Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.i.949.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0.500000 | + | 2.59808i | 0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −1.50000 | + | 2.59808i | −0.344124 | + | 0.596040i | −0.985194 | − | 0.171442i | \(-0.945157\pi\) |
0.641071 | + | 0.767482i | \(0.278491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | − | 1.00000i | − | 0.213201i | ||||||
\(23\) | −6.06218 | − | 3.50000i | −1.26405 | − | 0.729800i | −0.290196 | − | 0.956967i | \(-0.593720\pi\) |
−0.973856 | + | 0.227167i | \(0.927054\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.866025 | − | 2.50000i | 0.163663 | − | 0.472456i | ||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −0.866025 | − | 0.500000i | −0.150756 | − | 0.0870388i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.52628 | + | 5.50000i | 1.56611 | + | 0.904194i | 0.996616 | + | 0.0821995i | \(0.0261945\pi\) |
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | 2.59808 | − | 1.50000i | 0.421464 | − | 0.243332i | ||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0000 | −1.71791 | −0.858956 | − | 0.512050i | \(-0.828886\pi\) | ||||
−0.858956 | + | 0.512050i | \(0.828886\pi\) | |||||||
\(42\) | −1.73205 | − | 2.00000i | −0.267261 | − | 0.308607i | ||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.50000 | + | 6.06218i | 0.516047 | + | 0.893819i | ||||
\(47\) | −4.33013 | − | 2.50000i | −0.631614 | − | 0.364662i | 0.149763 | − | 0.988722i | \(-0.452149\pi\) |
−0.781377 | + | 0.624059i | \(0.785482\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.866025 | + | 0.500000i | −0.120096 | + | 0.0693375i | ||||
\(53\) | −9.52628 | + | 5.50000i | −1.30854 | + | 0.755483i | −0.981852 | − | 0.189651i | \(-0.939264\pi\) |
−0.326683 | + | 0.945134i | \(0.605931\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | − | 3.00000i | − | 0.397360i | ||||||
\(58\) | −6.92820 | − | 4.00000i | −0.909718 | − | 0.525226i | ||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | −2.59808 | + | 0.500000i | −0.327327 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.00000 | 0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −5.19615 | + | 3.00000i | −0.608164 | + | 0.351123i | −0.772246 | − | 0.635323i | \(-0.780867\pi\) |
0.164083 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(74\) | −5.50000 | − | 9.52628i | −0.639362 | − | 1.10741i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | 0.866025 | − | 2.50000i | 0.0986928 | − | 0.284901i | ||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 9.52628 | + | 5.50000i | 1.05200 | + | 0.607373i | ||||
\(83\) | 8.00000i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(84\) | 0.500000 | + | 2.59808i | 0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | −6.92820 | + | 4.00000i | −0.742781 | + | 0.428845i | ||||
\(88\) | 0.866025 | − | 0.500000i | 0.0923186 | − | 0.0533002i | ||||
\(89\) | −5.00000 | + | 8.66025i | −0.529999 | + | 0.917985i | 0.469389 | + | 0.882992i | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 1.73205i | 0.209657 | − | 0.181568i | ||||
\(92\) | − | 7.00000i | − | 0.729800i | ||||||
\(93\) | −1.73205 | − | 1.00000i | −0.179605 | − | 0.103695i | ||||
\(94\) | 2.50000 | + | 4.33013i | 0.257855 | + | 0.446619i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 16.0000i | 1.62455i | 0.583272 | + | 0.812277i | \(0.301772\pi\) | ||||
−0.583272 | + | 0.812277i | \(0.698228\pi\) | |||||||
\(98\) | 4.33013 | − | 5.50000i | 0.437409 | − | 0.555584i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8564 | + | 8.00000i | 1.36531 | + | 0.788263i | 0.990325 | − | 0.138767i | \(-0.0443138\pi\) |
0.374987 | + | 0.927030i | \(0.377647\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.0000 | 1.06841 | ||||||||
\(107\) | −8.66025 | − | 5.00000i | −0.837218 | − | 0.483368i | 0.0190994 | − | 0.999818i | \(-0.493920\pi\) |
−0.856318 | + | 0.516449i | \(0.827253\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 3.00000 | + | 5.19615i | 0.287348 | + | 0.497701i | 0.973176 | − | 0.230063i | \(-0.0738931\pi\) |
−0.685828 | + | 0.727764i | \(0.740560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0000 | −1.04407 | ||||||||
\(112\) | 2.59808 | − | 0.500000i | 0.245495 | − | 0.0472456i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −1.50000 | + | 2.59808i | −0.140488 | + | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.00000 | + | 6.92820i | 0.371391 | + | 0.643268i | ||||
\(117\) | 0.866025 | + | 0.500000i | 0.0800641 | + | 0.0462250i | ||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.52628 | − | 5.50000i | 0.858956 | − | 0.495918i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | + | 0.866025i | 0.222718 | + | 0.0771517i | ||||
\(127\) | 17.0000i | 1.50851i | 0.656584 | + | 0.754253i | \(0.272001\pi\) | ||||
−0.656584 | + | 0.754253i | \(0.727999\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.50000 | − | 4.33013i | 0.218426 | − | 0.378325i | −0.735901 | − | 0.677089i | \(-0.763241\pi\) |
0.954327 | + | 0.298764i | \(0.0965744\pi\) | |||||||
\(132\) | − | 1.00000i | − | 0.0870388i | ||||||
\(133\) | 7.79423 | − | 1.50000i | 0.675845 | − | 0.130066i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5885 | − | 9.00000i | 1.33181 | − | 0.768922i | 0.346235 | − | 0.938148i | \(-0.387460\pi\) |
0.985577 | + | 0.169226i | \(0.0541268\pi\) | |||||||
\(138\) | −6.06218 | − | 3.50000i | −0.516047 | − | 0.297940i | ||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | 5.19615 | + | 3.00000i | 0.436051 | + | 0.251754i | ||||
\(143\) | −0.866025 | + | 0.500000i | −0.0724207 | + | 0.0418121i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | −2.59808 | − | 6.50000i | −0.214286 | − | 0.536111i | ||||
\(148\) | 11.0000i | 0.904194i | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | 2.59808 | + | 1.50000i | 0.210732 | + | 0.121666i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 1.73205i | −0.161165 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.500000 | − | 0.866025i | 0.0400320 | − | 0.0693375i | ||||
\(157\) | 6.06218 | − | 3.50000i | 0.483814 | − | 0.279330i | −0.238190 | − | 0.971219i | \(-0.576554\pi\) |
0.722005 | + | 0.691888i | \(0.243221\pi\) | |||||||
\(158\) | 6.92820 | − | 4.00000i | 0.551178 | − | 0.318223i | ||||
\(159\) | 5.50000 | − | 9.52628i | 0.436178 | − | 0.755483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.50000 | + | 18.1865i | 0.275839 | + | 1.43330i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −13.8564 | − | 8.00000i | −1.08532 | − | 0.626608i | −0.152992 | − | 0.988227i | \(-0.548891\pi\) |
−0.932326 | + | 0.361619i | \(0.882224\pi\) | |||||||
\(164\) | −5.50000 | − | 9.52628i | −0.429478 | − | 0.743877i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | − | 6.92820i | 0.310460 | − | 0.537733i | ||||
\(167\) | 3.00000i | 0.232147i | 0.993241 | + | 0.116073i | \(0.0370308\pi\) | ||||
−0.993241 | + | 0.116073i | \(0.962969\pi\) | |||||||
\(168\) | 0.866025 | − | 2.50000i | 0.0668153 | − | 0.192879i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | + | 2.59808i | 0.114708 | + | 0.198680i | ||||
\(172\) | −6.92820 | + | 4.00000i | −0.528271 | + | 0.304997i | ||||
\(173\) | 12.9904 | + | 7.50000i | 0.987640 | + | 0.570214i | 0.904568 | − | 0.426329i | \(-0.140193\pi\) |
0.0830722 | + | 0.996544i | \(0.473527\pi\) | |||||||
\(174\) | 8.00000 | 0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −3.46410 | − | 2.00000i | −0.260378 | − | 0.150329i | ||||
\(178\) | 8.66025 | − | 5.00000i | 0.649113 | − | 0.374766i | ||||
\(179\) | −9.50000 | − | 16.4545i | −0.710063 | − | 1.22987i | −0.964833 | − | 0.262864i | \(-0.915333\pi\) |
0.254770 | − | 0.967002i | \(-0.418000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.0000 | −1.78391 | −0.891953 | − | 0.452128i | \(-0.850665\pi\) | ||||
−0.891953 | + | 0.452128i | \(0.850665\pi\) | |||||||
\(182\) | −2.59808 | + | 0.500000i | −0.192582 | + | 0.0370625i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.50000 | + | 6.06218i | −0.258023 | + | 0.446910i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | + | 1.73205i | 0.0733236 | + | 0.127000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 5.00000i | − | 0.364662i | ||||||
\(189\) | 2.00000 | − | 1.73205i | 0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 19.0526 | − | 11.0000i | 1.37143 | − | 0.791797i | 0.380325 | − | 0.924853i | \(-0.375812\pi\) |
0.991109 | + | 0.133056i | \(0.0424789\pi\) | |||||||
\(194\) | 8.00000 | − | 13.8564i | 0.574367 | − | 0.994832i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 1.00000i | 0.0712470i | 0.999365 | + | 0.0356235i | \(0.0113417\pi\) | ||||
−0.999365 | + | 0.0356235i | \(0.988658\pi\) | |||||||
\(198\) | −0.866025 | − | 0.500000i | −0.0615457 | − | 0.0355335i | ||||
\(199\) | −12.0000 | − | 20.7846i | −0.850657 | − | 1.47338i | −0.880616 | − | 0.473831i | \(-0.842871\pi\) |
0.0299585 | − | 0.999551i | \(-0.490462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8564 | − | 16.0000i | −0.972529 | − | 1.12298i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | − | 13.8564i | −0.557386 | − | 0.965422i | ||||
\(207\) | −6.06218 | + | 3.50000i | −0.421350 | + | 0.243267i | ||||
\(208\) | −0.866025 | − | 0.500000i | −0.0600481 | − | 0.0346688i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00000 | 0.344214 | 0.172107 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172107 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(212\) | −9.52628 | − | 5.50000i | −0.654268 | − | 0.377742i | ||||
\(213\) | 5.19615 | − | 3.00000i | 0.356034 | − | 0.205557i | ||||
\(214\) | 5.00000 | + | 8.66025i | 0.341793 | + | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.73205 | − | 5.00000i | 0.117579 | − | 0.339422i | ||||
\(218\) | − | 6.00000i | − | 0.406371i | ||||||
\(219\) | 3.00000 | − | 5.19615i | 0.202721 | − | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.52628 | + | 5.50000i | 0.639362 | + | 0.369136i | ||||
\(223\) | 12.0000i | 0.803579i | 0.915732 | + | 0.401790i | \(0.131612\pi\) | ||||
−0.915732 | + | 0.401790i | \(0.868388\pi\) | |||||||
\(224\) | −2.50000 | − | 0.866025i | −0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | −6.92820 | + | 4.00000i | −0.459841 | + | 0.265489i | −0.711977 | − | 0.702202i | \(-0.752200\pi\) |
0.252136 | + | 0.967692i | \(0.418867\pi\) | |||||||
\(228\) | 2.59808 | − | 1.50000i | 0.172062 | − | 0.0993399i | ||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.500000 | + | 2.59808i | 0.0328976 | + | 0.170941i | ||||
\(232\) | − | 8.00000i | − | 0.525226i | ||||||
\(233\) | −15.5885 | − | 9.00000i | −1.02123 | − | 0.589610i | −0.106773 | − | 0.994283i | \(-0.534052\pi\) |
−0.914461 | + | 0.404674i | \(0.867385\pi\) | |||||||
\(234\) | −0.500000 | − | 0.866025i | −0.0326860 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | − | 8.00000i | − | 0.519656i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | −8.66025 | + | 5.00000i | −0.556702 | + | 0.321412i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.0000 | −0.701334 | ||||||||
\(247\) | −2.59808 | − | 1.50000i | −0.165312 | − | 0.0954427i | ||||
\(248\) | 1.73205 | − | 1.00000i | 0.109985 | − | 0.0635001i | ||||
\(249\) | −4.00000 | − | 6.92820i | −0.253490 | − | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.0000 | 0.820553 | 0.410276 | − | 0.911961i | \(-0.365432\pi\) | ||||
0.410276 | + | 0.911961i | \(0.365432\pi\) | |||||||
\(252\) | −1.73205 | − | 2.00000i | −0.109109 | − | 0.125988i | ||||
\(253\) | − | 7.00000i | − | 0.440086i | ||||||
\(254\) | 8.50000 | − | 14.7224i | 0.533337 | − | 0.923768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −17.3205 | − | 10.0000i | −1.08042 | − | 0.623783i | −0.149413 | − | 0.988775i | \(-0.547738\pi\) |
−0.931011 | + | 0.364992i | \(0.881072\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | −5.50000 | − | 28.5788i | −0.341753 | − | 1.77580i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | −4.33013 | + | 2.50000i | −0.267516 | + | 0.154451i | ||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.50000 | − | 2.59808i | −0.459855 | − | 0.159298i | ||||
\(267\) | − | 10.0000i | − | 0.611990i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | + | 17.3205i | 0.609711 | + | 1.05605i | 0.991288 | + | 0.131713i | \(0.0420477\pi\) |
−0.381577 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | + | 27.7128i | −0.971931 | + | 1.68343i | −0.282218 | + | 0.959350i | \(0.591070\pi\) |
−0.689713 | + | 0.724083i | \(0.742263\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.866025 | + | 2.50000i | −0.0524142 | + | 0.151307i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.50000 | + | 6.06218i | 0.210675 | + | 0.364900i | ||||
\(277\) | 19.0526 | − | 11.0000i | 1.14476 | − | 0.660926i | 0.197153 | − | 0.980373i | \(-0.436830\pi\) |
0.947604 | + | 0.319447i | \(0.103497\pi\) | |||||||
\(278\) | 17.3205 | + | 10.0000i | 1.03882 | + | 0.599760i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | −4.33013 | − | 2.50000i | −0.257855 | − | 0.148873i | ||||
\(283\) | −12.1244 | + | 7.00000i | −0.720718 | + | 0.416107i | −0.815017 | − | 0.579437i | \(-0.803272\pi\) |
0.0942988 | + | 0.995544i | \(0.469939\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.00000 | 0.0591312 | ||||||||
\(287\) | 19.0526 | + | 22.0000i | 1.12464 | + | 1.29862i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −8.50000 | + | 14.7224i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.00000 | − | 13.8564i | −0.468968 | − | 0.812277i | ||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | 27.0000i | 1.57736i | 0.614806 | + | 0.788678i | \(0.289234\pi\) | ||||
−0.614806 | + | 0.788678i | \(0.710766\pi\) | |||||||
\(294\) | −1.00000 | + | 6.92820i | −0.0583212 | + | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.50000 | − | 9.52628i | 0.319681 | − | 0.553704i | ||||
\(297\) | −0.866025 | + | 0.500000i | −0.0502519 | + | 0.0290129i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.50000 | − | 6.06218i | 0.202410 | − | 0.350585i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | − | 13.8564i | 0.922225 | − | 0.798670i | ||||
\(302\) | 6.00000i | 0.345261i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.50000 | − | 2.59808i | −0.0860309 | − | 0.149010i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 2.59808 | − | 0.500000i | 0.148039 | − | 0.0284901i | ||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | −0.866025 | + | 0.500000i | −0.0490290 | + | 0.0283069i | ||||
\(313\) | 10.3923 | + | 6.00000i | 0.587408 | + | 0.339140i | 0.764072 | − | 0.645131i | \(-0.223197\pi\) |
−0.176664 | + | 0.984271i | \(0.556531\pi\) | |||||||
\(314\) | −7.00000 | −0.395033 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | −9.52628 | + | 5.50000i | −0.534207 | + | 0.308425i | ||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0000 | 0.558146 | ||||||||
\(322\) | 6.06218 | − | 17.5000i | 0.337832 | − | 0.975237i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.00000 | + | 13.8564i | 0.443079 | + | 0.767435i | ||||
\(327\) | −5.19615 | − | 3.00000i | −0.287348 | − | 0.165900i | ||||
\(328\) | 11.0000i | 0.607373i | ||||||||
\(329\) | 2.50000 | + | 12.9904i | 0.137829 | + | 0.716183i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.50000 | − | 11.2583i | 0.357272 | − | 0.618814i | −0.630232 | − | 0.776407i | \(-0.717040\pi\) |
0.987504 | + | 0.157593i | \(0.0503735\pi\) | |||||||
\(332\) | −6.92820 | + | 4.00000i | −0.380235 | + | 0.219529i | ||||
\(333\) | 9.52628 | − | 5.50000i | 0.522037 | − | 0.301398i | ||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | + | 1.73205i | −0.109109 | + | 0.0944911i | ||||
\(337\) | 12.0000i | 0.653682i | 0.945079 | + | 0.326841i | \(0.105984\pi\) | ||||
−0.945079 | + | 0.326841i | \(0.894016\pi\) | |||||||
\(338\) | −10.3923 | − | 6.00000i | −0.565267 | − | 0.326357i | ||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.00000 | + | 1.73205i | −0.0541530 | + | 0.0937958i | ||||
\(342\) | − | 3.00000i | − | 0.162221i | ||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.50000 | − | 12.9904i | −0.403202 | − | 0.698367i | ||||
\(347\) | −12.1244 | + | 7.00000i | −0.650870 | + | 0.375780i | −0.788789 | − | 0.614664i | \(-0.789292\pi\) |
0.137920 | + | 0.990443i | \(0.455958\pi\) | |||||||
\(348\) | −6.92820 | − | 4.00000i | −0.371391 | − | 0.214423i | ||||
\(349\) | −12.0000 | −0.642345 | −0.321173 | − | 0.947021i | \(-0.604077\pi\) | ||||
−0.321173 | + | 0.947021i | \(0.604077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0.866025 | + | 0.500000i | 0.0461593 | + | 0.0266501i | ||||
\(353\) | 20.7846 | − | 12.0000i | 1.10625 | − | 0.638696i | 0.168397 | − | 0.985719i | \(-0.446141\pi\) |
0.937856 | + | 0.347024i | \(0.112808\pi\) | |||||||
\(354\) | 2.00000 | + | 3.46410i | 0.106299 | + | 0.184115i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0000i | 1.00418i | ||||||||
\(359\) | 2.00000 | − | 3.46410i | 0.105556 | − | 0.182828i | −0.808409 | − | 0.588621i | \(-0.799671\pi\) |
0.913965 | + | 0.405793i | \(0.133004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | 20.7846 | + | 12.0000i | 1.09241 | + | 0.630706i | ||||
\(363\) | 10.0000i | 0.524864i | ||||||||
\(364\) | 2.50000 | + | 0.866025i | 0.131036 | + | 0.0453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6506 | + | 12.5000i | −1.13015 | + | 0.652495i | −0.943974 | − | 0.330021i | \(-0.892944\pi\) |
−0.186180 | + | 0.982516i | \(0.559611\pi\) | |||||||
\(368\) | 6.06218 | − | 3.50000i | 0.316013 | − | 0.182450i | ||||
\(369\) | −5.50000 | + | 9.52628i | −0.286319 | + | 0.495918i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.5000 | + | 9.52628i | 1.42773 | + | 0.494580i | ||||
\(372\) | − | 2.00000i | − | 0.103695i | ||||||
\(373\) | −5.19615 | − | 3.00000i | −0.269047 | − | 0.155334i | 0.359408 | − | 0.933181i | \(-0.382979\pi\) |
−0.628454 | + | 0.777847i | \(0.716312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.50000 | + | 4.33013i | −0.128928 | + | 0.223309i | ||||
\(377\) | 8.00000i | 0.412021i | ||||||||
\(378\) | −2.59808 | + | 0.500000i | −0.133631 | + | 0.0257172i | ||||
\(379\) | 19.0000 | 0.975964 | 0.487982 | − | 0.872854i | \(-0.337733\pi\) | ||||
0.487982 | + | 0.872854i | \(0.337733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.50000 | − | 14.7224i | −0.435468 | − | 0.754253i | ||||
\(382\) | −5.19615 | + | 3.00000i | −0.265858 | + | 0.153493i | ||||
\(383\) | −30.3109 | − | 17.5000i | −1.54881 | − | 0.894208i | −0.998233 | − | 0.0594268i | \(-0.981073\pi\) |
−0.550581 | − | 0.834781i | \(-0.685594\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | 6.92820 | + | 4.00000i | 0.352180 | + | 0.203331i | ||||
\(388\) | −13.8564 | + | 8.00000i | −0.703452 | + | 0.406138i | ||||
\(389\) | 5.00000 | + | 8.66025i | 0.253510 | + | 0.439092i | 0.964490 | − | 0.264120i | \(-0.0850816\pi\) |
−0.710980 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.92820 | + | 1.00000i | 0.349927 | + | 0.0505076i | ||||
\(393\) | 5.00000i | 0.252217i | ||||||||
\(394\) | 0.500000 | − | 0.866025i | 0.0251896 | − | 0.0436297i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | 12.1244 | + | 7.00000i | 0.608504 | + | 0.351320i | 0.772380 | − | 0.635161i | \(-0.219066\pi\) |
−0.163876 | + | 0.986481i | \(0.552400\pi\) | |||||||
\(398\) | 24.0000i | 1.20301i | ||||||||
\(399\) | −6.00000 | + | 5.19615i | −0.300376 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.50000 | − | 4.33013i | 0.124844 | − | 0.216236i | −0.796828 | − | 0.604206i | \(-0.793490\pi\) |
0.921672 | + | 0.387970i | \(0.126824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73205 | + | 1.00000i | −0.0862796 | + | 0.0498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | + | 20.7846i | 0.198517 | + | 1.03152i | ||||
\(407\) | 11.0000i | 0.545250i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00000 | + | 1.73205i | 0.0494468 | + | 0.0856444i | 0.889689 | − | 0.456566i | \(-0.150921\pi\) |
−0.840243 | + | 0.542211i | \(0.817588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | + | 15.5885i | −0.443937 | + | 0.768922i | ||||
\(412\) | 16.0000i | 0.788263i | ||||||||
\(413\) | 3.46410 | − | 10.0000i | 0.170457 | − | 0.492068i | ||||
\(414\) | 7.00000 | 0.344031 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 17.3205 | − | 10.0000i | 0.848189 | − | 0.489702i | ||||
\(418\) | 2.59808 | + | 1.50000i | 0.127076 | + | 0.0733674i | ||||
\(419\) | 5.00000 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | −4.33013 | − | 2.50000i | −0.210787 | − | 0.121698i | ||||
\(423\) | −4.33013 | + | 2.50000i | −0.210538 | + | 0.121554i | ||||
\(424\) | 5.50000 | + | 9.52628i | 0.267104 | + | 0.462637i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 10.0000i | − | 0.483368i | ||||||
\(429\) | 0.500000 | − | 0.866025i | 0.0241402 | − | 0.0418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 32.0000i | − | 1.53782i | −0.639356 | − | 0.768911i | \(-0.720799\pi\) | ||
0.639356 | − | 0.768911i | \(-0.279201\pi\) | |||||||
\(434\) | −4.00000 | + | 3.46410i | −0.192006 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.00000 | + | 5.19615i | −0.143674 | + | 0.248851i | ||||
\(437\) | 18.1865 | − | 10.5000i | 0.869980 | − | 0.502283i | ||||
\(438\) | −5.19615 | + | 3.00000i | −0.248282 | + | 0.143346i | ||||
\(439\) | 16.0000 | − | 27.7128i | 0.763638 | − | 1.32266i | −0.177325 | − | 0.984152i | \(-0.556744\pi\) |
0.940963 | − | 0.338508i | \(-0.109922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.8564 | − | 8.00000i | −0.658338 | − | 0.380091i | 0.133306 | − | 0.991075i | \(-0.457441\pi\) |
−0.791643 | + | 0.610984i | \(0.790774\pi\) | |||||||
\(444\) | −5.50000 | − | 9.52628i | −0.261018 | − | 0.452097i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | − | 10.3923i | 0.284108 | − | 0.492090i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.73205 | + | 2.00000i | 0.0818317 | + | 0.0944911i | ||||
\(449\) | −11.0000 | −0.519122 | −0.259561 | − | 0.965727i | \(-0.583578\pi\) | ||||
−0.259561 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.50000 | − | 9.52628i | −0.258985 | − | 0.448575i | ||||
\(452\) | −5.19615 | + | 3.00000i | −0.244406 | + | 0.141108i | ||||
\(453\) | 5.19615 | + | 3.00000i | 0.244137 | + | 0.140952i | ||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −15.5885 | − | 9.00000i | −0.729197 | − | 0.421002i | 0.0889312 | − | 0.996038i | \(-0.471655\pi\) |
−0.818128 | + | 0.575036i | \(0.804988\pi\) | |||||||
\(458\) | −12.1244 | + | 7.00000i | −0.566534 | + | 0.327089i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0.866025 | − | 2.50000i | 0.0402911 | − | 0.116311i | ||||
\(463\) | − | 13.0000i | − | 0.604161i | −0.953282 | − | 0.302081i | \(-0.902319\pi\) | ||
0.953282 | − | 0.302081i | \(-0.0976812\pi\) | |||||||
\(464\) | −4.00000 | + | 6.92820i | −0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.00000 | + | 15.5885i | 0.416917 | + | 0.722121i | ||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 1.00000i | 0.0462250i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | + | 6.06218i | −0.161271 | + | 0.279330i | ||||
\(472\) | 3.46410 | − | 2.00000i | 0.159448 | − | 0.0920575i | ||||
\(473\) | −6.92820 | + | 4.00000i | −0.318559 | + | 0.183920i | ||||
\(474\) | −4.00000 | + | 6.92820i | −0.183726 | + | 0.318223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0000i | 0.503655i | ||||||||
\(478\) | −15.5885 | − | 9.00000i | −0.712999 | − | 0.411650i | ||||
\(479\) | 11.0000 | + | 19.0526i | 0.502603 | + | 0.870534i | 0.999995 | + | 0.00300810i | \(0.000957509\pi\) |
−0.497393 | + | 0.867526i | \(0.665709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.50000 | + | 9.52628i | −0.250778 | + | 0.434361i | ||||
\(482\) | 7.00000i | 0.318841i | ||||||||
\(483\) | −12.1244 | − | 14.0000i | −0.551677 | − | 0.637022i | ||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 13.8564 | − | 8.00000i | 0.627894 | − | 0.362515i | −0.152042 | − | 0.988374i | \(-0.548585\pi\) |
0.779936 | + | 0.625859i | \(0.215252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 9.52628 | + | 5.50000i | 0.429478 | + | 0.247959i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.50000 | + | 2.59808i | 0.0674882 | + | 0.116893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 10.3923 | + | 12.0000i | 0.466159 | + | 0.538274i | ||||
\(498\) | 8.00000i | 0.358489i | ||||||||
\(499\) | −16.0000 | + | 27.7128i | −0.716258 | + | 1.24060i | 0.246214 | + | 0.969216i | \(0.420813\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.50000 | − | 2.59808i | −0.0670151 | − | 0.116073i | ||||
\(502\) | −11.2583 | − | 6.50000i | −0.502484 | − | 0.290109i | ||||
\(503\) | 36.0000i | 1.60516i | 0.596544 | + | 0.802580i | \(0.296540\pi\) | ||||
−0.596544 | + | 0.802580i | \(0.703460\pi\) | |||||||
\(504\) | 0.500000 | + | 2.59808i | 0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.50000 | + | 6.06218i | −0.155594 | + | 0.269497i | ||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | −14.7224 | + | 8.50000i | −0.653202 | + | 0.377127i | ||||
\(509\) | −17.0000 | + | 29.4449i | −0.753512 | + | 1.30512i | 0.192599 | + | 0.981278i | \(0.438308\pi\) |
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0000 | + | 5.19615i | 0.663561 | + | 0.229864i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.59808 | − | 1.50000i | −0.114708 | − | 0.0662266i | ||||
\(514\) | 10.0000 | + | 17.3205i | 0.441081 | + | 0.763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.00000 | − | 6.92820i | 0.176090 | − | 0.304997i | ||||
\(517\) | − | 5.00000i | − | 0.219900i | ||||||
\(518\) | −9.52628 | + | 27.5000i | −0.418561 | + | 1.20828i | ||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.5000 | + | 28.5788i | 0.722878 | + | 1.25206i | 0.959841 | + | 0.280543i | \(0.0905145\pi\) |
−0.236963 | + | 0.971519i | \(0.576152\pi\) | |||||||
\(522\) | −6.92820 | + | 4.00000i | −0.303239 | + | 0.175075i | ||||
\(523\) | −1.73205 | − | 1.00000i | −0.0757373 | − | 0.0437269i | 0.461653 | − | 0.887061i | \(-0.347256\pi\) |
−0.537390 | + | 0.843334i | \(0.680590\pi\) | |||||||
\(524\) | 5.00000 | 0.218426 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.866025 | − | 0.500000i | 0.0376889 | − | 0.0217597i | ||||
\(529\) | 13.0000 | + | 22.5167i | 0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 5.19615 | + | 6.00000i | 0.225282 | + | 0.260133i | ||||
\(533\) | − | 11.0000i | − | 0.476463i | ||||||
\(534\) | −5.00000 | + | 8.66025i | −0.216371 | + | 0.374766i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4545 | + | 9.50000i | 0.710063 | + | 0.409955i | ||||
\(538\) | − | 20.0000i | − | 0.862261i | ||||||
\(539\) | −6.50000 | + | 2.59808i | −0.279975 | + | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 27.7128 | − | 16.0000i | 1.19037 | − | 0.687259i | ||||
\(543\) | 20.7846 | − | 12.0000i | 0.891953 | − | 0.514969i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.00000 | − | 1.73205i | 0.0855921 | − | 0.0741249i | ||||
\(547\) | − | 16.0000i | − | 0.684111i | −0.939680 | − | 0.342055i | \(-0.888877\pi\) | ||
0.939680 | − | 0.342055i | \(-0.111123\pi\) | |||||||
\(548\) | 15.5885 | + | 9.00000i | 0.665906 | + | 0.384461i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | − | 7.00000i | − | 0.297940i | ||||||
\(553\) | 20.7846 | − | 4.00000i | 0.883852 | − | 0.170097i | ||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.0000 | − | 17.3205i | −0.424094 | − | 0.734553i | ||||
\(557\) | 28.5788 | − | 16.5000i | 1.21092 | − | 0.699127i | 0.247964 | − | 0.968769i | \(-0.420239\pi\) |
0.962961 | + | 0.269642i | \(0.0869053\pi\) | |||||||
\(558\) | −1.73205 | − | 1.00000i | −0.0733236 | − | 0.0423334i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.866025 | + | 0.500000i | 0.0365311 | + | 0.0210912i | ||||
\(563\) | −32.9090 | + | 19.0000i | −1.38695 | + | 0.800755i | −0.992970 | − | 0.118366i | \(-0.962235\pi\) |
−0.393977 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(564\) | 2.50000 | + | 4.33013i | 0.105269 | + | 0.182331i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.0000 | 0.588464 | ||||||||
\(567\) | −0.866025 | + | 2.50000i | −0.0363696 | + | 0.104990i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | + | 27.7128i | 0.669579 | + | 1.15975i | 0.978022 | + | 0.208502i | \(0.0668588\pi\) |
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(572\) | −0.866025 | − | 0.500000i | −0.0362103 | − | 0.0209061i | ||||
\(573\) | 6.00000i | 0.250654i | ||||||||
\(574\) | −5.50000 | − | 28.5788i | −0.229566 | − | 1.19286i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 12.1244 | − | 7.00000i | 0.504744 | − | 0.291414i | −0.225927 | − | 0.974144i | \(-0.572541\pi\) |
0.730670 | + | 0.682730i | \(0.239208\pi\) | |||||||
\(578\) | 14.7224 | − | 8.50000i | 0.612372 | − | 0.353553i | ||||
\(579\) | −11.0000 | + | 19.0526i | −0.457144 | + | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.0000 | − | 13.8564i | 0.663792 | − | 0.574861i | ||||
\(582\) | 16.0000i | 0.663221i | ||||||||
\(583\) | −9.52628 | − | 5.50000i | −0.394538 | − | 0.227787i | ||||
\(584\) | 3.00000 | + | 5.19615i | 0.124141 | + | 0.215018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.5000 | − | 23.3827i | 0.557680 | − | 0.965930i | ||||
\(587\) | 18.0000i | 0.742940i | 0.928445 | + | 0.371470i | \(0.121146\pi\) | ||||
−0.928445 | + | 0.371470i | \(0.878854\pi\) | |||||||
\(588\) | 4.33013 | − | 5.50000i | 0.178571 | − | 0.226816i | ||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.500000 | − | 0.866025i | −0.0205673 | − | 0.0356235i | ||||
\(592\) | −9.52628 | + | 5.50000i | −0.391528 | + | 0.226049i | ||||
\(593\) | −13.8564 | − | 8.00000i | −0.569014 | − | 0.328521i | 0.187741 | − | 0.982219i | \(-0.439883\pi\) |
−0.756756 | + | 0.653698i | \(0.773217\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.7846 | + | 12.0000i | 0.850657 | + | 0.491127i | ||||
\(598\) | −6.06218 | + | 3.50000i | −0.247901 | + | 0.143126i | ||||
\(599\) | 1.00000 | + | 1.73205i | 0.0408589 | + | 0.0707697i | 0.885732 | − | 0.464198i | \(-0.153657\pi\) |
−0.844873 | + | 0.534967i | \(0.820324\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | −20.7846 | + | 4.00000i | −0.847117 | + | 0.163028i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.00000 | − | 5.19615i | 0.122068 | − | 0.211428i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.0429 | − | 18.5000i | −1.30058 | − | 0.750892i | −0.320079 | − | 0.947391i | \(-0.603709\pi\) |
−0.980504 | + | 0.196499i | \(0.937043\pi\) | |||||||
\(608\) | 3.00000i | 0.121666i | ||||||||
\(609\) | 20.0000 | + | 6.92820i | 0.810441 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.50000 | − | 4.33013i | 0.101139 | − | 0.175178i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.5070 | + | 20.5000i | −1.43412 | + | 0.827987i | −0.997431 | − | 0.0716275i | \(-0.977181\pi\) |
−0.436684 | + | 0.899615i | \(0.643847\pi\) | |||||||
\(614\) | −10.0000 | + | 17.3205i | −0.403567 | + | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50000 | − | 0.866025i | −0.100728 | − | 0.0348932i | ||||
\(617\) | − | 28.0000i | − | 1.12724i | −0.826035 | − | 0.563619i | \(-0.809409\pi\) | ||
0.826035 | − | 0.563619i | \(-0.190591\pi\) | |||||||
\(618\) | 13.8564 | + | 8.00000i | 0.557386 | + | 0.321807i | ||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50000 | − | 6.06218i | 0.140450 | − | 0.243267i | ||||
\(622\) | 12.0000i | 0.481156i | ||||||||
\(623\) | 25.9808 | − | 5.00000i | 1.04090 | − | 0.200321i | ||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.00000 | − | 10.3923i | −0.239808 | − | 0.415360i | ||||
\(627\) | 2.59808 | − | 1.50000i | 0.103757 | − | 0.0599042i | ||||
\(628\) | 6.06218 | + | 3.50000i | 0.241907 | + | 0.139665i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0000 | −1.03504 | −0.517522 | − | 0.855670i | \(-0.673145\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(632\) | 6.92820 | + | 4.00000i | 0.275589 | + | 0.159111i | ||||
\(633\) | −4.33013 | + | 2.50000i | −0.172107 | + | 0.0993661i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.0000 | 0.436178 | ||||||||
\(637\) | −6.92820 | − | 1.00000i | −0.274505 | − | 0.0396214i | ||||
\(638\) | − | 8.00000i | − | 0.316723i | ||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | + | 2.59808i | 0.0592464 | + | 0.102618i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550431i | \(0.814464\pi\) | |||||||
\(642\) | −8.66025 | − | 5.00000i | −0.341793 | − | 0.197334i | ||||
\(643\) | − | 10.0000i | − | 0.394362i | −0.980367 | − | 0.197181i | \(-0.936821\pi\) | ||
0.980367 | − | 0.197181i | \(-0.0631786\pi\) | |||||||
\(644\) | −14.0000 | + | 12.1244i | −0.551677 | + | 0.477767i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.7224 | − | 8.50000i | 0.578799 | − | 0.334169i | −0.181857 | − | 0.983325i | \(-0.558211\pi\) |
0.760656 | + | 0.649155i | \(0.224878\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −2.00000 | + | 3.46410i | −0.0785069 | + | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.00000 | + | 5.19615i | 0.0391931 | + | 0.203653i | ||||
\(652\) | − | 16.0000i | − | 0.626608i | ||||||
\(653\) | −6.06218 | − | 3.50000i | −0.237231 | − | 0.136966i | 0.376672 | − | 0.926347i | \(-0.377068\pi\) |
−0.613904 | + | 0.789381i | \(0.710402\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.50000 | − | 9.52628i | 0.214739 | − | 0.371939i | ||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | 4.33013 | − | 12.5000i | 0.168806 | − | 0.487301i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000 | + | 20.7846i | 0.466746 | + | 0.808428i | 0.999278 | − | 0.0379819i | \(-0.0120929\pi\) |
−0.532533 | + | 0.846410i | \(0.678760\pi\) | |||||||
\(662\) | −11.2583 | + | 6.50000i | −0.437567 | + | 0.252630i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.0000 | −0.426241 | ||||||||
\(667\) | −48.4974 | − | 28.0000i | −1.87783 | − | 1.08416i | ||||
\(668\) | −2.59808 | + | 1.50000i | −0.100523 | + | 0.0580367i | ||||
\(669\) | −6.00000 | − | 10.3923i | −0.231973 | − | 0.401790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.59808 | − | 0.500000i | 0.100223 | − | 0.0192879i | ||||
\(673\) | 28.0000i | 1.07932i | 0.841883 | + | 0.539660i | \(0.181447\pi\) | ||||
−0.841883 | + | 0.539660i | \(0.818553\pi\) | |||||||
\(674\) | 6.00000 | − | 10.3923i | 0.231111 | − | 0.400297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | −11.2583 | − | 6.50000i | −0.432693 | − | 0.249815i | 0.267800 | − | 0.963474i | \(-0.413703\pi\) |
−0.700493 | + | 0.713659i | \(0.747037\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 32.0000 | − | 27.7128i | 1.22805 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | − | 6.92820i | 0.153280 | − | 0.265489i | ||||
\(682\) | 1.73205 | − | 1.00000i | 0.0663237 | − | 0.0382920i | ||||
\(683\) | 3.46410 | − | 2.00000i | 0.132550 | − | 0.0765279i | −0.432259 | − | 0.901750i | \(-0.642283\pi\) |
0.564809 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(684\) | −1.50000 | + | 2.59808i | −0.0573539 | + | 0.0993399i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | −6.92820 | − | 4.00000i | −0.264135 | − | 0.152499i | ||||
\(689\) | −5.50000 | − | 9.52628i | −0.209533 | − | 0.362922i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.00000 | − | 10.3923i | 0.228251 | − | 0.395342i | −0.729039 | − | 0.684472i | \(-0.760033\pi\) |
0.957290 | + | 0.289130i | \(0.0933661\pi\) | |||||||
\(692\) | 15.0000i | 0.570214i | ||||||||
\(693\) | −1.73205 | − | 2.00000i | −0.0657952 | − | 0.0759737i | ||||
\(694\) | 14.0000 | 0.531433 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.00000 | + | 6.92820i | 0.151620 | + | 0.262613i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 10.3923 | + | 6.00000i | 0.393355 | + | 0.227103i | ||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0.866025 | + | 0.500000i | 0.0326860 | + | 0.0188713i | ||||
\(703\) | −28.5788 | + | 16.5000i | −1.07787 | + | 0.622309i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 4.00000i | − | 0.150329i | ||||||
\(709\) | 22.0000 | − | 38.1051i | 0.826227 | − | 1.43107i | −0.0747503 | − | 0.997202i | \(-0.523816\pi\) |
0.900978 | − | 0.433865i | \(-0.142851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00000 | + | 6.92820i | 0.150012 | + | 0.259828i | ||||
\(712\) | 8.66025 | + | 5.00000i | 0.324557 | + | 0.187383i | ||||
\(713\) | − | 14.0000i | − | 0.524304i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.50000 | − | 16.4545i | 0.355032 | − | 0.614933i | ||||
\(717\) | −15.5885 | + | 9.00000i | −0.582162 | + | 0.336111i | ||||
\(718\) | −3.46410 | + | 2.00000i | −0.129279 | + | 0.0746393i | ||||
\(719\) | 1.00000 | − | 1.73205i | 0.0372937 | − | 0.0645946i | −0.846776 | − | 0.531949i | \(-0.821460\pi\) |
0.884070 | + | 0.467355i | \(0.154793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | − | 41.5692i | −0.297936 | − | 1.54812i | ||||
\(722\) | − | 10.0000i | − | 0.372161i | ||||||
\(723\) | 6.06218 | + | 3.50000i | 0.225455 | + | 0.130166i | ||||
\(724\) | −12.0000 | − | 20.7846i | −0.445976 | − | 0.772454i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | − | 11.0000i | − | 0.407967i | −0.978974 | − | 0.203984i | \(-0.934611\pi\) | ||
0.978974 | − | 0.203984i | \(-0.0653890\pi\) | |||||||
\(728\) | −1.73205 | − | 2.00000i | −0.0641941 | − | 0.0741249i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.52628 | − | 5.50000i | −0.351861 | − | 0.203147i | 0.313644 | − | 0.949541i | \(-0.398450\pi\) |
−0.665505 | + | 0.746394i | \(0.731784\pi\) | |||||||
\(734\) | 25.0000 | 0.922767 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.52628 | − | 5.50000i | 0.350667 | − | 0.202458i | ||||
\(739\) | −9.50000 | − | 16.4545i | −0.349463 | − | 0.605288i | 0.636691 | − | 0.771119i | \(-0.280303\pi\) |
−0.986154 | + | 0.165831i | \(0.946969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.00000 | 0.110208 | ||||||||
\(742\) | −19.0526 | − | 22.0000i | −0.699441 | − | 0.807645i | ||||
\(743\) | 49.0000i | 1.79764i | 0.438322 | + | 0.898818i | \(0.355573\pi\) | ||||
−0.438322 | + | 0.898818i | \(0.644427\pi\) | |||||||
\(744\) | −1.00000 | + | 1.73205i | −0.0366618 | + | 0.0635001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.00000 | + | 5.19615i | 0.109838 | + | 0.190245i | ||||
\(747\) | 6.92820 | + | 4.00000i | 0.253490 | + | 0.146352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.00000 | + | 25.9808i | 0.182696 | + | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | + | 22.5167i | −0.474377 | + | 0.821645i | −0.999570 | − | 0.0293387i | \(-0.990660\pi\) |
0.525193 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(752\) | 4.33013 | − | 2.50000i | 0.157903 | − | 0.0911656i | ||||
\(753\) | −11.2583 | + | 6.50000i | −0.410276 | + | 0.236873i | ||||
\(754\) | 4.00000 | − | 6.92820i | 0.145671 | − | 0.252310i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.50000 | + | 0.866025i | 0.0909241 | + | 0.0314970i | ||||
\(757\) | − | 2.00000i | − | 0.0726912i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363456i | \(-0.0115717\pi\) | |||||||
\(758\) | −16.4545 | − | 9.50000i | −0.597654 | − | 0.345056i | ||||
\(759\) | 3.50000 | + | 6.06218i | 0.127042 | + | 0.220043i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | + | 23.3827i | −0.489375 | + | 0.847622i | −0.999925 | − | 0.0122260i | \(-0.996108\pi\) |
0.510551 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(762\) | 17.0000i | 0.615845i | ||||||||
\(763\) | 5.19615 | − | 15.0000i | 0.188113 | − | 0.543036i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.5000 | + | 30.3109i | 0.632301 | + | 1.09518i | ||||
\(767\) | −3.46410 | + | 2.00000i | −0.125081 | + | 0.0722158i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | 0.720282 | ||||||||
\(772\) | 19.0526 | + | 11.0000i | 0.685717 | + | 0.395899i | ||||
\(773\) | 28.5788 | − | 16.5000i | 1.02791 | − | 0.593464i | 0.111524 | − | 0.993762i | \(-0.464427\pi\) |
0.916385 | + | 0.400298i | \(0.131093\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i | −0.143777 | − | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.0000 | 0.574367 | ||||||||
\(777\) | 19.0526 | + | 22.0000i | 0.683507 | + | 0.789246i | ||||
\(778\) | − | 10.0000i | − | 0.358517i | ||||||
\(779\) | 16.5000 | − | 28.5788i | 0.591174 | − | 1.02394i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00000 | − | 5.19615i | −0.107348 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000i | 0.285897i | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.50000 | − | 4.33013i | 0.0891720 | − | 0.154451i | ||||
\(787\) | −19.0526 | + | 11.0000i | −0.679150 | + | 0.392108i | −0.799535 | − | 0.600620i | \(-0.794921\pi\) |
0.120384 | + | 0.992727i | \(0.461587\pi\) | |||||||
\(788\) | −0.866025 | + | 0.500000i | −0.0308509 | + | 0.0178118i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | − | 10.3923i | 0.426671 | − | 0.369508i | ||||
\(792\) | − | 1.00000i | − | 0.0355335i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.00000 | − | 12.1244i | −0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0000 | − | 20.7846i | 0.425329 | − | 0.736691i | ||||
\(797\) | 18.0000i | 0.637593i | 0.947823 | + | 0.318796i | \(0.103279\pi\) | ||||
−0.947823 | + | 0.318796i | \(0.896721\pi\) | |||||||
\(798\) | 7.79423 | − | 1.50000i | 0.275913 | − | 0.0530994i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.00000 | + | 8.66025i | 0.176666 | + | 0.305995i | ||||
\(802\) | −4.33013 | + | 2.50000i | −0.152902 | + | 0.0882781i | ||||
\(803\) | −5.19615 | − | 3.00000i | −0.183368 | − | 0.105868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | −17.3205 | − | 10.0000i | −0.609711 | − | 0.352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5000 | − | 33.7750i | −0.685583 | − | 1.18747i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.287670 | − | 0.957730i | \(-0.407120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | 6.92820 | − | 20.0000i | 0.243132 | − | 0.701862i | ||||
\(813\) | − | 32.0000i | − | 1.12229i | ||||||
\(814\) | 5.50000 | − | 9.52628i | 0.192775 | − | 0.333896i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.7846 | − | 12.0000i | −0.727161 | − | 0.419827i | ||||
\(818\) | − | 2.00000i | − | 0.0699284i | ||||||
\(819\) | −0.500000 | − | 2.59808i | −0.0174714 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | 15.5885 | − | 9.00000i | 0.543710 | − | 0.313911i | ||||
\(823\) | −20.7846 | + | 12.0000i | −0.724506 | + | 0.418294i | −0.816409 | − | 0.577474i | \(-0.804038\pi\) |
0.0919029 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(824\) | 8.00000 | − | 13.8564i | 0.278693 | − | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | + | 6.92820i | −0.278356 | + | 0.241063i | ||||
\(827\) | 10.0000i | 0.347734i | 0.984769 | + | 0.173867i | \(0.0556263\pi\) | ||||
−0.984769 | + | 0.173867i | \(0.944374\pi\) | |||||||
\(828\) | −6.06218 | − | 3.50000i | −0.210675 | − | 0.121633i | ||||
\(829\) | −4.00000 | − | 6.92820i | −0.138926 | − | 0.240626i | 0.788165 | − | 0.615465i | \(-0.211032\pi\) |
−0.927090 | + | 0.374838i | \(0.877698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.0000 | + | 19.0526i | −0.381586 | + | 0.660926i | ||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.0000 | −0.692543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.50000 | − | 2.59808i | −0.0518786 | − | 0.0898563i | ||||
\(837\) | −1.73205 | + | 1.00000i | −0.0598684 | + | 0.0345651i | ||||
\(838\) | −4.33013 | − | 2.50000i | −0.149582 | − | 0.0863611i | ||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −19.0526 | − | 11.0000i | −0.656595 | − | 0.379085i | ||||
\(843\) | 0.866025 | − | 0.500000i | 0.0298275 | − | 0.0172209i | ||||
\(844\) | 2.50000 | + | 4.33013i | 0.0860535 | + | 0.149049i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.00000 | 0.171904 | ||||||||
\(847\) | −25.9808 | + | 5.00000i | −0.892710 | + | 0.171802i | ||||
\(848\) | − | 11.0000i | − | 0.377742i | ||||||
\(849\) | 7.00000 | − | 12.1244i | 0.240239 | − | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.5000 | − | 66.6840i | −1.31976 | − | 2.28590i | ||||
\(852\) | 5.19615 | + | 3.00000i | 0.178017 | + | 0.102778i | ||||
\(853\) | − | 41.0000i | − | 1.40381i | −0.712269 | − | 0.701907i | \(-0.752332\pi\) | ||
0.712269 | − | 0.701907i | \(-0.247668\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.00000 | + | 8.66025i | −0.170896 | + | 0.296001i | ||||
\(857\) | 12.1244 | − | 7.00000i | 0.414160 | − | 0.239115i | −0.278416 | − | 0.960461i | \(-0.589809\pi\) |
0.692576 | + | 0.721345i | \(0.256476\pi\) | |||||||
\(858\) | −0.866025 | + | 0.500000i | −0.0295656 | + | 0.0170697i | ||||
\(859\) | 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 | ||||||||
\(861\) | −27.5000 | − | 9.52628i | −0.937197 | − | 0.324655i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.8993 | + | 26.5000i | 1.56243 | + | 0.902070i | 0.997010 | + | 0.0772684i | \(0.0246198\pi\) |
0.565422 | + | 0.824802i | \(0.308713\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.0000 | + | 27.7128i | −0.543702 | + | 0.941720i | ||||
\(867\) | − | 17.0000i | − | 0.577350i | ||||||
\(868\) | 5.19615 | − | 1.00000i | 0.176369 | − | 0.0339422i | ||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.19615 | − | 3.00000i | 0.175964 | − | 0.101593i | ||||
\(873\) | 13.8564 | + | 8.00000i | 0.468968 | + | 0.270759i | ||||
\(874\) | −21.0000 | −0.710336 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | 14.7224 | + | 8.50000i | 0.497141 | + | 0.287025i | 0.727532 | − | 0.686074i | \(-0.240667\pi\) |
−0.230391 | + | 0.973098i | \(0.574001\pi\) | |||||||
\(878\) | −27.7128 | + | 16.0000i | −0.935262 | + | 0.539974i | ||||
\(879\) | −13.5000 | − | 23.3827i | −0.455344 | − | 0.788678i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.0000 | −1.78562 | −0.892808 | − | 0.450438i | \(-0.851268\pi\) | ||||
−0.892808 | + | 0.450438i | \(0.851268\pi\) | |||||||
\(882\) | −2.59808 | − | 6.50000i | −0.0874818 | − | 0.218866i | ||||
\(883\) | − | 42.0000i | − | 1.41341i | −0.707507 | − | 0.706706i | \(-0.750180\pi\) | ||
0.707507 | − | 0.706706i | \(-0.249820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.00000 | + | 13.8564i | 0.268765 | + | 0.465515i | ||||
\(887\) | 38.1051 | + | 22.0000i | 1.27944 | + | 0.738688i | 0.976746 | − | 0.214399i | \(-0.0687792\pi\) |
0.302698 | + | 0.953086i | \(0.402113\pi\) | |||||||
\(888\) | 11.0000i | 0.369136i | ||||||||
\(889\) | 34.0000 | − | 29.4449i | 1.14032 | − | 0.987549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | −10.3923 | + | 6.00000i | −0.347960 | + | 0.200895i | ||||
\(893\) | 12.9904 | − | 7.50000i | 0.434707 | − | 0.250978i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | 7.00000i | 0.233723i | ||||||||
\(898\) | 9.52628 | + | 5.50000i | 0.317896 | + | 0.183537i | ||||
\(899\) | 8.00000 | + | 13.8564i | 0.266815 | + | 0.462137i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 11.0000i | 0.366260i | ||||||||
\(903\) | −6.92820 | + | 20.0000i | −0.230556 | + | 0.665558i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.00000 | − | 5.19615i | −0.0996683 | − | 0.172631i | ||||
\(907\) | 8.66025 | − | 5.00000i | 0.287559 | − | 0.166022i | −0.349281 | − | 0.937018i | \(-0.613574\pi\) |
0.636841 | + | 0.770996i | \(0.280241\pi\) | |||||||
\(908\) | −6.92820 | − | 4.00000i | −0.229920 | − | 0.132745i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | 2.59808 | + | 1.50000i | 0.0860309 | + | 0.0496700i | ||||
\(913\) | −6.92820 | + | 4.00000i | −0.229290 | + | 0.132381i | ||||
\(914\) | 9.00000 | + | 15.5885i | 0.297694 | + | 0.515620i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | −12.9904 | + | 2.50000i | −0.428980 | + | 0.0825573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0000 | + | 31.1769i | −0.593765 | + | 1.02843i | 0.399955 | + | 0.916535i | \(0.369026\pi\) |
−0.993720 | + | 0.111897i | \(0.964307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | + | 17.3205i | 0.329511 | + | 0.570730i | ||||
\(922\) | 10.3923 | + | 6.00000i | 0.342252 | + | 0.197599i | ||||
\(923\) | − | 6.00000i | − | 0.197492i | ||||||
\(924\) | −2.00000 | + | 1.73205i | −0.0657952 | + | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.50000 | + | 11.2583i | −0.213603 | + | 0.369972i | ||||
\(927\) | 13.8564 | − | 8.00000i | 0.455104 | − | 0.262754i | ||||
\(928\) | 6.92820 | − | 4.00000i | 0.227429 | − | 0.131306i | ||||
\(929\) | −10.5000 | + | 18.1865i | −0.344494 | + | 0.596681i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.640768 | + | 0.767735i | \(0.278616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5000 | − | 12.9904i | −0.540766 | − | 0.425743i | ||||
\(932\) | − | 18.0000i | − | 0.589610i | ||||||
\(933\) | 10.3923 | + | 6.00000i | 0.340229 | + | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 0.866025i | 0.0163430 | − | 0.0283069i | ||||
\(937\) | − | 12.0000i | − | 0.392023i | −0.980602 | − | 0.196011i | \(-0.937201\pi\) | ||
0.980602 | − | 0.196011i | \(-0.0627990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | − | 46.7654i | −0.880175 | − | 1.52451i | −0.851146 | − | 0.524929i | \(-0.824092\pi\) |
−0.0290288 | − | 0.999579i | \(-0.509241\pi\) | |||||||
\(942\) | 6.06218 | − | 3.50000i | 0.197516 | − | 0.114036i | ||||
\(943\) | 66.6840 | + | 38.5000i | 2.17153 | + | 1.25373i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 19.0526 | + | 11.0000i | 0.619125 | + | 0.357452i | 0.776528 | − | 0.630082i | \(-0.216979\pi\) |
−0.157403 | + | 0.987534i | \(0.550312\pi\) | |||||||
\(948\) | 6.92820 | − | 4.00000i | 0.225018 | − | 0.129914i | ||||
\(949\) | −3.00000 | − | 5.19615i | −0.0973841 | − | 0.168674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20.0000i | − | 0.647864i | −0.946080 | − | 0.323932i | \(-0.894995\pi\) | ||
0.946080 | − | 0.323932i | \(-0.105005\pi\) | |||||||
\(954\) | 5.50000 | − | 9.52628i | 0.178069 | − | 0.308425i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.00000 | + | 15.5885i | 0.291081 | + | 0.504167i | ||||
\(957\) | −6.92820 | − | 4.00000i | −0.223957 | − | 0.129302i | ||||
\(958\) | − | 22.0000i | − | 0.710788i | ||||||
\(959\) | −45.0000 | − | 15.5885i | −1.45313 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 9.52628 | − | 5.50000i | 0.307140 | − | 0.177327i | ||||
\(963\) | −8.66025 | + | 5.00000i | −0.279073 | + | 0.161123i | ||||
\(964\) | 3.50000 | − | 6.06218i | 0.112727 | − | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.50000 | + | 18.1865i | 0.112611 | + | 0.585142i | ||||
\(967\) | 20.0000i | 0.643157i | 0.946883 | + | 0.321578i | \(0.104213\pi\) | ||||
−0.946883 | + | 0.321578i | \(0.895787\pi\) | |||||||
\(968\) | −8.66025 | − | 5.00000i | −0.278351 | − | 0.160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5000 | − | 38.9711i | 0.722059 | − | 1.25064i | −0.238114 | − | 0.971237i | \(-0.576529\pi\) |
0.960173 | − | 0.279406i | \(-0.0901376\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 34.6410 | + | 40.0000i | 1.11054 | + | 1.28234i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.7654 | + | 27.0000i | −1.49616 | + | 0.863807i | −0.999990 | − | 0.00442082i | \(-0.998593\pi\) |
−0.496167 | + | 0.868227i | \(0.665259\pi\) | |||||||
\(978\) | −13.8564 | − | 8.00000i | −0.443079 | − | 0.255812i | ||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −17.3205 | − | 10.0000i | −0.552720 | − | 0.319113i | ||||
\(983\) | 42.4352 | − | 24.5000i | 1.35347 | − | 0.781429i | 0.364740 | − | 0.931110i | \(-0.381158\pi\) |
0.988734 | + | 0.149681i | \(0.0478246\pi\) | |||||||
\(984\) | −5.50000 | − | 9.52628i | −0.175334 | − | 0.303687i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.66025 | − | 10.0000i | −0.275659 | − | 0.318304i | ||||
\(988\) | − | 3.00000i | − | 0.0954427i | ||||||
\(989\) | 28.0000 | − | 48.4974i | 0.890348 | − | 1.54213i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0000 | − | 19.0526i | −0.349427 | − | 0.605224i | 0.636721 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(992\) | 1.73205 | + | 1.00000i | 0.0549927 | + | 0.0317500i | ||||
\(993\) | 13.0000i | 0.412543i | ||||||||
\(994\) | −3.00000 | − | 15.5885i | −0.0951542 | − | 0.494436i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.00000 | − | 6.92820i | 0.126745 | − | 0.219529i | ||||
\(997\) | −12.1244 | + | 7.00000i | −0.383982 | + | 0.221692i | −0.679549 | − | 0.733630i | \(-0.737825\pi\) |
0.295567 | + | 0.955322i | \(0.404491\pi\) | |||||||
\(998\) | 27.7128 | − | 16.0000i | 0.877234 | − | 0.506471i | ||||
\(999\) | −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 | 1050.2.o.i.499.1 | 4 | ||
5.2 | odd | 4 | 210.2.i.d.121.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1050.2.i.b.751.1 | 2 | |||
5.4 | even | 2 | inner | 1050.2.o.i.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.i.949.2 | 4 | ||
15.2 | even | 4 | 630.2.k.c.541.1 | 2 | |||
20.7 | even | 4 | 1680.2.bg.g.961.1 | 2 | |||
35.2 | odd | 12 | 1470.2.a.a.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.i.949.1 | 4 | ||
35.12 | even | 12 | 1470.2.a.h.1.1 | 1 | |||
35.17 | even | 12 | 1470.2.i.m.361.1 | 2 | |||
35.18 | odd | 12 | 1050.2.i.b.151.1 | 2 | |||
35.23 | odd | 12 | 7350.2.a.cp.1.1 | 1 | |||
35.27 | even | 4 | 1470.2.i.m.961.1 | 2 | |||
35.32 | odd | 12 | 210.2.i.d.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.bu.1.1 | 1 | |||
105.2 | even | 12 | 4410.2.a.bj.1.1 | 1 | |||
105.32 | even | 12 | 630.2.k.c.361.1 | 2 | |||
105.47 | odd | 12 | 4410.2.a.ba.1.1 | 1 | |||
140.67 | even | 12 | 1680.2.bg.g.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.d.121.1 | ✓ | 2 | 5.2 | odd | 4 | ||
210.2.i.d.151.1 | yes | 2 | 35.32 | odd | 12 | ||
630.2.k.c.361.1 | 2 | 105.32 | even | 12 | |||
630.2.k.c.541.1 | 2 | 15.2 | even | 4 | |||
1050.2.i.b.151.1 | 2 | 35.18 | odd | 12 | |||
1050.2.i.b.751.1 | 2 | 5.3 | odd | 4 | |||
1050.2.o.i.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.i.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.i.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.i.949.2 | 4 | 7.4 | even | 3 | inner | ||
1470.2.a.a.1.1 | 1 | 35.2 | odd | 12 | |||
1470.2.a.h.1.1 | 1 | 35.12 | even | 12 | |||
1470.2.i.m.361.1 | 2 | 35.17 | even | 12 | |||
1470.2.i.m.961.1 | 2 | 35.27 | even | 4 | |||
1680.2.bg.g.961.1 | 2 | 20.7 | even | 4 | |||
1680.2.bg.g.1201.1 | 2 | 140.67 | even | 12 | |||
4410.2.a.ba.1.1 | 1 | 105.47 | odd | 12 | |||
4410.2.a.bj.1.1 | 1 | 105.2 | even | 12 | |||
7350.2.a.bu.1.1 | 1 | 35.33 | even | 12 | |||
7350.2.a.cp.1.1 | 1 | 35.23 | odd | 12 |