Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(49,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.j (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: | \(3.59326809096\) |
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 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.49 |
Dual form | 450.2.j.a.349.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | −3.46410 | + | 2.00000i | −1.30931 | + | 0.755929i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | −3.46410 | − | 2.00000i | −0.960769 | − | 0.554700i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | − | 3.46410i | −1.30931 | − | 0.755929i | ||||
\(22\) | 2.59808 | + | 1.50000i | 0.553912 | + | 0.319801i | ||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 2.59808 | − | 4.50000i | 0.452267 | − | 0.783349i | ||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 4.33013 | − | 2.50000i | 0.702439 | − | 0.405554i | ||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 6.92820 | 1.06904 | ||||||||
\(43\) | −9.52628 | + | 5.50000i | −1.45274 | + | 0.838742i | −0.998636 | − | 0.0522047i | \(-0.983375\pi\) |
−0.454108 | + | 0.890947i | \(0.650042\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0.866025 | − | 1.50000i | 0.125000 | − | 0.216506i | ||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | −3.46410 | + | 2.00000i | −0.480384 | + | 0.277350i | ||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 3.46410i | −0.267261 | − | 0.462910i | ||||
\(57\) | −4.33013 | − | 7.50000i | −0.573539 | − | 0.993399i | ||||
\(58\) | −5.19615 | − | 3.00000i | −0.682288 | − | 0.393919i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | − | 12.0000i | − | 1.51186i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.19615i | 0.639602i | ||||||||
\(67\) | −4.33013 | − | 2.50000i | −0.529009 | − | 0.305424i | 0.211604 | − | 0.977356i | \(-0.432131\pi\) |
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 2.59808 | + | 1.50000i | 0.315063 | + | 0.181902i | ||||
\(69\) | 10.3923i | 1.25109i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | 7.00000i | 0.819288i | 0.912245 | + | 0.409644i | \(0.134347\pi\) | ||||
−0.912245 | + | 0.409644i | \(0.865653\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | 10.3923 | + | 6.00000i | 1.18431 | + | 0.683763i | ||||
\(78\) | 3.46410 | + | 6.00000i | 0.392232 | + | 0.679366i | ||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 3.00000i | 0.331295i | ||||||||
\(83\) | −10.3923 | + | 6.00000i | −1.14070 | + | 0.658586i | −0.946605 | − | 0.322396i | \(-0.895512\pi\) |
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(84\) | −6.00000 | + | 3.46410i | −0.654654 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.50000 | − | 9.52628i | 0.593080 | − | 1.02725i | ||||
\(87\) | −5.19615 | + | 9.00000i | −0.557086 | + | 0.964901i | ||||
\(88\) | 2.59808 | − | 1.50000i | 0.276956 | − | 0.159901i | ||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | −3.46410 | −0.359211 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.73205i | 0.176777i | ||||||||
\(97\) | 9.52628 | − | 5.50000i | 0.967247 | − | 0.558440i | 0.0688512 | − | 0.997627i | \(-0.478067\pi\) |
0.898396 | + | 0.439187i | \(0.144733\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 2.59808 | − | 4.50000i | 0.257248 | − | 0.445566i | ||||
\(103\) | −3.46410 | − | 2.00000i | −0.341328 | − | 0.197066i | 0.319531 | − | 0.947576i | \(-0.396475\pi\) |
−0.660859 | + | 0.750510i | \(0.729808\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | − | 9.00000i | − | 0.870063i | −0.900415 | − | 0.435031i | \(-0.856737\pi\) | ||
0.900415 | − | 0.435031i | \(-0.143263\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | − | 3.46410i | 0.569495 | − | 0.328798i | ||||
\(112\) | 3.46410 | + | 2.00000i | 0.327327 | + | 0.188982i | ||||
\(113\) | 15.5885 | + | 9.00000i | 1.46644 | + | 0.846649i | 0.999295 | − | 0.0375328i | \(-0.0119499\pi\) |
0.467143 | + | 0.884182i | \(0.345283\pi\) | |||||||
\(114\) | 7.50000 | + | 4.33013i | 0.702439 | + | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 10.3923 | − | 6.00000i | 0.960769 | − | 0.554700i | ||||
\(118\) | − | 3.00000i | − | 0.276172i | ||||||
\(119\) | −6.00000 | − | 10.3923i | −0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −8.66025 | − | 5.00000i | −0.784063 | − | 0.452679i | ||||
\(123\) | 5.19615 | 0.468521 | ||||||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.00000 | + | 10.3923i | 0.534522 | + | 0.925820i | ||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −16.5000 | − | 9.52628i | −1.45274 | − | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | −2.59808 | − | 4.50000i | −0.226134 | − | 0.391675i | ||||
\(133\) | 17.3205 | − | 10.0000i | 1.50188 | − | 0.867110i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −7.79423 | + | 4.50000i | −0.665906 | + | 0.384461i | −0.794524 | − | 0.607233i | \(-0.792279\pi\) |
0.128618 | + | 0.991694i | \(0.458946\pi\) | |||||||
\(138\) | −5.19615 | − | 9.00000i | −0.442326 | − | 0.766131i | ||||
\(139\) | −0.500000 | + | 0.866025i | −0.0424094 | + | 0.0734553i | −0.886451 | − | 0.462822i | \(-0.846837\pi\) |
0.844042 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | 12.0000i | 1.00349i | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.50000 | − | 6.06218i | −0.289662 | − | 0.501709i | ||||
\(147\) | 15.5885 | 1.28571 | ||||||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | − | 5.00000i | − | 0.405554i | ||||||
\(153\) | −7.79423 | − | 4.50000i | −0.630126 | − | 0.363803i | ||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | − | 3.46410i | −0.480384 | − | 0.277350i | ||||
\(157\) | −6.92820 | − | 4.00000i | −0.552931 | − | 0.319235i | 0.197372 | − | 0.980329i | \(-0.436759\pi\) |
−0.750303 | + | 0.661094i | \(0.770093\pi\) | |||||||
\(158\) | −12.1244 | − | 7.00000i | −0.964562 | − | 0.556890i | ||||
\(159\) | 9.00000 | − | 5.19615i | 0.713746 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 7.79423 | + | 4.50000i | 0.612372 | + | 0.353553i | ||||
\(163\) | 16.0000i | 1.25322i | 0.779334 | + | 0.626608i | \(0.215557\pi\) | ||||
−0.779334 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 15.5885 | + | 9.00000i | 1.20627 | + | 0.696441i | 0.961943 | − | 0.273252i | \(-0.0880992\pi\) |
0.244328 | + | 0.969693i | \(0.421432\pi\) | |||||||
\(168\) | 3.46410 | − | 6.00000i | 0.267261 | − | 0.462910i | ||||
\(169\) | 1.50000 | + | 2.59808i | 0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.50000 | − | 12.9904i | 0.573539 | − | 0.993399i | ||||
\(172\) | 11.0000i | 0.838742i | ||||||||
\(173\) | 15.5885 | − | 9.00000i | 1.18517 | − | 0.684257i | 0.227964 | − | 0.973670i | \(-0.426793\pi\) |
0.957205 | + | 0.289412i | \(0.0934598\pi\) | |||||||
\(174\) | − | 10.3923i | − | 0.787839i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | −5.19615 | −0.390567 | ||||||||
\(178\) | 5.19615 | − | 3.00000i | 0.389468 | − | 0.224860i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | −13.8564 | + | 8.00000i | −1.02711 | + | 0.592999i | ||||
\(183\) | −8.66025 | + | 15.0000i | −0.640184 | + | 1.10883i | ||||
\(184\) | −3.00000 | + | 5.19615i | −0.221163 | + | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.00000 | − | 1.73205i | 0.219971 | − | 0.127000i | ||||
\(187\) | 7.79423 | − | 4.50000i | 0.569970 | − | 0.329073i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.0000 | − | 10.3923i | 1.30931 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | −0.866025 | − | 1.50000i | −0.0625000 | − | 0.108253i | ||||
\(193\) | −11.2583 | − | 6.50000i | −0.810392 | − | 0.467880i | 0.0366998 | − | 0.999326i | \(-0.488315\pi\) |
−0.847092 | + | 0.531446i | \(0.821649\pi\) | |||||||
\(194\) | −5.50000 | + | 9.52628i | −0.394877 | + | 0.683947i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | − | 7.79423i | −0.321429 | − | 0.556731i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −7.79423 | + | 4.50000i | −0.553912 | + | 0.319801i | ||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | −10.3923 | − | 6.00000i | −0.731200 | − | 0.422159i | ||||
\(203\) | −20.7846 | − | 12.0000i | −1.45879 | − | 0.842235i | ||||
\(204\) | 5.19615i | 0.363803i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | −15.5885 | + | 9.00000i | −1.08347 | + | 0.625543i | ||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 7.50000 | + | 12.9904i | 0.518786 | + | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | −5.19615 | − | 3.00000i | −0.356873 | − | 0.206041i | ||||
\(213\) | 5.19615 | + | 9.00000i | 0.356034 | + | 0.616670i | ||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | − | 8.00000i | − | 0.543075i | ||||||
\(218\) | −3.46410 | + | 2.00000i | −0.234619 | + | 0.135457i | ||||
\(219\) | −10.5000 | + | 6.06218i | −0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | −3.46410 | + | 6.00000i | −0.232495 | + | 0.402694i | ||||
\(223\) | 19.0526 | − | 11.0000i | 1.27585 | − | 0.736614i | 0.299770 | − | 0.954011i | \(-0.403090\pi\) |
0.976083 | + | 0.217397i | \(0.0697566\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −2.59808 | + | 1.50000i | −0.172440 | + | 0.0995585i | −0.583736 | − | 0.811943i | \(-0.698410\pi\) |
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(228\) | −8.66025 | −0.573539 | ||||||||
\(229\) | 10.0000 | − | 17.3205i | 0.660819 | − | 1.14457i | −0.319582 | − | 0.947559i | \(-0.603543\pi\) |
0.980401 | − | 0.197013i | \(-0.0631241\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.7846i | 1.36753i | ||||||||
\(232\) | −5.19615 | + | 3.00000i | −0.341144 | + | 0.196960i | ||||
\(233\) | − | 21.0000i | − | 1.37576i | −0.725826 | − | 0.687878i | \(-0.758542\pi\) | ||
0.725826 | − | 0.687878i | \(-0.241458\pi\) | |||||||
\(234\) | −6.00000 | + | 10.3923i | −0.392232 | + | 0.679366i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50000 | + | 2.59808i | 0.0976417 | + | 0.169120i | ||||
\(237\) | −12.1244 | + | 21.0000i | −0.787562 | + | 1.36410i | ||||
\(238\) | 10.3923 | + | 6.00000i | 0.673633 | + | 0.388922i | ||||
\(239\) | 3.00000 | − | 5.19615i | 0.194054 | − | 0.336111i | −0.752536 | − | 0.658551i | \(-0.771170\pi\) |
0.946590 | + | 0.322440i | \(0.104503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.50000 | + | 2.59808i | −0.286910 | + | 0.165647i | ||||
\(247\) | 17.3205 | + | 10.0000i | 1.10208 | + | 0.636285i | ||||
\(248\) | −1.73205 | − | 1.00000i | −0.109985 | − | 0.0635001i | ||||
\(249\) | −18.0000 | − | 10.3923i | −1.14070 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(252\) | −10.3923 | − | 6.00000i | −0.654654 | − | 0.377964i | ||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | −1.00000 | − | 1.73205i | −0.0627456 | − | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.79423 | − | 4.50000i | −0.486191 | − | 0.280702i | 0.236802 | − | 0.971558i | \(-0.423901\pi\) |
−0.722993 | + | 0.690856i | \(0.757234\pi\) | |||||||
\(258\) | 19.0526 | 1.18616 | ||||||||
\(259\) | 8.00000 | + | 13.8564i | 0.497096 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0000 | −1.11417 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | −20.7846 | + | 12.0000i | −1.28163 | + | 0.739952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.304487 | + | 0.952517i | \(0.598485\pi\) | |||||||
\(264\) | 4.50000 | + | 2.59808i | 0.276956 | + | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.0000 | + | 17.3205i | −0.613139 | + | 1.06199i | ||||
\(267\) | −5.19615 | − | 9.00000i | −0.317999 | − | 0.550791i | ||||
\(268\) | −4.33013 | + | 2.50000i | −0.264505 | + | 0.152712i | ||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 2.59808 | − | 1.50000i | 0.157532 | − | 0.0909509i | ||||
\(273\) | 13.8564 | + | 24.0000i | 0.838628 | + | 1.45255i | ||||
\(274\) | 4.50000 | − | 7.79423i | 0.271855 | − | 0.470867i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | + | 5.19615i | 0.541736 | + | 0.312772i | ||||
\(277\) | −19.0526 | + | 11.0000i | −1.14476 | + | 0.660926i | −0.947604 | − | 0.319447i | \(-0.896503\pi\) |
−0.197153 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(278\) | − | 1.00000i | − | 0.0599760i | ||||||
\(279\) | −3.00000 | − | 5.19615i | −0.179605 | − | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3205 | + | 10.0000i | 1.02960 | + | 0.594438i | 0.916869 | − | 0.399188i | \(-0.130708\pi\) |
0.112728 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 12.0000i | 0.708338i | ||||||||
\(288\) | −2.59808 | + | 1.50000i | −0.153093 | + | 0.0883883i | ||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5000 | + | 9.52628i | 0.967247 | + | 0.558440i | ||||
\(292\) | 6.06218 | + | 3.50000i | 0.354762 | + | 0.204822i | ||||
\(293\) | −15.5885 | − | 9.00000i | −0.910687 | − | 0.525786i | −0.0300351 | − | 0.999549i | \(-0.509562\pi\) |
−0.880652 | + | 0.473763i | \(0.842895\pi\) | |||||||
\(294\) | −13.5000 | + | 7.79423i | −0.787336 | + | 0.454569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 7.79423 | + | 13.5000i | 0.452267 | + | 0.783349i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | − | 38.1051i | 1.26806 | − | 2.19634i | ||||
\(302\) | −8.66025 | − | 5.00000i | −0.498342 | − | 0.287718i | ||||
\(303\) | −10.3923 | + | 18.0000i | −0.597022 | + | 1.03407i | ||||
\(304\) | 2.50000 | + | 4.33013i | 0.143385 | + | 0.248350i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.00000 | 0.514496 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | 10.3923 | − | 6.00000i | 0.592157 | − | 0.341882i | ||||
\(309\) | − | 6.92820i | − | 0.394132i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 6.92820 | 0.392232 | ||||||||
\(313\) | 0.866025 | − | 0.500000i | 0.0489506 | − | 0.0282617i | −0.475325 | − | 0.879810i | \(-0.657669\pi\) |
0.524276 | + | 0.851549i | \(0.324336\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | 20.7846 | − | 12.0000i | 1.16738 | − | 0.673987i | 0.214318 | − | 0.976764i | \(-0.431247\pi\) |
0.953062 | + | 0.302777i | \(0.0979136\pi\) | |||||||
\(318\) | −5.19615 | + | 9.00000i | −0.291386 | + | 0.504695i | ||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | − | 7.79423i | 0.753497 | − | 0.435031i | ||||
\(322\) | 20.7846 | − | 12.0000i | 1.15828 | − | 0.668734i | ||||
\(323\) | − | 15.0000i | − | 0.834622i | ||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.00000 | − | 13.8564i | −0.443079 | − | 0.767435i | ||||
\(327\) | 3.46410 | + | 6.00000i | 0.191565 | + | 0.331801i | ||||
\(328\) | 2.59808 | + | 1.50000i | 0.143455 | + | 0.0828236i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | 10.3923 | + | 6.00000i | 0.569495 | + | 0.328798i | ||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.92820i | 0.377964i | ||||||||
\(337\) | 26.8468 | + | 15.5000i | 1.46244 | + | 0.844339i | 0.999124 | − | 0.0418554i | \(-0.0133269\pi\) |
0.463314 | + | 0.886194i | \(0.346660\pi\) | |||||||
\(338\) | −2.59808 | − | 1.50000i | −0.141317 | − | 0.0815892i | ||||
\(339\) | 31.1769i | 1.69330i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 15.0000i | 0.811107i | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | −5.50000 | − | 9.52628i | −0.296540 | − | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 15.5885i | −0.483843 | + | 0.838041i | ||||
\(347\) | −18.1865 | − | 10.5000i | −0.976304 | − | 0.563670i | −0.0751519 | − | 0.997172i | \(-0.523944\pi\) |
−0.901152 | + | 0.433503i | \(0.857278\pi\) | |||||||
\(348\) | 5.19615 | + | 9.00000i | 0.278543 | + | 0.482451i | ||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | + | 10.3923i | 0.960769 | + | 0.554700i | ||||
\(352\) | − | 3.00000i | − | 0.159901i | ||||||
\(353\) | −7.79423 | + | 4.50000i | −0.414845 | + | 0.239511i | −0.692869 | − | 0.721063i | \(-0.743654\pi\) |
0.278024 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(354\) | 4.50000 | − | 2.59808i | 0.239172 | − | 0.138086i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.00000 | + | 5.19615i | −0.159000 | + | 0.275396i | ||||
\(357\) | 10.3923 | − | 18.0000i | 0.550019 | − | 0.952661i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 13.8564 | − | 8.00000i | 0.728277 | − | 0.420471i | ||||
\(363\) | 3.46410 | 0.181818 | ||||||||
\(364\) | 8.00000 | − | 13.8564i | 0.419314 | − | 0.726273i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 17.3205i | − | 0.905357i | ||||||
\(367\) | 6.92820 | − | 4.00000i | 0.361649 | − | 0.208798i | −0.308155 | − | 0.951336i | \(-0.599711\pi\) |
0.669804 | + | 0.742538i | \(0.266378\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 4.50000 | + | 7.79423i | 0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 20.7846i | 0.623009 | + | 1.07908i | ||||
\(372\) | −1.73205 | + | 3.00000i | −0.0898027 | + | 0.155543i | ||||
\(373\) | −8.66025 | − | 5.00000i | −0.448411 | − | 0.258890i | 0.258748 | − | 0.965945i | \(-0.416690\pi\) |
−0.707159 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(374\) | −4.50000 | + | 7.79423i | −0.232689 | + | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | −10.3923 | + | 18.0000i | −0.534522 | + | 0.925820i | ||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | + | 1.73205i | −0.153695 | + | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3923 | + | 6.00000i | 0.531022 | + | 0.306586i | 0.741433 | − | 0.671027i | \(-0.234147\pi\) |
−0.210411 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.0000 | 0.661683 | ||||||||
\(387\) | − | 33.0000i | − | 1.67748i | ||||||
\(388\) | − | 11.0000i | − | 0.558440i | ||||||
\(389\) | 18.0000 | + | 31.1769i | 0.912636 | + | 1.58073i | 0.810326 | + | 0.585980i | \(0.199290\pi\) |
0.102311 | + | 0.994753i | \(0.467376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | 7.79423 | + | 4.50000i | 0.393668 | + | 0.227284i | ||||
\(393\) | −20.7846 | −1.04844 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.50000 | − | 7.79423i | 0.226134 | − | 0.391675i | ||||
\(397\) | 8.00000i | 0.401508i | 0.979642 | + | 0.200754i | \(0.0643393\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(398\) | 17.3205 | − | 10.0000i | 0.868199 | − | 0.501255i | ||||
\(399\) | 30.0000 | + | 17.3205i | 1.50188 | + | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5000 | + | 28.5788i | −0.823971 | + | 1.42716i | 0.0787327 | + | 0.996896i | \(0.474913\pi\) |
−0.902703 | + | 0.430263i | \(0.858421\pi\) | |||||||
\(402\) | 4.33013 | + | 7.50000i | 0.215967 | + | 0.374066i | ||||
\(403\) | 6.92820 | − | 4.00000i | 0.345118 | − | 0.199254i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | −10.3923 | + | 6.00000i | −0.515127 | + | 0.297409i | ||||
\(408\) | −2.59808 | − | 4.50000i | −0.128624 | − | 0.222783i | ||||
\(409\) | −15.5000 | + | 26.8468i | −0.766426 | + | 1.32749i | 0.173064 | + | 0.984911i | \(0.444633\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.5000 | − | 7.79423i | −0.665906 | − | 0.384461i | ||||
\(412\) | −3.46410 | + | 2.00000i | −0.170664 | + | 0.0985329i | ||||
\(413\) | − | 12.0000i | − | 0.590481i | ||||||
\(414\) | 9.00000 | − | 15.5885i | 0.442326 | − | 0.766131i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | −1.73205 | −0.0848189 | ||||||||
\(418\) | −12.9904 | − | 7.50000i | −0.635380 | − | 0.366837i | ||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | − | 1.73205i | −0.0487370 | − | 0.0844150i | 0.840628 | − | 0.541613i | \(-0.182186\pi\) |
−0.889365 | + | 0.457198i | \(0.848853\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.00000 | − | 5.19615i | −0.436051 | − | 0.251754i | ||||
\(427\) | −34.6410 | − | 20.0000i | −1.67640 | − | 0.967868i | ||||
\(428\) | −7.79423 | − | 4.50000i | −0.376748 | − | 0.217516i | ||||
\(429\) | −18.0000 | + | 10.3923i | −0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 2.59808 | + | 4.50000i | 0.125000 | + | 0.216506i | ||||
\(433\) | 13.0000i | 0.624740i | 0.949960 | + | 0.312370i | \(0.101123\pi\) | ||||
−0.949960 | + | 0.312370i | \(0.898877\pi\) | |||||||
\(434\) | 4.00000 | + | 6.92820i | 0.192006 | + | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | − | 3.46410i | 0.0957826 | − | 0.165900i | ||||
\(437\) | −25.9808 | − | 15.0000i | −1.24283 | − | 0.717547i | ||||
\(438\) | 6.06218 | − | 10.5000i | 0.289662 | − | 0.501709i | ||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | 12.0000i | 0.570782i | ||||||||
\(443\) | −2.59808 | + | 1.50000i | −0.123438 | + | 0.0712672i | −0.560448 | − | 0.828190i | \(-0.689371\pi\) |
0.437009 | + | 0.899457i | \(0.356038\pi\) | |||||||
\(444\) | − | 6.92820i | − | 0.328798i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.0000 | + | 19.0526i | −0.520865 | + | 0.902165i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.46410 | − | 2.00000i | 0.163663 | − | 0.0944911i | ||||
\(449\) | 15.0000 | 0.707894 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | −8.66025 | + | 15.0000i | −0.406894 | + | 0.704761i | ||||
\(454\) | 1.50000 | − | 2.59808i | 0.0703985 | − | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.50000 | − | 4.33013i | 0.351220 | − | 0.202777i | ||||
\(457\) | −0.866025 | + | 0.500000i | −0.0405110 | + | 0.0233890i | −0.520119 | − | 0.854094i | \(-0.674112\pi\) |
0.479608 | + | 0.877483i | \(0.340779\pi\) | |||||||
\(458\) | 20.0000i | 0.934539i | ||||||||
\(459\) | − | 15.5885i | − | 0.727607i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | −10.3923 | − | 18.0000i | −0.483494 | − | 0.837436i | ||||
\(463\) | 17.3205 | + | 10.0000i | 0.804952 | + | 0.464739i | 0.845200 | − | 0.534450i | \(-0.179481\pi\) |
−0.0402476 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | + | 18.1865i | 0.486403 | + | 0.842475i | ||||
\(467\) | 21.0000i | 0.971764i | 0.874024 | + | 0.485882i | \(0.161502\pi\) | ||||
−0.874024 | + | 0.485882i | \(0.838498\pi\) | |||||||
\(468\) | − | 12.0000i | − | 0.554700i | ||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 13.8564i | − | 0.638470i | ||||||
\(472\) | −2.59808 | − | 1.50000i | −0.119586 | − | 0.0690431i | ||||
\(473\) | 28.5788 | + | 16.5000i | 1.31406 | + | 0.758671i | ||||
\(474\) | − | 24.2487i | − | 1.11378i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 15.5885 | + | 9.00000i | 0.713746 | + | 0.412082i | ||||
\(478\) | 6.00000i | 0.274434i | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 14.7224 | + | 8.50000i | 0.670588 | + | 0.387164i | ||||
\(483\) | −20.7846 | − | 36.0000i | −0.945732 | − | 1.63806i | ||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.5885i | 0.707107i | ||||||||
\(487\) | 2.00000i | 0.0906287i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) | ||||
−0.998973 | + | 0.0453143i | \(0.985571\pi\) | |||||||
\(488\) | −8.66025 | + | 5.00000i | −0.392031 | + | 0.226339i | ||||
\(489\) | −24.0000 | + | 13.8564i | −1.08532 | + | 0.626608i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5000 | − | 28.5788i | 0.744635 | − | 1.28974i | −0.205731 | − | 0.978609i | \(-0.565957\pi\) |
0.950365 | − | 0.311136i | \(-0.100710\pi\) | |||||||
\(492\) | 2.59808 | − | 4.50000i | 0.117130 | − | 0.202876i | ||||
\(493\) | −15.5885 | + | 9.00000i | −0.702069 | + | 0.405340i | ||||
\(494\) | −20.0000 | −0.899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −20.7846 | + | 12.0000i | −0.932317 | + | 0.538274i | ||||
\(498\) | 20.7846 | 0.931381 | ||||||||
\(499\) | −15.5000 | + | 26.8468i | −0.693875 | + | 1.20183i | 0.276683 | + | 0.960961i | \(0.410765\pi\) |
−0.970558 | + | 0.240866i | \(0.922569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1769i | 1.39288i | ||||||||
\(502\) | 18.1865 | − | 10.5000i | 0.811705 | − | 0.468638i | ||||
\(503\) | − | 6.00000i | − | 0.267527i | −0.991013 | − | 0.133763i | \(-0.957294\pi\) | ||
0.991013 | − | 0.133763i | \(-0.0427062\pi\) | |||||||
\(504\) | 12.0000 | 0.534522 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | + | 15.5885i | 0.400099 | + | 0.692991i | ||||
\(507\) | −2.59808 | + | 4.50000i | −0.115385 | + | 0.199852i | ||||
\(508\) | 1.73205 | + | 1.00000i | 0.0768473 | + | 0.0443678i | ||||
\(509\) | −6.00000 | + | 10.3923i | −0.265945 | + | 0.460631i | −0.967811 | − | 0.251679i | \(-0.919017\pi\) |
0.701866 | + | 0.712309i | \(0.252351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | − | 24.2487i | −0.619324 | − | 1.07270i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 25.9808 | 1.14708 | ||||||||
\(514\) | 9.00000 | 0.396973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.5000 | + | 9.52628i | −0.726372 | + | 0.419371i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.8564 | − | 8.00000i | −0.608816 | − | 0.351500i | ||||
\(519\) | 27.0000 | + | 15.5885i | 1.18517 | + | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 15.5885 | − | 9.00000i | 0.682288 | − | 0.393919i | ||||
\(523\) | − | 20.0000i | − | 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | − | 20.7846i | 0.523225 | − | 0.906252i | ||||
\(527\) | −5.19615 | − | 3.00000i | −0.226348 | − | 0.130682i | ||||
\(528\) | −5.19615 | −0.226134 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.50000 | − | 7.79423i | −0.195283 | − | 0.338241i | ||||
\(532\) | − | 20.0000i | − | 0.867110i | ||||||
\(533\) | −10.3923 | + | 6.00000i | −0.450141 | + | 0.259889i | ||||
\(534\) | 9.00000 | + | 5.19615i | 0.389468 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.50000 | − | 4.33013i | 0.107984 | − | 0.187033i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.19615 | − | 3.00000i | 0.224022 | − | 0.129339i | ||||
\(539\) | −27.0000 | −1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 13.8564 | − | 8.00000i | 0.595184 | − | 0.343629i | ||||
\(543\) | −13.8564 | − | 24.0000i | −0.594635 | − | 1.02994i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −24.0000 | − | 13.8564i | −1.02711 | − | 0.592999i | ||||
\(547\) | −0.866025 | + | 0.500000i | −0.0370286 | + | 0.0213785i | −0.518400 | − | 0.855138i | \(-0.673472\pi\) |
0.481371 | + | 0.876517i | \(0.340139\pi\) | |||||||
\(548\) | 9.00000i | 0.384461i | ||||||||
\(549\) | −30.0000 | −1.28037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | −10.3923 | −0.442326 | ||||||||
\(553\) | −48.4974 | − | 28.0000i | −2.06232 | − | 1.19068i | ||||
\(554\) | 11.0000 | − | 19.0526i | 0.467345 | − | 0.809466i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.500000 | + | 0.866025i | 0.0212047 | + | 0.0367277i | ||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 5.19615 | + | 3.00000i | 0.219971 | + | 0.127000i | ||||
\(559\) | 44.0000 | 1.86100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | −5.19615 | − | 3.00000i | −0.219186 | − | 0.126547i | ||||
\(563\) | −2.59808 | − | 1.50000i | −0.109496 | − | 0.0632175i | 0.444252 | − | 0.895902i | \(-0.353470\pi\) |
−0.553748 | + | 0.832684i | \(0.686803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 31.1769 | + | 18.0000i | 1.30931 | + | 0.755929i | ||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −19.5000 | − | 33.7750i | −0.817483 | − | 1.41592i | −0.907532 | − | 0.419984i | \(-0.862036\pi\) |
0.0900490 | − | 0.995937i | \(-0.471298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5000 | + | 25.1147i | −0.606806 | + | 1.05102i | 0.384957 | + | 0.922934i | \(0.374216\pi\) |
−0.991763 | + | 0.128085i | \(0.959117\pi\) | |||||||
\(572\) | 10.3923 | + | 6.00000i | 0.434524 | + | 0.250873i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | − | 10.3923i | −0.250435 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | − | 7.00000i | − | 0.291414i | −0.989328 | − | 0.145707i | \(-0.953454\pi\) | ||
0.989328 | − | 0.145707i | \(-0.0465456\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | − | 22.5167i | − | 0.935760i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | − | 41.5692i | 0.995688 | − | 1.72458i | ||||
\(582\) | −19.0526 | −0.789754 | ||||||||
\(583\) | −15.5885 | + | 9.00000i | −0.645608 | + | 0.372742i | ||||
\(584\) | −7.00000 | −0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | 0.743573 | ||||||||
\(587\) | 33.7750 | − | 19.5000i | 1.39404 | − | 0.804851i | 0.400283 | − | 0.916392i | \(-0.368912\pi\) |
0.993760 | + | 0.111540i | \(0.0355784\pi\) | |||||||
\(588\) | 7.79423 | − | 13.5000i | 0.321429 | − | 0.556731i | ||||
\(589\) | 5.00000 | − | 8.66025i | 0.206021 | − | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.46410 | + | 2.00000i | −0.142374 | + | 0.0821995i | ||||
\(593\) | 18.0000i | 0.739171i | 0.929197 | + | 0.369586i | \(0.120500\pi\) | ||||
−0.929197 | + | 0.369586i | \(0.879500\pi\) | |||||||
\(594\) | −13.5000 | − | 7.79423i | −0.553912 | − | 0.319801i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.3205 | − | 30.0000i | −0.708881 | − | 1.22782i | ||||
\(598\) | 20.7846 | + | 12.0000i | 0.849946 | + | 0.490716i | ||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | + | 21.6506i | 0.509886 | + | 0.883148i | 0.999934 | + | 0.0114528i | \(0.00364562\pi\) |
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(602\) | 44.0000i | 1.79331i | ||||||||
\(603\) | 12.9904 | − | 7.50000i | 0.529009 | − | 0.305424i | ||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 20.7846i | − | 0.844317i | ||||||
\(607\) | −6.92820 | − | 4.00000i | −0.281207 | − | 0.162355i | 0.352763 | − | 0.935713i | \(-0.385242\pi\) |
−0.633970 | + | 0.773358i | \(0.718576\pi\) | |||||||
\(608\) | −4.33013 | − | 2.50000i | −0.175610 | − | 0.101388i | ||||
\(609\) | − | 41.5692i | − | 1.68447i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.79423 | + | 4.50000i | −0.315063 | + | 0.181902i | ||||
\(613\) | − | 2.00000i | − | 0.0807792i | −0.999184 | − | 0.0403896i | \(-0.987140\pi\) | ||
0.999184 | − | 0.0403896i | \(-0.0128599\pi\) | |||||||
\(614\) | 3.50000 | + | 6.06218i | 0.141249 | + | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | + | 10.3923i | −0.241747 | + | 0.418718i | ||||
\(617\) | 33.7750 | + | 19.5000i | 1.35973 | + | 0.785040i | 0.989587 | − | 0.143934i | \(-0.0459755\pi\) |
0.370143 | + | 0.928975i | \(0.379309\pi\) | |||||||
\(618\) | 3.46410 | + | 6.00000i | 0.139347 | + | 0.241355i | ||||
\(619\) | −9.50000 | − | 16.4545i | −0.381837 | − | 0.661361i | 0.609488 | − | 0.792796i | \(-0.291375\pi\) |
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | − | 15.5885i | −1.08347 | − | 0.625543i | ||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | 20.7846 | − | 12.0000i | 0.832718 | − | 0.480770i | ||||
\(624\) | −6.00000 | + | 3.46410i | −0.240192 | + | 0.138675i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.500000 | + | 0.866025i | −0.0199840 | + | 0.0346133i | ||||
\(627\) | −12.9904 | + | 22.5000i | −0.518786 | + | 0.898563i | ||||
\(628\) | −6.92820 | + | 4.00000i | −0.276465 | + | 0.159617i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | −12.1244 | + | 7.00000i | −0.482281 | + | 0.278445i | ||||
\(633\) | 6.92820 | 0.275371 | ||||||||
\(634\) | −12.0000 | + | 20.7846i | −0.476581 | + | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 10.3923i | − | 0.412082i | ||||||
\(637\) | −31.1769 | + | 18.0000i | −1.23527 | + | 0.713186i | ||||
\(638\) | 18.0000i | 0.712627i | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | − | 7.79423i | −0.177739 | − | 0.307854i | 0.763367 | − | 0.645966i | \(-0.223545\pi\) |
−0.941106 | + | 0.338112i | \(0.890212\pi\) | |||||||
\(642\) | −7.79423 | + | 13.5000i | −0.307614 | + | 0.532803i | ||||
\(643\) | 19.9186 | + | 11.5000i | 0.785512 | + | 0.453516i | 0.838380 | − | 0.545086i | \(-0.183503\pi\) |
−0.0528680 | + | 0.998602i | \(0.516836\pi\) | |||||||
\(644\) | −12.0000 | + | 20.7846i | −0.472866 | + | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.50000 | + | 12.9904i | 0.295084 | + | 0.511100i | ||||
\(647\) | 6.00000i | 0.235884i | 0.993020 | + | 0.117942i | \(0.0376297\pi\) | ||||
−0.993020 | + | 0.117942i | \(0.962370\pi\) | |||||||
\(648\) | 7.79423 | − | 4.50000i | 0.306186 | − | 0.176777i | ||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | − | 6.92820i | 0.470317 | − | 0.271538i | ||||
\(652\) | 13.8564 | + | 8.00000i | 0.542659 | + | 0.313304i | ||||
\(653\) | 36.3731 | + | 21.0000i | 1.42339 | + | 0.821794i | 0.996587 | − | 0.0825519i | \(-0.0263070\pi\) |
0.426801 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(654\) | −6.00000 | − | 3.46410i | −0.234619 | − | 0.135457i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | −18.1865 | − | 10.5000i | −0.709524 | − | 0.409644i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | − | 31.1769i | −0.701180 | − | 1.21448i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) |
0.266872 | − | 0.963732i | \(-0.414010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | −3.46410 | − | 2.00000i | −0.134636 | − | 0.0777322i | ||||
\(663\) | 20.7846 | 0.807207 | ||||||||
\(664\) | −6.00000 | − | 10.3923i | −0.232845 | − | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0000 | −0.464991 | ||||||||
\(667\) | 36.0000i | 1.39393i | ||||||||
\(668\) | 15.5885 | − | 9.00000i | 0.603136 | − | 0.348220i | ||||
\(669\) | 33.0000 | + | 19.0526i | 1.27585 | + | 0.736614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0000 | − | 25.9808i | 0.579069 | − | 1.00298i | ||||
\(672\) | −3.46410 | − | 6.00000i | −0.133631 | − | 0.231455i | ||||
\(673\) | −12.1244 | + | 7.00000i | −0.467360 | + | 0.269830i | −0.715134 | − | 0.698988i | \(-0.753634\pi\) |
0.247774 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(674\) | −31.0000 | −1.19408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −31.1769 | + | 18.0000i | −1.19823 | + | 0.691796i | −0.960159 | − | 0.279453i | \(-0.909847\pi\) |
−0.238067 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(678\) | −15.5885 | − | 27.0000i | −0.598671 | − | 1.03693i | ||||
\(679\) | −22.0000 | + | 38.1051i | −0.844283 | + | 1.46234i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | −5.19615 | + | 3.00000i | −0.198971 | + | 0.114876i | ||||
\(683\) | 21.0000i | 0.803543i | 0.915740 | + | 0.401771i | \(0.131605\pi\) | ||||
−0.915740 | + | 0.401771i | \(0.868395\pi\) | |||||||
\(684\) | −7.50000 | − | 12.9904i | −0.286770 | − | 0.496700i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.00000 | − | 6.92820i | −0.152721 | − | 0.264520i | ||||
\(687\) | 34.6410 | 1.32164 | ||||||||
\(688\) | 9.52628 | + | 5.50000i | 0.363186 | + | 0.209686i | ||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | −31.1769 | + | 18.0000i | −1.18431 | + | 0.683763i | ||||
\(694\) | 21.0000 | 0.797149 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.00000 | − | 5.19615i | −0.341144 | − | 0.196960i | ||||
\(697\) | 7.79423 | + | 4.50000i | 0.295227 | + | 0.170450i | ||||
\(698\) | 13.8564 | + | 8.00000i | 0.524473 | + | 0.302804i | ||||
\(699\) | 31.5000 | − | 18.1865i | 1.19144 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | −20.7846 | −0.784465 | ||||||||
\(703\) | 20.0000i | 0.754314i | ||||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.50000 | − | 7.79423i | 0.169360 | − | 0.293340i | ||||
\(707\) | −41.5692 | − | 24.0000i | −1.56337 | − | 0.902613i | ||||
\(708\) | −2.59808 | + | 4.50000i | −0.0976417 | + | 0.169120i | ||||
\(709\) | −17.0000 | − | 29.4449i | −0.638448 | − | 1.10583i | −0.985773 | − | 0.168080i | \(-0.946243\pi\) |
0.347325 | − | 0.937745i | \(-0.387090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.0000 | −1.57512 | ||||||||
\(712\) | − | 6.00000i | − | 0.224860i | ||||||
\(713\) | −10.3923 | + | 6.00000i | −0.389195 | + | 0.224702i | ||||
\(714\) | 20.7846i | 0.777844i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3923 | 0.388108 | ||||||||
\(718\) | −20.7846 | + | 12.0000i | −0.775675 | + | 0.447836i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | −5.19615 | + | 3.00000i | −0.193381 | + | 0.111648i | ||||
\(723\) | 14.7224 | − | 25.5000i | 0.547533 | − | 0.948355i | ||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.00000 | + | 1.73205i | −0.111340 | + | 0.0642824i | ||||
\(727\) | −24.2487 | + | 14.0000i | −0.899335 | + | 0.519231i | −0.876984 | − | 0.480519i | \(-0.840448\pi\) |
−0.0223506 | + | 0.999750i | \(0.507115\pi\) | |||||||
\(728\) | 16.0000i | 0.592999i | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.5000 | − | 28.5788i | −0.610275 | − | 1.05703i | ||||
\(732\) | 8.66025 | + | 15.0000i | 0.320092 | + | 0.554416i | ||||
\(733\) | 27.7128 | + | 16.0000i | 1.02360 | + | 0.590973i | 0.915144 | − | 0.403128i | \(-0.132077\pi\) |
0.108453 | + | 0.994102i | \(0.465410\pi\) | |||||||
\(734\) | −4.00000 | + | 6.92820i | −0.147643 | + | 0.255725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 15.0000i | 0.552532i | ||||||||
\(738\) | −7.79423 | − | 4.50000i | −0.286910 | − | 0.165647i | ||||
\(739\) | −29.0000 | −1.06678 | −0.533391 | − | 0.845869i | \(-0.679083\pi\) | ||||
−0.533391 | + | 0.845869i | \(0.679083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.6410i | 1.27257i | ||||||||
\(742\) | −20.7846 | − | 12.0000i | −0.763027 | − | 0.440534i | ||||
\(743\) | −5.19615 | − | 3.00000i | −0.190628 | − | 0.110059i | 0.401648 | − | 0.915794i | \(-0.368437\pi\) |
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(744\) | − | 3.46410i | − | 0.127000i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | − | 36.0000i | − | 1.31717i | ||||||
\(748\) | − | 9.00000i | − | 0.329073i | ||||||
\(749\) | 18.0000 | + | 31.1769i | 0.657706 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.1865 | − | 31.5000i | −0.662754 | − | 1.14792i | ||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 20.7846i | − | 0.755929i | ||||||
\(757\) | 38.0000i | 1.38113i | 0.723269 | + | 0.690567i | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | 25.1147 | − | 14.5000i | 0.912208 | − | 0.526664i | ||||
\(759\) | 27.0000 | − | 15.5885i | 0.980038 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 1.73205 | − | 3.00000i | 0.0627456 | − | 0.108679i | ||||
\(763\) | −13.8564 | + | 8.00000i | −0.501636 | + | 0.289619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | 10.3923 | − | 6.00000i | 0.375244 | − | 0.216647i | ||||
\(768\) | −1.73205 | −0.0625000 | ||||||||
\(769\) | 25.0000 | − | 43.3013i | 0.901523 | − | 1.56148i | 0.0760054 | − | 0.997107i | \(-0.475783\pi\) |
0.825518 | − | 0.564376i | \(-0.190883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.5885i | − | 0.561405i | ||||||
\(772\) | −11.2583 | + | 6.50000i | −0.405196 | + | 0.233940i | ||||
\(773\) | 30.0000i | 1.07903i | 0.841978 | + | 0.539513i | \(0.181391\pi\) | ||||
−0.841978 | + | 0.539513i | \(0.818609\pi\) | |||||||
\(774\) | 16.5000 | + | 28.5788i | 0.593080 | + | 1.02725i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.50000 | + | 9.52628i | 0.197438 | + | 0.341974i | ||||
\(777\) | −13.8564 | + | 24.0000i | −0.497096 | + | 0.860995i | ||||
\(778\) | −31.1769 | − | 18.0000i | −1.11775 | − | 0.645331i | ||||
\(779\) | −7.50000 | + | 12.9904i | −0.268715 | + | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | − | 18.0000i | − | 0.643679i | ||||||
\(783\) | −15.5885 | − | 27.0000i | −0.557086 | − | 0.964901i | ||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0000 | − | 10.3923i | 0.642039 | − | 0.370681i | ||||
\(787\) | 3.46410 | + | 2.00000i | 0.123482 | + | 0.0712923i | 0.560469 | − | 0.828176i | \(-0.310621\pi\) |
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.0000 | − | 20.7846i | −1.28163 | − | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.0000 | −2.56003 | ||||||||
\(792\) | 9.00000i | 0.319801i | ||||||||
\(793\) | − | 40.0000i | − | 1.42044i | ||||||
\(794\) | −4.00000 | − | 6.92820i | −0.141955 | − | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | + | 17.3205i | −0.354441 | + | 0.613909i | ||||
\(797\) | 41.5692 | + | 24.0000i | 1.47246 | + | 0.850124i | 0.999520 | − | 0.0309726i | \(-0.00986046\pi\) |
0.472937 | + | 0.881096i | \(0.343194\pi\) | |||||||
\(798\) | −34.6410 | −1.22628 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00000 | − | 15.5885i | 0.317999 | − | 0.550791i | ||||
\(802\) | − | 33.0000i | − | 1.16527i | ||||||
\(803\) | 18.1865 | − | 10.5000i | 0.641789 | − | 0.370537i | ||||
\(804\) | −7.50000 | − | 4.33013i | −0.264505 | − | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | + | 6.92820i | −0.140894 | + | 0.244036i | ||||
\(807\) | −5.19615 | − | 9.00000i | −0.182913 | − | 0.316815i | ||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | 39.0000 | 1.37117 | 0.685583 | − | 0.727994i | \(-0.259547\pi\) | ||||
0.685583 | + | 0.727994i | \(0.259547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | −20.7846 | + | 12.0000i | −0.729397 | + | 0.421117i | ||||
\(813\) | −13.8564 | − | 24.0000i | −0.485965 | − | 0.841717i | ||||
\(814\) | 6.00000 | − | 10.3923i | 0.210300 | − | 0.364250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.50000 | + | 2.59808i | 0.157532 | + | 0.0909509i | ||||
\(817\) | 47.6314 | − | 27.5000i | 1.66641 | − | 0.962103i | ||||
\(818\) | − | 31.0000i | − | 1.08389i | ||||||
\(819\) | −24.0000 | + | 41.5692i | −0.838628 | + | 1.45255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0000 | + | 41.5692i | 0.837606 | + | 1.45078i | 0.891891 | + | 0.452250i | \(0.149379\pi\) |
−0.0542853 | + | 0.998525i | \(0.517288\pi\) | |||||||
\(822\) | 15.5885 | 0.543710 | ||||||||
\(823\) | −3.46410 | − | 2.00000i | −0.120751 | − | 0.0697156i | 0.438408 | − | 0.898776i | \(-0.355543\pi\) |
−0.559159 | + | 0.829060i | \(0.688876\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | + | 10.3923i | 0.208767 | + | 0.361595i | ||||
\(827\) | − | 36.0000i | − | 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 18.0000i | 0.625543i | ||||||||
\(829\) | −44.0000 | −1.52818 | −0.764092 | − | 0.645108i | \(-0.776812\pi\) | ||||
−0.764092 | + | 0.645108i | \(0.776812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.0000 | − | 19.0526i | −1.14476 | − | 0.660926i | ||||
\(832\) | 3.46410 | + | 2.00000i | 0.120096 | + | 0.0693375i | ||||
\(833\) | 23.3827 | + | 13.5000i | 0.810162 | + | 0.467747i | ||||
\(834\) | 1.50000 | − | 0.866025i | 0.0519408 | − | 0.0299880i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.0000 | 0.518786 | ||||||||
\(837\) | 5.19615 | − | 9.00000i | 0.179605 | − | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0000 | − | 25.9808i | −0.517858 | − | 0.896956i | −0.999785 | − | 0.0207443i | \(-0.993396\pi\) |
0.481927 | − | 0.876211i | \(-0.339937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 1.73205 | + | 1.00000i | 0.0596904 | + | 0.0344623i | ||||
\(843\) | −5.19615 | + | 9.00000i | −0.178965 | + | 0.309976i | ||||
\(844\) | −2.00000 | − | 3.46410i | −0.0688428 | − | 0.119239i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00000i | 0.274883i | ||||||||
\(848\) | −5.19615 | + | 3.00000i | −0.178437 | + | 0.103020i | ||||
\(849\) | 34.6410i | 1.18888i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | − | 20.7846i | 0.411355 | − | 0.712487i | ||||
\(852\) | 10.3923 | 0.356034 | ||||||||
\(853\) | −38.1051 | + | 22.0000i | −1.30469 | + | 0.753266i | −0.981205 | − | 0.192966i | \(-0.938189\pi\) |
−0.323489 | + | 0.946232i | \(0.604856\pi\) | |||||||
\(854\) | 40.0000 | 1.36877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | 0.307614 | ||||||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 10.3923 | − | 18.0000i | 0.354787 | − | 0.614510i | ||||
\(859\) | −9.50000 | + | 16.4545i | −0.324136 | + | 0.561420i | −0.981337 | − | 0.192295i | \(-0.938407\pi\) |
0.657201 | + | 0.753715i | \(0.271740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.0000 | + | 10.3923i | −0.613438 | + | 0.354169i | ||||
\(862\) | −20.7846 | + | 12.0000i | −0.707927 | + | 0.408722i | ||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.50000 | − | 11.2583i | −0.220879 | − | 0.382574i | ||||
\(867\) | 6.92820 | + | 12.0000i | 0.235294 | + | 0.407541i | ||||
\(868\) | −6.92820 | − | 4.00000i | −0.235159 | − | 0.135769i | ||||
\(869\) | 21.0000 | − | 36.3731i | 0.712376 | − | 1.23387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | + | 17.3205i | 0.338837 | + | 0.586883i | ||||
\(872\) | 4.00000i | 0.135457i | ||||||||
\(873\) | 33.0000i | 1.11688i | ||||||||
\(874\) | 30.0000 | 1.01477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.1244i | 0.409644i | ||||||||
\(877\) | −1.73205 | − | 1.00000i | −0.0584872 | − | 0.0337676i | 0.470471 | − | 0.882415i | \(-0.344084\pi\) |
−0.528958 | + | 0.848648i | \(0.677417\pi\) | |||||||
\(878\) | 8.66025 | + | 5.00000i | 0.292269 | + | 0.168742i | ||||
\(879\) | − | 31.1769i | − | 1.05157i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | −23.3827 | − | 13.5000i | −0.787336 | − | 0.454569i | ||||
\(883\) | − | 41.0000i | − | 1.37976i | −0.723924 | − | 0.689880i | \(-0.757663\pi\) | ||
0.723924 | − | 0.689880i | \(-0.242337\pi\) | |||||||
\(884\) | −6.00000 | − | 10.3923i | −0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.50000 | − | 2.59808i | 0.0503935 | − | 0.0872841i | ||||
\(887\) | 36.3731 | + | 21.0000i | 1.22129 | + | 0.705111i | 0.965193 | − | 0.261540i | \(-0.0842305\pi\) |
0.256096 | + | 0.966651i | \(0.417564\pi\) | |||||||
\(888\) | 3.46410 | + | 6.00000i | 0.116248 | + | 0.201347i | ||||
\(889\) | −4.00000 | − | 6.92820i | −0.134156 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | − | 22.0000i | − | 0.736614i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | + | 3.46410i | −0.0668153 | + | 0.115728i | ||||
\(897\) | 20.7846 | − | 36.0000i | 0.693978 | − | 1.20201i | ||||
\(898\) | −12.9904 | + | 7.50000i | −0.433495 | + | 0.250278i | ||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 7.79423 | − | 4.50000i | 0.259519 | − | 0.149834i | ||||
\(903\) | 76.2102 | 2.53612 | ||||||||
\(904\) | −9.00000 | + | 15.5885i | −0.299336 | + | 0.518464i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 17.3205i | − | 0.575435i | ||||||
\(907\) | 4.33013 | − | 2.50000i | 0.143780 | − | 0.0830111i | −0.426385 | − | 0.904542i | \(-0.640213\pi\) |
0.570164 | + | 0.821531i | \(0.306880\pi\) | |||||||
\(908\) | 3.00000i | 0.0995585i | ||||||||
\(909\) | −36.0000 | −1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000 | + | 25.9808i | 0.496972 | + | 0.860781i | 0.999994 | − | 0.00349271i | \(-0.00111177\pi\) |
−0.503022 | + | 0.864274i | \(0.667778\pi\) | |||||||
\(912\) | −4.33013 | + | 7.50000i | −0.143385 | + | 0.248350i | ||||
\(913\) | 31.1769 | + | 18.0000i | 1.03181 | + | 0.595713i | ||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | − | 17.3205i | −0.330409 | − | 0.572286i | ||||
\(917\) | − | 48.0000i | − | 1.58510i | ||||||
\(918\) | 7.79423 | + | 13.5000i | 0.257248 | + | 0.445566i | ||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5000 | − | 6.06218i | 0.345987 | − | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7846 | − | 12.0000i | −0.684134 | − | 0.394985i | ||||
\(924\) | 18.0000 | + | 10.3923i | 0.592157 | + | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.0000 | −0.657241 | ||||||||
\(927\) | 10.3923 | − | 6.00000i | 0.341328 | − | 0.197066i | ||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5000 | + | 38.9711i | −0.737408 | + | 1.27723i | ||||
\(932\) | −18.1865 | − | 10.5000i | −0.595720 | − | 0.343939i | ||||
\(933\) | 10.3923 | 0.340229 | ||||||||
\(934\) | −10.5000 | − | 18.1865i | −0.343570 | − | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | + | 10.3923i | 0.196116 | + | 0.339683i | ||||
\(937\) | − | 10.0000i | − | 0.326686i | −0.986569 | − | 0.163343i | \(-0.947772\pi\) | ||
0.986569 | − | 0.163343i | \(-0.0522277\pi\) | |||||||
\(938\) | −17.3205 | + | 10.0000i | −0.565535 | + | 0.326512i | ||||
\(939\) | 1.50000 | + | 0.866025i | 0.0489506 | + | 0.0282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 6.92820 | + | 12.0000i | 0.225733 | + | 0.390981i | ||||
\(943\) | 15.5885 | − | 9.00000i | 0.507630 | − | 0.293080i | ||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.0000 | −1.07292 | ||||||||
\(947\) | 23.3827 | − | 13.5000i | 0.759835 | − | 0.438691i | −0.0694014 | − | 0.997589i | \(-0.522109\pi\) |
0.829237 | + | 0.558898i | \(0.188776\pi\) | |||||||
\(948\) | 12.1244 | + | 21.0000i | 0.393781 | + | 0.682048i | ||||
\(949\) | 14.0000 | − | 24.2487i | 0.454459 | − | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.0000 | + | 20.7846i | 1.16738 | + | 0.673987i | ||||
\(952\) | 10.3923 | − | 6.00000i | 0.336817 | − | 0.194461i | ||||
\(953\) | − | 51.0000i | − | 1.65205i | −0.563632 | − | 0.826026i | \(-0.690596\pi\) | ||
0.563632 | − | 0.826026i | \(-0.309404\pi\) | |||||||
\(954\) | −18.0000 | −0.582772 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | 31.1769 | 1.00781 | ||||||||
\(958\) | 5.19615 | + | 3.00000i | 0.167880 | + | 0.0969256i | ||||
\(959\) | 18.0000 | − | 31.1769i | 0.581250 | − | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | − | 16.0000i | − | 0.515861i | ||||||
\(963\) | 23.3827 | + | 13.5000i | 0.753497 | + | 0.435031i | ||||
\(964\) | −17.0000 | −0.547533 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 36.0000 | + | 20.7846i | 1.15828 | + | 0.668734i | ||||
\(967\) | 19.0526 | + | 11.0000i | 0.612689 | + | 0.353736i | 0.774017 | − | 0.633165i | \(-0.218244\pi\) |
−0.161328 | + | 0.986901i | \(0.551578\pi\) | |||||||
\(968\) | 1.73205 | + | 1.00000i | 0.0556702 | + | 0.0321412i | ||||
\(969\) | 22.5000 | − | 12.9904i | 0.722804 | − | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.0000 | 1.92549 | 0.962746 | − | 0.270408i | \(-0.0871586\pi\) | ||||
0.962746 | + | 0.270408i | \(0.0871586\pi\) | |||||||
\(972\) | −7.79423 | − | 13.5000i | −0.250000 | − | 0.433013i | ||||
\(973\) | − | 4.00000i | − | 0.128234i | ||||||
\(974\) | −1.00000 | − | 1.73205i | −0.0320421 | − | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000 | − | 8.66025i | 0.160046 | − | 0.277208i | ||||
\(977\) | 7.79423 | + | 4.50000i | 0.249359 | + | 0.143968i | 0.619471 | − | 0.785020i | \(-0.287347\pi\) |
−0.370111 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(978\) | 13.8564 | − | 24.0000i | 0.443079 | − | 0.767435i | ||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | + | 10.3923i | −0.191565 | + | 0.331801i | ||||
\(982\) | 33.0000i | 1.05307i | ||||||||
\(983\) | −31.1769 | + | 18.0000i | −0.994389 | + | 0.574111i | −0.906583 | − | 0.422027i | \(-0.861319\pi\) |
−0.0878058 | + | 0.996138i | \(0.527985\pi\) | |||||||
\(984\) | 5.19615i | 0.165647i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.3205 | − | 10.0000i | 0.551039 | − | 0.318142i | ||||
\(989\) | −66.0000 | −2.09868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −1.73205 | + | 1.00000i | −0.0549927 | + | 0.0317500i | ||||
\(993\) | −3.46410 | + | 6.00000i | −0.109930 | + | 0.190404i | ||||
\(994\) | 12.0000 | − | 20.7846i | 0.380617 | − | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.0000 | + | 10.3923i | −0.570352 | + | 0.329293i | ||||
\(997\) | 22.5167 | − | 13.0000i | 0.713110 | − | 0.411714i | −0.0991016 | − | 0.995077i | \(-0.531597\pi\) |
0.812211 | + | 0.583363i | \(0.198264\pi\) | |||||||
\(998\) | − | 31.0000i | − | 0.981288i | ||||||
\(999\) | 20.7846i | 0.657596i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))