | − | 0.171442i | \(-0.0548427\pi\) |
−0.641071 | + | 0.767482i | \(0.721509\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.50000 | − | 6.06218i | −0.729800 | − | 1.26405i | −0.956967 | − | 0.290196i | \(-0.906280\pi\) |
0.227167 | − | 0.973856i | \(-0.427054\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.500000 | + | 2.59808i | −0.0845154 | + | 0.439155i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.50000 | − | 9.52628i | −0.904194 | − | 1.56611i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
−0.0821995 | − | 0.996616i | \(-0.526194\pi\) | |||||||
\(38\) | −1.50000 | + | 2.59808i | −0.243332 | + | 0.421464i | ||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −11.0000 | −1.71791 | −0.858956 | − | 0.512050i | \(-0.828886\pi\) | ||||
−0.858956 | + | 0.512050i | \(0.828886\pi\) | |||||||
\(42\) | 2.00000 | + | 1.73205i | 0.308607 | + | 0.267261i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 3.50000 | − | 6.06218i | 0.516047 | − | 0.893819i | ||||
\(47\) | 2.50000 | + | 4.33013i | 0.364662 | + | 0.631614i | 0.988722 | − | 0.149763i | \(-0.0478510\pi\) |
−0.624059 | + | 0.781377i | \(0.714518\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | 5.50000 | − | 9.52628i | 0.755483 | − | 1.30854i | −0.189651 | − | 0.981852i | \(-0.560736\pi\) |
0.945134 | − | 0.326683i | \(-0.105931\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | −4.00000 | − | 6.92820i | −0.525226 | − | 0.909718i | ||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | −2.50000 | + | 0.866025i | −0.298807 | + | 0.103510i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 3.00000 | − | 5.19615i | 0.351123 | − | 0.608164i | −0.635323 | − | 0.772246i | \(-0.719133\pi\) |
0.986447 | + | 0.164083i | \(0.0524664\pi\) | |||||||
\(74\) | 5.50000 | − | 9.52628i | 0.639362 | − | 1.10741i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | 2.50000 | − | 0.866025i | 0.284901 | − | 0.0986928i | ||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −5.50000 | − | 9.52628i | −0.607373 | − | 1.05200i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −0.500000 | + | 2.59808i | −0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | −4.00000 | + | 6.92820i | −0.428845 | + | 0.742781i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 5.00000 | + | 8.66025i | 0.529999 | + | 0.917985i | 0.999388 | + | 0.0349934i | \(0.0111410\pi\) |
−0.469389 | + | 0.882992i | \(0.655526\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | 7.00000 | 0.729800 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | −2.50000 | + | 4.33013i | −0.257855 | + | 0.446619i | ||||
\(95\) | −1.50000 | + | 2.59808i | −0.153897 | + | 0.266557i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | + | 13.8564i | 0.788263 | + | 1.36531i | 0.927030 | + | 0.374987i | \(0.122353\pi\) |
−0.138767 | + | 0.990325i | \(0.544314\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | 11.0000 | 1.06841 | ||||||||
\(107\) | 5.00000 | + | 8.66025i | 0.483368 | + | 0.837218i | 0.999818 | − | 0.0190994i | \(-0.00607989\pi\) |
−0.516449 | + | 0.856318i | \(0.672747\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −3.00000 | + | 5.19615i | −0.287348 | + | 0.497701i | −0.973176 | − | 0.230063i | \(-0.926107\pi\) |
0.685828 | + | 0.727764i | \(0.259440\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | −11.0000 | −1.04407 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 1.50000 | + | 2.59808i | 0.140488 | + | 0.243332i | ||||
\(115\) | 3.50000 | − | 6.06218i | 0.326377 | − | 0.565301i | ||||
\(116\) | 4.00000 | − | 6.92820i | 0.371391 | − | 0.643268i | ||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.50000 | + | 9.52628i | −0.495918 | + | 0.858956i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | −17.0000 | −1.50851 | −0.754253 | − | 0.656584i | \(-0.772001\pi\) | ||||
−0.754253 | + | 0.656584i | \(0.772001\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | −0.500000 | + | 0.866025i | −0.0438529 | + | 0.0759555i | ||||
\(131\) | 2.50000 | + | 4.33013i | 0.218426 | + | 0.378325i | 0.954327 | − | 0.298764i | \(-0.0965744\pi\) |
−0.735901 | + | 0.677089i | \(0.763241\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −1.50000 | + | 7.79423i | −0.130066 | + | 0.675845i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | −3.50000 | − | 6.06218i | −0.297940 | − | 0.516047i | ||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | −2.00000 | − | 1.73205i | −0.169031 | − | 0.146385i | ||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | 0.500000 | − | 0.866025i | 0.0418121 | − | 0.0724207i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −4.00000 | − | 6.92820i | −0.332182 | − | 0.575356i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 6.50000 | + | 2.59808i | 0.536111 | + | 0.214286i | ||||
\(148\) | 11.0000 | 0.904194 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −3.00000 | + | 5.19615i | −0.244137 | + | 0.422857i | −0.961888 | − | 0.273442i | \(-0.911838\pi\) |
0.717752 | + | 0.696299i | \(0.245171\pi\) | |||||||
\(152\) | −1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | + | 1.73205i | 0.161165 | + | 0.139573i | ||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0.500000 | + | 0.866025i | 0.0400320 | + | 0.0693375i | ||||
\(157\) | 3.50000 | − | 6.06218i | 0.279330 | − | 0.483814i | −0.691888 | − | 0.722005i | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | −5.50000 | − | 9.52628i | −0.436178 | − | 0.755483i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.50000 | − | 18.1865i | 0.275839 | − | 1.43330i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.00000 | − | 13.8564i | −0.626608 | − | 1.08532i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.361619 | − | 0.932326i | \(-0.382224\pi\) | |||||||
\(164\) | 5.50000 | − | 9.52628i | 0.429478 | − | 0.743877i | ||||
\(165\) | 0.500000 | − | 0.866025i | 0.0389249 | − | 0.0674200i | ||||
\(166\) | 4.00000 | + | 6.92820i | 0.310460 | + | 0.537733i | ||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | −2.50000 | + | 0.866025i | −0.192879 | + | 0.0668153i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 2.59808i | 0.114708 | − | 0.198680i | ||||
\(172\) | −4.00000 | + | 6.92820i | −0.304997 | + | 0.528271i | ||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | −2.50000 | + | 0.866025i | −0.188982 | + | 0.0654654i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | −5.00000 | + | 8.66025i | −0.374766 | + | 0.649113i | ||||
\(179\) | 9.50000 | − | 16.4545i | 0.710063 | − | 1.22987i | −0.254770 | − | 0.967002i | \(-0.582000\pi\) |
0.964833 | − | 0.262864i | \(-0.0846670\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −24.0000 | −1.78391 | −0.891953 | − | 0.452128i | \(-0.850665\pi\) | ||||
−0.891953 | + | 0.452128i | \(0.850665\pi\) | |||||||
\(182\) | −0.500000 | + | 2.59808i | −0.0370625 | + | 0.192582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.50000 | + | 6.06218i | 0.258023 | + | 0.446910i | ||||
\(185\) | 5.50000 | − | 9.52628i | 0.404368 | − | 0.700386i | ||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.00000 | −0.364662 | ||||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −11.0000 | + | 19.0526i | −0.791797 | + | 1.37143i | 0.133056 | + | 0.991109i | \(0.457521\pi\) |
−0.924853 | + | 0.380325i | \(0.875812\pi\) | |||||||
\(194\) | −8.00000 | − | 13.8564i | −0.574367 | − | 0.994832i | ||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | −1.00000 | −0.0712470 | −0.0356235 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356235 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(198\) | −0.500000 | − | 0.866025i | −0.0355335 | − | 0.0615457i | ||||
\(199\) | 12.0000 | − | 20.7846i | 0.850657 | − | 1.47338i | −0.0299585 | − | 0.999551i | \(-0.509538\pi\) |
0.880616 | − | 0.473831i | \(-0.157129\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0000 | − | 13.8564i | −1.12298 | − | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.50000 | − | 9.52628i | −0.384137 | − | 0.665344i | ||||
\(206\) | −8.00000 | + | 13.8564i | −0.557386 | + | 0.965422i | ||||
\(207\) | −3.50000 | + | 6.06218i | −0.243267 | + | 0.421350i | ||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | −0.500000 | + | 2.59808i | −0.0345033 | + | 0.179284i | ||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | 5.50000 | + | 9.52628i | 0.377742 | + | 0.654268i | ||||
\(213\) | −3.00000 | + | 5.19615i | −0.205557 | + | 0.356034i | ||||
\(214\) | −5.00000 | + | 8.66025i | −0.341793 | + | 0.592003i | ||||
\(215\) | 4.00000 | + | 6.92820i | 0.272798 | + | 0.472500i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 5.00000 | − | 1.73205i | 0.339422 | − | 0.117579i | ||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −3.00000 | − | 5.19615i | −0.202721 | − | 0.351123i | ||||
\(220\) | −0.500000 | + | 0.866025i | −0.0337100 | + | 0.0583874i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.50000 | − | 9.52628i | −0.369136 | − | 0.639362i | ||||
\(223\) | 12.0000 | 0.803579 | 0.401790 | − | 0.915732i | \(-0.368388\pi\) | ||||
0.401790 | + | 0.915732i | \(0.368388\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | −4.00000 | + | 6.92820i | −0.265489 | + | 0.459841i | −0.967692 | − | 0.252136i | \(-0.918867\pi\) |
0.702202 | + | 0.711977i | \(0.252200\pi\) | |||||||
\(228\) | −1.50000 | + | 2.59808i | −0.0993399 | + | 0.172062i | ||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 7.00000 | 0.461566 | ||||||||
\(231\) | 0.500000 | − | 2.59808i | 0.0328976 | − | 0.170941i | ||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −9.00000 | − | 15.5885i | −0.589610 | − | 1.02123i | −0.994283 | − | 0.106773i | \(-0.965948\pi\) |
0.404674 | − | 0.914461i | \(-0.367385\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | −2.50000 | + | 4.33013i | −0.163082 | + | 0.282466i | ||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0000 | −1.16432 | −0.582162 | − | 0.813073i | \(-0.697793\pi\) | ||||
−0.582162 | + | 0.813073i | \(0.697793\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | −3.50000 | + | 6.06218i | −0.225455 | + | 0.390499i | −0.956456 | − | 0.291877i | \(-0.905720\pi\) |
0.731001 | + | 0.682376i | \(0.239053\pi\) | |||||||
\(242\) | −5.00000 | + | 8.66025i | −0.321412 | + | 0.556702i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | + | 4.33013i | −0.351382 | + | 0.276642i | ||||
\(246\) | −11.0000 | −0.701334 | ||||||||
\(247\) | 1.50000 | + | 2.59808i | 0.0954427 | + | 0.165312i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 4.00000 | − | 6.92820i | 0.253490 | − | 0.439057i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 13.0000 | 0.820553 | 0.410276 | − | 0.911961i | \(-0.365432\pi\) | ||||
0.410276 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(252\) | 2.00000 | + | 1.73205i | 0.125988 | + | 0.109109i | ||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | −8.50000 | − | 14.7224i | −0.533337 | − | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.0000 | + | 17.3205i | 0.623783 | + | 1.08042i | 0.988775 | + | 0.149413i | \(0.0477384\pi\) |
−0.364992 | + | 0.931011i | \(0.618928\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | 5.50000 | − | 28.5788i | 0.341753 | − | 1.77580i | ||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 4.00000 | + | 6.92820i | 0.247594 | + | 0.428845i | ||||
\(262\) | −2.50000 | + | 4.33013i | −0.154451 | + | 0.267516i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | 11.0000 | 0.675725 | ||||||||
\(266\) | −7.50000 | + | 2.59808i | −0.459855 | + | 0.159298i | ||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | + | 17.3205i | −0.609711 | + | 1.05605i | 0.381577 | + | 0.924337i | \(0.375381\pi\) |
−0.991288 | + | 0.131713i | \(0.957952\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | −16.0000 | − | 27.7128i | −0.971931 | − | 1.68343i | −0.689713 | − | 0.724083i | \(-0.742263\pi\) |
−0.282218 | − | 0.959350i | \(-0.591070\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.50000 | − | 0.866025i | 0.151307 | − | 0.0524142i | ||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | 3.50000 | − | 6.06218i | 0.210675 | − | 0.364900i | ||||
\(277\) | 11.0000 | − | 19.0526i | 0.660926 | − | 1.14476i | −0.319447 | − | 0.947604i | \(-0.603497\pi\) |
0.980373 | − | 0.197153i | \(-0.0631696\pi\) | |||||||
\(278\) | 10.0000 | + | 17.3205i | 0.599760 | + | 1.03882i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0.500000 | − | 2.59808i | 0.0298807 | − | 0.155265i | ||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 2.50000 | + | 4.33013i | 0.148873 | + | 0.257855i | ||||
\(283\) | 7.00000 | − | 12.1244i | 0.416107 | − | 0.720718i | −0.579437 | − | 0.815017i | \(-0.696728\pi\) |
0.995544 | + | 0.0942988i | \(0.0300609\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 1.50000 | + | 2.59808i | 0.0888523 | + | 0.153897i | ||||
\(286\) | 1.00000 | 0.0591312 | ||||||||
\(287\) | −22.0000 | − | 19.0526i | −1.29862 | − | 1.12464i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 4.00000 | − | 6.92820i | 0.234888 | − | 0.406838i | ||||
\(291\) | −8.00000 | + | 13.8564i | −0.468968 | + | 0.812277i | ||||
\(292\) | 3.00000 | + | 5.19615i | 0.175562 | + | 0.304082i | ||||
\(293\) | 27.0000 | 1.57736 | 0.788678 | − | 0.614806i | \(-0.210766\pi\) | ||||
0.788678 | + | 0.614806i | \(0.210766\pi\) | |||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 5.50000 | + | 9.52628i | 0.319681 | + | 0.553704i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.50000 | − | 6.06218i | −0.202410 | − | 0.350585i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 16.0000 | + | 13.8564i | 0.922225 | + | 0.798670i | ||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.50000 | − | 2.59808i | 0.0860309 | − | 0.149010i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | −0.500000 | + | 2.59808i | −0.0284901 | + | 0.148039i | ||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | 6.00000 | + | 10.3923i | 0.339140 | + | 0.587408i | 0.984271 | − | 0.176664i | \(-0.0565306\pi\) |
−0.645131 | + | 0.764072i | \(0.723197\pi\) | |||||||
\(314\) | 7.00000 | 0.395033 | ||||||||
\(315\) | 2.50000 | − | 0.866025i | 0.140859 | − | 0.0487950i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 5.50000 | − | 9.52628i | 0.308425 | − | 0.534207i | ||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 10.0000 | 0.558146 | ||||||||
\(322\) | 17.5000 | − | 6.06218i | 0.975237 | − | 0.337832i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −0.500000 | + | 0.866025i | −0.0277350 | + | 0.0480384i | ||||
\(326\) | 8.00000 | − | 13.8564i | 0.443079 | − | 0.767435i | ||||
\(327\) | 3.00000 | + | 5.19615i | 0.165900 | + | 0.287348i | ||||
\(328\) | 11.0000 | 0.607373 | ||||||||
\(329\) | −2.50000 | + | 12.9904i | −0.137829 | + | 0.716183i | ||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 6.50000 | + | 11.2583i | 0.357272 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503735\pi\) |
−0.630232 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(332\) | −4.00000 | + | 6.92820i | −0.219529 | + | 0.380235i | ||||
\(333\) | −5.50000 | + | 9.52628i | −0.301398 | + | 0.522037i | ||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | − | 1.73205i | −0.109109 | − | 0.0944911i | ||||
\(337\) | −12.0000 | −0.653682 | −0.326841 | − | 0.945079i | \(-0.605984\pi\) | ||||
−0.326841 | + | 0.945079i | \(0.605984\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00000 | − | 1.73205i | −0.0541530 | − | 0.0937958i | ||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −3.50000 | − | 6.06218i | −0.188434 | − | 0.326377i | ||||
\(346\) | −7.50000 | + | 12.9904i | −0.403202 | + | 0.698367i | ||||
\(347\) | −7.00000 | + | 12.1244i | −0.375780 | + | 0.650870i | −0.990443 | − | 0.137920i | \(-0.955958\pi\) |
0.614664 | + | 0.788789i | \(0.289292\pi\) | |||||||
\(348\) | −4.00000 | − | 6.92820i | −0.214423 | − | 0.371391i | ||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | −2.00000 | − | 1.73205i | −0.106904 | − | 0.0925820i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | −2.00000 | + | 3.46410i | −0.106299 | + | 0.184115i | ||||
\(355\) | −3.00000 | − | 5.19615i | −0.159223 | − | 0.275783i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0000 | 1.00418 | ||||||||
\(359\) | −2.00000 | − | 3.46410i | −0.105556 | − | 0.182828i | 0.808409 | − | 0.588621i | \(-0.200329\pi\) |
−0.913965 | + | 0.405793i | \(0.866996\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | −12.0000 | − | 20.7846i | −0.630706 | − | 1.09241i | ||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | −2.50000 | + | 0.866025i | −0.131036 | + | 0.0453921i | ||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.5000 | + | 21.6506i | −0.652495 | + | 1.13015i | 0.330021 | + | 0.943974i | \(0.392944\pi\) |
−0.982516 | + | 0.186180i | \(0.940389\pi\) | |||||||
\(368\) | −3.50000 | + | 6.06218i | −0.182450 | + | 0.316013i | ||||
\(369\) | 5.50000 | + | 9.52628i | 0.286319 | + | 0.495918i | ||||
\(370\) | 11.0000 | 0.571863 | ||||||||
\(371\) | 27.5000 | − | 9.52628i | 1.42773 | − | 0.494580i | ||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −2.50000 | − | 4.33013i | −0.128928 | − | 0.223309i | ||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0.500000 | − | 2.59808i | 0.0257172 | − | 0.133631i | ||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | −1.50000 | − | 2.59808i | −0.0769484 | − | 0.133278i | ||||
\(381\) | −8.50000 | + | 14.7224i | −0.435468 | + | 0.754253i | ||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | −17.5000 | − | 30.3109i | −0.894208 | − | 1.54881i | −0.834781 | − | 0.550581i | \(-0.814406\pi\) |
−0.0594268 | − | 0.998233i | \(-0.518927\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.00000 | + | 1.73205i | 0.101929 | + | 0.0882735i | ||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | 8.00000 | − | 13.8564i | 0.406138 | − | 0.703452i | ||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 0.500000 | + | 0.866025i | 0.0253185 | + | 0.0438529i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | 5.00000 | 0.252217 | ||||||||
\(394\) | −0.500000 | − | 0.866025i | −0.0251896 | − | 0.0436297i | ||||
\(395\) | −4.00000 | + | 6.92820i | −0.201262 | + | 0.348596i | ||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | 24.0000 | 1.20301 | ||||||||
\(399\) | 6.00000 | + | 5.19615i | 0.300376 | + | 0.260133i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 2.50000 | + | 4.33013i | 0.124844 | + | 0.216236i | 0.921672 | − | 0.387970i | \(-0.126824\pi\) |
−0.796828 | + | 0.604206i | \(0.793490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00000 | − | 1.73205i | 0.0498135 | − | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 4.00000 | − | 20.7846i | 0.198517 | − | 1.03152i | ||||
\(407\) | −11.0000 | −0.545250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | + | 1.73205i | −0.0494468 | + | 0.0856444i | −0.889689 | − | 0.456566i | \(-0.849079\pi\) |
0.840243 | + | 0.542211i | \(0.182412\pi\) | |||||||
\(410\) | 5.50000 | − | 9.52628i | 0.271626 | − | 0.470469i | ||||
\(411\) | −9.00000 | − | 15.5885i | −0.443937 | − | 0.768922i | ||||
\(412\) | −16.0000 | −0.788263 | ||||||||
\(413\) | −10.0000 | + | 3.46410i | −0.492068 | + | 0.170457i | ||||
\(414\) | −7.00000 | −0.344031 | ||||||||
\(415\) | 4.00000 | + | 6.92820i | 0.196352 | + | 0.340092i | ||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | 10.0000 | − | 17.3205i | 0.489702 | − | 0.848189i | ||||
\(418\) | 1.50000 | + | 2.59808i | 0.0733674 | + | 0.127076i | ||||
\(419\) | −5.00000 | −0.244266 | −0.122133 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122133 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(420\) | −2.50000 | + | 0.866025i | −0.121988 | + | 0.0422577i | ||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 2.50000 | + | 4.33013i | 0.121698 | + | 0.210787i | ||||
\(423\) | 2.50000 | − | 4.33013i | 0.121554 | − | 0.210538i | ||||
\(424\) | −5.50000 | + | 9.52628i | −0.267104 | + | 0.462637i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.0000 | −0.483368 | ||||||||
\(429\) | −0.500000 | − | 0.866025i | −0.0241402 | − | 0.0418121i | ||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −32.0000 | −1.53782 | −0.768911 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768911 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(434\) | 4.00000 | + | 3.46410i | 0.192006 | + | 0.166282i | ||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | −3.00000 | − | 5.19615i | −0.143674 | − | 0.248851i | ||||
\(437\) | 10.5000 | − | 18.1865i | 0.502283 | − | 0.869980i | ||||
\(438\) | 3.00000 | − | 5.19615i | 0.143346 | − | 0.248282i | ||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.00000 | − | 13.8564i | −0.380091 | − | 0.658338i | 0.610984 | − | 0.791643i | \(-0.290774\pi\) |
−0.991075 | + | 0.133306i | \(0.957441\pi\) | |||||||
\(444\) | 5.50000 | − | 9.52628i | 0.261018 | − | 0.452097i | ||||
\(445\) | −5.00000 | + | 8.66025i | −0.237023 | + | 0.410535i | ||||
\(446\) | 6.00000 | + | 10.3923i | 0.284108 | + | 0.492090i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | + | 1.73205i | 0.0944911 | + | 0.0818317i | ||||
\(449\) | 11.0000 | 0.519122 | 0.259561 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259561 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | −5.50000 | + | 9.52628i | −0.258985 | + | 0.448575i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | 3.00000 | + | 5.19615i | 0.140952 | + | 0.244137i | ||||
\(454\) | −8.00000 | −0.375459 | ||||||||
\(455\) | −0.500000 | + | 2.59808i | −0.0234404 | + | 0.121800i | ||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | 9.00000 | + | 15.5885i | 0.421002 | + | 0.729197i | 0.996038 | − | 0.0889312i | \(-0.0283451\pi\) |
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(458\) | 7.00000 | − | 12.1244i | 0.327089 | − | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.50000 | + | 6.06218i | 0.163188 | + | 0.282650i | ||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 2.50000 | − | 0.866025i | 0.116311 | − | 0.0402911i | ||||
\(463\) | −13.0000 | −0.604161 | −0.302081 | − | 0.953282i | \(-0.597681\pi\) | ||||
−0.302081 | + | 0.953282i | \(0.597681\pi\) | |||||||
\(464\) | 4.00000 | + | 6.92820i | 0.185695 | + | 0.321634i | ||||
\(465\) | 1.00000 | − | 1.73205i | 0.0463739 | − | 0.0803219i | ||||
\(466\) | 9.00000 | − | 15.5885i | 0.416917 | − | 0.722121i | ||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.00000 | −0.230633 | ||||||||
\(471\) | −3.50000 | − | 6.06218i | −0.161271 | − | 0.279330i | ||||
\(472\) | 2.00000 | − | 3.46410i | 0.0920575 | − | 0.159448i | ||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 4.00000 | + | 6.92820i | 0.183726 | + | 0.318223i | ||||
\(475\) | −3.00000 | −0.137649 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.0000 | −0.503655 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | −11.0000 | + | 19.0526i | −0.502603 | + | 0.870534i | 0.497393 | + | 0.867526i | \(0.334291\pi\) |
−0.999995 | + | 0.00300810i | \(0.999042\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | −5.50000 | − | 9.52628i | −0.250778 | − | 0.434361i | ||||
\(482\) | −7.00000 | −0.318841 | ||||||||
\(483\) | −14.0000 | − | 12.1244i | −0.637022 | − | 0.551677i | ||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | −8.00000 | − | 13.8564i | −0.363261 | − | 0.629187i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 8.00000 | − | 13.8564i | 0.362515 | − | 0.627894i | −0.625859 | − | 0.779936i | \(-0.715252\pi\) |
0.988374 | + | 0.152042i | \(0.0485850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | −6.50000 | − | 2.59808i | −0.293640 | − | 0.117369i | ||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | −5.50000 | − | 9.52628i | −0.247959 | − | 0.429478i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.50000 | + | 2.59808i | −0.0674882 | + | 0.116893i | ||||
\(495\) | −0.500000 | − | 0.866025i | −0.0224733 | − | 0.0389249i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −12.0000 | − | 10.3923i | −0.538274 | − | 0.466159i | ||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | −1.50000 | + | 2.59808i | −0.0670151 | + | 0.116073i | ||||
\(502\) | 6.50000 | + | 11.2583i | 0.290109 | + | 0.502484i | ||||
\(503\) | 36.0000 | 1.60516 | 0.802580 | − | 0.596544i | \(-0.203460\pi\) | ||||
0.802580 | + | 0.596544i | \(0.203460\pi\) | |||||||
\(504\) | −0.500000 | + | 2.59808i | −0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.50000 | − | 6.06218i | −0.155594 | − | 0.269497i | ||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 8.50000 | − | 14.7224i | 0.377127 | − | 0.653202i | ||||
\(509\) | 17.0000 | + | 29.4449i | 0.753512 | + | 1.30512i | 0.946111 | + | 0.323843i | \(0.104975\pi\) |
−0.192599 | + | 0.981278i | \(0.561692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0000 | − | 5.19615i | 0.663561 | − | 0.229864i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.50000 | − | 2.59808i | −0.0662266 | − | 0.114708i | ||||
\(514\) | −10.0000 | + | 17.3205i | −0.441081 | + | 0.763975i | ||||
\(515\) | −8.00000 | + | 13.8564i | −0.352522 | + | 0.610586i | ||||
\(516\) | 4.00000 | + | 6.92820i | 0.176090 | + | 0.304997i | ||||
\(517\) | 5.00000 | 0.219900 | ||||||||
\(518\) | 27.5000 | − | 9.52628i | 1.20828 | − | 0.418561i | ||||
\(519\) | 15.0000 | 0.658427 | ||||||||
\(520\) | −0.500000 | − | 0.866025i | −0.0219265 | − | 0.0379777i | ||||
\(521\) | 16.5000 | − | 28.5788i | 0.722878 | − | 1.25206i | −0.236963 | − | 0.971519i | \(-0.576152\pi\) |
0.959841 | − | 0.280543i | \(-0.0905145\pi\) | |||||||
\(522\) | −4.00000 | + | 6.92820i | −0.175075 | + | 0.303239i | ||||
\(523\) | −1.00000 | − | 1.73205i | −0.0437269 | − | 0.0757373i | 0.843334 | − | 0.537390i | \(-0.180590\pi\) |
−0.887061 | + | 0.461653i | \(0.847256\pi\) | |||||||
\(524\) | −5.00000 | −0.218426 | ||||||||
\(525\) | −0.500000 | + | 2.59808i | −0.0218218 | + | 0.113389i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.500000 | + | 0.866025i | −0.0217597 | + | 0.0376889i | ||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | 5.50000 | + | 9.52628i | 0.238905 | + | 0.413795i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | −6.00000 | − | 5.19615i | −0.260133 | − | 0.225282i | ||||
\(533\) | −11.0000 | −0.476463 | ||||||||
\(534\) | 5.00000 | + | 8.66025i | 0.216371 | + | 0.374766i | ||||
\(535\) | −5.00000 | + | 8.66025i | −0.216169 | + | 0.374415i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.50000 | − | 16.4545i | −0.409955 | − | 0.710063i | ||||
\(538\) | −20.0000 | −0.862261 | ||||||||
\(539\) | 6.50000 | + | 2.59808i | 0.279975 | + | 0.111907i | ||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 16.0000 | − | 27.7128i | 0.687259 | − | 1.19037i | ||||
\(543\) | −12.0000 | + | 20.7846i | −0.514969 | + | 0.891953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 2.00000 | + | 1.73205i | 0.0855921 | + | 0.0741249i | ||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 9.00000 | + | 15.5885i | 0.384461 | + | 0.665906i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | + | 0.866025i | −0.0213201 | + | 0.0369274i | ||||
\(551\) | −12.0000 | − | 20.7846i | −0.511217 | − | 0.885454i | ||||
\(552\) | 7.00000 | 0.297940 | ||||||||
\(553\) | −4.00000 | + | 20.7846i | −0.170097 | + | 0.883852i | ||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | −5.50000 | − | 9.52628i | −0.233462 | − | 0.404368i | ||||
\(556\) | −10.0000 | + | 17.3205i | −0.424094 | + | 0.734553i | ||||
\(557\) | 16.5000 | − | 28.5788i | 0.699127 | − | 1.21092i | −0.269642 | − | 0.962961i | \(-0.586905\pi\) |
0.968769 | − | 0.247964i | \(-0.0797613\pi\) | |||||||
\(558\) | −1.00000 | − | 1.73205i | −0.0423334 | − | 0.0733236i | ||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 2.50000 | − | 0.866025i | 0.105644 | − | 0.0365963i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.500000 | − | 0.866025i | −0.0210912 | − | 0.0365311i | ||||
\(563\) | 19.0000 | − | 32.9090i | 0.800755 | − | 1.38695i | −0.118366 | − | 0.992970i | \(-0.537765\pi\) |
0.919120 | − | 0.393977i | \(-0.128901\pi\) | |||||||
\(564\) | −2.50000 | + | 4.33013i | −0.105269 | + | 0.182331i | ||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 14.0000 | 0.588464 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 4.50000 | + | 7.79423i | 0.188650 | + | 0.326751i | 0.944800 | − | 0.327647i | \(-0.106256\pi\) |
−0.756151 | + | 0.654398i | \(0.772922\pi\) | |||||||
\(570\) | −1.50000 | + | 2.59808i | −0.0628281 | + | 0.108821i | ||||
\(571\) | 16.0000 | − | 27.7128i | 0.669579 | − | 1.15975i | −0.308443 | − | 0.951243i | \(-0.599808\pi\) |
0.978022 | − | 0.208502i | \(-0.0668588\pi\) | |||||||
\(572\) | 0.500000 | + | 0.866025i | 0.0209061 | + | 0.0362103i | ||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 5.50000 | − | 28.5788i | 0.229566 | − | 1.19286i | ||||
\(575\) | 7.00000 | 0.291920 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 7.00000 | − | 12.1244i | 0.291414 | − | 0.504744i | −0.682730 | − | 0.730670i | \(-0.739208\pi\) |
0.974144 | + | 0.225927i | \(0.0725410\pi\) | |||||||
\(578\) | −8.50000 | + | 14.7224i | −0.353553 | + | 0.612372i | ||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | 16.0000 | + | 13.8564i | 0.663792 | + | 0.574861i | ||||
\(582\) | −16.0000 | −0.663221 | ||||||||
\(583\) | −5.50000 | − | 9.52628i | −0.227787 | − | 0.394538i | ||||
\(584\) | −3.00000 | + | 5.19615i | −0.124141 | + | 0.215018i | ||||
\(585\) | 0.500000 | − | 0.866025i | 0.0206725 | − | 0.0358057i | ||||
\(586\) | 13.5000 | + | 23.3827i | 0.557680 | + | 0.965930i | ||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | −5.50000 | + | 4.33013i | −0.226816 | + | 0.178571i | ||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | −2.00000 | − | 3.46410i | −0.0823387 | − | 0.142615i | ||||
\(591\) | −0.500000 | + | 0.866025i | −0.0205673 | + | 0.0356235i | ||||
\(592\) | −5.50000 | + | 9.52628i | −0.226049 | + | 0.391528i | ||||
\(593\) | −8.00000 | − | 13.8564i | −0.328521 | − | 0.569014i | 0.653698 | − | 0.756756i | \(-0.273217\pi\) |
−0.982219 | + | 0.187741i | \(0.939883\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.0000 | − | 20.7846i | −0.491127 | − | 0.850657i | ||||
\(598\) | 3.50000 | − | 6.06218i | 0.143126 | − | 0.247901i | ||||
\(599\) | −1.00000 | + | 1.73205i | −0.0408589 | + | 0.0707697i | −0.885732 | − | 0.464198i | \(-0.846343\pi\) |
0.844873 | + | 0.534967i | \(0.179676\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | −4.00000 | + | 20.7846i | −0.163028 | + | 0.847117i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.00000 | − | 5.19615i | −0.122068 | − | 0.211428i | ||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5000 | + | 32.0429i | 0.750892 | + | 1.30058i | 0.947391 | + | 0.320079i | \(0.103709\pi\) |
−0.196499 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(608\) | 3.00000 | 0.121666 | ||||||||
\(609\) | −20.0000 | + | 6.92820i | −0.810441 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.50000 | + | 4.33013i | 0.101139 | + | 0.175178i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5000 | − | 35.5070i | 0.827987 | − | 1.43412i | −0.0716275 | − | 0.997431i | \(-0.522819\pi\) |
0.899615 | − | 0.436684i | \(-0.143847\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | −11.0000 | −0.443563 | ||||||||
\(616\) | −2.50000 | + | 0.866025i | −0.100728 | + | 0.0348932i | ||||
\(617\) | 28.0000 | 1.12724 | 0.563619 | − | 0.826035i | \(-0.309409\pi\) | ||||
0.563619 | + | 0.826035i | \(0.309409\pi\) | |||||||
\(618\) | 8.00000 | + | 13.8564i | 0.321807 | + | 0.557386i | ||||
\(619\) | −14.5000 | + | 25.1147i | −0.582804 | + | 1.00945i | 0.412341 | + | 0.911030i | \(0.364711\pi\) |
−0.995145 | + | 0.0984169i | \(0.968622\pi\) | |||||||
\(620\) | −1.00000 | + | 1.73205i | −0.0401610 | + | 0.0695608i | ||||
\(621\) | 3.50000 | + | 6.06218i | 0.140450 | + | 0.243267i | ||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | −5.00000 | + | 25.9808i | −0.200321 | + | 1.04090i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −6.00000 | + | 10.3923i | −0.239808 | + | 0.415360i | ||||
\(627\) | 1.50000 | − | 2.59808i | 0.0599042 | − | 0.103757i | ||||
\(628\) | 3.50000 | + | 6.06218i | 0.139665 | + | 0.241907i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.00000 | + | 1.73205i | 0.0796819 | + | 0.0690066i | ||||
\(631\) | −26.0000 | −1.03504 | −0.517522 | − | 0.855670i | \(-0.673145\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 2.50000 | − | 4.33013i | 0.0993661 | − | 0.172107i | ||||
\(634\) | −9.00000 | + | 15.5885i | −0.357436 | + | 0.619097i | ||||
\(635\) | −8.50000 | − | 14.7224i | −0.337312 | − | 0.584242i | ||||
\(636\) | 11.0000 | 0.436178 | ||||||||
\(637\) | 1.00000 | + | 6.92820i | 0.0396214 | + | 0.274505i | ||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 1.50000 | − | 2.59808i | 0.0592464 | − | 0.102618i | −0.834881 | − | 0.550431i | \(-0.814464\pi\) |
0.894127 | + | 0.447813i | \(0.147797\pi\) | |||||||
\(642\) | 5.00000 | + | 8.66025i | 0.197334 | + | 0.341793i | ||||
\(643\) | −10.0000 | −0.394362 | −0.197181 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197181 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(644\) | 14.0000 | + | 12.1244i | 0.551677 | + | 0.477767i | ||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.50000 | − | 14.7224i | 0.334169 | − | 0.578799i | −0.649155 | − | 0.760656i | \(-0.724878\pi\) |
0.983325 | + | 0.181857i | \(0.0582109\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 2.00000 | + | 3.46410i | 0.0785069 | + | 0.135978i | ||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 1.00000 | − | 5.19615i | 0.0391931 | − | 0.203653i | ||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | −3.50000 | − | 6.06218i | −0.136966 | − | 0.237231i | 0.789381 | − | 0.613904i | \(-0.210402\pi\) |
−0.926347 | + | 0.376672i | \(0.877068\pi\) | |||||||
\(654\) | −3.00000 | + | 5.19615i | −0.117309 | + | 0.203186i | ||||
\(655\) | −2.50000 | + | 4.33013i | −0.0976831 | + | 0.169192i | ||||
\(656\) | 5.50000 | + | 9.52628i | 0.214739 | + | 0.371939i | ||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −12.5000 | + | 4.33013i | −0.487301 | + | 0.168806i | ||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0.500000 | + | 0.866025i | 0.0194625 | + | 0.0337100i | ||||
\(661\) | 12.0000 | − | 20.7846i | 0.466746 | − | 0.808428i | −0.532533 | − | 0.846410i | \(-0.678760\pi\) |
0.999278 | + | 0.0379819i | \(0.0120929\pi\) | |||||||
\(662\) | −6.50000 | + | 11.2583i | −0.252630 | + | 0.437567i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | −7.50000 | + | 2.59808i | −0.290838 | + | 0.100749i | ||||
\(666\) | −11.0000 | −0.426241 | ||||||||
\(667\) | 28.0000 | + | 48.4974i | 1.08416 | + | 1.87783i | ||||
\(668\) | 1.50000 | − | 2.59808i | 0.0580367 | − | 0.100523i | ||||
\(669\) | 6.00000 | − | 10.3923i | 0.231973 | − | 0.401790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.500000 | − | 2.59808i | 0.0192879 | − | 0.100223i | ||||
\(673\) | 28.0000 | 1.07932 | 0.539660 | − | 0.841883i | \(-0.318553\pi\) | ||||
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(674\) | −6.00000 | − | 10.3923i | −0.231111 | − | 0.400297i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 6.50000 | + | 11.2583i | 0.249815 | + | 0.432693i | 0.963474 | − | 0.267800i | \(-0.0862968\pi\) |
−0.713659 | + | 0.700493i | \(0.752963\pi\) | |||||||
\(678\) | 6.00000 | 0.230429 | ||||||||
\(679\) | −32.0000 | − | 27.7128i | −1.22805 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | + | 6.92820i | 0.153280 | + | 0.265489i | ||||
\(682\) | 1.00000 | − | 1.73205i | 0.0382920 | − | 0.0663237i | ||||
\(683\) | −2.00000 | + | 3.46410i | −0.0765279 | + | 0.132550i | −0.901750 | − | 0.432259i | \(-0.857717\pi\) |
0.825222 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(684\) | 1.50000 | + | 2.59808i | 0.0573539 | + | 0.0993399i | ||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | 5.50000 | − | 9.52628i | 0.209533 | − | 0.362922i | ||||
\(690\) | 3.50000 | − | 6.06218i | 0.133243 | − | 0.230783i | ||||
\(691\) | 6.00000 | + | 10.3923i | 0.228251 | + | 0.395342i | 0.957290 | − | 0.289130i | \(-0.0933661\pi\) |
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(692\) | −15.0000 | −0.570214 | ||||||||
\(693\) | −2.00000 | − | 1.73205i | −0.0759737 | − | 0.0657952i | ||||
\(694\) | −14.0000 | −0.531433 | ||||||||
\(695\) | 10.0000 | + | 17.3205i | 0.379322 | + | 0.657004i | ||||
\(696\) | 4.00000 | − | 6.92820i | 0.151620 | − | 0.262613i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.00000 | + | 10.3923i | 0.227103 | + | 0.393355i | ||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 0.500000 | − | 2.59808i | 0.0188982 | − | 0.0981981i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −0.500000 | − | 0.866025i | −0.0188713 | − | 0.0326860i | ||||
\(703\) | 16.5000 | − | 28.5788i | 0.622309 | − | 1.07787i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 2.50000 | + | 4.33013i | 0.0941554 | + | 0.163082i | ||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −22.0000 | − | 38.1051i | −0.826227 | − | 1.43107i | −0.900978 | − | 0.433865i | \(-0.857149\pi\) |
0.0747503 | − | 0.997202i | \(-0.476184\pi\) | |||||||
\(710\) | 3.00000 | − | 5.19615i | 0.112588 | − | 0.195008i | ||||
\(711\) | 4.00000 | − | 6.92820i | 0.150012 | − | 0.259828i | ||||
\(712\) | −5.00000 | − | 8.66025i | −0.187383 | − | 0.324557i | ||||
\(713\) | −14.0000 | −0.524304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.00000 | 0.0373979 | ||||||||
\(716\) | 9.50000 | + | 16.4545i | 0.355032 | + | 0.614933i | ||||
\(717\) | −9.00000 | + | 15.5885i | −0.336111 | + | 0.582162i | ||||
\(718\) | 2.00000 | − | 3.46410i | 0.0746393 | − | 0.129279i | ||||
\(719\) | −1.00000 | − | 1.73205i | −0.0372937 | − | 0.0645946i | 0.846776 | − | 0.531949i | \(-0.178540\pi\) |
−0.884070 | + | 0.467355i | \(0.845207\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −8.00000 | + | 41.5692i | −0.297936 | + | 1.54812i | ||||
\(722\) | 10.0000 | 0.372161 | ||||||||
\(723\) | 3.50000 | + | 6.06218i | 0.130166 | + | 0.225455i | ||||
\(724\) | 12.0000 | − | 20.7846i | 0.445976 | − | 0.772454i | ||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | 5.00000 | + | 8.66025i | 0.185567 | + | 0.321412i | ||||
\(727\) | 11.0000 | 0.407967 | 0.203984 | − | 0.978974i | \(-0.434611\pi\) | ||||
0.203984 | + | 0.978974i | \(0.434611\pi\) | |||||||
\(728\) | −2.00000 | − | 1.73205i | −0.0741249 | − | 0.0641941i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.00000 | + | 5.19615i | 0.111035 | + | 0.192318i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50000 | − | 9.52628i | −0.203147 | − | 0.351861i | 0.746394 | − | 0.665505i | \(-0.231784\pi\) |
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(734\) | −25.0000 | −0.922767 | ||||||||
\(735\) | 1.00000 | + | 6.92820i | 0.0368856 | + | 0.255551i | ||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.50000 | + | 9.52628i | −0.202458 | + | 0.350667i | ||||
\(739\) | 9.50000 | − | 16.4545i | 0.349463 | − | 0.605288i | −0.636691 | − | 0.771119i | \(-0.719697\pi\) |
0.986154 | + | 0.165831i | \(0.0530307\pi\) | |||||||
\(740\) | 5.50000 | + | 9.52628i | 0.202184 | + | 0.350193i | ||||
\(741\) | 3.00000 | 0.110208 | ||||||||
\(742\) | 22.0000 | + | 19.0526i | 0.807645 | + | 0.699441i | ||||
\(743\) | 49.0000 | 1.79764 | 0.898818 | − | 0.438322i | \(-0.144427\pi\) | ||||
0.898818 | + | 0.438322i | \(0.144427\pi\) | |||||||
\(744\) | 1.00000 | + | 1.73205i | 0.0366618 | + | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.00000 | − | 5.19615i | 0.109838 | − | 0.190245i | ||||
\(747\) | −4.00000 | − | 6.92820i | −0.146352 | − | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.00000 | + | 25.9808i | −0.182696 | + | 0.949316i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −13.0000 | − | 22.5167i | −0.474377 | − | 0.821645i | 0.525193 | − | 0.850983i | \(-0.323993\pi\) |
−0.999570 | + | 0.0293387i | \(0.990660\pi\) | |||||||
\(752\) | 2.50000 | − | 4.33013i | 0.0911656 | − | 0.157903i | ||||
\(753\) | 6.50000 | − | 11.2583i | 0.236873 | − | 0.410276i | ||||
\(754\) | −4.00000 | − | 6.92820i | −0.145671 | − | 0.252310i | ||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | 2.50000 | − | 0.866025i | 0.0909241 | − | 0.0314970i | ||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −9.50000 | − | 16.4545i | −0.345056 | − | 0.597654i | ||||
\(759\) | −3.50000 | + | 6.06218i | −0.127042 | + | 0.220043i | ||||
\(760\) | 1.50000 | − | 2.59808i | 0.0544107 | − | 0.0942421i | ||||
\(761\) | −13.5000 | − | 23.3827i | −0.489375 | − | 0.847622i | 0.510551 | − | 0.859848i | \(-0.329442\pi\) |
−0.999925 | + | 0.0122260i | \(0.996108\pi\) | |||||||
\(762\) | −17.0000 | −0.615845 | ||||||||
\(763\) | −15.0000 | + | 5.19615i | −0.543036 | + | 0.188113i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.5000 | − | 30.3109i | 0.632301 | − | 1.09518i | ||||
\(767\) | −2.00000 | + | 3.46410i | −0.0722158 | + | 0.125081i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | −0.500000 | + | 2.59808i | −0.0180187 | + | 0.0936282i | ||||
\(771\) | 20.0000 | 0.720282 | ||||||||
\(772\) | −11.0000 | − | 19.0526i | −0.395899 | − | 0.685717i | ||||
\(773\) | −16.5000 | + | 28.5788i | −0.593464 | + | 1.02791i | 0.400298 | + | 0.916385i | \(0.368907\pi\) |
−0.993762 | + | 0.111524i | \(0.964427\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | 1.00000 | + | 1.73205i | 0.0359211 | + | 0.0622171i | ||||
\(776\) | 16.0000 | 0.574367 | ||||||||
\(777\) | −22.0000 | − | 19.0526i | −0.789246 | − | 0.683507i | ||||
\(778\) | −10.0000 | −0.358517 | ||||||||
\(779\) | −16.5000 | − | 28.5788i | −0.591174 | − | 1.02394i | ||||
\(780\) | −0.500000 | + | 0.866025i | −0.0179029 | + | 0.0310087i | ||||
\(781\) | −3.00000 | + | 5.19615i | −0.107348 | + | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 7.00000 | 0.249841 | ||||||||
\(786\) | 2.50000 | + | 4.33013i | 0.0891720 | + | 0.154451i | ||||
\(787\) | −11.0000 | + | 19.0526i | −0.392108 | + | 0.679150i | −0.992727 | − | 0.120384i | \(-0.961587\pi\) |
0.600620 | + | 0.799535i | \(0.294921\pi\) | |||||||
\(788\) | 0.500000 | − | 0.866025i | 0.0178118 | − | 0.0308509i | ||||
\(789\) | 12.0000 | + | 20.7846i | 0.427211 | + | 0.739952i | ||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 12.0000 | + | 10.3923i | 0.426671 | + | 0.369508i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 5.50000 | − | 9.52628i | 0.195065 | − | 0.337862i | ||||
\(796\) | 12.0000 | + | 20.7846i | 0.425329 | + | 0.736691i | ||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | −1.50000 | + | 7.79423i | −0.0530994 | + | 0.275913i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 5.00000 | − | 8.66025i | 0.176666 | − | 0.305995i | ||||
\(802\) | −2.50000 | + | 4.33013i | −0.0882781 | + | 0.152902i | ||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5000 | − | 6.06218i | 0.616794 | − | 0.213664i | ||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | 10.0000 | + | 17.3205i | 0.352017 | + | 0.609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5000 | − | 33.7750i | 0.685583 | − | 1.18747i | −0.287670 | − | 0.957730i | \(-0.592880\pi\) |
0.973253 | − | 0.229736i | \(-0.0737862\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | 20.0000 | − | 6.92820i | 0.701862 | − | 0.243132i | ||||
\(813\) | −32.0000 | −1.12229 | ||||||||
\(814\) | −5.50000 | − | 9.52628i | −0.192775 | − | 0.333896i | ||||
\(815\) | 8.00000 | − | 13.8564i | 0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 20.7846i | 0.419827 | + | 0.727161i | ||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 0.500000 | − | 2.59808i | 0.0174714 | − | 0.0907841i | ||||
\(820\) | 11.0000 | 0.384137 | ||||||||
\(821\) | −21.0000 | − | 36.3731i | −0.732905 | − | 1.26943i | −0.955636 | − | 0.294549i | \(-0.904831\pi\) |
0.222731 | − | 0.974880i | \(-0.428503\pi\) | |||||||
\(822\) | 9.00000 | − | 15.5885i | 0.313911 | − | 0.543710i | ||||
\(823\) | 12.0000 | − | 20.7846i | 0.418294 | − | 0.724506i | −0.577474 | − | 0.816409i | \(-0.695962\pi\) |
0.995768 | + | 0.0919029i | \(0.0292950\pi\) | |||||||
\(824\) | −8.00000 | − | 13.8564i | −0.278693 | − | 0.482711i | ||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | −8.00000 | − | 6.92820i | −0.278356 | − | 0.241063i | ||||
\(827\) | −10.0000 | −0.347734 | −0.173867 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173867 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(828\) | −3.50000 | − | 6.06218i | −0.121633 | − | 0.210675i | ||||
\(829\) | 4.00000 | − | 6.92820i | 0.138926 | − | 0.240626i | −0.788165 | − | 0.615465i | \(-0.788968\pi\) |
0.927090 | + | 0.374838i | \(0.122302\pi\) | |||||||
\(830\) | −4.00000 | + | 6.92820i | −0.138842 | + | 0.240481i | ||||
\(831\) | −11.0000 | − | 19.0526i | −0.381586 | − | 0.660926i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.0000 | 0.692543 | ||||||||
\(835\) | −1.50000 | − | 2.59808i | −0.0519096 | − | 0.0899101i | ||||
\(836\) | −1.50000 | + | 2.59808i | −0.0518786 | + | 0.0898563i | ||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | −2.50000 | − | 4.33013i | −0.0863611 | − | 0.149582i | ||||
\(839\) | −40.0000 | −1.38095 | −0.690477 | − | 0.723355i | \(-0.742599\pi\) | ||||
−0.690477 | + | 0.723355i | \(0.742599\pi\) | |||||||
\(840\) | −2.00000 | − | 1.73205i | −0.0690066 | − | 0.0597614i | ||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 11.0000 | + | 19.0526i | 0.379085 | + | 0.656595i | ||||
\(843\) | −0.500000 | + | 0.866025i | −0.0172209 | + | 0.0298275i | ||||
\(844\) | −2.50000 | + | 4.33013i | −0.0860535 | + | 0.149049i | ||||
\(845\) | −6.00000 | − | 10.3923i | −0.206406 | − | 0.357506i | ||||
\(846\) | 5.00000 | 0.171904 | ||||||||
\(847\) | −5.00000 | + | 25.9808i | −0.171802 | + | 0.892710i | ||||
\(848\) | −11.0000 | −0.377742 | ||||||||
\(849\) | −7.00000 | − | 12.1244i | −0.240239 | − | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.5000 | + | 66.6840i | −1.31976 | + | 2.28590i | ||||
\(852\) | −3.00000 | − | 5.19615i | −0.102778 | − | 0.178017i | ||||
\(853\) | −41.0000 | −1.40381 | −0.701907 | − | 0.712269i | \(-0.747668\pi\) | ||||
−0.701907 | + | 0.712269i | \(0.747668\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | 0.102598 | ||||||||
\(856\) | −5.00000 | − | 8.66025i | −0.170896 | − | 0.296001i | ||||
\(857\) | 7.00000 | − | 12.1244i | 0.239115 | − | 0.414160i | −0.721345 | − | 0.692576i | \(-0.756476\pi\) |
0.960461 | + | 0.278416i | \(0.0898092\pi\) | |||||||
\(858\) | 0.500000 | − | 0.866025i | 0.0170697 | − | 0.0295656i | ||||
\(859\) | −6.00000 | − | 10.3923i | −0.204717 | − | 0.354581i | 0.745325 | − | 0.666701i | \(-0.232294\pi\) |
−0.950043 | + | 0.312120i | \(0.898961\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | −27.5000 | + | 9.52628i | −0.937197 | + | 0.324655i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5000 | + | 45.8993i | 0.902070 | + | 1.56243i | 0.824802 | + | 0.565422i | \(0.191287\pi\) |
0.0772684 | + | 0.997010i | \(0.475380\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −7.50000 | + | 12.9904i | −0.255008 | + | 0.441686i | ||||
\(866\) | −16.0000 | − | 27.7128i | −0.543702 | − | 0.941720i | ||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | −1.00000 | + | 5.19615i | −0.0339422 | + | 0.176369i | ||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | −4.00000 | − | 6.92820i | −0.135613 | − | 0.234888i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.00000 | − | 5.19615i | 0.101593 | − | 0.175964i | ||||
\(873\) | 8.00000 | + | 13.8564i | 0.270759 | + | 0.468968i | ||||
\(874\) | 21.0000 | 0.710336 | ||||||||
\(875\) | −2.00000 | − | 1.73205i | −0.0676123 | − | 0.0585540i | ||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −8.50000 | − | 14.7224i | −0.287025 | − | 0.497141i | 0.686074 | − | 0.727532i | \(-0.259333\pi\) |
−0.973098 | + | 0.230391i | \(0.925999\pi\) | |||||||
\(878\) | 16.0000 | − | 27.7128i | 0.539974 | − | 0.935262i | ||||
\(879\) | 13.5000 | − | 23.3827i | 0.455344 | − | 0.788678i | ||||
\(880\) | −0.500000 | − | 0.866025i | −0.0168550 | − | 0.0291937i | ||||
\(881\) | −53.0000 | −1.78562 | −0.892808 | − | 0.450438i | \(-0.851268\pi\) | ||||
−0.892808 | + | 0.450438i | \(0.851268\pi\) | |||||||
\(882\) | 6.50000 | + | 2.59808i | 0.218866 | + | 0.0874818i | ||||
\(883\) | −42.0000 | −1.41341 | −0.706706 | − | 0.707507i | \(-0.749820\pi\) | ||||
−0.706706 | + | 0.707507i | \(0.749820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.00000 | + | 3.46410i | −0.0672293 | + | 0.116445i | ||||
\(886\) | 8.00000 | − | 13.8564i | 0.268765 | − | 0.465515i | ||||
\(887\) | −22.0000 | − | 38.1051i | −0.738688 | − | 1.27944i | −0.953086 | − | 0.302698i | \(-0.902113\pi\) |
0.214399 | − | 0.976746i | \(-0.431221\pi\) | |||||||
\(888\) | 11.0000 | 0.369136 | ||||||||
\(889\) | −34.0000 | − | 29.4449i | −1.14032 | − | 0.987549i | ||||
\(890\) | −10.0000 | −0.335201 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | −6.00000 | + | 10.3923i | −0.200895 | + | 0.347960i | ||||
\(893\) | −7.50000 | + | 12.9904i | −0.250978 | + | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.0000 | 0.635100 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | −7.00000 | −0.233723 | ||||||||
\(898\) | 5.50000 | + | 9.52628i | 0.183537 | + | 0.317896i | ||||
\(899\) | −8.00000 | + | 13.8564i | −0.266815 | + | 0.462137i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −11.0000 | −0.366260 | ||||||||
\(903\) | 20.0000 | − | 6.92820i | 0.665558 | − | 0.230556i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −12.0000 | − | 20.7846i | −0.398893 | − | 0.690904i | ||||
\(906\) | −3.00000 | + | 5.19615i | −0.0996683 | + | 0.172631i | ||||
\(907\) | 5.00000 | − | 8.66025i | 0.166022 | − | 0.287559i | −0.770996 | − | 0.636841i | \(-0.780241\pi\) |
0.937018 | + | 0.349281i | \(0.113574\pi\) | |||||||
\(908\) | −4.00000 | − | 6.92820i | −0.132745 | − | 0.229920i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.50000 | + | 0.866025i | −0.0828742 | + | 0.0287085i | ||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | −1.50000 | − | 2.59808i | −0.0496700 | − | 0.0860309i | ||||
\(913\) | 4.00000 | − | 6.92820i | 0.132381 | − | 0.229290i | ||||
\(914\) | −9.00000 | + | 15.5885i | −0.297694 | + | 0.515620i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | −2.50000 | + | 12.9904i | −0.0825573 | + | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0000 | + | 31.1769i | 0.593765 | + | 1.02843i | 0.993720 | + | 0.111897i | \(0.0356925\pi\) |
−0.399955 | + | 0.916535i | \(0.630974\pi\) | |||||||
\(920\) | −3.50000 | + | 6.06218i | −0.115392 | + | 0.199864i | ||||
\(921\) | 10.0000 | − | 17.3205i | 0.329511 | − | 0.570730i | ||||
\(922\) | −6.00000 | − | 10.3923i | −0.197599 | − | 0.342252i | ||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 2.00000 | + | 1.73205i | 0.0657952 | + | 0.0569803i | ||||
\(925\) | 11.0000 | 0.361678 | ||||||||
\(926\) | −6.50000 | − | 11.2583i | −0.213603 | − | 0.369972i | ||||
\(927\) | 8.00000 | − | 13.8564i | 0.262754 | − | 0.455104i | ||||
\(928\) | −4.00000 | + | 6.92820i | −0.131306 | + | 0.227429i | ||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 2.00000 | 0.0655826 | ||||||||
\(931\) | −16.5000 | + | 12.9904i | −0.540766 | + | 0.425743i | ||||
\(932\) | 18.0000 | 0.589610 | ||||||||
\(933\) | 6.00000 | + | 10.3923i | 0.196431 | + | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 0.866025i | 0.0163430 | + | 0.0283069i | ||||
\(937\) | 12.0000 | 0.392023 | 0.196011 | − | 0.980602i | \(-0.437201\pi\) | ||||
0.196011 | + | 0.980602i | \(0.437201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.0000 | 0.391605 | ||||||||
\(940\) | −2.50000 | − | 4.33013i | −0.0815410 | − | 0.141233i | ||||
\(941\) | −27.0000 | + | 46.7654i | −0.880175 | + | 1.52451i | −0.0290288 | + | 0.999579i | \(0.509241\pi\) |
−0.851146 | + | 0.524929i | \(0.824092\pi\) | |||||||
\(942\) | 3.50000 | − | 6.06218i | 0.114036 | − | 0.197516i | ||||
\(943\) | 38.5000 | + | 66.6840i | 1.25373 | + | 2.17153i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0.500000 | − | 2.59808i | 0.0162650 | − | 0.0845154i | ||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −11.0000 | − | 19.0526i | −0.357452 | − | 0.619125i | 0.630082 | − | 0.776528i | \(-0.283021\pi\) |
−0.987534 | + | 0.157403i | \(0.949688\pi\) | |||||||
\(948\) | −4.00000 | + | 6.92820i | −0.129914 | + | 0.225018i | ||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | −1.50000 | − | 2.59808i | −0.0486664 | − | 0.0842927i | ||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.0000 | −0.647864 | −0.323932 | − | 0.946080i | \(-0.605005\pi\) | ||||
−0.323932 | + | 0.946080i | \(0.605005\pi\) | |||||||
\(954\) | −5.50000 | − | 9.52628i | −0.178069 | − | 0.308425i | ||||
\(955\) | −3.00000 | + | 5.19615i | −0.0970777 | + | 0.168144i | ||||
\(956\) | 9.00000 | − | 15.5885i | 0.291081 | − | 0.504167i | ||||
\(957\) | 4.00000 | + | 6.92820i | 0.129302 | + | 0.223957i | ||||
\(958\) | −22.0000 | −0.710788 | ||||||||
\(959\) | 45.0000 | − | 15.5885i | 1.45313 | − | 0.503378i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 5.50000 | − | 9.52628i | 0.177327 | − | 0.307140i | ||||
\(963\) | 5.00000 | − | 8.66025i | 0.161123 | − | 0.279073i | ||||
\(964\) | −3.50000 | − | 6.06218i | −0.112727 | − | 0.195250i | ||||
\(965\) | −22.0000 | −0.708205 | ||||||||
\(966\) | 3.50000 | − | 18.1865i | 0.112611 | − | 0.585142i | ||||
\(967\) | −20.0000 | −0.643157 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(968\) | −5.00000 | − | 8.66025i | −0.160706 | − | 0.278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.00000 | − | 13.8564i | 0.256865 | − | 0.444902i | ||||
\(971\) | 22.5000 | + | 38.9711i | 0.722059 | + | 1.25064i | 0.960173 | + | 0.279406i | \(0.0901376\pi\) |
−0.238114 | + | 0.971237i | \(0.576529\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 40.0000 | + | 34.6410i | 1.28234 | + | 1.11054i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0000 | + | 46.7654i | −0.863807 | + | 1.49616i | 0.00442082 | + | 0.999990i | \(0.498593\pi\) |
−0.868227 | + | 0.496167i | \(0.834741\pi\) | |||||||
\(978\) | −8.00000 | − | 13.8564i | −0.255812 | − | 0.443079i | ||||
\(979\) | 10.0000 | 0.319601 | ||||||||
\(980\) | −1.00000 | − | 6.92820i | −0.0319438 | − | 0.221313i | ||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 10.0000 | + | 17.3205i | 0.319113 | + | 0.552720i | ||||
\(983\) | −24.5000 | + | 42.4352i | −0.781429 | + | 1.35347i | 0.149681 | + | 0.988734i | \(0.452175\pi\) |
−0.931110 | + | 0.364740i | \(0.881158\pi\) | |||||||
\(984\) | 5.50000 | − | 9.52628i | 0.175334 | − | 0.303687i | ||||
\(985\) | −0.500000 | − | 0.866025i | −0.0159313 | − | 0.0275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0000 | + | 8.66025i | 0.318304 | + | 0.275659i | ||||
\(988\) | −3.00000 | −0.0954427 | ||||||||
\(989\) | −28.0000 | − | 48.4974i | −0.890348 | − | 1.54213i | ||||
\(990\) | 0.500000 | − | 0.866025i | 0.0158910 | − | 0.0275241i | ||||
\(991\) | −11.0000 | + | 19.0526i | −0.349427 | + | 0.605224i | −0.986148 | − | 0.165870i | \(-0.946957\pi\) |
0.636721 | + | 0.771094i | \(0.280290\pi\) | |||||||
\(992\) | −1.00000 | − | 1.73205i | −0.0317500 | − | 0.0549927i | ||||
\(993\) | 13.0000 | 0.412543 | ||||||||
\(994\) | 3.00000 | − | 15.5885i | 0.0951542 | − | 0.494436i | ||||
\(995\) | 24.0000 | 0.760851 | ||||||||
\(996\) | 4.00000 | + | 6.92820i | 0.126745 | + | 0.219529i | ||||
\(997\) | −7.00000 | + | 12.1244i | −0.221692 | + | 0.383982i | −0.955322 | − | 0.295567i | \(-0.904491\pi\) |
0.733630 | + | 0.679549i | \(0.237825\pi\) | |||||||
\(998\) | −16.0000 | + | 27.7128i | −0.506471 | + | 0.877234i | ||||
\(999\) | 5.50000 | + | 9.52628i | 0.174012 | + | 0.301398i |
(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 | 210.2.i.d.151.1 | yes | 2 | |
3.2 | odd | 2 | 630.2.k.c.361.1 | 2 | |||
4.3 | odd | 2 | 1680.2.bg.g.1201.1 | 2 | |||
5.2 | odd | 4 | 1050.2.o.i.949.1 | 4 | |||
5.3 | odd | 4 | 1050.2.o.i.949.2 | 4 | |||
5.4 | even | 2 | 1050.2.i.b.151.1 | 2 | |||
7.2 | even | 3 | inner | 210.2.i.d.121.1 | ✓ | 2 | |
7.3 | odd | 6 | 1470.2.a.h.1.1 | 1 | |||
7.4 | even | 3 | 1470.2.a.a.1.1 | 1 | |||
7.5 | odd | 6 | 1470.2.i.m.961.1 | 2 | |||
7.6 | odd | 2 | 1470.2.i.m.361.1 | 2 | |||
21.2 | odd | 6 | 630.2.k.c.541.1 | 2 | |||
21.11 | odd | 6 | 4410.2.a.bj.1.1 | 1 | |||
21.17 | even | 6 | 4410.2.a.ba.1.1 | 1 | |||
28.23 | odd | 6 | 1680.2.bg.g.961.1 | 2 | |||
35.2 | odd | 12 | 1050.2.o.i.499.2 | 4 | |||
35.4 | even | 6 | 7350.2.a.cp.1.1 | 1 | |||
35.9 | even | 6 | 1050.2.i.b.751.1 | 2 | |||
35.23 | odd | 12 | 1050.2.o.i.499.1 | 4 | |||
35.24 | odd | 6 | 7350.2.a.bu.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.d.121.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
210.2.i.d.151.1 | yes | 2 | 1.1 | even | 1 | trivial | |
630.2.k.c.361.1 | 2 | 3.2 | odd | 2 | |||
630.2.k.c.541.1 | 2 | 21.2 | odd | 6 | |||
1050.2.i.b.151.1 | 2 | 5.4 | even | 2 | |||
1050.2.i.b.751.1 | 2 | 35.9 | even | 6 | |||
1050.2.o.i.499.1 | 4 | 35.23 | odd | 12 | |||
1050.2.o.i.499.2 | 4 | 35.2 | odd | 12 | |||
1050.2.o.i.949.1 | 4 | 5.2 | odd | 4 | |||
1050.2.o.i.949.2 | 4 | 5.3 | odd | 4 | |||
1470.2.a.a.1.1 | 1 | 7.4 | even | 3 | |||
1470.2.a.h.1.1 | 1 | 7.3 | odd | 6 | |||
1470.2.i.m.361.1 | 2 | 7.6 | odd | 2 | |||
1470.2.i.m.961.1 | 2 | 7.5 | odd | 6 | |||
1680.2.bg.g.961.1 | 2 | 28.23 | odd | 6 | |||
1680.2.bg.g.1201.1 | 2 | 4.3 | odd | 2 | |||
4410.2.a.ba.1.1 | 1 | 21.17 | even | 6 | |||
4410.2.a.bj.1.1 | 1 | 21.11 | odd | 6 | |||
7350.2.a.bu.1.1 | 1 | 35.24 | odd | 6 | |||
7350.2.a.cp.1.1 | 1 | 35.4 | even | 6 |