Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,2,Mod(25,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("42.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.335371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.37 |
Dual form | 42.2.e.a.25.1 |
$q$-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 \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.00000 | + | 1.73205i | 0.534522 | + | 0.462910i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −4.00000 | + | 6.92820i | −0.917663 | + | 1.58944i | −0.114708 | + | 0.993399i | \(0.536593\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 5.00000 | 1.06600 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.50000 | − | 4.33013i | 0.435194 | − | 0.753778i | ||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 2.00000 | + | 1.73205i | 0.338062 | + | 0.292770i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | −4.00000 | − | 6.92820i | −0.648886 | − | 1.12390i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −0.500000 | + | 2.59808i | −0.0771517 | + | 0.400892i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0.500000 | − | 2.59808i | 0.0668153 | − | 0.347183i | ||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 2.50000 | − | 4.33013i | 0.328266 | − | 0.568574i | ||||
\(59\) | 5.50000 | + | 9.52628i | 0.716039 | + | 1.24022i | 0.962557 | + | 0.271078i | \(0.0873801\pi\) |
−0.246518 | + | 0.969138i | \(0.579287\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | 3.00000 | 0.381000 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.50000 | + | 4.33013i | 0.307729 | + | 0.533002i | ||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 2.00000 | − | 3.46410i | 0.242536 | − | 0.420084i | ||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | −2.50000 | + | 0.866025i | −0.298807 | + | 0.103510i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −5.00000 | − | 8.66025i | −0.585206 | − | 1.01361i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.409644 | − | 0.912245i | \(-0.365653\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | −12.5000 | + | 4.33013i | −1.42451 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | + | 2.59808i | −0.168763 | + | 0.292306i | −0.937985 | − | 0.346675i | \(-0.887311\pi\) |
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.00000 | −0.768350 | −0.384175 | − | 0.923260i | \(-0.625514\pi\) | ||||
−0.384175 | + | 0.923260i | \(0.625514\pi\) | |||||||
\(84\) | −2.00000 | − | 1.73205i | −0.218218 | − | 0.188982i | ||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | −2.50000 | − | 4.33013i | −0.268028 | − | 0.464238i | ||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 1.50000 | − | 2.59808i | 0.155543 | − | 0.269408i | ||||
\(94\) | 3.00000 | + | 5.19615i | 0.309426 | + | 0.535942i | ||||
\(95\) | −4.00000 | − | 6.92820i | −0.410391 | − | 0.710819i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 5.50000 | − | 4.33013i | 0.555584 | − | 0.437409i | ||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | −2.00000 | − | 3.46410i | −0.198030 | − | 0.342997i | ||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.500000 | + | 2.59808i | −0.0487950 | + | 0.253546i | ||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | −1.50000 | + | 2.59808i | −0.145010 | + | 0.251166i | −0.929377 | − | 0.369132i | \(-0.879655\pi\) |
0.784366 | + | 0.620298i | \(0.212988\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | −2.50000 | + | 4.33013i | −0.238366 | + | 0.412861i | ||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 16.0000 | 1.50515 | 0.752577 | − | 0.658505i | \(-0.228811\pi\) | ||||
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 4.00000 | − | 6.92820i | 0.374634 | − | 0.648886i | ||||
\(115\) | 2.00000 | + | 3.46410i | 0.186501 | + | 0.323029i | ||||
\(116\) | 2.50000 | + | 4.33013i | 0.232119 | + | 0.402042i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.0000 | −1.01263 | ||||||||
\(119\) | 10.0000 | − | 3.46410i | 0.916698 | − | 0.317554i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 3.00000 | + | 5.19615i | 0.271607 | + | 0.470438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.50000 | + | 2.59808i | −0.134704 | + | 0.233314i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −2.50000 | + | 0.866025i | −0.222718 | + | 0.0771517i | ||||
\(127\) | 9.00000 | 0.798621 | 0.399310 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399310 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | −5.00000 | −0.435194 | ||||||||
\(133\) | 16.0000 | + | 13.8564i | 1.38738 | + | 1.20150i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | −2.00000 | + | 3.46410i | −0.170251 | + | 0.294884i | ||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0.500000 | − | 2.59808i | 0.0422577 | − | 0.219578i | ||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −1.00000 | + | 1.73205i | −0.0839181 | + | 0.145350i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 2.50000 | − | 4.33013i | 0.207614 | − | 0.359597i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | −1.00000 | − | 6.92820i | −0.0824786 | − | 0.571429i | ||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | −2.00000 | − | 3.46410i | −0.163299 | − | 0.282843i | ||||
\(151\) | −9.50000 | − | 16.4545i | −0.773099 | − | 1.33905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.162758 | − | 0.986666i | \(-0.447961\pi\) | |||||||
\(152\) | −4.00000 | + | 6.92820i | −0.324443 | + | 0.561951i | ||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 2.50000 | − | 12.9904i | 0.201456 | − | 1.04679i | ||||
\(155\) | 3.00000 | 0.240966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | −1.50000 | − | 2.59808i | −0.119334 | − | 0.206692i | ||||
\(159\) | −4.50000 | + | 7.79423i | −0.356873 | + | 0.618123i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −8.00000 | − | 6.92820i | −0.630488 | − | 0.546019i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | 3.50000 | − | 6.06218i | 0.271653 | − | 0.470516i | ||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 2.50000 | − | 0.866025i | 0.192879 | − | 0.0668153i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 2.00000 | − | 3.46410i | 0.153393 | − | 0.265684i | ||||
\(171\) | −4.00000 | − | 6.92820i | −0.305888 | − | 0.529813i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | −11.0000 | + | 19.0526i | −0.836315 | + | 1.44854i | 0.0566411 | + | 0.998395i | \(0.481961\pi\) |
−0.892956 | + | 0.450145i | \(0.851372\pi\) | |||||||
\(174\) | 5.00000 | 0.379049 | ||||||||
\(175\) | 10.0000 | − | 3.46410i | 0.755929 | − | 0.261861i | ||||
\(176\) | 5.00000 | 0.376889 | ||||||||
\(177\) | −5.50000 | + | 9.52628i | −0.413405 | + | 0.716039i | ||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | −6.00000 | − | 10.3923i | −0.448461 | − | 0.776757i | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 2.00000 | + | 3.46410i | 0.147043 | + | 0.254686i | ||||
\(186\) | 1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | ||||
\(187\) | 10.0000 | − | 17.3205i | 0.731272 | − | 1.26660i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | −0.500000 | + | 2.59808i | −0.0363696 | + | 0.188982i | ||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | −12.0000 | + | 20.7846i | −0.868290 | + | 1.50392i | −0.00454614 | + | 0.999990i | \(0.501447\pi\) |
−0.863743 | + | 0.503932i | \(0.831886\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | −3.50000 | + | 6.06218i | −0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −2.50000 | + | 4.33013i | −0.177667 | + | 0.307729i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −2.50000 | + | 12.9904i | −0.175466 | + | 0.911746i | ||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40.0000 | 2.76686 | ||||||||
\(210\) | −2.00000 | − | 1.73205i | −0.138013 | − | 0.119523i | ||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 4.50000 | − | 7.79423i | 0.309061 | − | 0.535310i | ||||
\(213\) | 1.00000 | + | 1.73205i | 0.0685189 | + | 0.118678i | ||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −7.50000 | + | 2.59808i | −0.509133 | + | 0.176369i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 5.00000 | − | 8.66025i | 0.337869 | − | 0.585206i | ||||
\(220\) | −2.50000 | − | 4.33013i | −0.168550 | − | 0.291937i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.00000 | + | 3.46410i | −0.134231 | + | 0.232495i | ||||
\(223\) | −7.00000 | −0.468755 | −0.234377 | − | 0.972146i | \(-0.575305\pi\) | ||||
−0.234377 | + | 0.972146i | \(0.575305\pi\) | |||||||
\(224\) | −2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | −8.00000 | + | 13.8564i | −0.532152 | + | 0.921714i | ||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 4.00000 | + | 6.92820i | 0.264906 | + | 0.458831i | ||||
\(229\) | 10.0000 | − | 17.3205i | 0.660819 | − | 1.14457i | −0.319582 | − | 0.947559i | \(-0.603543\pi\) |
0.980401 | − | 0.197013i | \(-0.0631241\pi\) | |||||||
\(230\) | −4.00000 | −0.263752 | ||||||||
\(231\) | −10.0000 | − | 8.66025i | −0.657952 | − | 0.569803i | ||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | 2.00000 | − | 3.46410i | 0.131024 | − | 0.226941i | −0.793047 | − | 0.609160i | \(-0.791507\pi\) |
0.924072 | + | 0.382219i | \(0.124840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | 5.50000 | − | 9.52628i | 0.358020 | − | 0.620108i | ||||
\(237\) | −3.00000 | −0.194871 | ||||||||
\(238\) | −2.00000 | + | 10.3923i | −0.129641 | + | 0.673633i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0.500000 | − | 0.866025i | 0.0322749 | − | 0.0559017i | ||||
\(241\) | 12.5000 | + | 21.6506i | 0.805196 | + | 1.39464i | 0.916159 | + | 0.400815i | \(0.131273\pi\) |
−0.110963 | + | 0.993825i | \(0.535394\pi\) | |||||||
\(242\) | −7.00000 | − | 12.1244i | −0.449977 | − | 0.779383i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 5.50000 | − | 4.33013i | 0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.50000 | − | 2.59808i | −0.0952501 | − | 0.164978i | ||||
\(249\) | −3.50000 | − | 6.06218i | −0.221803 | − | 0.384175i | ||||
\(250\) | 4.50000 | − | 7.79423i | 0.284605 | − | 0.492950i | ||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0.500000 | − | 2.59808i | 0.0314970 | − | 0.163663i | ||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | −4.50000 | + | 7.79423i | −0.282355 | + | 0.489053i | ||||
\(255\) | −2.00000 | − | 3.46410i | −0.125245 | − | 0.216930i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | −8.00000 | − | 6.92820i | −0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.50000 | − | 4.33013i | 0.154746 | − | 0.268028i | ||||
\(262\) | −0.500000 | − | 0.866025i | −0.0308901 | − | 0.0535032i | ||||
\(263\) | 15.0000 | + | 25.9808i | 0.924940 | + | 1.60204i | 0.791658 | + | 0.610964i | \(0.209218\pi\) |
0.133281 | + | 0.991078i | \(0.457449\pi\) | |||||||
\(264\) | 2.50000 | − | 4.33013i | 0.153864 | − | 0.266501i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | −20.0000 | + | 6.92820i | −1.22628 | + | 0.424795i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | −15.5000 | − | 26.8468i | −0.945052 | − | 1.63688i | −0.755648 | − | 0.654978i | \(-0.772678\pi\) |
−0.189404 | − | 0.981899i | \(-0.560656\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | −7.50000 | + | 12.9904i | −0.455593 | + | 0.789109i | −0.998722 | − | 0.0505395i | \(-0.983906\pi\) |
0.543130 | + | 0.839649i | \(0.317239\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 10.0000 | − | 17.3205i | 0.603023 | − | 1.04447i | ||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | 8.00000 | + | 13.8564i | 0.480673 | + | 0.832551i | 0.999754 | − | 0.0221745i | \(-0.00705893\pi\) |
−0.519081 | + | 0.854725i | \(0.673726\pi\) | |||||||
\(278\) | 7.00000 | − | 12.1244i | 0.419832 | − | 0.727171i | ||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 2.00000 | + | 1.73205i | 0.119523 | + | 0.103510i | ||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | −3.00000 | + | 5.19615i | −0.178647 | + | 0.309426i | ||||
\(283\) | −5.00000 | − | 8.66025i | −0.297219 | − | 0.514799i | 0.678280 | − | 0.734804i | \(-0.262726\pi\) |
−0.975499 | + | 0.220005i | \(0.929393\pi\) | |||||||
\(284\) | −1.00000 | − | 1.73205i | −0.0593391 | − | 0.102778i | ||||
\(285\) | 4.00000 | − | 6.92820i | 0.236940 | − | 0.410391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 2.50000 | + | 4.33013i | 0.146805 | + | 0.254274i | ||||
\(291\) | 3.50000 | + | 6.06218i | 0.205174 | + | 0.355371i | ||||
\(292\) | −5.00000 | + | 8.66025i | −0.292603 | + | 0.506803i | ||||
\(293\) | −21.0000 | −1.22683 | −0.613417 | − | 0.789760i | \(-0.710205\pi\) | ||||
−0.613417 | + | 0.789760i | \(0.710205\pi\) | |||||||
\(294\) | 6.50000 | + | 2.59808i | 0.379088 | + | 0.151523i | ||||
\(295\) | −11.0000 | −0.640445 | ||||||||
\(296\) | 2.00000 | − | 3.46410i | 0.116248 | − | 0.201347i | ||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | 9.00000 | + | 15.5885i | 0.521356 | + | 0.903015i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 1.00000 | − | 5.19615i | 0.0576390 | − | 0.299501i | ||||
\(302\) | 19.0000 | 1.09333 | ||||||||
\(303\) | 5.00000 | − | 8.66025i | 0.287242 | − | 0.497519i | ||||
\(304\) | −4.00000 | − | 6.92820i | −0.229416 | − | 0.397360i | ||||
\(305\) | 3.00000 | + | 5.19615i | 0.171780 | + | 0.297531i | ||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 10.0000 | + | 8.66025i | 0.569803 | + | 0.493464i | ||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | −1.50000 | + | 2.59808i | −0.0851943 | + | 0.147561i | ||||
\(311\) | 16.0000 | + | 27.7128i | 0.907277 | + | 1.57145i | 0.817832 | + | 0.575458i | \(0.195176\pi\) |
0.0894452 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | −2.50000 | + | 0.866025i | −0.140859 | + | 0.0487950i | ||||
\(316\) | 3.00000 | 0.168763 | ||||||||
\(317\) | −1.50000 | + | 2.59808i | −0.0842484 | + | 0.145922i | −0.905071 | − | 0.425261i | \(-0.860182\pi\) |
0.820822 | + | 0.571184i | \(0.193516\pi\) | |||||||
\(318\) | −4.50000 | − | 7.79423i | −0.252347 | − | 0.437079i | ||||
\(319\) | 12.5000 | + | 21.6506i | 0.699866 | + | 1.21220i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 10.0000 | − | 3.46410i | 0.557278 | − | 0.193047i | ||||
\(323\) | −32.0000 | −1.78053 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −1.00000 | + | 1.73205i | −0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | − | 10.3923i | −0.661581 | − | 0.572946i | ||||
\(330\) | −5.00000 | −0.275241 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | 3.50000 | + | 6.06218i | 0.192087 | + | 0.332705i | ||||
\(333\) | 2.00000 | + | 3.46410i | 0.109599 | + | 0.189832i | ||||
\(334\) | 7.00000 | − | 12.1244i | 0.383023 | − | 0.663415i | ||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | −0.500000 | + | 2.59808i | −0.0272772 | + | 0.141737i | ||||
\(337\) | 9.00000 | 0.490261 | 0.245131 | − | 0.969490i | \(-0.421169\pi\) | ||||
0.245131 | + | 0.969490i | \(0.421169\pi\) | |||||||
\(338\) | 6.50000 | − | 11.2583i | 0.353553 | − | 0.612372i | ||||
\(339\) | 8.00000 | + | 13.8564i | 0.434500 | + | 0.752577i | ||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | −7.50000 | + | 12.9904i | −0.406148 | + | 0.703469i | ||||
\(342\) | 8.00000 | 0.432590 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | −2.00000 | + | 3.46410i | −0.107676 | + | 0.186501i | ||||
\(346\) | −11.0000 | − | 19.0526i | −0.591364 | − | 1.02427i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | −2.50000 | + | 4.33013i | −0.134014 | + | 0.232119i | ||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | −2.00000 | + | 10.3923i | −0.106904 | + | 0.555492i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | −12.0000 | − | 20.7846i | −0.638696 | − | 1.10625i | −0.985719 | − | 0.168397i | \(-0.946141\pi\) |
0.347024 | − | 0.937856i | \(-0.387192\pi\) | |||||||
\(354\) | −5.50000 | − | 9.52628i | −0.292322 | − | 0.506316i | ||||
\(355\) | −1.00000 | + | 1.73205i | −0.0530745 | + | 0.0919277i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 8.00000 | + | 6.92820i | 0.423405 | + | 0.366679i | ||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −5.00000 | + | 8.66025i | −0.263890 | + | 0.457071i | −0.967272 | − | 0.253741i | \(-0.918339\pi\) |
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −8.50000 | − | 14.7224i | −0.443696 | − | 0.768505i | 0.554264 | − | 0.832341i | \(-0.313000\pi\) |
−0.997960 | + | 0.0638362i | \(0.979666\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 22.5000 | − | 7.79423i | 1.16814 | − | 0.404656i | ||||
\(372\) | −3.00000 | −0.155543 | ||||||||
\(373\) | 16.0000 | − | 27.7128i | 0.828449 | − | 1.43492i | −0.0708063 | − | 0.997490i | \(-0.522557\pi\) |
0.899255 | − | 0.437425i | \(-0.144109\pi\) | |||||||
\(374\) | 10.0000 | + | 17.3205i | 0.517088 | + | 0.895622i | ||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | − | 1.73205i | −0.102869 | − | 0.0890871i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | −4.00000 | + | 6.92820i | −0.205196 | + | 0.355409i | ||||
\(381\) | 4.50000 | + | 7.79423i | 0.230542 | + | 0.399310i | ||||
\(382\) | −12.0000 | − | 20.7846i | −0.613973 | − | 1.06343i | ||||
\(383\) | 17.0000 | − | 29.4449i | 0.868659 | − | 1.50456i | 0.00529229 | − | 0.999986i | \(-0.498315\pi\) |
0.863367 | − | 0.504576i | \(-0.168351\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.50000 | − | 12.9904i | 0.127412 | − | 0.662051i | ||||
\(386\) | 5.00000 | 0.254493 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | −3.50000 | − | 6.06218i | −0.177686 | − | 0.307760i | ||||
\(389\) | 1.00000 | + | 1.73205i | 0.0507020 | + | 0.0878185i | 0.890263 | − | 0.455448i | \(-0.150521\pi\) |
−0.839561 | + | 0.543266i | \(0.817187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | −1.00000 | −0.0504433 | ||||||||
\(394\) | −1.00000 | + | 1.73205i | −0.0503793 | + | 0.0872595i | ||||
\(395\) | −1.50000 | − | 2.59808i | −0.0754732 | − | 0.130723i | ||||
\(396\) | −2.50000 | − | 4.33013i | −0.125630 | − | 0.217597i | ||||
\(397\) | −18.0000 | + | 31.1769i | −0.903394 | + | 1.56472i | −0.0803356 | + | 0.996768i | \(0.525599\pi\) |
−0.823058 | + | 0.567957i | \(0.807734\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −4.00000 | + | 20.7846i | −0.200250 | + | 1.04053i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −12.0000 | + | 20.7846i | −0.599251 | + | 1.03793i | 0.393680 | + | 0.919247i | \(0.371202\pi\) |
−0.992932 | + | 0.118686i | \(0.962132\pi\) | |||||||
\(402\) | −1.00000 | − | 1.73205i | −0.0498755 | − | 0.0863868i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.00000 | + | 8.66025i | −0.248759 | + | 0.430864i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.0000 | − | 8.66025i | −0.496292 | − | 0.429801i | ||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | 12.5000 | + | 21.6506i | 0.618085 | + | 1.07056i | 0.989835 | + | 0.142222i | \(0.0454247\pi\) |
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.00000 | + | 1.73205i | −0.0493264 | + | 0.0854358i | ||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 27.5000 | − | 9.52628i | 1.35319 | − | 0.468758i | ||||
\(414\) | −4.00000 | −0.196589 | ||||||||
\(415\) | 3.50000 | − | 6.06218i | 0.171808 | − | 0.297581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | − | 12.1244i | −0.342791 | − | 0.593732i | ||||
\(418\) | −20.0000 | + | 34.6410i | −0.978232 | + | 1.69435i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 2.50000 | − | 0.866025i | 0.121988 | − | 0.0422577i | ||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | −1.00000 | + | 1.73205i | −0.0486792 | + | 0.0843149i | ||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 4.50000 | + | 7.79423i | 0.218539 | + | 0.378521i | ||||
\(425\) | −8.00000 | + | 13.8564i | −0.388057 | + | 0.672134i | ||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | −12.0000 | − | 10.3923i | −0.580721 | − | 0.502919i | ||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.00000 | − | 1.73205i | −0.0482243 | − | 0.0835269i | ||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 1.50000 | − | 7.79423i | 0.0720023 | − | 0.374135i | ||||
\(435\) | 5.00000 | 0.239732 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 16.0000 | + | 27.7128i | 0.765384 | + | 1.32568i | ||||
\(438\) | 5.00000 | + | 8.66025i | 0.238909 | + | 0.413803i | ||||
\(439\) | −7.50000 | + | 12.9904i | −0.357955 | + | 0.619997i | −0.987619 | − | 0.156871i | \(-0.949859\pi\) |
0.629664 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(440\) | 5.00000 | 0.238366 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.50000 | + | 14.7224i | −0.403847 | + | 0.699484i | −0.994187 | − | 0.107671i | \(-0.965661\pi\) |
0.590339 | + | 0.807155i | \(0.298994\pi\) | |||||||
\(444\) | −2.00000 | − | 3.46410i | −0.0949158 | − | 0.164399i | ||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | 3.50000 | − | 6.06218i | 0.165730 | − | 0.287052i | ||||
\(447\) | 18.0000 | 0.851371 | ||||||||
\(448\) | 0.500000 | − | 2.59808i | 0.0236228 | − | 0.122748i | ||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | 2.00000 | − | 3.46410i | 0.0942809 | − | 0.163299i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.00000 | − | 13.8564i | −0.376288 | − | 0.651751i | ||||
\(453\) | 9.50000 | − | 16.4545i | 0.446349 | − | 0.773099i | ||||
\(454\) | 3.00000 | 0.140797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.00000 | −0.374634 | ||||||||
\(457\) | −15.5000 | + | 26.8468i | −0.725059 | + | 1.25584i | 0.233890 | + | 0.972263i | \(0.424854\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 10.0000 | + | 17.3205i | 0.467269 | + | 0.809334i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | 2.00000 | − | 3.46410i | 0.0932505 | − | 0.161515i | ||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 12.5000 | − | 4.33013i | 0.581553 | − | 0.201456i | ||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 2.50000 | − | 4.33013i | 0.116060 | − | 0.201021i | ||||
\(465\) | 1.50000 | + | 2.59808i | 0.0695608 | + | 0.120483i | ||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | 10.0000 | − | 17.3205i | 0.462745 | − | 0.801498i | −0.536352 | − | 0.843995i | \(-0.680198\pi\) |
0.999097 | + | 0.0424970i | \(0.0135313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | − | 1.73205i | 0.230879 | − | 0.0799787i | ||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | −2.00000 | + | 3.46410i | −0.0921551 | + | 0.159617i | ||||
\(472\) | 5.50000 | + | 9.52628i | 0.253158 | + | 0.438483i | ||||
\(473\) | −5.00000 | − | 8.66025i | −0.229900 | − | 0.398199i | ||||
\(474\) | 1.50000 | − | 2.59808i | 0.0688973 | − | 0.119334i | ||||
\(475\) | −32.0000 | −1.46826 | ||||||||
\(476\) | −8.00000 | − | 6.92820i | −0.366679 | − | 0.317554i | ||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 6.00000 | − | 10.3923i | 0.274434 | − | 0.475333i | ||||
\(479\) | −19.0000 | − | 32.9090i | −0.868132 | − | 1.50365i | −0.863903 | − | 0.503658i | \(-0.831987\pi\) |
−0.00422900 | − | 0.999991i | \(-0.501346\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −25.0000 | −1.13872 | ||||||||
\(483\) | 2.00000 | − | 10.3923i | 0.0910032 | − | 0.472866i | ||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | −3.50000 | + | 6.06218i | −0.158927 | + | 0.275269i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −2.50000 | − | 4.33013i | −0.113286 | − | 0.196217i | 0.803807 | − | 0.594890i | \(-0.202804\pi\) |
−0.917093 | + | 0.398673i | \(0.869471\pi\) | |||||||
\(488\) | 3.00000 | − | 5.19615i | 0.135804 | − | 0.235219i | ||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 1.00000 | + | 6.92820i | 0.0451754 | + | 0.312984i | ||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | − | 17.3205i | −0.450377 | − | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.50000 | + | 4.33013i | −0.112367 | + | 0.194625i | ||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | 1.00000 | − | 5.19615i | 0.0448561 | − | 0.233079i | ||||
\(498\) | 7.00000 | 0.313678 | ||||||||
\(499\) | −5.00000 | + | 8.66025i | −0.223831 | + | 0.387686i | −0.955968 | − | 0.293471i | \(-0.905190\pi\) |
0.732137 | + | 0.681157i | \(0.238523\pi\) | |||||||
\(500\) | 4.50000 | + | 7.79423i | 0.201246 | + | 0.348569i | ||||
\(501\) | −7.00000 | − | 12.1244i | −0.312737 | − | 0.541676i | ||||
\(502\) | −10.5000 | + | 18.1865i | −0.468638 | + | 0.811705i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 2.00000 | + | 1.73205i | 0.0890871 | + | 0.0771517i | ||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 10.0000 | − | 17.3205i | 0.444554 | − | 0.769991i | ||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | −4.50000 | − | 7.79423i | −0.199655 | − | 0.345813i | ||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | −25.0000 | + | 8.66025i | −1.10593 | + | 0.383107i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.00000 | − | 6.92820i | 0.176604 | − | 0.305888i | ||||
\(514\) | 3.00000 | + | 5.19615i | 0.132324 | + | 0.229192i | ||||
\(515\) | −4.00000 | − | 6.92820i | −0.176261 | − | 0.305293i | ||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | −30.0000 | −1.31940 | ||||||||
\(518\) | 10.0000 | − | 3.46410i | 0.439375 | − | 0.152204i | ||||
\(519\) | −22.0000 | −0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | 2.50000 | + | 4.33013i | 0.109422 | + | 0.189525i | ||||
\(523\) | −4.00000 | + | 6.92820i | −0.174908 | + | 0.302949i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) |
0.765222 | + | 0.643767i | \(0.222629\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 8.00000 | + | 6.92820i | 0.349149 | + | 0.302372i | ||||
\(526\) | −30.0000 | −1.30806 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 2.50000 | + | 4.33013i | 0.108799 | + | 0.188445i | ||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 4.50000 | − | 7.79423i | 0.195468 | − | 0.338560i | ||||
\(531\) | −11.0000 | −0.477359 | ||||||||
\(532\) | 4.00000 | − | 20.7846i | 0.173422 | − | 0.901127i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | −1.50000 | − | 2.59808i | −0.0648507 | − | 0.112325i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 6.00000 | − | 10.3923i | 0.258919 | − | 0.448461i | ||||
\(538\) | 31.0000 | 1.33650 | ||||||||
\(539\) | 5.00000 | + | 34.6410i | 0.215365 | + | 1.49209i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 9.00000 | − | 15.5885i | 0.386940 | − | 0.670200i | −0.605096 | − | 0.796152i | \(-0.706865\pi\) |
0.992036 | + | 0.125952i | \(0.0401986\pi\) | |||||||
\(542\) | −7.50000 | − | 12.9904i | −0.322153 | − | 0.557985i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | − | 3.46410i | 0.0857493 | − | 0.148522i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 1.00000 | − | 1.73205i | 0.0427179 | − | 0.0739895i | ||||
\(549\) | 3.00000 | + | 5.19615i | 0.128037 | + | 0.221766i | ||||
\(550\) | 10.0000 | + | 17.3205i | 0.426401 | + | 0.738549i | ||||
\(551\) | 20.0000 | − | 34.6410i | 0.852029 | − | 1.47576i | ||||
\(552\) | 4.00000 | 0.170251 | ||||||||
\(553\) | 6.00000 | + | 5.19615i | 0.255146 | + | 0.220963i | ||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | −2.00000 | + | 3.46410i | −0.0848953 | + | 0.147043i | ||||
\(556\) | 7.00000 | + | 12.1244i | 0.296866 | + | 0.514187i | ||||
\(557\) | 11.5000 | + | 19.9186i | 0.487271 | + | 0.843978i | 0.999893 | − | 0.0146368i | \(-0.00465919\pi\) |
−0.512622 | + | 0.858614i | \(0.671326\pi\) | |||||||
\(558\) | −1.50000 | + | 2.59808i | −0.0635001 | + | 0.109985i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.50000 | + | 0.866025i | −0.105644 | + | 0.0365963i | ||||
\(561\) | 20.0000 | 0.844401 | ||||||||
\(562\) | −1.00000 | + | 1.73205i | −0.0421825 | + | 0.0730622i | ||||
\(563\) | −8.50000 | − | 14.7224i | −0.358232 | − | 0.620477i | 0.629433 | − | 0.777055i | \(-0.283287\pi\) |
−0.987666 | + | 0.156578i | \(0.949954\pi\) | |||||||
\(564\) | −3.00000 | − | 5.19615i | −0.126323 | − | 0.218797i | ||||
\(565\) | −8.00000 | + | 13.8564i | −0.336563 | + | 0.582943i | ||||
\(566\) | 10.0000 | 0.420331 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | 2.00000 | 0.0839181 | ||||||||
\(569\) | −12.0000 | + | 20.7846i | −0.503066 | + | 0.871336i | 0.496928 | + | 0.867792i | \(0.334461\pi\) |
−0.999994 | + | 0.00354413i | \(0.998872\pi\) | |||||||
\(570\) | 4.00000 | + | 6.92820i | 0.167542 | + | 0.290191i | ||||
\(571\) | 15.0000 | + | 25.9808i | 0.627730 | + | 1.08726i | 0.988006 | + | 0.154415i | \(0.0493493\pi\) |
−0.360276 | + | 0.932846i | \(0.617317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.0000 | 0.667246 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −15.5000 | − | 26.8468i | −0.645273 | − | 1.11765i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) |
0.338965 | − | 0.940799i | \(-0.389923\pi\) | |||||||
\(578\) | 0.500000 | + | 0.866025i | 0.0207973 | + | 0.0360219i | ||||
\(579\) | 2.50000 | − | 4.33013i | 0.103896 | − | 0.179954i | ||||
\(580\) | −5.00000 | −0.207614 | ||||||||
\(581\) | −3.50000 | + | 18.1865i | −0.145204 | + | 0.754505i | ||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | 22.5000 | − | 38.9711i | 0.931855 | − | 1.61402i | ||||
\(584\) | −5.00000 | − | 8.66025i | −0.206901 | − | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.5000 | − | 18.1865i | 0.433751 | − | 0.751279i | ||||
\(587\) | 35.0000 | 1.44460 | 0.722302 | − | 0.691577i | \(-0.243084\pi\) | ||||
0.722302 | + | 0.691577i | \(0.243084\pi\) | |||||||
\(588\) | −5.50000 | + | 4.33013i | −0.226816 | + | 0.178571i | ||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 5.50000 | − | 9.52628i | 0.226431 | − | 0.392191i | ||||
\(591\) | 1.00000 | + | 1.73205i | 0.0411345 | + | 0.0712470i | ||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | −18.0000 | + | 31.1769i | −0.739171 | + | 1.28028i | 0.213697 | + | 0.976900i | \(0.431449\pi\) |
−0.952869 | + | 0.303383i | \(0.901884\pi\) | |||||||
\(594\) | −5.00000 | −0.205152 | ||||||||
\(595\) | −2.00000 | + | 10.3923i | −0.0819920 | + | 0.426043i | ||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | −2.00000 | + | 3.46410i | −0.0818546 | + | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | + | 25.9808i | 0.612883 | + | 1.06155i | 0.990752 | + | 0.135686i | \(0.0433238\pi\) |
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(600\) | −2.00000 | + | 3.46410i | −0.0816497 | + | 0.141421i | ||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | 4.00000 | + | 3.46410i | 0.163028 | + | 0.141186i | ||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | −9.50000 | + | 16.4545i | −0.386550 | + | 0.669523i | ||||
\(605\) | −7.00000 | − | 12.1244i | −0.284590 | − | 0.492925i | ||||
\(606\) | 5.00000 | + | 8.66025i | 0.203111 | + | 0.351799i | ||||
\(607\) | 13.5000 | − | 23.3827i | 0.547948 | − | 0.949074i | −0.450467 | − | 0.892793i | \(-0.648742\pi\) |
0.998415 | − | 0.0562808i | \(-0.0179242\pi\) | |||||||
\(608\) | 8.00000 | 0.324443 | ||||||||
\(609\) | −12.5000 | + | 4.33013i | −0.506526 | + | 0.175466i | ||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00000 | + | 3.46410i | 0.0808452 | + | 0.140028i | ||||
\(613\) | −6.00000 | − | 10.3923i | −0.242338 | − | 0.419741i | 0.719042 | − | 0.694967i | \(-0.244581\pi\) |
−0.961380 | + | 0.275225i | \(0.911248\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.5000 | + | 4.33013i | −0.503639 | + | 0.174466i | ||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 4.00000 | − | 6.92820i | 0.160904 | − | 0.278693i | ||||
\(619\) | −5.00000 | − | 8.66025i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663842i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(620\) | −1.50000 | − | 2.59808i | −0.0602414 | − | 0.104341i | ||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | −32.0000 | −1.28308 | ||||||||
\(623\) | −12.0000 | − | 10.3923i | −0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | 20.0000 | + | 34.6410i | 0.798723 | + | 1.38343i | ||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0.500000 | − | 2.59808i | 0.0199205 | − | 0.103510i | ||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | −1.50000 | + | 2.59808i | −0.0596668 | + | 0.103346i | ||||
\(633\) | 1.00000 | + | 1.73205i | 0.0397464 | + | 0.0688428i | ||||
\(634\) | −1.50000 | − | 2.59808i | −0.0595726 | − | 0.103183i | ||||
\(635\) | −4.50000 | + | 7.79423i | −0.178577 | + | 0.309305i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.0000 | −0.989759 | ||||||||
\(639\) | −1.00000 | + | 1.73205i | −0.0395594 | + | 0.0685189i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −13.0000 | − | 22.5167i | −0.513469 | − | 0.889355i | −0.999878 | − | 0.0156233i | \(-0.995027\pi\) |
0.486409 | − | 0.873731i | \(-0.338307\pi\) | |||||||
\(642\) | 1.50000 | − | 2.59808i | 0.0592003 | − | 0.102538i | ||||
\(643\) | 14.0000 | 0.552106 | 0.276053 | − | 0.961142i | \(-0.410973\pi\) | ||||
0.276053 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(644\) | −2.00000 | + | 10.3923i | −0.0788110 | + | 0.409514i | ||||
\(645\) | −2.00000 | −0.0787499 | ||||||||
\(646\) | 16.0000 | − | 27.7128i | 0.629512 | − | 1.09035i | ||||
\(647\) | 9.00000 | + | 15.5885i | 0.353827 | + | 0.612845i | 0.986916 | − | 0.161233i | \(-0.0515470\pi\) |
−0.633090 | + | 0.774078i | \(0.718214\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 27.5000 | − | 47.6314i | 1.07947 | − | 1.86970i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | − | 5.19615i | −0.235159 | − | 0.203653i | ||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 19.5000 | − | 33.7750i | 0.763094 | − | 1.32172i | −0.178154 | − | 0.984003i | \(-0.557013\pi\) |
0.941248 | − | 0.337715i | \(-0.109654\pi\) | |||||||
\(654\) | −1.00000 | − | 1.73205i | −0.0391031 | − | 0.0677285i | ||||
\(655\) | −0.500000 | − | 0.866025i | −0.0195366 | − | 0.0338384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 15.0000 | − | 5.19615i | 0.584761 | − | 0.202567i | ||||
\(659\) | −40.0000 | −1.55818 | −0.779089 | − | 0.626913i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626913i | \(0.784318\pi\) | |||||||
\(660\) | 2.50000 | − | 4.33013i | 0.0973124 | − | 0.168550i | ||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 2.00000 | + | 3.46410i | 0.0777322 | + | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.00000 | −0.271653 | ||||||||
\(665\) | −20.0000 | + | 6.92820i | −0.775567 | + | 0.268664i | ||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −10.0000 | + | 17.3205i | −0.387202 | + | 0.670653i | ||||
\(668\) | 7.00000 | + | 12.1244i | 0.270838 | + | 0.469105i | ||||
\(669\) | −3.50000 | − | 6.06218i | −0.135318 | − | 0.234377i | ||||
\(670\) | 1.00000 | − | 1.73205i | 0.0386334 | − | 0.0669150i | ||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | −2.00000 | − | 1.73205i | −0.0771517 | − | 0.0668153i | ||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | −4.50000 | + | 7.79423i | −0.173334 | + | 0.300222i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | 13.5000 | − | 23.3827i | 0.518847 | − | 0.898670i | −0.480913 | − | 0.876768i | \(-0.659695\pi\) |
0.999760 | − | 0.0219013i | \(-0.00697196\pi\) | |||||||
\(678\) | −16.0000 | −0.614476 | ||||||||
\(679\) | 3.50000 | − | 18.1865i | 0.134318 | − | 0.697935i | ||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | −7.50000 | − | 12.9904i | −0.287190 | − | 0.497427i | ||||
\(683\) | 4.50000 | + | 7.79423i | 0.172188 | + | 0.298238i | 0.939184 | − | 0.343413i | \(-0.111583\pi\) |
−0.766997 | + | 0.641651i | \(0.778250\pi\) | |||||||
\(684\) | −4.00000 | + | 6.92820i | −0.152944 | + | 0.264906i | ||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 20.0000 | 0.763048 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.00000 | − | 3.46410i | −0.0761387 | − | 0.131876i | ||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 22.0000 | 0.836315 | ||||||||
\(693\) | 2.50000 | − | 12.9904i | 0.0949671 | − | 0.493464i | ||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 7.00000 | − | 12.1244i | 0.265525 | − | 0.459903i | ||||
\(696\) | −2.50000 | − | 4.33013i | −0.0947623 | − | 0.164133i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.00000 | − | 12.1244i | 0.264954 | − | 0.458914i | ||||
\(699\) | 4.00000 | 0.151294 | ||||||||
\(700\) | −8.00000 | − | 6.92820i | −0.302372 | − | 0.261861i | ||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | + | 27.7128i | 0.603451 | + | 1.04521i | ||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | −3.00000 | + | 5.19615i | −0.112987 | + | 0.195698i | ||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | −25.0000 | + | 8.66025i | −0.940222 | + | 0.325702i | ||||
\(708\) | 11.0000 | 0.413405 | ||||||||
\(709\) | −19.0000 | + | 32.9090i | −0.713560 | + | 1.23592i | 0.249952 | + | 0.968258i | \(0.419585\pi\) |
−0.963512 | + | 0.267664i | \(0.913748\pi\) | |||||||
\(710\) | −1.00000 | − | 1.73205i | −0.0375293 | − | 0.0650027i | ||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | −10.0000 | + | 3.46410i | −0.374241 | + | 0.129641i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | 45.0000 | 1.67473 | ||||||||
\(723\) | −12.5000 | + | 21.6506i | −0.464880 | + | 0.805196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0000 | − | 17.3205i | −0.371391 | − | 0.643268i | ||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | 7.00000 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.00000 | + | 8.66025i | −0.185058 | + | 0.320530i | ||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | −3.00000 | − | 5.19615i | −0.110883 | − | 0.192055i | ||||
\(733\) | 3.00000 | − | 5.19615i | 0.110808 | − | 0.191924i | −0.805289 | − | 0.592883i | \(-0.797990\pi\) |
0.916096 | + | 0.400959i | \(0.131323\pi\) | |||||||
\(734\) | 17.0000 | 0.627481 | ||||||||
\(735\) | 6.50000 | + | 2.59808i | 0.239756 | + | 0.0958315i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 5.00000 | − | 8.66025i | 0.184177 | − | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0000 | + | 25.9808i | 0.551784 | + | 0.955718i | 0.998146 | + | 0.0608653i | \(0.0193860\pi\) |
−0.446362 | + | 0.894852i | \(0.647281\pi\) | |||||||
\(740\) | 2.00000 | − | 3.46410i | 0.0735215 | − | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.50000 | + | 23.3827i | −0.165200 | + | 0.858405i | ||||
\(743\) | 30.0000 | 1.10059 | 0.550297 | − | 0.834969i | \(-0.314515\pi\) | ||||
0.550297 | + | 0.834969i | \(0.314515\pi\) | |||||||
\(744\) | 1.50000 | − | 2.59808i | 0.0549927 | − | 0.0952501i | ||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | 16.0000 | + | 27.7128i | 0.585802 | + | 1.01464i | ||||
\(747\) | 3.50000 | − | 6.06218i | 0.128058 | − | 0.221803i | ||||
\(748\) | −20.0000 | −0.731272 | ||||||||
\(749\) | 6.00000 | + | 5.19615i | 0.219235 | + | 0.189863i | ||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | −22.5000 | + | 38.9711i | −0.821037 | + | 1.42208i | 0.0838743 | + | 0.996476i | \(0.473271\pi\) |
−0.904911 | + | 0.425601i | \(0.860063\pi\) | |||||||
\(752\) | 3.00000 | + | 5.19615i | 0.109399 | + | 0.189484i | ||||
\(753\) | 10.5000 | + | 18.1865i | 0.382641 | + | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.0000 | 0.691481 | ||||||||
\(756\) | 2.50000 | − | 0.866025i | 0.0909241 | − | 0.0314970i | ||||
\(757\) | −54.0000 | −1.96266 | −0.981332 | − | 0.192323i | \(-0.938398\pi\) | ||||
−0.981332 | + | 0.192323i | \(0.938398\pi\) | |||||||
\(758\) | −8.00000 | + | 13.8564i | −0.290573 | + | 0.503287i | ||||
\(759\) | −10.0000 | − | 17.3205i | −0.362977 | − | 0.628695i | ||||
\(760\) | −4.00000 | − | 6.92820i | −0.145095 | − | 0.251312i | ||||
\(761\) | −4.00000 | + | 6.92820i | −0.145000 | + | 0.251147i | −0.929373 | − | 0.369142i | \(-0.879652\pi\) |
0.784373 | + | 0.620289i | \(0.212985\pi\) | |||||||
\(762\) | −9.00000 | −0.326036 | ||||||||
\(763\) | 5.00000 | − | 1.73205i | 0.181012 | − | 0.0627044i | ||||
\(764\) | 24.0000 | 0.868290 | ||||||||
\(765\) | 2.00000 | − | 3.46410i | 0.0723102 | − | 0.125245i | ||||
\(766\) | 17.0000 | + | 29.4449i | 0.614235 | + | 1.06389i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −35.0000 | −1.26213 | −0.631066 | − | 0.775729i | \(-0.717382\pi\) | ||||
−0.631066 | + | 0.775729i | \(0.717382\pi\) | |||||||
\(770\) | 10.0000 | + | 8.66025i | 0.360375 | + | 0.312094i | ||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −5.00000 | − | 8.66025i | −0.179838 | − | 0.311488i | 0.761987 | − | 0.647592i | \(-0.224224\pi\) |
−0.941825 | + | 0.336104i | \(0.890891\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | 6.00000 | − | 10.3923i | 0.215526 | − | 0.373303i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 2.00000 | − | 10.3923i | 0.0717496 | − | 0.372822i | ||||
\(778\) | −2.00000 | −0.0717035 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | − | 8.66025i | −0.178914 | − | 0.309888i | ||||
\(782\) | −8.00000 | + | 13.8564i | −0.286079 | + | 0.495504i | ||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0.500000 | − | 0.866025i | 0.0178344 | − | 0.0308901i | ||||
\(787\) | 9.00000 | + | 15.5885i | 0.320815 | + | 0.555668i | 0.980656 | − | 0.195737i | \(-0.0627098\pi\) |
−0.659841 | + | 0.751405i | \(0.729376\pi\) | |||||||
\(788\) | −1.00000 | − | 1.73205i | −0.0356235 | − | 0.0617018i | ||||
\(789\) | −15.0000 | + | 25.9808i | −0.534014 | + | 0.924940i | ||||
\(790\) | 3.00000 | 0.106735 | ||||||||
\(791\) | 8.00000 | − | 41.5692i | 0.284447 | − | 1.47803i | ||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.0000 | − | 31.1769i | −0.638796 | − | 1.10643i | ||||
\(795\) | −4.50000 | − | 7.79423i | −0.159599 | − | 0.276433i | ||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | 21.0000 | 0.743858 | 0.371929 | − | 0.928261i | \(-0.378696\pi\) | ||||
0.371929 | + | 0.928261i | \(0.378696\pi\) | |||||||
\(798\) | −16.0000 | − | 13.8564i | −0.566394 | − | 0.490511i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 2.00000 | − | 3.46410i | 0.0707107 | − | 0.122474i | ||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | −12.0000 | − | 20.7846i | −0.423735 | − | 0.733930i | ||||
\(803\) | −25.0000 | + | 43.3013i | −0.882231 | + | 1.52807i | ||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 10.0000 | − | 3.46410i | 0.352454 | − | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5000 | − | 26.8468i | 0.545626 | − | 0.945052i | ||||
\(808\) | −5.00000 | − | 8.66025i | −0.175899 | − | 0.304667i | ||||
\(809\) | −20.0000 | − | 34.6410i | −0.703163 | − | 1.21791i | −0.967351 | − | 0.253442i | \(-0.918437\pi\) |
0.264188 | − | 0.964471i | \(-0.414896\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | 12.5000 | − | 4.33013i | 0.438664 | − | 0.151958i | ||||
\(813\) | −15.0000 | −0.526073 | ||||||||
\(814\) | 10.0000 | − | 17.3205i | 0.350500 | − | 0.607083i | ||||
\(815\) | 2.00000 | + | 3.46410i | 0.0700569 | + | 0.121342i | ||||
\(816\) | −2.00000 | − | 3.46410i | −0.0700140 | − | 0.121268i | ||||
\(817\) | −8.00000 | + | 13.8564i | −0.279885 | + | 0.484774i | ||||
\(818\) | −25.0000 | −0.874105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | − | 21.6506i | 0.436253 | − | 0.755612i | −0.561144 | − | 0.827718i | \(-0.689639\pi\) |
0.997397 | + | 0.0721058i | \(0.0229719\pi\) | |||||||
\(822\) | −1.00000 | − | 1.73205i | −0.0348790 | − | 0.0604122i | ||||
\(823\) | −20.0000 | − | 34.6410i | −0.697156 | − | 1.20751i | −0.969448 | − | 0.245295i | \(-0.921115\pi\) |
0.272292 | − | 0.962215i | \(-0.412218\pi\) | |||||||
\(824\) | −4.00000 | + | 6.92820i | −0.139347 | + | 0.241355i | ||||
\(825\) | 20.0000 | 0.696311 | ||||||||
\(826\) | −5.50000 | + | 28.5788i | −0.191369 | + | 0.994385i | ||||
\(827\) | 9.00000 | 0.312961 | 0.156480 | − | 0.987681i | \(-0.449985\pi\) | ||||
0.156480 | + | 0.987681i | \(0.449985\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | 16.0000 | + | 27.7128i | 0.555703 | + | 0.962506i | 0.997848 | + | 0.0655624i | \(0.0208842\pi\) |
−0.442145 | + | 0.896943i | \(0.645783\pi\) | |||||||
\(830\) | 3.50000 | + | 6.06218i | 0.121487 | + | 0.210421i | ||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | − | 27.7128i | −0.138592 | − | 0.960192i | ||||
\(834\) | 14.0000 | 0.484780 | ||||||||
\(835\) | 7.00000 | − | 12.1244i | 0.242245 | − | 0.419581i | ||||
\(836\) | −20.0000 | − | 34.6410i | −0.691714 | − | 1.19808i | ||||
\(837\) | 1.50000 | + | 2.59808i | 0.0518476 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.0000 | −0.966667 | −0.483334 | − | 0.875436i | \(-0.660574\pi\) | ||||
−0.483334 | + | 0.875436i | \(0.660574\pi\) | |||||||
\(840\) | −0.500000 | + | 2.59808i | −0.0172516 | + | 0.0896421i | ||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −15.0000 | + | 25.9808i | −0.516934 | + | 0.895356i | ||||
\(843\) | 1.00000 | + | 1.73205i | 0.0344418 | + | 0.0596550i | ||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | 6.50000 | − | 11.2583i | 0.223607 | − | 0.387298i | ||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 28.0000 | + | 24.2487i | 0.962091 | + | 0.833196i | ||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 5.00000 | − | 8.66025i | 0.171600 | − | 0.297219i | ||||
\(850\) | −8.00000 | − | 13.8564i | −0.274398 | − | 0.475271i | ||||
\(851\) | −8.00000 | − | 13.8564i | −0.274236 | − | 0.474991i | ||||
\(852\) | 1.00000 | − | 1.73205i | 0.0342594 | − | 0.0593391i | ||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 15.0000 | − | 5.19615i | 0.513289 | − | 0.177809i | ||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | −1.50000 | + | 2.59808i | −0.0512689 | + | 0.0888004i | ||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0000 | − | 29.4449i | 0.580033 | − | 1.00465i | −0.415442 | − | 0.909620i | \(-0.636373\pi\) |
0.995475 | − | 0.0950262i | \(-0.0302935\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −5.00000 | + | 8.66025i | −0.170202 | + | 0.294798i | −0.938490 | − | 0.345305i | \(-0.887775\pi\) |
0.768288 | + | 0.640104i | \(0.221109\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −11.0000 | − | 19.0526i | −0.374011 | − | 0.647806i | ||||
\(866\) | −7.00000 | + | 12.1244i | −0.237870 | + | 0.412002i | ||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 6.00000 | + | 5.19615i | 0.203653 | + | 0.176369i | ||||
\(869\) | 15.0000 | 0.508840 | ||||||||
\(870\) | −2.50000 | + | 4.33013i | −0.0847579 | + | 0.146805i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.00000 | + | 1.73205i | 0.0338643 | + | 0.0586546i | ||||
\(873\) | −3.50000 | + | 6.06218i | −0.118457 | + | 0.205174i | ||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | −4.50000 | + | 23.3827i | −0.152128 | + | 0.790479i | ||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 16.0000 | − | 27.7128i | 0.540282 | − | 0.935795i | −0.458606 | − | 0.888640i | \(-0.651651\pi\) |
0.998888 | − | 0.0471555i | \(-0.0150156\pi\) | |||||||
\(878\) | −7.50000 | − | 12.9904i | −0.253113 | − | 0.438404i | ||||
\(879\) | −10.5000 | − | 18.1865i | −0.354156 | − | 0.613417i | ||||
\(880\) | −2.50000 | + | 4.33013i | −0.0842750 | + | 0.145969i | ||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 1.00000 | + | 6.92820i | 0.0336718 | + | 0.233285i | ||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.50000 | − | 9.52628i | −0.184880 | − | 0.320222i | ||||
\(886\) | −8.50000 | − | 14.7224i | −0.285563 | − | 0.494610i | ||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | 4.00000 | 0.134231 | ||||||||
\(889\) | 4.50000 | − | 23.3827i | 0.150925 | − | 0.784230i | ||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | −2.50000 | + | 4.33013i | −0.0837532 | + | 0.145065i | ||||
\(892\) | 3.50000 | + | 6.06218i | 0.117189 | + | 0.202977i | ||||
\(893\) | 24.0000 | + | 41.5692i | 0.803129 | + | 1.39106i | ||||
\(894\) | −9.00000 | + | 15.5885i | −0.301005 | + | 0.521356i | ||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.00000 | + | 13.8564i | −0.266963 | + | 0.462394i | ||||
\(899\) | 7.50000 | + | 12.9904i | 0.250139 | + | 0.433253i | ||||
\(900\) | 2.00000 | + | 3.46410i | 0.0666667 | + | 0.115470i | ||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.00000 | − | 1.73205i | 0.166390 | − | 0.0576390i | ||||
\(904\) | 16.0000 | 0.532152 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.50000 | + | 16.4545i | 0.315616 | + | 0.546664i | ||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | −1.50000 | + | 2.59808i | −0.0497792 | + | 0.0862202i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 4.00000 | − | 6.92820i | 0.132453 | − | 0.229416i | ||||
\(913\) | 17.5000 | + | 30.3109i | 0.579165 | + | 1.00314i | ||||
\(914\) | −15.5000 | − | 26.8468i | −0.512694 | − | 0.888013i | ||||
\(915\) | −3.00000 | + | 5.19615i | −0.0991769 | + | 0.171780i | ||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | 2.00000 | + | 1.73205i | 0.0660458 | + | 0.0571974i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 16.0000 | − | 27.7128i | 0.527791 | − | 0.914161i | −0.471684 | − | 0.881768i | \(-0.656354\pi\) |
0.999475 | − | 0.0323936i | \(-0.0103130\pi\) | |||||||
\(920\) | 2.00000 | + | 3.46410i | 0.0659380 | + | 0.114208i | ||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 7.00000 | − | 12.1244i | 0.230533 | − | 0.399294i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.50000 | + | 12.9904i | −0.0822440 | + | 0.427352i | ||||
\(925\) | 16.0000 | 0.526077 | ||||||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | −4.00000 | − | 6.92820i | −0.131377 | − | 0.227552i | ||||
\(928\) | 2.50000 | + | 4.33013i | 0.0820665 | + | 0.142143i | ||||
\(929\) | 3.00000 | − | 5.19615i | 0.0984268 | − | 0.170480i | −0.812607 | − | 0.582812i | \(-0.801952\pi\) |
0.911034 | + | 0.412332i | \(0.135286\pi\) | |||||||
\(930\) | −3.00000 | −0.0983739 | ||||||||
\(931\) | 44.0000 | − | 34.6410i | 1.44204 | − | 1.13531i | ||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | −16.0000 | + | 27.7128i | −0.523816 | + | 0.907277i | ||||
\(934\) | 10.0000 | + | 17.3205i | 0.327210 | + | 0.566744i | ||||
\(935\) | 10.0000 | + | 17.3205i | 0.327035 | + | 0.566441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | −1.00000 | + | 5.19615i | −0.0326512 | + | 0.169660i | ||||
\(939\) | −1.00000 | −0.0326338 | ||||||||
\(940\) | 3.00000 | − | 5.19615i | 0.0978492 | − | 0.169480i | ||||
\(941\) | 5.50000 | + | 9.52628i | 0.179295 | + | 0.310548i | 0.941639 | − | 0.336624i | \(-0.109285\pi\) |
−0.762344 | + | 0.647172i | \(0.775952\pi\) | |||||||
\(942\) | −2.00000 | − | 3.46410i | −0.0651635 | − | 0.112867i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −11.0000 | −0.358020 | ||||||||
\(945\) | −2.00000 | − | 1.73205i | −0.0650600 | − | 0.0563436i | ||||
\(946\) | 10.0000 | 0.325128 | ||||||||
\(947\) | 16.0000 | − | 27.7128i | 0.519930 | − | 0.900545i | −0.479801 | − | 0.877377i | \(-0.659291\pi\) |
0.999732 | − | 0.0231683i | \(-0.00737536\pi\) | |||||||
\(948\) | 1.50000 | + | 2.59808i | 0.0487177 | + | 0.0843816i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 16.0000 | − | 27.7128i | 0.519109 | − | 0.899122i | ||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | 10.0000 | − | 3.46410i | 0.324102 | − | 0.112272i | ||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 4.50000 | − | 7.79423i | 0.145693 | − | 0.252347i | ||||
\(955\) | −12.0000 | − | 20.7846i | −0.388311 | − | 0.672574i | ||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | −12.5000 | + | 21.6506i | −0.404068 | + | 0.699866i | ||||
\(958\) | 38.0000 | 1.22772 | ||||||||
\(959\) | 5.00000 | − | 1.73205i | 0.161458 | − | 0.0559308i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.50000 | − | 2.59808i | −0.0483368 | − | 0.0837218i | ||||
\(964\) | 12.5000 | − | 21.6506i | 0.402598 | − | 0.697320i | ||||
\(965\) | 5.00000 | 0.160956 | ||||||||
\(966\) | 8.00000 | + | 6.92820i | 0.257396 | + | 0.222911i | ||||
\(967\) | −61.0000 | −1.96163 | −0.980814 | − | 0.194946i | \(-0.937547\pi\) | ||||
−0.980814 | + | 0.194946i | \(0.937547\pi\) | |||||||
\(968\) | −7.00000 | + | 12.1244i | −0.224989 | + | 0.389692i | ||||
\(969\) | −16.0000 | − | 27.7128i | −0.513994 | − | 0.890264i | ||||
\(970\) | −3.50000 | − | 6.06218i | −0.112378 | − | 0.194645i | ||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.00000 | + | 36.3731i | −0.224410 | + | 1.16607i | ||||
\(974\) | 5.00000 | 0.160210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.00000 | + | 5.19615i | 0.0960277 | + | 0.166325i | ||||
\(977\) | 15.0000 | + | 25.9808i | 0.479893 | + | 0.831198i | 0.999734 | − | 0.0230645i | \(-0.00734232\pi\) |
−0.519841 | + | 0.854263i | \(0.674009\pi\) | |||||||
\(978\) | −2.00000 | + | 3.46410i | −0.0639529 | + | 0.110770i | ||||
\(979\) | −30.0000 | −0.958804 | ||||||||
\(980\) | −6.50000 | − | 2.59808i | −0.207635 | − | 0.0829925i | ||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | −4.50000 | + | 7.79423i | −0.143601 | + | 0.248724i | ||||
\(983\) | 30.0000 | + | 51.9615i | 0.956851 | + | 1.65732i | 0.730073 | + | 0.683369i | \(0.239486\pi\) |
0.226778 | + | 0.973946i | \(0.427181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00000 | + | 1.73205i | −0.0318626 | + | 0.0551877i | ||||
\(986\) | 20.0000 | 0.636930 | ||||||||
\(987\) | 3.00000 | − | 15.5885i | 0.0954911 | − | 0.496186i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | − | 6.92820i | 0.127193 | − | 0.220304i | ||||
\(990\) | −2.50000 | − | 4.33013i | −0.0794552 | − | 0.137620i | ||||
\(991\) | −23.5000 | − | 40.7032i | −0.746502 | − | 1.29298i | −0.949490 | − | 0.313798i | \(-0.898398\pi\) |
0.202988 | − | 0.979181i | \(-0.434935\pi\) | |||||||
\(992\) | −1.50000 | + | 2.59808i | −0.0476250 | + | 0.0824890i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 4.00000 | + | 3.46410i | 0.126872 | + | 0.109875i | ||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | −3.50000 | + | 6.06218i | −0.110902 | + | 0.192087i | ||||
\(997\) | −19.0000 | − | 32.9090i | −0.601736 | − | 1.04224i | −0.992558 | − | 0.121771i | \(-0.961143\pi\) |
0.390822 | − | 0.920466i | \(-0.372191\pi\) | |||||||
\(998\) | −5.00000 | − | 8.66025i | −0.158272 | − | 0.274136i | ||||
\(999\) | −2.00000 | + | 3.46410i | −0.0632772 | + | 0.109599i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))